Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 367.7 | ||
Character | \(\chi\) | \(=\) | 690.367 |
Dual form | 690.2.j.b.643.7 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.19853 | − | 0.408021i | −0.983211 | − | 0.182473i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.64584 | + | 1.64584i | −0.622070 | + | 0.622070i | −0.946060 | − | 0.323990i | \(-0.894976\pi\) |
0.323990 | + | 0.946060i | \(0.394976\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.26608 | − | 1.84311i | −0.400369 | − | 0.582842i | ||||
\(11\) | 6.11317i | 1.84319i | 0.388154 | + | 0.921595i | \(0.373113\pi\) | ||||
−0.388154 | + | 0.921595i | \(0.626887\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −0.241478 | + | 0.241478i | −0.0669738 | + | 0.0669738i | −0.739800 | − | 0.672826i | \(-0.765080\pi\) |
0.672826 | + | 0.739800i | \(0.265080\pi\) | |||||||
\(14\) | −2.32757 | −0.622070 | ||||||||
\(15\) | −1.84311 | + | 1.26608i | −0.475888 | + | 0.326900i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.327163 | + | 0.327163i | −0.0793486 | + | 0.0793486i | −0.745667 | − | 0.666319i | \(-0.767869\pi\) |
0.666319 | + | 0.745667i | \(0.267869\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 0.759529 | 0.174248 | 0.0871240 | − | 0.996197i | \(-0.472232\pi\) | ||||
0.0871240 | + | 0.996197i | \(0.472232\pi\) | |||||||
\(20\) | 0.408021 | − | 2.19853i | 0.0912363 | − | 0.491605i | ||||
\(21\) | 2.32757i | 0.507918i | ||||||||
\(22\) | −4.32266 | + | 4.32266i | −0.921595 | + | 0.921595i | ||||
\(23\) | −4.49658 | + | 1.66757i | −0.937601 | + | 0.347712i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 4.66704 | + | 1.79409i | 0.933408 | + | 0.358818i | ||||
\(26\) | −0.341501 | −0.0669738 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −1.64584 | − | 1.64584i | −0.311035 | − | 0.311035i | ||||
\(29\) | 7.09541i | 1.31758i | 0.752325 | + | 0.658792i | \(0.228932\pi\) | ||||
−0.752325 | + | 0.658792i | \(0.771068\pi\) | |||||||
\(30\) | −2.19853 | − | 0.408021i | −0.401394 | − | 0.0744941i | ||||
\(31\) | −8.30560 | −1.49173 | −0.745865 | − | 0.666097i | \(-0.767964\pi\) | ||||
−0.745865 | + | 0.666097i | \(0.767964\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 4.32266 | + | 4.32266i | 0.752479 | + | 0.752479i | ||||
\(34\) | −0.462678 | −0.0793486 | ||||||||
\(35\) | 4.28997 | − | 2.94689i | 0.725137 | − | 0.498116i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.92602 | − | 1.92602i | 0.316636 | − | 0.316636i | −0.530838 | − | 0.847474i | \(-0.678123\pi\) |
0.847474 | + | 0.530838i | \(0.178123\pi\) | |||||||
\(38\) | 0.537068 | + | 0.537068i | 0.0871240 | + | 0.0871240i | ||||
\(39\) | 0.341501i | 0.0546839i | ||||||||
\(40\) | 1.84311 | − | 1.26608i | 0.291421 | − | 0.200185i | ||||
\(41\) | 6.75167 | 1.05443 | 0.527217 | − | 0.849731i | \(-0.323235\pi\) | ||||
0.527217 | + | 0.849731i | \(0.323235\pi\) | |||||||
\(42\) | −1.64584 | + | 1.64584i | −0.253959 | + | 0.253959i | ||||
\(43\) | 0.144662 | + | 0.144662i | 0.0220608 | + | 0.0220608i | 0.718051 | − | 0.695990i | \(-0.245034\pi\) |
−0.695990 | + | 0.718051i | \(0.745034\pi\) | |||||||
\(44\) | −6.11317 | −0.921595 | ||||||||
\(45\) | −0.408021 | + | 2.19853i | −0.0608242 | + | 0.327737i | ||||
\(46\) | −4.35871 | − | 2.00041i | −0.642657 | − | 0.294945i | ||||
\(47\) | 1.46451 | + | 1.46451i | 0.213621 | + | 0.213621i | 0.805804 | − | 0.592183i | \(-0.201734\pi\) |
−0.592183 | + | 0.805804i | \(0.701734\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 1.58240i | 0.226057i | ||||||||
\(50\) | 2.03148 | + | 4.56871i | 0.287295 | + | 0.646113i | ||||
\(51\) | 0.462678i | 0.0647879i | ||||||||
\(52\) | −0.241478 | − | 0.241478i | −0.0334869 | − | 0.0334869i | ||||
\(53\) | −1.45249 | − | 1.45249i | −0.199515 | − | 0.199515i | 0.600277 | − | 0.799792i | \(-0.295057\pi\) |
−0.799792 | + | 0.600277i | \(0.795057\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 2.49430 | − | 13.4400i | 0.336332 | − | 1.81224i | ||||
\(56\) | − | 2.32757i | − | 0.311035i | ||||||
\(57\) | 0.537068 | − | 0.537068i | 0.0711365 | − | 0.0711365i | ||||
\(58\) | −5.01721 | + | 5.01721i | −0.658792 | + | 0.658792i | ||||
\(59\) | 1.68540i | 0.219420i | 0.993964 | + | 0.109710i | \(0.0349922\pi\) | ||||
−0.993964 | + | 0.109710i | \(0.965008\pi\) | |||||||
\(60\) | −1.26608 | − | 1.84311i | −0.163450 | − | 0.237944i | ||||
\(61\) | − | 8.05915i | − | 1.03187i | −0.856628 | − | 0.515934i | \(-0.827445\pi\) | ||
0.856628 | − | 0.515934i | \(-0.172555\pi\) | |||||||
\(62\) | −5.87295 | − | 5.87295i | −0.745865 | − | 0.745865i | ||||
\(63\) | 1.64584 | + | 1.64584i | 0.207357 | + | 0.207357i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0.629423 | − | 0.432367i | 0.0780703 | − | 0.0536285i | ||||
\(66\) | 6.11317i | 0.752479i | ||||||||
\(67\) | 3.13950 | − | 3.13950i | 0.383551 | − | 0.383551i | −0.488829 | − | 0.872380i | \(-0.662576\pi\) |
0.872380 | + | 0.488829i | \(0.162576\pi\) | |||||||
\(68\) | −0.327163 | − | 0.327163i | −0.0396743 | − | 0.0396743i | ||||
\(69\) | −2.00041 | + | 4.35871i | −0.240821 | + | 0.524727i | ||||
\(70\) | 5.11723 | + | 0.949699i | 0.611626 | + | 0.113511i | ||||
\(71\) | 6.24090 | 0.740658 | 0.370329 | − | 0.928901i | \(-0.379245\pi\) | ||||
0.370329 | + | 0.928901i | \(0.379245\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 6.62866 | − | 6.62866i | 0.775826 | − | 0.775826i | −0.203292 | − | 0.979118i | \(-0.565164\pi\) |
0.979118 | + | 0.203292i | \(0.0651641\pi\) | |||||||
\(74\) | 2.72380 | 0.316636 | ||||||||
\(75\) | 4.56871 | − | 2.03148i | 0.527549 | − | 0.234575i | ||||
\(76\) | 0.759529i | 0.0871240i | ||||||||
\(77\) | −10.0613 | − | 10.0613i | −1.14659 | − | 1.14659i | ||||
\(78\) | −0.241478 | + | 0.241478i | −0.0273419 | + | 0.0273419i | ||||
\(79\) | 3.83429 | 0.431391 | 0.215695 | − | 0.976461i | \(-0.430798\pi\) | ||||
0.215695 | + | 0.976461i | \(0.430798\pi\) | |||||||
\(80\) | 2.19853 | + | 0.408021i | 0.245803 | + | 0.0456181i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.77416 | + | 4.77416i | 0.527217 | + | 0.527217i | ||||
\(83\) | 2.14295 | + | 2.14295i | 0.235219 | + | 0.235219i | 0.814867 | − | 0.579648i | \(-0.196810\pi\) |
−0.579648 | + | 0.814867i | \(0.696810\pi\) | |||||||
\(84\) | −2.32757 | −0.253959 | ||||||||
\(85\) | 0.852765 | − | 0.585786i | 0.0924953 | − | 0.0635375i | ||||
\(86\) | 0.204583i | 0.0220608i | ||||||||
\(87\) | 5.01721 | + | 5.01721i | 0.537901 | + | 0.537901i | ||||
\(88\) | −4.32266 | − | 4.32266i | −0.460797 | − | 0.460797i | ||||
\(89\) | −4.64280 | −0.492136 | −0.246068 | − | 0.969253i | \(-0.579139\pi\) | ||||
−0.246068 | + | 0.969253i | \(0.579139\pi\) | |||||||
\(90\) | −1.84311 | + | 1.26608i | −0.194281 | + | 0.133456i | ||||
\(91\) | − | 0.794868i | − | 0.0833248i | ||||||
\(92\) | −1.66757 | − | 4.49658i | −0.173856 | − | 0.468801i | ||||
\(93\) | −5.87295 | + | 5.87295i | −0.608996 | + | 0.608996i | ||||
\(94\) | 2.07114i | 0.213621i | ||||||||
\(95\) | −1.66985 | − | 0.309904i | −0.171323 | − | 0.0317955i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 11.2007 | − | 11.2007i | 1.13726 | − | 1.13726i | 0.148317 | − | 0.988940i | \(-0.452614\pi\) |
0.988940 | − | 0.148317i | \(-0.0473856\pi\) | |||||||
\(98\) | −1.11893 | + | 1.11893i | −0.113029 | + | 0.113029i | ||||
\(99\) | 6.11317 | 0.614396 | ||||||||
\(100\) | −1.79409 | + | 4.66704i | −0.179409 | + | 0.466704i | ||||
\(101\) | −16.0613 | −1.59816 | −0.799080 | − | 0.601224i | \(-0.794680\pi\) | ||||
−0.799080 | + | 0.601224i | \(0.794680\pi\) | |||||||
\(102\) | −0.327163 | + | 0.327163i | −0.0323939 | + | 0.0323939i | ||||
\(103\) | 1.60298 | + | 1.60298i | 0.157946 | + | 0.157946i | 0.781656 | − | 0.623710i | \(-0.214375\pi\) |
−0.623710 | + | 0.781656i | \(0.714375\pi\) | |||||||
\(104\) | − | 0.341501i | − | 0.0334869i | ||||||
\(105\) | 0.949699 | − | 5.11723i | 0.0926812 | − | 0.499391i | ||||
\(106\) | − | 2.05413i | − | 0.199515i | ||||||
\(107\) | −9.95278 | + | 9.95278i | −0.962171 | + | 0.962171i | −0.999310 | − | 0.0371390i | \(-0.988176\pi\) |
0.0371390 | + | 0.999310i | \(0.488176\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 14.4446 | 1.38354 | 0.691771 | − | 0.722117i | \(-0.256831\pi\) | ||||
0.691771 | + | 0.722117i | \(0.256831\pi\) | |||||||
\(110\) | 11.2672 | − | 7.73975i | 1.07429 | − | 0.737956i | ||||
\(111\) | − | 2.72380i | − | 0.258532i | ||||||
\(112\) | 1.64584 | − | 1.64584i | 0.155518 | − | 0.155518i | ||||
\(113\) | 0.885110 | + | 0.885110i | 0.0832642 | + | 0.0832642i | 0.747512 | − | 0.664248i | \(-0.231248\pi\) |
−0.664248 | + | 0.747512i | \(0.731248\pi\) | |||||||
\(114\) | 0.759529 | 0.0711365 | ||||||||
\(115\) | 10.5662 | − | 1.83150i | 0.985308 | − | 0.170788i | ||||
\(116\) | −7.09541 | −0.658792 | ||||||||
\(117\) | 0.241478 | + | 0.241478i | 0.0223246 | + | 0.0223246i | ||||
\(118\) | −1.19176 | + | 1.19176i | −0.109710 | + | 0.109710i | ||||
\(119\) | − | 1.07692i | − | 0.0987208i | ||||||
\(120\) | 0.408021 | − | 2.19853i | 0.0372471 | − | 0.200697i | ||||
\(121\) | −26.3708 | −2.39735 | ||||||||
\(122\) | 5.69868 | − | 5.69868i | 0.515934 | − | 0.515934i | ||||
\(123\) | 4.77416 | − | 4.77416i | 0.430471 | − | 0.430471i | ||||
\(124\) | − | 8.30560i | − | 0.745865i | ||||||
