Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 22.3 | ||
Root | \(-0.623490 + 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.22 |
Dual form | 507.2.e.j.484.3 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.623490 | − | 1.07992i | 0.440874 | − | 0.763616i | −0.556881 | − | 0.830593i | \(-0.688002\pi\) |
0.997755 | + | 0.0669766i | \(0.0213353\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.222521 | + | 0.385418i | 0.111260 | + | 0.192709i | ||||
\(5\) | 2.80194 | 1.25306 | 0.626532 | − | 0.779395i | \(-0.284474\pi\) | ||||
0.626532 | + | 0.779395i | \(0.284474\pi\) | |||||||
\(6\) | 0.623490 | + | 1.07992i | 0.254539 | + | 0.440874i | ||||
\(7\) | −2.40097 | − | 4.15860i | −0.907481 | − | 1.57180i | −0.817552 | − | 0.575855i | \(-0.804669\pi\) |
−0.0899290 | − | 0.995948i | \(-0.528664\pi\) | |||||||
\(8\) | 3.04892 | 1.07796 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.74698 | − | 3.02586i | 0.552443 | − | 0.956860i | ||||
\(11\) | 0.733406 | − | 1.27030i | 0.221130 | − | 0.383009i | −0.734021 | − | 0.679127i | \(-0.762359\pi\) |
0.955151 | + | 0.296118i | \(0.0956921\pi\) | |||||||
\(12\) | −0.445042 | −0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.98792 | −1.60034 | ||||||||
\(15\) | −1.40097 | + | 2.42655i | −0.361729 | + | 0.626532i | ||||
\(16\) | 1.45593 | − | 2.52174i | 0.363982 | − | 0.630435i | ||||
\(17\) | 1.22252 | + | 2.11747i | 0.296505 | + | 0.513562i | 0.975334 | − | 0.220735i | \(-0.0708456\pi\) |
−0.678829 | + | 0.734296i | \(0.737512\pi\) | |||||||
\(18\) | −1.24698 | −0.293916 | ||||||||
\(19\) | 1.27144 | + | 2.20220i | 0.291688 | + | 0.505218i | 0.974209 | − | 0.225648i | \(-0.0724498\pi\) |
−0.682521 | + | 0.730866i | \(0.739116\pi\) | |||||||
\(20\) | 0.623490 | + | 1.07992i | 0.139417 | + | 0.241477i | ||||
\(21\) | 4.80194 | 1.04787 | ||||||||
\(22\) | −0.914542 | − | 1.58403i | −0.194981 | − | 0.337717i | ||||
\(23\) | 1.75786 | − | 3.04471i | 0.366540 | − | 0.634866i | −0.622482 | − | 0.782634i | \(-0.713876\pi\) |
0.989022 | + | 0.147768i | \(0.0472089\pi\) | |||||||
\(24\) | −1.52446 | + | 2.64044i | −0.311179 | + | 0.538978i | ||||
\(25\) | 2.85086 | 0.570171 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.06853 | − | 1.85075i | 0.201934 | − | 0.349759i | ||||
\(29\) | −0.925428 | + | 1.60289i | −0.171848 | + | 0.297649i | −0.939066 | − | 0.343737i | \(-0.888307\pi\) |
0.767218 | + | 0.641386i | \(0.221640\pi\) | |||||||
\(30\) | 1.74698 | + | 3.02586i | 0.318953 | + | 0.552443i | ||||
\(31\) | 7.63102 | 1.37057 | 0.685286 | − | 0.728274i | \(-0.259677\pi\) | ||||
0.685286 | + | 0.728274i | \(0.259677\pi\) | |||||||
\(32\) | 1.23341 | + | 2.13632i | 0.218037 | + | 0.377652i | ||||
\(33\) | 0.733406 | + | 1.27030i | 0.127670 | + | 0.221130i | ||||
\(34\) | 3.04892 | 0.522885 | ||||||||
\(35\) | −6.72737 | − | 11.6521i | −1.13713 | − | 1.96957i | ||||
\(36\) | 0.222521 | − | 0.385418i | 0.0370868 | − | 0.0642363i | ||||
\(37\) | −2.27748 | + | 3.94471i | −0.374415 | + | 0.648506i | −0.990239 | − | 0.139377i | \(-0.955490\pi\) |
0.615824 | + | 0.787884i | \(0.288823\pi\) | |||||||
\(38\) | 3.17092 | 0.514390 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.54288 | 1.35075 | ||||||||
\(41\) | 0.623490 | − | 1.07992i | 0.0973727 | − | 0.168655i | −0.813224 | − | 0.581951i | \(-0.802289\pi\) |
0.910596 | + | 0.413297i | \(0.135623\pi\) | |||||||
\(42\) | 2.99396 | − | 5.18569i | 0.461978 | − | 0.800169i | ||||
\(43\) | −1.19202 | − | 2.06464i | −0.181782 | − | 0.314855i | 0.760706 | − | 0.649097i | \(-0.224853\pi\) |
−0.942487 | + | 0.334242i | \(0.891520\pi\) | |||||||
\(44\) | 0.652793 | 0.0984122 | ||||||||
\(45\) | −1.40097 | − | 2.42655i | −0.208844 | − | 0.361729i | ||||
\(46\) | −2.19202 | − | 3.79669i | −0.323196 | − | 0.559792i | ||||
\(47\) | −12.8170 | −1.86955 | −0.934776 | − | 0.355238i | \(-0.884400\pi\) | ||||
−0.934776 | + | 0.355238i | \(0.884400\pi\) | |||||||
\(48\) | 1.45593 | + | 2.52174i | 0.210145 | + | 0.363982i | ||||
\(49\) | −8.02930 | + | 13.9072i | −1.14704 | + | 1.98674i | ||||
\(50\) | 1.77748 | − | 3.07868i | 0.251374 | − | 0.435392i | ||||
\(51\) | −2.44504 | −0.342374 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.85086 | −1.21576 | −0.607879 | − | 0.794030i | \(-0.707980\pi\) | ||||
−0.607879 | + | 0.794030i | \(0.707980\pi\) | |||||||
\(54\) | 0.623490 | − | 1.07992i | 0.0848462 | − | 0.146958i | ||||
\(55\) | 2.05496 | − | 3.55929i | 0.277090 | − | 0.479935i | ||||
\(56\) | −7.32036 | − | 12.6792i | −0.978224 | − | 1.69433i | ||||
\(57\) | −2.54288 | −0.336812 | ||||||||
\(58\) | 1.15399 | + | 1.99877i | 0.151526 | + | 0.262451i | ||||
\(59\) | 1.08815 | + | 1.88472i | 0.141665 | + | 0.245370i | 0.928124 | − | 0.372272i | \(-0.121421\pi\) |
−0.786459 | + | 0.617642i | \(0.788088\pi\) | |||||||
\(60\) | −1.24698 | −0.160984 | ||||||||
\(61\) | 3.91454 | + | 6.78019i | 0.501206 | + | 0.868114i | 0.999999 | + | 0.00139289i | \(0.000443372\pi\) |
−0.498793 | + | 0.866721i | \(0.666223\pi\) | |||||||
\(62\) | 4.75786 | − | 8.24086i | 0.604249 | − | 1.04659i | ||||
\(63\) | −2.40097 | + | 4.15860i | −0.302494 | + | 0.523934i | ||||
\(64\) | 8.89977 | 1.11247 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.82908 | 0.225145 | ||||||||
\(67\) | −1.79105 | + | 3.10219i | −0.218812 | + | 0.378993i | −0.954445 | − | 0.298387i | \(-0.903551\pi\) |
0.735633 | + | 0.677380i | \(0.236885\pi\) | |||||||
\(68\) | −0.544073 | + | 0.942362i | −0.0659785 | + | 0.114278i | ||||
\(69\) | 1.75786 | + | 3.04471i | 0.211622 | + | 0.366540i | ||||
\(70\) | −16.7778 | −2.00533 | ||||||||
\(71\) | −4.41939 | − | 7.65460i | −0.524485 | − | 0.908434i | −0.999594 | − | 0.0285072i | \(-0.990925\pi\) |
0.475109 | − | 0.879927i | \(-0.342409\pi\) | |||||||
\(72\) | −1.52446 | − | 2.64044i | −0.179659 | − | 0.311179i | ||||
\(73\) | 7.69202 | 0.900283 | 0.450142 | − | 0.892957i | \(-0.351374\pi\) | ||||
0.450142 | + | 0.892957i | \(0.351374\pi\) | |||||||
\(74\) | 2.83997 | + | 4.91897i | 0.330140 | + | 0.571819i | ||||
\(75\) | −1.42543 | + | 2.46891i | −0.164594 | + | 0.285086i | ||||
\(76\) | −0.565843 | + | 0.980069i | −0.0649067 | + | 0.112422i | ||||
\(77\) | −7.04354 | −0.802686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.02177 | −0.452485 | −0.226242 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226242 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(80\) | 4.07942 | − | 7.06576i | 0.456093 | − | 0.789976i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.777479 | − | 1.34663i | −0.0858582 | − | 0.148711i | ||||
\(83\) | 0.652793 | 0.0716533 | 0.0358267 | − | 0.999358i | \(-0.488594\pi\) | ||||
0.0358267 | + | 0.999358i | \(0.488594\pi\) | |||||||
\(84\) | 1.06853 | + | 1.85075i | 0.116586 | + | 0.201934i | ||||
\(85\) | 3.42543 | + | 5.93301i | 0.371540 | + | 0.643526i | ||||
\(86\) | −2.97285 | −0.320571 | ||||||||
\(87\) | −0.925428 | − | 1.60289i | −0.0992162 | − | 0.171848i | ||||
\(88\) | 2.23609 | − | 3.87303i | 0.238368 | − | 0.412866i | ||||
\(89\) | 3.14795 | − | 5.45241i | 0.333682 | − | 0.577954i | −0.649549 | − | 0.760320i | \(-0.725042\pi\) |
0.983231 | + | 0.182366i | \(0.0583755\pi\) | |||||||
\(90\) | −3.49396 | −0.368296 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.56465 | 0.163126 | ||||||||
\(93\) | −3.81551 | + | 6.60866i | −0.395650 | + | 0.685286i | ||||
\(94\) | −7.99127 | + | 13.8413i | −0.824237 | + | 1.42762i | ||||
\(95\) | 3.56249 | + | 6.17042i | 0.365504 | + | 0.633071i | ||||
\(96\) | −2.46681 | −0.251768 | ||||||||
\(97\) | −5.01573 | − | 8.68750i | −0.509270 | − | 0.882082i | −0.999942 | − | 0.0107376i | \(-0.996582\pi\) |
0.490672 | − | 0.871344i | \(-0.336751\pi\) | |||||||
\(98\) | 10.0124 | + | 17.3419i | 1.01140 | + | 1.75180i | ||||
\(99\) | −1.46681 | −0.147420 | ||||||||
\(100\) | 0.634375 | + | 1.09877i | 0.0634375 | + | 0.109877i | ||||
\(101\) | −6.94385 | + | 12.0271i | −0.690938 | + | 1.19674i | 0.280592 | + | 0.959827i | \(0.409469\pi\) |
−0.971531 | + | 0.236913i | \(0.923864\pi\) | |||||||
\(102\) | −1.52446 | + | 2.64044i | −0.150944 | + | 0.261443i | ||||
\(103\) | −17.4034 | −1.71481 | −0.857405 | − | 0.514642i | \(-0.827925\pi\) | ||||
−0.857405 | + | 0.514642i | \(0.827925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.4547 | 1.31305 | ||||||||
\(106\) | −5.51842 | + | 9.55818i | −0.535996 | + | 0.928373i | ||||
\(107\) | −5.27628 | + | 9.13879i | −0.510077 | + | 0.883480i | 0.489854 | + | 0.871804i | \(0.337050\pi\) |
−0.999932 | + | 0.0116758i | \(0.996283\pi\) | |||||||
\(108\) | 0.222521 | + | 0.385418i | 0.0214121 | + | 0.0370868i | ||||
\(109\) | −1.07069 | −0.102553 | −0.0512766 | − | 0.998684i | \(-0.516329\pi\) | ||||
−0.0512766 | + | 0.998684i | \(0.516329\pi\) | |||||||
\(110\) | −2.56249 | − | 4.43836i | −0.244324 | − | 0.423181i | ||||
\(111\) | −2.27748 | − | 3.94471i | −0.216169 | − | 0.374415i | ||||
\(112\) | −13.9825 | −1.32123 | ||||||||
\(113\) | 8.26540 | + | 14.3161i | 0.777543 | + | 1.34674i | 0.933354 | + | 0.358957i | \(0.116868\pi\) |
−0.155811 | + | 0.987787i | \(0.549799\pi\) | |||||||
\(114\) | −1.58546 | + | 2.74609i | −0.148492 | + | 0.257195i | ||||
\(115\) | 4.92543 | − | 8.53109i | 0.459298 | − | 0.795528i | ||||
