Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,2,Mod(101,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.h (of order \(2\), degree \(1\), 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: | \(1.08596546749\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 20x^{12} + 36x^{10} + 240x^{8} - 156x^{6} + 268x^{4} + 136x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.15 | ||
Root | \(1.32216 + 1.07919i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.101 |
Dual form | 136.2.h.a.101.13 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09558 | + | 0.894257i | 0.774695 | + | 0.632335i | ||||
\(3\) | −1.88797 | −1.09002 | −0.545011 | − | 0.838429i | \(-0.683474\pi\) | ||||
−0.545011 | + | 0.838429i | \(0.683474\pi\) | |||||||
\(4\) | 0.400610 | + | 1.95947i | 0.200305 | + | 0.979734i | ||||
\(5\) | 2.41361 | 1.07940 | 0.539699 | − | 0.841858i | \(-0.318538\pi\) | ||||
0.539699 | + | 0.841858i | \(0.318538\pi\) | |||||||
\(6\) | −2.06843 | − | 1.68833i | −0.844434 | − | 0.689259i | ||||
\(7\) | 2.57100i | 0.971747i | 0.874029 | + | 0.485874i | \(0.161499\pi\) | ||||
−0.874029 | + | 0.485874i | \(0.838501\pi\) | |||||||
\(8\) | −1.31336 | + | 2.50501i | −0.464345 | + | 0.885655i | ||||
\(9\) | 0.564439 | 0.188146 | ||||||||
\(10\) | 2.64431 | + | 2.15839i | 0.836205 | + | 0.682542i | ||||
\(11\) | 0.736213 | 0.221976 | 0.110988 | − | 0.993822i | \(-0.464598\pi\) | ||||
0.110988 | + | 0.993822i | \(0.464598\pi\) | |||||||
\(12\) | −0.756340 | − | 3.69942i | −0.218337 | − | 1.06793i | ||||
\(13\) | − | 4.07497i | − | 1.13019i | −0.825024 | − | 0.565097i | \(-0.808839\pi\) | ||
0.825024 | − | 0.565097i | \(-0.191161\pi\) | |||||||
\(14\) | −2.29914 | + | 2.81675i | −0.614470 | + | 0.752808i | ||||
\(15\) | −4.55683 | −1.17657 | ||||||||
\(16\) | −3.67902 | + | 1.56996i | −0.919756 | + | 0.392491i | ||||
\(17\) | 3.99239 | − | 1.02997i | 0.968296 | − | 0.249804i | ||||
\(18\) | 0.618390 | + | 0.504753i | 0.145756 | + | 0.118971i | ||||
\(19\) | − | 0.853468i | − | 0.195799i | −0.995196 | − | 0.0978995i | \(-0.968788\pi\) | ||
0.995196 | − | 0.0978995i | \(-0.0312124\pi\) | |||||||
\(20\) | 0.966916 | + | 4.72939i | 0.216209 | + | 1.05752i | ||||
\(21\) | − | 4.85398i | − | 1.05923i | ||||||
\(22\) | 0.806583 | + | 0.658363i | 0.171964 | + | 0.140363i | ||||
\(23\) | − | 8.20450i | − | 1.71076i | −0.518004 | − | 0.855378i | \(-0.673325\pi\) | ||
0.518004 | − | 0.855378i | \(-0.326675\pi\) | |||||||
\(24\) | 2.47960 | − | 4.72939i | 0.506145 | − | 0.965382i | ||||
\(25\) | 0.825510 | 0.165102 | ||||||||
\(26\) | 3.64407 | − | 4.46448i | 0.714661 | − | 0.875556i | ||||
\(27\) | 4.59827 | 0.884938 | ||||||||
\(28\) | −5.03779 | + | 1.02997i | −0.952054 | + | 0.194646i | ||||
\(29\) | −5.86012 | −1.08820 | −0.544099 | − | 0.839021i | \(-0.683128\pi\) | ||||
−0.544099 | + | 0.839021i | \(0.683128\pi\) | |||||||
\(30\) | −4.99239 | − | 4.07497i | −0.911481 | − | 0.743985i | ||||
\(31\) | − | 3.51111i | − | 0.630614i | −0.948990 | − | 0.315307i | \(-0.897892\pi\) | ||
0.948990 | − | 0.315307i | \(-0.102108\pi\) | |||||||
\(32\) | −5.43463 | − | 1.56996i | −0.960716 | − | 0.277533i | ||||
\(33\) | −1.38995 | −0.241959 | ||||||||
\(34\) | 5.29505 | + | 2.44180i | 0.908094 | + | 0.418766i | ||||
\(35\) | 6.20539i | 1.04890i | ||||||||
\(36\) | 0.226120 | + | 1.10600i | 0.0376866 | + | 0.184333i | ||||
\(37\) | 4.38770 | 0.721333 | 0.360666 | − | 0.932695i | \(-0.382549\pi\) | ||||
0.360666 | + | 0.932695i | \(0.382549\pi\) | |||||||
\(38\) | 0.763219 | − | 0.935046i | 0.123811 | − | 0.151684i | ||||
\(39\) | 7.69344i | 1.23194i | ||||||||
\(40\) | −3.16995 | + | 6.04611i | −0.501213 | + | 0.955975i | ||||
\(41\) | 11.7156i | 1.82967i | 0.403827 | + | 0.914836i | \(0.367680\pi\) | ||||
−0.403827 | + | 0.914836i | \(0.632320\pi\) | |||||||
\(42\) | 4.34070 | − | 5.31794i | 0.669785 | − | 0.820577i | ||||
\(43\) | − | 1.09108i | − | 0.166389i | −0.996533 | − | 0.0831944i | \(-0.973488\pi\) | ||
0.996533 | − | 0.0831944i | \(-0.0265123\pi\) | |||||||
\(44\) | 0.294934 | + | 1.44258i | 0.0444630 | + | 0.217478i | ||||
\(45\) | 1.36234 | 0.203085 | ||||||||
\(46\) | 7.33693 | − | 8.98872i | 1.08177 | − | 1.32531i | ||||
\(47\) | −5.42795 | −0.791748 | −0.395874 | − | 0.918305i | \(-0.629558\pi\) | ||||
−0.395874 | + | 0.918305i | \(0.629558\pi\) | |||||||
\(48\) | 6.94589 | − | 2.96405i | 1.00255 | − | 0.427823i | ||||
\(49\) | 0.389949 | 0.0557070 | ||||||||
\(50\) | 0.904416 | + | 0.738218i | 0.127904 | + | 0.104400i | ||||
\(51\) | −7.53752 | + | 1.94455i | −1.05546 | + | 0.272292i | ||||
\(52\) | 7.98478 | − | 1.63247i | 1.10729 | − | 0.226383i | ||||
\(53\) | 4.66811i | 0.641214i | 0.947212 | + | 0.320607i | \(0.103887\pi\) | ||||
−0.947212 | + | 0.320607i | \(0.896113\pi\) | |||||||
\(54\) | 5.03779 | + | 4.11204i | 0.685557 | + | 0.559577i | ||||
\(55\) | 1.77693 | 0.239601 | ||||||||
\(56\) | −6.44038 | − | 3.37666i | −0.860633 | − | 0.451226i | ||||
\(57\) | 1.61132i | 0.213425i | ||||||||
\(58\) | −6.42026 | − | 5.24045i | −0.843021 | − | 0.688105i | ||||
\(59\) | 12.5060i | 1.62814i | 0.580767 | + | 0.814070i | \(0.302753\pi\) | ||||
−0.580767 | + | 0.814070i | \(0.697247\pi\) | |||||||
\(60\) | −1.82551 | − | 8.92895i | −0.235672 | − | 1.15272i | ||||
\(61\) | −8.16364 | −1.04525 | −0.522624 | − | 0.852564i | \(-0.675047\pi\) | ||||
−0.522624 | + | 0.852564i | \(0.675047\pi\) | |||||||
\(62\) | 3.13983 | − | 3.84672i | 0.398759 | − | 0.488534i | ||||
\(63\) | 1.45117i | 0.182831i | ||||||||
\(64\) | −4.55015 | − | 6.57998i | −0.568768 | − | 0.822498i | ||||
\(65\) | − | 9.83539i | − | 1.21993i | ||||||
\(66\) | −1.52281 | − | 1.24297i | −0.187444 | − | 0.152999i | ||||
\(67\) | − | 10.5614i | − | 1.29028i | −0.764063 | − | 0.645142i | \(-0.776798\pi\) | ||
0.764063 | − | 0.645142i | \(-0.223202\pi\) | |||||||
\(68\) | 3.61758 | + | 7.41034i | 0.438696 | + | 0.898636i | ||||
\(69\) | 15.4899i | 1.86476i | ||||||||
\(70\) | −5.54922 | + | 6.79853i | −0.663258 | + | 0.812580i | ||||
\(71\) | − | 0.511064i | − | 0.0606522i | −0.999540 | − | 0.0303261i | \(-0.990345\pi\) | ||
0.999540 | − | 0.0303261i | \(-0.00965458\pi\) | |||||||
\(72\) | −0.741314 | + | 1.41392i | −0.0873647 | + | 0.166633i | ||||
\(73\) | − | 13.3269i | − | 1.55980i | −0.625904 | − | 0.779900i | \(-0.715270\pi\) | ||
0.625904 | − | 0.779900i | \(-0.284730\pi\) | |||||||
\(74\) | 4.80709 | + | 3.92373i | 0.558813 | + | 0.456124i | ||||
\(75\) | −1.55854 | −0.179965 | ||||||||
\(76\) | 1.67234 | − | 0.341908i | 0.191831 | − | 0.0392195i | ||||
\(77\) | 1.89280i | 0.215705i | ||||||||
\(78\) | −6.87991 | + | 8.42881i | −0.778996 | + | 0.954375i | ||||
\(79\) | 1.45117i | 0.163270i | 0.996662 | + | 0.0816349i | \(0.0260141\pi\) | ||||
−0.996662 | + | 0.0816349i | \(0.973986\pi\) | |||||||
\(80\) | −8.87973 | + | 3.78928i | −0.992783 | + | 0.423654i | ||||
\(81\) | −10.3747 | −1.15275 | ||||||||
\(82\) | −10.4768 | + | 12.8354i | −1.15697 | + | 1.41744i | ||||
\(83\) | 4.35603i | 0.478137i | 0.971003 | + | 0.239068i | \(0.0768420\pi\) | ||||
−0.971003 | + | 0.239068i | \(0.923158\pi\) | |||||||
\(84\) | 9.51121 | − | 1.94455i | 1.03776 | − | 0.212168i | ||||
\(85\) | 9.63607 | − | 2.48594i | 1.04518 | − | 0.269638i | ||||
\(86\) | 0.975710 | − | 1.19538i | 0.105213 | − | 0.128901i | ||||
\(87\) | 11.0637 | 1.18616 | ||||||||
\(88\) | −0.966916 | + | 1.84422i | −0.103074 | + | 0.196594i | ||||
\(89\) | 5.72371 | 0.606712 | 0.303356 | − | 0.952877i | \(-0.401893\pi\) | ||||
0.303356 | + | 0.952877i | \(0.401893\pi\) | |||||||
\(90\) | 1.49255 | + | 1.21828i | 0.157329 | + | 0.128418i | ||||
\(91\) | 10.4768 | 1.09826 | ||||||||
\(92\) | 16.0765 | − | 3.28680i | 1.67609 | − | 0.342673i | ||||
\(93\) | 6.62888i | 0.687383i | ||||||||
\(94\) | −5.94678 | − | 4.85398i | −0.613363 | − | 0.500650i | ||||
\(95\) | − | 2.05994i | − | 0.211345i | ||||||
\(96\) | 10.2604 | + | 2.96405i | 1.04720 | + | 0.302517i | ||||
\(97\) | 11.8953i | 1.20779i | 0.797065 | + | 0.603894i | \(0.206385\pi\) | ||||
−0.797065 | + | 0.603894i | \(0.793615\pi\) | |||||||
\(98\) | 0.427222 | + | 0.348714i | 0.0431559 | + | 0.0352255i | ||||
\(99\) | 0.415547 | 0.0417640 | ||||||||
\(100\) | 0.330707 | + | 1.61756i | 0.0330707 | + | 0.161756i | ||||
\(101\) | − | 8.33582i | − | 0.829445i | −0.909948 | − | 0.414722i | \(-0.863879\pi\) | ||
0.909948 | − | 0.414722i | \(-0.136121\pi\) | |||||||
\(102\) | −9.99692 | − | 4.61006i | −0.989842 | − | 0.456463i | ||||
\(103\) | 15.5446 | 1.53165 | 0.765826 | − | 0.643048i | \(-0.222330\pi\) | ||||
0.765826 | + | 0.643048i | \(0.222330\pi\) | |||||||
\(104\) | 10.2078 | + | 5.35193i | 1.00096 | + | 0.524800i | ||||
\(105\) | − | 11.7156i | − | 1.14333i | ||||||
\(106\) | −4.17449 | + | 5.11431i | −0.405462 | + | 0.496746i | ||||
\(107\) | −14.9889 | −1.44903 | −0.724517 | − | 0.689257i | \(-0.757937\pi\) | ||||
−0.724517 | + | 0.689257i | \(0.757937\pi\) | |||||||
\(108\) | 1.84211 | + | 9.01016i | 0.177257 | + | 0.867003i | ||||
\(109\) | −0.941184 | −0.0901491 | −0.0450745 | − | 0.998984i | \(-0.514353\pi\) | ||||
−0.0450745 | + | 0.998984i | \(0.514353\pi\) | |||||||
\(110\) | 1.94678 | + | 1.58903i | 0.185618 | + | 0.151508i | ||||
\(111\) | −8.28385 | −0.786268 | ||||||||
\(112\) | −4.03638 | − | 9.45878i | −0.381402 | − | 0.893770i | ||||
