Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11x^{14} + 85x^{12} + 334x^{10} + 952x^{8} + 1050x^{6} + 853x^{4} + 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.1 | ||
Root | \(-1.14241 - 1.97871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.i.508.1 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14241 | + | 1.97871i | −0.807803 | + | 1.39916i | 0.106579 | + | 0.994304i | \(0.466010\pi\) |
−0.914382 | + | 0.404852i | \(0.867323\pi\) | |||||||
\(3\) | −1.57521 | − | 2.72835i | −0.909448 | − | 1.57521i | −0.814832 | − | 0.579697i | \(-0.803171\pi\) |
−0.0946163 | − | 0.995514i | \(-0.530162\pi\) | |||||||
\(4\) | −1.61019 | − | 2.78892i | −0.805093 | − | 1.39446i | ||||
\(5\) | −1.06250 | + | 1.84030i | −0.475162 | + | 0.823005i | −0.999595 | − | 0.0284464i | \(-0.990944\pi\) |
0.524433 | + | 0.851452i | \(0.324277\pi\) | |||||||
\(6\) | 7.19813 | 2.93862 | ||||||||
\(7\) | 0.331665 | + | 2.62488i | 0.125358 | + | 0.992112i | ||||
\(8\) | 2.78832 | 0.985820 | ||||||||
\(9\) | −3.46258 | + | 5.99736i | −1.15419 | + | 1.99912i | ||||
\(10\) | −2.42760 | − | 4.20473i | −0.767676 | − | 1.32965i | ||||
\(11\) | −0.154233 | − | 0.267139i | −0.0465029 | − | 0.0805454i | 0.841837 | − | 0.539732i | \(-0.181474\pi\) |
−0.888340 | + | 0.459186i | \(0.848141\pi\) | |||||||
\(12\) | −5.07276 | + | 8.78629i | −1.46438 | + | 2.53638i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.57276 | − | 2.34241i | −1.48938 | − | 0.626036i | ||||
\(15\) | 6.69462 | 1.72854 | ||||||||
\(16\) | 0.0349749 | − | 0.0605784i | 0.00874373 | − | 0.0151446i | ||||
\(17\) | 0.887368 | + | 1.53697i | 0.215218 | + | 0.372769i | 0.953340 | − | 0.301898i | \(-0.0976204\pi\) |
−0.738122 | + | 0.674667i | \(0.764287\pi\) | |||||||
\(18\) | −7.91135 | − | 13.7029i | −1.86472 | − | 3.22979i | ||||
\(19\) | −0.890653 | + | 1.54266i | −0.204330 | + | 0.353909i | −0.949919 | − | 0.312496i | \(-0.898835\pi\) |
0.745589 | + | 0.666406i | \(0.232168\pi\) | |||||||
\(20\) | 6.84326 | 1.53020 | ||||||||
\(21\) | 6.63914 | − | 5.03964i | 1.44878 | − | 1.09974i | ||||
\(22\) | 0.704786 | 0.150261 | ||||||||
\(23\) | −0.575211 | + | 0.996294i | −0.119940 | + | 0.207742i | −0.919744 | − | 0.392520i | \(-0.871603\pi\) |
0.799804 | + | 0.600261i | \(0.204937\pi\) | |||||||
\(24\) | −4.39219 | − | 7.60750i | −0.896553 | − | 1.55288i | ||||
\(25\) | 0.242207 | + | 0.419515i | 0.0484414 | + | 0.0839029i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.3659 | 2.37982 | ||||||||
\(28\) | 6.78655 | − | 5.15153i | 1.28254 | − | 0.973548i | ||||
\(29\) | 2.01052 | 0.373345 | 0.186672 | − | 0.982422i | \(-0.440230\pi\) | ||||
0.186672 | + | 0.982422i | \(0.440230\pi\) | |||||||
\(30\) | −7.64798 | + | 13.2467i | −1.39632 | + | 2.41850i | ||||
\(31\) | 2.30242 | + | 3.98791i | 0.413527 | + | 0.716251i | 0.995273 | − | 0.0971205i | \(-0.0309632\pi\) |
−0.581745 | + | 0.813371i | \(0.697630\pi\) | |||||||
\(32\) | 2.86823 | + | 4.96792i | 0.507037 | + | 0.878213i | ||||
\(33\) | −0.485898 | + | 0.841600i | −0.0845840 | + | 0.146504i | ||||
\(34\) | −4.05494 | −0.695416 | ||||||||
\(35\) | −5.18295 | − | 2.17856i | −0.876078 | − | 0.368244i | ||||
\(36\) | 22.3016 | 3.71693 | ||||||||
\(37\) | 2.77071 | − | 4.79901i | 0.455502 | − | 0.788953i | −0.543215 | − | 0.839594i | \(-0.682793\pi\) |
0.998717 | + | 0.0506410i | \(0.0161264\pi\) | |||||||
\(38\) | −2.03497 | − | 3.52468i | −0.330117 | − | 0.571779i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.96258 | + | 5.13134i | −0.468425 | + | 0.811336i | ||||
\(41\) | −6.72984 | −1.05102 | −0.525512 | − | 0.850786i | \(-0.676126\pi\) | ||||
−0.525512 | + | 0.850786i | \(0.676126\pi\) | |||||||
\(42\) | 2.38737 | + | 18.8942i | 0.368379 | + | 2.91544i | ||||
\(43\) | 1.52611 | 0.232729 | 0.116365 | − | 0.993207i | \(-0.462876\pi\) | ||||
0.116365 | + | 0.993207i | \(0.462876\pi\) | |||||||
\(44\) | −0.496686 | + | 0.860286i | −0.0748783 | + | 0.129693i | ||||
\(45\) | −7.35795 | − | 12.7443i | −1.09686 | − | 1.89981i | ||||
\(46\) | −1.31425 | − | 2.27635i | −0.193776 | − | 0.335629i | ||||
\(47\) | −4.75908 | + | 8.24297i | −0.694183 | + | 1.20236i | 0.276272 | + | 0.961079i | \(0.410901\pi\) |
−0.970455 | + | 0.241281i | \(0.922432\pi\) | |||||||
\(48\) | −0.220372 | −0.0318079 | ||||||||
\(49\) | −6.78000 | + | 1.74116i | −0.968571 | + | 0.248738i | ||||
\(50\) | −1.10680 | −0.156524 | ||||||||
\(51\) | 2.79558 | − | 4.84209i | 0.391460 | − | 0.678028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.72037 | − | 6.44387i | −0.511032 | − | 0.885134i | −0.999918 | − | 0.0127862i | \(-0.995930\pi\) |
0.488886 | − | 0.872348i | \(-0.337403\pi\) | |||||||
\(54\) | −14.1269 | + | 24.4685i | −1.92243 | + | 3.32974i | ||||
\(55\) | 0.655486 | 0.0883857 | ||||||||
\(56\) | 0.924789 | + | 7.31901i | 0.123580 | + | 0.978044i | ||||
\(57\) | 5.61186 | 0.743309 | ||||||||
\(58\) | −2.29683 | + | 3.97823i | −0.301589 | + | 0.522368i | ||||
\(59\) | 4.06053 | + | 7.03304i | 0.528636 | + | 0.915624i | 0.999442 | + | 0.0333877i | \(0.0106296\pi\) |
−0.470807 | + | 0.882236i | \(0.656037\pi\) | |||||||
\(60\) | −10.7796 | − | 18.6708i | −1.39164 | − | 2.41039i | ||||
\(61\) | 1.72037 | − | 2.97977i | 0.220271 | − | 0.381521i | −0.734619 | − | 0.678480i | \(-0.762639\pi\) |
0.954890 | + | 0.296959i | \(0.0959725\pi\) | |||||||
\(62\) | −10.5212 | −1.33620 | ||||||||
\(63\) | −16.8908 | − | 7.09974i | −2.12804 | − | 0.894483i | ||||
\(64\) | −12.9669 | −1.62086 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.11019 | − | 1.92290i | −0.136654 | − | 0.236692i | ||||
\(67\) | −6.30747 | − | 10.9249i | −0.770580 | − | 1.33468i | −0.937245 | − | 0.348671i | \(-0.886633\pi\) |
0.166665 | − | 0.986014i | \(-0.446700\pi\) | |||||||
\(68\) | 2.85765 | − | 4.94960i | 0.346541 | − | 0.600227i | ||||
\(69\) | 3.62431 | 0.436316 | ||||||||
\(70\) | 10.2318 | − | 7.76673i | 1.22293 | − | 0.928302i | ||||
\(71\) | −1.35070 | −0.160299 | −0.0801494 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801494 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(72\) | −9.65478 | + | 16.7226i | −1.13783 | + | 1.97077i | ||||
\(73\) | −5.94059 | − | 10.2894i | −0.695293 | − | 1.20428i | −0.970082 | − | 0.242778i | \(-0.921941\pi\) |
0.274789 | − | 0.961505i | \(-0.411392\pi\) | |||||||
\(74\) | 6.33056 | + | 10.9648i | 0.735912 | + | 1.27464i | ||||
\(75\) | 0.763054 | − | 1.32165i | 0.0881099 | − | 0.152611i | ||||
\(76\) | 5.73646 | 0.658018 | ||||||||
\(77\) | 0.650054 | − | 0.493443i | 0.0740805 | − | 0.0562330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.96258 | − | 6.86339i | 0.445825 | − | 0.772191i | −0.552284 | − | 0.833656i | \(-0.686244\pi\) |
0.998109 | + | 0.0614644i | \(0.0195771\pi\) | |||||||
\(80\) | 0.0743214 | + | 0.128728i | 0.00830939 | + | 0.0143923i | ||||
\(81\) | −9.09116 | − | 15.7464i | −1.01013 | − | 1.74960i | ||||
\(82\) | 7.68821 | − | 13.3164i | 0.849021 | − | 1.47055i | ||||
\(83\) | −11.2290 | −1.23255 | −0.616273 | − | 0.787533i | \(-0.711358\pi\) | ||||
−0.616273 | + | 0.787533i | \(0.711358\pi\) | |||||||
\(84\) | −24.7454 | − | 10.4013i | −2.69995 | − | 1.13487i | ||||
\(85\) | −3.77130 | −0.409055 | ||||||||
\(86\) | −1.74344 | + | 3.01972i | −0.188000 | + | 0.325625i | ||||
\(87\) | −3.16700 | − | 5.48540i | −0.339538 | − | 0.588096i | ||||
\(88\) | −0.430050 | − | 0.744869i | −0.0458435 | − | 0.0794033i | ||||
\(89\) | 0.829583 | − | 1.43688i | 0.0879357 | − | 0.152309i | −0.818703 | − | 0.574218i | \(-0.805306\pi\) |
0.906638 | + | 0.421909i | \(0.138640\pi\) | |||||||
\(90\) | 33.6231 | 3.54418 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.70479 | 0.386251 | ||||||||
\(93\) | 7.25360 | − | 12.5636i | 0.752164 | − | 1.30279i | ||||
\(94\) | −10.8736 | − | 18.8336i | −1.12153 | − | 1.94254i | ||||
\(95\) | −1.89263 | − | 3.27813i | −0.194180 | − | 0.336329i | ||||
\(96\) | 9.03614 | − | 15.6511i | 0.922247 | − | 1.59738i | ||||
\(97\) | −7.66641 | −0.778406 | −0.389203 | − | 0.921152i | \(-0.627250\pi\) | ||||
−0.389203 | + | 0.921152i | \(0.627250\pi\) | |||||||
\(98\) | 4.30026 | − | 15.4047i | 0.434392 | − | 1.55611i | ||||
\(99\) | 2.13617 | 0.214693 | ||||||||
\(100\) | 0.779996 | − | 1.35099i | 0.0779996 | − | 0.135099i | ||||
\(101\) | −4.55864 | − | 7.89579i | −0.453601 | − | 0.785660i | 0.545005 | − | 0.838433i | \(-0.316528\pi\) |
−0.998607 | + | 0.0527721i | \(0.983194\pi\) | |||||||
\(102\) | 6.38738 | + | 11.0633i | 0.632445 | + | 1.09543i | ||||
\(103\) | −3.02085 | + | 5.23226i | −0.297653 | + | 0.515550i | −0.975599 | − | 0.219562i | \(-0.929537\pi\) |
0.677946 | + | 0.735112i | \(0.262870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.22037 | + | 17.5726i | 0.216686 | + | 1.71491i | ||||
\(106\) | 17.0007 | 1.65125 | ||||||||
\(107\) | −6.04305 | + | 10.4669i | −0.584204 | + | 1.01187i | 0.410770 | + | 0.911739i | \(0.365260\pi\) |
−0.994974 | + | 0.100132i | \(0.968074\pi\) | |||||||
\(108\) | −19.9114 | − | 34.4876i | −1.91598 | − | 3.31857i | ||||
\(109\) | −0.680941 | − | 1.17942i | −0.0652223 | − | 0.112968i | 0.831570 | − | 0.555420i | \(-0.187442\pi\) |
−0.896793 | + | 0.442451i | \(0.854109\pi\) | |||||||
\(110\) | −0.748831 | + | 1.29701i | −0.0713983 | + | 0.123665i | ||||
\(111\) | −17.4578 | −1.65702 | ||||||||
\(112\) | 0.170611 | + | 0.0717133i | 0.0161212 | + | 0.00677627i | ||||
\(113\) | −9.42009 | −0.886168 | −0.443084 | − | 0.896480i | \(-0.646116\pi\) | ||||
−0.443084 | + | 0.896480i | \(0.646116\pi\) | |||||||
\(114\) | −6.41103 | + | 11.1042i | −0.600448 | + | 1.04001i | ||||
