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 | 367.12 | ||
Character | \(\chi\) | \(=\) | 690.367 |
Dual form | 690.2.j.b.643.12 |
$q$-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 | −0.323990 | − | 0.946060i | \(-0.605024\pi\) |
0.946060 | + | 0.323990i | \(0.105024\pi\) | |||||||
\(8\) | −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 | \(-0.626887\pi\) | ||
0.388154 | − | 0.921595i | \(-0.373113\pi\) | |||||||
\(12\) | 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 | −0.666319 | − | 0.745667i | \(-0.732131\pi\) |
0.745667 | + | 0.666319i | \(0.232131\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | −0.759529 | −0.174248 | −0.0871240 | − | 0.996197i | \(-0.527768\pi\) | ||||
−0.0871240 | + | 0.996197i | \(0.527768\pi\) | |||||||
\(20\) | −0.408021 | + | 2.19853i | −0.0912363 | + | 0.491605i | ||||
\(21\) | − | 2.32757i | − | 0.507918i | ||||||
\(22\) | 4.32266 | − | 4.32266i | 0.921595 | − | 0.921595i | ||||
\(23\) | −1.66757 | + | 4.49658i | −0.347712 | + | 0.937601i | ||||
\(24\) | 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 | −0.847474 | − | 0.530838i | \(-0.821877\pi\) |
0.530838 | + | 0.847474i | \(0.321877\pi\) | |||||||
\(38\) | −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 | 0.695990 | − | 0.718051i | \(-0.254966\pi\) |
−0.718051 | + | 0.695990i | \(0.754966\pi\) | |||||||
\(44\) | 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 | 0.799792 | − | 0.600277i | \(-0.204943\pi\) |
−0.600277 | + | 0.799792i | \(0.704943\pi\) | |||||||
\(54\) | − | 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 | \(0.172555\pi\) | ||||
−0.856628 | + | 0.515934i | \(0.827445\pi\) | |||||||
\(62\) | −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 | −0.872380 | − | 0.488829i | \(-0.837424\pi\) |
0.488829 | + | 0.872380i | \(0.337424\pi\) | |||||||
\(68\) | 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 | \(-0.569202\pi\) | ||||
−0.215695 | + | 0.976461i | \(0.569202\pi\) | |||||||
\(80\) | −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 | 0.579648 | − | 0.814867i | \(-0.303190\pi\) |
−0.814867 | + | 0.579648i | \(0.803190\pi\) | |||||||
\(84\) | 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 | \(-0.420861\pi\) | ||||
0.246068 | + | 0.969253i | \(0.420861\pi\) | |||||||
\(90\) | 1.84311 | − | 1.26608i | 0.194281 | − | 0.133456i | ||||
\(91\) | 0.794868i | 0.0833248i | ||||||||
\(92\) | −4.49658 | − | 1.66757i | −0.468801 | − | 0.173856i | ||||
\(93\) | −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 | \(0.547386\pi\) |
−0.988940 | + | 0.148317i | \(0.952614\pi\) | |||||||
\(98\) | −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 | 0.623710 | − | 0.781656i | \(-0.285625\pi\) |
−0.781656 | + | 0.623710i | \(0.785625\pi\) | |||||||
\(104\) | − | 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 | −0.0371390 | − | 0.999310i | \(-0.511824\pi\) |
0.999310 | + | 0.0371390i | \(0.0118244\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | −14.4446 | −1.38354 | −0.691771 | − | 0.722117i | \(-0.743169\pi\) | ||||
−0.691771 | + | 0.722117i | \(0.743169\pi\) | |||||||
\(110\) | 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 | 0.664248 | − | 0.747512i | \(-0.268752\pi\) |
−0.747512 | + | 0.664248i | \(0.768752\pi\) | |||||||
\(114\) | −0.759529 | −0.0711365 | ||||||||
\(115\) | −5.50089 | + | 9.20544i | −0.512961 | + | 0.858412i | ||||
\(116\) | −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 | \(-0.369706\pi\) |
0.917388 | − | 0.397994i | \(-0.130294\pi\) | |||||||
\(138\) | −1.66757 | + | 4.49658i | −0.141953 | + | 0.382774i | ||||
