Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1121,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.8 | ||
Character | \(\chi\) | \(=\) | 1155.1121 |
Dual form | 1155.2.l.e.1121.7 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04560 | −1.44646 | −0.723228 | − | 0.690609i | \(-0.757342\pi\) | ||||
−0.723228 | + | 0.690609i | \(0.757342\pi\) | |||||||
\(3\) | −1.22443 | + | 1.22506i | −0.706926 | + | 0.707287i | ||||
\(4\) | 2.18447 | 1.09224 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 2.50470 | − | 2.50597i | 1.02254 | − | 1.02306i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −0.377355 | −0.133415 | ||||||||
\(9\) | −0.00153018 | − | 3.00000i | −0.000510061 | − | 1.00000i | ||||
\(10\) | 2.04560i | 0.646875i | ||||||||
\(11\) | −0.566637 | − | 3.26786i | −0.170847 | − | 0.985298i | ||||
\(12\) | −2.67474 | + | 2.67610i | −0.772130 | + | 0.772524i | ||||
\(13\) | 2.37539i | 0.658814i | 0.944188 | + | 0.329407i | \(0.106849\pi\) | ||||
−0.944188 | + | 0.329407i | \(0.893151\pi\) | |||||||
\(14\) | − | 2.04560i | − | 0.546709i | ||||||
\(15\) | 1.22506 | + | 1.22443i | 0.316308 | + | 0.316147i | ||||
\(16\) | −3.59703 | −0.899257 | ||||||||
\(17\) | −4.73436 | −1.14825 | −0.574125 | − | 0.818768i | \(-0.694658\pi\) | ||||
−0.574125 | + | 0.818768i | \(0.694658\pi\) | |||||||
\(18\) | 0.00313014 | + | 6.13679i | 0.000737781 | + | 1.44646i | ||||
\(19\) | 0.636972i | 0.146131i | 0.997327 | + | 0.0730657i | \(0.0232783\pi\) | ||||
−0.997327 | + | 0.0730657i | \(0.976722\pi\) | |||||||
\(20\) | − | 2.18447i | − | 0.488463i | ||||||
\(21\) | −1.22506 | − | 1.22443i | −0.267329 | − | 0.267193i | ||||
\(22\) | 1.15911 | + | 6.68473i | 0.247123 | + | 1.42519i | ||||
\(23\) | − | 4.83595i | − | 1.00837i | −0.863597 | − | 0.504183i | \(-0.831794\pi\) | ||
0.863597 | − | 0.504183i | \(-0.168206\pi\) | |||||||
\(24\) | 0.462046 | − | 0.462281i | 0.0943147 | − | 0.0943628i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 4.85909i | − | 0.952946i | ||||||
\(27\) | 3.67704 | + | 3.67142i | 0.707648 | + | 0.706566i | ||||
\(28\) | 2.18447i | 0.412826i | ||||||||
\(29\) | 4.70001 | 0.872769 | 0.436385 | − | 0.899760i | \(-0.356259\pi\) | ||||
0.436385 | + | 0.899760i | \(0.356259\pi\) | |||||||
\(30\) | −2.50597 | − | 2.50470i | −0.457526 | − | 0.457293i | ||||
\(31\) | 1.83079 | 0.328820 | 0.164410 | − | 0.986392i | \(-0.447428\pi\) | ||||
0.164410 | + | 0.986392i | \(0.447428\pi\) | |||||||
\(32\) | 8.11278 | 1.43415 | ||||||||
\(33\) | 4.69713 | + | 3.30711i | 0.817665 | + | 0.575695i | ||||
\(34\) | 9.68459 | 1.66089 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.00334264 | − | 6.55341i | −0.000557107 | − | 1.09224i | ||||
\(37\) | 5.92338 | 0.973798 | 0.486899 | − | 0.873458i | \(-0.338128\pi\) | ||||
0.486899 | + | 0.873458i | \(0.338128\pi\) | |||||||
\(38\) | − | 1.30299i | − | 0.211373i | ||||||
\(39\) | −2.90999 | − | 2.90850i | −0.465971 | − | 0.465733i | ||||
\(40\) | 0.377355i | 0.0596650i | ||||||||
\(41\) | −6.62936 | −1.03533 | −0.517666 | − | 0.855583i | \(-0.673199\pi\) | ||||
−0.517666 | + | 0.855583i | \(0.673199\pi\) | |||||||
\(42\) | 2.50597 | + | 2.50470i | 0.386680 | + | 0.386483i | ||||
\(43\) | 10.1301i | 1.54482i | 0.635123 | + | 0.772411i | \(0.280949\pi\) | ||||
−0.635123 | + | 0.772411i | \(0.719051\pi\) | |||||||
\(44\) | −1.23780 | − | 7.13855i | −0.186606 | − | 1.07618i | ||||
\(45\) | −3.00000 | + | 0.00153018i | −0.447214 | + | 0.000228106i | ||||
\(46\) | 9.89242i | 1.45856i | ||||||||
\(47\) | 11.3883i | 1.66115i | 0.556909 | + | 0.830574i | \(0.311987\pi\) | ||||
−0.556909 | + | 0.830574i | \(0.688013\pi\) | |||||||
\(48\) | 4.40432 | − | 4.40656i | 0.635708 | − | 0.636033i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 2.04560 | 0.289291 | ||||||||
\(51\) | 5.79690 | − | 5.79986i | 0.811728 | − | 0.812142i | ||||
\(52\) | 5.18897i | 0.719580i | ||||||||
\(53\) | − | 6.88591i | − | 0.945852i | −0.881102 | − | 0.472926i | \(-0.843198\pi\) | ||
0.881102 | − | 0.472926i | \(-0.156802\pi\) | |||||||
\(54\) | −7.52176 | − | 7.51025i | −1.02358 | − | 1.02202i | ||||
\(55\) | −3.26786 | + | 0.566637i | −0.440638 | + | 0.0764053i | ||||
\(56\) | − | 0.377355i | − | 0.0504262i | ||||||
\(57\) | −0.780327 | − | 0.779929i | −0.103357 | − | 0.103304i | ||||
\(58\) | −9.61432 | −1.26242 | ||||||||
\(59\) | − | 1.96672i | − | 0.256045i | −0.991771 | − | 0.128023i | \(-0.959137\pi\) | ||
0.991771 | − | 0.128023i | \(-0.0408630\pi\) | |||||||
\(60\) | 2.67610 | + | 2.67474i | 0.345483 | + | 0.345307i | ||||
\(61\) | − | 3.95587i | − | 0.506497i | −0.967401 | − | 0.253248i | \(-0.918501\pi\) | ||
0.967401 | − | 0.253248i | \(-0.0814990\pi\) | |||||||
\(62\) | −3.74507 | −0.475624 | ||||||||
\(63\) | 3.00000 | − | 0.00153018i | 0.377964 | − | 0.000192785i | ||||
\(64\) | −9.40144 | −1.17518 | ||||||||
\(65\) | 2.37539 | 0.294631 | ||||||||
\(66\) | −9.60843 | − | 6.76503i | −1.18272 | − | 0.832717i | ||||
\(67\) | 0.542784 | 0.0663116 | 0.0331558 | − | 0.999450i | \(-0.489444\pi\) | ||||
0.0331558 | + | 0.999450i | \(0.489444\pi\) | |||||||
\(68\) | −10.3421 | −1.25416 | ||||||||
\(69\) | 5.92432 | + | 5.92130i | 0.713204 | + | 0.712840i | ||||
\(70\) | −2.04560 | −0.244496 | ||||||||
\(71\) | 6.29497i | 0.747076i | 0.927615 | + | 0.373538i | \(0.121855\pi\) | ||||
−0.927615 | + | 0.373538i | \(0.878145\pi\) | |||||||
\(72\) | 0.000577422 | 1.13206i | 6.80499e−5 | 0.133415i | ||||||
\(73\) | 6.85940i | 0.802832i | 0.915896 | + | 0.401416i | \(0.131482\pi\) | ||||
−0.915896 | + | 0.401416i | \(0.868518\pi\) | |||||||
\(74\) | −12.1169 | −1.40856 | ||||||||
\(75\) | 1.22443 | − | 1.22506i | 0.141385 | − | 0.141457i | ||||
\(76\) | 1.39145i | 0.159610i | ||||||||
\(77\) | 3.26786 | − | 0.566637i | 0.372407 | − | 0.0645742i | ||||
\(78\) | 5.95266 | + | 5.94963i | 0.674006 | + | 0.673662i | ||||
\(79\) | − | 6.24475i | − | 0.702590i | −0.936265 | − | 0.351295i | \(-0.885741\pi\) | ||
0.936265 | − | 0.351295i | \(-0.114259\pi\) | |||||||
\(80\) | 3.59703i | 0.402160i | ||||||||
\(81\) | −9.00000 | + | 0.00918110i | −0.999999 | + | 0.00102012i | ||||
\(82\) | 13.5610 | 1.49756 | ||||||||
\(83\) | 2.16097 | 0.237197 | 0.118599 | − | 0.992942i | \(-0.462160\pi\) | ||||
0.118599 | + | 0.992942i | \(0.462160\pi\) | |||||||
\(84\) | −2.67610 | − | 2.67474i | −0.291987 | − | 0.291838i | ||||
\(85\) | 4.73436i | 0.513513i | ||||||||
\(86\) | − | 20.7221i | − | 2.23452i | ||||||
\(87\) | −5.75484 | + | 5.75778i | −0.616984 | + | 0.617298i | ||||
\(88\) | 0.213823 | + | 1.23314i | 0.0227936 | + | 0.131454i | ||||
\(89\) | 12.4798i | 1.32286i | 0.750008 | + | 0.661428i | \(0.230049\pi\) | ||||
−0.750008 | + | 0.661428i | \(0.769951\pi\) | |||||||
\(90\) | 6.13679 | − | 0.00313014i | 0.646875 | − | 0.000329946i | ||||
\(91\) | −2.37539 | −0.249008 | ||||||||
\(92\) | − | 10.5640i | − | 1.10137i | ||||||
\(93\) | −2.24168 | + | 2.24283i | −0.232452 | + | 0.232570i | ||||
\(94\) | − | 23.2958i | − | 2.40278i | ||||||
\(95\) | 0.636972 | 0.0653519 | ||||||||
\(96\) | −9.93355 | + | 9.93862i | −1.01384 | + | 1.01436i | ||||
\(97\) | −14.6880 | −1.49134 | −0.745668 | − | 0.666318i | \(-0.767869\pi\) | ||||
−0.745668 | + | 0.666318i | \(0.767869\pi\) | |||||||
\(98\) | 2.04560 | 0.206637 | ||||||||
\(99\) | −9.80272 | + | 1.70491i | −0.985210 | + | 0.171350i | ||||
\(100\) | −2.18447 | −0.218447 | ||||||||
\(101\) | −17.4470 | −1.73604 | −0.868019 | − | 0.496531i | \(-0.834607\pi\) | ||||
−0.868019 | + | 0.496531i | \(0.834607\pi\) | |||||||
\(102\) | −11.8581 | + | 11.8642i | −1.17413 | + | 1.17473i | ||||
\(103\) | −14.0733 | −1.38668 | −0.693340 | − | 0.720611i | \(-0.743861\pi\) | ||||
−0.693340 | + | 0.720611i | \(0.743861\pi\) | |||||||
\(104\) | − | 0.896364i | − | 0.0878957i | ||||||
\(105\) | −1.22443 | + | 1.22506i | −0.119492 | + | 0.119553i | ||||
\(106\) | 14.0858i | 1.36813i | ||||||||
\(107\) | −4.73757 | −0.457998 | −0.228999 | − | 0.973427i | \(-0.573545\pi\) | ||||
−0.228999 | + | 0.973427i | \(0.573545\pi\) | |||||||
\(108\) | 8.03240 | + | 8.02012i | 0.772918 | + | 0.771736i | ||||
\(109\) | 7.36247i | 0.705197i | 0.935775 | + | 0.352598i | \(0.114702\pi\) | ||||
−0.935775 | + | 0.352598i | \(0.885298\pi\) | |||||||
\(110\) | 6.68473 | − | 1.15911i | 0.637364 | − | 0.110517i | ||||
\(111\) | −7.25278 | + | 7.25648i | −0.688404 | + | 0.688755i | ||||
\(112\) | − | 3.59703i | − | 0.339887i | ||||||
\(113\) | − | 2.79872i | − | 0.263281i | −0.991298 | − | 0.131641i | \(-0.957976\pi\) | ||
0.991298 | − | 0.131641i | \(-0.0420245\pi\) | |||||||
\(114\) | 1.59624 | + | 1.59542i | 0.149501 | + | 0.149425i | ||||
\(115\) | −4.83595 | −0.450955 | ||||||||