\(113\) | 9.83539i | 0.925236i | 0.886558 | + | 0.462618i | \(0.153090\pi\) | ||||
−0.886558 | + | 0.462618i | \(0.846910\pi\) | |||||||
\(114\) | −1.44094 | + | 1.76534i | −0.134956 | + | 0.165339i | ||||
\(115\) | − | 19.8025i | − | 1.84659i | ||||||
\(116\) | −2.34762 | − | 11.4827i | −0.217971 | − | 1.06614i | ||||
\(117\) | − | 2.30007i | − | 0.212642i | ||||||
\(118\) | −11.1836 | + | 13.7014i | −1.02953 | + | 1.26131i | ||||
\(119\) | 2.64805 | + | 10.2644i | 0.242747 | + | 0.940940i | ||||
\(120\) | 5.98478 | − | 11.4149i | 0.546333 | − | 1.04203i | ||||
\(121\) | −10.4580 | −0.950726 | ||||||||
\(122\) | −8.94396 | − | 7.30039i | −0.809748 | − | 0.660946i | ||||
\(123\) | − | 22.1187i | − | 1.99438i | ||||||
\(124\) | 6.87991 | − | 1.40659i | 0.617834 | − | 0.126315i | ||||
\(125\) | −10.0756 | −0.901188 | ||||||||
\(126\) | −1.29772 | + | 1.58988i | −0.115610 | + | 0.141638i | ||||
\(127\) | −11.0984 | −0.984827 | −0.492413 | − | 0.870362i | \(-0.663885\pi\) | ||||
−0.492413 | + | 0.870362i | \(0.663885\pi\) | |||||||
\(128\) | 0.899126 | − | 11.2779i | 0.0794722 | − | 0.996837i | ||||
\(129\) | 2.05994i | 0.181367i | ||||||||
\(130\) | 8.79537 | − | 10.7755i | 0.771405 | − | 0.945074i | ||||
\(131\) | 18.4354 | 1.61071 | 0.805356 | − | 0.592792i | \(-0.201974\pi\) | ||||
0.805356 | + | 0.592792i | \(0.201974\pi\) | |||||||
\(132\) | −0.556827 | − | 2.72356i | −0.0484656 | − | 0.237055i | ||||
\(133\) | 2.19427 | 0.190267 | ||||||||
\(134\) | 9.44463 | − | 11.5709i | 0.815892 | − | 0.999577i | ||||
\(135\) | 11.0984 | 0.955201 | ||||||||
\(136\) | −2.66338 | + | 11.3537i | −0.228383 | + | 0.973571i | ||||
\(137\) | −13.5340 | −1.15629 | −0.578143 | − | 0.815935i | \(-0.696223\pi\) | ||||
−0.578143 | + | 0.815935i | \(0.696223\pi\) | |||||||
\(138\) | −13.8519 | + | 16.9705i | −1.17915 | + | 1.44462i | ||||
\(139\) | −2.71030 | −0.229885 | −0.114942 | − | 0.993372i | \(-0.536668\pi\) | ||||
−0.114942 | + | 0.993372i | \(0.536668\pi\) | |||||||
\(140\) | −12.1593 | + | 2.48594i | −1.02765 | + | 0.210100i | ||||
\(141\) | 10.2478 | 0.863022 | ||||||||
\(142\) | 0.457023 | − | 0.559914i | 0.0383525 | − | 0.0469870i | ||||
\(143\) | − | 3.00005i | − | 0.250876i | ||||||
\(144\) | −2.07658 | + | 0.886149i | −0.173049 | + | 0.0738457i | ||||
\(145\) | −14.1440 | −1.17460 | ||||||||
\(146\) | 11.9177 | − | 14.6008i | 0.986316 | − | 1.20837i | ||||
\(147\) | −0.736213 | −0.0607218 | ||||||||
\(148\) | 1.75775 | + | 8.59755i | 0.144487 | + | 0.706714i | ||||
\(149\) | 1.70694i | 0.139838i | 0.997553 | + | 0.0699188i | \(0.0222740\pi\) | ||||
−0.997553 | + | 0.0699188i | \(0.977726\pi\) | |||||||
\(150\) | −1.70751 | − | 1.39373i | −0.139418 | − | 0.113798i | ||||
\(151\) | 3.47786 | 0.283024 | 0.141512 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141512 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(152\) | 2.13794 | + | 1.12091i | 0.173410 | + | 0.0909182i | ||||
\(153\) | 2.25346 | − | 0.581354i | 0.182181 | − | 0.0469997i | ||||
\(154\) | −1.69265 | + | 2.07373i | −0.136398 | + | 0.167106i | ||||
\(155\) | − | 8.47445i | − | 0.680684i | ||||||
\(156\) | −15.0750 | + | 3.08207i | −1.20697 | + | 0.246763i | ||||
\(157\) | − | 22.0508i | − | 1.75984i | −0.475118 | − | 0.879922i | \(-0.657595\pi\) | ||
0.475118 | − | 0.879922i | \(-0.342405\pi\) | |||||||
\(158\) | −1.29772 | + | 1.58988i | −0.103241 | + | 0.126484i | ||||
\(159\) | − | 8.81326i | − | 0.698937i | ||||||
\(160\) | −13.1171 | − | 3.78928i | −1.03700 | − | 0.299569i | ||||
\(161\) | 21.0938 | 1.66242 | ||||||||
\(162\) | −11.3664 | − | 9.27767i | −0.893028 | − | 0.728922i | ||||
\(163\) | 6.94414 | 0.543907 | 0.271953 | − | 0.962310i | \(-0.412330\pi\) | ||||
0.271953 | + | 0.962310i | \(0.412330\pi\) | |||||||
\(164\) | −22.9564 | + | 4.69339i | −1.79259 | + | 0.366492i | ||||
\(165\) | −3.35479 | −0.261170 | ||||||||
\(166\) | −3.89541 | + | 4.77240i | −0.302343 | + | 0.370410i | ||||
\(167\) | 11.3843i | 0.880941i | 0.897767 | + | 0.440470i | \(0.145188\pi\) | ||||
−0.897767 | + | 0.440470i | \(0.854812\pi\) | |||||||
\(168\) | 12.1593 | + | 6.37505i | 0.938108 | + | 0.491846i | ||||
\(169\) | −3.60541 | −0.277339 | ||||||||
\(170\) | 12.7802 | + | 5.89356i | 0.980196 | + | 0.452015i | ||||
\(171\) | − | 0.481730i | − | 0.0368388i | ||||||
\(172\) | 2.13794 | − | 0.437099i | 0.163017 | − | 0.0333285i | ||||
\(173\) | 5.68789 | 0.432442 | 0.216221 | − | 0.976344i | \(-0.430627\pi\) | ||||
0.216221 | + | 0.976344i | \(0.430627\pi\) | |||||||
\(174\) | 12.1213 | + | 9.89383i | 0.918911 | + | 0.750049i | ||||
\(175\) | 2.12239i | 0.160437i | ||||||||
\(176\) | −2.70854 | + | 1.15583i | −0.204164 | + | 0.0871237i | ||||
\(177\) | − | 23.6109i | − | 1.77471i | ||||||
\(178\) | 6.27080 | + | 5.11846i | 0.470016 | + | 0.383645i | ||||
\(179\) | 16.5292i | 1.23545i | 0.786394 | + | 0.617725i | \(0.211946\pi\) | ||||
−0.786394 | + | 0.617725i | \(0.788054\pi\) | |||||||
\(180\) | 0.545765 | + | 2.66945i | 0.0406789 | + | 0.198969i | ||||
\(181\) | −20.6345 | −1.53375 | −0.766874 | − | 0.641798i | \(-0.778189\pi\) | ||||
−0.766874 | + | 0.641798i | \(0.778189\pi\) | |||||||
\(182\) | 11.4782 | + | 9.36892i | 0.850819 | + | 0.694470i | ||||
\(183\) | 15.4127 | 1.13934 | ||||||||
\(184\) | 20.5524 | + | 10.7755i | 1.51514 | + | 0.794381i | ||||
\(185\) | 10.5902 | 0.778606 | ||||||||
\(186\) | −5.92792 | + | 7.26250i | −0.434656 | + | 0.532512i | ||||
\(187\) | 2.93925 | − | 0.758276i | 0.214939 | − | 0.0554506i | ||||
\(188\) | −2.17449 | − | 10.6359i | −0.158591 | − | 0.775702i | ||||
\(189\) | 11.8222i | 0.859936i | ||||||||
\(190\) | 1.84211 | − | 2.25684i | 0.133641 | − | 0.163728i | ||||
\(191\) | −17.3215 | −1.25334 | −0.626670 | − | 0.779285i | \(-0.715583\pi\) | ||||
−0.626670 | + | 0.779285i | \(0.715583\pi\) | |||||||
\(192\) | 8.59055 | + | 12.4228i | 0.619969 | + | 0.896540i | ||||
\(193\) | 12.3439i | 0.888537i | 0.895894 | + | 0.444268i | \(0.146536\pi\) | ||||
−0.895894 | + | 0.444268i | \(0.853464\pi\) | |||||||
\(194\) | −10.6375 | + | 13.0323i | −0.763727 | + | 0.935667i | ||||
\(195\) | 18.5689i | 1.32975i | ||||||||
\(196\) | 0.156217 | + | 0.764092i | 0.0111584 | + | 0.0545780i | ||||
\(197\) | 5.96937 | 0.425300 | 0.212650 | − | 0.977128i | \(-0.431791\pi\) | ||||
0.212650 | + | 0.977128i | \(0.431791\pi\) | |||||||
\(198\) | 0.455267 | + | 0.371606i | 0.0323544 | + | 0.0264089i | ||||
\(199\) | − | 12.8979i | − | 0.914307i | −0.889388 | − | 0.457154i | \(-0.848869\pi\) | ||
0.889388 | − | 0.457154i | \(-0.151131\pi\) | |||||||
\(200\) | −1.08420 | + | 2.06791i | −0.0766642 | + | 0.146223i | ||||
\(201\) | 19.9397i | 1.40644i | ||||||||
\(202\) | 7.45436 | − | 9.13259i | 0.524487 | − | 0.642567i | ||||
\(203\) | − | 15.0664i | − | 1.05745i | ||||||
\(204\) | −6.82989 | − | 13.9905i | −0.478188 | − | 0.979532i | ||||
\(205\) | 28.2769i | 1.97495i | ||||||||
\(206\) | 17.0304 | + | 13.9008i | 1.18656 | + | 0.968517i | ||||
\(207\) | − | 4.63094i | − | 0.321873i | ||||||
\(208\) | 6.39756 | + | 14.9919i | 0.443591 | + | 1.03950i | ||||
\(209\) | − | 0.628334i | − | 0.0434627i | ||||||
\(210\) | 10.4768 | − | 12.8354i | 0.722965 | − | 0.885730i | ||||
\(211\) | −4.31995 | −0.297398 | −0.148699 | − | 0.988883i | \(-0.547509\pi\) | ||||
−0.148699 | + | 0.988883i | \(0.547509\pi\) | |||||||
\(212\) | −9.14701 | + | 1.87009i | −0.628219 | + | 0.128438i | ||||
\(213\) | 0.964875i | 0.0661122i | ||||||||
\(214\) | −16.4216 | − | 13.4039i | −1.12256 | − | 0.916275i | ||||
\(215\) | − | 2.63345i | − | 0.179600i | ||||||
\(216\) | −6.03921 | + | 11.5187i | −0.410916 | + | 0.783749i | ||||
\(217\) | 9.02707 | 0.612798 | ||||||||
\(218\) | −1.03115 | − | 0.841660i | −0.0698381 | − | 0.0570044i | ||||
\(219\) | 25.1609i | 1.70021i | ||||||||
\(220\) | 0.711855 | + | 3.48184i | 0.0479933 | + | 0.234745i | ||||
\(221\) | −4.19710 | − | 16.2689i | −0.282327 | − | 1.09436i | ||||
\(222\) | −9.07565 | − | 7.40789i | −0.609118 | − | 0.497185i | ||||
\(223\) | 15.5793 | 1.04326 | 0.521632 | − | 0.853171i | \(-0.325323\pi\) | ||||
0.521632 | + | 0.853171i | \(0.325323\pi\) | |||||||
\(224\) | 4.03638 | − | 13.9724i | 0.269692 | − | 0.933573i | ||||
\(225\) | 0.465950 | 0.0310633 | ||||||||
\(226\) | −8.79537 | + | 10.7755i | −0.585059 | + | 0.716776i | ||||
\(227\) | −5.47171 | −0.363170 | −0.181585 | − | 0.983375i | \(-0.558123\pi\) | ||||
−0.181585 | + | 0.983375i | \(0.558123\pi\) | |||||||
\(228\) | −3.15733 | + | 0.645512i | −0.209100 | + | 0.0427501i | ||||
\(229\) | 2.88870i | 0.190890i | 0.995435 | + | 0.0954452i | \(0.0304275\pi\) | ||||
−0.995435 | + | 0.0954452i | \(0.969573\pi\) | |||||||
\(230\) | 17.7085 | − | 21.6953i | 1.16766 | − | 1.43054i | ||||
\(231\) | − | 3.57356i | − | 0.235123i | ||||||
\(232\) | 7.69648 | − | 14.6797i | 0.505298 | − | 0.963767i | ||||
\(233\) | − | 8.67268i | − | 0.568166i | −0.958800 | − | 0.284083i | \(-0.908311\pi\) | ||
0.958800 | − | 0.284083i | \(-0.0916892\pi\) | |||||||
\(234\) | 2.05686 | − | 2.51992i | 0.134461 | − | 0.164733i | ||||
\(235\) | −13.1009 | −0.854612 | ||||||||
\(236\) | −24.5051 | + | 5.01002i | −1.59514 | + | 0.326124i | ||||
\(237\) | − | 2.73978i | − | 0.177968i | ||||||
\(238\) | −6.27788 | + | 13.6136i | −0.406934 | + | 0.882438i | ||||
