Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.20 | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.e.191.20 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.878679 | − | 1.49262i | −0.507306 | − | 0.861766i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | −1.67676 | − | 0.434124i | −0.684536 | − | 0.177230i | ||||
\(7\) | 2.38487 | 0.901395 | 0.450697 | − | 0.892677i | \(-0.351175\pi\) | ||||
0.450697 | + | 0.892677i | \(0.351175\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.45585 | + | 2.62307i | −0.485282 | + | 0.874358i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.76715 | 1.73886 | 0.869431 | − | 0.494054i | \(-0.164485\pi\) | ||||
0.869431 | + | 0.494054i | \(0.164485\pi\) | |||||||
\(12\) | −1.49262 | + | 0.878679i | −0.430883 | + | 0.253653i | ||||
\(13\) | −1.58054 | + | 1.58054i | −0.438362 | + | 0.438362i | −0.891460 | − | 0.453098i | \(-0.850319\pi\) |
0.453098 | + | 0.891460i | \(0.350319\pi\) | |||||||
\(14\) | 1.68635 | − | 1.68635i | 0.450697 | − | 0.450697i | ||||
\(15\) | 0.434124 | − | 1.67676i | 0.112090 | − | 0.432939i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.766912 | − | 0.766912i | −0.186003 | − | 0.186003i | 0.607962 | − | 0.793966i | \(-0.291987\pi\) |
−0.793966 | + | 0.607962i | \(0.791987\pi\) | |||||||
\(18\) | 0.825355 | + | 2.88423i | 0.194538 | + | 0.679820i | ||||
\(19\) | 4.27127 | − | 4.27127i | 0.979898 | − | 0.979898i | −0.0199043 | − | 0.999802i | \(-0.506336\pi\) |
0.999802 | + | 0.0199043i | \(0.00633614\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | −2.09553 | − | 3.55970i | −0.457283 | − | 0.776791i | ||||
\(22\) | 4.07799 | − | 4.07799i | 0.869431 | − | 0.869431i | ||||
\(23\) | 5.87049 | + | 5.87049i | 1.22408 | + | 1.22408i | 0.966168 | + | 0.257913i | \(0.0830347\pi\) |
0.257913 | + | 0.966168i | \(0.416965\pi\) | |||||||
\(24\) | −0.434124 | + | 1.67676i | −0.0886151 | + | 0.342268i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 2.23522i | 0.438362i | ||||||||
\(27\) | 5.19448 | − | 0.131812i | 0.999678 | − | 0.0253671i | ||||
\(28\) | − | 2.38487i | − | 0.450697i | ||||||
\(29\) | −0.666860 | + | 0.666860i | −0.123833 | + | 0.123833i | −0.766307 | − | 0.642474i | \(-0.777908\pi\) |
0.642474 | + | 0.766307i | \(0.277908\pi\) | |||||||
\(30\) | −0.878679 | − | 1.49262i | −0.160424 | − | 0.272514i | ||||
\(31\) | −4.93081 | − | 4.93081i | −0.885599 | − | 0.885599i | 0.108497 | − | 0.994097i | \(-0.465396\pi\) |
−0.994097 | + | 0.108497i | \(0.965396\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −5.06748 | − | 8.60819i | −0.882135 | − | 1.49849i | ||||
\(34\) | −1.08458 | −0.186003 | ||||||||
\(35\) | 1.68635 | + | 1.68635i | 0.285046 | + | 0.285046i | ||||
\(36\) | 2.62307 | + | 1.45585i | 0.437179 | + | 0.242641i | ||||
\(37\) | 5.79440 | − | 1.85066i | 0.952593 | − | 0.304247i | ||||
\(38\) | − | 6.04049i | − | 0.979898i | ||||||
\(39\) | 3.74793 | + | 0.970360i | 0.600149 | + | 0.155382i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 2.85384 | 0.445695 | 0.222847 | − | 0.974853i | \(-0.428465\pi\) | ||||
0.222847 | + | 0.974853i | \(0.428465\pi\) | |||||||
\(42\) | −3.99886 | − | 1.03533i | −0.617037 | − | 0.159754i | ||||
\(43\) | −6.47528 | + | 6.47528i | −0.987472 | + | 0.987472i | −0.999922 | − | 0.0124508i | \(-0.996037\pi\) |
0.0124508 | + | 0.999922i | \(0.496037\pi\) | |||||||
\(44\) | − | 5.76715i | − | 0.869431i | ||||||
\(45\) | −2.88423 | + | 0.825355i | −0.429956 | + | 0.123037i | ||||
\(46\) | 8.30212 | 1.22408 | ||||||||
\(47\) | − | 8.44283i | − | 1.23151i | −0.787936 | − | 0.615757i | \(-0.788850\pi\) | ||
0.787936 | − | 0.615757i | \(-0.211150\pi\) | |||||||
\(48\) | 0.878679 | + | 1.49262i | 0.126826 | + | 0.215442i | ||||
\(49\) | −1.31242 | −0.187488 | ||||||||
\(50\) | 0.707107 | + | 0.707107i | 0.100000 | + | 0.100000i | ||||
\(51\) | −0.470841 | + | 1.81858i | −0.0659309 | + | 0.254652i | ||||
\(52\) | 1.58054 | + | 1.58054i | 0.219181 | + | 0.219181i | ||||
\(53\) | 7.21707i | 0.991341i | 0.868511 | + | 0.495670i | \(0.165078\pi\) | ||||
−0.868511 | + | 0.495670i | \(0.834922\pi\) | |||||||
\(54\) | 3.57985 | − | 3.76626i | 0.487156 | − | 0.512523i | ||||
\(55\) | 4.07799 | + | 4.07799i | 0.549877 | + | 0.549877i | ||||
\(56\) | −1.68635 | − | 1.68635i | −0.225349 | − | 0.225349i | ||||
\(57\) | −10.1285 | − | 2.62232i | −1.34155 | − | 0.347335i | ||||
\(58\) | 0.943082i | 0.123833i | ||||||||
\(59\) | −5.63841 | − | 5.63841i | −0.734059 | − | 0.734059i | 0.237362 | − | 0.971421i | \(-0.423717\pi\) |
−0.971421 | + | 0.237362i | \(0.923717\pi\) | |||||||
\(60\) | −1.67676 | − | 0.434124i | −0.216469 | − | 0.0560451i | ||||
\(61\) | −8.82247 | − | 8.82247i | −1.12960 | − | 1.12960i | −0.990242 | − | 0.139360i | \(-0.955496\pi\) |
−0.139360 | − | 0.990242i | \(-0.544504\pi\) | |||||||
\(62\) | −6.97322 | −0.885599 | ||||||||
\(63\) | −3.47200 | + | 6.25568i | −0.437430 | + | 0.788141i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −2.23522 | −0.277244 | ||||||||
\(66\) | −9.67016 | − | 2.50366i | −1.19031 | − | 0.308179i | ||||
\(67\) | − | 2.96422i | − | 0.362137i | −0.983471 | − | 0.181068i | \(-0.942045\pi\) | ||
0.983471 | − | 0.181068i | \(-0.0579555\pi\) | |||||||
\(68\) | −0.766912 | + | 0.766912i | −0.0930017 | + | 0.0930017i | ||||
\(69\) | 3.60415 | − | 13.9207i | 0.433888 | − | 1.67585i | ||||
\(70\) | 2.38487 | 0.285046 | ||||||||
\(71\) | − | 10.2106i | − | 1.21177i | −0.795552 | − | 0.605886i | \(-0.792819\pi\) | ||
0.795552 | − | 0.605886i | \(-0.207181\pi\) | |||||||
