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 | 170.8 | ||
Root | \(1.14241 + 1.97871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.i.508.8 |
$q$-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 | \(-0.533990\pi\) |
0.914382 | − | 0.404852i | \(-0.132677\pi\) | |||||||
\(3\) | −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 | −0.524433 | − | 0.851452i | \(-0.675723\pi\) |
0.999595 | + | 0.0284464i | \(0.00905598\pi\) | |||||||
\(6\) | −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 | 0.888340 | − | 0.459186i | \(-0.151859\pi\) |
−0.841837 | + | 0.539732i | \(0.818526\pi\) | |||||||
\(12\) | −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 | −0.745589 | − | 0.666406i | \(-0.767832\pi\) |
0.949919 | + | 0.312496i | \(0.101165\pi\) | |||||||
\(20\) | −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 | 0.581745 | − | 0.813371i | \(-0.302370\pi\) |
−0.995273 | + | 0.0971205i | \(0.969037\pi\) | |||||||
\(32\) | −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 | −0.998717 | − | 0.0506410i | \(-0.983874\pi\) |
0.543215 | + | 0.839594i | \(0.317207\pi\) | |||||||
\(38\) | −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 | \(-0.323874\pi\) | ||||
0.525512 | + | 0.850786i | \(0.323874\pi\) | |||||||
\(42\) | 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 | \(-0.589099\pi\) |
0.970455 | − | 0.241281i | \(-0.0775675\pi\) | |||||||
\(48\) | −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 | \(-0.989370\pi\) |
0.470807 | − | 0.882236i | \(-0.343963\pi\) | |||||||
\(60\) | 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 | \(0.113367\pi\) |
−0.166665 | + | 0.986014i | \(0.553300\pi\) | |||||||
\(68\) | 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 | \(-0.474460\pi\) | ||||
0.0801494 | + | 0.996783i | \(0.474460\pi\) | |||||||
\(72\) | 9.65478 | − | 16.7226i | 1.13783 | − | 1.97077i | ||||
\(73\) | 5.94059 | + | 10.2894i | 0.695293 | + | 1.20428i | 0.970082 | + | 0.242778i | \(0.0780588\pi\) |
−0.274789 | + | 0.961505i | \(0.588608\pi\) | |||||||
\(74\) | 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 | \(-0.288642\pi\) | ||||
0.616273 | + | 0.787533i | \(0.288642\pi\) | |||||||
\(84\) | 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 | −0.906638 | − | 0.421909i | \(-0.861360\pi\) |
0.818703 | + | 0.574218i | \(0.194694\pi\) | |||||||
\(90\) | 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 | \(-0.372750\pi\) | ||||
0.389203 | + | 0.921152i | \(0.372750\pi\) | |||||||
\(98\) | −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 | 0.896793 | − | 0.442451i | \(-0.145891\pi\) |
−0.831570 | + | 0.555420i | \(0.812558\pi\) | |||||||
\(110\) | 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 | 0.876529 | − | 0.481349i | \(-0.159853\pi\) |
−0.855125 | + | 0.518421i | \(0.826520\pi\) | |||||||
\(138\) | 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 | \(0.498662\pi\) |
−0.868120 | + | 0.496355i | \(0.834672\pi\) | |||||||
\(150\) | −1.74344 | − | 3.01972i | −0.142351 | − | 0.246559i | ||||
\(151\) | −8.75211 | − | 15.1591i | −0.712236 | − | 1.23363i | −0.964016 | − | 0.265845i | \(-0.914349\pi\) |
0.251779 | − | 0.967785i | \(-0.418984\pi\) | |||||||
\(152\) | −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 | −0.993080 | − | 0.117444i | \(-0.962530\pi\) |
0.598249 | + | 0.801310i | \(0.295863\pi\) | |||||||
\(164\) | −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 | \(-0.427324\pi\) | ||||
0.226339 | + | 0.974049i | \(0.427324\pi\) | |||||||
\(168\) | 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 | 0.862149 | − | 0.506655i | \(-0.169118\pi\) |
−0.869850 | + | 0.493316i | \(0.835785\pi\) | |||||||
\(194\) | 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 | \(-0.630996\pi\) | ||||
−0.400017 | + | 0.916508i | \(0.630996\pi\) | |||||||
\(198\) | −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 | \(-0.650599\pi\) | ||||
−0.455666 | + | 0.890151i | \(0.650599\pi\) | |||||||
