Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.10 | ||
Character | \(\chi\) | \(=\) | 570.521 |
Dual form | 570.2.s.b.221.10 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.32792 | + | 1.11204i | 0.766675 | + | 0.642035i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 1.62701 | − | 0.593994i | 0.664225 | − | 0.242497i | ||||
\(7\) | −0.387589 | −0.146495 | −0.0732475 | − | 0.997314i | \(-0.523336\pi\) | ||||
−0.0732475 | + | 0.997314i | \(0.523336\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.526745 | + | 2.95339i | 0.175582 | + | 0.984465i | ||||
\(10\) | 0.866025 | − | 0.500000i | 0.273861 | − | 0.158114i | ||||
\(11\) | 6.28666i | 1.89550i | 0.319015 | + | 0.947750i | \(0.396648\pi\) | ||||
−0.319015 | + | 0.947750i | \(0.603352\pi\) | |||||||
\(12\) | 0.299093 | − | 1.70603i | 0.0863406 | − | 0.492489i | ||||
\(13\) | 5.96278 | − | 3.44261i | 1.65378 | − | 0.954809i | 0.678280 | − | 0.734804i | \(-0.262726\pi\) |
0.975499 | − | 0.220006i | \(-0.0706076\pi\) | |||||||
\(14\) | −0.193795 | + | 0.335662i | −0.0517938 | + | 0.0897095i | ||||
\(15\) | 0.593994 | + | 1.62701i | 0.153369 | + | 0.420093i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.63331 | − | 2.67504i | −1.12374 | − | 0.648793i | −0.181389 | − | 0.983411i | \(-0.558059\pi\) |
−0.942354 | + | 0.334619i | \(0.891393\pi\) | |||||||
\(18\) | 2.82109 | + | 1.02052i | 0.664937 | + | 0.240540i | ||||
\(19\) | 0.936449 | + | 4.25712i | 0.214836 | + | 0.976650i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −0.514688 | − | 0.431014i | −0.112314 | − | 0.0940549i | ||||
\(22\) | 5.44441 | + | 3.14333i | 1.16075 | + | 0.670160i | ||||
\(23\) | 5.57852 | − | 3.22076i | 1.16320 | − | 0.671575i | 0.211133 | − | 0.977457i | \(-0.432285\pi\) |
0.952069 | + | 0.305882i | \(0.0989513\pi\) | |||||||
\(24\) | −1.32792 | − | 1.11204i | −0.271061 | − | 0.226994i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | − | 6.88523i | − | 1.35030i | ||||||
\(27\) | −2.58481 | + | 4.50763i | −0.497447 | + | 0.867494i | ||||
\(28\) | 0.193795 | + | 0.335662i | 0.0366237 | + | 0.0634342i | ||||
\(29\) | −2.15245 | − | 3.72815i | −0.399699 | − | 0.692299i | 0.593989 | − | 0.804473i | \(-0.297552\pi\) |
−0.993689 | + | 0.112173i | \(0.964219\pi\) | |||||||
\(30\) | 1.70603 | + | 0.299093i | 0.311477 | + | 0.0546066i | ||||
\(31\) | − | 5.87016i | − | 1.05431i | −0.849769 | − | 0.527156i | \(-0.823258\pi\) | ||
0.849769 | − | 0.527156i | \(-0.176742\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −6.99100 | + | 8.34818i | −1.21698 | + | 1.45323i | ||||
\(34\) | −4.63331 | + | 2.67504i | −0.794606 | + | 0.458766i | ||||
\(35\) | −0.335662 | − | 0.193795i | −0.0567373 | − | 0.0327573i | ||||
\(36\) | 2.29434 | − | 1.93287i | 0.382390 | − | 0.322145i | ||||
\(37\) | − | 2.54580i | − | 0.418527i | −0.977859 | − | 0.209264i | \(-0.932893\pi\) | ||
0.977859 | − | 0.209264i | \(-0.0671067\pi\) | |||||||
\(38\) | 4.15500 | + | 1.31757i | 0.674030 | + | 0.213738i | ||||
\(39\) | 11.7464 | + | 2.05932i | 1.88093 | + | 0.329755i | ||||
\(40\) | −0.866025 | − | 0.500000i | −0.136931 | − | 0.0790569i | ||||
\(41\) | 1.40194 | − | 2.42823i | 0.218946 | − | 0.379226i | −0.735540 | − | 0.677481i | \(-0.763071\pi\) |
0.954486 | + | 0.298256i | \(0.0964048\pi\) | |||||||
\(42\) | −0.630613 | + | 0.230226i | −0.0973057 | + | 0.0355246i | ||||
\(43\) | −0.588721 | + | 1.01969i | −0.0897791 | + | 0.155502i | −0.907418 | − | 0.420230i | \(-0.861949\pi\) |
0.817639 | + | 0.575732i | \(0.195283\pi\) | |||||||
\(44\) | 5.44441 | − | 3.14333i | 0.820775 | − | 0.473875i | ||||
\(45\) | −1.02052 | + | 2.82109i | −0.152131 | + | 0.420543i | ||||
\(46\) | − | 6.44153i | − | 0.949751i | ||||||
\(47\) | −6.74336 | + | 3.89328i | −0.983620 | + | 0.567893i | −0.903361 | − | 0.428881i | \(-0.858908\pi\) |
−0.0802589 | + | 0.996774i | \(0.525575\pi\) | |||||||
\(48\) | −1.62701 | + | 0.593994i | −0.234839 | + | 0.0857356i | ||||
\(49\) | −6.84977 | −0.978539 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −3.17792 | − | 8.70465i | −0.444997 | − | 1.21890i | ||||
\(52\) | −5.96278 | − | 3.44261i | −0.826889 | − | 0.477405i | ||||
\(53\) | 1.97481 | + | 3.42047i | 0.271261 | + | 0.469837i | 0.969185 | − | 0.246334i | \(-0.0792261\pi\) |
−0.697924 | + | 0.716172i | \(0.745893\pi\) | |||||||
\(54\) | 2.61132 | + | 4.49233i | 0.355355 | + | 0.611328i | ||||
\(55\) | −3.14333 | + | 5.44441i | −0.423846 | + | 0.734124i | ||||
\(56\) | 0.387589 | 0.0517938 | ||||||||
\(57\) | −3.49055 | + | 6.69448i | −0.462334 | + | 0.886706i | ||||
\(58\) | −4.30489 | −0.565260 | ||||||||
\(59\) | −0.556791 | + | 0.964390i | −0.0724880 | + | 0.125553i | −0.899991 | − | 0.435908i | \(-0.856427\pi\) |
0.827503 | + | 0.561461i | \(0.189761\pi\) | |||||||
\(60\) | 1.11204 | − | 1.32792i | 0.143563 | − | 0.171434i | ||||
\(61\) | 1.28373 | + | 2.22348i | 0.164365 | + | 0.284688i | 0.936429 | − | 0.350856i | \(-0.114109\pi\) |
−0.772065 | + | 0.635544i | \(0.780776\pi\) | |||||||
\(62\) | −5.08371 | − | 2.93508i | −0.645632 | − | 0.372756i | ||||
\(63\) | −0.204161 | − | 1.14470i | −0.0257218 | − | 0.144219i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.88523 | 0.854008 | ||||||||
\(66\) | 3.73424 | + | 10.2285i | 0.459653 | + | 1.25904i | ||||
\(67\) | 6.95760 | − | 4.01697i | 0.850006 | − | 0.490751i | −0.0106470 | − | 0.999943i | \(-0.503389\pi\) |
0.860653 | + | 0.509192i | \(0.170056\pi\) | |||||||
\(68\) | 5.35008i | 0.648793i | ||||||||
\(69\) | 10.9894 | + | 1.92661i | 1.32297 | + | 0.231937i | ||||
\(70\) | −0.335662 | + | 0.193795i | −0.0401193 | + | 0.0231629i | ||||
\(71\) | 4.17799 | − | 7.23648i | 0.495836 | − | 0.858813i | −0.504153 | − | 0.863614i | \(-0.668195\pi\) |
0.999988 | + | 0.00480188i | \(0.00152849\pi\) | |||||||
\(72\) | −0.526745 | − | 2.95339i | −0.0620775 | − | 0.348061i | ||||
\(73\) | −0.890700 | + | 1.54274i | −0.104249 | + | 0.180564i | −0.913431 | − | 0.406994i | \(-0.866577\pi\) |
0.809182 | + | 0.587557i | \(0.199910\pi\) | |||||||
\(74\) | −2.20473 | − | 1.27290i | −0.256294 | − | 0.147972i | ||||
\(75\) | −0.299093 | + | 1.70603i | −0.0345362 | + | 0.196996i | ||||
\(76\) | 3.21855 | − | 2.93955i | 0.369193 | − | 0.337189i | ||||
\(77\) | − | 2.43664i | − | 0.277681i | ||||||
\(78\) | 7.65663 | − | 9.14304i | 0.866943 | − | 1.03524i | ||||
\(79\) | −12.3862 | − | 7.15117i | −1.39355 | − | 0.804569i | −0.399848 | − | 0.916581i | \(-0.630937\pi\) |
−0.993707 | + | 0.112012i | \(0.964270\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −8.44508 | + | 3.11137i | −0.938342 | + | 0.345708i | ||||
\(82\) | −1.40194 | − | 2.42823i | −0.154818 | − | 0.268153i | ||||
\(83\) | 3.22583i | 0.354081i | 0.984204 | + | 0.177040i | \(0.0566523\pi\) | ||||
−0.984204 | + | 0.177040i | \(0.943348\pi\) | |||||||
\(84\) | −0.115925 | + | 0.661239i | −0.0126485 | + | 0.0721471i | ||||
\(85\) | −2.67504 | − | 4.63331i | −0.290149 | − | 0.502553i | ||||
\(86\) | 0.588721 | + | 1.01969i | 0.0634834 | + | 0.109956i | ||||
\(87\) | 1.28756 | − | 7.34428i | 0.138041 | − | 0.787390i | ||||
\(88\) | − | 6.28666i | − | 0.670160i | ||||||
\(89\) | −7.49847 | − | 12.9877i | −0.794836 | − | 1.37670i | −0.922943 | − | 0.384936i | \(-0.874223\pi\) |
0.128107 | − | 0.991760i | \(-0.459110\pi\) | |||||||
\(90\) | 1.93287 | + | 2.29434i | 0.203743 | + | 0.241845i | ||||
\(91\) | −2.31111 | + | 1.33432i | −0.242270 | + | 0.139875i | ||||
\(92\) | −5.57852 | − | 3.22076i | −0.581601 | − | 0.335788i | ||||
\(93\) | 6.52784 | − | 7.79511i | 0.676905 | − | 0.808315i | ||||
\(94\) | 7.78656i | 0.803122i | ||||||||
\(95\) | −1.31757 | + | 4.15500i | −0.135180 | + | 0.426294i | ||||
\(96\) | −0.299093 | + | 1.70603i | −0.0305260 | + | 0.174121i | ||||
\(97\) | −5.33880 | − | 3.08236i | −0.542073 | − | 0.312966i | 0.203846 | − | 0.979003i | \(-0.434656\pi\) |
−0.745919 | + | 0.666037i | \(0.767989\pi\) | |||||||
\(98\) | −3.42489 | + | 5.93208i | −0.345966 | + | 0.599230i | ||||
\(99\) | −18.5670 | + | 3.31146i | −1.86605 | + | 0.332815i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.63539 | + | 2.09889i | −0.361734 | + | 0.208847i | −0.669841 | − | 0.742504i | \(-0.733638\pi\) |
0.308107 | + | 0.951352i | \(0.400305\pi\) | |||||||
\(102\) | −9.12741 | − | 1.60017i | −0.903748 | − | 0.158441i | ||||
\(103\) | − | 14.4685i | − | 1.42562i | −0.701356 | − | 0.712811i | \(-0.747422\pi\) | ||
0.701356 | − | 0.712811i | \(-0.252578\pi\) | |||||||
\(104\) | −5.96278 | + | 3.44261i | −0.584699 | + | 0.337576i | ||||
\(105\) | −0.230226 | − | 0.630613i | −0.0224677 | − | 0.0615415i | ||||
\(106\) | 3.94962 | 0.383621 | ||||||||
\(107\) | 2.46390 | 0.238194 | 0.119097 | − | 0.992883i | \(-0.462000\pi\) | ||||
0.119097 | + | 0.992883i | \(0.462000\pi\) | |||||||
\(108\) | 5.19613 | − | 0.0153044i | 0.499998 | − | 0.00147267i | ||||
\(109\) | 2.32388 | + | 1.34169i | 0.222587 | + | 0.128511i | 0.607148 | − | 0.794589i | \(-0.292314\pi\) |
−0.384561 | + | 0.923100i | \(0.625647\pi\) | |||||||
\(110\) | 3.14333 | + | 5.44441i | 0.299705 | + | 0.519104i | ||||
\(111\) | 2.83103 | − | 3.38062i | 0.268709 | − | 0.320874i | ||||
\(112\) | 0.193795 | − | 0.335662i | 0.0183119 | − | 0.0317171i | ||||
\(113\) | 0.146598 | 0.0137908 | 0.00689539 | − | 0.999976i | \(-0.497805\pi\) | ||||
0.00689539 | + | 0.999976i | \(0.497805\pi\) | |||||||
\(114\) | 4.05232 | + | 6.37014i | 0.379534 | + | 0.596619i | ||||
\(115\) | 6.44153 | 0.600675 | ||||||||
\(116\) | −2.15245 | + | 3.72815i | −0.199850 | + | 0.346150i | ||||
\(117\) | 13.3083 | + | 15.7971i | 1.23035 | + | 1.46044i | ||||
\(118\) | 0.556791 | + | 0.964390i | 0.0512567 | + | 0.0887793i | ||||
\(119\) | 1.79582 | + | 1.03682i | 0.164623 | + | 0.0950449i | ||||
\(120\) | −0.593994 | − | 1.62701i | −0.0542240 | − | 0.148525i | ||||
\(121\) | −28.5221 | −2.59292 | ||||||||
