Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(128,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.128");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.y (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 263.6 | ||
Character | \(\chi\) | \(=\) | 735.263 |
Dual form | 735.2.y.j.422.6 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0952630 | + | 0.355526i | −0.0673611 | + | 0.251395i | −0.991393 | − | 0.130921i | \(-0.958207\pi\) |
0.924032 | + | 0.382316i | \(0.124873\pi\) | |||||||
\(3\) | 0.0448327 | − | 1.73147i | 0.0258842 | − | 0.999665i | ||||
\(4\) | 1.61473 | + | 0.932263i | 0.807363 | + | 0.466132i | ||||
\(5\) | −2.22214 | + | 0.249219i | −0.993770 | + | 0.111454i | ||||
\(6\) | 0.611312 | + | 0.180884i | 0.249567 | + | 0.0738457i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00579 | + | 1.00579i | −0.355602 | + | 0.355602i | ||||
\(9\) | −2.99598 | − | 0.155253i | −0.998660 | − | 0.0517510i | ||||
\(10\) | 0.123083 | − | 0.813769i | 0.0389223 | − | 0.257336i | ||||
\(11\) | 2.93366 | + | 1.69375i | 0.884531 | + | 0.510684i | 0.872150 | − | 0.489239i | \(-0.162725\pi\) |
0.0123815 | + | 0.999923i | \(0.496059\pi\) | |||||||
\(12\) | 1.68658 | − | 2.75406i | 0.486873 | − | 0.795028i | ||||
\(13\) | 1.59420 | + | 1.59420i | 0.442151 | + | 0.442151i | 0.892734 | − | 0.450583i | \(-0.148784\pi\) |
−0.450583 | + | 0.892734i | \(0.648784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.331892 | + | 3.85874i | 0.0856941 | + | 0.996321i | ||||
\(16\) | 1.60275 | + | 2.77605i | 0.400689 | + | 0.694013i | ||||
\(17\) | 0.192179 | − | 0.0514941i | 0.0466101 | − | 0.0124891i | −0.235439 | − | 0.971889i | \(-0.575653\pi\) |
0.282049 | + | 0.959400i | \(0.408986\pi\) | |||||||
\(18\) | 0.340602 | − | 1.05036i | 0.0802808 | − | 0.247572i | ||||
\(19\) | 6.36261 | − | 3.67345i | 1.45968 | − | 0.842748i | 0.460687 | − | 0.887563i | \(-0.347603\pi\) |
0.998995 | + | 0.0448148i | \(0.0142698\pi\) | |||||||
\(20\) | −3.82048 | − | 1.66919i | −0.854286 | − | 0.373243i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.881641 | + | 0.881641i | −0.187966 | + | 0.187966i | ||||
\(23\) | 3.02498 | + | 0.810540i | 0.630752 | + | 0.169009i | 0.560011 | − | 0.828485i | \(-0.310797\pi\) |
0.0707408 | + | 0.997495i | \(0.477464\pi\) | |||||||
\(24\) | 1.69641 | + | 1.78660i | 0.346278 | + | 0.364687i | ||||
\(25\) | 4.87578 | − | 1.10760i | 0.975156 | − | 0.221520i | ||||
\(26\) | −0.718647 | + | 0.414911i | −0.140938 | + | 0.0813707i | ||||
\(27\) | −0.403134 | + | 5.18049i | −0.0775831 | + | 0.996986i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.49165 | 1.76256 | 0.881278 | − | 0.472598i | \(-0.156684\pi\) | ||||
0.881278 | + | 0.472598i | \(0.156684\pi\) | |||||||
\(30\) | −1.40350 | − | 0.249598i | −0.256243 | − | 0.0455702i | ||||
\(31\) | −0.461291 | + | 0.798980i | −0.0828503 | + | 0.143501i | −0.904473 | − | 0.426531i | \(-0.859736\pi\) |
0.821623 | + | 0.570031i | \(0.193069\pi\) | |||||||
\(32\) | −3.88752 | + | 1.04166i | −0.687224 | + | 0.184141i | ||||
\(33\) | 3.06420 | − | 5.00361i | 0.533409 | − | 0.871016i | ||||
\(34\) | 0.0732300i | 0.0125588i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.69295 | − | 3.04373i | −0.782159 | − | 0.507289i | ||||
\(37\) | −8.08083 | − | 2.16525i | −1.32848 | − | 0.355965i | −0.476332 | − | 0.879266i | \(-0.658034\pi\) |
−0.852148 | + | 0.523300i | \(0.824701\pi\) | |||||||
\(38\) | 0.699888 | + | 2.61202i | 0.113537 | + | 0.423725i | ||||
\(39\) | 2.83178 | − | 2.68883i | 0.453447 | − | 0.430558i | ||||
\(40\) | 1.98435 | − | 2.48568i | 0.313753 | − | 0.393020i | ||||
\(41\) | 1.39256i | 0.217481i | 0.994070 | + | 0.108741i | \(0.0346818\pi\) | ||||
−0.994070 | + | 0.108741i | \(0.965318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.864526 | + | 0.864526i | 0.131839 | + | 0.131839i | 0.769947 | − | 0.638108i | \(-0.220283\pi\) |
−0.638108 | + | 0.769947i | \(0.720283\pi\) | |||||||
\(44\) | 3.15804 | + | 5.46988i | 0.476092 | + | 0.824616i | ||||
\(45\) | 6.69617 | − | 0.401663i | 0.998206 | − | 0.0598764i | ||||
\(46\) | −0.576337 | + | 0.998245i | −0.0849762 | + | 0.147183i | ||||
\(47\) | −0.238409 | + | 0.889755i | −0.0347755 | + | 0.129784i | −0.981131 | − | 0.193342i | \(-0.938067\pi\) |
0.946356 | + | 0.323126i | \(0.104734\pi\) | |||||||
\(48\) | 4.87851 | − | 2.65066i | 0.704152 | − | 0.382591i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0707006 | + | 1.83898i | −0.00999858 | + | 0.260071i | ||||
\(51\) | −0.0805446 | − | 0.335060i | −0.0112785 | − | 0.0469178i | ||||
\(52\) | 1.08798 | + | 4.06040i | 0.150876 | + | 0.563077i | ||||
\(53\) | −2.39420 | − | 8.93528i | −0.328869 | − | 1.22736i | −0.910365 | − | 0.413806i | \(-0.864199\pi\) |
0.581496 | − | 0.813549i | \(-0.302468\pi\) | |||||||
\(54\) | −1.80340 | − | 0.636833i | −0.245411 | − | 0.0866621i | ||||
\(55\) | −6.94110 | − | 3.03262i | −0.935938 | − | 0.408918i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.07522 | − | 11.1814i | −0.804683 | − | 1.48101i | ||||
\(58\) | −0.904203 | + | 3.37453i | −0.118728 | + | 0.443098i | ||||
\(59\) | −3.12516 | + | 5.41293i | −0.406861 | + | 0.704704i | −0.994536 | − | 0.104393i | \(-0.966710\pi\) |
0.587675 | + | 0.809097i | \(0.300043\pi\) | |||||||
\(60\) | −3.06144 | + | 6.54022i | −0.395231 | + | 0.844338i | ||||
\(61\) | −0.916307 | − | 1.58709i | −0.117321 | − | 0.203206i | 0.801384 | − | 0.598150i | \(-0.204097\pi\) |
−0.918705 | + | 0.394944i | \(0.870764\pi\) | |||||||
\(62\) | −0.240114 | − | 0.240114i | −0.0304945 | − | 0.0304945i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.92967i | 0.616209i | ||||||||
\(65\) | −3.93983 | − | 3.14522i | −0.488676 | − | 0.390116i | ||||
\(66\) | 1.48701 | + | 1.56606i | 0.183038 | + | 0.192769i | ||||
\(67\) | −0.298494 | − | 1.11399i | −0.0364668 | − | 0.136096i | 0.945292 | − | 0.326224i | \(-0.105776\pi\) |
−0.981759 | + | 0.190128i | \(0.939110\pi\) | |||||||
\(68\) | 0.358322 | + | 0.0960121i | 0.0434529 | + | 0.0116432i | ||||
\(69\) | 1.53904 | − | 5.20132i | 0.185279 | − | 0.626166i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.77651i | 1.16026i | 0.814524 | + | 0.580129i | \(0.196998\pi\) | ||||
−0.814524 | + | 0.580129i | \(0.803002\pi\) | |||||||
\(72\) | 3.16949 | − | 2.85719i | 0.373528 | − | 0.336723i | ||||
\(73\) | 6.56741 | − | 1.75973i | 0.768658 | − | 0.205961i | 0.146879 | − | 0.989154i | \(-0.453077\pi\) |
0.621778 | + | 0.783193i | \(0.286410\pi\) | |||||||
\(74\) | 1.53961 | − | 2.66668i | 0.178976 | − | 0.309995i | ||||
\(75\) | −1.69918 | − | 8.49192i | −0.196205 | − | 0.980563i | ||||
\(76\) | 13.6985 | 1.57133 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.686187 | + | 1.26292i | 0.0776954 | + | 0.142997i | ||||
\(79\) | 2.95931 | − | 1.70856i | 0.332948 | − | 0.192228i | −0.324201 | − | 0.945988i | \(-0.605095\pi\) |
0.657149 | + | 0.753760i | \(0.271762\pi\) | |||||||
\(80\) | −4.25339 | − | 5.76933i | −0.475543 | − | 0.645031i | ||||
\(81\) | 8.95179 | + | 0.930269i | 0.994644 | + | 0.103363i | ||||
\(82\) | −0.495092 | − | 0.132659i | −0.0546737 | − | 0.0146498i | ||||
\(83\) | 6.26911 | − | 6.26911i | 0.688124 | − | 0.688124i | −0.273693 | − | 0.961817i | \(-0.588245\pi\) |
0.961817 | + | 0.273693i | \(0.0882453\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.414214 | + | 0.162321i | −0.0449278 | + | 0.0176062i | ||||
\(86\) | −0.389719 | + | 0.225004i | −0.0420245 | + | 0.0242628i | ||||
\(87\) | 0.425536 | − | 16.4345i | 0.0456223 | − | 1.76197i | ||||
\(88\) | −4.65422 | + | 1.24709i | −0.496141 | + | 0.132941i | ||||
\(89\) | 6.18833 | + | 10.7185i | 0.655962 | + | 1.13616i | 0.981652 | + | 0.190683i | \(0.0610703\pi\) |
−0.325690 | + | 0.945477i | \(0.605596\pi\) | |||||||
\(90\) | −0.495095 | + | 2.41893i | −0.0521876 | + | 0.254977i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.12888 | + | 4.12888i | 0.430465 | + | 0.430465i | ||||
\(93\) | 1.36273 | + | 0.834532i | 0.141308 | + | 0.0865370i | ||||
\(94\) | −0.293620 | − | 0.169521i | −0.0302845 | − | 0.0174848i | ||||
\(95\) | −13.2231 | + | 9.74860i | −1.35666 | + | 1.00019i | ||||
\(96\) | 1.62931 | + | 6.77783i | 0.166291 | + | 0.691760i | ||||
\(97\) | −6.71326 | + | 6.71326i | −0.681628 | + | 0.681628i | −0.960367 | − | 0.278739i | \(-0.910084\pi\) |
0.278739 | + | 0.960367i | \(0.410084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.52622 | − | 5.52990i | −0.856918 | − | 0.555775i | ||||
\(100\) | 8.90563 | + | 2.75704i | 0.890563 | + | 0.275704i | ||||
\(101\) | −10.7840 | − | 6.22616i | −1.07305 | − | 0.619526i | −0.144037 | − | 0.989572i | \(-0.546008\pi\) |
−0.929013 | + | 0.370047i | \(0.879342\pi\) | |||||||
\(102\) | 0.126796 | + | 0.00328310i | 0.0125546 | + | 0.000325075i | ||||
\(103\) | −3.58311 | + | 13.3724i | −0.353055 | + | 1.31762i | 0.529861 | + | 0.848085i | \(0.322244\pi\) |
−0.882915 | + | 0.469533i | \(0.844422\pi\) | |||||||
\(104\) | −3.20687 | −0.314459 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.40481 | 0.330704 | ||||||||
\(107\) | −1.91016 | + | 7.12882i | −0.184662 | + | 0.689169i | 0.810040 | + | 0.586374i | \(0.199445\pi\) |
−0.994703 | + | 0.102795i | \(0.967221\pi\) | |||||||
\(108\) | −5.48053 | + | 7.98925i | −0.527364 | + | 0.768766i | ||||
\(109\) | −5.78212 | − | 3.33831i | −0.553826 | − | 0.319752i | 0.196838 | − | 0.980436i | \(-0.436933\pi\) |
−0.750664 | + | 0.660684i | \(0.770266\pi\) | |||||||
\(110\) | 1.73940 | − | 2.17885i | 0.165846 | − | 0.207745i | ||||
\(111\) | −4.11135 | + | 13.8946i | −0.390233 | + | 1.31882i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.23451 | − | 8.23451i | 0.774637 | − | 0.774637i | −0.204276 | − | 0.978913i | \(-0.565484\pi\) |
0.978913 | + | 0.204276i | \(0.0654841\pi\) | |||||||
\(114\) | 4.55401 | − | 1.09473i | 0.426522 | − | 0.102531i | ||||
\(115\) | −6.92392 | − | 1.04725i | −0.645659 | − | 0.0976564i | ||||
\(116\) | 15.3264 | + | 8.84872i | 1.42302 | + | 0.821583i | ||||
\(117\) | −4.52868 | − | 5.02369i | −0.418677 | − | 0.464440i | ||||