\(72\) | 2.88423 | − | 0.825355i | 0.339910 | − | 0.0972690i | ||||
\(73\) | − | 1.48258i | − | 0.173523i | −0.996229 | − | 0.0867615i | \(-0.972348\pi\) | ||
0.996229 | − | 0.0867615i | \(-0.0276518\pi\) | |||||||
\(74\) | 2.78864 | − | 5.40587i | 0.324173 | − | 0.628420i | ||||
\(75\) | 1.49262 | − | 0.878679i | 0.172353 | − | 0.101461i | ||||
\(76\) | −4.27127 | − | 4.27127i | −0.489949 | − | 0.489949i | ||||
\(77\) | 13.7539 | 1.56740 | ||||||||
\(78\) | 3.33634 | − | 1.96404i | 0.377766 | − | 0.222384i | ||||
\(79\) | −3.85057 | + | 3.85057i | −0.433223 | + | 0.433223i | −0.889723 | − | 0.456500i | \(-0.849103\pi\) |
0.456500 | + | 0.889723i | \(0.349103\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | −4.76103 | − | 7.63758i | −0.529003 | − | 0.848620i | ||||
\(82\) | 2.01797 | − | 2.01797i | 0.222847 | − | 0.222847i | ||||
\(83\) | 16.2511i | 1.78378i | 0.452248 | + | 0.891892i | \(0.350622\pi\) | ||||
−0.452248 | + | 0.891892i | \(0.649378\pi\) | |||||||
\(84\) | −3.55970 | + | 2.09553i | −0.388396 | + | 0.228641i | ||||
\(85\) | − | 1.08458i | − | 0.117639i | ||||||
\(86\) | 9.15744i | 0.987472i | ||||||||
\(87\) | 1.58133 | + | 0.409414i | 0.169536 | + | 0.0438938i | ||||
\(88\) | −4.07799 | − | 4.07799i | −0.434716 | − | 0.434716i | ||||
\(89\) | −3.88764 | + | 3.88764i | −0.412089 | + | 0.412089i | −0.882466 | − | 0.470377i | \(-0.844118\pi\) |
0.470377 | + | 0.882466i | \(0.344118\pi\) | |||||||
\(90\) | −1.45585 | + | 2.62307i | −0.153460 | + | 0.276496i | ||||
\(91\) | −3.76937 | + | 3.76937i | −0.395137 | + | 0.395137i | ||||
\(92\) | 5.87049 | − | 5.87049i | 0.612040 | − | 0.612040i | ||||
\(93\) | −3.02724 | + | 11.6924i | −0.313910 | + | 1.21245i | ||||
\(94\) | −5.96998 | − | 5.96998i | −0.615757 | − | 0.615757i | ||||
\(95\) | 6.04049 | 0.619742 | ||||||||
\(96\) | 1.67676 | + | 0.434124i | 0.171134 | + | 0.0443076i | ||||
\(97\) | 11.4270 | − | 11.4270i | 1.16024 | − | 1.16024i | 0.175815 | − | 0.984423i | \(-0.443744\pi\) |
0.984423 | − | 0.175815i | \(-0.0562561\pi\) | |||||||
\(98\) | −0.928018 | + | 0.928018i | −0.0937440 | + | 0.0937440i | ||||
\(99\) | −8.39609 | + | 15.1277i | −0.843838 | + | 1.52039i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.32729 | −0.231574 | −0.115787 | − | 0.993274i | \(-0.536939\pi\) | ||||
−0.115787 | + | 0.993274i | \(0.536939\pi\) | |||||||
\(102\) | 0.952995 | + | 1.61886i | 0.0943606 | + | 0.160291i | ||||
\(103\) | 3.07081 | + | 3.07081i | 0.302576 | + | 0.302576i | 0.842021 | − | 0.539445i | \(-0.181366\pi\) |
−0.539445 | + | 0.842021i | \(0.681366\pi\) | |||||||
\(104\) | 2.23522 | 0.219181 | ||||||||
\(105\) | 1.03533 | − | 3.99886i | 0.101038 | − | 0.390248i | ||||
\(106\) | 5.10324 | + | 5.10324i | 0.495670 | + | 0.495670i | ||||
\(107\) | 10.7333i | 1.03762i | 0.854888 | + | 0.518812i | \(0.173625\pi\) | ||||
−0.854888 | + | 0.518812i | \(0.826375\pi\) | |||||||
\(108\) | −0.131812 | − | 5.19448i | −0.0126836 | − | 0.499839i | ||||
\(109\) | −6.01820 | + | 6.01820i | −0.576439 | + | 0.576439i | −0.933920 | − | 0.357481i | \(-0.883636\pi\) |
0.357481 | + | 0.933920i | \(0.383636\pi\) | |||||||
\(110\) | 5.76715 | 0.549877 | ||||||||
\(111\) | −7.85376 | − | 7.02271i | −0.745446 | − | 0.666567i | ||||
\(112\) | −2.38487 | −0.225349 | ||||||||
\(113\) | 12.0416 | − | 12.0416i | 1.13278 | − | 1.13278i | 0.143069 | − | 0.989713i | \(-0.454303\pi\) |
0.989713 | − | 0.143069i | \(-0.0456972\pi\) | |||||||
\(114\) | −9.01618 | + | 5.30766i | −0.844443 | + | 0.497108i | ||||
\(115\) | 8.30212i | 0.774177i | ||||||||
\(116\) | 0.666860 | + | 0.666860i | 0.0619164 | + | 0.0619164i | ||||
\(117\) | −1.84485 | − | 6.44688i | −0.170556 | − | 0.596014i | ||||
\(118\) | −7.97392 | −0.734059 | ||||||||
\(119\) | −1.82898 | − | 1.82898i | −0.167662 | − | 0.167662i | ||||
\(120\) | −1.49262 | + | 0.878679i | −0.136257 | + | 0.0802121i | ||||
\(121\) | 22.2601 | 2.02364 | ||||||||
\(122\) | −12.4769 | −1.12960 | ||||||||
\(123\) | −2.50761 | − | 4.25971i | −0.226104 | − | 0.384085i | ||||
\(124\) | −4.93081 | + | 4.93081i | −0.442800 | + | 0.442800i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 1.96836 | + | 6.87850i | 0.175355 | + | 0.612786i | ||||
\(127\) | −10.6143 | −0.941868 | −0.470934 | − | 0.882169i | \(-0.656083\pi\) | ||||
−0.470934 | + | 0.882169i | \(0.656083\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 15.3549 | + | 3.97546i | 1.35192 | + | 0.350020i | ||||
\(130\) | −1.58054 | + | 1.58054i | −0.138622 | + | 0.138622i | ||||
\(131\) | −4.84087 | + | 4.84087i | −0.422949 | + | 0.422949i | −0.886218 | − | 0.463269i | \(-0.846676\pi\) |
0.463269 | + | 0.886218i | \(0.346676\pi\) | |||||||
\(132\) | −8.60819 | + | 5.06748i | −0.749246 | + | 0.441067i | ||||
\(133\) | 10.1864 | − | 10.1864i | 0.883274 | − | 0.883274i | ||||
\(134\) | −2.09602 | − | 2.09602i | −0.181068 | − | 0.181068i | ||||
\(135\) | 3.76626 | + | 3.57985i | 0.324148 | + | 0.308104i | ||||
\(136\) | 1.08458i | 0.0930017i | ||||||||
\(137\) | 22.0782i | 1.88627i | 0.332415 | + | 0.943133i | \(0.392136\pi\) | ||||
−0.332415 | + | 0.943133i | \(0.607864\pi\) | |||||||
\(138\) | −7.29490 | − | 12.3919i | −0.620983 | − | 1.05487i | ||||
\(139\) | − | 4.31292i | − | 0.365817i | −0.983130 | − | 0.182909i | \(-0.941449\pi\) | ||
0.983130 | − | 0.182909i | \(-0.0585512\pi\) | |||||||
\(140\) | 1.68635 | − | 1.68635i | 0.142523 | − | 0.142523i | ||||
\(141\) | −12.6020 | + | 7.41854i | −1.06128 | + | 0.624754i | ||||
\(142\) | −7.21996 | − | 7.21996i | −0.605886 | − | 0.605886i | ||||