\(122\) | 2.56746 | 0.232447 | ||||||||
\(123\) | 4.56195 | − | 1.66549i | 0.411337 | − | 0.150172i | ||||
\(124\) | −5.08371 | + | 2.93508i | −0.456530 | + | 0.263578i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.09342 | − | 0.395544i | −0.0974099 | − | 0.0352378i | ||||
\(127\) | −14.1674 | + | 8.17952i | −1.25715 | + | 0.725815i | −0.972519 | − | 0.232822i | \(-0.925204\pi\) |
−0.284630 | + | 0.958638i | \(0.591871\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.91571 | + | 0.699393i | −0.168669 | + | 0.0615781i | ||||
\(130\) | 3.44261 | − | 5.96278i | 0.301937 | − | 0.522971i | ||||
\(131\) | −2.32705 | − | 1.34352i | −0.203316 | − | 0.117384i | 0.394886 | − | 0.918730i | \(-0.370784\pi\) |
−0.598201 | + | 0.801346i | \(0.704118\pi\) | |||||||
\(132\) | 10.7252 | + | 1.88029i | 0.933512 | + | 0.163659i | ||||
\(133\) | −0.362957 | − | 1.65001i | −0.0314724 | − | 0.143074i | ||||
\(134\) | − | 8.03394i | − | 0.694027i | ||||||
\(135\) | −4.49233 | + | 2.61132i | −0.386638 | + | 0.224747i | ||||
\(136\) | 4.63331 | + | 2.67504i | 0.397303 | + | 0.229383i | ||||
\(137\) | 11.8037 | − | 6.81488i | 1.00846 | − | 0.582234i | 0.0977189 | − | 0.995214i | \(-0.468845\pi\) |
0.910740 | + | 0.412980i | \(0.135512\pi\) | |||||||
\(138\) | 7.16322 | − | 8.55383i | 0.609774 | − | 0.728151i | ||||
\(139\) | 11.3319 | + | 19.6275i | 0.961162 | + | 1.66478i | 0.719590 | + | 0.694399i | \(0.244330\pi\) |
0.241572 | + | 0.970383i | \(0.422337\pi\) | |||||||
\(140\) | 0.387589i | 0.0327573i | ||||||||
\(141\) | −13.2841 | − | 2.32890i | −1.11872 | − | 0.196129i | ||||
\(142\) | −4.17799 | − | 7.23648i | −0.350609 | − | 0.607272i | ||||
\(143\) | 21.6425 | + | 37.4860i | 1.80984 | + | 3.13474i | ||||
\(144\) | −2.82109 | − | 1.02052i | −0.235091 | − | 0.0850436i | ||||
\(145\) | − | 4.30489i | − | 0.357502i | ||||||
\(146\) | 0.890700 | + | 1.54274i | 0.0737148 | + | 0.127678i | ||||
\(147\) | −9.09595 | − | 7.61721i | −0.750222 | − | 0.628257i | ||||
\(148\) | −2.20473 | + | 1.27290i | −0.181228 | + | 0.104632i | ||||
\(149\) | 2.36838 | + | 1.36738i | 0.194025 | + | 0.112020i | 0.593866 | − | 0.804564i | \(-0.297601\pi\) |
−0.399840 | + | 0.916585i | \(0.630934\pi\) | |||||||
\(150\) | 1.32792 | + | 1.11204i | 0.108424 | + | 0.0907975i | ||||
\(151\) | 5.03506i | 0.409747i | 0.978788 | + | 0.204874i | \(0.0656784\pi\) | ||||
−0.978788 | + | 0.204874i | \(0.934322\pi\) | |||||||
\(152\) | −0.936449 | − | 4.25712i | −0.0759560 | − | 0.345298i | ||||
\(153\) | 5.45988 | − | 15.0931i | 0.441405 | − | 1.22020i | ||||
\(154\) | −2.11019 | − | 1.21832i | −0.170044 | − | 0.0981751i | ||||
\(155\) | 2.93508 | − | 5.08371i | 0.235751 | − | 0.408333i | ||||
\(156\) | −4.08978 | − | 11.2024i | −0.327445 | − | 0.896906i | ||||
\(157\) | 0.931580 | − | 1.61354i | 0.0743482 | − | 0.128775i | −0.826454 | − | 0.563004i | \(-0.809646\pi\) |
0.900803 | + | 0.434229i | \(0.142979\pi\) | |||||||
\(158\) | −12.3862 | + | 7.15117i | −0.985392 | + | 0.568916i | ||||
\(159\) | −1.18130 | + | 6.73817i | −0.0936833 | + | 0.534372i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −2.16218 | + | 1.24833i | −0.170403 | + | 0.0983824i | ||||
\(162\) | −1.52801 | + | 8.86934i | −0.120052 | + | 0.696841i | ||||
\(163\) | −15.6424 | −1.22521 | −0.612604 | − | 0.790390i | \(-0.709878\pi\) | ||||
−0.612604 | + | 0.790390i | \(0.709878\pi\) | |||||||
\(164\) | −2.80388 | −0.218946 | ||||||||
\(165\) | −10.2285 | + | 3.73424i | −0.796286 | + | 0.290710i | ||||
\(166\) | 2.79365 | + | 1.61291i | 0.216829 | + | 0.125186i | ||||
\(167\) | 2.58979 | + | 4.48565i | 0.200404 | + | 0.347110i | 0.948659 | − | 0.316302i | \(-0.102441\pi\) |
−0.748255 | + | 0.663412i | \(0.769108\pi\) | |||||||
\(168\) | 0.514688 | + | 0.431014i | 0.0397090 | + | 0.0332534i | ||||
\(169\) | 17.2032 | − | 29.7968i | 1.32332 | − | 2.29206i | ||||
\(170\) | −5.35008 | −0.410333 | ||||||||
\(171\) | −12.0797 | + | 5.00812i | −0.923756 | + | 0.382980i | ||||
\(172\) | 1.17744 | 0.0897791 | ||||||||
\(173\) | −4.91408 | + | 8.51144i | −0.373611 | + | 0.647113i | −0.990118 | − | 0.140236i | \(-0.955214\pi\) |
0.616507 | + | 0.787349i | \(0.288547\pi\) | |||||||
\(174\) | −5.71655 | − | 4.78720i | −0.433371 | − | 0.362917i | ||||
\(175\) | −0.193795 | − | 0.335662i | −0.0146495 | − | 0.0253737i | ||||
\(176\) | −5.44441 | − | 3.14333i | −0.410388 | − | 0.236937i | ||||
\(177\) | −1.81181 | + | 0.661461i | −0.136184 | + | 0.0497184i | ||||
\(178\) | −14.9969 | −1.12407 | ||||||||
\(179\) | 19.6374 | 1.46777 | 0.733884 | − | 0.679275i | \(-0.237706\pi\) | ||||
0.733884 | + | 0.679275i | \(0.237706\pi\) | |||||||
\(180\) | 2.95339 | − | 0.526745i | 0.220133 | − | 0.0392612i | ||||
\(181\) | −19.3105 | + | 11.1489i | −1.43534 | + | 0.828691i | −0.997521 | − | 0.0703737i | \(-0.977581\pi\) |
−0.437815 | + | 0.899065i | \(0.644247\pi\) | |||||||
\(182\) | 2.66864i | 0.197813i | ||||||||
\(183\) | −0.767908 | + | 4.38017i | −0.0567654 | + | 0.323791i | ||||
\(184\) | −5.57852 | + | 3.22076i | −0.411254 | + | 0.237438i | ||||
\(185\) | 1.27290 | − | 2.20473i | 0.0935855 | − | 0.162095i | ||||
\(186\) | −3.48684 | − | 9.55083i | −0.255667 | − | 0.700301i | ||||
\(187\) | 16.8171 | − | 29.1280i | 1.22979 | − | 2.13005i | ||||
\(188\) | 6.74336 | + | 3.89328i | 0.491810 | + | 0.283947i | ||||
\(189\) | 1.00184 | − | 1.74711i | 0.0728735 | − | 0.127084i | ||||
\(190\) | 2.93955 | + | 3.21855i | 0.213257 | + | 0.233498i | ||||
\(191\) | − | 17.2742i | − | 1.24992i | −0.780658 | − | 0.624958i | \(-0.785116\pi\) | ||
0.780658 | − | 0.624958i | \(-0.214884\pi\) | |||||||
\(192\) | 1.32792 | + | 1.11204i | 0.0958344 | + | 0.0802544i | ||||
\(193\) | 8.44254 | + | 4.87430i | 0.607707 | + | 0.350860i | 0.772068 | − | 0.635540i | \(-0.219223\pi\) |
−0.164360 | + | 0.986400i | \(0.552556\pi\) | |||||||
\(194\) | −5.33880 | + | 3.08236i | −0.383304 | + | 0.221300i | ||||
\(195\) | 9.14304 | + | 7.65663i | 0.654746 | + | 0.548303i | ||||
\(196\) | 3.42489 | + | 5.93208i | 0.244635 | + | 0.423720i | ||||
\(197\) | 7.99412i | 0.569557i | 0.958593 | + | 0.284779i | \(0.0919201\pi\) | ||||
−0.958593 | + | 0.284779i | \(0.908080\pi\) | |||||||
\(198\) | −6.41568 | + | 17.7352i | −0.455943 | + | 1.26039i | ||||
\(199\) | 2.50783 | + | 4.34368i | 0.177775 | + | 0.307915i | 0.941118 | − | 0.338078i | \(-0.109777\pi\) |
−0.763343 | + | 0.645993i | \(0.776443\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 13.7062 | + | 2.40289i | 0.966758 | + | 0.169487i | ||||
\(202\) | 4.19778i | 0.295355i | ||||||||
\(203\) | 0.834265 | + | 1.44499i | 0.0585539 | + | 0.101418i | ||||
\(204\) | −5.94949 | + | 7.10448i | −0.416548 | + | 0.497413i | ||||
\(205\) | 2.42823 | − | 1.40194i | 0.169595 | − | 0.0979157i | ||||
\(206\) | −12.5301 | − | 7.23425i | −0.873012 | − | 0.504034i | ||||
\(207\) | 12.4506 | + | 14.7791i | 0.865379 | + | 1.02722i | ||||
\(208\) | 6.88523i | 0.477405i | ||||||||
\(209\) | −26.7631 | + | 5.88714i | −1.85124 | + | 0.407222i | ||||
\(210\) | −0.661239 | − | 0.115925i | −0.0456299 | − | 0.00799959i | ||||
\(211\) | −0.901047 | − | 0.520219i | −0.0620306 | − | 0.0358134i | 0.468664 | − | 0.883377i | \(-0.344736\pi\) |
−0.530695 | + | 0.847563i | \(0.678069\pi\) | |||||||
\(212\) | 1.97481 | − | 3.42047i | 0.135630 | − | 0.234919i | ||||
\(213\) | 13.5953 | − | 4.96340i | 0.931533 | − | 0.340086i | ||||
\(214\) | 1.23195 | − | 2.13380i | 0.0842144 | − | 0.145864i | ||||
\(215\) | −1.01969 | + | 0.588721i | −0.0695426 | + | 0.0401504i | ||||
\(216\) | 2.58481 | − | 4.50763i | 0.175874 | − | 0.306706i | ||||
\(217\) | 2.27521i | 0.154451i | ||||||||
\(218\) | 2.32388 | − | 1.34169i | 0.157393 | − | 0.0908708i | ||||
\(219\) | −2.89836 | + | 1.05814i | −0.195853 | + | 0.0715025i | ||||
\(220\) | 6.28666 | 0.423846 | ||||||||
\(221\) | −36.8365 | −2.47789 | ||||||||
\(222\) | −1.51219 | − | 4.14205i | −0.101492 | − | 0.277996i | ||||
\(223\) | −3.44225 | − | 1.98738i | −0.230510 | − | 0.133085i | 0.380297 | − | 0.924864i | \(-0.375822\pi\) |
−0.610807 | + | 0.791779i | \(0.709155\pi\) | |||||||
\(224\) | −0.193795 | − | 0.335662i | −0.0129484 | − | 0.0224274i | ||||
\(225\) | −2.29434 | + | 1.93287i | −0.152956 | + | 0.128858i | ||||
\(226\) | 0.0732990 | − | 0.126958i | 0.00487578 | − | 0.00844509i | ||||
\(227\) | 20.9613 | 1.39125 | 0.695626 | − | 0.718404i | \(-0.255127\pi\) | ||||
0.695626 | + | 0.718404i | \(0.255127\pi\) | |||||||
\(228\) | 7.54286 | − | 0.324338i | 0.499538 | − | 0.0214798i | ||||
\(229\) | −8.17578 | −0.540271 | −0.270135 | − | 0.962822i | \(-0.587068\pi\) | ||||
−0.270135 | + | 0.962822i | \(0.587068\pi\) | |||||||
\(230\) | 3.22076 | − | 5.57852i | 0.212371 | − | 0.367837i | ||||
\(231\) | 2.70964 | − | 3.23567i | 0.178281 | − | 0.212891i | ||||
\(232\) | 2.15245 | + | 3.72815i | 0.141315 | + | 0.244765i | ||||
\(233\) | −3.05627 | − | 1.76454i | −0.200223 | − | 0.115599i | 0.396537 | − | 0.918019i | \(-0.370212\pi\) |
−0.596759 | + | 0.802420i | \(0.703545\pi\) | |||||||
\(234\) | 20.3348 | − | 3.62676i | 1.32933 | − | 0.237089i | ||||
\(235\) | −7.78656 | −0.507939 | ||||||||
\(236\) | 1.11358 | 0.0724880 | ||||||||
\(237\) | −8.49550 | − | 23.2701i | −0.551842 | − | 1.51155i | ||||
\(238\) | 1.79582 | − | 1.03682i | 0.116406 | − | 0.0672069i | ||||
\(239\) | − | 15.8539i | − | 1.02550i | −0.858537 | − | 0.512751i | \(-0.828626\pi\) | ||
0.858537 | − | 0.512751i | \(-0.171374\pi\) | |||||||
\(240\) | −1.70603 | − | 0.299093i | −0.110124 | − | 0.0193063i | ||||
\(241\) | 3.16963 | − | 1.82999i | 0.204174 | − | 0.117880i | −0.394427 | − | 0.918927i | \(-0.629057\pi\) |
0.598601 | + | 0.801047i | \(0.295724\pi\) | |||||||
\(242\) | −14.2610 | + | 24.7009i | −0.916735 | + | 1.58783i | ||||
\(243\) | −14.6744 | − | 5.25960i | −0.941360 | − | 0.337403i | ||||
\(244\) | 1.28373 | − | 2.22348i | 0.0821823 | − | 0.142344i | ||||