\(139\) | 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 | \(-0.758142\pi\) | ||||
−0.724960 | + | 0.688791i | \(0.758142\pi\) | |||||||
\(150\) | 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 | −0.887841 | − | 0.460150i | \(-0.847796\pi\) |
0.460150 | + | 0.887841i | \(0.347796\pi\) | |||||||
\(158\) | −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 | \(-0.722739\pi\) | ||
0.644030 | − | 0.765000i | \(-0.277261\pi\) | |||||||
\(182\) | −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 | \(-0.728485\pi\) | ||
0.657734 | − | 0.753251i | \(-0.271515\pi\) | |||||||
\(192\) | −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 | \(-0.547228\pi\) | ||||
−0.147829 | + | 0.989013i | \(0.547228\pi\) | |||||||
\(200\) | −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 | ||||||
\(207\) | 4.49658 | + | 1.66757i | 0.312534 | + | 0.115904i | ||||
\(208\) | 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 | −0.777228 | − | 0.629219i | \(-0.783375\pi\) |
0.629219 | + | 0.777228i | \(0.283375\pi\) | |||||||
\(228\) | −0.537068 | − | 0.537068i | −0.0355682 | − | 0.0355682i | ||||
\(229\) | −5.86090 | −0.387299 | −0.193650 | − | 0.981071i | \(-0.562032\pi\) | ||||
−0.193650 | + | 0.981071i | \(0.562032\pi\) | |||||||
\(230\) | −10.3989 | + | 2.61951i | −0.685686 | + | 0.172725i | ||||
\(231\) | −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 | \(-0.794876\pi\) | ||
0.799451 | − | 0.600731i | \(-0.205124\pi\) | |||||||
\(242\) | −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 | \(-0.724762\pi\) | ||
0.648880 | − | 0.760890i | \(-0.275238\pi\) | |||||||
\(252\) | 1.64584 | − | 1.64584i | 0.103678 | − | 0.103678i | ||||
\(253\) | 27.4883 | + | 10.1941i | 1.72818 | + | 0.640900i | ||||
\(254\) | − | 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 | \(-0.999312\pi\) |
−0.00216013 | − | 0.999998i | \(-0.500688\pi\) | |||||||
\(264\) | 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 | \(0.283222\pi\) | ||||
−0.629592 | + | 0.776926i | \(0.716778\pi\) | |||||||
\(282\) | 1.46451 | + | 1.46451i | 0.0872106 | + | 0.0872106i | ||||
\(283\) | −5.48295 | − | 5.48295i | −0.325928 | − | 0.325928i | 0.525108 | − | 0.851036i | \(-0.324025\pi\) |
−0.851036 | + | 0.525108i | \(0.824025\pi\) | |||||||
\(284\) | 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 | \(0.0279894\pi\) |
0.0878182 | + | 0.996137i | \(0.472011\pi\) | |||||||
\(294\) | 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 | 0.567228 | − | 0.823561i | \(-0.308016\pi\) |
−0.823561 | + | 0.567228i | \(0.808016\pi\) | |||||||
\(314\) | −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 | ||||||
\(322\) | −3.88139 | + | 10.4661i | −0.216301 | + | 0.583254i | ||||
\(323\) | −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 | −0.131363 | − | 0.991334i | \(-0.541935\pi\) |
0.991334 | + | 0.131363i | \(0.0419354\pi\) | |||||||
\(338\) | −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 | ||||||||
\(345\) | 2.61951 | + | 10.3989i | 0.141030 | + | 0.559861i | ||||
\(346\) | 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 | \(-0.169670\pi\) | ||||
0.861269 | + | 0.508150i | \(0.169670\pi\) | |||||||
\(360\) | 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 | \(-0.427272\pi\) |
0.974011 | − | 0.226499i | \(-0.0727281\pi\) | |||||||
\(368\) | 1.66757 | − | 4.49658i | 0.0869281 | − | 0.234400i | ||||
\(369\) | − | 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 | 0.983194 | − | 0.182564i | \(-0.0584398\pi\) |
−0.182564 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(374\) | − | 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 | \(-0.592009\pi\) | ||||