\(143\) | −9.11520 | + | 9.11520i | −0.762251 | + | 0.762251i | ||||
\(144\) | 1.45585 | − | 2.62307i | 0.121320 | − | 0.218589i | ||||
\(145\) | −0.943082 | −0.0783187 | ||||||||
\(146\) | −1.04834 | − | 1.04834i | −0.0867615 | − | 0.0867615i | ||||
\(147\) | 1.15319 | + | 1.95894i | 0.0951137 | + | 0.161571i | ||||
\(148\) | −1.85066 | − | 5.79440i | −0.152123 | − | 0.476297i | ||||
\(149\) | − | 19.4968i | − | 1.59724i | −0.601837 | − | 0.798619i | \(-0.705564\pi\) | ||
0.601837 | − | 0.798619i | \(-0.294436\pi\) | |||||||
\(150\) | 0.434124 | − | 1.67676i | 0.0354460 | − | 0.136907i | ||||
\(151\) | − | 3.98542i | − | 0.324329i | −0.986764 | − | 0.162165i | \(-0.948152\pi\) | ||
0.986764 | − | 0.162165i | \(-0.0518476\pi\) | |||||||
\(152\) | −6.04049 | −0.489949 | ||||||||
\(153\) | 3.12817 | − | 0.895161i | 0.252898 | − | 0.0723695i | ||||
\(154\) | 9.72547 | − | 9.72547i | 0.783701 | − | 0.783701i | ||||
\(155\) | − | 6.97322i | − | 0.560102i | ||||||
\(156\) | 0.970360 | − | 3.74793i | 0.0776910 | − | 0.300075i | ||||
\(157\) | 22.7620 | 1.81661 | 0.908305 | − | 0.418310i | \(-0.137377\pi\) | ||||
0.908305 | + | 0.418310i | \(0.137377\pi\) | |||||||
\(158\) | 5.44553i | 0.433223i | ||||||||
\(159\) | 10.7724 | − | 6.34149i | 0.854304 | − | 0.502913i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 14.0003 | + | 14.0003i | 1.10338 | + | 1.10338i | ||||
\(162\) | −8.76714 | − | 2.03403i | −0.688811 | − | 0.159808i | ||||
\(163\) | −7.51726 | − | 7.51726i | −0.588798 | − | 0.588798i | 0.348508 | − | 0.937306i | \(-0.386688\pi\) |
−0.937306 | + | 0.348508i | \(0.886688\pi\) | |||||||
\(164\) | − | 2.85384i | − | 0.222847i | ||||||
\(165\) | 2.50366 | − | 9.67016i | 0.194910 | − | 0.752821i | ||||
\(166\) | 11.4912 | + | 11.4912i | 0.891892 | + | 0.891892i | ||||
\(167\) | 12.5348 | + | 12.5348i | 0.969973 | + | 0.969973i | 0.999562 | − | 0.0295892i | \(-0.00941992\pi\) |
−0.0295892 | + | 0.999562i | \(0.509420\pi\) | |||||||
\(168\) | −1.03533 | + | 3.99886i | −0.0798772 | + | 0.308518i | ||||
\(169\) | 8.00381i | 0.615677i | ||||||||
\(170\) | −0.766912 | − | 0.766912i | −0.0588195 | − | 0.0588195i | ||||
\(171\) | 4.98555 | + | 17.4222i | 0.381255 | + | 1.33231i | ||||
\(172\) | 6.47528 | + | 6.47528i | 0.493736 | + | 0.493736i | ||||
\(173\) | −15.9099 | −1.20960 | −0.604802 | − | 0.796376i | \(-0.706748\pi\) | ||||
−0.604802 | + | 0.796376i | \(0.706748\pi\) | |||||||
\(174\) | 1.40767 | − | 0.828666i | 0.106715 | − | 0.0628210i | ||||
\(175\) | 2.38487i | 0.180279i | ||||||||
\(176\) | −5.76715 | −0.434716 | ||||||||
\(177\) | −3.46167 | + | 13.3704i | −0.260195 | + | 1.00498i | ||||
\(178\) | 5.49796i | 0.412089i | ||||||||
\(179\) | −9.10948 | + | 9.10948i | −0.680875 | + | 0.680875i | −0.960197 | − | 0.279322i | \(-0.909890\pi\) |
0.279322 | + | 0.960197i | \(0.409890\pi\) | |||||||
\(180\) | 0.825355 | + | 2.88423i | 0.0615183 | + | 0.214978i | ||||
\(181\) | 4.67113 | 0.347202 | 0.173601 | − | 0.984816i | \(-0.444460\pi\) | ||||
0.173601 | + | 0.984816i | \(0.444460\pi\) | |||||||
\(182\) | 5.33069i | 0.395137i | ||||||||
\(183\) | −5.41650 | + | 20.9207i | −0.400399 | + | 1.54651i | ||||
\(184\) | − | 8.30212i | − | 0.612040i | ||||||
\(185\) | 5.40587 | + | 2.78864i | 0.397448 | + | 0.205025i | ||||
\(186\) | 6.12722 | + | 10.4084i | 0.449270 | + | 0.763180i | ||||
\(187\) | −4.42290 | − | 4.42290i | −0.323434 | − | 0.323434i | ||||
\(188\) | −8.44283 | −0.615757 | ||||||||
\(189\) | 12.3881 | − | 0.314353i | 0.901104 | − | 0.0228658i | ||||
\(190\) | 4.27127 | − | 4.27127i | 0.309871 | − | 0.309871i | ||||
\(191\) | −2.51857 | − | 2.51857i | −0.182237 | − | 0.182237i | 0.610093 | − | 0.792330i | \(-0.291132\pi\) |
−0.792330 | + | 0.610093i | \(0.791132\pi\) | |||||||
\(192\) | 1.49262 | − | 0.878679i | 0.107721 | − | 0.0634132i | ||||
\(193\) | −4.71089 | + | 4.71089i | −0.339098 | + | 0.339098i | −0.856028 | − | 0.516930i | \(-0.827075\pi\) |
0.516930 | + | 0.856028i | \(0.327075\pi\) | |||||||
\(194\) | − | 16.1603i | − | 1.16024i | ||||||
\(195\) | 1.96404 | + | 3.33634i | 0.140648 | + | 0.238920i | ||||
\(196\) | 1.31242i | 0.0937440i | ||||||||
\(197\) | 10.7908i | 0.768811i | 0.923164 | + | 0.384406i | \(0.125594\pi\) | ||||
−0.923164 | + | 0.384406i | \(0.874406\pi\) | |||||||
\(198\) | 4.75995 | + | 16.6338i | 0.338275 | + | 1.18211i | ||||
\(199\) | 4.64611 | + | 4.64611i | 0.329354 | + | 0.329354i | 0.852341 | − | 0.522987i | \(-0.175182\pi\) |
−0.522987 | + | 0.852341i | \(0.675182\pi\) | |||||||
\(200\) | 0.707107 | − | 0.707107i | 0.0500000 | − | 0.0500000i | ||||
\(201\) | −4.42446 | + | 2.60459i | −0.312077 | + | 0.183714i | ||||
\(202\) | −1.64564 | + | 1.64564i | −0.115787 | + | 0.115787i | ||||
\(203\) | −1.59037 | + | 1.59037i | −0.111622 | + | 0.111622i | ||||
\(204\) | 1.81858 | + | 0.470841i | 0.127326 | + | 0.0329654i | ||||
\(205\) | 2.01797 | + | 2.01797i | 0.140941 | + | 0.140941i | ||||
\(206\) | 4.34279 | 0.302576 | ||||||||
\(207\) | −23.9452 | + | 6.85219i | −1.66431 | + | 0.476260i | ||||
\(208\) | 1.58054 | − | 1.58054i | 0.109591 | − | 0.109591i | ||||
\(209\) | 24.6331 | − | 24.6331i | 1.70391 | − | 1.70391i | ||||
\(210\) | −2.09553 | − | 3.55970i | −0.144605 | − | 0.245643i | ||||
\(211\) | 3.92953 | 0.270520 | 0.135260 | − | 0.990810i | \(-0.456813\pi\) | ||||
0.135260 | + | 0.990810i | \(0.456813\pi\) | |||||||
\(212\) | 7.21707 | 0.495670 | ||||||||
\(213\) | −15.2405 | + | 8.97181i | −1.04426 | + | 0.614738i | ||||
\(214\) | 7.58956 | + | 7.58956i | 0.518812 | + | 0.518812i | ||||