\(245\) | −5.93208 | − | 3.42489i | −0.378987 | − | 0.218808i | ||||
\(246\) | 0.838620 | − | 4.78351i | 0.0534684 | − | 0.304985i | ||||
\(247\) | 20.2395 | + | 22.1604i | 1.28781 | + | 1.41004i | ||||
\(248\) | 5.87016i | 0.372756i | ||||||||
\(249\) | −3.58724 | + | 4.28364i | −0.227332 | + | 0.271465i | ||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | 9.75160 | − | 5.63009i | 0.615516 | − | 0.355368i | −0.159605 | − | 0.987181i | \(-0.551022\pi\) |
0.775121 | + | 0.631813i | \(0.217689\pi\) | |||||||
\(252\) | −0.889262 | + | 0.749160i | −0.0560183 | + | 0.0471927i | ||||
\(253\) | 20.2478 | + | 35.0703i | 1.27297 | + | 2.20485i | ||||
\(254\) | 16.3590i | 1.02646i | ||||||||
\(255\) | 1.60017 | − | 9.12741i | 0.100207 | − | 0.571581i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.6499 | − | 23.6423i | −0.851456 | − | 1.47477i | −0.879894 | − | 0.475170i | \(-0.842386\pi\) |
0.0284374 | − | 0.999596i | \(-0.490947\pi\) | |||||||
\(258\) | −0.352164 | + | 2.00875i | −0.0219248 | + | 0.125059i | ||||
\(259\) | 0.986725i | 0.0613121i | ||||||||
\(260\) | −3.44261 | − | 5.96278i | −0.213502 | − | 0.369796i | ||||
\(261\) | 9.87690 | − | 8.32080i | 0.611365 | − | 0.515045i | ||||
\(262\) | −2.32705 | + | 1.34352i | −0.143766 | + | 0.0830032i | ||||
\(263\) | 16.4659 | + | 9.50659i | 1.01533 | + | 0.586202i | 0.912748 | − | 0.408523i | \(-0.133956\pi\) |
0.102583 | + | 0.994724i | \(0.467289\pi\) | |||||||
\(264\) | 6.99100 | − | 8.34818i | 0.430266 | − | 0.513795i | ||||
\(265\) | 3.94962i | 0.242623i | ||||||||
\(266\) | −1.61043 | − | 0.510676i | −0.0987419 | − | 0.0313116i | ||||
\(267\) | 4.48547 | − | 25.5853i | 0.274507 | − | 1.56579i | ||||
\(268\) | −6.95760 | − | 4.01697i | −0.425003 | − | 0.245376i | ||||
\(269\) | 9.43473 | − | 16.3414i | 0.575246 | − | 0.996355i | −0.420769 | − | 0.907168i | \(-0.638240\pi\) |
0.996015 | − | 0.0891869i | \(-0.0284268\pi\) | |||||||
\(270\) | 0.0153044 | + | 5.19613i | 0.000931395 | + | 0.316226i | ||||
\(271\) | 9.90543 | − | 17.1567i | 0.601712 | − | 1.04220i | −0.390850 | − | 0.920454i | \(-0.627819\pi\) |
0.992562 | − | 0.121741i | \(-0.0388478\pi\) | |||||||
\(272\) | 4.63331 | − | 2.67504i | 0.280936 | − | 0.162198i | ||||
\(273\) | −4.55278 | − | 0.798171i | −0.275547 | − | 0.0483075i | ||||
\(274\) | − | 13.6298i | − | 0.823403i | ||||||
\(275\) | −5.44441 | + | 3.14333i | −0.328310 | + | 0.189550i | ||||
\(276\) | −3.82623 | − | 10.4804i | −0.230312 | − | 0.630849i | ||||
\(277\) | 13.1915 | 0.792598 | 0.396299 | − | 0.918121i | \(-0.370294\pi\) | ||||
0.396299 | + | 0.918121i | \(0.370294\pi\) | |||||||
\(278\) | 22.6639 | 1.35929 | ||||||||
\(279\) | 17.3369 | − | 3.09208i | 1.03793 | − | 0.185118i | ||||
\(280\) | 0.335662 | + | 0.193795i | 0.0200596 | + | 0.0115814i | ||||
\(281\) | 8.39558 | + | 14.5416i | 0.500838 | + | 0.867477i | 1.00000 | 0.000967983i | \(0.000308119\pi\) | |
−0.499161 | + | 0.866509i | \(0.666359\pi\) | |||||||
\(282\) | −8.65895 | + | 10.3399i | −0.515633 | + | 0.615734i | ||||
\(283\) | 3.98624 | − | 6.90437i | 0.236958 | − | 0.410422i | −0.722882 | − | 0.690971i | \(-0.757183\pi\) |
0.959840 | + | 0.280549i | \(0.0905164\pi\) | |||||||
\(284\) | −8.35597 | −0.495836 | ||||||||
\(285\) | −6.37014 | + | 4.05232i | −0.377335 | + | 0.240039i | ||||
\(286\) | 43.2851 | 2.55950 | ||||||||
\(287\) | −0.543377 | + | 0.941156i | −0.0320745 | + | 0.0555547i | ||||
\(288\) | −2.29434 | + | 1.93287i | −0.135195 | + | 0.113896i | ||||
\(289\) | 5.81170 | + | 10.0662i | 0.341864 | + | 0.592127i | ||||
\(290\) | −3.72815 | − | 2.15245i | −0.218924 | − | 0.126396i | ||||
\(291\) | −3.66180 | − | 10.0301i | −0.214659 | − | 0.587973i | ||||
\(292\) | 1.78140 | 0.104249 | ||||||||
\(293\) | 4.52893 | 0.264583 | 0.132292 | − | 0.991211i | \(-0.457766\pi\) | ||||
0.132292 | + | 0.991211i | \(0.457766\pi\) | |||||||
\(294\) | −11.1447 | + | 4.06872i | −0.649970 | + | 0.237293i | ||||
\(295\) | −0.964390 | + | 0.556791i | −0.0561489 | + | 0.0324176i | ||||
\(296\) | 2.54580i | 0.147972i | ||||||||
\(297\) | −28.3380 | − | 16.2498i | −1.64433 | − | 0.942911i | ||||
\(298\) | 2.36838 | − | 1.36738i | 0.137196 | − | 0.0792104i | ||||
\(299\) | 22.1757 | − | 38.4094i | 1.28245 | − | 2.22127i | ||||
\(300\) | 1.62701 | − | 0.593994i | 0.0939356 | − | 0.0342943i | ||||
\(301\) | 0.228182 | − | 0.395223i | 0.0131522 | − | 0.0227802i | ||||
\(302\) | 4.36049 | + | 2.51753i | 0.250918 | + | 0.144868i | ||||
\(303\) | −7.16155 | − | 1.25553i | −0.411420 | − | 0.0721281i | ||||
\(304\) | −4.15500 | − | 1.31757i | −0.238305 | − | 0.0755679i | ||||
\(305\) | 2.56746i | 0.147012i | ||||||||
\(306\) | −10.3410 | − | 12.2749i | −0.591157 | − | 0.701711i | ||||
\(307\) | 20.5036 | + | 11.8378i | 1.17020 | + | 0.675618i | 0.953728 | − | 0.300670i | \(-0.0972104\pi\) |
0.216476 | + | 0.976288i | \(0.430544\pi\) | |||||||
\(308\) | −2.11019 | + | 1.21832i | −0.120239 | + | 0.0694203i | ||||
\(309\) | 16.0895 | − | 19.2130i | 0.915300 | − | 1.09299i | ||||
\(310\) | −2.93508 | − | 5.08371i | −0.166701 | − | 0.288735i | ||||
\(311\) | 21.2557i | 1.20530i | 0.798006 | + | 0.602650i | \(0.205888\pi\) | ||||
−0.798006 | + | 0.602650i | \(0.794112\pi\) | |||||||
\(312\) | −11.7464 | − | 2.05932i | −0.665010 | − | 0.116586i | ||||
\(313\) | 16.1860 | + | 28.0351i | 0.914889 | + | 1.58463i | 0.807063 | + | 0.590465i | \(0.201056\pi\) |
0.107826 | + | 0.994170i | \(0.465611\pi\) | |||||||
\(314\) | −0.931580 | − | 1.61354i | −0.0525721 | − | 0.0910575i | ||||
\(315\) | 0.395544 | − | 1.09342i | 0.0222864 | − | 0.0616074i | ||||
\(316\) | 14.3023i | 0.804569i | ||||||||
\(317\) | −0.273517 | − | 0.473746i | −0.0153623 | − | 0.0266082i | 0.858242 | − | 0.513245i | \(-0.171557\pi\) |
−0.873604 | + | 0.486637i | \(0.838223\pi\) | |||||||
\(318\) | 5.24478 | + | 4.39212i | 0.294112 | + | 0.246298i | ||||
\(319\) | 23.4376 | − | 13.5317i | 1.31225 | − | 0.757630i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | 3.27186 | + | 2.73995i | 0.182618 | + | 0.152929i | ||||
\(322\) | 2.49667i | 0.139134i | ||||||||
\(323\) | 7.04911 | − | 22.2296i | 0.392223 | − | 1.23689i | ||||
\(324\) | 6.91707 | + | 5.75797i | 0.384281 | + | 0.319887i | ||||
\(325\) | 5.96278 | + | 3.44261i | 0.330756 | + | 0.190962i | ||||
\(326\) | −7.82120 | + | 13.5467i | −0.433176 | + | 0.750284i | ||||
\(327\) | 1.59391 | + | 4.36590i | 0.0881436 | + | 0.241435i | ||||
\(328\) | −1.40194 | + | 2.42823i | −0.0774091 | + | 0.134077i | ||||
\(329\) | 2.61365 | − | 1.50899i | 0.144095 | − | 0.0831935i | ||||
\(330\) | −1.88029 | + | 10.7252i | −0.103507 | + | 0.590405i | ||||
\(331\) | 12.2880i | 0.675410i | 0.941252 | + | 0.337705i | \(0.109651\pi\) | ||||
−0.941252 | + | 0.337705i | \(0.890349\pi\) | |||||||
\(332\) | 2.79365 | − | 1.61291i | 0.153321 | − | 0.0885202i | ||||
\(333\) | 7.51876 | − | 1.34099i | 0.412025 | − | 0.0734857i | ||||
\(334\) | 5.17958 | 0.283414 | ||||||||
\(335\) | 8.03394 | 0.438941 | ||||||||
\(336\) | 0.630613 | − | 0.230226i | 0.0344027 | − | 0.0125598i | ||||
\(337\) | 12.8425 | + | 7.41464i | 0.699577 | + | 0.403901i | 0.807190 | − | 0.590292i | \(-0.200987\pi\) |
−0.107613 | + | 0.994193i | \(0.534321\pi\) | |||||||
\(338\) | −17.2032 | − | 29.7968i | −0.935730 | − | 1.62073i | ||||
\(339\) | 0.194670 | + | 0.163022i | 0.0105730 | + | 0.00885416i | ||||
\(340\) | −2.67504 | + | 4.63331i | −0.145074 | + | 0.251276i | ||||
\(341\) | 36.9037 | 1.99845 | ||||||||
\(342\) | −1.70268 | + | 12.9654i | −0.0920706 | + | 0.701087i | ||||
\(343\) | 5.36802 | 0.289846 | ||||||||
\(344\) | 0.588721 | − | 1.01969i | 0.0317417 | − | 0.0549782i | ||||
\(345\) | 8.55383 | + | 7.16322i | 0.460523 | + | 0.385655i | ||||
\(346\) | 4.91408 | + | 8.51144i | 0.264183 | + | 0.457578i | ||||
\(347\) | −8.34699 | − | 4.81914i | −0.448090 | − | 0.258705i | 0.258933 | − | 0.965895i | \(-0.416629\pi\) |
−0.707023 | + | 0.707190i | \(0.749962\pi\) | |||||||
\(348\) | −7.00412 | + | 2.55708i | −0.375460 | + | 0.137074i | ||||
\(349\) | −25.2299 | −1.35053 | −0.675263 | − | 0.737577i | \(-0.735970\pi\) | ||||
−0.675263 | + | 0.737577i | \(0.735970\pi\) | |||||||
\(350\) | −0.387589 | −0.0207175 | ||||||||
\(351\) | 0.105374 | + | 35.7765i | 0.00562446 | + | 1.90961i | ||||
\(352\) | −5.44441 | + | 3.14333i | −0.290188 | + | 0.167540i | ||||
\(353\) | − | 10.0563i | − | 0.535241i | −0.963524 | − | 0.267620i | \(-0.913763\pi\) | ||
0.963524 | − | 0.267620i | \(-0.0862373\pi\) | |||||||
\(354\) | −0.333064 | + | 1.89980i | −0.0177022 | + | 0.100973i | ||||
\(355\) | 7.23648 | − | 4.17799i | 0.384073 | − | 0.221744i | ||||
\(356\) | −7.49847 | + | 12.9877i | −0.397418 | + | 0.688348i | ||||
\(357\) | 1.23173 | + | 3.37383i | 0.0651899 | + | 0.178562i | ||||
\(358\) | 9.81870 | − | 17.0065i | 0.518934 | − | 0.898821i | ||||
\(359\) | 9.76791 | + | 5.63951i | 0.515531 | + | 0.297642i | 0.735104 | − | 0.677954i | \(-0.237133\pi\) |
−0.219573 | + | 0.975596i | \(0.570467\pi\) | |||||||
\(360\) | 1.02052 | − | 2.82109i | 0.0537863 | − | 0.148684i | ||||
\(361\) | −17.2461 | + | 7.97315i | −0.907691 | + | 0.419639i | ||||
\(362\) | 22.2978i | 1.17195i | ||||||||
\(363\) | −37.8751 | − | 31.7176i | −1.98793 | − | 1.66474i | ||||
\(364\) | 2.31111 | + | 1.33432i | 0.121135 | + | 0.0699374i | ||||
\(365\) | −1.54274 | + | 0.890700i | −0.0807505 | + | 0.0466213i | ||||
\(366\) | 3.40938 | + | 2.85511i | 0.178211 | + | 0.149239i | ||||
\(367\) | −13.2097 | − | 22.8799i | −0.689540 | − | 1.19432i | −0.971987 | − | 0.235036i | \(-0.924479\pi\) |
0.282447 | − | 0.959283i | \(-0.408854\pi\) | |||||||
\(368\) | 6.44153i | 0.335788i | ||||||||
\(369\) | 7.90999 | + | 2.86142i | 0.411777 | + | 0.148960i | ||||
\(370\) | −1.27290 | − | 2.20473i | −0.0661750 | − | 0.114618i | ||||
\(371\) | −0.765414 | − | 1.32574i | −0.0397383 | − | 0.0688288i | ||||