−0.285048 | + | 0.958513i | \(0.592009\pi\) | |||||||
\(380\) | 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 | 0.998335 | − | 0.0576815i | \(-0.0183708\pi\) |
−0.0576815 | + | 0.998335i | \(0.518371\pi\) | |||||||
\(384\) | − | 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 | \(-0.681513\pi\) | ||||
−0.539833 | + | 0.841772i | \(0.681513\pi\) | |||||||
\(390\) | −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 | \(0.0749528\pi\) | ||||
−0.972405 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(402\) | −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 | \(-0.539838\pi\) | ||||
−0.124827 | + | 0.992178i | \(0.539838\pi\) | |||||||
\(420\) | 5.11723 | + | 0.949699i | 0.249695 | + | 0.0463406i | ||||
\(421\) | 5.71253i | 0.278412i | 0.990263 | + | 0.139206i | \(0.0444550\pi\) | ||||
−0.990263 | + | 0.139206i | \(0.955545\pi\) | |||||||
\(422\) | 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 | \(-0.974771\pi\) | ||
0.996861 | − | 0.0791753i | \(-0.0252287\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −11.6374 | − | 11.6374i | −0.559256 | − | 0.559256i | 0.369840 | − | 0.929096i | \(-0.379413\pi\) |
−0.929096 | + | 0.369840i | \(0.879413\pi\) | |||||||
\(434\) | −19.3319 | −0.927961 | ||||||||
\(435\) | 8.98334 | + | 13.0776i | 0.430718 | + | 0.627023i | ||||
\(436\) | − | 14.4446i | − | 0.691771i | ||||||
\(437\) | 1.26657 | − | 3.41528i | 0.0605882 | − | 0.163375i | ||||
\(438\) | 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 | −0.124672 | − | 0.992198i | \(-0.539788\pi\) |
0.992198 | + | 0.124672i | \(0.0397878\pi\) | |||||||
\(458\) | −4.14428 | − | 4.14428i | −0.193650 | − | 0.193650i | ||||
\(459\) | −0.462678 | −0.0215960 | ||||||||
\(460\) | −9.20544 | − | 5.50089i | −0.429206 | − | 0.256481i | ||||
\(461\) | 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 | \(0.535903\pi\) |
−0.993646 | + | 0.112554i | \(0.964097\pi\) | |||||||
\(468\) | −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 | \(-0.580957\pi\) | ||||
−0.251600 | + | 0.967831i | \(0.580957\pi\) | |||||||
\(480\) | −2.19853 | − | 0.408021i | −0.100349 | − | 0.0186235i | ||||
\(481\) | − | 0.930181i | − | 0.0424126i | ||||||
\(482\) | 13.1887 | − | 13.1887i | 0.600731 | − | 0.600731i | ||||
\(483\) | 10.4661 | + | 3.88139i | 0.476225 | + | 0.176609i | ||||
\(484\) | − | 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 | 0.759064 | − | 0.651016i | \(-0.225657\pi\) |
−0.651016 | + | 0.759064i | \(0.725657\pi\) | |||||||
\(504\) | 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 | \(0.0606567\pi\) | ||||
−0.981899 | + | 0.189407i | \(0.939343\pi\) | |||||||
\(522\) | 5.01721 | + | 5.01721i | 0.219597 | + | 0.219597i | ||||
\(523\) | −22.1099 | − | 22.1099i | −0.966800 | − | 0.966800i | 0.0326665 | − | 0.999466i | \(-0.489600\pi\) |
−0.999466 | + | 0.0326665i | \(0.989600\pi\) | |||||||
\(524\) | 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 | ||||||
\(552\) | −4.49658 | − | 1.66757i | −0.191387 | − | 0.0709765i | ||||
\(553\) | −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 | −0.758522 | − | 0.651647i | \(-0.774078\pi\) |
0.651647 | + | 0.758522i | \(0.274078\pi\) | |||||||
\(558\) | −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 | \(-0.954751\pi\) |
−0.141675 | − | 0.989913i | \(-0.545249\pi\) | |||||||
\(564\) | 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 | \(-0.382207\pi\) | ||||
0.361668 | + | 0.932307i | \(0.382207\pi\) | |||||||
\(570\) | −1.66985 | − | 0.309904i | −0.0699421 | − | 0.0129805i | ||||
\(571\) | 43.9751i | 1.84030i | 0.391565 | + | 0.920151i | \(0.371934\pi\) | ||||
