Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(11,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("370.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.l (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.116304318664704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.6 | ||
Root | \(0.828615 + 1.14604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.11 |
Dual form | 370.2.l.c.101.6 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 1.40680 | − | 2.43665i | 0.812218 | − | 1.40680i | −0.0990900 | − | 0.995078i | \(-0.531593\pi\) |
0.911308 | − | 0.411725i | \(-0.135073\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | − | 2.81361i | − | 1.14865i | ||||||
\(7\) | −0.712432 | + | 1.23397i | −0.269274 | + | 0.466396i | −0.968674 | − | 0.248334i | \(-0.920117\pi\) |
0.699401 | + | 0.714730i | \(0.253450\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.45819 | − | 4.25771i | −0.819397 | − | 1.41924i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.135694 | 0.0409134 | 0.0204567 | − | 0.999791i | \(-0.493488\pi\) | ||||
0.0204567 | + | 0.999791i | \(0.493488\pi\) | |||||||
\(12\) | −1.40680 | − | 2.43665i | −0.406109 | − | 0.703402i | ||||
\(13\) | 2.09999 | + | 1.21243i | 0.582433 | + | 0.336268i | 0.762100 | − | 0.647460i | \(-0.224169\pi\) |
−0.179667 | + | 0.983728i | \(0.557502\pi\) | |||||||
\(14\) | 1.42486i | 0.380811i | ||||||||
\(15\) | 2.43665 | − | 1.40680i | 0.629142 | − | 0.363235i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.46516 | + | 1.42326i | −0.597890 | + | 0.345192i | −0.768211 | − | 0.640197i | \(-0.778853\pi\) |
0.170321 | + | 0.985389i | \(0.445520\pi\) | |||||||
\(18\) | −4.25771 | − | 2.45819i | −1.00355 | − | 0.579401i | ||||
\(19\) | −2.07501 | − | 1.19801i | −0.476040 | − | 0.274842i | 0.242725 | − | 0.970095i | \(-0.421959\pi\) |
−0.718765 | + | 0.695253i | \(0.755292\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | 2.00450 | + | 3.47190i | 0.437418 | + | 0.757631i | ||||
\(22\) | 0.117515 | − | 0.0678472i | 0.0250543 | − | 0.0144651i | ||||
\(23\) | 3.45016i | 0.719407i | 0.933067 | + | 0.359704i | \(0.117122\pi\) | ||||
−0.933067 | + | 0.359704i | \(0.882878\pi\) | |||||||
\(24\) | −2.43665 | − | 1.40680i | −0.497380 | − | 0.287163i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 2.42486 | 0.475555 | ||||||||
\(27\) | −5.39194 | −1.03768 | ||||||||
\(28\) | 0.712432 | + | 1.23397i | 0.134637 | + | 0.233198i | ||||
\(29\) | 2.74145i | 0.509074i | 0.967063 | + | 0.254537i | \(0.0819231\pi\) | ||||
−0.967063 | + | 0.254537i | \(0.918077\pi\) | |||||||
\(30\) | 1.40680 | − | 2.43665i | 0.256846 | − | 0.444870i | ||||
\(31\) | 4.04405i | 0.726332i | 0.931724 | + | 0.363166i | \(0.118304\pi\) | ||||
−0.931724 | + | 0.363166i | \(0.881696\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0.190895 | − | 0.330641i | 0.0332306 | − | 0.0575571i | ||||
\(34\) | −1.42326 | + | 2.46516i | −0.244088 | + | 0.422772i | ||||
\(35\) | −1.23397 | + | 0.712432i | −0.208579 | + | 0.120423i | ||||
\(36\) | −4.91638 | −0.819397 | ||||||||
\(37\) | −5.97276 | + | 1.15156i | −0.981916 | + | 0.189315i | ||||
\(38\) | −2.39602 | −0.388685 | ||||||||
\(39\) | 5.90855 | − | 3.41131i | 0.946126 | − | 0.546246i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −0.490256 | + | 0.849148i | −0.0765651 | + | 0.132615i | −0.901766 | − | 0.432225i | \(-0.857729\pi\) |
0.825201 | + | 0.564840i | \(0.191062\pi\) | |||||||
\(42\) | 3.47190 | + | 2.00450i | 0.535726 | + | 0.309301i | ||||
\(43\) | − | 11.8861i | − | 1.81262i | −0.422613 | − | 0.906310i | \(-0.638887\pi\) | ||
0.422613 | − | 0.906310i | \(-0.361113\pi\) | |||||||
\(44\) | 0.0678472 | − | 0.117515i | 0.0102284 | − | 0.0177160i | ||||
\(45\) | − | 4.91638i | − | 0.732891i | ||||||
\(46\) | 1.72508 | + | 2.98792i | 0.254349 | + | 0.440545i | ||||
\(47\) | 0.163866 | 0.0239024 | 0.0119512 | − | 0.999929i | \(-0.496196\pi\) | ||||
0.0119512 | + | 0.999929i | \(0.496196\pi\) | |||||||
\(48\) | −2.81361 | −0.406109 | ||||||||
\(49\) | 2.48488 | + | 4.30394i | 0.354983 | + | 0.614849i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 8.00900i | 1.12148i | ||||||||
\(52\) | 2.09999 | − | 1.21243i | 0.291217 | − | 0.168134i | ||||
\(53\) | 0.462004 | + | 0.800215i | 0.0634612 | + | 0.109918i | 0.896010 | − | 0.444033i | \(-0.146453\pi\) |
−0.832549 | + | 0.553951i | \(0.813119\pi\) | |||||||
\(54\) | −4.66956 | + | 2.69597i | −0.635447 | + | 0.366875i | ||||
\(55\) | 0.117515 | + | 0.0678472i | 0.0158457 | + | 0.00914852i | ||||
\(56\) | 1.23397 | + | 0.712432i | 0.164896 | + | 0.0952027i | ||||
\(57\) | −5.83827 | + | 3.37072i | −0.773297 | + | 0.446463i | ||||
\(58\) | 1.37072 | + | 2.37416i | 0.179985 | + | 0.311743i | ||||
\(59\) | 12.5215 | − | 7.22929i | 1.63016 | − | 0.941174i | 0.646119 | − | 0.763237i | \(-0.276391\pi\) |
0.984042 | − | 0.177937i | \(-0.0569424\pi\) | |||||||
\(60\) | − | 2.81361i | − | 0.363235i | ||||||
\(61\) | 8.11798 | + | 4.68692i | 1.03940 | + | 0.600098i | 0.919663 | − | 0.392708i | \(-0.128462\pi\) |
0.119737 | + | 0.992806i | \(0.461795\pi\) | |||||||
\(62\) | 2.02202 | + | 3.50225i | 0.256797 | + | 0.444786i | ||||
\(63\) | 7.00517 | 0.882569 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.21243 | + | 2.09999i | 0.150384 | + | 0.260472i | ||||
\(66\) | − | 0.381791i | − | 0.0469952i | ||||||
\(67\) | 3.94640 | − | 6.83536i | 0.482129 | − | 0.835073i | −0.517660 | − | 0.855586i | \(-0.673197\pi\) |
0.999790 | + | 0.0205137i | \(0.00653018\pi\) | |||||||
\(68\) | 2.84653i | 0.345192i | ||||||||
\(69\) | 8.40684 | + | 4.85369i | 1.01206 | + | 0.584316i | ||||
\(70\) | −0.712432 | + | 1.23397i | −0.0851519 | + | 0.147487i | ||||
\(71\) | −2.98434 | + | 5.16904i | −0.354177 | + | 0.613452i | −0.986977 | − | 0.160863i | \(-0.948572\pi\) |
0.632800 | + | 0.774315i | \(0.281905\pi\) | |||||||
\(72\) | −4.25771 | + | 2.45819i | −0.501776 | + | 0.289701i | ||||
\(73\) | −9.17382 | −1.07371 | −0.536857 | − | 0.843673i | \(-0.680389\pi\) | ||||
−0.536857 | + | 0.843673i | \(0.680389\pi\) | |||||||
\(74\) | −4.59679 | + | 3.98366i | −0.534366 | + | 0.463091i | ||||
\(75\) | 2.81361 | 0.324887 | ||||||||
\(76\) | −2.07501 | + | 1.19801i | −0.238020 | + | 0.137421i | ||||
\(77\) | −0.0966730 | + | 0.167443i | −0.0110169 | + | 0.0190819i | ||||
\(78\) | 3.41131 | − | 5.90855i | 0.386254 | − | 0.669012i | ||||
\(79\) | 4.63367 | + | 2.67525i | 0.521328 | + | 0.300989i | 0.737478 | − | 0.675371i | \(-0.236017\pi\) |
−0.216150 | + | 0.976360i | \(0.569350\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | −0.210831 | + | 0.365171i | −0.0234257 | + | 0.0405745i | ||||
\(82\) | 0.980511i | 0.108279i | ||||||||
\(83\) | −6.00344 | − | 10.3983i | −0.658963 | − | 1.14136i | −0.980884 | − | 0.194591i | \(-0.937662\pi\) |
0.321921 | − | 0.946766i | \(-0.395671\pi\) | |||||||
\(84\) | 4.00900 | 0.437418 | ||||||||
\(85\) | −2.84653 | −0.308749 | ||||||||
\(86\) | −5.94307 | − | 10.2937i | −0.640858 | − | 1.11000i | ||||
\(87\) | 6.67996 | + | 3.85668i | 0.716167 | + | 0.413479i | ||||
\(88\) | − | 0.135694i | − | 0.0144651i | ||||||
\(89\) | −8.45591 | + | 4.88202i | −0.896325 | + | 0.517493i | −0.876006 | − | 0.482300i | \(-0.839801\pi\) |
−0.0203188 | + | 0.999794i | \(0.506468\pi\) | |||||||
\(90\) | −2.45819 | − | 4.25771i | −0.259116 | − | 0.448802i | ||||
\(91\) | −2.99220 | + | 1.72755i | −0.313668 | + | 0.181096i | ||||
\(92\) | 2.98792 | + | 1.72508i | 0.311512 | + | 0.179852i | ||||
\(93\) | 9.85395 | + | 5.68918i | 1.02181 | + | 0.589940i | ||||
\(94\) | 0.141912 | − | 0.0819332i | 0.0146372 | − | 0.00845076i | ||||
\(95\) | −1.19801 | − | 2.07501i | −0.122913 | − | 0.212892i | ||||
\(96\) | −2.43665 | + | 1.40680i | −0.248690 | + | 0.143581i | ||||
\(97\) | 14.5305i | 1.47535i | 0.675156 | + | 0.737675i | \(0.264076\pi\) | ||||
−0.675156 | + | 0.737675i | \(0.735924\pi\) | |||||||
\(98\) | 4.30394 | + | 2.48488i | 0.434764 | + | 0.251011i | ||||
\(99\) | −0.333563 | − | 0.577748i | −0.0335243 | − | 0.0580659i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.2395 | −1.01886 | −0.509432 | − | 0.860511i | \(-0.670145\pi\) | ||||
−0.509432 | + | 0.860511i | \(0.670145\pi\) | |||||||
\(102\) | 4.00450 | + | 6.93600i | 0.396505 | + | 0.686766i | ||||
\(103\) | − | 18.9067i | − | 1.86293i | −0.363826 | − | 0.931467i | \(-0.618530\pi\) | ||
0.363826 | − | 0.931467i | \(-0.381470\pi\) | |||||||
\(104\) | 1.21243 | − | 2.09999i | 0.118889 | − | 0.205921i | ||||
\(105\) | 4.00900i | 0.391239i | ||||||||
\(106\) | 0.800215 | + | 0.462004i | 0.0777237 | + | 0.0448738i | ||||
\(107\) | −6.32318 | + | 10.9521i | −0.611285 | + | 1.05878i | 0.379739 | + | 0.925094i | \(0.376014\pi\) |
−0.991024 | + | 0.133684i | \(0.957319\pi\) | |||||||
\(108\) | −2.69597 | + | 4.66956i | −0.259420 | + | 0.449329i | ||||
\(109\) | 10.6071 | − | 6.12399i | 1.01597 | − | 0.586572i | 0.103038 | − | 0.994677i | \(-0.467144\pi\) |
0.912935 | + | 0.408105i | \(0.133810\pi\) | |||||||
\(110\) | 0.135694 | 0.0129380 | ||||||||
\(111\) | −5.59656 | + | 16.1736i | −0.531202 | + | 1.53513i | ||||
\(112\) | 1.42486 | 0.134637 | ||||||||
\(113\) | −4.17418 | + | 2.40996i | −0.392674 | + | 0.226710i | −0.683318 | − | 0.730121i | \(-0.739464\pi\) |
0.290644 | + | 0.956831i | \(0.406130\pi\) | |||||||
\(114\) | −3.37072 | + | 5.83827i | −0.315697 | + | 0.546804i | ||||
\(115\) | −1.72508 | + | 2.98792i | −0.160864 | + | 0.278625i | ||||
\(116\) | 2.37416 | + | 1.37072i | 0.220436 | + | 0.127269i | ||||