\(372\) | −10.0147 | − | 1.75572i | −0.519237 | − | 0.0910299i | ||||
\(373\) | 9.42090i | 0.487796i | 0.969801 | + | 0.243898i | \(0.0784262\pi\) | ||||
−0.969801 | + | 0.243898i | \(0.921574\pi\) | |||||||
\(374\) | −16.8171 | − | 29.1280i | −0.869590 | − | 1.50617i | ||||
\(375\) | −1.11204 | + | 1.32792i | −0.0574254 | + | 0.0685735i | ||||
\(376\) | 6.74336 | − | 3.89328i | 0.347762 | − | 0.200781i | ||||
\(377\) | −25.6691 | − | 14.8201i | −1.32203 | − | 0.763273i | ||||
\(378\) | −1.01212 | − | 1.74118i | −0.0520578 | − | 0.0895565i | ||||
\(379\) | 18.4868i | 0.949601i | 0.880093 | + | 0.474801i | \(0.157480\pi\) | ||||
−0.880093 | + | 0.474801i | \(0.842520\pi\) | |||||||
\(380\) | 4.25712 | − | 0.936449i | 0.218386 | − | 0.0480388i | ||||
\(381\) | −27.9091 | − | 4.89287i | −1.42982 | − | 0.250669i | ||||
\(382\) | −14.9599 | − | 8.63710i | −0.765415 | − | 0.441912i | ||||
\(383\) | −8.39580 | + | 14.5419i | −0.429005 | + | 0.743059i | −0.996785 | − | 0.0801217i | \(-0.974469\pi\) |
0.567780 | + | 0.823180i | \(0.307802\pi\) | |||||||
\(384\) | 1.62701 | − | 0.593994i | 0.0830282 | − | 0.0303121i | ||||
\(385\) | 1.21832 | − | 2.11019i | 0.0620914 | − | 0.107545i | ||||
\(386\) | 8.44254 | − | 4.87430i | 0.429714 | − | 0.248096i | ||||
\(387\) | −3.32167 | − | 1.20161i | −0.168850 | − | 0.0610811i | ||||
\(388\) | 6.16472i | 0.312966i | ||||||||
\(389\) | −3.31963 | + | 1.91659i | −0.168312 | + | 0.0971748i | −0.581790 | − | 0.813339i | \(-0.697647\pi\) |
0.413478 | + | 0.910514i | \(0.364314\pi\) | |||||||
\(390\) | 11.2024 | − | 4.08978i | 0.567253 | − | 0.207094i | ||||
\(391\) | −34.4627 | −1.74285 | ||||||||
\(392\) | 6.84977 | 0.345966 | ||||||||
\(393\) | −1.59609 | − | 4.37186i | −0.0805121 | − | 0.220531i | ||||
\(394\) | 6.92311 | + | 3.99706i | 0.348781 | + | 0.201369i | ||||
\(395\) | −7.15117 | − | 12.3862i | −0.359814 | − | 0.623217i | ||||
\(396\) | 12.1513 | + | 14.4237i | 0.610626 | + | 0.724821i | ||||
\(397\) | 6.16028 | − | 10.6699i | 0.309176 | − | 0.535508i | −0.669007 | − | 0.743257i | \(-0.733280\pi\) |
0.978182 | + | 0.207748i | \(0.0666135\pi\) | |||||||
\(398\) | 5.01565 | 0.251412 | ||||||||
\(399\) | 1.35290 | − | 2.59471i | 0.0677296 | − | 0.129898i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 3.20325 | − | 5.54818i | 0.159962 | − | 0.277063i | −0.774892 | − | 0.632093i | \(-0.782196\pi\) |
0.934855 | + | 0.355030i | \(0.115529\pi\) | |||||||
\(402\) | 8.93405 | − | 10.6684i | 0.445590 | − | 0.532093i | ||||
\(403\) | −20.2087 | − | 35.0025i | −1.00667 | − | 1.74360i | ||||
\(404\) | 3.63539 | + | 2.09889i | 0.180867 | + | 0.104424i | ||||
\(405\) | −8.86934 | − | 1.52801i | −0.440721 | − | 0.0759277i | ||||
\(406\) | 1.66853 | 0.0828078 | ||||||||
\(407\) | 16.0046 | 0.793318 | ||||||||
\(408\) | 3.17792 | + | 8.70465i | 0.157330 | + | 0.430945i | ||||
\(409\) | −28.7986 | + | 16.6269i | −1.42400 | + | 0.822147i | −0.996638 | − | 0.0819327i | \(-0.973891\pi\) |
−0.427363 | + | 0.904080i | \(0.640557\pi\) | |||||||
\(410\) | − | 2.80388i | − | 0.138474i | ||||||
\(411\) | 23.2528 | + | 4.07656i | 1.14698 | + | 0.201082i | ||||
\(412\) | −12.5301 | + | 7.23425i | −0.617313 | + | 0.356406i | ||||
\(413\) | 0.215806 | − | 0.373787i | 0.0106191 | − | 0.0183929i | ||||
\(414\) | 19.0244 | − | 3.39304i | 0.934997 | − | 0.166759i | ||||
\(415\) | −1.61291 | + | 2.79365i | −0.0791748 | + | 0.137135i | ||||
\(416\) | 5.96278 | + | 3.44261i | 0.292349 | + | 0.168788i | ||||
\(417\) | −6.77860 | + | 38.6653i | −0.331949 | + | 1.89345i | ||||
\(418\) | −8.28312 | + | 26.1211i | −0.405141 | + | 1.27762i | ||||
\(419\) | 26.2177i | 1.28082i | 0.768034 | + | 0.640409i | \(0.221235\pi\) | ||||
−0.768034 | + | 0.640409i | \(0.778765\pi\) | |||||||
\(420\) | −0.431014 | + | 0.514688i | −0.0210313 | + | 0.0251142i | ||||
\(421\) | 16.2792 | + | 9.39883i | 0.793402 | + | 0.458071i | 0.841159 | − | 0.540788i | \(-0.181874\pi\) |
−0.0477568 | + | 0.998859i | \(0.515207\pi\) | |||||||
\(422\) | −0.901047 | + | 0.520219i | −0.0438623 | + | 0.0253239i | ||||
\(423\) | −15.0504 | − | 17.8650i | −0.731777 | − | 0.868628i | ||||
\(424\) | −1.97481 | − | 3.42047i | −0.0959052 | − | 0.166113i | ||||
\(425\) | − | 5.35008i | − | 0.259517i | ||||||
\(426\) | 2.49921 | − | 14.2556i | 0.121087 | − | 0.690684i | ||||
\(427\) | −0.497560 | − | 0.861799i | −0.0240786 | − | 0.0417054i | ||||
\(428\) | −1.23195 | − | 2.13380i | −0.0595485 | − | 0.103141i | ||||
\(429\) | −12.9463 | + | 73.8457i | −0.625051 | + | 3.56531i | ||||
\(430\) | 1.17744i | 0.0567813i | ||||||||
\(431\) | 16.8907 | + | 29.2555i | 0.813595 | + | 1.40919i | 0.910333 | + | 0.413877i | \(0.135826\pi\) |
−0.0967380 | + | 0.995310i | \(0.530841\pi\) | |||||||
\(432\) | −2.61132 | − | 4.49233i | −0.125637 | − | 0.216137i | ||||
\(433\) | 18.8094 | − | 10.8596i | 0.903920 | − | 0.521879i | 0.0254504 | − | 0.999676i | \(-0.491898\pi\) |
0.878470 | + | 0.477797i | \(0.158565\pi\) | |||||||
\(434\) | 1.97039 | + | 1.13761i | 0.0945818 | + | 0.0546068i | ||||
\(435\) | 4.78720 | − | 5.71655i | 0.229529 | − | 0.274088i | ||||
\(436\) | − | 2.68338i | − | 0.128511i | ||||||
\(437\) | 18.9352 | + | 20.7324i | 0.905792 | + | 0.991763i | ||||
\(438\) | −0.532803 | + | 3.03912i | −0.0254583 | + | 0.145215i | ||||
\(439\) | −4.46634 | − | 2.57864i | −0.213167 | − | 0.123072i | 0.389616 | − | 0.920978i | \(-0.372608\pi\) |
−0.602782 | + | 0.797906i | \(0.705941\pi\) | |||||||
\(440\) | 3.14333 | − | 5.44441i | 0.149852 | − | 0.259552i | ||||
\(441\) | −3.60808 | − | 20.2301i | −0.171813 | − | 0.963338i | ||||
\(442\) | −18.4183 | + | 31.9014i | −0.876068 | + | 1.51739i | ||||
\(443\) | −28.7183 | + | 16.5805i | −1.36445 | + | 0.787765i | −0.990212 | − | 0.139568i | \(-0.955429\pi\) |
−0.374237 | + | 0.927333i | \(0.622095\pi\) | |||||||
\(444\) | −4.34322 | − | 0.761431i | −0.206120 | − | 0.0361359i | ||||
\(445\) | − | 14.9969i | − | 0.710923i | ||||||
\(446\) | −3.44225 | + | 1.98738i | −0.162995 | + | 0.0941053i | ||||
\(447\) | 1.62444 | + | 4.44950i | 0.0768332 | + | 0.210454i | ||||
\(448\) | −0.387589 | −0.0183119 | ||||||||
\(449\) | −28.6061 | −1.35001 | −0.675004 | − | 0.737815i | \(-0.735858\pi\) | ||||
−0.675004 | + | 0.737815i | \(0.735858\pi\) | |||||||
\(450\) | 0.526745 | + | 2.95339i | 0.0248310 | + | 0.139224i | ||||
\(451\) | 15.2655 | + | 8.81352i | 0.718822 | + | 0.415012i | ||||
\(452\) | −0.0732990 | − | 0.126958i | −0.00344769 | − | 0.00597158i | ||||
\(453\) | −5.59918 | + | 6.68616i | −0.263072 | + | 0.314143i | ||||
\(454\) | 10.4807 | − | 18.1530i | 0.491882 | − | 0.851964i | ||||
\(455\) | −2.66864 | −0.125108 | ||||||||
\(456\) | 3.49055 | − | 6.69448i | 0.163460 | − | 0.313498i | ||||
\(457\) | 12.0944 | 0.565752 | 0.282876 | − | 0.959156i | \(-0.408711\pi\) | ||||
0.282876 | + | 0.959156i | \(0.408711\pi\) | |||||||
\(458\) | −4.08789 | + | 7.08043i | −0.191015 | + | 0.330847i | ||||
\(459\) | 24.0343 | − | 13.9708i | 1.12183 | − | 0.652100i | ||||
\(460\) | −3.22076 | − | 5.57852i | −0.150169 | − | 0.260100i | ||||
\(461\) | −23.9736 | − | 13.8412i | −1.11656 | − | 0.644647i | −0.176040 | − | 0.984383i | \(-0.556329\pi\) |
−0.940521 | + | 0.339736i | \(0.889662\pi\) | |||||||
\(462\) | −1.44735 | − | 3.96445i | −0.0673368 | − | 0.184443i | ||||
\(463\) | 22.5239 | 1.04678 | 0.523388 | − | 0.852094i | \(-0.324668\pi\) | ||||
0.523388 | + | 0.852094i | \(0.324668\pi\) | |||||||
\(464\) | 4.30489 | 0.199850 | ||||||||
\(465\) | 9.55083 | − | 3.48684i | 0.442909 | − | 0.161698i | ||||
\(466\) | −3.05627 | + | 1.76454i | −0.141579 | + | 0.0817407i | ||||
\(467\) | 22.4617i | 1.03940i | 0.854348 | + | 0.519701i | \(0.173957\pi\) | ||||
−0.854348 | + | 0.519701i | \(0.826043\pi\) | |||||||
\(468\) | 7.02653 | − | 19.4238i | 0.324802 | − | 0.897867i | ||||
\(469\) | −2.69669 | + | 1.55693i | −0.124522 | + | 0.0718926i | ||||
\(470\) | −3.89328 | + | 6.74336i | −0.179584 | + | 0.311048i | ||||
\(471\) | 3.03139 | − | 1.10671i | 0.139679 | − | 0.0509943i | ||||
\(472\) | 0.556791 | − | 0.964390i | 0.0256284 | − | 0.0443896i | ||||
\(473\) | −6.41047 | − | 3.70109i | −0.294754 | − | 0.170176i | ||||
\(474\) | −24.4002 | − | 4.27772i | −1.12074 | − | 0.196482i | ||||
\(475\) | −3.21855 | + | 2.93955i | −0.147677 | + | 0.134876i | ||||
\(476\) | − | 2.07363i | − | 0.0950449i | ||||||
\(477\) | −9.06177 | + | 7.63410i | −0.414910 | + | 0.349542i | ||||
\(478\) | −13.7299 | − | 7.92694i | −0.627989 | − | 0.362570i | ||||
\(479\) | −14.0462 | + | 8.10959i | −0.641788 | + | 0.370537i | −0.785303 | − | 0.619111i | \(-0.787493\pi\) |
0.143515 | + | 0.989648i | \(0.454160\pi\) | |||||||
\(480\) | −1.11204 | + | 1.32792i | −0.0507573 | + | 0.0606110i | ||||
\(481\) | −8.76421 | − | 15.1801i | −0.399614 | − | 0.692151i | ||||
\(482\) | − | 3.65997i | − | 0.166707i | ||||||
\(483\) | −4.25939 | − | 0.746734i | −0.193809 | − | 0.0339776i | ||||
\(484\) | 14.2610 | + | 24.7009i | 0.648229 | + | 1.12277i | ||||
\(485\) | −3.08236 | − | 5.33880i | −0.139963 | − | 0.242423i | ||||
\(486\) | −11.8921 | + | 10.0786i | −0.539438 | + | 0.457173i | ||||
\(487\) | 26.2560i | 1.18977i | 0.803809 | + | 0.594887i | \(0.202803\pi\) | ||||
−0.803809 | + | 0.594887i | \(0.797197\pi\) | |||||||
\(488\) | −1.28373 | − | 2.22348i | −0.0581117 | − | 0.100652i | ||||
\(489\) | −20.7719 | − | 17.3949i | −0.939337 | − | 0.786627i | ||||
\(490\) | −5.93208 | + | 3.42489i | −0.267984 | + | 0.154721i | ||||
\(491\) | 20.1138 | + | 11.6127i | 0.907723 | + | 0.524074i | 0.879698 | − | 0.475533i | \(-0.157745\pi\) |
0.0280250 | + | 0.999607i | \(0.491078\pi\) | |||||||
\(492\) | −3.72333 | − | 3.11802i | −0.167861 | − | 0.140571i | ||||
\(493\) | 23.0315i | 1.03729i | ||||||||
\(494\) | 29.3112 | − | 6.44766i | 1.31878 | − | 0.290094i | ||||
\(495\) | −17.7352 | − | 6.41568i | −0.797139 | − | 0.288363i | ||||