\(125\) | −9.52858 | − | 5.84861i | −0.852262 | − | 0.523115i | ||||
\(126\) | 2.32757i | 0.207357i | ||||||||
\(127\) | −6.44789 | − | 6.44789i | −0.572158 | − | 0.572158i | 0.360573 | − | 0.932731i | \(-0.382581\pi\) |
−0.932731 | + | 0.360573i | \(0.882581\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0.204583 | 0.0180125 | ||||||||
\(130\) | 0.750799 | + | 0.139340i | 0.0658494 | + | 0.0122209i | ||||
\(131\) | 10.5482 | 0.921604 | 0.460802 | − | 0.887503i | \(-0.347562\pi\) | ||||
0.460802 | + | 0.887503i | \(0.347562\pi\) | |||||||
\(132\) | −4.32266 | + | 4.32266i | −0.376239 | + | 0.376239i | ||||
\(133\) | −1.25007 | + | 1.25007i | −0.108395 | + | 0.108395i | ||||
\(134\) | 4.43992 | 0.383551 | ||||||||
\(135\) | 1.26608 | + | 1.84311i | 0.108967 | + | 0.158629i | ||||
\(136\) | − | 0.462678i | − | 0.0396743i | ||||||
\(137\) | −15.3962 | + | 15.3962i | −1.31538 | + | 1.31538i | −0.397994 | + | 0.917388i | \(0.630294\pi\) |
−0.917388 | + | 0.397994i | \(0.869706\pi\) | |||||||
\(138\) | −4.49658 | + | 1.66757i | −0.382774 | + | 0.141953i | ||||
\(139\) | 5.75151i | 0.487837i | 0.969796 | + | 0.243918i | \(0.0784329\pi\) | ||||
−0.969796 | + | 0.243918i | \(0.921567\pi\) | |||||||
\(140\) | 2.94689 | + | 4.28997i | 0.249058 | + | 0.362569i | ||||
\(141\) | 2.07114 | 0.174421 | ||||||||
\(142\) | 4.41298 | + | 4.41298i | 0.370329 | + | 0.370329i | ||||
\(143\) | −1.47619 | − | 1.47619i | −0.123445 | − | 0.123445i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 2.89508 | − | 15.5994i | 0.240423 | − | 1.29546i | ||||
\(146\) | 9.37434 | 0.775826 | ||||||||
\(147\) | 1.11893 | + | 1.11893i | 0.0922874 | + | 0.0922874i | ||||
\(148\) | 1.92602 | + | 1.92602i | 0.158318 | + | 0.158318i | ||||
\(149\) | 17.6985 | 1.44992 | 0.724960 | − | 0.688791i | \(-0.241858\pi\) | ||||
0.724960 | + | 0.688791i | \(0.241858\pi\) | |||||||
\(150\) | 4.66704 | + | 1.79409i | 0.381062 | + | 0.146487i | ||||
\(151\) | −11.9117 | −0.969359 | −0.484680 | − | 0.874692i | \(-0.661064\pi\) | ||||
−0.484680 | + | 0.874692i | \(0.661064\pi\) | |||||||
\(152\) | −0.537068 | + | 0.537068i | −0.0435620 | + | 0.0435620i | ||||
\(153\) | 0.327163 | + | 0.327163i | 0.0264495 | + | 0.0264495i | ||||
\(154\) | − | 14.2288i | − | 1.14659i | ||||||
\(155\) | 18.2601 | + | 3.38886i | 1.46669 | + | 0.272200i | ||||
\(156\) | −0.341501 | −0.0273419 | ||||||||
\(157\) | 5.35896 | − | 5.35896i | 0.427692 | − | 0.427692i | −0.460150 | − | 0.887841i | \(-0.652204\pi\) |
0.887841 | + | 0.460150i | \(0.152204\pi\) | |||||||
\(158\) | 2.71125 | + | 2.71125i | 0.215695 | + | 0.215695i | ||||
\(159\) | −2.05413 | −0.162903 | ||||||||
\(160\) | 1.26608 | + | 1.84311i | 0.100092 | + | 0.145710i | ||||
\(161\) | 4.65610 | − | 10.1452i | 0.366952 | − | 0.799555i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 1.79995 | − | 1.79995i | 0.140983 | − | 0.140983i | −0.633093 | − | 0.774076i | \(-0.718215\pi\) |
0.774076 | + | 0.633093i | \(0.218215\pi\) | |||||||
\(164\) | 6.75167i | 0.527217i | ||||||||
\(165\) | −7.73975 | − | 11.2672i | −0.602539 | − | 0.877152i | ||||
\(166\) | 3.03059i | 0.235219i | ||||||||
\(167\) | 9.84687 | + | 9.84687i | 0.761974 | + | 0.761974i | 0.976679 | − | 0.214705i | \(-0.0688791\pi\) |
−0.214705 | + | 0.976679i | \(0.568879\pi\) | |||||||
\(168\) | −1.64584 | − | 1.64584i | −0.126980 | − | 0.126980i | ||||
\(169\) | 12.8834i | 0.991029i | ||||||||
\(170\) | 1.01721 | + | 0.188782i | 0.0780164 | + | 0.0144789i | ||||
\(171\) | − | 0.759529i | − | 0.0580827i | ||||||
\(172\) | −0.144662 | + | 0.144662i | −0.0110304 | + | 0.0110304i | ||||
\(173\) | 12.1316 | − | 12.1316i | 0.922351 | − | 0.922351i | −0.0748442 | − | 0.997195i | \(-0.523846\pi\) |
0.997195 | + | 0.0748442i | \(0.0238459\pi\) | |||||||
\(174\) | 7.09541i | 0.537901i | ||||||||
\(175\) | −10.6340 | + | 4.72842i | −0.803855 | + | 0.357435i | ||||
\(176\) | − | 6.11317i | − | 0.460797i | ||||||
\(177\) | 1.19176 | + | 1.19176i | 0.0895778 | + | 0.0895778i | ||||
\(178\) | −3.28296 | − | 3.28296i | −0.246068 | − | 0.246068i | ||||
\(179\) | 1.62037i | 0.121112i | 0.998165 | + | 0.0605561i | \(0.0192874\pi\) | ||||
−0.998165 | + | 0.0605561i | \(0.980713\pi\) | |||||||
\(180\) | −2.19853 | − | 0.408021i | −0.163868 | − | 0.0304121i | ||||
\(181\) | 20.5841i | 1.53000i | 0.644030 | + | 0.765000i | \(0.277261\pi\) | ||||
−0.644030 | + | 0.765000i | \(0.722739\pi\) | |||||||
\(182\) | 0.562057 | − | 0.562057i | 0.0416624 | − | 0.0416624i | ||||
\(183\) | −5.69868 | − | 5.69868i | −0.421258 | − | 0.421258i | ||||
\(184\) | 2.00041 | − | 4.35871i | 0.147472 | − | 0.321328i | ||||
\(185\) | −5.02026 | + | 3.44855i | −0.369097 | + | 0.253542i | ||||
\(186\) | −8.30560 | −0.608996 | ||||||||
\(187\) | −2.00000 | − | 2.00000i | −0.146254 | − | 0.146254i | ||||
\(188\) | −1.46451 | + | 1.46451i | −0.106811 | + | 0.106811i | ||||
\(189\) | 2.32757 | 0.169306 | ||||||||
\(190\) | −0.961624 | − | 1.39989i | −0.0697635 | − | 0.101559i | ||||
\(191\) | 20.8203i | 1.50650i | 0.657734 | + | 0.753251i | \(0.271515\pi\) | ||||
−0.657734 | + | 0.753251i | \(0.728485\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 5.74993 | − | 5.74993i | 0.413889 | − | 0.413889i | −0.469202 | − | 0.883091i | \(-0.655458\pi\) |
0.883091 | + | 0.469202i | \(0.155458\pi\) | |||||||
\(194\) | 15.8402 | 1.13726 | ||||||||
\(195\) | 0.139340 | − | 0.750799i | 0.00997831 | − | 0.0537658i | ||||
\(196\) | −1.58240 | −0.113029 | ||||||||
\(197\) | 1.24668 | + | 1.24668i | 0.0888223 | + | 0.0888223i | 0.750122 | − | 0.661300i | \(-0.229995\pi\) |
−0.661300 | + | 0.750122i | \(0.729995\pi\) | |||||||
\(198\) | 4.32266 | + | 4.32266i | 0.307198 | + | 0.307198i | ||||
\(199\) | 4.17076 | 0.295658 | 0.147829 | − | 0.989013i | \(-0.452772\pi\) | ||||
0.147829 | + | 0.989013i | \(0.452772\pi\) | |||||||
\(200\) | −4.56871 | + | 2.03148i | −0.323056 | + | 0.143647i | ||||
\(201\) | − | 4.43992i | − | 0.313168i | ||||||
\(202\) | −11.3571 | − | 11.3571i | −0.799080 | − | 0.799080i | ||||
\(203\) | −11.6779 | − | 11.6779i | −0.819630 | − | 0.819630i | ||||
\(204\) | −0.462678 | −0.0323939 | ||||||||
\(205\) | −14.8437 | − | 2.75483i | −1.03673 | − | 0.192405i | ||||
\(206\) | 2.26695i | 0.157946i | ||||||||
\(207\) | 1.66757 | + | 4.49658i | 0.115904 | + | 0.312534i | ||||
\(208\) | 0.241478 | − | 0.241478i | 0.0167435 | − | 0.0167435i | ||||
\(209\) | 4.64313i | 0.321172i | ||||||||
\(210\) | 4.28997 | − | 2.94689i | 0.296036 | − | 0.203355i | ||||
\(211\) | 6.87441 | 0.473254 | 0.236627 | − | 0.971601i | \(-0.423958\pi\) | ||||
0.236627 | + | 0.971601i | \(0.423958\pi\) | |||||||
\(212\) | 1.45249 | − | 1.45249i | 0.0997574 | − | 0.0997574i | ||||
\(213\) | 4.41298 | − | 4.41298i | 0.302373 | − | 0.302373i | ||||
\(214\) | −14.0754 | −0.962171 | ||||||||
\(215\) | −0.259018 | − | 0.377069i | −0.0176649 | − | 0.0257159i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 13.6697 | − | 13.6697i | 0.927961 | − | 0.927961i | ||||
\(218\) | 10.2139 | + | 10.2139i | 0.691771 | + | 0.691771i | ||||
\(219\) | − | 9.37434i | − | 0.633459i | ||||||
\(220\) | 13.4400 | + | 2.49430i | 0.906122 | + | 0.168166i | ||||
\(221\) | − | 0.158005i | − | 0.0106286i | ||||||
\(222\) | 1.92602 | − | 1.92602i | 0.129266 | − | 0.129266i | ||||
\(223\) | 11.2802 | − | 11.2802i | 0.755379 | − | 0.755379i | −0.220098 | − | 0.975478i | \(-0.570638\pi\) |
0.975478 | + | 0.220098i | \(0.0706379\pi\) | |||||||
\(224\) | 2.32757 | 0.155518 | ||||||||
\(225\) | 1.79409 | − | 4.66704i | 0.119606 | − | 0.311136i | ||||
\(226\) | 1.25173i | 0.0832642i | ||||||||
\(227\) | 2.22998 | − | 2.22998i | 0.148009 | − | 0.148009i | −0.629219 | − | 0.777228i | \(-0.716625\pi\) |
0.777228 | + | 0.629219i | \(0.216625\pi\) | |||||||
\(228\) | 0.537068 | + | 0.537068i | 0.0355682 | + | 0.0355682i | ||||
\(229\) | 5.86090 | 0.387299 | 0.193650 | − | 0.981071i | \(-0.437968\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437968\pi\) | |||||||
\(230\) | 8.76653 | + | 6.17640i | 0.578048 | + | 0.407260i | ||||
\(231\) | −14.2288 | −0.936190 | ||||||||
\(232\) | −5.01721 | − | 5.01721i | −0.329396 | − | 0.329396i | ||||
\(233\) | 13.1762 | − | 13.1762i | 0.863199 | − | 0.863199i | −0.128510 | − | 0.991708i | \(-0.541019\pi\) |
0.991708 | + | 0.128510i | \(0.0410193\pi\) | |||||||
\(234\) | 0.341501i | 0.0223246i | ||||||||
\(235\) | −2.62222 | − | 3.81733i | −0.171055 | − | 0.249015i | ||||
\(236\) | −1.68540 | −0.109710 | ||||||||
\(237\) | 2.71125 | − | 2.71125i | 0.176115 | − | 0.176115i | ||||
\(238\) | 0.761495 | − | 0.761495i | 0.0493604 | − | 0.0493604i | ||||
\(239\) | 22.8269i | 1.47655i | 0.674499 | + | 0.738276i | \(0.264360\pi\) | ||||
−0.674499 | + | 0.738276i | \(0.735640\pi\) | |||||||
\(240\) | 1.84311 | − | 1.26608i | 0.118972 | − | 0.0817250i | ||||
\(241\) | 18.6517i | 1.20146i | 0.799451 | + | 0.600731i | \(0.205124\pi\) | ||||
−0.799451 | + | 0.600731i | \(0.794876\pi\) | |||||||
\(242\) | −18.6470 | − | 18.6470i | −1.19867 | − | 1.19867i | ||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 8.05915 | 0.515934 | ||||||||
\(245\) | 0.645653 | − | 3.47895i | 0.0412492 | − | 0.222262i | ||||
\(246\) | 6.75167 | 0.430471 | ||||||||
\(247\) | −0.183409 | + | 0.183409i | −0.0116701 | + | 0.0116701i | ||||
\(248\) | 5.87295 | − | 5.87295i | 0.372933 | − | 0.372933i | ||||