\(118\) | −1.62673 | − | 1.62673i | −0.149752 | − | 0.149752i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.21491 | − | 3.54728i | −0.384767 | − | 0.323821i | ||||
\(121\) | 0.237567 | + | 0.411478i | 0.0215970 | + | 0.0374071i | ||||
\(122\) | 0.651543 | − | 0.174580i | 0.0589879 | − | 0.0158058i | ||||
\(123\) | 2.41118 | + | 0.0624322i | 0.217408 | + | 0.00562932i | ||||
\(124\) | −1.48972 | + | 0.860089i | −0.133781 | + | 0.0772383i | ||||
\(125\) | −10.5586 | + | 3.67638i | −0.944391 | + | 0.328825i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.88180 | − | 1.88180i | 0.166983 | − | 0.166983i | −0.618669 | − | 0.785652i | \(-0.712328\pi\) |
0.785652 | + | 0.618669i | \(0.212328\pi\) | |||||||
\(128\) | −9.52767 | − | 2.55293i | −0.842135 | − | 0.225649i | ||||
\(129\) | 1.53566 | − | 1.45814i | 0.135207 | − | 0.128382i | ||||
\(130\) | 1.49353 | − | 1.10109i | 0.130991 | − | 0.0965719i | ||||
\(131\) | −7.76894 | + | 4.48540i | −0.678776 | + | 0.391891i | −0.799394 | − | 0.600808i | \(-0.794846\pi\) |
0.120618 | + | 0.992699i | \(0.461512\pi\) | |||||||
\(132\) | 9.61252 | − | 5.22282i | 0.836663 | − | 0.454588i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.424489 | 0.0366703 | ||||||||
\(135\) | −0.395261 | − | 11.6122i | −0.0340187 | − | 0.999421i | ||||
\(136\) | −0.141500 | + | 0.245084i | −0.0121335 | + | 0.0210158i | ||||
\(137\) | −8.87285 | + | 2.37747i | −0.758059 | + | 0.203121i | −0.617090 | − | 0.786893i | \(-0.711688\pi\) |
−0.140969 | + | 0.990014i | \(0.545022\pi\) | |||||||
\(138\) | 1.70259 | + | 1.04266i | 0.144934 | + | 0.0887575i | ||||
\(139\) | − | 1.83916i | − | 0.155995i | −0.996954 | − | 0.0779976i | \(-0.975147\pi\) | ||
0.996954 | − | 0.0779976i | \(-0.0248526\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.52990 | + | 0.452688i | 0.128840 | + | 0.0381232i | ||||
\(142\) | −3.47581 | − | 0.931340i | −0.291683 | − | 0.0781563i | ||||
\(143\) | 1.97666 | + | 7.37700i | 0.165297 | + | 0.616896i | ||||
\(144\) | −4.37083 | − | 8.56583i | −0.364236 | − | 0.713819i | ||||
\(145\) | −21.0917 | + | 2.36550i | −1.75157 | + | 0.196444i | ||||
\(146\) | 2.50253i | 0.207110i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.0297 | − | 11.0297i | −0.906640 | − | 0.906640i | ||||
\(149\) | −0.493614 | − | 0.854964i | −0.0404384 | − | 0.0700414i | 0.845098 | − | 0.534612i | \(-0.179542\pi\) |
−0.885536 | + | 0.464570i | \(0.846209\pi\) | |||||||
\(150\) | 3.18097 | + | 0.204862i | 0.259725 | + | 0.0167270i | ||||
\(151\) | 4.35542 | − | 7.54381i | 0.354439 | − | 0.613907i | −0.632583 | − | 0.774493i | \(-0.718005\pi\) |
0.987022 | + | 0.160586i | \(0.0513385\pi\) | |||||||
\(152\) | −2.70474 | + | 10.0942i | −0.219383 | + | 0.818749i | ||||
\(153\) | −0.583758 | + | 0.124439i | −0.0471940 | + | 0.0100603i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.825930 | − | 1.89040i | 0.0663403 | − | 0.151841i | ||||
\(156\) | 7.07925 | − | 1.70177i | 0.566793 | − | 0.136251i | ||||
\(157\) | 1.92641 | + | 7.18947i | 0.153744 | + | 0.573782i | 0.999210 | + | 0.0397515i | \(0.0126566\pi\) |
−0.845465 | + | 0.534031i | \(0.820677\pi\) | |||||||
\(158\) | 0.325524 | + | 1.21487i | 0.0258973 | + | 0.0966502i | ||||
\(159\) | −15.5785 | + | 3.74490i | −1.23546 | + | 0.296990i | ||||
\(160\) | 8.37901 | − | 3.28355i | 0.662419 | − | 0.259588i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.18351 | + | 3.09398i | −0.0929853 | + | 0.243086i | ||||
\(163\) | 5.17967 | − | 19.3308i | 0.405703 | − | 1.51411i | −0.397052 | − | 0.917796i | \(-0.629967\pi\) |
0.802755 | − | 0.596309i | \(-0.203367\pi\) | |||||||
\(164\) | −1.29823 | + | 2.24860i | −0.101375 | + | 0.175586i | ||||
\(165\) | −5.56207 | + | 11.8824i | −0.433007 | + | 0.925040i | ||||
\(166\) | 1.63162 | + | 2.82605i | 0.126638 | + | 0.219344i | ||||
\(167\) | −17.4876 | − | 17.4876i | −1.35323 | − | 1.35323i | −0.882018 | − | 0.471215i | \(-0.843816\pi\) |
−0.471215 | − | 0.882018i | \(-0.656184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.91707i | − | 0.609005i | ||||||
\(170\) | −0.0182503 | − | 0.162727i | −0.00139974 | − | 0.0124806i | ||||
\(171\) | −19.6326 | + | 10.0178i | −1.50134 | + | 0.766079i | ||||
\(172\) | 0.590008 | + | 2.20194i | 0.0449877 | + | 0.167896i | ||||
\(173\) | 14.8579 | + | 3.98116i | 1.12962 | + | 0.302682i | 0.774772 | − | 0.632241i | \(-0.217865\pi\) |
0.354852 | + | 0.934922i | \(0.384531\pi\) | |||||||
\(174\) | 5.80236 | + | 1.71689i | 0.439876 | + | 0.130157i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.8587i | 0.818502i | ||||||||
\(177\) | 9.23222 | + | 5.65380i | 0.693936 | + | 0.424965i | ||||
\(178\) | −4.40023 | + | 1.17904i | −0.329811 | + | 0.0883726i | ||||
\(179\) | 8.82622 | − | 15.2875i | 0.659703 | − | 1.14264i | −0.320990 | − | 0.947083i | \(-0.604016\pi\) |
0.980693 | − | 0.195556i | \(-0.0626511\pi\) | |||||||
\(180\) | 11.1869 | + | 5.59401i | 0.833825 | + | 0.416953i | ||||
\(181\) | −11.9237 | −0.886282 | −0.443141 | − | 0.896452i | \(-0.646136\pi\) | ||||
−0.443141 | + | 0.896452i | \(0.646136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.78908 | + | 1.51541i | −0.206175 | + | 0.112022i | ||||
\(184\) | −3.85774 | + | 2.22727i | −0.284397 | + | 0.164196i | ||||
\(185\) | 18.4963 | + | 2.79758i | 1.35988 | + | 0.205683i | ||||
\(186\) | −0.426516 | + | 0.404986i | −0.0312736 | + | 0.0296950i | ||||
\(187\) | 0.651004 | + | 0.174436i | 0.0476061 | + | 0.0127560i | ||||
\(188\) | −1.21445 | + | 1.21445i | −0.0885729 | + | 0.0885729i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.20621 | − | 5.62983i | −0.160055 | − | 0.408431i | ||||
\(191\) | −15.4022 | + | 8.89245i | −1.11446 | + | 0.643435i | −0.939981 | − | 0.341226i | \(-0.889158\pi\) |
−0.174480 | + | 0.984661i | \(0.555825\pi\) | |||||||
\(192\) | 8.53558 | + | 0.221010i | 0.616002 | + | 0.0159500i | ||||
\(193\) | −19.5879 | + | 5.24857i | −1.40997 | + | 0.377801i | −0.881915 | − | 0.471409i | \(-0.843746\pi\) |
−0.528056 | + | 0.849210i | \(0.677079\pi\) | |||||||
\(194\) | −1.74721 | − | 3.02626i | −0.125443 | − | 0.217273i | ||||
\(195\) | −5.62249 | + | 6.68069i | −0.402635 | + | 0.478414i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.10678 | + | 4.10678i | 0.292596 | + | 0.292596i | 0.838105 | − | 0.545509i | \(-0.183664\pi\) |
−0.545509 | + | 0.838105i | \(0.683664\pi\) | |||||||
\(198\) | 2.77826 | − | 2.50450i | 0.197442 | − | 0.177987i | ||||
\(199\) | −11.6175 | − | 6.70739i | −0.823546 | − | 0.475474i | 0.0280920 | − | 0.999605i | \(-0.491057\pi\) |
−0.851638 | + | 0.524131i | \(0.824390\pi\) | |||||||
\(200\) | −3.79001 | + | 6.01805i | −0.267994 | + | 0.425540i | ||||
\(201\) | −1.94223 | + | 0.466890i | −0.136994 | + | 0.0329319i | ||||
\(202\) | 3.24088 | − | 3.24088i | 0.228027 | − | 0.228027i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.182307 | − | 0.616119i | 0.0127640 | − | 0.0431370i | ||||
\(205\) | −0.347053 | − | 3.09446i | −0.0242392 | − | 0.216126i | ||||
\(206\) | −4.41289 | − | 2.54778i | −0.307460 | − | 0.177512i | ||||
\(207\) | −8.93694 | − | 2.89800i | −0.621160 | − | 0.201425i | ||||
\(208\) | −1.87047 | + | 6.98068i | −0.129694 | + | 0.484023i | ||||
\(209\) | 24.8876 | 1.72151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.11525 | 0.558677 | 0.279338 | − | 0.960193i | \(-0.409885\pi\) | ||||
0.279338 | + | 0.960193i | \(0.409885\pi\) | |||||||
\(212\) | 4.46405 | − | 16.6601i | 0.306592 | − | 1.14422i | ||||
\(213\) | 16.9277 | + | 0.438307i | 1.15987 | + | 0.0300323i | ||||
\(214\) | −2.35251 | − | 1.35823i | −0.160815 | − | 0.0928464i | ||||
\(215\) | −2.13655 | − | 1.70564i | −0.145712 | − | 0.116324i | ||||
\(216\) | −4.80504 | − | 5.61598i | −0.326941 | − | 0.382119i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.73768 | − | 1.73768i | 0.117690 | − | 0.117690i | ||||
\(219\) | −2.75249 | − | 11.4502i | −0.185996 | − | 0.773731i | ||||
\(220\) | −8.38079 | − | 11.3678i | −0.565033 | − | 0.766416i | ||||
\(221\) | 0.388462 | + | 0.224279i | 0.0261308 | + | 0.0150866i | ||||
\(222\) | −4.54825 | − | 2.78534i | −0.305259 | − | 0.186940i | ||||
\(223\) | −11.5431 | − | 11.5431i | −0.772984 | − | 0.772984i | 0.205643 | − | 0.978627i | \(-0.434072\pi\) |
−0.978627 | + | 0.205643i | \(0.934072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.7797 | + | 2.56137i | −0.985313 | + | 0.170758i | ||||
\(226\) | 2.14314 | + | 3.71203i | 0.142559 | + | 0.246920i | ||||
\(227\) | −9.62471 | + | 2.57893i | −0.638815 | + | 0.171170i | −0.563666 | − | 0.826002i | \(-0.690610\pi\) |
−0.0751483 | + | 0.997172i | \(0.523943\pi\) | |||||||
\(228\) | 0.614140 | − | 23.7185i | 0.0406724 | − | 1.57080i | ||||
\(229\) | 4.15793 | − | 2.40058i | 0.274764 | − | 0.158635i | −0.356287 | − | 0.934377i | \(-0.615957\pi\) |
0.631051 | + | 0.775742i | \(0.282624\pi\) | |||||||
\(230\) | 1.03192 | − | 2.36187i | 0.0680426 | − | 0.155737i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.54665 | + | 9.54665i | −0.626768 | + | 0.626768i | ||||
\(233\) | 19.5056 | + | 5.22651i | 1.27785 | + | 0.342400i | 0.833035 | − | 0.553220i | \(-0.186601\pi\) |
0.444820 | + | 0.895620i | \(0.353268\pi\) | |||||||
\(234\) | 2.21747 | − | 1.13149i | 0.144960 | − | 0.0739680i | ||||
\(235\) | 0.308033 | − | 2.03657i | 0.0200939 | − | 0.132851i | ||||
\(236\) | −10.0926 | + | 5.82694i | −0.656969 | + | 0.379301i | ||||
\(237\) | −2.82564 | − | 5.20055i | −0.183545 | − | 0.337812i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8618 | −0.831961 | −0.415981 | − | 0.909373i | \(-0.636562\pi\) | ||||
−0.415981 | + | 0.909373i | \(0.636562\pi\) | |||||||
\(240\) | −10.1801 | + | 7.10596i | −0.657124 | + | 0.458688i | ||||
\(241\) | 8.09281 | − | 14.0172i | 0.521304 | − | 0.902924i | −0.478389 | − | 0.878148i | \(-0.658779\pi\) |
0.999693 | − | 0.0247765i | \(-0.00788740\pi\) | |||||||
\(242\) | −0.168923 | + | 0.0452627i | −0.0108588 | + | 0.00290960i | ||||
\(243\) | 2.01207 | − | 15.4581i | 0.129074 | − | 0.991635i | ||||
