Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,2,Mod(29,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.29");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.894324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.20138089353117696.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 85.3 | ||
Root | \(-1.40471 + 0.163666i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.85 |
Dual form | 112.2.m.d.29.3 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.163666 | − | 1.40471i | 0.115730 | − | 0.993281i | ||||
\(3\) | −2.05500 | + | 2.05500i | −1.18645 | + | 1.18645i | −0.208411 | + | 0.978041i | \(0.566829\pi\) |
−0.978041 | + | 0.208411i | \(0.933171\pi\) | |||||||
\(4\) | −1.94643 | − | 0.459808i | −0.973213 | − | 0.229904i | ||||
\(5\) | 2.72766 | + | 2.72766i | 1.21985 | + | 1.21985i | 0.967685 | + | 0.252164i | \(0.0811421\pi\) |
0.252164 | + | 0.967685i | \(0.418858\pi\) | |||||||
\(6\) | 2.55034 | + | 3.22301i | 1.04117 | + | 1.31579i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −0.964462 | + | 2.65891i | −0.340989 | + | 0.940067i | ||||
\(9\) | − | 5.44602i | − | 1.81534i | ||||||
\(10\) | 4.27801 | − | 3.38515i | 1.35282 | − | 1.07048i | ||||
\(11\) | 0.919616 | + | 0.919616i | 0.277275 | + | 0.277275i | 0.832020 | − | 0.554746i | \(-0.187184\pi\) |
−0.554746 | + | 0.832020i | \(0.687184\pi\) | |||||||
\(12\) | 4.94480 | − | 3.05500i | 1.42744 | − | 0.881901i | ||||
\(13\) | −1.12607 | + | 1.12607i | −0.312316 | + | 0.312316i | −0.845806 | − | 0.533490i | \(-0.820880\pi\) |
0.533490 | + | 0.845806i | \(0.320880\pi\) | |||||||
\(14\) | 1.40471 | + | 0.163666i | 0.375425 | + | 0.0437417i | ||||
\(15\) | −11.2107 | −2.89458 | ||||||||
\(16\) | 3.57715 | + | 1.78996i | 0.894288 | + | 0.447491i | ||||
\(17\) | −1.50885 | −0.365950 | −0.182975 | − | 0.983118i | \(-0.558573\pi\) | ||||
−0.182975 | + | 0.983118i | \(0.558573\pi\) | |||||||
\(18\) | −7.65008 | − | 0.891330i | −1.80314 | − | 0.210088i | ||||
\(19\) | 1.46271 | − | 1.46271i | 0.335569 | − | 0.335569i | −0.519127 | − | 0.854697i | \(-0.673743\pi\) |
0.854697 | + | 0.519127i | \(0.173743\pi\) | |||||||
\(20\) | −4.05500 | − | 6.56340i | −0.906725 | − | 1.46762i | ||||
\(21\) | −2.05500 | − | 2.05500i | −0.448437 | − | 0.448437i | ||||
\(22\) | 1.44230 | − | 1.14128i | 0.307500 | − | 0.243323i | ||||
\(23\) | − | 4.77031i | − | 0.994677i | −0.867556 | − | 0.497339i | \(-0.834311\pi\) | ||
0.867556 | − | 0.497339i | \(-0.165689\pi\) | |||||||
\(24\) | −3.48209 | − | 7.44602i | −0.710779 | − | 1.51991i | ||||
\(25\) | 9.88030i | 1.97606i | ||||||||
\(26\) | 1.39751 | + | 1.76611i | 0.274074 | + | 0.346362i | ||||
\(27\) | 5.02656 | + | 5.02656i | 0.967362 | + | 0.967362i | ||||
\(28\) | 0.459808 | − | 1.94643i | 0.0868955 | − | 0.367840i | ||||
\(29\) | 4.10069 | − | 4.10069i | 0.761478 | − | 0.761478i | −0.215111 | − | 0.976590i | \(-0.569011\pi\) |
0.976590 | + | 0.215111i | \(0.0690115\pi\) | |||||||
\(30\) | −1.83481 | + | 15.7478i | −0.334989 | + | 2.87514i | ||||
\(31\) | 4.10999 | 0.738176 | 0.369088 | − | 0.929394i | \(-0.379670\pi\) | ||||
0.369088 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(32\) | 3.09984 | − | 4.73191i | 0.547980 | − | 0.836492i | ||||
\(33\) | −3.77961 | −0.657946 | ||||||||
\(34\) | −0.246948 | + | 2.11950i | −0.0423513 | + | 0.363491i | ||||
\(35\) | −2.72766 | + | 2.72766i | −0.461059 | + | 0.461059i | ||||
\(36\) | −2.50412 | + | 10.6003i | −0.417354 | + | 1.76671i | ||||
\(37\) | −1.65467 | − | 1.65467i | −0.272025 | − | 0.272025i | 0.557890 | − | 0.829915i | \(-0.311611\pi\) |
−0.829915 | + | 0.557890i | \(0.811611\pi\) | |||||||
\(38\) | −1.81529 | − | 2.29409i | −0.294479 | − | 0.372150i | ||||
\(39\) | − | 4.62815i | − | 0.741097i | ||||||
\(40\) | −9.88334 | + | 4.62189i | −1.56269 | + | 0.730785i | ||||
\(41\) | − | 7.45533i | − | 1.16433i | −0.813072 | − | 0.582163i | \(-0.802206\pi\) | ||
0.813072 | − | 0.582163i | \(-0.197794\pi\) | |||||||
\(42\) | −3.22301 | + | 2.55034i | −0.497321 | + | 0.393526i | ||||
\(43\) | 5.68992 | + | 5.68992i | 0.867705 | + | 0.867705i | 0.992218 | − | 0.124513i | \(-0.0397369\pi\) |
−0.124513 | + | 0.992218i | \(0.539737\pi\) | |||||||
\(44\) | −1.36712 | − | 2.21281i | −0.206101 | − | 0.333594i | ||||
\(45\) | 14.8549 | − | 14.8549i | 2.21444 | − | 2.21444i | ||||
\(46\) | −6.70090 | − | 0.780738i | −0.987994 | − | 0.115114i | ||||
\(47\) | 3.59748 | 0.524747 | 0.262373 | − | 0.964966i | \(-0.415495\pi\) | ||||
0.262373 | + | 0.964966i | \(0.415495\pi\) | |||||||
\(48\) | −11.0294 | + | 3.67267i | −1.59196 | + | 0.530104i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 13.8790 | + | 1.61707i | 1.96278 | + | 0.228689i | ||||
\(51\) | 3.10069 | − | 3.10069i | 0.434183 | − | 0.434183i | ||||
\(52\) | 2.70960 | − | 1.67404i | 0.375753 | − | 0.232148i | ||||
\(53\) | −0.675714 | − | 0.675714i | −0.0928165 | − | 0.0928165i | 0.659174 | − | 0.751990i | \(-0.270906\pi\) |
−0.751990 | + | 0.659174i | \(0.770906\pi\) | |||||||
\(54\) | 7.88355 | − | 6.23819i | 1.07281 | − | 0.848910i | ||||
\(55\) | 5.01680i | 0.676466i | ||||||||
\(56\) | −2.65891 | − | 0.964462i | −0.355312 | − | 0.128882i | ||||
\(57\) | 6.01174i | 0.796275i | ||||||||
\(58\) | −5.08913 | − | 6.43142i | −0.668236 | − | 0.844487i | ||||
\(59\) | 1.13843 | + | 1.13843i | 0.148211 | + | 0.148211i | 0.777318 | − | 0.629108i | \(-0.216580\pi\) |
−0.629108 | + | 0.777318i | \(0.716580\pi\) | |||||||
\(60\) | 21.8208 | + | 5.15476i | 2.81705 | + | 0.665476i | ||||
\(61\) | −3.21881 | + | 3.21881i | −0.412127 | + | 0.412127i | −0.882479 | − | 0.470352i | \(-0.844127\pi\) |
0.470352 | + | 0.882479i | \(0.344127\pi\) | |||||||
\(62\) | 0.672667 | − | 5.77335i | 0.0854288 | − | 0.733216i | ||||
\(63\) | 5.44602 | 0.686134 | ||||||||
\(64\) | −6.13963 | − | 5.12884i | −0.767453 | − | 0.641105i | ||||
\(65\) | −6.14310 | −0.761957 | ||||||||
\(66\) | −0.618595 | + | 5.30926i | −0.0761438 | + | 0.653525i | ||||
\(67\) | −1.52640 | + | 1.52640i | −0.186480 | + | 0.186480i | −0.794172 | − | 0.607692i | \(-0.792095\pi\) |
0.607692 | + | 0.794172i | \(0.292095\pi\) | |||||||
\(68\) | 2.93687 | + | 0.693782i | 0.356148 | + | 0.0841334i | ||||
\(69\) | 9.80296 | + | 9.80296i | 1.18014 | + | 1.18014i | ||||
\(70\) | 3.38515 | + | 4.27801i | 0.404603 | + | 0.511320i | ||||
\(71\) | − | 13.8202i | − | 1.64016i | −0.572251 | − | 0.820079i | \(-0.693930\pi\) | ||
0.572251 | − | 0.820079i | \(-0.306070\pi\) | |||||||
\(72\) | 14.4805 | + | 5.25248i | 1.70654 | + | 0.619010i | ||||
\(73\) | 14.4749i | 1.69416i | 0.531468 | + | 0.847078i | \(0.321641\pi\) | ||||
−0.531468 | + | 0.847078i | \(0.678359\pi\) | |||||||
\(74\) | −2.59514 | + | 2.05351i | −0.301679 | + | 0.238716i | ||||
\(75\) | −20.3040 | − | 20.3040i | −2.34450 | − | 2.34450i | ||||
\(76\) | −3.51963 | + | 2.17450i | −0.403729 | + | 0.249432i | ||||
\(77\) | −0.919616 | + | 0.919616i | −0.104800 | + | 0.104800i | ||||
\(78\) | −6.50122 | − | 0.757473i | −0.736118 | − | 0.0857669i | ||||
\(79\) | −1.77961 | −0.200222 | −0.100111 | − | 0.994976i | \(-0.531920\pi\) | ||||
−0.100111 | + | 0.994976i | \(0.531920\pi\) | |||||||
\(80\) | 4.87485 | + | 14.6397i | 0.545025 | + | 1.63677i | ||||
\(81\) | −4.32107 | −0.480119 | ||||||||
\(82\) | −10.4726 | − | 1.22019i | −1.15650 | − | 0.134747i | ||||
\(83\) | −7.16133 | + | 7.16133i | −0.786058 | + | 0.786058i | −0.980845 | − | 0.194787i | \(-0.937598\pi\) |
0.194787 | + | 0.980845i | \(0.437598\pi\) | |||||||
\(84\) | 3.05500 | + | 4.94480i | 0.333327 | + | 0.539522i | ||||
\(85\) | −4.11564 | − | 4.11564i | −0.446404 | − | 0.446404i | ||||
\(86\) | 8.92394 | − | 7.06145i | 0.962294 | − | 0.761455i | ||||
\(87\) | 16.8538i | 1.80692i | ||||||||
\(88\) | −3.33211 | + | 1.55824i | −0.355204 | + | 0.166109i | ||||
\(89\) | 8.45899i | 0.896651i | 0.893870 | + | 0.448325i | \(0.147979\pi\) | ||||
−0.893870 | + | 0.448325i | \(0.852021\pi\) | |||||||
\(90\) | −18.4356 | − | 23.2981i | −1.94328 | − | 2.45584i | ||||
\(91\) | −1.12607 | − | 1.12607i | −0.118045 | − | 0.118045i | ||||
\(92\) | −2.19342 | + | 9.28505i | −0.228680 | + | 0.968033i | ||||
\(93\) | −8.44602 | + | 8.44602i | −0.875811 | + | 0.875811i | ||||
\(94\) | 0.588786 | − | 5.05342i | 0.0607287 | − | 0.521221i | ||||
\(95\) | 7.97958 | 0.818688 | ||||||||
\(96\) | 3.35389 | + | 16.0942i | 0.342305 | + | 1.64261i | ||||
\(97\) | 16.2227 | 1.64717 | 0.823585 | − | 0.567194i | \(-0.191971\pi\) | ||||
0.823585 | + | 0.567194i | \(0.191971\pi\) | |||||||
\(98\) | −0.163666 | + | 1.40471i | −0.0165328 | + | 0.141897i | ||||
\(99\) | 5.00824 | − | 5.00824i | 0.503348 | − | 0.503348i | ||||
\(100\) | 4.54304 | − | 19.2313i | 0.454304 | − | 1.92313i | ||||
\(101\) | −11.5664 | − | 11.5664i | −1.15090 | − | 1.15090i | −0.986372 | − | 0.164533i | \(-0.947388\pi\) |
−0.164533 | − | 0.986372i | \(-0.552612\pi\) | |||||||
\(102\) | −3.84809 | − | 4.86304i | −0.381018 | − | 0.481513i | ||||
\(103\) | − | 17.1875i | − | 1.69354i | −0.531963 | − | 0.846768i | \(-0.678545\pi\) | ||
0.531963 | − | 0.846768i | \(-0.321455\pi\) | |||||||
\(104\) | −1.90808 | − | 4.08018i | −0.187102 | − | 0.400095i | ||||
\(105\) | − | 11.2107i | − | 1.09405i | ||||||
\(106\) | −1.05977 | + | 0.838591i | −0.102934 | + | 0.0814512i | ||||
\(107\) | 4.10143 | + | 4.10143i | 0.396501 | + | 0.396501i | 0.876997 | − | 0.480496i | \(-0.159543\pi\) |
−0.480496 | + | 0.876997i | \(0.659543\pi\) | |||||||
\(108\) | −7.47258 | − | 12.0951i | −0.719049 | − | 1.16385i | ||||
\(109\) | −3.27351 | + | 3.27351i | −0.313545 | + | 0.313545i | −0.846281 | − | 0.532736i | \(-0.821164\pi\) |
0.532736 | + | 0.846281i | \(0.321164\pi\) | |||||||
\(110\) | 7.04716 | + | 0.821082i | 0.671920 | + | 0.0782871i | ||||
\(111\) | 6.80066 | 0.645490 | ||||||||
\(112\) | −1.78996 | + | 3.57715i | −0.169136 | + | 0.338009i | ||||
\(113\) | −9.17193 | −0.862822 | −0.431411 | − | 0.902155i | \(-0.641984\pi\) | ||||
−0.431411 | + | 0.902155i | \(0.641984\pi\) | |||||||