\(116\) | −0.823708 | −0.0764794 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.71379 | 0.249825 | ||||||||
\(119\) | 5.87047 | − | 10.1680i | 0.538145 | − | 0.932095i | ||||
\(120\) | −4.27144 | + | 7.39835i | −0.389927 | + | 0.675374i | ||||
\(121\) | 4.42423 | + | 7.66299i | 0.402203 | + | 0.696636i | ||||
\(122\) | 9.76271 | 0.883874 | ||||||||
\(123\) | 0.623490 | + | 1.07992i | 0.0562182 | + | 0.0973727i | ||||
\(124\) | 1.69806 | + | 2.94113i | 0.152490 | + | 0.264121i | ||||
\(125\) | −6.02177 | −0.538604 | ||||||||
\(126\) | 2.99396 | + | 5.18569i | 0.266723 | + | 0.461978i | ||||
\(127\) | 4.76875 | − | 8.25972i | 0.423158 | − | 0.732931i | −0.573088 | − | 0.819494i | \(-0.694255\pi\) |
0.996246 | + | 0.0865622i | \(0.0275881\pi\) | |||||||
\(128\) | 3.08211 | − | 5.33836i | 0.272422 | − | 0.471849i | ||||
\(129\) | 2.38404 | 0.209903 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.50902 | −0.481326 | −0.240663 | − | 0.970609i | \(-0.577365\pi\) | ||||
−0.240663 | + | 0.970609i | \(0.577365\pi\) | |||||||
\(132\) | −0.326396 | + | 0.565335i | −0.0284092 | + | 0.0492061i | ||||
\(133\) | 6.10537 | − | 10.5748i | 0.529402 | − | 0.916952i | ||||
\(134\) | 2.23341 | + | 3.86837i | 0.192937 | + | 0.334177i | ||||
\(135\) | 2.80194 | 0.241152 | ||||||||
\(136\) | 3.72737 | + | 6.45599i | 0.319619 | + | 0.553596i | ||||
\(137\) | −8.09179 | − | 14.0154i | −0.691329 | − | 1.19742i | −0.971403 | − | 0.237438i | \(-0.923692\pi\) |
0.280074 | − | 0.959978i | \(-0.409641\pi\) | |||||||
\(138\) | 4.38404 | 0.373195 | ||||||||
\(139\) | 5.25451 | + | 9.10108i | 0.445682 | + | 0.771944i | 0.998099 | − | 0.0616238i | \(-0.0196279\pi\) |
−0.552418 | + | 0.833568i | \(0.686295\pi\) | |||||||
\(140\) | 2.99396 | − | 5.18569i | 0.253036 | − | 0.438271i | ||||
\(141\) | 6.40850 | − | 11.0999i | 0.539693 | − | 0.934776i | ||||
\(142\) | −11.0218 | −0.924926 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91185 | −0.242654 | ||||||||
\(145\) | −2.59299 | + | 4.49119i | −0.215336 | + | 0.372973i | ||||
\(146\) | 4.79590 | − | 8.30674i | 0.396911 | − | 0.687470i | ||||
\(147\) | −8.02930 | − | 13.9072i | −0.662246 | − | 1.14704i | ||||
\(148\) | −2.02715 | −0.166630 | ||||||||
\(149\) | 7.17510 | + | 12.4276i | 0.587807 | + | 1.01811i | 0.994519 | + | 0.104555i | \(0.0333418\pi\) |
−0.406712 | + | 0.913556i | \(0.633325\pi\) | |||||||
\(150\) | 1.77748 | + | 3.07868i | 0.145131 | + | 0.251374i | ||||
\(151\) | −1.96615 | −0.160003 | −0.0800014 | − | 0.996795i | \(-0.525492\pi\) | ||||
−0.0800014 | + | 0.996795i | \(0.525492\pi\) | |||||||
\(152\) | 3.87651 | + | 6.71431i | 0.314426 | + | 0.544603i | ||||
\(153\) | 1.22252 | − | 2.11747i | 0.0988350 | − | 0.171187i | ||||
\(154\) | −4.39158 | + | 7.60643i | −0.353883 | + | 0.612944i | ||||
\(155\) | 21.3817 | 1.71742 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7017 | 0.854089 | 0.427045 | − | 0.904231i | \(-0.359555\pi\) | ||||
0.427045 | + | 0.904231i | \(0.359555\pi\) | |||||||
\(158\) | −2.50753 | + | 4.34317i | −0.199489 | + | 0.345524i | ||||
\(159\) | 4.42543 | − | 7.66507i | 0.350959 | − | 0.607879i | ||||
\(160\) | 3.45593 | + | 5.98584i | 0.273215 | + | 0.473222i | ||||
\(161\) | −16.8823 | −1.33051 | ||||||||
\(162\) | 0.623490 | + | 1.07992i | 0.0489860 | + | 0.0848462i | ||||
\(163\) | 1.94989 | + | 3.37730i | 0.152727 | + | 0.264531i | 0.932229 | − | 0.361869i | \(-0.117861\pi\) |
−0.779502 | + | 0.626400i | \(0.784528\pi\) | |||||||
\(164\) | 0.554958 | 0.0433349 | ||||||||
\(165\) | 2.05496 | + | 3.55929i | 0.159978 | + | 0.277090i | ||||
\(166\) | 0.407010 | − | 0.704961i | 0.0315901 | − | 0.0547156i | ||||
\(167\) | 10.5097 | − | 18.2033i | 0.813264 | − | 1.40861i | −0.0973035 | − | 0.995255i | \(-0.531022\pi\) |
0.910568 | − | 0.413360i | \(-0.135645\pi\) | |||||||
\(168\) | 14.6407 | 1.12956 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.54288 | 0.655209 | ||||||||
\(171\) | 1.27144 | − | 2.20220i | 0.0972293 | − | 0.168406i | ||||
\(172\) | 0.530499 | − | 0.918852i | 0.0404502 | − | 0.0700618i | ||||
\(173\) | −6.61745 | − | 11.4618i | −0.503115 | − | 0.871421i | −0.999994 | − | 0.00360102i | \(-0.998854\pi\) |
0.496878 | − | 0.867820i | \(-0.334480\pi\) | |||||||
\(174\) | −2.30798 | −0.174967 | ||||||||
\(175\) | −6.84481 | − | 11.8556i | −0.517419 | − | 0.896197i | ||||
\(176\) | −2.13557 | − | 3.69892i | −0.160975 | − | 0.278816i | ||||
\(177\) | −2.17629 | −0.163580 | ||||||||
\(178\) | −3.92543 | − | 6.79904i | −0.294223 | − | 0.509610i | ||||
\(179\) | −4.26391 | + | 7.38530i | −0.318699 | + | 0.552003i | −0.980217 | − | 0.197926i | \(-0.936579\pi\) |
0.661518 | + | 0.749930i | \(0.269913\pi\) | |||||||
\(180\) | 0.623490 | − | 1.07992i | 0.0464722 | − | 0.0804922i | ||||
\(181\) | −3.63640 | −0.270291 | −0.135146 | − | 0.990826i | \(-0.543150\pi\) | ||||
−0.135146 | + | 0.990826i | \(0.543150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.82908 | −0.578743 | ||||||||
\(184\) | 5.35958 | − | 9.28307i | 0.395114 | − | 0.684357i | ||||
\(185\) | −6.38135 | + | 11.0528i | −0.469167 | + | 0.812620i | ||||
\(186\) | 4.75786 | + | 8.24086i | 0.348864 | + | 0.604249i | ||||
\(187\) | 3.58642 | 0.262265 | ||||||||
\(188\) | −2.85205 | − | 4.93990i | −0.208007 | − | 0.360279i | ||||
\(189\) | −2.40097 | − | 4.15860i | −0.174645 | − | 0.302494i | ||||
\(190\) | 8.88471 | 0.644564 | ||||||||
\(191\) | −10.6908 | − | 18.5171i | −0.773561 | − | 1.33985i | −0.935600 | − | 0.353062i | \(-0.885140\pi\) |
0.162039 | − | 0.986784i | \(-0.448193\pi\) | |||||||
\(192\) | −4.44989 | + | 7.70743i | −0.321143 | + | 0.556236i | ||||
\(193\) | −4.21379 | + | 7.29850i | −0.303315 | + | 0.525358i | −0.976885 | − | 0.213766i | \(-0.931427\pi\) |
0.673569 | + | 0.739124i | \(0.264760\pi\) | |||||||
\(194\) | −12.5090 | −0.898096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.14675 | −0.510482 | ||||||||
\(197\) | −13.2383 | + | 22.9293i | −0.943186 | + | 1.63365i | −0.183844 | + | 0.982955i | \(0.558854\pi\) |
−0.759343 | + | 0.650691i | \(0.774479\pi\) | |||||||
\(198\) | −0.914542 | + | 1.58403i | −0.0649937 | + | 0.112572i | ||||
\(199\) | 7.12618 | + | 12.3429i | 0.505161 | + | 0.874965i | 0.999982 | + | 0.00597014i | \(0.00190036\pi\) |
−0.494821 | + | 0.868995i | \(0.664766\pi\) | |||||||
\(200\) | 8.69202 | 0.614619 | ||||||||
\(201\) | −1.79105 | − | 3.10219i | −0.126331 | − | 0.218812i | ||||
\(202\) | 8.65883 | + | 14.9975i | 0.609233 | + | 1.05522i | ||||
\(203\) | 8.88769 | 0.623794 | ||||||||
\(204\) | −0.544073 | − | 0.942362i | −0.0380927 | − | 0.0659785i | ||||
\(205\) | 1.74698 | − | 3.02586i | 0.122014 | − | 0.211335i | ||||
\(206\) | −10.8509 | + | 18.7942i | −0.756015 | + | 1.30946i | ||||
\(207\) | −3.51573 | −0.244360 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.72992 | 0.258004 | ||||||||
\(210\) | 8.38889 | − | 14.5300i | 0.578888 | − | 1.00266i | ||||
\(211\) | −0.925428 | + | 1.60289i | −0.0637091 | + | 0.110347i | −0.896121 | − | 0.443811i | \(-0.853626\pi\) |
0.832412 | + | 0.554158i | \(0.186960\pi\) | |||||||
\(212\) | −1.96950 | − | 3.41127i | −0.135266 | − | 0.234287i | ||||
\(213\) | 8.83877 | 0.605623 | ||||||||
\(214\) | 6.57942 | + | 11.3959i | 0.449760 | + | 0.779007i | ||||
\(215\) | −3.33997 | − | 5.78500i | −0.227784 | − | 0.394534i | ||||
\(216\) | 3.04892 | 0.207453 | ||||||||
\(217\) | −18.3218 | − | 31.7344i | −1.24377 | − | 2.15427i | ||||
\(218\) | −0.667563 | + | 1.15625i | −0.0452131 | + | 0.0783113i | ||||
\(219\) | −3.84601 | + | 6.66149i | −0.259889 | + | 0.450142i | ||||
\(220\) | 1.82908 | 0.123317 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.67994 | −0.381213 | ||||||||
\(223\) | 9.32520 | − | 16.1517i | 0.624462 | − | 1.08160i | −0.364183 | − | 0.931327i | \(-0.618652\pi\) |
0.988645 | − | 0.150272i | \(-0.0480149\pi\) | |||||||
\(224\) | 5.92274 | − | 10.2585i | 0.395730 | − | 0.685424i | ||||
\(225\) | −1.42543 | − | 2.46891i | −0.0950285 | − | 0.164594i | ||||
\(226\) | 20.6136 | 1.37119 | ||||||||
\(227\) | 4.87867 | + | 8.45010i | 0.323808 | + | 0.560853i | 0.981270 | − | 0.192635i | \(-0.0617033\pi\) |
−0.657462 | + | 0.753488i | \(0.728370\pi\) | |||||||
\(228\) | −0.565843 | − | 0.980069i | −0.0374739 | − | 0.0649067i | ||||
\(229\) | 2.86294 | 0.189188 | 0.0945941 | − | 0.995516i | \(-0.469845\pi\) | ||||
0.0945941 | + | 0.995516i | \(0.469845\pi\) | |||||||
\(230\) | −6.14191 | − | 10.6381i | −0.404985 | − | 0.701455i | ||||
\(231\) | 3.52177 | − | 6.09989i | 0.231715 | − | 0.401343i | ||||
\(232\) | −2.82155 | + | 4.88707i | −0.185244 | + | 0.320852i | ||||
\(233\) | −5.78554 | −0.379024 | −0.189512 | − | 0.981878i | \(-0.560691\pi\) | ||||
−0.189512 | + | 0.981878i | \(0.560691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.9124 | −2.34267 | ||||||||
\(236\) | −0.484271 | + | 0.838781i | −0.0315233 | + | 0.0546000i | ||||
\(237\) | 2.01089 | − | 3.48296i | 0.130621 | − | 0.226242i | ||||
\(238\) | −7.32036 | − | 12.6792i | −0.474508 | − | 0.821872i | ||||
\(239\) | −7.09246 | −0.458773 | −0.229386 | − | 0.973335i | \(-0.573672\pi\) | ||||
−0.229386 | + | 0.973335i | \(0.573672\pi\) | |||||||
\(240\) | 4.07942 | + | 7.06576i | 0.263325 | + | 0.456093i | ||||
\(241\) | 1.94989 | + | 3.37730i | 0.125603 | + | 0.217551i | 0.921969 | − | 0.387265i | \(-0.126580\pi\) |