\(215\) | −9.15744 | −0.624532 | ||||||||
\(216\) | −3.76626 | − | 3.57985i | −0.256261 | − | 0.243578i | ||||
\(217\) | −11.7593 | − | 11.7593i | −0.798275 | − | 0.798275i | ||||
\(218\) | 8.51102i | 0.576439i | ||||||||
\(219\) | −2.21293 | + | 1.30271i | −0.149536 | + | 0.0880292i | ||||
\(220\) | 4.07799 | − | 4.07799i | 0.274938 | − | 0.274938i | ||||
\(221\) | 2.42426 | 0.163074 | ||||||||
\(222\) | −10.5193 | + | 0.587635i | −0.706006 | + | 0.0394395i | ||||
\(223\) | 15.8876 | 1.06391 | 0.531956 | − | 0.846772i | \(-0.321457\pi\) | ||||
0.531956 | + | 0.846772i | \(0.321457\pi\) | |||||||
\(224\) | −1.68635 | + | 1.68635i | −0.112674 | + | 0.112674i | ||||
\(225\) | −2.62307 | − | 1.45585i | −0.174872 | − | 0.0970564i | ||||
\(226\) | − | 17.0294i | − | 1.13278i | ||||||
\(227\) | 2.98325 | + | 2.98325i | 0.198005 | + | 0.198005i | 0.799144 | − | 0.601139i | \(-0.205286\pi\) |
−0.601139 | + | 0.799144i | \(0.705286\pi\) | |||||||
\(228\) | −2.62232 | + | 10.1285i | −0.173667 | + | 0.670775i | ||||
\(229\) | 23.9167 | 1.58046 | 0.790229 | − | 0.612812i | \(-0.209962\pi\) | ||||
0.790229 | + | 0.612812i | \(0.209962\pi\) | |||||||
\(230\) | 5.87049 | + | 5.87049i | 0.387088 | + | 0.387088i | ||||
\(231\) | −12.0853 | − | 20.5294i | −0.795152 | − | 1.35073i | ||||
\(232\) | 0.943082 | 0.0619164 | ||||||||
\(233\) | −25.6460 | −1.68013 | −0.840063 | − | 0.542489i | \(-0.817482\pi\) | ||||
−0.840063 | + | 0.542489i | \(0.817482\pi\) | |||||||
\(234\) | −5.86314 | − | 3.25413i | −0.383285 | − | 0.212729i | ||||
\(235\) | 5.96998 | − | 5.96998i | 0.389439 | − | 0.389439i | ||||
\(236\) | −5.63841 | + | 5.63841i | −0.367029 | + | 0.367029i | ||||
\(237\) | 9.13087 | + | 2.36403i | 0.593114 | + | 0.153561i | ||||
\(238\) | −2.58657 | −0.167662 | ||||||||
\(239\) | 11.0015 | + | 11.0015i | 0.711626 | + | 0.711626i | 0.966875 | − | 0.255249i | \(-0.0821574\pi\) |
−0.255249 | + | 0.966875i | \(0.582157\pi\) | |||||||
\(240\) | −0.434124 | + | 1.67676i | −0.0280226 | + | 0.108235i | ||||
\(241\) | −20.6461 | + | 20.6461i | −1.32993 | + | 1.32993i | −0.424503 | + | 0.905427i | \(0.639551\pi\) |
−0.905427 | + | 0.424503i | \(0.860449\pi\) | |||||||
\(242\) | 15.7402 | − | 15.7402i | 1.01182 | − | 1.01182i | ||||
\(243\) | −7.21661 | + | 13.8174i | −0.462946 | + | 0.886387i | ||||
\(244\) | −8.82247 | + | 8.82247i | −0.564801 | + | 0.564801i | ||||
\(245\) | −0.928018 | − | 0.928018i | −0.0592889 | − | 0.0592889i | ||||
\(246\) | −4.78521 | − | 1.23892i | −0.305094 | − | 0.0789906i | ||||
\(247\) | 13.5018i | 0.859100i | ||||||||
\(248\) | 6.97322i | 0.442800i | ||||||||
\(249\) | 24.2567 | − | 14.2795i | 1.53721 | − | 0.904924i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −3.73539 | + | 3.73539i | −0.235776 | + | 0.235776i | −0.815098 | − | 0.579323i | \(-0.803317\pi\) |
0.579323 | + | 0.815098i | \(0.303317\pi\) | |||||||
\(252\) | 6.25568 | + | 3.47200i | 0.394071 | + | 0.218715i | ||||
\(253\) | 33.8560 | + | 33.8560i | 2.12851 | + | 2.12851i | ||||
\(254\) | −7.50545 | + | 7.50545i | −0.470934 | + | 0.470934i | ||||
\(255\) | −1.61886 | + | 0.952995i | −0.101377 | + | 0.0596789i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.24794 | − | 9.24794i | −0.576870 | − | 0.576870i | 0.357169 | − | 0.934040i | \(-0.383742\pi\) |
−0.934040 | + | 0.357169i | \(0.883742\pi\) | |||||||
\(258\) | 13.6686 | − | 8.04645i | 0.850970 | − | 0.500950i | ||||
\(259\) | 13.8189 | − | 4.41358i | 0.858662 | − | 0.274246i | ||||
\(260\) | 2.23522i | 0.138622i | ||||||||
\(261\) | −0.778377 | − | 2.72007i | −0.0481803 | − | 0.168368i | ||||
\(262\) | 6.84602i | 0.422949i | ||||||||
\(263\) | −13.9407 | −0.859620 | −0.429810 | − | 0.902919i | \(-0.641419\pi\) | ||||
−0.429810 | + | 0.902919i | \(0.641419\pi\) | |||||||
\(264\) | −2.50366 | + | 9.67016i | −0.154090 | + | 0.595157i | ||||
\(265\) | −5.10324 | + | 5.10324i | −0.313489 | + | 0.313489i | ||||
\(266\) | − | 14.4058i | − | 0.883274i | ||||||
\(267\) | 9.21878 | + | 2.38679i | 0.564180 | + | 0.146069i | ||||
\(268\) | −2.96422 | −0.181068 | ||||||||
\(269\) | − | 10.1133i | − | 0.616617i | −0.951287 | − | 0.308308i | \(-0.900237\pi\) | ||
0.951287 | − | 0.308308i | \(-0.0997628\pi\) | |||||||
\(270\) | 5.19448 | − | 0.131812i | 0.316126 | − | 0.00802180i | ||||
\(271\) | 29.2907 | 1.77928 | 0.889640 | − | 0.456662i | \(-0.150955\pi\) | ||||
0.889640 | + | 0.456662i | \(0.150955\pi\) | |||||||
\(272\) | 0.766912 | + | 0.766912i | 0.0465009 | + | 0.0465009i | ||||
\(273\) | 8.93831 | + | 2.31418i | 0.540971 | + | 0.140060i | ||||
\(274\) | 15.6116 | + | 15.6116i | 0.943133 | + | 0.943133i | ||||
\(275\) | 5.76715i | 0.347773i | ||||||||
\(276\) | −13.9207 | − | 3.60415i | −0.837927 | − | 0.216944i | ||||
\(277\) | −11.9085 | − | 11.9085i | −0.715514 | − | 0.715514i | 0.252169 | − | 0.967683i | \(-0.418856\pi\) |
−0.967683 | + | 0.252169i | \(0.918856\pi\) | |||||||
\(278\) | −3.04969 | − | 3.04969i | −0.182909 | − | 0.182909i | ||||
\(279\) | 20.1124 | − | 5.75538i | 1.20410 | − | 0.344565i | ||||
\(280\) | − | 2.38487i | − | 0.142523i | ||||||
\(281\) | −3.54960 | − | 3.54960i | −0.211751 | − | 0.211751i | 0.593260 | − | 0.805011i | \(-0.297841\pi\) |
−0.805011 | + | 0.593260i | \(0.797841\pi\) | |||||||
\(282\) | −3.66523 | + | 14.1566i | −0.218261 | + | 0.843015i | ||||
\(283\) | −9.57331 | − | 9.57331i | −0.569074 | − | 0.569074i | 0.362795 | − | 0.931869i | \(-0.381823\pi\) |
−0.931869 | + | 0.362795i | \(0.881823\pi\) | |||||||
\(284\) | −10.2106 | −0.605886 | ||||||||
\(285\) | −5.30766 | − | 9.01618i | −0.314398 | − | 0.534072i | ||||
