Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(-0.885704 - 2.72592i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.81 |
Dual form | 605.2.g.o.366.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90030 | − | 1.38065i | −1.34371 | − | 0.976264i | −0.999299 | − | 0.0374455i | \(-0.988078\pi\) |
−0.344413 | − | 0.938818i | \(-0.611922\pi\) | |||||||
\(3\) | 0.885704 | − | 2.72592i | 0.511361 | − | 1.57381i | −0.278445 | − | 0.960452i | \(-0.589819\pi\) |
0.789806 | − | 0.613356i | \(-0.210181\pi\) | |||||||
\(4\) | 1.08691 | + | 3.34515i | 0.543453 | + | 1.67258i | ||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | −5.44662 | + | 3.95720i | −2.22357 | + | 1.61552i | ||||
\(7\) | −1.04556 | − | 3.21790i | −0.395184 | − | 1.21625i | −0.928818 | − | 0.370537i | \(-0.879174\pi\) |
0.533633 | − | 0.845716i | \(-0.320826\pi\) | |||||||
\(8\) | 1.10133 | − | 3.38955i | 0.389380 | − | 1.19839i | ||||
\(9\) | −4.21910 | − | 3.06535i | −1.40637 | − | 1.02178i | ||||
\(10\) | −2.34889 | −0.742786 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 10.0813 | 2.91022 | ||||||||
\(13\) | −1.19953 | − | 0.871507i | −0.332689 | − | 0.241713i | 0.408882 | − | 0.912587i | \(-0.365919\pi\) |
−0.741571 | + | 0.670875i | \(0.765919\pi\) | |||||||
\(14\) | −2.45591 | + | 7.55851i | −0.656369 | + | 2.02010i | ||||
\(15\) | −0.885704 | − | 2.72592i | −0.228688 | − | 0.703829i | ||||
\(16\) | −1.08151 | + | 0.785763i | −0.270377 | + | 0.196441i | ||||
\(17\) | 3.01957 | − | 2.19385i | 0.732354 | − | 0.532086i | −0.157953 | − | 0.987447i | \(-0.550490\pi\) |
0.890307 | + | 0.455360i | \(0.150490\pi\) | |||||||
\(18\) | 3.78537 | + | 11.6502i | 0.892219 | + | 2.74597i | ||||
\(19\) | −0.993518 | + | 3.05773i | −0.227929 | + | 0.701492i | 0.770052 | + | 0.637981i | \(0.220230\pi\) |
−0.997981 | + | 0.0635118i | \(0.979770\pi\) | |||||||
\(20\) | 2.84556 | + | 2.06742i | 0.636286 | + | 0.462289i | ||||
\(21\) | −9.69779 | −2.11623 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51730 | −0.524894 | −0.262447 | − | 0.964946i | \(-0.584530\pi\) | ||||
−0.262447 | + | 0.964946i | \(0.584530\pi\) | |||||||
\(24\) | −8.26418 | − | 6.00428i | −1.68692 | − | 1.22562i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 1.07621 | + | 3.31224i | 0.211063 | + | 0.649584i | ||||
\(27\) | −5.13636 | + | 3.73179i | −0.988494 | + | 0.718183i | ||||
\(28\) | 9.62795 | − | 6.99512i | 1.81951 | − | 1.32195i | ||||
\(29\) | 1.45170 | + | 4.46786i | 0.269573 | + | 0.829661i | 0.990604 | + | 0.136759i | \(0.0436684\pi\) |
−0.721031 | + | 0.692903i | \(0.756332\pi\) | |||||||
\(30\) | −2.08042 | + | 6.40289i | −0.379832 | + | 1.16900i | ||||
\(31\) | −7.45517 | − | 5.41650i | −1.33899 | − | 0.972831i | −0.999481 | − | 0.0322277i | \(-0.989740\pi\) |
−0.339507 | − | 0.940604i | \(-0.610260\pi\) | |||||||
\(32\) | −3.98793 | −0.704972 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.76700 | −1.50353 | ||||||||
\(35\) | −2.73731 | − | 1.98877i | −0.462690 | − | 0.336164i | ||||
\(36\) | 5.66832 | − | 17.4453i | 0.944720 | − | 2.90755i | ||||
\(37\) | −0.833662 | − | 2.56575i | −0.137053 | − | 0.421807i | 0.858850 | − | 0.512226i | \(-0.171179\pi\) |
−0.995904 | + | 0.0904198i | \(0.971179\pi\) | |||||||
\(38\) | 6.10963 | − | 4.43890i | 0.991112 | − | 0.720085i | ||||
\(39\) | −3.43808 | + | 2.49791i | −0.550533 | + | 0.399986i | ||||
\(40\) | −1.10133 | − | 3.38955i | −0.174136 | − | 0.535935i | ||||
\(41\) | 1.40662 | − | 4.32913i | 0.219677 | − | 0.676096i | −0.779112 | − | 0.626885i | \(-0.784329\pi\) |
0.998788 | − | 0.0492106i | \(-0.0156705\pi\) | |||||||
\(42\) | 18.4287 | + | 13.3892i | 2.84360 | + | 2.06600i | ||||
\(43\) | 5.38350 | 0.820976 | 0.410488 | − | 0.911866i | \(-0.365358\pi\) | ||||
0.410488 | + | 0.911866i | \(0.365358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.21509 | −0.777420 | ||||||||
\(46\) | 4.78362 | + | 3.47550i | 0.705306 | + | 0.512435i | ||||
\(47\) | −3.25376 | + | 10.0140i | −0.474609 | + | 1.46070i | 0.371875 | + | 0.928283i | \(0.378715\pi\) |
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(48\) | 1.18403 | + | 3.64406i | 0.170900 | + | 0.525975i | ||||
\(49\) | −3.59858 | + | 2.61452i | −0.514083 | + | 0.373503i | ||||
\(50\) | −1.90030 | + | 1.38065i | −0.268742 | + | 0.195253i | ||||
\(51\) | −3.30580 | − | 10.1742i | −0.462904 | − | 1.42467i | ||||
\(52\) | 1.61155 | − | 4.95985i | 0.223482 | − | 0.687807i | ||||
\(53\) | 2.03654 | + | 1.47963i | 0.279741 | + | 0.203243i | 0.718804 | − | 0.695213i | \(-0.244690\pi\) |
−0.439064 | + | 0.898456i | \(0.644690\pi\) | |||||||
\(54\) | 14.9129 | 2.02939 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.0588 | −1.61142 | ||||||||
\(57\) | 7.45517 | + | 5.41650i | 0.987461 | + | 0.717432i | ||||
\(58\) | 3.40988 | − | 10.4945i | 0.447739 | − | 1.37800i | ||||
\(59\) | 3.68128 | + | 11.3298i | 0.479262 | + | 1.47502i | 0.840122 | + | 0.542397i | \(0.182483\pi\) |
−0.360860 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(60\) | 8.15594 | − | 5.92563i | 1.05293 | − | 0.764996i | ||||
\(61\) | 11.0673 | − | 8.04083i | 1.41702 | − | 1.02952i | 0.424763 | − | 0.905305i | \(-0.360358\pi\) |
0.992255 | − | 0.124219i | \(-0.0396424\pi\) | |||||||
\(62\) | 6.68876 | + | 20.5859i | 0.849473 | + | 2.61441i | ||||
\(63\) | −5.45269 | + | 16.7817i | −0.686974 | + | 2.11429i | ||||
\(64\) | 9.74126 | + | 7.07744i | 1.21766 | + | 0.884680i | ||||
\(65\) | −1.48270 | −0.183906 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.83159 | 0.956781 | 0.478391 | − | 0.878147i | \(-0.341220\pi\) | ||||
0.478391 | + | 0.878147i | \(0.341220\pi\) | |||||||
\(68\) | 10.6208 | + | 7.71643i | 1.28796 | + | 0.935754i | ||||
\(69\) | −2.22959 | + | 6.86196i | −0.268411 | + | 0.826083i | ||||
\(70\) | 2.45591 | + | 7.55851i | 0.293537 | + | 0.903415i | ||||
\(71\) | −2.03654 | + | 1.47963i | −0.241693 | + | 0.175600i | −0.702037 | − | 0.712140i | \(-0.747726\pi\) |
0.460344 | + | 0.887741i | \(0.347726\pi\) | |||||||
\(72\) | −15.0368 | + | 10.9249i | −1.77211 | + | 1.28751i | ||||
\(73\) | −0.916356 | − | 2.82026i | −0.107251 | − | 0.330086i | 0.883001 | − | 0.469371i | \(-0.155519\pi\) |
−0.990252 | + | 0.139285i | \(0.955519\pi\) | |||||||
\(74\) | −1.95818 | + | 6.02667i | −0.227634 | + | 0.700587i | ||||
\(75\) | −2.31880 | − | 1.68471i | −0.267752 | − | 0.194533i | ||||
\(76\) | −11.3085 | −1.29717 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.98210 | 1.13025 | ||||||||
\(79\) | −5.47462 | − | 3.97755i | −0.615943 | − | 0.447509i | 0.235559 | − | 0.971860i | \(-0.424308\pi\) |
−0.851502 | + | 0.524351i | \(0.824308\pi\) | |||||||
\(80\) | −0.413100 | + | 1.27139i | −0.0461860 | + | 0.142146i | ||||
\(81\) | 0.788584 | + | 2.42701i | 0.0876205 | + | 0.269668i | ||||
\(82\) | −8.64998 | + | 6.28458i | −0.955230 | + | 0.694015i | ||||
\(83\) | −6.10963 | + | 4.43890i | −0.670618 | + | 0.487233i | −0.870232 | − | 0.492642i | \(-0.836031\pi\) |
0.199614 | + | 0.979875i | \(0.436031\pi\) | |||||||
\(84\) | −10.5406 | − | 32.4406i | −1.15007 | − | 3.53956i | ||||
\(85\) | 1.15337 | − | 3.54972i | 0.125101 | − | 0.385021i | ||||
\(86\) | −10.2302 | − | 7.43271i | −1.10316 | − | 0.801489i | ||||
\(87\) | 13.4648 | 1.44358 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8016 | 1.14497 | 0.572484 | − | 0.819916i | \(-0.305980\pi\) | ||||
0.572484 | + | 0.819916i | \(0.305980\pi\) | |||||||
\(90\) | 9.91022 | + | 7.20019i | 1.04463 | + | 0.758967i | ||||
\(91\) | −1.55025 | + | 4.77117i | −0.162510 | + | 0.500155i | ||||
\(92\) | −2.73607 | − | 8.42077i | −0.285256 | − | 0.877926i | ||||
\(93\) | −21.3680 | + | 15.5247i | −2.21576 | + | 1.60984i | ||||
\(94\) | 20.0089 | − | 14.5373i | 2.06376 | − | 1.49941i | ||||
\(95\) | 0.993518 | + | 3.05773i | 0.101933 | + | 0.313717i | ||||
\(96\) | −3.53212 | + | 10.8708i | −0.360496 | + | 1.10949i | ||||
\(97\) | −8.91270 | − | 6.47546i | −0.904948 | − | 0.657483i | 0.0347843 | − | 0.999395i | \(-0.488926\pi\) |
−0.939732 | + | 0.341912i | \(0.888926\pi\) | |||||||
\(98\) | 10.4481 | 1.05542 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.51730 | 0.351730 | ||||||||
\(101\) | 10.3007 | + | 7.48391i | 1.02496 | + | 0.744677i | 0.967294 | − | 0.253659i | \(-0.0816340\pi\) |
0.0576666 | + | 0.998336i | \(0.481634\pi\) | |||||||
\(102\) | −7.76497 | + | 23.8981i | −0.768847 | + | 2.36627i | ||||
\(103\) | −5.66832 | − | 17.4453i | −0.558516 | − | 1.71894i | −0.686472 | − | 0.727156i | \(-0.740842\pi\) |
0.127956 | − | 0.991780i | \(-0.459158\pi\) | |||||||
\(104\) | −4.27510 | + | 3.10604i | −0.419208 | + | 0.304572i | ||||
\(105\) | −7.84568 | + | 5.70022i | −0.765660 | + | 0.556284i | ||||
\(106\) | −1.82718 | − | 5.62348i | −0.177471 | − | 0.546201i | ||||
\(107\) | 2.20447 | − | 6.78465i | 0.213114 | − | 0.655897i | −0.786168 | − | 0.618012i | \(-0.787938\pi\) |
0.999282 | − | 0.0378844i | \(-0.0120619\pi\) | |||||||
\(108\) | −18.0662 | − | 13.1258i | −1.73842 | − | 1.26303i | ||||
\(109\) | 4.14588 | 0.397103 | 0.198551 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198551 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.73240 | −0.733927 | ||||||||
\(112\) | 3.65929 | + | 2.65863i | 0.345770 | + | 0.251217i | ||||
\(113\) | 0.452646 | − | 1.39310i | 0.0425813 | − | 0.131052i | −0.927506 | − | 0.373809i | \(-0.878052\pi\) |
0.970087 | + | 0.242757i | \(0.0780517\pi\) | |||||||
\(114\) | −6.68876 | − | 20.5859i | −0.626460 | − | 1.92804i | ||||
\(115\) | −2.03654 | + | 1.47963i | −0.189908 | + | 0.137977i | ||||
\(116\) | −13.3678 | + | 9.71230i | −1.24117 | + | 0.901764i | ||||