\(116\) | 10.2670 | 0.953270 | ||||||||
\(117\) | 7.12616 | − | 0.00363478i | 0.658814 | − | 0.000336035i | ||||
\(118\) | 4.02312i | 0.370359i | ||||||||
\(119\) | − | 4.73436i | − | 0.433998i | ||||||
\(120\) | −0.462281 | − | 0.462046i | −0.0422003 | − | 0.0421788i | ||||
\(121\) | −10.3578 | + | 3.70338i | −0.941622 | + | 0.336671i | ||||
\(122\) | 8.09211i | 0.732625i | ||||||||
\(123\) | 8.11721 | − | 8.12135i | 0.731904 | − | 0.732277i | ||||
\(124\) | 3.99931 | 0.359149 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −6.13679 | + | 0.00313014i | −0.546709 | + | 0.000278855i | ||||
\(127\) | 13.1403i | 1.16601i | 0.812467 | + | 0.583007i | \(0.198124\pi\) | ||||
−0.812467 | + | 0.583007i | \(0.801876\pi\) | |||||||
\(128\) | 3.00600 | 0.265695 | ||||||||
\(129\) | −12.4099 | − | 12.4036i | −1.09263 | − | 1.09208i | ||||
\(130\) | −4.85909 | −0.426170 | ||||||||
\(131\) | 6.43379 | 0.562123 | 0.281061 | − | 0.959690i | \(-0.409314\pi\) | ||||
0.281061 | + | 0.959690i | \(0.409314\pi\) | |||||||
\(132\) | 10.2607 | + | 7.22430i | 0.893083 | + | 0.628794i | ||||
\(133\) | −0.636972 | −0.0552325 | ||||||||
\(134\) | −1.11032 | −0.0959168 | ||||||||
\(135\) | 3.67142 | − | 3.67704i | 0.315986 | − | 0.316470i | ||||
\(136\) | 1.78653 | 0.153194 | ||||||||
\(137\) | 16.6169i | 1.41968i | 0.704363 | + | 0.709840i | \(0.251233\pi\) | ||||
−0.704363 | + | 0.709840i | \(0.748767\pi\) | |||||||
\(138\) | −12.1188 | − | 12.1126i | −1.03162 | − | 1.03109i | ||||
\(139\) | 9.29709i | 0.788569i | 0.918988 | + | 0.394285i | \(0.129008\pi\) | ||||
−0.918988 | + | 0.394285i | \(0.870992\pi\) | |||||||
\(140\) | 2.18447 | 0.184622 | ||||||||
\(141\) | −13.9513 | − | 13.9441i | −1.17491 | − | 1.17431i | ||||
\(142\) | − | 12.8770i | − | 1.08061i | ||||||
\(143\) | 7.76244 | − | 1.34598i | 0.649128 | − | 0.112557i | ||||
\(144\) | 0.00550411 | + | 10.7911i | 0.000458676 | + | 0.899257i | ||||
\(145\) | − | 4.70001i | − | 0.390314i | ||||||
\(146\) | − | 14.0316i | − | 1.16126i | ||||||
\(147\) | 1.22443 | − | 1.22506i | 0.100989 | − | 0.101041i | ||||
\(148\) | 12.9395 | 1.06362 | ||||||||
\(149\) | −15.5271 | −1.27203 | −0.636014 | − | 0.771678i | \(-0.719418\pi\) | ||||
−0.636014 | + | 0.771678i | \(0.719418\pi\) | |||||||
\(150\) | −2.50470 | + | 2.50597i | −0.204508 | + | 0.204612i | ||||
\(151\) | − | 4.91642i | − | 0.400092i | −0.979786 | − | 0.200046i | \(-0.935891\pi\) | ||
0.979786 | − | 0.200046i | \(-0.0641092\pi\) | |||||||
\(152\) | − | 0.240364i | − | 0.0194961i | ||||||
\(153\) | 0.00724443 | + | 14.2031i | 0.000585678 | + | 1.14825i | ||||
\(154\) | −6.68473 | + | 1.15911i | −0.538671 | + | 0.0934038i | ||||
\(155\) | − | 1.83079i | − | 0.147053i | ||||||
\(156\) | −6.35678 | − | 6.35354i | −0.508950 | − | 0.508690i | ||||
\(157\) | 6.37551 | 0.508821 | 0.254410 | − | 0.967096i | \(-0.418119\pi\) | ||||
0.254410 | + | 0.967096i | \(0.418119\pi\) | |||||||
\(158\) | 12.7743i | 1.01627i | ||||||||
\(159\) | 8.43563 | + | 8.43133i | 0.668989 | + | 0.668648i | ||||
\(160\) | − | 8.11278i | − | 0.641372i | ||||||
\(161\) | 4.83595 | 0.381126 | ||||||||
\(162\) | 18.4104 | − | 0.0187808i | 1.44646 | − | 0.00147556i | ||||
\(163\) | −17.0281 | −1.33374 | −0.666872 | − | 0.745173i | \(-0.732367\pi\) | ||||
−0.666872 | + | 0.745173i | \(0.732367\pi\) | |||||||
\(164\) | −14.4817 | −1.13083 | ||||||||
\(165\) | 3.30711 | − | 4.69713i | 0.257459 | − | 0.365671i | ||||
\(166\) | −4.42047 | −0.343095 | ||||||||
\(167\) | 17.5347 | 1.35687 | 0.678437 | − | 0.734659i | \(-0.262658\pi\) | ||||
0.678437 | + | 0.734659i | \(0.262658\pi\) | |||||||
\(168\) | 0.462281 | + | 0.462046i | 0.0356658 | + | 0.0356476i | ||||
\(169\) | 7.35753 | 0.565964 | ||||||||
\(170\) | − | 9.68459i | − | 0.742774i | ||||||
\(171\) | 1.91092 | 0.000974684i | 0.146131 | 7.45359e-5i | ||||||
\(172\) | 22.1289i | 1.68731i | ||||||||
\(173\) | −21.7187 | −1.65124 | −0.825620 | − | 0.564227i | \(-0.809174\pi\) | ||||
−0.825620 | + | 0.564227i | \(0.809174\pi\) | |||||||
\(174\) | 11.7721 | − | 11.7781i | 0.892440 | − | 0.892895i | ||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | 2.03821 | + | 11.7546i | 0.153636 | + | 0.886035i | ||||
\(177\) | 2.40935 | + | 2.40812i | 0.181098 | + | 0.181005i | ||||
\(178\) | − | 25.5287i | − | 1.91345i | ||||||
\(179\) | 22.4731i | 1.67972i | 0.542804 | + | 0.839859i | \(0.317363\pi\) | ||||
−0.542804 | + | 0.839859i | \(0.682637\pi\) | |||||||
\(180\) | −6.55341 | + | 0.00334264i | −0.488463 | + | 0.000249146i | ||||
\(181\) | −2.04960 | −0.152346 | −0.0761728 | − | 0.997095i | \(-0.524270\pi\) | ||||
−0.0761728 | + | 0.997095i | \(0.524270\pi\) | |||||||
\(182\) | 4.85909 | 0.360180 | ||||||||
\(183\) | 4.84616 | + | 4.84369i | 0.358239 | + | 0.358056i | ||||
\(184\) | 1.82487i | 0.134531i | ||||||||
\(185\) | − | 5.92338i | − | 0.435496i | ||||||
\(186\) | 4.58558 | − | 4.58792i | 0.336231 | − | 0.336403i | ||||
\(187\) | 2.68266 | + | 15.4712i | 0.196175 | + | 1.13137i | ||||
\(188\) | 24.8773i | 1.81436i | ||||||||
\(189\) | −3.67142 | + | 3.67704i | −0.267057 | + | 0.267466i | ||||
\(190\) | −1.30299 | −0.0945287 | ||||||||
\(191\) | − | 2.33032i | − | 0.168616i | −0.996440 | − | 0.0843080i | \(-0.973132\pi\) | ||
0.996440 | − | 0.0843080i | \(-0.0268680\pi\) | |||||||
\(192\) | 11.5114 | − | 11.5173i | 0.830765 | − | 0.831189i | ||||
\(193\) | − | 5.98755i | − | 0.430993i | −0.976505 | − | 0.215497i | \(-0.930863\pi\) | ||
0.976505 | − | 0.215497i | \(-0.0691371\pi\) | |||||||
\(194\) | 30.0456 | 2.15715 | ||||||||
\(195\) | −2.90850 | + | 2.90999i | −0.208282 | + | 0.208388i | ||||
\(196\) | −2.18447 | −0.156034 | ||||||||
\(197\) | −15.4447 | −1.10039 | −0.550194 | − | 0.835037i | \(-0.685446\pi\) | ||||
−0.550194 | + | 0.835037i | \(0.685446\pi\) | |||||||
\(198\) | 20.0524 | − | 3.48756i | 1.42506 | − | 0.247850i | ||||
\(199\) | 20.7622 | 1.47179 | 0.735896 | − | 0.677095i | \(-0.236761\pi\) | ||||
0.735896 | + | 0.677095i | \(0.236761\pi\) | |||||||
\(200\) | 0.377355 | 0.0266830 | ||||||||
\(201\) | −0.664602 | + | 0.664941i | −0.0468774 | + | 0.0469013i | ||||
\(202\) | 35.6895 | 2.51110 | ||||||||
\(203\) | 4.70001i | 0.329876i | ||||||||
\(204\) | 12.6632 | − | 12.6696i | 0.886599 | − | 0.887051i | ||||
\(205\) | 6.62936i | 0.463015i | ||||||||
\(206\) | 28.7882 | 2.00577 | ||||||||
\(207\) | −14.5079 | + | 0.00739989i | −1.00837 | + | 0.000514328i | ||||
\(208\) | − | 8.54433i | − | 0.592443i | ||||||
\(209\) | 2.08154 | − | 0.360932i | 0.143983 | − | 0.0249662i | ||||
\(210\) | 2.50470 | − | 2.50597i | 0.172840 | − | 0.172929i | ||||
\(211\) | − | 17.1746i | − | 1.18235i | −0.806545 | − | 0.591173i | \(-0.798665\pi\) | ||
0.806545 | − | 0.591173i | \(-0.201335\pi\) | |||||||
\(212\) | − | 15.0421i | − | 1.03309i | ||||||
\(213\) | −7.71170 | − | 7.70777i | −0.528397 | − | 0.528128i | ||||
\(214\) | 9.69117 | 0.662475 | ||||||||
\(215\) | 10.1301 | 0.690865 | ||||||||
\(216\) | −1.38755 | − | 1.38543i | −0.0944109 | − | 0.0942665i | ||||
\(217\) | 1.83079i | 0.124282i | ||||||||
\(218\) | − | 15.0607i | − | 1.02004i | ||||||
\(219\) | −8.40316 | − | 8.39887i | −0.567833 | − | 0.567543i | ||||
\(220\) | −7.13855 | + | 1.23780i | −0.481281 | + | 0.0834526i | ||||
\(221\) | − | 11.2459i | − | 0.756483i | ||||||
\(222\) | 14.8363 | − | 14.8438i | 0.995746 | − | 0.996254i | ||||
\(223\) | 4.43349 | 0.296889 | 0.148444 | − | 0.988921i | \(-0.452573\pi\) | ||||
0.148444 | + | 0.988921i | \(0.452573\pi\) | |||||||
\(224\) | 8.11278i | 0.542058i | ||||||||
\(225\) | 0.00153018 | + | 3.00000i | 0.000102012 | + | 0.200000i | ||||
\(226\) | 5.72505i | 0.380825i | ||||||||
\(227\) | −6.23302 | −0.413700 | −0.206850 | − | 0.978373i | \(-0.566321\pi\) | ||||
−0.206850 | + | 0.978373i | \(0.566321\pi\) | |||||||
\(228\) | −1.70460 | − | 1.70373i | −0.112890 | − | 0.112832i | ||||
\(229\) | 0.909472 | 0.0600996 | 0.0300498 | − | 0.999548i | \(-0.490433\pi\) | ||||
0.0300498 | + | 0.999548i | \(0.490433\pi\) | |||||||
\(230\) | 9.89242 | 0.652287 | ||||||||
\(231\) | −3.30711 | + | 4.69713i | −0.217592 | + | 0.309048i | ||||
\(232\) | −1.77357 | −0.116441 | ||||||||
\(233\) | −27.6897 | −1.81401 | −0.907005 | − | 0.421120i | \(-0.861637\pi\) | ||||
−0.907005 | + | 0.421120i | \(0.861637\pi\) | |||||||
\(234\) | −14.5773 | + | 0.00743530i | −0.952946 | + | 0.000486061i | ||||
\(235\) | 11.3883 | 0.742888 | ||||||||
\(236\) | − | 4.29625i | − | 0.279662i | ||||||
\(237\) | 7.65018 | + | 7.64628i | 0.496933 | + | 0.496679i | ||||
\(238\) | 9.68459i | 0.627759i | ||||||||
\(239\) | 23.6267 | 1.52829 | 0.764143 | − | 0.645047i | \(-0.223162\pi\) | ||||
0.764143 | + | 0.645047i | \(0.223162\pi\) | |||||||