\(117\) | − | 11.9216i | − | 1.10215i | ||||||
\(118\) | 7.22929 | − | 12.5215i | 0.665510 | − | 1.15270i | ||||
\(119\) | − | 4.05591i | − | 0.371805i | ||||||
\(120\) | −1.40680 | − | 2.43665i | −0.128423 | − | 0.222435i | ||||
\(121\) | −10.9816 | −0.998326 | ||||||||
\(122\) | 9.37383 | 0.848667 | ||||||||
\(123\) | 1.37939 | + | 2.38917i | 0.124375 | + | 0.215424i | ||||
\(124\) | 3.50225 | + | 2.02202i | 0.314511 | + | 0.181583i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 6.06666 | − | 3.50259i | 0.540461 | − | 0.312035i | ||||
\(127\) | −3.46769 | − | 6.00621i | −0.307708 | − | 0.532965i | 0.670153 | − | 0.742223i | \(-0.266229\pi\) |
−0.977860 | + | 0.209258i | \(0.932895\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −28.9624 | − | 16.7215i | −2.55000 | − | 1.47224i | ||||
\(130\) | 2.09999 | + | 1.21243i | 0.184182 | + | 0.106337i | ||||
\(131\) | −16.0549 | + | 9.26933i | −1.40273 | + | 0.809865i | −0.994672 | − | 0.103092i | \(-0.967126\pi\) |
−0.408055 | + | 0.912957i | \(0.633793\pi\) | |||||||
\(132\) | −0.190895 | − | 0.330641i | −0.0166153 | − | 0.0287786i | ||||
\(133\) | 2.95661 | − | 1.70700i | 0.256370 | − | 0.148015i | ||||
\(134\) | − | 7.89280i | − | 0.681834i | ||||||
\(135\) | −4.66956 | − | 2.69597i | −0.401892 | − | 0.232032i | ||||
\(136\) | 1.42326 | + | 2.46516i | 0.122044 | + | 0.211386i | ||||
\(137\) | 3.81263 | 0.325735 | 0.162868 | − | 0.986648i | \(-0.447926\pi\) | ||||
0.162868 | + | 0.986648i | \(0.447926\pi\) | |||||||
\(138\) | 9.70738 | 0.826347 | ||||||||
\(139\) | 4.93152 | + | 8.54164i | 0.418286 | + | 0.724493i | 0.995767 | − | 0.0919114i | \(-0.0292976\pi\) |
−0.577481 | + | 0.816404i | \(0.695964\pi\) | |||||||
\(140\) | 1.42486i | 0.120423i | ||||||||
\(141\) | 0.230528 | − | 0.399286i | 0.0194139 | − | 0.0336259i | ||||
\(142\) | 5.96869i | 0.500881i | ||||||||
\(143\) | 0.284957 | + | 0.164520i | 0.0238293 | + | 0.0137579i | ||||
\(144\) | −2.45819 | + | 4.25771i | −0.204849 | + | 0.354809i | ||||
\(145\) | −1.37072 | + | 2.37416i | −0.113832 | + | 0.197164i | ||||
\(146\) | −7.94477 | + | 4.58691i | −0.657513 | + | 0.379616i | ||||
\(147\) | 13.9830 | 1.15330 | ||||||||
\(148\) | −1.98910 | + | 5.74834i | −0.163503 | + | 0.472511i | ||||
\(149\) | −8.48318 | −0.694969 | −0.347484 | − | 0.937686i | \(-0.612964\pi\) | ||||
−0.347484 | + | 0.937686i | \(0.612964\pi\) | |||||||
\(150\) | 2.43665 | − | 1.40680i | 0.198952 | − | 0.114865i | ||||
\(151\) | 2.94779 | − | 5.10573i | 0.239888 | − | 0.415498i | −0.720794 | − | 0.693149i | \(-0.756223\pi\) |
0.960682 | + | 0.277651i | \(0.0895560\pi\) | |||||||
\(152\) | −1.19801 | + | 2.07501i | −0.0971713 | + | 0.168306i | ||||
\(153\) | 12.1197 | + | 6.99730i | 0.979819 | + | 0.565698i | ||||
\(154\) | 0.193346i | 0.0155803i | ||||||||
\(155\) | −2.02202 | + | 3.50225i | −0.162413 | + | 0.281307i | ||||
\(156\) | − | 6.82261i | − | 0.546246i | ||||||
\(157\) | −8.59034 | − | 14.8789i | −0.685584 | − | 1.18747i | −0.973253 | − | 0.229736i | \(-0.926214\pi\) |
0.287669 | − | 0.957730i | \(-0.407120\pi\) | |||||||
\(158\) | 5.35050 | 0.425663 | ||||||||
\(159\) | 2.59980 | 0.206177 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −4.25738 | − | 2.45800i | −0.335529 | − | 0.193718i | ||||
\(162\) | 0.421663i | 0.0331290i | ||||||||
\(163\) | 9.41656 | − | 5.43665i | 0.737562 | − | 0.425832i | −0.0836202 | − | 0.996498i | \(-0.526648\pi\) |
0.821182 | + | 0.570666i | \(0.193315\pi\) | |||||||
\(164\) | 0.490256 | + | 0.849148i | 0.0382825 | + | 0.0663073i | ||||
\(165\) | 0.330641 | − | 0.190895i | 0.0257403 | − | 0.0148612i | ||||
\(166\) | −10.3983 | − | 6.00344i | −0.807062 | − | 0.465957i | ||||
\(167\) | 11.8695 | + | 6.85285i | 0.918488 | + | 0.530289i | 0.883152 | − | 0.469086i | \(-0.155417\pi\) |
0.0353354 | + | 0.999376i | \(0.488750\pi\) | |||||||
\(168\) | 3.47190 | − | 2.00450i | 0.267863 | − | 0.154651i | ||||
\(169\) | −3.56002 | − | 6.16613i | −0.273848 | − | 0.474318i | ||||
\(170\) | −2.46516 | + | 1.42326i | −0.189069 | + | 0.109159i | ||||
\(171\) | 11.7797i | 0.900819i | ||||||||
\(172\) | −10.2937 | − | 5.94307i | −0.784888 | − | 0.453155i | ||||
\(173\) | −3.72448 | − | 6.45098i | −0.283167 | − | 0.490459i | 0.688996 | − | 0.724765i | \(-0.258052\pi\) |
−0.972163 | + | 0.234306i | \(0.924718\pi\) | |||||||
\(174\) | 7.71336 | 0.584748 | ||||||||
\(175\) | −1.42486 | −0.107710 | ||||||||
\(176\) | −0.0678472 | − | 0.117515i | −0.00511418 | − | 0.00885802i | ||||
\(177\) | − | 40.6808i | − | 3.05775i | ||||||
\(178\) | −4.88202 | + | 8.45591i | −0.365923 | + | 0.633797i | ||||
\(179\) | 23.9080i | 1.78697i | 0.449092 | + | 0.893486i | \(0.351748\pi\) | ||||
−0.449092 | + | 0.893486i | \(0.648252\pi\) | |||||||
\(180\) | −4.25771 | − | 2.45819i | −0.317351 | − | 0.183223i | ||||
\(181\) | 8.02572 | − | 13.9010i | 0.596547 | − | 1.03325i | −0.396779 | − | 0.917914i | \(-0.629872\pi\) |
0.993327 | − | 0.115336i | \(-0.0367945\pi\) | |||||||
\(182\) | −1.72755 | + | 2.99220i | −0.128054 | + | 0.221797i | ||||
\(183\) | 22.8408 | − | 13.1871i | 1.68844 | − | 0.974821i | ||||
\(184\) | 3.45016 | 0.254349 | ||||||||
\(185\) | −5.74834 | − | 1.98910i | −0.422627 | − | 0.146242i | ||||
\(186\) | 11.3784 | 0.834302 | ||||||||
\(187\) | −0.334509 | + | 0.193129i | −0.0244617 | + | 0.0141230i | ||||
\(188\) | 0.0819332 | − | 0.141912i | 0.00597559 | − | 0.0103500i | ||||
\(189\) | 3.84139 | − | 6.65348i | 0.279420 | − | 0.483970i | ||||
\(190\) | −2.07501 | − | 1.19801i | −0.150537 | − | 0.0869127i | ||||
\(191\) | 1.16751i | 0.0844777i | 0.999108 | + | 0.0422389i | \(0.0134490\pi\) | ||||
−0.999108 | + | 0.0422389i | \(0.986551\pi\) | |||||||
\(192\) | −1.40680 | + | 2.43665i | −0.101527 | + | 0.175850i | ||||
\(193\) | 3.22571i | 0.232192i | 0.993238 | + | 0.116096i | \(0.0370380\pi\) | ||||
−0.993238 | + | 0.116096i | \(0.962962\pi\) | |||||||
\(194\) | 7.26525 | + | 12.5838i | 0.521615 | + | 0.903463i | ||||
\(195\) | 6.82261 | 0.488577 | ||||||||
\(196\) | 4.96977 | 0.354983 | ||||||||
\(197\) | 1.85075 | + | 3.20559i | 0.131860 | + | 0.228389i | 0.924394 | − | 0.381440i | \(-0.124572\pi\) |
−0.792533 | + | 0.609829i | \(0.791238\pi\) | |||||||
\(198\) | −0.577748 | − | 0.333563i | −0.0410588 | − | 0.0237053i | ||||
\(199\) | − | 22.9628i | − | 1.62779i | −0.581012 | − | 0.813895i | \(-0.697343\pi\) | ||
0.581012 | − | 0.813895i | \(-0.302657\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | −11.1036 | − | 19.2320i | −0.783189 | − | 1.35652i | ||||
\(202\) | −8.86764 | + | 5.11973i | −0.623925 | + | 0.360223i | ||||
\(203\) | −3.38286 | − | 1.95309i | −0.237430 | − | 0.137080i | ||||
\(204\) | 6.93600 | + | 4.00450i | 0.485617 | + | 0.280371i | ||||
\(205\) | −0.849148 | + | 0.490256i | −0.0593070 | + | 0.0342409i | ||||
\(206\) | −9.45336 | − | 16.3737i | −0.658647 | − | 1.14081i | ||||
\(207\) | 14.6898 | − | 8.48114i | 1.02101 | − | 0.589480i | ||||
\(208\) | − | 2.42486i | − | 0.168134i | ||||||
\(209\) | −0.281568 | − | 0.162563i | −0.0194764 | − | 0.0112447i | ||||
\(210\) | 2.00450 | + | 3.47190i | 0.138324 | + | 0.239584i | ||||
\(211\) | 15.3087 | 1.05389 | 0.526947 | − | 0.849898i | \(-0.323337\pi\) | ||||
0.526947 | + | 0.849898i | \(0.323337\pi\) | |||||||
\(212\) | 0.924008 | 0.0634612 | ||||||||
\(213\) | 8.39677 | + | 14.5436i | 0.575337 | + | 0.996513i | ||||
\(214\) | 12.6464i | 0.864488i | ||||||||
\(215\) | 5.94307 | − | 10.2937i | 0.405314 | − | 0.702025i | ||||
\(216\) | 5.39194i | 0.366875i | ||||||||
\(217\) | −4.99022 | − | 2.88111i | −0.338758 | − | 0.195582i | ||||
\(218\) | 6.12399 | − | 10.6071i | 0.414769 | − | 0.718401i | ||||
\(219\) | −12.9058 | + | 22.3534i | −0.872091 | + | 1.51051i | ||||
\(220\) | 0.117515 | − | 0.0678472i | 0.00792285 | − | 0.00457426i | ||||
\(221\) | −6.90244 | −0.464308 | ||||||||
\(222\) | 3.24003 | + | 16.8050i | 0.217457 | + | 1.12788i | ||||
\(223\) | −9.77305 | −0.654452 | −0.327226 | − | 0.944946i | \(-0.606114\pi\) | ||||
−0.327226 | + | 0.944946i | \(0.606114\pi\) | |||||||
\(224\) | 1.23397 | − | 0.712432i | 0.0824479 | − | 0.0476013i | ||||
\(225\) | 2.45819 | − | 4.25771i | 0.163879 | − | 0.283847i | ||||
\(226\) | −2.40996 | + | 4.17418i | −0.160308 | + | 0.277662i | ||||
\(227\) | −9.75238 | − | 5.63054i | −0.647288 | − | 0.373712i | 0.140128 | − | 0.990133i | \(-0.455248\pi\) |
−0.787416 | + | 0.616421i | \(0.788582\pi\) | |||||||
\(228\) | 6.74145i | 0.446463i | ||||||||
\(229\) | 0.119732 | − | 0.207382i | 0.00791212 | − | 0.0137042i | −0.862042 | − | 0.506836i | \(-0.830815\pi\) |
0.869954 | + | 0.493132i | \(0.164148\pi\) | |||||||
\(230\) | 3.45016i | 0.227497i | ||||||||
\(231\) | 0.272000 | + | 0.471118i | 0.0178963 | + | 0.0309973i | ||||
\(232\) | 2.74145 | 0.179985 | ||||||||
\(233\) | −23.8459 | −1.56220 | −0.781098 | − | 0.624408i | \(-0.785340\pi\) | ||||
−0.781098 | + | 0.624408i | \(0.785340\pi\) | |||||||
\(234\) | −5.96078 | − | 10.3244i | −0.389668 | − | 0.674925i | ||||
\(235\) | 0.141912 | + | 0.0819332i | 0.00925735 | + | 0.00534473i | ||||
\(236\) | − | 14.4586i | − | 0.941174i | ||||||
\(237\) | 13.0373 | − | 7.52710i | 0.846865 | − | 0.488938i | ||||
\(238\) | −2.02795 | − | 3.51252i | −0.131453 | − | 0.227683i | ||||
\(239\) | −10.4042 | + | 6.00686i | −0.672991 | + | 0.388551i | −0.797209 | − | 0.603704i | \(-0.793691\pi\) |
0.124218 | + | 0.992255i | \(0.460358\pi\) | |||||||
\(240\) | −2.43665 | − | 1.40680i | −0.157285 | − | 0.0908088i | ||||