\(117\) | 2.38944 | + | 7.35395i | 0.220904 | + | 0.679873i | ||||
\(118\) | 8.64694 | − | 26.6126i | 0.796016 | − | 2.44988i | ||||
\(119\) | −10.2167 | − | 7.42289i | −0.936566 | − | 0.680455i | ||||
\(120\) | −10.2151 | −0.932506 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −32.1326 | −2.90915 | ||||||||
\(123\) | −10.5550 | − | 7.66865i | −0.951711 | − | 0.691459i | ||||
\(124\) | 10.0159 | − | 30.8259i | 0.899459 | − | 2.76825i | ||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | 33.5312 | − | 24.3619i | 2.98720 | − | 2.17033i | ||||
\(127\) | −9.13897 | + | 6.63985i | −0.810952 | + | 0.589191i | −0.914107 | − | 0.405474i | \(-0.867106\pi\) |
0.103154 | + | 0.994665i | \(0.467106\pi\) | |||||||
\(128\) | −6.27516 | − | 19.3130i | −0.554651 | − | 1.70704i | ||||
\(129\) | 4.76819 | − | 14.6750i | 0.419816 | − | 1.29206i | ||||
\(130\) | 2.81756 | + | 2.04708i | 0.247116 | + | 0.179541i | ||||
\(131\) | −14.6799 | −1.28259 | −0.641294 | − | 0.767295i | \(-0.721602\pi\) | ||||
−0.641294 | + | 0.767295i | \(0.721602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8783 | 0.943266 | ||||||||
\(134\) | −14.8823 | − | 10.8126i | −1.28564 | − | 0.934071i | ||||
\(135\) | −1.96192 | + | 6.03816i | −0.168855 | + | 0.519682i | ||||
\(136\) | −4.11061 | − | 12.6512i | −0.352482 | − | 1.08483i | ||||
\(137\) | 12.6573 | − | 9.19606i | 1.08139 | − | 0.785673i | 0.103462 | − | 0.994633i | \(-0.467008\pi\) |
0.977924 | + | 0.208961i | \(0.0670081\pi\) | |||||||
\(138\) | 13.7108 | − | 9.96148i | 1.16714 | − | 0.847978i | ||||
\(139\) | 2.36252 | + | 7.27109i | 0.200386 | + | 0.616726i | 0.999871 | + | 0.0160398i | \(0.00510584\pi\) |
−0.799485 | + | 0.600686i | \(0.794894\pi\) | |||||||
\(140\) | 3.67755 | − | 11.3183i | 0.310810 | − | 0.956574i | ||||
\(141\) | 24.4156 | + | 17.7389i | 2.05616 | + | 1.49389i | ||||
\(142\) | 5.91288 | 0.496198 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.97164 | 0.580970 | ||||||||
\(145\) | 3.80059 | + | 2.76129i | 0.315622 | + | 0.229313i | ||||
\(146\) | −2.15242 | + | 6.62448i | −0.178136 | + | 0.548246i | ||||
\(147\) | 3.93969 | + | 12.1251i | 0.324940 | + | 1.00006i | ||||
\(148\) | 7.67672 | − | 5.57746i | 0.631022 | − | 0.458464i | ||||
\(149\) | −5.24461 | + | 3.81043i | −0.429655 | + | 0.312163i | −0.781511 | − | 0.623891i | \(-0.785551\pi\) |
0.351856 | + | 0.936054i | \(0.385551\pi\) | |||||||
\(150\) | 2.08042 | + | 6.40289i | 0.169866 | + | 0.522794i | ||||
\(151\) | 3.36157 | − | 10.3459i | 0.273561 | − | 0.841934i | −0.716036 | − | 0.698064i | \(-0.754045\pi\) |
0.989597 | − | 0.143870i | \(-0.0459547\pi\) | |||||||
\(152\) | 9.27016 | + | 6.73516i | 0.751909 | + | 0.546294i | ||||
\(153\) | −19.4648 | −1.57364 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.21509 | −0.740174 | ||||||||
\(156\) | −12.0928 | − | 8.78591i | −0.968197 | − | 0.703436i | ||||
\(157\) | 3.22310 | − | 9.91970i | 0.257232 | − | 0.791678i | −0.736150 | − | 0.676818i | \(-0.763358\pi\) |
0.993382 | − | 0.114859i | \(-0.0366418\pi\) | |||||||
\(158\) | 4.91182 | + | 15.1170i | 0.390763 | + | 1.20265i | ||||
\(159\) | 5.83713 | − | 4.24092i | 0.462915 | − | 0.336327i | ||||
\(160\) | −3.22630 | + | 2.34404i | −0.255061 | + | 0.185313i | ||||
\(161\) | 2.63199 | + | 8.10044i | 0.207430 | + | 0.638404i | ||||
\(162\) | 1.85230 | − | 5.70080i | 0.145531 | − | 0.447897i | ||||
\(163\) | 8.28747 | + | 6.02120i | 0.649124 | + | 0.471617i | 0.862973 | − | 0.505250i | \(-0.168600\pi\) |
−0.213848 | + | 0.976867i | \(0.568600\pi\) | |||||||
\(164\) | 16.0105 | 1.25021 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7386 | 1.37679 | ||||||||
\(167\) | 0.846784 | + | 0.615225i | 0.0655261 | + | 0.0476075i | 0.620066 | − | 0.784550i | \(-0.287106\pi\) |
−0.554540 | + | 0.832157i | \(0.687106\pi\) | |||||||
\(168\) | −10.6805 | + | 32.8712i | −0.824018 | + | 2.53607i | ||||
\(169\) | −3.33788 | − | 10.2729i | −0.256760 | − | 0.790226i | ||||
\(170\) | −7.09266 | + | 5.15312i | −0.543982 | + | 0.395226i | ||||
\(171\) | 13.5648 | − | 9.85540i | 1.03733 | − | 0.753661i | ||||
\(172\) | 5.85136 | + | 18.0086i | 0.446162 | + | 1.37315i | ||||
\(173\) | 3.68128 | − | 11.3298i | 0.279883 | − | 0.861390i | −0.708003 | − | 0.706209i | \(-0.750404\pi\) |
0.987886 | − | 0.155181i | \(-0.0495962\pi\) | |||||||
\(174\) | −25.5871 | − | 18.5901i | −1.93975 | − | 1.40931i | ||||
\(175\) | −3.38350 | −0.255769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.1447 | 2.56647 | ||||||||
\(178\) | −20.5263 | − | 14.9132i | −1.53851 | − | 1.11779i | ||||
\(179\) | −1.04929 | + | 3.22939i | −0.0784277 | + | 0.241376i | −0.982582 | − | 0.185831i | \(-0.940502\pi\) |
0.904154 | + | 0.427207i | \(0.140502\pi\) | |||||||
\(180\) | −5.66832 | − | 17.4453i | −0.422492 | − | 1.30030i | ||||
\(181\) | 4.60961 | − | 3.34908i | 0.342629 | − | 0.248935i | −0.403141 | − | 0.915138i | \(-0.632082\pi\) |
0.745770 | + | 0.666203i | \(0.232082\pi\) | |||||||
\(182\) | 9.53322 | − | 6.92629i | 0.706649 | − | 0.513411i | ||||
\(183\) | −12.1163 | − | 37.2902i | −0.895665 | − | 2.75657i | ||||
\(184\) | −2.77239 | + | 8.53253i | −0.204383 | + | 0.629027i | ||||
\(185\) | −2.18256 | − | 1.58572i | −0.160465 | − | 0.116584i | ||||
\(186\) | 62.0397 | 4.54897 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −37.0350 | −2.70106 | ||||||||
\(189\) | 17.3789 | + | 12.6265i | 1.26413 | + | 0.918443i | ||||
\(190\) | 2.33367 | − | 7.18230i | 0.169302 | − | 0.521058i | ||||
\(191\) | −2.78632 | − | 8.57540i | −0.201611 | − | 0.620494i | −0.999836 | − | 0.0181343i | \(-0.994227\pi\) |
0.798225 | − | 0.602360i | \(-0.205773\pi\) | |||||||
\(192\) | 27.9204 | − | 20.2853i | 2.01498 | − | 1.46397i | ||||
\(193\) | −21.2220 | + | 15.4187i | −1.52759 | + | 1.10986i | −0.570032 | + | 0.821623i | \(0.693069\pi\) |
−0.957559 | + | 0.288237i | \(0.906931\pi\) | |||||||
\(194\) | 7.99646 | + | 24.6106i | 0.574112 | + | 1.76694i | ||||
\(195\) | −1.31323 | + | 4.04171i | −0.0940423 | + | 0.289433i | ||||
\(196\) | −12.6573 | − | 9.19606i | −0.904093 | − | 0.656862i | ||||
\(197\) | −16.6978 | −1.18967 | −0.594834 | − | 0.803849i | \(-0.702782\pi\) | ||||
−0.594834 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7912 | −1.19029 | −0.595147 | − | 0.803617i | \(-0.702906\pi\) | ||||
−0.595147 | + | 0.803617i | \(0.702906\pi\) | |||||||
\(200\) | −2.88333 | − | 2.09486i | −0.203882 | − | 0.148129i | ||||
\(201\) | 6.93647 | − | 21.3483i | 0.489261 | − | 1.50579i | ||||
\(202\) | −9.24179 | − | 28.4433i | −0.650250 | − | 2.00126i | ||||
\(203\) | 12.8593 | − | 9.34283i | 0.902546 | − | 0.655738i | ||||
\(204\) | 30.4412 | − | 22.1168i | 2.13131 | − | 1.54849i | ||||
\(205\) | −1.40662 | − | 4.32913i | −0.0982425 | − | 0.302359i | ||||
\(206\) | −13.3143 | + | 40.9771i | −0.927650 | + | 2.85501i | ||||
\(207\) | 10.6208 | + | 7.71643i | 0.738193 | + | 0.536329i | ||||
\(208\) | 1.98210 | 0.137434 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 22.7791 | 1.57191 | ||||||||
\(211\) | −6.18516 | − | 4.49378i | −0.425804 | − | 0.309365i | 0.354165 | − | 0.935183i | \(-0.384765\pi\) |
−0.779969 | + | 0.625818i | \(0.784765\pi\) | |||||||
\(212\) | −2.73607 | + | 8.42077i | −0.187914 | + | 0.578341i | ||||
\(213\) | 2.22959 | + | 6.86196i | 0.152769 | + | 0.470174i | ||||
\(214\) | −13.5563 | + | 9.84925i | −0.926692 | + | 0.673281i | ||||
\(215\) | 4.35534 | − | 3.16434i | 0.297032 | − | 0.215806i | ||||
\(216\) | 6.99224 | + | 21.5199i | 0.475762 | + | 1.46424i | ||||
\(217\) | −9.63493 | + | 29.6533i | −0.654062 | + | 2.01299i | ||||
\(218\) | −7.87839 | − | 5.72398i | −0.533592 | − | 0.387677i | ||||
\(219\) | −8.49940 | −0.574336 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.53401 | −0.372258 | ||||||||
\(222\) | 14.6938 | + | 10.6757i | 0.986186 | + | 0.716506i | ||||
\(223\) | −1.17103 | + | 3.60406i | −0.0784181 | + | 0.241346i | −0.982579 | − | 0.185846i | \(-0.940497\pi\) |
0.904161 | + | 0.427192i | \(0.140497\pi\) | |||||||
\(224\) | 4.16961 | + | 12.8328i | 0.278594 | + | 0.857424i | ||||
\(225\) | −4.21910 | + | 3.06535i | −0.281273 | + | 0.204357i | ||||
\(226\) | −2.78354 | + | 2.02236i | −0.185158 | + | 0.134525i | ||||
\(227\) | −6.04007 | − | 18.5894i | −0.400894 | − | 1.23382i | −0.924276 | − | 0.381726i | \(-0.875330\pi\) |
0.523382 | − | 0.852098i | \(-0.324670\pi\) | |||||||
\(228\) | −10.0159 | + | 30.8259i | −0.663322 | + | 2.04150i | ||||
\(229\) | −4.17662 | − | 3.03449i | −0.275999 | − | 0.200525i | 0.441172 | − | 0.897423i | \(-0.354563\pi\) |
−0.717170 | + | 0.696898i | \(0.754563\pi\) | |||||||
\(230\) | 5.91288 | 0.389884 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.7429 | 1.09922 | ||||||||
\(233\) | −5.05611 | − | 3.67348i | −0.331237 | − | 0.240658i | 0.409718 | − | 0.912212i | \(-0.365627\pi\) |
−0.740955 | + | 0.671554i | \(0.765627\pi\) | |||||||
\(234\) | 5.61255 | − | 17.2736i | 0.366904 | − | 1.12921i | ||||
\(235\) | 3.25376 | + | 10.0140i | 0.212252 | + | 0.653244i | ||||
\(236\) | −33.8988 | + | 24.6289i | −2.20662 | + | 1.60321i | ||||
\(237\) | −15.6914 | + | 11.4004i | −1.01926 | + | 0.740538i | ||||
\(238\) | 9.16643 | + | 28.2114i | 0.594171 | + | 1.82867i | ||||
\(239\) | 1.42478 | − | 4.38501i | 0.0921610 | − | 0.283643i | −0.894342 | − | 0.447383i | \(-0.852356\pi\) |
0.986503 | + | 0.163741i | \(0.0523560\pi\) | |||||||
\(240\) | 3.09982 | + | 2.25215i | 0.200093 | + | 0.145376i | ||||
\(241\) | 7.87827 | 0.507484 | 0.253742 | − | 0.967272i | \(-0.418339\pi\) | ||||