\(115\) | −1.22232 | − | 2.11712i | −0.113982 | − | 0.197422i | ||||
\(116\) | −3.23731 | − | 5.60719i | −0.300577 | − | 0.520615i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.5551 | −1.70814 | ||||||||
\(119\) | −3.74004 | + | 2.83899i | −0.342849 | + | 0.260250i | ||||
\(120\) | 18.6667 | 1.70403 | ||||||||
\(121\) | 5.45242 | − | 9.44388i | 0.495675 | − | 0.858534i | ||||
\(122\) | 3.93073 | + | 6.80822i | 0.355871 | + | 0.616387i | ||||
\(123\) | 10.6009 | + | 18.3613i | 0.955852 | + | 1.65558i | ||||
\(124\) | 7.41466 | − | 12.8426i | 0.665856 | − | 1.15330i | ||||
\(125\) | −11.6543 | −1.04239 | ||||||||
\(126\) | 33.3444 | − | 25.3111i | 2.97056 | − | 2.25489i | ||||
\(127\) | −13.3998 | −1.18904 | −0.594519 | − | 0.804081i | \(-0.702658\pi\) | ||||
−0.594519 | + | 0.804081i | \(0.702658\pi\) | |||||||
\(128\) | 9.07695 | − | 15.7217i | 0.802297 | − | 1.38962i | ||||
\(129\) | −2.40394 | − | 4.16375i | −0.211655 | − | 0.366598i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.69854 | + | 11.6022i | −0.585254 | + | 1.01369i | 0.409590 | + | 0.912270i | \(0.365672\pi\) |
−0.994844 | + | 0.101420i | \(0.967662\pi\) | |||||||
\(132\) | 3.12954 | 0.272392 | ||||||||
\(133\) | −4.34469 | − | 1.82621i | −0.376732 | − | 0.158353i | ||||
\(134\) | 28.8228 | 2.48991 | ||||||||
\(135\) | −13.1387 | + | 22.7569i | −1.13080 | + | 1.95860i | ||||
\(136\) | 2.47427 | + | 4.28555i | 0.212167 | + | 0.367483i | ||||
\(137\) | −0.250522 | − | 0.433917i | −0.0214036 | − | 0.0370720i | 0.855125 | − | 0.518421i | \(-0.173480\pi\) |
−0.876529 | + | 0.481349i | \(0.840147\pi\) | |||||||
\(138\) | −4.14044 | + | 7.17145i | −0.352458 | + | 0.610475i | ||||
\(139\) | 1.41936 | 0.120388 | 0.0601941 | − | 0.998187i | \(-0.480828\pi\) | ||||
0.0601941 | + | 0.998187i | \(0.480828\pi\) | |||||||
\(140\) | 2.26967 | + | 17.9627i | 0.191822 | + | 1.51813i | ||||
\(141\) | 29.9862 | 2.52529 | ||||||||
\(142\) | 1.54305 | − | 2.67264i | 0.129490 | − | 0.224283i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.242207 | + | 0.419515i | 0.0201839 | + | 0.0349596i | ||||
\(145\) | −2.13617 | + | 3.69996i | −0.177399 | + | 0.307265i | ||||
\(146\) | 27.1463 | 2.24664 | ||||||||
\(147\) | 15.4304 | + | 15.7555i | 1.27268 | + | 1.29949i | ||||
\(148\) | −17.8454 | −1.46689 | ||||||||
\(149\) | 10.5454 | − | 18.2652i | 0.863916 | − | 1.49635i | −0.00420426 | − | 0.999991i | \(-0.501338\pi\) |
0.868120 | − | 0.496355i | \(-0.165328\pi\) | |||||||
\(150\) | 1.74344 | + | 3.01972i | 0.142351 | + | 0.246559i | ||||
\(151\) | 8.75211 | + | 15.1591i | 0.712236 | + | 1.23363i | 0.964016 | + | 0.265845i | \(0.0856510\pi\) |
−0.251779 | + | 0.967785i | \(0.581016\pi\) | |||||||
\(152\) | −2.48343 | + | 4.30142i | −0.201432 | + | 0.348891i | ||||
\(153\) | −12.2903 | −0.993614 | ||||||||
\(154\) | 0.233753 | + | 1.84998i | 0.0188363 | + | 0.149075i | ||||
\(155\) | −9.78526 | −0.785971 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0377894 | − | 0.0654532i | −0.00301593 | − | 0.00522374i | 0.864514 | − | 0.502610i | \(-0.167627\pi\) |
−0.867529 | + | 0.497386i | \(0.834293\pi\) | |||||||
\(158\) | 9.05375 | + | 15.6816i | 0.720278 | + | 1.24756i | ||||
\(159\) | −11.7207 | + | 20.3009i | −0.929515 | + | 1.60997i | ||||
\(160\) | −12.1899 | −0.963699 | ||||||||
\(161\) | −2.80593 | − | 1.17942i | −0.221138 | − | 0.0929516i | ||||
\(162\) | 41.5432 | 3.26394 | ||||||||
\(163\) | 5.04086 | − | 8.73102i | 0.394830 | − | 0.683866i | −0.598249 | − | 0.801310i | \(-0.704137\pi\) |
0.993080 | + | 0.117444i | \(0.0374701\pi\) | |||||||
\(164\) | 10.8363 | + | 18.7690i | 0.846172 | + | 1.46561i | ||||
\(165\) | −1.03253 | − | 1.78839i | −0.0803822 | − | 0.139226i | ||||
\(166\) | 12.8281 | − | 22.2189i | 0.995655 | − | 1.72452i | ||||
\(167\) | −5.84989 | −0.452678 | −0.226339 | − | 0.974049i | \(-0.572676\pi\) | ||||
−0.226339 | + | 0.974049i | \(0.572676\pi\) | |||||||
\(168\) | 18.5120 | − | 14.0521i | 1.42824 | − | 1.08415i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.30835 | − | 7.46229i | 0.330436 | − | 0.572331i | ||||
\(171\) | −6.16791 | − | 10.6831i | −0.471672 | − | 0.816960i | ||||
\(172\) | −2.45732 | − | 4.25620i | −0.187369 | − | 0.324532i | ||||
\(173\) | −8.49511 | + | 14.7140i | −0.645871 | + | 1.11868i | 0.338229 | + | 0.941064i | \(0.390172\pi\) |
−0.984100 | + | 0.177617i | \(0.943161\pi\) | |||||||
\(174\) | 14.4720 | 1.09712 | ||||||||
\(175\) | −1.02084 | + | 0.774903i | −0.0771686 | + | 0.0585771i | ||||
\(176\) | −0.0215771 | −0.00162644 | ||||||||
\(177\) | 12.7924 | − | 22.1570i | 0.961534 | − | 1.66543i | ||||
\(178\) | 1.89544 | + | 3.28300i | 0.142069 | + | 0.246072i | ||||
\(179\) | 7.65079 | + | 13.2516i | 0.571847 | + | 0.990468i | 0.996376 | + | 0.0850537i | \(0.0271062\pi\) |
−0.424529 | + | 0.905414i | \(0.639560\pi\) | |||||||
\(180\) | −23.6953 | + | 41.0415i | −1.76615 | + | 3.05905i | ||||
\(181\) | 5.84958 | 0.434796 | 0.217398 | − | 0.976083i | \(-0.430243\pi\) | ||||
0.217398 | + | 0.976083i | \(0.430243\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8398 | −0.801301 | ||||||||
\(184\) | −1.60387 | + | 2.77799i | −0.118239 | + | 0.204796i | ||||
\(185\) | 5.88774 | + | 10.1979i | 0.432875 | + | 0.749761i | ||||
\(186\) | 16.5731 | + | 28.7055i | 1.21520 | + | 2.10479i | ||||
\(187\) | 0.273722 | − | 0.474101i | 0.0200165 | − | 0.0346697i | ||||
\(188\) | 30.6520 | 2.23553 | ||||||||
\(189\) | 4.10134 | + | 32.4590i | 0.298329 | + | 2.36105i | ||||
\(190\) | 8.64861 | 0.627436 | ||||||||
\(191\) | 13.4090 | − | 23.2250i | 0.970238 | − | 1.68050i | 0.275407 | − | 0.961328i | \(-0.411188\pi\) |
0.694831 | − | 0.719173i | \(-0.255479\pi\) | |||||||
\(192\) | 20.4255 | + | 35.3780i | 1.47409 | + | 2.55319i | ||||
\(193\) | 0.106992 | + | 0.185315i | 0.00770145 | + | 0.0133393i | 0.869850 | − | 0.493316i | \(-0.164215\pi\) |
−0.862149 | + | 0.506655i | \(0.830882\pi\) | |||||||
\(194\) | 8.75816 | − | 15.1696i | 0.628799 | − | 1.08911i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7730 | + | 16.1053i | 1.12664 | + | 1.15038i | ||||
\(197\) | 11.2290 | 0.800035 | 0.400017 | − | 0.916508i | \(-0.369004\pi\) | ||||
0.400017 | + | 0.916508i | \(0.369004\pi\) | |||||||
\(198\) | −2.44038 | + | 4.22685i | −0.173430 | + | 0.300389i | ||||
\(199\) | −10.2100 | − | 17.6843i | −0.723771 | − | 1.25361i | −0.959478 | − | 0.281784i | \(-0.909074\pi\) |
0.235707 | − | 0.971824i | \(-0.424259\pi\) | |||||||
\(200\) | 0.675351 | + | 1.16974i | 0.0477545 | + | 0.0827132i | ||||
\(201\) | −19.8712 | + | 34.4179i | −1.40161 | + | 2.42765i | ||||
\(202\) | 20.8313 | 1.46568 | ||||||||
\(203\) | 0.666820 | + | 5.27738i | 0.0468016 | + | 0.370399i | ||||
\(204\) | −18.0056 | −1.26065 | ||||||||
\(205\) | 7.15042 | − | 12.3849i | 0.499407 | − | 0.864999i | ||||
\(206\) | −6.90207 | − | 11.9547i | −0.480890 | − | 0.832926i | ||||
\(207\) | −3.98343 | − | 6.89950i | −0.276867 | − | 0.479548i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.549471 | 0.0380077 | ||||||||
\(210\) | −37.3075 | − | 15.6816i | −2.57446 | − | 1.08213i | ||||
\(211\) | 8.41738 | 0.579476 | 0.289738 | − | 0.957106i | \(-0.406432\pi\) | ||||
0.289738 | + | 0.957106i | \(0.406432\pi\) | |||||||
\(212\) | −11.9810 | + | 20.7517i | −0.822857 | + | 1.42523i | ||||
\(213\) | 2.12764 | + | 3.68518i | 0.145783 | + | 0.252504i | ||||
\(214\) | −13.8072 | − | 23.9148i | −0.943844 | − | 1.63479i | ||||
\(215\) | −1.62148 | + | 2.80849i | −0.110584 | + | 0.191537i | ||||
\(216\) | 34.4801 | 2.34607 | ||||||||
\(217\) | −9.70417 | + | 7.36624i | −0.658762 | + | 0.500053i | ||||
\(218\) | 3.11164 | 0.210747 | ||||||||
\(219\) | −18.7154 | + | 32.4159i | −1.26467 | + | 2.19047i | ||||
\(220\) | −1.05545 | − | 1.82810i | −0.0711587 | − | 0.123250i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 19.9439 | − | 34.5439i | 1.33855 | − | 2.31843i | ||||
\(223\) | 13.6091 | 0.911333 | 0.455666 | − | 0.890151i | \(-0.349401\pi\) | ||||
0.455666 | + | 0.890151i | \(0.349401\pi\) | |||||||
\(224\) | −12.0889 | + | 9.17646i | −0.807725 | + | 0.613128i | ||||
\(225\) | −3.35464 | −0.223643 | ||||||||
\(226\) | 10.7616 | − | 18.6396i | 0.715849 | − | 1.23989i | ||||
\(227\) | 1.80138 | + | 3.12008i | 0.119562 | + | 0.207087i | 0.919594 | − | 0.392870i | \(-0.128518\pi\) |
−0.800032 | + | 0.599957i | \(0.795184\pi\) | |||||||
\(228\) | −9.03614 | − | 15.6511i | −0.598433 | − | 1.03652i | ||||
\(229\) | 9.19208 | − | 15.9212i | 0.607430 | − | 1.05210i | −0.384232 | − | 0.923236i | \(-0.625534\pi\) |
0.991662 | − | 0.128863i | \(-0.0411328\pi\) | |||||||
\(230\) | 5.58554 | 0.368299 | ||||||||
\(231\) | −2.37025 | − | 0.996294i | −0.155951 | − | 0.0655514i | ||||
\(232\) | 5.60598 | 0.368051 | ||||||||
\(233\) | −10.1348 | + | 17.5541i | −0.663955 | + | 1.15000i | 0.315612 | + | 0.948888i | \(0.397790\pi\) |
−0.979567 | + | 0.201116i | \(0.935543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1130 | − | 17.5162i | −0.659699 | − | 1.14263i | ||||
\(236\) | 13.0764 | − | 22.6490i | 0.851202 | − | 1.47432i | ||||
\(237\) | −24.9676 | −1.62182 | ||||||||
\(238\) | −1.34488 | − | 10.6437i | −0.0871758 | − | 0.689931i | ||||
\(239\) | −20.8097 | −1.34607 | −0.673033 | − | 0.739612i | \(-0.735009\pi\) | ||||
−0.673033 | + | 0.739612i | \(0.735009\pi\) | |||||||
\(240\) | 0.234144 | − | 0.405549i | 0.0151139 | − | 0.0261781i | ||||
\(241\) | −6.35736 | − | 11.0113i | −0.409514 | − | 0.709299i | 0.585322 | − | 0.810801i | \(-0.300968\pi\) |
−0.994835 | + | 0.101503i | \(0.967635\pi\) | |||||||
\(242\) | 12.4578 | + | 21.5775i | 0.800816 | + | 1.38705i | ||||