\(249\) | 3.03059 | 0.192056 | ||||||||
\(250\) | −2.60213 | − | 10.8733i | −0.164573 | − | 0.687689i | ||||
\(251\) | 24.1095i | 1.52178i | 0.648880 | + | 0.760890i | \(0.275238\pi\) | ||||
−0.648880 | + | 0.760890i | \(0.724762\pi\) | |||||||
\(252\) | −1.64584 | + | 1.64584i | −0.103678 | + | 0.103678i | ||||
\(253\) | −10.1941 | − | 27.4883i | −0.640900 | − | 1.72818i | ||||
\(254\) | − | 9.11869i | − | 0.572158i | ||||||
\(255\) | 0.188782 | − | 1.01721i | 0.0118220 | − | 0.0637001i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.3759 | − | 16.3759i | −1.02150 | − | 1.02150i | −0.999764 | − | 0.0217381i | \(-0.993080\pi\) |
−0.0217381 | − | 0.999764i | \(-0.506920\pi\) | |||||||
\(258\) | 0.144662 | + | 0.144662i | 0.00900627 | + | 0.00900627i | ||||
\(259\) | 6.33986i | 0.393939i | ||||||||
\(260\) | 0.432367 | + | 0.629423i | 0.0268143 | + | 0.0390351i | ||||
\(261\) | 7.09541 | 0.439195 | ||||||||
\(262\) | 7.45873 | + | 7.45873i | 0.460802 | + | 0.460802i | ||||
\(263\) | 16.2523 | + | 16.2523i | 1.00216 | + | 1.00216i | 0.999998 | + | 0.00216013i | \(0.000687592\pi\) |
0.00216013 | + | 0.999998i | \(0.499312\pi\) | |||||||
\(264\) | −6.11317 | −0.376239 | ||||||||
\(265\) | 2.60069 | + | 3.78598i | 0.159759 | + | 0.232571i | ||||
\(266\) | −1.76786 | −0.108395 | ||||||||
\(267\) | −3.28296 | + | 3.28296i | −0.200914 | + | 0.200914i | ||||
\(268\) | 3.13950 | + | 3.13950i | 0.191775 | + | 0.191775i | ||||
\(269\) | 27.3620i | 1.66829i | 0.551546 | + | 0.834144i | \(0.314038\pi\) | ||||
−0.551546 | + | 0.834144i | \(0.685962\pi\) | |||||||
\(270\) | −0.408021 | + | 2.19853i | −0.0248314 | + | 0.133798i | ||||
\(271\) | −30.7037 | −1.86512 | −0.932559 | − | 0.361017i | \(-0.882430\pi\) | ||||
−0.932559 | + | 0.361017i | \(0.882430\pi\) | |||||||
\(272\) | 0.327163 | − | 0.327163i | 0.0198371 | − | 0.0198371i | ||||
\(273\) | −0.562057 | − | 0.562057i | −0.0340172 | − | 0.0340172i | ||||
\(274\) | −21.7734 | −1.31538 | ||||||||
\(275\) | −10.9676 | + | 28.5304i | −0.661370 | + | 1.72045i | ||||
\(276\) | −4.35871 | − | 2.00041i | −0.262364 | − | 0.120411i | ||||
\(277\) | 2.21937 | + | 2.21937i | 0.133349 | + | 0.133349i | 0.770631 | − | 0.637282i | \(-0.219941\pi\) |
−0.637282 | + | 0.770631i | \(0.719941\pi\) | |||||||
\(278\) | −4.06693 | + | 4.06693i | −0.243918 | + | 0.243918i | ||||
\(279\) | 8.30560i | 0.497243i | ||||||||
\(280\) | −0.949699 | + | 5.11723i | −0.0567554 | + | 0.305813i | ||||
\(281\) | − | 26.0473i | − | 1.55385i | −0.629592 | − | 0.776926i | \(-0.716778\pi\) | ||
0.629592 | − | 0.776926i | \(-0.283222\pi\) | |||||||
\(282\) | 1.46451 | + | 1.46451i | 0.0872106 | + | 0.0872106i | ||||
\(283\) | 5.48295 | + | 5.48295i | 0.325928 | + | 0.325928i | 0.851036 | − | 0.525108i | \(-0.175975\pi\) |
−0.525108 | + | 0.851036i | \(0.675975\pi\) | |||||||
\(284\) | 6.24090i | 0.370329i | ||||||||
\(285\) | −1.39989 | + | 0.961624i | −0.0829226 | + | 0.0569617i | ||||
\(286\) | − | 2.08765i | − | 0.123445i | ||||||
\(287\) | −11.1122 | + | 11.1122i | −0.655932 | + | 0.655932i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 16.7859i | 0.987408i | ||||||||
\(290\) | 13.0776 | − | 8.98334i | 0.767943 | − | 0.527520i | ||||
\(291\) | − | 15.8402i | − | 0.928566i | ||||||
\(292\) | 6.62866 | + | 6.62866i | 0.387913 | + | 0.387913i | ||||
\(293\) | −18.5543 | − | 18.5543i | −1.08395 | − | 1.08395i | −0.996137 | − | 0.0878182i | \(-0.972011\pi\) |
−0.0878182 | − | 0.996137i | \(-0.527989\pi\) | |||||||
\(294\) | 1.58240i | 0.0922874i | ||||||||
\(295\) | 0.687677 | − | 3.70539i | 0.0400381 | − | 0.215736i | ||||
\(296\) | 2.72380i | 0.158318i | ||||||||
\(297\) | 4.32266 | − | 4.32266i | 0.250826 | − | 0.250826i | ||||
\(298\) | 12.5148 | + | 12.5148i | 0.724960 | + | 0.724960i | ||||
\(299\) | 0.683142 | − | 1.48850i | 0.0395071 | − | 0.0860824i | ||||
\(300\) | 2.03148 | + | 4.56871i | 0.117288 | + | 0.263774i | ||||
\(301\) | −0.476182 | −0.0274467 | ||||||||
\(302\) | −8.42283 | − | 8.42283i | −0.484680 | − | 0.484680i | ||||
\(303\) | −11.3571 | + | 11.3571i | −0.652446 | + | 0.652446i | ||||
\(304\) | −0.759529 | −0.0435620 | ||||||||
\(305\) | −3.28830 | + | 17.7183i | −0.188288 | + | 1.01454i | ||||
\(306\) | 0.462678i | 0.0264495i | ||||||||
\(307\) | 20.3743 | + | 20.3743i | 1.16282 | + | 1.16282i | 0.983855 | + | 0.178966i | \(0.0572752\pi\) |
0.178966 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(308\) | 10.0613 | − | 10.0613i | 0.573297 | − | 0.573297i | ||||
\(309\) | 2.26695 | 0.128962 | ||||||||
\(310\) | 10.5155 | + | 15.3081i | 0.597243 | + | 0.869443i | ||||
\(311\) | 16.5017 | 0.935724 | 0.467862 | − | 0.883801i | \(-0.345024\pi\) | ||||
0.467862 | + | 0.883801i | \(0.345024\pi\) | |||||||
\(312\) | −0.241478 | − | 0.241478i | −0.0136710 | − | 0.0136710i | ||||
\(313\) | 4.53498 | + | 4.53498i | 0.256332 | + | 0.256332i | 0.823561 | − | 0.567228i | \(-0.191984\pi\) |
−0.567228 | + | 0.823561i | \(0.691984\pi\) | |||||||
\(314\) | 7.57872 | 0.427692 | ||||||||
\(315\) | −2.94689 | − | 4.28997i | −0.166039 | − | 0.241712i | ||||
\(316\) | 3.83429i | 0.215695i | ||||||||
\(317\) | −12.5140 | − | 12.5140i | −0.702856 | − | 0.702856i | 0.262167 | − | 0.965023i | \(-0.415563\pi\) |
−0.965023 | + | 0.262167i | \(0.915563\pi\) | |||||||
\(318\) | −1.45249 | − | 1.45249i | −0.0814516 | − | 0.0814516i | ||||
\(319\) | −43.3754 | −2.42856 | ||||||||
\(320\) | −0.408021 | + | 2.19853i | −0.0228091 | + | 0.122901i | ||||
\(321\) | 14.0754i | 0.785609i | ||||||||
\(322\) | 10.4661 | − | 3.88139i | 0.583254 | − | 0.216301i | ||||
\(323\) | −0.248490 | + | 0.248490i | −0.0138263 | + | 0.0138263i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −1.56022 | + | 0.693752i | −0.0865453 | + | 0.0384824i | ||||
\(326\) | 2.54552 | 0.140983 | ||||||||
\(327\) | 10.2139 | − | 10.2139i | 0.564828 | − | 0.564828i | ||||
\(328\) | −4.77416 | + | 4.77416i | −0.263609 | + | 0.263609i | ||||
\(329\) | −4.82072 | −0.265775 | ||||||||
\(330\) | 2.49430 | − | 13.4400i | 0.137307 | − | 0.739846i | ||||
\(331\) | 24.3710 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266390\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266390\pi\) | |||||||
\(332\) | −2.14295 | + | 2.14295i | −0.117610 | + | 0.117610i | ||||
\(333\) | −1.92602 | − | 1.92602i | −0.105545 | − | 0.105545i | ||||
\(334\) | 13.9256i | 0.761974i | ||||||||
\(335\) | −8.18325 | + | 5.62129i | −0.447099 | + | 0.307124i | ||||
\(336\) | − | 2.32757i | − | 0.126980i | ||||||
\(337\) | −15.7870 | + | 15.7870i | −0.859971 | + | 0.859971i | −0.991334 | − | 0.131363i | \(-0.958065\pi\) |
0.131363 | + | 0.991334i | \(0.458065\pi\) | |||||||
\(338\) | −9.10992 | + | 9.10992i | −0.495515 | + | 0.495515i | ||||
\(339\) | 1.25173 | 0.0679849 | ||||||||
\(340\) | 0.585786 | + | 0.852765i | 0.0317687 | + | 0.0462477i | ||||
\(341\) | − | 50.7735i | − | 2.74954i | ||||||
\(342\) | 0.537068 | − | 0.537068i | 0.0290413 | − | 0.0290413i | ||||
\(343\) | −14.1253 | − | 14.1253i | −0.762694 | − | 0.762694i | ||||
\(344\) | −0.204583 | −0.0110304 | ||||||||
\(345\) | 6.17640 | − | 8.76653i | 0.332526 | − | 0.471974i | ||||
\(346\) | 17.1567 | 0.922351 | ||||||||
\(347\) | −11.4749 | − | 11.4749i | −0.616007 | − | 0.616007i | 0.328498 | − | 0.944505i | \(-0.393458\pi\) |
−0.944505 | + | 0.328498i | \(0.893458\pi\) | |||||||
\(348\) | −5.01721 | + | 5.01721i | −0.268951 | + | 0.268951i | ||||
\(349\) | − | 5.86005i | − | 0.313682i | −0.987624 | − | 0.156841i | \(-0.949869\pi\) | ||
0.987624 | − | 0.156841i | \(-0.0501309\pi\) | |||||||
\(350\) | −10.8629 | − | 4.17588i | −0.580645 | − | 0.223210i | ||||
\(351\) | 0.341501 | 0.0182280 | ||||||||
\(352\) | 4.32266 | − | 4.32266i | 0.230399 | − | 0.230399i | ||||
\(353\) | 3.94327 | − | 3.94327i | 0.209879 | − | 0.209879i | −0.594337 | − | 0.804216i | \(-0.702586\pi\) |
0.804216 | + | 0.594337i | \(0.202586\pi\) | |||||||
\(354\) | 1.68540i | 0.0895778i | ||||||||
\(355\) | −13.7208 | − | 2.54642i | −0.728224 | − | 0.135150i | ||||
\(356\) | − | 4.64280i | − | 0.246068i | ||||||
\(357\) | −0.761495 | − | 0.761495i | −0.0403026 | − | 0.0403026i | ||||
\(358\) | −1.14577 | + | 1.14577i | −0.0605561 | + | 0.0605561i | ||||
\(359\) | −32.6374 | −1.72254 | −0.861269 | − | 0.508150i | \(-0.830330\pi\) | ||||
−0.861269 | + | 0.508150i | \(0.830330\pi\) | |||||||
\(360\) | −1.26608 | − | 1.84311i | −0.0667282 | − | 0.0971403i | ||||
\(361\) | −18.4231 | −0.969638 | ||||||||
\(362\) | −14.5551 | + | 14.5551i | −0.765000 | + | 0.765000i | ||||
\(363\) | −18.6470 | + | 18.6470i | −0.978713 | + | 0.978713i | ||||
\(364\) | 0.794868 | 0.0416624 | ||||||||
\(365\) | −17.2779 | + | 11.8687i | −0.904368 | + | 0.621234i | ||||
\(366\) | − | 8.05915i | − | 0.421258i | ||||||
\(367\) | −22.9985 | + | 22.9985i | −1.20051 | + | 1.20051i | −0.226499 | + | 0.974011i | \(0.572728\pi\) |
−0.974011 | + | 0.226499i | \(0.927272\pi\) | |||||||
\(368\) | 4.49658 | − | 1.66757i | 0.234400 | − | 0.0869281i | ||||
\(369\) | − | 6.75167i | − | 0.351478i | ||||||
\(370\) | −5.98836 | − | 1.11137i | −0.311320 | − | 0.0577774i | ||||
\(371\) | 4.78114 | 0.248224 | ||||||||
\(372\) | −5.87295 | − | 5.87295i | −0.304498 | − | 0.304498i | ||||