\(286\) | 12.8908i | 0.762251i | ||||||||
\(287\) | 6.80602 | 0.401747 | ||||||||
\(288\) | −0.825355 | − | 2.88423i | −0.0486345 | − | 0.169955i | ||||
\(289\) | − | 15.8237i | − | 0.930805i | ||||||
\(290\) | −0.666860 | + | 0.666860i | −0.0391593 | + | 0.0391593i | ||||
\(291\) | −27.0969 | − | 7.01555i | −1.58845 | − | 0.411259i | ||||
\(292\) | −1.48258 | −0.0867615 | ||||||||
\(293\) | − | 4.08873i | − | 0.238866i | −0.992842 | − | 0.119433i | \(-0.961892\pi\) | ||
0.992842 | − | 0.119433i | \(-0.0381077\pi\) | |||||||
\(294\) | 2.20061 | + | 0.569751i | 0.128342 | + | 0.0332285i | ||||
\(295\) | − | 7.97392i | − | 0.464259i | ||||||
\(296\) | −5.40587 | − | 2.78864i | −0.314210 | − | 0.162087i | ||||
\(297\) | 29.9574 | − | 0.760178i | 1.73830 | − | 0.0441100i | ||||
\(298\) | −13.7863 | − | 13.7863i | −0.798619 | − | 0.798619i | ||||
\(299\) | −18.5570 | −1.07318 | ||||||||
\(300\) | −0.878679 | − | 1.49262i | −0.0507306 | − | 0.0861766i | ||||
\(301\) | −15.4427 | + | 15.4427i | −0.890102 | + | 0.890102i | ||||
\(302\) | −2.81812 | − | 2.81812i | −0.162165 | − | 0.162165i | ||||
\(303\) | 2.04494 | + | 3.47376i | 0.117479 | + | 0.199563i | ||||
\(304\) | −4.27127 | + | 4.27127i | −0.244974 | + | 0.244974i | ||||
\(305\) | − | 12.4769i | − | 0.714423i | ||||||
\(306\) | 1.57898 | − | 2.84493i | 0.0902641 | − | 0.162634i | ||||
\(307\) | − | 2.82576i | − | 0.161275i | −0.996744 | − | 0.0806373i | \(-0.974304\pi\) | ||
0.996744 | − | 0.0806373i | \(-0.0256956\pi\) | |||||||
\(308\) | − | 13.7539i | − | 0.783701i | ||||||
\(309\) | 1.88531 | − | 7.28183i | 0.107251 | − | 0.414249i | ||||
\(310\) | −4.93081 | − | 4.93081i | −0.280051 | − | 0.280051i | ||||
\(311\) | −9.24050 | + | 9.24050i | −0.523981 | + | 0.523981i | −0.918771 | − | 0.394790i | \(-0.870817\pi\) |
0.394790 | + | 0.918771i | \(0.370817\pi\) | |||||||
\(312\) | −1.96404 | − | 3.33634i | −0.111192 | − | 0.188883i | ||||
\(313\) | −3.34887 | + | 3.34887i | −0.189290 | + | 0.189290i | −0.795389 | − | 0.606099i | \(-0.792733\pi\) |
0.606099 | + | 0.795389i | \(0.292733\pi\) | |||||||
\(314\) | 16.0952 | − | 16.0952i | 0.908305 | − | 0.908305i | ||||
\(315\) | −6.87850 | + | 1.96836i | −0.387560 | + | 0.110905i | ||||
\(316\) | 3.85057 | + | 3.85057i | 0.216612 | + | 0.216612i | ||||
\(317\) | −25.0019 | −1.40425 | −0.702123 | − | 0.712056i | \(-0.747764\pi\) | ||||
−0.702123 | + | 0.712056i | \(0.747764\pi\) | |||||||
\(318\) | 3.13310 | − | 12.1013i | 0.175696 | − | 0.678608i | ||||
\(319\) | −3.84588 | + | 3.84588i | −0.215328 | + | 0.215328i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 16.0207 | − | 9.43109i | 0.894189 | − | 0.526392i | ||||
\(322\) | 19.7994 | 1.10338 | ||||||||
\(323\) | −6.55138 | −0.364529 | ||||||||
\(324\) | −7.63758 | + | 4.76103i | −0.424310 | + | 0.264501i | ||||
\(325\) | −1.58054 | − | 1.58054i | −0.0876724 | − | 0.0876724i | ||||
\(326\) | −10.6310 | −0.588798 | ||||||||
\(327\) | 14.2710 | + | 3.69484i | 0.789187 | + | 0.204325i | ||||
\(328\) | −2.01797 | − | 2.01797i | −0.111424 | − | 0.111424i | ||||
\(329\) | − | 20.1350i | − | 1.11008i | ||||||
\(330\) | −5.06748 | − | 8.60819i | −0.278956 | − | 0.473865i | ||||
\(331\) | −16.1922 | + | 16.1922i | −0.890002 | + | 0.890002i | −0.994523 | − | 0.104520i | \(-0.966669\pi\) |
0.104520 | + | 0.994523i | \(0.466669\pi\) | |||||||
\(332\) | 16.2511 | 0.891892 | ||||||||
\(333\) | −3.58133 | + | 17.8934i | −0.196256 | + | 0.980553i | ||||
\(334\) | 17.7269 | 0.969973 | ||||||||
\(335\) | 2.09602 | − | 2.09602i | 0.114518 | − | 0.114518i | ||||
\(336\) | 2.09553 | + | 3.55970i | 0.114321 | + | 0.194198i | ||||
\(337\) | 11.4390i | 0.623121i | 0.950226 | + | 0.311560i | \(0.100852\pi\) | ||||
−0.950226 | + | 0.311560i | \(0.899148\pi\) | |||||||
\(338\) | 5.65955 | + | 5.65955i | 0.307839 | + | 0.307839i | ||||
\(339\) | −28.5544 | − | 7.39289i | −1.55086 | − | 0.401526i | ||||
\(340\) | −1.08458 | −0.0588195 | ||||||||
\(341\) | −28.4367 | − | 28.4367i | −1.53994 | − | 1.53994i | ||||
\(342\) | 15.8447 | + | 8.79403i | 0.856781 | + | 0.475527i | ||||
\(343\) | −19.8240 | −1.07040 | ||||||||
\(344\) | 9.15744 | 0.493736 | ||||||||
\(345\) | 12.3919 | − | 7.29490i | 0.667159 | − | 0.392744i | ||||
\(346\) | −11.2500 | + | 11.2500i | −0.604802 | + | 0.604802i | ||||
\(347\) | −5.80793 | + | 5.80793i | −0.311786 | + | 0.311786i | −0.845601 | − | 0.533815i | \(-0.820758\pi\) |
0.533815 | + | 0.845601i | \(0.320758\pi\) | |||||||
\(348\) | 0.409414 | − | 1.58133i | 0.0219469 | − | 0.0847679i | ||||
\(349\) | 11.5690 | 0.619277 | 0.309638 | − | 0.950854i | \(-0.399792\pi\) | ||||
0.309638 | + | 0.950854i | \(0.399792\pi\) | |||||||
\(350\) | 1.68635 | + | 1.68635i | 0.0901395 | + | 0.0901395i | ||||
\(351\) | −8.00173 | + | 8.41840i | −0.427101 | + | 0.449341i | ||||
\(352\) | −4.07799 | + | 4.07799i | −0.217358 | + | 0.217358i | ||||
\(353\) | −8.48939 | + | 8.48939i | −0.451845 | + | 0.451845i | −0.895966 | − | 0.444122i | \(-0.853516\pi\) |
0.444122 | + | 0.895966i | \(0.353516\pi\) | |||||||
\(354\) | 7.00652 | + | 11.9021i | 0.372392 | + | 0.632587i | ||||
\(355\) | 7.21996 | − | 7.21996i | 0.383196 | − | 0.383196i | ||||
\(356\) | 3.88764 | + | 3.88764i | 0.206045 | + | 0.206045i | ||||
\(357\) | −1.12289 | + | 4.33707i | −0.0594297 | + | 0.229542i | ||||
\(358\) | 12.8828i | 0.680875i | ||||||||
\(359\) | 22.1081i | 1.16682i | 0.812177 | + | 0.583411i | \(0.198282\pi\) | ||||
−0.812177 | + | 0.583411i | \(0.801718\pi\) | |||||||
\(360\) | 2.62307 | + | 1.45585i | 0.138248 | + | 0.0767298i | ||||