0.253742 | + | 0.967272i | \(0.418339\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7324 | −0.752634 | ||||||||
\(244\) | 38.9269 | + | 28.2821i | 2.49204 | + | 1.81057i | ||||
\(245\) | −1.37453 | + | 4.23038i | −0.0878158 | + | 0.270269i | ||||
\(246\) | 9.46991 | + | 29.1454i | 0.603780 | + | 1.85824i | ||||
\(247\) | 3.85659 | − | 2.80198i | 0.245389 | − | 0.178285i | ||||
\(248\) | −26.5701 | + | 19.3043i | −1.68720 | + | 1.22583i | ||||
\(249\) | 6.68876 | + | 20.5859i | 0.423883 | + | 1.30458i | ||||
\(250\) | −0.725848 | + | 2.23393i | −0.0459067 | + | 0.141286i | ||||
\(251\) | −8.62067 | − | 6.26328i | −0.544132 | − | 0.395335i | 0.281485 | − | 0.959566i | \(-0.409173\pi\) |
−0.825617 | + | 0.564231i | \(0.809173\pi\) | |||||||
\(252\) | −62.0638 | −3.90965 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 26.5340 | 1.66489 | ||||||||
\(255\) | −8.65469 | − | 6.28800i | −0.541978 | − | 0.393770i | ||||
\(256\) | −7.29803 | + | 22.4610i | −0.456127 | + | 1.40381i | ||||
\(257\) | 0.868046 | + | 2.67157i | 0.0541472 | + | 0.166648i | 0.974473 | − | 0.224505i | \(-0.0720764\pi\) |
−0.920326 | + | 0.391153i | \(0.872076\pi\) | |||||||
\(258\) | −29.3219 | + | 21.3036i | −1.82550 | + | 1.32631i | ||||
\(259\) | −7.38469 | + | 5.36529i | −0.458862 | + | 0.333383i | ||||
\(260\) | −1.61155 | − | 4.95985i | −0.0999442 | − | 0.307597i | ||||
\(261\) | 7.57073 | − | 23.3003i | 0.468617 | − | 1.44225i | ||||
\(262\) | 27.8961 | + | 20.2677i | 1.72343 | + | 1.25214i | ||||
\(263\) | 27.6453 | 1.70468 | 0.852340 | − | 0.522987i | \(-0.175183\pi\) | ||||
0.852340 | + | 0.522987i | \(0.175183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.51730 | 0.154637 | ||||||||
\(266\) | −20.6719 | − | 15.0190i | −1.26748 | − | 0.920876i | ||||
\(267\) | 9.56703 | − | 29.4443i | 0.585493 | − | 1.80196i | ||||
\(268\) | 8.51221 | + | 26.1979i | 0.519966 | + | 1.60029i | ||||
\(269\) | 11.7923 | − | 8.56759i | 0.718988 | − | 0.522375i | −0.167073 | − | 0.985945i | \(-0.553431\pi\) |
0.886061 | + | 0.463569i | \(0.153431\pi\) | |||||||
\(270\) | 12.0648 | − | 8.76557i | 0.734239 | − | 0.533456i | ||||
\(271\) | −0.668274 | − | 2.05674i | −0.0405948 | − | 0.124938i | 0.928705 | − | 0.370819i | \(-0.120923\pi\) |
−0.969300 | + | 0.245881i | \(0.920923\pi\) | |||||||
\(272\) | −1.54185 | + | 4.74534i | −0.0934886 | + | 0.287728i | ||||
\(273\) | 11.6328 | + | 8.45169i | 0.704046 | + | 0.511519i | ||||
\(274\) | −36.7491 | −2.22009 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.3777 | −1.52756 | ||||||||
\(277\) | 12.3797 | + | 8.99441i | 0.743827 | + | 0.540422i | 0.893907 | − | 0.448252i | \(-0.147953\pi\) |
−0.150080 | + | 0.988674i | \(0.547953\pi\) | |||||||
\(278\) | 5.54931 | − | 17.0790i | 0.332826 | − | 1.02433i | ||||
\(279\) | 14.8506 | + | 45.7055i | 0.889082 | + | 2.73631i | ||||
\(280\) | −9.75574 | + | 7.08796i | −0.583017 | + | 0.423587i | ||||
\(281\) | −1.73003 | + | 1.25694i | −0.103205 | + | 0.0749827i | −0.638191 | − | 0.769878i | \(-0.720317\pi\) |
0.534986 | + | 0.844861i | \(0.320317\pi\) | |||||||
\(282\) | −21.9056 | − | 67.4184i | −1.30446 | − | 4.01471i | ||||
\(283\) | 1.33835 | − | 4.11902i | 0.0795566 | − | 0.244850i | −0.903366 | − | 0.428871i | \(-0.858911\pi\) |
0.982922 | + | 0.184021i | \(0.0589114\pi\) | |||||||
\(284\) | −7.16314 | − | 5.20432i | −0.425054 | − | 0.308820i | ||||
\(285\) | 9.21509 | 0.545855 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.4014 | −0.909116 | ||||||||
\(288\) | 16.8255 | + | 12.2244i | 0.991449 | + | 0.720330i | ||||
\(289\) | −0.948440 | + | 2.91900i | −0.0557906 | + | 0.171706i | ||||
\(290\) | −3.40988 | − | 10.4945i | −0.200235 | − | 0.616260i | ||||
\(291\) | −25.5456 | + | 18.5599i | −1.49751 | + | 1.08800i | ||||
\(292\) | 8.43820 | − | 6.13071i | 0.493808 | − | 0.358773i | ||||
\(293\) | −4.17384 | − | 12.8458i | −0.243839 | − | 0.750458i | −0.995825 | − | 0.0912798i | \(-0.970904\pi\) |
0.751987 | − | 0.659178i | \(-0.229096\pi\) | |||||||
\(294\) | 9.25391 | − | 28.4806i | 0.539699 | − | 1.66102i | ||||
\(295\) | 9.63772 | + | 7.00222i | 0.561130 | + | 0.407685i | ||||
\(296\) | −9.61488 | −0.558854 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2272 | 0.882086 | ||||||||
\(299\) | 3.01957 | + | 2.19385i | 0.174626 | + | 0.126873i | ||||
\(300\) | 3.11529 | − | 9.58788i | 0.179861 | − | 0.553556i | ||||
\(301\) | −5.62877 | − | 17.3236i | −0.324437 | − | 0.998515i | ||||
\(302\) | −20.6719 | + | 15.0190i | −1.18954 | + | 0.864248i | ||||
\(303\) | 29.5239 | − | 21.4504i | 1.69610 | − | 1.23229i | ||||
\(304\) | −1.32815 | − | 4.08764i | −0.0761749 | − | 0.234442i | ||||
\(305\) | 4.22732 | − | 13.0103i | 0.242055 | − | 0.744970i | ||||
\(306\) | 36.9889 | + | 26.8740i | 2.11451 | + | 1.53628i | ||||
\(307\) | −2.37887 | −0.135769 | −0.0678847 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678847 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −52.5749 | −2.99088 | ||||||||
\(310\) | 17.5114 | + | 12.7228i | 0.994581 | + | 0.722605i | ||||
\(311\) | −6.84308 | + | 21.0608i | −0.388036 | + | 1.19425i | 0.546219 | + | 0.837643i | \(0.316067\pi\) |
−0.934254 | + | 0.356608i | \(0.883933\pi\) | |||||||
\(312\) | 4.68033 | + | 14.4046i | 0.264972 | + | 0.815499i | ||||
\(313\) | 22.0735 | − | 16.0373i | 1.24767 | − | 0.906483i | 0.249582 | − | 0.968354i | \(-0.419707\pi\) |
0.998084 | + | 0.0618710i | \(0.0197068\pi\) | |||||||
\(314\) | −19.8204 | + | 14.4004i | −1.11853 | + | 0.812661i | ||||
\(315\) | 5.45269 | + | 16.7817i | 0.307224 | + | 0.945539i | ||||
\(316\) | 7.35510 | − | 22.6367i | 0.413757 | − | 1.27341i | ||||
\(317\) | 12.4553 | + | 9.04929i | 0.699558 | + | 0.508259i | 0.879788 | − | 0.475366i | \(-0.157684\pi\) |
−0.180230 | + | 0.983625i | \(0.557684\pi\) | |||||||
\(318\) | −16.9475 | −0.950368 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.0409 | 0.673104 | ||||||||
\(321\) | −16.5419 | − | 12.0184i | −0.923278 | − | 0.670801i | ||||
\(322\) | 6.18227 | − | 19.0271i | 0.344524 | − | 1.06034i | ||||
\(323\) | 3.70820 | + | 11.4127i | 0.206330 | + | 0.635018i | ||||
\(324\) | −7.26162 | + | 5.27587i | −0.403423 | + | 0.293104i | ||||
\(325\) | −1.19953 | + | 0.871507i | −0.0665377 | + | 0.0483425i | ||||
\(326\) | −7.43550 | − | 22.8841i | −0.411814 | − | 1.26743i | ||||
\(327\) | 3.67202 | − | 11.3013i | 0.203063 | − | 0.624964i | ||||
\(328\) | −13.1246 | − | 9.53561i | −0.724687 | − | 0.526516i | ||||
\(329\) | 35.6262 | 1.96413 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9129 | 1.42430 | 0.712150 | − | 0.702027i | \(-0.247721\pi\) | ||||
0.712150 | + | 0.702027i | \(0.247721\pi\) | |||||||
\(332\) | −21.4894 | − | 15.6130i | −1.17938 | − | 0.856873i | ||||
\(333\) | −4.34763 | + | 13.3806i | −0.238248 | + | 0.733253i | ||||
\(334\) | −0.759733 | − | 2.33822i | −0.0415707 | − | 0.127942i | ||||
\(335\) | 6.33589 | − | 4.60329i | 0.346167 | − | 0.251505i | ||||
\(336\) | 10.4883 | − | 7.62016i | 0.572181 | − | 0.415714i | ||||
\(337\) | 4.32071 | + | 13.2978i | 0.235364 | + | 0.724375i | 0.997073 | + | 0.0764562i | \(0.0243605\pi\) |
−0.761709 | + | 0.647919i | \(0.775639\pi\) | |||||||
\(338\) | −7.84033 | + | 24.1301i | −0.426458 | + | 1.31250i | ||||
\(339\) | −3.39657 | − | 2.46775i | −0.184476 | − | 0.134030i | ||||
\(340\) | 13.1280 | 0.711964 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −39.3839 | −2.12964 | ||||||||
\(343\) | −6.98538 | − | 5.07517i | −0.377175 | − | 0.274034i | ||||
\(344\) | 5.92903 | − | 18.2477i | 0.319672 | − | 0.983848i | ||||
\(345\) | 2.22959 | + | 6.86196i | 0.120037 | + | 0.369436i | ||||
\(346\) | −22.6380 | + | 16.4475i | −1.21703 | + | 0.884221i | ||||
\(347\) | 25.1173 | − | 18.2488i | 1.34837 | − | 0.979646i | 0.349276 | − | 0.937020i | \(-0.386428\pi\) |
0.999091 | − | 0.0426260i | \(-0.0135724\pi\) | |||||||
\(348\) | 14.6350 | + | 45.0418i | 0.784517 | + | 2.41449i | ||||
\(349\) | 1.13198 | − | 3.48389i | 0.0605938 | − | 0.186488i | −0.916178 | − | 0.400772i | \(-0.868742\pi\) |
0.976771 | + | 0.214284i | \(0.0687418\pi\) | |||||||
\(350\) | 6.42965 | + | 4.67142i | 0.343679 | + | 0.249698i | ||||
\(351\) | 9.41348 | 0.502454 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5749 | 1.30799 | 0.653994 | − | 0.756500i | \(-0.273092\pi\) | ||||
0.653994 | + | 0.756500i | \(0.273092\pi\) | |||||||
\(354\) | −64.8850 | − | 47.1417i | −3.44860 | − | 2.50555i | ||||
\(355\) | −0.777890 | + | 2.39410i | −0.0412861 | + | 0.127066i | ||||
\(356\) | 11.7403 | + | 36.1331i | 0.622237 | + | 1.91505i | ||||
\(357\) | −29.2832 | + | 21.2755i | −1.54983 | + | 1.12602i | ||||
\(358\) | 6.45260 | − | 4.68809i | 0.341030 | − | 0.247773i | ||||
\(359\) | −2.03535 | − | 6.26415i | −0.107421 | − | 0.330609i | 0.882870 | − | 0.469618i | \(-0.155608\pi\) |
−0.990291 | + | 0.139009i | \(0.955608\pi\) | |||||||
\(360\) | −5.74355 | + | 17.6768i | −0.302712 | + | 0.931651i | ||||
\(361\) | 7.00866 | + | 5.09209i | 0.368877 | + | 0.268005i | ||||
\(362\) | −13.3835 | −0.703421 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.6453 | −0.924864 | ||||||||
\(365\) | −2.39905 | − | 1.74301i | −0.125572 | − | 0.0912335i | ||||
\(366\) | −28.4600 | + | 87.5908i | −1.48763 | + | 4.57844i | ||||
\(367\) | 2.52418 | + | 7.76862i | 0.131761 | + | 0.405519i | 0.995072 | − | 0.0991534i | \(-0.0316134\pi\) |
−0.863311 | + | 0.504672i | \(0.831613\pi\) | |||||||
\(368\) | 2.72249 | − | 1.97800i | 0.141920 | − | 0.103111i | ||||
\(369\) | −19.2050 | + | 13.9532i | −0.999771 | + | 0.726376i | ||||
\(370\) | 1.95818 | + | 6.02667i | 0.101801 | + | 0.313312i | ||||
\(371\) | 2.63199 | − | 8.10044i | 0.136646 | − | 0.420554i | ||||