\(496\) | 5.08371 | + | 2.93508i | 0.228265 | + | 0.131789i | ||||
\(497\) | −1.61934 | + | 2.80478i | −0.0726374 | + | 0.125812i | ||||
\(498\) | 1.91612 | + | 5.24846i | 0.0858635 | + | 0.235189i | ||||
\(499\) | −5.68385 | + | 9.84472i | −0.254444 | + | 0.440710i | −0.964744 | − | 0.263189i | \(-0.915226\pi\) |
0.710300 | + | 0.703899i | \(0.248559\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | −1.54917 | + | 8.83653i | −0.0692120 | + | 0.394787i | ||||
\(502\) | − | 11.2602i | − | 0.502567i | ||||||
\(503\) | −11.7374 | + | 6.77660i | −0.523346 | + | 0.302154i | −0.738302 | − | 0.674470i | \(-0.764372\pi\) |
0.214957 | + | 0.976624i | \(0.431039\pi\) | |||||||
\(504\) | 0.204161 | + | 1.14470i | 0.00909403 | + | 0.0509892i | ||||
\(505\) | −4.19778 | −0.186799 | ||||||||
\(506\) | 40.4957 | 1.80025 | ||||||||
\(507\) | 55.9796 | − | 20.4372i | 2.48614 | − | 0.907647i | ||||
\(508\) | 14.1674 | + | 8.17952i | 0.628575 | + | 0.362908i | ||||
\(509\) | −15.5217 | − | 26.8843i | −0.687986 | − | 1.19163i | −0.972488 | − | 0.232951i | \(-0.925162\pi\) |
0.284502 | − | 0.958675i | \(-0.408172\pi\) | |||||||
\(510\) | −7.10448 | − | 5.94949i | −0.314592 | − | 0.263448i | ||||
\(511\) | 0.345226 | − | 0.597948i | 0.0152719 | − | 0.0264517i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −21.6101 | − | 6.78268i | −0.954108 | − | 0.299463i | ||||
\(514\) | −27.2998 | −1.20414 | ||||||||
\(515\) | 7.23425 | − | 12.5301i | 0.318779 | − | 0.552141i | ||||
\(516\) | 1.56355 | + | 1.30936i | 0.0688314 | + | 0.0576413i | ||||
\(517\) | −24.4757 | − | 42.3932i | −1.07644 | − | 1.86445i | ||||
\(518\) | 0.854529 | + | 0.493363i | 0.0375459 | + | 0.0216771i | ||||
\(519\) | −15.9906 | + | 5.83787i | −0.701908 | + | 0.256254i | ||||
\(520\) | −6.88523 | −0.301937 | ||||||||
\(521\) | 7.63094 | 0.334317 | 0.167159 | − | 0.985930i | \(-0.446541\pi\) | ||||
0.167159 | + | 0.985930i | \(0.446541\pi\) | |||||||
\(522\) | −2.26758 | − | 12.7140i | −0.0992492 | − | 0.556479i | ||||
\(523\) | −14.6044 | + | 8.43187i | −0.638607 | + | 0.368700i | −0.784078 | − | 0.620663i | \(-0.786864\pi\) |
0.145471 | + | 0.989363i | \(0.453530\pi\) | |||||||
\(524\) | 2.68705i | 0.117384i | ||||||||
\(525\) | 0.115925 | − | 0.661239i | 0.00505939 | − | 0.0288589i | ||||
\(526\) | 16.4659 | − | 9.50659i | 0.717948 | − | 0.414507i | ||||
\(527\) | −15.7029 | + | 27.1983i | −0.684030 | + | 1.18477i | ||||
\(528\) | −3.73424 | − | 10.2285i | −0.162512 | − | 0.445137i | ||||
\(529\) | 9.24662 | − | 16.0156i | 0.402027 | − | 0.696331i | ||||
\(530\) | 3.42047 | + | 1.97481i | 0.148576 | + | 0.0857802i | ||||
\(531\) | −3.14151 | − | 1.13644i | −0.136330 | − | 0.0493171i | ||||
\(532\) | −1.24747 | + | 1.13934i | −0.0540849 | + | 0.0493965i | ||||
\(533\) | − | 19.3053i | − | 0.836207i | ||||||
\(534\) | −19.9147 | − | 16.6772i | −0.861795 | − | 0.721691i | ||||
\(535\) | 2.13380 | + | 1.23195i | 0.0922522 | + | 0.0532618i | ||||
\(536\) | −6.95760 | + | 4.01697i | −0.300522 | + | 0.173507i | ||||
\(537\) | 26.0769 | + | 21.8375i | 1.12530 | + | 0.942359i | ||||
\(538\) | −9.43473 | − | 16.3414i | −0.406760 | − | 0.704529i | ||||
\(539\) | − | 43.0622i | − | 1.85482i | ||||||
\(540\) | 4.50763 | + | 2.58481i | 0.193978 | + | 0.111233i | ||||
\(541\) | −11.3322 | − | 19.6279i | −0.487208 | − | 0.843869i | 0.512684 | − | 0.858577i | \(-0.328651\pi\) |
−0.999892 | + | 0.0147085i | \(0.995318\pi\) | |||||||
\(542\) | −9.90543 | − | 17.1567i | −0.425475 | − | 0.736944i | ||||
\(543\) | −38.0408 | − | 6.66911i | −1.63249 | − | 0.286199i | ||||
\(544\) | − | 5.35008i | − | 0.229383i | ||||||
\(545\) | 1.34169 | + | 2.32388i | 0.0574717 | + | 0.0995440i | ||||
\(546\) | −2.96763 | + | 3.54374i | −0.127003 | + | 0.151658i | ||||
\(547\) | −1.44092 | + | 0.831914i | −0.0616091 | + | 0.0355701i | −0.530488 | − | 0.847692i | \(-0.677991\pi\) |
0.468879 | + | 0.883262i | \(0.344658\pi\) | |||||||
\(548\) | −11.8037 | − | 6.81488i | −0.504230 | − | 0.291117i | ||||
\(549\) | −5.89063 | + | 4.96257i | −0.251406 | + | 0.211797i | ||||
\(550\) | 6.28666i | 0.268064i | ||||||||
\(551\) | 13.8555 | − | 12.6544i | 0.590264 | − | 0.539097i | ||||
\(552\) | −10.9894 | − | 1.92661i | −0.467742 | − | 0.0820021i | ||||
\(553\) | 4.80075 | + | 2.77172i | 0.204149 | + | 0.117865i | ||||
\(554\) | 6.59573 | − | 11.4241i | 0.280226 | − | 0.485365i | ||||
\(555\) | 4.14205 | − | 1.51219i | 0.175820 | − | 0.0641889i | ||||
\(556\) | 11.3319 | − | 19.6275i | 0.480581 | − | 0.832391i | ||||
\(557\) | 7.03591 | − | 4.06218i | 0.298121 | − | 0.172120i | −0.343477 | − | 0.939161i | \(-0.611605\pi\) |
0.641599 | + | 0.767041i | \(0.278272\pi\) | |||||||
\(558\) | 5.99063 | − | 16.5602i | 0.253604 | − | 0.701051i | ||||
\(559\) | 8.10695i | 0.342888i | ||||||||
\(560\) | 0.335662 | − | 0.193795i | 0.0141843 | − | 0.00818932i | ||||
\(561\) | 54.7232 | − | 19.9785i | 2.31042 | − | 0.843492i | ||||
\(562\) | 16.7912 | 0.708292 | ||||||||
\(563\) | −6.21069 | −0.261749 | −0.130875 | − | 0.991399i | \(-0.541779\pi\) | ||||
−0.130875 | + | 0.991399i | \(0.541779\pi\) | |||||||
\(564\) | 4.62517 | + | 12.6688i | 0.194755 | + | 0.533454i | ||||
\(565\) | 0.126958 | + | 0.0732990i | 0.00534114 | + | 0.00308371i | ||||
\(566\) | −3.98624 | − | 6.90437i | −0.167554 | − | 0.290213i | ||||
\(567\) | 3.27322 | − | 1.20593i | 0.137462 | − | 0.0506444i | ||||
\(568\) | −4.17799 | + | 7.23648i | −0.175304 | + | 0.303636i | ||||
\(569\) | −24.7474 | −1.03747 | −0.518733 | − | 0.854936i | \(-0.673596\pi\) | ||||
−0.518733 | + | 0.854936i | \(0.673596\pi\) | |||||||
\(570\) | 0.324338 | + | 7.54286i | 0.0135850 | + | 0.315936i | ||||
\(571\) | −2.91055 | −0.121803 | −0.0609014 | − | 0.998144i | \(-0.519398\pi\) | ||||
−0.0609014 | + | 0.998144i | \(0.519398\pi\) | |||||||
\(572\) | 21.6425 | − | 37.4860i | 0.904920 | − | 1.56737i | ||||
\(573\) | 19.2096 | − | 22.9388i | 0.802491 | − | 0.958280i | ||||
\(574\) | 0.543377 | + | 0.941156i | 0.0226801 | + | 0.0392831i | ||||
\(575\) | 5.57852 | + | 3.22076i | 0.232641 | + | 0.134315i | ||||
\(576\) | 0.526745 | + | 2.95339i | 0.0219477 | + | 0.123058i | ||||
\(577\) | 11.1520 | 0.464264 | 0.232132 | − | 0.972684i | \(-0.425430\pi\) | ||||
0.232132 | + | 0.972684i | \(0.425430\pi\) | |||||||
\(578\) | 11.6234 | 0.483469 | ||||||||
\(579\) | 5.79061 | + | 15.8611i | 0.240650 | + | 0.659165i | ||||
\(580\) | −3.72815 | + | 2.15245i | −0.154803 | + | 0.0893755i | ||||
\(581\) | − | 1.25030i | − | 0.0518710i | ||||||
\(582\) | −10.5172 | − | 1.84382i | −0.435952 | − | 0.0764289i | ||||
\(583\) | −21.5033 | + | 12.4149i | −0.890577 | + | 0.514175i | ||||
\(584\) | 0.890700 | − | 1.54274i | 0.0368574 | − | 0.0638389i | ||||
\(585\) | 3.62676 | + | 20.3348i | 0.149948 | + | 0.840740i | ||||
\(586\) | 2.26447 | − | 3.92217i | 0.0935443 | − | 0.162023i | ||||
\(587\) | −28.0297 | − | 16.1829i | −1.15691 | − | 0.667942i | −0.206348 | − | 0.978479i | \(-0.566158\pi\) |
−0.950561 | + | 0.310537i | \(0.899491\pi\) | |||||||
\(588\) | −2.04872 | + | 11.6859i | −0.0844877 | + | 0.481920i | ||||
\(589\) | 24.9900 | − | 5.49711i | 1.02969 | − | 0.226504i | ||||
\(590\) | 1.11358i | 0.0458454i | ||||||||
\(591\) | −8.88976 | + | 10.6156i | −0.365676 | + | 0.436665i | ||||
\(592\) | 2.20473 | + | 1.27290i | 0.0906138 | + | 0.0523159i | ||||
\(593\) | −11.3927 | + | 6.57758i | −0.467842 | + | 0.270109i | −0.715336 | − | 0.698781i | \(-0.753726\pi\) |
0.247494 | + | 0.968889i | \(0.420393\pi\) | |||||||
\(594\) | −28.2417 | + | 16.4165i | −1.15877 | + | 0.673576i | ||||
\(595\) | 1.03682 | + | 1.79582i | 0.0425054 | + | 0.0736215i | ||||
\(596\) | − | 2.73477i | − | 0.112020i | ||||||
\(597\) | −1.50014 | + | 8.55686i | −0.0613968 | + | 0.350209i | ||||
\(598\) | −22.1757 | − | 38.4094i | −0.906831 | − | 1.57068i | ||||
\(599\) | 19.9168 | + | 34.4969i | 0.813777 | + | 1.40950i | 0.910203 | + | 0.414163i | \(0.135926\pi\) |
−0.0964255 | + | 0.995340i | \(0.530741\pi\) | |||||||
\(600\) | 0.299093 | − | 1.70603i | 0.0122104 | − | 0.0696484i | ||||
\(601\) | 2.09040i | 0.0852692i | 0.999091 | + | 0.0426346i | \(0.0135751\pi\) | ||||
−0.999091 | + | 0.0426346i | \(0.986425\pi\) | |||||||
\(602\) | −0.228182 | − | 0.395223i | −0.00930000 | − | 0.0161081i | ||||
\(603\) | 15.5286 | + | 18.4326i | 0.632373 | + | 0.750634i | ||||
\(604\) | 4.36049 | − | 2.51753i | 0.177426 | − | 0.102437i | ||||
\(605\) | −24.7009 | − | 14.2610i | −1.00423 | − | 0.579794i | ||||
\(606\) | −4.66809 | + | 5.57432i | −0.189628 | + | 0.226441i | ||||
\(607\) | − | 5.53538i | − | 0.224674i | −0.993670 | − | 0.112337i | \(-0.964166\pi\) | ||
0.993670 | − | 0.112337i | \(-0.0358336\pi\) | |||||||
\(608\) | −3.21855 | + | 2.93955i | −0.130529 | + | 0.119214i | ||||
\(609\) | −0.499045 | + | 2.84656i | −0.0202223 | + | 0.115349i | ||||
\(610\) | 2.22348 | + | 1.28373i | 0.0900263 | + | 0.0519767i | ||||
\(611\) | −26.8061 | + | 46.4296i | −1.08446 | + | 1.87834i | ||||
\(612\) | −15.8009 | + | 2.81813i | −0.638714 | + | 0.113916i | ||||
\(613\) | −10.6274 | + | 18.4073i | −0.429238 | + | 0.743462i | −0.996806 | − | 0.0798646i | \(-0.974551\pi\) |
0.567568 | + | 0.823327i | \(0.307885\pi\) | |||||||
\(614\) | 20.5036 | − | 11.8378i | 0.827459 | − | 0.477734i | ||||
\(615\) | 4.78351 | + | 0.838620i | 0.192890 | + | 0.0338164i | ||||
\(616\) | 2.43664i | 0.0981751i | ||||||||
\(617\) | −3.00091 | + | 1.73258i | −0.120812 | + | 0.0697509i | −0.559188 | − | 0.829041i | \(-0.688887\pi\) |
0.438376 | + | 0.898792i | \(0.355554\pi\) | |||||||
\(618\) | −8.59420 | − | 23.5404i | −0.345709 | − | 0.946935i | ||||
\(619\) | 20.0769 | 0.806960 | 0.403480 | − | 0.914989i | \(-0.367801\pi\) | ||||
0.403480 | + | 0.914989i | \(0.367801\pi\) | |||||||
\(620\) | −5.87016 | −0.235751 | ||||||||
\(621\) | 0.0985836 | + | 33.4710i | 0.00395602 | + | 1.34315i | ||||