\(243\) | −10.0922 | + | 17.4801i | −0.647412 | + | 1.12135i | ||||
\(244\) | −11.0805 | −0.709355 | ||||||||
\(245\) | 3.99946 | − | 14.3272i | 0.255516 | − | 0.915330i | ||||
\(246\) | −48.4422 | −3.08856 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.41990 | + | 11.1196i | 0.407664 | + | 0.706094i | ||||
\(249\) | 17.6881 | + | 30.6367i | 1.12094 | + | 1.94152i | ||||
\(250\) | 13.3140 | − | 23.0605i | 0.842050 | − | 1.45847i | ||||
\(251\) | 13.7436 | 0.867486 | 0.433743 | − | 0.901037i | \(-0.357193\pi\) | ||||
0.433743 | + | 0.901037i | \(0.357193\pi\) | |||||||
\(252\) | 7.39666 | + | 58.5390i | 0.465946 | + | 3.68761i | ||||
\(253\) | 0.354865 | 0.0223102 | ||||||||
\(254\) | 15.3080 | − | 26.5142i | 0.960510 | − | 1.66365i | ||||
\(255\) | 5.94059 | + | 10.2894i | 0.372014 | + | 0.644347i | ||||
\(256\) | 7.77229 | + | 13.4620i | 0.485768 | + | 0.841375i | ||||
\(257\) | 3.66736 | − | 6.35206i | 0.228764 | − | 0.396231i | −0.728678 | − | 0.684856i | \(-0.759865\pi\) |
0.957442 | + | 0.288626i | \(0.0931983\pi\) | |||||||
\(258\) | 10.9851 | 0.683904 | ||||||||
\(259\) | 13.5158 | + | 5.68112i | 0.839830 | + | 0.353008i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.96159 | + | 12.0578i | −0.430912 | + | 0.746361i | ||||
\(262\) | −15.3049 | − | 26.5089i | −0.945540 | − | 1.63772i | ||||
\(263\) | 3.33942 | + | 5.78405i | 0.205918 | + | 0.356660i | 0.950425 | − | 0.310955i | \(-0.100649\pi\) |
−0.744507 | + | 0.667615i | \(0.767315\pi\) | |||||||
\(264\) | −1.35484 | + | 2.34665i | −0.0833846 | + | 0.144426i | ||||
\(265\) | 15.8115 | 0.971293 | ||||||||
\(266\) | 8.57693 | − | 6.51058i | 0.525886 | − | 0.399189i | ||||
\(267\) | −5.22708 | −0.319892 | ||||||||
\(268\) | −20.3124 | + | 35.1821i | −1.24078 | + | 2.14909i | ||||
\(269\) | −8.11263 | − | 14.0515i | −0.494636 | − | 0.856735i | 0.505345 | − | 0.862917i | \(-0.331365\pi\) |
−0.999981 | + | 0.00618287i | \(0.998032\pi\) | |||||||
\(270\) | −30.0195 | − | 51.9953i | −1.82693 | − | 3.16433i | ||||
\(271\) | −9.36904 | + | 16.2277i | −0.569129 | + | 0.985760i | 0.427524 | + | 0.904004i | \(0.359386\pi\) |
−0.996652 | + | 0.0817555i | \(0.973947\pi\) | |||||||
\(272\) | 0.124143 | 0.00752725 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.14479 | 0.0691595 | ||||||||
\(275\) | 0.0747124 | − | 0.129406i | 0.00450533 | − | 0.00780346i | ||||
\(276\) | −5.83582 | − | 10.1079i | −0.351275 | − | 0.608426i | ||||
\(277\) | −15.0163 | − | 26.0090i | −0.902243 | − | 1.56273i | −0.824575 | − | 0.565752i | \(-0.808586\pi\) |
−0.0776679 | − | 0.996979i | \(-0.524747\pi\) | |||||||
\(278\) | −1.62148 | + | 2.80849i | −0.0972501 | + | 0.168442i | ||||
\(279\) | −31.8893 | −1.90916 | ||||||||
\(280\) | −14.4517 | − | 6.07453i | −0.863656 | − | 0.363023i | ||||
\(281\) | −2.23065 | −0.133070 | −0.0665348 | − | 0.997784i | \(-0.521194\pi\) | ||||
−0.0665348 | + | 0.997784i | \(0.521194\pi\) | |||||||
\(282\) | −34.2565 | + | 59.3339i | −2.03994 | + | 3.53328i | ||||
\(283\) | −6.88774 | − | 11.9299i | −0.409433 | − | 0.709159i | 0.585393 | − | 0.810750i | \(-0.300940\pi\) |
−0.994826 | + | 0.101590i | \(0.967607\pi\) | |||||||
\(284\) | 2.17488 | + | 3.76700i | 0.129055 | + | 0.223531i | ||||
\(285\) | −5.96258 | + | 10.3275i | −0.353193 | + | 0.611748i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.23205 | − | 17.6650i | −0.131754 | − | 1.04273i | ||||
\(288\) | −39.7259 | −2.34087 | ||||||||
\(289\) | 6.92516 | − | 11.9947i | 0.407362 | − | 0.705572i | ||||
\(290\) | −4.88075 | − | 8.45371i | −0.286608 | − | 0.496419i | ||||
\(291\) | 12.0762 | + | 20.9166i | 0.707920 | + | 1.22615i | ||||
\(292\) | −19.1309 | + | 33.1357i | −1.11955 | + | 1.93912i | ||||
\(293\) | 1.01231 | 0.0591400 | 0.0295700 | − | 0.999563i | \(-0.490586\pi\) | ||||
0.0295700 | + | 0.999563i | \(0.490586\pi\) | |||||||
\(294\) | −48.8033 | + | 12.5331i | −2.84626 | + | 0.730946i | ||||
\(295\) | −17.2572 | −1.00475 | ||||||||
\(296\) | 7.72563 | − | 13.3812i | 0.449043 | − | 0.777766i | ||||
\(297\) | −1.90723 | − | 3.30341i | −0.110668 | − | 0.191683i | ||||
\(298\) | 24.0943 | + | 41.7326i | 1.39575 | + | 2.41751i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.91464 | −0.283747 | ||||||||
\(301\) | 0.506157 | + | 4.00585i | 0.0291744 | + | 0.230893i | ||||
\(302\) | −39.9939 | −2.30139 | ||||||||
\(303\) | −14.3616 | + | 24.8751i | −0.825054 | + | 1.42904i | ||||
\(304\) | 0.0623010 | + | 0.107909i | 0.00357321 | + | 0.00618898i | ||||
\(305\) | 3.65577 | + | 6.33199i | 0.209329 | + | 0.362568i | ||||
\(306\) | 14.0405 | − | 24.3189i | 0.802645 | − | 1.39022i | ||||
\(307\) | −24.0527 | −1.37276 | −0.686379 | − | 0.727244i | \(-0.740801\pi\) | ||||
−0.686379 | + | 0.727244i | \(0.740801\pi\) | |||||||
\(308\) | −2.42288 | − | 1.01842i | −0.138057 | − | 0.0580296i | ||||
\(309\) | 19.0339 | 1.08280 | ||||||||
\(310\) | 11.1787 | − | 19.3622i | 0.634910 | − | 1.09970i | ||||
\(311\) | 4.49548 | + | 7.78639i | 0.254915 | + | 0.441526i | 0.964872 | − | 0.262719i | \(-0.0846192\pi\) |
−0.709957 | + | 0.704245i | \(0.751286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.61806 | − | 13.1949i | 0.430598 | − | 0.745818i | −0.566326 | − | 0.824181i | \(-0.691636\pi\) |
0.996925 | + | 0.0783626i | \(0.0249692\pi\) | |||||||
\(314\) | 0.172684 | 0.00974510 | ||||||||
\(315\) | 31.0120 | − | 23.5406i | 1.74733 | − | 1.32636i | ||||
\(316\) | −25.5220 | −1.43572 | ||||||||
\(317\) | 3.41775 | − | 5.91972i | 0.191960 | − | 0.332484i | −0.753940 | − | 0.656944i | \(-0.771849\pi\) |
0.945900 | + | 0.324459i | \(0.105182\pi\) | |||||||
\(318\) | −26.7797 | − | 46.3838i | −1.50173 | − | 2.60107i | ||||
\(319\) | −0.310088 | − | 0.537088i | −0.0173616 | − | 0.0300712i | ||||
\(320\) | 13.7772 | − | 23.8628i | 0.770170 | − | 1.33397i | ||||
\(321\) | 38.0763 | 2.12521 | ||||||||
\(322\) | 5.53925 | − | 4.20473i | 0.308690 | − | 0.234321i | ||||
\(323\) | −3.16135 | −0.175902 | ||||||||
\(324\) | −29.2769 | + | 50.7091i | −1.62650 | + | 2.81717i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.5174 | + | 19.9487i | 0.637890 | + | 1.10486i | ||||
\(327\) | −2.14525 | + | 3.71568i | −0.118633 | + | 0.205478i | ||||
\(328\) | −18.7649 | −1.03612 | ||||||||
\(329\) | −23.2152 | − | 9.75811i | −1.27990 | − | 0.537982i | ||||
\(330\) | 4.71827 | 0.259732 | ||||||||
\(331\) | 6.90727 | − | 11.9637i | 0.379658 | − | 0.657587i | −0.611354 | − | 0.791357i | \(-0.709375\pi\) |
0.991012 | + | 0.133770i | \(0.0427084\pi\) | |||||||
\(332\) | 18.0808 | + | 31.3169i | 0.992314 | + | 1.71874i | ||||
\(333\) | 19.1876 | + | 33.2339i | 1.05147 | + | 1.82121i | ||||
\(334\) | 6.68295 | − | 11.5752i | 0.365675 | − | 0.633367i | ||||
\(335\) | 26.8066 | 1.46460 | ||||||||
\(336\) | −0.0730896 | − | 0.578449i | −0.00398736 | − | 0.0315570i | ||||
\(337\) | 27.0432 | 1.47314 | 0.736568 | − | 0.676364i | \(-0.236445\pi\) | ||||
0.736568 | + | 0.676364i | \(0.236445\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.8386 | + | 25.7013i | 0.805924 | + | 1.39590i | ||||
\(340\) | 6.07249 | + | 10.5179i | 0.329327 | + | 0.570411i | ||||
\(341\) | 0.710218 | − | 1.23013i | 0.0384604 | − | 0.0666154i | ||||
\(342\) | 28.1850 | 1.52407 | ||||||||
\(343\) | −6.81903 | − | 17.2192i | −0.368193 | − | 0.929749i | ||||
\(344\) | 4.25528 | 0.229429 | ||||||||
\(345\) | −3.85082 | + | 6.66981i | −0.207321 | + | 0.359091i | ||||
\(346\) | −19.4097 | − | 33.6186i | −1.04347 | − | 1.80735i | ||||
\(347\) | 9.65568 | + | 16.7241i | 0.518344 | + | 0.897799i | 0.999773 | + | 0.0213132i | \(0.00678472\pi\) |
−0.481429 | + | 0.876485i | \(0.659882\pi\) | |||||||
\(348\) | −10.1989 | + | 17.6650i | −0.546719 | + | 0.946944i | ||||
\(349\) | 14.1573 | 0.757821 | 0.378911 | − | 0.925433i | \(-0.376299\pi\) | ||||
0.378911 | + | 0.925433i | \(0.376299\pi\) | |||||||
\(350\) | −0.367085 | − | 2.90521i | −0.0196215 | − | 0.155290i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.884750 | − | 1.53243i | 0.0471573 | − | 0.0816789i | ||||
\(353\) | −8.48235 | − | 14.6919i | −0.451470 | − | 0.781969i | 0.547008 | − | 0.837128i | \(-0.315767\pi\) |
−0.998478 | + | 0.0551585i | \(0.982434\pi\) | |||||||
\(354\) | 29.2282 | + | 50.6247i | 1.55346 | + | 2.69067i | ||||
\(355\) | 1.43511 | − | 2.48569i | 0.0761680 | − | 0.131927i | ||||
\(356\) | −5.34313 | −0.283186 | ||||||||
\(357\) | 13.6371 | + | 5.73212i | 0.721752 | + | 0.303376i | ||||
\(358\) | −34.9613 | −1.84776 | ||||||||
\(359\) | 11.3816 | − | 19.7136i | 0.600700 | − | 1.04044i | −0.392016 | − | 0.919959i | \(-0.628222\pi\) |
0.992715 | − | 0.120484i | \(-0.0384446\pi\) | |||||||
\(360\) | −20.5163 | − | 35.5353i | −1.08131 | − | 1.87288i | ||||
\(361\) | 7.91348 | + | 13.7065i | 0.416499 | + | 0.721397i | ||||
\(362\) | −6.68260 | + | 11.5746i | −0.351229 | + | 0.608347i | ||||
\(363\) | −34.3549 | −1.80316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.2474 | 1.32151 | ||||||||
\(366\) | 12.3835 | − | 21.4488i | 0.647293 | − | 1.12114i | ||||
\(367\) | −8.29168 | − | 14.3616i | −0.432822 | − | 0.749670i | 0.564293 | − | 0.825575i | \(-0.309149\pi\) |
−0.997115 | + | 0.0759048i | \(0.975815\pi\) | |||||||
\(368\) | 0.0402359 | + | 0.0696907i | 0.00209744 | + | 0.00363288i | ||||
\(369\) | 23.3026 | − | 40.3613i | 1.21308 | − | 2.10112i | ||||
\(370\) | −26.9048 | −1.39871 | ||||||||
\(371\) | 15.6805 | − | 11.9027i | 0.814090 | − | 0.617959i | ||||
\(372\) | −46.7186 | −2.42225 | ||||||||
\(373\) | −13.8230 | + | 23.9422i | −0.715730 | + | 1.23968i | 0.246947 | + | 0.969029i | \(0.420573\pi\) |