\(244\) | − | 3.41696i | − | 0.218748i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.251892 | + | 0.851289i | −0.0160601 | + | 0.0542762i | ||||
\(247\) | 15.9995 | + | 4.28704i | 1.01802 | + | 0.272778i | ||||
\(248\) | −0.339645 | − | 1.26757i | −0.0215675 | − | 0.0804910i | ||||
\(249\) | −10.5737 | − | 11.1358i | −0.670082 | − | 0.705705i | ||||
\(250\) | −0.301203 | − | 4.10409i | −0.0190498 | − | 0.259565i | ||||
\(251\) | 8.02862i | 0.506762i | 0.967367 | + | 0.253381i | \(0.0815426\pi\) | ||||
−0.967367 | + | 0.253381i | \(0.918457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.50140 | + | 7.50140i | 0.471609 | + | 0.471609i | ||||
\(254\) | 0.489763 | + | 0.848294i | 0.0307304 | + | 0.0532267i | ||||
\(255\) | 0.262485 | + | 0.724476i | 0.0164374 | + | 0.0453684i | ||||
\(256\) | −3.11440 | + | 5.39430i | −0.194650 | + | 0.337144i | ||||
\(257\) | 6.07998 | − | 22.6908i | 0.379259 | − | 1.41541i | −0.467763 | − | 0.883854i | \(-0.654940\pi\) |
0.847022 | − | 0.531558i | \(-0.178393\pi\) | |||||||
\(258\) | 0.372116 | + | 0.684874i | 0.0231669 | + | 0.0426384i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.42958 | − | 8.75163i | −0.212693 | − | 0.542753i | ||||
\(261\) | −28.4368 | − | 1.47361i | −1.76019 | − | 0.0912140i | ||||
\(262\) | −0.854585 | − | 3.18936i | −0.0527964 | − | 0.197039i | ||||
\(263\) | −5.06438 | − | 18.9005i | −0.312283 | − | 1.16546i | −0.926493 | − | 0.376313i | \(-0.877192\pi\) |
0.614210 | − | 0.789143i | \(-0.289475\pi\) | |||||||
\(264\) | 1.95065 | + | 8.11455i | 0.120054 | + | 0.499416i | ||||
\(265\) | 7.54709 | + | 19.2587i | 0.463614 | + | 1.18305i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.8362 | − | 10.2344i | 1.15276 | − | 0.626334i | ||||
\(268\) | 0.556549 | − | 2.07707i | 0.0339967 | − | 0.126877i | ||||
\(269\) | −5.73161 | + | 9.92745i | −0.349463 | + | 0.605287i | −0.986154 | − | 0.165832i | \(-0.946969\pi\) |
0.636691 | + | 0.771119i | \(0.280303\pi\) | |||||||
\(270\) | 4.16610 | + | 0.965689i | 0.253541 | + | 0.0587700i | ||||
\(271\) | −4.21138 | − | 7.29432i | −0.255823 | − | 0.443099i | 0.709296 | − | 0.704911i | \(-0.249013\pi\) |
−0.965119 | + | 0.261813i | \(0.915680\pi\) | |||||||
\(272\) | 0.450965 | + | 0.450965i | 0.0273438 | + | 0.0273438i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.38102i | − | 0.204255i | ||||||
\(275\) | 16.1799 | + | 5.00903i | 0.975683 | + | 0.302056i | ||||
\(276\) | 7.33414 | − | 6.96392i | 0.441463 | − | 0.419179i | ||||
\(277\) | 4.65976 | + | 17.3905i | 0.279978 | + | 1.04489i | 0.952432 | + | 0.304752i | \(0.0985737\pi\) |
−0.672454 | + | 0.740139i | \(0.734760\pi\) | |||||||
\(278\) | 0.653868 | + | 0.175203i | 0.0392164 | + | 0.0105080i | ||||
\(279\) | 1.50606 | − | 2.32211i | 0.0901656 | − | 0.139021i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.41251i | − | 0.263228i | −0.991301 | − | 0.131614i | \(-0.957984\pi\) | ||
0.991301 | − | 0.131614i | \(-0.0420160\pi\) | |||||||
\(282\) | −0.306685 | + | 0.500793i | −0.0182628 | + | 0.0298218i | ||||
\(283\) | −2.83104 | + | 0.758575i | −0.168288 | + | 0.0450926i | −0.341979 | − | 0.939708i | \(-0.611097\pi\) |
0.173691 | + | 0.984800i | \(0.444431\pi\) | |||||||
\(284\) | −9.11428 | + | 15.7864i | −0.540833 | + | 0.936751i | ||||
\(285\) | 16.2866 | + | 23.3324i | 0.964734 | + | 1.38209i | ||||
\(286\) | −2.81102 | −0.166219 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 11.8087 | − | 2.51724i | 0.695832 | − | 0.148330i | ||||
\(289\) | −14.6882 | + | 8.48021i | −0.864009 | + | 0.498836i | ||||
\(290\) | 1.16826 | − | 7.72401i | 0.0686028 | − | 0.453570i | ||||
\(291\) | 11.3228 | + | 11.9248i | 0.663756 | + | 0.699043i | ||||
\(292\) | 12.2451 | + | 3.28107i | 0.716591 | + | 0.192010i | ||||
\(293\) | −7.37595 | + | 7.37595i | −0.430908 | + | 0.430908i | −0.888937 | − | 0.458029i | \(-0.848555\pi\) |
0.458029 | + | 0.888937i | \(0.348555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.59552 | − | 12.8071i | 0.325784 | − | 0.745660i | ||||
\(296\) | 10.3054 | − | 5.94985i | 0.598992 | − | 0.345828i | ||||
\(297\) | −9.95710 | + | 14.5150i | −0.577770 | + | 0.842245i | ||||
\(298\) | 0.350985 | − | 0.0940462i | 0.0203320 | − | 0.00544795i | ||||
\(299\) | 3.53025 | + | 6.11457i | 0.204160 | + | 0.353615i | ||||
\(300\) | 5.17299 | − | 15.2962i | 0.298663 | − | 0.883128i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.26711 | + | 2.26711i | 0.130458 | + | 0.130458i | ||||
\(303\) | −11.2639 | + | 18.3931i | −0.647093 | + | 1.05665i | ||||
\(304\) | 20.3954 | + | 11.7753i | 1.16976 | + | 0.675359i | ||||
\(305\) | 2.43169 | + | 3.29837i | 0.139238 | + | 0.188864i | ||||
\(306\) | 0.0113692 | − | 0.219396i | 0.000649932 | − | 0.0125420i | ||||
\(307\) | 11.3608 | − | 11.3608i | 0.648396 | − | 0.648396i | −0.304209 | − | 0.952605i | \(-0.598392\pi\) |
0.952605 | + | 0.304209i | \(0.0983922\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.9932 | + | 6.80357i | 1.30804 | + | 0.387042i | ||||
\(310\) | 0.593408 | + | 0.473725i | 0.0337033 | + | 0.0269058i | ||||
\(311\) | 7.74479 | + | 4.47145i | 0.439167 | + | 0.253553i | 0.703244 | − | 0.710949i | \(-0.251734\pi\) |
−0.264078 | + | 0.964501i | \(0.585067\pi\) | |||||||
\(312\) | −0.143773 | + | 5.55260i | −0.00813952 | + | 0.314354i | ||||
\(313\) | 1.65617 | − | 6.18089i | 0.0936120 | − | 0.349365i | −0.903193 | − | 0.429234i | \(-0.858784\pi\) |
0.996805 | + | 0.0798692i | \(0.0254503\pi\) | |||||||
\(314\) | −2.73956 | −0.154602 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.37130 | 0.358414 | ||||||||
\(317\) | 0.653184 | − | 2.43772i | 0.0366865 | − | 0.136916i | −0.945154 | − | 0.326626i | \(-0.894088\pi\) |
0.981840 | + | 0.189710i | \(0.0607549\pi\) | |||||||
\(318\) | 0.152647 | − | 5.89532i | 0.00855999 | − | 0.330593i | ||||
\(319\) | 27.8453 | + | 16.0765i | 1.55904 | + | 0.900110i | ||||
\(320\) | −1.22857 | − | 10.9544i | −0.0686792 | − | 0.612370i | ||||
\(321\) | 12.2577 | + | 3.62699i | 0.684158 | + | 0.202439i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.03360 | − | 1.03360i | 0.0575108 | − | 0.0575108i | ||||
\(324\) | 13.5874 | + | 9.84756i | 0.754858 | + | 0.547086i | ||||
\(325\) | 9.53869 | + | 6.00722i | 0.529111 | + | 0.333221i | ||||
\(326\) | 6.37918 | + | 3.68302i | 0.353310 | + | 0.203984i | ||||
\(327\) | −6.03941 | + | 9.86190i | −0.333980 | + | 0.545364i | ||||
\(328\) | −1.40063 | − | 1.40063i | −0.0773368 | − | 0.0773368i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.69463 | − | 3.10941i | −0.203383 | − | 0.171167i | ||||
\(331\) | 1.80929 | + | 3.13378i | 0.0994474 | + | 0.172248i | 0.911456 | − | 0.411397i | \(-0.134959\pi\) |
−0.812009 | + | 0.583645i | \(0.801626\pi\) | |||||||
\(332\) | 15.9674 | − | 4.27844i | 0.876322 | − | 0.234810i | ||||
\(333\) | 23.8738 | + | 7.74162i | 1.30828 | + | 0.424238i | ||||
\(334\) | 7.88323 | − | 4.55139i | 0.431351 | − | 0.249041i | ||||
\(335\) | 0.940923 | + | 2.40106i | 0.0514081 | + | 0.131184i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0941 | + | 17.0941i | −0.931175 | + | 0.931175i | −0.997779 | − | 0.0666042i | \(-0.978784\pi\) |
0.0666042 | + | 0.997779i | \(0.478784\pi\) | |||||||
\(338\) | 2.81473 | + | 0.754203i | 0.153101 | + | 0.0410233i | ||||
\(339\) | −13.8886 | − | 14.6270i | −0.754327 | − | 0.794428i | ||||
\(340\) | −0.820168 | − | 0.124051i | −0.0444799 | − | 0.00672762i | ||||
\(341\) | −2.70654 | + | 1.56262i | −0.146567 | + | 0.0846207i | ||||
\(342\) | −1.69133 | − | 7.93421i | −0.0914565 | − | 0.429033i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.73907 | −0.0937644 | ||||||||
\(345\) | −2.12370 | + | 11.9416i | −0.114336 | + | 0.642914i | ||||
\(346\) | −2.83081 | + | 4.90311i | −0.152185 | + | 0.263593i | ||||
\(347\) | 7.49364 | − | 2.00792i | 0.402280 | − | 0.107791i | −0.0520055 | − | 0.998647i | \(-0.516561\pi\) |
0.454285 | + | 0.890856i | \(0.349895\pi\) | |||||||
\(348\) | 16.0084 | − | 26.1405i | 0.858141 | − | 1.40128i | ||||
\(349\) | 14.8272i | 0.793681i | 0.917888 | + | 0.396841i | \(0.129893\pi\) | ||||
−0.917888 | + | 0.396841i | \(0.870107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.90140 | + | 7.61605i | −0.475122 | + | 0.406515i | ||||
\(352\) | −13.1690 | − | 3.52862i | −0.701909 | − | 0.188076i | ||||
\(353\) | −2.76558 | − | 10.3213i | −0.147197 | − | 0.549346i | −0.999648 | − | 0.0265388i | \(-0.991551\pi\) |
0.852451 | − | 0.522807i | \(-0.175115\pi\) | |||||||
\(354\) | −2.88956 | + | 2.74370i | −0.153578 | + | 0.145826i | ||||
\(355\) | −2.43650 | − | 21.7247i | −0.129316 | − | 1.15303i | ||||
\(356\) | 23.0766i | 1.22306i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.59428 | + | 4.59428i | 0.242815 | + | 0.242815i | ||||
\(359\) | −3.04752 | − | 5.27846i | −0.160842 | − | 0.278587i | 0.774329 | − | 0.632783i | \(-0.218088\pi\) |
−0.935171 | + | 0.354197i | \(0.884754\pi\) | |||||||
\(360\) | −6.33098 | + | 7.13896i | −0.333672 | + | 0.376256i | ||||
\(361\) | 17.4885 | − | 30.2910i | 0.920448 | − | 1.59426i | ||||
\(362\) | 1.13589 | − | 4.23919i | 0.0597009 | − | 0.222807i | ||||
\(363\) | 0.723114 | − | 0.392893i | 0.0379536 | − | 0.0206215i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.1551 | + | 5.54710i | −0.740913 | + | 0.290348i | ||||
\(366\) | −0.273070 | − | 1.13595i | −0.0142736 | − | 0.0593773i | ||||
\(367\) | 1.29117 | + | 4.81870i | 0.0673984 | + | 0.251534i | 0.991402 | − | 0.130849i | \(-0.0417702\pi\) |
−0.924004 | + | 0.382383i | \(0.875104\pi\) | |||||||
\(368\) | 2.59820 | + | 9.69660i | 0.135440 | + | 0.505470i | ||||
\(369\) | 0.216199 | − | 4.17208i | 0.0112549 | − | 0.217190i | ||||
\(370\) | −2.75663 | + | 6.30942i | −0.143310 | + | 0.328011i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.42243 | + | 2.61796i | 0.0737496 | + | 0.135735i | ||||
\(373\) | −2.58813 | + | 9.65902i | −0.134008 | + | 0.500125i | 0.865992 | + | 0.500058i | \(0.166688\pi\) |
−1.00000 | 6.70928e-5i | \(0.999979\pi\) | ||||||||
\(374\) | −0.124033 | + | 0.214832i | −0.00641360 | + | 0.0111087i | ||||