\(114\) | 8.44476 | + | 0.983920i | 0.790924 | + | 0.0921525i | ||||
\(115\) | 13.0118 | − | 13.0118i | 1.21336 | − | 1.21336i | ||||
\(116\) | −9.86721 | + | 6.09616i | −0.916147 | + | 0.566014i | ||||
\(117\) | 6.13262 | + | 6.13262i | 0.566961 | + | 0.566961i | ||||
\(118\) | 1.78548 | − | 1.41284i | 0.164367 | − | 0.130062i | ||||
\(119\) | − | 1.50885i | − | 0.138316i | ||||||
\(120\) | 10.8123 | − | 29.8082i | 0.987021 | − | 2.72110i | ||||
\(121\) | − | 9.30861i | − | 0.846238i | ||||||
\(122\) | 3.99469 | + | 5.04831i | 0.361662 | + | 0.457053i | ||||
\(123\) | 15.3207 | + | 15.3207i | 1.38142 | + | 1.38142i | ||||
\(124\) | −7.99980 | − | 1.88981i | −0.718403 | − | 0.169710i | ||||
\(125\) | −13.3118 | + | 13.3118i | −1.19064 | + | 1.19064i | ||||
\(126\) | 0.891330 | − | 7.65008i | 0.0794060 | − | 0.681524i | ||||
\(127\) | −12.9787 | −1.15167 | −0.575835 | − | 0.817566i | \(-0.695323\pi\) | ||||
−0.575835 | + | 0.817566i | \(0.695323\pi\) | |||||||
\(128\) | −8.20939 | + | 7.78499i | −0.725614 | + | 0.688102i | ||||
\(129\) | −23.3855 | −2.05898 | ||||||||
\(130\) | −1.00542 | + | 8.62928i | −0.0881810 | + | 0.756838i | ||||
\(131\) | −6.81965 | + | 6.81965i | −0.595836 | + | 0.595836i | −0.939202 | − | 0.343366i | \(-0.888433\pi\) |
0.343366 | + | 0.939202i | \(0.388433\pi\) | |||||||
\(132\) | 7.35674 | + | 1.73790i | 0.640322 | + | 0.151264i | ||||
\(133\) | 1.46271 | + | 1.46271i | 0.126833 | + | 0.126833i | ||||
\(134\) | 1.89434 | + | 2.39398i | 0.163646 | + | 0.206808i | ||||
\(135\) | 27.4215i | 2.36007i | ||||||||
\(136\) | 1.45523 | − | 4.01190i | 0.124785 | − | 0.344018i | ||||
\(137\) | − | 22.6543i | − | 1.93548i | −0.251943 | − | 0.967742i | \(-0.581069\pi\) | ||
0.251943 | − | 0.967742i | \(-0.418931\pi\) | |||||||
\(138\) | 15.3747 | − | 12.1659i | 1.30878 | − | 1.03563i | ||||
\(139\) | −6.64728 | − | 6.64728i | −0.563815 | − | 0.563815i | 0.366574 | − | 0.930389i | \(-0.380531\pi\) |
−0.930389 | + | 0.366574i | \(0.880531\pi\) | |||||||
\(140\) | 6.56340 | − | 4.05500i | 0.554708 | − | 0.342710i | ||||
\(141\) | −7.39281 | + | 7.39281i | −0.622587 | + | 0.622587i | ||||
\(142\) | −19.4134 | − | 2.26190i | −1.62914 | − | 0.189815i | ||||
\(143\) | −2.07111 | −0.173195 | ||||||||
\(144\) | 9.74818 | − | 19.4812i | 0.812348 | − | 1.62344i | ||||
\(145\) | 22.3706 | 1.85778 | ||||||||
\(146\) | 20.3330 | + | 2.36905i | 1.68277 | + | 0.196064i | ||||
\(147\) | 2.05500 | − | 2.05500i | 0.169493 | − | 0.169493i | ||||
\(148\) | 2.45986 | + | 3.98151i | 0.202199 | + | 0.327278i | ||||
\(149\) | 7.77031 | + | 7.77031i | 0.636568 | + | 0.636568i | 0.949707 | − | 0.313139i | \(-0.101381\pi\) |
−0.313139 | + | 0.949707i | \(0.601381\pi\) | |||||||
\(150\) | −31.8443 | + | 25.1981i | −2.60008 | + | 2.05742i | ||||
\(151\) | 5.46829i | 0.445004i | 0.974932 | + | 0.222502i | \(0.0714223\pi\) | ||||
−0.974932 | + | 0.222502i | \(0.928578\pi\) | |||||||
\(152\) | 2.47850 | + | 5.29996i | 0.201033 | + | 0.429883i | ||||
\(153\) | 8.21724i | 0.664324i | ||||||||
\(154\) | 1.14128 | + | 1.44230i | 0.0919673 | + | 0.116224i | ||||
\(155\) | 11.2107 | + | 11.2107i | 0.900463 | + | 0.900463i | ||||
\(156\) | −2.12806 | + | 9.00836i | −0.170381 | + | 0.721246i | ||||
\(157\) | −5.61722 | + | 5.61722i | −0.448303 | + | 0.448303i | −0.894790 | − | 0.446487i | \(-0.852675\pi\) |
0.446487 | + | 0.894790i | \(0.352675\pi\) | |||||||
\(158\) | −0.291263 | + | 2.49984i | −0.0231716 | + | 0.198877i | ||||
\(159\) | 2.77718 | 0.220245 | ||||||||
\(160\) | 21.3624 | − | 4.45173i | 1.68885 | − | 0.351940i | ||||
\(161\) | 4.77031 | 0.375953 | ||||||||
\(162\) | −0.707214 | + | 6.06986i | −0.0555640 | + | 0.476893i | ||||
\(163\) | −6.31758 | + | 6.31758i | −0.494831 | + | 0.494831i | −0.909824 | − | 0.414994i | \(-0.863784\pi\) |
0.414994 | + | 0.909824i | \(0.363784\pi\) | |||||||
\(164\) | −3.42802 | + | 14.5112i | −0.267683 | + | 1.13314i | ||||
\(165\) | −10.3095 | − | 10.3095i | −0.802595 | − | 0.802595i | ||||
\(166\) | 8.88753 | + | 11.2317i | 0.689806 | + | 0.871746i | ||||
\(167\) | − | 11.8175i | − | 0.914463i | −0.889348 | − | 0.457231i | \(-0.848841\pi\) | ||
0.889348 | − | 0.457231i | \(-0.151159\pi\) | |||||||
\(168\) | 7.44602 | − | 3.48209i | 0.574473 | − | 0.268649i | ||||
\(169\) | 10.4639i | 0.804917i | ||||||||
\(170\) | −6.45488 | + | 5.10769i | −0.495067 | + | 0.391742i | ||||
\(171\) | −7.96597 | − | 7.96597i | −0.609173 | − | 0.609173i | ||||
\(172\) | −8.45874 | − | 13.6913i | −0.644973 | − | 1.04395i | ||||
\(173\) | 5.63858 | − | 5.63858i | 0.428694 | − | 0.428694i | −0.459490 | − | 0.888183i | \(-0.651968\pi\) |
0.888183 | + | 0.459490i | \(0.151968\pi\) | |||||||
\(174\) | 23.6747 | + | 2.75840i | 1.79477 | + | 0.209114i | ||||
\(175\) | −9.88030 | −0.746880 | ||||||||
\(176\) | 1.64353 | + | 4.93569i | 0.123886 | + | 0.372041i | ||||
\(177\) | −4.67893 | −0.351690 | ||||||||
\(178\) | 11.8824 | + | 1.38445i | 0.890626 | + | 0.103769i | ||||
\(179\) | 11.7278 | − | 11.7278i | 0.876575 | − | 0.876575i | −0.116604 | − | 0.993179i | \(-0.537201\pi\) |
0.993179 | + | 0.116604i | \(0.0372007\pi\) | |||||||
\(180\) | −35.7444 | + | 22.0836i | −2.66423 | + | 1.64601i | ||||
\(181\) | −4.18574 | − | 4.18574i | −0.311124 | − | 0.311124i | 0.534221 | − | 0.845345i | \(-0.320605\pi\) |
−0.845345 | + | 0.534221i | \(0.820605\pi\) | |||||||
\(182\) | −1.76611 | + | 1.39751i | −0.130913 | + | 0.103590i | ||||
\(183\) | − | 13.2293i | − | 0.977937i | ||||||
\(184\) | 12.6838 | + | 4.60078i | 0.935064 | + | 0.339174i | ||||
\(185\) | − | 9.02674i | − | 0.663659i | ||||||
\(186\) | 10.4819 | + | 13.2465i | 0.768569 | + | 0.971284i | ||||
\(187\) | −1.38756 | − | 1.38756i | −0.101469 | − | 0.101469i | ||||
\(188\) | −7.00223 | − | 1.65415i | −0.510690 | − | 0.120641i | ||||
\(189\) | −5.02656 | + | 5.02656i | −0.365629 | + | 0.365629i | ||||
\(190\) | 1.30599 | − | 11.2090i | 0.0947464 | − | 0.813187i | ||||
\(191\) | 12.3676 | 0.894891 | 0.447445 | − | 0.894311i | \(-0.352334\pi\) | ||||
0.447445 | + | 0.894311i | \(0.352334\pi\) | |||||||
\(192\) | 23.1567 | − | 2.07717i | 1.67119 | − | 0.149907i | ||||
\(193\) | 23.6837 | 1.70479 | 0.852395 | − | 0.522898i | \(-0.175149\pi\) | ||||
0.852395 | + | 0.522898i | \(0.175149\pi\) | |||||||
\(194\) | 2.65512 | − | 22.7883i | 0.190626 | − | 1.63610i | ||||
\(195\) | 12.6240 | − | 12.6240i | 0.904026 | − | 0.904026i | ||||
\(196\) | 1.94643 | + | 0.459808i | 0.139030 | + | 0.0328434i | ||||
\(197\) | −11.4195 | − | 11.4195i | −0.813606 | − | 0.813606i | 0.171566 | − | 0.985173i | \(-0.445117\pi\) |
−0.985173 | + | 0.171566i | \(0.945117\pi\) | |||||||
\(198\) | −6.21546 | − | 7.85482i | −0.441713 | − | 0.558218i | ||||
\(199\) | 5.49683i | 0.389660i | 0.980837 | + | 0.194830i | \(0.0624155\pi\) | ||||
−0.980837 | + | 0.194830i | \(0.937585\pi\) | |||||||
\(200\) | −26.2708 | − | 9.52917i | −1.85763 | − | 0.673814i | ||||
\(201\) | − | 6.27351i | − | 0.442499i | ||||||
\(202\) | −18.1406 | + | 14.3545i | −1.27636 | + | 1.00998i | ||||
\(203\) | 4.10069 | + | 4.10069i | 0.287812 | + | 0.287812i | ||||
\(204\) | −7.46098 | + | 4.60954i | −0.522373 | + | 0.322732i | ||||
\(205\) | 20.3356 | − | 20.3356i | 1.42030 | − | 1.42030i | ||||
\(206\) | −24.1435 | − | 2.81302i | −1.68216 | − | 0.195992i | ||||
\(207\) | −25.9792 | −1.80568 | ||||||||
\(208\) | −6.04377 | + | 2.01251i | −0.419060 | + | 0.139542i | ||||
\(209\) | 2.69027 | 0.186090 | ||||||||
\(210\) | −15.7478 | − | 1.83481i | −1.08670 | − | 0.126614i | ||||
\(211\) | 0.907874 | − | 0.907874i | 0.0625007 | − | 0.0625007i | −0.675166 | − | 0.737666i | \(-0.735928\pi\) |
0.737666 | + | 0.675166i | \(0.235928\pi\) | |||||||
\(212\) | 1.00453 | + | 1.62593i | 0.0689914 | + | 0.111669i | ||||
\(213\) | 28.4005 | + | 28.4005i | 1.94597 | + | 1.94597i | ||||
\(214\) | 6.43260 | − | 5.09006i | 0.439723 | − | 0.347949i | ||||
\(215\) | 31.0404i | 2.11694i | ||||||||
\(216\) | −18.2131 | + | 8.51726i | −1.23925 | + | 0.579526i | ||||
\(217\) | 4.10999i | 0.279004i | ||||||||
\(218\) | 4.06257 | + | 5.13410i | 0.275152 | + | 0.347725i | ||||
\(219\) | −29.7458 | − | 29.7458i | −2.01004 | − | 2.01004i | ||||
\(220\) | 2.30677 | − | 9.76484i | 0.155522 | − | 0.658345i | ||||
\(221\) | 1.69908 | − | 1.69908i | 0.114292 | − | 0.114292i | ||||
\(222\) | 1.11304 | − | 9.55297i | 0.0747023 | − | 0.641153i | ||||
\(223\) | −3.20318 | −0.214501 | −0.107250 | − | 0.994232i | \(-0.534205\pi\) | ||||
−0.107250 | + | 0.994232i | \(0.534205\pi\) | |||||||
\(224\) | 4.73191 | + | 3.09984i | 0.316164 | + | 0.207117i | ||||
\(225\) | 53.8083 | 3.58722 | ||||||||
\(226\) | −1.50114 | + | 12.8839i | −0.0998540 | + | 0.857025i | ||||
\(227\) | −13.7931 | + | 13.7931i | −0.915480 | + | 0.915480i | −0.996696 | − | 0.0812167i | \(-0.974119\pi\) |
0.0812167 | + | 0.996696i | \(0.474119\pi\) | |||||||
\(228\) | 2.76425 | − | 11.7014i | 0.183067 | − | 0.774945i | ||||
\(229\) | 7.02177 | + | 7.02177i | 0.464012 | + | 0.464012i | 0.899968 | − | 0.435956i | \(-0.143590\pi\) |
−0.435956 | + | 0.899968i | \(0.643590\pi\) | |||||||
\(230\) | −16.1482 | − | 20.4074i | −1.06478 | − | 1.34562i | ||||
\(231\) | − | 3.77961i | − | 0.248680i | ||||||
\(232\) | 6.94841 | + | 14.8583i | 0.456185 | + | 0.975496i | ||||
\(233\) | 2.93857i | 0.192512i | 0.995357 | + | 0.0962561i | \(0.0306868\pi\) | ||||
−0.995357 | + | 0.0962561i | \(0.969313\pi\) | |||||||
\(234\) | 9.61826 | − | 7.61085i | 0.628765 | − | 0.497537i | ||||
\(235\) | 9.81272 | + | 9.81272i | 0.640111 | + | 0.640111i | ||||
\(236\) | −1.69241 | − | 2.73932i | −0.110166 | − | 0.178315i | ||||
\(237\) | 3.65710 | − | 3.65710i | 0.237554 | − | 0.237554i | ||||
\(238\) | −2.11950 | − | 0.246948i | −0.137387 | − | 0.0160073i | ||||
\(239\) | 16.2109 | 1.04859 | 0.524297 | − | 0.851536i | \(-0.324328\pi\) | ||||
0.524297 | + | 0.851536i | \(0.324328\pi\) | |||||||
\(240\) | −40.1023 | − | 20.0667i | −2.58859 | − | 1.29530i | ||||
\(241\) | −14.1166 | −0.909329 | −0.454665 | − | 0.890663i | \(-0.650241\pi\) | ||||