−0.796365 | + | 0.604816i | \(0.793247\pi\) | |||||||
\(242\) | 11.0339 | 0.709283 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −1.74214 | + | 3.01747i | −0.111529 | + | 0.193174i | ||||
\(245\) | −22.4976 | + | 38.9670i | −1.43732 | + | 2.48951i | ||||
\(246\) | 1.55496 | 0.0991405 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 23.2664 | 1.47742 | ||||||||
\(249\) | −0.326396 | + | 0.565335i | −0.0206845 | + | 0.0358267i | ||||
\(250\) | −3.75451 | + | 6.50301i | −0.237456 | + | 0.411286i | ||||
\(251\) | 1.22252 | + | 2.11747i | 0.0771648 | + | 0.133653i | 0.902026 | − | 0.431682i | \(-0.142080\pi\) |
−0.824861 | + | 0.565336i | \(0.808747\pi\) | |||||||
\(252\) | −2.13706 | −0.134622 | ||||||||
\(253\) | −2.57846 | − | 4.46602i | −0.162106 | − | 0.280776i | ||||
\(254\) | −5.94653 | − | 10.2997i | −0.373119 | − | 0.646261i | ||||
\(255\) | −6.85086 | −0.429017 | ||||||||
\(256\) | 5.05645 | + | 8.75803i | 0.316028 | + | 0.547377i | ||||
\(257\) | 7.06518 | − | 12.2372i | 0.440714 | − | 0.763339i | −0.557029 | − | 0.830493i | \(-0.688059\pi\) |
0.997743 | + | 0.0671545i | \(0.0213920\pi\) | |||||||
\(258\) | 1.48643 | − | 2.57457i | 0.0925409 | − | 0.160285i | ||||
\(259\) | 21.8726 | 1.35910 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.85086 | 0.114565 | ||||||||
\(262\) | −3.43482 | + | 5.94928i | −0.212204 | + | 0.367548i | ||||
\(263\) | 11.8617 | − | 20.5451i | 0.731426 | − | 1.26687i | −0.224847 | − | 0.974394i | \(-0.572188\pi\) |
0.956274 | − | 0.292473i | \(-0.0944783\pi\) | |||||||
\(264\) | 2.23609 | + | 3.87303i | 0.137622 | + | 0.238368i | ||||
\(265\) | −24.7995 | −1.52342 | ||||||||
\(266\) | −7.61327 | − | 13.1866i | −0.466799 | − | 0.808520i | ||||
\(267\) | 3.14795 | + | 5.45241i | 0.192651 | + | 0.333682i | ||||
\(268\) | −1.59419 | −0.0973805 | ||||||||
\(269\) | 2.95808 | + | 5.12355i | 0.180357 | + | 0.312388i | 0.942002 | − | 0.335606i | \(-0.108941\pi\) |
−0.761645 | + | 0.647995i | \(0.775608\pi\) | |||||||
\(270\) | 1.74698 | − | 3.02586i | 0.106318 | − | 0.184148i | ||||
\(271\) | 1.59515 | − | 2.76287i | 0.0968982 | − | 0.167833i | −0.813501 | − | 0.581563i | \(-0.802441\pi\) |
0.910399 | + | 0.413731i | \(0.135775\pi\) | |||||||
\(272\) | 7.11960 | 0.431689 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.1806 | −1.21915 | ||||||||
\(275\) | 2.09083 | − | 3.62143i | 0.126082 | − | 0.218381i | ||||
\(276\) | −0.782323 | + | 1.35502i | −0.0470903 | + | 0.0815629i | ||||
\(277\) | −10.9683 | − | 18.9977i | −0.659022 | − | 1.14146i | −0.980869 | − | 0.194667i | \(-0.937637\pi\) |
0.321848 | − | 0.946791i | \(-0.395696\pi\) | |||||||
\(278\) | 13.1045 | 0.785958 | ||||||||
\(279\) | −3.81551 | − | 6.60866i | −0.228429 | − | 0.395650i | ||||
\(280\) | −20.5112 | − | 35.5264i | −1.22578 | − | 2.12311i | ||||
\(281\) | 11.9903 | 0.715282 | 0.357641 | − | 0.933859i | \(-0.383581\pi\) | ||||
0.357641 | + | 0.933859i | \(0.383581\pi\) | |||||||
\(282\) | −7.99127 | − | 13.8413i | −0.475873 | − | 0.824237i | ||||
\(283\) | 7.18329 | − | 12.4418i | 0.427002 | − | 0.739590i | −0.569603 | − | 0.821920i | \(-0.692903\pi\) |
0.996605 | + | 0.0823303i | \(0.0262362\pi\) | |||||||
\(284\) | 1.96681 | − | 3.40662i | 0.116709 | − | 0.202146i | ||||
\(285\) | −7.12498 | −0.422047 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.98792 | −0.353456 | ||||||||
\(288\) | 1.23341 | − | 2.13632i | 0.0726791 | − | 0.125884i | ||||
\(289\) | 5.51089 | − | 9.54513i | 0.324170 | − | 0.561478i | ||||
\(290\) | 3.23341 | + | 5.60042i | 0.189872 | + | 0.328868i | ||||
\(291\) | 10.0315 | 0.588055 | ||||||||
\(292\) | 1.71164 | + | 2.96464i | 0.100166 | + | 0.173492i | ||||
\(293\) | −9.37920 | − | 16.2452i | −0.547939 | − | 0.949058i | −0.998416 | − | 0.0562695i | \(-0.982079\pi\) |
0.450477 | − | 0.892788i | \(-0.351254\pi\) | |||||||
\(294\) | −20.0248 | −1.16787 | ||||||||
\(295\) | 3.04892 | + | 5.28088i | 0.177515 | + | 0.307465i | ||||
\(296\) | −6.94385 | + | 12.0271i | −0.403603 | + | 0.699061i | ||||
\(297\) | 0.733406 | − | 1.27030i | 0.0425565 | − | 0.0737101i | ||||
\(298\) | 17.8944 | 1.03659 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.26875 | −0.0732513 | ||||||||
\(301\) | −5.72401 | + | 9.91428i | −0.329927 | + | 0.571450i | ||||
\(302\) | −1.22587 | + | 2.12327i | −0.0705411 | + | 0.122181i | ||||
\(303\) | −6.94385 | − | 12.0271i | −0.398913 | − | 0.690938i | ||||
\(304\) | 7.40449 | 0.424676 | ||||||||
\(305\) | 10.9683 | + | 18.9977i | 0.628043 | + | 1.08780i | ||||
\(306\) | −1.52446 | − | 2.64044i | −0.0871475 | − | 0.150944i | ||||
\(307\) | 25.6262 | 1.46257 | 0.731283 | − | 0.682074i | \(-0.238922\pi\) | ||||
0.731283 | + | 0.682074i | \(0.238922\pi\) | |||||||
\(308\) | −1.56734 | − | 2.71470i | −0.0893072 | − | 0.154685i | ||||
\(309\) | 8.70171 | − | 15.0718i | 0.495023 | − | 0.857405i | ||||
\(310\) | 13.3312 | − | 23.0904i | 0.757164 | − | 1.31145i | ||||
\(311\) | 11.3817 | 0.645394 | 0.322697 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322697 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.5743 | 1.55859 | 0.779297 | − | 0.626655i | \(-0.215576\pi\) | ||||
0.779297 | + | 0.626655i | \(0.215576\pi\) | |||||||
\(314\) | 6.67241 | − | 11.5569i | 0.376546 | − | 0.652196i | ||||
\(315\) | −6.72737 | + | 11.6521i | −0.379044 | + | 0.656524i | ||||
\(316\) | −0.894928 | − | 1.55006i | −0.0503436 | − | 0.0871977i | ||||
\(317\) | −11.2597 | −0.632405 | −0.316203 | − | 0.948692i | \(-0.602408\pi\) | ||||
−0.316203 | + | 0.948692i | \(0.602408\pi\) | |||||||
\(318\) | −5.51842 | − | 9.55818i | −0.309458 | − | 0.535996i | ||||
\(319\) | 1.35743 | + | 2.35113i | 0.0760014 | + | 0.131638i | ||||
\(320\) | 24.9366 | 1.39400 | ||||||||
\(321\) | −5.27628 | − | 9.13879i | −0.294493 | − | 0.510077i | ||||
\(322\) | −10.5260 | + | 18.2315i | −0.586588 | + | 1.01600i | ||||
\(323\) | −3.10872 | + | 5.38446i | −0.172974 | + | 0.299599i | ||||
\(324\) | −0.445042 | −0.0247245 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.86294 | 0.269333 | ||||||||
\(327\) | 0.535344 | − | 0.927243i | 0.0296046 | − | 0.0512766i | ||||
\(328\) | 1.90097 | − | 3.29257i | 0.104963 | − | 0.181802i | ||||
\(329\) | 30.7732 | + | 53.3008i | 1.69658 | + | 2.93857i | ||||
\(330\) | 5.12498 | 0.282121 | ||||||||
\(331\) | 5.95324 | + | 10.3113i | 0.327220 | + | 0.566761i | 0.981959 | − | 0.189094i | \(-0.0605550\pi\) |
−0.654739 | + | 0.755855i | \(0.727222\pi\) | |||||||
\(332\) | 0.145260 | + | 0.251598i | 0.00797218 | + | 0.0138082i | ||||
\(333\) | 4.55496 | 0.249610 | ||||||||
\(334\) | −13.1054 | − | 22.6992i | −0.717094 | − | 1.24204i | ||||
\(335\) | −5.01842 | + | 8.69215i | −0.274185 | + | 0.474903i | ||||
\(336\) | 6.99127 | − | 12.1092i | 0.381405 | − | 0.660613i | ||||
\(337\) | 17.1672 | 0.935157 | 0.467578 | − | 0.883952i | \(-0.345127\pi\) | ||||
0.467578 | + | 0.883952i | \(0.345127\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5308 | −0.897830 | ||||||||
\(340\) | −1.52446 | + | 2.64044i | −0.0826754 | + | 0.143198i | ||||
\(341\) | 5.59664 | − | 9.69366i | 0.303075 | − | 0.524941i | ||||
\(342\) | −1.58546 | − | 2.74609i | −0.0857317 | − | 0.148492i | ||||
\(343\) | 43.4989 | 2.34872 | ||||||||
\(344\) | −3.63437 | − | 6.29492i | −0.195952 | − | 0.339399i | ||||
\(345\) | 4.92543 | + | 8.53109i | 0.265176 | + | 0.459298i | ||||
\(346\) | −16.5036 | −0.887242 | ||||||||
\(347\) | 12.1380 | + | 21.0237i | 0.651603 | + | 1.12861i | 0.982734 | + | 0.185025i | \(0.0592366\pi\) |
−0.331131 | + | 0.943585i | \(0.607430\pi\) | |||||||
\(348\) | 0.411854 | − | 0.713352i | 0.0220777 | − | 0.0382397i | ||||
\(349\) | 2.28621 | − | 3.95983i | 0.122378 | − | 0.211965i | −0.798327 | − | 0.602224i | \(-0.794281\pi\) |
0.920705 | + | 0.390259i | \(0.127615\pi\) | |||||||
\(350\) | −17.0707 | −0.912467 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.61835 | 0.192859 | ||||||||
\(353\) | 3.03803 | − | 5.26203i | 0.161698 | − | 0.280069i | −0.773780 | − | 0.633455i | \(-0.781636\pi\) |
0.935478 | + | 0.353385i | \(0.114970\pi\) | |||||||
\(354\) | −1.35690 | + | 2.35021i | −0.0721182 | + | 0.124912i | ||||
\(355\) | −12.3828 | − | 21.4477i | −0.657213 | − | 1.13833i | ||||
\(356\) | 2.80194 | 0.148502 | ||||||||
\(357\) | 5.87047 | + | 10.1680i | 0.310698 | + | 0.538145i | ||||
\(358\) | 5.31700 | + | 9.20932i | 0.281012 | + | 0.486728i | ||||
\(359\) | −14.9661 | −0.789883 | −0.394942 | − | 0.918706i | \(-0.629235\pi\) | ||||
−0.394942 | + | 0.918706i | \(0.629235\pi\) | |||||||
\(360\) | −4.27144 | − | 7.39835i | −0.225125 | − | 0.389927i | ||||
\(361\) | 6.26689 | − | 10.8546i | 0.329836 | − | 0.571293i | ||||
\(362\) | −2.26726 | + | 3.92701i | −0.119164 | + | 0.206399i | ||||
\(363\) | −8.84846 | −0.464424 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.5526 | 1.12811 | ||||||||
\(366\) | −4.88135 | + | 8.45475i | −0.255152 | + | 0.441937i | ||||
\(367\) | −18.5417 | + | 32.1151i | −0.967868 | + | 1.67640i | −0.266164 | + | 0.963928i | \(0.585756\pi\) |
−0.701704 | + | 0.712468i | \(0.747577\pi\) | |||||||
\(368\) | −5.11865 | − | 8.86575i | −0.266828 | − | 0.462159i | ||||
\(369\) | −1.24698 | −0.0649152 | ||||||||
\(370\) | 7.95742 | + | 13.7827i | 0.413687 | + | 0.716526i | ||||
\(371\) | 21.2506 | + | 36.8072i | 1.10328 | + | 1.91093i | ||||