\(241\) | 7.10709 | + | 4.10328i | 0.457808 | + | 0.264316i | 0.711122 | − | 0.703068i | \(-0.248187\pi\) |
−0.253314 | + | 0.967384i | \(0.581521\pi\) | |||||||
\(242\) | −9.51033 | + | 5.49079i | −0.611347 | + | 0.352962i | ||||
\(243\) | −7.49472 | − | 12.9812i | −0.480786 | − | 0.832747i | ||||
\(244\) | 8.11798 | − | 4.68692i | 0.519700 | − | 0.300049i | ||||
\(245\) | 4.96977i | 0.317507i | ||||||||
\(246\) | 2.38917 | + | 1.37939i | 0.152328 | + | 0.0879465i | ||||
\(247\) | −2.90501 | − | 5.03162i | −0.184841 | − | 0.320154i | ||||
\(248\) | 4.04405 | 0.256797 | ||||||||
\(249\) | −33.7826 | −2.14089 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | − | 13.4091i | − | 0.846375i | −0.906042 | − | 0.423187i | \(-0.860911\pi\) | ||
0.906042 | − | 0.423187i | \(-0.139089\pi\) | |||||||
\(252\) | 3.50259 | − | 6.06666i | 0.220642 | − | 0.382163i | ||||
\(253\) | 0.468167i | 0.0294334i | ||||||||
\(254\) | −6.00621 | − | 3.46769i | −0.376863 | − | 0.217582i | ||||
\(255\) | −4.00450 | + | 6.93600i | −0.250772 | + | 0.434349i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.0771 | − | 8.12744i | 0.878108 | − | 0.506976i | 0.00807398 | − | 0.999967i | \(-0.497430\pi\) |
0.870034 | + | 0.492991i | \(0.164097\pi\) | |||||||
\(258\) | −33.4429 | −2.08207 | ||||||||
\(259\) | 2.83420 | − | 8.19060i | 0.176109 | − | 0.508939i | ||||
\(260\) | 2.42486 | 0.150384 | ||||||||
\(261\) | 11.6723 | − | 6.73900i | 0.722497 | − | 0.417134i | ||||
\(262\) | −9.26933 | + | 16.0549i | −0.572661 | + | 0.991878i | ||||
\(263\) | −3.09553 | + | 5.36161i | −0.190878 | + | 0.330611i | −0.945542 | − | 0.325501i | \(-0.894467\pi\) |
0.754663 | + | 0.656112i | \(0.227800\pi\) | |||||||
\(264\) | −0.330641 | − | 0.190895i | −0.0203495 | − | 0.0117488i | ||||
\(265\) | 0.924008i | 0.0567614i | ||||||||
\(266\) | 1.70700 | − | 2.95661i | 0.104663 | − | 0.181281i | ||||
\(267\) | 27.4722i | 1.68127i | ||||||||
\(268\) | −3.94640 | − | 6.83536i | −0.241065 | − | 0.417536i | ||||
\(269\) | 13.8306 | 0.843269 | 0.421634 | − | 0.906766i | \(-0.361457\pi\) | ||||
0.421634 | + | 0.906766i | \(0.361457\pi\) | |||||||
\(270\) | −5.39194 | −0.328143 | ||||||||
\(271\) | 5.32088 | + | 9.21603i | 0.323220 | + | 0.559834i | 0.981151 | − | 0.193245i | \(-0.0619012\pi\) |
−0.657930 | + | 0.753079i | \(0.728568\pi\) | |||||||
\(272\) | 2.46516 | + | 1.42326i | 0.149473 | + | 0.0862980i | ||||
\(273\) | 9.72129i | 0.588359i | ||||||||
\(274\) | 3.30184 | − | 1.90632i | 0.199471 | − | 0.115165i | ||||
\(275\) | 0.0678472 | + | 0.117515i | 0.00409134 | + | 0.00708641i | ||||
\(276\) | 8.40684 | − | 4.85369i | 0.506032 | − | 0.292158i | ||||
\(277\) | −17.9019 | − | 10.3357i | −1.07562 | − | 0.621011i | −0.145911 | − | 0.989298i | \(-0.546611\pi\) |
−0.929712 | + | 0.368287i | \(0.879945\pi\) | |||||||
\(278\) | 8.54164 | + | 4.93152i | 0.512294 | + | 0.295773i | ||||
\(279\) | 17.2184 | − | 9.94104i | 1.03084 | − | 0.595155i | ||||
\(280\) | 0.712432 | + | 1.23397i | 0.0425759 | + | 0.0737437i | ||||
\(281\) | −12.3130 | + | 7.10889i | −0.734529 | + | 0.424081i | −0.820077 | − | 0.572253i | \(-0.806069\pi\) |
0.0855476 | + | 0.996334i | \(0.472736\pi\) | |||||||
\(282\) | − | 0.461056i | − | 0.0274555i | ||||||
\(283\) | −23.5507 | − | 13.5970i | −1.39994 | − | 0.808258i | −0.405558 | − | 0.914069i | \(-0.632923\pi\) |
−0.994386 | + | 0.105811i | \(0.966256\pi\) | |||||||
\(284\) | 2.98434 | + | 5.16904i | 0.177088 | + | 0.306726i | ||||
\(285\) | −6.74145 | −0.399329 | ||||||||
\(286\) | 0.329041 | 0.0194566 | ||||||||
\(287\) | −0.698547 | − | 1.20992i | −0.0412339 | − | 0.0714193i | ||||
\(288\) | 4.91638i | 0.289701i | ||||||||
\(289\) | −4.44865 | + | 7.70528i | −0.261685 | + | 0.453252i | ||||
\(290\) | 2.74145i | 0.160983i | ||||||||
\(291\) | 35.4058 | + | 20.4416i | 2.07553 | + | 1.19831i | ||||
\(292\) | −4.58691 | + | 7.94477i | −0.268429 | + | 0.464932i | ||||
\(293\) | −4.06312 | + | 7.03753i | −0.237370 | + | 0.411137i | −0.959959 | − | 0.280141i | \(-0.909619\pi\) |
0.722589 | + | 0.691278i | \(0.242952\pi\) | |||||||
\(294\) | 12.1096 | − | 6.99148i | 0.706246 | − | 0.407752i | ||||
\(295\) | 14.4586 | 0.841812 | ||||||||
\(296\) | 1.15156 | + | 5.97276i | 0.0669329 | + | 0.347160i | ||||
\(297\) | −0.731657 | −0.0424550 | ||||||||
\(298\) | −7.34665 | + | 4.24159i | −0.425580 | + | 0.245709i | ||||
\(299\) | −4.18308 | + | 7.24530i | −0.241914 | + | 0.419007i | ||||
\(300\) | 1.40680 | − | 2.43665i | 0.0812218 | − | 0.140680i | ||||
\(301\) | 14.6671 | + | 8.46807i | 0.845399 | + | 0.488091i | ||||
\(302\) | − | 5.89559i | − | 0.339253i | ||||||
\(303\) | −14.4049 | + | 24.9500i | −0.827541 | + | 1.43334i | ||||
\(304\) | 2.39602i | 0.137421i | ||||||||
\(305\) | 4.68692 | + | 8.11798i | 0.268372 | + | 0.464834i | ||||
\(306\) | 13.9946 | 0.800018 | ||||||||
\(307\) | 18.6234 | 1.06290 | 0.531448 | − | 0.847091i | \(-0.321648\pi\) | ||||
0.531448 | + | 0.847091i | \(0.321648\pi\) | |||||||
\(308\) | 0.0966730 | + | 0.167443i | 0.00550846 | + | 0.00954093i | ||||
\(309\) | −46.0691 | − | 26.5980i | −2.62078 | − | 1.51311i | ||||
\(310\) | 4.04405i | 0.229686i | ||||||||
\(311\) | 12.1810 | − | 7.03271i | 0.690722 | − | 0.398789i | −0.113160 | − | 0.993577i | \(-0.536097\pi\) |
0.803883 | + | 0.594788i | \(0.202764\pi\) | |||||||
\(312\) | −3.41131 | − | 5.90855i | −0.193127 | − | 0.334506i | ||||
\(313\) | 29.1305 | − | 16.8185i | 1.64655 | − | 0.950637i | 0.668123 | − | 0.744051i | \(-0.267098\pi\) |
0.978428 | − | 0.206586i | \(-0.0662354\pi\) | |||||||
\(314\) | −14.8789 | − | 8.59034i | −0.839665 | − | 0.484781i | ||||
\(315\) | 6.06666 | + | 3.50259i | 0.341817 | + | 0.197348i | ||||
\(316\) | 4.63367 | − | 2.67525i | 0.260664 | − | 0.150495i | ||||
\(317\) | 14.2227 | + | 24.6344i | 0.798825 | + | 1.38361i | 0.920381 | + | 0.391022i | \(0.127878\pi\) |
−0.121556 | + | 0.992585i | \(0.538788\pi\) | |||||||
\(318\) | 2.25149 | − | 1.29990i | 0.126257 | − | 0.0728947i | ||||
\(319\) | 0.371999i | 0.0208280i | ||||||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | 17.7910 | + | 30.8148i | 0.992994 | + | 1.71992i | ||||
\(322\) | −4.91600 | −0.273958 | ||||||||
\(323\) | 6.82032 | 0.379493 | ||||||||
\(324\) | 0.210831 | + | 0.365171i | 0.0117129 | + | 0.0202873i | ||||
\(325\) | 2.42486i | 0.134507i | ||||||||
\(326\) | 5.43665 | − | 9.41656i | 0.301108 | − | 0.521535i | ||||
\(327\) | − | 34.4610i | − | 1.90570i | ||||||
\(328\) | 0.849148 | + | 0.490256i | 0.0468863 | + | 0.0270698i | ||||
\(329\) | −0.116744 | + | 0.202206i | −0.00643628 | + | 0.0111480i | ||||
\(330\) | 0.190895 | − | 0.330641i | 0.0105084 | − | 0.0182012i | ||||
\(331\) | 26.5630 | − | 15.3361i | 1.46003 | − | 0.842951i | 0.461021 | − | 0.887389i | \(-0.347483\pi\) |
0.999012 | + | 0.0444385i | \(0.0141499\pi\) | |||||||
\(332\) | −12.0069 | −0.658963 | ||||||||
\(333\) | 19.5852 | + | 22.5996i | 1.07326 | + | 1.23845i | ||||
\(334\) | 13.7057 | 0.749942 | ||||||||
\(335\) | 6.83536 | − | 3.94640i | 0.373456 | − | 0.215615i | ||||
\(336\) | 2.00450 | − | 3.47190i | 0.109355 | − | 0.189408i | ||||
\(337\) | −8.94414 | + | 15.4917i | −0.487218 | + | 0.843887i | −0.999892 | − | 0.0146966i | \(-0.995322\pi\) |
0.512674 | + | 0.858584i | \(0.328655\pi\) | |||||||
\(338\) | −6.16613 | − | 3.56002i | −0.335394 | − | 0.193640i | ||||
\(339\) | 13.5614i | 0.736553i | ||||||||
\(340\) | −1.42326 | + | 2.46516i | −0.0771873 | + | 0.133692i | ||||
\(341\) | 0.548755i | 0.0297167i | ||||||||
\(342\) | 5.88987 | + | 10.2015i | 0.318488 | + | 0.551637i | ||||
\(343\) | −17.0553 | −0.920898 | ||||||||
\(344\) | −11.8861 | −0.640858 | ||||||||
\(345\) | 4.85369 | + | 8.40684i | 0.261314 | + | 0.452609i | ||||
\(346\) | −6.45098 | − | 3.72448i | −0.346807 | − | 0.200229i | ||||
\(347\) | 1.63302i | 0.0876649i | 0.999039 | + | 0.0438325i | \(0.0139568\pi\) | ||||
−0.999039 | + | 0.0438325i | \(0.986043\pi\) | |||||||
\(348\) | 6.67996 | − | 3.85668i | 0.358084 | − | 0.206740i | ||||
\(349\) | 14.4163 | + | 24.9697i | 0.771685 | + | 1.33660i | 0.936639 | + | 0.350297i | \(0.113919\pi\) |
−0.164954 | + | 0.986301i | \(0.552747\pi\) | |||||||
\(350\) | −1.23397 | + | 0.712432i | −0.0659583 | + | 0.0380811i | ||||
\(351\) | −11.3230 | − | 6.53736i | −0.604379 | − | 0.348939i | ||||
\(352\) | −0.117515 | − | 0.0678472i | −0.00626356 | − | 0.00361627i | ||||
\(353\) | −9.81009 | + | 5.66386i | −0.522138 | + | 0.301457i | −0.737809 | − | 0.675009i | \(-0.764140\pi\) |
0.215671 | + | 0.976466i | \(0.430806\pi\) | |||||||
\(354\) | −20.3404 | − | 35.2306i | −1.08108 | − | 1.87248i | ||||
\(355\) | −5.16904 | + | 2.98434i | −0.274344 | + | 0.158393i | ||||
\(356\) | 9.76404i | 0.517493i | ||||||||
\(357\) | −9.88285 | − | 5.70587i | −0.523056 | − | 0.301986i | ||||
\(358\) | 11.9540 | + | 20.7050i | 0.631790 | + | 1.09429i | ||||
\(359\) | −2.21623 | −0.116968 | −0.0584842 | − | 0.998288i | \(-0.518627\pi\) | ||||
−0.0584842 | + | 0.998288i | \(0.518627\pi\) | |||||||
\(360\) | −4.91638 | −0.259116 | ||||||||
\(361\) | −6.62955 | − | 11.4827i | −0.348924 | − | 0.604354i | ||||
\(362\) | − | 16.0514i | − | 0.843645i | ||||||
\(363\) | −15.4489 | + | 26.7583i | −0.810859 | + | 1.40445i | ||||
\(364\) | 3.45510i | 0.181096i | ||||||||
\(365\) | −7.94477 | − | 4.58691i | −0.415848 | − | 0.240090i | ||||
\(366\) | 13.1871 | − | 22.8408i | 0.689303 | − | 1.19391i | ||||
\(367\) | 0.931550 | − | 1.61349i | 0.0486265 | − | 0.0842236i | −0.840688 | − | 0.541520i | \(-0.817849\pi\) |
0.889314 | + | 0.457297i | \(0.151182\pi\) | |||||||