−0.391565 | + | 0.920151i | \(0.628066\pi\) | |||||||
\(572\) | −1.47619 | + | 1.47619i | −0.0617227 | + | 0.0617227i | ||||
\(573\) | −14.7221 | − | 14.7221i | −0.615027 | − | 0.615027i | ||||
\(574\) | 15.7150 | 0.655932 | ||||||||
\(575\) | −15.8499 | + | 17.9939i | −0.660986 | + | 0.750399i | ||||
\(576\) | −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 | ||||
\(598\) | 0.569476 | − | 1.53558i | 0.0232876 | − | 0.0627947i | ||||
\(599\) | − | 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 | 0.799649 | − | 0.600468i | \(-0.205019\pi\) |
−0.600468 | + | 0.799649i | \(0.705019\pi\) | |||||||
\(614\) | 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 | \(0.536979\pi\) |
−0.993260 | + | 0.115911i | \(0.963021\pi\) | |||||||
\(618\) | −1.60298 | − | 1.60298i | −0.0644812 | − | 0.0644812i | ||||
\(619\) | −14.2298 | −0.571945 | −0.285972 | − | 0.958238i | \(-0.592317\pi\) | ||||
−0.285972 | + | 0.958238i | \(0.592317\pi\) | |||||||
\(620\) | 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 | \(0.128905\pi\) | ||||
−0.919115 | + | 0.393990i | \(0.871095\pi\) | |||||||
\(632\) | 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 | \(0.210967\pi\) | ||||
−0.788289 | + | 0.615306i | \(0.789033\pi\) | |||||||
\(642\) | 9.95278 | − | 9.95278i | 0.392805 | − | 0.392805i | ||||
\(643\) | −21.5814 | − | 21.5814i | −0.851087 | − | 0.851087i | 0.139180 | − | 0.990267i | \(-0.455553\pi\) |
−0.990267 | + | 0.139180i | \(0.955553\pi\) | |||||||
\(644\) | −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 | \(-0.476373\pi\) | ||||
0.0741592 | + | 0.997246i | \(0.476373\pi\) | |||||||
\(660\) | 11.2672 | − | 7.73975i | 0.438576 | − | 0.301269i | ||||
\(661\) | − | 4.54043i | − | 0.176602i | −0.996094 | − | 0.0883010i | \(-0.971856\pi\) | ||
0.996094 | − | 0.0883010i | \(-0.0281438\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | −31.9050 | − | 11.8321i | −1.23537 | − | 0.458140i | ||||
\(668\) | −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 | \(0.609561\pi\) |
−0.941347 | + | 0.337440i | \(0.890439\pi\) | |||||||
\(678\) | −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 | ||||||||
\(690\) | −5.50089 | + | 9.20544i | −0.209415 | + | 0.350445i | ||||
\(691\) | −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 | \(-0.966580\pi\) | ||
0.994493 | − | 0.104800i | \(-0.0334203\pi\) | |||||||
\(702\) | 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 | \(-0.780567\pi\) | ||||
−0.771647 | + | 0.636051i | \(0.780567\pi\) | |||||||
\(710\) | 7.90147 | + | 11.5026i | 0.296537 | + | 0.431687i | ||||
\(711\) | 3.83429i | 0.143797i | ||||||||
\(712\) | −3.28296 | + | 3.28296i | −0.123034 | + | 0.123034i | ||||
\(713\) | 13.8502 | − | 37.3468i | 0.518693 | − | 1.39865i | ||||
\(714\) | − | 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 | −0.772788 | − | 0.634664i | \(-0.781139\pi\) |
0.634664 | + | 0.772788i | \(0.281139\pi\) | |||||||
\(728\) | −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 | 0.580308 | − | 0.814397i | \(-0.302932\pi\) |
−0.814397 | + | 0.580308i | \(0.802932\pi\) | |||||||
\(734\) | 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 | 0.977389 | − | 0.211448i | \(-0.0678178\pi\) |
−0.211448 | + | 0.977389i | \(0.567818\pi\) | |||||||
\(744\) | − | 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 | \(0.0714142\pi\) | ||||
−0.974938 | + | 0.222477i | \(0.928586\pi\) | |||||||
\(752\) | −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 | −0.412543 | − | 0.910938i | \(-0.635359\pi\) |
0.910938 | + | 0.412543i | \(0.135359\pi\) | |||||||