\(361\) | − | 17.4876i | − | 0.920399i | ||||||
\(362\) | 3.30299 | − | 3.30299i | 0.173601 | − | 0.173601i | ||||
\(363\) | −19.5595 | − | 33.2259i | −1.02661 | − | 1.74391i | ||||
\(364\) | 3.76937 | + | 3.76937i | 0.197569 | + | 0.197569i | ||||
\(365\) | 1.04834 | − | 1.04834i | 0.0548728 | − | 0.0548728i | ||||
\(366\) | 10.9632 | + | 18.6232i | 0.573053 | + | 0.973452i | ||||
\(367\) | −21.8077 | −1.13835 | −0.569176 | − | 0.822216i | \(-0.692738\pi\) | ||||
−0.569176 | + | 0.822216i | \(0.692738\pi\) | |||||||
\(368\) | −5.87049 | − | 5.87049i | −0.306020 | − | 0.306020i | ||||
\(369\) | −4.15475 | + | 7.48583i | −0.216288 | + | 0.389697i | ||||
\(370\) | 5.79440 | − | 1.85066i | 0.301236 | − | 0.0962113i | ||||
\(371\) | 17.2117i | 0.893589i | ||||||||
\(372\) | 11.6924 | + | 3.02724i | 0.606225 | + | 0.156955i | ||||
\(373\) | − | 18.7132i | − | 0.968931i | −0.874810 | − | 0.484465i | \(-0.839014\pi\) | ||
0.874810 | − | 0.484465i | \(-0.160986\pi\) | |||||||
\(374\) | −6.25492 | −0.323434 | ||||||||
\(375\) | 1.67676 | + | 0.434124i | 0.0865877 | + | 0.0224180i | ||||
\(376\) | −5.96998 | + | 5.96998i | −0.307878 | + | 0.307878i | ||||
\(377\) | − | 2.10799i | − | 0.108567i | ||||||
\(378\) | 8.53746 | − | 8.98202i | 0.439119 | − | 0.461985i | ||||
\(379\) | −5.00400 | −0.257038 | −0.128519 | − | 0.991707i | \(-0.541022\pi\) | ||||
−0.128519 | + | 0.991707i | \(0.541022\pi\) | |||||||
\(380\) | − | 6.04049i | − | 0.309871i | ||||||
\(381\) | 9.32657 | + | 15.8432i | 0.477815 | + | 0.811670i | ||||
\(382\) | −3.56179 | −0.182237 | ||||||||
\(383\) | 7.07401 | + | 7.07401i | 0.361465 | + | 0.361465i | 0.864352 | − | 0.502887i | \(-0.167729\pi\) |
−0.502887 | + | 0.864352i | \(0.667729\pi\) | |||||||
\(384\) | 0.434124 | − | 1.67676i | 0.0221538 | − | 0.0855670i | ||||
\(385\) | 9.72547 | + | 9.72547i | 0.495656 | + | 0.495656i | ||||
\(386\) | 6.66221i | 0.339098i | ||||||||
\(387\) | −7.55813 | − | 26.4122i | −0.384201 | − | 1.34261i | ||||
\(388\) | −11.4270 | − | 11.4270i | −0.580119 | − | 0.580119i | ||||
\(389\) | −8.14631 | − | 8.14631i | −0.413034 | − | 0.413034i | 0.469760 | − | 0.882794i | \(-0.344340\pi\) |
−0.882794 | + | 0.469760i | \(0.844340\pi\) | |||||||
\(390\) | 3.74793 | + | 0.970360i | 0.189784 | + | 0.0491361i | ||||
\(391\) | − | 9.00429i | − | 0.455367i | ||||||
\(392\) | 0.928018 | + | 0.928018i | 0.0468720 | + | 0.0468720i | ||||
\(393\) | 11.4792 | + | 2.97202i | 0.579047 | + | 0.149919i | ||||
\(394\) | 7.63023 | + | 7.63023i | 0.384406 | + | 0.384406i | ||||
\(395\) | −5.44553 | −0.273994 | ||||||||
\(396\) | 15.1277 | + | 8.39609i | 0.760194 | + | 0.421919i | ||||
\(397\) | 24.1303i | 1.21106i | 0.795821 | + | 0.605532i | \(0.207040\pi\) | ||||
−0.795821 | + | 0.605532i | \(0.792960\pi\) | |||||||
\(398\) | 6.57059 | 0.329354 | ||||||||
\(399\) | −24.1551 | − | 6.25389i | −1.20927 | − | 0.313086i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −2.25525 | + | 2.25525i | −0.112622 | + | 0.112622i | −0.761172 | − | 0.648550i | \(-0.775376\pi\) |
0.648550 | + | 0.761172i | \(0.275376\pi\) | |||||||
\(402\) | −1.28684 | + | 4.97029i | −0.0641815 | + | 0.247895i | ||||
\(403\) | 15.5867 | 0.776426 | ||||||||
\(404\) | 2.32729i | 0.115787i | ||||||||
\(405\) | 2.03403 | − | 8.76714i | 0.101072 | − | 0.435643i | ||||
\(406\) | 2.24912i | 0.111622i | ||||||||
\(407\) | 33.4172 | − | 10.6730i | 1.65643 | − | 0.529043i | ||||
\(408\) | 1.61886 | − | 0.952995i | 0.0801457 | − | 0.0471803i | ||||
\(409\) | 0.672279 | + | 0.672279i | 0.0332420 | + | 0.0332420i | 0.723532 | − | 0.690290i | \(-0.242517\pi\) |
−0.690290 | + | 0.723532i | \(0.742517\pi\) | |||||||
\(410\) | 2.85384 | 0.140941 | ||||||||
\(411\) | 32.9544 | − | 19.3996i | 1.62552 | − | 0.956914i | ||||
\(412\) | 3.07081 | − | 3.07081i | 0.151288 | − | 0.151288i | ||||
\(413\) | −13.4469 | − | 13.4469i | −0.661676 | − | 0.661676i | ||||
\(414\) | −12.0866 | + | 21.7771i | −0.594024 | + | 1.07028i | ||||
\(415\) | −11.4912 | + | 11.4912i | −0.564082 | + | 0.564082i | ||||
\(416\) | − | 2.23522i | − | 0.109591i | ||||||
\(417\) | −6.43756 | + | 3.78967i | −0.315249 | + | 0.185581i | ||||
\(418\) | − | 34.8365i | − | 1.70391i | ||||||
\(419\) | 8.78968i | 0.429404i | 0.976680 | + | 0.214702i | \(0.0688780\pi\) | ||||
−0.976680 | + | 0.214702i | \(0.931122\pi\) | |||||||
\(420\) | −3.99886 | − | 1.03533i | −0.195124 | − | 0.0505188i | ||||
\(421\) | −22.8305 | − | 22.8305i | −1.11269 | − | 1.11269i | −0.992786 | − | 0.119903i | \(-0.961742\pi\) |
−0.119903 | − | 0.992786i | \(-0.538258\pi\) | |||||||
\(422\) | 2.77860 | − | 2.77860i | 0.135260 | − | 0.135260i | ||||
\(423\) | 22.1462 | + | 12.2915i | 1.07678 | + | 0.597631i | ||||
\(424\) | 5.10324 | − | 5.10324i | 0.247835 | − | 0.247835i | ||||
\(425\) | 0.766912 | − | 0.766912i | 0.0372007 | − | 0.0372007i | ||||
\(426\) | −4.43265 | + | 17.1207i | −0.214762 | + | 0.829501i | ||||
\(427\) | −21.0404 | − | 21.0404i | −1.01822 | − | 1.01822i | ||||
\(428\) | 10.7333 | 0.518812 | ||||||||
\(429\) | 21.6149 | + | 5.59622i | 1.04358 | + | 0.270188i | ||||
\(430\) | −6.47528 | + | 6.47528i | −0.312266 | + | 0.312266i | ||||
\(431\) | 21.2557 | − | 21.2557i | 1.02385 | − | 1.02385i | 0.0241401 | − | 0.999709i | \(-0.492315\pi\) |
0.999709 | − | 0.0241401i | \(-0.00768479\pi\) | |||||||
\(432\) | −5.19448 | + | 0.131812i | −0.249920 | + | 0.00634179i | ||||
\(433\) | −20.9909 | −1.00876 | −0.504379 | − | 0.863483i | \(-0.668278\pi\) | ||||
−0.504379 | + | 0.863483i | \(0.668278\pi\) | |||||||