\(368\) | 2.98792 | − | 1.72508i | 0.155756 | − | 0.0899259i | ||||
\(369\) | 4.82057 | 0.250949 | ||||||||
\(370\) | −5.97276 | + | 1.15156i | −0.310509 | + | 0.0598666i | ||||
\(371\) | −1.31659 | −0.0683537 | ||||||||
\(372\) | 9.85395 | − | 5.68918i | 0.510903 | − | 0.294970i | ||||
\(373\) | −2.19037 | + | 3.79383i | −0.113413 | + | 0.196437i | −0.917144 | − | 0.398555i | \(-0.869512\pi\) |
0.803731 | + | 0.594992i | \(0.202845\pi\) | |||||||
\(374\) | −0.193129 | + | 0.334509i | −0.00998646 | + | 0.0172971i | ||||
\(375\) | 2.43665 | + | 1.40680i | 0.125828 | + | 0.0726470i | ||||
\(376\) | − | 0.163866i | − | 0.00845076i | ||||||
\(377\) | −3.32382 | + | 5.75702i | −0.171185 | + | 0.296502i | ||||
\(378\) | − | 7.68278i | − | 0.395160i | ||||||
\(379\) | 9.65335 | + | 16.7201i | 0.495859 | + | 0.858854i | 0.999989 | − | 0.00477467i | \(-0.00151983\pi\) |
−0.504129 | + | 0.863628i | \(0.668186\pi\) | |||||||
\(380\) | −2.39602 | −0.122913 | ||||||||
\(381\) | −19.5134 | −0.999703 | ||||||||
\(382\) | 0.583753 | + | 1.01109i | 0.0298674 | + | 0.0517318i | ||||
\(383\) | −23.4066 | − | 13.5138i | −1.19602 | − | 0.690523i | −0.236355 | − | 0.971667i | \(-0.575953\pi\) |
−0.959666 | + | 0.281144i | \(0.909286\pi\) | |||||||
\(384\) | 2.81361i | 0.143581i | ||||||||
\(385\) | −0.167443 | + | 0.0966730i | −0.00853367 | + | 0.00492691i | ||||
\(386\) | 1.61286 | + | 2.79355i | 0.0820922 | + | 0.142188i | ||||
\(387\) | −50.6078 | + | 29.2184i | −2.57254 | + | 1.48526i | ||||
\(388\) | 12.5838 | + | 7.26525i | 0.638845 | + | 0.368837i | ||||
\(389\) | 9.73946 | + | 5.62308i | 0.493810 | + | 0.285101i | 0.726154 | − | 0.687532i | \(-0.241306\pi\) |
−0.232344 | + | 0.972634i | \(0.574639\pi\) | |||||||
\(390\) | 5.90855 | − | 3.41131i | 0.299191 | − | 0.172738i | ||||
\(391\) | −4.91048 | − | 8.50520i | −0.248334 | − | 0.430126i | ||||
\(392\) | 4.30394 | − | 2.48488i | 0.217382 | − | 0.125506i | ||||
\(393\) | 52.1605i | 2.63115i | ||||||||
\(394\) | 3.20559 | + | 1.85075i | 0.161495 | + | 0.0932393i | ||||
\(395\) | 2.67525 | + | 4.63367i | 0.134606 | + | 0.233145i | ||||
\(396\) | −0.667126 | −0.0335243 | ||||||||
\(397\) | 7.59996 | 0.381431 | 0.190715 | − | 0.981645i | \(-0.438919\pi\) | ||||
0.190715 | + | 0.981645i | \(0.438919\pi\) | |||||||
\(398\) | −11.4814 | − | 19.8864i | −0.575511 | − | 0.996814i | ||||
\(399\) | − | 9.60564i | − | 0.480884i | ||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | − | 20.1495i | − | 1.00622i | −0.864223 | − | 0.503108i | \(-0.832190\pi\) | ||
0.864223 | − | 0.503108i | \(-0.167810\pi\) | |||||||
\(402\) | −19.2320 | − | 11.1036i | −0.959206 | − | 0.553798i | ||||
\(403\) | −4.90313 | + | 8.49247i | −0.244242 | + | 0.423040i | ||||
\(404\) | −5.11973 | + | 8.86764i | −0.254716 | + | 0.441181i | ||||
\(405\) | −0.365171 | + | 0.210831i | −0.0181455 | + | 0.0104763i | ||||
\(406\) | −3.90619 | −0.193861 | ||||||||
\(407\) | −0.810471 | + | 0.156260i | −0.0401736 | + | 0.00774552i | ||||
\(408\) | 8.00900 | 0.396505 | ||||||||
\(409\) | 16.7570 | − | 9.67464i | 0.828579 | − | 0.478380i | −0.0247872 | − | 0.999693i | \(-0.507891\pi\) |
0.853366 | + | 0.521313i | \(0.174557\pi\) | |||||||
\(410\) | −0.490256 | + | 0.849148i | −0.0242120 | + | 0.0419364i | ||||
\(411\) | 5.36362 | − | 9.29007i | 0.264568 | − | 0.458245i | ||||
\(412\) | −16.3737 | − | 9.45336i | −0.806674 | − | 0.465733i | ||||
\(413\) | 20.6015i | 1.01373i | ||||||||
\(414\) | 8.48114 | − | 14.6898i | 0.416825 | − | 0.721963i | ||||
\(415\) | − | 12.0069i | − | 0.589395i | ||||||
\(416\) | −1.21243 | − | 2.09999i | −0.0594443 | − | 0.102961i | ||||
\(417\) | 27.7507 | 1.35896 | ||||||||
\(418\) | −0.325126 | −0.0159024 | ||||||||
\(419\) | 10.2368 | + | 17.7306i | 0.500099 | + | 0.866196i | 1.00000 | 0.000113822i | \(3.62306e-5\pi\) | |
−0.499901 | + | 0.866082i | \(0.666630\pi\) | |||||||
\(420\) | 3.47190 | + | 2.00450i | 0.169411 | + | 0.0978097i | ||||
\(421\) | 28.6857i | 1.39805i | 0.715095 | + | 0.699027i | \(0.246384\pi\) | ||||
−0.715095 | + | 0.699027i | \(0.753616\pi\) | |||||||
\(422\) | 13.2577 | − | 7.65434i | 0.645375 | − | 0.372608i | ||||
\(423\) | −0.402815 | − | 0.697696i | −0.0195855 | − | 0.0339231i | ||||
\(424\) | 0.800215 | − | 0.462004i | 0.0388619 | − | 0.0224369i | ||||
\(425\) | −2.46516 | − | 1.42326i | −0.119578 | − | 0.0690384i | ||||
\(426\) | 14.5436 | + | 8.39677i | 0.704641 | + | 0.406825i | ||||
\(427\) | −11.5670 | + | 6.67821i | −0.559767 | + | 0.323181i | ||||
\(428\) | 6.32318 | + | 10.9521i | 0.305643 | + | 0.529389i | ||||
\(429\) | 0.801758 | − | 0.462895i | 0.0387093 | − | 0.0223488i | ||||
\(430\) | − | 11.8861i | − | 0.573201i | ||||||
\(431\) | 11.3724 | + | 6.56586i | 0.547789 | + | 0.316266i | 0.748230 | − | 0.663440i | \(-0.230904\pi\) |
−0.200441 | + | 0.979706i | \(0.564237\pi\) | |||||||
\(432\) | 2.69597 | + | 4.66956i | 0.129710 | + | 0.224664i | ||||
\(433\) | 13.0628 | 0.627756 | 0.313878 | − | 0.949463i | \(-0.398372\pi\) | ||||
0.313878 | + | 0.949463i | \(0.398372\pi\) | |||||||
\(434\) | −5.76221 | −0.276595 | ||||||||
\(435\) | 3.85668 | + | 6.67996i | 0.184914 | + | 0.320280i | ||||
\(436\) | − | 12.2480i | − | 0.586572i | ||||||
\(437\) | 4.13332 | − | 7.15911i | 0.197723 | − | 0.342467i | ||||
\(438\) | 25.8115i | 1.23332i | ||||||||
\(439\) | 28.8758 | + | 16.6715i | 1.37817 | + | 0.795685i | 0.991939 | − | 0.126718i | \(-0.0404445\pi\) |
0.386228 | + | 0.922403i | \(0.373778\pi\) | |||||||
\(440\) | 0.0678472 | − | 0.117515i | 0.00323449 | − | 0.00560230i | ||||
\(441\) | 12.2166 | − | 21.1598i | 0.581744 | − | 1.00761i | ||||
\(442\) | −5.97768 | + | 3.45122i | −0.284329 | + | 0.164158i | ||||
\(443\) | −12.9896 | −0.617156 | −0.308578 | − | 0.951199i | \(-0.599853\pi\) | ||||
−0.308578 | + | 0.951199i | \(0.599853\pi\) | |||||||
\(444\) | 11.2085 | + | 12.9336i | 0.531930 | + | 0.613799i | ||||
\(445\) | −9.76404 | −0.462860 | ||||||||
\(446\) | −8.46371 | + | 4.88652i | −0.400768 | + | 0.231384i | ||||
\(447\) | −11.9342 | + | 20.6706i | −0.564466 | + | 0.977685i | ||||
\(448\) | 0.712432 | − | 1.23397i | 0.0336592 | − | 0.0582995i | ||||
\(449\) | 7.61850 | + | 4.39854i | 0.359539 | + | 0.207580i | 0.668879 | − | 0.743372i | \(-0.266775\pi\) |
−0.309339 | + | 0.950952i | \(0.600108\pi\) | |||||||
\(450\) | − | 4.91638i | − | 0.231760i | ||||||
\(451\) | −0.0665250 | + | 0.115225i | −0.00313254 | + | 0.00542572i | ||||
\(452\) | 4.81993i | 0.226710i | ||||||||
\(453\) | −8.29393 | − | 14.3655i | −0.389683 | − | 0.674950i | ||||
\(454\) | −11.2611 | −0.528509 | ||||||||
\(455\) | −3.45510 | −0.161977 | ||||||||
\(456\) | 3.37072 | + | 5.83827i | 0.157849 | + | 0.273402i | ||||
\(457\) | 12.1483 | + | 7.01381i | 0.568273 | + | 0.328092i | 0.756459 | − | 0.654041i | \(-0.226928\pi\) |
−0.188187 | + | 0.982133i | \(0.560261\pi\) | |||||||
\(458\) | − | 0.239464i | − | 0.0111894i | ||||||
\(459\) | 13.2920 | − | 7.67415i | 0.620419 | − | 0.358199i | ||||
\(460\) | 1.72508 | + | 2.98792i | 0.0804322 | + | 0.139313i | ||||
\(461\) | 15.7345 | − | 9.08430i | 0.732827 | − | 0.423098i | −0.0866282 | − | 0.996241i | \(-0.527609\pi\) |
0.819456 | + | 0.573143i | \(0.194276\pi\) | |||||||
\(462\) | 0.471118 | + | 0.272000i | 0.0219184 | + | 0.0126546i | ||||
\(463\) | 22.4748 | + | 12.9759i | 1.04449 | + | 0.603039i | 0.921103 | − | 0.389319i | \(-0.127290\pi\) |
0.123391 | + | 0.992358i | \(0.460623\pi\) | |||||||
\(464\) | 2.37416 | − | 1.37072i | 0.110218 | − | 0.0636343i | ||||
\(465\) | 5.68918 | + | 9.85395i | 0.263829 | + | 0.456966i | ||||
\(466\) | −20.6511 | + | 11.9229i | −0.956646 | + | 0.552320i | ||||
\(467\) | − | 37.6856i | − | 1.74388i | −0.489610 | − | 0.871941i | \(-0.662861\pi\) | ||
0.489610 | − | 0.871941i | \(-0.337139\pi\) | |||||||
\(468\) | −10.3244 | − | 5.96078i | −0.477244 | − | 0.275537i | ||||
\(469\) | 5.62308 | + | 9.73946i | 0.259650 | + | 0.449726i | ||||
\(470\) | 0.163866 | 0.00755859 | ||||||||
\(471\) | −48.3397 | −2.22737 | ||||||||
\(472\) | −7.22929 | − | 12.5215i | −0.332755 | − | 0.576349i | ||||
\(473\) | − | 1.61288i | − | 0.0741605i | ||||||
\(474\) | 7.52710 | − | 13.0373i | 0.345731 | − | 0.598824i | ||||
\(475\) | − | 2.39602i | − | 0.109937i | ||||||
\(476\) | −3.51252 | − | 2.02795i | −0.160996 | − | 0.0929512i | ||||
\(477\) | 2.27139 | − | 3.93416i | 0.104000 | − | 0.180133i | ||||
\(478\) | −6.00686 | + | 10.4042i | −0.274747 | + | 0.475876i | ||||
\(479\) | 7.08315 | − | 4.08946i | 0.323637 | − | 0.186852i | −0.329375 | − | 0.944199i | \(-0.606838\pi\) |
0.653013 | + | 0.757347i | \(0.273505\pi\) | |||||||
\(480\) | −2.81361 | −0.128423 | ||||||||
\(481\) | −13.9389 | − | 4.82331i | −0.635561 | − | 0.219924i | ||||
\(482\) | 8.20657 | 0.373799 | ||||||||
\(483\) | −11.9786 | + | 6.91584i | −0.545045 | + | 0.314682i | ||||
\(484\) | −5.49079 | + | 9.51033i | −0.249582 | + | 0.432288i | ||||
\(485\) | −7.26525 | + | 12.5838i | −0.329898 | + | 0.571400i | ||||
\(486\) | −12.9812 | − | 7.49472i | −0.588841 | − | 0.339967i | ||||
\(487\) | − | 32.8178i | − | 1.48712i | −0.668671 | − | 0.743558i | \(-0.733137\pi\) | ||
0.668671 | − | 0.743558i | \(-0.266863\pi\) | |||||||
\(488\) | 4.68692 | − | 8.11798i | 0.212167 | − | 0.367484i | ||||
\(489\) | − | 30.5932i | − | 1.38347i | ||||||
\(490\) | 2.48488 | + | 4.30394i | 0.112256 | + | 0.194432i | ||||
\(491\) | −25.5005 | −1.15082 | −0.575410 | − | 0.817865i | \(-0.695158\pi\) | ||||
−0.575410 | + | 0.817865i | \(0.695158\pi\) | |||||||
\(492\) | 2.75877 | 0.124375 | ||||||||