\(375\) | 5.89216 | + | 18.4467i | 0.304270 | + | 0.952586i | ||||
\(376\) | −0.655120 | − | 1.13470i | −0.0337852 | − | 0.0585177i | ||||
\(377\) | 15.1316 | + | 15.1316i | 0.779315 | + | 0.779315i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4715i | 1.10292i | 0.834202 | + | 0.551459i | \(0.185929\pi\) | ||||
−0.834202 | + | 0.551459i | \(0.814071\pi\) | |||||||
\(380\) | −30.4399 | + | 3.41393i | −1.56154 | + | 0.175131i | ||||
\(381\) | −3.17391 | − | 3.34264i | −0.162604 | − | 0.171249i | ||||
\(382\) | −1.69424 | − | 6.32299i | −0.0866849 | − | 0.323513i | ||||
\(383\) | −20.0203 | − | 5.36443i | −1.02299 | − | 0.274110i | −0.291943 | − | 0.956436i | \(-0.594302\pi\) |
−0.731048 | + | 0.682326i | \(0.760968\pi\) | |||||||
\(384\) | −4.84748 | + | 16.3824i | −0.247372 | + | 0.836012i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 7.46402i | − | 0.379909i | ||||||
\(387\) | −2.45588 | − | 2.72432i | −0.124840 | − | 0.138485i | ||||
\(388\) | −17.0986 | + | 4.58156i | −0.868050 | + | 0.232593i | ||||
\(389\) | 6.81615 | − | 11.8059i | 0.345592 | − | 0.598583i | −0.639869 | − | 0.768484i | \(-0.721011\pi\) |
0.985461 | + | 0.169901i | \(0.0543447\pi\) | |||||||
\(390\) | −1.83955 | − | 2.63536i | −0.0931490 | − | 0.133447i | ||||
\(391\) | 0.623074 | 0.0315102 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.41804 | + | 13.6528i | 0.374190 | + | 0.688692i | ||||
\(394\) | −1.85129 | + | 1.06884i | −0.0932667 | + | 0.0538476i | ||||
\(395\) | −6.15018 | + | 4.53416i | −0.309449 | + | 0.228139i | ||||
\(396\) | −8.61220 | − | 16.8780i | −0.432780 | − | 0.848149i | ||||
\(397\) | 33.5540 | + | 8.99077i | 1.68403 | + | 0.451234i | 0.968838 | − | 0.247697i | \(-0.0796738\pi\) |
0.715189 | + | 0.698931i | \(0.246340\pi\) | |||||||
\(398\) | 3.49137 | − | 3.49137i | 0.175007 | − | 0.175007i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.8894 | + | 11.7602i | 0.544472 | + | 0.588011i | ||||
\(401\) | 13.4243 | − | 7.75055i | 0.670380 | − | 0.387044i | −0.125841 | − | 0.992050i | \(-0.540163\pi\) |
0.796221 | + | 0.605006i | \(0.206829\pi\) | |||||||
\(402\) | 0.0190310 | − | 0.734991i | 0.000949180 | − | 0.0366580i | ||||
\(403\) | −2.00912 | + | 0.538342i | −0.100081 | + | 0.0268167i | ||||
\(404\) | −11.6088 | − | 20.1071i | −0.577561 | − | 1.00036i | ||||
\(405\) | −20.1239 | + | 0.163776i | −0.999967 | + | 0.00813810i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0390 | − | 20.0390i | −0.993296 | − | 0.993296i | ||||
\(408\) | 0.418013 | + | 0.255990i | 0.0206947 | + | 0.0126734i | ||||
\(409\) | 27.7487 | + | 16.0207i | 1.37208 | + | 0.792172i | 0.991190 | − | 0.132447i | \(-0.0422834\pi\) |
0.380893 | + | 0.924619i | \(0.375617\pi\) | |||||||
\(410\) | 1.13322 | + | 0.171401i | 0.0559659 | + | 0.00846488i | ||||
\(411\) | 3.71873 | + | 15.4697i | 0.183431 | + | 0.763062i | ||||
\(412\) | −18.2523 | + | 18.2523i | −0.899226 | + | 0.899226i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.88167 | − | 2.90124i | 0.0924792 | − | 0.142588i | ||||
\(415\) | −12.3684 | + | 15.4932i | −0.607142 | + | 0.760531i | ||||
\(416\) | −7.85809 | − | 4.53687i | −0.385275 | − | 0.222438i | ||||
\(417\) | −3.18444 | − | 0.0824543i | −0.155943 | − | 0.00403780i | ||||
\(418\) | −2.37087 | + | 8.84820i | −0.115963 | + | 0.432780i | ||||
\(419\) | 5.95062 | 0.290707 | 0.145353 | − | 0.989380i | \(-0.453568\pi\) | ||||
0.145353 | + | 0.989380i | \(0.453568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.6388 | −0.518504 | −0.259252 | − | 0.965810i | \(-0.583476\pi\) | ||||
−0.259252 | + | 0.965810i | \(0.583476\pi\) | |||||||
\(422\) | −0.773083 | + | 2.88518i | −0.0376331 | + | 0.140449i | ||||
\(423\) | 0.852406 | − | 2.62867i | 0.0414454 | − | 0.127810i | ||||
\(424\) | 11.3951 | + | 6.57898i | 0.553396 | + | 0.319504i | ||||
\(425\) | 0.879985 | − | 0.463931i | 0.0426856 | − | 0.0225039i | ||||
\(426\) | −1.76842 | + | 5.97650i | −0.0856801 | + | 0.289563i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.73032 | + | 9.73032i | −0.470333 | + | 0.470333i | ||||
\(429\) | 12.8617 | − | 3.09180i | 0.620968 | − | 0.149273i | ||||
\(430\) | 0.809933 | − | 0.597116i | 0.0390585 | − | 0.0287955i | ||||
\(431\) | −9.76349 | − | 5.63695i | −0.470291 | − | 0.271523i | 0.246071 | − | 0.969252i | \(-0.420860\pi\) |
−0.716361 | + | 0.697729i | \(0.754194\pi\) | |||||||
\(432\) | −15.0274 | + | 7.18394i | −0.723008 | + | 0.345637i | ||||
\(433\) | 9.75098 | + | 9.75098i | 0.468602 | + | 0.468602i | 0.901462 | − | 0.432859i | \(-0.142495\pi\) |
−0.432859 | + | 0.901462i | \(0.642495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.15020 | + | 36.6258i | 0.151041 | + | 1.75607i | ||||
\(436\) | −6.22436 | − | 10.7809i | −0.298093 | − | 0.516312i | ||||
\(437\) | 22.2242 | − | 5.95496i | 1.06313 | − | 0.284865i | ||||
\(438\) | 4.33305 | + | 0.112195i | 0.207041 | + | 0.00536088i | ||||
\(439\) | 24.6276 | − | 14.2188i | 1.17541 | − | 0.678625i | 0.220464 | − | 0.975395i | \(-0.429243\pi\) |
0.954949 | + | 0.296770i | \(0.0959096\pi\) | |||||||
\(440\) | 10.0315 | − | 3.93113i | 0.478233 | − | 0.187409i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.116743 | + | 0.116743i | −0.00555290 | + | 0.00555290i | ||||
\(443\) | −26.2443 | − | 7.03213i | −1.24690 | − | 0.334106i | −0.425763 | − | 0.904835i | \(-0.639994\pi\) |
−0.821139 | + | 0.570728i | \(0.806661\pi\) | |||||||
\(444\) | −19.5922 | + | 18.6032i | −0.929804 | + | 0.882868i | ||||
\(445\) | −16.4226 | − | 22.2757i | −0.778505 | − | 1.05597i | ||||
\(446\) | 5.20351 | − | 3.00425i | 0.246393 | − | 0.142255i | ||||
\(447\) | −1.50247 | + | 0.816347i | −0.0710646 | + | 0.0386119i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.40628 | 0.113559 | 0.0567796 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567796 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(450\) | 0.497325 | − | 5.49857i | 0.0234441 | − | 0.259205i | ||||
\(451\) | −2.35865 | + | 4.08529i | −0.111064 | + | 0.192369i | ||||
\(452\) | 20.9732 | − | 5.61975i | 0.986496 | − | 0.264331i | ||||
\(453\) | −12.8666 | − | 7.87949i | −0.604527 | − | 0.370211i | ||||
\(454\) | − | 3.66752i | − | 0.172125i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 17.3566 | + | 5.13572i | 0.812796 | + | 0.240502i | ||||
\(457\) | −8.49105 | − | 2.27517i | −0.397194 | − | 0.106428i | 0.0546923 | − | 0.998503i | \(-0.482582\pi\) |
−0.451887 | + | 0.892075i | \(0.649249\pi\) | |||||||
\(458\) | 0.457373 | + | 1.70694i | 0.0213716 | + | 0.0797601i | ||||
\(459\) | 0.189291 | + | 1.01634i | 0.00883535 | + | 0.0474386i | ||||
\(460\) | −10.2039 | − | 8.14593i | −0.475760 | − | 0.379806i | ||||
\(461\) | − | 35.4227i | − | 1.64980i | −0.565278 | − | 0.824900i | \(-0.691231\pi\) | ||
0.565278 | − | 0.824900i | \(-0.308769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0869 | − | 20.0869i | −0.933519 | − | 0.933519i | 0.0644045 | − | 0.997924i | \(-0.479485\pi\) |
−0.997924 | + | 0.0644045i | \(0.979485\pi\) | |||||||
\(464\) | 15.2128 | + | 26.3493i | 0.706236 | + | 1.22324i | ||||
\(465\) | −3.23615 | − | 1.51483i | −0.150073 | − | 0.0702484i | ||||
\(466\) | −3.71632 | + | 6.43686i | −0.172155 | + | 0.298182i | ||||
\(467\) | 2.12502 | − | 7.93069i | 0.0983343 | − | 0.366989i | −0.899170 | − | 0.437600i | \(-0.855828\pi\) |
0.997504 | + | 0.0706117i | \(0.0224951\pi\) | |||||||
\(468\) | −2.62918 | − | 12.3338i | −0.121534 | − | 0.570130i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.694711 | + | 0.303524i | 0.0320446 | + | 0.0140005i | ||||
\(471\) | 12.5347 | − | 3.01320i | 0.577569 | − | 0.138841i | ||||
\(472\) | −2.30103 | − | 8.58756i | −0.105914 | − | 0.395275i | ||||
\(473\) | 1.07193 | + | 4.00051i | 0.0492876 | + | 0.183944i | ||||
\(474\) | 2.11811 | − | 0.509170i | 0.0972881 | − | 0.0233870i | ||||
\(475\) | 26.9540 | − | 24.9582i | 1.23673 | − | 1.14516i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.78575 | + | 27.1416i | 0.264911 | + | 1.24273i | ||||
\(478\) | 1.22525 | − | 4.57271i | 0.0560418 | − | 0.209151i | ||||
\(479\) | 20.1914 | − | 34.9726i | 0.922571 | − | 1.59794i | 0.127149 | − | 0.991884i | \(-0.459417\pi\) |
0.795422 | − | 0.606056i | \(-0.207249\pi\) | |||||||
\(480\) | −5.30972 | − | 14.6552i | −0.242355 | − | 0.668916i | ||||
\(481\) | −9.43060 | − | 16.3343i | −0.429998 | − | 0.744779i | ||||
\(482\) | 4.21252 | + | 4.21252i | 0.191875 | + | 0.191875i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.885900i | 0.0402682i | ||||||||
\(485\) | 13.2447 | − | 16.5909i | 0.601411 | − | 0.753352i | ||||
\(486\) | 5.30407 | + | 2.18792i | 0.240597 | + | 0.0992462i | ||||
\(487\) | 7.24668 | + | 27.0450i | 0.328378 | + | 1.22552i | 0.910872 | + | 0.412690i | \(0.135411\pi\) |
−0.582493 | + | 0.812835i | \(0.697923\pi\) | |||||||
\(488\) | 2.51790 | + | 0.674670i | 0.113980 | + | 0.0305409i | ||||
\(489\) | −33.2385 | − | 9.83510i | −1.50310 | − | 0.444759i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.6924i | − | 1.65590i | −0.560798 | − | 0.827952i | \(-0.689506\pi\) | ||
0.560798 | − | 0.827952i | \(-0.310494\pi\) | |||||||
\(492\) | 3.83519 | + | 2.34866i | 0.172904 | + | 0.105886i | ||||
\(493\) | 1.82409 | − | 0.488764i | 0.0821530 | − | 0.0220128i | ||||
\(494\) | −3.04831 | + | 5.27983i | −0.137150 | + | 0.237551i | ||||
\(495\) | 20.3246 | + | 10.1633i | 0.913522 | + | 0.456805i | ||||
\(496\) | −2.95735 | −0.132789 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.96636 | − | 2.69840i | 0.222548 | − | 0.120918i | ||||
\(499\) | −6.60386 | + | 3.81274i | −0.295629 | + | 0.170682i | −0.640478 | − | 0.767977i | \(-0.721264\pi\) |
0.344849 | + | 0.938658i | \(0.387930\pi\) | |||||||
\(500\) | −20.4766 | − | 3.90706i | −0.915742 | − | 0.174729i | ||||
\(501\) | −31.0633 | + | 29.4953i | −1.38781 | + | 1.31775i | ||||
\(502\) | −2.85438 | − | 0.764830i | −0.127397 | − | 0.0341360i | ||||
\(503\) | 15.7533 | − | 15.7533i | 0.702406 | − | 0.702406i | −0.262521 | − | 0.964926i | \(-0.584554\pi\) |