\(372\) | −75.1577 | − | 54.6053i | −3.89675 | − | 2.83115i | ||||
\(373\) | −27.0409 | −1.40012 | −0.700061 | − | 0.714083i | \(-0.746844\pi\) | ||||
−0.700061 | + | 0.714083i | \(0.746844\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.86620 | −0.148010 | ||||||||
\(376\) | 30.3596 | + | 22.0576i | 1.56568 | + | 1.13753i | ||||
\(377\) | 2.15242 | − | 6.62448i | 0.110856 | − | 0.341178i | ||||
\(378\) | −15.5923 | − | 47.9882i | −0.801982 | − | 2.46825i | ||||
\(379\) | −26.4241 | + | 19.1982i | −1.35731 | + | 0.986147i | −0.358704 | + | 0.933451i | \(0.616781\pi\) |
−0.998611 | + | 0.0526956i | \(0.983219\pi\) | |||||||
\(380\) | −9.14873 | + | 6.64694i | −0.469320 | + | 0.340981i | ||||
\(381\) | 10.0053 | + | 30.7930i | 0.512585 | + | 1.57757i | ||||
\(382\) | −6.54476 | + | 20.1427i | −0.334859 | + | 1.03059i | ||||
\(383\) | 2.14104 | + | 1.55556i | 0.109402 | + | 0.0794854i | 0.641141 | − | 0.767423i | \(-0.278461\pi\) |
−0.531739 | + | 0.846908i | \(0.678461\pi\) | |||||||
\(384\) | −58.2034 | −2.97018 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 61.6157 | 3.13616 | ||||||||
\(387\) | −22.7135 | − | 16.5023i | −1.15459 | − | 0.838861i | ||||
\(388\) | 11.9741 | − | 36.8526i | 0.607894 | − | 1.87091i | ||||
\(389\) | −8.97735 | − | 27.6294i | −0.455170 | − | 1.40087i | −0.870936 | − | 0.491397i | \(-0.836487\pi\) |
0.415766 | − | 0.909472i | \(-0.363513\pi\) | |||||||
\(390\) | 8.07569 | − | 5.86733i | 0.408928 | − | 0.297104i | ||||
\(391\) | −7.60118 | + | 5.52258i | −0.384408 | + | 0.279289i | ||||
\(392\) | 4.89882 | + | 15.0770i | 0.247428 | + | 0.761505i | ||||
\(393\) | −13.0020 | + | 40.0161i | −0.655866 | + | 2.01855i | ||||
\(394\) | 31.7307 | + | 23.0537i | 1.59857 | + | 1.16143i | ||||
\(395\) | −6.76700 | −0.340485 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.35977 | −0.469753 | −0.234877 | − | 0.972025i | \(-0.575469\pi\) | ||||
−0.234877 | + | 0.972025i | \(0.575469\pi\) | |||||||
\(398\) | 31.9082 | + | 23.1826i | 1.59941 | + | 1.16204i | ||||
\(399\) | 9.63493 | − | 29.6533i | 0.482350 | − | 1.48452i | ||||
\(400\) | 0.413100 | + | 1.27139i | 0.0206550 | + | 0.0635696i | ||||
\(401\) | −3.98909 | + | 2.89824i | −0.199206 | + | 0.144731i | −0.682916 | − | 0.730497i | \(-0.739289\pi\) |
0.483711 | + | 0.875228i | \(0.339289\pi\) | |||||||
\(402\) | −42.6557 | + | 30.9912i | −2.12747 | + | 1.54570i | ||||
\(403\) | 4.22215 | + | 12.9945i | 0.210321 | + | 0.647300i | ||||
\(404\) | −13.8389 | + | 42.5918i | −0.688512 | + | 2.11902i | ||||
\(405\) | 2.06454 | + | 1.49998i | 0.102588 | + | 0.0745344i | ||||
\(406\) | −37.3356 | −1.85294 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −38.1268 | −1.88756 | ||||||||
\(409\) | 30.9922 | + | 22.5171i | 1.53247 | + | 1.11340i | 0.954848 | + | 0.297093i | \(0.0960172\pi\) |
0.577617 | + | 0.816308i | \(0.303983\pi\) | |||||||
\(410\) | −3.30400 | + | 10.1687i | −0.163173 | + | 0.502194i | ||||
\(411\) | −13.8571 | − | 42.6477i | −0.683520 | − | 2.10366i | ||||
\(412\) | 52.1963 | − | 37.9228i | 2.57153 | − | 1.86832i | ||||
\(413\) | 32.6093 | − | 23.6920i | 1.60460 | − | 1.16581i | ||||
\(414\) | −9.52892 | − | 29.3270i | −0.468321 | − | 1.44134i | ||||
\(415\) | −2.33367 | + | 7.18230i | −0.114555 | + | 0.352565i | ||||
\(416\) | 4.78362 | + | 3.47550i | 0.234536 | + | 0.170401i | ||||
\(417\) | 21.9129 | 1.07308 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.3777 | 1.82602 | 0.913009 | − | 0.407938i | \(-0.133752\pi\) | ||||
0.913009 | + | 0.407938i | \(0.133752\pi\) | |||||||
\(420\) | −27.5956 | − | 20.0494i | −1.34653 | − | 0.978310i | ||||
\(421\) | 9.08889 | − | 27.9727i | 0.442966 | − | 1.36331i | −0.441734 | − | 0.897146i | \(-0.645636\pi\) |
0.884699 | − | 0.466162i | \(-0.154364\pi\) | |||||||
\(422\) | 5.54931 | + | 17.0790i | 0.270136 | + | 0.831394i | ||||
\(423\) | 44.4245 | − | 32.2763i | 2.15999 | − | 1.56933i | ||||
\(424\) | 7.25821 | − | 5.27340i | 0.352490 | − | 0.256099i | ||||
\(425\) | −1.15337 | − | 3.54972i | −0.0559469 | − | 0.172187i | ||||
\(426\) | 5.23706 | − | 16.1180i | 0.253736 | − | 0.780921i | ||||
\(427\) | −37.4461 | − | 27.2062i | −1.81214 | − | 1.31660i | ||||
\(428\) | 25.0917 | 1.21286 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.6453 | −0.609809 | ||||||||
\(431\) | −1.43051 | − | 1.03932i | −0.0689050 | − | 0.0500624i | 0.552800 | − | 0.833314i | \(-0.313560\pi\) |
−0.621705 | + | 0.783252i | \(0.713560\pi\) | |||||||
\(432\) | 2.62273 | − | 8.07193i | 0.126186 | − | 0.388361i | ||||
\(433\) | 3.10603 | + | 9.55937i | 0.149266 | + | 0.459394i | 0.997535 | − | 0.0701721i | \(-0.0223548\pi\) |
−0.848269 | + | 0.529566i | \(0.822355\pi\) | |||||||
\(434\) | 59.2499 | − | 43.0475i | 2.84408 | − | 2.06635i | ||||
\(435\) | 10.8932 | − | 7.91441i | 0.522291 | − | 0.379467i | ||||
\(436\) | 4.50618 | + | 13.8686i | 0.215807 | + | 0.664185i | ||||
\(437\) | 2.50099 | − | 7.69725i | 0.119638 | − | 0.368209i | ||||
\(438\) | 16.1514 | + | 11.7347i | 0.771742 | + | 0.560704i | ||||
\(439\) | 39.1972 | 1.87078 | 0.935390 | − | 0.353618i | \(-0.115049\pi\) | ||||
0.935390 | + | 0.353618i | \(0.115049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.1972 | 1.10463 | ||||||||
\(442\) | 10.5163 | + | 7.64050i | 0.500207 | + | 0.363422i | ||||
\(443\) | −4.32997 | + | 13.3263i | −0.205723 | + | 0.633150i | 0.793960 | + | 0.607970i | \(0.208016\pi\) |
−0.999683 | + | 0.0251803i | \(0.991984\pi\) | |||||||
\(444\) | −8.40439 | − | 25.8661i | −0.398855 | − | 1.22755i | ||||
\(445\) | 8.73869 | − | 6.34903i | 0.414254 | − | 0.300973i | ||||
\(446\) | 7.20124 | − | 5.23201i | 0.340989 | − | 0.247743i | ||||
\(447\) | 5.74175 | + | 17.6713i | 0.271575 | + | 0.835823i | ||||
\(448\) | 12.5894 | − | 38.7463i | 0.594795 | − | 1.83059i | ||||
\(449\) | −2.08408 | − | 1.51417i | −0.0983537 | − | 0.0714581i | 0.537521 | − | 0.843250i | \(-0.319361\pi\) |
−0.635875 | + | 0.771792i | \(0.719361\pi\) | |||||||
\(450\) | 12.2497 | 0.577456 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.15212 | 0.242335 | ||||||||
\(453\) | −25.2246 | − | 18.3267i | −1.18515 | − | 0.861065i | ||||
\(454\) | −14.1875 | + | 43.6646i | −0.665852 | + | 2.04928i | ||||
\(455\) | 1.55025 | + | 4.77117i | 0.0726767 | + | 0.223676i | ||||
\(456\) | 26.5701 | − | 19.3043i | 1.24426 | − | 0.904008i | ||||
\(457\) | −12.2337 | + | 8.88833i | −0.572270 | + | 0.415778i | −0.835929 | − | 0.548837i | \(-0.815071\pi\) |
0.263659 | + | 0.964616i | \(0.415071\pi\) | |||||||
\(458\) | 3.74725 | + | 11.5329i | 0.175098 | + | 0.538895i | ||||
\(459\) | −7.32265 | + | 22.5368i | −0.341792 | + | 1.05193i | ||||
\(460\) | −7.16314 | − | 5.20432i | −0.333983 | − | 0.242653i | ||||
\(461\) | 9.83622 | 0.458118 | 0.229059 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229059 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2093 | 0.985678 | 0.492839 | − | 0.870120i | \(-0.335959\pi\) | ||||
0.492839 | + | 0.870120i | \(0.335959\pi\) | |||||||
\(464\) | −5.08070 | − | 3.69135i | −0.235866 | − | 0.171367i | ||||
\(465\) | −8.16184 | + | 25.1196i | −0.378496 | + | 1.16489i | ||||
\(466\) | 4.53633 | + | 13.9614i | 0.210142 | + | 0.646749i | ||||
\(467\) | 7.73743 | − | 5.62157i | 0.358045 | − | 0.260135i | −0.394191 | − | 0.919029i | \(-0.628975\pi\) |
0.752236 | + | 0.658893i | \(0.228975\pi\) | |||||||
\(468\) | −22.0030 | + | 15.9861i | −1.01709 | + | 0.738958i | ||||
\(469\) | −8.18840 | − | 25.2013i | −0.378105 | − | 1.16369i | ||||
\(470\) | 7.64273 | − | 23.5219i | 0.352533 | − | 1.08498i | ||||
\(471\) | −24.1855 | − | 17.5718i | −1.11441 | − | 0.809667i | ||||
\(472\) | 42.4573 | 1.95426 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 45.5582 | 2.09256 | ||||||||
\(475\) | 2.60106 | + | 1.88978i | 0.119345 | + | 0.0867092i | ||||
\(476\) | 13.7261 | − | 42.2445i | 0.629134 | − | 1.93627i | ||||
\(477\) | −4.05677 | − | 12.4854i | −0.185747 | − | 0.571669i | ||||
\(478\) | −8.76163 | + | 6.36570i | −0.400748 | + | 0.291160i | ||||
\(479\) | 13.9128 | − | 10.1083i | 0.635693 | − | 0.461858i | −0.222675 | − | 0.974893i | \(-0.571479\pi\) |
0.858368 | + | 0.513035i | \(0.171479\pi\) | |||||||
\(480\) | 3.53212 | + | 10.8708i | 0.161219 | + | 0.496180i | ||||
\(481\) | −1.23607 | + | 3.80423i | −0.0563598 | + | 0.173458i | ||||
\(482\) | −14.9710 | − | 10.8771i | −0.681912 | − | 0.495438i | ||||
\(483\) | 24.4123 | 1.11080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.0167 | −0.500243 | ||||||||
\(486\) | 22.2950 | + | 16.1983i | 1.01132 | + | 0.734769i | ||||
\(487\) | 4.80581 | − | 14.7907i | 0.217772 | − | 0.670233i | −0.781173 | − | 0.624314i | \(-0.785379\pi\) |
0.998945 | − | 0.0459186i | \(-0.0146215\pi\) | |||||||
\(488\) | −15.0661 | − | 46.3687i | −0.682010 | − | 2.09901i | ||||
\(489\) | 23.7535 | − | 17.2579i | 1.07417 | − | 0.780431i | ||||
\(490\) | 8.45268 | − | 6.14123i | 0.381853 | − | 0.277433i | ||||
\(491\) | −2.79931 | − | 8.61539i | −0.126331 | − | 0.388807i | 0.867810 | − | 0.496896i | \(-0.165527\pi\) |
−0.994141 | + | 0.108089i | \(0.965527\pi\) | |||||||
\(492\) | 14.1805 | − | 43.6432i | 0.639308 | − | 1.96759i | ||||
\(493\) | 14.1853 | + | 10.3062i | 0.638874 | + | 0.464169i | ||||
\(494\) | −11.1972 | −0.503785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.3189 | 0.553136 | ||||||||
\(497\) | 6.89064 | + | 5.00635i | 0.309088 | + | 0.224565i | ||||
\(498\) | 15.7112 | − | 48.3541i | 0.704035 | − | 2.16680i | ||||
\(499\) | 7.59212 | + | 23.3661i | 0.339870 | + | 1.04601i | 0.964273 | + | 0.264910i | \(0.0853423\pi\) |