\(493\) | −3.90180 | − | 6.75812i | −0.175728 | − | 0.304370i | ||||
\(494\) | −5.03162 | − | 2.90501i | −0.226383 | − | 0.130702i | ||||
\(495\) | − | 0.667126i | − | 0.0299851i | ||||||
\(496\) | 3.50225 | − | 2.02202i | 0.157256 | − | 0.0907916i | ||||
\(497\) | −4.25228 | − | 7.36517i | −0.190741 | − | 0.330373i | ||||
\(498\) | −29.2566 | + | 16.8913i | −1.31102 | + | 0.756918i | ||||
\(499\) | −14.3171 | − | 8.26601i | −0.640923 | − | 0.370037i | 0.144047 | − | 0.989571i | \(-0.453988\pi\) |
−0.784970 | + | 0.619534i | \(0.787322\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | 33.3960 | − | 19.2812i | 1.49202 | − | 0.861421i | ||||
\(502\) | −6.70455 | − | 11.6126i | −0.299239 | − | 0.518297i | ||||
\(503\) | 14.2980 | − | 8.25495i | 0.637516 | − | 0.368070i | −0.146141 | − | 0.989264i | \(-0.546685\pi\) |
0.783657 | + | 0.621194i | \(0.213352\pi\) | |||||||
\(504\) | − | 7.00517i | − | 0.312035i | ||||||
\(505\) | −8.86764 | − | 5.11973i | −0.394605 | − | 0.227825i | ||||
\(506\) | 0.234084 | + | 0.405445i | 0.0104063 | + | 0.0180242i | ||||
\(507\) | −20.0330 | −0.889696 | ||||||||
\(508\) | −6.93538 | −0.307708 | ||||||||
\(509\) | 5.24366 | + | 9.08229i | 0.232421 | + | 0.402566i | 0.958520 | − | 0.285025i | \(-0.0920018\pi\) |
−0.726099 | + | 0.687590i | \(0.758669\pi\) | |||||||
\(510\) | 8.00900i | 0.354645i | ||||||||
\(511\) | 6.53572 | − | 11.3202i | 0.289123 | − | 0.500776i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 11.1883 | + | 6.45959i | 0.493977 | + | 0.285198i | ||||
\(514\) | 8.12744 | − | 14.0771i | 0.358486 | − | 0.620916i | ||||
\(515\) | 9.45336 | − | 16.3737i | 0.416565 | − | 0.721511i | ||||
\(516\) | −28.9624 | + | 16.7215i | −1.27500 | + | 0.736122i | ||||
\(517\) | 0.0222358 | 0.000977928 | ||||||||
\(518\) | −1.64081 | − | 8.51037i | −0.0720931 | − | 0.373924i | ||||
\(519\) | −20.9584 | −0.919972 | ||||||||
\(520\) | 2.09999 | − | 1.21243i | 0.0920908 | − | 0.0531686i | ||||
\(521\) | 1.61567 | − | 2.79842i | 0.0707837 | − | 0.122601i | −0.828461 | − | 0.560046i | \(-0.810783\pi\) |
0.899245 | + | 0.437445i | \(0.144117\pi\) | |||||||
\(522\) | 6.73900 | − | 11.6723i | 0.294958 | − | 0.510883i | ||||
\(523\) | 9.84484 | + | 5.68392i | 0.430485 | + | 0.248541i | 0.699553 | − | 0.714581i | \(-0.253382\pi\) |
−0.269068 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(524\) | 18.5387i | 0.809865i | ||||||||
\(525\) | −2.00450 | + | 3.47190i | −0.0874836 | + | 0.151526i | ||||
\(526\) | 6.19105i | 0.269943i | ||||||||
\(527\) | −5.75574 | − | 9.96924i | −0.250724 | − | 0.434267i | ||||
\(528\) | −0.381791 | −0.0166153 | ||||||||
\(529\) | 11.0964 | 0.482453 | ||||||||
\(530\) | 0.462004 | + | 0.800215i | 0.0200682 | + | 0.0347591i | ||||
\(531\) | −61.5605 | − | 35.5420i | −2.67150 | − | 1.54239i | ||||
\(532\) | − | 3.41400i | − | 0.148015i | ||||||
\(533\) | −2.05907 | + | 1.18880i | −0.0891881 | + | 0.0514928i | ||||
\(534\) | 13.7361 | + | 23.7916i | 0.594419 | + | 1.02956i | ||||
\(535\) | −10.9521 | + | 6.32318i | −0.473500 | + | 0.273375i | ||||
\(536\) | −6.83536 | − | 3.94640i | −0.295243 | − | 0.170458i | ||||
\(537\) | 58.2557 | + | 33.6339i | 2.51392 | + | 1.45141i | ||||
\(538\) | 11.9777 | − | 6.91532i | 0.516395 | − | 0.298141i | ||||
\(539\) | 0.337185 | + | 0.584021i | 0.0145236 | + | 0.0251556i | ||||
\(540\) | −4.66956 | + | 2.69597i | −0.200946 | + | 0.116016i | ||||
\(541\) | 1.49314i | 0.0641950i | 0.999485 | + | 0.0320975i | \(0.0102187\pi\) | ||||
−0.999485 | + | 0.0320975i | \(0.989781\pi\) | |||||||
\(542\) | 9.21603 | + | 5.32088i | 0.395862 | + | 0.228551i | ||||
\(543\) | −22.5812 | − | 39.1118i | −0.969053 | − | 1.67845i | ||||
\(544\) | 2.84653 | 0.122044 | ||||||||
\(545\) | 12.2480 | 0.524646 | ||||||||
\(546\) | 4.86064 | + | 8.41888i | 0.208016 | + | 0.360295i | ||||
\(547\) | − | 2.00176i | − | 0.0855891i | −0.999084 | − | 0.0427946i | \(-0.986374\pi\) | ||
0.999084 | − | 0.0427946i | \(-0.0136261\pi\) | |||||||
\(548\) | 1.90632 | − | 3.30184i | 0.0814338 | − | 0.141047i | ||||
\(549\) | − | 46.0853i | − | 1.96687i | ||||||
\(550\) | 0.117515 | + | 0.0678472i | 0.00501085 | + | 0.00289302i | ||||
\(551\) | 3.28428 | − | 5.68854i | 0.139915 | − | 0.242340i | ||||
\(552\) | 4.85369 | − | 8.40684i | 0.206587 | − | 0.357819i | ||||
\(553\) | −6.60234 | + | 3.81186i | −0.280760 | + | 0.162097i | ||||
\(554\) | −20.6714 | −0.878242 | ||||||||
\(555\) | −12.9336 | + | 11.2085i | −0.548999 | + | 0.475772i | ||||
\(556\) | 9.86304 | 0.418286 | ||||||||
\(557\) | 26.5034 | − | 15.3018i | 1.12299 | − | 0.648357i | 0.180825 | − | 0.983515i | \(-0.442123\pi\) |
0.942162 | + | 0.335159i | \(0.108790\pi\) | |||||||
\(558\) | 9.94104 | − | 17.2184i | 0.420838 | − | 0.728912i | ||||
\(559\) | 14.4111 | − | 24.9608i | 0.609526 | − | 1.05573i | ||||
\(560\) | 1.23397 | + | 0.712432i | 0.0521446 | + | 0.0301057i | ||||
\(561\) | 1.08678i | 0.0458838i | ||||||||
\(562\) | −7.10889 | + | 12.3130i | −0.299870 | + | 0.519391i | ||||
\(563\) | 21.0846i | 0.888610i | 0.895876 | + | 0.444305i | \(0.146549\pi\) | ||||
−0.895876 | + | 0.444305i | \(0.853451\pi\) | |||||||
\(564\) | −0.230528 | − | 0.399286i | −0.00970697 | − | 0.0168130i | ||||
\(565\) | −4.81993 | −0.202776 | ||||||||
\(566\) | −27.1940 | −1.14305 | ||||||||
\(567\) | −0.300406 | − | 0.520318i | −0.0126159 | − | 0.0218513i | ||||
\(568\) | 5.16904 | + | 2.98434i | 0.216888 | + | 0.125220i | ||||
\(569\) | − | 40.6362i | − | 1.70356i | −0.523902 | − | 0.851779i | \(-0.675524\pi\) | ||
0.523902 | − | 0.851779i | \(-0.324476\pi\) | |||||||
\(570\) | −5.83827 | + | 3.37072i | −0.244538 | + | 0.141184i | ||||
\(571\) | −6.07118 | − | 10.5156i | −0.254071 | − | 0.440064i | 0.710572 | − | 0.703625i | \(-0.248436\pi\) |
−0.964643 | + | 0.263561i | \(0.915103\pi\) | |||||||
\(572\) | 0.284957 | − | 0.164520i | 0.0119147 | − | 0.00687894i | ||||
\(573\) | 2.84481 | + | 1.64245i | 0.118844 | + | 0.0686143i | ||||
\(574\) | −1.20992 | − | 0.698547i | −0.0505010 | − | 0.0291568i | ||||
\(575\) | −2.98792 | + | 1.72508i | −0.124605 | + | 0.0719407i | ||||
\(576\) | 2.45819 | + | 4.25771i | 0.102425 | + | 0.177405i | ||||
\(577\) | −0.653769 | + | 0.377454i | −0.0272168 | + | 0.0157136i | −0.513547 | − | 0.858062i | \(-0.671669\pi\) |
0.486330 | + | 0.873775i | \(0.338335\pi\) | |||||||
\(578\) | 8.89729i | 0.370078i | ||||||||
\(579\) | 7.85995 | + | 4.53794i | 0.326648 | + | 0.188591i | ||||
\(580\) | 1.37072 | + | 2.37416i | 0.0569162 | + | 0.0985818i | ||||
\(581\) | 17.1082 | 0.709766 | ||||||||
\(582\) | 40.8831 | 1.69466 | ||||||||
\(583\) | 0.0626914 | + | 0.108585i | 0.00259641 | + | 0.00449712i | ||||
\(584\) | 9.17382i | 0.379616i | ||||||||
\(585\) | 5.96078 | − | 10.3244i | 0.246448 | − | 0.426860i | ||||
\(586\) | 8.12624i | 0.335692i | ||||||||
\(587\) | 18.0383 | + | 10.4144i | 0.744521 | + | 0.429849i | 0.823711 | − | 0.567010i | \(-0.191900\pi\) |
−0.0791898 | + | 0.996860i | \(0.525233\pi\) | |||||||
\(588\) | 6.99148 | − | 12.1096i | 0.288324 | − | 0.499392i | ||||
\(589\) | 4.84480 | − | 8.39145i | 0.199627 | − | 0.345763i | ||||
\(590\) | 12.5215 | − | 7.22929i | 0.515502 | − | 0.297625i | ||||
\(591\) | 10.4146 | 0.428397 | ||||||||
\(592\) | 3.98366 | + | 4.59679i | 0.163727 | + | 0.188927i | ||||
\(593\) | 24.1914 | 0.993421 | 0.496711 | − | 0.867916i | \(-0.334541\pi\) | ||||
0.496711 | + | 0.867916i | \(0.334541\pi\) | |||||||
\(594\) | −0.633634 | + | 0.365829i | −0.0259983 | + | 0.0150101i | ||||
\(595\) | 2.02795 | − | 3.51252i | 0.0831380 | − | 0.143999i | ||||
\(596\) | −4.24159 | + | 7.34665i | −0.173742 | + | 0.300930i | ||||
\(597\) | −55.9524 | − | 32.3041i | −2.28998 | − | 1.32212i | ||||
\(598\) | 8.36615i | 0.342118i | ||||||||
\(599\) | 16.3882 | − | 28.3852i | 0.669603 | − | 1.15979i | −0.308413 | − | 0.951253i | \(-0.599798\pi\) |
0.978015 | − | 0.208533i | \(-0.0668690\pi\) | |||||||
\(600\) | − | 2.81361i | − | 0.114865i | ||||||
\(601\) | −9.68763 | − | 16.7795i | −0.395167 | − | 0.684449i | 0.597956 | − | 0.801529i | \(-0.295980\pi\) |
−0.993122 | + | 0.117080i | \(0.962647\pi\) | |||||||
\(602\) | 16.9361 | 0.690265 | ||||||||
\(603\) | −38.8040 | −1.58022 | ||||||||
\(604\) | −2.94779 | − | 5.10573i | −0.119944 | − | 0.207749i | ||||
\(605\) | −9.51033 | − | 5.49079i | −0.386650 | − | 0.223233i | ||||
\(606\) | 28.8098i | 1.17032i | ||||||||
\(607\) | −13.7171 | + | 7.91956i | −0.556759 | + | 0.321445i | −0.751844 | − | 0.659342i | \(-0.770835\pi\) |
0.195085 | + | 0.980786i | \(0.437502\pi\) | |||||||
\(608\) | 1.19801 | + | 2.07501i | 0.0485857 | + | 0.0841528i | ||||
\(609\) | −9.51803 | + | 5.49524i | −0.385690 | + | 0.222678i | ||||
\(610\) | 8.11798 | + | 4.68692i | 0.328687 | + | 0.189768i | ||||
\(611\) | 0.344118 | + | 0.198677i | 0.0139215 | + | 0.00803760i | ||||
\(612\) | 12.1197 | − | 6.99730i | 0.489909 | − | 0.282849i | ||||
\(613\) | 14.9248 | + | 25.8506i | 0.602808 | + | 1.04409i | 0.992394 | + | 0.123105i | \(0.0392850\pi\) |
−0.389585 | + | 0.920990i | \(0.627382\pi\) | |||||||
\(614\) | 16.1284 | − | 9.31172i | 0.650888 | − | 0.375791i | ||||
\(615\) | 2.75877i | 0.111244i | ||||||||
\(616\) | 0.167443 | + | 0.0966730i | 0.00674645 | + | 0.00389507i | ||||
\(617\) | 18.6383 | + | 32.2824i | 0.750349 | + | 1.29964i | 0.947654 | + | 0.319300i | \(0.103448\pi\) |
−0.197305 | + | 0.980342i | \(0.563219\pi\) | |||||||
\(618\) | −53.1961 | −2.13986 | ||||||||
\(619\) | −0.794892 | −0.0319494 | −0.0159747 | − | 0.999872i | \(-0.505085\pi\) | ||||