\(373\) | −15.4627 | − | 15.4627i | −0.800629 | − | 0.800629i | 0.182564 | − | 0.983194i | \(-0.441560\pi\) |
−0.983194 | + | 0.182564i | \(0.941560\pi\) | |||||||
\(374\) | − | 2.82843i | − | 0.146254i | ||||||
\(375\) | −10.8733 | + | 2.60213i | −0.561495 | + | 0.134374i | ||||
\(376\) | −2.07114 | −0.106811 | ||||||||
\(377\) | −1.71338 | − | 1.71338i | −0.0882436 | − | 0.0882436i | ||||
\(378\) | 1.64584 | + | 1.64584i | 0.0846530 | + | 0.0846530i | ||||
\(379\) | 11.0986 | 0.570095 | 0.285048 | − | 0.958513i | \(-0.407991\pi\) | ||||
0.285048 | + | 0.958513i | \(0.407991\pi\) | |||||||
\(380\) | 0.309904 | − | 1.66985i | 0.0158977 | − | 0.0856613i | ||||
\(381\) | −9.11869 | −0.467165 | ||||||||
\(382\) | −14.7221 | + | 14.7221i | −0.753251 | + | 0.753251i | ||||
\(383\) | −18.4090 | − | 18.4090i | −0.940653 | − | 0.940653i | 0.0576815 | − | 0.998335i | \(-0.481629\pi\) |
−0.998335 | + | 0.0576815i | \(0.981629\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 18.0148 | + | 26.2253i | 0.918121 | + | 1.33656i | ||||
\(386\) | 8.13163 | 0.413889 | ||||||||
\(387\) | 0.144662 | − | 0.144662i | 0.00735359 | − | 0.00735359i | ||||
\(388\) | 11.2007 | + | 11.2007i | 0.568628 | + | 0.568628i | ||||
\(389\) | 21.2944 | 1.07967 | 0.539833 | − | 0.841772i | \(-0.318487\pi\) | ||||
0.539833 | + | 0.841772i | \(0.318487\pi\) | |||||||
\(390\) | 0.629423 | − | 0.432367i | 0.0318721 | − | 0.0218937i | ||||
\(391\) | 0.925546 | − | 2.01668i | 0.0468069 | − | 0.101988i | ||||
\(392\) | −1.11893 | − | 1.11893i | −0.0565143 | − | 0.0565143i | ||||
\(393\) | 7.45873 | − | 7.45873i | 0.376243 | − | 0.376243i | ||||
\(394\) | 1.76307i | 0.0888223i | ||||||||
\(395\) | −8.42978 | − | 1.56447i | −0.424148 | − | 0.0787170i | ||||
\(396\) | 6.11317i | 0.307198i | ||||||||
\(397\) | −17.4767 | − | 17.4767i | −0.877130 | − | 0.877130i | 0.116107 | − | 0.993237i | \(-0.462959\pi\) |
−0.993237 | + | 0.116107i | \(0.962959\pi\) | |||||||
\(398\) | 2.94918 | + | 2.94918i | 0.147829 | + | 0.147829i | ||||
\(399\) | 1.76786i | 0.0885037i | ||||||||
\(400\) | −4.66704 | − | 1.79409i | −0.233352 | − | 0.0897045i | ||||
\(401\) | − | 9.34370i | − | 0.466602i | −0.972405 | − | 0.233301i | \(-0.925047\pi\) | ||
0.972405 | − | 0.233301i | \(-0.0749528\pi\) | |||||||
\(402\) | 3.13950 | − | 3.13950i | 0.156584 | − | 0.156584i | ||||
\(403\) | 2.00562 | − | 2.00562i | 0.0999069 | − | 0.0999069i | ||||
\(404\) | − | 16.0613i | − | 0.799080i | ||||||
\(405\) | 2.19853 | + | 0.408021i | 0.109246 | + | 0.0202747i | ||||
\(406\) | − | 16.5151i | − | 0.819630i | ||||||
\(407\) | 11.7741 | + | 11.7741i | 0.583620 | + | 0.583620i | ||||
\(408\) | −0.327163 | − | 0.327163i | −0.0161970 | − | 0.0161970i | ||||
\(409\) | − | 15.8867i | − | 0.785545i | −0.919636 | − | 0.392773i | \(-0.871516\pi\) | ||
0.919636 | − | 0.392773i | \(-0.128484\pi\) | |||||||
\(410\) | −8.54815 | − | 12.4441i | −0.422163 | − | 0.614568i | ||||
\(411\) | 21.7734i | 1.07401i | ||||||||
\(412\) | −1.60298 | + | 1.60298i | −0.0789730 | + | 0.0789730i | ||||
\(413\) | −2.77390 | − | 2.77390i | −0.136495 | − | 0.136495i | ||||
\(414\) | −2.00041 | + | 4.35871i | −0.0983148 | + | 0.214219i | ||||
\(415\) | −3.83697 | − | 5.58570i | −0.188349 | − | 0.274191i | ||||
\(416\) | 0.341501 | 0.0167435 | ||||||||
\(417\) | 4.06693 | + | 4.06693i | 0.199159 | + | 0.199159i | ||||
\(418\) | −3.28319 | + | 3.28319i | −0.160586 | + | 0.160586i | ||||
\(419\) | 5.11030 | 0.249654 | 0.124827 | − | 0.992178i | \(-0.460162\pi\) | ||||
0.124827 | + | 0.992178i | \(0.460162\pi\) | |||||||
\(420\) | 5.11723 | + | 0.949699i | 0.249695 | + | 0.0463406i | ||||
\(421\) | − | 5.71253i | − | 0.278412i | −0.990263 | − | 0.139206i | \(-0.955545\pi\) | ||
0.990263 | − | 0.139206i | \(-0.0444550\pi\) | |||||||
\(422\) | 4.86094 | + | 4.86094i | 0.236627 | + | 0.236627i | ||||
\(423\) | 1.46451 | − | 1.46451i | 0.0712071 | − | 0.0712071i | ||||
\(424\) | 2.05413 | 0.0997574 | ||||||||
\(425\) | −2.11384 | + | 0.939921i | −0.102536 | + | 0.0455929i | ||||
\(426\) | 6.24090 | 0.302373 | ||||||||
\(427\) | 13.2641 | + | 13.2641i | 0.641895 | + | 0.641895i | ||||
\(428\) | −9.95278 | − | 9.95278i | −0.481086 | − | 0.481086i | ||||
\(429\) | −2.08765 | −0.100793 | ||||||||
\(430\) | 0.0834743 | − | 0.449782i | 0.00402549 | − | 0.0216904i | ||||
\(431\) | 3.28744i | 0.158351i | 0.996861 | + | 0.0791753i | \(0.0252287\pi\) | ||||
−0.996861 | + | 0.0791753i | \(0.974771\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 11.6374 | + | 11.6374i | 0.559256 | + | 0.559256i | 0.929096 | − | 0.369840i | \(-0.120587\pi\) |
−0.369840 | + | 0.929096i | \(0.620587\pi\) | |||||||
\(434\) | 19.3319 | 0.927961 | ||||||||
\(435\) | −8.98334 | − | 13.0776i | −0.430718 | − | 0.627023i | ||||
\(436\) | 14.4446i | 0.691771i | ||||||||
\(437\) | −3.41528 | + | 1.26657i | −0.163375 | + | 0.0605882i | ||||
\(438\) | 6.62866 | − | 6.62866i | 0.316730 | − | 0.316730i | ||||
\(439\) | 12.3751i | 0.590631i | 0.955400 | + | 0.295316i | \(0.0954248\pi\) | ||||
−0.955400 | + | 0.295316i | \(0.904575\pi\) | |||||||
\(440\) | 7.73975 | + | 11.2672i | 0.368978 | + | 0.537144i | ||||
\(441\) | 1.58240 | 0.0753524 | ||||||||
\(442\) | 0.111726 | − | 0.111726i | 0.00531428 | − | 0.00531428i | ||||
\(443\) | 24.4511 | − | 24.4511i | 1.16171 | − | 1.16171i | 0.177606 | − | 0.984102i | \(-0.443165\pi\) |
0.984102 | − | 0.177606i | \(-0.0568354\pi\) | |||||||
\(444\) | 2.72380 | 0.129266 | ||||||||
\(445\) | 10.2073 | + | 1.89436i | 0.483873 | + | 0.0898013i | ||||
\(446\) | 15.9526 | 0.755379 | ||||||||
\(447\) | 12.5148 | − | 12.5148i | 0.591927 | − | 0.591927i | ||||
\(448\) | 1.64584 | + | 1.64584i | 0.0777588 | + | 0.0777588i | ||||
\(449\) | 41.0277i | 1.93622i | 0.250534 | + | 0.968108i | \(0.419394\pi\) | ||||
−0.250534 | + | 0.968108i | \(0.580606\pi\) | |||||||
\(450\) | 4.56871 | − | 2.03148i | 0.215371 | − | 0.0957649i | ||||
\(451\) | 41.2741i | 1.94352i | ||||||||
\(452\) | −0.885110 | + | 0.885110i | −0.0416321 | + | 0.0416321i | ||||
\(453\) | −8.42283 | + | 8.42283i | −0.395739 | + | 0.395739i | ||||
\(454\) | 3.15367 | 0.148009 | ||||||||
\(455\) | −0.324323 | + | 1.74754i | −0.0152045 | + | 0.0819259i | ||||
\(456\) | 0.759529i | 0.0355682i | ||||||||
\(457\) | −18.5456 | + | 18.5456i | −0.867526 | + | 0.867526i | −0.992198 | − | 0.124672i | \(-0.960212\pi\) |
0.124672 | + | 0.992198i | \(0.460212\pi\) | |||||||
\(458\) | 4.14428 | + | 4.14428i | 0.193650 | + | 0.193650i | ||||
\(459\) | 0.462678 | 0.0215960 | ||||||||
\(460\) | 1.83150 | + | 10.5662i | 0.0853940 | + | 0.492654i | ||||
\(461\) | 21.4962 | 1.00118 | 0.500588 | − | 0.865686i | \(-0.333117\pi\) | ||||
0.500588 | + | 0.865686i | \(0.333117\pi\) | |||||||
\(462\) | −10.0613 | − | 10.0613i | −0.468095 | − | 0.468095i | ||||
\(463\) | −14.7714 | + | 14.7714i | −0.686485 | + | 0.686485i | −0.961453 | − | 0.274968i | \(-0.911333\pi\) |
0.274968 | + | 0.961453i | \(0.411333\pi\) | |||||||
\(464\) | − | 7.09541i | − | 0.329396i | ||||||
\(465\) | 15.3081 | − | 10.5155i | 0.709897 | − | 0.487647i | ||||
\(466\) | 18.6339 | 0.863199 | ||||||||
\(467\) | 23.9052 | − | 23.9052i | 1.10620 | − | 1.10620i | 0.112554 | − | 0.993646i | \(-0.464097\pi\) |
0.993646 | − | 0.112554i | \(-0.0359030\pi\) | |||||||
\(468\) | −0.241478 | + | 0.241478i | −0.0111623 | + | 0.0111623i | ||||
\(469\) | 10.3342i | 0.477191i | ||||||||
\(470\) | 0.845067 | − | 4.55345i | 0.0389800 | − | 0.210035i | ||||
\(471\) | − | 7.57872i | − | 0.349209i | ||||||
\(472\) | −1.19176 | − | 1.19176i | −0.0548550 | − | 0.0548550i | ||||
\(473\) | −0.884344 | + | 0.884344i | −0.0406622 | + | 0.0406622i | ||||
\(474\) | 3.83429 | 0.176115 | ||||||||
\(475\) | 3.54475 | + | 1.36266i | 0.162644 | + | 0.0625233i | ||||
\(476\) | 1.07692 | 0.0493604 | ||||||||
\(477\) | −1.45249 | + | 1.45249i | −0.0665049 | + | 0.0665049i | ||||
\(478\) | −16.1411 | + | 16.1411i | −0.738276 | + | 0.738276i | ||||
\(479\) | 11.0131 | 0.503199 | 0.251600 | − | 0.967831i | \(-0.419043\pi\) | ||||
0.251600 | + | 0.967831i | \(0.419043\pi\) | |||||||
\(480\) | 2.19853 | + | 0.408021i | 0.100349 | + | 0.0186235i | ||||
\(481\) | 0.930181i | 0.0424126i | ||||||||
\(482\) | −13.1887 | + | 13.1887i | −0.600731 | + | 0.600731i | ||||
\(483\) | −3.88139 | − | 10.4661i | −0.176609 | − | 0.476225i | ||||
\(484\) | − | 26.3708i | − | 1.19867i | ||||||
\(485\) | −29.1951 | + | 20.0549i | −1.32568 | + | 0.910645i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 25.8202 | + | 25.8202i | 1.17002 | + | 1.17002i | 0.982203 | + | 0.187820i | \(0.0601422\pi\) |
0.187820 | + | 0.982203i | \(0.439858\pi\) | |||||||
\(488\) | 5.69868 | + | 5.69868i | 0.257967 | + | 0.257967i | ||||
\(489\) | − | 2.54552i | − | 0.115112i | ||||||
\(490\) | 2.91653 | − | 2.00344i | 0.131756 | − | 0.0905063i | ||||
\(491\) | −21.1318 | −0.953665 | −0.476832 | − | 0.878994i | \(-0.658215\pi\) | ||||
−0.476832 | + | 0.878994i | \(0.658215\pi\) | |||||||
\(492\) | 4.77416 | + | 4.77416i | 0.215236 | + | 0.215236i | ||||
\(493\) | −2.32135 | − | 2.32135i | −0.104548 | − | 0.104548i | ||||
\(494\) | −0.259380 | −0.0116701 | ||||||||
\(495\) | −13.4400 | − | 2.49430i | −0.604081 | − | 0.112111i | ||||
\(496\) | 8.30560 | 0.372933 | ||||||||
\(497\) | −10.2715 | + | 10.2715i | −0.460742 | + | 0.460742i | ||||