−0.454665 | + | 0.890663i | \(0.650241\pi\) | |||||||
\(242\) | −13.0759 | − | 1.52351i | −0.840552 | − | 0.0979347i | ||||
\(243\) | −6.19990 | + | 6.19990i | −0.397724 | + | 0.397724i | ||||
\(244\) | 7.74522 | − | 4.78515i | 0.495837 | − | 0.306338i | ||||
\(245\) | −2.72766 | − | 2.72766i | −0.174264 | − | 0.174264i | ||||
\(246\) | 24.0286 | − | 19.0136i | 1.53201 | − | 1.21227i | ||||
\(247\) | 3.29424i | 0.209608i | ||||||||
\(248\) | −3.96393 | + | 10.9281i | −0.251710 | + | 0.693936i | ||||
\(249\) | − | 29.4330i | − | 1.86524i | ||||||
\(250\) | 16.5206 | + | 20.8779i | 1.04485 | + | 1.32044i | ||||
\(251\) | −14.1967 | − | 14.1967i | −0.896091 | − | 0.896091i | 0.0989969 | − | 0.995088i | \(-0.468437\pi\) |
−0.995088 | + | 0.0989969i | \(0.968437\pi\) | |||||||
\(252\) | −10.6003 | − | 2.50412i | −0.667755 | − | 0.157745i | ||||
\(253\) | 4.38685 | − | 4.38685i | 0.275799 | − | 0.275799i | ||||
\(254\) | −2.12417 | + | 18.2313i | −0.133282 | + | 1.14393i | ||||
\(255\) | 16.9153 | 1.05927 | ||||||||
\(256\) | 9.59206 | + | 12.8060i | 0.599503 | + | 0.800372i | ||||
\(257\) | −3.23679 | −0.201905 | −0.100953 | − | 0.994891i | \(-0.532189\pi\) | ||||
−0.100953 | + | 0.994891i | \(0.532189\pi\) | |||||||
\(258\) | −3.82742 | + | 32.8499i | −0.238285 | + | 2.04515i | ||||
\(259\) | 1.65467 | − | 1.65467i | 0.102816 | − | 0.102816i | ||||
\(260\) | 11.9571 | + | 2.82464i | 0.741547 | + | 0.175177i | ||||
\(261\) | −22.3324 | − | 22.3324i | −1.38234 | − | 1.38234i | ||||
\(262\) | 8.46350 | + | 10.6958i | 0.522877 | + | 0.660788i | ||||
\(263\) | 24.0161i | 1.48090i | 0.672114 | + | 0.740448i | \(0.265386\pi\) | ||||
−0.672114 | + | 0.740448i | \(0.734614\pi\) | |||||||
\(264\) | 3.64529 | − | 10.0497i | 0.224352 | − | 0.618514i | ||||
\(265\) | − | 3.68624i | − | 0.226444i | ||||||
\(266\) | 2.29409 | − | 1.81529i | 0.140659 | − | 0.111303i | ||||
\(267\) | −17.3832 | − | 17.3832i | −1.06383 | − | 1.06383i | ||||
\(268\) | 3.67289 | − | 2.26918i | 0.224357 | − | 0.138612i | ||||
\(269\) | −0.0875040 | + | 0.0875040i | −0.00533521 | + | 0.00533521i | −0.709769 | − | 0.704434i | \(-0.751201\pi\) |
0.704434 | + | 0.709769i | \(0.251201\pi\) | |||||||
\(270\) | 38.5193 | + | 4.48798i | 2.34421 | + | 0.273130i | ||||
\(271\) | −10.1138 | −0.614372 | −0.307186 | − | 0.951650i | \(-0.599387\pi\) | ||||
−0.307186 | + | 0.951650i | \(0.599387\pi\) | |||||||
\(272\) | −5.39739 | − | 2.70079i | −0.327265 | − | 0.163760i | ||||
\(273\) | 4.62815 | 0.280109 | ||||||||
\(274\) | −31.8227 | − | 3.70774i | −1.92248 | − | 0.223993i | ||||
\(275\) | −9.08608 | + | 9.08608i | −0.547911 | + | 0.547911i | ||||
\(276\) | −14.5733 | − | 23.5882i | −0.877208 | − | 1.41984i | ||||
\(277\) | −11.0080 | − | 11.0080i | −0.661406 | − | 0.661406i | 0.294305 | − | 0.955711i | \(-0.404912\pi\) |
−0.955711 | + | 0.294305i | \(0.904912\pi\) | |||||||
\(278\) | −10.4254 | + | 8.24957i | −0.625277 | + | 0.494776i | ||||
\(279\) | − | 22.3831i | − | 1.34004i | ||||||
\(280\) | −4.62189 | − | 9.88334i | −0.276211 | − | 0.590643i | ||||
\(281\) | − | 4.21999i | − | 0.251743i | −0.992047 | − | 0.125872i | \(-0.959827\pi\) | ||
0.992047 | − | 0.125872i | \(-0.0401727\pi\) | |||||||
\(282\) | 9.17481 | + | 11.5947i | 0.546352 | + | 0.690455i | ||||
\(283\) | −16.5834 | − | 16.5834i | −0.985781 | − | 0.985781i | 0.0141195 | − | 0.999900i | \(-0.495505\pi\) |
−0.999900 | + | 0.0141195i | \(0.995505\pi\) | |||||||
\(284\) | −6.35464 | + | 26.9000i | −0.377079 | + | 1.59622i | ||||
\(285\) | −16.3980 | + | 16.3980i | −0.971334 | + | 0.971334i | ||||
\(286\) | −0.338971 | + | 2.90931i | −0.0200438 | + | 0.172031i | ||||
\(287\) | 7.45533 | 0.440074 | ||||||||
\(288\) | −25.7701 | − | 16.8818i | −1.51852 | − | 0.994770i | ||||
\(289\) | −14.7234 | −0.866080 | ||||||||
\(290\) | 3.66131 | − | 31.4242i | 0.215000 | − | 1.84529i | ||||
\(291\) | −33.3377 | + | 33.3377i | −1.95429 | + | 1.95429i | ||||
\(292\) | 6.65566 | − | 28.1743i | 0.389493 | − | 1.64878i | ||||
\(293\) | −13.5242 | − | 13.5242i | −0.790093 | − | 0.790093i | 0.191416 | − | 0.981509i | \(-0.438692\pi\) |
−0.981509 | + | 0.191416i | \(0.938692\pi\) | |||||||
\(294\) | −2.55034 | − | 3.22301i | −0.148739 | − | 0.187970i | ||||
\(295\) | 6.21049i | 0.361589i | ||||||||
\(296\) | 5.99547 | − | 2.80375i | 0.348480 | − | 0.162965i | ||||
\(297\) | 9.24501i | 0.536450i | ||||||||
\(298\) | 12.1868 | − | 9.64330i | 0.705961 | − | 0.558621i | ||||
\(299\) | 5.37171 | + | 5.37171i | 0.310654 | + | 0.310654i | ||||
\(300\) | 30.1843 | + | 48.8561i | 1.74269 | + | 2.82071i | ||||
\(301\) | −5.68992 | + | 5.68992i | −0.327962 | + | 0.327962i | ||||
\(302\) | 7.68137 | + | 0.894976i | 0.442013 | + | 0.0515001i | ||||
\(303\) | 47.5380 | 2.73099 | ||||||||
\(304\) | 7.85056 | − | 2.61415i | 0.450260 | − | 0.149932i | ||||
\(305\) | −17.5597 | −1.00546 | ||||||||
\(306\) | 11.5428 | + | 1.34488i | 0.659860 | + | 0.0768820i | ||||
\(307\) | −8.93389 | + | 8.93389i | −0.509884 | + | 0.509884i | −0.914491 | − | 0.404607i | \(-0.867408\pi\) |
0.404607 | + | 0.914491i | \(0.367408\pi\) | |||||||
\(308\) | 2.21281 | − | 1.36712i | 0.126087 | − | 0.0778988i | ||||
\(309\) | 35.3203 | + | 35.3203i | 2.00930 | + | 2.00930i | ||||
\(310\) | 17.5826 | − | 13.9130i | 0.998623 | − | 0.790203i | ||||
\(311\) | 19.7737i | 1.12126i | 0.828066 | + | 0.560631i | \(0.189442\pi\) | ||||
−0.828066 | + | 0.560631i | \(0.810558\pi\) | |||||||
\(312\) | 12.3058 | + | 4.46368i | 0.696682 | + | 0.252706i | ||||
\(313\) | 8.72743i | 0.493303i | 0.969104 | + | 0.246652i | \(0.0793304\pi\) | ||||
−0.969104 | + | 0.246652i | \(0.920670\pi\) | |||||||
\(314\) | 6.97122 | + | 8.80992i | 0.393409 | + | 0.497173i | ||||
\(315\) | 14.8549 | + | 14.8549i | 0.836979 | + | 0.836979i | ||||
\(316\) | 3.46389 | + | 0.818280i | 0.194859 | + | 0.0460319i | ||||
\(317\) | 19.0197 | − | 19.0197i | 1.06825 | − | 1.06825i | 0.0707615 | − | 0.997493i | \(-0.477457\pi\) |
0.997493 | − | 0.0707615i | \(-0.0225429\pi\) | |||||||
\(318\) | 0.454531 | − | 3.90114i | 0.0254888 | − | 0.218765i | ||||
\(319\) | 7.54211 | 0.422277 | ||||||||
\(320\) | −2.75710 | − | 30.7366i | −0.154126 | − | 1.71823i | ||||
\(321\) | −16.8569 | −0.940858 | ||||||||
\(322\) | 0.780738 | − | 6.70090i | 0.0435088 | − | 0.373427i | ||||
\(323\) | −2.20702 | + | 2.20702i | −0.122802 | + | 0.122802i | ||||
\(324\) | 8.41065 | + | 1.98686i | 0.467258 | + | 0.110381i | ||||
\(325\) | −11.1259 | − | 11.1259i | −0.617156 | − | 0.617156i | ||||
\(326\) | 7.84039 | + | 9.90834i | 0.434239 | + | 0.548772i | ||||
\(327\) | − | 13.4541i | − | 0.744013i | ||||||
\(328\) | 19.8231 | + | 7.19038i | 1.09455 | + | 0.397022i | ||||
\(329\) | 3.59748i | 0.198336i | ||||||||
\(330\) | −16.1692 | + | 12.7946i | −0.890086 | + | 0.704318i | ||||
\(331\) | 22.3328 | + | 22.3328i | 1.22752 | + | 1.22752i | 0.964899 | + | 0.262620i | \(0.0845866\pi\) |
0.262620 | + | 0.964899i | \(0.415413\pi\) | |||||||
\(332\) | 17.2318 | − | 10.6462i | 0.945720 | − | 0.584284i | ||||
\(333\) | −9.01134 | + | 9.01134i | −0.493818 | + | 0.493818i | ||||
\(334\) | −16.6001 | − | 1.93412i | −0.908318 | − | 0.105830i | ||||
\(335\) | −8.32703 | −0.454954 | ||||||||
\(336\) | −3.67267 | − | 11.0294i | −0.200360 | − | 0.601704i | ||||
\(337\) | −23.4825 | −1.27918 | −0.639588 | − | 0.768718i | \(-0.720895\pi\) | ||||
−0.639588 | + | 0.768718i | \(0.720895\pi\) | |||||||
\(338\) | 14.6988 | + | 1.71259i | 0.799508 | + | 0.0931527i | ||||
\(339\) | 18.8483 | − | 18.8483i | 1.02370 | − | 1.02370i | ||||
\(340\) | 6.11839 | + | 9.90320i | 0.331816 | + | 0.537076i | ||||
\(341\) | 3.77961 | + | 3.77961i | 0.204678 | + | 0.204678i | ||||
\(342\) | −12.4936 | + | 9.88612i | −0.675579 | + | 0.534580i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −20.6167 | + | 9.64129i | −1.11158 | + | 0.519824i | ||||
\(345\) | 53.4784i | 2.87918i | ||||||||
\(346\) | −6.99774 | − | 8.84343i | −0.376201 | − | 0.475426i | ||||
\(347\) | −6.29716 | − | 6.29716i | −0.338049 | − | 0.338049i | 0.517584 | − | 0.855633i | \(-0.326832\pi\) |
−0.855633 | + | 0.517584i | \(0.826832\pi\) | |||||||
\(348\) | 7.74950 | − | 32.8047i | 0.415417 | − | 1.75851i | ||||
\(349\) | 6.94033 | − | 6.94033i | 0.371507 | − | 0.371507i | −0.496519 | − | 0.868026i | \(-0.665389\pi\) |
0.868026 | + | 0.496519i | \(0.165389\pi\) | |||||||
\(350\) | −1.61707 | + | 13.8790i | −0.0864361 | + | 0.741862i | ||||
\(351\) | −11.3206 | −0.604246 | ||||||||
\(352\) | 7.20220 | − | 1.50088i | 0.383879 | − | 0.0799969i | ||||
\(353\) | 30.0934 | 1.60171 | 0.800856 | − | 0.598857i | \(-0.204378\pi\) | ||||
0.800856 | + | 0.598857i | \(0.204378\pi\) | |||||||
\(354\) | −0.765783 | + | 6.57254i | −0.0407009 | + | 0.349327i | ||||
\(355\) | 37.6969 | − | 37.6969i | 2.00074 | − | 2.00074i | ||||
\(356\) | 3.88951 | − | 16.4648i | 0.206144 | − | 0.872633i | ||||
\(357\) | 3.10069 | + | 3.10069i | 0.164106 | + | 0.164106i | ||||
\(358\) | −14.5547 | − | 18.3936i | −0.769239 | − | 0.972131i | ||||
\(359\) | 10.3716i | 0.547394i | 0.961816 | + | 0.273697i | \(0.0882465\pi\) | ||||
−0.961816 | + | 0.273697i | \(0.911754\pi\) | |||||||
\(360\) | 25.1709 | + | 53.8249i | 1.32662 | + | 2.83682i | ||||
\(361\) | 14.7209i | 0.774786i | ||||||||
\(362\) | −6.56482 | + | 5.19469i | −0.345039 | + | 0.273027i | ||||
\(363\) | 19.1292 | + | 19.1292i | 1.00402 | + | 1.00402i | ||||
\(364\) | 1.67404 | + | 2.70960i | 0.0877436 | + | 0.142021i | ||||
\(365\) | −39.4826 | + | 39.4826i | −2.06661 | + | 2.06661i | ||||
\(366\) | −18.5833 | − | 2.16519i | −0.971366 | − | 0.113176i | ||||
\(367\) | −8.12973 | −0.424368 | −0.212184 | − | 0.977230i | \(-0.568058\pi\) | ||||
−0.212184 | + | 0.977230i | \(0.568058\pi\) | |||||||
\(368\) | 8.53868 | − | 17.0641i | 0.445109 | − | 0.889529i | ||||
\(369\) | −40.6019 | −2.11365 | ||||||||
\(370\) | −12.6800 | − | 1.47737i | −0.659200 | − | 0.0768050i | ||||
\(371\) | 0.675714 | − | 0.675714i | 0.0350813 | − | 0.0350813i | ||||