−0.624403 | + | 0.781102i | \(0.714658\pi\) | |||||||
\(500\) | 2.84556 | − | 2.06742i | 0.127257 | − | 0.0924578i | ||||
\(501\) | 2.42705 | − | 1.76336i | 0.108433 | − | 0.0787809i | ||||
\(502\) | 7.73445 | + | 23.8042i | 0.345205 | + | 1.06243i | ||||
\(503\) | −3.50184 | + | 10.7776i | −0.156139 | + | 0.480547i | −0.998275 | − | 0.0587190i | \(-0.981298\pi\) |
0.842135 | + | 0.539266i | \(0.181298\pi\) | |||||||
\(504\) | 50.8771 | + | 36.9644i | 2.26625 | + | 1.64652i | ||||
\(505\) | 12.7324 | 0.566584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.9596 | −1.37496 | ||||||||
\(508\) | −32.1445 | − | 23.3544i | −1.42618 | − | 1.03618i | ||||
\(509\) | −8.18553 | + | 25.1925i | −0.362817 | + | 1.11664i | 0.588519 | + | 0.808483i | \(0.299711\pi\) |
−0.951337 | + | 0.308154i | \(0.900289\pi\) | |||||||
\(510\) | 7.76497 | + | 23.8981i | 0.343839 | + | 1.05823i | ||||
\(511\) | −8.11720 | + | 5.89749i | −0.359084 | + | 0.260890i | ||||
\(512\) | 12.0220 | − | 8.73446i | 0.531300 | − | 0.386012i | ||||
\(513\) | −6.30774 | − | 19.4132i | −0.278494 | − | 0.857115i | ||||
\(514\) | 2.03895 | − | 6.27524i | 0.0899342 | − | 0.276789i | ||||
\(515\) | −14.8399 | − | 10.7818i | −0.653922 | − | 0.475102i | ||||
\(516\) | 54.2727 | 2.38922 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 21.4406 | 0.942048 | ||||||||
\(519\) | −27.6236 | − | 20.0697i | −1.21254 | − | 0.880964i | ||||
\(520\) | −1.63294 | + | 5.02568i | −0.0716092 | + | 0.220390i | ||||
\(521\) | 8.24970 | + | 25.3900i | 0.361426 | + | 1.11235i | 0.952189 | + | 0.305510i | \(0.0988268\pi\) |
−0.590763 | + | 0.806845i | \(0.701173\pi\) | |||||||
\(522\) | −46.5561 | + | 33.8250i | −2.03771 | + | 1.48048i | ||||
\(523\) | 3.92707 | − | 2.85318i | 0.171719 | − | 0.124761i | −0.498606 | − | 0.866829i | \(-0.666155\pi\) |
0.670325 | + | 0.742068i | \(0.266155\pi\) | |||||||
\(524\) | −15.9557 | − | 49.1065i | −0.697027 | − | 2.14523i | ||||
\(525\) | −2.99678 | + | 9.22314i | −0.130790 | + | 0.402531i | ||||
\(526\) | −52.5342 | − | 38.1683i | −2.29060 | − | 1.66422i | ||||
\(527\) | −34.3944 | −1.49824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6632 | −0.724486 | ||||||||
\(530\) | −4.78362 | − | 3.47550i | −0.207787 | − | 0.150966i | ||||
\(531\) | 19.1982 | − | 59.0861i | 0.833132 | − | 2.56412i | ||||
\(532\) | 11.8237 | + | 36.3895i | 0.512621 | + | 1.57769i | ||||
\(533\) | −5.46014 | + | 3.96702i | −0.236505 | + | 0.171831i | ||||
\(534\) | −58.8323 | + | 42.7442i | −2.54592 | + | 1.84972i | ||||
\(535\) | −2.20447 | − | 6.78465i | −0.0953074 | − | 0.293326i | ||||
\(536\) | 8.62518 | − | 26.5456i | 0.372551 | − | 1.14659i | ||||
\(537\) | 7.87367 | + | 5.72056i | 0.339774 | + | 0.246860i | ||||
\(538\) | −34.2376 | −1.47609 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −22.3310 | −0.960973 | ||||||||
\(541\) | −16.0384 | − | 11.6526i | −0.689545 | − | 0.500984i | 0.186965 | − | 0.982366i | \(-0.440135\pi\) |
−0.876511 | + | 0.481383i | \(0.840135\pi\) | |||||||
\(542\) | −1.56971 | + | 4.83106i | −0.0674246 | + | 0.207512i | ||||
\(543\) | −5.04655 | − | 15.5317i | −0.216568 | − | 0.666529i | ||||
\(544\) | −12.0418 | + | 8.74890i | −0.516289 | + | 0.375106i | ||||
\(545\) | 3.35408 | − | 2.43688i | 0.143673 | − | 0.104385i | ||||
\(546\) | −10.4369 | − | 32.1214i | −0.446657 | − | 1.37467i | ||||
\(547\) | 4.52887 | − | 13.9384i | 0.193641 | − | 0.595964i | −0.806349 | − | 0.591440i | \(-0.798560\pi\) |
0.999990 | − | 0.00452464i | \(-0.00144024\pi\) | |||||||
\(548\) | 44.5196 | + | 32.3454i | 1.90178 | + | 1.38172i | ||||
\(549\) | −71.3419 | −3.04480 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.1038 | −0.643445 | ||||||||
\(552\) | 20.8035 | + | 15.1146i | 0.885454 | + | 0.643320i | ||||
\(553\) | −7.07531 | + | 21.7756i | −0.300873 | + | 0.925991i | ||||
\(554\) | −11.1071 | − | 34.1841i | −0.471895 | − | 1.45234i | ||||
\(555\) | −6.25564 | + | 4.54499i | −0.265537 | + | 0.192924i | ||||
\(556\) | −21.7551 | + | 15.8060i | −0.922621 | + | 0.670324i | ||||
\(557\) | 1.80386 | + | 5.55171i | 0.0764321 | + | 0.235234i | 0.981972 | − | 0.189028i | \(-0.0605337\pi\) |
−0.905540 | + | 0.424262i | \(0.860534\pi\) | |||||||
\(558\) | 34.8825 | − | 107.357i | 1.47669 | − | 4.54480i | ||||
\(559\) | −6.45765 | − | 4.69176i | −0.273130 | − | 0.198440i | ||||
\(560\) | 4.52313 | 0.191137 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.02295 | 0.211880 | ||||||||
\(563\) | 31.7965 | + | 23.1015i | 1.34006 | + | 0.973612i | 0.999442 | + | 0.0334116i | \(0.0106372\pi\) |
0.340621 | + | 0.940201i | \(0.389363\pi\) | |||||||
\(564\) | −32.8021 | + | 100.954i | −1.38122 | + | 4.25095i | ||||
\(565\) | −0.452646 | − | 1.39310i | −0.0190430 | − | 0.0586082i | ||||
\(566\) | −8.23016 | + | 5.97956i | −0.345940 | + | 0.251340i | ||||
\(567\) | 6.98538 | − | 5.07517i | 0.293358 | − | 0.213137i | ||||
\(568\) | 2.77239 | + | 8.53253i | 0.116327 | + | 0.358017i | ||||
\(569\) | −2.50615 | + | 7.71314i | −0.105063 | + | 0.323351i | −0.989745 | − | 0.142843i | \(-0.954375\pi\) |
0.884682 | + | 0.466195i | \(0.154375\pi\) | |||||||
\(570\) | −17.5114 | − | 12.7228i | −0.733472 | − | 0.532898i | ||||
\(571\) | 35.6274 | 1.49096 | 0.745480 | − | 0.666528i | \(-0.232220\pi\) | ||||
0.745480 | + | 0.666528i | \(0.232220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.8437 | −1.07963 | ||||||||
\(574\) | 29.2672 | + | 21.2639i | 1.22159 | + | 0.887537i | ||||
\(575\) | −0.777890 | + | 2.39410i | −0.0324402 | + | 0.0998408i | ||||
\(576\) | −19.4045 | − | 59.7208i | −0.808519 | − | 2.48837i | ||||
\(577\) | 25.7696 | − | 18.7227i | 1.07280 | − | 0.779435i | 0.0963872 | − | 0.995344i | \(-0.469271\pi\) |
0.976414 | + | 0.215909i | \(0.0692713\pi\) | |||||||
\(578\) | 5.83242 | − | 4.23750i | 0.242597 | − | 0.176257i | ||||
\(579\) | 23.2336 | + | 71.5057i | 0.965556 | + | 2.97168i | ||||
\(580\) | −5.10606 | + | 15.7148i | −0.212018 | + | 0.652523i | ||||
\(581\) | 20.6719 | + | 15.0190i | 0.857616 | + | 0.623095i | ||||
\(582\) | 74.1688 | 3.07440 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.5686 | −0.437332 | ||||||||
\(585\) | 6.25564 | + | 4.54499i | 0.258639 | + | 0.187912i | ||||
\(586\) | −9.80392 | + | 30.1734i | −0.404996 | + | 1.24645i | ||||
\(587\) | −13.7149 | − | 42.2101i | −0.566074 | − | 1.74220i | −0.664739 | − | 0.747076i | \(-0.731457\pi\) |
0.0986650 | − | 0.995121i | \(-0.468543\pi\) | |||||||
\(588\) | −36.2783 | + | 26.3577i | −1.49609 | + | 1.08697i | ||||
\(589\) | 23.9690 | − | 17.4145i | 0.987627 | − | 0.717553i | ||||
\(590\) | −8.64694 | − | 26.6126i | −0.355989 | − | 1.09562i | ||||
\(591\) | −14.7893 | + | 45.5168i | −0.608350 | + | 1.87231i | ||||
\(592\) | 2.91768 | + | 2.11982i | 0.119916 | + | 0.0871241i | ||||
\(593\) | −41.9463 | −1.72253 | −0.861264 | − | 0.508158i | \(-0.830327\pi\) | ||||
−0.861264 | + | 0.508158i | \(0.830327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.6286 | −0.517721 | ||||||||
\(596\) | −18.4469 | − | 13.4025i | −0.755614 | − | 0.548986i | ||||
\(597\) | −14.8720 | + | 45.7713i | −0.608670 | + | 1.87329i | ||||
\(598\) | −2.70915 | − | 8.33792i | −0.110786 | − | 0.340963i | ||||
\(599\) | −13.4383 | + | 9.76351i | −0.549075 | + | 0.398926i | −0.827444 | − | 0.561548i | \(-0.810206\pi\) |
0.278370 | + | 0.960474i | \(0.410206\pi\) | |||||||
\(600\) | −8.26418 | + | 6.00428i | −0.337384 | + | 0.245124i | ||||
\(601\) | −4.07816 | − | 12.5513i | −0.166351 | − | 0.511977i | 0.832782 | − | 0.553601i | \(-0.186747\pi\) |
−0.999133 | + | 0.0416241i | \(0.986747\pi\) | |||||||
\(602\) | −13.2214 | + | 40.6913i | −0.538864 | + | 1.65845i | ||||
\(603\) | −33.0422 | − | 24.0066i | −1.34558 | − | 0.977624i | ||||
\(604\) | 38.2622 | 1.55687 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −85.7195 | −3.48212 | ||||||||
\(607\) | 7.31420 | + | 5.31408i | 0.296874 | + | 0.215692i | 0.726244 | − | 0.687437i | \(-0.241264\pi\) |
−0.429370 | + | 0.903129i | \(0.641264\pi\) | |||||||
\(608\) | 3.96208 | − | 12.1940i | 0.160683 | − | 0.494533i | ||||
\(609\) | −14.0782 | − | 43.3284i | −0.570479 | − | 1.75575i | ||||
\(610\) | −25.9958 | + | 18.8871i | −1.05254 | + | 0.764715i | ||||
\(611\) | 12.6303 | − | 9.17643i | 0.510966 | − | 0.371238i | ||||
\(612\) | −21.1564 | − | 65.1127i | −0.855197 | − | 2.63203i | ||||
\(613\) | −2.36805 | + | 7.28812i | −0.0956448 | + | 0.294364i | −0.987421 | − | 0.158112i | \(-0.949459\pi\) |
0.891776 | + | 0.452476i | \(0.149459\pi\) | |||||||
\(614\) | 4.52056 | + | 3.28438i | 0.182435 | + | 0.132547i | ||||
\(615\) | −13.0467 | −0.526093 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.67989 | −0.107888 | −0.0539441 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539441 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(618\) | 99.9078 | + | 72.5872i | 4.01888 | + | 2.91989i | ||||
\(619\) | 2.52598 | − | 7.77416i | 0.101528 | − | 0.312470i | −0.887372 | − | 0.461054i | \(-0.847471\pi\) |
0.988900 | + | 0.148584i | \(0.0474715\pi\) | |||||||
\(620\) | −10.0159 | − | 30.8259i | −0.402250 | − | 1.23800i | ||||
\(621\) | 12.9298 | − | 9.39404i | 0.518855 | − | 0.376970i | ||||
\(622\) | 42.0814 | − | 30.5739i | 1.68731 | − | 1.22590i | ||||
\(623\) | −11.2937 | − | 34.7585i | −0.452474 | − | 1.39257i | ||||
\(624\) | 1.75555 | − | 5.40303i | 0.0702783 | − | 0.216294i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | −64.0880 | −2.56147 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.6861 | 1.46394 | ||||||||
\(629\) | −8.14617 | − | 5.91854i | −0.324809 | − | 0.235988i | ||||