\(434\) | −16.6302 | −0.798275 | ||||||||
\(435\) | 0.828666 | + | 1.40767i | 0.0397315 | + | 0.0674924i | ||||
\(436\) | 6.01820 | + | 6.01820i | 0.288220 | + | 0.288220i | ||||
\(437\) | 50.1489 | 2.39895 | ||||||||
\(438\) | −0.643624 | + | 2.48594i | −0.0307535 | + | 0.118783i | ||||
\(439\) | −1.49381 | − | 1.49381i | −0.0712955 | − | 0.0712955i | 0.670560 | − | 0.741855i | \(-0.266054\pi\) |
−0.741855 | + | 0.670560i | \(0.766054\pi\) | |||||||
\(440\) | − | 5.76715i | − | 0.274938i | ||||||
\(441\) | 1.91067 | − | 3.44256i | 0.0909845 | − | 0.163932i | ||||
\(442\) | 1.71421 | − | 1.71421i | 0.0815369 | − | 0.0815369i | ||||
\(443\) | 5.07352 | 0.241050 | 0.120525 | − | 0.992710i | \(-0.461542\pi\) | ||||
0.120525 | + | 0.992710i | \(0.461542\pi\) | |||||||
\(444\) | −7.02271 | + | 7.85376i | −0.333283 | + | 0.372723i | ||||
\(445\) | −5.49796 | −0.260628 | ||||||||
\(446\) | 11.2342 | − | 11.2342i | 0.531956 | − | 0.531956i | ||||
\(447\) | −29.1013 | + | 17.1314i | −1.37645 | + | 0.810288i | ||||
\(448\) | 2.38487i | 0.112674i | ||||||||
\(449\) | −3.64509 | − | 3.64509i | −0.172022 | − | 0.172022i | 0.615845 | − | 0.787867i | \(-0.288815\pi\) |
−0.787867 | + | 0.615845i | \(0.788815\pi\) | |||||||
\(450\) | −2.88423 | + | 0.825355i | −0.135964 | + | 0.0389076i | ||||
\(451\) | 16.4585 | 0.775002 | ||||||||
\(452\) | −12.0416 | − | 12.0416i | −0.566391 | − | 0.566391i | ||||
\(453\) | −5.94873 | + | 3.50191i | −0.279496 | + | 0.164534i | ||||
\(454\) | 4.21895 | 0.198005 | ||||||||
\(455\) | −5.33069 | −0.249907 | ||||||||
\(456\) | 5.30766 | + | 9.01618i | 0.248554 | + | 0.422221i | ||||
\(457\) | −14.4628 | + | 14.4628i | −0.676539 | + | 0.676539i | −0.959215 | − | 0.282676i | \(-0.908778\pi\) |
0.282676 | + | 0.959215i | \(0.408778\pi\) | |||||||
\(458\) | 16.9116 | − | 16.9116i | 0.790229 | − | 0.790229i | ||||
\(459\) | −4.08480 | − | 3.88262i | −0.190662 | − | 0.181225i | ||||
\(460\) | 8.30212 | 0.387088 | ||||||||
\(461\) | −3.48415 | − | 3.48415i | −0.162273 | − | 0.162273i | 0.621300 | − | 0.783573i | \(-0.286605\pi\) |
−0.783573 | + | 0.621300i | \(0.786605\pi\) | |||||||
\(462\) | −23.0620 | − | 5.97089i | −1.07294 | − | 0.277791i | ||||
\(463\) | 13.8483 | − | 13.8483i | 0.643586 | − | 0.643586i | −0.307849 | − | 0.951435i | \(-0.599609\pi\) |
0.951435 | + | 0.307849i | \(0.0996091\pi\) | |||||||
\(464\) | 0.666860 | − | 0.666860i | 0.0309582 | − | 0.0309582i | ||||
\(465\) | −10.4084 | + | 6.12722i | −0.482677 | + | 0.284143i | ||||
\(466\) | −18.1345 | + | 18.1345i | −0.840063 | + | 0.840063i | ||||
\(467\) | −4.04485 | − | 4.04485i | −0.187173 | − | 0.187173i | 0.607300 | − | 0.794473i | \(-0.292253\pi\) |
−0.794473 | + | 0.607300i | \(0.792253\pi\) | |||||||
\(468\) | −6.44688 | + | 1.84485i | −0.298007 | + | 0.0852780i | ||||
\(469\) | − | 7.06926i | − | 0.326428i | ||||||
\(470\) | − | 8.44283i | − | 0.389439i | ||||||
\(471\) | −20.0005 | − | 33.9751i | −0.921576 | − | 1.56549i | ||||
\(472\) | 7.97392i | 0.367029i | ||||||||
\(473\) | −37.3440 | + | 37.3440i | −1.71708 | + | 1.71708i | ||||
\(474\) | 8.12813 | − | 4.78488i | 0.373337 | − | 0.219777i | ||||
\(475\) | 4.27127 | + | 4.27127i | 0.195980 | + | 0.195980i | ||||
\(476\) | −1.82898 | + | 1.82898i | −0.0838312 | + | 0.0838312i | ||||
\(477\) | −18.9309 | − | 10.5069i | −0.866786 | − | 0.481080i | ||||
\(478\) | 15.5584 | 0.711626 | ||||||||
\(479\) | −4.03608 | − | 4.03608i | −0.184413 | − | 0.184413i | 0.608862 | − | 0.793276i | \(-0.291626\pi\) |
−0.793276 | + | 0.608862i | \(0.791626\pi\) | |||||||
\(480\) | 0.878679 | + | 1.49262i | 0.0401060 | + | 0.0681286i | ||||
\(481\) | −6.23322 | + | 12.0833i | −0.284211 | + | 0.550951i | ||||
\(482\) | 29.1979i | 1.32993i | ||||||||
\(483\) | 8.59541 | − | 33.1990i | 0.391105 | − | 1.51061i | ||||
\(484\) | − | 22.2601i | − | 1.01182i | ||||||
\(485\) | 16.1603 | 0.733799 | ||||||||
\(486\) | 4.66746 | + | 14.8733i | 0.211720 | + | 0.674666i | ||||
\(487\) | 5.50666 | − | 5.50666i | 0.249531 | − | 0.249531i | −0.571247 | − | 0.820778i | \(-0.693540\pi\) |
0.820778 | + | 0.571247i | \(0.193540\pi\) | |||||||
\(488\) | 12.4769i | 0.564801i | ||||||||
\(489\) | −4.61518 | + | 17.8257i | −0.208705 | + | 0.806106i | ||||
\(490\) | −1.31242 | −0.0592889 | ||||||||
\(491\) | 14.6275i | 0.660132i | 0.943958 | + | 0.330066i | \(0.107071\pi\) | ||||
−0.943958 | + | 0.330066i | \(0.892929\pi\) | |||||||
\(492\) | −4.25971 | + | 2.50761i | −0.192042 | + | 0.113052i | ||||
\(493\) | 1.02285 | 0.0460666 | ||||||||
\(494\) | 9.54722 | + | 9.54722i | 0.429550 | + | 0.429550i | ||||
\(495\) | −16.6338 | + | 4.75995i | −0.747634 | + | 0.213944i | ||||
\(496\) | 4.93081 | + | 4.93081i | 0.221400 | + | 0.221400i | ||||
\(497\) | − | 24.3508i | − | 1.09228i | ||||||
\(498\) | 7.05497 | − | 27.2492i | 0.316141 | − | 1.22106i | ||||
\(499\) | −3.49525 | − | 3.49525i | −0.156469 | − | 0.156469i | 0.624531 | − | 0.781000i | \(-0.285290\pi\) |
−0.781000 | + | 0.624531i | \(0.785290\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | 7.69567 | − | 29.7238i | 0.343817 | − | 1.32796i | ||||
\(502\) | 5.28264i | 0.235776i | ||||||||
\(503\) | 22.0215 | + | 22.0215i | 0.981892 | + | 0.981892i | 0.999839 | − | 0.0179468i | \(-0.00571296\pi\) |
−0.0179468 | + | 0.999839i | \(0.505713\pi\) | |||||||
\(504\) | 6.87850 | − | 1.96836i | 0.306393 | − | 0.0876777i | ||||
\(505\) | −1.64564 | − | 1.64564i | −0.0732301 | − | 0.0732301i | ||||
\(506\) | 47.8796 | 2.12851 | ||||||||
\(507\) | 11.9467 | − | 7.03278i | 0.530570 | − | 0.312337i | ||||