\(240\) | −4.40656 | − | 4.40432i | −0.284442 | − | 0.284297i | ||||
\(241\) | − | 11.4547i | − | 0.737865i | −0.929456 | − | 0.368932i | \(-0.879723\pi\) | ||
0.929456 | − | 0.368932i | \(-0.120277\pi\) | |||||||
\(242\) | 21.1880 | − | 7.57563i | 1.36202 | − | 0.486980i | ||||
\(243\) | 11.0086 | − | 11.0368i | 0.706205 | − | 0.708008i | ||||
\(244\) | − | 8.64148i | − | 0.553214i | ||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | −16.6045 | + | 16.6130i | −1.05867 | + | 1.05921i | ||||
\(247\) | −1.51306 | −0.0962734 | ||||||||
\(248\) | −0.690858 | −0.0438696 | ||||||||
\(249\) | −2.64596 | + | 2.64731i | −0.167681 | + | 0.167766i | ||||
\(250\) | − | 2.04560i | − | 0.129375i | ||||||
\(251\) | 22.5704i | 1.42463i | 0.701860 | + | 0.712315i | \(0.252353\pi\) | ||||
−0.701860 | + | 0.712315i | \(0.747647\pi\) | |||||||
\(252\) | 6.55341 | − | 0.00334264i | 0.412826 | − | 0.000210567i | ||||
\(253\) | −15.8032 | + | 2.74023i | −0.993540 | + | 0.172277i | ||||
\(254\) | − | 26.8798i | − | 1.68659i | ||||||
\(255\) | −5.79986 | − | 5.79690i | −0.363201 | − | 0.363016i | ||||
\(256\) | 12.6538 | 0.790863 | ||||||||
\(257\) | − | 3.44901i | − | 0.215143i | −0.994197 | − | 0.107572i | \(-0.965692\pi\) | ||
0.994197 | − | 0.107572i | \(-0.0343075\pi\) | |||||||
\(258\) | 25.3857 | + | 25.3728i | 1.58045 | + | 1.57964i | ||||
\(259\) | 5.92338i | 0.368061i | ||||||||
\(260\) | 5.18897 | 0.321806 | ||||||||
\(261\) | −0.00719187 | − | 14.1000i | −0.000445166 | − | 0.872769i | ||||
\(262\) | −13.1609 | −0.813086 | ||||||||
\(263\) | 21.1738 | 1.30563 | 0.652816 | − | 0.757516i | \(-0.273587\pi\) | ||||
0.652816 | + | 0.757516i | \(0.273587\pi\) | |||||||
\(264\) | −1.77248 | − | 1.24796i | −0.109089 | − | 0.0768064i | ||||
\(265\) | −6.88591 | −0.422998 | ||||||||
\(266\) | 1.30299 | 0.0798913 | ||||||||
\(267\) | −15.2885 | − | 15.2807i | −0.935640 | − | 0.935163i | ||||
\(268\) | 1.18570 | 0.0724279 | ||||||||
\(269\) | 24.0947i | 1.46908i | 0.678564 | + | 0.734541i | \(0.262603\pi\) | ||||
−0.678564 | + | 0.734541i | \(0.737397\pi\) | |||||||
\(270\) | −7.51025 | + | 7.52176i | −0.457060 | + | 0.457759i | ||||
\(271\) | − | 2.95183i | − | 0.179311i | −0.995973 | − | 0.0896553i | \(-0.971423\pi\) | ||
0.995973 | − | 0.0896553i | \(-0.0285765\pi\) | |||||||
\(272\) | 17.0296 | 1.03257 | ||||||||
\(273\) | 2.90850 | − | 2.90999i | 0.176031 | − | 0.176120i | ||||
\(274\) | − | 33.9916i | − | 2.05351i | ||||||
\(275\) | 0.566637 | + | 3.26786i | 0.0341695 | + | 0.197060i | ||||
\(276\) | 12.9415 | + | 12.9349i | 0.778987 | + | 0.778590i | ||||
\(277\) | 4.92236i | 0.295756i | 0.989006 | + | 0.147878i | \(0.0472443\pi\) | ||||
−0.989006 | + | 0.147878i | \(0.952756\pi\) | |||||||
\(278\) | − | 19.0181i | − | 1.14063i | ||||||
\(279\) | −0.00280145 | − | 5.49238i | −0.000167718 | − | 0.328820i | ||||
\(280\) | −0.377355 | −0.0225513 | ||||||||
\(281\) | 10.4955 | 0.626109 | 0.313054 | − | 0.949735i | \(-0.398648\pi\) | ||||
0.313054 | + | 0.949735i | \(0.398648\pi\) | |||||||
\(282\) | 28.5387 | + | 28.5241i | 1.69945 | + | 1.69859i | ||||
\(283\) | − | 9.10112i | − | 0.541006i | −0.962719 | − | 0.270503i | \(-0.912810\pi\) | ||
0.962719 | − | 0.270503i | \(-0.0871899\pi\) | |||||||
\(284\) | 13.7512i | 0.815983i | ||||||||
\(285\) | −0.779929 | + | 0.780327i | −0.0461990 | + | 0.0462226i | ||||
\(286\) | −15.8788 | + | 2.75334i | −0.938935 | + | 0.162808i | ||||
\(287\) | − | 6.62936i | − | 0.391319i | ||||||
\(288\) | −0.0124140 | − | 24.3383i | −0.000731504 | − | 1.43415i | ||||
\(289\) | 5.41413 | 0.318478 | ||||||||
\(290\) | 9.61432i | 0.564573i | ||||||||
\(291\) | 17.9844 | − | 17.9936i | 1.05426 | − | 1.05480i | ||||
\(292\) | 14.9842i | 0.876882i | ||||||||
\(293\) | −27.1116 | −1.58388 | −0.791939 | − | 0.610600i | \(-0.790928\pi\) | ||||
−0.791939 | + | 0.610600i | \(0.790928\pi\) | |||||||
\(294\) | −2.50470 | + | 2.50597i | −0.146077 | + | 0.146151i | ||||
\(295\) | −1.96672 | −0.114507 | ||||||||
\(296\) | −2.23522 | −0.129919 | ||||||||
\(297\) | 9.91415 | − | 14.0964i | 0.575278 | − | 0.817958i | ||||
\(298\) | 31.7621 | 1.83993 | ||||||||
\(299\) | 11.4873 | 0.664326 | ||||||||
\(300\) | 2.67474 | − | 2.67610i | 0.154426 | − | 0.154505i | ||||
\(301\) | −10.1301 | −0.583888 | ||||||||
\(302\) | 10.0570i | 0.578716i | ||||||||
\(303\) | 21.3626 | − | 21.3735i | 1.22725 | − | 1.22788i | ||||
\(304\) | − | 2.29120i | − | 0.131410i | ||||||
\(305\) | −3.95587 | −0.226512 | ||||||||
\(306\) | −0.0148192 | − | 29.0538i | −0.000847157 | − | 1.66089i | ||||
\(307\) | 5.75870i | 0.328666i | 0.986405 | + | 0.164333i | \(0.0525472\pi\) | ||||
−0.986405 | + | 0.164333i | \(0.947453\pi\) | |||||||
\(308\) | 7.13855 | − | 1.23780i | 0.406757 | − | 0.0705303i | ||||
\(309\) | 17.2318 | − | 17.2405i | 0.980280 | − | 0.980780i | ||||
\(310\) | 3.74507i | 0.212705i | ||||||||
\(311\) | − | 8.05967i | − | 0.457022i | −0.973541 | − | 0.228511i | \(-0.926614\pi\) | ||
0.973541 | − | 0.228511i | \(-0.0733857\pi\) | |||||||
\(312\) | 1.09810 | + | 1.09754i | 0.0621675 | + | 0.0621358i | ||||
\(313\) | −15.4684 | −0.874327 | −0.437164 | − | 0.899382i | \(-0.644017\pi\) | ||||
−0.437164 | + | 0.899382i | \(0.644017\pi\) | |||||||
\(314\) | −13.0417 | −0.735987 | ||||||||
\(315\) | −0.00153018 | − | 3.00000i | −8.62161e−5 | − | 0.169031i | ||||
\(316\) | − | 13.6415i | − | 0.767394i | ||||||
\(317\) | 1.78189i | 0.100081i | 0.998747 | + | 0.0500403i | \(0.0159350\pi\) | ||||
−0.998747 | + | 0.0500403i | \(0.984065\pi\) | |||||||
\(318\) | −17.2559 | − | 17.2471i | −0.967663 | − | 0.967170i | ||||
\(319\) | −2.66320 | − | 15.3590i | −0.149110 | − | 0.859937i | ||||
\(320\) | 9.40144i | 0.525556i | ||||||||
\(321\) | 5.80084 | − | 5.80380i | 0.323771 | − | 0.323936i | ||||
\(322\) | −9.89242 | −0.551283 | ||||||||
\(323\) | − | 3.01565i | − | 0.167795i | ||||||
\(324\) | −19.6602 | + | 0.0200558i | −1.09224 | + | 0.00111421i | ||||
\(325\) | − | 2.37539i | − | 0.131763i | ||||||
\(326\) | 34.8326 | 1.92920 | ||||||||
\(327\) | −9.01944 | − | 9.01485i | −0.498776 | − | 0.498522i | ||||
\(328\) | 2.50162 | 0.138129 | ||||||||
\(329\) | −11.3883 | −0.627855 | ||||||||
\(330\) | −6.76503 | + | 9.60843i | −0.372402 | + | 0.528927i | ||||
\(331\) | 26.3766 | 1.44979 | 0.724894 | − | 0.688861i | \(-0.241889\pi\) | ||||
0.724894 | + | 0.688861i | \(0.241889\pi\) | |||||||
\(332\) | 4.72058 | 0.259075 | ||||||||
\(333\) | −0.00906386 | − | 17.7701i | −0.000496697 | − | 0.973798i | ||||
\(334\) | −35.8689 | −1.96266 | ||||||||
\(335\) | − | 0.542784i | − | 0.0296554i | ||||||
\(336\) | 4.40656 | + | 4.40432i | 0.240398 | + | 0.240275i | ||||
\(337\) | 26.0748i | 1.42038i | 0.704008 | + | 0.710192i | \(0.251392\pi\) | ||||
−0.704008 | + | 0.710192i | \(0.748608\pi\) | |||||||
\(338\) | −15.0506 | −0.818642 | ||||||||
\(339\) | 3.42859 | + | 3.42684i | 0.186215 | + | 0.186120i | ||||
\(340\) | 10.3421i | 0.560877i | ||||||||
\(341\) | −1.03739 | − | 5.98278i | −0.0561780 | − | 0.323986i | ||||
\(342\) | −3.90896 | + | 0.00199381i | −0.211373 | + | 0.000107813i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 3.82263i | − | 0.206103i | ||||||
\(345\) | 5.92130 | − | 5.92432i | 0.318792 | − | 0.318955i | ||||
\(346\) | 44.4277 | 2.38845 | ||||||||
\(347\) | −32.5968 | −1.74989 | −0.874944 | − | 0.484225i | \(-0.839102\pi\) | ||||
−0.874944 | + | 0.484225i | \(0.839102\pi\) | |||||||
\(348\) | −12.5713 | + | 12.5777i | −0.673892 | + | 0.674235i | ||||
\(349\) | 23.6094i | 1.26378i | 0.775057 | + | 0.631891i | \(0.217721\pi\) | ||||
−0.775057 | + | 0.631891i | \(0.782279\pi\) | |||||||
\(350\) | 2.04560i | 0.109342i | ||||||||
\(351\) | −8.72105 | + | 8.73441i | −0.465495 | + | 0.466208i | ||||
\(352\) | −4.59700 | − | 26.5115i | −0.245021 | − | 1.41307i | ||||
\(353\) | 1.54586i | 0.0822778i | 0.999153 | + | 0.0411389i | \(0.0130986\pi\) | ||||
−0.999153 | + | 0.0411389i | \(0.986901\pi\) | |||||||
\(354\) | −4.92856 | − | 4.92604i | −0.261950 | − | 0.261816i | ||||
\(355\) | 6.29497 | 0.334102 | ||||||||
\(356\) | 27.2618i | 1.44487i | ||||||||
\(357\) | 5.79986 | + | 5.79690i | 0.306961 | + | 0.306804i | ||||
\(358\) | − | 45.9709i | − | 2.42964i | ||||||
\(359\) | −29.4604 | −1.55486 | −0.777430 | − | 0.628969i | \(-0.783477\pi\) | ||||
−0.777430 | + | 0.628969i | \(0.783477\pi\) | |||||||
\(360\) | 1.13206 | 0.000577422i | 0.0596650 | 3.04328e-5i | ||||||
\(361\) | 18.5943 | 0.978646 | ||||||||
\(362\) | 4.19266 | 0.220361 | ||||||||
\(363\) | 8.14563 | − | 17.2235i | 0.427535 | − | 0.903999i | ||||
\(364\) | −5.18897 | −0.271976 | ||||||||
\(365\) | 6.85940 | 0.359037 | ||||||||
\(366\) | −9.91330 | − | 9.90824i | −0.518176 | − | 0.517912i | ||||