\(239\) | −16.1107 | −1.04211 | −0.521057 | − | 0.853522i | \(-0.674462\pi\) | ||||
−0.521057 | + | 0.853522i | \(0.674462\pi\) | |||||||
\(240\) | 16.7647 | − | 7.15405i | 1.08216 | − | 0.461792i | ||||
\(241\) | 9.65567i | 0.621977i | 0.950414 | + | 0.310988i | \(0.100660\pi\) | ||||
−0.950414 | + | 0.310988i | \(0.899340\pi\) | |||||||
\(242\) | −11.4576 | − | 9.35213i | −0.736523 | − | 0.601178i | ||||
\(243\) | 5.79238 | 0.371581 | ||||||||
\(244\) | −3.27043 | − | 15.9964i | −0.209368 | − | 1.02406i | ||||
\(245\) | 0.941184 | 0.0601301 | ||||||||
\(246\) | 19.7798 | − | 24.2330i | 1.26112 | − | 1.54504i | ||||
\(247\) | −3.47786 | −0.221291 | ||||||||
\(248\) | 8.79537 | + | 4.61137i | 0.558506 | + | 0.292822i | ||||
\(249\) | − | 8.22407i | − | 0.521179i | ||||||
\(250\) | −11.0387 | − | 9.01016i | −0.698146 | − | 0.569853i | ||||
\(251\) | 19.7073i | 1.24391i | 0.783052 | + | 0.621956i | \(0.213662\pi\) | ||||
−0.783052 | + | 0.621956i | \(0.786338\pi\) | |||||||
\(252\) | −2.84353 | + | 0.581354i | −0.179125 | + | 0.0366219i | ||||
\(253\) | − | 6.04026i | − | 0.379748i | ||||||
\(254\) | −12.1593 | − | 9.92485i | −0.762940 | − | 0.622740i | ||||
\(255\) | −18.1926 | + | 4.69339i | −1.13927 | + | 0.293911i | ||||
\(256\) | 11.0704 | − | 11.5519i | 0.691902 | − | 0.721992i | ||||
\(257\) | 6.33840 | 0.395379 | 0.197689 | − | 0.980265i | \(-0.436656\pi\) | ||||
0.197689 | + | 0.980265i | \(0.436656\pi\) | |||||||
\(258\) | −1.84211 | + | 2.25684i | −0.114685 | + | 0.140504i | ||||
\(259\) | 11.2808i | 0.700953i | ||||||||
\(260\) | 19.2721 | − | 3.94016i | 1.19521 | − | 0.244358i | ||||
\(261\) | −3.30768 | −0.204740 | ||||||||
\(262\) | 20.1976 | + | 16.4860i | 1.24781 | + | 1.01851i | ||||
\(263\) | −15.5446 | −0.958519 | −0.479260 | − | 0.877673i | \(-0.659095\pi\) | ||||
−0.479260 | + | 0.877673i | \(0.659095\pi\) | |||||||
\(264\) | 1.82551 | − | 3.48184i | 0.112352 | − | 0.214292i | ||||
\(265\) | 11.2670i | 0.692126i | ||||||||
\(266\) | 2.40400 | + | 1.96224i | 0.147399 | + | 0.120313i | ||||
\(267\) | −10.8062 | −0.661329 | ||||||||
\(268\) | 20.6948 | − | 4.23101i | 1.26413 | − | 0.258450i | ||||
\(269\) | 22.8463 | 1.39296 | 0.696481 | − | 0.717575i | \(-0.254748\pi\) | ||||
0.696481 | + | 0.717575i | \(0.254748\pi\) | |||||||
\(270\) | 12.1593 | + | 9.92485i | 0.739989 | + | 0.604007i | ||||
\(271\) | 7.17019 | 0.435558 | 0.217779 | − | 0.975998i | \(-0.430119\pi\) | ||||
0.217779 | + | 0.975998i | \(0.430119\pi\) | |||||||
\(272\) | −13.0711 | + | 10.0572i | −0.792550 | + | 0.609806i | ||||
\(273\) | −19.7798 | −1.19713 | ||||||||
\(274\) | −14.8276 | − | 12.1029i | −0.895770 | − | 0.731161i | ||||
\(275\) | 0.607751 | 0.0366488 | ||||||||
\(276\) | −30.3519 | + | 6.20539i | −1.82697 | + | 0.373521i | ||||
\(277\) | 6.61070 | 0.397199 | 0.198599 | − | 0.980081i | \(-0.436361\pi\) | ||||
0.198599 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(278\) | −2.96936 | − | 2.42370i | −0.178090 | − | 0.145364i | ||||
\(279\) | − | 1.98181i | − | 0.118648i | ||||||
\(280\) | −15.5446 | − | 8.14995i | −0.928966 | − | 0.487052i | ||||
\(281\) | 14.8479 | 0.885754 | 0.442877 | − | 0.896582i | \(-0.353958\pi\) | ||||
0.442877 | + | 0.896582i | \(0.353958\pi\) | |||||||
\(282\) | 11.2273 | + | 9.16418i | 0.668579 | + | 0.545719i | ||||
\(283\) | 14.3388 | 0.852355 | 0.426177 | − | 0.904640i | \(-0.359860\pi\) | ||||
0.426177 | + | 0.904640i | \(0.359860\pi\) | |||||||
\(284\) | 1.00141 | − | 0.204737i | 0.0594230 | − | 0.0121489i | ||||
\(285\) | 3.88910i | 0.230371i | ||||||||
\(286\) | 2.68281 | − | 3.28680i | 0.158638 | − | 0.194353i | ||||
\(287\) | −30.1209 | −1.77798 | ||||||||
\(288\) | −3.06752 | − | 0.886149i | −0.180755 | − | 0.0522168i | ||||
\(289\) | 14.8783 | − | 8.22407i | 0.875196 | − | 0.483769i | ||||
\(290\) | −15.4960 | − | 12.6484i | −0.909956 | − | 0.742740i | ||||
\(291\) | − | 22.4581i | − | 1.31651i | ||||||
\(292\) | 26.1137 | − | 5.33890i | 1.52819 | − | 0.312436i | ||||
\(293\) | − | 19.5648i | − | 1.14299i | −0.820605 | − | 0.571495i | \(-0.806364\pi\) | ||
0.820605 | − | 0.571495i | \(-0.193636\pi\) | |||||||
\(294\) | −0.806583 | − | 0.658363i | −0.0470409 | − | 0.0383965i | ||||
\(295\) | 30.1846i | 1.75741i | ||||||||
\(296\) | −5.76265 | + | 10.9912i | −0.334947 | + | 0.638852i | ||||
\(297\) | 3.38531 | 0.196435 | ||||||||
\(298\) | −1.52644 | + | 1.87009i | −0.0884242 | + | 0.108331i | ||||
\(299\) | −33.4331 | −1.93349 | ||||||||
\(300\) | −0.624366 | − | 3.05391i | −0.0360478 | − | 0.176317i | ||||
\(301\) | 2.80518 | 0.161688 | ||||||||
\(302\) | 3.81029 | + | 3.11010i | 0.219257 | + | 0.178966i | ||||
\(303\) | 15.7378i | 0.904112i | ||||||||
\(304\) | 1.33991 | + | 3.13993i | 0.0768493 | + | 0.180087i | ||||
\(305\) | −19.7038 | −1.12824 | ||||||||
\(306\) | 2.98873 | + | 1.37825i | 0.170855 | + | 0.0787892i | ||||
\(307\) | 10.6087i | 0.605468i | 0.953075 | + | 0.302734i | \(0.0978994\pi\) | ||||
−0.953075 | + | 0.302734i | \(0.902101\pi\) | |||||||
\(308\) | −3.70889 | + | 0.758276i | −0.211333 | + | 0.0432068i | ||||
\(309\) | −29.3477 | −1.66953 | ||||||||
\(310\) | 7.57833 | − | 9.28447i | 0.430420 | − | 0.527323i | ||||
\(311\) | − | 15.2696i | − | 0.865860i | −0.901428 | − | 0.432930i | \(-0.857480\pi\) | ||
0.901428 | − | 0.432930i | \(-0.142520\pi\) | |||||||
\(312\) | −19.2721 | − | 10.1043i | −1.09107 | − | 0.572043i | ||||
\(313\) | − | 13.1472i | − | 0.743125i | −0.928408 | − | 0.371562i | \(-0.878822\pi\) | ||
0.928408 | − | 0.371562i | \(-0.121178\pi\) | |||||||
\(314\) | 19.7191 | − | 24.1585i | 1.11281 | − | 1.36334i | ||||
\(315\) | 3.50257i | 0.197347i | ||||||||
\(316\) | −2.84353 | + | 0.581354i | −0.159961 | + | 0.0327037i | ||||
\(317\) | 25.7911 | 1.44857 | 0.724287 | − | 0.689499i | \(-0.242169\pi\) | ||||
0.724287 | + | 0.689499i | \(0.242169\pi\) | |||||||
\(318\) | 7.88132 | − | 9.65567i | 0.441963 | − | 0.541463i | ||||
\(319\) | −4.31429 | −0.241554 | ||||||||
\(320\) | −10.9823 | − | 15.8815i | −0.613928 | − | 0.887803i | ||||
\(321\) | 28.2987 | 1.57948 | ||||||||
\(322\) | 23.1100 | + | 18.8633i | 1.28787 | + | 1.05121i | ||||
\(323\) | −0.879045 | − | 3.40737i | −0.0489114 | − | 0.189591i | ||||
\(324\) | −4.15622 | − | 20.3289i | −0.230901 | − | 1.12939i | ||||
\(325\) | − | 3.36393i | − | 0.186597i | ||||||
\(326\) | 7.60789 | + | 6.20984i | 0.421362 | + | 0.343931i | ||||
\(327\) | 1.77693 | 0.0982644 | ||||||||
\(328\) | −29.3477 | − | 15.3869i | −1.62046 | − | 0.849598i | ||||
\(329\) | − | 13.9553i | − | 0.769379i | ||||||
\(330\) | −3.67546 | − | 3.00005i | −0.202327 | − | 0.165147i | ||||
\(331\) | 17.4779i | 0.960670i | 0.877085 | + | 0.480335i | \(0.159485\pi\) | ||||
−0.877085 | + | 0.480335i | \(0.840515\pi\) | |||||||
\(332\) | −8.53551 | + | 1.74507i | −0.468447 | + | 0.0957732i | ||||
\(333\) | 2.47659 | 0.135716 | ||||||||
\(334\) | −10.1805 | + | 12.4724i | −0.557050 | + | 0.682461i | ||||
\(335\) | − | 25.4912i | − | 1.39273i | ||||||
\(336\) | 7.62057 | + | 17.8579i | 0.415736 | + | 0.974229i | ||||
\(337\) | − | 26.1195i | − | 1.42282i | −0.702777 | − | 0.711410i | \(-0.748057\pi\) | ||
0.702777 | − | 0.711410i | \(-0.251943\pi\) | |||||||
\(338\) | −3.95003 | − | 3.22416i | −0.214853 | − | 0.175371i | ||||
\(339\) | − | 18.5689i | − | 1.00853i | ||||||
\(340\) | 8.73143 | + | 17.8857i | 0.473528 | + | 0.969986i | ||||
\(341\) | − | 2.58492i | − | 0.139981i | ||||||
\(342\) | 0.430791 | − | 0.527776i | 0.0232945 | − | 0.0285389i | ||||
\(343\) | 18.9996i | 1.02588i | ||||||||
\(344\) | 2.73318 | + | 1.43299i | 0.147363 | + | 0.0772618i | ||||
\(345\) | 37.3865i | 2.01282i | ||||||||
\(346\) | 6.23157 | + | 5.08644i | 0.335011 | + | 0.273448i | ||||
\(347\) | 17.9138 | 0.961663 | 0.480832 | − | 0.876813i | \(-0.340335\pi\) | ||||
0.480832 | + | 0.876813i | \(0.340335\pi\) | |||||||
\(348\) | 4.43225 | + | 21.6790i | 0.237593 | + | 1.16212i | ||||
\(349\) | 22.5260i | 1.20579i | 0.797820 | + | 0.602895i | \(0.205986\pi\) | ||||
−0.797820 | + | 0.602895i | \(0.794014\pi\) | |||||||
\(350\) | −1.89796 | + | 2.32525i | −0.101450 | + | 0.124290i | ||||
\(351\) | − | 18.7378i | − | 1.00015i | ||||||
\(352\) | −4.00104 | − | 1.15583i | −0.213256 | − | 0.0616058i | ||||
\(353\) | 5.56775 | 0.296342 | 0.148171 | − | 0.988962i | \(-0.452661\pi\) | ||||
0.148171 | + | 0.988962i | \(0.452661\pi\) | |||||||
\(354\) | 21.1142 | − | 25.8678i | 1.12221 | − | 1.37486i | ||||
\(355\) | − | 1.23351i | − | 0.0654679i | ||||||
\(356\) | 2.29297 | + | 11.2154i | 0.121527 | + | 0.594416i | ||||
\(357\) | −4.99945 | − | 19.3790i | −0.264599 | − | 1.02564i | ||||
\(358\) | −14.7814 | + | 18.1091i | −0.781219 | + | 0.957098i | ||||
\(359\) | 22.1622 | 1.16967 | 0.584837 | − | 0.811150i | \(-0.301158\pi\) | ||||
0.584837 | + | 0.811150i | \(0.301158\pi\) | |||||||
\(360\) | −1.78924 | + | 3.41266i | −0.0943014 | + | 0.179863i | ||||
\(361\) | 18.2716 | 0.961663 | ||||||||
\(362\) | −22.6068 | − | 18.4525i | −1.18819 | − | 0.969842i | ||||
\(363\) | 19.7444 | 1.03631 | ||||||||
\(364\) | 4.19710 | + | 20.5289i | 0.219988 | + | 1.07601i | ||||
\(365\) | − | 32.1660i | − | 1.68365i | ||||||
\(366\) | 16.8859 | + | 13.7829i | 0.882642 | + | 0.720445i | ||||
\(367\) | − | 2.12239i | − | 0.110788i | −0.998465 | − | 0.0553939i | \(-0.982359\pi\) | ||