\(224\) | −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 | 0.800032 | − | 0.599957i | \(-0.204816\pi\) |
−0.919594 | + | 0.392870i | \(0.871482\pi\) | |||||||
\(228\) | 9.03614 | + | 15.6511i | 0.598433 | + | 1.03652i | ||||
\(229\) | −9.19208 | + | 15.9212i | −0.607430 | + | 1.05210i | 0.384232 | + | 0.923236i | \(0.374466\pi\) |
−0.991662 | + | 0.128863i | \(0.958867\pi\) | |||||||
\(230\) | 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 | \(-0.264991\pi\) | ||||
0.673033 | + | 0.739612i | \(0.264991\pi\) | |||||||
\(240\) | −0.234144 | + | 0.405549i | −0.0151139 | + | 0.0261781i | ||||
\(241\) | 6.35736 | + | 11.0113i | 0.409514 | + | 0.709299i | 0.994835 | − | 0.101503i | \(-0.0323651\pi\) |
−0.585322 | + | 0.810801i | \(0.699032\pi\) | |||||||
\(242\) | −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 | \(-0.640614\pi\) |
0.996652 | − | 0.0817555i | \(-0.0260527\pi\) | |||||||
\(272\) | 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 | \(-0.478806\pi\) | ||||
0.0665348 | + | 0.997784i | \(0.478806\pi\) | |||||||
\(282\) | −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 | \(-0.509414\pi\) | ||||
−0.0295700 | + | 0.999563i | \(0.509414\pi\) | |||||||
\(294\) | 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 | \(-0.259199\pi\) | ||||
0.686379 | + | 0.727244i | \(0.259199\pi\) | |||||||
\(308\) | −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 | −0.945900 | − | 0.324459i | \(-0.894818\pi\) |
0.753940 | + | 0.656944i | \(0.228151\pi\) | |||||||
\(318\) | 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 | −0.991012 | − | 0.133770i | \(-0.957292\pi\) |
0.611354 | + | 0.791357i | \(0.290625\pi\) | |||||||
\(332\) | −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 | \(-0.623701\pi\) | ||||
−0.378911 | + | 0.925433i | \(0.623701\pi\) | |||||||
\(350\) | −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 | 0.998478 | − | 0.0551585i | \(-0.0175664\pi\) |
−0.547008 | + | 0.837128i | \(0.684233\pi\) | |||||||
\(354\) | 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 | \(0.371778\pi\) |
−0.992715 | + | 0.120484i | \(0.961555\pi\) | |||||||
\(360\) | −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 | \(-0.423714\pi\) | ||||
0.237372 | + | 0.971419i | \(0.423714\pi\) | |||||||
\(380\) | −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 | −0.751629 | − | 0.659586i | \(-0.770732\pi\) |
0.947033 | + | 0.321137i | \(0.104065\pi\) | |||||||
\(384\) | 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 | \(-0.574712\pi\) |
0.958563 | − | 0.284882i | \(-0.0919544\pi\) | |||||||
\(398\) | −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 | \(-0.600592\pi\) |
0.978533 | − | 0.206092i | \(-0.0660746\pi\) | |||||||
\(402\) | −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 | \(-0.837321\pi\) |
0.0125273 | − | 0.999922i | \(-0.496012\pi\) | |||||||
\(410\) | −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 | \(-0.329429\pi\) | ||||
0.510584 | + | 0.859828i | \(0.329429\pi\) | |||||||
\(422\) | 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 | 0.994539 | − | 0.104368i | \(-0.0332820\pi\) |
−0.587655 | + | 0.809112i | \(0.699949\pi\) | |||||||
\(432\) | 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 | \(-0.513171\pi\) | ||||
−0.0413661 | + | 0.999144i | \(0.513171\pi\) | |||||||
\(450\) | −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 | \(-0.556046\pi\) |
0.940218 | − | 0.340573i | \(-0.110621\pi\) | |||||||
\(458\) | 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 | \(-0.557134\pi\) | ||||
−0.178530 | + | 0.983934i | \(0.557134\pi\) | |||||||
\(462\) | −4.67917 | + | 3.55186i | −0.217695 | + | 0.165248i | ||||
\(463\) | 14.4720 | 0.672570 | 0.336285 | − | 0.941760i | \(-0.390829\pi\) | ||||
0.336285 | + | 0.941760i | \(0.390829\pi\) | |||||||
\(464\) | 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 | 0.867680 | − | 0.497124i | \(-0.165611\pi\) |
−0.864362 | + | 0.502871i | \(0.832277\pi\) | |||||||