\(367\) | 16.8829 | 0.881280 | 0.440640 | − | 0.897684i | \(-0.354751\pi\) | ||||
0.440640 | + | 0.897684i | \(0.354751\pi\) | |||||||
\(368\) | 17.3951i | 0.906780i | ||||||||
\(369\) | 0.0101441 | + | 19.8881i | 0.000528083 | + | 1.03533i | ||||
\(370\) | 12.1169i | 0.629926i | ||||||||
\(371\) | 6.88591 | 0.357498 | ||||||||
\(372\) | −4.89689 | + | 4.89939i | −0.253892 | + | 0.254021i | ||||
\(373\) | − | 7.88226i | − | 0.408128i | −0.978958 | − | 0.204064i | \(-0.934585\pi\) | ||
0.978958 | − | 0.204064i | \(-0.0654150\pi\) | |||||||
\(374\) | −5.48764 | − | 31.6479i | −0.283759 | − | 1.63647i | ||||
\(375\) | −1.22506 | − | 1.22443i | −0.0632617 | − | 0.0632294i | ||||
\(376\) | − | 4.29741i | − | 0.221622i | ||||||
\(377\) | 11.1643i | 0.574993i | ||||||||
\(378\) | 7.51025 | − | 7.52176i | 0.386286 | − | 0.386877i | ||||
\(379\) | −4.34576 | −0.223227 | −0.111613 | − | 0.993752i | \(-0.535602\pi\) | ||||
−0.111613 | + | 0.993752i | \(0.535602\pi\) | |||||||
\(380\) | 1.39145 | 0.0713797 | ||||||||
\(381\) | −16.0976 | − | 16.0894i | −0.824706 | − | 0.824286i | ||||
\(382\) | 4.76690i | 0.243896i | ||||||||
\(383\) | − | 20.1719i | − | 1.03073i | −0.856970 | − | 0.515367i | \(-0.827656\pi\) | ||
0.856970 | − | 0.515367i | \(-0.172344\pi\) | |||||||
\(384\) | −3.68064 | + | 3.68252i | −0.187827 | + | 0.187923i | ||||
\(385\) | −0.566637 | − | 3.26786i | −0.0288785 | − | 0.166546i | ||||
\(386\) | 12.2481i | 0.623413i | ||||||||
\(387\) | 30.3902 | − | 0.0155009i | 1.54482 | − | 0.000787954i | ||||
\(388\) | −32.0854 | −1.62889 | ||||||||
\(389\) | − | 20.0116i | − | 1.01463i | −0.861762 | − | 0.507313i | \(-0.830639\pi\) | ||
0.861762 | − | 0.507313i | \(-0.169361\pi\) | |||||||
\(390\) | 5.94963 | − | 5.95266i | 0.301271 | − | 0.301425i | ||||
\(391\) | 22.8951i | 1.15786i | ||||||||
\(392\) | 0.377355 | 0.0190593 | ||||||||
\(393\) | −7.87774 | + | 7.88176i | −0.397379 | + | 0.397582i | ||||
\(394\) | 31.5936 | 1.59166 | ||||||||
\(395\) | −6.24475 | −0.314208 | ||||||||
\(396\) | −21.4138 | + | 3.72433i | −1.07608 | + | 0.187154i | ||||
\(397\) | −5.93402 | −0.297820 | −0.148910 | − | 0.988851i | \(-0.547576\pi\) | ||||
−0.148910 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(398\) | −42.4711 | −2.12888 | ||||||||
\(399\) | 0.779929 | − | 0.780327i | 0.0390453 | − | 0.0390652i | ||||
\(400\) | 3.59703 | 0.179851 | ||||||||
\(401\) | 6.75438i | 0.337297i | 0.985676 | + | 0.168649i | \(0.0539403\pi\) | ||||
−0.985676 | + | 0.168649i | \(0.946060\pi\) | |||||||
\(402\) | 1.35951 | − | 1.36020i | 0.0678061 | − | 0.0678407i | ||||
\(403\) | 4.34884i | 0.216631i | ||||||||
\(404\) | −38.1124 | −1.89616 | ||||||||
\(405\) | 0.00918110 | + | 9.00000i | 0.000456212 | + | 0.447213i | ||||
\(406\) | − | 9.61432i | − | 0.477151i | ||||||
\(407\) | −3.35641 | − | 19.3568i | −0.166371 | − | 0.959481i | ||||
\(408\) | −2.18749 | + | 2.18860i | −0.108297 | + | 0.108352i | ||||
\(409\) | 16.1388i | 0.798014i | 0.916948 | + | 0.399007i | \(0.130645\pi\) | ||||
−0.916948 | + | 0.399007i | \(0.869355\pi\) | |||||||
\(410\) | − | 13.5610i | − | 0.669731i | ||||||
\(411\) | −20.3567 | − | 20.3463i | −1.00412 | − | 1.00361i | ||||
\(412\) | −30.7426 | −1.51458 | ||||||||
\(413\) | 1.96672 | 0.0967761 | ||||||||
\(414\) | 29.6772 | − | 0.0151372i | 1.45856 | − | 0.000743953i | ||||
\(415\) | − | 2.16097i | − | 0.106078i | ||||||
\(416\) | 19.2710i | 0.944839i | ||||||||
\(417\) | −11.3895 | − | 11.3837i | −0.557745 | − | 0.557460i | ||||
\(418\) | −4.25799 | + | 0.738321i | −0.208265 | + | 0.0361125i | ||||
\(419\) | 25.6930i | 1.25519i | 0.778542 | + | 0.627593i | \(0.215960\pi\) | ||||
−0.778542 | + | 0.627593i | \(0.784040\pi\) | |||||||
\(420\) | −2.67474 | + | 2.67610i | −0.130514 | + | 0.130580i | ||||
\(421\) | 18.9921 | 0.925619 | 0.462810 | − | 0.886458i | \(-0.346841\pi\) | ||||
0.462810 | + | 0.886458i | \(0.346841\pi\) | |||||||
\(422\) | 35.1323i | 1.71021i | ||||||||
\(423\) | 34.1648 | − | 0.0174261i | 1.66115 | − | 0.000847287i | ||||
\(424\) | 2.59843i | 0.126191i | ||||||||
\(425\) | 4.73436 | 0.229650 | ||||||||
\(426\) | 15.7750 | + | 15.7670i | 0.764303 | + | 0.763913i | ||||
\(427\) | 3.95587 | 0.191438 | ||||||||
\(428\) | −10.3491 | −0.500242 | ||||||||
\(429\) | −7.85568 | + | 11.1575i | −0.379276 | + | 0.538689i | ||||
\(430\) | −20.7221 | −0.999307 | ||||||||
\(431\) | −21.6210 | −1.04145 | −0.520723 | − | 0.853725i | \(-0.674338\pi\) | ||||
−0.520723 | + | 0.853725i | \(0.674338\pi\) | |||||||
\(432\) | −13.2264 | − | 13.2062i | −0.636357 | − | 0.635384i | ||||
\(433\) | 10.2110 | 0.490711 | 0.245355 | − | 0.969433i | \(-0.421095\pi\) | ||||
0.245355 | + | 0.969433i | \(0.421095\pi\) | |||||||
\(434\) | − | 3.74507i | − | 0.179769i | ||||||
\(435\) | 5.75778 | + | 5.75484i | 0.276064 | + | 0.275923i | ||||
\(436\) | 16.0831i | 0.770241i | ||||||||
\(437\) | 3.08037 | 0.147354 | ||||||||
\(438\) | 17.1895 | + | 17.1807i | 0.821345 | + | 0.820927i | ||||
\(439\) | 18.4912i | 0.882536i | 0.897375 | + | 0.441268i | \(0.145471\pi\) | ||||
−0.897375 | + | 0.441268i | \(0.854529\pi\) | |||||||
\(440\) | 1.23314 | − | 0.213823i | 0.0587878 | − | 0.0101936i | ||||
\(441\) | 0.00153018 | + | 3.00000i | 7.28659e−5 | + | 0.142857i | ||||
\(442\) | 23.0047i | 1.09422i | ||||||||
\(443\) | 8.61282i | 0.409207i | 0.978845 | + | 0.204604i | \(0.0655906\pi\) | ||||
−0.978845 | + | 0.204604i | \(0.934409\pi\) | |||||||
\(444\) | −15.8435 | + | 15.8516i | −0.751899 | + | 0.752283i | ||||
\(445\) | 12.4798 | 0.591600 | ||||||||
\(446\) | −9.06914 | −0.429436 | ||||||||
\(447\) | 19.0118 | − | 19.0215i | 0.899230 | − | 0.899688i | ||||
\(448\) | − | 9.40144i | − | 0.444176i | ||||||
\(449\) | − | 16.6872i | − | 0.787516i | −0.919214 | − | 0.393758i | \(-0.871175\pi\) | ||
0.919214 | − | 0.393758i | \(-0.128825\pi\) | |||||||
\(450\) | −0.00313014 | − | 6.13679i | −0.000147556 | − | 0.289291i | ||||
\(451\) | 3.75644 | + | 21.6638i | 0.176884 | + | 1.02011i | ||||
\(452\) | − | 6.11372i | − | 0.287565i | ||||||
\(453\) | 6.02289 | + | 6.01982i | 0.282980 | + | 0.282836i | ||||
\(454\) | 12.7503 | 0.598399 | ||||||||
\(455\) | 2.37539i | 0.111360i | ||||||||
\(456\) | 0.294460 | + | 0.294310i | 0.0137894 | + | 0.0137823i | ||||
\(457\) | 24.2227i | 1.13309i | 0.824031 | + | 0.566544i | \(0.191720\pi\) | ||||
−0.824031 | + | 0.566544i | \(0.808280\pi\) | |||||||
\(458\) | −1.86041 | −0.0869315 | ||||||||
\(459\) | −17.4084 | − | 17.3818i | −0.812556 | − | 0.811314i | ||||
\(460\) | −10.5640 | −0.492549 | ||||||||
\(461\) | −23.5724 | −1.09788 | −0.548938 | − | 0.835863i | \(-0.684968\pi\) | ||||
−0.548938 | + | 0.835863i | \(0.684968\pi\) | |||||||
\(462\) | 6.76503 | − | 9.60843i | 0.314738 | − | 0.447025i | ||||
\(463\) | −6.36147 | −0.295643 | −0.147821 | − | 0.989014i | \(-0.547226\pi\) | ||||
−0.147821 | + | 0.989014i | \(0.547226\pi\) | |||||||
\(464\) | −16.9060 | −0.784844 | ||||||||
\(465\) | 2.24283 | + | 2.24168i | 0.104009 | + | 0.103955i | ||||
\(466\) | 56.6419 | 2.62389 | ||||||||
\(467\) | 38.5449i | 1.78364i | 0.452386 | + | 0.891822i | \(0.350573\pi\) | ||||
−0.452386 | + | 0.891822i | \(0.649427\pi\) | |||||||
\(468\) | 15.5669 | − | 0.00794007i | 0.719580 | − | 0.000367030i | ||||
\(469\) | 0.542784i | 0.0250634i | ||||||||
\(470\) | −23.2958 | −1.07455 | ||||||||
\(471\) | −7.80638 | + | 7.81036i | −0.359699 | + | 0.359882i | ||||
\(472\) | 0.742152i | 0.0341603i | ||||||||
\(473\) | 33.1037 | − | 5.74007i | 1.52211 | − | 0.263929i | ||||
\(474\) | −15.6492 | − | 15.6412i | −0.718791 | − | 0.718425i | ||||
\(475\) | − | 0.636972i | − | 0.0292263i | ||||||
\(476\) | − | 10.3421i | − | 0.474028i | ||||||
\(477\) | −20.6577 | + | 0.0105367i | −0.945852 | + | 0.000482442i | ||||
\(478\) | −48.3308 | −2.21060 | ||||||||
\(479\) | 24.8867 | 1.13710 | 0.568550 | − | 0.822648i | \(-0.307504\pi\) | ||||
0.568550 | + | 0.822648i | \(0.307504\pi\) | |||||||
\(480\) | 9.93862 | + | 9.93355i | 0.453634 | + | 0.453403i | ||||
\(481\) | 14.0703i | 0.641552i | ||||||||
\(482\) | 23.4318i | 1.06729i | ||||||||
\(483\) | −5.92130 | + | 5.92432i | −0.269428 | + | 0.269566i | ||||
\(484\) | −22.6264 | + | 8.08993i | −1.02847 | + | 0.367724i | ||||
\(485\) | 14.6880i | 0.666946i | ||||||||
\(486\) | −22.5193 | + | 22.5768i | −1.02149 | + | 1.02410i | ||||
\(487\) | −12.5901 | −0.570514 | −0.285257 | − | 0.958451i | \(-0.592079\pi\) | ||||
−0.285257 | + | 0.958451i | \(0.592079\pi\) | |||||||
\(488\) | 1.49276i | 0.0675743i | ||||||||
\(489\) | 20.8497 | − | 20.8604i | 0.942858 | − | 0.943339i | ||||
\(490\) | − | 2.04560i | − | 0.0924107i | ||||||
\(491\) | 18.3662 | 0.828854 | 0.414427 | − | 0.910082i | \(-0.363982\pi\) | ||||