\(498\) | 2.14295 | + | 2.14295i | 0.0960279 | + | 0.0960279i | ||||
\(499\) | − | 25.7570i | − | 1.15304i | −0.817083 | − | 0.576520i | \(-0.804410\pi\) | ||
0.817083 | − | 0.576520i | \(-0.195590\pi\) | |||||||
\(500\) | 5.84861 | − | 9.52858i | 0.261558 | − | 0.426131i | ||||
\(501\) | 13.9256 | 0.622149 | ||||||||
\(502\) | −17.0480 | + | 17.0480i | −0.760890 | + | 0.760890i | ||||
\(503\) | −2.42325 | − | 2.42325i | −0.108048 | − | 0.108048i | 0.651016 | − | 0.759064i | \(-0.274343\pi\) |
−0.759064 | + | 0.651016i | \(0.774343\pi\) | |||||||
\(504\) | −2.32757 | −0.103678 | ||||||||
\(505\) | 35.3112 | + | 6.55336i | 1.57133 | + | 0.291621i | ||||
\(506\) | 12.2288 | − | 26.6455i | 0.543639 | − | 1.18454i | ||||
\(507\) | 9.10992 | + | 9.10992i | 0.404586 | + | 0.404586i | ||||
\(508\) | 6.44789 | − | 6.44789i | 0.286079 | − | 0.286079i | ||||
\(509\) | − | 37.8408i | − | 1.67726i | −0.544698 | − | 0.838632i | \(-0.683356\pi\) | ||
0.544698 | − | 0.838632i | \(-0.316644\pi\) | |||||||
\(510\) | 0.852765 | − | 0.585786i | 0.0377611 | − | 0.0259391i | ||||
\(511\) | 21.8195i | 0.965237i | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −0.537068 | − | 0.537068i | −0.0237122 | − | 0.0237122i | ||||
\(514\) | − | 23.1590i | − | 1.02150i | ||||||
\(515\) | −2.87014 | − | 4.17824i | −0.126473 | − | 0.184115i | ||||
\(516\) | 0.204583i | 0.00900627i | ||||||||
\(517\) | −8.95282 | + | 8.95282i | −0.393745 | + | 0.393745i | ||||
\(518\) | −4.48296 | + | 4.48296i | −0.196970 | + | 0.196970i | ||||
\(519\) | − | 17.1567i | − | 0.753096i | ||||||
\(520\) | −0.139340 | + | 0.750799i | −0.00611044 | + | 0.0329247i | ||||
\(521\) | − | 8.64661i | − | 0.378815i | −0.981899 | − | 0.189407i | \(-0.939343\pi\) | ||
0.981899 | − | 0.189407i | \(-0.0606567\pi\) | |||||||
\(522\) | 5.01721 | + | 5.01721i | 0.219597 | + | 0.219597i | ||||
\(523\) | 22.1099 | + | 22.1099i | 0.966800 | + | 0.966800i | 0.999466 | − | 0.0326665i | \(-0.0103999\pi\) |
−0.0326665 | + | 0.999466i | \(0.510400\pi\) | |||||||
\(524\) | 10.5482i | 0.460802i | ||||||||
\(525\) | −4.17588 | + | 10.8629i | −0.182250 | + | 0.474095i | ||||
\(526\) | 22.9842i | 1.00216i | ||||||||
\(527\) | 2.71728 | − | 2.71728i | 0.118367 | − | 0.118367i | ||||
\(528\) | −4.32266 | − | 4.32266i | −0.188120 | − | 0.188120i | ||||
\(529\) | 17.4384 | − | 14.9967i | 0.758192 | − | 0.652031i | ||||
\(530\) | −0.838129 | + | 4.51606i | −0.0364060 | + | 0.196165i | ||||
\(531\) | 1.68540 | 0.0731400 | ||||||||
\(532\) | −1.25007 | − | 1.25007i | −0.0541973 | − | 0.0541973i | ||||
\(533\) | −1.63038 | + | 1.63038i | −0.0706195 | + | 0.0706195i | ||||
\(534\) | −4.64280 | −0.200914 | ||||||||
\(535\) | 25.9424 | − | 17.8205i | 1.12159 | − | 0.770447i | ||||
\(536\) | 4.43992i | 0.191775i | ||||||||
\(537\) | 1.14577 | + | 1.14577i | 0.0494438 | + | 0.0494438i | ||||
\(538\) | −19.3478 | + | 19.3478i | −0.834144 | + | 0.834144i | ||||
\(539\) | −9.67348 | −0.416666 | ||||||||
\(540\) | −1.84311 | + | 1.26608i | −0.0793147 | + | 0.0544833i | ||||
\(541\) | 31.2535 | 1.34369 | 0.671846 | − | 0.740691i | \(-0.265502\pi\) | ||||
0.671846 | + | 0.740691i | \(0.265502\pi\) | |||||||
\(542\) | −21.7108 | − | 21.7108i | −0.932559 | − | 0.932559i | ||||
\(543\) | 14.5551 | + | 14.5551i | 0.624620 | + | 0.624620i | ||||
\(544\) | 0.462678 | 0.0198371 | ||||||||
\(545\) | −31.7568 | − | 5.89370i | −1.36031 | − | 0.252458i | ||||
\(546\) | − | 0.794868i | − | 0.0340172i | ||||||
\(547\) | 12.6714 | + | 12.6714i | 0.541792 | + | 0.541792i | 0.924054 | − | 0.382262i | \(-0.124855\pi\) |
−0.382262 | + | 0.924054i | \(0.624855\pi\) | |||||||
\(548\) | −15.3962 | − | 15.3962i | −0.657691 | − | 0.657691i | ||||
\(549\) | −8.05915 | −0.343956 | ||||||||
\(550\) | −27.9293 | + | 12.4188i | −1.19091 | + | 0.529539i | ||||
\(551\) | 5.38917i | 0.229586i | ||||||||
\(552\) | −1.66757 | − | 4.49658i | −0.0709765 | − | 0.191387i | ||||
\(553\) | −6.31063 | + | 6.31063i | −0.268355 | + | 0.268355i | ||||
\(554\) | 3.13866i | 0.133349i | ||||||||
\(555\) | −1.11137 | + | 5.98836i | −0.0471750 | + | 0.254192i | ||||
\(556\) | −5.75151 | −0.243918 | ||||||||
\(557\) | 2.52234 | − | 2.52234i | 0.106875 | − | 0.106875i | −0.651647 | − | 0.758522i | \(-0.725922\pi\) |
0.758522 | + | 0.651647i | \(0.225922\pi\) | |||||||
\(558\) | −5.87295 | + | 5.87295i | −0.248622 | + | 0.248622i | ||||
\(559\) | −0.0698653 | −0.00295499 | ||||||||
\(560\) | −4.28997 | + | 2.94689i | −0.181284 | + | 0.124529i | ||||
\(561\) | −2.82843 | −0.119416 | ||||||||
\(562\) | 18.4182 | − | 18.4182i | 0.776926 | − | 0.776926i | ||||
\(563\) | 26.8499 | + | 26.8499i | 1.13159 | + | 1.13159i | 0.989913 | + | 0.141675i | \(0.0452489\pi\) |
0.141675 | + | 0.989913i | \(0.454751\pi\) | |||||||
\(564\) | 2.07114i | 0.0872106i | ||||||||
\(565\) | −1.58479 | − | 2.30708i | −0.0666728 | − | 0.0970597i | ||||
\(566\) | 7.75406i | 0.325928i | ||||||||
\(567\) | 1.64584 | − | 1.64584i | 0.0691189 | − | 0.0691189i | ||||
\(568\) | −4.41298 | + | 4.41298i | −0.185165 | + | 0.185165i | ||||
\(569\) | −17.2543 | −0.723337 | −0.361668 | − | 0.932307i | \(-0.617793\pi\) | ||||
−0.361668 | + | 0.932307i | \(0.617793\pi\) | |||||||
\(570\) | −1.66985 | − | 0.309904i | −0.0699421 | − | 0.0129805i | ||||
\(571\) | − | 43.9751i | − | 1.84030i | −0.391565 | − | 0.920151i | \(-0.628066\pi\) | ||
0.391565 | − | 0.920151i | \(-0.371934\pi\) | |||||||
\(572\) | 1.47619 | − | 1.47619i | 0.0617227 | − | 0.0617227i | ||||
\(573\) | 14.7221 | + | 14.7221i | 0.615027 | + | 0.615027i | ||||
\(574\) | −15.7150 | −0.655932 | ||||||||
\(575\) | −23.9775 | − | 0.284659i | −0.999930 | − | 0.0118711i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 3.00797 | + | 3.00797i | 0.125223 | + | 0.125223i | 0.766941 | − | 0.641718i | \(-0.221778\pi\) |
−0.641718 | + | 0.766941i | \(0.721778\pi\) | |||||||
\(578\) | −11.8694 | + | 11.8694i | −0.493704 | + | 0.493704i | ||||
\(579\) | − | 8.13163i | − | 0.337939i | ||||||
\(580\) | 15.5994 | + | 2.89508i | 0.647731 | + | 0.120211i | ||||
\(581\) | −7.05392 | −0.292646 | ||||||||
\(582\) | 11.2007 | − | 11.2007i | 0.464283 | − | 0.464283i | ||||
\(583\) | 8.87931 | − | 8.87931i | 0.367744 | − | 0.367744i | ||||
\(584\) | 9.37434i | 0.387913i | ||||||||
\(585\) | −0.432367 | − | 0.629423i | −0.0178762 | − | 0.0260234i | ||||
\(586\) | − | 26.2398i | − | 1.08395i | ||||||
\(587\) | −22.9088 | − | 22.9088i | −0.945548 | − | 0.945548i | 0.0530437 | − | 0.998592i | \(-0.483108\pi\) |
−0.998592 | + | 0.0530437i | \(0.983108\pi\) | |||||||
\(588\) | −1.11893 | + | 1.11893i | −0.0461437 | + | 0.0461437i | ||||
\(589\) | −6.30835 | −0.259931 | ||||||||
\(590\) | 3.10637 | − | 2.13384i | 0.127887 | − | 0.0878490i | ||||
\(591\) | 1.76307 | 0.0725231 | ||||||||
\(592\) | −1.92602 | + | 1.92602i | −0.0791590 | + | 0.0791590i | ||||
\(593\) | −11.7866 | + | 11.7866i | −0.484017 | + | 0.484017i | −0.906412 | − | 0.422395i | \(-0.861190\pi\) |
0.422395 | + | 0.906412i | \(0.361190\pi\) | |||||||
\(594\) | 6.11317 | 0.250826 | ||||||||
\(595\) | −0.439405 | + | 2.36763i | −0.0180138 | + | 0.0970634i | ||||
\(596\) | 17.6985i | 0.724960i | ||||||||
\(597\) | 2.94918 | − | 2.94918i | 0.120702 | − | 0.120702i | ||||
\(598\) | 1.53558 | − | 0.569476i | 0.0627947 | − | 0.0232876i | ||||
\(599\) | − | 46.9341i | − | 1.91767i | −0.283957 | − | 0.958837i | \(-0.591647\pi\) | ||
0.283957 | − | 0.958837i | \(-0.408353\pi\) | |||||||
\(600\) | −1.79409 | + | 4.66704i | −0.0732434 | + | 0.190531i | ||||
\(601\) | −2.50913 | −0.102350 | −0.0511748 | − | 0.998690i | \(-0.516297\pi\) | ||||
−0.0511748 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(602\) | −0.336712 | − | 0.336712i | −0.0137234 | − | 0.0137234i | ||||
\(603\) | −3.13950 | − | 3.13950i | −0.127850 | − | 0.127850i | ||||
\(604\) | − | 11.9117i | − | 0.484680i | ||||||
\(605\) | 57.9769 | + | 10.7599i | 2.35710 | + | 0.437450i | ||||
\(606\) | −16.0613 | −0.652446 | ||||||||
\(607\) | −4.62585 | − | 4.62585i | −0.187758 | − | 0.187758i | 0.606968 | − | 0.794726i | \(-0.292385\pi\) |
−0.794726 | + | 0.606968i | \(0.792385\pi\) | |||||||
\(608\) | −0.537068 | − | 0.537068i | −0.0217810 | − | 0.0217810i | ||||
\(609\) | −16.5151 | −0.669225 | ||||||||
\(610\) | −14.8539 | + | 10.2035i | −0.601416 | + | 0.413128i | ||||
\(611\) | −0.707295 | −0.0286141 | ||||||||
\(612\) | −0.327163 | + | 0.327163i | −0.0132248 | + | 0.0132248i | ||||
\(613\) | −4.93150 | − | 4.93150i | −0.199181 | − | 0.199181i | 0.600468 | − | 0.799649i | \(-0.294981\pi\) |
−0.799649 | + | 0.600468i | \(0.794981\pi\) | |||||||
\(614\) | 28.8136i | 1.16282i | ||||||||
\(615\) | −12.4441 | + | 8.54815i | −0.501793 | + | 0.344695i | ||||
\(616\) | 14.2288 | 0.573297 | ||||||||
\(617\) | 27.5512 | − | 27.5512i | 1.10917 | − | 1.10917i | 0.115911 | − | 0.993260i | \(-0.463021\pi\) |
0.993260 | − | 0.115911i | \(-0.0369787\pi\) | |||||||
\(618\) | 1.60298 | + | 1.60298i | 0.0644812 | + | 0.0644812i | ||||
\(619\) | 14.2298 | 0.571945 | 0.285972 | − | 0.958238i | \(-0.407683\pi\) | ||||
0.285972 | + | 0.958238i | \(0.407683\pi\) | |||||||
\(620\) | −3.38886 | + | 18.2601i | −0.136100 | + | 0.733343i | ||||
\(621\) | 4.35871 | + | 2.00041i | 0.174909 | + | 0.0802737i | ||||
\(622\) | 11.6684 | + | 11.6684i | 0.467862 | + | 0.467862i | ||||
