Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [451,2,Mod(16,451)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(451, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("451.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 451 = 11 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 451.l (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.60125313116\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 37.16 | ||
Character | \(\chi\) | \(=\) | 451.37 |
Dual form | 451.2.l.a.256.16 |
$q$-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 \(\left(\mathbb{Z}/451\mathbb{Z}\right)^\times\).
\(n\) | \(288\) | \(375\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.868271 | −0.613960 | −0.306980 | − | 0.951716i | \(-0.599319\pi\) | ||||
−0.306980 | + | 0.951716i | \(0.599319\pi\) | |||||||
\(3\) | −0.984882 | + | 3.03116i | −0.568622 | + | 1.75004i | 0.0883149 | + | 0.996093i | \(0.471852\pi\) |
−0.656937 | + | 0.753946i | \(0.728148\pi\) | |||||||
\(4\) | −1.24611 | −0.623053 | ||||||||
\(5\) | 0.0632253 | + | 0.194588i | 0.0282752 | + | 0.0870222i | 0.964198 | − | 0.265182i | \(-0.0854321\pi\) |
−0.935923 | + | 0.352205i | \(0.885432\pi\) | |||||||
\(6\) | 0.855145 | − | 2.63186i | 0.349111 | − | 1.07445i | ||||
\(7\) | 0.658084 | − | 2.02537i | 0.248732 | − | 0.765520i | −0.746268 | − | 0.665646i | \(-0.768156\pi\) |
0.995000 | − | 0.0998737i | \(-0.0318439\pi\) | |||||||
\(8\) | 2.81850 | 0.996490 | ||||||||
\(9\) | −5.79086 | − | 4.20730i | −1.93029 | − | 1.40243i | ||||
\(10\) | −0.0548967 | − | 0.168955i | −0.0173599 | − | 0.0534282i | ||||
\(11\) | 1.60295 | − | 2.90354i | 0.483307 | − | 0.875451i | ||||
\(12\) | 1.22727 | − | 3.77714i | 0.354281 | − | 1.09037i | ||||
\(13\) | −5.78851 | −1.60544 | −0.802721 | − | 0.596354i | \(-0.796615\pi\) | ||||
−0.802721 | + | 0.596354i | \(0.796615\pi\) | |||||||
\(14\) | −0.571396 | + | 1.75857i | −0.152712 | + | 0.469999i | ||||
\(15\) | −0.652095 | −0.168370 | ||||||||
\(16\) | 0.0449879 | 0.0112470 | ||||||||
\(17\) | −0.694463 | − | 0.504557i | −0.168432 | − | 0.122373i | 0.500376 | − | 0.865808i | \(-0.333195\pi\) |
−0.668808 | + | 0.743435i | \(0.733195\pi\) | |||||||
\(18\) | 5.02804 | + | 3.65308i | 1.18512 | + | 0.861040i | ||||
\(19\) | −0.254617 | + | 0.184990i | −0.0584132 | + | 0.0424396i | −0.616609 | − | 0.787270i | \(-0.711494\pi\) |
0.558196 | + | 0.829709i | \(0.311494\pi\) | |||||||
\(20\) | −0.0787854 | − | 0.242477i | −0.0176170 | − | 0.0542194i | ||||
\(21\) | 5.49109 | + | 3.98951i | 1.19825 | + | 0.870582i | ||||
\(22\) | −1.39179 | + | 2.52106i | −0.296731 | + | 0.537492i | ||||
\(23\) | 2.78413 | − | 2.02279i | 0.580531 | − | 0.421780i | −0.258385 | − | 0.966042i | \(-0.583190\pi\) |
0.838915 | + | 0.544262i | \(0.183190\pi\) | |||||||
\(24\) | −2.77589 | + | 8.54331i | −0.566626 | + | 1.74390i | ||||
\(25\) | 4.01122 | − | 2.91432i | 0.802244 | − | 0.582864i | ||||
\(26\) | 5.02599 | 0.985678 | ||||||||
\(27\) | 10.7209 | − | 7.78922i | 2.06325 | − | 1.49904i | ||||
\(28\) | −0.820042 | + | 2.52383i | −0.154973 | + | 0.476959i | ||||
\(29\) | −1.03881 | −0.192902 | −0.0964512 | − | 0.995338i | \(-0.530749\pi\) | ||||
−0.0964512 | + | 0.995338i | \(0.530749\pi\) | |||||||
\(30\) | 0.566195 | 0.103373 | ||||||||
\(31\) | 0.691206 | − | 2.12731i | 0.124144 | − | 0.382077i | −0.869600 | − | 0.493757i | \(-0.835623\pi\) |
0.993744 | + | 0.111680i | \(0.0356232\pi\) | |||||||
\(32\) | −5.67606 | −1.00340 | ||||||||
\(33\) | 7.22237 | + | 7.71843i | 1.25725 | + | 1.34361i | ||||
\(34\) | 0.602982 | + | 0.438092i | 0.103411 | + | 0.0751322i | ||||
\(35\) | 0.435720 | 0.0736502 | ||||||||
\(36\) | 7.21602 | + | 5.24274i | 1.20267 | + | 0.873791i | ||||
\(37\) | 8.75858 | 1.43990 | 0.719951 | − | 0.694025i | \(-0.244164\pi\) | ||||
0.719951 | + | 0.694025i | \(0.244164\pi\) | |||||||
\(38\) | 0.221077 | − | 0.160622i | 0.0358634 | − | 0.0260563i | ||||
\(39\) | 5.70099 | − | 17.5459i | 0.912890 | − | 2.80959i | ||||
\(40\) | 0.178201 | + | 0.548445i | 0.0281760 | + | 0.0867168i | ||||
\(41\) | −3.51709 | − | 5.35071i | −0.549277 | − | 0.835640i | ||||
\(42\) | −4.76776 | − | 3.46398i | −0.735681 | − | 0.534503i | ||||
\(43\) | −6.58553 | + | 4.78467i | −1.00428 | + | 0.729656i | −0.963003 | − | 0.269492i | \(-0.913144\pi\) |
−0.0412820 | + | 0.999148i | \(0.513144\pi\) | |||||||
\(44\) | −1.99744 | + | 3.61812i | −0.301126 | + | 0.545452i | ||||
\(45\) | 0.452560 | − | 1.39284i | 0.0674637 | − | 0.207632i | ||||
\(46\) | −2.41738 | + | 1.75633i | −0.356423 | + | 0.258956i | ||||
\(47\) | 2.08120 | + | 6.40526i | 0.303574 | + | 0.934303i | 0.980206 | + | 0.197982i | \(0.0634388\pi\) |
−0.676632 | + | 0.736321i | \(0.736561\pi\) | |||||||
\(48\) | −0.0443078 | + | 0.136365i | −0.00639528 | + | 0.0196827i | ||||
\(49\) | 1.99405 | + | 1.44876i | 0.284864 | + | 0.206966i | ||||
\(50\) | −3.48283 | + | 2.53042i | −0.492546 | + | 0.357856i | ||||
\(51\) | 2.21335 | − | 1.60810i | 0.309931 | − | 0.225178i | ||||
\(52\) | 7.21309 | 1.00028 | ||||||||
\(53\) | −0.565249 | + | 0.410677i | −0.0776429 | + | 0.0564108i | −0.625930 | − | 0.779880i | \(-0.715280\pi\) |
0.548287 | + | 0.836290i | \(0.315280\pi\) | |||||||
\(54\) | −9.30868 | + | 6.76316i | −1.26675 | + | 0.920349i | ||||
\(55\) | 0.666340 | + | 0.128336i | 0.0898493 | + | 0.0173049i | ||||
\(56\) | 1.85481 | − | 5.70852i | 0.247859 | − | 0.762833i | ||||
\(57\) | −0.309966 | − | 0.953977i | −0.0410560 | − | 0.126357i | ||||
\(58\) | 0.901970 | 0.118434 | ||||||||
\(59\) | −10.5746 | − | 7.68288i | −1.37669 | − | 1.00023i | −0.997181 | − | 0.0750393i | \(-0.976092\pi\) |
−0.379512 | − | 0.925187i | \(-0.623908\pi\) | |||||||
\(60\) | 0.812578 | 0.104903 | ||||||||
\(61\) | −0.201457 | −0.0257939 | −0.0128970 | − | 0.999917i | \(-0.504105\pi\) | ||||
−0.0128970 | + | 0.999917i | \(0.504105\pi\) | |||||||
\(62\) | −0.600155 | + | 1.84709i | −0.0762197 | + | 0.234580i | ||||
\(63\) | −12.3322 | + | 8.95990i | −1.55372 | + | 1.12884i | ||||
\(64\) | 4.83838 | 0.604798 | ||||||||
\(65\) | −0.365980 | − | 1.12637i | −0.0453943 | − | 0.139709i | ||||
\(66\) | −6.27098 | − | 6.70169i | −0.771904 | − | 0.824921i | ||||
\(67\) | 4.47028 | − | 13.7581i | 0.546132 | − | 1.68082i | −0.172152 | − | 0.985070i | \(-0.555072\pi\) |
0.718284 | − | 0.695750i | \(-0.244928\pi\) | |||||||
\(68\) | 0.865373 | + | 0.628731i | 0.104942 | + | 0.0762448i | ||||
\(69\) | 3.38935 | + | 10.4313i | 0.408029 | + | 1.25578i | ||||
\(70\) | −0.378323 | −0.0452183 | ||||||||
\(71\) | −9.62219 | − | 6.99093i | −1.14194 | − | 0.829671i | −0.154555 | − | 0.987984i | \(-0.549394\pi\) |
−0.987389 | + | 0.158313i | \(0.949394\pi\) | |||||||
\(72\) | −16.3215 | − | 11.8583i | −1.92351 | − | 1.39751i | ||||
\(73\) | −1.52825 | − | 4.70348i | −0.178869 | − | 0.550501i | 0.820920 | − | 0.571043i | \(-0.193461\pi\) |
−0.999789 | + | 0.0205418i | \(0.993461\pi\) | |||||||
\(74\) | −7.60483 | −0.884043 | ||||||||
\(75\) | 4.88318 | + | 15.0289i | 0.563861 | + | 1.73539i | ||||
\(76\) | 0.317280 | − | 0.230517i | 0.0363945 | − | 0.0264421i | ||||
\(77\) | −4.82589 | − | 5.15734i | −0.549961 | − | 0.587734i | ||||
\(78\) | −4.95001 | + | 15.2346i | −0.560478 | + | 1.72497i | ||||
\(79\) | −7.69735 | − | 5.59245i | −0.866019 | − | 0.629200i | 0.0634965 | − | 0.997982i | \(-0.479775\pi\) |
−0.929516 | + | 0.368782i | \(0.879775\pi\) | |||||||
\(80\) | 0.00284438 | + | 0.00875409i | 0.000318011 | + | 0.000978737i | ||||
\(81\) | 6.41574 | + | 19.7456i | 0.712860 | + | 2.19396i | ||||
\(82\) | 3.05379 | + | 4.64587i | 0.337234 | + | 0.513050i | ||||
\(83\) | 4.69566 | − | 3.41160i | 0.515416 | − | 0.374472i | −0.299458 | − | 0.954109i | \(-0.596806\pi\) |
0.814874 | + | 0.579638i | \(0.196806\pi\) | |||||||
\(84\) | −6.84247 | − | 4.97135i | −0.746575 | − | 0.542419i | ||||
\(85\) | 0.0542728 | − | 0.167035i | 0.00588671 | − | 0.0181174i | ||||
\(86\) | 5.71803 | − | 4.15439i | 0.616591 | − | 0.447980i | ||||
\(87\) | 1.02311 | − | 3.14880i | 0.109689 | − | 0.337587i | ||||
\(88\) | 4.51791 | − | 8.18363i | 0.481611 | − | 0.872378i | ||||
\(89\) | −5.73225 | − | 4.16472i | −0.607617 | − | 0.441460i | 0.240957 | − | 0.970536i | \(-0.422539\pi\) |
−0.848574 | + | 0.529076i | \(0.822539\pi\) | |||||||
\(90\) | −0.392945 | + | 1.20936i | −0.0414200 | + | 0.127478i | ||||
\(91\) | −3.80932 | + | 11.7239i | −0.399326 | + | 1.22900i | ||||
\(92\) | −3.46932 | + | 2.52061i | −0.361701 | + | 0.262791i | ||||
\(93\) | 5.76746 | + | 4.19031i | 0.598058 | + | 0.434515i | ||||
\(94\) | −1.80704 | − | 5.56150i | −0.186382 | − | 0.573625i | ||||
\(95\) | −0.0520950 | − | 0.0378492i | −0.00534484 | − | 0.00388325i | ||||
\(96\) | 5.59025 | − | 17.2050i | 0.570553 | − | 1.75598i | ||||
\(97\) | 7.45569 | − | 5.41688i | 0.757011 | − | 0.550001i | −0.140981 | − | 0.990012i | \(-0.545026\pi\) |
0.897992 | + | 0.440012i | \(0.145026\pi\) | |||||||
\(98\) | −1.73138 | − | 1.25792i | −0.174896 | − | 0.127069i | ||||
\(99\) | −21.4985 | + | 10.0699i | −2.16068 | + | 1.01206i | ||||
\(100\) | −4.99840 | + | 3.63155i | −0.499840 | + | 0.363155i | ||||
\(101\) | −1.19912 | − | 3.69052i | −0.119317 | − | 0.367220i | 0.873506 | − | 0.486814i | \(-0.161841\pi\) |
−0.992823 | + | 0.119593i | \(0.961841\pi\) | |||||||
\(102\) | −1.92179 | + | 1.39626i | −0.190286 | + | 0.138251i | ||||
\(103\) | 4.84420 | − | 14.9089i | 0.477313 | − | 1.46902i | −0.365500 | − | 0.930811i | \(-0.619102\pi\) |
0.842813 | − | 0.538207i | \(-0.180898\pi\) | |||||||
\(104\) | −16.3149 | −1.59981 | ||||||||
\(105\) | −0.429133 | + | 1.32074i | −0.0418791 | + | 0.128891i | ||||
\(106\) | 0.490789 | − | 0.356579i | 0.0476697 | − | 0.0346340i | ||||
\(107\) | −6.19269 | + | 4.49925i | −0.598670 | + | 0.434959i | −0.845407 | − | 0.534123i | \(-0.820642\pi\) |
0.246736 | + | 0.969083i | \(0.420642\pi\) | |||||||
\(108\) | −13.3594 | + | 9.70619i | −1.28551 | + | 0.933978i | ||||
\(109\) | 16.4370 | 1.57438 | 0.787188 | − | 0.616713i | \(-0.211536\pi\) | ||||
0.787188 | + | 0.616713i | \(0.211536\pi\) | |||||||
\(110\) | −0.578564 | − | 0.111431i | −0.0551639 | − | 0.0106245i | ||||