\(372\) | 20.3231 | − | 12.5560i | 1.05370 | − | 0.650999i | ||||
\(373\) | −3.18688 | − | 3.18688i | −0.165010 | − | 0.165010i | 0.619772 | − | 0.784782i | \(-0.287225\pi\) |
−0.784782 | + | 0.619772i | \(0.787225\pi\) | |||||||
\(374\) | −2.17622 | + | 1.72203i | −0.112530 | + | 0.0890440i | ||||
\(375\) | − | 54.7115i | − | 2.82529i | ||||||
\(376\) | −3.46963 | + | 9.56539i | −0.178933 | + | 0.493297i | ||||
\(377\) | 9.23534i | 0.475644i | ||||||||
\(378\) | 6.23819 | + | 7.88355i | 0.320858 | + | 0.405486i | ||||
\(379\) | −0.839080 | − | 0.839080i | −0.0431006 | − | 0.0431006i | 0.685228 | − | 0.728329i | \(-0.259703\pi\) |
−0.728329 | + | 0.685228i | \(0.759703\pi\) | |||||||
\(380\) | −15.5317 | − | 3.66907i | −0.796758 | − | 0.188219i | ||||
\(381\) | 26.6711 | − | 26.6711i | 1.36640 | − | 1.36640i | ||||
\(382\) | 2.02417 | − | 17.3730i | 0.103565 | − | 0.888878i | ||||
\(383\) | −34.3749 | −1.75647 | −0.878237 | − | 0.478225i | \(-0.841280\pi\) | ||||
−0.878237 | + | 0.478225i | \(0.841280\pi\) | |||||||
\(384\) | 0.872140 | − | 32.8684i | 0.0445062 | − | 1.67731i | ||||
\(385\) | −5.01680 | −0.255680 | ||||||||
\(386\) | 3.87623 | − | 33.2688i | 0.197295 | − | 1.69334i | ||||
\(387\) | 30.9874 | − | 30.9874i | 1.57518 | − | 1.57518i | ||||
\(388\) | −31.5764 | − | 7.45934i | −1.60305 | − | 0.378691i | ||||
\(389\) | 10.9633 | + | 10.9633i | 0.555860 | + | 0.555860i | 0.928126 | − | 0.372266i | \(-0.121419\pi\) |
−0.372266 | + | 0.928126i | \(0.621419\pi\) | |||||||
\(390\) | −15.6670 | − | 19.7993i | −0.793329 | − | 1.00257i | ||||
\(391\) | 7.19768i | 0.364003i | ||||||||
\(392\) | 0.964462 | − | 2.65891i | 0.0487127 | − | 0.134295i | ||||
\(393\) | − | 28.0287i | − | 1.41386i | ||||||
\(394\) | −17.9101 | + | 14.1721i | −0.902298 | + | 0.713981i | ||||
\(395\) | −4.85419 | − | 4.85419i | −0.244241 | − | 0.244241i | ||||
\(396\) | −12.0510 | + | 7.44535i | −0.605586 | + | 0.374143i | ||||
\(397\) | 26.4375 | − | 26.4375i | 1.32686 | − | 1.32686i | 0.418764 | − | 0.908095i | \(-0.362463\pi\) |
0.908095 | − | 0.418764i | \(-0.137537\pi\) | |||||||
\(398\) | 7.72146 | + | 0.899646i | 0.387042 | + | 0.0450952i | ||||
\(399\) | −6.01174 | −0.300963 | ||||||||
\(400\) | −17.6854 | + | 35.3433i | −0.884269 | + | 1.76717i | ||||
\(401\) | 4.97625 | 0.248502 | 0.124251 | − | 0.992251i | \(-0.460347\pi\) | ||||
0.124251 | + | 0.992251i | \(0.460347\pi\) | |||||||
\(402\) | −8.81247 | − | 1.02676i | −0.439526 | − | 0.0512102i | ||||
\(403\) | −4.62815 | + | 4.62815i | −0.230545 | + | 0.230545i | ||||
\(404\) | 17.1949 | + | 27.8316i | 0.855478 | + | 1.38467i | ||||
\(405\) | −11.7864 | − | 11.7864i | −0.585672 | − | 0.585672i | ||||
\(406\) | 6.43142 | − | 5.08913i | 0.319186 | − | 0.252569i | ||||
\(407\) | − | 3.04331i | − | 0.150851i | ||||||
\(408\) | 5.25396 | + | 11.2349i | 0.260110 | + | 0.556212i | ||||
\(409\) | 4.06359i | 0.200932i | 0.994941 | + | 0.100466i | \(0.0320333\pi\) | ||||
−0.994941 | + | 0.100466i | \(0.967967\pi\) | |||||||
\(410\) | −25.2374 | − | 31.8939i | −1.24639 | − | 1.57513i | ||||
\(411\) | 46.5544 | + | 46.5544i | 2.29636 | + | 2.29636i | ||||
\(412\) | −7.90295 | + | 33.4542i | −0.389350 | + | 1.64817i | ||||
\(413\) | −1.13843 | + | 1.13843i | −0.0560184 | + | 0.0560184i | ||||
\(414\) | −4.25192 | + | 36.4932i | −0.208970 | + | 1.79354i | ||||
\(415\) | −39.0674 | −1.91774 | ||||||||
\(416\) | 1.83783 | + | 8.81913i | 0.0901069 | + | 0.432393i | ||||
\(417\) | 27.3203 | 1.33788 | ||||||||
\(418\) | 0.440306 | − | 3.77905i | 0.0215361 | − | 0.184839i | ||||
\(419\) | 0.552238 | − | 0.552238i | 0.0269786 | − | 0.0269786i | −0.693489 | − | 0.720467i | \(-0.743927\pi\) |
0.720467 | + | 0.693489i | \(0.243927\pi\) | |||||||
\(420\) | −5.15476 | + | 21.8208i | −0.251526 | + | 1.06474i | ||||
\(421\) | −3.77763 | − | 3.77763i | −0.184110 | − | 0.184110i | 0.609034 | − | 0.793144i | \(-0.291557\pi\) |
−0.793144 | + | 0.609034i | \(0.791557\pi\) | |||||||
\(422\) | −1.12671 | − | 1.42389i | −0.0548475 | − | 0.0693139i | ||||
\(423\) | − | 19.5920i | − | 0.952593i | ||||||
\(424\) | 2.44836 | − | 1.14496i | 0.118903 | − | 0.0556044i | ||||
\(425\) | − | 14.9079i | − | 0.723140i | ||||||
\(426\) | 44.5427 | − | 35.2463i | 2.15810 | − | 1.70769i | ||||
\(427\) | −3.21881 | − | 3.21881i | −0.155769 | − | 0.155769i | ||||
\(428\) | −6.09727 | − | 9.86901i | −0.294723 | − | 0.477037i | ||||
\(429\) | 4.25612 | − | 4.25612i | 0.205487 | − | 0.205487i | ||||
\(430\) | 43.6028 | + | 5.08027i | 2.10271 | + | 0.244992i | ||||
\(431\) | 1.18186 | 0.0569283 | 0.0284641 | − | 0.999595i | \(-0.490938\pi\) | ||||
0.0284641 | + | 0.999595i | \(0.490938\pi\) | |||||||
\(432\) | 8.98342 | + | 26.9781i | 0.432215 | + | 1.29799i | ||||
\(433\) | −15.2584 | −0.733273 | −0.366637 | − | 0.930364i | \(-0.619491\pi\) | ||||
−0.366637 | + | 0.930364i | \(0.619491\pi\) | |||||||
\(434\) | 5.77335 | + | 0.672667i | 0.277130 | + | 0.0322891i | ||||
\(435\) | −45.9715 | + | 45.9715i | −2.20416 | + | 2.20416i | ||||
\(436\) | 7.87683 | − | 4.86646i | 0.377232 | − | 0.233061i | ||||
\(437\) | −6.97759 | − | 6.97759i | −0.333783 | − | 0.333783i | ||||
\(438\) | −46.6527 | + | 36.9159i | −2.22915 | + | 1.76391i | ||||
\(439\) | 4.34502i | 0.207376i | 0.994610 | + | 0.103688i | \(0.0330644\pi\) | ||||
−0.994610 | + | 0.103688i | \(0.966936\pi\) | |||||||
\(440\) | −13.3392 | − | 4.83851i | −0.635923 | − | 0.230667i | ||||
\(441\) | 5.44602i | 0.259334i | ||||||||
\(442\) | −2.10863 | − | 2.66479i | −0.100297 | − | 0.126751i | ||||
\(443\) | −4.31392 | − | 4.31392i | −0.204961 | − | 0.204961i | 0.597161 | − | 0.802121i | \(-0.296295\pi\) |
−0.802121 | + | 0.597161i | \(0.796295\pi\) | |||||||
\(444\) | −13.2370 | − | 3.12700i | −0.628200 | − | 0.148401i | ||||
\(445\) | −23.0733 | + | 23.0733i | −1.09378 | + | 1.09378i | ||||
\(446\) | −0.524253 | + | 4.49954i | −0.0248241 | + | 0.213060i | ||||
\(447\) | −31.9359 | −1.51052 | ||||||||
\(448\) | 5.12884 | − | 6.13963i | 0.242315 | − | 0.290070i | ||||
\(449\) | 3.72499 | 0.175793 | 0.0878967 | − | 0.996130i | \(-0.471985\pi\) | ||||
0.0878967 | + | 0.996130i | \(0.471985\pi\) | |||||||
\(450\) | 8.80661 | − | 75.5851i | 0.415147 | − | 3.56312i | ||||
\(451\) | 6.85604 | − | 6.85604i | 0.322838 | − | 0.322838i | ||||
\(452\) | 17.8525 | + | 4.21732i | 0.839710 | + | 0.198366i | ||||
\(453\) | −11.2373 | − | 11.2373i | −0.527976 | − | 0.527976i | ||||
\(454\) | 17.1178 | + | 21.6328i | 0.803380 | + | 1.01528i | ||||
\(455\) | − | 6.14310i | − | 0.287993i | ||||||
\(456\) | −15.9847 | − | 5.79809i | −0.748552 | − | 0.271521i | ||||
\(457\) | 10.7451i | 0.502636i | 0.967905 | + | 0.251318i | \(0.0808640\pi\) | ||||
−0.967905 | + | 0.251318i | \(0.919136\pi\) | |||||||
\(458\) | 11.0128 | − | 8.71433i | 0.514594 | − | 0.407194i | ||||
\(459\) | −7.58434 | − | 7.58434i | −0.354007 | − | 0.354007i | ||||
\(460\) | −31.3094 | + | 19.3436i | −1.45981 | + | 0.901899i | ||||
\(461\) | 7.88785 | − | 7.88785i | 0.367374 | − | 0.367374i | −0.499145 | − | 0.866519i | \(-0.666352\pi\) |
0.866519 | + | 0.499145i | \(0.166352\pi\) | |||||||
\(462\) | −5.30926 | − | 0.618595i | −0.247009 | − | 0.0287797i | ||||
\(463\) | 27.3485 | 1.27099 | 0.635496 | − | 0.772104i | \(-0.280796\pi\) | ||||
0.635496 | + | 0.772104i | \(0.280796\pi\) | |||||||
\(464\) | 22.0089 | − | 7.32870i | 1.02174 | − | 0.340226i | ||||
\(465\) | −46.0758 | −2.13671 | ||||||||
\(466\) | 4.12784 | + | 0.480945i | 0.191219 | + | 0.0222794i | ||||
\(467\) | 11.3915 | − | 11.3915i | 0.527135 | − | 0.527135i | −0.392582 | − | 0.919717i | \(-0.628418\pi\) |
0.919717 | + | 0.392582i | \(0.128418\pi\) | |||||||
\(468\) | −9.11686 | − | 14.7565i | −0.421427 | − | 0.682120i | ||||
\(469\) | −1.52640 | − | 1.52640i | −0.0704828 | − | 0.0704828i | ||||
\(470\) | 15.3900 | − | 12.1780i | 0.709890 | − | 0.561730i | ||||
\(471\) | − | 23.0867i | − | 1.06378i | ||||||
\(472\) | −4.12495 | + | 1.92901i | −0.189866 | + | 0.0887898i | ||||
\(473\) | 10.4651i | 0.481185i | ||||||||
\(474\) | −4.53862 | − | 5.73571i | −0.208466 | − | 0.263450i | ||||
\(475\) | 14.4520 | + | 14.4520i | 0.663105 | + | 0.663105i | ||||
\(476\) | −0.693782 | + | 2.93687i | −0.0317994 | + | 0.134611i | ||||
\(477\) | −3.67995 | + | 3.67995i | −0.168493 | + | 0.168493i | ||||
\(478\) | 2.65317 | − | 22.7716i | 0.121353 | − | 1.04155i | ||||
\(479\) | 11.3880 | 0.520330 | 0.260165 | − | 0.965564i | \(-0.416223\pi\) | ||||
0.260165 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(480\) | −34.7513 | + | 53.0479i | −1.58617 | + | 2.42130i | ||||
\(481\) | 3.72655 | 0.169916 | ||||||||
\(482\) | −2.31041 | + | 19.8297i | −0.105236 | + | 0.903219i | ||||
\(483\) | −9.80296 | + | 9.80296i | −0.446050 | + | 0.446050i | ||||
\(484\) | −4.28017 | + | 18.1185i | −0.194553 | + | 0.823570i | ||||
\(485\) | 44.2502 | + | 44.2502i | 2.00930 | + | 2.00930i | ||||
\(486\) | 7.69435 | + | 9.72378i | 0.349023 | + | 0.441080i | ||||
\(487\) | − | 31.3531i | − | 1.42075i | −0.703826 | − | 0.710373i | \(-0.748526\pi\) | ||
0.703826 | − | 0.710373i | \(-0.251474\pi\) | |||||||
\(488\) | −5.45412 | − | 11.6630i | −0.246896 | − | 0.527957i | ||||
\(489\) | − | 25.9652i | − | 1.17419i | ||||||
\(490\) | −4.27801 | + | 3.38515i | −0.193261 | + | 0.152926i | ||||
\(491\) | 20.2775 | + | 20.2775i | 0.915112 | + | 0.915112i | 0.996669 | − | 0.0815572i | \(-0.0259893\pi\) |
−0.0815572 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(492\) | −22.7760 | − | 36.8651i | −1.02682 | − | 1.66201i | ||||
\(493\) | −6.18733 | + | 6.18733i | −0.278663 | + | 0.278663i | ||||
\(494\) | 4.62746 | + | 0.539157i | 0.208199 | + | 0.0242578i | ||||
\(495\) | 27.3216 | 1.22802 | ||||||||
\(496\) | 14.7021 | + | 7.35674i | 0.660143 | + | 0.330327i | ||||
\(497\) | 13.8202 | 0.619921 | ||||||||
\(498\) | −41.3449 | − | 4.81719i | −1.85271 | − | 0.215864i | ||||
\(499\) | −18.5167 | + | 18.5167i | −0.828921 | + | 0.828921i | −0.987368 | − | 0.158446i | \(-0.949351\pi\) |