\(372\) | −3.39612 | −0.176081 | ||||||||
\(373\) | 18.2545 | + | 31.6177i | 0.945183 | + | 1.63710i | 0.755385 | + | 0.655282i | \(0.227450\pi\) |
0.189798 | + | 0.981823i | \(0.439217\pi\) | |||||||
\(374\) | 2.23609 | − | 3.87303i | 0.115626 | − | 0.200270i | ||||
\(375\) | 3.01089 | − | 5.21501i | 0.155481 | − | 0.269302i | ||||
\(376\) | −39.0780 | −2.01529 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.98792 | −0.307985 | ||||||||
\(379\) | 13.2925 | − | 23.0234i | 0.682792 | − | 1.18263i | −0.291333 | − | 0.956622i | \(-0.594099\pi\) |
0.974125 | − | 0.226009i | \(-0.0725679\pi\) | |||||||
\(380\) | −1.58546 | + | 2.74609i | −0.0813323 | + | 0.140872i | ||||
\(381\) | 4.76875 | + | 8.25972i | 0.244310 | + | 0.423158i | ||||
\(382\) | −26.6625 | −1.36417 | ||||||||
\(383\) | 7.17510 | + | 12.4276i | 0.366630 | + | 0.635022i | 0.989036 | − | 0.147672i | \(-0.0471781\pi\) |
−0.622406 | + | 0.782694i | \(0.713845\pi\) | |||||||
\(384\) | 3.08211 | + | 5.33836i | 0.157283 | + | 0.272422i | ||||
\(385\) | −19.7356 | −1.00582 | ||||||||
\(386\) | 5.25451 | + | 9.10108i | 0.267448 | + | 0.463233i | ||||
\(387\) | −1.19202 | + | 2.06464i | −0.0605939 | + | 0.104952i | ||||
\(388\) | 2.23221 | − | 3.86630i | 0.113323 | − | 0.196282i | ||||
\(389\) | −22.6582 | −1.14881 | −0.574407 | − | 0.818570i | \(-0.694767\pi\) | ||||
−0.574407 | + | 0.818570i | \(0.694767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.59611 | 0.434724 | ||||||||
\(392\) | −24.4807 | + | 42.4018i | −1.23646 | + | 2.14161i | ||||
\(393\) | 2.75451 | − | 4.77096i | 0.138947 | − | 0.240663i | ||||
\(394\) | 16.5078 | + | 28.5924i | 0.831652 | + | 1.44046i | ||||
\(395\) | −11.2687 | −0.566992 | ||||||||
\(396\) | −0.326396 | − | 0.565335i | −0.0164020 | − | 0.0284092i | ||||
\(397\) | −3.95377 | − | 6.84813i | −0.198434 | − | 0.343698i | 0.749587 | − | 0.661906i | \(-0.230252\pi\) |
−0.948021 | + | 0.318208i | \(0.896919\pi\) | |||||||
\(398\) | 17.7724 | 0.890850 | ||||||||
\(399\) | 6.10537 | + | 10.5748i | 0.305651 | + | 0.529402i | ||||
\(400\) | 4.15064 | − | 7.18911i | 0.207532 | − | 0.359456i | ||||
\(401\) | −1.46830 | + | 2.54318i | −0.0733236 | + | 0.127000i | −0.900356 | − | 0.435154i | \(-0.856694\pi\) |
0.827032 | + | 0.562154i | \(0.190027\pi\) | |||||||
\(402\) | −4.46681 | −0.222784 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.18060 | −0.307497 | ||||||||
\(405\) | −1.40097 | + | 2.42655i | −0.0696147 | + | 0.120576i | ||||
\(406\) | 5.54138 | − | 9.59796i | 0.275014 | − | 0.476339i | ||||
\(407\) | 3.34063 | + | 5.78615i | 0.165589 | + | 0.286809i | ||||
\(408\) | −7.45473 | −0.369064 | ||||||||
\(409\) | −5.87747 | − | 10.1801i | −0.290622 | − | 0.503372i | 0.683335 | − | 0.730105i | \(-0.260529\pi\) |
−0.973957 | + | 0.226733i | \(0.927196\pi\) | |||||||
\(410\) | −2.17845 | − | 3.77318i | −0.107586 | − | 0.186344i | ||||
\(411\) | 16.1836 | 0.798278 | ||||||||
\(412\) | −3.87263 | − | 6.70758i | −0.190791 | − | 0.330459i | ||||
\(413\) | 5.22521 | − | 9.05033i | 0.257116 | − | 0.445338i | ||||
\(414\) | −2.19202 | + | 3.79669i | −0.107732 | + | 0.186597i | ||||
\(415\) | 1.82908 | 0.0897862 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.5090 | −0.514629 | ||||||||
\(418\) | 2.32557 | − | 4.02800i | 0.113747 | − | 0.197016i | ||||
\(419\) | −3.67092 | + | 6.35821i | −0.179336 | + | 0.310619i | −0.941653 | − | 0.336584i | \(-0.890728\pi\) |
0.762317 | + | 0.647203i | \(0.224062\pi\) | |||||||
\(420\) | 2.99396 | + | 5.18569i | 0.146090 | + | 0.253036i | ||||
\(421\) | 25.6963 | 1.25236 | 0.626181 | − | 0.779677i | \(-0.284617\pi\) | ||||
0.626181 | + | 0.779677i | \(0.284617\pi\) | |||||||
\(422\) | 1.15399 | + | 1.99877i | 0.0561753 | + | 0.0972985i | ||||
\(423\) | 6.40850 | + | 11.0999i | 0.311592 | + | 0.539693i | ||||
\(424\) | −26.9855 | −1.31053 | ||||||||
\(425\) | 3.48523 | + | 6.03660i | 0.169058 | + | 0.292818i | ||||
\(426\) | 5.51089 | − | 9.54513i | 0.267003 | − | 0.462463i | ||||
\(427\) | 18.7974 | − | 32.5580i | 0.909669 | − | 1.57559i | ||||
\(428\) | −4.69633 | −0.227006 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.32975 | −0.401696 | ||||||||
\(431\) | −4.47099 | + | 7.74399i | −0.215360 | + | 0.373015i | −0.953384 | − | 0.301760i | \(-0.902426\pi\) |
0.738024 | + | 0.674775i | \(0.235759\pi\) | |||||||
\(432\) | 1.45593 | − | 2.52174i | 0.0700483 | − | 0.121327i | ||||
\(433\) | −1.45742 | − | 2.52432i | −0.0700391 | − | 0.121311i | 0.828879 | − | 0.559428i | \(-0.188979\pi\) |
−0.898918 | + | 0.438116i | \(0.855646\pi\) | |||||||
\(434\) | −45.6939 | −2.19338 | ||||||||
\(435\) | −2.59299 | − | 4.49119i | −0.124324 | − | 0.215336i | ||||
\(436\) | −0.238250 | − | 0.412662i | −0.0114101 | − | 0.0197629i | ||||
\(437\) | 8.94007 | 0.427661 | ||||||||
\(438\) | 4.79590 | + | 8.30674i | 0.229157 | + | 0.396911i | ||||
\(439\) | −4.52930 | + | 7.84498i | −0.216172 | + | 0.374421i | −0.953634 | − | 0.300967i | \(-0.902690\pi\) |
0.737463 | + | 0.675388i | \(0.236024\pi\) | |||||||
\(440\) | 6.26540 | − | 10.8520i | 0.298691 | − | 0.517348i | ||||
\(441\) | 16.0586 | 0.764696 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2325 | 0.533672 | 0.266836 | − | 0.963742i | \(-0.414022\pi\) | ||||
0.266836 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(444\) | 1.01357 | − | 1.75556i | 0.0481021 | − | 0.0833152i | ||||
\(445\) | 8.82036 | − | 15.2773i | 0.418125 | − | 0.724214i | ||||
\(446\) | −11.6283 | − | 20.1409i | −0.550618 | − | 0.953698i | ||||
\(447\) | −14.3502 | −0.678741 | ||||||||
\(448\) | −21.3681 | − | 37.0106i | −1.00955 | − | 1.74859i | ||||
\(449\) | −14.3790 | − | 24.9051i | −0.678585 | − | 1.17534i | −0.975407 | − | 0.220411i | \(-0.929260\pi\) |
0.296822 | − | 0.954933i | \(-0.404073\pi\) | |||||||
\(450\) | −3.55496 | −0.167582 | ||||||||
\(451\) | −0.914542 | − | 1.58403i | −0.0430641 | − | 0.0745892i | ||||
\(452\) | −3.67845 | + | 6.37126i | −0.173020 | + | 0.299679i | ||||
\(453\) | 0.983074 | − | 1.70273i | 0.0461888 | − | 0.0800014i | ||||
\(454\) | 12.1672 | 0.571035 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.75302 | −0.363068 | ||||||||
\(457\) | 9.53803 | − | 16.5204i | 0.446170 | − | 0.772790i | −0.551963 | − | 0.833869i | \(-0.686121\pi\) |
0.998133 | + | 0.0610792i | \(0.0194542\pi\) | |||||||
\(458\) | 1.78501 | − | 3.09173i | 0.0834081 | − | 0.144467i | ||||
\(459\) | 1.22252 | + | 2.11747i | 0.0570624 | + | 0.0988350i | ||||
\(460\) | 4.38404 | 0.204407 | ||||||||
\(461\) | −15.8666 | − | 27.4817i | −0.738981 | − | 1.27995i | −0.952955 | − | 0.303113i | \(-0.901974\pi\) |
0.213974 | − | 0.976839i | \(-0.431359\pi\) | |||||||
\(462\) | −4.39158 | − | 7.60643i | −0.204315 | − | 0.353883i | ||||
\(463\) | −36.4784 | −1.69530 | −0.847648 | − | 0.530559i | \(-0.821982\pi\) | ||||
−0.847648 | + | 0.530559i | \(0.821982\pi\) | |||||||
\(464\) | 2.69471 | + | 4.66737i | 0.125099 | + | 0.216677i | ||||
\(465\) | −10.6908 | + | 18.5171i | −0.495775 | + | 0.858708i | ||||
\(466\) | −3.60723 | + | 6.24790i | −0.167102 | + | 0.289428i | ||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.2010 | 0.794271 | ||||||||
\(470\) | −22.3910 | + | 38.7824i | −1.03282 | + | 1.78890i | ||||
\(471\) | −5.35086 | + | 9.26795i | −0.246554 | + | 0.427045i | ||||
\(472\) | 3.31767 | + | 5.74637i | 0.152708 | + | 0.264498i | ||||
\(473\) | −3.49694 | −0.160790 | ||||||||
\(474\) | −2.50753 | − | 4.34317i | −0.115175 | − | 0.199489i | ||||
\(475\) | 3.62469 | + | 6.27814i | 0.166312 | + | 0.288061i | ||||
\(476\) | 5.22521 | 0.239497 | ||||||||
\(477\) | 4.42543 | + | 7.66507i | 0.202626 | + | 0.350959i | ||||
\(478\) | −4.42208 | + | 7.65926i | −0.202261 | + | 0.350326i | ||||
\(479\) | −2.80827 | + | 4.86407i | −0.128313 | + | 0.222245i | −0.923023 | − | 0.384744i | \(-0.874290\pi\) |
0.794710 | + | 0.606989i | \(0.207623\pi\) | |||||||
\(480\) | −6.91185 | −0.315482 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.86294 | 0.221501 | ||||||||
\(483\) | 8.44116 | − | 14.6205i | 0.384086 | − | 0.665256i | ||||
\(484\) | −1.96897 | + | 3.41035i | −0.0894985 | + | 0.155016i | ||||
\(485\) | −14.0538 | − | 24.3418i | −0.638148 | − | 1.10531i | ||||
\(486\) | −1.24698 | −0.0565641 | ||||||||
\(487\) | 4.87867 | + | 8.45010i | 0.221073 | + | 0.382910i | 0.955134 | − | 0.296173i | \(-0.0957106\pi\) |
−0.734061 | + | 0.679084i | \(0.762377\pi\) | |||||||
\(488\) | 11.9351 | + | 20.6722i | 0.540277 | + | 0.935788i | ||||
\(489\) | −3.89977 | −0.176354 | ||||||||
\(490\) | 28.0541 | + | 48.5911i | 1.26735 | + | 2.19512i | ||||
\(491\) | 3.69418 | − | 6.39850i | 0.166716 | − | 0.288760i | −0.770547 | − | 0.637383i | \(-0.780017\pi\) |
0.937263 | + | 0.348622i | \(0.113350\pi\) | |||||||
\(492\) | −0.277479 | + | 0.480608i | −0.0125097 | + | 0.0216675i | ||||
\(493\) | −4.52542 | −0.203815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.10992 | −0.184727 | ||||||||
\(496\) | 11.1102 | − | 19.2435i | 0.498863 | − | 0.864056i | ||||
\(497\) | −21.2216 | + | 36.7569i | −0.951920 | + | 1.64877i | ||||
\(498\) | 0.407010 | + | 0.704961i | 0.0182385 | + | 0.0315901i | ||||
\(499\) | −43.2814 | −1.93754 | −0.968771 | − | 0.247956i | \(-0.920241\pi\) | ||||
−0.968771 | + | 0.247956i | \(0.920241\pi\) | |||||||