\(623\) | 7.64132 | − | 7.64132i | 0.306143 | − | 0.306143i | ||||
\(624\) | − | 0.341501i | − | 0.0136710i | ||||||
\(625\) | 18.5625 | + | 16.7462i | 0.742499 | + | 0.669847i | ||||
\(626\) | 6.41343i | 0.256332i | ||||||||
\(627\) | 3.28319 | + | 3.28319i | 0.131118 | + | 0.131118i | ||||
\(628\) | 5.35896 | + | 5.35896i | 0.213846 | + | 0.213846i | ||||
\(629\) | 1.26024i | 0.0502492i | ||||||||
\(630\) | 0.949699 | − | 5.11723i | 0.0378369 | − | 0.203875i | ||||
\(631\) | − | 19.7938i | − | 0.787979i | −0.919115 | − | 0.393990i | \(-0.871095\pi\) | ||
0.919115 | − | 0.393990i | \(-0.128905\pi\) | |||||||
\(632\) | −2.71125 | + | 2.71125i | −0.107848 | + | 0.107848i | ||||
\(633\) | 4.86094 | − | 4.86094i | 0.193205 | − | 0.193205i | ||||
\(634\) | − | 17.6975i | − | 0.702856i | ||||||
\(635\) | 11.5450 | + | 16.8067i | 0.458149 | + | 0.666955i | ||||
\(636\) | − | 2.05413i | − | 0.0814516i | ||||||
\(637\) | −0.382114 | − | 0.382114i | −0.0151399 | − | 0.0151399i | ||||
\(638\) | −30.6710 | − | 30.6710i | −1.21428 | − | 1.21428i | ||||
\(639\) | − | 6.24090i | − | 0.246886i | ||||||
\(640\) | −1.84311 | + | 1.26608i | −0.0728552 | + | 0.0500461i | ||||
\(641\) | − | 31.1566i | − | 1.23061i | −0.788289 | − | 0.615306i | \(-0.789033\pi\) | ||
0.788289 | − | 0.615306i | \(-0.210967\pi\) | |||||||
\(642\) | −9.95278 | + | 9.95278i | −0.392805 | + | 0.392805i | ||||
\(643\) | 21.5814 | + | 21.5814i | 0.851087 | + | 0.851087i | 0.990267 | − | 0.139180i | \(-0.0444468\pi\) |
−0.139180 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(644\) | 10.1452 | + | 4.65610i | 0.399778 | + | 0.183476i | ||||
\(645\) | −0.449782 | − | 0.0834743i | −0.0177101 | − | 0.00328680i | ||||
\(646\) | −0.351417 | −0.0138263 | ||||||||
\(647\) | 1.34183 | + | 1.34183i | 0.0527528 | + | 0.0527528i | 0.732991 | − | 0.680238i | \(-0.238124\pi\) |
−0.680238 | + | 0.732991i | \(0.738124\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −10.3031 | −0.404432 | ||||||||
\(650\) | −1.59380 | − | 0.612683i | −0.0625139 | − | 0.0240314i | ||||
\(651\) | − | 19.3319i | − | 0.757677i | ||||||
\(652\) | 1.79995 | + | 1.79995i | 0.0704916 | + | 0.0704916i | ||||
\(653\) | −25.9393 | + | 25.9393i | −1.01508 | + | 1.01508i | −0.0151973 | + | 0.999885i | \(0.504838\pi\) |
−0.999885 | + | 0.0151973i | \(0.995162\pi\) | |||||||
\(654\) | 14.4446 | 0.564828 | ||||||||
\(655\) | −23.1906 | − | 4.30391i | −0.906131 | − | 0.168168i | ||||
\(656\) | −6.75167 | −0.263609 | ||||||||
\(657\) | −6.62866 | − | 6.62866i | −0.258609 | − | 0.258609i | ||||
\(658\) | −3.40877 | − | 3.40877i | −0.132888 | − | 0.132888i | ||||
\(659\) | −3.80748 | −0.148318 | −0.0741592 | − | 0.997246i | \(-0.523627\pi\) | ||||
−0.0741592 | + | 0.997246i | \(0.523627\pi\) | |||||||
\(660\) | 11.2672 | − | 7.73975i | 0.438576 | − | 0.301269i | ||||
\(661\) | 4.54043i | 0.176602i | 0.996094 | + | 0.0883010i | \(0.0281438\pi\) | ||||
−0.996094 | + | 0.0883010i | \(0.971856\pi\) | |||||||
\(662\) | 17.2329 | + | 17.2329i | 0.669775 | + | 0.669775i | ||||
\(663\) | −0.111726 | − | 0.111726i | −0.00433909 | − | 0.00433909i | ||||
\(664\) | −3.03059 | −0.117610 | ||||||||
\(665\) | 3.25836 | − | 2.23825i | 0.126354 | − | 0.0867956i | ||||
\(666\) | − | 2.72380i | − | 0.105545i | ||||||
\(667\) | −11.8321 | − | 31.9050i | −0.458140 | − | 1.23537i | ||||
\(668\) | −9.84687 | + | 9.84687i | −0.380987 | + | 0.380987i | ||||
\(669\) | − | 15.9526i | − | 0.616765i | ||||||
\(670\) | −9.76128 | − | 1.81158i | −0.377111 | − | 0.0699875i | ||||
\(671\) | 49.2669 | 1.90193 | ||||||||
\(672\) | 1.64584 | − | 1.64584i | 0.0634898 | − | 0.0634898i | ||||
\(673\) | 22.6605 | − | 22.6605i | 0.873499 | − | 0.873499i | −0.119353 | − | 0.992852i | \(-0.538082\pi\) |
0.992852 | + | 0.119353i | \(0.0380821\pi\) | |||||||
\(674\) | −22.3261 | −0.859971 | ||||||||
\(675\) | −2.03148 | − | 4.56871i | −0.0781917 | − | 0.175850i | ||||
\(676\) | −12.8834 | −0.495515 | ||||||||
\(677\) | 33.2731 | − | 33.2731i | 1.27879 | − | 1.27879i | 0.337440 | − | 0.941347i | \(-0.390439\pi\) |
0.941347 | − | 0.337440i | \(-0.109561\pi\) | |||||||
\(678\) | 0.885110 | + | 0.885110i | 0.0339925 | + | 0.0339925i | ||||
\(679\) | 36.8691i | 1.41491i | ||||||||
\(680\) | −0.188782 | + | 1.01721i | −0.00723947 | + | 0.0390082i | ||||
\(681\) | − | 3.15367i | − | 0.120849i | ||||||
\(682\) | 35.9023 | − | 35.9023i | 1.37477 | − | 1.37477i | ||||
\(683\) | 16.5376 | − | 16.5376i | 0.632793 | − | 0.632793i | −0.315975 | − | 0.948768i | \(-0.602332\pi\) |
0.948768 | + | 0.315975i | \(0.102332\pi\) | |||||||
\(684\) | 0.759529 | 0.0290413 | ||||||||
\(685\) | 40.1308 | − | 27.5669i | 1.53332 | − | 1.05328i | ||||
\(686\) | − | 19.9762i | − | 0.762694i | ||||||
\(687\) | 4.14428 | − | 4.14428i | 0.158114 | − | 0.158114i | ||||
\(688\) | −0.144662 | − | 0.144662i | −0.00551519 | − | 0.00551519i | ||||
\(689\) | 0.701487 | 0.0267245 | ||||||||
\(690\) | 10.5662 | − | 1.83150i | 0.402250 | − | 0.0697239i | ||||
\(691\) | −38.2075 | −1.45348 | −0.726741 | − | 0.686912i | \(-0.758966\pi\) | ||||
−0.726741 | + | 0.686912i | \(0.758966\pi\) | |||||||
\(692\) | 12.1316 | + | 12.1316i | 0.461176 | + | 0.461176i | ||||
\(693\) | −10.0613 | + | 10.0613i | −0.382198 | + | 0.382198i | ||||
\(694\) | − | 16.2280i | − | 0.616007i | ||||||
\(695\) | 2.34674 | − | 12.6448i | 0.0890168 | − | 0.479646i | ||||
\(696\) | −7.09541 | −0.268951 | ||||||||
\(697\) | −2.20890 | + | 2.20890i | −0.0836679 | + | 0.0836679i | ||||
\(698\) | 4.14368 | − | 4.14368i | 0.156841 | − | 0.156841i | ||||
\(699\) | − | 18.6339i | − | 0.704799i | ||||||
\(700\) | −4.72842 | − | 10.6340i | −0.178717 | − | 0.401928i | ||||
\(701\) | 5.54946i | 0.209600i | 0.994493 | + | 0.104800i | \(0.0334203\pi\) | ||||
−0.994493 | + | 0.104800i | \(0.966580\pi\) | |||||||
\(702\) | 0.241478 | + | 0.241478i | 0.00911398 | + | 0.00911398i | ||||
\(703\) | 1.46287 | − | 1.46287i | 0.0551732 | − | 0.0551732i | ||||
\(704\) | 6.11317 | 0.230399 | ||||||||
\(705\) | −4.55345 | − | 0.845067i | −0.171493 | − | 0.0318271i | ||||
\(706\) | 5.57662 | 0.209879 | ||||||||
\(707\) | 26.4344 | − | 26.4344i | 0.994168 | − | 0.994168i | ||||
\(708\) | −1.19176 | + | 1.19176i | −0.0447889 | + | 0.0447889i | ||||
\(709\) | 41.0934 | 1.54329 | 0.771647 | − | 0.636051i | \(-0.219433\pi\) | ||||
0.771647 | + | 0.636051i | \(0.219433\pi\) | |||||||
\(710\) | −7.90147 | − | 11.5026i | −0.296537 | − | 0.431687i | ||||
\(711\) | − | 3.83429i | − | 0.143797i | ||||||
\(712\) | 3.28296 | − | 3.28296i | 0.123034 | − | 0.123034i | ||||
\(713\) | 37.3468 | − | 13.8502i | 1.39865 | − | 0.518693i | ||||
\(714\) | − | 1.07692i | − | 0.0403026i | ||||||
\(715\) | 2.64313 | + | 3.84777i | 0.0988475 | + | 0.143898i | ||||
\(716\) | −1.62037 | −0.0605561 | ||||||||
\(717\) | 16.1411 | + | 16.1411i | 0.602800 | + | 0.602800i | ||||
\(718\) | −23.0781 | − | 23.0781i | −0.861269 | − | 0.861269i | ||||
\(719\) | − | 1.72658i | − | 0.0643905i | −0.999482 | − | 0.0321952i | \(-0.989750\pi\) | ||
0.999482 | − | 0.0321952i | \(-0.0102498\pi\) | |||||||
\(720\) | 0.408021 | − | 2.19853i | 0.0152060 | − | 0.0819342i | ||||
\(721\) | −5.27650 | −0.196507 | ||||||||
\(722\) | −13.0271 | − | 13.0271i | −0.484819 | − | 0.484819i | ||||
\(723\) | 13.1887 | + | 13.1887i | 0.490495 | + | 0.490495i | ||||
\(724\) | −20.5841 | −0.765000 | ||||||||
\(725\) | −12.7298 | + | 33.1145i | −0.472773 | + | 1.22984i | ||||
\(726\) | −26.3708 | −0.978713 | ||||||||
\(727\) | 3.72425 | − | 3.72425i | 0.138125 | − | 0.138125i | −0.634664 | − | 0.772788i | \(-0.718861\pi\) |
0.772788 | + | 0.634664i | \(0.218861\pi\) | |||||||
\(728\) | 0.562057 | + | 0.562057i | 0.0208312 | + | 0.0208312i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −20.6097 | − | 3.82493i | −0.762801 | − | 0.141567i | ||||
\(731\) | −0.0946561 | −0.00350098 | ||||||||
\(732\) | 5.69868 | − | 5.69868i | 0.210629 | − | 0.210629i | ||||
\(733\) | 6.33773 | + | 6.33773i | 0.234089 | + | 0.234089i | 0.814397 | − | 0.580308i | \(-0.197068\pi\) |
−0.580308 | + | 0.814397i | \(0.697068\pi\) | |||||||
\(734\) | −32.5248 | −1.20051 | ||||||||
\(735\) | −2.00344 | − | 2.91653i | −0.0738981 | − | 0.107578i | ||||
\(736\) | 4.35871 | + | 2.00041i | 0.160664 | + | 0.0737361i | ||||
\(737\) | 19.1923 | + | 19.1923i | 0.706956 | + | 0.706956i | ||||
\(738\) | 4.77416 | − | 4.77416i | 0.175739 | − | 0.175739i | ||||
\(739\) | − | 27.5093i | − | 1.01195i | −0.862549 | − | 0.505973i | \(-0.831133\pi\) | ||
0.862549 | − | 0.505973i | \(-0.168867\pi\) | |||||||
\(740\) | −3.44855 | − | 5.02026i | −0.126771 | − | 0.184549i | ||||
\(741\) | 0.259380i | 0.00952856i | ||||||||
\(742\) | 3.38078 | + | 3.38078i | 0.124112 | + | 0.124112i | ||||
\(743\) | −20.8781 | − | 20.8781i | −0.765942 | − | 0.765942i | 0.211448 | − | 0.977389i | \(-0.432182\pi\) |
−0.977389 | + | 0.211448i | \(0.932182\pi\) | |||||||
\(744\) | − | 8.30560i | − | 0.304498i | ||||||
\(745\) | −38.9107 | − | 7.22137i | −1.42558 | − | 0.264571i | ||||
\(746\) | − | 21.8676i | − | 0.800629i | ||||||
\(747\) | 2.14295 | − | 2.14295i | 0.0784065 | − | 0.0784065i | ||||
\(748\) | 2.00000 | − | 2.00000i | 0.0731272 | − | 0.0731272i | ||||
\(749\) | − | 32.7614i | − | 1.19708i | ||||||
\(750\) | −9.52858 | − | 5.84861i | −0.347935 | − | 0.213561i | ||||