0.158446 | + | 0.987368i | \(0.449351\pi\) | |||||||
\(500\) | 32.0313 | − | 19.7896i | 1.43249 | − | 0.885017i | ||||
\(501\) | 24.2848 | + | 24.2848i | 1.08497 | + | 1.08497i | ||||
\(502\) | −22.2659 | + | 17.6188i | −0.993774 | + | 0.786366i | ||||
\(503\) | − | 31.9854i | − | 1.42616i | −0.701082 | − | 0.713080i | \(-0.747299\pi\) | ||
0.701082 | − | 0.713080i | \(-0.252701\pi\) | |||||||
\(504\) | −5.25248 | + | 14.4805i | −0.233964 | + | 0.645012i | ||||
\(505\) | − | 63.0987i | − | 2.80786i | ||||||
\(506\) | −5.44427 | − | 6.88023i | −0.242028 | − | 0.305864i | ||||
\(507\) | −21.5033 | − | 21.5033i | −0.954996 | − | 0.954996i | ||||
\(508\) | 25.2620 | + | 5.96769i | 1.12082 | + | 0.264774i | ||||
\(509\) | 12.1644 | − | 12.1644i | 0.539176 | − | 0.539176i | −0.384111 | − | 0.923287i | \(-0.625492\pi\) |
0.923287 | + | 0.384111i | \(0.125492\pi\) | |||||||
\(510\) | 2.76846 | − | 23.7610i | 0.122589 | − | 1.05216i | ||||
\(511\) | −14.4749 | −0.640331 | ||||||||
\(512\) | 19.5586 | − | 11.3782i | 0.864375 | − | 0.502849i | ||||
\(513\) | 14.7048 | 0.649234 | ||||||||
\(514\) | −0.529753 | + | 4.54675i | −0.0233664 | + | 0.200549i | ||||
\(515\) | 46.8817 | − | 46.8817i | 2.06586 | − | 2.06586i | ||||
\(516\) | 45.5182 | + | 10.7529i | 2.00383 | + | 0.473368i | ||||
\(517\) | 3.30830 | + | 3.30830i | 0.145499 | + | 0.145499i | ||||
\(518\) | −2.05351 | − | 2.59514i | −0.0902262 | − | 0.114024i | ||||
\(519\) | 23.1745i | 1.01725i | ||||||||
\(520\) | 5.92478 | − | 16.3340i | 0.259819 | − | 0.716291i | ||||
\(521\) | − | 34.4322i | − | 1.50850i | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(522\) | −35.0257 | + | 27.7155i | −1.53303 | + | 1.21308i | ||||
\(523\) | −15.4031 | − | 15.4031i | −0.673530 | − | 0.673530i | 0.284998 | − | 0.958528i | \(-0.408007\pi\) |
−0.958528 | + | 0.284998i | \(0.908007\pi\) | |||||||
\(524\) | 16.4097 | − | 10.1382i | 0.716861 | − | 0.442890i | ||||
\(525\) | 20.3040 | − | 20.3040i | 0.886138 | − | 0.886138i | ||||
\(526\) | 33.7357 | + | 3.93062i | 1.47094 | + | 0.171383i | ||||
\(527\) | −6.20137 | −0.270136 | ||||||||
\(528\) | −13.5203 | − | 6.76537i | −0.588394 | − | 0.294425i | ||||
\(529\) | 0.244184 | 0.0106167 | ||||||||
\(530\) | −5.17810 | − | 0.603314i | −0.224922 | − | 0.0262063i | ||||
\(531\) | 6.19990 | − | 6.19990i | 0.269053 | − | 0.269053i | ||||
\(532\) | −2.17450 | − | 3.51963i | −0.0942764 | − | 0.152595i | ||||
\(533\) | 8.39524 | + | 8.39524i | 0.363638 | + | 0.363638i | ||||
\(534\) | −27.2634 | + | 21.5733i | −1.17980 | + | 0.933569i | ||||
\(535\) | 22.3747i | 0.967341i | ||||||||
\(536\) | −2.58642 | − | 5.53073i | −0.111716 | − | 0.238891i | ||||
\(537\) | 48.2011i | 2.08003i | ||||||||
\(538\) | 0.108596 | + | 0.137239i | 0.00468192 | + | 0.00591681i | ||||
\(539\) | −0.919616 | − | 0.919616i | −0.0396106 | − | 0.0396106i | ||||
\(540\) | 12.6086 | − | 53.3740i | 0.542589 | − | 2.29685i | ||||
\(541\) | −23.7164 | + | 23.7164i | −1.01965 | + | 1.01965i | −0.0198437 | + | 0.999803i | \(0.506317\pi\) |
−0.999803 | + | 0.0198437i | \(0.993683\pi\) | |||||||
\(542\) | −1.65529 | + | 14.2070i | −0.0711010 | + | 0.610244i | ||||
\(543\) | 17.2034 | 0.738267 | ||||||||
\(544\) | −4.67720 | + | 7.13975i | −0.200533 | + | 0.306114i | ||||
\(545\) | −17.8581 | −0.764956 | ||||||||
\(546\) | 0.757473 | − | 6.50122i | 0.0324168 | − | 0.278226i | ||||
\(547\) | 27.8819 | − | 27.8819i | 1.19214 | − | 1.19214i | 0.215680 | − | 0.976464i | \(-0.430803\pi\) |
0.976464 | − | 0.215680i | \(-0.0691967\pi\) | |||||||
\(548\) | −10.4166 | + | 44.0949i | −0.444975 | + | 1.88364i | ||||
\(549\) | 17.5297 | + | 17.5297i | 0.748150 | + | 0.748150i | ||||
\(550\) | 11.2762 | + | 14.2504i | 0.480820 | + | 0.607639i | ||||
\(551\) | − | 11.9963i | − | 0.511058i | ||||||
\(552\) | −35.5198 | + | 16.6106i | −1.51182 | + | 0.706995i | ||||
\(553\) | − | 1.77961i | − | 0.0756769i | ||||||
\(554\) | −17.2647 | + | 13.6614i | −0.733506 | + | 0.580418i | ||||
\(555\) | 18.5499 | + | 18.5499i | 0.787400 | + | 0.787400i | ||||
\(556\) | 9.88197 | + | 15.9949i | 0.419089 | + | 0.678335i | ||||
\(557\) | 0.275943 | − | 0.275943i | 0.0116921 | − | 0.0116921i | −0.701237 | − | 0.712929i | \(-0.747368\pi\) |
0.712929 | + | 0.701237i | \(0.247368\pi\) | |||||||
\(558\) | −31.4418 | − | 3.66336i | −1.33104 | − | 0.155082i | ||||
\(559\) | −12.8145 | −0.541997 | ||||||||
\(560\) | −14.6397 | + | 4.87485i | −0.618640 | + | 0.206000i | ||||
\(561\) | 5.70288 | 0.240776 | ||||||||
\(562\) | −5.92786 | − | 0.690669i | −0.250052 | − | 0.0291341i | ||||
\(563\) | −13.8911 | + | 13.8911i | −0.585438 | + | 0.585438i | −0.936393 | − | 0.350954i | \(-0.885857\pi\) |
0.350954 | + | 0.936393i | \(0.385857\pi\) | |||||||
\(564\) | 17.7888 | − | 10.9903i | 0.749045 | − | 0.462775i | ||||
\(565\) | −25.0179 | − | 25.0179i | −1.05251 | − | 1.05251i | ||||
\(566\) | −26.0090 | + | 20.5807i | −1.09324 | + | 0.865073i | ||||
\(567\) | − | 4.32107i | − | 0.181468i | ||||||
\(568\) | 36.7467 | + | 13.3291i | 1.54186 | + | 0.559275i | ||||
\(569\) | − | 8.08076i | − | 0.338763i | −0.985551 | − | 0.169381i | \(-0.945823\pi\) | ||
0.985551 | − | 0.169381i | \(-0.0541770\pi\) | |||||||
\(570\) | 20.3507 | + | 25.7183i | 0.852395 | + | 1.07722i | ||||
\(571\) | −7.55816 | − | 7.55816i | −0.316299 | − | 0.316299i | 0.531045 | − | 0.847344i | \(-0.321800\pi\) |
−0.847344 | + | 0.531045i | \(0.821800\pi\) | |||||||
\(572\) | 4.03126 | + | 0.952312i | 0.168556 | + | 0.0398182i | ||||
\(573\) | −25.4154 | + | 25.4154i | −1.06175 | + | 1.06175i | ||||
\(574\) | 1.22019 | − | 10.4726i | 0.0509296 | − | 0.437117i | ||||
\(575\) | 47.1320 | 1.96554 | ||||||||
\(576\) | −27.9317 | + | 33.4365i | −1.16382 | + | 1.39319i | ||||
\(577\) | 1.95969 | 0.0815831 | 0.0407915 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407915 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(578\) | −2.40972 | + | 20.6821i | −0.100231 | + | 0.860261i | ||||
\(579\) | −48.6699 | + | 48.6699i | −2.02265 | + | 2.02265i | ||||
\(580\) | −43.5427 | − | 10.2862i | −1.80801 | − | 0.427110i | ||||
\(581\) | −7.16133 | − | 7.16133i | −0.297102 | − | 0.297102i | ||||
\(582\) | 41.3735 | + | 52.2860i | 1.71499 | + | 2.16733i | ||||
\(583\) | − | 1.24279i | − | 0.0514713i | ||||||
\(584\) | −38.4874 | − | 13.9605i | −1.59262 | − | 0.577688i | ||||
\(585\) | 33.4554i | 1.38321i | ||||||||
\(586\) | −21.2111 | + | 16.7842i | −0.876221 | + | 0.693347i | ||||
\(587\) | 24.6131 | + | 24.6131i | 1.01589 | + | 1.01589i | 0.999872 | + | 0.0160192i | \(0.00509930\pi\) |
0.0160192 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(588\) | −4.94480 | + | 3.05500i | −0.203920 | + | 0.125986i | ||||
\(589\) | 6.01174 | − | 6.01174i | 0.247709 | − | 0.247709i | ||||
\(590\) | 8.72395 | + | 1.01645i | 0.359159 | + | 0.0418465i | ||||
\(591\) | 46.9341 | 1.93061 | ||||||||
\(592\) | −2.95720 | − | 8.88078i | −0.121540 | − | 0.364998i | ||||
\(593\) | 16.5483 | 0.679558 | 0.339779 | − | 0.940505i | \(-0.389648\pi\) | ||||
0.339779 | + | 0.940505i | \(0.389648\pi\) | |||||||
\(594\) | 12.9866 | + | 1.51310i | 0.532845 | + | 0.0620831i | ||||
\(595\) | 4.11564 | − | 4.11564i | 0.168725 | − | 0.168725i | ||||
\(596\) | −11.5515 | − | 18.6972i | −0.473167 | − | 0.765866i | ||||
\(597\) | −11.2960 | − | 11.2960i | −0.462313 | − | 0.462313i | ||||
\(598\) | 8.42487 | − | 6.66654i | 0.344519 | − | 0.272615i | ||||
\(599\) | 10.2649i | 0.419412i | 0.977764 | + | 0.209706i | \(0.0672507\pi\) | ||||
−0.977764 | + | 0.209706i | \(0.932749\pi\) | |||||||
\(600\) | 73.5689 | − | 34.4041i | 3.00344 | − | 1.40454i | ||||
\(601\) | 35.6586i | 1.45455i | 0.686348 | + | 0.727273i | \(0.259213\pi\) | ||||
−0.686348 | + | 0.727273i | \(0.740787\pi\) | |||||||
\(602\) | 7.06145 | + | 8.92394i | 0.287803 | + | 0.363713i | ||||
\(603\) | 8.31283 | + | 8.31283i | 0.338524 | + | 0.338524i | ||||
\(604\) | 2.51436 | − | 10.6436i | 0.102308 | − | 0.433083i | ||||
\(605\) | 25.3908 | − | 25.3908i | 1.03228 | − | 1.03228i | ||||
\(606\) | 7.78037 | − | 66.7772i | 0.316056 | − | 2.71264i | ||||
\(607\) | 23.1111 | 0.938052 | 0.469026 | − | 0.883184i | \(-0.344605\pi\) | ||||
0.469026 | + | 0.883184i | \(0.344605\pi\) | |||||||
\(608\) | −2.38725 | − | 11.4556i | −0.0968157 | − | 0.464586i | ||||
\(609\) | −16.8538 | −0.682950 | ||||||||
\(610\) | −2.87393 | + | 24.6663i | −0.116362 | + | 0.998708i | ||||
\(611\) | −4.05103 | + | 4.05103i | −0.163887 | + | 0.163887i | ||||
\(612\) | 3.77835 | − | 15.9942i | 0.152731 | − | 0.646529i | ||||
\(613\) | −26.9200 | − | 26.9200i | −1.08729 | − | 1.08729i | −0.995807 | − | 0.0914813i | \(-0.970840\pi\) |
−0.0914813 | − | 0.995807i | \(-0.529160\pi\) | |||||||
\(614\) | 11.0874 | + | 14.0117i | 0.447449 | + | 0.565467i | ||||
\(615\) | 83.5793i | 3.37024i | ||||||||
\(616\) | −1.55824 | − | 3.33211i | −0.0627834 | − | 0.134255i | ||||
\(617\) | 47.9337i | 1.92974i | 0.262732 | + | 0.964869i | \(0.415377\pi\) | ||||
−0.262732 | + | 0.964869i | \(0.584623\pi\) | |||||||
\(618\) | 55.3955 | − | 43.8340i | 2.22833 | − | 1.76326i | ||||
\(619\) | 4.05053 | + | 4.05053i | 0.162805 | + | 0.162805i | 0.783808 | − | 0.621003i | \(-0.213275\pi\) |
−0.621003 | + | 0.783808i | \(0.713275\pi\) | |||||||
\(620\) | −16.6660 | − | 26.9755i | −0.669323 | − | 1.08336i | ||||
\(621\) | 23.9782 | − | 23.9782i | 0.962213 | − | 0.962213i | ||||
\(622\) | 27.7763 | + | 3.23629i | 1.11373 | + | 0.129763i | ||||
\(623\) | −8.45899 | −0.338902 | ||||||||
\(624\) | 8.28423 | − | 16.5556i | 0.331634 | − | 0.662755i | ||||
\(625\) | −23.2188 | −0.928752 | ||||||||
\(626\) | 12.2595 | + | 1.42839i | 0.489989 | + | 0.0570898i | ||||
\(627\) | −5.52849 | + | 5.52849i | −0.220787 | + | 0.220787i | ||||
\(628\) | 13.5164 | − | 8.35067i | 0.539361 | − | 0.333228i | ||||
\(629\) | 2.49664 | + | 2.49664i | 0.0995477 | + | 0.0995477i | ||||
\(630\) | 23.2981 | − | 18.4356i | 0.928219 | − | 0.734492i | ||||
\(631\) | 2.35784i | 0.0938640i | 0.998898 | + | 0.0469320i | \(0.0149444\pi\) | ||||