\(622\) | 18.4080 | + | 10.6278i | 0.738092 | + | 0.426138i | ||||
\(623\) | 2.90633 | + | 5.03390i | 0.116440 | + | 0.201679i | ||||
\(624\) | −7.65663 | + | 9.14304i | −0.306511 | + | 0.366014i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 32.3721 | 1.29385 | ||||||||
\(627\) | −42.0859 | − | 21.9439i | −1.68075 | − | 0.876354i | ||||
\(628\) | −1.86316 | −0.0743482 | ||||||||
\(629\) | −6.81012 | + | 11.7955i | −0.271537 | + | 0.470317i | ||||
\(630\) | −0.749160 | − | 0.889262i | −0.0298473 | − | 0.0354291i | ||||
\(631\) | −3.03717 | − | 5.26053i | −0.120908 | − | 0.209418i | 0.799218 | − | 0.601041i | \(-0.205247\pi\) |
−0.920126 | + | 0.391623i | \(0.871914\pi\) | |||||||
\(632\) | 12.3862 | + | 7.15117i | 0.492696 | + | 0.284458i | ||||
\(633\) | −0.618014 | − | 1.69281i | −0.0245639 | − | 0.0672831i | ||||
\(634\) | −0.547035 | −0.0217255 | ||||||||
\(635\) | −16.3590 | −0.649189 | ||||||||
\(636\) | 6.42608 | − | 2.34605i | 0.254811 | − | 0.0930269i | ||||
\(637\) | −40.8437 | + | 23.5811i | −1.61829 | + | 0.934319i | ||||
\(638\) | − | 27.0634i | − | 1.07145i | ||||||
\(639\) | 23.5729 | + | 8.52746i | 0.932530 | + | 0.337341i | ||||
\(640\) | 0.866025 | − | 0.500000i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | 2.26142 | − | 3.91689i | 0.0893206 | − | 0.154708i | −0.817904 | − | 0.575355i | \(-0.804864\pi\) |
0.907224 | + | 0.420648i | \(0.138197\pi\) | |||||||
\(642\) | 4.00880 | − | 1.46354i | 0.158215 | − | 0.0577614i | ||||
\(643\) | 5.12601 | − | 8.87852i | 0.202150 | − | 0.350135i | −0.747071 | − | 0.664745i | \(-0.768540\pi\) |
0.949221 | + | 0.314610i | \(0.101874\pi\) | |||||||
\(644\) | 2.16218 | + | 1.24833i | 0.0852017 | + | 0.0491912i | ||||
\(645\) | −2.00875 | − | 0.352164i | −0.0790945 | − | 0.0138664i | ||||
\(646\) | −15.7268 | − | 17.2195i | −0.618764 | − | 0.677492i | ||||
\(647\) | − | 32.4311i | − | 1.27500i | −0.770451 | − | 0.637500i | \(-0.779969\pi\) | ||
0.770451 | − | 0.637500i | \(-0.220031\pi\) | |||||||
\(648\) | 8.44508 | − | 3.11137i | 0.331754 | − | 0.122226i | ||||
\(649\) | −6.06279 | − | 3.50035i | −0.237985 | − | 0.137401i | ||||
\(650\) | 5.96278 | − | 3.44261i | 0.233880 | − | 0.135030i | ||||
\(651\) | −2.53012 | + | 3.02130i | −0.0991632 | + | 0.118414i | ||||
\(652\) | 7.82120 | + | 13.5467i | 0.306302 | + | 0.530531i | ||||
\(653\) | 34.6967i | 1.35778i | 0.734238 | + | 0.678892i | \(0.237540\pi\) | ||||
−0.734238 | + | 0.678892i | \(0.762460\pi\) | |||||||
\(654\) | 4.57793 | + | 0.802580i | 0.179011 | + | 0.0313834i | ||||
\(655\) | −1.34352 | − | 2.32705i | −0.0524958 | − | 0.0909255i | ||||
\(656\) | 1.40194 | + | 2.42823i | 0.0547365 | + | 0.0948065i | ||||
\(657\) | −5.02548 | − | 1.81796i | −0.196063 | − | 0.0709253i | ||||
\(658\) | − | 3.01799i | − | 0.117653i | ||||||
\(659\) | −3.29288 | − | 5.70344i | −0.128272 | − | 0.222174i | 0.794735 | − | 0.606957i | \(-0.207610\pi\) |
−0.923007 | + | 0.384782i | \(0.874277\pi\) | |||||||
\(660\) | 8.34818 | + | 6.99100i | 0.324953 | + | 0.272124i | ||||
\(661\) | 33.4091 | − | 19.2887i | 1.29946 | − | 0.750245i | 0.319152 | − | 0.947704i | \(-0.396602\pi\) |
0.980311 | + | 0.197458i | \(0.0632687\pi\) | |||||||
\(662\) | 10.6417 | + | 6.14400i | 0.413602 | + | 0.238793i | ||||
\(663\) | −48.9160 | − | 40.9636i | −1.89974 | − | 1.59090i | ||||
\(664\) | − | 3.22583i | − | 0.125186i | ||||||
\(665\) | 0.510676 | − | 1.61043i | 0.0198032 | − | 0.0624499i | ||||
\(666\) | 2.59805 | − | 7.18193i | 0.100672 | − | 0.278294i | ||||
\(667\) | −24.0149 | − | 13.8650i | −0.929862 | − | 0.536856i | ||||
\(668\) | 2.58979 | − | 4.48565i | 0.100202 | − | 0.173555i | ||||
\(669\) | −2.36099 | − | 6.46699i | −0.0912810 | − | 0.250028i | ||||
\(670\) | 4.01697 | − | 6.95760i | 0.155189 | − | 0.268795i | ||||
\(671\) | −13.9783 | + | 8.07037i | −0.539626 | + | 0.311553i | ||||
\(672\) | 0.115925 | − | 0.661239i | 0.00447191 | − | 0.0255079i | ||||
\(673\) | − | 27.8104i | − | 1.07201i | −0.844214 | − | 0.536006i | \(-0.819932\pi\) | ||
0.844214 | − | 0.536006i | \(-0.180068\pi\) | |||||||
\(674\) | 12.8425 | − | 7.41464i | 0.494676 | − | 0.285601i | ||||
\(675\) | −5.19613 | + | 0.0153044i | −0.199999 | + | 0.000589066i | ||||
\(676\) | −34.4064 | −1.32332 | ||||||||
\(677\) | 20.4612 | 0.786387 | 0.393193 | − | 0.919456i | \(-0.371370\pi\) | ||||
0.393193 | + | 0.919456i | \(0.371370\pi\) | |||||||
\(678\) | 0.238517 | − | 0.0870783i | 0.00916018 | − | 0.00334422i | ||||
\(679\) | 2.06926 | + | 1.19469i | 0.0794110 | + | 0.0458480i | ||||
\(680\) | 2.67504 | + | 4.63331i | 0.102583 | + | 0.177679i | ||||
\(681\) | 27.8350 | + | 23.3098i | 1.06664 | + | 0.893233i | ||||
\(682\) | 18.4518 | − | 31.9595i | 0.706558 | − | 1.22379i | ||||
\(683\) | −6.27342 | −0.240046 | −0.120023 | − | 0.992771i | \(-0.538297\pi\) | ||||
−0.120023 | + | 0.992771i | \(0.538297\pi\) | |||||||
\(684\) | 10.3770 | + | 7.95725i | 0.396774 | + | 0.304253i | ||||
\(685\) | 13.6298 | 0.520766 | ||||||||
\(686\) | 2.68401 | − | 4.64884i | 0.102476 | − | 0.177494i | ||||
\(687\) | −10.8568 | − | 9.09177i | −0.414212 | − | 0.346873i | ||||
\(688\) | −0.588721 | − | 1.01969i | −0.0224448 | − | 0.0388755i | ||||
\(689\) | 23.5507 | + | 13.5970i | 0.897211 | + | 0.518005i | ||||
\(690\) | 10.4804 | − | 3.82623i | 0.398984 | − | 0.145662i | ||||
\(691\) | −39.8978 | −1.51778 | −0.758891 | − | 0.651217i | \(-0.774259\pi\) | ||||
−0.758891 | + | 0.651217i | \(0.774259\pi\) | |||||||
\(692\) | 9.82817 | 0.373611 | ||||||||
\(693\) | 7.19636 | − | 1.28349i | 0.273367 | − | 0.0487557i | ||||
\(694\) | −8.34699 | + | 4.81914i | −0.316847 | + | 0.182932i | ||||
\(695\) | 22.6639i | 0.859690i | ||||||||
\(696\) | −1.28756 | + | 7.34428i | −0.0488049 | + | 0.278384i | ||||
\(697\) | −12.9912 | + | 7.50049i | −0.492078 | + | 0.284101i | ||||
\(698\) | −12.6150 | + | 21.8497i | −0.477483 | + | 0.827025i | ||||
\(699\) | −2.09625 | − | 5.74185i | −0.0792875 | − | 0.217177i | ||||
\(700\) | −0.193795 | + | 0.335662i | −0.00732475 | + | 0.0126868i | ||||
\(701\) | 8.46297 | + | 4.88610i | 0.319642 | + | 0.184545i | 0.651233 | − | 0.758878i | \(-0.274252\pi\) |
−0.331591 | + | 0.943423i | \(0.607585\pi\) | |||||||
\(702\) | 31.0361 | + | 17.7970i | 1.17138 | + | 0.671705i | ||||
\(703\) | 10.8378 | − | 2.38401i | 0.408755 | − | 0.0899147i | ||||
\(704\) | 6.28666i | 0.236937i | ||||||||
\(705\) | −10.3399 | − | 8.65895i | −0.389424 | − | 0.326115i | ||||
\(706\) | −8.70898 | − | 5.02813i | −0.327767 | − | 0.189236i | ||||
\(707\) | 1.40904 | − | 0.813507i | 0.0529923 | − | 0.0305951i | ||||
\(708\) | 1.47875 | + | 1.23834i | 0.0555747 | + | 0.0465398i | ||||
\(709\) | −9.26925 | − | 16.0548i | −0.348114 | − | 0.602951i | 0.637800 | − | 0.770202i | \(-0.279844\pi\) |
−0.985914 | + | 0.167251i | \(0.946511\pi\) | |||||||
\(710\) | − | 8.35597i | − | 0.313594i | ||||||
\(711\) | 14.5959 | − | 40.3481i | 0.547388 | − | 1.51317i | ||||
\(712\) | 7.49847 | + | 12.9877i | 0.281017 | + | 0.486736i | ||||
\(713\) | −18.9064 | − | 32.7468i | −0.708050 | − | 1.22638i | ||||
\(714\) | 3.53769 | + | 0.620209i | 0.132395 | + | 0.0232107i | ||||
\(715\) | 43.2851i | 1.61877i | ||||||||
\(716\) | −9.81870 | − | 17.0065i | −0.366942 | − | 0.635562i | ||||
\(717\) | 17.6301 | − | 21.0527i | 0.658408 | − | 0.786227i | ||||
\(718\) | 9.76791 | − | 5.63951i | 0.364535 | − | 0.210465i | ||||
\(719\) | −29.2721 | − | 16.9002i | −1.09166 | − | 0.630273i | −0.157645 | − | 0.987496i | \(-0.550390\pi\) |
−0.934019 | + | 0.357223i | \(0.883724\pi\) | |||||||
\(720\) | −1.93287 | − | 2.29434i | −0.0720339 | − | 0.0855051i | ||||
\(721\) | 5.60783i | 0.208847i | ||||||||
\(722\) | −1.71811 | + | 18.9222i | −0.0639416 | + | 0.704210i | ||||
\(723\) | 6.24403 | + | 1.09467i | 0.232218 | + | 0.0407113i | ||||
\(724\) | 19.3105 | + | 11.1489i | 0.717668 | + | 0.414346i | ||||
\(725\) | 2.15245 | − | 3.72815i | 0.0799398 | − | 0.138460i | ||||
\(726\) | −46.4058 | + | 16.9419i | −1.72228 | + | 0.628775i | ||||
\(727\) | −15.8883 | + | 27.5193i | −0.589264 | + | 1.02064i | 0.405065 | + | 0.914288i | \(0.367249\pi\) |
−0.994329 | + | 0.106347i | \(0.966084\pi\) | |||||||
\(728\) | 2.31111 | − | 1.33432i | 0.0856555 | − | 0.0494532i | ||||
\(729\) | −13.6375 | − | 23.3028i | −0.505093 | − | 0.863065i | ||||
\(730\) | 1.78140i | 0.0659325i | ||||||||
\(731\) | 5.45545 | − | 3.14971i | 0.201777 | − | 0.116496i | ||||
\(732\) | 4.17729 | − | 1.52505i | 0.154397 | − | 0.0563676i | ||||
\(733\) | 24.0223 | 0.887283 | 0.443642 | − | 0.896204i | \(-0.353686\pi\) | ||||
0.443642 | + | 0.896204i | \(0.353686\pi\) | |||||||
\(734\) | −26.4194 | −0.975157 | ||||||||
\(735\) | −4.06872 | − | 11.1447i | −0.150077 | − | 0.411077i | ||||
\(736\) | 5.57852 | + | 3.22076i | 0.205627 | + | 0.118719i | ||||
\(737\) | 25.2533 | + | 43.7400i | 0.930218 | + | 1.61119i | ||||
\(738\) | 6.43306 | − | 5.41954i | 0.236804 | − | 0.199496i | ||||
\(739\) | −12.2978 | + | 21.3005i | −0.452384 | + | 0.783551i | −0.998534 | − | 0.0541361i | \(-0.982760\pi\) |
0.546150 | + | 0.837687i | \(0.316093\pi\) | |||||||
\(740\) | −2.54580 | −0.0935855 | ||||||||
\(741\) | 2.23314 | + | 51.9343i | 0.0820365 | + | 1.90786i | ||||
\(742\) | −1.53083 | −0.0561985 | ||||||||
\(743\) | 1.48071 | − | 2.56467i | 0.0543220 | − | 0.0940885i | −0.837586 | − | 0.546306i | \(-0.816034\pi\) |
0.891908 | + | 0.452217i | \(0.149367\pi\) | |||||||
\(744\) | −6.52784 | + | 7.79511i | −0.239322 | + | 0.285782i | ||||
\(745\) | 1.36738 | + | 2.36838i | 0.0500971 | + | 0.0867707i | ||||
\(746\) | 8.15874 | + | 4.71045i | 0.298713 | + | 0.172462i | ||||
\(747\) | −9.52714 | + | 1.69919i | −0.348580 | + | 0.0621700i | ||||
\(748\) | −33.6342 | −1.22979 | ||||||||
\(749\) | −0.954981 | −0.0348942 | ||||||||
\(750\) | 0.593994 | + | 1.62701i | 0.0216896 | + | 0.0594101i | ||||