\(500\) | −1.33997 | − | 2.32090i | −0.0599253 | − | 0.103794i | ||||
\(501\) | 10.5097 | + | 18.2033i | 0.469538 | + | 0.813264i | ||||
\(502\) | 3.04892 | 0.136080 | ||||||||
\(503\) | −5.38351 | − | 9.32451i | −0.240039 | − | 0.415760i | 0.720686 | − | 0.693261i | \(-0.243827\pi\) |
−0.960725 | + | 0.277502i | \(0.910494\pi\) | |||||||
\(504\) | −7.32036 | + | 12.6792i | −0.326075 | + | 0.564778i | ||||
\(505\) | −19.4562 | + | 33.6992i | −0.865791 | + | 1.49959i | ||||
\(506\) | −6.43057 | −0.285874 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.24459 | 0.188323 | ||||||||
\(509\) | 20.7724 | − | 35.9788i | 0.920720 | − | 1.59473i | 0.122417 | − | 0.992479i | \(-0.460935\pi\) |
0.798303 | − | 0.602256i | \(-0.205731\pi\) | |||||||
\(510\) | −4.27144 | + | 7.39835i | −0.189142 | + | 0.327604i | ||||
\(511\) | −18.4683 | − | 31.9880i | −0.816990 | − | 1.41507i | ||||
\(512\) | 24.9390 | 1.10216 | ||||||||
\(513\) | 1.27144 | + | 2.20220i | 0.0561354 | + | 0.0972293i | ||||
\(514\) | −8.81013 | − | 15.2596i | −0.388598 | − | 0.673072i | ||||
\(515\) | −48.7633 | −2.14877 | ||||||||
\(516\) | 0.530499 | + | 0.918852i | 0.0233539 | + | 0.0404502i | ||||
\(517\) | −9.40007 | + | 16.2814i | −0.413415 | + | 0.716055i | ||||
\(518\) | 13.6374 | − | 23.6206i | 0.599191 | − | 1.03783i | ||||
\(519\) | 13.2349 | 0.580948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7198 | 1.12680 | 0.563402 | − | 0.826183i | \(-0.309492\pi\) | ||||
0.563402 | + | 0.826183i | \(0.309492\pi\) | |||||||
\(522\) | 1.15399 | − | 1.99877i | 0.0505087 | − | 0.0874837i | ||||
\(523\) | −4.29643 | + | 7.44163i | −0.187870 | + | 0.325400i | −0.944540 | − | 0.328397i | \(-0.893492\pi\) |
0.756670 | + | 0.653797i | \(0.226825\pi\) | |||||||
\(524\) | −1.22587 | − | 2.12327i | −0.0535525 | − | 0.0927557i | ||||
\(525\) | 13.6896 | 0.597464 | ||||||||
\(526\) | −14.7913 | − | 25.6194i | −0.644933 | − | 1.11706i | ||||
\(527\) | 9.32908 | + | 16.1584i | 0.406381 | + | 0.703873i | ||||
\(528\) | 4.27114 | 0.185878 | ||||||||
\(529\) | 5.31982 | + | 9.21420i | 0.231297 | + | 0.400618i | ||||
\(530\) | −15.4623 | + | 26.7814i | −0.671638 | + | 1.16331i | ||||
\(531\) | 1.08815 | − | 1.88472i | 0.0472215 | − | 0.0817901i | ||||
\(532\) | 5.43429 | 0.235606 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.85086 | 0.339740 | ||||||||
\(535\) | −14.7838 | + | 25.6063i | −0.639160 | + | 1.10706i | ||||
\(536\) | −5.46077 | + | 9.45833i | −0.235869 | + | 0.408538i | ||||
\(537\) | −4.26391 | − | 7.38530i | −0.184001 | − | 0.318699i | ||||
\(538\) | 7.37734 | 0.318060 | ||||||||
\(539\) | 11.7775 | + | 20.3992i | 0.507292 | + | 0.878655i | ||||
\(540\) | 0.623490 | + | 1.07992i | 0.0268307 | + | 0.0464722i | ||||
\(541\) | 31.3534 | 1.34799 | 0.673995 | − | 0.738736i | \(-0.264577\pi\) | ||||
0.673995 | + | 0.738736i | \(0.264577\pi\) | |||||||
\(542\) | −1.98911 | − | 3.44525i | −0.0854398 | − | 0.147986i | ||||
\(543\) | 1.81820 | − | 3.14921i | 0.0780264 | − | 0.135146i | ||||
\(544\) | −3.01573 | + | 5.22340i | −0.129298 | + | 0.223951i | ||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9342 | 0.852325 | 0.426163 | − | 0.904647i | \(-0.359865\pi\) | ||||
0.426163 | + | 0.904647i | \(0.359865\pi\) | |||||||
\(548\) | 3.60119 | − | 6.23744i | 0.153835 | − | 0.266450i | ||||
\(549\) | 3.91454 | − | 6.78019i | 0.167069 | − | 0.289371i | ||||
\(550\) | −2.60723 | − | 4.51585i | −0.111173 | − | 0.192557i | ||||
\(551\) | −4.70650 | −0.200503 | ||||||||
\(552\) | 5.35958 | + | 9.28307i | 0.228119 | + | 0.395114i | ||||
\(553\) | 9.65615 | + | 16.7249i | 0.410621 | + | 0.711217i | ||||
\(554\) | −27.3545 | −1.16218 | ||||||||
\(555\) | −6.38135 | − | 11.0528i | −0.270873 | − | 0.469167i | ||||
\(556\) | −2.33848 | + | 4.05036i | −0.0991736 | + | 0.171774i | ||||
\(557\) | −16.6174 | + | 28.7823i | −0.704104 | + | 1.21954i | 0.262910 | + | 0.964820i | \(0.415318\pi\) |
−0.967014 | + | 0.254723i | \(0.918016\pi\) | |||||||
\(558\) | −9.51573 | −0.402833 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −39.1782 | −1.65558 | ||||||||
\(561\) | −1.79321 | + | 3.10593i | −0.0757093 | + | 0.131132i | ||||
\(562\) | 7.47584 | − | 12.9485i | 0.315349 | − | 0.546201i | ||||
\(563\) | −1.93565 | − | 3.35264i | −0.0815779 | − | 0.141297i | 0.822350 | − | 0.568982i | \(-0.192663\pi\) |
−0.903928 | + | 0.427685i | \(0.859329\pi\) | |||||||
\(564\) | 5.70410 | 0.240186 | ||||||||
\(565\) | 23.1591 | + | 40.1128i | 0.974312 | + | 1.68756i | ||||
\(566\) | −8.95742 | − | 15.5147i | −0.376508 | − | 0.652132i | ||||
\(567\) | 4.80194 | 0.201662 | ||||||||
\(568\) | −13.4743 | − | 23.3382i | −0.565371 | − | 0.979251i | ||||
\(569\) | −10.0728 | + | 17.4467i | −0.422276 | + | 0.731403i | −0.996162 | − | 0.0875324i | \(-0.972102\pi\) |
0.573886 | + | 0.818935i | \(0.305435\pi\) | |||||||
\(570\) | −4.44235 | + | 7.69438i | −0.186070 | + | 0.322282i | ||||
\(571\) | −32.1269 | −1.34447 | −0.672234 | − | 0.740338i | \(-0.734665\pi\) | ||||
−0.672234 | + | 0.740338i | \(0.734665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3817 | 0.893231 | ||||||||
\(574\) | −3.73341 | + | 6.46645i | −0.155829 | + | 0.269904i | ||||
\(575\) | 5.01142 | − | 8.68003i | 0.208991 | − | 0.361982i | ||||
\(576\) | −4.44989 | − | 7.70743i | −0.185412 | − | 0.321143i | ||||
\(577\) | −16.7506 | −0.697338 | −0.348669 | − | 0.937246i | \(-0.613366\pi\) | ||||
−0.348669 | + | 0.937246i | \(0.613366\pi\) | |||||||
\(578\) | −6.87196 | − | 11.9026i | −0.285836 | − | 0.495082i | ||||
\(579\) | −4.21379 | − | 7.29850i | −0.175119 | − | 0.303315i | ||||
\(580\) | −2.30798 | −0.0958336 | ||||||||
\(581\) | −1.56734 | − | 2.71470i | −0.0650240 | − | 0.112625i | ||||
\(582\) | 6.25451 | − | 10.8331i | 0.259258 | − | 0.449048i | ||||
\(583\) | −6.49127 | + | 11.2432i | −0.268841 | + | 0.465646i | ||||
\(584\) | 23.4523 | 0.970465 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.3913 | −0.966287 | ||||||||
\(587\) | 3.36898 | − | 5.83524i | 0.139053 | − | 0.240846i | −0.788086 | − | 0.615566i | \(-0.788928\pi\) |
0.927138 | + | 0.374719i | \(0.122261\pi\) | |||||||
\(588\) | 3.57338 | − | 6.18927i | 0.147364 | − | 0.255241i | ||||
\(589\) | 9.70237 | + | 16.8050i | 0.399779 | + | 0.692438i | ||||
\(590\) | 7.60388 | 0.313047 | ||||||||
\(591\) | −13.2383 | − | 22.9293i | −0.544549 | − | 0.943186i | ||||
\(592\) | 6.63169 | + | 11.4864i | 0.272561 | + | 0.472089i | ||||
\(593\) | 18.1172 | 0.743985 | 0.371992 | − | 0.928236i | \(-0.378675\pi\) | ||||
0.371992 | + | 0.928236i | \(0.378675\pi\) | |||||||
\(594\) | −0.914542 | − | 1.58403i | −0.0375241 | − | 0.0649937i | ||||
\(595\) | 16.4487 | − | 28.4900i | 0.674331 | − | 1.16797i | ||||
\(596\) | −3.19322 | + | 5.53082i | −0.130799 | + | 0.226551i | ||||
\(597\) | −14.2524 | −0.583310 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7851 | −1.09441 | −0.547204 | − | 0.836999i | \(-0.684308\pi\) | ||||
−0.547204 | + | 0.836999i | \(0.684308\pi\) | |||||||
\(600\) | −4.34601 | + | 7.52751i | −0.177425 | + | 0.307309i | ||||
\(601\) | 2.35086 | − | 4.07180i | 0.0958934 | − | 0.166092i | −0.814088 | − | 0.580742i | \(-0.802763\pi\) |
0.909981 | + | 0.414650i | \(0.136096\pi\) | |||||||
\(602\) | 7.13773 | + | 12.3629i | 0.290912 | + | 0.503874i | ||||
\(603\) | 3.58211 | 0.145875 | ||||||||
\(604\) | −0.437509 | − | 0.757788i | −0.0178020 | − | 0.0308340i | ||||
\(605\) | 12.3964 | + | 21.4712i | 0.503986 | + | 0.872930i | ||||
\(606\) | −17.3177 | −0.703482 | ||||||||
\(607\) | −13.8198 | − | 23.9366i | −0.560929 | − | 0.971558i | −0.997416 | − | 0.0718472i | \(-0.977111\pi\) |
0.436486 | − | 0.899711i | \(-0.356223\pi\) | |||||||
\(608\) | −3.13640 | + | 5.43240i | −0.127198 | + | 0.220313i | ||||
\(609\) | −4.44385 | + | 7.69697i | −0.180074 | + | 0.311897i | ||||
\(610\) | 27.3545 | 1.10755 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.08815 | 0.0439857 | ||||||||
\(613\) | −24.0891 | + | 41.7236i | −0.972950 | + | 1.68520i | −0.286409 | + | 0.958108i | \(0.592461\pi\) |
−0.686541 | + | 0.727091i | \(0.740872\pi\) | |||||||
\(614\) | 15.9777 | − | 27.6742i | 0.644807 | − | 1.11684i | ||||
\(615\) | 1.74698 | + | 3.02586i | 0.0704450 | + | 0.122014i | ||||
\(616\) | −21.4752 | −0.865259 | ||||||||
\(617\) | −15.1521 | − | 26.2443i | −0.610002 | − | 1.05655i | −0.991239 | − | 0.132077i | \(-0.957835\pi\) |
0.381238 | − | 0.924477i | \(-0.375498\pi\) | |||||||
\(618\) | −10.8509 | − | 18.7942i | −0.436485 | − | 0.756015i | ||||
\(619\) | −10.9041 | −0.438272 | −0.219136 | − | 0.975694i | \(-0.570324\pi\) | ||||
−0.219136 | + | 0.975694i | \(0.570324\pi\) | |||||||
\(620\) | 4.75786 | + | 8.24086i | 0.191080 | + | 0.330961i | ||||
\(621\) | 1.75786 | − | 3.04471i | 0.0705407 | − | 0.122180i | ||||
\(622\) | 7.09634 | − | 12.2912i | 0.284537 | − | 0.492833i | ||||
\(623\) | −30.2325 | −1.21124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1269 | −1.24508 | ||||||||
\(626\) | 17.1923 | − | 29.7780i | 0.687143 | − | 1.19017i | ||||
\(627\) | −1.86496 | + | 3.23021i | −0.0744794 | + | 0.129002i | ||||
\(628\) | 2.38135 | + | 4.12463i | 0.0950264 | + | 0.164591i | ||||
\(629\) | −11.1371 | −0.444064 | ||||||||
\(630\) | 8.38889 | + | 14.5300i | 0.334221 | + | 0.578888i | ||||