\(111\) | −8.62617 | + | 26.5486i | −0.818760 | + | 2.51988i | ||||
\(112\) | 0.0296059 | − | 0.0911174i | 0.00279749 | − | 0.00860979i | ||||
\(113\) | 9.30824 | 0.875645 | 0.437823 | − | 0.899061i | \(-0.355750\pi\) | ||||
0.437823 | + | 0.899061i | \(0.355750\pi\) | |||||||
\(114\) | 0.269135 | + | 0.828311i | 0.0252068 | + | 0.0775784i | ||||
\(115\) | 0.569637 | + | 0.413865i | 0.0531189 | + | 0.0385931i | ||||
\(116\) | 1.29447 | 0.120188 | ||||||||
\(117\) | 33.5204 | + | 24.3540i | 3.09896 | + | 2.25153i | ||||
\(118\) | 9.18160 | + | 6.67082i | 0.845235 | + | 0.614099i | ||||
\(119\) | −1.47893 | + | 1.07451i | −0.135573 | + | 0.0984998i | ||||
\(120\) | −1.83793 | −0.167779 | ||||||||
\(121\) | −5.86112 | − | 9.30845i | −0.532829 | − | 0.846223i | ||||
\(122\) | 0.174919 | 0.0158364 | ||||||||
\(123\) | 19.6827 | − | 5.39102i | 1.77473 | − | 0.486092i | ||||
\(124\) | −0.861316 | + | 2.65086i | −0.0773484 | + | 0.238054i | ||||
\(125\) | 1.64833 | + | 1.19758i | 0.147431 | + | 0.107115i | ||||
\(126\) | 10.7077 | − | 7.77962i | 0.953920 | − | 0.693064i | ||||
\(127\) | 4.21423 | + | 12.9701i | 0.373953 | + | 1.15091i | 0.944182 | + | 0.329423i | \(0.106854\pi\) |
−0.570230 | + | 0.821485i | \(0.693146\pi\) | |||||||
\(128\) | 7.15109 | 0.632073 | ||||||||
\(129\) | −8.01711 | − | 24.6741i | −0.705867 | − | 2.17243i | ||||
\(130\) | 0.317770 | + | 0.977996i | 0.0278703 | + | 0.0857759i | ||||
\(131\) | −0.259230 | − | 0.797829i | −0.0226491 | − | 0.0697067i | 0.939093 | − | 0.343663i | \(-0.111668\pi\) |
−0.961742 | + | 0.273956i | \(0.911668\pi\) | |||||||
\(132\) | −8.99984 | − | 9.61797i | −0.783335 | − | 0.837137i | ||||
\(133\) | 0.207115 | + | 0.637434i | 0.0179591 | + | 0.0552725i | ||||
\(134\) | −3.88142 | + | 11.9458i | −0.335303 | + | 1.03196i | ||||
\(135\) | 2.19352 | + | 1.59369i | 0.188788 | + | 0.137163i | ||||
\(136\) | −1.95734 | − | 1.42209i | −0.167841 | − | 0.121943i | ||||
\(137\) | −0.685615 | + | 0.498129i | −0.0585761 | + | 0.0425580i | −0.616688 | − | 0.787208i | \(-0.711526\pi\) |
0.558112 | + | 0.829766i | \(0.311526\pi\) | |||||||
\(138\) | −2.94287 | − | 9.05723i | −0.250514 | − | 0.771002i | ||||
\(139\) | −6.29048 | + | 19.3601i | −0.533552 | + | 1.64210i | 0.213206 | + | 0.977007i | \(0.431610\pi\) |
−0.746758 | + | 0.665096i | \(0.768390\pi\) | |||||||
\(140\) | −0.542953 | −0.0458879 | ||||||||
\(141\) | −21.4651 | −1.80769 | ||||||||
\(142\) | 8.35467 | + | 6.07002i | 0.701108 | + | 0.509385i | ||||
\(143\) | −9.27867 | + | 16.8072i | −0.775921 | + | 1.40549i | ||||
\(144\) | −0.260519 | − | 0.189278i | −0.0217099 | − | 0.0157732i | ||||
\(145\) | −0.0656792 | − | 0.202140i | −0.00545436 | − | 0.0167868i | ||||
\(146\) | 1.32694 | + | 4.08390i | 0.109818 | + | 0.337986i | ||||
\(147\) | −6.35533 | + | 4.61742i | −0.524179 | + | 0.380838i | ||||
\(148\) | −10.9141 | −0.897135 | ||||||||
\(149\) | 1.88449 | + | 5.79988i | 0.154384 | + | 0.475144i | 0.998098 | − | 0.0616483i | \(-0.0196357\pi\) |
−0.843714 | + | 0.536793i | \(0.819636\pi\) | |||||||
\(150\) | −4.23993 | − | 13.0491i | −0.346188 | − | 1.06546i | ||||
\(151\) | −6.47553 | − | 19.9296i | −0.526971 | − | 1.62185i | −0.760385 | − | 0.649473i | \(-0.774990\pi\) |
0.233414 | − | 0.972378i | \(-0.425010\pi\) | |||||||
\(152\) | −0.717638 | + | 0.521395i | −0.0582081 | + | 0.0422907i | ||||
\(153\) | 1.89871 | + | 5.84363i | 0.153502 | + | 0.472430i | ||||
\(154\) | 4.19018 | + | 4.47797i | 0.337654 | + | 0.360845i | ||||
\(155\) | 0.457651 | 0.0367594 | ||||||||
\(156\) | −7.10404 | + | 21.8640i | −0.568778 | + | 1.75052i | ||||
\(157\) | −0.108460 | + | 0.0788004i | −0.00865601 | + | 0.00628896i | −0.592105 | − | 0.805861i | \(-0.701703\pi\) |
0.583449 | + | 0.812150i | \(0.301703\pi\) | |||||||
\(158\) | 6.68339 | + | 4.85576i | 0.531702 | + | 0.386304i | ||||
\(159\) | −0.688123 | − | 2.11782i | −0.0545717 | − | 0.167954i | ||||
\(160\) | −0.358871 | − | 1.10449i | −0.0283712 | − | 0.0873177i | ||||
\(161\) | −2.26471 | − | 6.97007i | −0.178484 | − | 0.549318i | ||||
\(162\) | −5.57060 | − | 17.1445i | −0.437668 | − | 1.34700i | ||||
\(163\) | 5.08780 | + | 3.69651i | 0.398507 | + | 0.289533i | 0.768933 | − | 0.639330i | \(-0.220788\pi\) |
−0.370425 | + | 0.928862i | \(0.620788\pi\) | |||||||
\(164\) | 4.38266 | + | 6.66755i | 0.342228 | + | 0.520648i | ||||
\(165\) | −1.04527 | + | 1.89338i | −0.0813744 | + | 0.147400i | ||||
\(166\) | −4.07711 | + | 2.96219i | −0.316445 | + | 0.229911i | ||||
\(167\) | −15.1659 | − | 11.0187i | −1.17357 | − | 0.852649i | −0.182138 | − | 0.983273i | \(-0.558302\pi\) |
−0.991432 | + | 0.130624i | \(0.958302\pi\) | |||||||
\(168\) | 15.4766 | + | 11.2444i | 1.19405 | + | 0.867527i | ||||
\(169\) | 20.5068 | 1.57745 | ||||||||
\(170\) | −0.0471235 | + | 0.145031i | −0.00361421 | + | 0.0111234i | ||||
\(171\) | 2.25276 | 0.172273 | ||||||||
\(172\) | 8.20627 | − | 5.96220i | 0.625722 | − | 0.454614i | ||||
\(173\) | −2.81593 | + | 8.66653i | −0.214091 | + | 0.658904i | 0.785126 | + | 0.619336i | \(0.212598\pi\) |
−0.999217 | + | 0.0395682i | \(0.987402\pi\) | |||||||
\(174\) | −0.888334 | + | 2.73401i | −0.0673444 | + | 0.207265i | ||||
\(175\) | −3.26287 | − | 10.0421i | −0.246650 | − | 0.759110i | ||||
\(176\) | 0.0721133 | − | 0.130624i | 0.00543575 | − | 0.00984619i | ||||
\(177\) | 33.7027 | − | 24.4865i | 2.53325 | − | 1.84051i | ||||
\(178\) | 4.97715 | + | 3.61611i | 0.373053 | + | 0.271039i | ||||
\(179\) | −13.1239 | − | 9.53505i | −0.980924 | − | 0.712683i | −0.0230091 | − | 0.999735i | \(-0.507325\pi\) |
−0.957915 | + | 0.287052i | \(0.907325\pi\) | |||||||
\(180\) | −0.563938 | + | 1.73562i | −0.0420334 | + | 0.129366i | ||||
\(181\) | 12.1360 | + | 8.81730i | 0.902060 | + | 0.655385i | 0.938994 | − | 0.343933i | \(-0.111759\pi\) |
−0.0369344 | + | 0.999318i | \(0.511759\pi\) | |||||||
\(182\) | 3.30753 | − | 10.1795i | 0.245170 | − | 0.754556i | ||||
\(183\) | 0.198411 | − | 0.610647i | 0.0146670 | − | 0.0451403i | ||||
\(184\) | 7.84706 | − | 5.70123i | 0.578493 | − | 0.420300i | ||||
\(185\) | 0.553764 | + | 1.70431i | 0.0407136 | + | 0.125303i | ||||
\(186\) | −5.00772 | − | 3.63832i | −0.367184 | − | 0.266775i | ||||
\(187\) | −2.57819 | + | 1.20762i | −0.188536 | + | 0.0883102i | ||||
\(188\) | −2.59339 | − | 7.98163i | −0.189142 | − | 0.582120i | ||||
\(189\) | −8.72081 | − | 26.8399i | −0.634345 | − | 1.95231i | ||||
\(190\) | 0.0452326 | + | 0.0328634i | 0.00328152 | + | 0.00238416i | ||||
\(191\) | 0.758867 | + | 2.33555i | 0.0549097 | + | 0.168995i | 0.974750 | − | 0.223298i | \(-0.0716822\pi\) |
−0.919841 | + | 0.392292i | \(0.871682\pi\) | |||||||
\(192\) | −4.76524 | + | 14.6659i | −0.343901 | + | 1.05842i | ||||
\(193\) | 0.256099 | + | 0.788193i | 0.0184344 | + | 0.0567354i | 0.959851 | − | 0.280512i | \(-0.0905042\pi\) |
−0.941416 | + | 0.337247i | \(0.890504\pi\) | |||||||
\(194\) | −6.47356 | + | 4.70332i | −0.464775 | + | 0.337679i | ||||
\(195\) | 3.77465 | 0.270308 | ||||||||
\(196\) | −2.48480 | − | 1.80531i | −0.177486 | − | 0.128951i | ||||
\(197\) | −6.31065 | − | 19.4222i | −0.449615 | − | 1.38377i | −0.877342 | − | 0.479866i | \(-0.840685\pi\) |
0.427726 | − | 0.903908i | \(-0.359315\pi\) | |||||||
\(198\) | 18.6666 | − | 8.74342i | 1.32657 | − | 0.621367i | ||||
\(199\) | −9.09828 | + | 6.61028i | −0.644960 | + | 0.468591i | −0.861551 | − | 0.507672i | \(-0.830506\pi\) |
0.216591 | + | 0.976262i | \(0.430506\pi\) | |||||||
\(200\) | 11.3056 | − | 8.21401i | 0.799428 | − | 0.580818i | ||||
\(201\) | 37.3003 | + | 27.1002i | 2.63096 | + | 1.91150i | ||||
\(202\) | 1.04116 | + | 3.20437i | 0.0732560 | + | 0.225459i | ||||
\(203\) | −0.683625 | + | 2.10398i | −0.0479811 | + | 0.147671i | ||||
\(204\) | −2.75807 | + | 2.00386i | −0.193104 | + | 0.140298i | ||||
\(205\) | 0.818812 | − | 1.02268i | 0.0571883 | − | 0.0714272i | ||||
\(206\) | −4.20608 | + | 12.9450i | −0.293051 | + | 0.901919i | ||||
\(207\) | −24.6330 | −1.71211 | ||||||||
\(208\) | −0.260413 | −0.0180564 | ||||||||
\(209\) | 0.128989 | + | 1.03582i | 0.00892234 | + | 0.0716492i | ||||
\(210\) | 0.372604 | − | 1.14676i | 0.0257121 | − | 0.0791337i | ||||
\(211\) | −1.82923 | −0.125929 | −0.0629647 | − | 0.998016i | \(-0.520056\pi\) | ||||
−0.0629647 | + | 0.998016i | \(0.520056\pi\) | |||||||
\(212\) | 0.704359 | − | 0.511747i | 0.0483756 | − | 0.0351469i | ||||
\(213\) | 30.6673 | − | 22.2811i | 2.10129 | − | 1.52668i | ||||
\(214\) | 5.37694 | − | 3.90657i | 0.367560 | − | 0.267048i | ||||
\(215\) | −1.34741 | − | 0.978951i | −0.0918926 | − | 0.0667639i | ||||
\(216\) | 30.2170 | − | 21.9539i | 2.05600 | − | 1.49377i | ||||
\(217\) | −3.85374 | − | 2.79990i | −0.261609 | − | 0.190070i | ||||
\(218\) | −14.2717 | −0.966604 | ||||||||
\(219\) | 15.7621 | 1.06511 | ||||||||
\(220\) | −0.830330 | − | 0.159920i | −0.0559808 | − | 0.0107818i | ||||
\(221\) | 4.01990 | + | 2.92063i | 0.270408 | + | 0.196463i | ||||
\(222\) | 7.48986 | − | 23.0514i | 0.502686 | − | 1.54711i | ||||
\(223\) | −4.98039 | − | 15.3281i | −0.333512 | − | 1.02644i | −0.967450 | − | 0.253061i | \(-0.918563\pi\) |
0.633939 | − | 0.773383i | \(-0.281437\pi\) | |||||||
\(224\) | −3.73533 | + | 11.4962i | −0.249577 | + | 0.768119i | ||||
\(225\) | −35.4898 | −2.36599 | ||||||||
\(226\) | −8.08207 | −0.537612 | ||||||||
\(227\) | −3.04165 | + | 9.36125i | −0.201882 | + | 0.621328i | 0.797945 | + | 0.602730i | \(0.205920\pi\) |
−0.999827 | + | 0.0185982i | \(0.994080\pi\) | |||||||
\(228\) | 0.386250 | + | 1.18876i | 0.0255800 | + | 0.0787273i | ||||
\(229\) | −1.07401 | + | 3.30546i | −0.0709724 | + | 0.218431i | −0.980251 | − | 0.197757i | \(-0.936634\pi\) |
0.909279 | + | 0.416188i | \(0.136634\pi\) | |||||||
\(230\) | −0.494599 | − | 0.359347i | −0.0326129 | − | 0.0236947i | ||||
\(231\) | 20.3856 | − | 9.54864i | 1.34128 | − | 0.628254i | ||||
\(232\) | −2.92789 | −0.192225 | ||||||||
\(233\) | −7.69657 | −0.504219 | −0.252110 | − | 0.967699i | \(-0.581124\pi\) | ||||
−0.252110 | + | 0.967699i | \(0.581124\pi\) | |||||||
\(234\) | −29.1048 | − | 21.1459i | −1.90264 | − | 1.38235i | ||||