\(480\) | 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 | 0.617819 | − | 0.786320i | \(-0.288016\pi\) |
−0.989883 | + | 0.141887i | \(0.954683\pi\) | |||||||
\(488\) | −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 | \(-0.515315\pi\) |
0.889070 | − | 0.457770i | \(-0.151352\pi\) | |||||||
\(500\) | −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 | −0.944246 | − | 0.329241i | \(-0.893207\pi\) |
0.757254 | + | 0.653120i | \(0.226540\pi\) | |||||||
\(510\) | −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 | −0.517985 | − | 0.855390i | \(-0.673318\pi\) |
0.999782 | + | 0.0208936i | \(0.00665111\pi\) | |||||||
\(542\) | −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 | 0.943826 | − | 0.330442i | \(-0.107198\pi\) |
−0.758084 | + | 0.652156i | \(0.773865\pi\) | |||||||
\(558\) | 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 | 0.986365 | − | 0.164573i | \(-0.0526247\pi\) |
−0.635707 | + | 0.771930i | \(0.719291\pi\) | |||||||
\(578\) | −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 | \(-0.224626\pi\) | ||||
0.761168 | + | 0.648555i | \(0.224626\pi\) | |||||||
\(588\) | 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 | −0.982840 | − | 0.184460i | \(-0.940946\pi\) |
0.651167 | + | 0.758934i | \(0.274280\pi\) | |||||||
\(594\) | 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 | 0.975733 | − | 0.218962i | \(-0.0702669\pi\) |
−0.677493 | + | 0.735529i | \(0.736934\pi\) | |||||||
\(614\) | 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 | \(-0.285932\pi\) | ||||
0.622955 | + | 0.782257i | \(0.285932\pi\) | |||||||
\(618\) | 21.7444 | − | 37.6625i | 0.874689 | − | 1.51501i | ||||
\(619\) | −6.54123 | − | 11.3297i | −0.262914 | − | 0.455380i | 0.704101 | − | 0.710100i | \(-0.251350\pi\) |
−0.967015 | + | 0.254719i | \(0.918017\pi\) | |||||||
\(620\) | 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 | \(-0.251480\pi\) | ||||
0.703812 | + | 0.710387i | \(0.251480\pi\) | |||||||
\(632\) | −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 | \(-0.667561\pi\) | ||||
−0.502432 | + | 0.864617i | \(0.667561\pi\) | |||||||
\(644\) | −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 | \(-0.985047\pi\) |
0.458782 | − | 0.888549i | \(-0.348286\pi\) | |||||||
\(662\) | 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 | 0.988454 | − | 0.151521i | \(-0.0484170\pi\) |
−0.625448 | + | 0.780266i | \(0.715084\pi\) | |||||||
\(684\) | 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 | \(-0.581212\pi\) |
0.964180 | − | 0.265250i | \(-0.0854545\pi\) | |||||||
\(692\) | 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 | \(0.560733\pi\) |
−0.755488 | + | 0.655163i | \(0.772600\pi\) | |||||||
\(710\) | −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 | −0.614626 | − | 0.788819i | \(-0.710693\pi\) |
0.990450 | + | 0.137872i | \(0.0440263\pi\) | |||||||
\(734\) | −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 | 0.986158 | − | 0.165810i | \(-0.0530238\pi\) |
−0.636674 | + | 0.771133i | \(0.719690\pi\) | |||||||
\(740\) | 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 | \(-0.547771\pi\) | ||||
−0.149515 | + | 0.988759i | \(0.547771\pi\) | |||||||
\(744\) | 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 | −0.730710 | − | 0.682688i | \(-0.760811\pi\) |
0.956580 | + | 0.291470i | \(0.0941443\pi\) | |||||||
\(762\) | 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 | \(-0.527663\pi\) | ||||
−0.0867969 | + | 0.996226i | \(0.527663\pi\) | |||||||
\(770\) | −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 | \(0.00312563\pi\) |
−0.491472 | + | 0.870893i | \(0.663541\pi\) | |||||||
\(774\) | 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 | \(-0.820783\pi\) |
−0.0394193 | − | 0.999223i | \(-0.512551\pi\) | |||||||
\(788\) | 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 | \(-0.610852\pi\) | ||||
−0.341256 | + | 0.939970i | \(0.610852\pi\) | |||||||
\(812\) | −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 | −0.986657 | − | 0.162813i | \(-0.947943\pi\) |