0.964926 | + | 0.262521i | \(0.0845538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.5152 | + | 11.1478i | 1.13541 | + | 0.496070i | ||||
\(506\) | −3.38155 | + | 1.95234i | −0.150328 | + | 0.0867921i | ||||
\(507\) | −13.7082 | − | 0.354943i | −0.608801 | − | 0.0157636i | ||||
\(508\) | 4.79292 | − | 1.28426i | 0.212651 | − | 0.0569798i | ||||
\(509\) | 7.20456 | + | 12.4787i | 0.319336 | + | 0.553107i | 0.980350 | − | 0.197267i | \(-0.0632067\pi\) |
−0.661013 | + | 0.750374i | \(0.729873\pi\) | |||||||
\(510\) | −0.282575 | + | 0.0243044i | −0.0125126 | + | 0.00107622i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15.5706 | − | 15.5706i | −0.688130 | − | 0.688130i | ||||
\(513\) | 16.4653 | + | 34.4423i | 0.726961 | + | 1.52067i | ||||
\(514\) | 7.48797 | + | 4.32318i | 0.330280 | + | 0.190687i | ||||
\(515\) | 4.62951 | − | 30.6082i | 0.204001 | − | 1.34876i | ||||
\(516\) | 3.83904 | − | 0.922862i | 0.169005 | − | 0.0406267i | ||||
\(517\) | −2.20643 | + | 2.20643i | −0.0970387 | + | 0.0970387i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.55938 | − | 25.5475i | 0.331820 | − | 1.12141i | ||||
\(520\) | 7.12610 | − | 0.799214i | 0.312500 | − | 0.0350479i | ||||
\(521\) | 21.9841 | + | 12.6925i | 0.963140 | + | 0.556069i | 0.897138 | − | 0.441750i | \(-0.145642\pi\) |
0.0660022 | + | 0.997819i | \(0.478976\pi\) | |||||||
\(522\) | 3.23288 | − | 9.96965i | 0.141499 | − | 0.436360i | ||||
\(523\) | −5.87340 | + | 21.9198i | −0.256826 | + | 0.958486i | 0.710240 | + | 0.703960i | \(0.248586\pi\) |
−0.967066 | + | 0.254527i | \(0.918080\pi\) | |||||||
\(524\) | −16.7263 | −0.730692 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.20208 | 0.314026 | ||||||||
\(527\) | −0.0475075 | + | 0.177300i | −0.00206946 | + | 0.00772333i | ||||
\(528\) | 18.8014 | + | 0.486822i | 0.818228 | + | 0.0211862i | ||||
\(529\) | −11.4251 | − | 6.59627i | −0.496742 | − | 0.286794i | ||||
\(530\) | −7.56594 | + | 0.848544i | −0.328644 | + | 0.0368584i | ||||
\(531\) | 10.2033 | − | 15.7318i | 0.442785 | − | 0.682704i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.22002 | + | 2.22002i | −0.0961595 | + | 0.0961595i | ||||
\(534\) | 1.84420 | + | 7.67173i | 0.0798062 | + | 0.331988i | ||||
\(535\) | 2.46800 | − | 16.3173i | 0.106701 | − | 0.705457i | ||||
\(536\) | 1.42067 | + | 0.820225i | 0.0613637 | + | 0.0354283i | ||||
\(537\) | −26.0741 | − | 15.9677i | −1.12518 | − | 0.689058i | ||||
\(538\) | −2.98346 | − | 2.98346i | −0.128626 | − | 0.128626i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.1874 | − | 19.1191i | 0.438396 | − | 0.822753i | ||||
\(541\) | 13.4713 | + | 23.3330i | 0.579178 | + | 1.00316i | 0.995574 | + | 0.0939817i | \(0.0299595\pi\) |
−0.416396 | + | 0.909183i | \(0.636707\pi\) | |||||||
\(542\) | 2.99451 | − | 0.802377i | 0.128625 | − | 0.0344650i | ||||
\(543\) | −0.534571 | + | 20.6455i | −0.0229407 | + | 0.885985i | ||||
\(544\) | −0.693459 | + | 0.400369i | −0.0297318 | + | 0.0171657i | ||||
\(545\) | 13.6806 | + | 5.97716i | 0.586013 | + | 0.256033i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.9286 | − | 17.9286i | 0.766572 | − | 0.766572i | −0.210929 | − | 0.977501i | \(-0.567649\pi\) |
0.977501 | + | 0.210929i | \(0.0676489\pi\) | |||||||
\(548\) | −16.5437 | − | 4.43286i | −0.706710 | − | 0.189362i | ||||
\(549\) | 2.49884 | + | 4.89715i | 0.106648 | + | 0.209005i | ||||
\(550\) | −3.32218 | + | 5.27519i | −0.141658 | + | 0.224935i | ||||
\(551\) | 60.3917 | − | 34.8671i | 2.57277 | − | 1.48539i | ||||
\(552\) | 3.68350 | + | 6.77942i | 0.156780 | + | 0.288551i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.62667 | −0.281540 | ||||||||
\(555\) | 5.67317 | − | 31.9004i | 0.240813 | − | 1.35410i | ||||
\(556\) | 1.71458 | − | 2.96973i | 0.0727142 | − | 0.125945i | ||||
\(557\) | −7.04793 | + | 1.88849i | −0.298630 | + | 0.0800177i | −0.405023 | − | 0.914306i | \(-0.632737\pi\) |
0.106393 | + | 0.994324i | \(0.466070\pi\) | |||||||
\(558\) | 0.682099 | + | 0.756656i | 0.0288756 | + | 0.0320318i | ||||
\(559\) | 2.75645i | 0.116585i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.331217 | − | 1.11937i | 0.0139840 | − | 0.0472600i | ||||
\(562\) | 1.56876 | + | 0.420349i | 0.0661743 | + | 0.0177313i | ||||
\(563\) | 8.51184 | + | 31.7666i | 0.358731 | + | 1.33880i | 0.875723 | + | 0.482813i | \(0.160385\pi\) |
−0.516992 | + | 0.855990i | \(0.672948\pi\) | |||||||
\(564\) | 2.04834 | + | 2.15723i | 0.0862506 | + | 0.0908359i | ||||
\(565\) | −16.2460 | + | 20.3504i | −0.683474 | + | 0.856147i | ||||
\(566\) | − | 1.07877i | − | 0.0453442i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.83316 | − | 9.83316i | −0.412590 | − | 0.412590i | ||||
\(569\) | −22.5957 | − | 39.1369i | −0.947260 | − | 1.64070i | −0.751162 | − | 0.660118i | \(-0.770506\pi\) |
−0.196098 | − | 0.980584i | \(-0.562827\pi\) | |||||||
\(570\) | −9.84680 | + | 3.56759i | −0.412437 | + | 0.149430i | ||||
\(571\) | −7.62340 | + | 13.2041i | −0.319029 | + | 0.552575i | −0.980286 | − | 0.197585i | \(-0.936690\pi\) |
0.661256 | + | 0.750160i | \(0.270024\pi\) | |||||||
\(572\) | −3.68554 | + | 13.7546i | −0.154100 | + | 0.575109i | ||||
\(573\) | 14.7065 | + | 27.0671i | 0.614372 | + | 1.13074i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6469 | + | 0.601553i | 0.652520 | + | 0.0250865i | ||||
\(576\) | 0.765346 | − | 14.7692i | 0.0318894 | − | 0.615383i | ||||
\(577\) | −2.24072 | − | 8.36250i | −0.0932826 | − | 0.348135i | 0.903471 | − | 0.428649i | \(-0.141010\pi\) |
−0.996753 | + | 0.0805142i | \(0.974344\pi\) | |||||||
\(578\) | −1.61570 | − | 6.02987i | −0.0672042 | − | 0.250810i | ||||
\(579\) | 8.20957 | + | 34.1512i | 0.341178 | + | 1.41928i | ||||
\(580\) | −36.2627 | − | 15.8434i | −1.50573 | − | 0.657862i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.31822 | + | 2.88958i | −0.220447 | + | 0.119777i | ||||
\(583\) | 8.11035 | − | 30.2682i | 0.335896 | − | 1.25358i | ||||
\(584\) | −4.83554 | + | 8.37540i | −0.200096 | + | 0.346576i | ||||
\(585\) | 11.3153 | + | 10.0347i | 0.467832 | + | 0.414883i | ||||
\(586\) | −1.91969 | − | 3.32500i | −0.0793016 | − | 0.137354i | ||||
\(587\) | 3.77086 | + | 3.77086i | 0.155640 | + | 0.155640i | 0.780632 | − | 0.624992i | \(-0.214898\pi\) |
−0.624992 | + | 0.780632i | \(0.714898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.77812i | 0.279288i | ||||||||
\(590\) | 4.02022 | + | 3.20940i | 0.165510 | + | 0.132129i | ||||
\(591\) | 7.29489 | − | 6.92665i | 0.300071 | − | 0.284924i | ||||
\(592\) | −6.94074 | − | 25.9032i | −0.285262 | − | 1.06461i | ||||
\(593\) | −11.4475 | − | 3.06735i | −0.470093 | − | 0.125961i | 0.0159927 | − | 0.999872i | \(-0.494909\pi\) |
−0.486086 | + | 0.873911i | \(0.661576\pi\) | |||||||
\(594\) | −4.21191 | − | 4.92275i | −0.172817 | − | 0.201983i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.84071i | − | 0.0753985i | ||||||
\(597\) | −12.1345 | + | 19.8147i | −0.496632 | + | 0.810962i | ||||
\(598\) | −2.51019 | + | 0.672604i | −0.102649 | + | 0.0275048i | ||||
\(599\) | −3.37794 | + | 5.85076i | −0.138019 | + | 0.239056i | −0.926747 | − | 0.375687i | \(-0.877407\pi\) |
0.788728 | + | 0.614743i | \(0.210740\pi\) | |||||||
\(600\) | 10.2502 | + | 6.83210i | 0.418461 | + | 0.278919i | ||||
\(601\) | 21.2564 | 0.867068 | 0.433534 | − | 0.901137i | \(-0.357266\pi\) | ||||
0.433534 | + | 0.901137i | \(0.357266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.721331 | + | 3.38385i | 0.0293749 | + | 0.137801i | ||||
\(604\) | 14.0656 | − | 8.12080i | 0.572322 | − | 0.330431i | ||||
\(605\) | −0.630455 | − | 0.855155i | −0.0256316 | − | 0.0347670i | ||||
\(606\) | −5.46619 | − | 5.75678i | −0.222049 | − | 0.233853i | ||||
\(607\) | −3.72230 | − | 0.997386i | −0.151083 | − | 0.0404827i | 0.182485 | − | 0.983209i | \(-0.441586\pi\) |
−0.333568 | + | 0.942726i | \(0.608253\pi\) | |||||||
\(608\) | −20.9083 | + | 20.9083i | −0.847944 | + | 0.847944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.40431 | + | 0.550318i | −0.0568588 | + | 0.0222817i | ||||
\(611\) | −1.79852 | + | 1.03837i | −0.0727602 | + | 0.0420081i | ||||
\(612\) | −1.05862 | − | 0.343281i | −0.0427921 | − | 0.0138763i | ||||
\(613\) | −21.3417 | + | 5.71850i | −0.861985 | + | 0.230968i | −0.662619 | − | 0.748957i | \(-0.730555\pi\) |
−0.199366 | + | 0.979925i | \(0.563888\pi\) | |||||||
\(614\) | 2.95680 | + | 5.12133i | 0.119327 | + | 0.206680i | ||||
\(615\) | −5.37352 | + | 0.462179i | −0.216681 | + | 0.0186369i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.47009 | − | 5.47009i | −0.220218 | − | 0.220218i | 0.588373 | − | 0.808590i | \(-0.299769\pi\) |
−0.808590 | + | 0.588373i | \(0.799769\pi\) | |||||||
\(618\) | −4.60925 | + | 7.52656i | −0.185411 | + | 0.302763i | ||||
\(619\) | −37.2349 | − | 21.4976i | −1.49660 | − | 0.864060i | −0.496603 | − | 0.867978i | \(-0.665419\pi\) |
−0.999992 | + | 0.00391818i | \(0.998753\pi\) | |||||||
\(620\) | 3.09601 | − | 2.28250i | 0.124339 | − | 0.0916675i | ||||
\(621\) | −5.41847 | + | 15.3441i | −0.217436 | + | 0.615738i | ||||
\(622\) | −2.32751 | + | 2.32751i | −0.0933247 | + | 0.0933247i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.0030 | + | 3.55162i | 0.480504 | + | 0.142179i | ||||
\(625\) | 22.5464 | − | 10.8008i | 0.901858 | − | 0.432033i | ||||
\(626\) | 2.03970 | + | 1.17762i | 0.0815227 | + | 0.0470672i | ||||
\(627\) | 1.11578 | − | 43.0922i | 0.0445599 | − | 1.72094i | ||||
\(628\) | −3.59185 | + | 13.4050i | −0.143330 | + | 0.534916i | ||||
\(629\) | −1.66446 | −0.0663664 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0091 | −1.51312 | −0.756560 | − | 0.653925i | \(-0.773121\pi\) | ||||
−0.756560 | + | 0.653925i | \(0.773121\pi\) | |||||||
\(632\) | −1.25800 | + | 4.69491i | −0.0500405 | + | 0.186754i | ||||
\(633\) | 0.363828 | − | 14.0513i | 0.0144609 | − | 0.558490i | ||||
\(634\) | 0.804448 | + | 0.464448i | 0.0319487 | + | 0.0184456i | ||||
\(635\) | −3.71263 | + | 4.65059i | −0.147331 | + | 0.184553i | ||||
\(636\) | −28.6463 | − | 8.47629i | −1.13590 | − | 0.336107i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.36823 | + | 8.36823i | −0.331301 | + | 0.331301i | ||||