−0.0159747 | + | 0.999872i | \(0.505085\pi\) | |||||||
\(620\) | 2.02202 | + | 3.50225i | 0.0812064 | + | 0.140654i | ||||
\(621\) | − | 18.6030i | − | 0.746514i | ||||||
\(622\) | 7.03271 | − | 12.1810i | 0.281986 | − | 0.488414i | ||||
\(623\) | − | 13.9124i | − | 0.557390i | ||||||
\(624\) | −5.90855 | − | 3.41131i | −0.236531 | − | 0.136562i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 16.8185 | − | 29.1305i | 0.672202 | − | 1.16429i | ||||
\(627\) | −0.792220 | + | 0.457389i | −0.0316382 | + | 0.0182663i | ||||
\(628\) | −17.1807 | −0.685584 | ||||||||
\(629\) | 13.0849 | − | 11.3396i | 0.521728 | − | 0.452139i | ||||
\(630\) | 7.00517 | 0.279093 | ||||||||
\(631\) | −4.04038 | + | 2.33271i | −0.160845 | + | 0.0928638i | −0.578262 | − | 0.815851i | \(-0.696269\pi\) |
0.417417 | + | 0.908715i | \(0.362935\pi\) | |||||||
\(632\) | 2.67525 | − | 4.63367i | 0.106416 | − | 0.184317i | ||||
\(633\) | 21.5363 | − | 37.3020i | 0.855991 | − | 1.48262i | ||||
\(634\) | 24.6344 | + | 14.2227i | 0.978357 | + | 0.564855i | ||||
\(635\) | − | 6.93538i | − | 0.275222i | ||||||
\(636\) | 1.29990 | − | 2.25149i | 0.0515443 | − | 0.0892774i | ||||
\(637\) | 12.0510i | 0.477478i | ||||||||
\(638\) | 0.186000 | + | 0.322161i | 0.00736380 | + | 0.0127545i | ||||
\(639\) | 29.3444 | 1.16084 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −1.51762 | − | 2.62860i | −0.0599425 | − | 0.103824i | 0.834497 | − | 0.551013i | \(-0.185758\pi\) |
−0.894439 | + | 0.447189i | \(0.852425\pi\) | |||||||
\(642\) | 30.8148 | + | 17.7910i | 1.21616 | + | 0.702153i | ||||
\(643\) | − | 44.1008i | − | 1.73916i | −0.493788 | − | 0.869582i | \(-0.664388\pi\) | ||
0.493788 | − | 0.869582i | \(-0.335612\pi\) | |||||||
\(644\) | −4.25738 | + | 2.45800i | −0.167764 | + | 0.0968588i | ||||
\(645\) | −16.7215 | − | 28.9624i | −0.658407 | − | 1.14039i | ||||
\(646\) | 5.90657 | − | 3.41016i | 0.232391 | − | 0.134171i | ||||
\(647\) | 38.6108 | + | 22.2919i | 1.51795 | + | 0.876386i | 0.999777 | + | 0.0211074i | \(0.00671920\pi\) |
0.518168 | + | 0.855279i | \(0.326614\pi\) | |||||||
\(648\) | 0.365171 | + | 0.210831i | 0.0143453 | + | 0.00828224i | ||||
\(649\) | 1.69910 | − | 0.980975i | 0.0666955 | − | 0.0385067i | ||||
\(650\) | 1.21243 | + | 2.09999i | 0.0475555 | + | 0.0823685i | ||||
\(651\) | −14.0405 | + | 8.10630i | −0.550292 | + | 0.317711i | ||||
\(652\) | − | 10.8733i | − | 0.425832i | ||||||
\(653\) | −11.5544 | − | 6.67094i | −0.452159 | − | 0.261054i | 0.256583 | − | 0.966522i | \(-0.417403\pi\) |
−0.708741 | + | 0.705468i | \(0.750737\pi\) | |||||||
\(654\) | −17.2305 | − | 29.8441i | −0.673766 | − | 1.16700i | ||||
\(655\) | −18.5387 | −0.724365 | ||||||||
\(656\) | 0.980511 | 0.0382825 | ||||||||
\(657\) | 22.5510 | + | 39.0595i | 0.879799 | + | 1.52386i | ||||
\(658\) | 0.233487i | 0.00910228i | ||||||||
\(659\) | 5.97659 | − | 10.3517i | 0.232815 | − | 0.403247i | −0.725821 | − | 0.687884i | \(-0.758540\pi\) |
0.958635 | + | 0.284637i | \(0.0918731\pi\) | |||||||
\(660\) | − | 0.381791i | − | 0.0148612i | ||||||
\(661\) | 27.9383 | + | 16.1302i | 1.08667 | + | 0.627391i | 0.932689 | − | 0.360682i | \(-0.117456\pi\) |
0.153984 | + | 0.988073i | \(0.450789\pi\) | |||||||
\(662\) | 15.3361 | − | 26.5630i | 0.596056 | − | 1.03240i | ||||
\(663\) | −9.71037 | + | 16.8189i | −0.377119 | + | 0.653190i | ||||
\(664\) | −10.3983 | + | 6.00344i | −0.403531 | + | 0.232979i | ||||
\(665\) | 3.41400 | 0.132389 | ||||||||
\(666\) | 28.2611 | + | 9.77920i | 1.09509 | + | 0.378936i | ||||
\(667\) | −9.45842 | −0.366232 | ||||||||
\(668\) | 11.8695 | − | 6.85285i | 0.459244 | − | 0.265145i | ||||
\(669\) | −13.7488 | + | 23.8135i | −0.531558 | + | 0.920685i | ||||
\(670\) | 3.94640 | − | 6.83536i | 0.152463 | − | 0.264073i | ||||
\(671\) | 1.10156 | + | 0.635989i | 0.0425254 | + | 0.0245521i | ||||
\(672\) | − | 4.00900i | − | 0.154651i | ||||||
\(673\) | 2.70006 | − | 4.67664i | 0.104080 | − | 0.180271i | −0.809282 | − | 0.587420i | \(-0.800144\pi\) |
0.913362 | + | 0.407149i | \(0.133477\pi\) | |||||||
\(674\) | 17.8883i | 0.689031i | ||||||||
\(675\) | −2.69597 | − | 4.66956i | −0.103768 | − | 0.179731i | ||||
\(676\) | −7.12004 | −0.273848 | ||||||||
\(677\) | −13.3269 | −0.512195 | −0.256097 | − | 0.966651i | \(-0.582437\pi\) | ||||
−0.256097 | + | 0.966651i | \(0.582437\pi\) | |||||||
\(678\) | 6.78069 | + | 11.7445i | 0.260411 | + | 0.451045i | ||||
\(679\) | −17.9302 | − | 10.3520i | −0.688097 | − | 0.397273i | ||||
\(680\) | 2.84653i | 0.109159i | ||||||||
\(681\) | −27.4394 | + | 15.8421i | −1.05148 | + | 0.607071i | ||||
\(682\) | 0.274377 | + | 0.475236i | 0.0105065 | + | 0.0181977i | ||||
\(683\) | 7.95908 | − | 4.59518i | 0.304546 | − | 0.175830i | −0.339937 | − | 0.940448i | \(-0.610406\pi\) |
0.644483 | + | 0.764618i | \(0.277073\pi\) | |||||||
\(684\) | 10.2015 | + | 5.88987i | 0.390066 | + | 0.225205i | ||||
\(685\) | 3.30184 | + | 1.90632i | 0.126157 | + | 0.0728366i | ||||
\(686\) | −14.7703 | + | 8.52764i | −0.563933 | + | 0.325587i | ||||
\(687\) | −0.336879 | − | 0.583492i | −0.0128527 | − | 0.0222616i | ||||
\(688\) | −10.2937 | + | 5.94307i | −0.392444 | + | 0.226578i | ||||
\(689\) | 2.24059i | 0.0853598i | ||||||||
\(690\) | 8.40684 | + | 4.85369i | 0.320043 | + | 0.184777i | ||||
\(691\) | −1.39847 | − | 2.42223i | −0.0532005 | − | 0.0921459i | 0.838199 | − | 0.545365i | \(-0.183609\pi\) |
−0.891399 | + | 0.453219i | \(0.850276\pi\) | |||||||
\(692\) | −7.44895 | −0.283167 | ||||||||
\(693\) | 0.950563 | 0.0361089 | ||||||||
\(694\) | 0.816508 | + | 1.41423i | 0.0309942 | + | 0.0536836i | ||||
\(695\) | 9.86304i | 0.374126i | ||||||||
\(696\) | 3.85668 | − | 6.67996i | 0.146187 | − | 0.253203i | ||||
\(697\) | − | 2.79105i | − | 0.105719i | ||||||
\(698\) | 24.9697 | + | 14.4163i | 0.945118 | + | 0.545664i | ||||
\(699\) | −33.5465 | + | 58.1042i | −1.26884 | + | 2.19770i | ||||
\(700\) | −0.712432 | + | 1.23397i | −0.0269274 | + | 0.0466396i | ||||
\(701\) | −23.7829 | + | 13.7311i | −0.898268 | + | 0.518615i | −0.876638 | − | 0.481151i | \(-0.840219\pi\) |
−0.0216300 | + | 0.999766i | \(0.506886\pi\) | |||||||
\(702\) | −13.0747 | −0.493474 | ||||||||
\(703\) | 13.7731 | + | 4.76593i | 0.519463 | + | 0.179750i | ||||
\(704\) | −0.135694 | −0.00511418 | ||||||||
\(705\) | 0.399286 | − | 0.230528i | 0.0150380 | − | 0.00868218i | ||||
\(706\) | −5.66386 | + | 9.81009i | −0.213162 | + | 0.369208i | ||||
\(707\) | 7.29492 | − | 12.6352i | 0.274354 | − | 0.475194i | ||||
\(708\) | −35.2306 | − | 20.3404i | −1.32405 | − | 0.764439i | ||||
\(709\) | 51.1521i | 1.92106i | 0.278179 | + | 0.960529i | \(0.410269\pi\) | ||||
−0.278179 | + | 0.960529i | \(0.589731\pi\) | |||||||
\(710\) | −2.98434 | + | 5.16904i | −0.112000 | + | 0.193990i | ||||
\(711\) | − | 26.3051i | − | 0.986518i | ||||||
\(712\) | 4.88202 | + | 8.45591i | 0.182962 | + | 0.316899i | ||||
\(713\) | −13.9526 | −0.522529 | ||||||||
\(714\) | −11.4117 | −0.427073 | ||||||||
\(715\) | 0.164520 | + | 0.284957i | 0.00615271 | + | 0.0106568i | ||||
\(716\) | 20.7050 | + | 11.9540i | 0.773781 | + | 0.446743i | ||||
\(717\) | 33.8019i | 1.26235i | ||||||||
\(718\) | −1.91932 | + | 1.10812i | −0.0716282 | + | 0.0413546i | ||||
\(719\) | 21.6217 | + | 37.4498i | 0.806352 | + | 1.39664i | 0.915374 | + | 0.402604i | \(0.131895\pi\) |
−0.109022 | + | 0.994039i | \(0.534772\pi\) | |||||||
\(720\) | −4.25771 | + | 2.45819i | −0.158676 | + | 0.0916114i | ||||
\(721\) | 23.3303 | + | 13.4697i | 0.868865 | + | 0.501639i | ||||
\(722\) | −11.4827 | − | 6.62955i | −0.427343 | − | 0.246726i | ||||
\(723\) | 19.9966 | − | 11.5450i | 0.743680 | − | 0.429364i | ||||
\(724\) | −8.02572 | − | 13.9010i | −0.298274 | − | 0.516625i | ||||
\(725\) | −2.37416 | + | 1.37072i | −0.0881742 | + | 0.0509074i | ||||
\(726\) | 30.8979i | 1.14673i | ||||||||
\(727\) | −17.4389 | − | 10.0684i | −0.646774 | − | 0.373415i | 0.140445 | − | 0.990088i | \(-0.455147\pi\) |
−0.787219 | + | 0.616673i | \(0.788480\pi\) | |||||||
\(728\) | 1.72755 | + | 2.99220i | 0.0640272 | + | 0.110898i | ||||
\(729\) | −43.4394 | −1.60887 | ||||||||
\(730\) | −9.17382 | −0.339538 | ||||||||
\(731\) | 16.9171 | + | 29.3013i | 0.625702 | + | 1.08375i | ||||
\(732\) | − | 26.3743i | − | 0.974821i | ||||||
\(733\) | 8.33337 | − | 14.4338i | 0.307800 | − | 0.533125i | −0.670081 | − | 0.742288i | \(-0.733741\pi\) |
0.977881 | + | 0.209163i | \(0.0670739\pi\) | |||||||
\(734\) | − | 1.86310i | − | 0.0687683i | ||||||
\(735\) | 12.1096 | + | 6.99148i | 0.446669 | + | 0.257885i | ||||
\(736\) | 1.72508 | − | 2.98792i | 0.0635872 | − | 0.110136i | ||||
\(737\) | 0.535505 | − | 0.927521i | 0.0197256 | − | 0.0341657i | ||||
\(738\) | 4.17473 | − | 2.41028i | 0.153674 | − | 0.0887238i | ||||
\(739\) | −23.6949 | −0.871629 | −0.435815 | − | 0.900036i | \(-0.643540\pi\) | ||||
−0.435815 | + | 0.900036i | \(0.643540\pi\) | |||||||
\(740\) | −4.59679 | + | 3.98366i | −0.168981 | + | 0.146442i | ||||
\(741\) | −16.3471 | −0.600525 | ||||||||
\(742\) | −1.14020 | + | 0.658293i | −0.0418579 | + | 0.0241667i | ||||
\(743\) | −13.8131 | + | 23.9250i | −0.506754 | + | 0.877724i | 0.493215 | + | 0.869907i | \(0.335821\pi\) |
−0.999969 | + | 0.00781654i | \(0.997512\pi\) | |||||||
\(744\) | 5.68918 | − | 9.85395i | 0.208575 | − | 0.361263i | ||||
\(745\) | −7.34665 | − | 4.24159i | −0.269160 | − | 0.155400i | ||||
\(746\) | 4.38074i | 0.160390i | ||||||||
\(747\) | −29.5152 | + | 51.1218i | −1.07990 | + | 1.87045i | ||||