\(631\) | 5.22617 | + | 9.05199i | 0.208050 | + | 0.360354i | 0.951100 | − | 0.308882i | \(-0.0999548\pi\) |
−0.743050 | + | 0.669236i | \(0.766621\pi\) | |||||||
\(632\) | −12.2620 | −0.487758 | ||||||||
\(633\) | −0.925428 | − | 1.60289i | −0.0367824 | − | 0.0637091i | ||||
\(634\) | −7.02028 | + | 12.1595i | −0.278811 | + | 0.482915i | ||||
\(635\) | 13.3617 | − | 23.1432i | 0.530244 | − | 0.918410i | ||||
\(636\) | 3.93900 | 0.156192 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.38537 | 0.134028 | ||||||||
\(639\) | −4.41939 | + | 7.65460i | −0.174828 | + | 0.302811i | ||||
\(640\) | 8.63587 | − | 14.9578i | 0.341363 | − | 0.591257i | ||||
\(641\) | 8.79709 | + | 15.2370i | 0.347464 | + | 0.601826i | 0.985798 | − | 0.167934i | \(-0.0537095\pi\) |
−0.638334 | + | 0.769760i | \(0.720376\pi\) | |||||||
\(642\) | −13.1588 | −0.519338 | ||||||||
\(643\) | −11.3029 | − | 19.5772i | −0.445743 | − | 0.772049i | 0.552361 | − | 0.833605i | \(-0.313727\pi\) |
−0.998104 | + | 0.0615560i | \(0.980394\pi\) | |||||||
\(644\) | −3.75667 | − | 6.50674i | −0.148033 | − | 0.256401i | ||||
\(645\) | 6.67994 | 0.263022 | ||||||||
\(646\) | 3.87651 | + | 6.71431i | 0.152519 | + | 0.264171i | ||||
\(647\) | 12.3959 | − | 21.4703i | 0.487333 | − | 0.844085i | −0.512561 | − | 0.858651i | \(-0.671303\pi\) |
0.999894 | + | 0.0145658i | \(0.00463659\pi\) | |||||||
\(648\) | −1.52446 | + | 2.64044i | −0.0598864 | + | 0.103726i | ||||
\(649\) | 3.19221 | 0.125305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6437 | 1.43618 | ||||||||
\(652\) | −0.867781 | + | 1.50304i | −0.0339849 | + | 0.0588636i | ||||
\(653\) | 10.9053 | − | 18.8885i | 0.426757 | − | 0.739164i | −0.569826 | − | 0.821765i | \(-0.692989\pi\) |
0.996583 | + | 0.0826012i | \(0.0263228\pi\) | |||||||
\(654\) | −0.667563 | − | 1.15625i | −0.0261038 | − | 0.0452131i | ||||
\(655\) | −15.4359 | −0.603132 | ||||||||
\(656\) | −1.81551 | − | 3.14456i | −0.0708838 | − | 0.122774i | ||||
\(657\) | −3.84601 | − | 6.66149i | −0.150047 | − | 0.259889i | ||||
\(658\) | 76.7472 | 2.99192 | ||||||||
\(659\) | −8.27628 | − | 14.3349i | −0.322398 | − | 0.558410i | 0.658584 | − | 0.752507i | \(-0.271156\pi\) |
−0.980982 | + | 0.194097i | \(0.937822\pi\) | |||||||
\(660\) | −0.914542 | + | 1.58403i | −0.0355985 | + | 0.0616584i | ||||
\(661\) | 7.97703 | − | 13.8166i | 0.310271 | − | 0.537405i | −0.668150 | − | 0.744026i | \(-0.732914\pi\) |
0.978421 | + | 0.206622i | \(0.0662470\pi\) | |||||||
\(662\) | 14.8471 | 0.577050 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.99031 | 0.0772391 | ||||||||
\(665\) | 17.1069 | − | 29.6299i | 0.663376 | − | 1.14900i | ||||
\(666\) | 2.83997 | − | 4.91897i | 0.110047 | − | 0.190606i | ||||
\(667\) | 3.25355 | + | 5.63532i | 0.125978 | + | 0.218200i | ||||
\(668\) | 9.35450 | 0.361937 | ||||||||
\(669\) | 9.32520 | + | 16.1517i | 0.360533 | + | 0.624462i | ||||
\(670\) | 6.25786 | + | 10.8389i | 0.241762 | + | 0.418745i | ||||
\(671\) | 11.4838 | 0.443327 | ||||||||
\(672\) | 5.92274 | + | 10.2585i | 0.228475 | + | 0.395730i | ||||
\(673\) | 3.69418 | − | 6.39850i | 0.142400 | − | 0.246644i | −0.786000 | − | 0.618227i | \(-0.787851\pi\) |
0.928400 | + | 0.371583i | \(0.121185\pi\) | |||||||
\(674\) | 10.7036 | − | 18.5391i | 0.412286 | − | 0.714101i | ||||
\(675\) | 2.85086 | 0.109729 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1454 | −0.851118 | −0.425559 | − | 0.904931i | \(-0.639922\pi\) | ||||
−0.425559 | + | 0.904931i | \(0.639922\pi\) | |||||||
\(678\) | −10.3068 | + | 17.8519i | −0.395830 | + | 0.685597i | ||||
\(679\) | −24.0852 | + | 41.7168i | −0.924306 | + | 1.60094i | ||||
\(680\) | 10.4438 | + | 18.0893i | 0.400503 | + | 0.693692i | ||||
\(681\) | −9.75733 | −0.373902 | ||||||||
\(682\) | −6.97889 | − | 12.0878i | −0.267236 | − | 0.462866i | ||||
\(683\) | −4.55011 | − | 7.88103i | −0.174105 | − | 0.301559i | 0.765746 | − | 0.643143i | \(-0.222370\pi\) |
−0.939851 | + | 0.341584i | \(0.889037\pi\) | |||||||
\(684\) | 1.13169 | 0.0432711 | ||||||||
\(685\) | −22.6727 | − | 39.2703i | −0.866279 | − | 1.50044i | ||||
\(686\) | 27.1211 | − | 46.9751i | 1.03549 | − | 1.79352i | ||||
\(687\) | −1.43147 | + | 2.47938i | −0.0546139 | + | 0.0945941i | ||||
\(688\) | −6.94198 | −0.264661 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.2838 | 0.467637 | ||||||||
\(691\) | −6.88553 | + | 11.9261i | −0.261938 | + | 0.453690i | −0.966757 | − | 0.255697i | \(-0.917695\pi\) |
0.704819 | + | 0.709387i | \(0.251028\pi\) | |||||||
\(692\) | 2.94504 | − | 5.10096i | 0.111954 | − | 0.193909i | ||||
\(693\) | 3.52177 | + | 6.09989i | 0.133781 | + | 0.231715i | ||||
\(694\) | 30.2717 | 1.14910 | ||||||||
\(695\) | 14.7228 | + | 25.5007i | 0.558468 | + | 0.967295i | ||||
\(696\) | −2.82155 | − | 4.88707i | −0.106951 | − | 0.185244i | ||||
\(697\) | 3.04892 | 0.115486 | ||||||||
\(698\) | −2.85086 | − | 4.93783i | −0.107906 | − | 0.186899i | ||||
\(699\) | 2.89277 | − | 5.01043i | 0.109415 | − | 0.189512i | ||||
\(700\) | 3.04623 | − | 5.27622i | 0.115137 | − | 0.199422i | ||||
\(701\) | 46.5090 | 1.75662 | 0.878311 | − | 0.478090i | \(-0.158671\pi\) | ||||
0.878311 | + | 0.478090i | \(0.158671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.5827 | −0.436850 | ||||||||
\(704\) | 6.52715 | − | 11.3054i | 0.246001 | − | 0.426086i | ||||
\(705\) | 17.9562 | − | 31.1011i | 0.676270 | − | 1.17133i | ||||
\(706\) | −3.78836 | − | 6.56164i | −0.142577 | − | 0.246951i | ||||
\(707\) | 66.6878 | 2.50805 | ||||||||
\(708\) | −0.484271 | − | 0.838781i | −0.0182000 | − | 0.0315233i | ||||
\(709\) | −3.62283 | − | 6.27492i | −0.136058 | − | 0.235660i | 0.789943 | − | 0.613180i | \(-0.210110\pi\) |
−0.926001 | + | 0.377521i | \(0.876777\pi\) | |||||||
\(710\) | −30.8823 | −1.15899 | ||||||||
\(711\) | 2.01089 | + | 3.48296i | 0.0754141 | + | 0.130621i | ||||
\(712\) | 9.59783 | − | 16.6239i | 0.359694 | − | 0.623008i | ||||
\(713\) | 13.4143 | − | 23.2343i | 0.502370 | − | 0.870130i | ||||
\(714\) | 14.6407 | 0.547915 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.79523 | −0.141835 | ||||||||
\(717\) | 3.54623 | − | 6.14225i | 0.132436 | − | 0.229386i | ||||
\(718\) | −9.33124 | + | 16.1622i | −0.348239 | + | 0.603167i | ||||
\(719\) | −12.7573 | − | 22.0963i | −0.475768 | − | 0.824055i | 0.523846 | − | 0.851813i | \(-0.324497\pi\) |
−0.999615 | + | 0.0277580i | \(0.991163\pi\) | |||||||
\(720\) | −8.15883 | −0.304062 | ||||||||
\(721\) | 41.7851 | + | 72.3739i | 1.55616 | + | 2.69534i | ||||
\(722\) | −7.81468 | − | 13.5354i | −0.290832 | − | 0.503736i | ||||
\(723\) | −3.89977 | −0.145034 | ||||||||
\(724\) | −0.809175 | − | 1.40153i | −0.0300728 | − | 0.0520875i | ||||
\(725\) | −2.63826 | + | 4.56960i | −0.0979825 | + | 0.169711i | ||||
\(726\) | −5.51693 | + | 9.55560i | −0.204752 | + | 0.354641i | ||||
\(727\) | −14.4873 | −0.537303 | −0.268651 | − | 0.963238i | \(-0.586578\pi\) | ||||
−0.268651 | + | 0.963238i | \(0.586578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.4378 | − | 23.2750i | 0.497355 | − | 0.861445i | ||||
\(731\) | 2.91454 | − | 5.04814i | 0.107798 | − | 0.186712i | ||||
\(732\) | −1.74214 | − | 3.01747i | −0.0643912 | − | 0.111529i | ||||
\(733\) | 37.5036 | 1.38523 | 0.692614 | − | 0.721308i | \(-0.256459\pi\) | ||||
0.692614 | + | 0.721308i | \(0.256459\pi\) | |||||||
\(734\) | 23.1211 | + | 40.0469i | 0.853415 | + | 1.47816i | ||||
\(735\) | −22.4976 | − | 38.9670i | −0.829837 | − | 1.43732i | ||||
\(736\) | 8.67264 | 0.319678 | ||||||||
\(737\) | 2.62714 | + | 4.55034i | 0.0967719 | + | 0.167614i | ||||
\(738\) | −0.777479 | + | 1.34663i | −0.0286194 | + | 0.0495703i | ||||
\(739\) | −21.5938 | + | 37.4016i | −0.794341 | + | 1.37584i | 0.128915 | + | 0.991656i | \(0.458851\pi\) |
−0.923257 | + | 0.384184i | \(0.874483\pi\) | |||||||
\(740\) | −5.67994 | −0.208799 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.9982 | 1.94563 | ||||||||
\(743\) | −6.73825 | + | 11.6710i | −0.247202 | + | 0.428167i | −0.962749 | − | 0.270398i | \(-0.912845\pi\) |
0.715546 | + | 0.698566i | \(0.246178\pi\) | |||||||
\(744\) | −11.6332 | + | 20.1493i | −0.426493 | + | 0.738708i | ||||
\(745\) | 20.1042 | + | 34.8214i | 0.736560 | + | 1.27576i | ||||
\(746\) | 45.5260 | 1.66683 | ||||||||
\(747\) | −0.326396 | − | 0.565335i | −0.0119422 | − | 0.0206845i | ||||
\(748\) | 0.798053 | + | 1.38227i | 0.0291797 | + | 0.0505407i | ||||
\(749\) | 50.6728 | 1.85154 | ||||||||
\(750\) | −3.75451 | − | 6.50301i | −0.137095 | − | 0.237456i | ||||
\(751\) | −17.7947 | + | 30.8213i | −0.649338 | + | 1.12469i | 0.333943 | + | 0.942593i | \(0.391621\pi\) |
−0.983281 | + | 0.182093i | \(0.941713\pi\) | |||||||
\(752\) | −18.6606 | + | 32.3211i | −0.680483 | + | 1.17863i | ||||
\(753\) | −2.44504 | −0.0891023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.50902 | −0.200494 | ||||||||
\(756\) | 1.06853 | − | 1.85075i | 0.0388621 | − | 0.0673112i | ||||
\(757\) | 6.10537 | − | 10.5748i | 0.221903 | − | 0.384348i | −0.733483 | − | 0.679708i | \(-0.762106\pi\) |
0.955386 | + | 0.295360i | \(0.0954397\pi\) | |||||||
\(758\) | −16.5755 | − | 28.7097i | −0.602050 | − | 1.04278i | ||||
\(759\) | 5.15691 | 0.187184 | ||||||||
\(760\) | 10.8617 | + | 18.8131i | 0.393997 | + | 0.682422i | ||||