\(639\) | 1.51783 | − | 29.2902i | 0.0600445 | − | 1.15870i | ||||
\(640\) | 21.8080 | + | 3.29848i | 0.862038 | + | 0.130384i | ||||
\(641\) | −26.6744 | − | 15.4005i | −1.05357 | − | 0.608282i | −0.129927 | − | 0.991524i | \(-0.541474\pi\) |
−0.923648 | + | 0.383242i | \(0.874808\pi\) | |||||||
\(642\) | −2.45720 | + | 4.01242i | −0.0969778 | + | 0.158357i | ||||
\(643\) | −6.17366 | − | 6.17366i | −0.243465 | − | 0.243465i | 0.574817 | − | 0.818282i | \(-0.305073\pi\) |
−0.818282 | + | 0.574817i | \(0.805073\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.04905 | + | 3.62291i | −0.120056 | + | 0.142652i | ||||
\(646\) | 0.269007 | + | 0.465934i | 0.0105839 | + | 0.0183319i | ||||
\(647\) | −32.0054 | + | 8.57582i | −1.25826 | + | 0.337150i | −0.825523 | − | 0.564369i | \(-0.809120\pi\) |
−0.432739 | + | 0.901519i | \(0.642453\pi\) | |||||||
\(648\) | −9.93932 | + | 8.06800i | −0.390453 | + | 0.316941i | ||||
\(649\) | −18.3363 | + | 10.5865i | −0.719762 | + | 0.415555i | ||||
\(650\) | −3.04441 | + | 2.81899i | −0.119412 | + | 0.110570i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26.3851 | − | 26.3851i | 1.03332 | − | 1.03332i | ||||
\(653\) | 23.4857 | + | 6.29299i | 0.919068 | + | 0.246264i | 0.687187 | − | 0.726481i | \(-0.258845\pi\) |
0.231881 | + | 0.972744i | \(0.425512\pi\) | |||||||
\(654\) | −2.93083 | − | 3.08664i | −0.114605 | − | 0.120697i | ||||
\(655\) | 16.1458 | − | 11.9033i | 0.630869 | − | 0.465102i | ||||
\(656\) | −3.86582 | + | 2.23193i | −0.150935 | + | 0.0871423i | ||||
\(657\) | −19.9490 | + | 4.25252i | −0.778286 | + | 0.165906i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.0375362 | −0.00146220 | −0.000731101 | − | 1.00000i | \(-0.500233\pi\) | ||||
−0.000731101 | 1.00000i | \(0.500233\pi\) | ||||||||
\(660\) | −20.0587 | + | 14.0014i | −0.780784 | + | 0.545006i | ||||
\(661\) | −9.84684 | + | 17.0552i | −0.382998 | + | 0.663371i | −0.991489 | − | 0.130189i | \(-0.958442\pi\) |
0.608492 | + | 0.793560i | \(0.291775\pi\) | |||||||
\(662\) | −1.28650 | + | 0.344716i | −0.0500011 | + | 0.0133978i | ||||
\(663\) | 0.405748 | − | 0.662556i | 0.0157579 | − | 0.0257315i | ||||
\(664\) | 12.6109i | 0.489396i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.02664 | + | 7.75029i | −0.194778 | + | 0.300318i | ||||
\(667\) | 28.7120 | + | 7.69337i | 1.11173 | + | 0.297888i | ||||
\(668\) | −11.9347 | − | 44.5408i | −0.461766 | − | 1.72334i | ||||
\(669\) | −20.5041 | + | 19.4691i | −0.792733 | + | 0.752717i | ||||
\(670\) | −0.943273 | + | 0.105791i | −0.0364418 | + | 0.00408706i | ||||
\(671\) | − | 6.20798i | − | 0.239656i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.33276 | − | 4.33276i | −0.167016 | − | 0.167016i | 0.618651 | − | 0.785666i | \(-0.287680\pi\) |
−0.785666 | + | 0.618651i | \(0.787680\pi\) | |||||||
\(674\) | −4.44897 | − | 7.70584i | −0.171368 | − | 0.296818i | ||||
\(675\) | 3.77232 | + | 25.7054i | 0.145197 | + | 0.989403i | ||||
\(676\) | 7.38079 | − | 12.7839i | 0.283877 | − | 0.491689i | ||||
\(677\) | −1.33467 | + | 4.98104i | −0.0512954 | + | 0.191437i | −0.986819 | − | 0.161827i | \(-0.948261\pi\) |
0.935524 | + | 0.353264i | \(0.114928\pi\) | |||||||
\(678\) | 6.52335 | − | 3.54436i | 0.250528 | − | 0.136120i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.253352 | − | 0.579876i | 0.00971559 | − | 0.0222372i | ||||
\(681\) | 4.03385 | + | 16.7805i | 0.154577 | + | 0.643031i | ||||
\(682\) | −0.297720 | − | 1.11111i | −0.0114003 | − | 0.0425465i | ||||
\(683\) | 12.3547 | + | 46.1083i | 0.472739 | + | 1.76429i | 0.629861 | + | 0.776708i | \(0.283112\pi\) |
−0.157122 | + | 0.987579i | \(0.550222\pi\) | |||||||
\(684\) | −41.0404 | − | 2.12673i | −1.56922 | − | 0.0813176i | ||||
\(685\) | 19.1242 | − | 7.49436i | 0.730697 | − | 0.286345i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.97013 | − | 7.30696i | −0.151470 | − | 0.278778i | ||||
\(688\) | −1.01435 | + | 3.78559i | −0.0386716 | + | 0.144324i | ||||
\(689\) | 10.4278 | − | 18.0614i | 0.397267 | − | 0.688086i | ||||
\(690\) | −4.04324 | − | 1.89262i | −0.153924 | − | 0.0720509i | ||||
\(691\) | 6.10922 | + | 10.5815i | 0.232406 | + | 0.402539i | 0.958516 | − | 0.285040i | \(-0.0920069\pi\) |
−0.726110 | + | 0.687579i | \(0.758674\pi\) | |||||||
\(692\) | 20.2799 | + | 20.2799i | 0.770928 | + | 0.770928i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.85547i | 0.108392i | ||||||||
\(695\) | 0.458353 | + | 4.08685i | 0.0173863 | + | 0.155023i | ||||
\(696\) | 16.1017 | + | 16.9577i | 0.610335 | + | 0.642782i | ||||
\(697\) | 0.0717086 | + | 0.267620i | 0.00271616 | + | 0.0101368i | ||||
\(698\) | −5.27145 | − | 1.41248i | −0.199527 | − | 0.0534632i | ||||
\(699\) | 9.92404 | − | 33.5391i | 0.375362 | − | 1.26856i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7907i | 0.823024i | 0.911404 | + | 0.411512i | \(0.134999\pi\) | ||||
−0.911404 | + | 0.411512i | \(0.865001\pi\) | |||||||
\(702\) | −1.85973 | − | 3.89021i | −0.0701911 | − | 0.146826i | ||||
\(703\) | −59.3691 | + | 15.9079i | −2.23915 | + | 0.599978i | ||||
\(704\) | −8.34962 | + | 14.4620i | −0.314688 | + | 0.545056i | ||||
\(705\) | −3.51245 | − | 0.624655i | −0.132287 | − | 0.0235259i | ||||
\(706\) | 3.93294 | 0.148018 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.63670 | + | 17.7362i | 0.362169 | + | 0.666567i | ||||
\(709\) | −12.2649 | + | 7.08112i | −0.460617 | + | 0.265937i | −0.712304 | − | 0.701872i | \(-0.752348\pi\) |
0.251687 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(710\) | 7.95583 | + | 1.20333i | 0.298577 | + | 0.0451600i | ||||
\(711\) | −9.13129 | + | 4.65936i | −0.342450 | + | 0.174740i | ||||
\(712\) | −17.0048 | − | 4.55642i | −0.637282 | − | 0.170759i | ||||
\(713\) | −2.04300 | + | 2.04300i | −0.0765110 | + | 0.0765110i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.23090 | − | 15.9001i | −0.233023 | − | 0.594629i | ||||
\(716\) | 28.5039 | − | 16.4567i | 1.06524 | − | 0.615016i | ||||
\(717\) | −0.576629 | + | 22.2698i | −0.0215346 | + | 0.831683i | ||||
\(718\) | 2.16695 | − | 0.580632i | 0.0808698 | − | 0.0216690i | ||||
\(719\) | −19.6576 | − | 34.0480i | −0.733106 | − | 1.26978i | −0.955549 | − | 0.294831i | \(-0.904737\pi\) |
0.222443 | − | 0.974946i | \(-0.428597\pi\) | |||||||
\(720\) | 11.8474 | + | 17.9451i | 0.441525 | + | 0.668776i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.10324 | + | 9.10324i | 0.338787 | + | 0.338787i | ||||
\(723\) | −23.9075 | − | 14.6409i | −0.889128 | − | 0.544500i | ||||
\(724\) | −19.2535 | − | 11.1160i | −0.715551 | − | 0.413124i | ||||
\(725\) | 46.2792 | − | 10.5129i | 1.71877 | − | 0.390441i | ||||
\(726\) | 0.0707978 | + | 0.294514i | 0.00262755 | + | 0.0109304i | ||||
\(727\) | 10.0141 | − | 10.0141i | 0.371403 | − | 0.371403i | −0.496585 | − | 0.867988i | \(-0.665413\pi\) |
0.867988 | + | 0.496585i | \(0.165413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6750 | − | 4.17686i | −0.987962 | − | 0.154699i | ||||
\(730\) | −0.623678 | − | 5.56095i | −0.0230834 | − | 0.205820i | ||||
\(731\) | 0.210661 | + | 0.121625i | 0.00779159 | + | 0.00449848i | ||||
\(732\) | −5.91636 | − | 0.153191i | −0.218675 | − | 0.00566212i | ||||
\(733\) | −11.1907 | + | 41.7644i | −0.413339 | + | 1.54260i | 0.374799 | + | 0.927106i | \(0.377712\pi\) |
−0.788139 | + | 0.615498i | \(0.788955\pi\) | |||||||
\(734\) | −1.83618 | −0.0677745 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.6040 | −0.464589 | ||||||||
\(737\) | 1.01115 | − | 3.77365i | 0.0372461 | − | 0.139004i | ||||
\(738\) | 1.46269 | + | 0.474309i | 0.0538423 | + | 0.0174596i | ||||
\(739\) | −13.9513 | − | 8.05476i | −0.513205 | − | 0.296299i | 0.220945 | − | 0.975286i | \(-0.429086\pi\) |
−0.734150 | + | 0.678987i | \(0.762419\pi\) | |||||||
\(740\) | 27.2584 | + | 21.7608i | 1.00204 | + | 0.799942i | ||||
\(741\) | 8.14019 | − | 27.5104i | 0.299037 | − | 1.01062i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1679 | + | 23.1679i | −0.849946 | + | 0.849946i | −0.990126 | − | 0.140180i | \(-0.955232\pi\) |
0.140180 | + | 0.990126i | \(0.455232\pi\) | |||||||
\(744\) | −2.20999 | + | 0.531257i | −0.0810222 | + | 0.0194768i | ||||
\(745\) | 1.30995 | + | 1.77683i | 0.0479929 | + | 0.0650979i | ||||
\(746\) | −3.18748 | − | 1.84029i | −0.116702 | − | 0.0673780i | ||||
\(747\) | −19.7554 | + | 17.8088i | −0.722813 | + | 0.651591i | ||||
\(748\) | 0.888574 | + | 0.888574i | 0.0324895 | + | 0.0324895i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.11961 | + | 0.337528i | −0.259971 | + | 0.0123248i | ||||
\(751\) | −14.3770 | − | 24.9017i | −0.524625 | − | 0.908677i | −0.999589 | − | 0.0286715i | \(-0.990872\pi\) |
0.474964 | − | 0.880005i | \(-0.342461\pi\) | |||||||
\(752\) | −2.85212 | + | 0.764222i | −0.104006 | + | 0.0278683i | ||||
\(753\) | 13.9013 | + | 0.359944i | 0.506592 | + | 0.0131171i | ||||
\(754\) | −6.82115 | + | 3.93819i | −0.248412 | + | 0.143420i | ||||
\(755\) | −7.79827 | + | 17.8488i | −0.283808 | + | 0.649585i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.29026 | + | 1.29026i | −0.0468952 | + | 0.0468952i | −0.730166 | − | 0.683270i | \(-0.760557\pi\) |
0.683270 | + | 0.730166i | \(0.260557\pi\) | |||||||
\(758\) | −7.63369 | − | 2.04544i | −0.277268 | − | 0.0742938i | ||||
\(759\) | 13.3248 | − | 12.6521i | 0.483658 | − | 0.459244i | ||||
\(760\) | 3.49462 | − | 23.1048i | 0.126763 | − | 0.838099i | ||||
\(761\) | −29.4421 | + | 16.9984i | −1.06728 | + | 0.616193i | −0.927436 | − | 0.373981i | \(-0.877992\pi\) |
−0.139841 | + | 0.990174i | \(0.544659\pi\) | |||||||
\(762\) | 1.49075 | − | 0.809978i | 0.0540043 | − | 0.0293424i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −33.1604 | −1.19970 | ||||||||
\(765\) | 1.26618 | − | 0.422004i | 0.0457787 | − | 0.0152576i | ||||
\(766\) | 3.81439 | − | 6.60672i | 0.137820 | − | 0.238711i | ||||
\(767\) | −13.6114 | + | 3.64716i | −0.491479 | + | 0.131691i | ||||
\(768\) | 9.20045 | + | 5.63434i | 0.331993 | + | 0.203312i | ||||