0.998465 | − | 0.0553939i | \(-0.0176414\pi\) | |||||||
\(368\) | 12.8808 | + | 30.1846i | 0.671456 | + | 1.57348i | ||||
\(369\) | 6.61275i | 0.344246i | ||||||||
\(370\) | 11.6024 | + | 9.47034i | 0.603182 | + | 0.492340i | ||||
\(371\) | −12.0017 | −0.623098 | ||||||||
\(372\) | −12.9891 | + | 2.65559i | −0.673452 | + | 0.137686i | ||||
\(373\) | 17.6720i | 0.915023i | 0.889204 | + | 0.457512i | \(0.151259\pi\) | ||||
−0.889204 | + | 0.457512i | \(0.848741\pi\) | |||||||
\(374\) | 3.89829 | + | 1.79769i | 0.201576 | + | 0.0929561i | ||||
\(375\) | 19.0224 | 0.982314 | ||||||||
\(376\) | 7.12888 | − | 13.5971i | 0.367644 | − | 0.701215i | ||||
\(377\) | 23.8798i | 1.22987i | ||||||||
\(378\) | −10.5721 | + | 12.9522i | −0.543768 | + | 0.666188i | ||||
\(379\) | 3.23194 | 0.166013 | 0.0830067 | − | 0.996549i | \(-0.473548\pi\) | ||||
0.0830067 | + | 0.996549i | \(0.473548\pi\) | |||||||
\(380\) | 4.03638 | − | 0.825231i | 0.207062 | − | 0.0423335i | ||||
\(381\) | 20.9535 | 1.07348 | ||||||||
\(382\) | −18.9772 | − | 15.4899i | −0.970956 | − | 0.792531i | ||||
\(383\) | 7.92400 | 0.404897 | 0.202449 | − | 0.979293i | \(-0.435110\pi\) | ||||
0.202449 | + | 0.979293i | \(0.435110\pi\) | |||||||
\(384\) | −1.69752 | + | 21.2924i | −0.0866264 | + | 1.08657i | ||||
\(385\) | 4.56849i | 0.232832i | ||||||||
\(386\) | −11.0387 | + | 13.5238i | −0.561853 | + | 0.688345i | ||||
\(387\) | − | 0.615851i | − | 0.0313054i | ||||||
\(388\) | −23.3085 | + | 4.76539i | −1.18331 | + | 0.241926i | ||||
\(389\) | − | 4.78602i | − | 0.242661i | −0.992612 | − | 0.121330i | \(-0.961284\pi\) | ||
0.992612 | − | 0.121330i | \(-0.0387160\pi\) | |||||||
\(390\) | −16.6054 | + | 20.3438i | −0.840848 | + | 1.03015i | ||||
\(391\) | −8.45038 | − | 32.7556i | −0.427354 | − | 1.65652i | ||||
\(392\) | −0.512145 | + | 0.976826i | −0.0258672 | + | 0.0493371i | ||||
\(393\) | −34.8056 | −1.75571 | ||||||||
\(394\) | 6.53995 | + | 5.33815i | 0.329478 | + | 0.268932i | ||||
\(395\) | 3.50257i | 0.176233i | ||||||||
\(396\) | 0.166472 | + | 0.814251i | 0.00836554 | + | 0.0409176i | ||||
\(397\) | −5.00982 | −0.251436 | −0.125718 | − | 0.992066i | \(-0.540123\pi\) | ||||
−0.125718 | + | 0.992066i | \(0.540123\pi\) | |||||||
\(398\) | 11.5340 | − | 14.1307i | 0.578148 | − | 0.708309i | ||||
\(399\) | −4.14272 | −0.207395 | ||||||||
\(400\) | −3.03707 | + | 1.29602i | −0.151854 | + | 0.0648010i | ||||
\(401\) | − | 7.61142i | − | 0.380096i | −0.981775 | − | 0.190048i | \(-0.939136\pi\) | ||
0.981775 | − | 0.190048i | \(-0.0608644\pi\) | |||||||
\(402\) | −17.8312 | + | 21.8456i | −0.889339 | + | 1.08956i | ||||
\(403\) | −14.3077 | −0.712717 | ||||||||
\(404\) | 16.3338 | − | 3.33941i | 0.812635 | − | 0.166142i | ||||
\(405\) | −25.0405 | −1.24427 | ||||||||
\(406\) | 13.4732 | − | 16.5065i | 0.668664 | − | 0.819203i | ||||
\(407\) | 3.23028 | 0.160119 | ||||||||
\(408\) | 5.02839 | − | 21.4355i | 0.248942 | − | 1.06121i | ||||
\(409\) | −18.6582 | −0.922590 | −0.461295 | − | 0.887247i | \(-0.652615\pi\) | ||||
−0.461295 | + | 0.887247i | \(0.652615\pi\) | |||||||
\(410\) | −25.2868 | + | 30.9797i | −1.24883 | + | 1.52998i | ||||
\(411\) | 25.5518 | 1.26038 | ||||||||
\(412\) | 6.22731 | + | 30.4591i | 0.306797 | + | 1.50061i | ||||
\(413\) | −32.1529 | −1.58214 | ||||||||
\(414\) | 4.14125 | − | 5.07358i | 0.203531 | − | 0.249353i | ||||
\(415\) | 10.5138i | 0.516100i | ||||||||
\(416\) | −6.39756 | + | 22.1460i | −0.313666 | + | 1.08580i | ||||
\(417\) | 5.11697 | 0.250579 | ||||||||
\(418\) | 0.561892 | − | 0.688392i | 0.0274830 | − | 0.0336704i | ||||
\(419\) | 1.05688 | 0.0516319 | 0.0258159 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258159 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(420\) | 22.9564 | − | 4.69339i | 1.12016 | − | 0.229014i | ||||
\(421\) | 1.37215i | 0.0668743i | 0.999441 | + | 0.0334371i | \(0.0106454\pi\) | ||||
−0.999441 | + | 0.0334371i | \(0.989355\pi\) | |||||||
\(422\) | −4.73287 | − | 3.86315i | −0.230393 | − | 0.188055i | ||||
\(423\) | −3.06375 | −0.148964 | ||||||||
\(424\) | −11.6937 | − | 6.13093i | −0.567895 | − | 0.297744i | ||||
\(425\) | 3.29576 | − | 0.850249i | 0.159868 | − | 0.0412432i | ||||
\(426\) | −0.862846 | + | 1.05710i | −0.0418050 | + | 0.0512168i | ||||
\(427\) | − | 20.9887i | − | 1.01572i | ||||||
\(428\) | −6.00471 | − | 29.3703i | −0.290249 | − | 1.41967i | ||||
\(429\) | 5.66400i | 0.273461i | ||||||||
\(430\) | 2.35498 | − | 2.88517i | 0.113567 | − | 0.139135i | ||||
\(431\) | 14.9578i | 0.720493i | 0.932857 | + | 0.360247i | \(0.117307\pi\) | ||||
−0.932857 | + | 0.360247i | \(0.882693\pi\) | |||||||
\(432\) | −16.9171 | + | 7.21912i | −0.813927 | + | 0.347330i | ||||
\(433\) | −1.48117 | −0.0711806 | −0.0355903 | − | 0.999366i | \(-0.511331\pi\) | ||||
−0.0355903 | + | 0.999366i | \(0.511331\pi\) | |||||||
\(434\) | 9.88992 | + | 8.07252i | 0.474731 | + | 0.387493i | ||||
\(435\) | 26.7036 | 1.28034 | ||||||||
\(436\) | −0.377048 | − | 1.84422i | −0.0180573 | − | 0.0883221i | ||||
\(437\) | −7.00228 | −0.334964 | ||||||||
\(438\) | −22.5003 | + | 27.5659i | −1.07511 | + | 1.31715i | ||||
\(439\) | − | 19.6083i | − | 0.935855i | −0.883767 | − | 0.467927i | \(-0.845001\pi\) | ||
0.883767 | − | 0.467927i | \(-0.154999\pi\) | |||||||
\(440\) | −2.33376 | + | 4.45123i | −0.111257 | + | 0.212204i | ||||
\(441\) | 0.220102 | 0.0104811 | ||||||||
\(442\) | 9.95028 | − | 21.5772i | 0.473287 | − | 1.02632i | ||||
\(443\) | − | 32.3084i | − | 1.53502i | −0.641037 | − | 0.767510i | \(-0.721495\pi\) | ||
0.641037 | − | 0.767510i | \(-0.278505\pi\) | |||||||
\(444\) | −3.31859 | − | 16.2319i | −0.157493 | − | 0.770333i | ||||
\(445\) | 13.8148 | 0.654884 | ||||||||
\(446\) | 17.0684 | + | 13.9319i | 0.808212 | + | 0.659692i | ||||
\(447\) | − | 3.22265i | − | 0.152426i | ||||||
\(448\) | 16.9171 | − | 11.6984i | 0.799260 | − | 0.552699i | ||||
\(449\) | 17.4468i | 0.823366i | 0.911327 | + | 0.411683i | \(0.135059\pi\) | ||||
−0.911327 | + | 0.411683i | \(0.864941\pi\) | |||||||
\(450\) | 0.510487 | + | 0.416679i | 0.0240646 | + | 0.0196424i | ||||
\(451\) | 8.62518i | 0.406144i | ||||||||
\(452\) | −19.2721 | + | 3.94016i | −0.906485 | + | 0.185329i | ||||
\(453\) | −6.56610 | −0.308502 | ||||||||
\(454\) | −5.99472 | − | 4.89312i | −0.281346 | − | 0.229645i | ||||
\(455\) | 25.2868 | 1.18546 | ||||||||
\(456\) | −4.03638 | − | 2.11626i | −0.189021 | − | 0.0991027i | ||||
\(457\) | −2.35230 | −0.110036 | −0.0550179 | − | 0.998485i | \(-0.517522\pi\) | ||||
−0.0550179 | + | 0.998485i | \(0.517522\pi\) | |||||||
\(458\) | −2.58324 | + | 3.16481i | −0.120707 | + | 0.147882i | ||||
\(459\) | 18.3581 | − | 4.73608i | 0.856882 | − | 0.221061i | ||||
\(460\) | 38.8023 | − | 7.93306i | 1.80917 | − | 0.369881i | ||||
\(461\) | − | 4.32881i | − | 0.201613i | −0.994906 | − | 0.100806i | \(-0.967858\pi\) | ||
0.994906 | − | 0.100806i | \(-0.0321422\pi\) | |||||||
\(462\) | 3.19568 | − | 3.91514i | 0.148677 | − | 0.182149i | ||||
\(463\) | 5.29610 | 0.246131 | 0.123065 | − | 0.992399i | \(-0.460728\pi\) | ||||
0.123065 | + | 0.992399i | \(0.460728\pi\) | |||||||
\(464\) | 21.5595 | − | 9.20018i | 1.00088 | − | 0.427108i | ||||
\(465\) | 15.9995i | 0.741960i | ||||||||
\(466\) | 7.75561 | − | 9.50166i | 0.359272 | − | 0.440156i | ||||
\(467\) | − | 4.40327i | − | 0.203759i | −0.994797 | − | 0.101879i | \(-0.967514\pi\) | ||
0.994797 | − | 0.101879i | \(-0.0324856\pi\) | |||||||
\(468\) | 4.50692 | − | 0.921432i | 0.208332 | − | 0.0425932i | ||||
\(469\) | 27.1535 | 1.25383 | ||||||||
\(470\) | −14.3532 | − | 11.7156i | −0.662063 | − | 0.540401i | ||||
\(471\) | 41.6313i | 1.91827i | ||||||||
\(472\) | −31.3276 | − | 16.4249i | −1.44197 | − | 0.756018i | ||||
\(473\) | − | 0.803270i | − | 0.0369344i | ||||||
\(474\) | 2.45006 | − | 3.00165i | 0.112535 | − | 0.137871i | ||||
\(475\) | − | 0.704546i | − | 0.0323268i | ||||||
\(476\) | −19.0520 | + | 9.30081i | −0.873247 | + | 0.426302i | ||||
\(477\) | 2.63486i | 0.120642i | ||||||||
\(478\) | −17.6506 | − | 14.4071i | −0.807320 | − | 0.658965i | ||||
\(479\) | 16.4286i | 0.750641i | 0.926895 | + | 0.375320i | \(0.122467\pi\) | ||||
−0.926895 | + | 0.375320i | \(0.877533\pi\) | |||||||
\(480\) | 24.7647 | + | 7.15405i | 1.13035 | + | 0.326536i | ||||
\(481\) | − | 17.8797i | − | 0.815246i | ||||||
\(482\) | −8.63465 | + | 10.5786i | −0.393298 | + | 0.481842i | ||||
\(483\) | −39.8245 | −1.81208 | ||||||||
\(484\) | −4.18957 | − | 20.4921i | −0.190435 | − | 0.931459i | ||||
\(485\) | 28.7107i | 1.30368i | ||||||||
\(486\) | 6.34604 | + | 5.17987i | 0.287862 | + | 0.234964i | ||||
\(487\) | 4.75584i | 0.215508i | 0.994178 | + | 0.107754i | \(0.0343658\pi\) | ||||
−0.994178 | + | 0.107754i | \(0.965634\pi\) | |||||||
\(488\) | 10.7218 | − | 20.4500i | 0.485355 | − | 0.925728i | ||||
\(489\) | −13.1103 | −0.592870 | ||||||||
\(490\) | 1.03115 | + | 0.841660i | 0.0465825 | + | 0.0380223i | ||||
\(491\) | 1.89082i | 0.0853316i | 0.999089 | + | 0.0426658i | \(0.0135851\pi\) | ||||
−0.999089 | + | 0.0426658i | \(0.986415\pi\) | |||||||
\(492\) | 43.3410 | − | 8.86099i | 1.95396 | − | 0.399484i | ||||
\(493\) | −23.3959 | + | 6.03574i | −1.05370 | + | 0.271836i | ||||
\(494\) | −3.81029 | − | 3.11010i | −0.171433 | − | 0.139930i | ||||
\(495\) | 1.00297 | 0.0450801 | ||||||||