\(761\) | −15.4535 | − | 26.7663i | −0.560190 | − | 0.970278i | −0.997479 | − | 0.0709569i | \(-0.977395\pi\) |
0.437289 | − | 0.899321i | \(-0.355939\pi\) | |||||||
\(762\) | 11.8931 | 0.430840 | ||||||||
\(763\) | 2.57069 | + | 4.45256i | 0.0930651 | + | 0.161194i | ||||
\(764\) | 4.75786 | − | 8.24086i | 0.172134 | − | 0.298144i | ||||
\(765\) | 3.42543 | − | 5.93301i | 0.123847 | − | 0.214509i | ||||
\(766\) | 17.8944 | 0.646551 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10.1129 | −0.364918 | ||||||||
\(769\) | −5.99462 | + | 10.3830i | −0.216172 | + | 0.374420i | −0.953634 | − | 0.300968i | \(-0.902690\pi\) |
0.737463 | + | 0.675388i | \(0.236024\pi\) | |||||||
\(770\) | −12.3049 | + | 21.3127i | −0.443439 | + | 0.768058i | ||||
\(771\) | 7.06518 | + | 12.2372i | 0.254446 | + | 0.440714i | ||||
\(772\) | −3.75063 | −0.134988 | ||||||||
\(773\) | −21.9831 | − | 38.0758i | −0.790676 | − | 1.36949i | −0.925549 | − | 0.378628i | \(-0.876396\pi\) |
0.134873 | − | 0.990863i | \(-0.456938\pi\) | |||||||
\(774\) | 1.48643 | + | 2.57457i | 0.0534285 | + | 0.0925409i | ||||
\(775\) | 21.7549 | 0.781460 | ||||||||
\(776\) | −15.2925 | − | 26.4875i | −0.548970 | − | 0.950845i | ||||
\(777\) | −10.9363 | + | 18.9422i | −0.392338 | + | 0.679549i | ||||
\(778\) | −14.1271 | + | 24.4689i | −0.506482 | + | 0.877253i | ||||
\(779\) | 3.17092 | 0.113610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9648 | −0.463918 | ||||||||
\(782\) | 5.35958 | − | 9.28307i | 0.191658 | − | 0.331962i | ||||
\(783\) | −0.925428 | + | 1.60289i | −0.0330721 | + | 0.0572825i | ||||
\(784\) | 23.3802 | + | 40.4956i | 0.835006 | + | 1.44627i | ||||
\(785\) | 29.9855 | 1.07023 | ||||||||
\(786\) | −3.43482 | − | 5.94928i | −0.122516 | − | 0.212204i | ||||
\(787\) | −15.1881 | − | 26.3066i | −0.541399 | − | 0.937730i | −0.998824 | − | 0.0484819i | \(-0.984562\pi\) |
0.457425 | − | 0.889248i | \(-0.348772\pi\) | |||||||
\(788\) | −11.7832 | −0.419757 | ||||||||
\(789\) | 11.8617 | + | 20.5451i | 0.422289 | + | 0.731426i | ||||
\(790\) | −7.02595 | + | 12.1693i | −0.249972 | + | 0.432964i | ||||
\(791\) | 39.6899 | − | 68.7450i | 1.41121 | − | 2.44429i | ||||
\(792\) | −4.47219 | −0.158912 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9.86054 | −0.349938 | ||||||||
\(795\) | 12.3998 | − | 21.4770i | 0.439775 | − | 0.761712i | ||||
\(796\) | −3.17145 | + | 5.49311i | −0.112409 | + | 0.194698i | ||||
\(797\) | −26.2881 | − | 45.5324i | −0.931173 | − | 1.61284i | −0.781320 | − | 0.624131i | \(-0.785453\pi\) |
−0.149854 | − | 0.988708i | \(-0.547880\pi\) | |||||||
\(798\) | 15.2265 | 0.539014 | ||||||||
\(799\) | −15.6691 | − | 27.1396i | −0.554331 | − | 0.960130i | ||||
\(800\) | 3.51626 | + | 6.09034i | 0.124319 | + | 0.215326i | ||||
\(801\) | −6.29590 | −0.222455 | ||||||||
\(802\) | 1.83095 | + | 3.17129i | 0.0646529 | + | 0.111982i | ||||
\(803\) | 5.64138 | − | 9.77115i | 0.199080 | − | 0.344816i | ||||
\(804\) | 0.797093 | − | 1.38061i | 0.0281113 | − | 0.0486902i | ||||
\(805\) | −47.3032 | −1.66722 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.91617 | −0.208259 | ||||||||
\(808\) | −21.1712 | + | 36.6696i | −0.744801 | + | 1.29003i | ||||
\(809\) | −24.7107 | + | 42.8002i | −0.868783 | + | 1.50478i | −0.00554214 | + | 0.999985i | \(0.501764\pi\) |
−0.863241 | + | 0.504792i | \(0.831569\pi\) | |||||||
\(810\) | 1.74698 | + | 3.02586i | 0.0613826 | + | 0.106318i | ||||
\(811\) | −1.36526 | −0.0479406 | −0.0239703 | − | 0.999713i | \(-0.507631\pi\) | ||||
−0.0239703 | + | 0.999713i | \(0.507631\pi\) | |||||||
\(812\) | 1.97770 | + | 3.42547i | 0.0694036 | + | 0.120211i | ||||
\(813\) | 1.59515 | + | 2.76287i | 0.0559442 | + | 0.0968982i | ||||
\(814\) | 8.33140 | 0.292016 | ||||||||
\(815\) | 5.46346 | + | 9.46299i | 0.191377 | + | 0.331474i | ||||
\(816\) | −3.55980 | + | 6.16576i | −0.124618 | + | 0.215845i | ||||
\(817\) | 3.03116 | − | 5.25013i | 0.106047 | − | 0.183679i | ||||
\(818\) | −14.6582 | −0.512511 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.55496 | 0.0543015 | ||||||||
\(821\) | −0.332970 | + | 0.576720i | −0.0116207 | + | 0.0201277i | −0.871777 | − | 0.489902i | \(-0.837032\pi\) |
0.860157 | + | 0.510030i | \(0.170366\pi\) | |||||||
\(822\) | 10.0903 | − | 17.4769i | 0.351940 | − | 0.609577i | ||||
\(823\) | 5.02960 | + | 8.71152i | 0.175321 | + | 0.303665i | 0.940272 | − | 0.340423i | \(-0.110570\pi\) |
−0.764951 | + | 0.644088i | \(0.777237\pi\) | |||||||
\(824\) | −53.0616 | −1.84849 | ||||||||
\(825\) | 2.09083 | + | 3.62143i | 0.0727935 | + | 0.126082i | ||||
\(826\) | −6.51573 | − | 11.2856i | −0.226711 | − | 0.392675i | ||||
\(827\) | −37.3038 | −1.29718 | −0.648590 | − | 0.761138i | \(-0.724641\pi\) | ||||
−0.648590 | + | 0.761138i | \(0.724641\pi\) | |||||||
\(828\) | −0.782323 | − | 1.35502i | −0.0271876 | − | 0.0470903i | ||||
\(829\) | 21.3104 | − | 36.9107i | 0.740142 | − | 1.28196i | −0.212289 | − | 0.977207i | \(-0.568092\pi\) |
0.952430 | − | 0.304756i | \(-0.0985750\pi\) | |||||||
\(830\) | 1.14042 | − | 1.97526i | 0.0395844 | − | 0.0685622i | ||||
\(831\) | 21.9366 | 0.760973 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.2640 | −1.36042 | ||||||||
\(834\) | −6.55227 | + | 11.3489i | −0.226887 | + | 0.392979i | ||||
\(835\) | 29.4475 | − | 51.0046i | 1.01907 | − | 1.76509i | ||||
\(836\) | 0.829986 | + | 1.43758i | 0.0287057 | + | 0.0497197i | ||||
\(837\) | 7.63102 | 0.263767 | ||||||||
\(838\) | 4.57756 | + | 7.92856i | 0.158129 | + | 0.273888i | ||||
\(839\) | −2.07002 | − | 3.58539i | −0.0714652 | − | 0.123781i | 0.828078 | − | 0.560612i | \(-0.189434\pi\) |
−0.899544 | + | 0.436831i | \(0.856101\pi\) | |||||||
\(840\) | 41.0224 | 1.41541 | ||||||||
\(841\) | 12.7872 | + | 22.1480i | 0.440937 | + | 0.763725i | ||||
\(842\) | 16.0214 | − | 27.7499i | 0.552134 | − | 0.956324i | ||||
\(843\) | −5.99516 | + | 10.3839i | −0.206484 | + | 0.357641i | ||||
\(844\) | −0.823708 | −0.0283532 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.9825 | 0.549491 | ||||||||
\(847\) | 21.2449 | − | 36.7972i | 0.729983 | − | 1.26437i | ||||
\(848\) | −12.8862 | + | 22.3196i | −0.442514 | + | 0.766457i | ||||
\(849\) | 7.18329 | + | 12.4418i | 0.246530 | + | 0.427002i | ||||
\(850\) | 8.69202 | 0.298134 | ||||||||
\(851\) | 8.00700 | + | 13.8685i | 0.274476 | + | 0.475407i | ||||
\(852\) | 1.96681 | + | 3.40662i | 0.0673819 | + | 0.116709i | ||||
\(853\) | 17.3502 | 0.594059 | 0.297030 | − | 0.954868i | \(-0.404004\pi\) | ||||
0.297030 | + | 0.954868i | \(0.404004\pi\) | |||||||
\(854\) | −23.4400 | − | 40.5992i | −0.802099 | − | 1.38928i | ||||
\(855\) | 3.56249 | − | 6.17042i | 0.121835 | − | 0.211024i | ||||
\(856\) | −16.0869 | + | 27.8634i | −0.549841 | + | 0.952352i | ||||
\(857\) | 41.0180 | 1.40115 | 0.700575 | − | 0.713579i | \(-0.252927\pi\) | ||||
0.700575 | + | 0.713579i | \(0.252927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.59286 | 0.224945 | 0.112473 | − | 0.993655i | \(-0.464123\pi\) | ||||
0.112473 | + | 0.993655i | \(0.464123\pi\) | |||||||
\(860\) | 1.48643 | − | 2.57457i | 0.0506867 | − | 0.0877920i | ||||
\(861\) | 2.99396 | − | 5.18569i | 0.102034 | − | 0.176728i | ||||
\(862\) | 5.57524 | + | 9.65659i | 0.189893 | + | 0.328905i | ||||
\(863\) | −16.6455 | −0.566619 | −0.283310 | − | 0.959028i | \(-0.591432\pi\) | ||||
−0.283310 | + | 0.959028i | \(0.591432\pi\) | |||||||
\(864\) | 1.23341 | + | 2.13632i | 0.0419613 | + | 0.0726791i | ||||
\(865\) | −18.5417 | − | 32.1151i | −0.630436 | − | 1.09195i | ||||
\(866\) | −3.63474 | −0.123514 | ||||||||
\(867\) | 5.51089 | + | 9.54513i | 0.187159 | + | 0.324170i | ||||
\(868\) | 8.15399 | − | 14.1231i | 0.276764 | − | 0.479370i | ||||
\(869\) | −2.94959 | + | 5.10884i | −0.100058 | + | 0.173306i | ||||
\(870\) | −6.46681 | −0.219245 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.26444 | −0.110548 | ||||||||
\(873\) | −5.01573 | + | 8.68750i | −0.169757 | + | 0.294027i | ||||
\(874\) | 5.57404 | − | 9.65452i | 0.188545 | − | 0.326569i | ||||
\(875\) | 14.4581 | + | 25.0421i | 0.488772 | + | 0.846579i | ||||
\(876\) | −3.42327 | −0.115662 | ||||||||
\(877\) | −27.2482 | − | 47.1953i | −0.920108 | − | 1.59367i | −0.799246 | − | 0.601004i | \(-0.794768\pi\) |
−0.120861 | − | 0.992669i | \(-0.538566\pi\) | |||||||
\(878\) | 5.64795 | + | 9.78253i | 0.190609 | + | 0.330145i | ||||
\(879\) | 18.7584 | 0.632705 | ||||||||
\(880\) | −5.98374 | − | 10.3641i | −0.201712 | − | 0.349375i | ||||
\(881\) | 4.50335 | − | 7.80004i | 0.151722 | − | 0.262790i | −0.780139 | − | 0.625607i | \(-0.784852\pi\) |
0.931861 | + | 0.362817i | \(0.118185\pi\) | |||||||
\(882\) | 10.0124 | − | 17.3419i | 0.337134 | − | 0.583934i | ||||
\(883\) | 18.8907 | 0.635722 | 0.317861 | − | 0.948137i | \(-0.397035\pi\) | ||||
0.317861 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.09783 | −0.204976 | ||||||||
\(886\) | 7.00335 | − | 12.1302i | 0.235282 | − | 0.407521i | ||||
\(887\) | 23.4562 | − | 40.6274i | 0.787583 | − | 1.36413i | −0.139861 | − | 0.990171i | \(-0.544666\pi\) |
0.927444 | − | 0.373962i | \(-0.122001\pi\) | |||||||
\(888\) | −6.94385 | − | 12.0271i | −0.233020 | − | 0.403603i | ||||
\(889\) | −45.7985 | −1.53603 | ||||||||
\(890\) | −10.9988 | − | 19.0505i | −0.368681 | − | 0.638574i | ||||
\(891\) | 0.733406 | + | 1.27030i | 0.0245700 | + | 0.0425565i | ||||