−0.962677 | + | 0.270652i | \(0.912761\pi\) | |||||||
\(374\) | 0.625404 | + | 1.08323i | 0.0323389 | + | 0.0560126i | ||||
\(375\) | 18.3580 | + | 31.7970i | 0.948004 | + | 1.64199i | ||||
\(376\) | −13.2698 | + | 22.9840i | −0.684340 | + | 1.18531i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −68.9122 | − | 28.9660i | −3.54446 | − | 1.48985i | ||||
\(379\) | −9.24228 | −0.474744 | −0.237372 | − | 0.971419i | \(-0.576286\pi\) | ||||
−0.237372 | + | 0.971419i | \(0.576286\pi\) | |||||||
\(380\) | −6.09497 | + | 10.5568i | −0.312665 | + | 0.541552i | ||||
\(381\) | 21.1075 | + | 36.5592i | 1.08137 | + | 1.87299i | ||||
\(382\) | 30.6369 | + | 53.0648i | 1.56752 | + | 2.71503i | ||||
\(383\) | −3.82413 | + | 6.62358i | −0.195404 | + | 0.338449i | −0.947033 | − | 0.321137i | \(-0.895935\pi\) |
0.751629 | + | 0.659586i | \(0.229268\pi\) | |||||||
\(384\) | −57.1925 | −2.91859 | ||||||||
\(385\) | 0.217402 | + | 1.72057i | 0.0110798 | + | 0.0876885i | ||||
\(386\) | −0.488913 | −0.0248850 | ||||||||
\(387\) | −5.28427 | + | 9.15262i | −0.268614 | + | 0.465254i | ||||
\(388\) | 12.3443 | + | 21.3810i | 0.626689 | + | 1.08546i | ||||
\(389\) | −3.26868 | − | 5.66153i | −0.165729 | − | 0.287051i | 0.771185 | − | 0.636611i | \(-0.219664\pi\) |
−0.936914 | + | 0.349560i | \(0.886331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.04169 | −0.103253 | ||||||||
\(392\) | −18.9048 | + | 4.85492i | −0.954837 | + | 0.245211i | ||||
\(393\) | 42.2064 | 2.12903 | ||||||||
\(394\) | −12.8281 | + | 22.2189i | −0.646271 | + | 1.11937i | ||||
\(395\) | 8.42044 | + | 14.5846i | 0.423678 | + | 0.733833i | ||||
\(396\) | −3.43963 | − | 5.95762i | −0.172848 | − | 0.299381i | ||||
\(397\) | −14.4654 | + | 25.0548i | −0.725996 | + | 1.25746i | 0.232566 | + | 0.972581i | \(0.425288\pi\) |
−0.958563 | + | 0.284882i | \(0.908046\pi\) | |||||||
\(398\) | 46.6561 | 2.33866 | ||||||||
\(399\) | 1.86126 | + | 14.7305i | 0.0931795 | + | 0.737446i | ||||
\(400\) | 0.0338847 | 0.00169423 | ||||||||
\(401\) | −13.3716 | + | 23.1603i | −0.667747 | + | 1.15657i | 0.310786 | + | 0.950480i | \(0.399408\pi\) |
−0.978533 | + | 0.206092i | \(0.933925\pi\) | |||||||
\(402\) | −45.4020 | − | 78.6385i | −2.26444 | − | 3.92213i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.6805 | + | 25.4274i | −0.730382 | + | 1.26506i | ||||
\(405\) | 38.6373 | 1.91990 | ||||||||
\(406\) | −11.2042 | − | 4.70947i | −0.556053 | − | 0.233727i | ||||
\(407\) | −1.70934 | −0.0847287 | ||||||||
\(408\) | 7.79498 | − | 13.5013i | 0.385909 | − | 0.668414i | ||||
\(409\) | 17.3862 | + | 30.1138i | 0.859694 | + | 1.48903i | 0.872221 | + | 0.489112i | \(0.162679\pi\) |
−0.0125273 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(410\) | 16.3374 | + | 28.2972i | 0.806846 | + | 1.39750i | ||||
\(411\) | −0.789250 | + | 1.36702i | −0.0389309 | + | 0.0674302i | ||||
\(412\) | 19.4565 | 0.958553 | ||||||||
\(413\) | −17.1142 | + | 12.9910i | −0.842133 | + | 0.639246i | ||||
\(414\) | 18.2028 | 0.894617 | ||||||||
\(415\) | 11.9308 | − | 20.6647i | 0.585659 | − | 1.01439i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.23579 | − | 3.87250i | −0.109487 | − | 0.189637i | ||||
\(418\) | −0.627719 | + | 1.08724i | −0.0307027 | + | 0.0531787i | ||||
\(419\) | −4.19246 | −0.204815 | −0.102407 | − | 0.994743i | \(-0.532655\pi\) | ||||
−0.102407 | + | 0.994743i | \(0.532655\pi\) | |||||||
\(420\) | 45.4333 | − | 34.4876i | 2.21692 | − | 1.68282i | ||||
\(421\) | −20.9526 | −1.02117 | −0.510584 | − | 0.859828i | \(-0.670571\pi\) | ||||
−0.510584 | + | 0.859828i | \(0.670571\pi\) | |||||||
\(422\) | −9.61607 | + | 16.6555i | −0.468103 | + | 0.810778i | ||||
\(423\) | −32.9574 | − | 57.0838i | −1.60244 | − | 2.77551i | ||||
\(424\) | −10.3736 | − | 17.9676i | −0.503786 | − | 0.872583i | ||||
\(425\) | −0.429853 | + | 0.744528i | −0.0208509 | + | 0.0361149i | ||||
\(426\) | −9.72252 | −0.471058 | ||||||||
\(427\) | 8.39213 | + | 3.52748i | 0.406124 | + | 0.170707i | ||||
\(428\) | 38.9217 | 1.88135 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.70479 | − | 6.41688i | −0.178661 | − | 0.309449i | ||||
\(431\) | −8.44713 | − | 14.6309i | −0.406884 | − | 0.704744i | 0.587655 | − | 0.809112i | \(-0.300051\pi\) |
−0.994539 | + | 0.104368i | \(0.966718\pi\) | |||||||
\(432\) | 0.432497 | − | 0.749106i | 0.0208085 | − | 0.0360414i | ||||
\(433\) | −3.42241 | −0.164471 | −0.0822353 | − | 0.996613i | \(-0.526206\pi\) | ||||
−0.0822353 | + | 0.996613i | \(0.526206\pi\) | |||||||
\(434\) | −3.48952 | − | 27.6169i | −0.167502 | − | 1.32566i | ||||
\(435\) | 13.4597 | 0.645342 | ||||||||
\(436\) | −2.19288 | + | 3.79818i | −0.105020 | + | 0.181900i | ||||
\(437\) | −1.02463 | − | 1.77470i | −0.0490145 | − | 0.0848956i | ||||
\(438\) | −42.7611 | − | 74.0644i | −2.04320 | − | 3.53893i | ||||
\(439\) | −9.03253 | + | 15.6448i | −0.431099 | + | 0.746685i | −0.996968 | − | 0.0778096i | \(-0.975207\pi\) |
0.565869 | + | 0.824495i | \(0.308541\pi\) | |||||||
\(440\) | 1.82771 | 0.0871324 | ||||||||
\(441\) | 13.0339 | − | 46.6910i | 0.620661 | − | 2.22338i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.22173 | + | 5.58020i | −0.153069 | + | 0.265123i | −0.932354 | − | 0.361546i | \(-0.882249\pi\) |
0.779285 | + | 0.626669i | \(0.215582\pi\) | |||||||
\(444\) | 28.1103 | + | 48.6885i | 1.33406 | + | 2.31065i | ||||
\(445\) | 1.76286 | + | 3.05336i | 0.0835674 | + | 0.144743i | ||||
\(446\) | −15.5471 | + | 26.9284i | −0.736178 | + | 1.27510i | ||||
\(447\) | −66.4451 | −3.14275 | ||||||||
\(448\) | −4.30065 | − | 34.0364i | −0.203187 | − | 1.60807i | ||||
\(449\) | 1.75306 | 0.0827322 | 0.0413661 | − | 0.999144i | \(-0.486829\pi\) | ||||
0.0413661 | + | 0.999144i | \(0.486829\pi\) | |||||||
\(450\) | 3.83237 | − | 6.63785i | 0.180659 | − | 0.312911i | ||||
\(451\) | 1.03796 | + | 1.79780i | 0.0488757 | + | 0.0846551i | ||||
\(452\) | 15.1681 | + | 26.2719i | 0.713447 | + | 1.23573i | ||||
\(453\) | 27.5728 | − | 47.7575i | 1.29548 | − | 2.24385i | ||||
\(454\) | −8.23163 | −0.386330 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.6477 | 0.732770 | ||||||||
\(457\) | −16.3550 | + | 28.3277i | −0.765054 | + | 1.32511i | 0.175164 | + | 0.984539i | \(0.443954\pi\) |
−0.940218 | + | 0.340573i | \(0.889379\pi\) | |||||||
\(458\) | 21.0022 | + | 36.3769i | 0.981368 | + | 1.69978i | ||||
\(459\) | 10.9731 | + | 19.0060i | 0.512180 | + | 0.887123i | ||||
\(460\) | −3.93632 | + | 6.81790i | −0.183532 | + | 0.317886i | ||||
\(461\) | 7.66641 | 0.357060 | 0.178530 | − | 0.983934i | \(-0.442866\pi\) | ||||
0.178530 | + | 0.983934i | \(0.442866\pi\) | |||||||
\(462\) | 4.67917 | − | 3.55186i | 0.217695 | − | 0.165248i | ||||
\(463\) | −14.4720 | −0.672570 | −0.336285 | − | 0.941760i | \(-0.609171\pi\) | ||||
−0.336285 | + | 0.941760i | \(0.609171\pi\) | |||||||
\(464\) | 0.0703179 | − | 0.121794i | 0.00326443 | − | 0.00565415i | ||||
\(465\) | 15.4138 | + | 26.6976i | 0.714800 | + | 1.23807i | ||||
\(466\) | −23.1562 | − | 40.1077i | −1.07269 | − | 1.85795i | ||||
\(467\) | 1.68801 | − | 2.92373i | 0.0781120 | − | 0.135294i | −0.824323 | − | 0.566119i | \(-0.808444\pi\) |
0.902435 | + | 0.430825i | \(0.141777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.5845 | − | 20.1798i | 1.22756 | − | 0.931815i | ||||
\(470\) | 46.2126 | 2.13163 | ||||||||
\(471\) | −0.119053 | + | 0.206205i | −0.00548566 | + | 0.00950144i | ||||
\(472\) | 11.3221 | + | 19.6104i | 0.521140 | + | 0.902641i | ||||
\(473\) | −0.235376 | − | 0.407683i | −0.0108226 | − | 0.0187453i | ||||
\(474\) | 28.5231 | − | 49.4035i | 1.31011 | − | 2.26918i | ||||
\(475\) | −0.862889 | −0.0395921 | ||||||||
\(476\) | 13.9399 | + | 5.85939i | 0.638934 | + | 0.268565i | ||||
\(477\) | 51.5283 | 2.35932 | ||||||||
\(478\) | 23.7731 | − | 41.1763i | 1.08736 | − | 1.88336i | ||||
\(479\) | −0.0726124 | − | 0.125768i | −0.00331775 | − | 0.00574651i | 0.864362 | − | 0.502871i | \(-0.167723\pi\) |
−0.867680 | + | 0.497124i | \(0.834389\pi\) | |||||||
\(480\) | 19.2017 | + | 33.2584i | 0.876435 | + | 1.51803i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 29.0508 | 1.32323 | ||||||||
\(483\) | 1.20206 | + | 9.51339i | 0.0546956 | + | 0.432874i | ||||
\(484\) | −35.1177 | −1.59626 | ||||||||
\(485\) | 8.14553 | − | 14.1085i | 0.369869 | − | 0.640633i | ||||
\(486\) | −23.0587 | − | 39.9388i | −1.04596 | − | 1.81166i | ||||
\(487\) | 8.21073 | + | 14.2214i | 0.372064 | + | 0.644433i | 0.989883 | − | 0.141887i | \(-0.0453169\pi\) |
−0.617819 | + | 0.786320i | \(0.711984\pi\) | |||||||
\(488\) | 4.79695 | − | 8.30856i | 0.217148 | − | 0.376111i | ||||
\(489\) | −31.7616 | −1.43631 | ||||||||
\(490\) | 23.7803 | + | 24.2812i | 1.07428 | + | 1.09691i | ||||
\(491\) | 18.2077 | 0.821701 | 0.410850 | − | 0.911703i | \(-0.365232\pi\) | ||||
0.410850 | + | 0.911703i | \(0.365232\pi\) | |||||||
\(492\) | 34.1389 | − | 59.1303i | 1.53910 | − | 2.66580i | ||||
\(493\) | 1.78407 | + | 3.09010i | 0.0803506 | + | 0.139171i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.26967 | + | 3.93119i | −0.102014 | + | 0.176694i | ||||
\(496\) | 0.322108 | 0.0144631 | ||||||||
\(497\) | −0.447981 | − | 3.54543i | −0.0200947 | − | 0.159034i | ||||
\(498\) | −80.8279 | −3.62199 | ||||||||
\(499\) | −18.7860 | + | 32.5383i | −0.840976 | + | 1.45661i | 0.0480945 | + | 0.998843i | \(0.484685\pi\) |
−0.889070 | + | 0.457770i | \(0.848648\pi\) | |||||||
\(500\) | 18.7656 | + | 32.5030i | 0.839225 | + | 1.45358i | ||||
\(501\) | 9.21481 | + | 15.9605i | 0.411687 | + | 0.713063i | ||||
\(502\) | −15.7007 | + | 27.1945i | −0.700758 | + | 1.21375i | ||||