\(751\) | − | 12.1937i | − | 0.444954i | −0.974938 | − | 0.222477i | \(-0.928586\pi\) | ||
0.974938 | − | 0.222477i | \(-0.0714142\pi\) | |||||||
\(752\) | −1.46451 | − | 1.46451i | −0.0534053 | − | 0.0534053i | ||||
\(753\) | 17.0480 | + | 17.0480i | 0.621264 | + | 0.621264i | ||||
\(754\) | − | 2.42309i | − | 0.0882436i | ||||||
\(755\) | 26.1882 | + | 4.86022i | 0.953085 | + | 0.176881i | ||||
\(756\) | 2.32757i | 0.0846530i | ||||||||
\(757\) | −13.7127 | + | 13.7127i | −0.498396 | + | 0.498396i | −0.910938 | − | 0.412543i | \(-0.864641\pi\) |
0.412543 | + | 0.910938i | \(0.364641\pi\) | |||||||
\(758\) | 7.84787 | + | 7.84787i | 0.285048 | + | 0.285048i | ||||
\(759\) | −26.6455 | − | 12.2288i | −0.967171 | − | 0.443879i | ||||
\(760\) | 1.39989 | − | 0.961624i | 0.0507795 | − | 0.0348818i | ||||
\(761\) | 15.5354 | 0.563159 | 0.281580 | − | 0.959538i | \(-0.409142\pi\) | ||||
0.281580 | + | 0.959538i | \(0.409142\pi\) | |||||||
\(762\) | −6.44789 | − | 6.44789i | −0.233582 | − | 0.233582i | ||||
\(763\) | −23.7735 | + | 23.7735i | −0.860660 | + | 0.860660i | ||||
\(764\) | −20.8203 | −0.753251 | ||||||||
\(765\) | −0.585786 | − | 0.852765i | −0.0211792 | − | 0.0308318i | ||||
\(766\) | − | 26.0342i | − | 0.940653i | ||||||
\(767\) | −0.406985 | − | 0.406985i | −0.0146954 | − | 0.0146954i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −30.1885 | −1.08863 | −0.544313 | − | 0.838882i | \(-0.683210\pi\) | ||||
−0.544313 | + | 0.838882i | \(0.683210\pi\) | |||||||
\(770\) | −5.80567 | + | 31.2825i | −0.209222 | + | 1.12734i | ||||
\(771\) | −23.1590 | −0.834053 | ||||||||
\(772\) | 5.74993 | + | 5.74993i | 0.206945 | + | 0.206945i | ||||
\(773\) | −8.94529 | − | 8.94529i | −0.321740 | − | 0.321740i | 0.527694 | − | 0.849434i | \(-0.323057\pi\) |
−0.849434 | + | 0.527694i | \(0.823057\pi\) | |||||||
\(774\) | 0.204583 | 0.00735359 | ||||||||
\(775\) | −38.7626 | − | 14.9010i | −1.39239 | − | 0.535260i | ||||
\(776\) | 15.8402i | 0.568628i | ||||||||
\(777\) | 4.48296 | + | 4.48296i | 0.160825 | + | 0.160825i | ||||
\(778\) | 15.0574 | + | 15.0574i | 0.539833 | + | 0.539833i | ||||
\(779\) | 5.12810 | 0.183733 | ||||||||
\(780\) | 0.750799 | + | 0.139340i | 0.0268829 | + | 0.00498916i | ||||
\(781\) | 38.1517i | 1.36517i | ||||||||
\(782\) | 2.08047 | − | 0.771547i | 0.0743973 | − | 0.0275905i | ||||
\(783\) | 5.01721 | − | 5.01721i | 0.179300 | − | 0.179300i | ||||
\(784\) | − | 1.58240i | − | 0.0565143i | ||||||
\(785\) | −13.9684 | + | 9.59525i | −0.498553 | + | 0.342469i | ||||
\(786\) | 10.5482 | 0.376243 | ||||||||
\(787\) | 37.6119 | − | 37.6119i | 1.34072 | − | 1.34072i | 0.445375 | − | 0.895344i | \(-0.353070\pi\) |
0.895344 | − | 0.445375i | \(-0.146930\pi\) | |||||||
\(788\) | −1.24668 | + | 1.24668i | −0.0444111 | + | 0.0444111i | ||||
\(789\) | 22.9842 | 0.818258 | ||||||||
\(790\) | −4.85451 | − | 7.06700i | −0.172716 | − | 0.251433i | ||||
\(791\) | −2.91351 | −0.103592 | ||||||||
\(792\) | −4.32266 | + | 4.32266i | −0.153599 | + | 0.153599i | ||||
\(793\) | 1.94610 | + | 1.94610i | 0.0691082 | + | 0.0691082i | ||||
\(794\) | − | 24.7158i | − | 0.877130i | ||||||
\(795\) | 4.51606 | + | 0.838129i | 0.160168 | + | 0.0297254i | ||||
\(796\) | 4.17076i | 0.147829i | ||||||||
\(797\) | −16.1680 | + | 16.1680i | −0.572700 | + | 0.572700i | −0.932882 | − | 0.360182i | \(-0.882715\pi\) |
0.360182 | + | 0.932882i | \(0.382715\pi\) | |||||||
\(798\) | −1.25007 | + | 1.25007i | −0.0442519 | + | 0.0442519i | ||||
\(799\) | −0.958269 | −0.0339011 | ||||||||
\(800\) | −2.03148 | − | 4.56871i | −0.0718237 | − | 0.161528i | ||||
\(801\) | 4.64280i | 0.164045i | ||||||||
\(802\) | 6.60699 | − | 6.60699i | 0.233301 | − | 0.233301i | ||||
\(803\) | 40.5221 | + | 40.5221i | 1.42999 | + | 1.42999i | ||||
\(804\) | 4.43992 | 0.156584 | ||||||||
\(805\) | −14.3760 | + | 20.4047i | −0.506689 | + | 0.719173i | ||||
\(806\) | 2.83637 | 0.0999069 | ||||||||
\(807\) | 19.3478 | + | 19.3478i | 0.681076 | + | 0.681076i | ||||
\(808\) | 11.3571 | − | 11.3571i | 0.399540 | − | 0.399540i | ||||
\(809\) | 11.0745i | 0.389357i | 0.980867 | + | 0.194679i | \(0.0623664\pi\) | ||||
−0.980867 | + | 0.194679i | \(0.937634\pi\) | |||||||
\(810\) | 1.26608 | + | 1.84311i | 0.0444855 | + | 0.0647602i | ||||
\(811\) | −5.55602 | −0.195098 | −0.0975491 | − | 0.995231i | \(-0.531100\pi\) | ||||
−0.0975491 | + | 0.995231i | \(0.531100\pi\) | |||||||
\(812\) | 11.6779 | − | 11.6779i | 0.409815 | − | 0.409815i | ||||
\(813\) | −21.7108 | + | 21.7108i | −0.761431 | + | 0.761431i | ||||
\(814\) | 16.6511i | 0.583620i | ||||||||
\(815\) | −4.69166 | + | 3.22283i | −0.164342 | + | 0.112891i | ||||
\(816\) | − | 0.462678i | − | 0.0161970i | ||||||
\(817\) | 0.109875 | + | 0.109875i | 0.00384405 | + | 0.00384405i | ||||
\(818\) | 11.2336 | − | 11.2336i | 0.392773 | − | 0.392773i | ||||
\(819\) | −0.794868 | −0.0277749 | ||||||||
\(820\) | 2.75483 | − | 14.8437i | 0.0962027 | − | 0.518366i | ||||
\(821\) | 11.9158 | 0.415863 | 0.207931 | − | 0.978143i | \(-0.433327\pi\) | ||||
0.207931 | + | 0.978143i | \(0.433327\pi\) | |||||||
\(822\) | −15.3962 | + | 15.3962i | −0.537003 | + | 0.537003i | ||||
\(823\) | −18.2633 | + | 18.2633i | −0.636619 | + | 0.636619i | −0.949720 | − | 0.313101i | \(-0.898632\pi\) |
0.313101 | + | 0.949720i | \(0.398632\pi\) | |||||||
\(824\) | −2.26695 | −0.0789730 | ||||||||
\(825\) | 12.4188 | + | 27.9293i | 0.432366 | + | 0.972373i | ||||
\(826\) | − | 3.92288i | − | 0.136495i | ||||||
\(827\) | −19.7059 | + | 19.7059i | −0.685241 | + | 0.685241i | −0.961176 | − | 0.275936i | \(-0.911012\pi\) |
0.275936 | + | 0.961176i | \(0.411012\pi\) | |||||||
\(828\) | −4.49658 | + | 1.66757i | −0.156267 | + | 0.0579520i | ||||
\(829\) | − | 3.61941i | − | 0.125707i | −0.998023 | − | 0.0628537i | \(-0.979980\pi\) | ||
0.998023 | − | 0.0628537i | \(-0.0200201\pi\) | |||||||
\(830\) | 1.23654 | − | 6.66283i | 0.0429211 | − | 0.231270i | ||||
\(831\) | 3.13866 | 0.108879 | ||||||||
\(832\) | 0.241478 | + | 0.241478i | 0.00837173 | + | 0.00837173i | ||||
\(833\) | −0.517702 | − | 0.517702i | −0.0179373 | − | 0.0179373i | ||||
\(834\) | 5.75151i | 0.199159i | ||||||||
\(835\) | −17.6309 | − | 25.6663i | −0.610141 | − | 0.888220i | ||||
\(836\) | −4.64313 | −0.160586 | ||||||||
\(837\) | 5.87295 | + | 5.87295i | 0.202999 | + | 0.202999i | ||||
\(838\) | 3.61353 | + | 3.61353i | 0.124827 | + | 0.124827i | ||||
\(839\) | 50.9017 | 1.75732 | 0.878660 | − | 0.477447i | \(-0.158438\pi\) | ||||
0.878660 | + | 0.477447i | \(0.158438\pi\) | |||||||
\(840\) | 2.94689 | + | 4.28997i | 0.101677 | + | 0.148018i | ||||
\(841\) | −21.3448 | −0.736027 | ||||||||
\(842\) | 4.03937 | − | 4.03937i | 0.139206 | − | 0.139206i | ||||
\(843\) | −18.4182 | − | 18.4182i | −0.634357 | − | 0.634357i | ||||
\(844\) | 6.87441i | 0.236627i | ||||||||
\(845\) | 5.25669 | − | 28.3244i | 0.180836 | − | 0.974391i | ||||
\(846\) | 2.07114 | 0.0712071 | ||||||||
\(847\) | 43.4022 | − | 43.4022i | 1.49132 | − | 1.49132i | ||||
\(848\) | 1.45249 | + | 1.45249i | 0.0498787 | + | 0.0498787i | ||||
\(849\) | 7.75406 | 0.266119 | ||||||||
\(850\) | −2.15933 | − | 0.830086i | −0.0740646 | − | 0.0284717i | ||||
\(851\) | −5.44873 | + | 11.8723i | −0.186780 | + | 0.406976i | ||||
\(852\) | 4.41298 | + | 4.41298i | 0.151186 | + | 0.151186i | ||||
\(853\) | 6.62856 | − | 6.62856i | 0.226958 | − | 0.226958i | −0.584463 | − | 0.811420i | \(-0.698695\pi\) |
0.811420 | + | 0.584463i | \(0.198695\pi\) | |||||||
\(854\) | 18.7583i | 0.641895i | ||||||||
\(855\) | −0.309904 | + | 1.66985i | −0.0105985 | + | 0.0571075i | ||||
\(856\) | − | 14.0754i | − | 0.481086i | ||||||
\(857\) | −8.37639 | − | 8.37639i | −0.286132 | − | 0.286132i | 0.549417 | − | 0.835549i | \(-0.314850\pi\) |
−0.835549 | + | 0.549417i | \(0.814850\pi\) | |||||||
\(858\) | −1.47619 | − | 1.47619i | −0.0503964 | − | 0.0503964i | ||||
\(859\) | − | 5.10209i | − | 0.174081i | −0.996205 | − | 0.0870405i | \(-0.972259\pi\) | ||
0.996205 | − | 0.0870405i | \(-0.0277409\pi\) | |||||||
\(860\) | 0.377069 | − | 0.259018i | 0.0128579 | − | 0.00883245i | ||||
\(861\) | 15.7150i | 0.535567i | ||||||||
\(862\) | −2.32457 | + | 2.32457i | −0.0791753 | + | 0.0791753i | ||||
\(863\) | −6.91979 | + | 6.91979i | −0.235553 | + | 0.235553i | −0.815006 | − | 0.579453i | \(-0.803266\pi\) |
0.579453 | + | 0.815006i | \(0.303266\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | −31.6217 | + | 21.7218i | −1.07517 | + | 0.738562i | ||||
\(866\) | 16.4577i | 0.559256i | ||||||||
\(867\) | 11.8694 | + | 11.8694i | 0.403107 | + | 0.403107i | ||||
\(868\) | 13.6697 | + | 13.6697i | 0.463980 | + | 0.463980i | ||||
\(869\) | 23.4396i | 0.795135i | ||||||||
\(870\) | 2.89508 | − | 15.5994i | 0.0981522 | − | 0.528870i | ||||
\(871\) | 1.51624i | 0.0513757i | ||||||||
\(872\) | −10.2139 | + | 10.2139i | −0.345885 | + | 0.345885i | ||||
\(873\) | −11.2007 | − | 11.2007i | −0.379086 | − | 0.379086i | ||||
\(874\) | −3.31057 | − | 1.51937i | −0.111982 | − | 0.0513935i | ||||
\(875\) | 25.3084 | − | 6.05666i | 0.855581 | − | 0.204752i | ||||
\(876\) | 9.37434 | 0.316730 | ||||||||
\(877\) | −11.0291 | − | 11.0291i | −0.372427 | − | 0.372427i | 0.495934 | − | 0.868360i | \(-0.334826\pi\) |