\(235\) | −1.11480 | + | 0.809950i | −0.0727215 | + | 0.0528353i | ||||
\(236\) | 13.1770 | + | 9.57368i | 0.857752 | + | 0.623193i | ||||
\(237\) | 24.5326 | − | 17.8240i | 1.59356 | − | 1.15779i | ||||
\(238\) | 1.28411 | − | 0.932963i | 0.0832367 | − | 0.0604750i | ||||
\(239\) | 8.25481 | − | 5.99747i | 0.533959 | − | 0.387944i | −0.287878 | − | 0.957667i | \(-0.592950\pi\) |
0.821837 | + | 0.569723i | \(0.192950\pi\) | |||||||
\(240\) | −0.0293364 | −0.00189366 | ||||||||
\(241\) | −8.49611 | + | 26.1483i | −0.547282 | + | 1.68436i | 0.168218 | + | 0.985750i | \(0.446199\pi\) |
−0.715500 | + | 0.698612i | \(0.753801\pi\) | |||||||
\(242\) | 5.08904 | + | 8.08226i | 0.327136 | + | 0.519547i | ||||
\(243\) | −26.4153 | −1.69454 | ||||||||
\(244\) | 0.251036 | 0.0160710 | ||||||||
\(245\) | −0.155837 | + | 0.479616i | −0.00995604 | + | 0.0306415i | ||||
\(246\) | −17.0900 | + | 4.68087i | −1.08962 | + | 0.298441i | ||||
\(247\) | 1.47385 | − | 1.07082i | 0.0937790 | − | 0.0681344i | ||||
\(248\) | 1.94816 | − | 5.99583i | 0.123709 | − | 0.380736i | ||||
\(249\) | 5.71641 | + | 17.5933i | 0.362263 | + | 1.11493i | ||||
\(250\) | −1.43120 | − | 1.03983i | −0.0905170 | − | 0.0657644i | ||||
\(251\) | −7.51195 | + | 5.45775i | −0.474150 | + | 0.344490i | −0.799057 | − | 0.601256i | \(-0.794667\pi\) |
0.324906 | + | 0.945746i | \(0.394667\pi\) | |||||||
\(252\) | 15.3673 | − | 11.1650i | 0.968047 | − | 0.703327i | ||||
\(253\) | −1.41044 | − | 11.3263i | −0.0886735 | − | 0.712076i | ||||
\(254\) | −3.65910 | − | 11.2615i | −0.229592 | − | 0.706612i | ||||
\(255\) | 0.452855 | + | 0.329019i | 0.0283589 | + | 0.0206039i | ||||
\(256\) | −15.8859 | −0.992866 | ||||||||
\(257\) | −4.96105 | + | 3.60441i | −0.309462 | + | 0.224837i | −0.731665 | − | 0.681664i | \(-0.761257\pi\) |
0.422204 | + | 0.906501i | \(0.361257\pi\) | |||||||
\(258\) | 6.96102 | + | 21.4238i | 0.433374 | + | 1.33379i | ||||
\(259\) | 5.76389 | − | 17.7394i | 0.358150 | − | 1.10227i | ||||
\(260\) | 0.456050 | + | 1.40358i | 0.0282830 | + | 0.0870461i | ||||
\(261\) | 6.01561 | + | 4.37060i | 0.372357 | + | 0.270533i | ||||
\(262\) | 0.225082 | + | 0.692732i | 0.0139056 | + | 0.0427971i | ||||
\(263\) | −6.37292 | − | 19.6138i | −0.392971 | − | 1.20944i | −0.930530 | − | 0.366215i | \(-0.880653\pi\) |
0.537559 | − | 0.843226i | \(-0.319347\pi\) | |||||||
\(264\) | 20.3563 | + | 21.7544i | 1.25284 | + | 1.33889i | ||||
\(265\) | −0.115651 | − | 0.0840251i | −0.00710437 | − | 0.00516162i | ||||
\(266\) | −0.179832 | − | 0.553466i | −0.0110262 | − | 0.0339352i | ||||
\(267\) | 18.2695 | − | 13.2736i | 1.11808 | − | 0.812330i | ||||
\(268\) | −5.57044 | + | 17.1441i | −0.340269 | + | 1.04724i | ||||
\(269\) | −4.23593 | + | 13.0368i | −0.258269 | + | 0.794871i | 0.734899 | + | 0.678177i | \(0.237230\pi\) |
−0.993168 | + | 0.116694i | \(0.962770\pi\) | |||||||
\(270\) | −1.90457 | − | 1.38375i | −0.115908 | − | 0.0842124i | ||||
\(271\) | −0.397548 | + | 1.22353i | −0.0241493 | + | 0.0743240i | −0.962405 | − | 0.271619i | \(-0.912441\pi\) |
0.938256 | + | 0.345943i | \(0.112441\pi\) | |||||||
\(272\) | −0.0312424 | − | 0.0226990i | −0.00189435 | − | 0.00137633i | ||||
\(273\) | −31.7852 | − | 23.0933i | −1.92373 | − | 1.39767i | ||||
\(274\) | 0.595300 | − | 0.432511i | 0.0359634 | − | 0.0261289i | ||||
\(275\) | −2.03208 | − | 16.3182i | −0.122539 | − | 0.984027i | ||||
\(276\) | −4.22348 | − | 12.9985i | −0.254224 | − | 0.782420i | ||||
\(277\) | −2.58858 | + | 7.96682i | −0.155532 | + | 0.478680i | −0.998214 | − | 0.0597319i | \(-0.980975\pi\) |
0.842682 | + | 0.538412i | \(0.180975\pi\) | |||||||
\(278\) | 5.46185 | − | 16.8098i | 0.327580 | − | 1.00819i | ||||
\(279\) | −12.9529 | + | 9.41086i | −0.775472 | + | 0.563413i | ||||
\(280\) | 1.22808 | 0.0733917 | ||||||||
\(281\) | 2.64444 | − | 8.13875i | 0.157754 | − | 0.485517i | −0.840675 | − | 0.541539i | \(-0.817842\pi\) |
0.998430 | + | 0.0560221i | \(0.0178417\pi\) | |||||||
\(282\) | 18.6375 | 1.10985 | ||||||||
\(283\) | 9.43360 | + | 6.85392i | 0.560770 | + | 0.407423i | 0.831741 | − | 0.555165i | \(-0.187345\pi\) |
−0.270971 | + | 0.962588i | \(0.587345\pi\) | |||||||
\(284\) | 11.9903 | + | 8.71143i | 0.711491 | + | 0.516929i | ||||
\(285\) | 0.166034 | − | 0.120631i | 0.00983503 | − | 0.00714557i | ||||
\(286\) | 8.05640 | − | 14.5932i | 0.476385 | − | 0.862913i | ||||
\(287\) | −13.1517 | + | 3.60220i | −0.776322 | + | 0.212631i | ||||
\(288\) | 32.8693 | + | 23.8809i | 1.93684 | + | 1.40720i | ||||
\(289\) | −5.02559 | − | 15.4672i | −0.295623 | − | 0.909833i | ||||
\(290\) | 0.0570274 | + | 0.175512i | 0.00334876 | + | 0.0103064i | ||||
\(291\) | 9.07642 | + | 27.9343i | 0.532069 | + | 1.63754i | ||||
\(292\) | 1.90436 | + | 5.86103i | 0.111444 | + | 0.342991i | ||||
\(293\) | −14.3423 | − | 10.4203i | −0.837885 | − | 0.608759i | 0.0838942 | − | 0.996475i | \(-0.473264\pi\) |
−0.921779 | + | 0.387716i | \(0.873264\pi\) | |||||||
\(294\) | 5.51815 | − | 4.00917i | 0.321825 | − | 0.233820i | ||||
\(295\) | 0.826412 | − | 2.54343i | 0.0481156 | − | 0.148084i | ||||
\(296\) | 24.6861 | 1.43485 | ||||||||
\(297\) | −5.43122 | − | 43.6144i | −0.315151 | − | 2.53077i | ||||
\(298\) | −1.63625 | − | 5.03587i | −0.0947855 | − | 0.291720i | ||||
\(299\) | −16.1159 | + | 11.7089i | −0.932009 | + | 0.677144i | ||||
\(300\) | −6.08496 | − | 18.7276i | −0.351315 | − | 1.08124i | ||||
\(301\) | 5.35692 | + | 16.4869i | 0.308767 | + | 0.950289i | ||||
\(302\) | 5.62252 | + | 17.3043i | 0.323539 | + | 0.995752i | ||||
\(303\) | 12.3675 | 0.710496 | ||||||||
\(304\) | −0.0114547 | + | 0.00832232i | −0.000656972 | + | 0.000477318i | ||||
\(305\) | −0.0127372 | − | 0.0392010i | −0.000729329 | − | 0.00224464i | ||||
\(306\) | −1.64860 | − | 5.07386i | −0.0942440 | − | 0.290053i | ||||
\(307\) | 23.3540 | + | 16.9677i | 1.33288 | + | 0.968395i | 0.999674 | + | 0.0255418i | \(0.00813108\pi\) |
0.333208 | + | 0.942853i | \(0.391869\pi\) | |||||||
\(308\) | 6.01356 | + | 6.42659i | 0.342655 | + | 0.366189i | ||||
\(309\) | 40.4203 | + | 29.3670i | 2.29943 | + | 1.67063i | ||||
\(310\) | −0.397365 | −0.0225688 | ||||||||
\(311\) | −13.2349 | −0.750484 | −0.375242 | − | 0.926927i | \(-0.622440\pi\) | ||||
−0.375242 | + | 0.926927i | \(0.622440\pi\) | |||||||
\(312\) | 16.0683 | − | 49.4530i | 0.909686 | − | 2.79972i | ||||
\(313\) | 9.82918 | + | 30.2511i | 0.555578 | + | 1.70989i | 0.694412 | + | 0.719578i | \(0.255665\pi\) |
−0.138834 | + | 0.990316i | \(0.544335\pi\) | |||||||
\(314\) | 0.0941723 | − | 0.0684202i | 0.00531445 | − | 0.00386117i | ||||
\(315\) | −2.52319 | − | 1.83321i | −0.142166 | − | 0.103290i | ||||
\(316\) | 9.59171 | + | 6.96878i | 0.539576 | + | 0.392025i | ||||
\(317\) | −8.59384 | + | 26.4491i | −0.482678 | + | 1.48553i | 0.352637 | + | 0.935760i | \(0.385285\pi\) |
−0.835315 | + | 0.549771i | \(0.814715\pi\) | |||||||
\(318\) | 0.597477 | + | 1.83885i | 0.0335049 | + | 0.103117i | ||||
\(319\) | −1.66516 | + | 3.01623i | −0.0932311 | + | 0.168877i | ||||
\(320\) | 0.305908 | + | 0.941489i | 0.0171008 | + | 0.0526309i | ||||
\(321\) | −7.53887 | − | 23.2022i | −0.420778 | − | 1.29502i | ||||
\(322\) | 1.96638 | + | 6.05191i | 0.109582 | + | 0.337260i | ||||
\(323\) | 0.270160 | 0.0150321 | ||||||||
\(324\) | −7.99468 | − | 24.6051i | −0.444149 | − | 1.36695i | ||||
\(325\) | −23.2190 | + | 16.8696i | −1.28796 | + | 0.935755i | ||||
\(326\) | −4.41759 | − | 3.20957i | −0.244668 | − | 0.177762i | ||||
\(327\) | −16.1885 | + | 49.8230i | −0.895224 | + | 2.75522i | ||||
\(328\) | −9.91291 | − | 15.0810i | −0.547349 | − | 0.832707i | ||||
\(329\) | 14.3427 | 0.790736 | ||||||||
\(330\) | 0.907581 | − | 1.64397i | 0.0499607 | − | 0.0904976i | ||||
\(331\) | 16.5745 | 0.911017 | 0.455508 | − | 0.890232i | \(-0.349458\pi\) | ||||
0.455508 | + | 0.890232i | \(0.349458\pi\) | |||||||
\(332\) | −5.85129 | + | 4.25121i | −0.321131 | + | 0.233315i | ||||
\(333\) | −50.7197 | − | 36.8500i | −2.77942 | − | 2.01937i | ||||
\(334\) | 13.1681 | + | 9.56718i | 0.720526 | + | 0.523493i | ||||
\(335\) | 2.95979 | 0.161711 | ||||||||
\(336\) | 0.247033 | + | 0.179480i | 0.0134767 | + | 0.00979143i | ||||
\(337\) | −4.29664 | − | 13.2237i | −0.234053 | − | 0.720340i | −0.997246 | − | 0.0741695i | \(-0.976369\pi\) |
0.763193 | − | 0.646171i | \(-0.223631\pi\) | |||||||
\(338\) | −17.8055 | −0.968489 | ||||||||
\(339\) | −9.16751 | + | 28.2147i | −0.497911 | + | 1.53241i | ||||
\(340\) | −0.0676296 | + | 0.208143i | −0.00366773 | + | 0.0112881i | ||||
\(341\) | −5.06878 | − | 5.41692i | −0.274490 | − | 0.293343i | ||||
\(342\) | −1.95601 | −0.105769 | ||||||||
\(343\) | 16.3067 | − | 11.8475i | 0.880482 | − | 0.639707i | ||||
\(344\) | −18.5613 | + | 13.4856i | −1.00076 | + | 0.727094i | ||||
\(345\) | −1.81551 | + | 1.31905i | −0.0977440 | + | 0.0710152i | ||||
\(346\) | 2.44499 | − | 7.52490i | 0.131443 | − | 0.404541i | ||||
\(347\) | 6.75781 | 0.362778 | 0.181389 | − | 0.983411i | \(-0.441941\pi\) | ||||
0.181389 | + | 0.983411i | \(0.441941\pi\) | |||||||
\(348\) | −1.27490 | + | 3.92373i | −0.0683417 | + | 0.210334i | ||||
\(349\) | −3.46068 | + | 2.51433i | −0.185246 | + | 0.134589i | −0.676543 | − | 0.736403i | \(-0.736523\pi\) |
0.491297 | + | 0.870992i | \(0.336523\pi\) | |||||||
\(350\) | 2.83306 | + | 8.71926i | 0.151433 | + | 0.466064i | ||||
\(351\) | −62.0582 | + | 45.0879i | −3.31242 | + | 2.40662i | ||||
\(352\) | −9.09843 | + | 16.4807i | −0.484948 | + | 0.878423i | ||||
\(353\) | 20.8082 | + | 15.1180i | 1.10751 | + | 0.804652i | 0.982269 | − | 0.187475i | \(-0.0600304\pi\) |
0.125239 | + | 0.992127i | \(0.460030\pi\) | |||||||
\(354\) | −29.2631 | + | 21.2609i | −1.55532 | + | 1.13000i | ||||
\(355\) | 0.751982 | − | 2.31436i | 0.0399111 | − | 0.122834i | ||||
\(356\) | 7.14298 | + | 5.18968i | 0.378577 | + | 0.275053i | ||||
\(357\) | −1.80042 | − | 5.54113i | −0.0952885 | − | 0.293268i | ||||
\(358\) | 11.3951 | + | 8.27901i | 0.602249 | + | 0.437559i | ||||
\(359\) | 15.4598 | − | 11.2322i | 0.815935 | − | 0.592812i | −0.0996099 | − | 0.995027i | \(-0.531759\pi\) |