\(892\) | 8.30021 | 0.277912 | ||||||||
\(893\) | −16.2960 | − | 28.2255i | −0.545326 | − | 0.944532i | ||||
\(894\) | −8.94720 | + | 15.4970i | −0.299239 | + | 0.518297i | ||||
\(895\) | −11.9472 | + | 20.6932i | −0.399351 | + | 0.691696i | ||||
\(896\) | −29.6002 | −0.988872 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.8605 | −1.19668 | ||||||||
\(899\) | −7.06196 | + | 12.2317i | −0.235529 | + | 0.407949i | ||||
\(900\) | 0.634375 | − | 1.09877i | 0.0211458 | − | 0.0366257i | ||||
\(901\) | −10.8204 | − | 18.7414i | −0.360478 | − | 0.624367i | ||||
\(902\) | −2.28083 | −0.0759434 | ||||||||
\(903\) | −5.72401 | − | 9.91428i | −0.190483 | − | 0.329927i | ||||
\(904\) | 25.2005 | + | 43.6486i | 0.838157 | + | 1.45173i | ||||
\(905\) | −10.1890 | −0.338693 | ||||||||
\(906\) | −1.22587 | − | 2.12327i | −0.0407269 | − | 0.0705411i | ||||
\(907\) | 17.6506 | − | 30.5718i | 0.586080 | − | 1.01512i | −0.408660 | − | 0.912687i | \(-0.634004\pi\) |
0.994740 | − | 0.102433i | \(-0.0326628\pi\) | |||||||
\(908\) | −2.17121 | + | 3.76065i | −0.0720542 | + | 0.124801i | ||||
\(909\) | 13.8877 | 0.460626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.80731 | −0.324931 | −0.162465 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162465 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(912\) | −3.70224 | + | 6.41247i | −0.122594 | + | 0.212338i | ||||
\(913\) | 0.478762 | − | 0.829240i | 0.0158447 | − | 0.0274439i | ||||
\(914\) | −11.8937 | − | 20.6005i | −0.393410 | − | 0.681406i | ||||
\(915\) | −21.9366 | −0.725202 | ||||||||
\(916\) | 0.637063 | + | 1.10343i | 0.0210492 | + | 0.0364582i | ||||
\(917\) | 13.2270 | + | 22.9098i | 0.436794 | + | 0.756549i | ||||
\(918\) | 3.04892 | 0.100629 | ||||||||
\(919\) | −9.23274 | − | 15.9916i | −0.304560 | − | 0.527513i | 0.672603 | − | 0.740003i | \(-0.265176\pi\) |
−0.977163 | + | 0.212490i | \(0.931843\pi\) | |||||||
\(920\) | 15.0172 | − | 26.0106i | 0.495103 | − | 0.857544i | ||||
\(921\) | −12.8131 | + | 22.1930i | −0.422207 | + | 0.731283i | ||||
\(922\) | −39.5706 | −1.30319 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.13467 | 0.103123 | ||||||||
\(925\) | −6.49276 | + | 11.2458i | −0.213481 | + | 0.369759i | ||||
\(926\) | −22.7439 | + | 39.3936i | −0.747412 | + | 1.29455i | ||||
\(927\) | 8.70171 | + | 15.0718i | 0.285802 | + | 0.495023i | ||||
\(928\) | −4.56571 | −0.149877 | ||||||||
\(929\) | 12.8134 | + | 22.1934i | 0.420393 | + | 0.728141i | 0.995978 | − | 0.0896005i | \(-0.0285590\pi\) |
−0.575585 | + | 0.817742i | \(0.695226\pi\) | |||||||
\(930\) | 13.3312 | + | 23.0904i | 0.437149 | + | 0.757164i | ||||
\(931\) | −40.8351 | −1.33831 | ||||||||
\(932\) | −1.28740 | − | 2.22985i | −0.0421703 | − | 0.0730412i | ||||
\(933\) | −5.69083 | + | 9.85680i | −0.186309 | + | 0.322697i | ||||
\(934\) | 8.10537 | − | 14.0389i | 0.265216 | − | 0.459367i | ||||
\(935\) | 10.0489 | 0.328635 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.54932 | 0.246625 | 0.123313 | − | 0.992368i | \(-0.460648\pi\) | ||||
0.123313 | + | 0.992368i | \(0.460648\pi\) | |||||||
\(938\) | 10.7247 | − | 18.5757i | 0.350173 | − | 0.606518i | ||||
\(939\) | −13.7872 | + | 23.8801i | −0.449927 | + | 0.779297i | ||||
\(940\) | −7.99127 | − | 13.8413i | −0.260647 | − | 0.451453i | ||||
\(941\) | −12.6418 | −0.412110 | −0.206055 | − | 0.978540i | \(-0.566063\pi\) | ||||
−0.206055 | + | 0.978540i | \(0.566063\pi\) | |||||||
\(942\) | 6.67241 | + | 11.5569i | 0.217399 | + | 0.376546i | ||||
\(943\) | −2.19202 | − | 3.79669i | −0.0713820 | − | 0.123637i | ||||
\(944\) | 6.33704 | 0.206253 | ||||||||
\(945\) | −6.72737 | − | 11.6521i | −0.218841 | − | 0.379044i | ||||
\(946\) | −2.18031 | + | 3.77640i | −0.0708879 | + | 0.122782i | ||||
\(947\) | −13.9901 | + | 24.2315i | −0.454616 | + | 0.787419i | −0.998666 | − | 0.0516344i | \(-0.983557\pi\) |
0.544050 | + | 0.839053i | \(0.316890\pi\) | |||||||
\(948\) | 1.78986 | 0.0581318 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.03982 | 0.293290 | ||||||||
\(951\) | 5.62983 | − | 9.75114i | 0.182560 | − | 0.316203i | ||||
\(952\) | 17.8986 | − | 31.0012i | 0.580096 | − | 1.00476i | ||||
\(953\) | −2.00120 | − | 3.46617i | −0.0648251 | − | 0.112280i | 0.831791 | − | 0.555089i | \(-0.187316\pi\) |
−0.896616 | + | 0.442808i | \(0.853982\pi\) | |||||||
\(954\) | 11.0368 | 0.357331 | ||||||||
\(955\) | −29.9550 | − | 51.8836i | −0.969322 | − | 1.67891i | ||||
\(956\) | −1.57822 | − | 2.73356i | −0.0510433 | − | 0.0884096i | ||||
\(957\) | −2.71486 | −0.0877589 | ||||||||
\(958\) | 3.50186 | + | 6.06540i | 0.113140 | + | 0.195964i | ||||
\(959\) | −38.8563 | + | 67.3011i | −1.25474 | + | 2.17326i | ||||
\(960\) | −12.4683 | + | 21.5957i | −0.402413 | + | 0.696999i | ||||
\(961\) | 27.2325 | 0.878468 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5526 | 0.340052 | ||||||||
\(964\) | −0.867781 | + | 1.50304i | −0.0279493 | + | 0.0484097i | ||||
\(965\) | −11.8068 | + | 20.4499i | −0.380074 | + | 0.658307i | ||||
\(966\) | −10.5260 | − | 18.2315i | −0.338667 | − | 0.586588i | ||||
\(967\) | 12.2239 | 0.393094 | 0.196547 | − | 0.980494i | \(-0.437027\pi\) | ||||
0.196547 | + | 0.980494i | \(0.437027\pi\) | |||||||
\(968\) | 13.4891 | + | 23.3638i | 0.433557 | + | 0.750942i | ||||
\(969\) | −3.10872 | − | 5.38446i | −0.0998665 | − | 0.172974i | ||||
\(970\) | −35.0495 | −1.12537 | ||||||||
\(971\) | 11.8201 | + | 20.4729i | 0.379324 | + | 0.657008i | 0.990964 | − | 0.134128i | \(-0.0428233\pi\) |
−0.611640 | + | 0.791136i | \(0.709490\pi\) | |||||||
\(972\) | 0.222521 | − | 0.385418i | 0.00713736 | − | 0.0123623i | ||||
\(973\) | 25.2318 | − | 43.7028i | 0.808896 | − | 1.40105i | ||||
\(974\) | 12.1672 | 0.389862 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7972 | 0.729719 | ||||||||
\(977\) | −9.36563 | + | 16.2217i | −0.299633 | + | 0.518979i | −0.976052 | − | 0.217538i | \(-0.930198\pi\) |
0.676419 | + | 0.736517i | \(0.263531\pi\) | |||||||
\(978\) | −2.43147 | + | 4.21143i | −0.0777498 | + | 0.134667i | ||||
\(979\) | −4.61745 | − | 7.99766i | −0.147574 | − | 0.255606i | ||||
\(980\) | −20.0248 | −0.639667 | ||||||||
\(981\) | 0.535344 | + | 0.927243i | 0.0170922 | + | 0.0296046i | ||||
\(982\) | −4.60656 | − | 7.97880i | −0.147001 | − | 0.254614i | ||||
\(983\) | 12.0954 | 0.385785 | 0.192892 | − | 0.981220i | \(-0.438213\pi\) | ||||
0.192892 | + | 0.981220i | \(0.438213\pi\) | |||||||
\(984\) | 1.90097 | + | 3.29257i | 0.0606007 | + | 0.104963i | ||||
\(985\) | −37.0928 | + | 64.2465i | −1.18187 | + | 2.04706i | ||||
\(986\) | −2.82155 | + | 4.88707i | −0.0898565 | + | 0.155636i | ||||
\(987\) | −61.5465 | −1.95905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.38165 | −0.266521 | ||||||||
\(990\) | −2.56249 | + | 4.43836i | −0.0814413 | + | 0.141060i | ||||
\(991\) | 14.2763 | − | 24.7272i | 0.453501 | − | 0.785487i | −0.545100 | − | 0.838371i | \(-0.683508\pi\) |
0.998601 | + | 0.0528844i | \(0.0168415\pi\) | |||||||
\(992\) | 9.41215 | + | 16.3023i | 0.298836 | + | 0.517599i | ||||
\(993\) | −11.9065 | −0.377841 | ||||||||
\(994\) | 26.4629 | + | 45.8351i | 0.839353 | + | 1.45380i | ||||
\(995\) | 19.9671 | + | 34.5840i | 0.633000 | + | 1.09639i | ||||
\(996\) | −0.290520 | −0.00920548 | ||||||||
\(997\) | 11.9673 | + | 20.7280i | 0.379010 | + | 0.656464i | 0.990918 | − | 0.134464i | \(-0.0429314\pi\) |
−0.611909 | + | 0.790928i | \(0.709598\pi\) | |||||||
\(998\) | −26.9855 | + | 46.7403i | −0.854212 | + | 1.47954i | ||||
\(999\) | −2.27748 | + | 3.94471i | −0.0720562 | + | 0.124805i |
(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 | 507.2.e.j.22.3 | 6 | ||
13.2 | odd | 12 | 507.2.j.h.361.5 | 12 | |||
13.3 | even | 3 | inner | 507.2.e.j.484.3 | 6 | ||
13.4 | even | 6 | 507.2.a.j.1.3 | ✓ | 3 | ||
13.5 | odd | 4 | 507.2.j.h.316.2 | 12 | |||
13.6 | odd | 12 | 507.2.b.g.337.5 | 6 | |||
13.7 | odd | 12 | 507.2.b.g.337.2 | 6 | |||
13.8 | odd | 4 | 507.2.j.h.316.5 | 12 | |||
13.9 | even | 3 | 507.2.a.k.1.1 | yes | 3 | ||
13.10 | even | 6 | 507.2.e.k.484.1 | 6 | |||
13.11 | odd | 12 | 507.2.j.h.361.2 | 12 | |||
13.12 | even | 2 | 507.2.e.k.22.1 | 6 | |||
39.17 | odd | 6 | 1521.2.a.q.1.1 | 3 | |||
39.20 | even | 12 | 1521.2.b.m.1351.5 | 6 | |||
39.32 | even | 12 | 1521.2.b.m.1351.2 | 6 | |||
39.35 | odd | 6 | 1521.2.a.p.1.3 | 3 | |||
52.35 | odd | 6 | 8112.2.a.cf.1.3 | 3 | |||
52.43 | odd | 6 | 8112.2.a.by.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.3 | ✓ | 3 | 13.4 | even | 6 | ||
507.2.a.k.1.1 | yes | 3 | 13.9 | even | 3 | ||
507.2.b.g.337.2 | 6 | 13.7 | odd | 12 | |||
507.2.b.g.337.5 | 6 | 13.6 | odd | 12 | |||
507.2.e.j.22.3 | 6 | 1.1 | even | 1 | trivial | ||
507.2.e.j.484.3 | 6 | 13.3 | even | 3 | inner | ||
507.2.e.k.22.1 | 6 | 13.12 | even | 2 | |||
507.2.e.k.484.1 | 6 | 13.10 | even | 6 | |||
507.2.j.h.316.2 | 12 | 13.5 | odd | 4 | |||
507.2.j.h.316.5 | 12 | 13.8 | odd | 4 | |||
507.2.j.h.361.2 | 12 | 13.11 | odd | 12 | |||
507.2.j.h.361.5 | 12 | 13.2 | odd | 12 | |||
1521.2.a.p.1.3 | 3 | 39.35 | odd | 6 | |||
1521.2.a.q.1.1 | 3 | 39.17 | odd | 6 | |||
1521.2.b.m.1351.2 | 6 | 39.32 | even | 12 | |||
1521.2.b.m.1351.5 | 6 | 39.20 | even | 12 | |||
8112.2.a.by.1.1 | 3 | 52.43 | odd | 6 | |||
8112.2.a.cf.1.3 | 3 | 52.35 | odd | 6 |