−0.998898 | + | 0.0469320i | \(0.985056\pi\) | |||||||
\(632\) | 1.71637 | − | 4.73184i | 0.0682735 | − | 0.188222i | ||||
\(633\) | 3.73136i | 0.148308i | ||||||||
\(634\) | −23.6043 | − | 29.8301i | −0.937448 | − | 1.18471i | ||||
\(635\) | −35.4014 | − | 35.4014i | −1.40486 | − | 1.40486i | ||||
\(636\) | −5.40558 | − | 1.27697i | −0.214345 | − | 0.0506351i | ||||
\(637\) | 1.12607 | − | 1.12607i | 0.0446166 | − | 0.0446166i | ||||
\(638\) | 1.23439 | − | 10.5945i | 0.0488699 | − | 0.419440i | ||||
\(639\) | −75.2652 | −2.97744 | ||||||||
\(640\) | −43.6273 | − | 1.15762i | −1.72452 | − | 0.0457590i | ||||
\(641\) | −49.8415 | −1.96862 | −0.984311 | − | 0.176440i | \(-0.943542\pi\) | ||||
−0.984311 | + | 0.176440i | \(0.943542\pi\) | |||||||
\(642\) | −2.75890 | + | 23.6790i | −0.108885 | + | 0.934536i | ||||
\(643\) | −6.07975 | + | 6.07975i | −0.239762 | + | 0.239762i | −0.816751 | − | 0.576990i | \(-0.804227\pi\) |
0.576990 | + | 0.816751i | \(0.304227\pi\) | |||||||
\(644\) | −9.28505 | − | 2.19342i | −0.365882 | − | 0.0864330i | ||||
\(645\) | −63.7879 | − | 63.7879i | −2.51165 | − | 2.51165i | ||||
\(646\) | 2.73901 | + | 3.46144i | 0.107765 | + | 0.136188i | ||||
\(647\) | − | 0.463264i | − | 0.0182128i | −0.999959 | − | 0.00910640i | \(-0.997101\pi\) | ||
0.999959 | − | 0.00910640i | \(-0.00289870\pi\) | |||||||
\(648\) | 4.16751 | − | 11.4894i | 0.163715 | − | 0.451344i | ||||
\(649\) | 2.09383i | 0.0821901i | ||||||||
\(650\) | −17.4497 | + | 13.8078i | −0.684432 | + | 0.541586i | ||||
\(651\) | −8.44602 | − | 8.44602i | −0.331026 | − | 0.331026i | ||||
\(652\) | 15.2016 | − | 9.39183i | 0.595339 | − | 0.367812i | ||||
\(653\) | 6.63668 | − | 6.63668i | 0.259713 | − | 0.259713i | −0.565224 | − | 0.824937i | \(-0.691210\pi\) |
0.824937 | + | 0.565224i | \(0.191210\pi\) | |||||||
\(654\) | −18.8991 | − | 2.20198i | −0.739014 | − | 0.0861044i | ||||
\(655\) | −37.2034 | −1.45366 | ||||||||
\(656\) | 13.3448 | − | 26.6689i | 0.521026 | − | 1.04124i | ||||
\(657\) | 78.8305 | 3.07547 | ||||||||
\(658\) | 5.05342 | + | 0.588786i | 0.197003 | + | 0.0229533i | ||||
\(659\) | −4.62922 | + | 4.62922i | −0.180329 | + | 0.180329i | −0.791499 | − | 0.611170i | \(-0.790699\pi\) |
0.611170 | + | 0.791499i | \(0.290699\pi\) | |||||||
\(660\) | 15.3263 | + | 24.8071i | 0.596576 | + | 0.965615i | ||||
\(661\) | −2.25711 | − | 2.25711i | −0.0877916 | − | 0.0877916i | 0.661847 | − | 0.749639i | \(-0.269773\pi\) |
−0.749639 | + | 0.661847i | \(0.769773\pi\) | |||||||
\(662\) | 35.0262 | − | 27.7160i | 1.36133 | − | 1.07721i | ||||
\(663\) | 6.98320i | 0.271205i | ||||||||
\(664\) | −12.1345 | − | 25.9482i | −0.470911 | − | 1.00698i | ||||
\(665\) | 7.97958i | 0.309435i | ||||||||
\(666\) | 11.1835 | + | 14.1332i | 0.433351 | + | 0.547650i | ||||
\(667\) | −19.5615 | − | 19.5615i | −0.757425 | − | 0.757425i | ||||
\(668\) | −5.43376 | + | 23.0018i | −0.210239 | + | 0.889968i | ||||
\(669\) | 6.58253 | − | 6.58253i | 0.254495 | − | 0.254495i | ||||
\(670\) | −1.36286 | + | 11.6971i | −0.0526517 | + | 0.451898i | ||||
\(671\) | −5.92014 | −0.228544 | ||||||||
\(672\) | −16.0942 | + | 3.35389i | −0.620848 | + | 0.129379i | ||||
\(673\) | 6.82222 | 0.262977 | 0.131489 | − | 0.991318i | \(-0.458024\pi\) | ||||
0.131489 | + | 0.991318i | \(0.458024\pi\) | |||||||
\(674\) | −3.84330 | + | 32.9862i | −0.148038 | + | 1.27058i | ||||
\(675\) | −49.6639 | + | 49.6639i | −1.91157 | + | 1.91157i | ||||
\(676\) | 4.81139 | − | 20.3673i | 0.185054 | − | 0.783356i | ||||
\(677\) | 4.77844 | + | 4.77844i | 0.183650 | + | 0.183650i | 0.792944 | − | 0.609294i | \(-0.208547\pi\) |
−0.609294 | + | 0.792944i | \(0.708547\pi\) | |||||||
\(678\) | −23.3916 | − | 29.5612i | −0.898347 | − | 1.13529i | ||||
\(679\) | 16.2227i | 0.622571i | ||||||||
\(680\) | 14.9125 | − | 6.97375i | 0.571868 | − | 0.267431i | ||||
\(681\) | − | 56.6895i | − | 2.17235i | ||||||
\(682\) | 5.92786 | − | 4.69067i | 0.226990 | − | 0.179615i | ||||
\(683\) | −29.2736 | − | 29.2736i | −1.12012 | − | 1.12012i | −0.991723 | − | 0.128400i | \(-0.959016\pi\) |
−0.128400 | − | 0.991723i | \(-0.540984\pi\) | |||||||
\(684\) | 11.8424 | + | 19.1680i | 0.452804 | + | 0.732906i | ||||
\(685\) | 61.7932 | − | 61.7932i | 2.36100 | − | 2.36100i | ||||
\(686\) | −1.40471 | − | 0.163666i | −0.0536321 | − | 0.00624881i | ||||
\(687\) | −28.8594 | −1.10106 | ||||||||
\(688\) | 10.1690 | + | 30.5385i | 0.387688 | + | 1.16427i | ||||
\(689\) | 1.52181 | 0.0579762 | ||||||||
\(690\) | 75.1216 | + | 8.75261i | 2.85983 | + | 0.333206i | ||||
\(691\) | −4.65064 | + | 4.65064i | −0.176919 | + | 0.176919i | −0.790011 | − | 0.613092i | \(-0.789925\pi\) |
0.613092 | + | 0.790011i | \(0.289925\pi\) | |||||||
\(692\) | −13.5678 | + | 8.38243i | −0.515769 | + | 0.318652i | ||||
\(693\) | 5.00824 | + | 5.00824i | 0.190247 | + | 0.190247i | ||||
\(694\) | −9.87632 | + | 7.81505i | −0.374900 | + | 0.296655i | ||||
\(695\) | − | 36.2631i | − | 1.37554i | ||||||
\(696\) | −44.8127 | − | 16.2548i | −1.69862 | − | 0.616138i | ||||
\(697\) | 11.2490i | 0.426086i | ||||||||
\(698\) | −8.61326 | − | 10.8851i | −0.326017 | − | 0.412005i | ||||
\(699\) | −6.03875 | − | 6.03875i | −0.228407 | − | 0.228407i | ||||
\(700\) | 19.2313 | + | 4.54304i | 0.726874 | + | 0.171711i | ||||
\(701\) | −4.01206 | + | 4.01206i | −0.151533 | + | 0.151533i | −0.778802 | − | 0.627269i | \(-0.784173\pi\) |
0.627269 | + | 0.778802i | \(0.284173\pi\) | |||||||
\(702\) | −1.85279 | + | 15.9021i | −0.0699292 | + | 0.600186i | ||||
\(703\) | −4.84060 | −0.182567 | ||||||||
\(704\) | −0.929538 | − | 10.3627i | −0.0350333 | − | 0.390557i | ||||
\(705\) | −40.3302 | −1.51892 | ||||||||
\(706\) | 4.92528 | − | 42.2726i | 0.185365 | − | 1.59095i | ||||
\(707\) | 11.5664 | − | 11.5664i | 0.435001 | − | 0.435001i | ||||
\(708\) | 9.10719 | + | 2.15141i | 0.342269 | + | 0.0808549i | ||||
\(709\) | 36.0117 | + | 36.0117i | 1.35245 | + | 1.35245i | 0.882915 | + | 0.469533i | \(0.155578\pi\) |
0.469533 | + | 0.882915i | \(0.344422\pi\) | |||||||
\(710\) | −46.7835 | − | 59.1230i | −1.75575 | − | 2.21885i | ||||
\(711\) | 9.69181i | 0.363471i | ||||||||
\(712\) | −22.4917 | − | 8.15837i | −0.842912 | − | 0.305748i | ||||
\(713\) | − | 19.6059i | − | 0.734248i | ||||||
\(714\) | 4.86304 | − | 3.84809i | 0.181995 | − | 0.144011i | ||||
\(715\) | −5.64929 | − | 5.64929i | −0.211271 | − | 0.211271i | ||||
\(716\) | −28.2198 | + | 17.4347i | −1.05462 | + | 0.651566i | ||||
\(717\) | −33.3133 | + | 33.3133i | −1.24411 | + | 1.24411i | ||||
\(718\) | 14.5691 | + | 1.69749i | 0.543716 | + | 0.0633496i | ||||
\(719\) | 7.62249 | 0.284271 | 0.142135 | − | 0.989847i | \(-0.454603\pi\) | ||||
0.142135 | + | 0.989847i | \(0.454603\pi\) | |||||||
\(720\) | 79.7281 | − | 26.5485i | 2.97129 | − | 0.989406i | ||||
\(721\) | 17.1875 | 0.640096 | ||||||||
\(722\) | 20.6787 | + | 2.40932i | 0.769580 | + | 0.0896657i | ||||
\(723\) | 29.0095 | − | 29.0095i | 1.07888 | − | 1.07888i | ||||
\(724\) | 6.22260 | + | 10.0719i | 0.231261 | + | 0.374318i | ||||
\(725\) | 40.5160 | + | 40.5160i | 1.50473 | + | 1.50473i | ||||
\(726\) | 30.0018 | − | 23.7402i | 1.11347 | − | 0.881080i | ||||
\(727\) | − | 25.4856i | − | 0.945207i | −0.881275 | − | 0.472604i | \(-0.843314\pi\) | ||
0.881275 | − | 0.472604i | \(-0.156686\pi\) | |||||||
\(728\) | 4.08018 | − | 1.90808i | 0.151222 | − | 0.0707180i | ||||
\(729\) | − | 38.4448i | − | 1.42388i | ||||||
\(730\) | 48.9997 | + | 61.9236i | 1.81356 | + | 2.29190i | ||||
\(731\) | −8.58525 | − | 8.58525i | −0.317537 | − | 0.317537i | ||||
\(732\) | −6.08293 | + | 25.7498i | −0.224832 | + | 0.951742i | ||||
\(733\) | −14.9748 | + | 14.9748i | −0.553106 | + | 0.553106i | −0.927336 | − | 0.374230i | \(-0.877907\pi\) |
0.374230 | + | 0.927336i | \(0.377907\pi\) | |||||||
\(734\) | −1.33056 | + | 11.4199i | −0.0491120 | + | 0.421517i | ||||
\(735\) | 11.2107 | 0.413512 | ||||||||
\(736\) | −22.5727 | − | 14.7872i | −0.832039 | − | 0.545063i | ||||
\(737\) | −2.80741 | −0.103412 | ||||||||
\(738\) | −6.64516 | + | 57.0339i | −0.244612 | + | 2.09945i | ||||
\(739\) | −12.3417 | + | 12.3417i | −0.453996 | + | 0.453996i | −0.896679 | − | 0.442682i | \(-0.854027\pi\) |
0.442682 | + | 0.896679i | \(0.354027\pi\) | |||||||
\(740\) | −4.15057 | + | 17.5699i | −0.152578 | + | 0.645882i | ||||
\(741\) | −6.76966 | − | 6.76966i | −0.248690 | − | 0.248690i | ||||
\(742\) | −0.838591 | − | 1.05977i | −0.0307857 | − | 0.0389056i | ||||
\(743\) | 10.6724i | 0.391531i | 0.980651 | + | 0.195766i | \(0.0627192\pi\) | ||||
−0.980651 | + | 0.195766i | \(0.937281\pi\) | |||||||
\(744\) | −14.3114 | − | 30.6031i | −0.524680 | − | 1.12196i | ||||
\(745\) | 42.3896i | 1.55303i | ||||||||
\(746\) | −4.99823 | + | 3.95506i | −0.182998 | + | 0.144805i | ||||
\(747\) | 39.0007 | + | 39.0007i | 1.42696 | + | 1.42696i | ||||
\(748\) | 2.06278 | + | 3.33880i | 0.0754226 | + | 0.122079i | ||||
\(749\) | −4.10143 | + | 4.10143i | −0.149863 | + | 0.149863i | ||||
\(750\) | −76.8538 | − | 8.95442i | −2.80630 | − | 0.326969i | ||||
\(751\) | −2.82952 | −0.103251 | −0.0516254 | − | 0.998667i | \(-0.516440\pi\) | ||||
−0.0516254 | + | 0.998667i | \(0.516440\pi\) | |||||||
\(752\) | 12.8687 | + | 6.43936i | 0.469275 | + | 0.234819i | ||||
\(753\) | 58.3485 | 2.12634 | ||||||||
\(754\) | 12.9730 | + | 1.51151i | 0.472448 | + | 0.0550461i | ||||
\(755\) | −14.9157 | + | 14.9157i | −0.542837 | + | 0.542837i | ||||
\(756\) | 12.0951 | − | 7.47258i | 0.439894 | − | 0.271775i | ||||
\(757\) | 15.6590 | + | 15.6590i | 0.569136 | + | 0.569136i | 0.931886 | − | 0.362750i | \(-0.118162\pi\) |
−0.362750 | + | 0.931886i | \(0.618162\pi\) | |||||||
\(758\) | −1.31599 | + | 1.04134i | −0.0477990 | + | 0.0378230i | ||||
\(759\) | 18.0299i | 0.654444i | ||||||||
\(760\) | −7.69600 | + | 21.2170i | −0.279163 | + | 0.769622i | ||||
\(761\) | 4.79367i | 0.173770i | 0.996218 | + | 0.0868852i | \(0.0276913\pi\) | ||||
−0.996218 | + | 0.0868852i | \(0.972309\pi\) | |||||||