0.915545 | + | 0.402215i | \(0.131759\pi\) | |||||||
\(360\) | 1.27554 | − | 3.92571i | 0.0672269 | − | 0.206903i | ||||
\(361\) | −5.84071 | + | 17.9759i | −0.307406 | + | 0.946098i | ||||
\(362\) | −10.5373 | − | 7.65581i | −0.553829 | − | 0.402380i | ||||
\(363\) | 33.9879 | − | 8.59823i | 1.78390 | − | 0.451290i | ||||
\(364\) | 4.74682 | − | 14.6092i | 0.248801 | − | 0.765730i | ||||
\(365\) | 0.818614 | − | 0.594758i | 0.0428482 | − | 0.0311311i | ||||
\(366\) | −0.172275 | + | 0.530207i | −0.00900495 | + | 0.0277144i | ||||
\(367\) | −16.7087 | − | 12.1396i | −0.872187 | − | 0.633681i | 0.0589857 | − | 0.998259i | \(-0.481213\pi\) |
−0.931173 | + | 0.364578i | \(0.881213\pi\) | |||||||
\(368\) | 0.125252 | − | 0.0910011i | 0.00652922 | − | 0.00474376i | ||||
\(369\) | −2.14511 | + | 45.7827i | −0.111670 | + | 2.38335i | ||||
\(370\) | −0.480818 | − | 1.47980i | −0.0249965 | − | 0.0769314i | ||||
\(371\) | 0.459794 | + | 1.41510i | 0.0238713 | + | 0.0734683i | ||||
\(372\) | −7.18686 | − | 5.22156i | −0.372622 | − | 0.270725i | ||||
\(373\) | −2.54906 | + | 7.84520i | −0.131985 | + | 0.406209i | −0.995109 | − | 0.0987836i | \(-0.968505\pi\) |
0.863124 | + | 0.504993i | \(0.168505\pi\) | |||||||
\(374\) | 2.23857 | − | 1.04855i | 0.115754 | − | 0.0542190i | ||||
\(375\) | −5.25347 | + | 3.81687i | −0.271288 | + | 0.197102i | ||||
\(376\) | 5.86585 | + | 18.0532i | 0.302508 | + | 0.931024i | ||||
\(377\) | 6.01317 | 0.309694 | ||||||||
\(378\) | 7.57203 | + | 23.3043i | 0.389463 | + | 1.19864i | ||||
\(379\) | −5.40959 | − | 3.93030i | −0.277872 | − | 0.201886i | 0.440117 | − | 0.897941i | \(-0.354937\pi\) |
−0.717989 | + | 0.696055i | \(0.754937\pi\) | |||||||
\(380\) | 0.0649159 | + | 0.0471641i | 0.00333011 | + | 0.00241947i | ||||
\(381\) | −43.4648 | −2.22677 | ||||||||
\(382\) | −0.658902 | − | 2.02789i | −0.0337124 | − | 0.103756i | ||||
\(383\) | −26.1121 | − | 18.9715i | −1.33426 | − | 0.969399i | −0.999634 | − | 0.0270495i | \(-0.991389\pi\) |
−0.334630 | − | 0.942350i | \(-0.608611\pi\) | |||||||
\(384\) | −7.04298 | + | 21.6761i | −0.359411 | + | 1.10615i | ||||
\(385\) | 0.698437 | − | 1.26513i | 0.0355956 | − | 0.0644771i | ||||
\(386\) | −0.222364 | − | 0.684365i | −0.0113180 | − | 0.0348333i | ||||
\(387\) | 58.2665 | 2.96185 | ||||||||
\(388\) | −9.29058 | + | 6.75000i | −0.471658 | + | 0.342679i | ||||
\(389\) | 3.80166 | − | 11.7003i | 0.192752 | − | 0.593229i | −0.807244 | − | 0.590218i | \(-0.799042\pi\) |
0.999995 | − | 0.00301094i | \(-0.000958415\pi\) | |||||||
\(390\) | −3.27742 | −0.165959 | ||||||||
\(391\) | −2.95408 | −0.149394 | ||||||||
\(392\) | 5.62023 | + | 4.08334i | 0.283865 | + | 0.206240i | ||||
\(393\) | 2.67366 | 0.134868 | ||||||||
\(394\) | 5.47936 | + | 16.8637i | 0.276046 | + | 0.849583i | ||||
\(395\) | 0.601554 | − | 1.85139i | 0.0302675 | − | 0.0931537i | ||||
\(396\) | 26.7894 | − | 12.5482i | 1.34622 | − | 0.630569i | ||||
\(397\) | 22.6613 | − | 16.4644i | 1.13734 | − | 0.826326i | 0.150593 | − | 0.988596i | \(-0.451882\pi\) |
0.986746 | + | 0.162270i | \(0.0518816\pi\) | |||||||
\(398\) | 7.89977 | − | 5.73952i | 0.395980 | − | 0.287696i | ||||
\(399\) | −2.13614 | −0.106941 | ||||||||
\(400\) | 0.180456 | − | 0.131109i | 0.00902282 | − | 0.00655546i | ||||
\(401\) | −19.3100 | + | 14.0295i | −0.964294 | + | 0.700601i | −0.954144 | − | 0.299348i | \(-0.903231\pi\) |
−0.0101501 | + | 0.999948i | \(0.503231\pi\) | |||||||
\(402\) | −32.3867 | − | 23.5304i | −1.61530 | − | 1.17359i | ||||
\(403\) | −4.00105 | + | 12.3140i | −0.199307 | + | 0.613403i | ||||
\(404\) | 1.49423 | + | 4.59877i | 0.0743408 | + | 0.228798i | ||||
\(405\) | −3.43661 | + | 2.49685i | −0.170767 | + | 0.124069i | ||||
\(406\) | 0.593572 | − | 1.82683i | 0.0294585 | − | 0.0906639i | ||||
\(407\) | 14.0396 | − | 25.4309i | 0.695915 | − | 1.26056i | ||||
\(408\) | 6.23833 | − | 4.53242i | 0.308844 | − | 0.224388i | ||||
\(409\) | 11.0219 | + | 8.00790i | 0.544999 | + | 0.395965i | 0.825938 | − | 0.563761i | \(-0.190646\pi\) |
−0.280939 | + | 0.959726i | \(0.590646\pi\) | |||||||
\(410\) | −0.710951 | + | 0.887965i | −0.0351114 | + | 0.0438535i | ||||
\(411\) | −0.834655 | − | 2.56880i | −0.0411705 | − | 0.126710i | ||||
\(412\) | −6.03638 | + | 18.5781i | −0.297391 | + | 0.915276i | ||||
\(413\) | −22.5197 | + | 16.3615i | −1.10812 | + | 0.805097i | ||||
\(414\) | 21.3881 | 1.05117 | ||||||||
\(415\) | 0.960739 | + | 0.698018i | 0.0471608 | + | 0.0342644i | ||||
\(416\) | 32.8559 | 1.61089 | ||||||||
\(417\) | −52.4881 | − | 38.1349i | −2.57035 | − | 1.86747i | ||||
\(418\) | −0.111997 | − | 0.899373i | −0.00547797 | − | 0.0439898i | ||||
\(419\) | −22.3554 | −1.09213 | −0.546067 | − | 0.837742i | \(-0.683876\pi\) | ||||
−0.546067 | + | 0.837742i | \(0.683876\pi\) | |||||||
\(420\) | 0.534745 | − | 1.64578i | 0.0260929 | − | 0.0803056i | ||||
\(421\) | −12.5947 | −0.613829 | −0.306914 | − | 0.951737i | \(-0.599297\pi\) | ||||
−0.306914 | + | 0.951737i | \(0.599297\pi\) | |||||||
\(422\) | 1.58827 | 0.0773156 | ||||||||
\(423\) | 14.8970 | − | 45.8482i | 0.724316 | − | 2.22922i | ||||
\(424\) | −1.59315 | + | 1.15749i | −0.0773703 | + | 0.0562128i | ||||
\(425\) | −4.25608 | −0.206450 | ||||||||
\(426\) | −26.6276 | + | 19.3460i | −1.29011 | + | 0.937319i | ||||
\(427\) | −0.132576 | + | 0.408026i | −0.00641578 | + | 0.0197457i | ||||
\(428\) | 7.71674 | − | 5.60654i | 0.373003 | − | 0.271003i | ||||
\(429\) | −41.8067 | − | 44.6782i | −2.01845 | − | 2.15708i | ||||
\(430\) | 1.16992 | + | 0.849995i | 0.0564184 | + | 0.0409904i | ||||
\(431\) | −7.84147 | − | 24.1336i | −0.377710 | − | 1.16247i | −0.941632 | − | 0.336644i | \(-0.890708\pi\) |
0.563921 | − | 0.825828i | \(-0.309292\pi\) | |||||||
\(432\) | 0.482313 | − | 0.350421i | 0.0232053 | − | 0.0168596i | ||||
\(433\) | 0.00722729 | + | 0.00525093i | 0.000347321 | + | 0.000252344i | 0.587959 | − | 0.808891i | \(-0.299932\pi\) |
−0.587612 | + | 0.809143i | \(0.699932\pi\) | |||||||
\(434\) | 3.34609 | + | 2.43108i | 0.160617 | + | 0.116695i | ||||
\(435\) | 0.677403 | 0.0324790 | ||||||||
\(436\) | −20.4822 | −0.980919 | ||||||||
\(437\) | −0.334691 | + | 1.03007i | −0.0160104 | + | 0.0492750i | ||||
\(438\) | −13.6858 | −0.653933 | ||||||||
\(439\) | 1.64069 | − | 5.04953i | 0.0783060 | − | 0.241001i | −0.904239 | − | 0.427027i | \(-0.859561\pi\) |
0.982545 | + | 0.186026i | \(0.0595609\pi\) | |||||||
\(440\) | 1.87808 | + | 0.361716i | 0.0895339 | + | 0.0172441i | ||||
\(441\) | −5.45188 | − | 16.7792i | −0.259613 | − | 0.799008i | ||||
\(442\) | −3.49036 | − | 2.53590i | −0.166020 | − | 0.120620i | ||||
\(443\) | 32.5614 | 1.54704 | 0.773520 | − | 0.633772i | \(-0.218494\pi\) | ||||
0.773520 | + | 0.633772i | \(0.218494\pi\) | |||||||
\(444\) | 10.7491 | − | 33.0824i | 0.510130 | − | 1.57002i | ||||
\(445\) | 0.447980 | − | 1.37874i | 0.0212363 | − | 0.0653585i | ||||
\(446\) | 4.32433 | + | 13.3089i | 0.204763 | + | 0.630196i | ||||
\(447\) | −19.4363 | −0.919307 | ||||||||
\(448\) | 3.18406 | − | 9.79954i | 0.150433 | − | 0.462985i | ||||
\(449\) | 37.0576 | 1.74886 | 0.874429 | − | 0.485154i | \(-0.161236\pi\) | ||||
0.874429 | + | 0.485154i | \(0.161236\pi\) | |||||||
\(450\) | 30.8148 | 1.45262 | ||||||||
\(451\) | −21.1737 | + | 1.63511i | −0.997032 | + | 0.0769942i | ||||
\(452\) | −11.5990 | −0.545573 | ||||||||
\(453\) | 66.7874 | 3.13795 | ||||||||
\(454\) | 2.64098 | − | 8.12810i | 0.123947 | − | 0.381471i | ||||
\(455\) | −2.52217 | −0.118241 | ||||||||
\(456\) | −0.873639 | − | 2.68878i | −0.0409119 | − | 0.125914i | ||||
\(457\) | −4.22291 | + | 12.9968i | −0.197539 | + | 0.607963i | 0.802398 | + | 0.596789i | \(0.203557\pi\) |
−0.999938 | + | 0.0111743i | \(0.996443\pi\) | |||||||
\(458\) | 0.932530 | − | 2.87003i | 0.0435743 | − | 0.134108i | ||||
\(459\) | −11.3754 | −0.530958 | ||||||||
\(460\) | −0.709827 | − | 0.515720i | −0.0330959 | − | 0.0240456i | ||||
\(461\) | −7.65758 | − | 23.5676i | −0.356649 | − | 1.09765i | −0.955047 | − | 0.296454i | \(-0.904196\pi\) |
0.598398 | − | 0.801199i | \(-0.295804\pi\) | |||||||
\(462\) | −17.7003 | + | 8.29081i | −0.823491 | + | 0.385723i | ||||
\(463\) | 1.93927 | − | 5.96846i | 0.0901255 | − | 0.277378i | −0.895827 | − | 0.444403i | \(-0.853416\pi\) |
0.985953 | + | 0.167025i | \(0.0534160\pi\) | |||||||
\(464\) | −0.0467340 | −0.00216957 | ||||||||
\(465\) | −0.450732 | + | 1.38721i | −0.0209022 | + | 0.0643303i | ||||
\(466\) | 6.68271 | 0.309571 | ||||||||
\(467\) | 31.3178 | 1.44921 | 0.724607 | − | 0.689162i | \(-0.242021\pi\) | ||||
0.724607 | + | 0.689162i | \(0.242021\pi\) | |||||||
\(468\) | −41.7700 | − | 30.3476i | −1.93082 | − | 1.40282i | ||||
\(469\) | −24.9235 | − | 18.1080i | −1.15086 | − | 0.836149i | ||||
\(470\) | 0.967949 | − | 0.703256i | 0.0446481 | − | 0.0324388i | ||||
\(471\) | −0.132037 | − | 0.406367i | −0.00608392 | − | 0.0187244i | ||||
\(472\) | −29.8044 | − | 21.6542i | −1.37186 | − | 0.996715i | ||||
\(473\) | 3.33623 | + | 26.7910i | 0.153400 | + | 1.23185i | ||||
\(474\) | −21.3009 | + | 15.4760i | −0.978384 | + | 0.710837i | ||||
\(475\) | −0.482204 | + | 1.48407i | −0.0221250 | + | 0.0680939i | ||||
\(476\) | 1.84290 | − | 1.33895i | 0.0844693 | − | 0.0613706i | ||||
\(477\) | 5.00112 | 0.228985 | ||||||||
\(478\) | −7.16741 | + | 5.20743i | −0.327830 | + | 0.238182i | ||||
\(479\) | −10.6404 | + | 32.7476i | −0.486170 | + | 1.49628i | 0.344109 | + | 0.938930i | \(0.388181\pi\) |
−0.830279 | + | 0.557348i | \(0.811819\pi\) | |||||||
\(480\) | 3.70133 | 0.168942 | ||||||||
\(481\) | −50.6991 | −2.31168 | ||||||||
\(482\) | 7.37693 | − | 22.7038i | 0.336010 | − | 1.03413i | ||||
\(483\) | 23.3578 | 1.06282 | ||||||||
\(484\) | 7.30357 | + | 11.5993i | 0.331980 | + | 0.527241i | ||||
\(485\) | 1.52545 | + | 1.10830i | 0.0692669 | + | 0.0503254i | ||||
\(486\) | 22.9357 | 1.04038 | ||||||||
\(487\) | −8.78057 | − | 6.37946i | −0.397886 | − | 0.289081i | 0.370794 | − | 0.928715i | \(-0.379086\pi\) |
−0.768679 | + | 0.639634i | \(0.779086\pi\) | |||||||
\(488\) | −0.567806 | −0.0257034 | ||||||||
\(489\) | −16.2156 | + | 11.7813i | −0.733293 | + | 0.532769i | ||||