\(630\) | 12.8078 | − | 39.4183i | 0.510275 | − | 1.57046i | ||||
\(631\) | 1.72117 | + | 5.29721i | 0.0685186 | + | 0.210879i | 0.979453 | − | 0.201673i | \(-0.0646377\pi\) |
−0.910934 | + | 0.412551i | \(0.864638\pi\) | |||||||
\(632\) | −19.5115 | + | 14.1759i | −0.776125 | + | 0.563888i | ||||
\(633\) | −17.7279 | + | 12.8801i | −0.704620 | + | 0.511937i | ||||
\(634\) | −11.1749 | − | 34.3927i | −0.443810 | − | 1.36591i | ||||
\(635\) | −3.49077 | + | 10.7435i | −0.138527 | + | 0.426343i | ||||
\(636\) | 20.5310 | + | 14.9166i | 0.814106 | + | 0.591483i | ||||
\(637\) | 6.59516 | 0.261310 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1280 | 0.519335 | ||||||||
\(640\) | −16.4286 | − | 11.9361i | −0.649397 | − | 0.471814i | ||||
\(641\) | −4.10701 | + | 12.6401i | −0.162217 | + | 0.499253i | −0.998820 | − | 0.0485563i | \(-0.984538\pi\) |
0.836603 | + | 0.547809i | \(0.184538\pi\) | |||||||
\(642\) | 14.8413 | + | 45.6769i | 0.585741 | + | 1.80273i | ||||
\(643\) | −14.4116 | + | 10.4706i | −0.568337 | + | 0.412921i | −0.834501 | − | 0.551007i | \(-0.814244\pi\) |
0.266164 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(644\) | −24.2365 | + | 17.6088i | −0.955051 | + | 0.693886i | ||||
\(645\) | −4.76819 | − | 14.6750i | −0.187747 | − | 0.577827i | ||||
\(646\) | 8.71018 | − | 26.8072i | 0.342697 | − | 1.05471i | ||||
\(647\) | 20.9397 | + | 15.2136i | 0.823225 | + | 0.598108i | 0.917634 | − | 0.397426i | \(-0.130096\pi\) |
−0.0944095 | + | 0.995533i | \(0.530096\pi\) | |||||||
\(648\) | 9.09498 | 0.357285 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.48270 | 0.136603 | ||||||||
\(651\) | 72.2986 | + | 52.5280i | 2.83361 | + | 2.05874i | ||||
\(652\) | −11.1341 | + | 34.2673i | −0.436046 | + | 1.34201i | ||||
\(653\) | 4.12093 | + | 12.6829i | 0.161265 | + | 0.496321i | 0.998742 | − | 0.0501511i | \(-0.0159703\pi\) |
−0.837477 | + | 0.546473i | \(0.815970\pi\) | |||||||
\(654\) | −22.5810 | + | 16.4061i | −0.882988 | + | 0.641528i | ||||
\(655\) | −11.8763 | + | 8.62862i | −0.464045 | + | 0.337148i | ||||
\(656\) | 1.88039 | + | 5.78726i | 0.0734171 | + | 0.225955i | ||||
\(657\) | −4.77888 | + | 14.7079i | −0.186442 | + | 0.573810i | ||||
\(658\) | −67.7003 | − | 49.1871i | −2.63923 | − | 1.91751i | ||||
\(659\) | −24.4877 | −0.953907 | −0.476954 | − | 0.878929i | \(-0.658259\pi\) | ||||
−0.476954 | + | 0.878929i | \(0.658259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2738 | −0.905248 | −0.452624 | − | 0.891702i | \(-0.649512\pi\) | ||||
−0.452624 | + | 0.891702i | \(0.649512\pi\) | |||||||
\(662\) | −49.2421 | − | 35.7765i | −1.91385 | − | 1.39049i | ||||
\(663\) | −4.90149 | + | 15.0852i | −0.190358 | + | 0.585862i | ||||
\(664\) | 8.31717 | + | 25.5976i | 0.322769 | + | 0.993380i | ||||
\(665\) | 8.80071 | − | 6.39409i | 0.341277 | − | 0.247952i | ||||
\(666\) | 26.7357 | − | 19.4246i | 1.03599 | − | 0.752688i | ||||
\(667\) | −3.65436 | − | 11.2470i | −0.141497 | − | 0.435484i | ||||
\(668\) | −1.13765 | + | 3.50132i | −0.0440169 | + | 0.135470i | ||||
\(669\) | 8.78719 | + | 6.38427i | 0.339733 | + | 0.246830i | ||||
\(670\) | −18.3956 | −0.710683 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 38.6741 | 1.49188 | ||||||||
\(673\) | −9.17770 | − | 6.66799i | −0.353774 | − | 0.257032i | 0.396676 | − | 0.917959i | \(-0.370164\pi\) |
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(674\) | 10.1489 | − | 31.2350i | 0.390920 | − | 1.20313i | ||||
\(675\) | 1.96192 | + | 6.03816i | 0.0755142 | + | 0.232409i | ||||
\(676\) | 30.7366 | − | 22.3315i | 1.18218 | − | 0.858902i | ||||
\(677\) | 17.3094 | − | 12.5760i | 0.665254 | − | 0.483335i | −0.203179 | − | 0.979142i | \(-0.565127\pi\) |
0.868433 | + | 0.495806i | \(0.165127\pi\) | |||||||
\(678\) | 3.04739 | + | 9.37891i | 0.117034 | + | 0.360195i | ||||
\(679\) | −11.5186 | + | 35.4507i | −0.442044 | + | 1.36047i | ||||
\(680\) | −10.7617 | − | 7.81884i | −0.412693 | − | 0.299839i | ||||
\(681\) | −56.0230 | −2.14680 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.11590 | −0.195754 | −0.0978772 | − | 0.995198i | \(-0.531205\pi\) | ||||
−0.0978772 | + | 0.995198i | \(0.531205\pi\) | |||||||
\(684\) | 47.7115 | + | 34.6644i | 1.82429 | + | 1.32543i | ||||
\(685\) | 4.83466 | − | 14.8795i | 0.184723 | − | 0.568518i | ||||
\(686\) | 6.26726 | + | 19.2887i | 0.239285 | + | 0.736444i | ||||
\(687\) | −11.9710 | + | 8.69745i | −0.456723 | + | 0.331828i | ||||
\(688\) | −5.82231 | + | 4.23016i | −0.221974 | + | 0.161273i | ||||
\(689\) | −1.15337 | − | 3.54972i | −0.0439400 | − | 0.135234i | ||||
\(690\) | 5.23706 | − | 16.1180i | 0.199372 | − | 0.613603i | ||||
\(691\) | 18.5359 | + | 13.4671i | 0.705140 | + | 0.512315i | 0.881602 | − | 0.471993i | \(-0.156465\pi\) |
−0.176462 | + | 0.984307i | \(0.556465\pi\) | |||||||
\(692\) | 41.9012 | 1.59285 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −72.9254 | −2.76821 | ||||||||
\(695\) | 6.18516 | + | 4.49378i | 0.234616 | + | 0.170459i | ||||
\(696\) | 14.8292 | − | 45.6396i | 0.562100 | − | 1.72997i | ||||
\(697\) | −5.25006 | − | 16.1580i | −0.198860 | − | 0.612028i | ||||
\(698\) | −6.96112 | + | 5.05755i | −0.263482 | + | 0.191431i | ||||
\(699\) | −14.4918 | + | 10.5289i | −0.548131 | + | 0.398241i | ||||
\(700\) | −3.67755 | − | 11.3183i | −0.138998 | − | 0.427793i | ||||
\(701\) | −11.7177 | + | 36.0632i | −0.442570 | + | 1.36209i | 0.442557 | + | 0.896740i | \(0.354071\pi\) |
−0.885127 | + | 0.465349i | \(0.845929\pi\) | |||||||
\(702\) | −17.8884 | − | 12.9967i | −0.675154 | − | 0.490528i | ||||
\(703\) | 8.67364 | 0.327133 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.1793 | 1.13662 | ||||||||
\(706\) | −46.6995 | − | 33.9292i | −1.75756 | − | 1.27694i | ||||
\(707\) | 13.3125 | − | 40.9716i | 0.500667 | − | 1.54090i | ||||
\(708\) | 37.1121 | + | 114.219i | 1.39476 | + | 4.29262i | ||||
\(709\) | 4.26907 | − | 3.10166i | 0.160328 | − | 0.116485i | −0.504728 | − | 0.863278i | \(-0.668407\pi\) |
0.665057 | + | 0.746793i | \(0.268407\pi\) | |||||||
\(710\) | 4.78362 | − | 3.47550i | 0.179526 | − | 0.130433i | ||||
\(711\) | 10.9054 | + | 33.5633i | 0.408984 | + | 1.25872i | ||||
\(712\) | 11.8962 | − | 36.6126i | 0.445828 | − | 1.37212i | ||||
\(713\) | 18.7669 | + | 13.6350i | 0.702827 | + | 0.510633i | ||||
\(714\) | 85.0206 | 3.18181 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.9433 | −0.446341 | ||||||||
\(717\) | −10.6912 | − | 7.76764i | −0.399271 | − | 0.290088i | ||||
\(718\) | −4.78081 | + | 14.7138i | −0.178418 | + | 0.549115i | ||||
\(719\) | 9.55224 | + | 29.3988i | 0.356238 | + | 1.09639i | 0.955288 | + | 0.295677i | \(0.0955452\pi\) |
−0.599050 | + | 0.800712i | \(0.704455\pi\) | |||||||
\(720\) | 5.64017 | − | 4.09783i | 0.210197 | − | 0.152717i | ||||
\(721\) | −50.2107 | + | 36.4802i | −1.86994 | + | 1.35859i | ||||
\(722\) | −6.28815 | − | 19.3529i | −0.234021 | − | 0.720242i | ||||
\(723\) | 6.97782 | − | 21.4755i | 0.259508 | − | 0.798683i | ||||
\(724\) | 16.2134 | + | 11.7797i | 0.602566 | + | 0.437790i | ||||
\(725\) | 4.69779 | 0.174471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.24387 | 0.305748 | 0.152874 | − | 0.988246i | \(-0.451147\pi\) | ||||
0.152874 | + | 0.988246i | \(0.451147\pi\) | |||||||
\(728\) | 14.4648 | + | 10.5093i | 0.536101 | + | 0.389500i | ||||
\(729\) | −12.7572 | + | 39.2626i | −0.472488 | + | 1.45417i | ||||
\(730\) | 2.15242 | + | 6.62448i | 0.0796648 | + | 0.245183i | ||||
\(731\) | 16.2559 | − | 11.8106i | 0.601245 | − | 0.436830i | ||||
\(732\) | 111.572 | − | 81.0620i | 4.12383 | − | 2.99614i | ||||
\(733\) | 13.4064 | + | 41.2606i | 0.495176 | + | 1.52399i | 0.816683 | + | 0.577087i | \(0.195810\pi\) |
−0.321507 | + | 0.946907i | \(0.604190\pi\) | |||||||
\(734\) | 5.92903 | − | 18.2477i | 0.218844 | − | 0.673534i | ||||
\(735\) | 10.3142 | + | 7.49373i | 0.380446 | + | 0.276411i | ||||
\(736\) | 10.0388 | 0.370036 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 55.7596 | 2.05254 | ||||||||
\(739\) | −0.243525 | − | 0.176931i | −0.00895822 | − | 0.00650853i | 0.583297 | − | 0.812259i | \(-0.301762\pi\) |
−0.592255 | + | 0.805750i | \(0.701762\pi\) | |||||||
\(740\) | 2.93224 | − | 9.02452i | 0.107791 | − | 0.331748i | ||||
\(741\) | −4.22215 | − | 12.9945i | −0.155105 | − | 0.477363i | ||||
\(742\) | −16.1854 | + | 11.7594i | −0.594184 | + | 0.431700i | ||||
\(743\) | −25.4873 | + | 18.5176i | −0.935038 | + | 0.679345i | −0.947221 | − | 0.320581i | \(-0.896122\pi\) |
0.0121830 | + | 0.999926i | \(0.496122\pi\) | |||||||
\(744\) | 29.0887 | + | 89.5258i | 1.06644 | + | 3.28218i | ||||
\(745\) | −2.00326 | + | 6.16541i | −0.0733939 | + | 0.225883i | ||||
\(746\) | 51.3856 | + | 37.3338i | 1.88136 | + | 1.36689i | ||||
\(747\) | 39.3839 | 1.44098 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.1372 | −0.881955 | ||||||||
\(750\) | 5.44662 | + | 3.95720i | 0.198883 | + | 0.144497i | ||||
\(751\) | 10.2873 | − | 31.6612i | 0.375391 | − | 1.15533i | −0.567824 | − | 0.823150i | \(-0.692215\pi\) |
0.943215 | − | 0.332184i | \(-0.107785\pi\) | |||||||
\(752\) | −4.34969 | − | 13.3870i | −0.158617 | − | 0.488172i | ||||
\(753\) | −24.7086 | + | 17.9518i | −0.900430 | + | 0.654201i | ||||
\(754\) | −13.2363 | + | 9.61674i | −0.482038 | + | 0.350221i | ||||
\(755\) | −3.36157 | − | 10.3459i | −0.122340 | − | 0.376524i | ||||
\(756\) | −23.3484 | + | 71.8589i | −0.849173 | + | 2.61348i | ||||
\(757\) | −12.5453 | − | 9.11469i | −0.455967 | − | 0.331279i | 0.335980 | − | 0.941869i | \(-0.390932\pi\) |
−0.791947 | + | 0.610590i | \(0.790932\pi\) | |||||||