\(762\) | −33.1001 | − | 41.8304i | −1.19909 | − | 1.51535i | ||||
\(763\) | −3.27351 | − | 3.27351i | −0.118509 | − | 0.118509i | ||||
\(764\) | −24.0727 | − | 5.68674i | −0.870920 | − | 0.205739i | ||||
\(765\) | −22.4139 | + | 22.4139i | −0.810375 | + | 0.810375i | ||||
\(766\) | −5.62601 | + | 48.2868i | −0.203276 | + | 1.74467i | ||||
\(767\) | −2.56390 | −0.0925772 | ||||||||
\(768\) | −46.0278 | − | 6.60455i | −1.66089 | − | 0.238321i | ||||
\(769\) | 13.5489 | 0.488585 | 0.244293 | − | 0.969702i | \(-0.421444\pi\) | ||||
0.244293 | + | 0.969702i | \(0.421444\pi\) | |||||||
\(770\) | −0.821082 | + | 7.04716i | −0.0295897 | + | 0.253962i | ||||
\(771\) | 6.65159 | − | 6.65159i | 0.239551 | − | 0.239551i | ||||
\(772\) | −46.0986 | − | 10.8900i | −1.65913 | − | 0.391938i | ||||
\(773\) | 18.7803 | + | 18.7803i | 0.675480 | + | 0.675480i | 0.958974 | − | 0.283494i | \(-0.0914936\pi\) |
−0.283494 | + | 0.958974i | \(0.591494\pi\) | |||||||
\(774\) | −38.4568 | − | 48.6000i | −1.38230 | − | 1.74689i | ||||
\(775\) | 40.6080i | 1.45868i | ||||||||
\(776\) | −15.6462 | + | 43.1348i | −0.561666 | + | 1.54845i | ||||
\(777\) | 6.80066i | 0.243972i | ||||||||
\(778\) | 17.1945 | − | 13.6059i | 0.616454 | − | 0.487795i | ||||
\(779\) | −10.9050 | − | 10.9050i | −0.390712 | − | 0.390712i | ||||
\(780\) | −30.3764 | + | 18.7671i | −1.08765 | + | 0.671971i | ||||
\(781\) | 12.7093 | − | 12.7093i | 0.454774 | − | 0.454774i | ||||
\(782\) | 10.1107 | + | 1.17802i | 0.361557 | + | 0.0421259i | ||||
\(783\) | 41.2247 | 1.47325 | ||||||||
\(784\) | −3.57715 | − | 1.78996i | −0.127755 | − | 0.0639273i | ||||
\(785\) | −30.6438 | −1.09372 | ||||||||
\(786\) | −39.3723 | − | 4.58736i | −1.40436 | − | 0.163626i | ||||
\(787\) | 24.4838 | − | 24.4838i | 0.872752 | − | 0.872752i | −0.120020 | − | 0.992772i | \(-0.538296\pi\) |
0.992772 | + | 0.120020i | \(0.0382958\pi\) | |||||||
\(788\) | 16.9765 | + | 27.4780i | 0.604761 | + | 0.978864i | ||||
\(789\) | −49.3530 | − | 49.3530i | −1.75701 | − | 1.75701i | ||||
\(790\) | −7.61320 | + | 6.02426i | −0.270865 | + | 0.214334i | ||||
\(791\) | − | 9.17193i | − | 0.326116i | ||||||
\(792\) | 8.48622 | + | 18.1467i | 0.301545 | + | 0.644816i | ||||
\(793\) | − | 7.24923i | − | 0.257428i | ||||||
\(794\) | −32.8101 | − | 41.4640i | −1.16439 | − | 1.47150i | ||||
\(795\) | 7.57521 | + | 7.57521i | 0.268665 | + | 0.268665i | ||||
\(796\) | 2.52748 | − | 10.6992i | 0.0895843 | − | 0.379222i | ||||
\(797\) | −17.6690 | + | 17.6690i | −0.625870 | + | 0.625870i | −0.947026 | − | 0.321157i | \(-0.895928\pi\) |
0.321157 | + | 0.947026i | \(0.395928\pi\) | |||||||
\(798\) | −0.983920 | + | 8.44476i | −0.0348304 | + | 0.298941i | ||||
\(799\) | −5.42807 | −0.192031 | ||||||||
\(800\) | 46.7527 | + | 30.6274i | 1.65296 | + | 1.08284i | ||||
\(801\) | 46.0678 | 1.62773 | ||||||||
\(802\) | 0.814444 | − | 6.99019i | 0.0287590 | − | 0.246832i | ||||
\(803\) | −13.3113 | + | 13.3113i | −0.469746 | + | 0.469746i | ||||
\(804\) | −2.88461 | + | 12.2109i | −0.101732 | + | 0.430646i | ||||
\(805\) | 13.0118 | + | 13.0118i | 0.458605 | + | 0.458605i | ||||
\(806\) | 5.74374 | + | 7.25869i | 0.202315 | + | 0.255676i | ||||
\(807\) | − | 0.359641i | − | 0.0126600i | ||||||
\(808\) | 41.9096 | − | 19.5988i | 1.47437 | − | 0.689482i | ||||
\(809\) | − | 2.99378i | − | 0.105256i | −0.998614 | − | 0.0526278i | \(-0.983240\pi\) | ||
0.998614 | − | 0.0526278i | \(-0.0167597\pi\) | |||||||
\(810\) | −18.4856 | + | 14.6275i | −0.649517 | + | 0.513958i | ||||
\(811\) | −2.28628 | − | 2.28628i | −0.0802820 | − | 0.0802820i | 0.665825 | − | 0.746108i | \(-0.268080\pi\) |
−0.746108 | + | 0.665825i | \(0.768080\pi\) | |||||||
\(812\) | −6.09616 | − | 9.86721i | −0.213933 | − | 0.346271i | ||||
\(813\) | 20.7839 | − | 20.7839i | 0.728923 | − | 0.728923i | ||||
\(814\) | −4.27497 | − | 0.498088i | −0.149838 | − | 0.0174580i | ||||
\(815\) | −34.4644 | −1.20724 | ||||||||
\(816\) | 16.6417 | − | 5.54151i | 0.582577 | − | 0.193992i | ||||
\(817\) | 16.6454 | 0.582351 | ||||||||
\(818\) | 5.70817 | + | 0.665073i | 0.199582 | + | 0.0232537i | ||||
\(819\) | −6.13262 | + | 6.13262i | −0.214291 | + | 0.214291i | ||||
\(820\) | −48.9323 | + | 30.2313i | −1.70879 | + | 1.05572i | ||||
\(821\) | −28.6342 | − | 28.6342i | −0.999339 | − | 0.999339i | 0.000660747 | − | 1.00000i | \(-0.499790\pi\) |
−1.00000 | 0.000660747i | \(0.999790\pi\) | ||||||||
\(822\) | 73.0149 | − | 57.7761i | 2.54669 | − | 2.01517i | ||||
\(823\) | 41.0492i | 1.43088i | 0.698672 | + | 0.715442i | \(0.253775\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(824\) | 45.7001 | + | 16.5767i | 1.59204 | + | 0.577476i | ||||
\(825\) | − | 37.3437i | − | 1.30014i | ||||||
\(826\) | 1.41284 | + | 1.78548i | 0.0491590 | + | 0.0621249i | ||||
\(827\) | −20.3987 | − | 20.3987i | −0.709331 | − | 0.709331i | 0.257064 | − | 0.966394i | \(-0.417245\pi\) |
−0.966394 | + | 0.257064i | \(0.917245\pi\) | |||||||
\(828\) | 50.5666 | + | 11.9454i | 1.75731 | + | 0.415132i | ||||
\(829\) | −18.4892 | + | 18.4892i | −0.642155 | + | 0.642155i | −0.951085 | − | 0.308930i | \(-0.900029\pi\) |
0.308930 | + | 0.951085i | \(0.400029\pi\) | |||||||
\(830\) | −6.39402 | + | 54.8784i | −0.221940 | + | 1.90486i | ||||
\(831\) | 45.2428 | 1.56945 | ||||||||
\(832\) | 12.6891 | − | 1.13822i | 0.439916 | − | 0.0394608i | ||||
\(833\) | 1.50885 | 0.0522786 | ||||||||
\(834\) | 4.47141 | − | 38.3771i | 0.154832 | − | 1.32889i | ||||
\(835\) | 32.2341 | − | 32.2341i | 1.11551 | − | 1.11551i | ||||
\(836\) | −5.23641 | − | 1.23701i | −0.181105 | − | 0.0427828i | ||||
\(837\) | 20.6591 | + | 20.6591i | 0.714084 | + | 0.714084i | ||||
\(838\) | −0.685352 | − | 0.866117i | −0.0236751 | − | 0.0299195i | ||||
\(839\) | − | 41.9862i | − | 1.44953i | −0.688999 | − | 0.724763i | \(-0.741949\pi\) | ||
0.688999 | − | 0.724763i | \(-0.258051\pi\) | |||||||
\(840\) | 29.8082 | + | 10.8123i | 1.02848 | + | 0.373059i | ||||
\(841\) | − | 4.63123i | − | 0.159698i | ||||||
\(842\) | −5.92474 | + | 4.68820i | −0.204180 | + | 0.161566i | ||||
\(843\) | 8.67205 | + | 8.67205i | 0.298681 | + | 0.298681i | ||||
\(844\) | −2.18456 | + | 1.34966i | −0.0751956 | + | 0.0464573i | ||||
\(845\) | −28.5421 | + | 28.5421i | −0.981876 | + | 0.981876i | ||||
\(846\) | −27.5210 | − | 3.20654i | −0.946193 | − | 0.110243i | ||||
\(847\) | 9.30861 | 0.319848 | ||||||||
\(848\) | −1.20763 | − | 3.62664i | −0.0414701 | − | 0.124539i | ||||
\(849\) | 68.1577 | 2.33916 | ||||||||
\(850\) | −20.9413 | − | 2.43992i | −0.718281 | − | 0.0836886i | ||||
\(851\) | −7.89326 | + | 7.89326i | −0.270577 | + | 0.270577i | ||||
\(852\) | −42.2207 | − | 68.3382i | −1.44646 | − | 2.34123i | ||||
\(853\) | 10.9845 | + | 10.9845i | 0.376104 | + | 0.376104i | 0.869694 | − | 0.493591i | \(-0.164316\pi\) |
−0.493591 | + | 0.869694i | \(0.664316\pi\) | |||||||
\(854\) | −5.04831 | + | 3.99469i | −0.172750 | + | 0.136695i | ||||
\(855\) | − | 43.4570i | − | 1.48620i | ||||||
\(856\) | −14.8610 | + | 6.94968i | −0.507939 | + | 0.237535i | ||||
\(857\) | 47.3215i | 1.61647i | 0.588858 | + | 0.808237i | \(0.299578\pi\) | ||||
−0.588858 | + | 0.808237i | \(0.700422\pi\) | |||||||
\(858\) | −5.28204 | − | 6.67520i | −0.180326 | − | 0.227888i | ||||
\(859\) | 5.11128 | + | 5.11128i | 0.174395 | + | 0.174395i | 0.788907 | − | 0.614512i | \(-0.210647\pi\) |
−0.614512 | + | 0.788907i | \(0.710647\pi\) | |||||||
\(860\) | 14.2726 | − | 60.4178i | 0.486692 | − | 2.06023i | ||||
\(861\) | −15.3207 | + | 15.3207i | −0.522127 | + | 0.522127i | ||||
\(862\) | 0.193431 | − | 1.66017i | 0.00658828 | − | 0.0565458i | ||||
\(863\) | 10.1105 | 0.344167 | 0.172084 | − | 0.985082i | \(-0.444950\pi\) | ||||
0.172084 | + | 0.985082i | \(0.444950\pi\) | |||||||
\(864\) | 39.3668 | − | 8.20369i | 1.33929 | − | 0.279095i | ||||
\(865\) | 30.7603 | 1.04588 | ||||||||
\(866\) | −2.49729 | + | 21.4337i | −0.0848614 | + | 0.728346i | ||||
\(867\) | 30.2565 | − | 30.2565i | 1.02756 | − | 1.02756i | ||||
\(868\) | 1.88981 | − | 7.99980i | 0.0641442 | − | 0.271531i | ||||
\(869\) | −1.63656 | − | 1.63656i | −0.0555165 | − | 0.0555165i | ||||
\(870\) | 57.0526 | + | 72.1006i | 1.93427 | + | 2.44444i | ||||
\(871\) | − | 3.43769i | − | 0.116482i | ||||||
\(872\) | −5.54680 | − | 11.8611i | −0.187838 | − | 0.401669i | ||||
\(873\) | − | 88.3493i | − | 2.99017i | ||||||
\(874\) | −10.9435 | + | 8.65950i | −0.370169 | + | 0.292912i | ||||
\(875\) | −13.3118 | − | 13.3118i | −0.450021 | − | 0.450021i | ||||
\(876\) | 44.2207 | + | 71.5754i | 1.49408 | + | 2.41831i | ||||
\(877\) | −38.0640 | + | 38.0640i | −1.28533 | + | 1.28533i | −0.347738 | + | 0.937592i | \(0.613050\pi\) |
−0.937592 | + | 0.347738i | \(0.886950\pi\) | |||||||
\(878\) | 6.10350 | + | 0.711133i | 0.205983 | + | 0.0239996i | ||||
\(879\) | 55.5844 | 1.87482 | ||||||||
\(880\) | −8.97990 | + | 17.9459i | −0.302712 | + | 0.604955i | ||||
\(881\) | −21.5769 | −0.726946 | −0.363473 | − | 0.931605i | \(-0.618409\pi\) | ||||
−0.363473 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(882\) | 7.65008 | + | 0.891330i | 0.257592 | + | 0.0300126i | ||||
\(883\) | 21.5700 | − | 21.5700i | 0.725888 | − | 0.725888i | −0.243910 | − | 0.969798i | \(-0.578430\pi\) |
0.969798 | + | 0.243910i | \(0.0784300\pi\) | |||||||
\(884\) | −4.08838 | + | 2.52588i | −0.137507 | + | 0.0849546i | ||||
\(885\) | −12.7625 | − | 12.7625i | −0.429008 | − | 0.429008i | ||||
\(886\) | −6.76586 | + | 5.35377i | −0.227303 | + | 0.179863i | ||||
\(887\) | 33.7110i | 1.13191i | 0.824437 | + | 0.565953i | \(0.191492\pi\) | ||||
−0.824437 | + | 0.565953i | \(0.808508\pi\) | |||||||
\(888\) | −6.55898 | + | 18.0824i | −0.220105 | + | 0.606804i | ||||
\(889\) | − | 12.9787i | − | 0.435291i | ||||||
\(890\) | 28.6350 | + | 36.1876i | 0.959846 | + | 1.21301i | ||||
\(891\) | −3.97372 | − | 3.97372i | −0.133125 | − | 0.133125i | ||||
\(892\) | 6.23476 | + | 1.47285i | 0.208755 | + | 0.0493146i | ||||
\(893\) | 5.26208 | − | 5.26208i | 0.176089 | − | 0.176089i | ||||