0.634328 | + | 0.773064i | \(0.281277\pi\) | |||||||
\(822\) | −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 | \(-0.698164\pi\) | ||||
−0.583109 | + | 0.812394i | \(0.698164\pi\) | |||||||
\(828\) | −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 | \(-0.281543\pi\) | ||||
0.633682 | + | 0.773594i | \(0.281543\pi\) | |||||||
\(840\) | −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 | \(-0.564279\pi\) | ||||
−0.200568 | + | 0.979680i | \(0.564279\pi\) | |||||||
\(854\) | −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 | −0.977008 | − | 0.213203i | \(-0.931611\pi\) |
0.673143 | + | 0.739512i | \(0.264944\pi\) | |||||||
\(864\) | −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 | −0.780842 | − | 0.624728i | \(-0.785210\pi\) |
0.931452 | + | 0.363865i | \(0.118543\pi\) | |||||||
\(878\) | 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 | \(0.487307\pi\) |
−0.885270 | + | 0.465077i | \(0.846027\pi\) | |||||||
\(930\) | 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 | \(-0.978052\pi\) |
0.439145 | − | 0.898416i | \(-0.355281\pi\) | |||||||
\(942\) | 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 | \(0.522195\pi\) |
−0.829086 | + | 0.559122i | \(0.811138\pi\) | |||||||
\(948\) | 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 | \(-0.484154\pi\) | ||||
0.0497600 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(968\) | −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 | \(0.0762425\pi\) |
−0.280270 | + | 0.959921i | \(0.590424\pi\) | |||||||
\(978\) | 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 | 0.596502 | − | 0.802612i | \(-0.296557\pi\) |
−0.993333 | + | 0.115280i | \(0.963224\pi\) | |||||||
\(984\) | 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.170.8 | 16 | ||
7.2 | even | 3 | 8281.2.a.ck.1.1 | 8 | |||
7.4 | even | 3 | inner | 1183.2.e.i.508.8 | 16 | ||
7.5 | odd | 6 | 8281.2.a.cj.1.1 | 8 | |||
13.5 | odd | 4 | 91.2.r.a.51.1 | yes | 16 | ||
13.8 | odd | 4 | 91.2.r.a.51.8 | yes | 16 | ||
13.12 | even | 2 | inner | 1183.2.e.i.170.1 | 16 | ||
39.5 | even | 4 | 819.2.dl.e.415.8 | 16 | |||
39.8 | even | 4 | 819.2.dl.e.415.1 | 16 | |||
91.5 | even | 12 | 637.2.c.e.246.8 | 8 | |||
91.12 | odd | 6 | 8281.2.a.cj.1.8 | 8 | |||
91.18 | odd | 12 | 91.2.r.a.25.8 | yes | 16 | ||
91.25 | even | 6 | inner | 1183.2.e.i.508.1 | 16 | ||
91.31 | even | 12 | 637.2.r.f.116.8 | 16 | |||
91.34 | even | 4 | 637.2.r.f.324.8 | 16 | |||
91.44 | odd | 12 | 637.2.c.f.246.8 | 8 | |||
91.47 | even | 12 | 637.2.c.e.246.1 | 8 | |||
91.51 | even | 6 | 8281.2.a.ck.1.8 | 8 | |||
91.60 | odd | 12 | 91.2.r.a.25.1 | ✓ | 16 | ||
91.73 | even | 12 | 637.2.r.f.116.1 | 16 | |||
91.83 | even | 4 | 637.2.r.f.324.1 | 16 | |||
91.86 | odd | 12 | 637.2.c.f.246.1 | 8 | |||
273.200 | even | 12 | 819.2.dl.e.298.1 | 16 | |||
273.242 | even | 12 | 819.2.dl.e.298.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.1 | ✓ | 16 | 91.60 | odd | 12 | ||
91.2.r.a.25.8 | yes | 16 | 91.18 | odd | 12 | ||
91.2.r.a.51.1 | yes | 16 | 13.5 | odd | 4 | ||
91.2.r.a.51.8 | yes | 16 | 13.8 | odd | 4 | ||
637.2.c.e.246.1 | 8 | 91.47 | even | 12 | |||
637.2.c.e.246.8 | 8 | 91.5 | even | 12 | |||
637.2.c.f.246.1 | 8 | 91.86 | odd | 12 | |||
637.2.c.f.246.8 | 8 | 91.44 | odd | 12 | |||
637.2.r.f.116.1 | 16 | 91.73 | even | 12 | |||
637.2.r.f.116.8 | 16 | 91.31 | even | 12 | |||
637.2.r.f.324.1 | 16 | 91.83 | even | 4 | |||
637.2.r.f.324.8 | 16 | 91.34 | even | 4 | |||
819.2.dl.e.298.1 | 16 | 273.200 | even | 12 | |||
819.2.dl.e.298.8 | 16 | 273.242 | even | 12 | |||
819.2.dl.e.415.1 | 16 | 39.8 | even | 4 | |||
819.2.dl.e.415.8 | 16 | 39.5 | even | 4 | |||
1183.2.e.i.170.1 | 16 | 13.12 | even | 2 | inner | ||
1183.2.e.i.170.8 | 16 | 1.1 | even | 1 | trivial | ||
1183.2.e.i.508.1 | 16 | 91.25 | even | 6 | inner | ||
1183.2.e.i.508.8 | 16 | 7.4 | even | 3 | inner | ||
8281.2.a.cj.1.1 | 8 | 7.5 | odd | 6 | |||
8281.2.a.cj.1.8 | 8 | 91.12 | odd | 6 | |||
8281.2.a.ck.1.1 | 8 | 7.2 | even | 3 | |||
8281.2.a.ck.1.8 | 8 | 91.51 | even | 6 |