\(503\) | −4.20535 | −0.187507 | −0.0937537 | − | 0.995595i | \(-0.529887\pi\) | ||||
−0.0937537 | + | 0.995595i | \(0.529887\pi\) | |||||||
\(504\) | −47.0969 | − | 19.7964i | −2.09786 | − | 0.881800i | ||||
\(505\) | 19.3741 | 0.862137 | ||||||||
\(506\) | −0.405400 | + | 0.702174i | −0.0180222 | + | 0.0312154i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.5761 | + | 37.3710i | 0.957287 | + | 1.65807i | ||||
\(509\) | 4.21873 | − | 7.30705i | 0.186992 | − | 0.323879i | −0.757254 | − | 0.653120i | \(-0.773460\pi\) |
0.944246 | + | 0.329241i | \(0.106793\pi\) | |||||||
\(510\) | −27.1463 | −1.20206 | ||||||||
\(511\) | 25.0382 | − | 19.0060i | 1.10762 | − | 0.840775i | ||||
\(512\) | 0.791350 | 0.0349731 | ||||||||
\(513\) | −11.0137 | + | 19.0763i | −0.486268 | + | 0.842240i | ||||
\(514\) | 8.37924 | + | 14.5133i | 0.369593 | + | 0.640153i | ||||
\(515\) | −6.41927 | − | 11.1185i | −0.282867 | − | 0.489940i | ||||
\(516\) | −7.74159 | + | 13.4088i | −0.340804 | + | 0.590290i | ||||
\(517\) | 2.93602 | 0.129126 | ||||||||
\(518\) | −26.6818 | + | 20.2536i | −1.17233 | + | 0.889893i | ||||
\(519\) | 53.5263 | 2.34955 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.9140 | − | 22.3677i | −0.565773 | − | 0.979948i | −0.996977 | − | 0.0776936i | \(-0.975244\pi\) |
0.431204 | − | 0.902254i | \(-0.358089\pi\) | |||||||
\(522\) | −15.9059 | − | 27.5499i | −0.696184 | − | 1.20583i | ||||
\(523\) | 0.378202 | − | 0.655065i | 0.0165376 | − | 0.0286440i | −0.857638 | − | 0.514254i | \(-0.828069\pi\) |
0.874176 | + | 0.485610i | \(0.161402\pi\) | |||||||
\(524\) | 43.1436 | 1.88473 | ||||||||
\(525\) | 3.72225 | + | 1.56458i | 0.162452 | + | 0.0682839i | ||||
\(526\) | −15.2599 | −0.665364 | ||||||||
\(527\) | −4.08619 | + | 7.07749i | −0.177997 | + | 0.308300i | ||||
\(528\) | 0.0339885 | + | 0.0588698i | 0.00147916 | + | 0.00256198i | ||||
\(529\) | 10.8383 | + | 18.7724i | 0.471229 | + | 0.816192i | ||||
\(530\) | −18.0632 | + | 31.2863i | −0.784614 | + | 1.35899i | ||||
\(531\) | −56.2396 | −2.44059 | ||||||||
\(532\) | 1.90259 | + | 15.0575i | 0.0824876 | + | 0.652827i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.97145 | − | 10.3428i | 0.258410 | − | 0.447579i | ||||
\(535\) | −12.8414 | − | 22.2420i | −0.555183 | − | 0.961606i | ||||
\(536\) | −17.5873 | − | 30.4620i | −0.759654 | − | 1.31576i | ||||
\(537\) | 24.1032 | − | 41.7480i | 1.04013 | − | 1.80156i | ||||
\(538\) | 37.0717 | 1.59827 | ||||||||
\(539\) | 1.51083 | + | 1.54266i | 0.0650760 | + | 0.0664469i | ||||
\(540\) | 84.6231 | 3.64160 | ||||||||
\(541\) | −11.2063 | + | 19.4099i | −0.481797 | + | 0.834496i | −0.999782 | − | 0.0208936i | \(-0.993349\pi\) |
0.517985 | + | 0.855390i | \(0.326682\pi\) | |||||||
\(542\) | −21.4065 | − | 37.0772i | −0.919488 | − | 1.59260i | ||||
\(543\) | −9.21432 | − | 15.9597i | −0.395424 | − | 0.684895i | ||||
\(544\) | −5.09035 | + | 8.81675i | −0.218247 | + | 0.378015i | ||||
\(545\) | 2.89398 | 0.123965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8059 | −0.504784 | −0.252392 | − | 0.967625i | \(-0.581217\pi\) | ||||
−0.252392 | + | 0.967625i | \(0.581217\pi\) | |||||||
\(548\) | −0.806774 | + | 1.39737i | −0.0344637 | + | 0.0596929i | ||||
\(549\) | 11.9138 | + | 20.6354i | 0.508470 | + | 0.880697i | ||||
\(550\) | 0.170704 | + | 0.295668i | 0.00727884 | + | 0.0126073i | ||||
\(551\) | −1.79068 | + | 3.10154i | −0.0762854 | + | 0.132130i | ||||
\(552\) | 10.1058 | 0.430129 | ||||||||
\(553\) | 19.3298 | + | 8.12495i | 0.821988 | + | 0.345508i | ||||
\(554\) | 68.6190 | 2.91534 | ||||||||
\(555\) | 18.5489 | − | 32.1276i | 0.787355 | − | 1.36374i | ||||
\(556\) | −2.28543 | − | 3.95848i | −0.0969238 | − | 0.167877i | ||||
\(557\) | −4.38366 | − | 7.59273i | −0.185742 | − | 0.321714i | 0.758084 | − | 0.652156i | \(-0.226135\pi\) |
−0.943826 | + | 0.330442i | \(0.892802\pi\) | |||||||
\(558\) | 36.4305 | − | 63.0995i | 1.54223 | − | 2.67122i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.313247 | + | 0.237780i | −0.0132371 | + | 0.0100480i | ||||
\(561\) | −1.72468 | −0.0728161 | ||||||||
\(562\) | 2.54831 | − | 4.41380i | 0.107494 | − | 0.186185i | ||||
\(563\) | −18.3879 | − | 31.8488i | −0.774958 | − | 1.34227i | −0.934818 | − | 0.355127i | \(-0.884438\pi\) |
0.159860 | − | 0.987140i | \(-0.448896\pi\) | |||||||
\(564\) | −48.2834 | − | 83.6293i | −2.03310 | − | 3.52143i | ||||
\(565\) | 10.0088 | − | 17.3358i | 0.421074 | − | 0.729321i | ||||
\(566\) | 31.4744 | 1.32297 | ||||||||
\(567\) | 38.3171 | − | 29.0857i | 1.60917 | − | 1.22149i | ||||
\(568\) | −3.76619 | −0.158026 | ||||||||
\(569\) | 17.8918 | − | 30.9896i | 0.750065 | − | 1.29915i | −0.197726 | − | 0.980257i | \(-0.563356\pi\) |
0.947791 | − | 0.318893i | \(-0.103311\pi\) | |||||||
\(570\) | −13.6234 | − | 23.5964i | −0.570621 | − | 0.988344i | ||||
\(571\) | −7.46920 | − | 12.9370i | −0.312576 | − | 0.541398i | 0.666343 | − | 0.745645i | \(-0.267859\pi\) |
−0.978919 | + | 0.204248i | \(0.934525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −84.4877 | −3.52952 | ||||||||
\(574\) | 37.5038 | + | 15.7641i | 1.56538 | + | 0.657979i | ||||
\(575\) | −0.557280 | −0.0232402 | ||||||||
\(576\) | 44.8987 | − | 77.7669i | 1.87078 | − | 3.24029i | ||||
\(577\) | −8.42309 | − | 14.5892i | −0.350658 | − | 0.607357i | 0.635707 | − | 0.771930i | \(-0.280709\pi\) |
−0.986365 | + | 0.164573i | \(0.947375\pi\) | |||||||
\(578\) | 15.8227 | + | 27.4057i | 0.658137 | + | 1.13993i | ||||
\(579\) | 0.337070 | − | 0.583822i | 0.0140081 | − | 0.0242628i | ||||
\(580\) | 13.7585 | 0.571292 | ||||||||
\(581\) | −3.72428 | − | 29.4748i | −0.154509 | − | 1.22282i | ||||
\(582\) | −55.1838 | −2.28744 | ||||||||
\(583\) | −1.14761 | + | 1.98771i | −0.0475290 | + | 0.0823226i | ||||
\(584\) | −16.5643 | − | 28.6901i | −0.685434 | − | 1.18721i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.15647 | + | 2.00307i | −0.0477735 | + | 0.0827461i | ||||
\(587\) | −36.8833 | −1.52234 | −0.761168 | − | 0.648555i | \(-0.775374\pi\) | ||||
−0.761168 | + | 0.648555i | \(0.775374\pi\) | |||||||
\(588\) | 19.0950 | − | 68.4035i | 0.787463 | − | 2.82091i | ||||
\(589\) | −8.20264 | −0.337984 | ||||||||
\(590\) | 19.7147 | − | 34.1469i | 0.811642 | − | 1.40580i | ||||
\(591\) | −17.6881 | − | 30.6367i | −0.727590 | − | 1.26022i | ||||
\(592\) | −0.193811 | − | 0.335690i | −0.00796558 | − | 0.0137968i | ||||
\(593\) | 8.07676 | − | 13.9894i | 0.331673 | − | 0.574474i | −0.651167 | − | 0.758934i | \(-0.725720\pi\) |
0.982840 | + | 0.184460i | \(0.0590537\pi\) | |||||||
\(594\) | 8.71531 | 0.357593 | ||||||||
\(595\) | −1.25081 | − | 9.89920i | −0.0512781 | − | 0.405828i | ||||
\(596\) | −67.9204 | −2.78213 | ||||||||
\(597\) | −32.1660 | + | 55.7131i | −1.31646 | + | 2.28018i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.24238 | + | 2.15186i | 0.0507622 | + | 0.0879227i | 0.890290 | − | 0.455394i | \(-0.150502\pi\) |
−0.839528 | + | 0.543317i | \(0.817168\pi\) | |||||||
\(600\) | 2.12764 | − | 3.68518i | 0.0868605 | − | 0.150447i | ||||
\(601\) | 9.55999 | 0.389960 | 0.194980 | − | 0.980807i | \(-0.437536\pi\) | ||||
0.194980 | + | 0.980807i | \(0.437536\pi\) | |||||||
\(602\) | −8.50464 | − | 3.57478i | −0.346623 | − | 0.145697i | ||||
\(603\) | 87.3605 | 3.55759 | ||||||||
\(604\) | 28.1850 | − | 48.8179i | 1.14683 | − | 1.98637i | ||||
\(605\) | 11.5864 | + | 20.0682i | 0.471052 | + | 0.815886i | ||||
\(606\) | −32.8136 | − | 56.8349i | −1.33296 | − | 2.30876i | ||||
\(607\) | 9.74294 | − | 16.8753i | 0.395454 | − | 0.684946i | −0.597705 | − | 0.801716i | \(-0.703921\pi\) |
0.993159 | + | 0.116770i | \(0.0372540\pi\) | |||||||
\(608\) | −10.2184 | −0.414411 | ||||||||
\(609\) | 13.3481 | − | 10.1323i | 0.540894 | − | 0.410582i | ||||
\(610\) | −16.7055 | −0.676387 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 19.7897 | + | 34.2768i | 0.799951 | + | 1.38556i | ||||
\(613\) | −7.38409 | − | 12.7896i | −0.298241 | − | 0.516568i | 0.677493 | − | 0.735529i | \(-0.263066\pi\) |
−0.975733 | + | 0.218962i | \(0.929733\pi\) | |||||||
\(614\) | 27.4779 | − | 47.5931i | 1.10892 | − | 1.92070i | ||||
\(615\) | −45.0537 | −1.81674 | ||||||||
\(616\) | 1.81256 | − | 1.37588i | 0.0730301 | − | 0.0554357i | ||||
\(617\) | −30.9478 | −1.24591 | −0.622955 | − | 0.782257i | \(-0.714068\pi\) | ||||
−0.622955 | + | 0.782257i | \(0.714068\pi\) | |||||||
\(618\) | −21.7444 | + | 37.6625i | −0.874689 | + | 1.51501i | ||||
\(619\) | 6.54123 | + | 11.3297i | 0.262914 | + | 0.455380i | 0.967015 | − | 0.254719i | \(-0.0819831\pi\) |
−0.704101 | + | 0.710100i | \(0.748650\pi\) | |||||||
\(620\) | 15.7561 | + | 27.2903i | 0.632780 | + | 1.09601i | ||||
\(621\) | −7.11300 | + | 12.3201i | −0.285435 | + | 0.494388i | ||||
\(622\) | −20.5426 | −0.823685 | ||||||||
\(623\) | 4.04678 | + | 1.70099i | 0.162131 | + | 0.0681489i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1716 | − | 19.3498i | 0.446865 | − | 0.773994i | ||||
\(626\) | 17.4059 | + | 30.1478i | 0.695678 | + | 1.20495i | ||||
\(627\) | −0.865532 | − | 1.49915i | −0.0345660 | − | 0.0598701i | ||||
\(628\) | −0.121696 | + | 0.210784i | −0.00485620 | + | 0.00841119i | ||||
\(629\) | 9.83456 | 0.392130 | ||||||||
\(630\) | 11.1516 | + | 88.2566i | 0.444291 | + | 3.51623i | ||||
\(631\) | −35.3591 | −1.40762 | −0.703812 | − | 0.710387i | \(-0.748520\pi\) | ||||
−0.703812 | + | 0.710387i | \(0.748520\pi\) | |||||||
\(632\) | 11.0489 | − | 19.1373i | 0.439503 | − | 0.761242i | ||||
\(633\) | −13.2591 | − | 22.9655i | −0.527004 | − | 0.912797i | ||||