0.414427 | + | 0.910082i | \(0.363982\pi\) | |||||||
\(492\) | 17.7318 | − | 17.7409i | 0.799412 | − | 0.799820i | ||||
\(493\) | −22.2515 | −1.00216 | ||||||||
\(494\) | 3.09510 | 0.139255 | ||||||||
\(495\) | 1.70491 | + | 9.80272i | 0.0766300 | + | 0.440599i | ||||
\(496\) | −6.58541 | −0.295694 | ||||||||
\(497\) | −6.29497 | −0.282368 | ||||||||
\(498\) | 5.41257 | − | 5.41533i | 0.242543 | − | 0.242667i | ||||
\(499\) | 11.3997 | 0.510321 | 0.255160 | − | 0.966899i | \(-0.417872\pi\) | ||||
0.255160 | + | 0.966899i | \(0.417872\pi\) | |||||||
\(500\) | 2.18447i | 0.0976925i | ||||||||
\(501\) | −21.4700 | + | 21.4810i | −0.959210 | + | 0.959699i | ||||
\(502\) | − | 46.1699i | − | 2.06066i | ||||||
\(503\) | 16.3592 | 0.729421 | 0.364710 | − | 0.931121i | \(-0.381168\pi\) | ||||
0.364710 | + | 0.931121i | \(0.381168\pi\) | |||||||
\(504\) | −1.13206 | 0.000577422i | −0.0504262 | 2.57204e-5i | ||||||
\(505\) | 17.4470i | 0.776380i | ||||||||
\(506\) | 32.3271 | − | 5.60540i | 1.43711 | − | 0.249191i | ||||
\(507\) | −9.00880 | + | 9.01340i | −0.400095 | + | 0.400299i | ||||
\(508\) | 28.7046i | 1.27356i | ||||||||
\(509\) | − | 4.04066i | − | 0.179099i | −0.995982 | − | 0.0895496i | \(-0.971457\pi\) | ||
0.995982 | − | 0.0895496i | \(-0.0285428\pi\) | |||||||
\(510\) | 11.8642 | + | 11.8581i | 0.525355 | + | 0.525087i | ||||
\(511\) | −6.85940 | −0.303442 | ||||||||
\(512\) | −31.8966 | −1.40964 | ||||||||
\(513\) | −2.33859 | + | 2.34217i | −0.103251 | + | 0.103410i | ||||
\(514\) | 7.05529i | 0.311196i | ||||||||
\(515\) | 14.0733i | 0.620142i | ||||||||
\(516\) | −27.1091 | − | 27.0953i | −1.19341 | − | 1.19280i | ||||
\(517\) | 37.2152 | − | 6.45300i | 1.63672 | − | 0.283803i | ||||
\(518\) | − | 12.1169i | − | 0.532384i | ||||||
\(519\) | 26.5930 | − | 26.6066i | 1.16731 | − | 1.16790i | ||||
\(520\) | −0.896364 | −0.0393082 | ||||||||
\(521\) | 41.5493i | 1.82031i | 0.414269 | + | 0.910154i | \(0.364037\pi\) | ||||
−0.414269 | + | 0.910154i | \(0.635963\pi\) | |||||||
\(522\) | 0.0147117 | + | 28.8430i | 0.000643913 | + | 1.26242i | ||||
\(523\) | 14.3063i | 0.625571i | 0.949824 | + | 0.312785i | \(0.101262\pi\) | ||||
−0.949824 | + | 0.312785i | \(0.898738\pi\) | |||||||
\(524\) | 14.0544 | 0.613971 | ||||||||
\(525\) | 1.22506 | + | 1.22443i | 0.0534659 | + | 0.0534386i | ||||
\(526\) | −43.3131 | −1.88854 | ||||||||
\(527\) | −8.66762 | −0.377568 | ||||||||
\(528\) | −16.8957 | − | 11.8958i | −0.735290 | − | 0.517697i | ||||
\(529\) | −0.386438 | −0.0168016 | ||||||||
\(530\) | 14.0858 | 0.611848 | ||||||||
\(531\) | −5.90017 | + | 0.00300945i | −0.256045 | + | 0.000130599i | ||||
\(532\) | −1.39145 | −0.0603269 | ||||||||
\(533\) | − | 15.7473i | − | 0.682092i | ||||||
\(534\) | 31.2741 | + | 31.2581i | 1.35336 | + | 1.35267i | ||||
\(535\) | 4.73757i | 0.204823i | ||||||||
\(536\) | −0.204822 | −0.00884697 | ||||||||
\(537\) | −27.5308 | − | 27.5168i | −1.18804 | − | 1.18744i | ||||
\(538\) | − | 49.2882i | − | 2.12496i | ||||||
\(539\) | 0.566637 | + | 3.26786i | 0.0244068 | + | 0.140757i | ||||
\(540\) | 8.02012 | − | 8.03240i | 0.345131 | − | 0.345659i | ||||
\(541\) | 5.57042i | 0.239491i | 0.992805 | + | 0.119746i | \(0.0382079\pi\) | ||||
−0.992805 | + | 0.119746i | \(0.961792\pi\) | |||||||
\(542\) | 6.03825i | 0.259365i | ||||||||
\(543\) | 2.50960 | − | 2.51088i | 0.107697 | − | 0.107752i | ||||
\(544\) | −38.4088 | −1.64676 | ||||||||
\(545\) | 7.36247 | 0.315373 | ||||||||
\(546\) | −5.94963 | + | 5.95266i | −0.254620 | + | 0.254750i | ||||
\(547\) | 17.6879i | 0.756282i | 0.925748 | + | 0.378141i | \(0.123436\pi\) | ||||
−0.925748 | + | 0.378141i | \(0.876564\pi\) | |||||||
\(548\) | 36.2992i | 1.55063i | ||||||||
\(549\) | −11.8676 | + | 0.00605320i | −0.506497 | + | 0.000258344i | ||||
\(550\) | −1.15911 | − | 6.68473i | −0.0494246 | − | 0.285038i | ||||
\(551\) | 2.99377i | 0.127539i | ||||||||
\(552\) | −2.23557 | − | 2.23443i | −0.0951522 | − | 0.0951037i | ||||
\(553\) | 6.24475 | 0.265554 | ||||||||
\(554\) | − | 10.0692i | − | 0.427798i | ||||||
\(555\) | 7.25648 | + | 7.25278i | 0.308021 | + | 0.307863i | ||||
\(556\) | 20.3092i | 0.861304i | ||||||||
\(557\) | 15.1992 | 0.644009 | 0.322005 | − | 0.946738i | \(-0.395643\pi\) | ||||
0.322005 | + | 0.946738i | \(0.395643\pi\) | |||||||
\(558\) | 0.00573064 | + | 11.2352i | 0.000242597 | + | 0.475624i | ||||
\(559\) | −24.0629 | −1.01775 | ||||||||
\(560\) | −3.59703 | −0.152002 | ||||||||
\(561\) | −22.2379 | − | 15.6571i | −0.938884 | − | 0.661042i | ||||
\(562\) | −21.4696 | −0.905639 | ||||||||
\(563\) | 9.08289 | 0.382798 | 0.191399 | − | 0.981512i | \(-0.438698\pi\) | ||||
0.191399 | + | 0.981512i | \(0.438698\pi\) | |||||||
\(564\) | −30.4761 | − | 30.4606i | −1.28328 | − | 1.28262i | ||||
\(565\) | −2.79872 | −0.117743 | ||||||||
\(566\) | 18.6172i | 0.782541i | ||||||||
\(567\) | −0.00918110 | − | 9.00000i | −0.000385570 | − | 0.377964i | ||||
\(568\) | − | 2.37544i | − | 0.0996712i | ||||||
\(569\) | −22.4721 | −0.942079 | −0.471040 | − | 0.882112i | \(-0.656121\pi\) | ||||
−0.471040 | + | 0.882112i | \(0.656121\pi\) | |||||||
\(570\) | 1.59542 | − | 1.59624i | 0.0668248 | − | 0.0668589i | ||||
\(571\) | − | 31.0553i | − | 1.29962i | −0.760096 | − | 0.649811i | \(-0.774848\pi\) | ||
0.760096 | − | 0.649811i | \(-0.225152\pi\) | |||||||
\(572\) | 16.9568 | − | 2.94026i | 0.709001 | − | 0.122938i | ||||
\(573\) | 2.85478 | + | 2.85332i | 0.119260 | + | 0.119199i | ||||
\(574\) | 13.5610i | 0.566026i | ||||||||
\(575\) | 4.83595i | 0.201673i | ||||||||
\(576\) | 0.0143859 | + | 28.2043i | 0.000599413 | + | 1.17518i | ||||
\(577\) | 30.2733 | 1.26030 | 0.630148 | − | 0.776475i | \(-0.282994\pi\) | ||||
0.630148 | + | 0.776475i | \(0.282994\pi\) | |||||||
\(578\) | −11.0751 | −0.460665 | ||||||||
\(579\) | 7.33509 | + | 7.33135i | 0.304836 | + | 0.304681i | ||||
\(580\) | − | 10.2670i | − | 0.426315i | ||||||
\(581\) | 2.16097i | 0.0896521i | ||||||||
\(582\) | −36.7889 | + | 36.8076i | −1.52495 | + | 1.52573i | ||||
\(583\) | −22.5022 | + | 3.90181i | −0.931945 | + | 0.161596i | ||||
\(584\) | − | 2.58843i | − | 0.107110i | ||||||
\(585\) | −0.00363478 | − | 7.12616i | −0.000150280 | − | 0.294631i | ||||
\(586\) | 55.4595 | 2.29101 | ||||||||
\(587\) | − | 32.4208i | − | 1.33815i | −0.743195 | − | 0.669075i | \(-0.766690\pi\) | ||
0.743195 | − | 0.669075i | \(-0.233310\pi\) | |||||||
\(588\) | 2.67474 | − | 2.67610i | 0.110304 | − | 0.110361i | ||||
\(589\) | 1.16616i | 0.0480509i | ||||||||
\(590\) | 4.02312 | 0.165629 | ||||||||
\(591\) | 18.9110 | − | 18.9206i | 0.777893 | − | 0.778290i | ||||
\(592\) | −21.3066 | −0.875695 | ||||||||
\(593\) | 10.4749 | 0.430154 | 0.215077 | − | 0.976597i | \(-0.431000\pi\) | ||||
0.215077 | + | 0.976597i | \(0.431000\pi\) | |||||||
\(594\) | −20.2804 | + | 28.8356i | −0.832114 | + | 1.18314i | ||||
\(595\) | −4.73436 | −0.194090 | ||||||||
\(596\) | −33.9184 | −1.38935 | ||||||||
\(597\) | −25.4219 | + | 25.4348i | −1.04045 | + | 1.04098i | ||||
\(598\) | −23.4983 | −0.960918 | ||||||||
\(599\) | 23.8437i | 0.974225i | 0.873339 | + | 0.487113i | \(0.161950\pi\) | ||||
−0.873339 | + | 0.487113i | \(0.838050\pi\) | |||||||
\(600\) | −0.462046 | + | 0.462281i | −0.0188629 | + | 0.0188726i | ||||
\(601\) | − | 42.7707i | − | 1.74465i | −0.488924 | − | 0.872327i | \(-0.662610\pi\) | ||
0.488924 | − | 0.872327i | \(-0.337390\pi\) | |||||||
\(602\) | 20.7221 | 0.844568 | ||||||||
\(603\) | −0.000830559 | − | 1.62835i | −3.38230e−5 | − | 0.0663116i | ||||
\(604\) | − | 10.7398i | − | 0.436995i | ||||||
\(605\) | 3.70338 | + | 10.3578i | 0.150564 | + | 0.421106i | ||||
\(606\) | −43.6994 | + | 43.7217i | −1.77517 | + | 1.77607i | ||||
\(607\) | − | 47.0364i | − | 1.90915i | −0.297971 | − | 0.954575i | \(-0.596310\pi\) | ||
0.297971 | − | 0.954575i | \(-0.403690\pi\) | |||||||
\(608\) | 5.16761i | 0.209574i | ||||||||
\(609\) | −5.75778 | − | 5.75484i | −0.233317 | − | 0.233198i | ||||
\(610\) | 8.09211 | 0.327640 | ||||||||
\(611\) | −27.0515 | −1.09439 | ||||||||
\(612\) | 0.0158253 | + | 31.0262i | 0.000639698 | + | 1.25416i | ||||
\(613\) | − | 13.1181i | − | 0.529836i | −0.964271 | − | 0.264918i | \(-0.914655\pi\) | ||
0.964271 | − | 0.264918i | \(-0.0853448\pi\) | |||||||
\(614\) | − | 11.7800i | − | 0.475401i | ||||||
\(615\) | −8.12135 | − | 8.11721i | −0.327484 | − | 0.327317i | ||||
\(616\) | −1.23314 | + | 0.213823i | −0.0496848 | + | 0.00861518i | ||||
\(617\) | − | 35.8827i | − | 1.44458i | −0.691588 | − | 0.722292i | \(-0.743089\pi\) | ||
0.691588 | − | 0.722292i | \(-0.256911\pi\) | |||||||
\(618\) | −35.2492 | + | 35.2672i | −1.41793 | + | 1.41866i | ||||