\(490\) | 0.135309 | − | 0.416437i | 0.00611262 | − | 0.0188127i | ||||
\(491\) | 7.90228 | + | 24.3207i | 0.356625 | + | 1.09758i | 0.955061 | + | 0.296408i | \(0.0957890\pi\) |
−0.598436 | + | 0.801170i | \(0.704211\pi\) | |||||||
\(492\) | −24.5268 | + | 6.71778i | −1.10575 | + | 0.302861i | ||||
\(493\) | 0.721416 | + | 0.524139i | 0.0324909 | + | 0.0236060i | ||||
\(494\) | −1.27970 | + | 0.929759i | −0.0575766 | + | 0.0418318i | ||||
\(495\) | −3.31873 | − | 3.54667i | −0.149166 | − | 0.159411i | ||||
\(496\) | 0.0310960 | − | 0.0957035i | 0.00139625 | − | 0.00429721i | ||||
\(497\) | −20.4915 | + | 14.8879i | −0.919168 | + | 0.667815i | ||||
\(498\) | −4.96339 | − | 15.2758i | −0.222415 | − | 0.684523i | ||||
\(499\) | −3.10004 | + | 9.54094i | −0.138777 | + | 0.427111i | −0.996158 | − | 0.0875703i | \(-0.972090\pi\) |
0.857382 | + | 0.514681i | \(0.172090\pi\) | |||||||
\(500\) | −2.05399 | − | 1.49231i | −0.0918574 | − | 0.0667383i | ||||
\(501\) | 48.3358 | − | 35.1180i | 2.15949 | − | 1.56896i | ||||
\(502\) | 6.52241 | − | 4.73881i | 0.291110 | − | 0.211503i | ||||
\(503\) | −1.79368 | −0.0799760 | −0.0399880 | − | 0.999200i | \(-0.512732\pi\) | ||||
−0.0399880 | + | 0.999200i | \(0.512732\pi\) | |||||||
\(504\) | −34.7584 | + | 25.2535i | −1.54826 | + | 1.12488i | ||||
\(505\) | 0.642314 | − | 0.466669i | 0.0285826 | − | 0.0207665i | ||||
\(506\) | 1.22464 | + | 9.83426i | 0.0544420 | + | 0.437186i | ||||
\(507\) | −20.1968 | + | 62.1593i | −0.896970 | + | 2.76059i | ||||
\(508\) | −5.25138 | − | 16.1621i | −0.232992 | − | 0.717076i | ||||
\(509\) | 9.76292 | 0.432734 | 0.216367 | − | 0.976312i | \(-0.430579\pi\) | ||||
0.216367 | + | 0.976312i | \(0.430579\pi\) | |||||||
\(510\) | −0.393201 | − | 0.285677i | −0.0174112 | − | 0.0126500i | ||||
\(511\) | −10.5320 | −0.465910 | ||||||||
\(512\) | −0.508951 | −0.0224927 | ||||||||
\(513\) | −1.28881 | + | 3.96654i | −0.0569022 | + | 0.175127i | ||||
\(514\) | 4.30754 | − | 3.12961i | 0.189997 | − | 0.138041i | ||||
\(515\) | 3.20736 | 0.141333 | ||||||||
\(516\) | 9.99016 | + | 30.7465i | 0.439792 | + | 1.35354i | ||||
\(517\) | 21.9340 | + | 4.22446i | 0.964656 | + | 0.185792i | ||||
\(518\) | −5.00462 | + | 15.4026i | −0.219890 | + | 0.676752i | ||||
\(519\) | −23.4963 | − | 17.0710i | −1.03137 | − | 0.749335i | ||||
\(520\) | −1.03151 | − | 3.17468i | −0.0452349 | − | 0.139219i | ||||
\(521\) | −10.9960 | −0.481741 | −0.240871 | − | 0.970557i | \(-0.577433\pi\) | ||||
−0.240871 | + | 0.970557i | \(0.577433\pi\) | |||||||
\(522\) | −5.22318 | − | 3.79486i | −0.228612 | − | 0.166097i | ||||
\(523\) | −3.64689 | − | 2.64962i | −0.159468 | − | 0.115860i | 0.505190 | − | 0.863008i | \(-0.331422\pi\) |
−0.664657 | + | 0.747148i | \(0.731422\pi\) | |||||||
\(524\) | 0.323028 | + | 0.994179i | 0.0141116 | + | 0.0434309i | ||||
\(525\) | 33.6527 | 1.46872 | ||||||||
\(526\) | 5.53342 | + | 17.0301i | 0.241269 | + | 0.742549i | ||||
\(527\) | −1.55337 | + | 1.12859i | −0.0676657 | + | 0.0491620i | ||||
\(528\) | 0.324920 | + | 0.347236i | 0.0141403 | + | 0.0151115i | ||||
\(529\) | −3.44769 | + | 10.6109i | −0.149900 | + | 0.461343i | ||||
\(530\) | 0.100416 | + | 0.0729566i | 0.00436180 | + | 0.00316903i | ||||
\(531\) | 28.9117 | + | 88.9809i | 1.25466 | + | 3.86144i | ||||
\(532\) | −0.258087 | − | 0.794310i | −0.0111895 | − | 0.0344377i | ||||
\(533\) | 20.3587 | + | 30.9726i | 0.881832 | + | 1.34157i | ||||
\(534\) | −15.8629 | + | 11.5251i | −0.686454 | + | 0.498738i | ||||
\(535\) | −1.26703 | − | 0.920554i | −0.0547786 | − | 0.0397990i | ||||
\(536\) | 12.5995 | − | 38.7772i | 0.544215 | − | 1.67492i | ||||
\(537\) | 41.8277 | − | 30.3896i | 1.80500 | − | 1.31141i | ||||
\(538\) | 3.67794 | − | 11.3195i | 0.158567 | − | 0.488019i | ||||
\(539\) | 7.40290 | − | 3.46752i | 0.318866 | − | 0.149357i | ||||
\(540\) | −2.73336 | − | 1.98590i | −0.117625 | − | 0.0854595i | ||||
\(541\) | 11.3905 | − | 35.0564i | 0.489717 | − | 1.50719i | −0.335314 | − | 0.942107i | \(-0.608842\pi\) |
0.825031 | − | 0.565088i | \(-0.191158\pi\) | |||||||
\(542\) | 0.345179 | − | 1.06235i | 0.0148267 | − | 0.0456320i | ||||
\(543\) | −38.6791 | + | 28.1020i | −1.65988 | + | 1.20597i | ||||
\(544\) | 3.94181 | + | 2.86389i | 0.169004 | + | 0.122788i | ||||
\(545\) | 1.03923 | + | 3.19843i | 0.0445158 | + | 0.137006i | ||||
\(546\) | 27.5982 | + | 20.0512i | 1.18109 | + | 0.858114i | ||||
\(547\) | 11.8451 | − | 36.4556i | 0.506461 | − | 1.55873i | −0.291839 | − | 0.956467i | \(-0.594267\pi\) |
0.798300 | − | 0.602259i | \(-0.205733\pi\) | |||||||
\(548\) | 0.854349 | − | 0.620721i | 0.0364960 | − | 0.0265159i | ||||
\(549\) | 1.16661 | + | 0.847591i | 0.0497896 | + | 0.0361743i | ||||
\(550\) | 1.76440 | + | 14.1687i | 0.0752342 | + | 0.604154i | ||||
\(551\) | 0.264499 | − | 0.192170i | 0.0112680 | − | 0.00818671i | ||||
\(552\) | 9.55287 | + | 29.4007i | 0.406597 | + | 1.25138i | ||||
\(553\) | −16.3923 | + | 11.9097i | −0.697072 | + | 0.506452i | ||||
\(554\) | 2.24759 | − | 6.91736i | 0.0954908 | − | 0.293890i | ||||
\(555\) | −5.71142 | −0.242436 | ||||||||
\(556\) | 7.83860 | − | 24.1247i | 0.332431 | − | 1.02312i | ||||
\(557\) | −7.50747 | + | 5.45450i | −0.318102 | + | 0.231115i | −0.735365 | − | 0.677671i | \(-0.762989\pi\) |
0.417263 | + | 0.908786i | \(0.362989\pi\) | |||||||
\(558\) | 11.2467 | − | 8.17118i | 0.476109 | − | 0.345914i | ||||
\(559\) | 38.1204 | − | 27.6961i | 1.61232 | − | 1.17142i | ||||
\(560\) | 0.0196022 | 0.000828342 | ||||||||
\(561\) | −1.12128 | − | 9.00426i | −0.0473406 | − | 0.380160i | ||||
\(562\) | −2.29609 | + | 7.06664i | −0.0968548 | + | 0.298088i | ||||
\(563\) | −0.720488 | + | 2.21743i | −0.0303650 | + | 0.0934537i | −0.965090 | − | 0.261917i | \(-0.915645\pi\) |
0.934725 | + | 0.355371i | \(0.115645\pi\) | |||||||
\(564\) | 26.7477 | 1.12628 | ||||||||
\(565\) | 0.588516 | + | 1.81127i | 0.0247591 | + | 0.0762006i | ||||
\(566\) | −8.19093 | − | 5.95106i | −0.344290 | − | 0.250142i | ||||
\(567\) | 44.2144 | 1.85683 | ||||||||
\(568\) | −27.1201 | − | 19.7039i | −1.13794 | − | 0.826759i | ||||
\(569\) | 37.2929 | + | 27.0949i | 1.56340 | + | 1.13588i | 0.933150 | + | 0.359487i | \(0.117048\pi\) |
0.630251 | + | 0.776391i | \(0.282952\pi\) | |||||||
\(570\) | −0.144163 | + | 0.104740i | −0.00603832 | + | 0.00438709i | ||||
\(571\) | −22.8066 | −0.954428 | −0.477214 | − | 0.878787i | \(-0.658353\pi\) | ||||
−0.477214 | + | 0.878787i | \(0.658353\pi\) | |||||||
\(572\) | 11.5622 | − | 20.9435i | 0.483440 | − | 0.875692i | ||||
\(573\) | −7.82681 | −0.326970 | ||||||||
\(574\) | 11.4193 | − | 3.12769i | 0.476631 | − | 0.130547i | ||||
\(575\) | 5.27269 | − | 16.2277i | 0.219887 | − | 0.676741i | ||||
\(576\) | −28.0184 | − | 20.3566i | −1.16743 | − | 0.848190i | ||||
\(577\) | 8.48493 | − | 6.16467i | 0.353232 | − | 0.256638i | −0.396991 | − | 0.917822i | \(-0.629946\pi\) |
0.750224 | + | 0.661184i | \(0.229946\pi\) | |||||||
\(578\) | 4.36357 | + | 13.4297i | 0.181501 | + | 0.558602i | ||||
\(579\) | −2.64136 | −0.109771 | ||||||||
\(580\) | 0.0818432 | + | 0.251887i | 0.00339835 | + | 0.0104591i | ||||
\(581\) | −3.81962 | − | 11.7556i | −0.158465 | − | 0.487704i | ||||
\(582\) | −7.88079 | − | 24.2546i | −0.326669 | − | 1.00539i | ||||
\(583\) | 0.286355 | + | 2.29952i | 0.0118596 | + | 0.0952363i | ||||
\(584\) | −4.30738 | − | 13.2568i | −0.178241 | − | 0.548569i | ||||
\(585\) | −2.61965 | + | 8.06244i | −0.108309 | + | 0.333341i | ||||
\(586\) | 12.4530 | + | 9.04762i | 0.514428 | + | 0.373754i | ||||
\(587\) | 31.2617 | + | 22.7129i | 1.29031 | + | 0.937463i | 0.999812 | − | 0.0194128i | \(-0.00617968\pi\) |
0.290496 | + | 0.956876i | \(0.406180\pi\) | |||||||
\(588\) | 7.91941 | − | 5.75379i | 0.326591 | − | 0.237282i | ||||
\(589\) | 0.217539 | + | 0.669517i | 0.00896355 | + | 0.0275870i | ||||
\(590\) | −0.717550 | + | 2.20839i | −0.0295411 | + | 0.0909180i | ||||
\(591\) | 65.0869 | 2.67732 | ||||||||
\(592\) | 0.394031 | 0.0161946 | ||||||||
\(593\) | 20.3534 | + | 14.7876i | 0.835814 | + | 0.607255i | 0.921198 | − | 0.389093i | \(-0.127212\pi\) |
−0.0853839 | + | 0.996348i | \(0.527212\pi\) | |||||||
\(594\) | 4.71577 | + | 37.8691i | 0.193491 | + | 1.55379i | ||||
\(595\) | −0.302591 | − | 0.219846i | −0.0124050 | − | 0.00901279i | ||||
\(596\) | −2.34828 | − | 7.22726i | −0.0961892 | − | 0.296040i | ||||
\(597\) | −11.0761 | − | 34.0886i | −0.453313 | − | 1.39515i | ||||
\(598\) | 13.9930 | − | 10.1665i | 0.572217 | − | 0.415740i | ||||
\(599\) | 10.7746 | 0.440237 | 0.220119 | − | 0.975473i | \(-0.429356\pi\) | ||||
0.220119 | + | 0.975473i | \(0.429356\pi\) | |||||||
\(600\) | 13.7632 | + | 42.3589i | 0.561882 | + | 1.72930i | ||||
\(601\) | −0.416917 | − | 1.28314i | −0.0170064 | − | 0.0523403i | 0.942193 | − | 0.335070i | \(-0.108760\pi\) |
−0.959200 | + | 0.282730i | \(0.908760\pi\) | |||||||
\(602\) | −4.65126 | − | 14.3151i | −0.189571 | − | 0.583440i | ||||
\(603\) | −83.7713 | + | 60.8634i | −3.41143 | + | 2.47855i | ||||
\(604\) | 8.06919 | + | 24.8344i | 0.328331 | + | 1.01050i | ||||
\(605\) | 1.44074 | − | 1.72903i | 0.0585743 | − | 0.0702951i | ||||
\(606\) | −10.7384 | −0.436217 | ||||||||
\(607\) | −4.68370 | + | 14.4150i | −0.190106 | + | 0.585085i | −0.999999 | − | 0.00149221i | \(-0.999525\pi\) |
0.809893 | + | 0.586577i | \(0.199525\pi\) | |||||||
\(608\) | 1.44522 | − | 1.05002i | 0.0586115 | − | 0.0425837i | ||||
\(609\) | −5.70421 | − | 4.14435i | −0.231146 | − | 0.167938i | ||||
\(610\) | 0.0110593 | + | 0.0340371i | 0.000447779 | + | 0.00137812i | ||||
\(611\) | −12.0470 | − | 37.0769i | −0.487370 | − | 1.49997i | ||||
\(612\) | −2.36599 | − | 7.28178i | −0.0956396 | − | 0.294348i | ||||
\(613\) | −4.22699 | − | 13.0094i | −0.170727 | − | 0.525443i | 0.828686 | − | 0.559714i | \(-0.189089\pi\) |
−0.999413 | + | 0.0342712i | \(0.989089\pi\) | |||||||
\(614\) | −20.2776 | − | 14.7325i | −0.818337 | − | 0.594556i | ||||
\(615\) | 2.29347 | + | 3.48917i | 0.0924818 | + | 0.140697i | ||||
\(616\) | −13.6018 | − | 14.5360i | −0.548031 | − | 0.585671i | ||||