\(751\) | 8.92680 | − | 5.15389i | 0.325744 | − | 0.188068i | −0.328206 | − | 0.944606i | \(-0.606444\pi\) |
0.653950 | + | 0.756538i | \(0.273111\pi\) | |||||||
\(752\) | − | 7.78656i | − | 0.283947i | ||||||
\(753\) | 19.2102 | + | 3.36784i | 0.700060 | + | 0.122731i | ||||
\(754\) | −25.6691 | + | 14.8201i | −0.934815 | + | 0.539716i | ||||
\(755\) | −2.51753 | + | 4.36049i | −0.0916223 | + | 0.158695i | ||||
\(756\) | −2.01396 | + | 0.00593182i | −0.0732472 | + | 0.000215738i | ||||
\(757\) | 9.26031 | − | 16.0393i | 0.336572 | − | 0.582959i | −0.647214 | − | 0.762308i | \(-0.724066\pi\) |
0.983785 | + | 0.179349i | \(0.0573993\pi\) | |||||||
\(758\) | 16.0100 | + | 9.24338i | 0.581510 | + | 0.335735i | ||||
\(759\) | −12.1120 | + | 69.0869i | −0.439636 | + | 2.50770i | ||||
\(760\) | 1.31757 | − | 4.15500i | 0.0477933 | − | 0.150718i | ||||
\(761\) | 50.2106i | 1.82013i | 0.414462 | + | 0.910067i | \(0.363970\pi\) | ||||
−0.414462 | + | 0.910067i | \(0.636030\pi\) | |||||||
\(762\) | −18.1919 | + | 21.7235i | −0.659022 | + | 0.786960i | ||||
\(763\) | −0.900710 | − | 0.520025i | −0.0326079 | − | 0.0188262i | ||||
\(764\) | −14.9599 | + | 8.63710i | −0.541230 | + | 0.312479i | ||||
\(765\) | 12.2749 | − | 10.3410i | 0.443801 | − | 0.373881i | ||||
\(766\) | 8.39580 | + | 14.5419i | 0.303352 | + | 0.525422i | ||||
\(767\) | 7.66726i | 0.276849i | ||||||||
\(768\) | 0.299093 | − | 1.70603i | 0.0107926 | − | 0.0615611i | ||||
\(769\) | −17.5253 | − | 30.3547i | −0.631979 | − | 1.09462i | −0.987147 | − | 0.159817i | \(-0.948910\pi\) |
0.355168 | − | 0.934802i | \(-0.384424\pi\) | |||||||
\(770\) | −1.21832 | − | 2.11019i | −0.0439052 | − | 0.0760461i | ||||
\(771\) | 8.16516 | − | 46.5743i | 0.294061 | − | 1.67733i | ||||
\(772\) | − | 9.74861i | − | 0.350860i | ||||||
\(773\) | −20.0359 | − | 34.7031i | −0.720640 | − | 1.24818i | −0.960744 | − | 0.277438i | \(-0.910515\pi\) |
0.240104 | − | 0.970747i | \(-0.422819\pi\) | |||||||
\(774\) | −2.70145 | + | 2.27584i | −0.0971018 | + | 0.0818035i | ||||
\(775\) | 5.08371 | − | 2.93508i | 0.182612 | − | 0.105431i | ||||
\(776\) | 5.33880 | + | 3.08236i | 0.191652 | + | 0.110650i | ||||
\(777\) | −1.09728 | + | 1.31029i | −0.0393645 | + | 0.0470065i | ||||
\(778\) | 3.83317i | 0.137426i | ||||||||
\(779\) | 11.6501 | + | 3.69431i | 0.417408 | + | 0.132362i | ||||
\(780\) | 2.05932 | − | 11.7464i | 0.0737355 | − | 0.420589i | ||||
\(781\) | 45.4933 | + | 26.2656i | 1.62788 | + | 0.939856i | ||||
\(782\) | −17.2313 | + | 29.8456i | −0.616192 | + | 1.06728i | ||||
\(783\) | 22.3688 | − | 0.0658837i | 0.799395 | − | 0.00235449i | ||||
\(784\) | 3.42489 | − | 5.93208i | 0.122317 | − | 0.211860i | ||||
\(785\) | 1.61354 | − | 0.931580i | 0.0575898 | − | 0.0332495i | ||||
\(786\) | −4.58419 | − | 0.803677i | −0.163513 | − | 0.0286662i | ||||
\(787\) | 1.76390i | 0.0628763i | 0.999506 | + | 0.0314382i | \(0.0100087\pi\) | ||||
−0.999506 | + | 0.0314382i | \(0.989991\pi\) | |||||||
\(788\) | 6.92311 | − | 3.99706i | 0.246626 | − | 0.142389i | ||||
\(789\) | 11.2937 | + | 30.9347i | 0.402067 | + | 1.10130i | ||||
\(790\) | −14.3023 | −0.508854 | ||||||||
\(791\) | −0.0568198 | −0.00202028 | ||||||||
\(792\) | 18.5670 | − | 3.31146i | 0.659749 | − | 0.117668i | ||||
\(793\) | 15.3092 | + | 8.83877i | 0.543646 | + | 0.313874i | ||||
\(794\) | −6.16028 | − | 10.6699i | −0.218620 | − | 0.378661i | ||||
\(795\) | −4.39212 | + | 5.24478i | −0.155773 | + | 0.186013i | ||||
\(796\) | 2.50783 | − | 4.34368i | 0.0888875 | − | 0.153958i | ||||
\(797\) | 24.2694 | 0.859666 | 0.429833 | − | 0.902908i | \(-0.358572\pi\) | ||||
0.429833 | + | 0.902908i | \(0.358572\pi\) | |||||||
\(798\) | −1.57063 | − | 2.46900i | −0.0555999 | − | 0.0874016i | ||||
\(799\) | 41.6587 | 1.47378 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 34.4081 | − | 28.9872i | 1.21575 | − | 1.02421i | ||||
\(802\) | −3.20325 | − | 5.54818i | −0.113111 | − | 0.195913i | ||||
\(803\) | −9.69866 | − | 5.59953i | −0.342258 | − | 0.197603i | ||||
\(804\) | −4.77211 | − | 13.0713i | −0.168299 | − | 0.460990i | ||||
\(805\) | −2.49667 | −0.0879959 | ||||||||
\(806\) | −40.4174 | −1.42364 | ||||||||
\(807\) | 30.7009 | − | 11.2083i | 1.08072 | − | 0.394552i | ||||
\(808\) | 3.63539 | − | 2.09889i | 0.127892 | − | 0.0738387i | ||||
\(809\) | 32.5685i | 1.14505i | 0.819888 | + | 0.572525i | \(0.194036\pi\) | ||||
−0.819888 | + | 0.572525i | \(0.805964\pi\) | |||||||
\(810\) | −5.75797 | + | 6.91707i | −0.202314 | + | 0.243041i | ||||
\(811\) | −40.2466 | + | 23.2364i | −1.41325 | + | 0.815940i | −0.995693 | − | 0.0927115i | \(-0.970447\pi\) |
−0.417556 | + | 0.908651i | \(0.637113\pi\) | |||||||
\(812\) | 0.834265 | − | 1.44499i | 0.0292770 | − | 0.0507092i | ||||
\(813\) | 32.2325 | − | 11.7675i | 1.13044 | − | 0.412705i | ||||
\(814\) | 8.00229 | − | 13.8604i | 0.280480 | − | 0.485806i | ||||
\(815\) | −13.5467 | − | 7.82120i | −0.474521 | − | 0.273965i | ||||
\(816\) | 9.12741 | + | 1.60017i | 0.319523 | + | 0.0560172i | ||||
\(817\) | −4.89227 | − | 1.55136i | −0.171159 | − | 0.0542753i | ||||
\(818\) | 33.2538i | 1.16269i | ||||||||
\(819\) | −5.15814 | − | 6.12278i | −0.180240 | − | 0.213947i | ||||
\(820\) | −2.42823 | − | 1.40194i | −0.0847975 | − | 0.0489578i | ||||
\(821\) | −15.0238 | + | 8.67398i | −0.524333 | + | 0.302724i | −0.738706 | − | 0.674028i | \(-0.764563\pi\) |
0.214373 | + | 0.976752i | \(0.431229\pi\) | |||||||
\(822\) | 15.1568 | − | 18.0992i | 0.528654 | − | 0.631283i | ||||
\(823\) | −1.52793 | − | 2.64645i | −0.0532603 | − | 0.0922496i | 0.838166 | − | 0.545415i | \(-0.183628\pi\) |
−0.891426 | + | 0.453166i | \(0.850295\pi\) | |||||||
\(824\) | 14.4685i | 0.504034i | ||||||||
\(825\) | −10.7252 | − | 1.88029i | −0.373405 | − | 0.0654634i | ||||
\(826\) | −0.215806 | − | 0.373787i | −0.00750885 | − | 0.0130057i | ||||
\(827\) | 1.06321 | + | 1.84154i | 0.0369715 | + | 0.0640366i | 0.883919 | − | 0.467640i | \(-0.154896\pi\) |
−0.846948 | + | 0.531676i | \(0.821562\pi\) | |||||||
\(828\) | 6.57372 | − | 18.1721i | 0.228453 | − | 0.631524i | ||||
\(829\) | 26.9654i | 0.936546i | 0.883584 | + | 0.468273i | \(0.155124\pi\) | ||||
−0.883584 | + | 0.468273i | \(0.844876\pi\) | |||||||
\(830\) | 1.61291 | + | 2.79365i | 0.0559851 | + | 0.0969690i | ||||
\(831\) | 17.5172 | + | 14.6694i | 0.607665 | + | 0.508876i | ||||
\(832\) | 5.96278 | − | 3.44261i | 0.206722 | − | 0.119351i | ||||
\(833\) | 31.7371 | + | 18.3234i | 1.09963 | + | 0.634869i | ||||
\(834\) | 30.0958 | + | 25.2031i | 1.04213 | + | 0.872711i | ||||
\(835\) | 5.17958i | 0.179247i | ||||||||
\(836\) | 18.4799 | + | 20.2339i | 0.639142 | + | 0.699805i | ||||
\(837\) | 26.4605 | + | 15.1733i | 0.914610 | + | 0.524464i | ||||
\(838\) | 22.7052 | + | 13.1089i | 0.784338 | + | 0.452838i | ||||
\(839\) | −6.48396 | + | 11.2305i | −0.223851 | + | 0.387722i | −0.955974 | − | 0.293451i | \(-0.905196\pi\) |
0.732123 | + | 0.681172i | \(0.238530\pi\) | |||||||
\(840\) | 0.230226 | + | 0.630613i | 0.00794354 | + | 0.0217582i | ||||
\(841\) | 5.23395 | − | 9.06547i | 0.180481 | − | 0.312602i | ||||
\(842\) | 16.2792 | − | 9.39883i | 0.561020 | − | 0.323905i | ||||
\(843\) | −5.02211 | + | 28.6462i | −0.172971 | + | 0.986629i | ||||
\(844\) | 1.04044i | 0.0358134i | ||||||||
\(845\) | 29.7968 | − | 17.2032i | 1.02504 | − | 0.591808i | ||||
\(846\) | −22.9968 | + | 4.10153i | −0.790646 | + | 0.141013i | ||||
\(847\) | 11.0549 | 0.379849 | ||||||||
\(848\) | −3.94962 | −0.135630 | ||||||||
\(849\) | 12.9713 | − | 4.73561i | 0.445175 | − | 0.162526i | ||||
\(850\) | −4.63331 | − | 2.67504i | −0.158921 | − | 0.0917532i | ||||
\(851\) | −8.19942 | − | 14.2018i | −0.281073 | − | 0.486832i | ||||
\(852\) | −11.0961 | − | 9.29215i | −0.380145 | − | 0.318344i | ||||
\(853\) | 19.8140 | − | 34.3188i | 0.678418 | − | 1.17505i | −0.297040 | − | 0.954865i | \(-0.595999\pi\) |
0.975457 | − | 0.220189i | \(-0.0706673\pi\) | |||||||
\(854\) | −0.995119 | −0.0340523 | ||||||||
\(855\) | −12.9654 | − | 1.70268i | −0.443406 | − | 0.0582306i | ||||
\(856\) | −2.46390 | −0.0842144 | ||||||||
\(857\) | −18.7067 | + | 32.4009i | −0.639008 | + | 1.10679i | 0.346642 | + | 0.937997i | \(0.387322\pi\) |
−0.985651 | + | 0.168798i | \(0.946012\pi\) | |||||||
\(858\) | 57.4791 | + | 48.1346i | 1.96231 | + | 1.64329i | ||||
\(859\) | −22.3252 | − | 38.6684i | −0.761726 | − | 1.31935i | −0.941960 | − | 0.335724i | \(-0.891019\pi\) |
0.180234 | − | 0.983624i | \(-0.442314\pi\) | |||||||
\(860\) | 1.01969 | + | 0.588721i | 0.0347713 | + | 0.0200752i | ||||
\(861\) | −1.76816 | + | 0.645525i | −0.0602588 | + | 0.0219994i | ||||
\(862\) | 33.7813 | 1.15060 | ||||||||
\(863\) | −20.1867 | −0.687163 | −0.343581 | − | 0.939123i | \(-0.611640\pi\) | ||||
−0.343581 | + | 0.939123i | \(0.611640\pi\) | |||||||
\(864\) | −5.19613 | + | 0.0153044i | −0.176776 | + | 0.000520666i | ||||
\(865\) | −8.51144 | + | 4.91408i | −0.289398 | + | 0.167084i | ||||
\(866\) | − | 21.7192i | − | 0.738048i | ||||||
\(867\) | −3.47647 | + | 19.8299i | −0.118067 | + | 0.673458i | ||||
\(868\) | 1.97039 | − | 1.13761i | 0.0668794 | − | 0.0386128i | ||||
\(869\) | 44.9570 | − | 77.8677i | 1.52506 | − | 2.64148i | ||||
\(870\) | −2.55708 | − | 7.00412i | −0.0866931 | − | 0.237462i | ||||
\(871\) | 27.6578 | − | 47.9047i | 0.937148 | − | 1.62319i | ||||
\(872\) | −2.32388 | − | 1.34169i | −0.0786964 | − | 0.0454354i | ||||
\(873\) | 6.29124 | − | 17.3912i | 0.212926 | − | 0.588603i | ||||
\(874\) | 27.4223 | − | 6.03216i | 0.927574 | − | 0.204041i | ||||
\(875\) | − | 0.387589i | − | 0.0131029i | ||||||
\(876\) | 2.36556 | + | 1.98098i | 0.0799247 | + | 0.0669312i | ||||
\(877\) | −46.0744 | − | 26.6011i | −1.55582 | − | 0.898254i | −0.997649 | − | 0.0685295i | \(-0.978169\pi\) |
−0.558173 | − | 0.829725i | \(-0.688497\pi\) | |||||||