\(619\) | −25.0255 | −1.00586 | −0.502931 | − | 0.864327i | \(-0.667745\pi\) | ||||
−0.502931 | + | 0.864327i | \(0.667745\pi\) | |||||||
\(620\) | − | 3.99931i | − | 0.160616i | ||||||
\(621\) | 17.7548 | − | 17.7820i | 0.712477 | − | 0.713568i | ||||
\(622\) | 16.4869i | 0.661063i | ||||||||
\(623\) | −12.4798 | −0.499993 | ||||||||
\(624\) | 10.4673 | + | 10.4620i | 0.419027 | + | 0.418814i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.6422 | 1.26468 | ||||||||
\(627\) | −2.10654 | + | 2.99194i | −0.0841271 | + | 0.119486i | ||||
\(628\) | 13.9271 | 0.555752 | ||||||||
\(629\) | −28.0434 | −1.11816 | ||||||||
\(630\) | 0.00313014 | + | 6.13679i | 0.000124708 | + | 0.244496i | ||||
\(631\) | −9.53055 | −0.379405 | −0.189703 | − | 0.981842i | \(-0.560752\pi\) | ||||
−0.189703 | + | 0.981842i | \(0.560752\pi\) | |||||||
\(632\) | 2.35649i | 0.0937361i | ||||||||
\(633\) | 21.0398 | + | 21.0291i | 0.836258 | + | 0.835832i | ||||
\(634\) | − | 3.64502i | − | 0.144762i | ||||||
\(635\) | 13.1403 | 0.521457 | ||||||||
\(636\) | 18.4274 | + | 18.4180i | 0.730694 | + | 0.730321i | ||||
\(637\) | − | 2.37539i | − | 0.0941163i | ||||||
\(638\) | 5.44783 | + | 31.4183i | 0.215682 | + | 1.24386i | ||||
\(639\) | 18.8849 | − | 0.00963246i | 0.747076 | − | 0.000381054i | ||||
\(640\) | − | 3.00600i | − | 0.118822i | ||||||
\(641\) | − | 24.8099i | − | 0.979933i | −0.871741 | − | 0.489966i | \(-0.837009\pi\) | ||
0.871741 | − | 0.489966i | \(-0.162991\pi\) | |||||||
\(642\) | −11.8662 | + | 11.8722i | −0.468321 | + | 0.468560i | ||||
\(643\) | −41.9082 | −1.65270 | −0.826348 | − | 0.563159i | \(-0.809586\pi\) | ||||
−0.826348 | + | 0.563159i | \(0.809586\pi\) | |||||||
\(644\) | 10.5640 | 0.416280 | ||||||||
\(645\) | −12.4036 | + | 12.4099i | −0.488391 | + | 0.488640i | ||||
\(646\) | 6.16881i | 0.242709i | ||||||||
\(647\) | − | 38.6385i | − | 1.51904i | −0.650487 | − | 0.759518i | \(-0.725435\pi\) | ||
0.650487 | − | 0.759518i | \(-0.274565\pi\) | |||||||
\(648\) | 3.39619 | − | 0.00346453i | 0.133415 | − | 0.000136100i | ||||
\(649\) | −6.42698 | + | 1.11442i | −0.252281 | + | 0.0437447i | ||||
\(650\) | 4.85909i | 0.190589i | ||||||||
\(651\) | −2.24283 | − | 2.24168i | −0.0879032 | − | 0.0878584i | ||||
\(652\) | −37.1974 | −1.45676 | ||||||||
\(653\) | 11.1028i | 0.434487i | 0.976117 | + | 0.217244i | \(0.0697066\pi\) | ||||
−0.976117 | + | 0.217244i | \(0.930293\pi\) | |||||||
\(654\) | 18.4502 | + | 18.4408i | 0.721458 | + | 0.721090i | ||||
\(655\) | − | 6.43379i | − | 0.251389i | ||||||
\(656\) | 23.8460 | 0.931030 | ||||||||
\(657\) | 20.5782 | − | 0.0104961i | 0.802832 | − | 0.000409493i | ||||
\(658\) | 23.2958 | 0.908164 | ||||||||
\(659\) | −3.84987 | −0.149970 | −0.0749848 | − | 0.997185i | \(-0.523891\pi\) | ||||
−0.0749848 | + | 0.997185i | \(0.523891\pi\) | |||||||
\(660\) | 7.22430 | − | 10.2607i | 0.281205 | − | 0.399399i | ||||
\(661\) | −24.6238 | −0.957756 | −0.478878 | − | 0.877881i | \(-0.658956\pi\) | ||||
−0.478878 | + | 0.877881i | \(0.658956\pi\) | |||||||
\(662\) | −53.9559 | −2.09705 | ||||||||
\(663\) | 13.7769 | + | 13.7699i | 0.535051 | + | 0.534778i | ||||
\(664\) | −0.815452 | −0.0316457 | ||||||||
\(665\) | 0.636972i | 0.0247007i | ||||||||
\(666\) | 0.0185410 | + | 36.3506i | 0.000718450 | + | 1.40856i | ||||
\(667\) | − | 22.7290i | − | 0.880071i | ||||||
\(668\) | 38.3040 | 1.48203 | ||||||||
\(669\) | −5.42851 | + | 5.43128i | −0.209878 | + | 0.209985i | ||||
\(670\) | 1.11032i | 0.0428953i | ||||||||
\(671\) | −12.9272 | + | 2.24154i | −0.499050 | + | 0.0865336i | ||||
\(672\) | −9.93862 | − | 9.93355i | −0.383391 | − | 0.383195i | ||||
\(673\) | − | 14.6708i | − | 0.565517i | −0.959191 | − | 0.282759i | \(-0.908750\pi\) | ||
0.959191 | − | 0.282759i | \(-0.0912496\pi\) | |||||||
\(674\) | − | 53.3385i | − | 2.05452i | ||||||
\(675\) | −3.67704 | − | 3.67142i | −0.141530 | − | 0.141313i | ||||
\(676\) | 16.0723 | 0.618166 | ||||||||
\(677\) | 46.1925 | 1.77532 | 0.887661 | − | 0.460498i | \(-0.152329\pi\) | ||||
0.887661 | + | 0.460498i | \(0.152329\pi\) | |||||||
\(678\) | −7.01351 | − | 7.00993i | −0.269352 | − | 0.269215i | ||||
\(679\) | − | 14.6880i | − | 0.563672i | ||||||
\(680\) | − | 1.78653i | − | 0.0685104i | ||||||
\(681\) | 7.63191 | − | 7.63581i | 0.292455 | − | 0.292605i | ||||
\(682\) | 2.12209 | + | 12.2384i | 0.0812591 | + | 0.468631i | ||||
\(683\) | 19.9481i | 0.763291i | 0.924309 | + | 0.381645i | \(0.124642\pi\) | ||||
−0.924309 | + | 0.381645i | \(0.875358\pi\) | |||||||
\(684\) | 4.17434 | − | 0.00212917i | 0.159610 | − | 8.14108e-5i | ||||
\(685\) | 16.6169 | 0.634901 | ||||||||
\(686\) | 2.04560i | 0.0781013i | ||||||||
\(687\) | −1.11359 | + | 1.11416i | −0.0424860 | + | 0.0425077i | ||||
\(688\) | − | 36.4382i | − | 1.38919i | ||||||
\(689\) | 16.3567 | 0.623140 | ||||||||
\(690\) | −12.1126 | + | 12.1188i | −0.461119 | + | 0.461354i | ||||
\(691\) | 30.0622 | 1.14362 | 0.571810 | − | 0.820386i | \(-0.306242\pi\) | ||||
0.571810 | + | 0.820386i | \(0.306242\pi\) | |||||||
\(692\) | −47.4438 | −1.80354 | ||||||||
\(693\) | −1.70491 | − | 9.80272i | −0.0647642 | − | 0.372374i | ||||
\(694\) | 66.6799 | 2.53114 | ||||||||
\(695\) | 9.29709 | 0.352659 | ||||||||
\(696\) | 2.17162 | − | 2.17272i | 0.0823149 | − | 0.0823569i | ||||
\(697\) | 31.3858 | 1.18882 | ||||||||
\(698\) | − | 48.2953i | − | 1.82801i | ||||||
\(699\) | 33.9041 | − | 33.9214i | 1.28237 | − | 1.28303i | ||||
\(700\) | − | 2.18447i | − | 0.0825653i | ||||||
\(701\) | 27.0757 | 1.02264 | 0.511318 | − | 0.859392i | \(-0.329157\pi\) | ||||
0.511318 | + | 0.859392i | \(0.329157\pi\) | |||||||
\(702\) | 17.8398 | − | 17.8671i | 0.673319 | − | 0.674350i | ||||
\(703\) | 3.77303i | 0.142302i | ||||||||
\(704\) | 5.32720 | + | 30.7226i | 0.200776 | + | 1.15790i | ||||
\(705\) | −13.9441 | + | 13.9513i | −0.525167 | + | 0.525435i | ||||
\(706\) | − | 3.16221i | − | 0.119011i | ||||||
\(707\) | − | 17.4470i | − | 0.656161i | ||||||
\(708\) | 5.26315 | + | 5.26047i | 0.197801 | + | 0.197700i | ||||
\(709\) | −7.84277 | −0.294541 | −0.147271 | − | 0.989096i | \(-0.547049\pi\) | ||||
−0.147271 | + | 0.989096i | \(0.547049\pi\) | |||||||
\(710\) | −12.8770 | −0.483265 | ||||||||
\(711\) | −18.7343 | + | 0.00955562i | −0.702590 | + | 0.000358364i | ||||
\(712\) | − | 4.70932i | − | 0.176489i | ||||||
\(713\) | − | 8.85362i | − | 0.331571i | ||||||
\(714\) | −11.8642 | − | 11.8581i | −0.444006 | − | 0.443779i | ||||
\(715\) | −1.34598 | − | 7.76244i | −0.0503369 | − | 0.290299i | ||||
\(716\) | 49.0919i | 1.83465i | ||||||||
\(717\) | −28.9293 | + | 28.9441i | −1.08039 | + | 1.08094i | ||||
\(718\) | 60.2642 | 2.24904 | ||||||||
\(719\) | 9.42161i | 0.351367i | 0.984447 | + | 0.175683i | \(0.0562135\pi\) | ||||
−0.984447 | + | 0.175683i | \(0.943787\pi\) | |||||||
\(720\) | 10.7911 | − | 0.00550411i | 0.402160 | − | 0.000205126i | ||||
\(721\) | − | 14.0733i | − | 0.524116i | ||||||
\(722\) | −38.0364 | −1.41557 | ||||||||
\(723\) | 14.0327 | + | 14.0256i | 0.521882 | + | 0.521616i | ||||
\(724\) | −4.47729 | −0.166397 | ||||||||
\(725\) | −4.70001 | −0.174554 | ||||||||
\(726\) | −16.6627 | + | 35.2323i | −0.618410 | + | 1.30759i | ||||
\(727\) | 4.00681 | 0.148604 | 0.0743022 | − | 0.997236i | \(-0.476327\pi\) | ||||
0.0743022 | + | 0.997236i | \(0.476327\pi\) | |||||||
\(728\) | 0.896364 | 0.0332215 | ||||||||
\(729\) | 0.0413149 | + | 27.0000i | 0.00153018 | + | 0.999999i | ||||
\(730\) | −14.0316 | −0.519332 | ||||||||
\(731\) | − | 47.9594i | − | 1.77384i | ||||||
\(732\) | 10.5863 | + | 10.5809i | 0.391281 | + | 0.391081i | ||||
\(733\) | 38.1353i | 1.40856i | 0.709923 | + | 0.704279i | \(0.248730\pi\) | ||||
−0.709923 | + | 0.704279i | \(0.751270\pi\) | |||||||
\(734\) | −34.5356 | −1.27473 | ||||||||
\(735\) | −1.22506 | − | 1.22443i | −0.0451869 | − | 0.0451639i | ||||
\(736\) | − | 39.2330i | − | 1.44615i | ||||||
\(737\) | −0.307561 | − | 1.77374i | −0.0113292 | − | 0.0653366i | ||||
\(738\) | −0.0207508 | − | 40.6830i | −0.000763849 | − | 1.49756i | ||||
\(739\) | 31.1709i | 1.14664i | 0.819332 | + | 0.573319i | \(0.194345\pi\) | ||||
−0.819332 | + | 0.573319i | \(0.805655\pi\) | |||||||
\(740\) | − | 12.9395i | − | 0.475664i | ||||||
\(741\) | 1.85263 | − | 1.85358i | 0.0680582 | − | 0.0680929i | ||||
\(742\) | −14.0858 | −0.517106 | ||||||||
\(743\) | 40.4561 | 1.48419 | 0.742095 | − | 0.670294i | \(-0.233832\pi\) | ||||
0.742095 | + | 0.670294i | \(0.233832\pi\) | |||||||
\(744\) | 0.845909 | − | 0.846341i | 0.0310125 | − | 0.0310284i | ||||
\(745\) | 15.5271i | 0.568868i | ||||||||
\(746\) | 16.1239i | 0.590339i | ||||||||
\(747\) | −0.00330668 | − | 6.48291i | −0.000120985 | − | 0.237197i | ||||