\(748\) | 0.386258i | 0.0141230i | ||||||||
\(749\) | −9.00967 | − | 15.6052i | −0.329206 | − | 0.570202i | ||||
\(750\) | 2.81361 | 0.102738 | ||||||||
\(751\) | −43.9061 | −1.60216 | −0.801078 | − | 0.598560i | \(-0.795740\pi\) | ||||
−0.801078 | + | 0.598560i | \(0.795740\pi\) | |||||||
\(752\) | −0.0819332 | − | 0.141912i | −0.00298780 | − | 0.00517502i | ||||
\(753\) | −32.6733 | − | 18.8640i | −1.19068 | − | 0.687441i | ||||
\(754\) | 6.64764i | 0.242093i | ||||||||
\(755\) | 5.10573 | − | 2.94779i | 0.185816 | − | 0.107281i | ||||
\(756\) | −3.84139 | − | 6.65348i | −0.139710 | − | 0.241985i | ||||
\(757\) | −46.2890 | + | 26.7250i | −1.68240 | + | 0.971335i | −0.722344 | + | 0.691534i | \(0.756935\pi\) |
−0.960058 | + | 0.279801i | \(0.909731\pi\) | |||||||
\(758\) | 16.7201 | + | 9.65335i | 0.607301 | + | 0.350625i | ||||
\(759\) | 1.14076 | + | 0.658619i | 0.0414070 | + | 0.0239064i | ||||
\(760\) | −2.07501 | + | 1.19801i | −0.0752686 | + | 0.0434563i | ||||
\(761\) | 21.8105 | + | 37.7769i | 0.790630 | + | 1.36941i | 0.925578 | + | 0.378558i | \(0.123580\pi\) |
−0.134948 | + | 0.990853i | \(0.543087\pi\) | |||||||
\(762\) | −16.8991 | + | 9.75671i | −0.612190 | + | 0.353448i | ||||
\(763\) | 17.4517i | 0.631794i | ||||||||
\(764\) | 1.01109 | + | 0.583753i | 0.0365799 | + | 0.0211194i | ||||
\(765\) | 6.99730 | + | 12.1197i | 0.252988 | + | 0.438188i | ||||
\(766\) | −27.0276 | −0.976546 | ||||||||
\(767\) | 35.0601 | 1.26595 | ||||||||
\(768\) | 1.40680 | + | 2.43665i | 0.0507636 | + | 0.0879252i | ||||
\(769\) | 0.845468i | 0.0304884i | 0.999884 | + | 0.0152442i | \(0.00485256\pi\) | ||||
−0.999884 | + | 0.0152442i | \(0.995147\pi\) | |||||||
\(770\) | −0.0966730 | + | 0.167443i | −0.00348385 | + | 0.00603421i | ||||
\(771\) | − | 45.7349i | − | 1.64710i | ||||||
\(772\) | 2.79355 | + | 1.61286i | 0.100542 | + | 0.0580480i | ||||
\(773\) | 9.74414 | − | 16.8773i | 0.350472 | − | 0.607036i | −0.635860 | − | 0.771804i | \(-0.719354\pi\) |
0.986332 | + | 0.164769i | \(0.0526878\pi\) | |||||||
\(774\) | −29.2184 | + | 50.6078i | −1.05023 | + | 1.81906i | ||||
\(775\) | −3.50225 | + | 2.02202i | −0.125804 | + | 0.0726332i | ||||
\(776\) | 14.5305 | 0.521615 | ||||||||
\(777\) | −15.9705 | − | 18.4285i | −0.572939 | − | 0.661120i | ||||
\(778\) | 11.2462 | 0.403194 | ||||||||
\(779\) | 2.03457 | − | 1.17466i | 0.0728961 | − | 0.0420866i | ||||
\(780\) | 3.41131 | − | 5.90855i | 0.122144 | − | 0.211560i | ||||
\(781\) | −0.404959 | + | 0.701410i | −0.0144906 | + | 0.0250984i | ||||
\(782\) | −8.50520 | − | 4.91048i | −0.304145 | − | 0.175598i | ||||
\(783\) | − | 14.7817i | − | 0.528256i | ||||||
\(784\) | 2.48488 | − | 4.30394i | 0.0887458 | − | 0.153712i | ||||
\(785\) | − | 17.1807i | − | 0.613205i | ||||||
\(786\) | 26.0802 | + | 45.1723i | 0.930251 | + | 1.61124i | ||||
\(787\) | −47.9472 | −1.70913 | −0.854566 | − | 0.519343i | \(-0.826177\pi\) | ||||
−0.854566 | + | 0.519343i | \(0.826177\pi\) | |||||||
\(788\) | 3.70150 | 0.131860 | ||||||||
\(789\) | 8.70959 | + | 15.0855i | 0.310070 | + | 0.537056i | ||||
\(790\) | 4.63367 | + | 2.67525i | 0.164859 | + | 0.0951811i | ||||
\(791\) | − | 6.86773i | − | 0.244189i | ||||||
\(792\) | −0.577748 | + | 0.333563i | −0.0205294 | + | 0.0118526i | ||||
\(793\) | 11.3651 | + | 19.6850i | 0.403588 | + | 0.699034i | ||||
\(794\) | 6.58176 | − | 3.79998i | 0.233578 | − | 0.134856i | ||||
\(795\) | 2.25149 | + | 1.29990i | 0.0798521 | + | 0.0461026i | ||||
\(796\) | −19.8864 | − | 11.4814i | −0.704854 | − | 0.406947i | ||||
\(797\) | −37.3841 | + | 21.5837i | −1.32421 | + | 0.764534i | −0.984398 | − | 0.175959i | \(-0.943697\pi\) |
−0.339814 | + | 0.940493i | \(0.610364\pi\) | |||||||
\(798\) | −4.80282 | − | 8.31873i | −0.170018 | − | 0.294480i | ||||
\(799\) | −0.403958 | + | 0.233225i | −0.0142910 | + | 0.00825091i | ||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 41.5725 | + | 24.0019i | 1.46889 | + | 0.848065i | ||||
\(802\) | −10.0747 | − | 17.4500i | −0.355751 | − | 0.616179i | ||||
\(803\) | −1.24484 | −0.0439294 | ||||||||
\(804\) | −22.2072 | −0.783189 | ||||||||
\(805\) | −2.45800 | − | 4.25738i | −0.0866331 | − | 0.150053i | ||||
\(806\) | 9.80626i | 0.345411i | ||||||||
\(807\) | 19.4570 | − | 33.7005i | 0.684918 | − | 1.18631i | ||||
\(808\) | 10.2395i | 0.360223i | ||||||||
\(809\) | −12.4451 | − | 7.18518i | −0.437546 | − | 0.252617i | 0.265010 | − | 0.964246i | \(-0.414625\pi\) |
−0.702556 | + | 0.711628i | \(0.747958\pi\) | |||||||
\(810\) | −0.210831 | + | 0.365171i | −0.00740786 | + | 0.0128308i | ||||
\(811\) | −2.97705 | + | 5.15639i | −0.104538 | + | 0.181065i | −0.913549 | − | 0.406728i | \(-0.866670\pi\) |
0.809011 | + | 0.587793i | \(0.200003\pi\) | |||||||
\(812\) | −3.38286 | + | 1.95309i | −0.118715 | + | 0.0685402i | ||||
\(813\) | 29.9417 | 1.05010 | ||||||||
\(814\) | −0.623759 | + | 0.540561i | −0.0218627 | + | 0.0189466i | ||||
\(815\) | 10.8733 | 0.380875 | ||||||||
\(816\) | 6.93600 | − | 4.00450i | 0.242809 | − | 0.140186i | ||||
\(817\) | −14.2397 | + | 24.6639i | −0.498184 | + | 0.862880i | ||||
\(818\) | 9.67464 | − | 16.7570i | 0.338266 | − | 0.585893i | ||||
\(819\) | 14.7108 | + | 8.49329i | 0.514037 | + | 0.296780i | ||||
\(820\) | 0.980511i | 0.0342409i | ||||||||
\(821\) | 6.82863 | − | 11.8275i | 0.238321 | − | 0.412784i | −0.721912 | − | 0.691985i | \(-0.756736\pi\) |
0.960233 | + | 0.279201i | \(0.0900697\pi\) | |||||||
\(822\) | − | 10.7272i | − | 0.374156i | ||||||
\(823\) | −6.14202 | − | 10.6383i | −0.214097 | − | 0.370828i | 0.738896 | − | 0.673820i | \(-0.235348\pi\) |
−0.952993 | + | 0.302992i | \(0.902014\pi\) | |||||||
\(824\) | −18.9067 | −0.658647 | ||||||||
\(825\) | 0.381791 | 0.0132923 | ||||||||
\(826\) | 10.3008 | + | 17.8414i | 0.358409 | + | 0.620783i | ||||
\(827\) | 37.2503 | + | 21.5065i | 1.29532 | + | 0.747853i | 0.979592 | − | 0.200998i | \(-0.0644183\pi\) |
0.315727 | + | 0.948850i | \(0.397752\pi\) | |||||||
\(828\) | − | 16.9623i | − | 0.589480i | ||||||
\(829\) | 11.7333 | − | 6.77420i | 0.407513 | − | 0.235278i | −0.282208 | − | 0.959353i | \(-0.591067\pi\) |
0.689720 | + | 0.724076i | \(0.257733\pi\) | |||||||
\(830\) | −6.00344 | − | 10.3983i | −0.208382 | − | 0.360929i | ||||
\(831\) | −50.3690 | + | 29.0806i | −1.74728 | + | 1.00879i | ||||
\(832\) | −2.09999 | − | 1.21243i | −0.0728042 | − | 0.0420335i | ||||
\(833\) | −12.2513 | − | 7.07328i | −0.424482 | − | 0.245075i | ||||
\(834\) | 24.0328 | − | 13.8754i | 0.832188 | − | 0.480464i | ||||
\(835\) | 6.85285 | + | 11.8695i | 0.237152 | + | 0.410760i | ||||
\(836\) | −0.281568 | + | 0.162563i | −0.00973822 | + | 0.00562236i | ||||
\(837\) | − | 21.8053i | − | 0.753701i | ||||||
\(838\) | 17.7306 | + | 10.2368i | 0.612493 | + | 0.353623i | ||||
\(839\) | −4.93536 | − | 8.54829i | −0.170388 | − | 0.295120i | 0.768168 | − | 0.640249i | \(-0.221169\pi\) |
−0.938555 | + | 0.345129i | \(0.887835\pi\) | |||||||
\(840\) | 4.00900 | 0.138324 | ||||||||
\(841\) | 21.4845 | 0.740843 | ||||||||
\(842\) | 14.3428 | + | 24.8425i | 0.494287 | + | 0.856130i | ||||
\(843\) | 40.0032i | 1.37778i | ||||||||
\(844\) | 7.65434 | − | 13.2577i | 0.263473 | − | 0.456349i | ||||
\(845\) | − | 7.12004i | − | 0.244937i | ||||||
\(846\) | −0.697696 | − | 0.402815i | −0.0239873 | − | 0.0138491i | ||||
\(847\) | 7.82363 | − | 13.5509i | 0.268823 | − | 0.465615i | ||||
\(848\) | 0.462004 | − | 0.800215i | 0.0158653 | − | 0.0274795i | ||||
\(849\) | −66.2624 | + | 38.2566i | −2.27412 | + | 1.31296i | ||||
\(850\) | −2.84653 | −0.0976350 | ||||||||
\(851\) | −3.97305 | − | 20.6070i | −0.136194 | − | 0.706398i | ||||
\(852\) | 16.7935 | 0.575337 | ||||||||
\(853\) | 25.9113 | − | 14.9599i | 0.887186 | − | 0.512217i | 0.0141647 | − | 0.999900i | \(-0.495491\pi\) |
0.873021 | + | 0.487683i | \(0.162158\pi\) | |||||||
\(854\) | −6.67821 | + | 11.5670i | −0.228524 | + | 0.395815i | ||||
\(855\) | −5.88987 | + | 10.2015i | −0.201429 | + | 0.348886i | ||||
\(856\) | 10.9521 | + | 6.32318i | 0.374334 | + | 0.216122i | ||||
\(857\) | − | 50.3628i | − | 1.72036i | −0.509991 | − | 0.860180i | \(-0.670351\pi\) | ||
0.509991 | − | 0.860180i | \(-0.329649\pi\) | |||||||
\(858\) | 0.462895 | − | 0.801758i | 0.0158030 | − | 0.0273716i | ||||
\(859\) | 28.2093i | 0.962488i | 0.876587 | + | 0.481244i | \(0.159815\pi\) | ||||
−0.876587 | + | 0.481244i | \(0.840185\pi\) | |||||||
\(860\) | −5.94307 | − | 10.2937i | −0.202657 | − | 0.351012i | ||||
\(861\) | −3.93087 | −0.133964 | ||||||||
\(862\) | 13.1317 | 0.447268 | ||||||||
\(863\) | 3.85665 | + | 6.67991i | 0.131282 | + | 0.227387i | 0.924171 | − | 0.381979i | \(-0.124757\pi\) |
−0.792889 | + | 0.609366i | \(0.791424\pi\) | |||||||
\(864\) | 4.66956 | + | 2.69597i | 0.158862 | + | 0.0917188i | ||||
\(865\) | − | 7.44895i | − | 0.253272i | ||||||
\(866\) | 11.3127 | − | 6.53138i | 0.384421 | − | 0.221945i | ||||
\(867\) | 12.5167 | + | 21.6796i | 0.425091 | + | 0.736279i | ||||
\(868\) | −4.99022 | + | 2.88111i | −0.169379 | + | 0.0977911i | ||||
\(869\) | 0.628763 | + | 0.363017i | 0.0213293 | + | 0.0123145i | ||||
\(870\) | 6.67996 | + | 3.85668i | 0.226472 | + | 0.130754i | ||||
\(871\) | 16.5748 | − | 9.56948i | 0.561616 | − | 0.324249i | ||||
\(872\) | −6.12399 | − | 10.6071i | −0.207385 | − | 0.359201i | ||||
\(873\) | 61.8667 | − | 35.7188i | 2.09387 | − | 1.20890i | ||||
\(874\) | − | 8.26663i | − | 0.279623i | ||||||
\(875\) | −1.23397 | − | 0.712432i | −0.0417157 | − | 0.0240846i | ||||