\(634\) | 7.80892 | + | 13.5254i | 0.310132 | + | 0.537164i | ||||
\(635\) | 14.2372 | − | 24.6596i | 0.564986 | − | 0.978585i | ||||
\(636\) | 75.4903 | 2.99338 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.41699 | 0.0560990 | ||||||||
\(639\) | 4.67691 | − | 8.10065i | 0.185016 | − | 0.320457i | ||||
\(640\) | 19.2884 | + | 33.4086i | 0.762443 | + | 1.32059i | ||||
\(641\) | 10.6188 | + | 18.3923i | 0.419417 | + | 0.726452i | 0.995881 | − | 0.0906706i | \(-0.0289010\pi\) |
−0.576464 | + | 0.817123i | \(0.695568\pi\) | |||||||
\(642\) | −43.4986 | + | 75.3418i | −1.71675 | + | 2.97351i | ||||
\(643\) | 25.4808 | 1.00486 | 0.502432 | − | 0.864617i | \(-0.332439\pi\) | ||||
0.502432 | + | 0.864617i | \(0.332439\pi\) | |||||||
\(644\) | 1.22875 | + | 9.72462i | 0.0484195 | + | 0.383204i | ||||
\(645\) | 10.2167 | 0.402283 | ||||||||
\(646\) | 3.61154 | − | 6.25537i | 0.142094 | − | 0.246114i | ||||
\(647\) | −11.3928 | − | 19.7329i | −0.447897 | − | 0.775781i | 0.550352 | − | 0.834933i | \(-0.314494\pi\) |
−0.998249 | + | 0.0591522i | \(0.981160\pi\) | |||||||
\(648\) | −25.3491 | − | 43.9059i | −0.995806 | − | 1.72479i | ||||
\(649\) | 1.25253 | − | 2.16945i | 0.0491662 | − | 0.0851583i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.3837 | + | 14.8729i | 1.38680 | + | 0.582916i | ||||
\(652\) | −32.4669 | −1.27150 | ||||||||
\(653\) | −8.13928 | + | 14.0976i | −0.318515 | + | 0.551684i | −0.980178 | − | 0.198117i | \(-0.936517\pi\) |
0.661664 | + | 0.749801i | \(0.269851\pi\) | |||||||
\(654\) | −4.90150 | − | 8.48964i | −0.191664 | − | 0.331971i | ||||
\(655\) | −14.2343 | − | 24.6546i | −0.556181 | − | 0.963334i | ||||
\(656\) | −0.235376 | + | 0.407683i | −0.00918988 | + | 0.0159173i | ||||
\(657\) | 82.2790 | 3.21001 | ||||||||
\(658\) | 45.8297 | − | 34.7884i | 1.78663 | − | 1.35619i | ||||
\(659\) | 20.5596 | 0.800888 | 0.400444 | − | 0.916321i | \(-0.368856\pi\) | ||||
0.400444 | + | 0.916321i | \(0.368856\pi\) | |||||||
\(660\) | −3.32513 | + | 5.75929i | −0.129430 | + | 0.224180i | ||||
\(661\) | 13.8863 | + | 24.0518i | 0.540115 | + | 0.935507i | 0.998897 | + | 0.0469576i | \(0.0149526\pi\) |
−0.458782 | + | 0.888549i | \(0.651714\pi\) | |||||||
\(662\) | 15.7818 | + | 27.3349i | 0.613378 | + | 1.06240i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.3101 | −1.21507 | ||||||||
\(665\) | 7.97698 | − | 6.05517i | 0.309334 | − | 0.234809i | ||||
\(666\) | −87.6802 | −3.39754 | ||||||||
\(667\) | −1.15647 | + | 2.00307i | −0.0447789 | + | 0.0775593i | ||||
\(668\) | 9.41941 | + | 16.3149i | 0.364448 | + | 0.631242i | ||||
\(669\) | −21.4372 | − | 37.1303i | −0.828810 | − | 1.43554i | ||||
\(670\) | −30.6241 | + | 53.0425i | −1.18311 | + | 2.04921i | ||||
\(671\) | −1.06135 | −0.0409730 | ||||||||
\(672\) | 44.0791 | + | 18.5279i | 1.70039 | + | 0.714729i | ||||
\(673\) | −5.20337 | −0.200575 | −0.100288 | − | 0.994958i | \(-0.531976\pi\) | ||||
−0.100288 | + | 0.994958i | \(0.531976\pi\) | |||||||
\(674\) | −30.8943 | + | 53.5105i | −1.19000 | + | 2.06115i | ||||
\(675\) | 2.99511 | + | 5.18768i | 0.115282 | + | 0.199674i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.4239 | + | 38.8394i | −0.861821 | + | 1.49272i | 0.00834820 | + | 0.999965i | \(0.497343\pi\) |
−0.870169 | + | 0.492753i | \(0.835991\pi\) | |||||||
\(678\) | −67.8070 | −2.60411 | ||||||||
\(679\) | −2.54268 | − | 20.1234i | −0.0975792 | − | 0.772266i | ||||
\(680\) | −10.5156 | −0.403254 | ||||||||
\(681\) | 5.67510 | − | 9.82957i | 0.217470 | − | 0.376670i | ||||
\(682\) | 1.62271 | + | 2.81062i | 0.0621370 | + | 0.107624i | ||||
\(683\) | −9.48691 | − | 16.4318i | −0.363006 | − | 0.628745i | 0.625448 | − | 0.780266i | \(-0.284916\pi\) |
−0.988454 | + | 0.151521i | \(0.951583\pi\) | |||||||
\(684\) | −19.8630 | + | 34.4037i | −0.759479 | + | 1.31546i | ||||
\(685\) | 1.06471 | 0.0406807 | ||||||||
\(686\) | 41.8618 | + | 6.17846i | 1.59829 | + | 0.235895i | ||||
\(687\) | −57.9179 | −2.20970 | ||||||||
\(688\) | 0.0533755 | − | 0.0924491i | 0.00203492 | − | 0.00352459i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.79840 | − | 15.2393i | −0.334949 | − | 0.580149i | ||||
\(691\) | −18.7111 | + | 32.4085i | −0.711803 | + | 1.23288i | 0.252376 | + | 0.967629i | \(0.418788\pi\) |
−0.964180 | + | 0.265250i | \(0.914545\pi\) | |||||||
\(692\) | 54.7148 | 2.07994 | ||||||||
\(693\) | 0.708493 | + | 5.60719i | 0.0269134 | + | 0.213000i | ||||
\(694\) | −44.1229 | −1.67488 | ||||||||
\(695\) | −1.50806 | + | 2.61204i | −0.0572040 | + | 0.0990802i | ||||
\(696\) | −8.83060 | − | 15.2951i | −0.334723 | − | 0.579757i | ||||
\(697\) | −5.97184 | − | 10.3435i | −0.226200 | − | 0.391789i | ||||
\(698\) | −16.1734 | + | 28.0131i | −0.612171 | + | 1.06031i | ||||
\(699\) | 63.8580 | 2.41533 | ||||||||
\(700\) | 3.80489 | + | 1.59932i | 0.143811 | + | 0.0604486i | ||||
\(701\) | −42.5513 | −1.60714 | −0.803570 | − | 0.595210i | \(-0.797069\pi\) | ||||
−0.803570 | + | 0.595210i | \(0.797069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.93548 | + | 8.54851i | 0.186145 | + | 0.322413i | ||||
\(704\) | 1.99991 | + | 3.46395i | 0.0753745 | + | 0.130552i | ||||
\(705\) | −31.8602 | + | 55.1835i | −1.19993 | + | 2.07833i | ||||
\(706\) | 38.7612 | 1.45880 | ||||||||
\(707\) | 19.2136 | − | 14.5846i | 0.722600 | − | 0.548512i | ||||
\(708\) | −82.3924 | −3.09650 | ||||||||
\(709\) | 25.1661 | − | 43.5889i | 0.945131 | − | 1.63702i | 0.189644 | − | 0.981853i | \(-0.439267\pi\) |
0.755488 | − | 0.655163i | \(-0.227400\pi\) | |||||||
\(710\) | 3.27897 | + | 5.67934i | 0.123057 | + | 0.213142i | ||||
\(711\) | 27.4415 | + | 47.5300i | 1.02914 | + | 1.78252i | ||||
\(712\) | 2.31315 | − | 4.00648i | 0.0866888 | − | 0.150149i | ||||
\(713\) | −5.29752 | −0.198394 | ||||||||
\(714\) | −26.9213 | + | 20.4354i | −1.00750 | + | 0.764776i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.6384 | − | 42.6749i | 0.920780 | − | 1.59484i | ||||
\(717\) | 32.7796 | + | 56.7760i | 1.22418 | + | 2.12034i | ||||
\(718\) | 26.0049 | + | 45.0418i | 0.970495 | + | 1.68095i | ||||
\(719\) | −14.4616 | + | 25.0482i | −0.539326 | + | 0.934141i | 0.459614 | + | 0.888119i | \(0.347988\pi\) |
−0.998940 | + | 0.0460219i | \(0.985346\pi\) | |||||||
\(720\) | −1.02938 | −0.0383625 | ||||||||
\(721\) | −14.7360 | − | 6.19400i | −0.548796 | − | 0.230677i | ||||
\(722\) | −36.1616 | −1.34580 | ||||||||
\(723\) | −20.0284 | + | 34.6902i | −0.744863 | + | 1.29014i | ||||
\(724\) | −9.41891 | − | 16.3140i | −0.350051 | − | 0.606306i | ||||
\(725\) | 0.486962 | + | 0.843444i | 0.0180853 | + | 0.0313247i | ||||
\(726\) | 39.2472 | − | 67.9782i | 1.45660 | − | 2.52291i | ||||
\(727\) | −19.8593 | −0.736539 | −0.368269 | − | 0.929719i | \(-0.620050\pi\) | ||||
−0.368269 | + | 0.929719i | \(0.620050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.04209 | 0.334892 | ||||||||
\(730\) | −28.8428 | + | 49.9572i | −1.06752 | + | 1.84900i | ||||
\(731\) | 1.35422 | + | 2.34558i | 0.0500876 | + | 0.0867543i | ||||
\(732\) | 17.4541 | + | 30.2314i | 0.645121 | + | 1.11738i | ||||
\(733\) | −10.1751 | + | 17.6237i | −0.375824 | + | 0.650947i | −0.990450 | − | 0.137872i | \(-0.955974\pi\) |
0.614626 | + | 0.788819i | \(0.289307\pi\) | |||||||
\(734\) | 37.8899 | 1.39854 | ||||||||
\(735\) | −45.3895 | + | 11.6564i | −1.67422 | + | 0.429954i | ||||
\(736\) | −6.59935 | −0.243255 | ||||||||
\(737\) | −1.94564 | + | 3.36994i | −0.0716684 | + | 0.124133i | ||||
\(738\) | 53.2421 | + | 92.2180i | 1.95987 | + | 3.39459i | ||||
\(739\) | −9.50055 | − | 16.4554i | −0.349483 | − | 0.605323i | 0.636674 | − | 0.771133i | \(-0.280310\pi\) |
−0.986158 | + | 0.165810i | \(0.946976\pi\) | |||||||
\(740\) | 18.9607 | − | 32.8409i | 0.697009 | − | 1.20726i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.63854 | + | 44.6248i | 0.206997 | + | 1.63823i | ||||
\(743\) | 8.15098 | 0.299030 | 0.149515 | − | 0.988759i | \(-0.452229\pi\) | ||||
0.149515 | + | 0.988759i | \(0.452229\pi\) | |||||||
\(744\) | 20.2254 | − | 35.0314i | 0.741498 | − | 1.28431i | ||||
\(745\) | 22.4090 | + | 38.8134i | 0.821000 | + | 1.42201i | ||||
\(746\) | −31.5831 | − | 54.7035i | −1.15634 | − | 2.00284i | ||||
\(747\) | 38.8814 | − | 67.3445i | 1.42260 | − | 2.46401i | ||||
\(748\) | −1.76297 | −0.0644607 | ||||||||
\(749\) | −29.4786 | − | 12.3908i | −1.07712 | − | 0.452750i | ||||
\(750\) | −83.8893 | −3.06320 | ||||||||
\(751\) | −18.3713 | + | 31.8201i | −0.670379 | + | 1.16113i | 0.307417 | + | 0.951575i | \(0.400535\pi\) |
−0.977797 | + | 0.209556i | \(0.932798\pi\) | |||||||
\(752\) | 0.332897 | + | 0.576595i | 0.0121395 | + | 0.0210262i | ||||
\(753\) | −21.6490 | − | 37.4972i | −0.788934 | − | 1.36647i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.1963 | −1.35371 | ||||||||
\(756\) | 83.9218 | − | 63.7034i | 3.05221 | − | 2.31687i | ||||
\(757\) | 38.3971 | 1.39557 | 0.697783 | − | 0.716310i | \(-0.254170\pi\) | ||||
0.697783 | + | 0.716310i | \(0.254170\pi\) | |||||||
\(758\) | 10.5584 | − | 18.2878i | 0.383500 | − | 0.664241i | ||||
\(759\) | −0.558987 | − | 0.968195i | −0.0202900 | − | 0.0351432i | ||||
\(760\) | −5.27726 | − | 9.14048i | −0.191426 | − | 0.331560i | ||||
\(761\) | −6.23089 | + | 10.7922i | −0.225870 | + | 0.391218i | −0.956580 | − | 0.291470i | \(-0.905856\pi\) |
0.730710 | + | 0.682688i | \(0.239189\pi\) | |||||||
\(762\) | −96.4533 | −3.49414 | ||||||||
\(763\) | 2.87000 | − | 2.17856i | 0.103901 | − | 0.0788692i | ||||
\(764\) | −86.3636 | −3.12453 | ||||||||
\(765\) | 13.0584 | − | 22.6178i | 0.472128 | − | 0.817749i | ||||