−0.868360 | + | 0.495934i | \(0.834826\pi\) | |||||||
\(878\) | −8.75052 | + | 8.75052i | −0.295316 | + | 0.295316i | ||||
\(879\) | −26.2398 | −0.885045 | ||||||||
\(880\) | −2.49430 | + | 13.4400i | −0.0840829 | + | 0.453061i | ||||
\(881\) | 53.9458i | 1.81748i | 0.417361 | + | 0.908741i | \(0.362955\pi\) | ||||
−0.417361 | + | 0.908741i | \(0.637045\pi\) | |||||||
\(882\) | 1.11893 | + | 1.11893i | 0.0376762 | + | 0.0376762i | ||||
\(883\) | −21.6479 | + | 21.6479i | −0.728511 | + | 0.728511i | −0.970323 | − | 0.241812i | \(-0.922258\pi\) |
0.241812 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(884\) | 0.158005 | 0.00531428 | ||||||||
\(885\) | −2.13384 | − | 3.10637i | −0.0717284 | − | 0.104419i | ||||
\(886\) | 34.5791 | 1.16171 | ||||||||
\(887\) | 27.1450 | + | 27.1450i | 0.911441 | + | 0.911441i | 0.996386 | − | 0.0849443i | \(-0.0270712\pi\) |
−0.0849443 | + | 0.996386i | \(0.527071\pi\) | |||||||
\(888\) | 1.92602 | + | 1.92602i | 0.0646330 | + | 0.0646330i | ||||
\(889\) | 21.2244 | 0.711845 | ||||||||
\(890\) | 5.87815 | + | 8.55718i | 0.197036 | + | 0.286837i | ||||
\(891\) | − | 6.11317i | − | 0.204799i | ||||||
\(892\) | 11.2802 | + | 11.2802i | 0.377690 | + | 0.377690i | ||||
\(893\) | 1.11234 | + | 1.11234i | 0.0372231 | + | 0.0372231i | ||||
\(894\) | 17.6985 | 0.591927 | ||||||||
\(895\) | 0.661145 | − | 3.56243i | 0.0220996 | − | 0.119079i | ||||
\(896\) | 2.32757i | 0.0777588i | ||||||||
\(897\) | −0.569476 | − | 1.53558i | −0.0190143 | − | 0.0512717i | ||||
\(898\) | −29.0109 | + | 29.0109i | −0.968108 | + | 0.968108i | ||||
\(899\) | − | 58.9316i | − | 1.96548i | ||||||
\(900\) | 4.66704 | + | 1.79409i | 0.155568 | + | 0.0598030i | ||||
\(901\) | 0.950401 | 0.0316624 | ||||||||
\(902\) | −29.1852 | + | 29.1852i | −0.971761 | + | 0.971761i | ||||
\(903\) | −0.336712 | + | 0.336712i | −0.0112051 | + | 0.0112051i | ||||
\(904\) | −1.25173 | −0.0416321 | ||||||||
\(905\) | 8.39873 | − | 45.2546i | 0.279183 | − | 1.50431i | ||||
\(906\) | −11.9117 | −0.395739 | ||||||||
\(907\) | −30.5493 | + | 30.5493i | −1.01437 | + | 1.01437i | −0.0144762 | + | 0.999895i | \(0.504608\pi\) |
−0.999895 | + | 0.0144762i | \(0.995392\pi\) | |||||||
\(908\) | 2.22998 | + | 2.22998i | 0.0740046 | + | 0.0740046i | ||||
\(909\) | 16.0613i | 0.532720i | ||||||||
\(910\) | −1.46503 | + | 1.00637i | −0.0485652 | + | 0.0333607i | ||||
\(911\) | 42.0891i | 1.39447i | 0.716840 | + | 0.697237i | \(0.245588\pi\) | ||||
−0.716840 | + | 0.697237i | \(0.754412\pi\) | |||||||
\(912\) | −0.537068 | + | 0.537068i | −0.0177841 | + | 0.0177841i | ||||
\(913\) | −13.1002 | + | 13.1002i | −0.433554 | + | 0.433554i | ||||
\(914\) | −26.2274 | −0.867526 | ||||||||
\(915\) | 10.2035 | + | 14.8539i | 0.337318 | + | 0.491054i | ||||
\(916\) | 5.86090i | 0.193650i | ||||||||
\(917\) | −17.3608 | + | 17.3608i | −0.573303 | + | 0.573303i | ||||
\(918\) | 0.327163 | + | 0.327163i | 0.0107980 | + | 0.0107980i | ||||
\(919\) | −6.51121 | −0.214785 | −0.107393 | − | 0.994217i | \(-0.534250\pi\) | ||||
−0.107393 | + | 0.994217i | \(0.534250\pi\) | |||||||
\(920\) | −6.17640 | + | 8.76653i | −0.203630 | + | 0.289024i | ||||
\(921\) | 28.8136 | 0.949440 | ||||||||
\(922\) | 15.2001 | + | 15.2001i | 0.500588 | + | 0.500588i | ||||
\(923\) | −1.50704 | + | 1.50704i | −0.0496047 | + | 0.0496047i | ||||
\(924\) | − | 14.2288i | − | 0.468095i | ||||||
\(925\) | 12.4443 | − | 5.53336i | 0.409165 | − | 0.181936i | ||||
\(926\) | −20.8899 | −0.686485 | ||||||||
\(927\) | 1.60298 | − | 1.60298i | 0.0526487 | − | 0.0526487i | ||||
\(928\) | 5.01721 | − | 5.01721i | 0.164698 | − | 0.164698i | ||||
\(929\) | − | 39.0887i | − | 1.28246i | −0.767349 | − | 0.641229i | \(-0.778425\pi\) | ||
0.767349 | − | 0.641229i | \(-0.221575\pi\) | |||||||
\(930\) | 18.2601 | + | 3.38886i | 0.598772 | + | 0.111125i | ||||
\(931\) | 1.20188i | 0.0393900i | ||||||||
\(932\) | 13.1762 | + | 13.1762i | 0.431599 | + | 0.431599i | ||||
\(933\) | 11.6684 | − | 11.6684i | 0.382008 | − | 0.382008i | ||||
\(934\) | 33.8070 | 1.10620 | ||||||||
\(935\) | 3.58101 | + | 5.21310i | 0.117112 | + | 0.170486i | ||||
\(936\) | −0.341501 | −0.0111623 | ||||||||
\(937\) | −3.08761 | + | 3.08761i | −0.100868 | + | 0.100868i | −0.755740 | − | 0.654872i | \(-0.772722\pi\) |
0.654872 | + | 0.755740i | \(0.272722\pi\) | |||||||
\(938\) | −7.30741 | + | 7.30741i | −0.238595 | + | 0.238595i | ||||
\(939\) | 6.41343 | 0.209294 | ||||||||
\(940\) | 3.81733 | − | 2.62222i | 0.124507 | − | 0.0855274i | ||||
\(941\) | 21.4791i | 0.700197i | 0.936713 | + | 0.350099i | \(0.113852\pi\) | ||||
−0.936713 | + | 0.350099i | \(0.886148\pi\) | |||||||
\(942\) | 5.35896 | − | 5.35896i | 0.174604 | − | 0.174604i | ||||
\(943\) | −30.3594 | + | 11.2589i | −0.988639 | + | 0.366640i | ||||
\(944\) | − | 1.68540i | − | 0.0548550i | ||||||
\(945\) | −5.11723 | − | 0.949699i | −0.166464 | − | 0.0308937i | ||||
\(946\) | −1.25065 | −0.0406622 | ||||||||
\(947\) | −8.49336 | − | 8.49336i | −0.275997 | − | 0.275997i | 0.555512 | − | 0.831509i | \(-0.312522\pi\) |
−0.831509 | + | 0.555512i | \(0.812522\pi\) | |||||||
\(948\) | 2.71125 | + | 2.71125i | 0.0880573 | + | 0.0880573i | ||||
\(949\) | 3.20135i | 0.103920i | ||||||||
\(950\) | 1.54297 | + | 3.47007i | 0.0500605 | + | 0.112584i | ||||
\(951\) | −17.6975 | −0.573879 | ||||||||
\(952\) | 0.761495 | + | 0.761495i | 0.0246802 | + | 0.0246802i | ||||
\(953\) | −36.6128 | − | 36.6128i | −1.18601 | − | 1.18601i | −0.978162 | − | 0.207843i | \(-0.933356\pi\) |
−0.207843 | − | 0.978162i | \(-0.566644\pi\) | |||||||
\(954\) | −2.05413 | −0.0665049 | ||||||||
\(955\) | 8.49511 | − | 45.7739i | 0.274895 | − | 1.48121i | ||||
\(956\) | −22.8269 | −0.738276 | ||||||||
\(957\) | −30.6710 | + | 30.6710i | −0.991454 | + | 0.991454i | ||||
\(958\) | 7.78741 | + | 7.78741i | 0.251600 | + | 0.251600i | ||||
\(959\) | − | 50.6793i | − | 1.63652i | ||||||
\(960\) | 1.26608 | + | 1.84311i | 0.0408625 | + | 0.0594860i | ||||
\(961\) | 37.9830 | 1.22526 | ||||||||
\(962\) | −0.657738 | + | 0.657738i | −0.0212063 | + | 0.0212063i | ||||
\(963\) | 9.95278 | + | 9.95278i | 0.320724 | + | 0.320724i | ||||
\(964\) | −18.6517 | −0.600731 | ||||||||
\(965\) | −14.9875 | + | 10.2953i | −0.482464 | + | 0.331417i | ||||
\(966\) | 4.65610 | − | 10.1452i | 0.149808 | − | 0.326417i | ||||
\(967\) | 16.2892 | + | 16.2892i | 0.523824 | + | 0.523824i | 0.918724 | − | 0.394900i | \(-0.129221\pi\) |
−0.394900 | + | 0.918724i | \(0.629221\pi\) | |||||||
\(968\) | 18.6470 | − | 18.6470i | 0.599337 | − | 0.599337i | ||||
\(969\) | 0.351417i | 0.0112892i | ||||||||
\(970\) | −34.8250 | − | 6.46312i | −1.11816 | − | 0.207518i | ||||
\(971\) | − | 18.4126i | − | 0.590889i | −0.955360 | − | 0.295444i | \(-0.904532\pi\) | ||
0.955360 | − | 0.295444i | \(-0.0954677\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −9.46608 | − | 9.46608i | −0.303469 | − | 0.303469i | ||||
\(974\) | 36.5152i | 1.17002i | ||||||||
\(975\) | −0.612683 | + | 1.59380i | −0.0196216 | + | 0.0510424i | ||||
\(976\) | 8.05915i | 0.257967i | ||||||||
\(977\) | −30.7089 | + | 30.7089i | −0.982464 | + | 0.982464i | −0.999849 | − | 0.0173847i | \(-0.994466\pi\) |
0.0173847 | + | 0.999849i | \(0.494466\pi\) | |||||||
\(978\) | 1.79995 | − | 1.79995i | 0.0575562 | − | 0.0575562i | ||||
\(979\) | − | 28.3822i | − | 0.907100i | ||||||
\(980\) | 3.47895 | + | 0.645653i | 0.111131 | + | 0.0206246i | ||||
\(981\) | − | 14.4446i | − | 0.461180i | ||||||
\(982\) | −14.9424 | − | 14.9424i | −0.476832 | − | 0.476832i | ||||
\(983\) | −16.1127 | − | 16.1127i | −0.513916 | − | 0.513916i | 0.401808 | − | 0.915724i | \(-0.368382\pi\) |
−0.915724 | + | 0.401808i | \(0.868382\pi\) | |||||||
\(984\) | 6.75167i | 0.215236i | ||||||||
\(985\) | −2.23219 | − | 3.24953i | −0.0711234 | − | 0.103539i | ||||
\(986\) | − | 3.28289i | − | 0.104548i | ||||||
\(987\) | −3.40877 | + | 3.40877i | −0.108502 | + | 0.108502i | ||||
\(988\) | −0.183409 | − | 0.183409i | −0.00583503 | − | 0.00583503i | ||||
\(989\) | −0.891719 | − | 0.409250i | −0.0283550 | − | 0.0130134i | ||||
\(990\) | −7.73975 | − | 11.2672i | −0.245985 | − | 0.358096i | ||||
\(991\) | −11.5298 | −0.366256 | −0.183128 | − | 0.983089i | \(-0.558622\pi\) | ||||
−0.183128 | + | 0.983089i | \(0.558622\pi\) | |||||||
\(992\) | 5.87295 | + | 5.87295i | 0.186466 | + | 0.186466i | ||||
\(993\) | 17.2329 | − | 17.2329i | 0.546869 | − | 0.546869i | ||||
\(994\) | −14.5262 | −0.460742 | ||||||||
\(995\) | −9.16953 | − | 1.70176i | −0.290694 | − | 0.0539494i | ||||
\(996\) | 3.03059i | 0.0960279i | ||||||||
\(997\) | −5.05273 | − | 5.05273i | −0.160021 | − | 0.160021i | 0.622555 | − | 0.782576i | \(-0.286095\pi\) |
−0.782576 | + | 0.622555i | \(0.786095\pi\) | |||||||
\(998\) | 18.2129 | − | 18.2129i | 0.576520 | − | 0.576520i | ||||
\(999\) | −2.72380 | −0.0861774 |
(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 | 690.2.j.b.367.7 | ✓ | 24 | |
5.3 | odd | 4 | inner | 690.2.j.b.643.12 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.367.12 | yes | 24 | |
115.68 | even | 4 | inner | 690.2.j.b.643.7 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.367.12 | yes | 24 | 23.22 | odd | 2 | inner | |
690.2.j.b.643.7 | yes | 24 | 115.68 | even | 4 | inner | |
690.2.j.b.643.12 | yes | 24 | 5.3 | odd | 4 | inner |