\(876\) | 12.9058 | + | 22.3534i | 0.436045 | + | 0.755253i | ||||
\(877\) | −46.2838 | −1.56289 | −0.781447 | − | 0.623972i | \(-0.785518\pi\) | ||||
−0.781447 | + | 0.623972i | \(0.785518\pi\) | |||||||
\(878\) | 33.3429 | 1.12527 | ||||||||
\(879\) | 11.4320 | + | 19.8008i | 0.385592 | + | 0.667866i | ||||
\(880\) | − | 0.135694i | − | 0.00457426i | ||||||
\(881\) | 8.51940 | − | 14.7560i | 0.287026 | − | 0.497143i | −0.686073 | − | 0.727533i | \(-0.740667\pi\) |
0.973098 | + | 0.230390i | \(0.0740001\pi\) | |||||||
\(882\) | − | 24.4333i | − | 0.822711i | ||||||
\(883\) | −12.7577 | − | 7.36566i | −0.429331 | − | 0.247874i | 0.269731 | − | 0.962936i | \(-0.413065\pi\) |
−0.699061 | + | 0.715062i | \(0.746399\pi\) | |||||||
\(884\) | −3.45122 | + | 5.97768i | −0.116077 | + | 0.201051i | ||||
\(885\) | 20.3404 | − | 35.2306i | 0.683735 | − | 1.18426i | ||||
\(886\) | −11.2493 | + | 6.49481i | −0.377929 | + | 0.218198i | ||||
\(887\) | 45.6244 | 1.53192 | 0.765958 | − | 0.642890i | \(-0.222265\pi\) | ||||
0.765958 | + | 0.642890i | \(0.222265\pi\) | |||||||
\(888\) | 16.1736 | + | 5.59656i | 0.542750 | + | 0.187808i | ||||
\(889\) | 9.88196 | 0.331430 | ||||||||
\(890\) | −8.45591 | + | 4.88202i | −0.283443 | + | 0.163646i | ||||
\(891\) | −0.0286087 | + | 0.0495517i | −0.000958426 | + | 0.00166004i | ||||
\(892\) | −4.88652 | + | 8.46371i | −0.163613 | + | 0.283386i | ||||
\(893\) | −0.340025 | − | 0.196313i | −0.0113785 | − | 0.00656938i | ||||
\(894\) | 23.8683i | 0.798276i | ||||||||
\(895\) | −11.9540 | + | 20.7050i | −0.399579 | + | 0.692091i | ||||
\(896\) | − | 1.42486i | − | 0.0476013i | ||||||
\(897\) | 11.7695 | + | 20.3854i | 0.392973 | + | 0.680650i | ||||
\(898\) | 8.79709 | 0.293563 | ||||||||
\(899\) | −11.0865 | −0.369757 | ||||||||
\(900\) | −2.45819 | − | 4.25771i | −0.0819397 | − | 0.141924i | ||||
\(901\) | −2.27783 | − | 1.31511i | −0.0758856 | − | 0.0438126i | ||||
\(902\) | 0.133050i | 0.00443008i | ||||||||
\(903\) | 41.2675 | − | 23.8258i | 1.37330 | − | 0.792873i | ||||
\(904\) | 2.40996 | + | 4.17418i | 0.0801542 | + | 0.138831i | ||||
\(905\) | 13.9010 | − | 8.02572i | 0.462083 | − | 0.266784i | ||||
\(906\) | −14.3655 | − | 8.29393i | −0.477262 | − | 0.275547i | ||||
\(907\) | −21.0518 | − | 12.1543i | −0.699014 | − | 0.403576i | 0.107966 | − | 0.994155i | \(-0.465566\pi\) |
−0.806980 | + | 0.590579i | \(0.798900\pi\) | |||||||
\(908\) | −9.75238 | + | 5.63054i | −0.323644 | + | 0.186856i | ||||
\(909\) | 25.1706 | + | 43.5967i | 0.834855 | + | 1.44601i | ||||
\(910\) | −2.99220 | + | 1.72755i | −0.0991905 | + | 0.0572677i | ||||
\(911\) | 1.13578i | 0.0376302i | 0.999823 | + | 0.0188151i | \(0.00598938\pi\) | ||||
−0.999823 | + | 0.0188151i | \(0.994011\pi\) | |||||||
\(912\) | 5.83827 | + | 3.37072i | 0.193324 | + | 0.111616i | ||||
\(913\) | −0.814634 | − | 1.41099i | −0.0269604 | − | 0.0466969i | ||||
\(914\) | 14.0276 | 0.463993 | ||||||||
\(915\) | 26.3743 | 0.871907 | ||||||||
\(916\) | −0.119732 | − | 0.207382i | −0.00395606 | − | 0.00685210i | ||||
\(917\) | − | 26.4150i | − | 0.872301i | ||||||
\(918\) | 7.67415 | − | 13.2920i | 0.253285 | − | 0.438702i | ||||
\(919\) | 22.3092i | 0.735911i | 0.929843 | + | 0.367955i | \(0.119942\pi\) | ||||
−0.929843 | + | 0.367955i | \(0.880058\pi\) | |||||||
\(920\) | 2.98792 | + | 1.72508i | 0.0985089 | + | 0.0568741i | ||||
\(921\) | 26.1995 | − | 45.3789i | 0.863304 | − | 1.49529i | ||||
\(922\) | 9.08430 | − | 15.7345i | 0.299176 | − | 0.518187i | ||||
\(923\) | −12.5342 | + | 7.23663i | −0.412568 | + | 0.238196i | ||||
\(924\) | 0.544000 | 0.0178963 | ||||||||
\(925\) | −3.98366 | − | 4.59679i | −0.130982 | − | 0.151141i | ||||
\(926\) | 25.9517 | 0.852826 | ||||||||
\(927\) | −80.4993 | + | 46.4763i | −2.64394 | + | 1.52648i | ||||
\(928\) | 1.37072 | − | 2.37416i | 0.0449962 | − | 0.0779358i | ||||
\(929\) | 19.2727 | − | 33.3813i | 0.632318 | − | 1.09521i | −0.354759 | − | 0.934958i | \(-0.615437\pi\) |
0.987077 | − | 0.160249i | \(-0.0512296\pi\) | |||||||
\(930\) | 9.85395 | + | 5.68918i | 0.323124 | + | 0.186556i | ||||
\(931\) | − | 11.9076i | − | 0.390257i | ||||||
\(932\) | −11.9229 | + | 20.6511i | −0.390549 | + | 0.676451i | ||||
\(933\) | − | 39.5746i | − | 1.29561i | ||||||
\(934\) | −18.8428 | − | 32.6367i | −0.616556 | − | 1.06791i | ||||
\(935\) | −0.386258 | −0.0126320 | ||||||||
\(936\) | −11.9216 | −0.389668 | ||||||||
\(937\) | 13.2183 | + | 22.8947i | 0.431822 | + | 0.747938i | 0.997030 | − | 0.0770107i | \(-0.0245376\pi\) |
−0.565208 | + | 0.824948i | \(0.691204\pi\) | |||||||
\(938\) | 9.73946 | + | 5.62308i | 0.318005 | + | 0.183600i | ||||
\(939\) | − | 94.6412i | − | 3.08850i | ||||||
\(940\) | 0.141912 | − | 0.0819332i | 0.00462867 | − | 0.00267237i | ||||
\(941\) | 11.8644 | + | 20.5497i | 0.386768 | + | 0.669902i | 0.992013 | − | 0.126137i | \(-0.0402580\pi\) |
−0.605244 | + | 0.796040i | \(0.706925\pi\) | |||||||
\(942\) | −41.8634 | + | 24.1698i | −1.36398 | + | 0.787496i | ||||
\(943\) | −2.92969 | − | 1.69146i | −0.0954039 | − | 0.0550815i | ||||
\(944\) | −12.5215 | − | 7.22929i | −0.407540 | − | 0.235293i | ||||
\(945\) | 6.65348 | − | 3.84139i | 0.216438 | − | 0.124960i | ||||
\(946\) | −0.806442 | − | 1.39680i | −0.0262197 | − | 0.0454139i | ||||
\(947\) | −21.8056 | + | 12.5895i | −0.708587 | + | 0.409103i | −0.810537 | − | 0.585687i | \(-0.800825\pi\) |
0.101951 | + | 0.994789i | \(0.467492\pi\) | |||||||
\(948\) | − | 15.0542i | − | 0.488938i | ||||||
\(949\) | −19.2650 | − | 11.1226i | −0.625367 | − | 0.361056i | ||||
\(950\) | −1.19801 | − | 2.07501i | −0.0388685 | − | 0.0673223i | ||||
\(951\) | 80.0341 | 2.59528 | ||||||||
\(952\) | −4.05591 | −0.131453 | ||||||||
\(953\) | 21.8586 | + | 37.8602i | 0.708069 | + | 1.22641i | 0.965572 | + | 0.260134i | \(0.0837668\pi\) |
−0.257503 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(954\) | − | 4.54278i | − | 0.147078i | ||||||
\(955\) | −0.583753 | + | 1.01109i | −0.0188898 | + | 0.0327181i | ||||
\(956\) | 12.0137i | 0.388551i | ||||||||
\(957\) | 0.906434 | + | 0.523330i | 0.0293009 | + | 0.0169169i | ||||
\(958\) | 4.08946 | − | 7.08315i | 0.132124 | − | 0.228846i | ||||
\(959\) | −2.71624 | + | 4.70466i | −0.0877119 | + | 0.151921i | ||||
\(960\) | −2.43665 | + | 1.40680i | −0.0786427 | + | 0.0454044i | ||||
\(961\) | 14.6457 | 0.472441 | ||||||||
\(962\) | −14.4831 | + | 2.79237i | −0.466955 | + | 0.0900296i | ||||
\(963\) | 62.1744 | 2.00354 | ||||||||
\(964\) | 7.10709 | − | 4.10328i | 0.228904 | − | 0.132158i | ||||
\(965\) | −1.61286 | + | 2.79355i | −0.0519197 | + | 0.0899275i | ||||
\(966\) | −6.91584 | + | 11.9786i | −0.222514 | + | 0.385405i | ||||
\(967\) | −16.2436 | − | 9.37825i | −0.522359 | − | 0.301584i | 0.215540 | − | 0.976495i | \(-0.430849\pi\) |
−0.737899 | + | 0.674911i | \(0.764182\pi\) | |||||||
\(968\) | 10.9816i | 0.352962i | ||||||||
\(969\) | 9.59485 | − | 16.6188i | 0.308231 | − | 0.533872i | ||||
\(970\) | 14.5305i | 0.466546i | ||||||||
\(971\) | −5.98784 | − | 10.3713i | −0.192159 | − | 0.332829i | 0.753806 | − | 0.657097i | \(-0.228216\pi\) |
−0.945966 | + | 0.324267i | \(0.894882\pi\) | |||||||
\(972\) | −14.9894 | −0.480786 | ||||||||
\(973\) | −14.0535 | −0.450534 | ||||||||
\(974\) | −16.4089 | − | 28.4210i | −0.525775 | − | 0.910669i | ||||
\(975\) | 5.90855 | + | 3.41131i | 0.189225 | + | 0.109249i | ||||
\(976\) | − | 9.37383i | − | 0.300049i | ||||||
\(977\) | −6.81645 | + | 3.93548i | −0.218077 | + | 0.125907i | −0.605060 | − | 0.796180i | \(-0.706851\pi\) |
0.386982 | + | 0.922087i | \(0.373517\pi\) | |||||||
\(978\) | −15.2966 | − | 26.4945i | −0.489132 | − | 0.847201i | ||||
\(979\) | −1.14742 | + | 0.662464i | −0.0366717 | + | 0.0211724i | ||||
\(980\) | 4.30394 | + | 2.48488i | 0.137484 | + | 0.0793767i | ||||
\(981\) | −52.1484 | − | 30.1079i | −1.66497 | − | 0.961271i | ||||
\(982\) | −22.0841 | + | 12.7502i | −0.704731 | + | 0.406876i | ||||
\(983\) | −20.2150 | − | 35.0134i | −0.644759 | − | 1.11675i | −0.984357 | − | 0.176184i | \(-0.943625\pi\) |
0.339599 | − | 0.940570i | \(-0.389709\pi\) | |||||||
\(984\) | 2.38917 | − | 1.37939i | 0.0761639 | − | 0.0439732i | ||||
\(985\) | 3.70150i | 0.117939i | ||||||||
\(986\) | −6.75812 | − | 3.90180i | −0.215222 | − | 0.124259i | ||||
\(987\) | 0.328471 | + | 0.568928i | 0.0104553 | + | 0.0181092i | ||||
\(988\) | −5.81001 | −0.184841 | ||||||||
\(989\) | 41.0091 | 1.30401 | ||||||||
\(990\) | −0.333563 | − | 0.577748i | −0.0106013 | − | 0.0183620i | ||||
\(991\) | 25.6435i | 0.814592i | 0.913296 | + | 0.407296i | \(0.133528\pi\) | ||||
−0.913296 | + | 0.407296i | \(0.866472\pi\) | |||||||
\(992\) | 2.02202 | − | 3.50225i | 0.0641993 | − | 0.111196i | ||||
\(993\) | − | 86.2997i | − | 2.73864i | ||||||
\(994\) | −7.36517 | − | 4.25228i | −0.233609 | − | 0.134874i | ||||
\(995\) | 11.4814 | − | 19.8864i | 0.363985 | − | 0.630440i | ||||
\(996\) | −16.8913 | + | 29.2566i | −0.535222 | + | 0.927031i | ||||
\(997\) | 25.0774 | − | 14.4784i | 0.794209 | − | 0.458537i | −0.0472332 | − | 0.998884i | \(-0.515040\pi\) |
0.841442 | + | 0.540347i | \(0.181707\pi\) | |||||||
\(998\) | −16.5320 | −0.523312 | ||||||||
\(999\) | 32.2048 | − | 6.20913i | 1.01892 | − | 0.196448i |
(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 | 370.2.l.c.11.6 | ✓ | 12 | |
37.27 | even | 6 | inner | 370.2.l.c.101.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.l.c.11.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
370.2.l.c.101.6 | yes | 12 | 37.27 | even | 6 | inner |