\(766\) | −8.73742 | − | 15.1336i | −0.315696 | − | 0.546801i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 24.4860 | − | 42.4110i | 0.883562 | − | 1.53037i | ||||
\(769\) | 4.81390 | 0.173594 | 0.0867969 | − | 0.996226i | \(-0.472337\pi\) | ||||
0.0867969 | + | 0.996226i | \(0.472337\pi\) | |||||||
\(770\) | −3.65287 | − | 1.53542i | −0.131640 | − | 0.0553326i | ||||
\(771\) | −23.1075 | −0.832196 | ||||||||
\(772\) | 0.344554 | − | 0.596785i | 0.0124008 | − | 0.0214787i | ||||
\(773\) | −14.1372 | − | 24.4863i | −0.508480 | − | 0.880713i | −0.999952 | − | 0.00981931i | \(-0.996874\pi\) |
0.491472 | − | 0.870893i | \(-0.336459\pi\) | |||||||
\(774\) | −12.0736 | − | 20.9120i | −0.433975 | − | 0.751668i | ||||
\(775\) | −1.11533 | + | 1.93180i | −0.0400637 | + | 0.0693923i | ||||
\(776\) | −21.3764 | −0.767369 | ||||||||
\(777\) | −5.79015 | − | 45.8247i | −0.207720 | − | 1.64395i | ||||
\(778\) | 14.9367 | 0.535505 | ||||||||
\(779\) | 5.99395 | − | 10.3818i | 0.214755 | − | 0.371967i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.208322 | + | 0.360825i | 0.00745436 | + | 0.0129113i | ||||
\(782\) | 2.33244 | − | 4.03991i | 0.0834081 | − | 0.144467i | ||||
\(783\) | 24.8619 | 0.888492 | ||||||||
\(784\) | −0.131653 | + | 0.471618i | −0.00470190 | + | 0.0168435i | ||||
\(785\) | 0.160604 | 0.00573222 | ||||||||
\(786\) | −48.2169 | + | 83.5141i | −1.71984 | + | 2.97885i | ||||
\(787\) | 24.8291 | + | 43.0053i | 0.885062 | + | 1.53297i | 0.845643 | + | 0.533749i | \(0.179217\pi\) |
0.0394193 | + | 0.999223i | \(0.487449\pi\) | |||||||
\(788\) | −18.0808 | − | 31.3169i | −0.644102 | − | 1.11562i | ||||
\(789\) | 10.5206 | − | 18.2222i | 0.374543 | − | 0.648728i | ||||
\(790\) | −38.4783 | −1.36900 | ||||||||
\(791\) | −3.12432 | − | 24.7266i | −0.111088 | − | 0.879177i | ||||
\(792\) | 5.95633 | 0.211649 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −33.0507 | − | 57.2455i | −1.17292 | − | 2.03157i | ||||
\(795\) | −24.9065 | − | 43.1393i | −0.883341 | − | 1.52999i | ||||
\(796\) | −32.8801 | + | 56.9501i | −1.16541 | + | 2.01854i | ||||
\(797\) | 5.37263 | 0.190308 | 0.0951542 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951542 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(798\) | −31.2736 | − | 13.1453i | −1.10707 | − | 0.465339i | ||||
\(799\) | −16.8922 | −0.597604 | ||||||||
\(800\) | −1.38941 | + | 2.40653i | −0.0491231 | + | 0.0850837i | ||||
\(801\) | 5.74500 | + | 9.95062i | 0.202989 | + | 0.351588i | ||||
\(802\) | −30.5517 | − | 52.9170i | −1.07882 | − | 1.86857i | ||||
\(803\) | −1.83246 | + | 3.17392i | −0.0646663 | + | 0.112005i | ||||
\(804\) | 127.985 | 4.51369 | ||||||||
\(805\) | 5.15178 | − | 3.91061i | 0.181576 | − | 0.137831i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.5582 | + | 44.2681i | −0.899692 | + | 1.55831i | ||||
\(808\) | −12.7109 | − | 22.0160i | −0.447169 | − | 0.774520i | ||||
\(809\) | −20.6184 | − | 35.7122i | −0.724905 | − | 1.25557i | −0.959013 | − | 0.283362i | \(-0.908550\pi\) |
0.234107 | − | 0.972211i | \(-0.424783\pi\) | |||||||
\(810\) | −44.1395 | + | 76.4518i | −1.55090 | + | 2.68624i | ||||
\(811\) | 19.4366 | 0.682512 | 0.341256 | − | 0.939970i | \(-0.389148\pi\) | ||||
0.341256 | + | 0.939970i | \(0.389148\pi\) | |||||||
\(812\) | 13.6445 | − | 10.3573i | 0.478828 | − | 0.363469i | ||||
\(813\) | 59.0328 | 2.07037 | ||||||||
\(814\) | 1.95276 | − | 3.38227i | 0.0684441 | − | 0.118549i | ||||
\(815\) | 10.7118 | + | 18.5533i | 0.375217 | + | 0.649895i | ||||
\(816\) | −0.195551 | − | 0.338704i | −0.00684564 | − | 0.0118570i | ||||
\(817\) | −1.35923 | + | 2.35426i | −0.0475535 | + | 0.0823651i | ||||
\(818\) | −79.4486 | −2.77785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46.0540 | −1.60828 | ||||||||
\(821\) | 10.0953 | − | 17.4856i | 0.352329 | − | 0.610251i | −0.634328 | − | 0.773064i | \(-0.718723\pi\) |
0.986657 | + | 0.162813i | \(0.0520566\pi\) | |||||||
\(822\) | −1.80329 | − | 3.12339i | −0.0628970 | − | 0.108941i | ||||
\(823\) | 21.4049 | + | 37.0743i | 0.746127 | + | 1.29233i | 0.949666 | + | 0.313263i | \(0.101422\pi\) |
−0.203539 | + | 0.979067i | \(0.565244\pi\) | |||||||
\(824\) | −8.42309 | + | 14.5892i | −0.293432 | + | 0.508240i | ||||
\(825\) | −0.470751 | −0.0163895 | ||||||||
\(826\) | −6.15408 | − | 48.7049i | −0.214128 | − | 1.69466i | ||||
\(827\) | 33.5376 | 1.16622 | 0.583109 | − | 0.812394i | \(-0.301836\pi\) | ||||
0.583109 | + | 0.812394i | \(0.301836\pi\) | |||||||
\(828\) | −12.8281 | + | 22.2189i | −0.445808 | + | 0.772162i | ||||
\(829\) | 19.8949 | + | 34.4590i | 0.690978 | + | 1.19681i | 0.971518 | + | 0.236967i | \(0.0761533\pi\) |
−0.280540 | + | 0.959842i | \(0.590513\pi\) | |||||||
\(830\) | 27.2596 | + | 47.2150i | 0.946195 | + | 1.63886i | ||||
\(831\) | −47.3077 | + | 81.9394i | −1.64109 | + | 2.84245i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.69246 | − | 8.87557i | −0.301176 | − | 0.307520i | ||||
\(834\) | 10.2167 | 0.353776 | ||||||||
\(835\) | 6.21548 | − | 10.7655i | 0.215096 | − | 0.372556i | ||||
\(836\) | −0.884750 | − | 1.53243i | −0.0305997 | − | 0.0530003i | ||||
\(837\) | 28.4715 | + | 49.3142i | 0.984120 | + | 1.70455i | ||||
\(838\) | 4.78949 | − | 8.29564i | 0.165450 | − | 0.286568i | ||||
\(839\) | −36.7098 | −1.26736 | −0.633682 | − | 0.773594i | \(-0.718457\pi\) | ||||
−0.633682 | + | 0.773594i | \(0.718457\pi\) | |||||||
\(840\) | 6.19111 | + | 48.9980i | 0.213614 | + | 1.69059i | ||||
\(841\) | −24.9578 | −0.860614 | ||||||||
\(842\) | 23.9364 | − | 41.4591i | 0.824903 | − | 1.42877i | ||||
\(843\) | 3.51375 | + | 6.08599i | 0.121020 | + | 0.209613i | ||||
\(844\) | −13.5535 | − | 23.4754i | −0.466532 | − | 0.808058i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 150.603 | 5.17783 | ||||||||
\(847\) | 26.5974 | + | 11.1798i | 0.913898 | + | 0.384141i | ||||
\(848\) | −0.520479 | −0.0178733 | ||||||||
\(849\) | −21.6993 | + | 37.5842i | −0.744717 | + | 1.28989i | ||||
\(850\) | −0.982134 | − | 1.70111i | −0.0336869 | − | 0.0583475i | ||||
\(851\) | 3.18749 | + | 5.52089i | 0.109266 | + | 0.189254i | ||||
\(852\) | 6.85179 | − | 11.8676i | 0.234738 | − | 0.406579i | ||||
\(853\) | 11.7156 | 0.401136 | 0.200568 | − | 0.979680i | \(-0.435721\pi\) | ||||
0.200568 | + | 0.979680i | \(0.435721\pi\) | |||||||
\(854\) | −16.5671 | + | 12.5757i | −0.566914 | + | 0.430333i | ||||
\(855\) | 26.2135 | 0.896483 | ||||||||
\(856\) | −16.8500 | + | 29.1850i | −0.575920 | + | 0.997523i | ||||
\(857\) | 13.8453 | + | 23.9807i | 0.472945 | + | 0.819164i | 0.999521 | − | 0.0309639i | \(-0.00985769\pi\) |
−0.526576 | + | 0.850128i | \(0.676524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.2819 | − | 33.3972i | 0.657890 | − | 1.13950i | −0.323271 | − | 0.946306i | \(-0.604783\pi\) |
0.981161 | − | 0.193192i | \(-0.0618840\pi\) | |||||||
\(860\) | 10.4436 | 0.356122 | ||||||||
\(861\) | −44.6803 | + | 33.9159i | −1.52270 | + | 1.15585i | ||||
\(862\) | 38.6002 | 1.31473 | ||||||||
\(863\) | 8.92660 | − | 15.4613i | 0.303865 | − | 0.526310i | −0.673143 | − | 0.739512i | \(-0.735056\pi\) |
0.977008 | + | 0.213203i | \(0.0683895\pi\) | |||||||
\(864\) | 35.4683 | + | 61.4329i | 1.20666 | + | 2.08999i | ||||
\(865\) | −18.0520 | − | 31.2670i | −0.613787 | − | 1.06311i | ||||
\(866\) | 3.90979 | − | 6.77195i | 0.132860 | − | 0.230120i | ||||
\(867\) | −43.6343 | −1.48190 | ||||||||
\(868\) | 36.1694 | + | 15.2032i | 1.22767 | + | 0.516029i | ||||
\(869\) | −2.44464 | −0.0829286 | ||||||||
\(870\) | −15.3764 | + | 26.6327i | −0.521310 | + | 0.902935i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.89868 | − | 3.28861i | −0.0642975 | − | 0.111366i | ||||
\(873\) | 26.5456 | − | 45.9783i | 0.898431 | − | 1.55613i | ||||
\(874\) | 4.68216 | 0.158376 | ||||||||
\(875\) | −3.86534 | − | 30.5912i | −0.130672 | − | 1.03417i | ||||
\(876\) | 120.541 | 4.07270 | ||||||||
\(877\) | −4.46017 | + | 7.72524i | −0.150609 | + | 0.260863i | −0.931452 | − | 0.363865i | \(-0.881457\pi\) |
0.780842 | + | 0.624728i | \(0.214790\pi\) | |||||||
\(878\) | −20.6376 | − | 35.7454i | −0.696487 | − | 1.20635i | ||||
\(879\) | −1.59461 | − | 2.76194i | −0.0537848 | − | 0.0931580i | ||||
\(880\) | 0.0229256 | − | 0.0397083i | 0.000772821 | − | 0.00133857i | ||||
\(881\) | −54.6144 | −1.84001 | −0.920003 | − | 0.391911i | \(-0.871814\pi\) | ||||
−0.920003 | + | 0.391911i | \(0.871814\pi\) | |||||||
\(882\) | 77.4978 | + | 79.1303i | 2.60949 | + | 2.66446i | ||||
\(883\) | 7.51632 | 0.252944 | 0.126472 | − | 0.991970i | \(-0.459635\pi\) | ||||
0.126472 | + | 0.991970i | \(0.459635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.1837 | + | 47.0835i | 0.913770 | + | 1.58270i | ||||
\(886\) | −7.36105 | − | 12.7497i | −0.247299 | − | 0.428335i | ||||
\(887\) | −22.5391 | + | 39.0389i | −0.756790 | + | 1.31080i | 0.187689 | + | 0.982229i | \(0.439900\pi\) |
−0.944479 | + | 0.328571i | \(0.893433\pi\) | |||||||
\(888\) | −48.6780 | −1.63353 | ||||||||
\(889\) | −4.44424 | − | 35.1728i | −0.149055 | − | 1.17966i | ||||
\(890\) | −8.05560 | −0.270024 | ||||||||
\(891\) | −2.80431 | + | 4.85720i | −0.0939479 | + | 0.162722i | ||||
\(892\) | −21.9132 | − | 37.9547i | −0.733708 | − | 1.27082i | ||||
\(893\) | −8.47737 | − | 14.6832i | −0.283684 | − | 0.491356i | ||||
\(894\) | 75.9074 | − | 131.475i | 2.53872 | − | 4.39720i | ||||
\(895\) | −32.5157 | −1.08688 | ||||||||
\(896\) | 44.2782 | + | 18.6116i | 1.47923 | + | 0.621769i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.00271 | + | 3.46880i | −0.0668314 | + | 0.115755i | ||||