\(617\) | 29.4960 | − | 21.4301i | 1.18746 | − | 0.862743i | 0.194470 | − | 0.980908i | \(-0.437701\pi\) |
0.992994 | + | 0.118165i | \(0.0377013\pi\) | |||||||
\(618\) | −35.0957 | − | 25.4986i | −1.41176 | − | 1.02570i | ||||
\(619\) | 9.57676 | + | 6.95793i | 0.384923 | + | 0.279663i | 0.763372 | − | 0.645959i | \(-0.223543\pi\) |
−0.378449 | + | 0.925622i | \(0.623543\pi\) | |||||||
\(620\) | −0.570281 | −0.0229030 | ||||||||
\(621\) | 14.0925 | − | 43.3724i | 0.565514 | − | 1.74047i | ||||
\(622\) | 11.4915 | 0.460768 | ||||||||
\(623\) | −12.2074 | + | 8.86921i | −0.489080 | + | 0.355338i | ||||
\(624\) | 0.256476 | − | 0.789352i | 0.0102673 | − | 0.0315994i | ||||
\(625\) | 7.53193 | − | 23.1809i | 0.301277 | − | 0.927235i | ||||
\(626\) | −8.53439 | − | 26.2662i | −0.341103 | − | 1.04981i | ||||
\(627\) | −3.26677 | − | 0.629176i | −0.130462 | − | 0.0251269i | ||||
\(628\) | 0.135152 | − | 0.0981936i | 0.00539315 | − | 0.00391835i | ||||
\(629\) | −6.08251 | − | 4.41920i | −0.242526 | − | 0.176205i | ||||
\(630\) | 2.19082 | + | 1.59172i | 0.0872842 | + | 0.0634157i | ||||
\(631\) | −0.986642 | + | 3.03657i | −0.0392776 | + | 0.120884i | −0.968773 | − | 0.247950i | \(-0.920243\pi\) |
0.929495 | + | 0.368834i | \(0.120243\pi\) | |||||||
\(632\) | −21.6950 | − | 15.7623i | −0.862980 | − | 0.626991i | ||||
\(633\) | 1.80157 | − | 5.54468i | 0.0716062 | − | 0.220381i | ||||
\(634\) | 7.46179 | − | 22.9650i | 0.296345 | − | 0.912057i | ||||
\(635\) | −2.25737 | + | 1.64008i | −0.0895810 | + | 0.0650844i | ||||
\(636\) | 0.857474 | + | 2.63903i | 0.0340010 | + | 0.104644i | ||||
\(637\) | −11.5426 | − | 8.38617i | −0.457334 | − | 0.332272i | ||||
\(638\) | 1.44581 | − | 2.61891i | 0.0572402 | − | 0.103684i | ||||
\(639\) | 26.3078 | + | 80.9670i | 1.04072 | + | 3.20300i | ||||
\(640\) | 0.452130 | + | 1.39151i | 0.0178720 | + | 0.0550044i | ||||
\(641\) | −4.89063 | − | 3.55325i | −0.193168 | − | 0.140345i | 0.486997 | − | 0.873403i | \(-0.338092\pi\) |
−0.680166 | + | 0.733058i | \(0.738092\pi\) | |||||||
\(642\) | 6.54578 | + | 20.1458i | 0.258341 | + | 0.795093i | ||||
\(643\) | −11.5463 | + | 35.5357i | −0.455340 | + | 1.40139i | 0.415396 | + | 0.909641i | \(0.363643\pi\) |
−0.870736 | + | 0.491751i | \(0.836357\pi\) | |||||||
\(644\) | 2.82207 | + | 8.68544i | 0.111205 | + | 0.342254i | ||||
\(645\) | 4.29439 | − | 3.12006i | 0.169091 | − | 0.122852i | ||||
\(646\) | −0.234572 | −0.00922912 | ||||||||
\(647\) | 29.3238 | + | 21.3050i | 1.15284 | + | 0.837585i | 0.988855 | − | 0.148879i | \(-0.0475664\pi\) |
0.163981 | + | 0.986464i | \(0.447566\pi\) | |||||||
\(648\) | 18.0828 | + | 55.6530i | 0.710358 | + | 2.18626i | ||||
\(649\) | −39.2581 | + | 18.3885i | −1.54101 | + | 0.721811i | ||||
\(650\) | 20.1604 | − | 14.6474i | 0.790754 | − | 0.574516i | ||||
\(651\) | 12.2824 | − | 8.92370i | 0.481386 | − | 0.349747i | ||||
\(652\) | −6.33994 | − | 4.60623i | −0.248291 | − | 0.180394i | ||||
\(653\) | 8.47582 | + | 26.0859i | 0.331684 | + | 1.02082i | 0.968332 | + | 0.249665i | \(0.0803205\pi\) |
−0.636648 | + | 0.771155i | \(0.719680\pi\) | |||||||
\(654\) | 14.0560 | − | 43.2599i | 0.549632 | − | 1.69159i | ||||
\(655\) | 0.138858 | − | 0.100886i | 0.00542562 | − | 0.00394194i | ||||
\(656\) | −0.158227 | − | 0.240717i | −0.00617771 | − | 0.00939844i | ||||
\(657\) | −10.9391 | + | 33.6670i | −0.426774 | + | 1.31348i | ||||
\(658\) | −12.4533 | −0.485481 | ||||||||
\(659\) | −9.52342 | −0.370980 | −0.185490 | − | 0.982646i | \(-0.559387\pi\) | ||||
−0.185490 | + | 0.982646i | \(0.559387\pi\) | |||||||
\(660\) | 1.30252 | − | 2.35936i | 0.0507005 | − | 0.0918378i | ||||
\(661\) | 12.2822 | − | 37.8006i | 0.477721 | − | 1.47027i | −0.364531 | − | 0.931191i | \(-0.618771\pi\) |
0.842252 | − | 0.539083i | \(-0.181229\pi\) | |||||||
\(662\) | −14.3912 | −0.559328 | ||||||||
\(663\) | −12.8120 | + | 9.30847i | −0.497577 | + | 0.361511i | ||||
\(664\) | 13.2347 | − | 9.61559i | 0.513607 | − | 0.373157i | ||||
\(665\) | −0.110942 | + | 0.0806039i | −0.00430214 | + | 0.00312569i | ||||
\(666\) | 44.0385 | + | 31.9958i | 1.70646 | + | 1.23981i | ||||
\(667\) | −2.89218 | + | 2.10130i | −0.111986 | + | 0.0813625i | ||||
\(668\) | 18.8983 | + | 13.7304i | 0.731196 | + | 0.531245i | ||||
\(669\) | 51.3669 | 1.98596 | ||||||||
\(670\) | −2.56990 | −0.0992840 | ||||||||
\(671\) | −0.322925 | + | 0.584939i | −0.0124664 | + | 0.0225813i | ||||
\(672\) | −31.1678 | − | 22.6447i | −1.20232 | − | 0.873538i | ||||
\(673\) | 0.369979 | − | 1.13868i | 0.0142616 | − | 0.0438928i | −0.943672 | − | 0.330881i | \(-0.892654\pi\) |
0.957934 | + | 0.286988i | \(0.0926541\pi\) | |||||||
\(674\) | 3.73065 | + | 11.4817i | 0.143699 | + | 0.442260i | ||||
\(675\) | 20.3037 | − | 62.4885i | 0.781492 | − | 2.40518i | ||||
\(676\) | −25.5536 | −0.982832 | ||||||||
\(677\) | −13.0875 | −0.502994 | −0.251497 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(678\) | 7.95989 | − | 24.4980i | 0.305698 | − | 0.940841i | ||||
\(679\) | −6.06473 | − | 18.6653i | −0.232743 | − | 0.716310i | ||||
\(680\) | 0.152968 | − | 0.470787i | 0.00586605 | − | 0.0180538i | ||||
\(681\) | −25.3797 | − | 18.4395i | −0.972553 | − | 0.706601i | ||||
\(682\) | 4.40108 | + | 4.70336i | 0.168526 | + | 0.180101i | ||||
\(683\) | −9.97397 | −0.381643 | −0.190822 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190822 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(684\) | −2.80718 | −0.107335 | ||||||||
\(685\) | −0.140278 | − | 0.101918i | −0.00535974 | − | 0.00389408i | ||||
\(686\) | −14.1587 | + | 10.2869i | −0.540581 | + | 0.392755i | ||||
\(687\) | −8.96158 | − | 6.51097i | −0.341906 | − | 0.248409i | ||||
\(688\) | −0.296270 | + | 0.215253i | −0.0112952 | + | 0.00820643i | ||||
\(689\) | 3.27194 | − | 2.37721i | 0.124651 | − | 0.0905644i | ||||
\(690\) | 1.57636 | − | 1.14529i | 0.0600110 | − | 0.0436005i | ||||
\(691\) | 17.0568 | 0.648871 | 0.324435 | − | 0.945908i | \(-0.394826\pi\) | ||||
0.324435 | + | 0.945908i | \(0.394826\pi\) | |||||||
\(692\) | 3.50894 | − | 10.7994i | 0.133390 | − | 0.410532i | ||||
\(693\) | 6.24751 | + | 50.1694i | 0.237323 | + | 1.90578i | ||||
\(694\) | −5.86761 | −0.222732 | ||||||||
\(695\) | −4.16496 | −0.157986 | ||||||||
\(696\) | 2.88363 | − | 8.87489i | 0.109304 | − | 0.336402i | ||||
\(697\) | −0.257250 | + | 5.49044i | −0.00974403 | + | 0.207965i | ||||
\(698\) | 3.00481 | − | 2.18312i | 0.113734 | − | 0.0826323i | ||||
\(699\) | 7.58022 | − | 23.3295i | 0.286710 | − | 0.882403i | ||||
\(700\) | 4.06588 | + | 12.5135i | 0.153676 | + | 0.472966i | ||||
\(701\) | −16.5794 | − | 12.0457i | −0.626197 | − | 0.454959i | 0.228884 | − | 0.973454i | \(-0.426492\pi\) |
−0.855081 | + | 0.518495i | \(0.826492\pi\) | |||||||
\(702\) | 53.8834 | − | 39.1486i | 2.03370 | − | 1.47757i | ||||
\(703\) | −2.23008 | + | 1.62025i | −0.0841092 | + | 0.0611089i | ||||
\(704\) | 7.75568 | − | 14.0485i | 0.292303 | − | 0.529471i | ||||
\(705\) | −1.35714 | − | 4.17684i | −0.0511127 | − | 0.157309i | ||||
\(706\) | −18.0671 | − | 13.1266i | −0.679966 | − | 0.494024i | ||||
\(707\) | −8.26381 | −0.310792 | ||||||||
\(708\) | −41.9971 | + | 30.5127i | −1.57835 | + | 1.14674i | ||||
\(709\) | 7.22984 | + | 22.2512i | 0.271522 | + | 0.835660i | 0.990119 | + | 0.140233i | \(0.0447850\pi\) |
−0.718596 | + | 0.695428i | \(0.755215\pi\) | |||||||
\(710\) | −0.652924 | + | 2.00949i | −0.0245038 | + | 0.0754150i | ||||
\(711\) | 21.0451 | + | 64.7702i | 0.789253 | + | 2.42907i | ||||
\(712\) | −16.1563 | − | 11.7383i | −0.605484 | − | 0.439910i | ||||
\(713\) | −2.37870 | − | 7.32088i | −0.0890829 | − | 0.274169i | ||||
\(714\) | 1.56326 | + | 4.81120i | 0.0585034 | + | 0.180055i | ||||
\(715\) | −3.85711 | − | 0.742875i | −0.144248 | − | 0.0277819i | ||||
\(716\) | 16.3537 | + | 11.8817i | 0.611167 | + | 0.444039i | ||||
\(717\) | 10.0492 | + | 30.9284i | 0.375296 | + | 1.15504i | ||||
\(718\) | −13.4233 | + | 9.75258i | −0.500952 | + | 0.363963i | ||||
\(719\) | 16.0706 | − | 49.4603i | 0.599333 | − | 1.84456i | 0.0674799 | − | 0.997721i | \(-0.478504\pi\) |
0.531853 | − | 0.846837i | \(-0.321496\pi\) | |||||||
\(720\) | 0.0203598 | − | 0.0626609i | 0.000758763 | − | 0.00233523i | ||||
\(721\) | −27.0082 | − | 19.6226i | −1.00584 | − | 0.730785i | ||||
\(722\) | 5.07132 | − | 15.6079i | 0.188735 | − | 0.580867i | ||||
\(723\) | −70.8920 | − | 51.5060i | −2.63650 | − | 1.91553i | ||||
\(724\) | −15.1227 | − | 10.9873i | −0.562031 | − | 0.408339i | ||||
\(725\) | −4.16690 | + | 3.02743i | −0.154755 | + | 0.112436i | ||||
\(726\) | −29.5107 | + | 7.46559i | −1.09524 | + | 0.277074i | ||||
\(727\) | −13.1520 | − | 40.4777i | −0.487780 | − | 1.50123i | −0.827913 | − | 0.560856i | \(-0.810472\pi\) |
0.340133 | − | 0.940377i | \(-0.389528\pi\) | |||||||
\(728\) | −10.7366 | + | 33.0438i | −0.397924 | + | 1.22468i | ||||
\(729\) | 6.76876 | − | 20.8321i | 0.250695 | − | 0.771559i | ||||
\(730\) | −0.710779 | + | 0.516411i | −0.0263071 | + | 0.0191132i | ||||
\(731\) | 6.98755 | 0.258444 | ||||||||
\(732\) | −0.247241 | + | 0.760931i | −0.00913830 | + | 0.0281248i | ||||
\(733\) | 20.7200 | 0.765310 | 0.382655 | − | 0.923891i | \(-0.375010\pi\) | ||||
0.382655 | + | 0.923891i | \(0.375010\pi\) | |||||||
\(734\) | 14.5077 | + | 10.5405i | 0.535489 | + | 0.389055i | ||||
\(735\) | −1.30031 | − | 0.944730i | −0.0479626 | − | 0.0348469i | ||||
\(736\) | −15.8029 | + | 11.4815i | −0.582502 | + | 0.423212i | ||||
\(737\) | −32.7816 | − | 35.0332i | −1.20753 | − | 1.29046i | ||||
\(738\) | 1.86254 | − | 39.7518i | 0.0685609 | − | 1.46328i | ||||
\(739\) | 33.3596 | + | 24.2372i | 1.22715 | + | 0.891579i | 0.996674 | − | 0.0814978i | \(-0.0259703\pi\) |
0.230480 | + | 0.973077i | \(0.425970\pi\) | |||||||
\(740\) | −0.690049 | − | 2.12375i | −0.0253667 | − | 0.0780706i | ||||
\(741\) | 1.79424 | + | 5.52210i | 0.0659130 | + | 0.202859i | ||||
\(742\) | −0.399226 | − | 1.22869i | −0.0146560 | − | 0.0451067i | ||||
\(743\) | 2.45693 | + | 7.56164i | 0.0901359 | + | 0.277410i | 0.985956 | − | 0.167008i | \(-0.0534106\pi\) |
−0.895820 | + | 0.444418i | \(0.853411\pi\) | |||||||