\(878\) | −4.46634 | + | 2.57864i | −0.150732 | + | 0.0870249i | ||||
\(879\) | 6.01406 | + | 5.03634i | 0.202849 | + | 0.169872i | ||||
\(880\) | −3.14333 | − | 5.44441i | −0.105962 | − | 0.183531i | ||||
\(881\) | − | 29.5768i | − | 0.996466i | −0.867043 | − | 0.498233i | \(-0.833982\pi\) | ||
0.867043 | − | 0.498233i | \(-0.166018\pi\) | |||||||
\(882\) | −19.3238 | − | 6.99035i | −0.650667 | − | 0.235377i | ||||
\(883\) | −8.68185 | − | 15.0374i | −0.292168 | − | 0.506049i | 0.682154 | − | 0.731208i | \(-0.261043\pi\) |
−0.974322 | + | 0.225159i | \(0.927710\pi\) | |||||||
\(884\) | 18.4183 | + | 31.9014i | 0.619474 | + | 1.07296i | ||||
\(885\) | −1.89980 | − | 0.333064i | −0.0638612 | − | 0.0111958i | ||||
\(886\) | 33.1611i | 1.11407i | ||||||||
\(887\) | 19.2230 | + | 33.2953i | 0.645446 | + | 1.11795i | 0.984198 | + | 0.177070i | \(0.0566620\pi\) |
−0.338752 | + | 0.940876i | \(0.610005\pi\) | |||||||
\(888\) | −2.83103 | + | 3.38062i | −0.0950030 | + | 0.113446i | ||||
\(889\) | 5.49111 | − | 3.17030i | 0.184166 | − | 0.106328i | ||||
\(890\) | −12.9877 | − | 7.49847i | −0.435350 | − | 0.251349i | ||||
\(891\) | −19.5601 | − | 53.0913i | −0.655289 | − | 1.77863i | ||||
\(892\) | 3.97476i | 0.133085i | ||||||||
\(893\) | −22.8890 | − | 25.0614i | −0.765950 | − | 0.838649i | ||||
\(894\) | 4.66560 | + | 0.817949i | 0.156041 | + | 0.0273563i | ||||
\(895\) | 17.0065 | + | 9.81870i | 0.568464 | + | 0.328203i | ||||
\(896\) | −0.193795 | + | 0.335662i | −0.00647422 | + | 0.0112137i | ||||
\(897\) | 72.1603 | − | 26.3444i | 2.40936 | − | 0.879615i | ||||
\(898\) | −14.3031 | + | 24.7736i | −0.477300 | + | 0.826707i | ||||
\(899\) | −21.8848 | + | 12.6352i | −0.729899 | + | 0.421408i | ||||
\(900\) | 2.82109 | + | 1.02052i | 0.0940362 | + | 0.0340174i | ||||
\(901\) | − | 21.1308i | − | 0.703968i | ||||||
\(902\) | 15.2655 | − | 8.81352i | 0.508284 | − | 0.293458i | ||||
\(903\) | 0.742510 | − | 0.271077i | 0.0247092 | − | 0.00902089i | ||||
\(904\) | −0.146598 | −0.00487578 | ||||||||
\(905\) | −22.2978 | −0.741204 | ||||||||
\(906\) | 2.99080 | + | 8.19211i | 0.0993625 | + | 0.272165i | ||||
\(907\) | −5.28915 | − | 3.05369i | −0.175623 | − | 0.101396i | 0.409611 | − | 0.912260i | \(-0.365664\pi\) |
−0.585235 | + | 0.810864i | \(0.698998\pi\) | |||||||
\(908\) | −10.4807 | − | 18.1530i | −0.347813 | − | 0.602430i | ||||
\(909\) | −8.11377 | − | 9.63115i | −0.269117 | − | 0.319445i | ||||
\(910\) | −1.33432 | + | 2.31111i | −0.0442323 | + | 0.0766126i | ||||
\(911\) | −30.0434 | −0.995381 | −0.497690 | − | 0.867355i | \(-0.665818\pi\) | ||||
−0.497690 | + | 0.867355i | \(0.665818\pi\) | |||||||
\(912\) | −4.05232 | − | 6.37014i | −0.134186 | − | 0.210937i | ||||
\(913\) | −20.2797 | −0.671160 | ||||||||
\(914\) | 6.04720 | − | 10.4741i | 0.200024 | − | 0.346451i | ||||
\(915\) | −2.85511 | + | 3.40938i | −0.0943870 | + | 0.112711i | ||||
\(916\) | 4.08789 | + | 7.08043i | 0.135068 | + | 0.233944i | ||||
\(917\) | 0.901941 | + | 0.520736i | 0.0297847 | + | 0.0171962i | ||||
\(918\) | −0.0818798 | − | 27.7997i | −0.00270243 | − | 0.917528i | ||||
\(919\) | −5.87159 | −0.193686 | −0.0968429 | − | 0.995300i | \(-0.530874\pi\) | ||||
−0.0968429 | + | 0.995300i | \(0.530874\pi\) | |||||||
\(920\) | −6.44153 | −0.212371 | ||||||||
\(921\) | 14.0631 | + | 38.5204i | 0.463396 | + | 1.26929i | ||||
\(922\) | −23.9736 | + | 13.8412i | −0.789528 | + | 0.455834i | ||||
\(923\) | − | 57.5328i | − | 1.89371i | ||||||
\(924\) | −4.15699 | − | 0.728782i | −0.136755 | − | 0.0239752i | ||||
\(925\) | 2.20473 | − | 1.27290i | 0.0724910 | − | 0.0418527i | ||||
\(926\) | 11.2620 | − | 19.5063i | 0.370091 | − | 0.641017i | ||||
\(927\) | 42.7312 | − | 7.62120i | 1.40348 | − | 0.250313i | ||||
\(928\) | 2.15245 | − | 3.72815i | 0.0706575 | − | 0.122382i | ||||
\(929\) | 32.7353 | + | 18.8998i | 1.07401 | + | 0.620081i | 0.929275 | − | 0.369390i | \(-0.120433\pi\) |
0.144737 | + | 0.989470i | \(0.453767\pi\) | |||||||
\(930\) | 1.75572 | − | 10.0147i | 0.0575724 | − | 0.328394i | ||||
\(931\) | −6.41446 | − | 29.1603i | −0.210226 | − | 0.955690i | ||||
\(932\) | 3.52908i | 0.115599i | ||||||||
\(933\) | −23.6371 | + | 28.2259i | −0.773845 | + | 0.924073i | ||||
\(934\) | 19.4524 | + | 11.2308i | 0.636501 | + | 0.367484i | ||||
\(935\) | 29.1280 | − | 16.8171i | 0.952588 | − | 0.549977i | ||||
\(936\) | −13.3083 | − | 15.7971i | −0.434994 | − | 0.516343i | ||||
\(937\) | 22.4831 | + | 38.9419i | 0.734491 | + | 1.27218i | 0.954946 | + | 0.296779i | \(0.0959125\pi\) |
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(938\) | 3.11387i | 0.101671i | ||||||||
\(939\) | −9.68226 | + | 55.2278i | −0.315968 | + | 1.80229i | ||||
\(940\) | 3.89328 | + | 6.74336i | 0.126985 | + | 0.219944i | ||||
\(941\) | 5.62832 | + | 9.74854i | 0.183478 | + | 0.317793i | 0.943063 | − | 0.332615i | \(-0.107931\pi\) |
−0.759585 | + | 0.650409i | \(0.774598\pi\) | |||||||
\(942\) | 0.557257 | − | 3.17861i | 0.0181564 | − | 0.103565i | ||||
\(943\) | − | 18.0613i | − | 0.588155i | ||||||
\(944\) | −0.556791 | − | 0.964390i | −0.0181220 | − | 0.0313882i | ||||
\(945\) | 1.74118 | − | 1.01212i | 0.0566405 | − | 0.0329242i | ||||
\(946\) | −6.41047 | + | 3.70109i | −0.208422 | + | 0.120333i | ||||
\(947\) | −35.4047 | − | 20.4409i | −1.15050 | − | 0.664240i | −0.201490 | − | 0.979491i | \(-0.564578\pi\) |
−0.949009 | + | 0.315250i | \(0.897912\pi\) | |||||||
\(948\) | −15.9047 | + | 18.9924i | −0.516562 | + | 0.616843i | ||||
\(949\) | 12.2653i | 0.398150i | ||||||||
\(950\) | 0.936449 | + | 4.25712i | 0.0303824 | + | 0.138119i | ||||
\(951\) | 0.163614 | − | 0.933259i | 0.00530555 | − | 0.0302630i | ||||
\(952\) | −1.79582 | − | 1.03682i | −0.0582029 | − | 0.0336034i | ||||
\(953\) | −17.8170 | + | 30.8599i | −0.577148 | + | 0.999651i | 0.418656 | + | 0.908145i | \(0.362501\pi\) |
−0.995805 | + | 0.0915056i | \(0.970832\pi\) | |||||||
\(954\) | 2.08044 | + | 11.6648i | 0.0673567 | + | 0.377661i | ||||
\(955\) | 8.63710 | − | 14.9599i | 0.279490 | − | 0.484091i | ||||
\(956\) | −13.7299 | + | 7.92694i | −0.444055 | + | 0.256375i | ||||
\(957\) | 46.1710 | + | 8.09446i | 1.49250 | + | 0.261657i | ||||
\(958\) | 16.2192i | 0.524018i | ||||||||
\(959\) | −4.57499 | + | 2.64137i | −0.147734 | + | 0.0852944i | ||||
\(960\) | 0.593994 | + | 1.62701i | 0.0191711 | + | 0.0525116i | ||||
\(961\) | −3.45878 | −0.111574 | ||||||||
\(962\) | −17.5284 | −0.565139 | ||||||||
\(963\) | 1.29785 | + | 7.27687i | 0.0418225 | + | 0.234494i | ||||
\(964\) | −3.16963 | − | 1.82999i | −0.102087 | − | 0.0589399i | ||||
\(965\) | 4.87430 | + | 8.44254i | 0.156909 | + | 0.271775i | ||||
\(966\) | −2.77639 | + | 3.31537i | −0.0893288 | + | 0.106670i | ||||
\(967\) | 9.57867 | − | 16.5907i | 0.308029 | − | 0.533522i | −0.669902 | − | 0.742450i | \(-0.733664\pi\) |
0.977931 | + | 0.208927i | \(0.0669972\pi\) | |||||||
\(968\) | 28.5221 | 0.916735 | ||||||||
\(969\) | 34.0808 | − | 21.6802i | 1.09483 | − | 0.696469i | ||||
\(970\) | −6.16472 | −0.197937 | ||||||||
\(971\) | −8.76880 | + | 15.1880i | −0.281404 | + | 0.487406i | −0.971731 | − | 0.236091i | \(-0.924133\pi\) |
0.690327 | + | 0.723498i | \(0.257467\pi\) | |||||||
\(972\) | 2.78223 | + | 15.3382i | 0.0892402 | + | 0.491972i | ||||
\(973\) | −4.39214 | − | 7.60740i | −0.140805 | − | 0.243882i | ||||
\(974\) | 22.7384 | + | 13.1280i | 0.728585 | + | 0.420649i | ||||
\(975\) | 4.08978 | + | 11.2024i | 0.130978 | + | 0.358763i | ||||
\(976\) | −2.56746 | −0.0821823 | ||||||||
\(977\) | 21.3473 | 0.682960 | 0.341480 | − | 0.939889i | \(-0.389072\pi\) | ||||
0.341480 | + | 0.939889i | \(0.389072\pi\) | |||||||
\(978\) | −25.4504 | + | 9.29150i | −0.813814 | + | 0.297109i | ||||
\(979\) | 81.6494 | − | 47.1403i | 2.60953 | − | 1.50661i | ||||
\(980\) | 6.84977i | 0.218808i | ||||||||
\(981\) | −2.73845 | + | 7.57005i | −0.0874321 | + | 0.241693i | ||||
\(982\) | 20.1138 | − | 11.6127i | 0.641857 | − | 0.370576i | ||||
\(983\) | 21.8784 | − | 37.8944i | 0.697811 | − | 1.20864i | −0.271413 | − | 0.962463i | \(-0.587491\pi\) |
0.969224 | − | 0.246181i | \(-0.0791758\pi\) | |||||||
\(984\) | −4.56195 | + | 1.66549i | −0.145430 | + | 0.0530938i | ||||
\(985\) | −3.99706 | + | 6.92311i | −0.127357 | + | 0.220589i | ||||
\(986\) | 19.9459 | + | 11.5158i | 0.635207 | + | 0.366737i | ||||
\(987\) | 5.14878 | + | 0.902658i | 0.163888 | + | 0.0287319i | ||||
\(988\) | 9.07178 | − | 28.6081i | 0.288612 | − | 0.910145i | ||||
\(989\) | 7.58452i | 0.241174i | ||||||||
\(990\) | −14.4237 | + | 12.1513i | −0.458417 | + | 0.386194i | ||||
\(991\) | 25.4172 | + | 14.6746i | 0.807405 | + | 0.466155i | 0.846054 | − | 0.533097i | \(-0.178972\pi\) |
−0.0386489 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(992\) | 5.08371 | − | 2.93508i | 0.161408 | − | 0.0931889i | ||||
\(993\) | −13.6647 | + | 16.3175i | −0.433637 | + | 0.517820i | ||||
\(994\) | 1.61934 | + | 2.80478i | 0.0513624 | + | 0.0889623i | ||||
\(995\) | 5.01565i | 0.159007i | ||||||||
\(996\) | 5.50336 | + | 0.964822i | 0.174381 | + | 0.0305715i | ||||
\(997\) | 3.34562 | + | 5.79479i | 0.105957 | + | 0.183523i | 0.914129 | − | 0.405424i | \(-0.132876\pi\) |
−0.808172 | + | 0.588947i | \(0.799543\pi\) | |||||||
\(998\) | 5.68385 | + | 9.84472i | 0.179919 | + | 0.311629i | ||||
\(999\) | 11.4755 | + | 6.58042i | 0.363070 | + | 0.208195i |
(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 | 570.2.s.b.521.10 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.a.521.11 | yes | 24 | ||
19.12 | odd | 6 | 570.2.s.a.221.11 | ✓ | 24 | ||
57.50 | even | 6 | inner | 570.2.s.b.221.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.11 | ✓ | 24 | 19.12 | odd | 6 | ||
570.2.s.a.521.11 | yes | 24 | 3.2 | odd | 2 | ||
570.2.s.b.221.10 | yes | 24 | 57.50 | even | 6 | inner | |
570.2.s.b.521.10 | yes | 24 | 1.1 | even | 1 | trivial |