\(899\) | 4.62907 | + | 8.01779i | 0.154388 | + | 0.267408i | ||||
\(900\) | 5.40160 | + | 9.35584i | 0.180053 | + | 0.311861i | ||||
\(901\) | 6.60268 | − | 11.4362i | 0.219967 | − | 0.380994i | ||||
\(902\) | −4.74309 | −0.157928 | ||||||||
\(903\) | 10.1320 | − | 7.69103i | 0.337173 | − | 0.255942i | ||||
\(904\) | −26.2662 | −0.873602 | ||||||||
\(905\) | −6.21515 | + | 10.7650i | −0.206599 | + | 0.357839i | ||||
\(906\) | 62.9988 | + | 109.117i | 2.09299 | + | 3.62517i | ||||
\(907\) | −3.18295 | − | 5.51303i | −0.105688 | − | 0.183057i | 0.808331 | − | 0.588728i | \(-0.200371\pi\) |
−0.914019 | + | 0.405671i | \(0.867038\pi\) | |||||||
\(908\) | 5.80111 | − | 10.0478i | 0.192517 | − | 0.333449i | ||||
\(909\) | 63.1385 | 2.09417 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.9161 | 0.692982 | 0.346491 | − | 0.938053i | \(-0.387373\pi\) | ||||
0.346491 | + | 0.938053i | \(0.387373\pi\) | |||||||
\(912\) | 0.196275 | − | 0.339958i | 0.00649930 | − | 0.0112571i | ||||
\(913\) | 1.73188 | + | 2.99971i | 0.0573169 | + | 0.0992758i | ||||
\(914\) | −37.3681 | − | 64.7234i | −1.23603 | − | 2.14086i | ||||
\(915\) | 11.5172 | − | 19.9484i | 0.380748 | − | 0.659475i | ||||
\(916\) | −59.2038 | −1.95615 | ||||||||
\(917\) | −32.6761 | − | 13.7348i | −1.07906 | − | 0.453563i | ||||
\(918\) | −50.1430 | −1.65496 | ||||||||
\(919\) | −2.44326 | + | 4.23185i | −0.0805957 | + | 0.139596i | −0.903506 | − | 0.428576i | \(-0.859016\pi\) |
0.822910 | + | 0.568171i | \(0.192349\pi\) | |||||||
\(920\) | −3.40821 | − | 5.90320i | −0.112366 | − | 0.194623i | ||||
\(921\) | 37.8880 | + | 65.6239i | 1.24845 | + | 2.16238i | ||||
\(922\) | −8.75816 | + | 15.1696i | −0.288435 | + | 0.499584i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.03796 | + | 8.21468i | 0.0341464 | + | 0.270243i | ||||
\(925\) | 2.68434 | 0.0882606 | ||||||||
\(926\) | 16.5329 | − | 28.6358i | 0.543305 | − | 0.941031i | ||||
\(927\) | −20.9198 | − | 36.2342i | −0.687098 | − | 1.19009i | ||||
\(928\) | 5.76664 | + | 9.98812i | 0.189299 | + | 0.327876i | ||||
\(929\) | 25.7675 | − | 44.6306i | 0.845404 | − | 1.46428i | −0.0398663 | − | 0.999205i | \(-0.512693\pi\) |
0.885270 | − | 0.465077i | \(-0.153973\pi\) | |||||||
\(930\) | −70.4355 | −2.30967 | ||||||||
\(931\) | 3.35261 | − | 12.0100i | 0.109877 | − | 0.393611i | ||||
\(932\) | 65.2759 | 2.13818 | ||||||||
\(933\) | 14.1626 | − | 24.5304i | 0.463664 | − | 0.803090i | ||||
\(934\) | 3.85680 | + | 6.68017i | 0.126198 | + | 0.218582i | ||||
\(935\) | 0.581657 | + | 1.00746i | 0.0190222 | + | 0.0329474i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3565 | 0.665016 | 0.332508 | − | 0.943100i | \(-0.392105\pi\) | ||||
0.332508 | + | 0.943100i | \(0.392105\pi\) | |||||||
\(938\) | 9.55952 | + | 75.6564i | 0.312129 | + | 2.47027i | ||||
\(939\) | −48.0002 | −1.56643 | ||||||||
\(940\) | −32.5676 | + | 56.4088i | −1.06224 | + | 1.83985i | ||||
\(941\) | 17.1317 | + | 29.6730i | 0.558479 | + | 0.967314i | 0.997624 | + | 0.0688974i | \(0.0219481\pi\) |
−0.439145 | + | 0.898416i | \(0.644719\pi\) | |||||||
\(942\) | −0.272013 | − | 0.471141i | −0.00886267 | − | 0.0153506i | ||||
\(943\) | 3.87108 | − | 6.70490i | 0.126060 | − | 0.218342i | ||||
\(944\) | 0.568067 | 0.0184890 | ||||||||
\(945\) | −64.0918 | − | 26.9399i | −2.08491 | − | 0.876354i | ||||
\(946\) | 1.07558 | 0.0349701 | ||||||||
\(947\) | 27.6578 | − | 47.9046i | 0.898756 | − | 1.55669i | 0.0696707 | − | 0.997570i | \(-0.477805\pi\) |
0.829086 | − | 0.559122i | \(-0.188862\pi\) | |||||||
\(948\) | 40.2025 | + | 69.6327i | 1.30572 | + | 2.26156i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.985770 | − | 1.70740i | 0.0319826 | − | 0.0553955i | ||||
\(951\) | −21.5347 | −0.698311 | ||||||||
\(952\) | −10.4284 | + | 7.91602i | −0.337988 | + | 0.256560i | ||||
\(953\) | 14.8378 | 0.480644 | 0.240322 | − | 0.970693i | \(-0.422747\pi\) | ||||
0.240322 | + | 0.970693i | \(0.422747\pi\) | |||||||
\(954\) | −58.8663 | + | 101.959i | −1.90587 | + | 3.30106i | ||||
\(955\) | 28.4939 | + | 49.3529i | 0.922041 | + | 1.59702i | ||||
\(956\) | 33.5075 | + | 58.0366i | 1.08371 | + | 1.87704i | ||||
\(957\) | −0.976908 | + | 1.69205i | −0.0315790 | + | 0.0546964i | ||||
\(958\) | 0.331812 | 0.0107203 | ||||||||
\(959\) | 1.05589 | − | 0.801506i | 0.0340965 | − | 0.0258820i | ||||
\(960\) | −86.8081 | −2.80172 | ||||||||
\(961\) | 4.89769 | − | 8.48305i | 0.157990 | − | 0.273647i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.8491 | − | 72.4847i | −1.34857 | − | 2.33579i | ||||
\(964\) | −20.4731 | + | 35.4604i | −0.659393 | + | 1.14210i | ||||
\(965\) | −0.454714 | −0.0146378 | ||||||||
\(966\) | −20.1974 | − | 8.48964i | −0.649842 | − | 0.273150i | ||||
\(967\) | −3.09473 | −0.0995199 | −0.0497600 | − | 0.998761i | \(-0.515846\pi\) | ||||
−0.0497600 | + | 0.998761i | \(0.515846\pi\) | |||||||
\(968\) | 15.2031 | − | 26.3326i | 0.488647 | − | 0.846361i | ||||
\(969\) | 4.97979 | + | 8.62524i | 0.159974 | + | 0.277083i | ||||
\(970\) | 18.6110 | + | 32.2352i | 0.597564 | + | 1.03501i | ||||
\(971\) | −27.4506 | + | 47.5459i | −0.880933 | + | 1.52582i | −0.0306280 | + | 0.999531i | \(0.509751\pi\) |
−0.850305 | + | 0.526290i | \(0.823583\pi\) | |||||||
\(972\) | 65.0010 | 2.08491 | ||||||||
\(973\) | 0.470751 | + | 3.72564i | 0.0150916 | + | 0.119439i | ||||
\(974\) | −37.5200 | −1.20222 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.120340 | − | 0.208435i | −0.00385198 | − | 0.00667183i | ||||
\(977\) | −21.6042 | − | 37.4196i | −0.691181 | − | 1.19716i | −0.971451 | − | 0.237239i | \(-0.923757\pi\) |
0.280270 | − | 0.959921i | \(-0.409576\pi\) | |||||||
\(978\) | 36.2847 | − | 62.8470i | 1.16026 | − | 2.00962i | ||||
\(979\) | −0.511795 | −0.0163570 | ||||||||
\(980\) | −46.3973 | + | 11.9152i | −1.48211 | + | 0.380618i | ||||
\(981\) | 9.43124 | 0.301116 | ||||||||
\(982\) | −20.8006 | + | 36.0276i | −0.663773 | + | 1.14969i | ||||
\(983\) | 12.4418 | + | 21.5498i | 0.396831 | + | 0.687332i | 0.993333 | − | 0.115280i | \(-0.0367765\pi\) |
−0.596502 | + | 0.802612i | \(0.703443\pi\) | |||||||
\(984\) | 29.5588 | + | 51.1973i | 0.942299 | + | 1.63211i | ||||
\(985\) | −11.9308 | + | 20.6647i | −0.380146 | + | 0.658433i | ||||
\(986\) | −8.15254 | −0.259630 | ||||||||
\(987\) | 9.94538 | + | 78.7102i | 0.316565 | + | 2.50537i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.877834 | + | 1.52045i | −0.0279135 | + | 0.0483476i | ||||
\(990\) | −5.18578 | − | 8.98203i | −0.164815 | − | 0.285468i | ||||
\(991\) | −2.39164 | − | 4.14244i | −0.0759730 | − | 0.131589i | 0.825536 | − | 0.564349i | \(-0.190873\pi\) |
−0.901509 | + | 0.432760i | \(0.857540\pi\) | |||||||
\(992\) | −13.2078 | + | 22.8765i | −0.419347 | + | 0.726331i | ||||
\(993\) | −43.5216 | −1.38112 | ||||||||
\(994\) | 7.52714 | + | 3.16390i | 0.238746 | + | 0.100353i | ||||
\(995\) | 43.3925 | 1.37564 | ||||||||
\(996\) | 56.9622 | − | 98.6614i | 1.80492 | − | 3.12621i | ||||
\(997\) | −1.72037 | − | 2.97977i | −0.0544847 | − | 0.0943703i | 0.837497 | − | 0.546442i | \(-0.184018\pi\) |
−0.891981 | + | 0.452072i | \(0.850685\pi\) | |||||||
\(998\) | −42.9225 | − | 74.3439i | −1.35869 | − | 2.35331i | ||||
\(999\) | 34.2623 | − | 59.3441i | 1.08401 | − | 1.87756i |
(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 | 1183.2.e.i.170.1 | 16 | ||
7.2 | even | 3 | 8281.2.a.ck.1.8 | 8 | |||
7.4 | even | 3 | inner | 1183.2.e.i.508.1 | 16 | ||
7.5 | odd | 6 | 8281.2.a.cj.1.8 | 8 | |||
13.5 | odd | 4 | 91.2.r.a.51.8 | yes | 16 | ||
13.8 | odd | 4 | 91.2.r.a.51.1 | yes | 16 | ||
13.12 | even | 2 | inner | 1183.2.e.i.170.8 | 16 | ||
39.5 | even | 4 | 819.2.dl.e.415.1 | 16 | |||
39.8 | even | 4 | 819.2.dl.e.415.8 | 16 | |||
91.5 | even | 12 | 637.2.c.e.246.1 | 8 | |||
91.12 | odd | 6 | 8281.2.a.cj.1.1 | 8 | |||
91.18 | odd | 12 | 91.2.r.a.25.1 | ✓ | 16 | ||
91.25 | even | 6 | inner | 1183.2.e.i.508.8 | 16 | ||
91.31 | even | 12 | 637.2.r.f.116.1 | 16 | |||
91.34 | even | 4 | 637.2.r.f.324.1 | 16 | |||
91.44 | odd | 12 | 637.2.c.f.246.1 | 8 | |||
91.47 | even | 12 | 637.2.c.e.246.8 | 8 | |||
91.51 | even | 6 | 8281.2.a.ck.1.1 | 8 | |||
91.60 | odd | 12 | 91.2.r.a.25.8 | yes | 16 | ||
91.73 | even | 12 | 637.2.r.f.116.8 | 16 | |||
91.83 | even | 4 | 637.2.r.f.324.8 | 16 | |||
91.86 | odd | 12 | 637.2.c.f.246.8 | 8 | |||
273.200 | even | 12 | 819.2.dl.e.298.8 | 16 | |||
273.242 | even | 12 | 819.2.dl.e.298.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.1 | ✓ | 16 | 91.18 | odd | 12 | ||
91.2.r.a.25.8 | yes | 16 | 91.60 | odd | 12 | ||
91.2.r.a.51.1 | yes | 16 | 13.8 | odd | 4 | ||
91.2.r.a.51.8 | yes | 16 | 13.5 | odd | 4 | ||
637.2.c.e.246.1 | 8 | 91.5 | even | 12 | |||
637.2.c.e.246.8 | 8 | 91.47 | even | 12 | |||
637.2.c.f.246.1 | 8 | 91.44 | odd | 12 | |||
637.2.c.f.246.8 | 8 | 91.86 | odd | 12 | |||
637.2.r.f.116.1 | 16 | 91.31 | even | 12 | |||
637.2.r.f.116.8 | 16 | 91.73 | even | 12 | |||
637.2.r.f.324.1 | 16 | 91.34 | even | 4 | |||
637.2.r.f.324.8 | 16 | 91.83 | even | 4 | |||
819.2.dl.e.298.1 | 16 | 273.242 | even | 12 | |||
819.2.dl.e.298.8 | 16 | 273.200 | even | 12 | |||
819.2.dl.e.415.1 | 16 | 39.5 | even | 4 | |||
819.2.dl.e.415.8 | 16 | 39.8 | even | 4 | |||
1183.2.e.i.170.1 | 16 | 1.1 | even | 1 | trivial | ||
1183.2.e.i.170.8 | 16 | 13.12 | even | 2 | inner | ||
1183.2.e.i.508.1 | 16 | 7.4 | even | 3 | inner | ||
1183.2.e.i.508.8 | 16 | 91.25 | even | 6 | inner | ||
8281.2.a.cj.1.1 | 8 | 91.12 | odd | 6 | |||
8281.2.a.cj.1.8 | 8 | 7.5 | odd | 6 | |||
8281.2.a.ck.1.1 | 8 | 91.51 | even | 6 | |||
8281.2.a.ck.1.8 | 8 | 7.2 | even | 3 |