\(496\) | 5.51232 | + | 12.9175i | 0.247510 | + | 0.580011i | ||||
\(497\) | 1.31395 | 0.0589386 | ||||||||
\(498\) | 7.35443 | − | 9.01016i | 0.329560 | − | 0.403755i | ||||
\(499\) | −36.9132 | −1.65246 | −0.826231 | − | 0.563331i | \(-0.809520\pi\) | ||||
−0.826231 | + | 0.563331i | \(0.809520\pi\) | |||||||
\(500\) | −4.03638 | − | 19.7428i | −0.180512 | − | 0.882924i | ||||
\(501\) | − | 21.4932i | − | 0.960244i | ||||||
\(502\) | −17.6234 | + | 21.5910i | −0.786569 | + | 0.963652i | ||||
\(503\) | 17.3295i | 0.772686i | 0.922355 | + | 0.386343i | \(0.126262\pi\) | ||||
−0.922355 | + | 0.386343i | \(0.873738\pi\) | |||||||
\(504\) | −3.63520 | − | 1.90592i | −0.161925 | − | 0.0848964i | ||||
\(505\) | − | 20.1194i | − | 0.895302i | ||||||
\(506\) | 5.40154 | − | 6.61761i | 0.240128 | − | 0.294189i | ||||
\(507\) | 6.80691 | 0.302305 | ||||||||
\(508\) | −4.44614 | − | 21.7470i | −0.197266 | − | 0.964868i | ||||
\(509\) | 10.2701i | 0.455213i | 0.973753 | + | 0.227607i | \(0.0730900\pi\) | ||||
−0.973753 | + | 0.227607i | \(0.926910\pi\) | |||||||
\(510\) | −24.1286 | − | 11.1269i | −1.06843 | − | 0.492706i | ||||
\(511\) | 34.2636 | 1.51573 | ||||||||
\(512\) | 22.4589 | − | 2.75624i | 0.992553 | − | 0.121810i | ||||
\(513\) | − | 3.92448i | − | 0.173270i | ||||||
\(514\) | 6.94425 | + | 5.66816i | 0.306298 | + | 0.250012i | ||||
\(515\) | 37.5185 | 1.65326 | ||||||||
\(516\) | −4.03638 | + | 0.825231i | −0.177692 | + | 0.0363288i | ||||
\(517\) | −3.99612 | −0.175749 | ||||||||
\(518\) | −10.0879 | + | 12.3590i | −0.443237 | + | 0.543025i | ||||
\(519\) | −10.7386 | −0.471371 | ||||||||
\(520\) | 24.6378 | + | 12.9175i | 1.08044 | + | 0.566468i | ||||
\(521\) | − | 26.1195i | − | 1.14432i | −0.820143 | − | 0.572158i | \(-0.806106\pi\) | ||
0.820143 | − | 0.572158i | \(-0.193894\pi\) | |||||||
\(522\) | −3.62384 | − | 2.95792i | −0.158611 | − | 0.129464i | ||||
\(523\) | − | 14.8223i | − | 0.648133i | −0.946034 | − | 0.324066i | \(-0.894950\pi\) | ||
0.946034 | − | 0.324066i | \(-0.105050\pi\) | |||||||
\(524\) | 7.38542 | + | 36.1236i | 0.322633 | + | 1.57807i | ||||
\(525\) | − | 4.00701i | − | 0.174880i | ||||||
\(526\) | −17.0304 | − | 13.9008i | −0.742560 | − | 0.606105i | ||||
\(527\) | −3.61633 | − | 14.0177i | −0.157530 | − | 0.610621i | ||||
\(528\) | 5.11365 | − | 2.18217i | 0.222543 | − | 0.0949667i | ||||
\(529\) | −44.3138 | −1.92669 | ||||||||
\(530\) | −10.0756 | + | 12.3439i | −0.437656 | + | 0.536187i | ||||
\(531\) | 7.05886i | 0.306329i | ||||||||
\(532\) | 0.879045 | + | 4.29959i | 0.0381114 | + | 0.186411i | ||||
\(533\) | 47.7408 | 2.06788 | ||||||||
\(534\) | −11.8391 | − | 9.66351i | −0.512328 | − | 0.418181i | ||||
\(535\) | −36.1774 | −1.56409 | ||||||||
\(536\) | 26.4565 | + | 13.8710i | 1.14275 | + | 0.599136i | ||||
\(537\) | − | 31.2067i | − | 1.34667i | ||||||
\(538\) | 25.0300 | + | 20.4304i | 1.07912 | + | 0.880818i | ||||
\(539\) | 0.287085 | 0.0123656 | ||||||||
\(540\) | 4.44614 | + | 21.7470i | 0.191331 | + | 0.935842i | ||||
\(541\) | 9.11519 | 0.391893 | 0.195946 | − | 0.980615i | \(-0.437222\pi\) | ||||
0.195946 | + | 0.980615i | \(0.437222\pi\) | |||||||
\(542\) | 7.85555 | + | 6.41199i | 0.337425 | + | 0.275419i | ||||
\(543\) | 38.9573 | 1.67182 | ||||||||
\(544\) | −23.3142 | − | 0.670405i | −0.999587 | − | 0.0287434i | ||||
\(545\) | −2.27165 | −0.0973068 | ||||||||
\(546\) | −21.6705 | − | 17.6883i | −0.927411 | − | 0.756987i | ||||
\(547\) | −26.1596 | −1.11850 | −0.559251 | − | 0.828999i | \(-0.688911\pi\) | ||||
−0.559251 | + | 0.828999i | \(0.688911\pi\) | |||||||
\(548\) | −5.42185 | − | 26.5194i | −0.231610 | − | 1.13285i | ||||
\(549\) | −4.60788 | −0.196659 | ||||||||
\(550\) | 0.665842 | + | 0.543485i | 0.0283916 | + | 0.0231743i | ||||
\(551\) | 5.00142i | 0.213068i | ||||||||
\(552\) | −38.8023 | − | 20.3438i | −1.65153 | − | 0.865892i | ||||
\(553\) | −3.73097 | −0.158657 | ||||||||
\(554\) | 7.24258 | + | 5.91167i | 0.307708 | + | 0.251163i | ||||
\(555\) | −19.9940 | −0.848697 | ||||||||
\(556\) | −1.08577 | − | 5.31074i | −0.0460470 | − | 0.225226i | ||||
\(557\) | 41.3488i | 1.75200i | 0.482307 | + | 0.876002i | \(0.339799\pi\) | ||||
−0.482307 | + | 0.876002i | \(0.660201\pi\) | |||||||
\(558\) | 1.77224 | − | 2.17124i | 0.0750251 | − | 0.0919158i | ||||
\(559\) | −4.44614 | −0.188052 | ||||||||
\(560\) | −9.74224 | − | 22.8298i | −0.411685 | − | 0.964735i | ||||
\(561\) | −5.54922 | + | 1.43160i | −0.234288 | + | 0.0604424i | ||||
\(562\) | 16.2672 | + | 13.2779i | 0.686189 | + | 0.560093i | ||||
\(563\) | − | 37.5179i | − | 1.58119i | −0.612338 | − | 0.790596i | \(-0.709771\pi\) | ||
0.612338 | − | 0.790596i | \(-0.290229\pi\) | |||||||
\(564\) | 4.10538 | + | 20.0803i | 0.172868 | + | 0.845532i | ||||
\(565\) | 23.7388i | 0.998699i | ||||||||
\(566\) | 15.7094 | + | 12.8226i | 0.660315 | + | 0.538974i | ||||
\(567\) | − | 26.6734i | − | 1.12018i | ||||||
\(568\) | 1.28022 | + | 0.671214i | 0.0537169 | + | 0.0281635i | ||||
\(569\) | 18.1288 | 0.760000 | 0.380000 | − | 0.924987i | \(-0.375924\pi\) | ||||
0.380000 | + | 0.924987i | \(0.375924\pi\) | |||||||
\(570\) | −3.47786 | + | 4.26084i | −0.145671 | + | 0.178467i | ||||
\(571\) | −15.4181 | −0.645226 | −0.322613 | − | 0.946531i | \(-0.604561\pi\) | ||||
−0.322613 | + | 0.946531i | \(0.604561\pi\) | |||||||
\(572\) | 5.87849 | − | 1.20185i | 0.245792 | − | 0.0502518i | ||||
\(573\) | 32.7025 | 1.36617 | ||||||||
\(574\) | −32.9999 | − | 26.9358i | −1.37739 | − | 1.12428i | ||||
\(575\) | − | 6.77290i | − | 0.282449i | ||||||
\(576\) | −2.56828 | − | 3.71400i | −0.107012 | − | 0.154750i | ||||
\(577\) | 18.4051 | 0.766215 | 0.383107 | − | 0.923704i | \(-0.374854\pi\) | ||||
0.383107 | + | 0.923704i | \(0.374854\pi\) | |||||||
\(578\) | 23.6549 | + | 4.29488i | 0.983914 | + | 0.178644i | ||||
\(579\) | − | 23.3050i | − | 0.968524i | ||||||
\(580\) | −5.66624 | − | 27.7148i | −0.235278 | − | 1.15079i | ||||
\(581\) | −11.1994 | −0.464628 | ||||||||
\(582\) | 20.0833 | − | 24.6047i | 0.832478 | − | 1.01990i | ||||
\(583\) | 3.43672i | 0.142334i | ||||||||
\(584\) | 33.3841 | + | 17.5031i | 1.38144 | + | 0.724285i | ||||
\(585\) | − | 5.55148i | − | 0.229525i | ||||||
\(586\) | 17.4960 | − | 21.4349i | 0.722753 | − | 0.885469i | ||||
\(587\) | 28.5683i | 1.17914i | 0.807718 | + | 0.589569i | \(0.200702\pi\) | ||||
−0.807718 | + | 0.589569i | \(0.799298\pi\) | |||||||
\(588\) | −0.294934 | − | 1.44258i | −0.0121629 | − | 0.0594912i | ||||
\(589\) | −2.99662 | −0.123474 | ||||||||
\(590\) | −26.9927 | + | 33.0697i | −1.11127 | + | 1.36146i | ||||
\(591\) | −11.2700 | −0.463586 | ||||||||
\(592\) | −16.1424 | + | 6.88852i | −0.663450 | + | 0.283117i | ||||
\(593\) | −21.7131 | −0.891651 | −0.445826 | − | 0.895120i | \(-0.647090\pi\) | ||||
−0.445826 | + | 0.895120i | \(0.647090\pi\) | |||||||
\(594\) | 3.70889 | + | 3.02733i | 0.152177 | + | 0.124213i | ||||
\(595\) | 6.39136 | + | 24.7743i | 0.262020 | + | 1.01565i | ||||
\(596\) | −3.34468 | + | 0.683815i | −0.137004 | + | 0.0280102i | ||||
\(597\) | 24.3509i | 0.996614i | ||||||||
\(598\) | −36.6288 | − | 29.8978i | −1.49786 | − | 1.22261i | ||||
\(599\) | 4.44614 | 0.181664 | 0.0908322 | − | 0.995866i | \(-0.471047\pi\) | ||||
0.0908322 | + | 0.995866i | \(0.471047\pi\) | |||||||
\(600\) | 2.04693 | − | 3.90416i | 0.0835656 | − | 0.159387i | ||||
\(601\) | − | 31.5661i | − | 1.28761i | −0.765190 | − | 0.643804i | \(-0.777355\pi\) | ||
0.765190 | − | 0.643804i | \(-0.222645\pi\) | |||||||
\(602\) | 3.07331 | + | 2.50855i | 0.125259 | + | 0.102241i | ||||
\(603\) | − | 5.96128i | − | 0.242762i | ||||||
\(604\) | 1.39326 | + | 6.81475i | 0.0566911 | + | 0.277288i | ||||
\(605\) | −25.2415 | −1.02621 | ||||||||
\(606\) | −14.0736 | + | 17.2421i | −0.571702 | + | 0.700411i | ||||
\(607\) | 32.8533i | 1.33347i | 0.745294 | + | 0.666736i | \(0.232309\pi\) | ||||
−0.745294 | + | 0.666736i | \(0.767691\pi\) | |||||||
\(608\) | −1.33991 | + | 4.63828i | −0.0543407 | + | 0.188107i | ||||
\(609\) | 28.4449i | 1.15265i | ||||||||
\(610\) | −21.5872 | − | 17.6203i | −0.874041 | − | 0.713425i | ||||
\(611\) | 22.1187i | 0.894829i | ||||||||
\(612\) | 2.04190 | + | 4.18268i | 0.0825390 | + | 0.169075i | ||||
\(613\) | 32.7902i | 1.32438i | 0.749335 | + | 0.662191i | \(0.230373\pi\) | ||||
−0.749335 | + | 0.662191i | \(0.769627\pi\) | |||||||
\(614\) | −9.48687 | + | 11.6227i | −0.382859 | + | 0.469053i | ||||
\(615\) | − | 53.3860i | − | 2.15273i | ||||||
\(616\) | −4.74149 | − | 2.48594i | −0.191040 | − | 0.100161i | ||||
\(617\) | 33.4463i | 1.34650i | 0.739415 | + | 0.673249i | \(0.235102\pi\) | ||||
−0.739415 | + | 0.673249i | \(0.764898\pi\) | |||||||
\(618\) | −32.1529 | − | 26.2444i | −1.29338 | − | 1.05570i | ||||
\(619\) | 29.0694 | 1.16840 | 0.584199 | − | 0.811610i | \(-0.301409\pi\) | ||||
0.584199 | + | 0.811610i | \(0.301409\pi\) | |||||||
\(620\) | 16.6054 | − | 3.39495i | 0.666889 | − | 0.136344i | ||||
\(621\) | − | 37.7265i | − | 1.51391i | ||||||
\(622\) | 13.6549 | − | 16.7291i | 0.547513 | − | 0.670777i | ||||
\(623\) | 14.7157i | 0.589570i | ||||||||
\(624\) | −12.0784 | − | 28.3043i | −0.483524 | − | 1.13308i | ||||
\(625\) | −28.4461 | −1.13784 | ||||||||
\(626\) | 11.7570 | − | 14.4039i | 0.469904 | − | 0.575695i | ||||