\(744\) | 16.2556 | + | 11.8104i | 0.595959 | + | 0.432990i | ||||
\(745\) | −1.00944 | + | 0.733398i | −0.0369829 | + | 0.0268696i | ||||
\(746\) | 2.21328 | − | 6.81176i | 0.0810338 | − | 0.249396i | ||||
\(747\) | −41.5455 | −1.52007 | ||||||||
\(748\) | 3.21269 | − | 1.50483i | 0.117468 | − | 0.0550219i | ||||
\(749\) | 5.03736 | + | 15.5034i | 0.184061 | + | 0.566482i | ||||
\(750\) | 4.56144 | − | 3.31408i | 0.166560 | − | 0.121013i | ||||
\(751\) | 1.54763 | + | 4.76312i | 0.0564739 | + | 0.173809i | 0.975315 | − | 0.220820i | \(-0.0708733\pi\) |
−0.918841 | + | 0.394629i | \(0.870873\pi\) | |||||||
\(752\) | 0.0936287 | + | 0.288160i | 0.00341429 | + | 0.0105081i | ||||
\(753\) | −9.14491 | − | 28.1451i | −0.333259 | − | 1.02567i | ||||
\(754\) | −5.22106 | −0.190140 | ||||||||
\(755\) | 3.46864 | − | 2.52011i | 0.126237 | − | 0.0917164i | ||||
\(756\) | 10.8670 | + | 33.4453i | 0.395230 | + | 1.21639i | ||||
\(757\) | −1.02446 | − | 3.15297i | −0.0372347 | − | 0.114597i | 0.930712 | − | 0.365754i | \(-0.119189\pi\) |
−0.967946 | + | 0.251157i | \(0.919189\pi\) | |||||||
\(758\) | 4.69699 | + | 3.41256i | 0.170602 | + | 0.123950i | ||||
\(759\) | 35.7208 | + | 6.87977i | 1.29658 | + | 0.249720i | ||||
\(760\) | −0.146830 | − | 0.106678i | −0.00532608 | − | 0.00386962i | ||||
\(761\) | −52.5475 | −1.90484 | −0.952422 | − | 0.304783i | \(-0.901416\pi\) | ||||
−0.952422 | + | 0.304783i | \(0.901416\pi\) | |||||||
\(762\) | 37.7393 | 1.36715 | ||||||||
\(763\) | 10.8169 | − | 33.2910i | 0.391598 | − | 1.20522i | ||||
\(764\) | −0.945628 | − | 2.91034i | −0.0342116 | − | 0.105293i | ||||
\(765\) | −1.01705 | + | 0.738931i | −0.0367716 | + | 0.0267161i | ||||
\(766\) | 22.6723 | + | 16.4724i | 0.819185 | + | 0.595173i | ||||
\(767\) | 61.2110 | + | 44.4724i | 2.21020 | + | 1.60581i | ||||
\(768\) | 15.6457 | − | 48.1525i | 0.564565 | − | 1.73755i | ||||
\(769\) | −0.664227 | − | 2.04428i | −0.0239527 | − | 0.0737187i | 0.938366 | − | 0.345644i | \(-0.112340\pi\) |
−0.962318 | + | 0.271925i | \(0.912340\pi\) | |||||||
\(770\) | −0.606433 | + | 1.09848i | −0.0218543 | + | 0.0395864i | ||||
\(771\) | −6.03949 | − | 18.5876i | −0.217507 | − | 0.669417i | ||||
\(772\) | −0.319127 | − | 0.982171i | −0.0114856 | − | 0.0353491i | ||||
\(773\) | −13.7384 | − | 42.2823i | −0.494135 | − | 1.52079i | −0.818301 | − | 0.574790i | \(-0.805084\pi\) |
0.324166 | − | 0.946000i | \(-0.394916\pi\) | |||||||
\(774\) | −50.5911 | −1.81846 | ||||||||
\(775\) | −3.42710 | − | 10.5475i | −0.123105 | − | 0.378878i | ||||
\(776\) | 21.0139 | − | 15.2675i | 0.754354 | − | 0.548070i | ||||
\(777\) | 48.0942 | + | 34.9425i | 1.72537 | + | 1.25355i | ||||
\(778\) | −3.30087 | + | 10.1590i | −0.118342 | + | 0.364219i | ||||
\(779\) | 1.88534 | + | 0.711755i | 0.0675493 | + | 0.0255013i | ||||
\(780\) | −4.70361 | −0.168416 | ||||||||
\(781\) | −35.7223 | + | 16.7323i | −1.27825 | + | 0.598730i | ||||
\(782\) | 2.56495 | 0.0917223 | ||||||||
\(783\) | −11.1370 | + | 8.09153i | −0.398005 | + | 0.289168i | ||||
\(784\) | 0.0897083 | + | 0.0651769i | 0.00320387 | + | 0.00232775i | ||||
\(785\) | −0.0221910 | − | 0.0161227i | −0.000792030 | − | 0.000575443i | ||||
\(786\) | −2.32146 | −0.0828037 | ||||||||
\(787\) | 0.398218 | + | 0.289322i | 0.0141949 | + | 0.0103132i | 0.594860 | − | 0.803829i | \(-0.297207\pi\) |
−0.580665 | + | 0.814142i | \(0.697207\pi\) | |||||||
\(788\) | 7.86374 | + | 24.2021i | 0.280134 | + | 0.862164i | ||||
\(789\) | 65.7292 | 2.34002 | ||||||||
\(790\) | −0.522312 | + | 1.60751i | −0.0185830 | + | 0.0571927i | ||||
\(791\) | 6.12560 | − | 18.8527i | 0.217801 | − | 0.670324i | ||||
\(792\) | −60.5936 | + | 28.3820i | −2.15310 | + | 1.00851i | ||||
\(793\) | 1.16613 | 0.0414106 | ||||||||
\(794\) | −19.6762 | + | 14.2956i | −0.698282 | + | 0.507331i | ||||
\(795\) | 0.368596 | − | 0.267800i | 0.0130727 | − | 0.00949790i | ||||
\(796\) | 11.3374 | − | 8.23711i | 0.401844 | − | 0.291957i | ||||
\(797\) | 1.68735 | − | 5.19314i | 0.0597692 | − | 0.183951i | −0.916714 | − | 0.399544i | \(-0.869169\pi\) |
0.976483 | + | 0.215593i | \(0.0691685\pi\) | |||||||
\(798\) | 1.85475 | 0.0656575 | ||||||||
\(799\) | 1.78650 | − | 5.49830i | 0.0632020 | − | 0.194516i | ||||
\(800\) | −22.7679 | + | 16.5419i | −0.804967 | + | 0.584843i | ||||
\(801\) | 15.6724 | + | 48.2346i | 0.553756 | + | 1.70429i | ||||
\(802\) | 16.7663 | − | 12.1814i | 0.592038 | − | 0.430141i | ||||
\(803\) | −16.1065 | − | 3.10208i | −0.568385 | − | 0.109470i | ||||
\(804\) | −46.4801 | − | 33.7697i | −1.63923 | − | 1.19097i | ||||
\(805\) | 1.21310 | − | 0.881370i | 0.0427562 | − | 0.0310642i | ||||
\(806\) | 3.47400 | − | 10.6919i | 0.122366 | − | 0.376605i | ||||
\(807\) | −35.3448 | − | 25.6795i | −1.24420 | − | 0.903962i | ||||
\(808\) | −3.37973 | − | 10.4017i | −0.118898 | − | 0.365932i | ||||
\(809\) | −19.7480 | − | 14.3477i | −0.694302 | − | 0.504440i | 0.183770 | − | 0.982969i | \(-0.441170\pi\) |
−0.878071 | + | 0.478530i | \(0.841170\pi\) | |||||||
\(810\) | 2.98391 | − | 2.16794i | 0.104844 | − | 0.0761736i | ||||
\(811\) | −2.31386 | + | 7.12133i | −0.0812507 | + | 0.250064i | −0.983427 | − | 0.181303i | \(-0.941969\pi\) |
0.902177 | + | 0.431367i | \(0.141969\pi\) | |||||||
\(812\) | 0.851869 | − | 2.62178i | 0.0298947 | − | 0.0920066i | ||||
\(813\) | −3.31716 | − | 2.41006i | −0.116338 | − | 0.0845245i | ||||
\(814\) | −12.1901 | + | 22.0809i | −0.427264 | + | 0.773936i | ||||
\(815\) | −0.397616 | + | 1.22374i | −0.0139279 | + | 0.0428656i | ||||
\(816\) | 0.0995742 | − | 0.0723449i | 0.00348579 | − | 0.00253258i | ||||
\(817\) | 0.791673 | − | 2.43652i | 0.0276971 | − | 0.0852430i | ||||
\(818\) | −9.57002 | − | 6.95303i | −0.334608 | − | 0.243107i | ||||
\(819\) | 71.3852 | − | 51.8644i | 2.49440 | − | 1.81229i | ||||
\(820\) | −1.02033 | + | 1.27437i | −0.0356313 | + | 0.0445029i | ||||
\(821\) | −13.9066 | − | 42.8002i | −0.485345 | − | 1.49374i | −0.831481 | − | 0.555553i | \(-0.812507\pi\) |
0.346136 | − | 0.938184i | \(-0.387493\pi\) | |||||||
\(822\) | 0.724707 | + | 2.23042i | 0.0252771 | + | 0.0777948i | ||||
\(823\) | −7.33433 | − | 5.32870i | −0.255659 | − | 0.185747i | 0.452572 | − | 0.891728i | \(-0.350506\pi\) |
−0.708231 | + | 0.705981i | \(0.750506\pi\) | |||||||
\(824\) | 13.6534 | − | 42.0208i | 0.475638 | − | 1.46386i | ||||
\(825\) | 51.4645 | + | 9.91199i | 1.79176 | + | 0.345091i | ||||
\(826\) | 19.5532 | − | 14.2062i | 0.680342 | − | 0.494298i | ||||
\(827\) | −15.2512 | − | 46.9383i | −0.530335 | − | 1.63220i | −0.753519 | − | 0.657427i | \(-0.771645\pi\) |
0.223184 | − | 0.974776i | \(-0.428355\pi\) | |||||||
\(828\) | 30.6953 | 1.06673 | ||||||||
\(829\) | −4.02928 | − | 12.4008i | −0.139943 | − | 0.430699i | 0.856383 | − | 0.516340i | \(-0.172706\pi\) |
−0.996326 | + | 0.0856414i | \(0.972706\pi\) | |||||||
\(830\) | −0.834182 | − | 0.606069i | −0.0289549 | − | 0.0210370i | ||||
\(831\) | −21.5992 | − | 15.6927i | −0.749268 | − | 0.544375i | ||||
\(832\) | −28.0070 | −0.970969 | ||||||||
\(833\) | −0.653811 | − | 2.01222i | −0.0226532 | − | 0.0697194i | ||||
\(834\) | 45.5739 | + | 33.1114i | 1.57810 | + | 1.14655i | ||||
\(835\) | 1.18522 | − | 3.64775i | 0.0410164 | − | 0.126236i | ||||
\(836\) | −0.160734 | − | 1.29074i | −0.00555909 | − | 0.0446412i | ||||
\(837\) | −9.15974 | − | 28.1908i | −0.316607 | − | 0.974415i | ||||
\(838\) | 19.4106 | 0.670527 | ||||||||
\(839\) | 11.1217 | − | 8.08039i | 0.383964 | − | 0.278966i | −0.379014 | − | 0.925391i | \(-0.623737\pi\) |
0.762977 | + | 0.646425i | \(0.223737\pi\) | |||||||
\(840\) | −1.20951 | + | 3.72249i | −0.0417321 | + | 0.128438i | ||||
\(841\) | −27.9209 | −0.962789 | ||||||||
\(842\) | 10.9356 | 0.376867 | ||||||||
\(843\) | 22.0654 | + | 16.0314i | 0.759971 | + | 0.552151i | ||||
\(844\) | 2.27941 | 0.0784606 | ||||||||
\(845\) | 1.29655 | + | 3.99037i | 0.0446026 | + | 0.137273i | ||||
\(846\) | −12.9346 | + | 39.8087i | −0.444701 | + | 1.36865i | ||||
\(847\) | −22.7102 | + | 5.74521i | −0.780332 | + | 0.197408i | ||||
\(848\) | −0.0254294 | + | 0.0184755i | −0.000873248 | + | 0.000634452i | ||||
\(849\) | −30.0663 | + | 21.8444i | −1.03187 | + | 0.749699i | ||||
\(850\) | 3.69543 | 0.126752 | ||||||||
\(851\) | 24.3850 | − | 17.7168i | 0.835908 | − | 0.607323i | ||||
\(852\) | −38.2147 | + | 27.7646i | −1.30921 | + | 0.951200i | ||||
\(853\) | 31.2833 | + | 22.7286i | 1.07112 | + | 0.778214i | 0.976113 | − | 0.217263i | \(-0.0697128\pi\) |
0.0950064 | + | 0.995477i | \(0.469713\pi\) | |||||||
\(854\) | 0.115112 | − | 0.354277i | 0.00393904 | − | 0.0121231i | ||||
\(855\) | 0.142432 | + | 0.438359i | 0.00487106 | + | 0.0149916i | ||||
\(856\) | −17.4541 | + | 12.6811i | −0.596569 | + | 0.433433i | ||||
\(857\) | −13.8399 | + | 42.5948i | −0.472762 | + | 1.45501i | 0.376191 | + | 0.926542i | \(0.377234\pi\) |
−0.848952 | + | 0.528469i | \(0.822766\pi\) | |||||||
\(858\) | 36.2996 | + | 38.7928i | 1.23925 | + | 1.32436i | ||||
\(859\) | −3.01842 | + | 2.19301i | −0.102987 | + | 0.0748246i | −0.638087 | − | 0.769964i | \(-0.720274\pi\) |
0.535100 | + | 0.844789i | \(0.320274\pi\) | |||||||
\(860\) | 1.67901 | + | 1.21988i | 0.0572539 | + | 0.0415974i | ||||
\(861\) | 2.03406 | − | 43.4127i | 0.0693207 | − | 1.47950i | ||||
\(862\) | 6.80852 | + | 20.9545i | 0.231899 | + | 0.713712i | ||||
\(863\) | −11.1328 | + | 34.2632i | −0.378965 | + | 1.16633i | 0.561799 | + | 0.827273i | \(0.310109\pi\) |
−0.940764 | + | 0.339061i | \(0.889891\pi\) | |||||||
\(864\) | −60.8527 | + | 44.2121i | −2.07025 | + | 1.50413i | ||||
\(865\) | −1.86444 | −0.0633928 | ||||||||
\(866\) | −0.00627525 | − | 0.00455923i | −0.000213242 | − | 0.000154929i | ||||
\(867\) | 51.8330 | 1.76034 | ||||||||
\(868\) | 4.80216 | + | 3.48897i | 0.162996 | + | 0.118423i | ||||
\(869\) | −28.5764 | + | 13.3852i | −0.969387 | + | 0.454061i | ||||
\(870\) | −0.588170 | −0.0199408 | ||||||||
\(871\) | −25.8762 | + | 79.6389i | −0.876783 | + | 2.69846i | ||||
\(872\) | 46.3276 | 1.56885 | ||||||||
\(873\) | −65.9653 | −2.23259 | ||||||||
\(874\) | 0.290602 | − | 0.894382i | 0.00982977 | − | 0.0302529i | ||||