\(769\) | − | 21.4206i | − | 0.772448i | −0.922405 | − | 0.386224i | \(-0.873779\pi\) | ||
0.922405 | − | 0.386224i | \(-0.126221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.0158 | − | 11.5446i | −1.40512 | − | 0.415768i | ||||
\(772\) | −36.5222 | − | 9.78610i | −1.31446 | − | 0.352209i | ||||
\(773\) | −3.47919 | − | 12.9845i | −0.125138 | − | 0.467021i | 0.874707 | − | 0.484653i | \(-0.161054\pi\) |
−0.999845 | + | 0.0176318i | \(0.994387\pi\) | |||||||
\(774\) | 1.20252 | − | 0.613604i | 0.0432238 | − | 0.0220555i | ||||
\(775\) | −1.36420 | + | 4.40657i | −0.0490037 | + | 0.158289i | ||||
\(776\) | − | 13.5043i | − | 0.484777i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.54798 | + | 3.54798i | 0.127201 | + | 0.127201i | ||||
\(779\) | 5.11550 | + | 8.86031i | 0.183282 | + | 0.317454i | ||||
\(780\) | −15.3069 | + | 5.54585i | −0.548076 | + | 0.198573i | ||||
\(781\) | −16.5590 | + | 28.6810i | −0.592526 | + | 1.02629i | ||||
\(782\) | −0.0593559 | + | 0.221519i | −0.00212256 | + | 0.00792151i | ||||
\(783\) | −3.82640 | + | 49.1714i | −0.136745 | + | 1.75724i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.07251 | − | 15.4959i | −0.216737 | − | 0.553072i | ||||
\(786\) | −5.56059 | + | 1.33670i | −0.198340 | + | 0.0476786i | ||||
\(787\) | 2.08930 | + | 7.79736i | 0.0744754 | + | 0.277946i | 0.993114 | − | 0.117153i | \(-0.0373769\pi\) |
−0.918638 | + | 0.395099i | \(0.870710\pi\) | |||||||
\(788\) | 2.80273 | + | 10.4599i | 0.0998431 | + | 0.372619i | ||||
\(789\) | −32.9527 | + | 7.92146i | −1.17315 | + | 0.282011i | ||||
\(790\) | −1.02613 | − | 2.61849i | −0.0365081 | − | 0.0931616i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 14.1376 | − | 3.01369i | 0.502356 | − | 0.107087i | ||||
\(793\) | 1.06936 | − | 3.99091i | 0.0379741 | − | 0.141721i | ||||
\(794\) | −6.39291 | + | 11.0728i | −0.226876 | + | 0.392960i | ||||
\(795\) | 33.6843 | − | 12.2041i | 1.19466 | − | 0.432836i | ||||
\(796\) | −12.5061 | − | 21.6612i | −0.443267 | − | 0.767761i | ||||
\(797\) | 7.78096 | + | 7.78096i | 0.275616 | + | 0.275616i | 0.831356 | − | 0.555740i | \(-0.187565\pi\) |
−0.555740 | + | 0.831356i | \(0.687565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.183268i | 0.00648357i | ||||||||
\(800\) | −17.8010 | + | 9.38472i | −0.629359 | + | 0.331800i | ||||
\(801\) | −16.8760 | − | 33.0732i | −0.596286 | − | 1.16858i | ||||
\(802\) | 1.47668 | + | 5.51105i | 0.0521434 | + | 0.194602i | ||||
\(803\) | 22.2471 | + | 5.96109i | 0.785083 | + | 0.210362i | ||||
\(804\) | −3.57144 | − | 1.05677i | −0.125955 | − | 0.0372694i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 0.765579i | − | 0.0269664i | ||||||
\(807\) | 16.9321 | + | 10.3692i | 0.596039 | + | 0.365013i | ||||
\(808\) | 17.1087 | − | 4.58427i | 0.601883 | − | 0.161274i | ||||
\(809\) | −14.3936 | + | 24.9304i | −0.506051 | + | 0.876506i | 0.493925 | + | 0.869505i | \(0.335562\pi\) |
−0.999975 | + | 0.00700090i | \(0.997772\pi\) | |||||||
\(810\) | 1.85884 | − | 7.17019i | 0.0653130 | − | 0.251935i | ||||
\(811\) | −9.83136 | −0.345226 | −0.172613 | − | 0.984990i | \(-0.555221\pi\) | ||||
−0.172613 | + | 0.984990i | \(0.555221\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.8187 | + | 6.96485i | −0.449572 | + | 0.244268i | ||||
\(814\) | 9.03336 | − | 5.21542i | 0.316619 | − | 0.182800i | ||||
\(815\) | −6.69233 | + | 44.2466i | −0.234422 | + | 1.54989i | ||||
\(816\) | 0.801051 | − | 0.760615i | 0.0280424 | − | 0.0266269i | ||||
\(817\) | 8.67644 | + | 2.32484i | 0.303550 | + | 0.0813360i | ||||
\(818\) | −8.33920 | + | 8.33920i | −0.291573 | + | 0.291573i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.32445 | − | 5.32025i | 0.0811734 | − | 0.185791i | ||||
\(821\) | −29.9149 | + | 17.2714i | −1.04404 | + | 0.602775i | −0.920974 | − | 0.389624i | \(-0.872605\pi\) |
−0.123063 | + | 0.992399i | \(0.539272\pi\) | |||||||
\(822\) | −5.85413 | − | 0.151580i | −0.204186 | − | 0.00528696i | ||||
\(823\) | 16.3184 | − | 4.37251i | 0.568825 | − | 0.152416i | 0.0370675 | − | 0.999313i | \(-0.488198\pi\) |
0.531758 | + | 0.846896i | \(0.321532\pi\) | |||||||
\(824\) | −9.84596 | − | 17.0537i | −0.343000 | − | 0.594094i | ||||
\(825\) | 9.39837 | − | 27.7904i | 0.327209 | − | 0.967537i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.8624 | + | 20.8624i | 0.725457 | + | 0.725457i | 0.969711 | − | 0.244254i | \(-0.0785431\pi\) |
−0.244254 | + | 0.969711i | \(0.578543\pi\) | |||||||
\(828\) | −11.7290 | − | 13.0111i | −0.407611 | − | 0.452165i | ||||
\(829\) | 30.0070 | + | 17.3245i | 1.04219 | + | 0.601706i | 0.920452 | − | 0.390856i | \(-0.127821\pi\) |
0.121734 | + | 0.992563i | \(0.461154\pi\) | |||||||
\(830\) | −4.32998 | − | 5.87323i | −0.150296 | − | 0.203863i | ||||
\(831\) | 30.3200 | − | 7.28858i | 1.05179 | − | 0.252838i | ||||
\(832\) | −7.85887 | + | 7.85887i | −0.272457 | + | 0.272457i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.332674 | − | 1.12430i | 0.0115196 | − | 0.0389313i | ||||
\(835\) | 43.2181 | + | 34.5016i | 1.49563 | + | 1.19398i | ||||
\(836\) | 40.1867 | + | 23.2018i | 1.38989 | + | 0.802451i | ||||
\(837\) | −3.95314 | − | 2.71181i | −0.136641 | − | 0.0937339i | ||||
\(838\) | −0.566873 | + | 2.11560i | −0.0195823 | + | 0.0730822i | ||||
\(839\) | −10.9282 | −0.377283 | −0.188642 | − | 0.982046i | \(-0.560408\pi\) | ||||
−0.188642 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.0915 | 2.10660 | ||||||||
\(842\) | 1.01348 | − | 3.78238i | 0.0349270 | − | 0.130349i | ||||
\(843\) | −7.64013 | − | 0.197825i | −0.263140 | − | 0.00681344i | ||||
\(844\) | 13.1039 | + | 7.56555i | 0.451055 | + | 0.260417i | ||||
\(845\) | 1.97309 | + | 17.5928i | 0.0678763 | + | 0.605211i | ||||
\(846\) | 0.853360 | + | 0.553468i | 0.0293391 | + | 0.0190286i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.9675 | − | 20.9675i | 0.720027 | − | 0.720027i | ||||
\(849\) | 1.18653 | + | 4.93587i | 0.0407215 | + | 0.169399i | ||||
\(850\) | 0.0811095 | + | 0.357053i | 0.00278203 | + | 0.0122468i | ||||
\(851\) | −22.6893 | − | 13.0997i | −0.777779 | − | 0.449051i | ||||
\(852\) | 26.9251 | + | 16.4889i | 0.922438 | + | 0.564899i | ||||
\(853\) | −8.08267 | − | 8.08267i | −0.276745 | − | 0.276745i | 0.555063 | − | 0.831808i | \(-0.312694\pi\) |
−0.831808 | + | 0.555063i | \(0.812694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41.1296 | − | 27.1537i | 1.40660 | − | 0.928636i | ||||
\(856\) | −5.24890 | − | 9.09135i | −0.179404 | − | 0.310736i | ||||
\(857\) | −19.5603 | + | 5.24115i | −0.668166 | + | 0.179034i | −0.576928 | − | 0.816795i | \(-0.695749\pi\) |
−0.0912372 | + | 0.995829i | \(0.529082\pi\) | |||||||
\(858\) | −0.126026 | + | 4.86720i | −0.00430244 | + | 0.166163i | ||||
\(859\) | 21.7038 | − | 12.5307i | 0.740525 | − | 0.427542i | −0.0817353 | − | 0.996654i | \(-0.526046\pi\) |
0.822260 | + | 0.569112i | \(0.192713\pi\) | |||||||
\(860\) | −1.85984 | − | 4.74597i | −0.0634202 | − | 0.161836i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.93418 | − | 2.93418i | 0.0999387 | − | 0.0999387i | ||||
\(863\) | 44.8273 | + | 12.0115i | 1.52594 | + | 0.408875i | 0.921692 | − | 0.387922i | \(-0.126807\pi\) |
0.604248 | + | 0.796796i | \(0.293474\pi\) | |||||||
\(864\) | −3.82911 | − | 20.5592i | −0.130269 | − | 0.699438i | ||||
\(865\) | −34.0084 | − | 5.14380i | −1.15632 | − | 0.174895i | ||||
\(866\) | −4.39564 | + | 2.53782i | −0.149370 | + | 0.0862387i | ||||
\(867\) | 14.0247 | + | 25.8123i | 0.476304 | + | 0.876631i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5755 | 0.392671 | ||||||||
\(870\) | −13.3215 | − | 2.36910i | −0.451642 | − | 0.0803201i | ||||
\(871\) | 1.30007 | − | 2.25178i | 0.0440511 | − | 0.0762988i | ||||
\(872\) | 9.17327 | − | 2.45797i | 0.310646 | − | 0.0832374i | ||||
\(873\) | 21.1550 | − | 19.0705i | 0.715990 | − | 0.645440i | ||||
\(874\) | 8.46858i | 0.286454i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.23006 | − | 21.0550i | 0.210494 | − | 0.711381i | ||||
\(877\) | −20.8851 | − | 5.59615i | −0.705240 | − | 0.188968i | −0.111663 | − | 0.993746i | \(-0.535618\pi\) |
−0.593576 | + | 0.804778i | \(0.702284\pi\) | |||||||
\(878\) | 2.70904 | + | 10.1103i | 0.0914258 | + | 0.341206i | ||||
\(879\) | 12.4406 | + | 13.1019i | 0.419609 | + | 0.441917i | ||||
\(880\) | −2.70619 | − | 24.1294i | −0.0912256 | − | 0.813402i | ||||
\(881\) | − | 29.1988i | − | 0.983734i | −0.870670 | − | 0.491867i | \(-0.836315\pi\) | ||
0.870670 | − | 0.491867i | \(-0.163685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.7944 | − | 24.7944i | −0.834397 | − | 0.834397i | 0.153718 | − | 0.988115i | \(-0.450875\pi\) |
−0.988115 | + | 0.153718i | \(0.950875\pi\) | |||||||
\(884\) | 0.418174 | + | 0.724298i | 0.0140647 | + | 0.0243608i | ||||
\(885\) | −21.9243 | − | 10.2627i | −0.736977 | − | 0.344975i | ||||
\(886\) | 5.00021 | − | 8.66062i | 0.167985 | − | 0.290959i | ||||
\(887\) | −6.79094 | + | 25.3441i | −0.228018 | + | 0.850973i | 0.753156 | + | 0.657843i | \(0.228531\pi\) |
−0.981173 | + | 0.193131i | \(0.938136\pi\) | |||||||
\(888\) | −9.83997 | − | 18.1103i | −0.330208 | − | 0.607743i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.48407 | − | 3.71661i | 0.317907 | − | 0.124581i | ||||
\(891\) | 24.6859 | + | 17.8912i | 0.827007 | + | 0.599377i | ||||
\(892\) | −7.87776 | − | 29.4002i | −0.263767 | − | 0.984392i | ||||
\(893\) | 1.75157 | + | 6.53694i | 0.0586140 | + | 0.218750i | ||||
\(894\) | −0.147103 | − | 0.611937i | −0.00491985 | − | 0.0204662i | ||||
\(895\) | −15.8031 | + | 36.1705i | −0.528240 | + | 1.20905i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.7455 | − | 5.83839i | 0.358781 | − | 0.194938i | ||||
\(898\) | −0.229229 | + | 0.855494i | −0.00764947 | + | 0.0285482i | ||||
\(899\) | −4.37842 | + | 7.58364i | −0.146028 | + | 0.252928i | ||||
\(900\) | −26.2530 | − | 9.64266i | −0.875101 | − | 0.321422i | ||||
\(901\) | −0.920228 | − | 1.59388i | −0.0306572 | − | 0.0530999i | ||||