\(627\) | 1.18628i | 0.0473753i | ||||||||
\(628\) | 43.2078 | − | 8.83376i | 1.72418 | − | 0.352505i | ||||
\(629\) | 17.5174 | − | 4.51919i | 0.698464 | − | 0.180192i | ||||
\(630\) | −3.13219 | + | 3.83736i | −0.124790 | + | 0.152884i | ||||
\(631\) | −35.3823 | −1.40855 | −0.704273 | − | 0.709929i | \(-0.748727\pi\) | ||||
−0.704273 | + | 0.709929i | \(0.748727\pi\) | |||||||
\(632\) | −3.63520 | − | 1.90592i | −0.144601 | − | 0.0758134i | ||||
\(633\) | 8.15595 | 0.324170 | ||||||||
\(634\) | 28.2563 | + | 23.0639i | 1.12220 | + | 0.915984i | ||||
\(635\) | −26.7873 | −1.06302 | ||||||||
\(636\) | 17.2693 | − | 3.53068i | 0.684772 | − | 0.140001i | ||||
\(637\) | − | 1.58903i | − | 0.0629597i | ||||||
\(638\) | −4.72667 | − | 3.85809i | −0.187131 | − | 0.152743i | ||||
\(639\) | − | 0.288465i | − | 0.0114115i | ||||||
\(640\) | 2.17014 | − | 27.2205i | 0.0857823 | − | 1.07598i | ||||
\(641\) | 3.40578i | 0.134520i | 0.997735 | + | 0.0672601i | \(0.0214257\pi\) | ||||
−0.997735 | + | 0.0672601i | \(0.978574\pi\) | |||||||
\(642\) | 31.0036 | + | 25.3063i | 1.22361 | + | 0.998759i | ||||
\(643\) | 39.7622 | 1.56807 | 0.784033 | − | 0.620719i | \(-0.213159\pi\) | ||||
0.784033 | + | 0.620719i | \(0.213159\pi\) | |||||||
\(644\) | 8.45038 | + | 41.3326i | 0.332992 | + | 1.62873i | ||||
\(645\) | 4.97188i | 0.195768i | ||||||||
\(646\) | 2.08400 | − | 4.51916i | 0.0819939 | − | 0.177804i | ||||
\(647\) | 19.5885 | 0.770105 | 0.385053 | − | 0.922895i | \(-0.374183\pi\) | ||||
0.385053 | + | 0.922895i | \(0.374183\pi\) | |||||||
\(648\) | 13.6258 | − | 25.9888i | 0.535272 | − | 1.02094i | ||||
\(649\) | 9.20706i | 0.361409i | ||||||||
\(650\) | 3.00822 | − | 3.68547i | 0.117992 | − | 0.144556i | ||||
\(651\) | −17.0429 | −0.667962 | ||||||||
\(652\) | 2.78189 | + | 13.6068i | 0.108947 | + | 0.532884i | ||||
\(653\) | −47.0453 | −1.84103 | −0.920513 | − | 0.390712i | \(-0.872229\pi\) | ||||
−0.920513 | + | 0.390712i | \(0.872229\pi\) | |||||||
\(654\) | 1.94678 | + | 1.58903i | 0.0761250 | + | 0.0621360i | ||||
\(655\) | 44.4959 | 1.73860 | ||||||||
\(656\) | −18.3931 | − | 43.1020i | −0.718129 | − | 1.68285i | ||||
\(657\) | − | 7.52224i | − | 0.293471i | ||||||
\(658\) | 12.4796 | − | 15.2892i | 0.486505 | − | 0.596034i | ||||
\(659\) | 26.4748i | 1.03131i | 0.856796 | + | 0.515656i | \(0.172452\pi\) | ||||
−0.856796 | + | 0.515656i | \(0.827548\pi\) | |||||||
\(660\) | −1.34396 | − | 6.57361i | −0.0523137 | − | 0.255877i | ||||
\(661\) | − | 34.0089i | − | 1.32279i | −0.750037 | − | 0.661396i | \(-0.769964\pi\) | ||
0.750037 | − | 0.661396i | \(-0.230036\pi\) | |||||||
\(662\) | −15.6297 | + | 19.1485i | −0.607465 | + | 0.744227i | ||||
\(663\) | 7.92400 | + | 30.7152i | 0.307743 | + | 1.19288i | ||||
\(664\) | −10.9119 | − | 5.72106i | −0.423464 | − | 0.222020i | ||||
\(665\) | 5.29610 | 0.205374 | ||||||||
\(666\) | 2.71331 | + | 2.21470i | 0.105139 | + | 0.0858180i | ||||
\(667\) | 48.0794i | 1.86164i | ||||||||
\(668\) | −22.3071 | + | 4.56065i | −0.863088 | + | 0.176457i | ||||
\(669\) | −29.4132 | −1.13718 | ||||||||
\(670\) | 22.7956 | − | 27.9277i | 0.880672 | − | 1.07894i | ||||
\(671\) | −6.01017 | −0.232020 | ||||||||
\(672\) | −7.62057 | + | 26.3796i | −0.293970 | + | 1.01761i | ||||
\(673\) | 14.2242i | 0.548301i | 0.961687 | + | 0.274151i | \(0.0883967\pi\) | ||||
−0.961687 | + | 0.274151i | \(0.911603\pi\) | |||||||
\(674\) | 23.3575 | − | 28.6161i | 0.899699 | − | 1.10225i | ||||
\(675\) | 3.79592 | 0.146105 | ||||||||
\(676\) | −1.44436 | − | 7.06468i | −0.0555524 | − | 0.271718i | ||||
\(677\) | −16.1654 | −0.621288 | −0.310644 | − | 0.950526i | \(-0.600545\pi\) | ||||
−0.310644 | + | 0.950526i | \(0.600545\pi\) | |||||||
\(678\) | 16.6054 | − | 20.3438i | 0.637727 | − | 0.781301i | ||||
\(679\) | −30.5829 | −1.17366 | ||||||||
\(680\) | −6.42836 | + | 27.4034i | −0.246516 | + | 1.05087i | ||||
\(681\) | 10.3304 | 0.395863 | ||||||||
\(682\) | 2.31159 | − | 2.83200i | 0.0885152 | − | 0.108443i | ||||
\(683\) | 15.6478 | 0.598746 | 0.299373 | − | 0.954136i | \(-0.403223\pi\) | ||||
0.299373 | + | 0.954136i | \(0.403223\pi\) | |||||||
\(684\) | 0.943935 | − | 0.192986i | 0.0360923 | − | 0.00737900i | ||||
\(685\) | −32.6658 | −1.24809 | ||||||||
\(686\) | −16.9905 | + | 20.8156i | −0.648700 | + | 0.794745i | ||||
\(687\) | − | 5.45378i | − | 0.208075i | ||||||
\(688\) | 1.71296 | + | 4.01413i | 0.0653061 | + | 0.153037i | ||||
\(689\) | 19.0224 | 0.724697 | ||||||||
\(690\) | −33.4331 | + | 40.9601i | −1.27278 | + | 1.55932i | ||||
\(691\) | −2.33710 | −0.0889075 | −0.0444537 | − | 0.999011i | \(-0.514155\pi\) | ||||
−0.0444537 | + | 0.999011i | \(0.514155\pi\) | |||||||
\(692\) | 2.27863 | + | 11.1452i | 0.0866203 | + | 0.423678i | ||||
\(693\) | 1.06837i | 0.0405841i | ||||||||
\(694\) | 19.6261 | + | 16.0195i | 0.744996 | + | 0.608093i | ||||
\(695\) | −6.54160 | −0.248137 | ||||||||
\(696\) | −14.5307 | + | 27.7148i | −0.550786 | + | 1.05053i | ||||
\(697\) | 12.0667 | + | 46.7733i | 0.457059 | + | 1.77166i | ||||
\(698\) | −20.1440 | + | 24.6792i | −0.762463 | + | 0.934120i | ||||
\(699\) | 16.3738i | 0.619314i | ||||||||
\(700\) | −4.15875 | + | 0.850249i | −0.157186 | + | 0.0321364i | ||||
\(701\) | 30.6904i | 1.15916i | 0.814916 | + | 0.579580i | \(0.196783\pi\) | ||||
−0.814916 | + | 0.579580i | \(0.803217\pi\) | |||||||
\(702\) | 16.7564 | − | 20.5289i | 0.632431 | − | 0.774813i | ||||
\(703\) | − | 3.74476i | − | 0.141236i | ||||||
\(704\) | −3.34987 | − | 4.84427i | −0.126253 | − | 0.182575i | ||||
\(705\) | 24.7342 | 0.931545 | ||||||||
\(706\) | 6.09994 | + | 4.97900i | 0.229574 | + | 0.187387i | ||||
\(707\) | 21.4314 | 0.806011 | ||||||||
\(708\) | 46.2649 | − | 9.45878i | 1.73874 | − | 0.355483i | ||||
\(709\) | 11.4092 | 0.428481 | 0.214240 | − | 0.976781i | \(-0.431272\pi\) | ||||
0.214240 | + | 0.976781i | \(0.431272\pi\) | |||||||
\(710\) | 1.10307 | − | 1.35141i | 0.0413977 | − | 0.0507177i | ||||
\(711\) | 0.819099i | 0.0307186i | ||||||||
\(712\) | −7.51731 | + | 14.3379i | −0.281723 | + | 0.537337i | ||||
\(713\) | −28.8069 | −1.07883 | ||||||||
\(714\) | 11.8525 | − | 25.7021i | 0.443567 | − | 0.961877i | ||||
\(715\) | − | 7.24094i | − | 0.270796i | ||||||
\(716\) | −32.3884 | + | 6.62176i | −1.21041 | + | 0.247467i | ||||
\(717\) | 30.4165 | 1.13593 | ||||||||
\(718\) | 24.2805 | + | 19.8187i | 0.906141 | + | 0.739626i | ||||
\(719\) | − | 7.71301i | − | 0.287647i | −0.989603 | − | 0.143823i | \(-0.954060\pi\) | ||
0.989603 | − | 0.143823i | \(-0.0459397\pi\) | |||||||
\(720\) | −5.01206 | + | 2.13882i | −0.186789 | + | 0.0797090i | ||||
\(721\) | 39.9651i | 1.48838i | ||||||||
\(722\) | 20.0181 | + | 16.3395i | 0.744995 | + | 0.608093i | ||||
\(723\) | − | 18.2296i | − | 0.677968i | ||||||
\(724\) | −8.26637 | − | 40.4326i | −0.307217 | − | 1.50266i | ||||
\(725\) | −4.83759 | −0.179664 | ||||||||
\(726\) | 21.6317 | + | 17.6566i | 0.802826 | + | 0.655296i | ||||
\(727\) | −13.2911 | −0.492938 | −0.246469 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246469 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(728\) | −13.7598 | + | 26.2444i | −0.509973 | + | 0.972682i | ||||
\(729\) | 20.1883 | 0.747716 | ||||||||
\(730\) | 28.7647 | − | 35.2406i | 1.06463 | − | 1.30431i | ||||
\(731\) | −1.12378 | − | 4.35603i | −0.0415646 | − | 0.161114i | ||||
\(732\) | 6.17449 | + | 30.2007i | 0.228216 | + | 1.11625i | ||||
\(733\) | − | 4.51326i | − | 0.166701i | −0.996520 | − | 0.0833505i | \(-0.973438\pi\) | ||
0.996520 | − | 0.0833505i | \(-0.0265621\pi\) | |||||||
\(734\) | 1.89796 | − | 2.32525i | 0.0700550 | − | 0.0858267i | ||||
\(735\) | −1.77693 | −0.0655430 | ||||||||
\(736\) | −12.8808 | + | 44.5884i | −0.474791 | + | 1.64355i | ||||
\(737\) | − | 7.77546i | − | 0.286413i | ||||||
\(738\) | −5.91349 | + | 7.24482i | −0.217679 | + | 0.266686i | ||||
\(739\) | − | 14.4505i | − | 0.531571i | −0.964032 | − | 0.265786i | \(-0.914369\pi\) | ||
0.964032 | − | 0.265786i | \(-0.0856314\pi\) | |||||||
\(740\) | 4.24253 | + | 20.7511i | 0.155959 | + | 0.762826i | ||||
\(741\) | 6.56610 | 0.241212 | ||||||||
\(742\) | −13.1489 | − | 10.7326i | −0.482711 | − | 0.394007i | ||||
\(743\) | − | 17.2867i | − | 0.634186i | −0.948394 | − | 0.317093i | \(-0.897293\pi\) | ||
0.948394 | − | 0.317093i | \(-0.102707\pi\) | |||||||
\(744\) | −16.6054 | − | 8.70614i | −0.608784 | − | 0.319182i | ||||
\(745\) | 4.11988i | 0.150941i | ||||||||
\(746\) | −15.8033 | + | 19.3612i | −0.578601 | + | 0.708864i | ||||
\(747\) | 2.45871i | 0.0899597i | ||||||||
\(748\) | 2.66331 | + | 5.45558i | 0.0973802 | + | 0.199476i | ||||
\(749\) | − | 38.5365i | − | 1.40809i | ||||||
\(750\) | 20.8407 | + | 17.0109i | 0.760994 | + | 0.621152i | ||||
\(751\) | − | 27.5979i | − | 1.00706i | −0.863978 | − | 0.503530i | \(-0.832034\pi\) | ||
0.863978 | − | 0.503530i | \(-0.167966\pi\) | |||||||
\(752\) | 19.9696 | − | 8.52168i | 0.728215 | − | 0.310754i | ||||
\(753\) | − | 37.2068i | − | 1.35589i | ||||||
\(754\) | −21.3547 | + | 26.1624i | −0.777692 | + | 0.952778i | ||||
\(755\) | 8.39419 | 0.305496 | ||||||||
\(756\) | −23.1651 | + | 4.73608i | −0.842508 | + | 0.172249i | ||||
\(757\) | − | 29.2683i | − | 1.06377i | −0.846815 | − | 0.531887i | \(-0.821483\pi\) | ||
0.846815 | − | 0.531887i | \(-0.178517\pi\) | |||||||