\(758\) | −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 | \(-0.316790\pi\) | ||||
0.544313 | + | 0.838882i | \(0.316790\pi\) | |||||||
\(770\) | 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 | 0.849434 | − | 0.527694i | \(-0.176943\pi\) |
−0.527694 | + | 0.849434i | \(0.676943\pi\) | |||||||
\(774\) | −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 | ||||||
\(782\) | −0.771547 | + | 2.08047i | −0.0275905 | + | 0.0743973i | ||||
\(783\) | 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 | \(0.646930\pi\) |
−0.895344 | + | 0.445375i | \(0.853070\pi\) | |||||||
\(788\) | −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 | −0.360182 | − | 0.932882i | \(-0.617285\pi\) |
0.932882 | + | 0.360182i | \(0.117285\pi\) | |||||||
\(798\) | −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 | ||||||||
\(805\) | 6.09711 | + | 24.2043i | 0.214895 | + | 0.853090i | ||||
\(806\) | 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 | −0.275936 | − | 0.961176i | \(-0.588988\pi\) |
0.961176 | + | 0.275936i | \(0.0889876\pi\) | |||||||
\(828\) | −1.66757 | + | 4.49658i | −0.0579520 | + | 0.156267i | ||||
\(829\) | − | 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 | \(-0.841562\pi\) | ||||
−0.878660 | + | 0.477447i | \(0.841562\pi\) | |||||||
\(840\) | 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 | \(-0.637045\pi\) | ||
0.417361 | − | 0.908741i | \(-0.362955\pi\) | |||||||
\(882\) | 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 | ||||||
\(897\) | −1.53558 | − | 0.569476i | −0.0512717 | − | 0.0190143i | ||||
\(898\) | −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 | \(-0.495392\pi\) |
0.999895 | − | 0.0144762i | \(-0.00460808\pi\) | |||||||
\(908\) | −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 | \(-0.754412\pi\) | ||
0.716840 | − | 0.697237i | \(-0.245588\pi\) | |||||||
\(912\) | 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 | \(-0.465750\pi\) | ||||
0.107393 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(920\) | −2.61951 | − | 10.3989i | −0.0863627 | − | 0.342843i | ||||
\(921\) | 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 | −0.654872 | − | 0.755740i | \(-0.727278\pi\) |
0.755740 | + | 0.654872i | \(0.227278\pi\) | |||||||
\(938\) | −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 | \(-0.886148\pi\) | ||
0.936713 | − | 0.350099i | \(-0.113852\pi\) | |||||||
\(942\) | −5.35896 | + | 5.35896i | −0.174604 | + | 0.174604i | ||||
\(943\) | −11.2589 | + | 30.3594i | −0.366640 | + | 0.988639i | ||||
\(944\) | − | 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 | \(0.0666445\pi\) |
0.207843 | + | 0.978162i | \(0.433356\pi\) | |||||||
\(954\) | 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 | \(0.0954677\pi\) | ||||
−0.955360 | + | 0.295444i | \(0.904532\pi\) | |||||||
\(972\) | −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 | −0.0173847 | − | 0.999849i | \(-0.505534\pi\) |
0.999849 | + | 0.0173847i | \(0.00553401\pi\) | |||||||
\(978\) | 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 | 0.915724 | − | 0.401808i | \(-0.131618\pi\) |
−0.401808 | + | 0.915724i | \(0.631618\pi\) | |||||||
\(984\) | 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.367.12 | yes | 24 | |
5.3 | odd | 4 | inner | 690.2.j.b.643.7 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.367.7 | ✓ | 24 | |
115.68 | even | 4 | inner | 690.2.j.b.643.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.7 | ✓ | 24 | 23.22 | odd | 2 | inner | |
690.2.j.b.367.12 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.643.7 | yes | 24 | 5.3 | odd | 4 | inner | |
690.2.j.b.643.12 | yes | 24 | 115.68 | even | 4 | inner |