\(748\) | 5.86019 | + | 33.7965i | 0.214270 | + | 1.23572i | ||||
\(749\) | − | 4.73757i | − | 0.173107i | ||||||
\(750\) | 2.50597 | + | 2.50470i | 0.0915053 | + | 0.0914586i | ||||
\(751\) | 38.5721 | 1.40752 | 0.703758 | − | 0.710440i | \(-0.251504\pi\) | ||||
0.703758 | + | 0.710440i | \(0.251504\pi\) | |||||||
\(752\) | − | 40.9639i | − | 1.49380i | ||||||
\(753\) | −27.6500 | − | 27.6359i | −1.00762 | − | 1.00711i | ||||
\(754\) | − | 22.8377i | − | 0.831702i | ||||||
\(755\) | −4.91642 | −0.178927 | ||||||||
\(756\) | −8.02012 | + | 8.03240i | −0.291689 | + | 0.292136i | ||||
\(757\) | −35.8603 | −1.30337 | −0.651683 | − | 0.758491i | \(-0.725937\pi\) | ||||
−0.651683 | + | 0.758491i | \(0.725937\pi\) | |||||||
\(758\) | 8.88968 | 0.322888 | ||||||||
\(759\) | 15.9930 | − | 22.7151i | 0.580511 | − | 0.824505i | ||||
\(760\) | −0.240364 | −0.00871893 | ||||||||
\(761\) | 12.7730 | 0.463021 | 0.231510 | − | 0.972832i | \(-0.425633\pi\) | ||||
0.231510 | + | 0.972832i | \(0.425633\pi\) | |||||||
\(762\) | 32.9293 | + | 32.9125i | 1.19290 | + | 1.19229i | ||||
\(763\) | −7.36247 | −0.266539 | ||||||||
\(764\) | − | 5.09052i | − | 0.184168i | ||||||
\(765\) | 14.2031 | − | 0.00724443i | 0.513513 | − | 0.000261923i | ||||
\(766\) | 41.2635i | 1.49091i | ||||||||
\(767\) | 4.67173 | 0.168686 | ||||||||
\(768\) | −15.4937 | + | 15.5016i | −0.559082 | + | 0.559367i | ||||
\(769\) | 1.97553i | 0.0712395i | 0.999365 | + | 0.0356197i | \(0.0113405\pi\) | ||||
−0.999365 | + | 0.0356197i | \(0.988659\pi\) | |||||||
\(770\) | 1.15911 | + | 6.68473i | 0.0417714 | + | 0.240901i | ||||
\(771\) | 4.22524 | + | 4.22308i | 0.152168 | + | 0.152091i | ||||
\(772\) | − | 13.0796i | − | 0.470747i | ||||||
\(773\) | 25.8041i | 0.928108i | 0.885807 | + | 0.464054i | \(0.153606\pi\) | ||||
−0.885807 | + | 0.464054i | \(0.846394\pi\) | |||||||
\(774\) | −62.1662 | + | 0.0317086i | −2.23452 | + | 0.00113974i | ||||
\(775\) | −1.83079 | −0.0657640 | ||||||||
\(776\) | 5.54257 | 0.198967 | ||||||||
\(777\) | −7.25648 | − | 7.25278i | −0.260325 | − | 0.260192i | ||||
\(778\) | 40.9356i | 1.46761i | ||||||||
\(779\) | − | 4.22272i | − | 0.151295i | ||||||
\(780\) | −6.35354 | + | 6.35678i | −0.227493 | + | 0.227609i | ||||
\(781\) | 20.5711 | − | 3.56696i | 0.736092 | − | 0.127636i | ||||
\(782\) | − | 46.8342i | − | 1.67479i | ||||||
\(783\) | 17.2821 | + | 17.2557i | 0.617613 | + | 0.616669i | ||||
\(784\) | 3.59703 | 0.128465 | ||||||||
\(785\) | − | 6.37551i | − | 0.227552i | ||||||
\(786\) | 16.1147 | − | 16.1229i | 0.574792 | − | 0.575085i | ||||
\(787\) | 15.7483i | 0.561367i | 0.959800 | + | 0.280683i | \(0.0905611\pi\) | ||||
−0.959800 | + | 0.280683i | \(0.909439\pi\) | |||||||
\(788\) | −33.7385 | −1.20188 | ||||||||
\(789\) | −25.9259 | + | 25.9391i | −0.922986 | + | 0.923457i | ||||
\(790\) | 12.7743 | 0.454488 | ||||||||
\(791\) | 2.79872 | 0.0995109 | ||||||||
\(792\) | 3.69910 | − | 0.643356i | 0.131442 | − | 0.0228607i | ||||
\(793\) | 9.39671 | 0.333687 | ||||||||
\(794\) | 12.1386 | 0.430783 | ||||||||
\(795\) | 8.43133 | − | 8.43563i | 0.299028 | − | 0.299181i | ||||
\(796\) | 45.3544 | 1.60754 | ||||||||
\(797\) | − | 30.7765i | − | 1.09016i | −0.838384 | − | 0.545080i | \(-0.816499\pi\) | ||
0.838384 | − | 0.545080i | \(-0.183501\pi\) | |||||||
\(798\) | −1.59542 | + | 1.59624i | −0.0564773 | + | 0.0565061i | ||||
\(799\) | − | 53.9161i | − | 1.90741i | ||||||
\(800\) | −8.11278 | −0.286830 | ||||||||
\(801\) | 37.4394 | − | 0.0190964i | 1.32286 | − | 0.000674738i | ||||
\(802\) | − | 13.8167i | − | 0.487886i | ||||||
\(803\) | 22.4156 | − | 3.88679i | 0.791029 | − | 0.137162i | ||||
\(804\) | −1.45180 | + | 1.45255i | −0.0512012 | + | 0.0512273i | ||||
\(805\) | − | 4.83595i | − | 0.170445i | ||||||
\(806\) | − | 8.89598i | − | 0.313348i | ||||||
\(807\) | −29.5174 | − | 29.5024i | −1.03906 | − | 1.03853i | ||||
\(808\) | 6.58370 | 0.231614 | ||||||||
\(809\) | −19.3715 | −0.681064 | −0.340532 | − | 0.940233i | \(-0.610607\pi\) | ||||
−0.340532 | + | 0.940233i | \(0.610607\pi\) | |||||||
\(810\) | −0.0187808 | − | 18.4104i | −0.000659891 | − | 0.646875i | ||||
\(811\) | − | 32.0378i | − | 1.12500i | −0.826797 | − | 0.562500i | \(-0.809840\pi\) | ||
0.826797 | − | 0.562500i | \(-0.190160\pi\) | |||||||
\(812\) | 10.2670i | 0.360302i | ||||||||
\(813\) | 3.61615 | + | 3.61431i | 0.126824 | + | 0.126759i | ||||
\(814\) | 6.86586 | + | 39.5962i | 0.240648 | + | 1.38785i | ||||
\(815\) | 17.0281i | 0.596468i | ||||||||
\(816\) | −20.8516 | + | 20.8622i | −0.729952 | + | 0.730325i | ||||
\(817\) | −6.45257 | −0.225747 | ||||||||
\(818\) | − | 33.0136i | − | 1.15429i | ||||||
\(819\) | 0.00363478 | + | 7.12616i | 0.000127009 | + | 0.249008i | ||||
\(820\) | 14.4817i | 0.505721i | ||||||||
\(821\) | −46.7599 | −1.63193 | −0.815966 | − | 0.578100i | \(-0.803794\pi\) | ||||
−0.815966 | + | 0.578100i | \(0.803794\pi\) | |||||||
\(822\) | 41.6416 | + | 41.6204i | 1.45242 | + | 1.45168i | ||||
\(823\) | −28.2494 | −0.984712 | −0.492356 | − | 0.870394i | \(-0.663864\pi\) | ||||
−0.492356 | + | 0.870394i | \(0.663864\pi\) | |||||||
\(824\) | 5.31061 | 0.185004 | ||||||||
\(825\) | −4.69713 | − | 3.30711i | −0.163533 | − | 0.115139i | ||||
\(826\) | −4.02312 | −0.139982 | ||||||||
\(827\) | −23.6293 | −0.821670 | −0.410835 | − | 0.911710i | \(-0.634763\pi\) | ||||
−0.410835 | + | 0.911710i | \(0.634763\pi\) | |||||||
\(828\) | −31.6920 | + | 0.0161649i | −1.10137 | + | 0.000561768i | ||||
\(829\) | 12.1268 | 0.421180 | 0.210590 | − | 0.977575i | \(-0.432462\pi\) | ||||
0.210590 | + | 0.977575i | \(0.432462\pi\) | |||||||
\(830\) | 4.42047i | 0.153437i | ||||||||
\(831\) | −6.03017 | − | 6.02710i | −0.209184 | − | 0.209078i | ||||
\(832\) | − | 22.3321i | − | 0.774225i | ||||||
\(833\) | 4.73436 | 0.164036 | ||||||||
\(834\) | 23.2983 | + | 23.2864i | 0.806754 | + | 0.806342i | ||||
\(835\) | − | 17.5347i | − | 0.606812i | ||||||
\(836\) | 4.54706 | − | 0.788445i | 0.157263 | − | 0.0272689i | ||||
\(837\) | 6.73190 | + | 6.72161i | 0.232689 | + | 0.232333i | ||||
\(838\) | − | 52.5576i | − | 1.81557i | ||||||
\(839\) | 2.31556i | 0.0799422i | 0.999201 | + | 0.0399711i | \(0.0127266\pi\) | ||||
−0.999201 | + | 0.0399711i | \(0.987273\pi\) | |||||||
\(840\) | 0.462046 | − | 0.462281i | 0.0159421 | − | 0.0159502i | ||||
\(841\) | −6.90994 | −0.238274 | ||||||||
\(842\) | −38.8502 | −1.33887 | ||||||||
\(843\) | −12.8510 | + | 12.8576i | −0.442613 | + | 0.442839i | ||||
\(844\) | − | 37.5174i | − | 1.29140i | ||||||
\(845\) | − | 7.35753i | − | 0.253107i | ||||||
\(846\) | −69.8874 | + | 0.0356468i | −2.40278 | + | 0.00122556i | ||||
\(847\) | −3.70338 | − | 10.3578i | −0.127250 | − | 0.355900i | ||||
\(848\) | 24.7688i | 0.850564i | ||||||||
\(849\) | 11.1494 | + | 11.1437i | 0.382646 | + | 0.382451i | ||||
\(850\) | −9.68459 | −0.332179 | ||||||||
\(851\) | − | 28.6452i | − | 0.981945i | ||||||
\(852\) | −16.8460 | − | 16.8374i | −0.577134 | − | 0.576840i | ||||
\(853\) | 47.5073i | 1.62662i | 0.581831 | + | 0.813310i | \(0.302336\pi\) | ||||
−0.581831 | + | 0.813310i | \(0.697664\pi\) | |||||||
\(854\) | −8.09211 | −0.276906 | ||||||||
\(855\) | −0.000974684 | − | 1.91092i | −3.33335e−5 | − | 0.0653519i | ||||
\(856\) | 1.78775 | 0.0611039 | ||||||||
\(857\) | 5.15358 | 0.176043 | 0.0880215 | − | 0.996119i | \(-0.471946\pi\) | ||||
0.0880215 | + | 0.996119i | \(0.471946\pi\) | |||||||
\(858\) | 16.0696 | − | 22.8238i | 0.548606 | − | 0.779190i | ||||
\(859\) | 22.6256 | 0.771974 | 0.385987 | − | 0.922504i | \(-0.373861\pi\) | ||||
0.385987 | + | 0.922504i | \(0.373861\pi\) | |||||||
\(860\) | 22.1289 | 0.754588 | ||||||||
\(861\) | 8.12135 | + | 8.11721i | 0.276775 | + | 0.276634i | ||||
\(862\) | 44.2279 | 1.50641 | ||||||||
\(863\) | 11.7358i | 0.399490i | 0.979848 | + | 0.199745i | \(0.0640114\pi\) | ||||
−0.979848 | + | 0.199745i | \(0.935989\pi\) | |||||||
\(864\) | 29.8311 | + | 29.7854i | 1.01487 | + | 1.01332i | ||||
\(865\) | 21.7187i | 0.738457i | ||||||||
\(866\) | −20.8877 | −0.709792 | ||||||||
\(867\) | −6.62924 | + | 6.63262i | −0.225141 | + | 0.225256i | ||||
\(868\) | 3.99931i | 0.135746i | ||||||||
\(869\) | −20.4070 | + | 3.53851i | −0.692260 | + | 0.120036i | ||||
\(870\) | −11.7781 | − | 11.7721i | −0.399315 | − | 0.399111i | ||||
\(871\) | 1.28932i | 0.0436870i | ||||||||
\(872\) | − | 2.77826i | − | 0.0940839i | ||||||
\(873\) | 0.0224753 | + | 44.0639i | 0.000760672 | + | 1.49134i | ||||
\(874\) | −6.30119 | −0.213141 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −18.3565 | − | 18.3471i | −0.620207 | − | 0.619891i | ||||
\(877\) | − | 34.3823i | − | 1.16101i | −0.814258 | − | 0.580503i | \(-0.802856\pi\) | ||