\(758\) | 76.7195 | 2.78658 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.4585 | 0.415645 | ||||||||
\(761\) | 42.3879 | + | 30.7966i | 1.53656 | + | 1.11638i | 0.952446 | + | 0.304707i | \(0.0985585\pi\) |
0.584116 | + | 0.811670i | \(0.301441\pi\) | |||||||
\(762\) | 23.5013 | − | 72.3295i | 0.851361 | − | 2.62022i | ||||
\(763\) | −4.33476 | − | 13.3410i | −0.156929 | − | 0.482977i | ||||
\(764\) | 25.6576 | − | 18.6413i | 0.928258 | − | 0.674419i | ||||
\(765\) | −15.7473 | + | 11.4411i | −0.569347 | + | 0.413655i | ||||
\(766\) | −1.92094 | − | 5.91204i | −0.0694064 | − | 0.213611i | ||||
\(767\) | 5.45822 | − | 16.7987i | 0.197085 | − | 0.606565i | ||||
\(768\) | 54.7630 | + | 39.7876i | 1.97609 | + | 1.43571i | ||||
\(769\) | 44.2652 | 1.59624 | 0.798122 | − | 0.602496i | \(-0.205827\pi\) | ||||
0.798122 | + | 0.602496i | \(0.205827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.05131 | 0.289961 | ||||||||
\(772\) | −74.6441 | − | 54.2321i | −2.68650 | − | 1.95186i | ||||
\(773\) | −10.9138 | + | 33.5891i | −0.392541 | + | 1.20812i | 0.538319 | + | 0.842741i | \(0.319060\pi\) |
−0.930860 | + | 0.365376i | \(0.880940\pi\) | |||||||
\(774\) | 20.3785 | + | 62.7187i | 0.732491 | + | 2.25438i | ||||
\(775\) | −7.45517 | + | 5.41650i | −0.267797 | + | 0.194566i | ||||
\(776\) | −31.7648 | + | 23.0784i | −1.14029 | + | 0.828468i | ||||
\(777\) | 8.08468 | + | 24.8821i | 0.290036 | + | 0.892640i | ||||
\(778\) | −21.0868 | + | 64.8986i | −0.756000 | + | 2.32673i | ||||
\(779\) | 11.8398 | + | 8.60213i | 0.424205 | + | 0.308203i | ||||
\(780\) | −14.9475 | −0.535206 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 22.0692 | 0.789194 | ||||||||
\(783\) | −24.1295 | − | 17.5311i | −0.862320 | − | 0.626512i | ||||
\(784\) | 1.83751 | − | 5.65526i | 0.0656252 | − | 0.201974i | ||||
\(785\) | −3.22310 | − | 9.91970i | −0.115038 | − | 0.354049i | ||||
\(786\) | 79.9558 | − | 58.0913i | 2.85193 | − | 2.07205i | ||||
\(787\) | 29.6844 | − | 21.5670i | 1.05814 | − | 0.768780i | 0.0843928 | − | 0.996433i | \(-0.473105\pi\) |
0.973742 | + | 0.227652i | \(0.0731050\pi\) | |||||||
\(788\) | −18.1489 | − | 55.8567i | −0.646529 | − | 1.98981i | ||||
\(789\) | 24.4855 | − | 75.3587i | 0.871708 | − | 2.68284i | ||||
\(790\) | 12.8593 | + | 9.34283i | 0.457514 | + | 0.332403i | ||||
\(791\) | −4.95613 | −0.176220 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2831 | −0.720274 | ||||||||
\(794\) | 17.7863 | + | 12.9225i | 0.631213 | + | 0.458603i | ||||
\(795\) | 2.22959 | − | 6.86196i | 0.0790753 | − | 0.243369i | ||||
\(796\) | −18.2504 | − | 56.1690i | −0.646869 | − | 1.99086i | ||||
\(797\) | 2.30903 | − | 1.67761i | 0.0817902 | − | 0.0594241i | −0.546139 | − | 0.837695i | \(-0.683903\pi\) |
0.627929 | + | 0.778271i | \(0.283903\pi\) | |||||||
\(798\) | −59.2499 | + | 43.0475i | −2.09742 | + | 1.52387i | ||||
\(799\) | 12.1443 | + | 37.3763i | 0.429635 | + | 1.32228i | ||||
\(800\) | −1.23234 | + | 3.79274i | −0.0435697 | + | 0.134094i | ||||
\(801\) | −45.5731 | − | 33.1108i | −1.61025 | − | 1.16991i | ||||
\(802\) | 11.5819 | 0.408971 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 78.9525 | 2.78444 | ||||||||
\(805\) | 6.89064 | + | 5.00635i | 0.242863 | + | 0.176451i | ||||
\(806\) | 9.91740 | − | 30.5226i | 0.349325 | − | 1.07511i | ||||
\(807\) | −12.9101 | − | 39.7331i | −0.454456 | − | 1.39867i | ||||
\(808\) | 36.7116 | − | 26.6726i | 1.29151 | − | 0.938338i | ||||
\(809\) | 21.1100 | − | 15.3373i | 0.742187 | − | 0.539231i | −0.151208 | − | 0.988502i | \(-0.548316\pi\) |
0.893395 | + | 0.449271i | \(0.148316\pi\) | |||||||
\(810\) | −1.85230 | − | 5.70080i | −0.0650832 | − | 0.200306i | ||||
\(811\) | 6.07072 | − | 18.6838i | 0.213172 | − | 0.656076i | −0.786106 | − | 0.618091i | \(-0.787906\pi\) |
0.999278 | − | 0.0379846i | \(-0.0120938\pi\) | |||||||
\(812\) | 45.2301 | + | 32.8616i | 1.58727 | + | 1.15322i | ||||
\(813\) | −6.19839 | −0.217387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.2439 | 0.358827 | ||||||||
\(816\) | 11.5698 | + | 8.40593i | 0.405023 | + | 0.294266i | ||||
\(817\) | −5.34861 | + | 16.4613i | −0.187124 | + | 0.575909i | ||||
\(818\) | −27.8061 | − | 85.5785i | −0.972218 | − | 2.99218i | ||||
\(819\) | 21.1660 | − | 15.3780i | 0.739599 | − | 0.537350i | ||||
\(820\) | 12.9527 | − | 9.41071i | 0.452329 | − | 0.328636i | ||||
\(821\) | 16.0416 | + | 49.3709i | 0.559855 | + | 1.72306i | 0.682763 | + | 0.730640i | \(0.260778\pi\) |
−0.122908 | + | 0.992418i | \(0.539222\pi\) | |||||||
\(822\) | −32.5488 | + | 100.175i | −1.13527 | + | 3.49400i | ||||
\(823\) | −12.8836 | − | 9.36045i | −0.449093 | − | 0.326285i | 0.340145 | − | 0.940373i | \(-0.389524\pi\) |
−0.789237 | + | 0.614088i | \(0.789524\pi\) | |||||||
\(824\) | −65.3744 | −2.27743 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −94.6775 | −3.29425 | ||||||||
\(827\) | 7.90542 | + | 5.74362i | 0.274898 | + | 0.199725i | 0.716689 | − | 0.697393i | \(-0.245657\pi\) |
−0.441791 | + | 0.897118i | \(0.645657\pi\) | |||||||
\(828\) | −14.2689 | + | 43.9151i | −0.495878 | + | 1.52616i | ||||
\(829\) | 0.314549 | + | 0.968083i | 0.0109247 | + | 0.0336229i | 0.956370 | − | 0.292157i | \(-0.0943731\pi\) |
−0.945446 | + | 0.325780i | \(0.894373\pi\) | |||||||
\(830\) | 14.3509 | − | 10.4265i | 0.498126 | − | 0.361910i | ||||
\(831\) | 35.4828 | − | 25.7798i | 1.23089 | − | 0.894290i | ||||
\(832\) | −5.51686 | − | 16.9791i | −0.191263 | − | 0.588646i | ||||
\(833\) | −5.13031 | + | 15.7895i | −0.177755 | + | 0.547073i | ||||
\(834\) | −41.6409 | − | 30.2539i | −1.44191 | − | 1.04761i | ||||
\(835\) | 1.04668 | 0.0362219 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 58.5056 | 2.02225 | ||||||||
\(838\) | −71.0286 | − | 51.6053i | −2.45364 | − | 1.78268i | ||||
\(839\) | 4.26133 | − | 13.1150i | 0.147117 | − | 0.452781i | −0.850160 | − | 0.526525i | \(-0.823495\pi\) |
0.997277 | + | 0.0737438i | \(0.0234947\pi\) | |||||||
\(840\) | 10.6805 | + | 32.8712i | 0.368512 | + | 1.13416i | ||||
\(841\) | 5.60712 | − | 4.07381i | 0.193349 | − | 0.140476i | ||||
\(842\) | −55.8920 | + | 40.6079i | −1.92617 | + | 1.39944i | ||||
\(843\) | 1.89402 | + | 5.82919i | 0.0652334 | + | 0.200768i | ||||
\(844\) | 8.30970 | − | 25.5746i | 0.286032 | − | 0.880315i | ||||
\(845\) | −8.73869 | − | 6.34903i | −0.300620 | − | 0.218413i | ||||
\(846\) | −128.982 | −4.43448 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.36518 | −0.115561 | ||||||||
\(849\) | −10.0427 | − | 7.29646i | −0.344665 | − | 0.250414i | ||||
\(850\) | −2.70915 | + | 8.33792i | −0.0929232 | + | 0.285988i | ||||
\(851\) | 2.09858 | + | 6.45877i | 0.0719385 | + | 0.221404i | ||||
\(852\) | −20.5310 | + | 14.9166i | −0.703379 | + | 0.511035i | ||||
\(853\) | −22.1075 | + | 16.0620i | −0.756946 | + | 0.549953i | −0.897972 | − | 0.440052i | \(-0.854960\pi\) |
0.141026 | + | 0.990006i | \(0.454960\pi\) | |||||||
\(854\) | 33.5966 | + | 103.400i | 1.14965 | + | 3.53826i | ||||
\(855\) | 5.18129 | − | 15.9464i | 0.177196 | − | 0.545354i | ||||
\(856\) | −20.5691 | − | 14.9443i | −0.703036 | − | 0.510786i | ||||
\(857\) | 22.2318 | 0.759424 | 0.379712 | − | 0.925105i | \(-0.376023\pi\) | ||||
0.379712 | + | 0.925105i | \(0.376023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5173 | 0.972998 | 0.486499 | − | 0.873681i | \(-0.338274\pi\) | ||||
0.486499 | + | 0.873681i | \(0.338274\pi\) | |||||||
\(860\) | 15.3191 | + | 11.1300i | 0.522376 | + | 0.379528i | ||||
\(861\) | −13.6411 | + | 41.9829i | −0.464887 | + | 1.43077i | ||||
\(862\) | 1.28345 | + | 3.95004i | 0.0437144 | + | 0.134539i | ||||
\(863\) | −42.2787 | + | 30.7173i | −1.43918 | + | 1.04563i | −0.450972 | + | 0.892538i | \(0.648923\pi\) |
−0.988212 | + | 0.153091i | \(0.951077\pi\) | |||||||
\(864\) | 20.4834 | − | 14.8821i | 0.696861 | − | 0.506299i | ||||
\(865\) | −3.68128 | − | 11.3298i | −0.125167 | − | 0.385226i | ||||
\(866\) | 7.29573 | − | 22.4539i | 0.247919 | − | 0.763016i | ||||
\(867\) | 7.11691 | + | 5.17074i | 0.241703 | + | 0.175607i | ||||
\(868\) | −109.667 | −3.72234 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −31.6274 | −1.07227 | ||||||||
\(871\) | −9.39420 | − | 6.82528i | −0.318310 | − | 0.231266i | ||||
\(872\) | 4.56599 | − | 14.0527i | 0.154624 | − | 0.475883i | ||||
\(873\) | 17.7540 | + | 54.6412i | 0.600882 | + | 1.84932i | ||||
\(874\) | −15.3798 | + | 11.1741i | −0.520229 | + | 0.377968i | ||||
\(875\) | −2.73731 | + | 1.98877i | −0.0925380 | + | 0.0672328i | ||||
\(876\) | −9.23806 | − | 28.4318i | −0.312125 | − | 0.960622i | ||||
\(877\) | −6.49166 | + | 19.9793i | −0.219208 | + | 0.674652i | 0.779620 | + | 0.626252i | \(0.215412\pi\) |
−0.998828 | + | 0.0483995i | \(0.984588\pi\) | |||||||
\(878\) | −74.4862 | − | 54.1174i | −2.51379 | − | 1.82637i | ||||
\(879\) | −38.7133 | −1.30577 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0743 | 1.55228 | 0.776141 | − | 0.630560i | \(-0.217175\pi\) | ||||
0.776141 | + | 0.630560i | \(0.217175\pi\) | |||||||
\(882\) | −44.0815 | − | 32.0271i | −1.48430 | − | 1.07841i | ||||
\(883\) | 0.192309 | − | 0.591867i | 0.00647172 | − | 0.0199179i | −0.947769 | − | 0.318959i | \(-0.896667\pi\) |
0.954240 | + | 0.299041i | \(0.0966668\pi\) | |||||||
\(884\) | −6.01495 | − | 18.5121i | −0.202305 | − | 0.622630i | ||||
\(885\) | 27.6236 | − | 20.0697i | 0.928558 | − | 0.674637i | ||||
\(886\) | 26.6271 | − | 19.3457i | 0.894554 | − | 0.649932i | ||||
\(887\) | 3.52516 | + | 10.8493i | 0.118363 | + | 0.364285i | 0.992634 | − | 0.121155i | \(-0.0386597\pi\) |
−0.874270 | + | 0.485439i | \(0.838660\pi\) | |||||||