\(758\) | 3.54086 | + | 2.89018i | 0.128610 | + | 0.104976i | ||||
\(759\) | 11.4038i | 0.413933i | ||||||||
\(760\) | 5.16016 | + | 2.70545i | 0.187179 | + | 0.0981370i | ||||
\(761\) | 5.48844 | 0.198956 | 0.0994779 | − | 0.995040i | \(-0.468283\pi\) | ||||
0.0994779 | + | 0.995040i | \(0.468283\pi\) | |||||||
\(762\) | 22.9564 | + | 18.7378i | 0.831621 | + | 0.678800i | ||||
\(763\) | − | 2.41979i | − | 0.0876021i | ||||||
\(764\) | −6.93916 | − | 33.9409i | −0.251050 | − | 1.22794i | ||||
\(765\) | 5.43897 | − | 1.40316i | 0.196646 | − | 0.0507314i | ||||
\(766\) | 8.68141 | + | 7.08609i | 0.313672 | + | 0.256031i | ||||
\(767\) | 50.9615 | 1.84011 | ||||||||
\(768\) | −20.9007 | + | 21.8096i | −0.754188 | + | 0.786986i | ||||
\(769\) | 41.5703 | 1.49906 | 0.749531 | − | 0.661969i | \(-0.230279\pi\) | ||||
0.749531 | + | 0.661969i | \(0.230279\pi\) | |||||||
\(770\) | −4.08540 | + | 5.00517i | −0.147228 | + | 0.180374i | ||||
\(771\) | −11.9667 | −0.430971 | ||||||||
\(772\) | −24.1876 | + | 4.94511i | −0.870529 | + | 0.177978i | ||||
\(773\) | − | 24.0984i | − | 0.866761i | −0.901211 | − | 0.433380i | \(-0.857321\pi\) | ||
0.901211 | − | 0.433380i | \(-0.142679\pi\) | |||||||
\(774\) | 0.550729 | − | 0.674716i | 0.0197955 | − | 0.0242522i | ||||
\(775\) | − | 2.89846i | − | 0.104116i | ||||||
\(776\) | −29.7979 | − | 15.6229i | −1.06968 | − | 0.560830i | ||||
\(777\) | − | 21.2978i | − | 0.764054i | ||||||
\(778\) | 4.27993 | − | 5.24348i | 0.153443 | − | 0.187988i | ||||
\(779\) | 9.99890 | 0.358248 | ||||||||
\(780\) | −36.3852 | + | 7.43890i | −1.30280 | + | 0.266356i | ||||
\(781\) | − | 0.376252i | − | 0.0134634i | ||||||
\(782\) | 20.0338 | − | 43.4433i | 0.716406 | − | 1.55353i | ||||
\(783\) | −26.9464 | −0.962987 | ||||||||
\(784\) | −1.43463 | + | 0.612206i | −0.0512368 | + | 0.0218645i | ||||
\(785\) | − | 53.2220i | − | 1.89957i | ||||||
\(786\) | −38.1325 | − | 31.1251i | −1.36014 | − | 1.11020i | ||||
\(787\) | 14.1491 | 0.504360 | 0.252180 | − | 0.967680i | \(-0.418853\pi\) | ||||
0.252180 | + | 0.967680i | \(0.418853\pi\) | |||||||
\(788\) | 2.39139 | + | 11.6968i | 0.0851897 | + | 0.416681i | ||||
\(789\) | 29.3477 | 1.04481 | ||||||||
\(790\) | −3.13219 | + | 3.83736i | −0.111438 | + | 0.136527i | ||||
\(791\) | −25.2868 | −0.899096 | ||||||||
\(792\) | −0.545765 | + | 1.04095i | −0.0193929 | + | 0.0369885i | ||||
\(793\) | 33.2666i | 1.18133i | ||||||||
\(794\) | −5.48868 | − | 4.48006i | −0.194786 | − | 0.158991i | ||||
\(795\) | − | 21.2718i | − | 0.754432i | ||||||
\(796\) | 25.2730 | − | 5.16702i | 0.895777 | − | 0.183140i | ||||
\(797\) | − | 19.0896i | − | 0.676189i | −0.941112 | − | 0.338094i | \(-0.890218\pi\) | ||
0.941112 | − | 0.338094i | \(-0.109782\pi\) | |||||||
\(798\) | −4.53869 | − | 3.70465i | −0.160668 | − | 0.131143i | ||||
\(799\) | −21.6705 | + | 5.59062i | −0.766647 | + | 0.197782i | ||||
\(800\) | −4.48634 | − | 1.29602i | −0.158616 | − | 0.0458213i | ||||
\(801\) | 3.23068 | 0.114151 | ||||||||
\(802\) | 6.80656 | − | 8.33895i | 0.240348 | − | 0.294458i | ||||
\(803\) | − | 9.81146i | − | 0.346239i | ||||||
\(804\) | −39.0712 | + | 7.98803i | −1.37793 | + | 0.281716i | ||||
\(805\) | 50.9122 | 1.79442 | ||||||||
\(806\) | −15.6753 | − | 12.7947i | −0.552138 | − | 0.450676i | ||||
\(807\) | −43.1331 | −1.51836 | ||||||||
\(808\) | 20.8813 | + | 10.9480i | 0.734601 | + | 0.385148i | ||||
\(809\) | − | 24.7737i | − | 0.870995i | −0.900190 | − | 0.435498i | \(-0.856572\pi\) | ||
0.900190 | − | 0.435498i | \(-0.143428\pi\) | |||||||
\(810\) | −27.4340 | − | 22.3927i | −0.963933 | − | 0.786798i | ||||
\(811\) | −28.7575 | −1.00981 | −0.504906 | − | 0.863174i | \(-0.668473\pi\) | ||||
−0.504906 | + | 0.863174i | \(0.668473\pi\) | |||||||
\(812\) | 29.5221 | − | 6.03574i | 1.03602 | − | 0.211813i | ||||
\(813\) | −13.5371 | −0.474768 | ||||||||
\(814\) | 3.53904 | + | 2.88870i | 0.124043 | + | 0.101249i | ||||
\(815\) | 16.7604 | 0.587092 | ||||||||
\(816\) | 24.6778 | − | 18.9877i | 0.863897 | − | 0.664702i | ||||
\(817\) | −0.931205 | −0.0325788 | ||||||||
\(818\) | −20.4417 | − | 16.6852i | −0.714726 | − | 0.583386i | ||||
\(819\) | 5.91349 | 0.206634 | ||||||||
\(820\) | −55.4077 | + | 11.3280i | −1.93492 | + | 0.395591i | ||||
\(821\) | 28.6880 | 1.00122 | 0.500609 | − | 0.865673i | \(-0.333109\pi\) | ||||
0.500609 | + | 0.865673i | \(0.333109\pi\) | |||||||
\(822\) | 27.9942 | + | 22.8499i | 0.976408 | + | 0.796981i | ||||
\(823\) | − | 35.5415i | − | 1.23890i | −0.785036 | − | 0.619450i | \(-0.787356\pi\) | ||
0.785036 | − | 0.619450i | \(-0.212644\pi\) | |||||||
\(824\) | −20.4157 | + | 38.9393i | −0.711214 | + | 1.35651i | ||||
\(825\) | −1.14742 | −0.0399479 | ||||||||
\(826\) | −35.2262 | − | 28.7529i | −1.22568 | − | 1.00044i | ||||
\(827\) | −35.4846 | −1.23392 | −0.616959 | − | 0.786995i | \(-0.711636\pi\) | ||||
−0.616959 | + | 0.786995i | \(0.711636\pi\) | |||||||
\(828\) | 9.07417 | − | 1.85520i | 0.315349 | − | 0.0644727i | ||||
\(829\) | − | 54.8280i | − | 1.90425i | −0.305703 | − | 0.952127i | \(-0.598891\pi\) | ||
0.305703 | − | 0.952127i | \(-0.401109\pi\) | |||||||
\(830\) | −9.40200 | + | 11.5187i | −0.326348 | + | 0.399820i | ||||
\(831\) | −12.4808 | −0.432955 | ||||||||
\(832\) | −26.8133 | + | 18.5417i | −0.929582 | + | 0.642819i | ||||
\(833\) | 1.55683 | − | 0.401635i | 0.0539409 | − | 0.0139158i | ||||
\(834\) | 5.60607 | + | 4.57588i | 0.194122 | + | 0.158450i | ||||
\(835\) | 27.4772i | 0.950887i | ||||||||
\(836\) | 1.23120 | − | 0.251717i | 0.0425819 | − | 0.00870580i | ||||
\(837\) | − | 16.1450i | − | 0.558054i | ||||||
\(838\) | 1.15790 | + | 0.945120i | 0.0399990 | + | 0.0326486i | ||||
\(839\) | − | 2.66018i | − | 0.0918395i | −0.998945 | − | 0.0459198i | \(-0.985378\pi\) | ||
0.998945 | − | 0.0459198i | \(-0.0146219\pi\) | |||||||
\(840\) | 29.3477 | + | 15.3869i | 1.01259 | + | 0.530898i | ||||
\(841\) | 5.34102 | 0.184173 | ||||||||
\(842\) | −1.22705 | + | 1.50330i | −0.0422869 | + | 0.0518072i | ||||
\(843\) | −28.0325 | −0.965490 | ||||||||
\(844\) | −1.73062 | − | 8.46481i | −0.0595703 | − | 0.291371i | ||||
\(845\) | −8.70205 | −0.299359 | ||||||||
\(846\) | −3.35659 | − | 2.73978i | −0.115402 | − | 0.0941954i | ||||
\(847\) | − | 26.8875i | − | 0.923866i | ||||||
\(848\) | −7.32877 | − | 17.1741i | −0.251671 | − | 0.589761i | ||||
\(849\) | −27.0713 | −0.929085 | ||||||||
\(850\) | 4.37112 | + | 2.01573i | 0.149928 | + | 0.0691390i | ||||
\(851\) | − | 35.9989i | − | 1.23402i | ||||||
\(852\) | −1.89064 | + | 0.386539i | −0.0647723 | + | 0.0132426i | ||||
\(853\) | −3.49362 | −0.119619 | −0.0598097 | − | 0.998210i | \(-0.519049\pi\) | ||||
−0.0598097 | + | 0.998210i | \(0.519049\pi\) | |||||||
\(854\) | 18.7693 | − | 22.9949i | 0.642273 | − | 0.786870i | ||||
\(855\) | − | 1.16271i | − | 0.0397638i | ||||||
\(856\) | 19.6859 | − | 37.5474i | 0.672851 | − | 1.28334i | ||||
\(857\) | 32.6540i | 1.11544i | 0.830030 | + | 0.557719i | \(0.188323\pi\) | ||||
−0.830030 | + | 0.557719i | \(0.811677\pi\) | |||||||
\(858\) | −5.06507 | + | 6.20539i | −0.172919 | + | 0.211849i | ||||
\(859\) | − | 44.7174i | − | 1.52574i | −0.646553 | − | 0.762869i | \(-0.723790\pi\) | ||
0.646553 | − | 0.762869i | \(-0.276210\pi\) | |||||||
\(860\) | 5.16016 | − | 1.05499i | 0.175960 | − | 0.0359748i | ||||
\(861\) | 56.8673 | 1.93803 | ||||||||
\(862\) | −13.3761 | + | 16.3876i | −0.455593 | + | 0.558163i | ||||
\(863\) | −2.12167 | −0.0722225 | −0.0361113 | − | 0.999348i | \(-0.511497\pi\) | ||||
−0.0361113 | + | 0.999348i | \(0.511497\pi\) | |||||||
\(864\) | −24.9899 | − | 7.21912i | −0.850174 | − | 0.245599i | ||||
\(865\) | 13.7283 | 0.466778 | ||||||||
\(866\) | −1.62275 | − | 1.32455i | −0.0551433 | − | 0.0450100i | ||||
\(867\) | −28.0899 | + | 15.5268i | −0.953982 | + | 0.527318i | ||||
\(868\) | 3.61633 | + | 17.6883i | 0.122746 | + | 0.600378i | ||||
\(869\) | 1.06837i | 0.0362420i | ||||||||
\(870\) | 29.2560 | + | 23.8798i | 0.991871 | + | 0.809602i | ||||
\(871\) | −43.0375 | −1.45827 | ||||||||
\(872\) | 1.23612 | − | 2.35768i | 0.0418602 | − | 0.0798410i | ||||
\(873\) | 6.71419i | 0.227241i | ||||||||
\(874\) | −7.67158 | − | 6.26183i | −0.259495 | − | 0.211810i | ||||
\(875\) | − | 25.9044i | − | 0.875727i | ||||||
\(876\) | −49.3019 | + | 10.0797i | −1.66576 | + | 0.340561i | ||||
\(877\) | −48.3375 | −1.63224 | −0.816121 | − | 0.577881i | \(-0.803880\pi\) | ||||
−0.816121 | + | 0.577881i | \(0.803880\pi\) | |||||||
\(878\) | 17.5349 | − | 21.4826i | 0.591774 | − | 0.725002i | ||||
\(879\) | 36.9379i | 1.24588i | ||||||||
\(880\) | −6.53737 | + | 2.78971i | −0.220375 | + | 0.0940413i | ||||
\(881\) | 12.6986i | 0.427827i | 0.976853 | + | 0.213913i | \(0.0686210\pi\) | ||||
−0.976853 | + | 0.213913i | \(0.931379\pi\) | |||||||
\(882\) | 0.241141 | + | 0.196828i | 0.00811963 | + | 0.00662754i | ||||
\(883\) | 33.2423i | 1.11869i | 0.828934 | + | 0.559346i | \(0.188948\pi\) | ||||
−0.828934 | + | 0.559346i | \(0.811052\pi\) | |||||||
\(884\) | 30.1969 | − | 14.7415i | 1.01563 | − | 0.495812i | ||||
\(885\) | − | 56.9876i | − | 1.91562i | ||||||
\(886\) | 28.8920 | − | 35.3966i | 0.970647 | − | 1.18917i | ||||
\(887\) | 39.5909i | 1.32933i | 0.747140 | + | 0.664666i | \(0.231426\pi\) | ||||
−0.747140 | + | 0.664666i | \(0.768574\pi\) | |||||||