\(894\) | −5.22683 | + | 44.8607i | −0.174811 | + | 1.50037i | ||||
\(895\) | 63.9788 | 2.13858 | ||||||||
\(896\) | −7.78499 | − | 8.20939i | −0.260078 | − | 0.274256i | ||||
\(897\) | −22.0777 | −0.737153 | ||||||||
\(898\) | 0.609656 | − | 5.23254i | 0.0203445 | − | 0.174612i | ||||
\(899\) | 16.8538 | − | 16.8538i | 0.562105 | − | 0.562105i | ||||
\(900\) | −104.734 | − | 24.7415i | −3.49113 | − | 0.824716i | ||||
\(901\) | 1.01955 | + | 1.01955i | 0.0339662 | + | 0.0339662i | ||||
\(902\) | −8.50865 | − | 10.7529i | −0.283307 | − | 0.358031i | ||||
\(903\) | − | 23.3855i | − | 0.778222i | ||||||
\(904\) | 8.84597 | − | 24.3873i | 0.294213 | − | 0.811111i | ||||
\(905\) | − | 22.8346i | − | 0.759047i | ||||||
\(906\) | −17.6244 | + | 13.9460i | −0.585530 | + | 0.463326i | ||||
\(907\) | 0.923962 | + | 0.923962i | 0.0306797 | + | 0.0306797i | 0.722280 | − | 0.691601i | \(-0.243094\pi\) |
−0.691601 | + | 0.722280i | \(0.743094\pi\) | |||||||
\(908\) | 33.1894 | − | 20.5051i | 1.10143 | − | 0.680485i | ||||
\(909\) | −62.9911 | + | 62.9911i | −2.08928 | + | 2.08928i | ||||
\(910\) | −8.62928 | − | 1.00542i | −0.286058 | − | 0.0333293i | ||||
\(911\) | −29.9873 | −0.993522 | −0.496761 | − | 0.867887i | \(-0.665477\pi\) | ||||
−0.496761 | + | 0.867887i | \(0.665477\pi\) | |||||||
\(912\) | −10.7608 | + | 21.5049i | −0.356326 | + | 0.712099i | ||||
\(913\) | −13.1713 | −0.435908 | ||||||||
\(914\) | 15.0938 | + | 1.75862i | 0.499259 | + | 0.0581699i | ||||
\(915\) | 36.0851 | − | 36.0851i | 1.19294 | − | 1.19294i | ||||
\(916\) | −10.4387 | − | 16.8960i | −0.344904 | − | 0.558261i | ||||
\(917\) | −6.81965 | − | 6.81965i | −0.225205 | − | 0.225205i | ||||
\(918\) | −11.8951 | + | 9.41250i | −0.392597 | + | 0.310659i | ||||
\(919\) | 13.0725i | 0.431220i | 0.976480 | + | 0.215610i | \(0.0691741\pi\) | ||||
−0.976480 | + | 0.215610i | \(0.930826\pi\) | |||||||
\(920\) | 22.0478 | + | 47.1466i | 0.726896 | + | 1.55438i | ||||
\(921\) | − | 36.7182i | − | 1.20991i | ||||||
\(922\) | −9.78917 | − | 12.3711i | −0.322389 | − | 0.407421i | ||||
\(923\) | 15.5626 | + | 15.5626i | 0.512248 | + | 0.512248i | ||||
\(924\) | −1.73790 | + | 7.35674i | −0.0571726 | + | 0.242019i | ||||
\(925\) | 16.3486 | − | 16.3486i | 0.537538 | − | 0.537538i | ||||
\(926\) | 4.47603 | − | 38.4167i | 0.147091 | − | 1.26245i | ||||
\(927\) | −93.6035 | −3.07434 | ||||||||
\(928\) | −6.69260 | − | 32.1156i | −0.219695 | − | 1.05424i | ||||
\(929\) | −20.7057 | −0.679333 | −0.339667 | − | 0.940546i | \(-0.610314\pi\) | ||||
−0.339667 | + | 0.940546i | \(0.610314\pi\) | |||||||
\(930\) | −7.54106 | + | 64.7232i | −0.247281 | + | 2.12236i | ||||
\(931\) | −1.46271 | + | 1.46271i | −0.0479385 | + | 0.0479385i | ||||
\(932\) | 1.35118 | − | 5.71971i | 0.0442593 | − | 0.187355i | ||||
\(933\) | −40.6348 | − | 40.6348i | −1.33033 | − | 1.33033i | ||||
\(934\) | −14.1373 | − | 17.8661i | −0.462588 | − | 0.584598i | ||||
\(935\) | − | 7.56961i | − | 0.247553i | ||||||
\(936\) | −22.2208 | + | 10.3914i | −0.726308 | + | 0.339654i | ||||
\(937\) | 5.93799i | 0.193986i | 0.995285 | + | 0.0969929i | \(0.0309224\pi\) | ||||
−0.995285 | + | 0.0969929i | \(0.969078\pi\) | |||||||
\(938\) | −2.39398 | + | 1.89434i | −0.0781661 | + | 0.0618523i | ||||
\(939\) | −17.9348 | − | 17.9348i | −0.585281 | − | 0.585281i | ||||
\(940\) | −14.5878 | − | 23.6117i | −0.475801 | − | 0.770129i | ||||
\(941\) | −13.9955 | + | 13.9955i | −0.456241 | + | 0.456241i | −0.897419 | − | 0.441178i | \(-0.854561\pi\) |
0.441178 | + | 0.897419i | \(0.354561\pi\) | |||||||
\(942\) | −32.4302 | − | 3.77852i | −1.05663 | − | 0.123111i | ||||
\(943\) | −35.5642 | −1.15813 | ||||||||
\(944\) | 2.03459 | + | 6.11007i | 0.0662201 | + | 0.198866i | ||||
\(945\) | −27.4215 | −0.892023 | ||||||||
\(946\) | 14.7004 | + | 1.71278i | 0.477952 | + | 0.0556873i | ||||
\(947\) | −30.2690 | + | 30.2690i | −0.983611 | + | 0.983611i | −0.999868 | − | 0.0162570i | \(-0.994825\pi\) |
0.0162570 | + | 0.999868i | \(0.494825\pi\) | |||||||
\(948\) | −8.79984 | + | 5.43671i | −0.285805 | + | 0.176576i | ||||
\(949\) | −16.2998 | − | 16.2998i | −0.529113 | − | 0.529113i | ||||
\(950\) | 22.6663 | − | 17.9356i | 0.735391 | − | 0.581909i | ||||
\(951\) | 78.1710i | 2.53487i | ||||||||
\(952\) | 4.01190 | + | 1.45523i | 0.130027 | + | 0.0471643i | ||||
\(953\) | − | 0.689500i | − | 0.0223351i | −0.999938 | − | 0.0111675i | \(-0.996445\pi\) | ||
0.999938 | − | 0.0111675i | \(-0.00355481\pi\) | |||||||
\(954\) | 4.56699 | + | 5.77155i | 0.147862 | + | 0.186861i | ||||
\(955\) | 33.7348 | + | 33.7348i | 1.09163 | + | 1.09163i | ||||
\(956\) | −31.5533 | − | 7.45388i | −1.02051 | − | 0.241076i | ||||
\(957\) | −15.4990 | + | 15.4990i | −0.501012 | + | 0.501012i | ||||
\(958\) | 1.86383 | − | 15.9968i | 0.0602176 | − | 0.516834i | ||||
\(959\) | 22.6543 | 0.731544 | ||||||||
\(960\) | 68.8294 | + | 57.4977i | 2.22146 | + | 1.85573i | ||||
\(961\) | −14.1080 | −0.455096 | ||||||||
\(962\) | 0.609910 | − | 5.23472i | 0.0196643 | − | 0.168774i | ||||
\(963\) | 22.3365 | − | 22.3365i | 0.719783 | − | 0.719783i | ||||
\(964\) | 27.4769 | + | 6.49092i | 0.884971 | + | 0.209058i | ||||
\(965\) | 64.6012 | + | 64.6012i | 2.07959 | + | 2.07959i | ||||
\(966\) | 12.1659 | + | 15.3747i | 0.391432 | + | 0.494674i | ||||
\(967\) | 14.1022i | 0.453497i | 0.973953 | + | 0.226749i | \(0.0728096\pi\) | ||||
−0.973953 | + | 0.226749i | \(0.927190\pi\) | |||||||
\(968\) | 24.7508 | + | 8.97780i | 0.795520 | + | 0.288557i | ||||
\(969\) | − | 9.07083i | − | 0.291397i | ||||||
\(970\) | 69.4010 | − | 54.9164i | 2.22833 | − | 1.76326i | ||||
\(971\) | −0.255230 | − | 0.255230i | −0.00819071 | − | 0.00819071i | 0.703000 | − | 0.711190i | \(-0.251844\pi\) |
−0.711190 | + | 0.703000i | \(0.751844\pi\) | |||||||
\(972\) | 14.9184 | − | 9.21689i | 0.478508 | − | 0.295632i | ||||
\(973\) | 6.64728 | − | 6.64728i | 0.213102 | − | 0.213102i | ||||
\(974\) | −44.0421 | − | 5.13145i | −1.41120 | − | 0.164422i | ||||
\(975\) | 45.7275 | 1.46445 | ||||||||
\(976\) | −17.2757 | + | 5.75263i | −0.552983 | + | 0.184137i | ||||
\(977\) | −9.83910 | −0.314781 | −0.157390 | − | 0.987536i | \(-0.550308\pi\) | ||||
−0.157390 | + | 0.987536i | \(0.550308\pi\) | |||||||
\(978\) | −36.4736 | − | 4.24963i | −1.16630 | − | 0.135888i | ||||
\(979\) | −7.77902 | + | 7.77902i | −0.248618 | + | 0.248618i | ||||
\(980\) | 4.05500 | + | 6.56340i | 0.129532 | + | 0.209660i | ||||
\(981\) | 17.8276 | + | 17.8276i | 0.569191 | + | 0.569191i | ||||
\(982\) | 31.8028 | − | 25.1653i | 1.01487 | − | 0.803057i | ||||
\(983\) | − | 26.6489i | − | 0.849968i | −0.905201 | − | 0.424984i | \(-0.860280\pi\) | ||
0.905201 | − | 0.424984i | \(-0.139720\pi\) | |||||||
\(984\) | −55.5125 | + | 25.9601i | −1.76967 | + | 0.827578i | ||||
\(985\) | − | 62.2971i | − | 1.98495i | ||||||
\(986\) | 7.67875 | + | 9.70406i | 0.244541 | + | 0.309040i | ||||
\(987\) | −7.39281 | − | 7.39281i | −0.235316 | − | 0.235316i | ||||
\(988\) | 1.51472 | − | 6.41201i | 0.0481896 | − | 0.203993i | ||||
\(989\) | 27.1427 | − | 27.1427i | 0.863086 | − | 0.863086i | ||||
\(990\) | 4.47163 | − | 38.3790i | 0.142118 | − | 1.21976i | ||||
\(991\) | 16.8287 | 0.534583 | 0.267291 | − | 0.963616i | \(-0.413871\pi\) | ||||
0.267291 | + | 0.963616i | \(0.413871\pi\) | |||||||
\(992\) | 12.7403 | − | 19.4481i | 0.404506 | − | 0.617478i | ||||
\(993\) | −91.7875 | −2.91279 | ||||||||
\(994\) | 2.26190 | − | 19.4134i | 0.0717432 | − | 0.615756i | ||||
\(995\) | −14.9935 | + | 14.9935i | −0.475326 | + | 0.475326i | ||||
\(996\) | −13.5335 | + | 57.2892i | −0.428826 | + | 1.81528i | ||||
\(997\) | −25.7816 | − | 25.7816i | −0.816511 | − | 0.816511i | 0.169089 | − | 0.985601i | \(-0.445917\pi\) |
−0.985601 | + | 0.169089i | \(0.945917\pi\) | |||||||
\(998\) | 22.9800 | + | 29.0412i | 0.727421 | + | 0.919282i | ||||
\(999\) | − | 16.6346i | − | 0.526294i |
(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 | 112.2.m.d.85.3 | yes | 12 | |
4.3 | odd | 2 | 448.2.m.d.113.6 | 12 | |||
7.2 | even | 3 | 784.2.x.l.165.2 | 24 | |||
7.3 | odd | 6 | 784.2.x.m.373.5 | 24 | |||
7.4 | even | 3 | 784.2.x.l.373.5 | 24 | |||
7.5 | odd | 6 | 784.2.x.m.165.2 | 24 | |||
7.6 | odd | 2 | 784.2.m.h.197.3 | 12 | |||
8.3 | odd | 2 | 896.2.m.h.225.1 | 12 | |||
8.5 | even | 2 | 896.2.m.g.225.6 | 12 | |||
16.3 | odd | 4 | 448.2.m.d.337.6 | 12 | |||
16.5 | even | 4 | 896.2.m.g.673.6 | 12 | |||
16.11 | odd | 4 | 896.2.m.h.673.1 | 12 | |||
16.13 | even | 4 | inner | 112.2.m.d.29.3 | ✓ | 12 | |
32.3 | odd | 8 | 7168.2.a.bi.1.11 | 12 | |||
32.13 | even | 8 | 7168.2.a.bj.1.11 | 12 | |||
32.19 | odd | 8 | 7168.2.a.bi.1.2 | 12 | |||
32.29 | even | 8 | 7168.2.a.bj.1.2 | 12 | |||
112.13 | odd | 4 | 784.2.m.h.589.3 | 12 | |||
112.45 | odd | 12 | 784.2.x.m.765.2 | 24 | |||
112.61 | odd | 12 | 784.2.x.m.557.5 | 24 | |||
112.93 | even | 12 | 784.2.x.l.557.5 | 24 | |||
112.109 | even | 12 | 784.2.x.l.765.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.3 | ✓ | 12 | 16.13 | even | 4 | inner | |
112.2.m.d.85.3 | yes | 12 | 1.1 | even | 1 | trivial | |
448.2.m.d.113.6 | 12 | 4.3 | odd | 2 | |||
448.2.m.d.337.6 | 12 | 16.3 | odd | 4 | |||
784.2.m.h.197.3 | 12 | 7.6 | odd | 2 | |||
784.2.m.h.589.3 | 12 | 112.13 | odd | 4 | |||
784.2.x.l.165.2 | 24 | 7.2 | even | 3 | |||
784.2.x.l.373.5 | 24 | 7.4 | even | 3 | |||
784.2.x.l.557.5 | 24 | 112.93 | even | 12 | |||
784.2.x.l.765.2 | 24 | 112.109 | even | 12 | |||
784.2.x.m.165.2 | 24 | 7.5 | odd | 6 | |||
784.2.x.m.373.5 | 24 | 7.3 | odd | 6 | |||
784.2.x.m.557.5 | 24 | 112.61 | odd | 12 | |||
784.2.x.m.765.2 | 24 | 112.45 | odd | 12 | |||
896.2.m.g.225.6 | 12 | 8.5 | even | 2 | |||
896.2.m.g.673.6 | 12 | 16.5 | even | 4 | |||
896.2.m.h.225.1 | 12 | 8.3 | odd | 2 | |||
896.2.m.h.673.1 | 12 | 16.11 | odd | 4 | |||
7168.2.a.bi.1.2 | 12 | 32.19 | odd | 8 | |||
7168.2.a.bi.1.11 | 12 | 32.3 | odd | 8 | |||
7168.2.a.bj.1.2 | 12 | 32.29 | even | 8 | |||
7168.2.a.bj.1.11 | 12 | 32.13 | even | 8 |