\(902\) | −1.22774 | − | 1.22774i | −0.0408792 | − | 0.0408792i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.5644i | 0.550925i | ||||||||
\(905\) | 26.4961 | − | 2.97162i | 0.880760 | − | 0.0987799i | ||||
\(906\) | 4.02708 | − | 3.82380i | 0.133791 | − | 0.127037i | ||||
\(907\) | 1.24159 | + | 4.63366i | 0.0412262 | + | 0.153858i | 0.983471 | − | 0.181068i | \(-0.0579554\pi\) |
−0.942244 | + | 0.334926i | \(0.891289\pi\) | |||||||
\(908\) | −17.9455 | − | 4.80849i | −0.595543 | − | 0.159575i | ||||
\(909\) | 31.3421 | + | 20.3277i | 1.03955 | + | 0.674227i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 16.2139i | − | 0.537190i | −0.963253 | − | 0.268595i | \(-0.913441\pi\) | ||
0.963253 | − | 0.268595i | \(-0.0865592\pi\) | |||||||
\(912\) | 21.3029 | − | 34.7861i | 0.705411 | − | 1.15188i | ||||
\(913\) | 29.0097 | − | 7.77313i | 0.960081 | − | 0.257253i | ||||
\(914\) | 1.61776 | − | 2.80205i | 0.0535109 | − | 0.0926836i | ||||
\(915\) | 5.82005 | − | 4.06253i | 0.192405 | − | 0.134303i | ||||
\(916\) | 8.95190 | 0.295779 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.379367 | − | 0.0295215i | −0.0125210 | − | 0.000974354i | ||||
\(919\) | −4.80348 | + | 2.77329i | −0.158452 | + | 0.0914823i | −0.577129 | − | 0.816653i | \(-0.695827\pi\) |
0.418677 | + | 0.908135i | \(0.362494\pi\) | |||||||
\(920\) | 8.01735 | − | 5.91072i | 0.264324 | − | 0.194871i | ||||
\(921\) | −19.1616 | − | 20.1803i | −0.631396 | − | 0.664962i | ||||
\(922\) | 12.5937 | + | 3.37447i | 0.414752 | + | 0.111132i | ||||
\(923\) | −15.5857 | + | 15.5857i | −0.513009 | + | 0.513009i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.7986 | − | 1.60697i | −1.37433 | − | 0.0528368i | ||||
\(926\) | 9.05498 | − | 5.22789i | 0.297565 | − | 0.171799i | ||||
\(927\) | 12.8110 | − | 39.5070i | 0.420769 | − | 1.29758i | ||||
\(928\) | −36.8990 | + | 9.88706i | −1.21127 | + | 0.324559i | ||||
\(929\) | 6.39892 | + | 11.0833i | 0.209942 | + | 0.363630i | 0.951696 | − | 0.307042i | \(-0.0993392\pi\) |
−0.741754 | + | 0.670672i | \(0.766006\pi\) | |||||||
\(930\) | 0.846846 | − | 1.00623i | 0.0277692 | − | 0.0329956i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.6237 | + | 26.6237i | 0.872090 | + | 0.872090i | ||||
\(933\) | 8.08941 | − | 13.2094i | 0.264835 | − | 0.432456i | ||||
\(934\) | 2.61713 | + | 1.51100i | 0.0856352 | + | 0.0494415i | ||||
\(935\) | −1.49009 | − | 0.225378i | −0.0487312 | − | 0.00737064i | ||||
\(936\) | 9.60771 | + | 0.497876i | 0.314038 | + | 0.0162736i | ||||
\(937\) | 24.4148 | − | 24.4148i | 0.797598 | − | 0.797598i | −0.185119 | − | 0.982716i | \(-0.559267\pi\) |
0.982716 | + | 0.185119i | \(0.0592669\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.6278 | − | 3.14471i | −0.346825 | − | 0.102624i | ||||
\(940\) | 2.39601 | − | 3.00134i | 0.0781492 | − | 0.0978929i | ||||
\(941\) | −3.22540 | − | 1.86219i | −0.105145 | − | 0.0607055i | 0.446505 | − | 0.894781i | \(-0.352668\pi\) |
−0.551650 | + | 0.834075i | \(0.686002\pi\) | |||||||
\(942\) | −0.122822 | + | 4.74347i | −0.00400175 | + | 0.154551i | ||||
\(943\) | −1.12873 | + | 4.21246i | −0.0367564 | + | 0.137177i | ||||
\(944\) | −20.0354 | −0.652098 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.52440 | −0.0495626 | ||||||||
\(947\) | −12.5754 | + | 46.9322i | −0.408647 | + | 1.52509i | 0.388582 | + | 0.921414i | \(0.372965\pi\) |
−0.797229 | + | 0.603677i | \(0.793702\pi\) | |||||||
\(948\) | 0.285642 | − | 11.0317i | 0.00927723 | − | 0.358294i | ||||
\(949\) | 13.2751 | + | 7.66439i | 0.430929 | + | 0.248797i | ||||
\(950\) | 6.30557 | + | 11.9604i | 0.204580 | + | 0.388047i | ||||
\(951\) | −4.19155 | − | 1.24026i | −0.135920 | − | 0.0402181i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.7199 | − | 21.7199i | 0.703578 | − | 0.703578i | −0.261599 | − | 0.965177i | \(-0.584250\pi\) |
0.965177 | + | 0.261599i | \(0.0842497\pi\) | |||||||
\(954\) | −10.2007 | − | 0.528606i | −0.330261 | − | 0.0171143i | ||||
\(955\) | 32.0095 | − | 23.5987i | 1.03580 | − | 0.763637i | ||||
\(956\) | −20.7683 | − | 11.9906i | −0.671695 | − | 0.387803i | ||||
\(957\) | 29.0843 | − | 47.4925i | 0.940162 | − | 1.53521i | ||||
\(958\) | 10.5102 | + | 10.5102i | 0.339569 | + | 0.339569i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −19.0223 | + | 1.63612i | −0.613942 | + | 0.0528055i | ||||
\(961\) | 15.0744 | + | 26.1097i | 0.486272 | + | 0.842247i | ||||
\(962\) | 6.70565 | − | 1.79677i | 0.216199 | − | 0.0579303i | ||||
\(963\) | 6.82958 | − | 21.0612i | 0.220080 | − | 0.678689i | ||||
\(964\) | 26.1353 | − | 15.0893i | 0.841763 | − | 0.485992i | ||||
\(965\) | 42.2190 | − | 16.5447i | 1.35908 | − | 0.532594i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.1187 | + | 42.1187i | −1.35445 | + | 1.35445i | −0.473831 | + | 0.880616i | \(0.657129\pi\) |
−0.880616 | + | 0.473831i | \(0.842871\pi\) | |||||||
\(968\) | −0.652806 | − | 0.174919i | −0.0209820 | − | 0.00562211i | ||||
\(969\) | −1.74330 | − | 1.83598i | −0.0560029 | − | 0.0589801i | ||||
\(970\) | 4.63675 | + | 6.28933i | 0.148877 | + | 0.201938i | ||||
\(971\) | 23.7650 | − | 13.7207i | 0.762655 | − | 0.440319i | −0.0675934 | − | 0.997713i | \(-0.521532\pi\) |
0.830248 | + | 0.557394i | \(0.188199\pi\) | |||||||
\(972\) | 17.6599 | − | 23.0848i | 0.566442 | − | 0.740444i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.3055 | −0.330211 | ||||||||
\(975\) | 10.8290 | − | 16.2466i | 0.346805 | − | 0.520309i | ||||
\(976\) | 2.93723 | − | 5.08744i | 0.0940185 | − | 0.162845i | ||||
\(977\) | 55.4023 | − | 14.8450i | 1.77248 | − | 0.474933i | 0.783297 | − | 0.621648i | \(-0.213537\pi\) |
0.989179 | + | 0.146715i | \(0.0468699\pi\) | |||||||
\(978\) | 6.66303 | − | 10.8802i | 0.213060 | − | 0.347912i | ||||
\(979\) | 41.9259i | 1.33996i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.8048 | + | 10.8992i | 0.536537 | + | 0.347984i | ||||
\(982\) | 13.0451 | + | 3.49543i | 0.416286 | + | 0.111544i | ||||
\(983\) | −6.23449 | − | 23.2674i | −0.198849 | − | 0.742116i | −0.991237 | − | 0.132098i | \(-0.957829\pi\) |
0.792387 | − | 0.610018i | \(-0.208838\pi\) | |||||||
\(984\) | −2.48794 | + | 2.36235i | −0.0793127 | + | 0.0753091i | ||||
\(985\) | −10.1493 | − | 8.10233i | −0.323384 | − | 0.258162i | ||||
\(986\) | 0.695074i | 0.0221357i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.8381 | + | 21.8381i | 0.694763 | + | 0.694763i | ||||
\(989\) | 1.91444 | + | 3.31591i | 0.0608756 | + | 0.105440i | ||||
\(990\) | −5.54949 | + | 6.25774i | −0.176374 | + | 0.198884i | ||||
\(991\) | −11.2380 | + | 19.4648i | −0.356986 | + | 0.618319i | −0.987456 | − | 0.157895i | \(-0.949529\pi\) |
0.630469 | + | 0.776214i | \(0.282862\pi\) | |||||||
\(992\) | 0.961016 | − | 3.58656i | 0.0305123 | − | 0.113873i | ||||
\(993\) | 5.50716 | − | 2.99223i | 0.174764 | − | 0.0949556i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.4874 | + | 12.0094i | 0.871408 | + | 0.380724i | ||||
\(996\) | −6.69213 | − | 27.8388i | −0.212048 | − | 0.882107i | ||||
\(997\) | 11.6511 | + | 43.4825i | 0.368994 | + | 1.37710i | 0.861925 | + | 0.507036i | \(0.169259\pi\) |
−0.492931 | + | 0.870068i | \(0.664074\pi\) | |||||||
\(998\) | −0.726425 | − | 2.71106i | −0.0229946 | − | 0.0858170i | ||||
\(999\) | 14.4747 | − | 40.9898i | 0.457960 | − | 1.29686i |
(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 | 735.2.y.j.263.6 | 48 | ||
3.2 | odd | 2 | inner | 735.2.y.j.263.7 | 48 | ||
5.2 | odd | 4 | inner | 735.2.y.j.557.6 | 48 | ||
7.2 | even | 3 | inner | 735.2.y.j.128.7 | 48 | ||
7.3 | odd | 6 | 735.2.j.h.638.6 | 24 | |||
7.4 | even | 3 | 105.2.j.a.8.6 | ✓ | 24 | ||
7.5 | odd | 6 | 735.2.y.g.128.7 | 48 | |||
7.6 | odd | 2 | 735.2.y.g.263.6 | 48 | |||
15.2 | even | 4 | inner | 735.2.y.j.557.7 | 48 | ||
21.2 | odd | 6 | inner | 735.2.y.j.128.6 | 48 | ||
21.5 | even | 6 | 735.2.y.g.128.6 | 48 | |||
21.11 | odd | 6 | 105.2.j.a.8.7 | yes | 24 | ||
21.17 | even | 6 | 735.2.j.h.638.7 | 24 | |||
21.20 | even | 2 | 735.2.y.g.263.7 | 48 | |||
35.2 | odd | 12 | inner | 735.2.y.j.422.7 | 48 | ||
35.4 | even | 6 | 525.2.j.b.218.7 | 24 | |||
35.12 | even | 12 | 735.2.y.g.422.7 | 48 | |||
35.17 | even | 12 | 735.2.j.h.197.7 | 24 | |||
35.18 | odd | 12 | 525.2.j.b.407.6 | 24 | |||
35.27 | even | 4 | 735.2.y.g.557.6 | 48 | |||
35.32 | odd | 12 | 105.2.j.a.92.7 | yes | 24 | ||
105.2 | even | 12 | inner | 735.2.y.j.422.6 | 48 | ||
105.17 | odd | 12 | 735.2.j.h.197.6 | 24 | |||
105.32 | even | 12 | 105.2.j.a.92.6 | yes | 24 | ||
105.47 | odd | 12 | 735.2.y.g.422.6 | 48 | |||
105.53 | even | 12 | 525.2.j.b.407.7 | 24 | |||
105.62 | odd | 4 | 735.2.y.g.557.7 | 48 | |||
105.74 | odd | 6 | 525.2.j.b.218.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.6 | ✓ | 24 | 7.4 | even | 3 | ||
105.2.j.a.8.7 | yes | 24 | 21.11 | odd | 6 | ||
105.2.j.a.92.6 | yes | 24 | 105.32 | even | 12 | ||
105.2.j.a.92.7 | yes | 24 | 35.32 | odd | 12 | ||
525.2.j.b.218.6 | 24 | 105.74 | odd | 6 | |||
525.2.j.b.218.7 | 24 | 35.4 | even | 6 | |||
525.2.j.b.407.6 | 24 | 35.18 | odd | 12 | |||
525.2.j.b.407.7 | 24 | 105.53 | even | 12 | |||
735.2.j.h.197.6 | 24 | 105.17 | odd | 12 | |||
735.2.j.h.197.7 | 24 | 35.17 | even | 12 | |||
735.2.j.h.638.6 | 24 | 7.3 | odd | 6 | |||
735.2.j.h.638.7 | 24 | 21.17 | even | 6 | |||
735.2.y.g.128.6 | 48 | 21.5 | even | 6 | |||
735.2.y.g.128.7 | 48 | 7.5 | odd | 6 | |||
735.2.y.g.263.6 | 48 | 7.6 | odd | 2 | |||
735.2.y.g.263.7 | 48 | 21.20 | even | 2 | |||
735.2.y.g.422.6 | 48 | 105.47 | odd | 12 | |||
735.2.y.g.422.7 | 48 | 35.12 | even | 12 | |||
735.2.y.g.557.6 | 48 | 35.27 | even | 4 | |||
735.2.y.g.557.7 | 48 | 105.62 | odd | 4 | |||
735.2.y.j.128.6 | 48 | 21.2 | odd | 6 | inner | ||
735.2.y.j.128.7 | 48 | 7.2 | even | 3 | inner | ||
735.2.y.j.263.6 | 48 | 1.1 | even | 1 | trivial | ||
735.2.y.j.263.7 | 48 | 3.2 | odd | 2 | inner | ||
735.2.y.j.422.6 | 48 | 105.2 | even | 12 | inner | ||
735.2.y.j.422.7 | 48 | 35.2 | odd | 12 | inner | ||
735.2.y.j.557.6 | 48 | 5.2 | odd | 4 | inner | ||
735.2.y.j.557.7 | 48 | 15.2 | even | 4 | inner |