\(888\) | 10.8797 | − | 20.7511i | 0.365099 | − | 0.696362i | ||||
\(889\) | − | 28.5341i | − | 0.957003i | ||||||
\(890\) | 15.1353 | + | 12.3540i | 0.507335 | + | 0.414106i | ||||
\(891\) | −7.63800 | −0.255883 | ||||||||
\(892\) | 6.24120 | + | 30.5270i | 0.208971 | + | 1.02212i | ||||
\(893\) | 4.63258i | 0.155023i | ||||||||
\(894\) | 2.88187 | − | 3.53068i | 0.0963843 | − | 0.118084i | ||||
\(895\) | 39.8950i | 1.33354i | ||||||||
\(896\) | 28.9956 | + | 2.31165i | 0.968674 | + | 0.0772269i | ||||
\(897\) | 63.1208 | 2.10754 | ||||||||
\(898\) | −15.6019 | + | 19.1145i | −0.520643 | + | 0.637857i | ||||
\(899\) | 20.5755i | 0.686233i | ||||||||
\(900\) | 0.186664 | + | 0.913014i | 0.00622214 | + | 0.0304338i | ||||
\(901\) | 4.80801 | + | 18.6369i | 0.160178 | + | 0.620886i | ||||
\(902\) | −7.71313 | + | 9.44961i | −0.256819 | + | 0.314638i | ||||
\(903\) | −5.29610 | −0.176243 | ||||||||
\(904\) | −24.6378 | − | 12.9175i | −0.819440 | − | 0.429628i | ||||
\(905\) | −49.8035 | −1.65553 | ||||||||
\(906\) | −7.19371 | − | 5.87178i | −0.238995 | − | 0.195077i | ||||
\(907\) | 52.1980 | 1.73321 | 0.866603 | − | 0.498998i | \(-0.166299\pi\) | ||||
0.866603 | + | 0.498998i | \(0.166299\pi\) | |||||||
\(908\) | −2.19202 | − | 10.7216i | −0.0727448 | − | 0.355810i | ||||
\(909\) | − | 4.70506i | − | 0.156057i | ||||||
\(910\) | 27.7038 | + | 22.6129i | 0.918373 | + | 0.749611i | ||||
\(911\) | 33.2042i | 1.10010i | 0.835131 | + | 0.550052i | \(0.185392\pi\) | ||||
−0.835131 | + | 0.550052i | \(0.814608\pi\) | |||||||
\(912\) | −2.52972 | − | 5.92810i | −0.0837674 | − | 0.196299i | ||||
\(913\) | 3.20697i | 0.106135i | ||||||||
\(914\) | −2.57714 | − | 2.10356i | −0.0852441 | − | 0.0695794i | ||||
\(915\) | 37.2003 | 1.22980 | ||||||||
\(916\) | −5.66031 | + | 1.15724i | −0.187022 | + | 0.0382363i | ||||
\(917\) | 47.3975i | 1.56520i | ||||||||
\(918\) | 24.3481 | + | 11.2281i | 0.803607 | + | 0.370582i | ||||
\(919\) | 2.50268 | 0.0825558 | 0.0412779 | − | 0.999148i | \(-0.486857\pi\) | ||||
0.0412779 | + | 0.999148i | \(0.486857\pi\) | |||||||
\(920\) | 49.6053 | + | 26.0079i | 1.63544 | + | 0.857454i | ||||
\(921\) | − | 20.0289i | − | 0.659973i | ||||||
\(922\) | 3.87106 | − | 4.74257i | 0.127487 | − | 0.156188i | ||||
\(923\) | −2.08257 | −0.0685488 | ||||||||
\(924\) | 7.00228 | − | 1.43160i | 0.230358 | − | 0.0470963i | ||||
\(925\) | 3.62209 | 0.119093 | ||||||||
\(926\) | 5.80233 | + | 4.73608i | 0.190676 | + | 0.155637i | ||||
\(927\) | 8.77396 | 0.288175 | ||||||||
\(928\) | 31.8476 | + | 9.20018i | 1.04545 | + | 0.302011i | ||||
\(929\) | 20.2991i | 0.665993i | 0.942928 | + | 0.332996i | \(0.108060\pi\) | ||||
−0.942928 | + | 0.332996i | \(0.891940\pi\) | |||||||
\(930\) | −14.3077 | + | 17.5288i | −0.469167 | + | 0.574793i | ||||
\(931\) | − | 0.332809i | − | 0.0109074i | ||||||
\(932\) | 16.9938 | − | 3.47436i | 0.556652 | − | 0.113807i | ||||
\(933\) | 28.8286i | 0.943806i | ||||||||
\(934\) | 3.93765 | − | 4.82415i | 0.128844 | − | 0.157851i | ||||
\(935\) | 7.09419 | − | 1.83018i | 0.232005 | − | 0.0598533i | ||||
\(936\) | 5.76171 | + | 3.02084i | 0.188327 | + | 0.0987391i | ||||
\(937\) | 36.2874 | 1.18546 | 0.592729 | − | 0.805402i | \(-0.298051\pi\) | ||||
0.592729 | + | 0.805402i | \(0.298051\pi\) | |||||||
\(938\) | 29.7489 | + | 24.2822i | 0.971336 | + | 0.792841i | ||||
\(939\) | 24.8216i | 0.810022i | ||||||||
\(940\) | −5.24837 | − | 25.6709i | −0.171183 | − | 0.837292i | ||||
\(941\) | 13.6402 | 0.444658 | 0.222329 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222329 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(942\) | −37.2290 | + | 45.6106i | −1.21299 | + | 1.48607i | ||||
\(943\) | 96.1207 | 3.13012 | ||||||||
\(944\) | −19.6339 | − | 46.0098i | −0.639030 | − | 1.49749i | ||||
\(945\) | 28.5341i | 0.928214i | ||||||||
\(946\) | 0.718330 | − | 0.880050i | 0.0233549 | − | 0.0286129i | ||||
\(947\) | 9.92155 | 0.322407 | 0.161203 | − | 0.986921i | \(-0.448462\pi\) | ||||
0.161203 | + | 0.986921i | \(0.448462\pi\) | |||||||
\(948\) | 5.36850 | − | 1.09758i | 0.174361 | − | 0.0356478i | ||||
\(949\) | −54.3069 | −1.76288 | ||||||||
\(950\) | 0.630045 | − | 0.771890i | 0.0204414 | − | 0.0250434i | ||||
\(951\) | −48.6929 | −1.57898 | ||||||||
\(952\) | −29.1904 | − | 6.84756i | −0.946065 | − | 0.221931i | ||||
\(953\) | 4.30663 | 0.139505 | 0.0697526 | − | 0.997564i | \(-0.477779\pi\) | ||||
0.0697526 | + | 0.997564i | \(0.477779\pi\) | |||||||
\(954\) | −2.35624 | + | 2.88672i | −0.0762862 | + | 0.0934609i | ||||
\(955\) | −41.8073 | −1.35285 | ||||||||
\(956\) | −6.45410 | − | 31.5684i | −0.208741 | − | 1.02099i | ||||
\(957\) | 8.14527 | 0.263299 | ||||||||
\(958\) | −14.6914 | + | 17.9989i | −0.474656 | + | 0.581518i | ||||
\(959\) | − | 34.7959i | − | 1.12362i | ||||||
\(960\) | 20.7342 | + | 29.9838i | 0.669194 | + | 0.967724i | ||||
\(961\) | 18.6721 | 0.602326 | ||||||||
\(962\) | 15.9891 | − | 19.5888i | 0.515509 | − | 0.631567i | ||||
\(963\) | −8.46033 | −0.272630 | ||||||||
\(964\) | −18.9200 | + | 3.86816i | −0.609371 | + | 0.124585i | ||||
\(965\) | 29.7935i | 0.959085i | ||||||||
\(966\) | −43.6311 | − | 35.6133i | −1.40381 | − | 1.14584i | ||||
\(967\) | −17.6400 | −0.567265 | −0.283633 | − | 0.958933i | \(-0.591540\pi\) | ||||
−0.283633 | + | 0.958933i | \(0.591540\pi\) | |||||||
\(968\) | 13.7352 | − | 26.1974i | 0.441465 | − | 0.842015i | ||||
\(969\) | 1.65961 | + | 6.43303i | 0.0533144 | + | 0.206659i | ||||
\(970\) | −25.6747 | + | 31.4550i | −0.824366 | + | 1.00996i | ||||
\(971\) | 10.5762i | 0.339407i | 0.985495 | + | 0.169704i | \(0.0542811\pi\) | ||||
−0.985495 | + | 0.169704i | \(0.945719\pi\) | |||||||
\(972\) | 2.32048 | + | 11.3500i | 0.0744296 | + | 0.364051i | ||||
\(973\) | − | 6.96819i | − | 0.223390i | ||||||
\(974\) | −4.25294 | + | 5.21042i | −0.136273 | + | 0.166953i | ||||
\(975\) | 6.35101i | 0.203395i | ||||||||
\(976\) | 30.0342 | − | 12.8166i | 0.961372 | − | 0.410250i | ||||
\(977\) | −40.2041 | −1.28624 | −0.643122 | − | 0.765764i | \(-0.722361\pi\) | ||||
−0.643122 | + | 0.765764i | \(0.722361\pi\) | |||||||
\(978\) | −14.3635 | − | 11.7240i | −0.459293 | − | 0.374892i | ||||
\(979\) | 4.21386 | 0.134676 | ||||||||
\(980\) | 0.377048 | + | 1.84422i | 0.0120443 | + | 0.0589114i | ||||
\(981\) | −0.531241 | −0.0169612 | ||||||||
\(982\) | −1.69088 | + | 2.07156i | −0.0539582 | + | 0.0661060i | ||||
\(983\) | − | 20.5056i | − | 0.654026i | −0.945020 | − | 0.327013i | \(-0.893958\pi\) | ||
0.945020 | − | 0.327013i | \(-0.106042\pi\) | |||||||
\(984\) | 55.4077 | + | 29.0500i | 1.76633 | + | 0.926080i | ||||
\(985\) | 14.4077 | 0.459069 | ||||||||
\(986\) | −31.0297 | − | 14.3093i | −0.988186 | − | 0.455700i | ||||
\(987\) | 26.3472i | 0.838639i | ||||||||
\(988\) | −1.39326 | − | 6.81475i | −0.0443256 | − | 0.216806i | ||||
\(989\) | −8.95180 | −0.284651 | ||||||||
\(990\) | 1.09884 | + | 0.896911i | 0.0349233 | + | 0.0285057i | ||||
\(991\) | 4.64662i | 0.147605i | 0.997273 | + | 0.0738024i | \(0.0235134\pi\) | ||||
−0.997273 | + | 0.0738024i | \(0.976487\pi\) | |||||||
\(992\) | −5.51232 | + | 19.0816i | −0.175016 | + | 0.605841i | ||||
\(993\) | − | 32.9977i | − | 1.04715i | ||||||
\(994\) | 1.43954 | + | 1.17501i | 0.0456595 | + | 0.0372689i | ||||
\(995\) | − | 31.1305i | − | 0.986902i | ||||||
\(996\) | 16.1148 | − | 3.29464i | 0.510617 | − | 0.104395i | ||||
\(997\) | −32.7934 | −1.03858 | −0.519289 | − | 0.854599i | \(-0.673803\pi\) | ||||
−0.519289 | + | 0.854599i | \(0.673803\pi\) | |||||||
\(998\) | −40.4415 | − | 33.0099i | −1.28015 | − | 1.04491i | ||||
\(999\) | 20.1758 | 0.638335 |
(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 | 136.2.h.a.101.15 | yes | 16 | |
3.2 | odd | 2 | 1224.2.l.b.1189.1 | 16 | |||
4.3 | odd | 2 | 544.2.h.a.305.13 | 16 | |||
8.3 | odd | 2 | 544.2.h.a.305.3 | 16 | |||
8.5 | even | 2 | inner | 136.2.h.a.101.14 | yes | 16 | |
12.11 | even | 2 | 4896.2.l.b.3025.3 | 16 | |||
17.16 | even | 2 | inner | 136.2.h.a.101.16 | yes | 16 | |
24.5 | odd | 2 | 1224.2.l.b.1189.4 | 16 | |||
24.11 | even | 2 | 4896.2.l.b.3025.13 | 16 | |||
51.50 | odd | 2 | 1224.2.l.b.1189.2 | 16 | |||
68.67 | odd | 2 | 544.2.h.a.305.4 | 16 | |||
136.67 | odd | 2 | 544.2.h.a.305.14 | 16 | |||
136.101 | even | 2 | inner | 136.2.h.a.101.13 | ✓ | 16 | |
204.203 | even | 2 | 4896.2.l.b.3025.14 | 16 | |||
408.101 | odd | 2 | 1224.2.l.b.1189.3 | 16 | |||
408.203 | even | 2 | 4896.2.l.b.3025.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.h.a.101.13 | ✓ | 16 | 136.101 | even | 2 | inner | |
136.2.h.a.101.14 | yes | 16 | 8.5 | even | 2 | inner | |
136.2.h.a.101.15 | yes | 16 | 1.1 | even | 1 | trivial | |
136.2.h.a.101.16 | yes | 16 | 17.16 | even | 2 | inner | |
544.2.h.a.305.3 | 16 | 8.3 | odd | 2 | |||
544.2.h.a.305.4 | 16 | 68.67 | odd | 2 | |||
544.2.h.a.305.13 | 16 | 4.3 | odd | 2 | |||
544.2.h.a.305.14 | 16 | 136.67 | odd | 2 | |||
1224.2.l.b.1189.1 | 16 | 3.2 | odd | 2 | |||
1224.2.l.b.1189.2 | 16 | 51.50 | odd | 2 | |||
1224.2.l.b.1189.3 | 16 | 408.101 | odd | 2 | |||
1224.2.l.b.1189.4 | 16 | 24.5 | odd | 2 | |||
4896.2.l.b.3025.3 | 16 | 12.11 | even | 2 | |||
4896.2.l.b.3025.4 | 16 | 408.203 | even | 2 | |||
4896.2.l.b.3025.13 | 16 | 24.11 | even | 2 | |||
4896.2.l.b.3025.14 | 16 | 204.203 | even | 2 |