0.814258 | − | 0.580503i | \(-0.197144\pi\) | |||||||
\(878\) | − | 37.8255i | − | 1.27655i | ||||||
\(879\) | 33.1964 | − | 33.2133i | 1.11969 | − | 1.12026i | ||||
\(880\) | 11.7546 | − | 2.03821i | 0.396247 | − | 0.0687079i | ||||
\(881\) | 45.6864i | 1.53921i | 0.638519 | + | 0.769606i | \(0.279548\pi\) | ||||
−0.638519 | + | 0.769606i | \(0.720452\pi\) | |||||||
\(882\) | −0.00313014 | − | 6.13679i | −0.000105397 | − | 0.206637i | ||||
\(883\) | 32.6587 | 1.09905 | 0.549527 | − | 0.835476i | \(-0.314808\pi\) | ||||
0.549527 | + | 0.835476i | \(0.314808\pi\) | |||||||
\(884\) | − | 24.5664i | − | 0.826258i | ||||||
\(885\) | 2.40812 | − | 2.40935i | 0.0809480 | − | 0.0809893i | ||||
\(886\) | − | 17.6184i | − | 0.591901i | ||||||
\(887\) | 10.1516 | 0.340857 | 0.170429 | − | 0.985370i | \(-0.445485\pi\) | ||||
0.170429 | + | 0.985370i | \(0.445485\pi\) | |||||||
\(888\) | 2.73687 | − | 2.73827i | 0.0918434 | − | 0.0918903i | ||||
\(889\) | −13.1403 | −0.440712 | ||||||||
\(890\) | −25.5287 | −0.855723 | ||||||||
\(891\) | 5.12973 | + | 29.4055i | 0.171852 | + | 0.985123i | ||||
\(892\) | 9.68483 | 0.324272 | ||||||||
\(893\) | −7.25400 | −0.242746 | ||||||||
\(894\) | −38.8906 | + | 38.9104i | −1.30070 | + | 1.30136i | ||||
\(895\) | 22.4731 | 0.751193 | ||||||||
\(896\) | 3.00600i | 0.100423i | ||||||||
\(897\) | −14.0654 | + | 14.0726i | −0.469629 | + | 0.469869i | ||||
\(898\) | 34.1353i | 1.13911i | ||||||||
\(899\) | 8.60473 | 0.286984 | ||||||||
\(900\) | 0.00334264 | + | 6.55341i | 0.000111421 | + | 0.218447i | ||||
\(901\) | 32.6003i | 1.08607i | ||||||||
\(902\) | −7.68417 | − | 44.3155i | −0.255855 | − | 1.47555i | ||||
\(903\) | 12.4036 | − | 12.4099i | 0.412766 | − | 0.412976i | ||||
\(904\) | 1.05611i | 0.0351257i | ||||||||
\(905\) | 2.04960i | 0.0681310i | ||||||||
\(906\) | −12.3204 | − | 12.3141i | −0.409319 | − | 0.409110i | ||||
\(907\) | −24.3139 | −0.807329 | −0.403664 | − | 0.914907i | \(-0.632264\pi\) | ||||
−0.403664 | + | 0.914907i | \(0.632264\pi\) | |||||||
\(908\) | −13.6159 | −0.451858 | ||||||||
\(909\) | 0.0266971 | + | 52.3409i | 0.000885485 | + | 1.73604i | ||||
\(910\) | − | 4.85909i | − | 0.161077i | ||||||
\(911\) | − | 36.9280i | − | 1.22348i | −0.791059 | − | 0.611740i | \(-0.790470\pi\) | ||
0.791059 | − | 0.611740i | \(-0.209530\pi\) | |||||||
\(912\) | 2.80686 | + | 2.80543i | 0.0929443 | + | 0.0928969i | ||||
\(913\) | −1.22448 | − | 7.06175i | −0.0405245 | − | 0.233710i | ||||
\(914\) | − | 49.5498i | − | 1.63896i | ||||||
\(915\) | 4.84369 | − | 4.84616i | 0.160127 | − | 0.160209i | ||||
\(916\) | 1.98672 | 0.0656430 | ||||||||
\(917\) | 6.43379i | 0.212462i | ||||||||
\(918\) | 35.6107 | + | 35.5562i | 1.17533 | + | 1.17353i | ||||
\(919\) | 36.7202i | 1.21129i | 0.795736 | + | 0.605644i | \(0.207084\pi\) | ||||
−0.795736 | + | 0.605644i | \(0.792916\pi\) | |||||||
\(920\) | 1.82487 | 0.0601642 | ||||||||
\(921\) | −7.05473 | − | 7.05113i | −0.232461 | − | 0.232343i | ||||
\(922\) | 48.2196 | 1.58803 | ||||||||
\(923\) | −14.9530 | −0.492184 | ||||||||
\(924\) | −7.22430 | + | 10.2607i | −0.237662 | + | 0.337554i | ||||
\(925\) | −5.92338 | −0.194760 | ||||||||
\(926\) | 13.0130 | 0.427634 | ||||||||
\(927\) | 0.0215347 | + | 42.2198i | 0.000707291 | + | 1.38668i | ||||
\(928\) | 38.1301 | 1.25168 | ||||||||
\(929\) | 20.9898i | 0.688653i | 0.938850 | + | 0.344326i | \(0.111893\pi\) | ||||
−0.938850 | + | 0.344326i | \(0.888107\pi\) | |||||||
\(930\) | −4.58792 | − | 4.58558i | −0.150444 | − | 0.150367i | ||||
\(931\) | − | 0.636972i | − | 0.0208759i | ||||||
\(932\) | −60.4873 | −1.98133 | ||||||||
\(933\) | 9.87356 | + | 9.86853i | 0.323246 | + | 0.323081i | ||||
\(934\) | − | 78.8474i | − | 2.57996i | ||||||
\(935\) | 15.4712 | − | 2.68266i | 0.505963 | − | 0.0877323i | ||||
\(936\) | −2.68909 | + | 0.00137160i | −0.0878957 | + | 4.48322e-5i | ||||
\(937\) | − | 34.8033i | − | 1.13697i | −0.822692 | − | 0.568487i | \(-0.807529\pi\) | ||
0.822692 | − | 0.568487i | \(-0.192471\pi\) | |||||||
\(938\) | − | 1.11032i | − | 0.0362532i | ||||||
\(939\) | 18.9400 | − | 18.9497i | 0.618085 | − | 0.618400i | ||||
\(940\) | 24.8773 | 0.811409 | ||||||||
\(941\) | 58.5246 | 1.90785 | 0.953924 | − | 0.300049i | \(-0.0970030\pi\) | ||||
0.953924 | + | 0.300049i | \(0.0970030\pi\) | |||||||
\(942\) | 15.9687 | − | 15.9769i | 0.520289 | − | 0.520554i | ||||
\(943\) | 32.0593i | 1.04399i | ||||||||
\(944\) | 7.07435i | 0.230251i | ||||||||
\(945\) | 3.67704 | + | 3.67142i | 0.119614 | + | 0.119431i | ||||
\(946\) | −67.7169 | + | 11.7419i | −2.20166 | + | 0.381761i | ||||
\(947\) | − | 36.3434i | − | 1.18100i | −0.807037 | − | 0.590500i | \(-0.798930\pi\) | ||
0.807037 | − | 0.590500i | \(-0.201070\pi\) | |||||||
\(948\) | 16.7116 | + | 16.7031i | 0.542768 | + | 0.542491i | ||||
\(949\) | −16.2937 | −0.528917 | ||||||||
\(950\) | 1.30299i | 0.0422745i | ||||||||
\(951\) | −2.18291 | − | 2.18180i | −0.0707858 | − | 0.0707497i | ||||
\(952\) | 1.78653i | 0.0579019i | ||||||||
\(953\) | 33.0869 | 1.07179 | 0.535896 | − | 0.844284i | \(-0.319974\pi\) | ||||
0.535896 | + | 0.844284i | \(0.319974\pi\) | |||||||
\(954\) | 42.2574 | − | 0.0215538i | 1.36813 | − | 0.000697832i | ||||
\(955\) | −2.33032 | −0.0754074 | ||||||||
\(956\) | 51.6119 | 1.66925 | ||||||||
\(957\) | 22.0765 | + | 15.5435i | 0.713633 | + | 0.502449i | ||||
\(958\) | −50.9081 | −1.64477 | ||||||||
\(959\) | −16.6169 | −0.536589 | ||||||||
\(960\) | −11.5173 | − | 11.5114i | −0.371719 | − | 0.371530i | ||||
\(961\) | −27.6482 | −0.891877 | ||||||||
\(962\) | − | 28.7822i | − | 0.927977i | ||||||
\(963\) | 0.00724935 | + | 14.2127i | 0.000233607 | + | 0.457998i | ||||
\(964\) | − | 25.0226i | − | 0.805922i | ||||||
\(965\) | −5.98755 | −0.192746 | ||||||||
\(966\) | 12.1126 | − | 12.1188i | 0.389716 | − | 0.389915i | ||||
\(967\) | − | 13.2363i | − | 0.425652i | −0.977090 | − | 0.212826i | \(-0.931733\pi\) | ||
0.977090 | − | 0.212826i | \(-0.0682667\pi\) | |||||||
\(968\) | 3.90858 | − | 1.39749i | 0.125627 | − | 0.0449170i | ||||
\(969\) | 3.69435 | + | 3.69246i | 0.118679 | + | 0.118619i | ||||
\(970\) | − | 30.0456i | − | 0.964708i | ||||||
\(971\) | 37.3725i | 1.19934i | 0.800248 | + | 0.599670i | \(0.204701\pi\) | ||||
−0.800248 | + | 0.599670i | \(0.795299\pi\) | |||||||
\(972\) | 24.0481 | − | 24.1095i | 0.771342 | − | 0.773312i | ||||
\(973\) | −9.29709 | −0.298051 | ||||||||
\(974\) | 25.7544 | 0.825223 | ||||||||
\(975\) | 2.90999 | + | 2.90850i | 0.0931941 | + | 0.0931466i | ||||
\(976\) | 14.2294i | 0.455470i | ||||||||
\(977\) | − | 7.28663i | − | 0.233120i | −0.993184 | − | 0.116560i | \(-0.962813\pi\) | ||
0.993184 | − | 0.116560i | \(-0.0371867\pi\) | |||||||
\(978\) | −42.6502 | + | 42.6720i | −1.36380 | + | 1.36450i | ||||
\(979\) | 40.7823 | − | 7.07152i | 1.30341 | − | 0.226007i | ||||
\(980\) | 2.18447i | 0.0697804i | ||||||||
\(981\) | 22.0874 | − | 0.0112659i | 0.705196 | − | 0.000359693i | ||||
\(982\) | −37.5698 | −1.19890 | ||||||||
\(983\) | − | 3.98229i | − | 0.127015i | −0.997981 | − | 0.0635076i | \(-0.979771\pi\) | ||
0.997981 | − | 0.0635076i | \(-0.0202287\pi\) | |||||||
\(984\) | −3.06307 | + | 3.06463i | −0.0976470 | + | 0.0976969i | ||||
\(985\) | 15.4447i | 0.492109i | ||||||||
\(986\) | 45.5176 | 1.44958 | ||||||||
\(987\) | 13.9441 | − | 13.9513i | 0.443847 | − | 0.444074i | ||||
\(988\) | −3.30523 | −0.105153 | ||||||||
\(989\) | 48.9886 | 1.55775 | ||||||||
\(990\) | −3.48756 | − | 20.0524i | −0.110842 | − | 0.637308i | ||||
\(991\) | −58.1994 | −1.84877 | −0.924383 | − | 0.381466i | \(-0.875419\pi\) | ||||
−0.924383 | + | 0.381466i | \(0.875419\pi\) | |||||||
\(992\) | 14.8528 | 0.471577 | ||||||||
\(993\) | −32.2963 | + | 32.3128i | −1.02489 | + | 1.02542i | ||||
\(994\) | 12.8770 | 0.408433 | ||||||||
\(995\) | − | 20.7622i | − | 0.658205i | ||||||
\(996\) | −5.78003 | + | 5.78297i | −0.183147 | + | 0.183241i | ||||
\(997\) | − | 30.0188i | − | 0.950705i | −0.879796 | − | 0.475352i | \(-0.842321\pi\) | ||
0.879796 | − | 0.475352i | \(-0.157679\pi\) | |||||||
\(998\) | −23.3192 | −0.738156 | ||||||||
\(999\) | 21.7805 | + | 21.7472i | 0.689106 | + | 0.688052i |
(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 | 1155.2.l.e.1121.8 | yes | 40 | |
3.2 | odd | 2 | 1155.2.l.f.1121.33 | yes | 40 | ||
11.10 | odd | 2 | 1155.2.l.f.1121.34 | yes | 40 | ||
33.32 | even | 2 | inner | 1155.2.l.e.1121.7 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.l.e.1121.7 | ✓ | 40 | 33.32 | even | 2 | inner | |
1155.2.l.e.1121.8 | yes | 40 | 1.1 | even | 1 | trivial | |
1155.2.l.f.1121.33 | yes | 40 | 3.2 | odd | 2 | ||
1155.2.l.f.1121.34 | yes | 40 | 11.10 | odd | 2 |