\(875\) | 3.51029 | − | 2.55038i | 0.118670 | − | 0.0862185i | ||||
\(876\) | −19.6413 | −0.663617 | ||||||||
\(877\) | 31.8505 | − | 23.1407i | 1.07551 | − | 0.781407i | 0.0986191 | − | 0.995125i | \(-0.468557\pi\) |
0.976895 | + | 0.213718i | \(0.0685575\pi\) | |||||||
\(878\) | −1.42457 | + | 4.38436i | −0.0480768 | + | 0.147965i | ||||
\(879\) | 45.7109 | − | 33.2109i | 1.54179 | − | 1.12018i | ||||
\(880\) | 0.0299773 | + | 0.00577358i | 0.00101053 | + | 0.000194627i | ||||
\(881\) | 33.2817 | + | 24.1806i | 1.12129 | + | 0.814664i | 0.984404 | − | 0.175922i | \(-0.0562908\pi\) |
0.136885 | + | 0.990587i | \(0.456291\pi\) | |||||||
\(882\) | 4.73371 | + | 14.5689i | 0.159392 | + | 0.490559i | ||||
\(883\) | −17.7151 | + | 12.8708i | −0.596161 | + | 0.433137i | −0.844514 | − | 0.535533i | \(-0.820111\pi\) |
0.248353 | + | 0.968670i | \(0.420111\pi\) | |||||||
\(884\) | −5.00922 | − | 3.63941i | −0.168478 | − | 0.122407i | ||||
\(885\) | 6.89563 | + | 5.00996i | 0.231794 | + | 0.168408i | ||||
\(886\) | −28.2721 | −0.949821 | ||||||||
\(887\) | 13.3922 | 0.449666 | 0.224833 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224833 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(888\) | −24.3129 | + | 74.8273i | −0.815886 | + | 2.51104i | ||||
\(889\) | 29.0426 | 0.974057 | ||||||||
\(890\) | −0.388968 | + | 1.19712i | −0.0130382 | + | 0.0401276i | ||||
\(891\) | 67.6163 | + | 13.0228i | 2.26523 | + | 0.436281i | ||||
\(892\) | 6.20609 | + | 19.1004i | 0.207795 | + | 0.639529i | ||||
\(893\) | −1.71482 | − | 1.24589i | −0.0573842 | − | 0.0416921i | ||||
\(894\) | 16.8760 | 0.564418 | ||||||||
\(895\) | 1.02564 | − | 3.15660i | 0.0342834 | − | 0.105513i | ||||
\(896\) | 4.70602 | − | 14.4836i | 0.157217 | − | 0.483864i | ||||
\(897\) | −19.6192 | − | 60.3818i | −0.655067 | − | 2.01609i | ||||
\(898\) | −32.1761 | −1.07373 | ||||||||
\(899\) | −0.718033 | + | 2.20988i | −0.0239477 | + | 0.0737036i | ||||
\(900\) | 44.2241 | 1.47414 | ||||||||
\(901\) | 0.599754 | 0.0199807 | ||||||||
\(902\) | 18.3845 | − | 1.41972i | 0.612138 | − | 0.0472714i | ||||
\(903\) | −55.2503 | −1.83861 | ||||||||
\(904\) | 26.2353 | 0.872572 | ||||||||
\(905\) | −0.948436 | + | 2.91899i | −0.0315271 | + | 0.0970304i | ||||
\(906\) | −57.9896 | −1.92658 | ||||||||
\(907\) | 5.63967 | + | 17.3571i | 0.187262 | + | 0.576333i | 0.999980 | − | 0.00632404i | \(-0.00201302\pi\) |
−0.812718 | + | 0.582657i | \(0.802013\pi\) | |||||||
\(908\) | 3.79022 | − | 11.6651i | 0.125783 | − | 0.387120i | ||||
\(909\) | −8.58319 | + | 26.4163i | −0.284686 | + | 0.876175i | ||||
\(910\) | 2.18993 | 0.0725954 | ||||||||
\(911\) | −33.1800 | − | 24.1067i | −1.09930 | − | 0.798690i | −0.118357 | − | 0.992971i | \(-0.537763\pi\) |
−0.980946 | + | 0.194281i | \(0.937763\pi\) | |||||||
\(912\) | −0.0139447 | − | 0.0429175i | −0.000461756 | − | 0.00142114i | ||||
\(913\) | −2.37882 | − | 19.1027i | −0.0787274 | − | 0.632206i | ||||
\(914\) | 3.66663 | − | 11.2847i | 0.121281 | − | 0.373265i | ||||
\(915\) | 0.131369 | 0.00434292 | ||||||||
\(916\) | 1.33833 | − | 4.11895i | 0.0442196 | − | 0.136094i | ||||
\(917\) | −1.78650 | −0.0589954 | ||||||||
\(918\) | 9.87693 | 0.325987 | ||||||||
\(919\) | 8.43530 | + | 6.12860i | 0.278255 | + | 0.202164i | 0.718156 | − | 0.695882i | \(-0.244986\pi\) |
−0.439901 | + | 0.898046i | \(0.644986\pi\) | |||||||
\(920\) | 1.60552 | + | 1.16648i | 0.0529325 | + | 0.0384577i | ||||
\(921\) | −74.4325 | + | 54.0784i | −2.45263 | + | 1.78194i | ||||
\(922\) | 6.64885 | + | 20.4631i | 0.218968 | + | 0.673915i | ||||
\(923\) | 55.6981 | + | 40.4670i | 1.83333 | + | 1.33199i | ||||
\(924\) | −25.4027 | + | 11.8986i | −0.835686 | + | 0.391435i | ||||
\(925\) | 35.1326 | − | 25.5253i | 1.15515 | − | 0.839267i | ||||
\(926\) | −1.68381 | + | 5.18224i | −0.0553335 | + | 0.170299i | ||||
\(927\) | −90.7784 | + | 65.9544i | −2.98155 | + | 2.16623i | ||||
\(928\) | 5.89636 | 0.193557 | ||||||||
\(929\) | 30.8016 | − | 22.3787i | 1.01057 | − | 0.734221i | 0.0462401 | − | 0.998930i | \(-0.485276\pi\) |
0.964328 | + | 0.264710i | \(0.0852761\pi\) | |||||||
\(930\) | 0.391357 | − | 1.20447i | 0.0128331 | − | 0.0394963i | ||||
\(931\) | −0.775726 | −0.0254234 | ||||||||
\(932\) | 9.59074 | 0.314155 | ||||||||
\(933\) | 13.0349 | − | 40.1171i | 0.426742 | − | 1.31338i | ||||
\(934\) | −27.1923 | −0.889761 | ||||||||
\(935\) | −0.397995 | − | 0.425331i | −0.0130158 | − | 0.0139098i | ||||
\(936\) | 94.4773 | + | 68.6418i | 3.08809 | + | 2.24363i | ||||
\(937\) | 21.0919 | 0.689043 | 0.344522 | − | 0.938778i | \(-0.388041\pi\) | ||||
0.344522 | + | 0.938778i | \(0.388041\pi\) | |||||||
\(938\) | 21.6404 | + | 15.7226i | 0.706583 | + | 0.513363i | ||||
\(939\) | −101.376 | −3.30829 | ||||||||
\(940\) | 1.38916 | − | 1.00928i | 0.0453093 | − | 0.0329192i | ||||
\(941\) | 0.196262 | − | 0.604034i | 0.00639797 | − | 0.0196909i | −0.947807 | − | 0.318846i | \(-0.896705\pi\) |
0.954205 | + | 0.299155i | \(0.0967048\pi\) | |||||||
\(942\) | 0.114644 | + | 0.352837i | 0.00373529 | + | 0.0114960i | ||||
\(943\) | −20.6154 | − | 7.78274i | −0.671329 | − | 0.253441i | ||||
\(944\) | −0.475729 | − | 0.345637i | −0.0154836 | − | 0.0112495i | ||||
\(945\) | 4.67133 | − | 3.39392i | 0.151958 | − | 0.110404i | ||||
\(946\) | −2.89675 | − | 23.2618i | −0.0941815 | − | 0.756307i | ||||
\(947\) | 10.8774 | − | 33.4772i | 0.353468 | − | 1.08786i | −0.603425 | − | 0.797420i | \(-0.706198\pi\) |
0.956893 | − | 0.290442i | \(-0.0938023\pi\) | |||||||
\(948\) | −30.5702 | + | 22.2105i | −0.992873 | + | 0.721364i | ||||
\(949\) | 8.84630 | + | 27.2261i | 0.287163 | + | 0.883797i | ||||
\(950\) | 0.418684 | − | 1.28858i | 0.0135839 | − | 0.0418069i | ||||
\(951\) | −71.7075 | − | 52.0985i | −2.32527 | − | 1.68941i | ||||
\(952\) | −4.16837 | + | 3.02850i | −0.135098 | + | 0.0981541i | ||||
\(953\) | −15.2306 | + | 11.0657i | −0.493369 | + | 0.358453i | −0.806478 | − | 0.591264i | \(-0.798629\pi\) |
0.313110 | + | 0.949717i | \(0.398629\pi\) | |||||||
\(954\) | −4.34233 | −0.140588 | ||||||||
\(955\) | −0.406490 | + | 0.295332i | −0.0131537 | + | 0.00955672i | ||||
\(956\) | −10.2864 | + | 7.47348i | −0.332685 | + | 0.241709i | ||||
\(957\) | −7.50269 | − | 8.01799i | −0.242527 | − | 0.259185i | ||||
\(958\) | 9.23871 | − | 28.4338i | 0.298489 | − | 0.918655i | ||||
\(959\) | 0.557705 | + | 1.71644i | 0.0180092 | + | 0.0554267i | ||||
\(960\) | −3.15508 | −0.101830 | ||||||||
\(961\) | 21.0318 | + | 15.2805i | 0.678446 | + | 0.492920i | ||||
\(962\) | 44.0206 | 1.41928 | ||||||||
\(963\) | 54.7907 | 1.76561 | ||||||||
\(964\) | 10.5870 | − | 32.5836i | 0.340986 | − | 1.04945i | ||||
\(965\) | −0.137181 | + | 0.0996675i | −0.00441600 | + | 0.00320841i | ||||
\(966\) | −20.2809 | −0.652528 | ||||||||
\(967\) | −11.4986 | − | 35.3890i | −0.369770 | − | 1.13804i | −0.946940 | − | 0.321411i | \(-0.895843\pi\) |
0.577170 | − | 0.816624i | \(-0.304157\pi\) | |||||||
\(968\) | −16.5196 | − | 26.2359i | −0.530959 | − | 0.843253i | ||||
\(969\) | −0.266076 | + | 0.818897i | −0.00854758 | + | 0.0263068i | ||||
\(970\) | −1.32450 | − | 0.962306i | −0.0425271 | − | 0.0308978i | ||||
\(971\) | 4.55553 | + | 14.0205i | 0.146194 | + | 0.449939i | 0.997163 | − | 0.0752777i | \(-0.0239843\pi\) |
−0.850969 | + | 0.525217i | \(0.823984\pi\) | |||||||
\(972\) | 32.9163 | 1.05579 | ||||||||
\(973\) | 35.0718 | + | 25.4812i | 1.12435 | + | 0.816889i | ||||
\(974\) | 7.62392 | + | 5.53910i | 0.244286 | + | 0.177484i | ||||
\(975\) | −28.2663 | − | 86.9948i | −0.905247 | − | 2.78606i | ||||
\(976\) | −0.00906313 | −0.000290104 | ||||||||
\(977\) | 5.73730 | + | 17.6576i | 0.183553 | + | 0.564917i | 0.999920 | − | 0.0126156i | \(-0.00401578\pi\) |
−0.816368 | + | 0.577532i | \(0.804016\pi\) | |||||||
\(978\) | 14.0795 | − | 10.2294i | 0.450213 | − | 0.327099i | ||||
\(979\) | −21.2809 | + | 9.96799i | −0.680142 | + | 0.318578i | ||||
\(980\) | 0.194189 | − | 0.597652i | 0.00620314 | − | 0.0190913i | ||||
\(981\) | −95.1841 | − | 69.1553i | −3.03900 | − | 2.20796i | ||||
\(982\) | −6.86132 | − | 21.1170i | −0.218954 | − | 0.673870i | ||||
\(983\) | 8.90157 | + | 27.3962i | 0.283916 | + | 0.873803i | 0.986722 | + | 0.162421i | \(0.0519304\pi\) |
−0.702806 | + | 0.711382i | \(0.748070\pi\) | |||||||
\(984\) | 55.4758 | − | 15.1946i | 1.76850 | − | 0.484386i | ||||
\(985\) | 3.38032 | − | 2.45595i | 0.107706 | − | 0.0782530i | ||||
\(986\) | −0.626385 | − | 0.455095i | −0.0199481 | − | 0.0144932i | ||||
\(987\) | −14.1258 | + | 43.4748i | −0.449630 | + | 1.38382i | ||||
\(988\) | −1.83657 | + | 1.33435i | −0.0584292 | + | 0.0424513i | ||||
\(989\) | −8.65660 | + | 26.6423i | −0.275264 | + | 0.847175i | ||||
\(990\) | 2.88156 | + | 3.07947i | 0.0915820 | + | 0.0978721i | ||||
\(991\) | −20.3863 | − | 14.8115i | −0.647592 | − | 0.470503i | 0.214858 | − | 0.976645i | \(-0.431071\pi\) |
−0.862450 | + | 0.506142i | \(0.831071\pi\) | |||||||
\(992\) | −3.92333 | + | 12.0748i | −0.124566 | + | 0.383374i | ||||
\(993\) | −16.3239 | + | 50.2399i | −0.518024 | + | 1.59431i | ||||
\(994\) | 17.7922 | − | 12.9268i | 0.564333 | − | 0.410012i | ||||
\(995\) | −1.86152 | − | 1.35247i | −0.0590142 | − | 0.0428763i | ||||
\(996\) | −7.12325 | − | 21.9231i | −0.225709 | − | 0.694660i | ||||
\(997\) | 1.70520 | + | 1.23890i | 0.0540041 | + | 0.0392363i | 0.614460 | − | 0.788948i | \(-0.289374\pi\) |
−0.560456 | + | 0.828184i | \(0.689374\pi\) | |||||||
\(998\) | 2.69167 | − | 8.28412i | 0.0852035 | − | 0.262229i | ||||
\(999\) | 93.9003 | − | 68.2225i | 2.97087 | − | 2.15847i |
(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 | 451.2.l.a.37.16 | yes | 160 | |
11.3 | even | 5 | 451.2.i.a.201.16 | yes | 160 | ||
41.10 | even | 5 | 451.2.i.a.92.16 | ✓ | 160 | ||
451.256 | even | 5 | inner | 451.2.l.a.256.16 | yes | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
451.2.i.a.92.16 | ✓ | 160 | 41.10 | even | 5 | ||
451.2.i.a.201.16 | yes | 160 | 11.3 | even | 5 | ||
451.2.l.a.37.16 | yes | 160 | 1.1 | even | 1 | trivial | |
451.2.l.a.256.16 | yes | 160 | 451.256 | even | 5 | inner |