\(888\) | −8.51594 | + | 26.2094i | −0.285776 | + | 0.879529i | ||||
\(889\) | 30.9217 | + | 22.4659i | 1.03708 | + | 0.753483i | ||||
\(890\) | −25.3718 | −0.850466 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.3290 | −0.446287 | ||||||||
\(893\) | −27.3876 | − | 19.8983i | −0.916491 | − | 0.665870i | ||||
\(894\) | 13.4868 | − | 41.5080i | 0.451065 | − | 1.38823i | ||||
\(895\) | 1.04929 | + | 3.22939i | 0.0350739 | + | 0.107946i | ||||
\(896\) | −55.5861 | + | 40.3857i | −1.85700 | + | 1.34919i | ||||
\(897\) | 8.65469 | − | 6.28800i | 0.288972 | − | 0.209950i | ||||
\(898\) | 1.86983 | + | 5.75474i | 0.0623970 | + | 0.192038i | ||||
\(899\) | 13.3775 | − | 41.1718i | 0.446165 | − | 1.37316i | ||||
\(900\) | −14.8399 | − | 10.7818i | −0.494662 | − | 0.359393i | ||||
\(901\) | 9.39558 | 0.313012 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −52.2081 | −1.73738 | ||||||||
\(904\) | −4.22348 | − | 3.06853i | −0.140471 | − | 0.102058i | ||||
\(905\) | 1.76071 | − | 5.41892i | 0.0585281 | − | 0.180131i | ||||
\(906\) | 22.6314 | + | 69.6524i | 0.751879 | + | 2.31405i | ||||
\(907\) | −31.4849 | + | 22.8751i | −1.04544 | + | 0.759557i | −0.971340 | − | 0.237694i | \(-0.923608\pi\) |
−0.0740999 | + | 0.997251i | \(0.523608\pi\) | |||||||
\(908\) | 55.6195 | − | 40.4100i | 1.84580 | − | 1.34105i | ||||
\(909\) | −20.5189 | − | 63.1507i | −0.680570 | − | 2.09458i | ||||
\(910\) | 3.64137 | − | 11.2070i | 0.120710 | − | 0.371508i | ||||
\(911\) | −30.8182 | − | 22.3907i | −1.02105 | − | 0.741838i | −0.0545536 | − | 0.998511i | \(-0.517374\pi\) |
−0.966498 | + | 0.256673i | \(0.917374\pi\) | |||||||
\(912\) | −12.3189 | −0.407920 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 35.5193 | 1.17488 | ||||||||
\(915\) | −31.7210 | − | 23.0466i | −1.04866 | − | 0.761898i | ||||
\(916\) | 5.61124 | − | 17.2696i | 0.185401 | − | 0.570605i | ||||
\(917\) | 15.3487 | + | 47.2384i | 0.506859 | + | 1.55995i | ||||
\(918\) | 45.0305 | − | 32.7166i | 1.48623 | − | 1.07981i | ||||
\(919\) | 15.5919 | − | 11.3282i | 0.514329 | − | 0.373682i | −0.300134 | − | 0.953897i | \(-0.597031\pi\) |
0.814463 | + | 0.580215i | \(0.197031\pi\) | |||||||
\(920\) | 2.77239 | + | 8.53253i | 0.0914029 | + | 0.281309i | ||||
\(921\) | −2.10698 | + | 6.48461i | −0.0694272 | + | 0.213675i | ||||
\(922\) | −18.6917 | − | 13.5803i | −0.615579 | − | 0.447244i | ||||
\(923\) | 3.73240 | 0.122853 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.69779 | −0.0887027 | ||||||||
\(926\) | −40.3039 | − | 29.2825i | −1.32447 | − | 0.962282i | ||||
\(927\) | −29.5608 | + | 90.9788i | −0.970904 | + | 2.98814i | ||||
\(928\) | −5.78926 | − | 17.8175i | −0.190042 | − | 0.584888i | ||||
\(929\) | −25.2195 | + | 18.3231i | −0.827426 | + | 0.601160i | −0.918830 | − | 0.394654i | \(-0.870864\pi\) |
0.0914042 | + | 0.995814i | \(0.470864\pi\) | |||||||
\(930\) | 50.1911 | − | 36.4660i | 1.64583 | − | 1.19577i | ||||
\(931\) | −4.41926 | − | 13.6011i | −0.144835 | − | 0.445757i | ||||
\(932\) | 6.79284 | − | 20.9062i | 0.222507 | − | 0.684806i | ||||
\(933\) | 51.3491 | + | 37.3073i | 1.68110 | + | 1.22139i | ||||
\(934\) | −22.4648 | −0.735070 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 27.5582 | 0.900767 | ||||||||
\(937\) | 20.9299 | + | 15.2065i | 0.683751 | + | 0.496774i | 0.874600 | − | 0.484845i | \(-0.161124\pi\) |
−0.190849 | + | 0.981619i | \(0.561124\pi\) | |||||||
\(938\) | −19.2337 | + | 59.1952i | −0.628002 | + | 1.93279i | ||||
\(939\) | −24.1658 | − | 74.3747i | −0.788622 | − | 2.42713i | ||||
\(940\) | −29.9620 | + | 21.7686i | −0.977252 | + | 0.710015i | ||||
\(941\) | 23.8365 | − | 17.3183i | 0.777049 | − | 0.564559i | −0.127043 | − | 0.991897i | \(-0.540549\pi\) |
0.904092 | + | 0.427338i | \(0.140549\pi\) | |||||||
\(942\) | 21.6992 | + | 66.7833i | 0.706999 | + | 2.17592i | ||||
\(943\) | −3.54089 | + | 10.8977i | −0.115307 | + | 0.354879i | ||||
\(944\) | −12.8839 | − | 9.36070i | −0.419335 | − | 0.304665i | ||||
\(945\) | 21.4815 | 0.698793 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.3881 | −0.467551 | −0.233776 | − | 0.972291i | \(-0.575108\pi\) | ||||
−0.233776 | + | 0.972291i | \(0.575108\pi\) | |||||||
\(948\) | −55.1913 | − | 40.0988i | −1.79253 | − | 1.30235i | ||||
\(949\) | −1.35868 | + | 4.18158i | −0.0441046 | + | 0.135740i | ||||
\(950\) | −2.33367 | − | 7.18230i | −0.0757142 | − | 0.233024i | ||||
\(951\) | 35.6993 | − | 25.9371i | 1.15763 | − | 0.841067i | ||||
\(952\) | −36.4123 | + | 26.4551i | −1.18013 | + | 0.857414i | ||||
\(953\) | 9.86355 | + | 30.3569i | 0.319512 | + | 0.983356i | 0.973857 | + | 0.227161i | \(0.0729442\pi\) |
−0.654346 | + | 0.756196i | \(0.727056\pi\) | |||||||
\(954\) | −9.52892 | + | 29.3270i | −0.308510 | + | 0.949496i | ||||
\(955\) | −7.29467 | − | 5.29989i | −0.236050 | − | 0.171500i | ||||
\(956\) | 16.2171 | 0.524499 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40.3944 | −1.30508 | ||||||||
\(959\) | −42.8260 | − | 31.1149i | −1.38292 | − | 1.00475i | ||||
\(960\) | 10.6646 | − | 32.8224i | 0.344200 | − | 1.05934i | ||||
\(961\) | 16.6616 | + | 51.2790i | 0.537470 | + | 1.65416i | ||||
\(962\) | 7.60118 | − | 5.52258i | 0.245072 | − | 0.178055i | ||||
\(963\) | −30.0982 | + | 21.8676i | −0.969901 | + | 0.704675i | ||||
\(964\) | 8.56295 | + | 26.3540i | 0.275794 | + | 0.848807i | ||||
\(965\) | −8.10607 | + | 24.9479i | −0.260944 | + | 0.803102i | ||||
\(966\) | −46.3905 | − | 33.7047i | −1.49259 | − | 1.08443i | ||||
\(967\) | −46.8425 | −1.50635 | −0.753176 | − | 0.657819i | \(-0.771479\pi\) | ||||
−0.753176 | + | 0.657819i | \(0.771479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.3944 | 1.10491 | ||||||||
\(970\) | 20.9350 | + | 15.2102i | 0.672182 | + | 0.488369i | ||||
\(971\) | −2.05867 | + | 6.33592i | −0.0660657 | + | 0.203329i | −0.978640 | − | 0.205582i | \(-0.934091\pi\) |
0.912574 | + | 0.408911i | \(0.134091\pi\) | |||||||
\(972\) | −12.7520 | − | 39.2467i | −0.409021 | − | 1.25884i | ||||
\(973\) | 20.9275 | − | 15.2047i | 0.670905 | − | 0.487441i | ||||
\(974\) | −29.5532 | + | 21.4717i | −0.946946 | + | 0.687997i | ||||
\(975\) | 1.31323 | + | 4.04171i | 0.0420570 | + | 0.129438i | ||||
\(976\) | −5.65116 | + | 17.3925i | −0.180889 | + | 0.556720i | ||||
\(977\) | 19.5750 | + | 14.2220i | 0.626259 | + | 0.455004i | 0.855102 | − | 0.518460i | \(-0.173494\pi\) |
−0.228843 | + | 0.973463i | \(0.573494\pi\) | |||||||
\(978\) | −68.9658 | −2.20528 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −15.6453 | −0.499770 | ||||||||
\(981\) | −17.4919 | − | 12.7086i | −0.558472 | − | 0.405754i | ||||
\(982\) | −6.57528 | + | 20.2366i | −0.209826 | + | 0.645777i | ||||
\(983\) | −8.58191 | − | 26.4124i | −0.273720 | − | 0.842425i | −0.989555 | − | 0.144155i | \(-0.953954\pi\) |
0.715835 | − | 0.698270i | \(-0.246046\pi\) | |||||||
\(984\) | −37.6178 | + | 27.3310i | −1.19921 | + | 0.871279i | ||||
\(985\) | −13.5088 | + | 9.81471i | −0.430426 | + | 0.312723i | ||||
\(986\) | −12.7270 | − | 39.1698i | −0.405311 | − | 1.24742i | ||||
\(987\) | 31.5542 | − | 97.1140i | 1.00438 | − | 3.09117i | ||||
\(988\) | 13.5648 | + | 9.85540i | 0.431554 | + | 0.313542i | ||||
\(989\) | −13.5519 | −0.430926 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.4227 | 1.44290 | 0.721450 | − | 0.692466i | \(-0.243476\pi\) | ||||
0.721450 | + | 0.692466i | \(0.243476\pi\) | |||||||
\(992\) | 29.7306 | + | 21.6006i | 0.943949 | + | 0.685819i | ||||
\(993\) | 22.9511 | − | 70.6364i | 0.728332 | − | 2.24158i | ||||
\(994\) | −6.18227 | − | 19.0271i | −0.196090 | − | 0.603502i | ||||
\(995\) | −13.5843 | + | 9.86959i | −0.430652 | + | 0.312887i | ||||
\(996\) | −61.5929 | + | 44.7499i | −1.95165 | + | 1.41795i | ||||
\(997\) | −15.6823 | − | 48.2653i | −0.496665 | − | 1.52858i | −0.814347 | − | 0.580379i | \(-0.802904\pi\) |
0.317682 | − | 0.948197i | \(-0.397096\pi\) | |||||||
\(998\) | 17.8331 | − | 54.8846i | 0.564497 | − | 1.73734i | ||||
\(999\) | 13.8568 | + | 10.0676i | 0.438410 | + | 0.318524i |
(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 | 605.2.g.o.81.1 | 12 | ||
11.2 | odd | 10 | 605.2.g.p.511.1 | 12 | |||
11.3 | even | 5 | inner | 605.2.g.o.366.1 | 12 | ||
11.4 | even | 5 | inner | 605.2.g.o.251.3 | 12 | ||
11.5 | even | 5 | 605.2.a.h.1.3 | yes | 3 | ||
11.6 | odd | 10 | 605.2.a.g.1.1 | ✓ | 3 | ||
11.7 | odd | 10 | 605.2.g.p.251.1 | 12 | |||
11.8 | odd | 10 | 605.2.g.p.366.3 | 12 | |||
11.9 | even | 5 | inner | 605.2.g.o.511.3 | 12 | ||
11.10 | odd | 2 | 605.2.g.p.81.3 | 12 | |||
33.5 | odd | 10 | 5445.2.a.bb.1.1 | 3 | |||
33.17 | even | 10 | 5445.2.a.bd.1.3 | 3 | |||
44.27 | odd | 10 | 9680.2.a.cb.1.1 | 3 | |||
44.39 | even | 10 | 9680.2.a.bz.1.1 | 3 | |||
55.39 | odd | 10 | 3025.2.a.u.1.3 | 3 | |||
55.49 | even | 10 | 3025.2.a.p.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.1 | ✓ | 3 | 11.6 | odd | 10 | ||
605.2.a.h.1.3 | yes | 3 | 11.5 | even | 5 | ||
605.2.g.o.81.1 | 12 | 1.1 | even | 1 | trivial | ||
605.2.g.o.251.3 | 12 | 11.4 | even | 5 | inner | ||
605.2.g.o.366.1 | 12 | 11.3 | even | 5 | inner | ||
605.2.g.o.511.3 | 12 | 11.9 | even | 5 | inner | ||
605.2.g.p.81.3 | 12 | 11.10 | odd | 2 | |||
605.2.g.p.251.1 | 12 | 11.7 | odd | 10 | |||
605.2.g.p.366.3 | 12 | 11.8 | odd | 10 | |||
605.2.g.p.511.1 | 12 | 11.2 | odd | 10 | |||
3025.2.a.p.1.1 | 3 | 55.49 | even | 10 | |||
3025.2.a.u.1.3 | 3 | 55.39 | odd | 10 | |||
5445.2.a.bb.1.1 | 3 | 33.5 | odd | 10 | |||
5445.2.a.bd.1.3 | 3 | 33.17 | even | 10 | |||
9680.2.a.bz.1.1 | 3 | 44.39 | even | 10 | |||
9680.2.a.cb.1.1 | 3 | 44.27 | odd | 10 |