\(508\) | 10.6143i | 0.470934i | ||||||||
\(509\) | −31.9079 | −1.41429 | −0.707147 | − | 0.707067i | \(-0.750018\pi\) | ||||
−0.707147 | + | 0.707067i | \(0.750018\pi\) | |||||||
\(510\) | −0.470841 | + | 1.81858i | −0.0208492 | + | 0.0805281i | ||||
\(511\) | − | 3.53576i | − | 0.156413i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 21.6240 | − | 22.7501i | 0.954725 | − | 1.00444i | ||||
\(514\) | −13.0786 | −0.576870 | ||||||||
\(515\) | 4.34279i | 0.191366i | ||||||||
\(516\) | 3.97546 | − | 15.3549i | 0.175010 | − | 0.675960i | ||||
\(517\) | − | 48.6911i | − | 2.14143i | ||||||
\(518\) | 6.65054 | − | 12.8923i | 0.292208 | − | 0.566454i | ||||
\(519\) | 13.9797 | + | 23.7474i | 0.613639 | + | 1.04240i | ||||
\(520\) | 1.58054 | + | 1.58054i | 0.0693111 | + | 0.0693111i | ||||
\(521\) | −9.90496 | −0.433944 | −0.216972 | − | 0.976178i | \(-0.569618\pi\) | ||||
−0.216972 | + | 0.976178i | \(0.569618\pi\) | |||||||
\(522\) | −2.47377 | − | 1.37298i | −0.108274 | − | 0.0600938i | ||||
\(523\) | 13.6371 | − | 13.6371i | 0.596307 | − | 0.596307i | −0.343021 | − | 0.939328i | \(-0.611450\pi\) |
0.939328 | + | 0.343021i | \(0.111450\pi\) | |||||||
\(524\) | 4.84087 | + | 4.84087i | 0.211474 | + | 0.211474i | ||||
\(525\) | 3.55970 | − | 2.09553i | 0.155358 | − | 0.0914565i | ||||
\(526\) | −9.85756 | + | 9.85756i | −0.429810 | + | 0.429810i | ||||
\(527\) | 7.56299i | 0.329449i | ||||||||
\(528\) | 5.06748 | + | 8.60819i | 0.220534 | + | 0.374623i | ||||
\(529\) | 45.9252i | 1.99675i | ||||||||
\(530\) | 7.21707i | 0.313489i | ||||||||
\(531\) | 22.9986 | − | 6.58131i | 0.998055 | − | 0.285605i | ||||
\(532\) | −10.1864 | − | 10.1864i | −0.441637 | − | 0.441637i | ||||
\(533\) | −4.51060 | + | 4.51060i | −0.195376 | + | 0.195376i | ||||
\(534\) | 8.20638 | − | 4.83094i | 0.355125 | − | 0.209055i | ||||
\(535\) | −7.58956 | + | 7.58956i | −0.328125 | + | 0.328125i | ||||
\(536\) | −2.09602 | + | 2.09602i | −0.0905341 | + | 0.0905341i | ||||
\(537\) | 21.6013 | + | 5.59271i | 0.932167 | + | 0.241343i | ||||
\(538\) | −7.15116 | − | 7.15116i | −0.308308 | − | 0.308308i | ||||
\(539\) | −7.56890 | −0.326016 | ||||||||
\(540\) | 3.57985 | − | 3.76626i | 0.154052 | − | 0.162074i | ||||
\(541\) | 19.1072 | − | 19.1072i | 0.821484 | − | 0.821484i | −0.164837 | − | 0.986321i | \(-0.552710\pi\) |
0.986321 | + | 0.164837i | \(0.0527099\pi\) | |||||||
\(542\) | 20.7116 | − | 20.7116i | 0.889640 | − | 0.889640i | ||||
\(543\) | −4.10442 | − | 6.97223i | −0.176138 | − | 0.299207i | ||||
\(544\) | 1.08458 | 0.0465009 | ||||||||
\(545\) | −8.51102 | −0.364572 | ||||||||
\(546\) | 7.95671 | − | 4.68397i | 0.340516 | − | 0.200455i | ||||
\(547\) | −27.2486 | − | 27.2486i | −1.16507 | − | 1.16507i | −0.983351 | − | 0.181714i | \(-0.941836\pi\) |
−0.181714 | − | 0.983351i | \(-0.558164\pi\) | |||||||
\(548\) | 22.0782 | 0.943133 | ||||||||
\(549\) | 35.9861 | − | 10.2978i | 1.53585 | − | 0.439501i | ||||
\(550\) | 4.07799 | + | 4.07799i | 0.173886 | + | 0.173886i | ||||
\(551\) | 5.69668i | 0.242687i | ||||||||
\(552\) | −12.3919 | + | 7.29490i | −0.527436 | + | 0.310492i | ||||
\(553\) | −9.18310 | + | 9.18310i | −0.390505 | + | 0.390505i | ||||
\(554\) | −16.8412 | −0.715514 | ||||||||
\(555\) | −0.587635 | − | 10.5193i | −0.0249437 | − | 0.446517i | ||||
\(556\) | −4.31292 | −0.182909 | ||||||||
\(557\) | −2.90028 | + | 2.90028i | −0.122889 | + | 0.122889i | −0.765876 | − | 0.642988i | \(-0.777695\pi\) |
0.642988 | + | 0.765876i | \(0.277695\pi\) | |||||||
\(558\) | 10.1519 | − | 18.2913i | 0.429765 | − | 0.774331i | ||||
\(559\) | − | 20.4689i | − | 0.865740i | ||||||
\(560\) | −1.68635 | − | 1.68635i | −0.0712615 | − | 0.0712615i | ||||
\(561\) | −2.71541 | + | 10.4880i | −0.114645 | + | 0.442805i | ||||
\(562\) | −5.01989 | −0.211751 | ||||||||
\(563\) | −2.02165 | − | 2.02165i | −0.0852024 | − | 0.0852024i | 0.663221 | − | 0.748424i | \(-0.269189\pi\) |
−0.748424 | + | 0.663221i | \(0.769189\pi\) | |||||||
\(564\) | 7.41854 | + | 12.6020i | 0.312377 | + | 0.530638i | ||||
\(565\) | 17.0294 | 0.716434 | ||||||||
\(566\) | −13.5387 | −0.569074 | ||||||||
\(567\) | −11.3544 | − | 18.2146i | −0.476840 | − | 0.764941i | ||||
\(568\) | −7.21996 | + | 7.21996i | −0.302943 | + | 0.302943i | ||||
\(569\) | −1.16582 | + | 1.16582i | −0.0488736 | + | 0.0488736i | −0.731121 | − | 0.682248i | \(-0.761003\pi\) |
0.682248 | + | 0.731121i | \(0.261003\pi\) | |||||||
\(570\) | −10.1285 | − | 2.62232i | −0.424235 | − | 0.109837i | ||||
\(571\) | 2.10782 | 0.0882095 | 0.0441048 | − | 0.999027i | \(-0.485956\pi\) | ||||
0.0441048 | + | 0.999027i | \(0.485956\pi\) | |||||||
\(572\) | 9.11520 | + | 9.11520i | 0.381126 | + | 0.381126i | ||||
\(573\) | −1.54626 | + | 5.97228i | −0.0645958 | + | 0.249496i | ||||
\(574\) | 4.81259 | − | 4.81259i | 0.200873 | − | 0.200873i | ||||
\(575\) | −5.87049 | + | 5.87049i | −0.244816 | + | 0.244816i | ||||
\(576\) | −2.62307 | − | 1.45585i | −0.109295 | − | 0.0606602i | ||||
\(577\) | −10.2491 | + | 10.2491i | −0.426674 | + | 0.426674i | −0.887494 | − | 0.460820i | \(-0.847555\pi\) |
0.460820 | + | 0.887494i | \(0.347555\pi\) | |||||||
\(578\) | −11.1890 | − | 11.1890i | −0.465403 | − | 0.465403i | ||||
\(579\) | 11.1710 | + | 2.89222i | 0.464249 | + | 0.120197i | ||||
\(580\) | 0.943082i | 0.0391593i | ||||||||
\(581\) | 38.7566i | 1.60789i | ||||||||
\(582\) | −24.1212 | + | 14.1997i | −0.999854 | + | 0.588596i | ||||
\(583\) | 41.6219i | 1.72381i | ||||||||
\(584\) | −1.04834 | + | 1.04834i | −0.0433808 | + | 0.0433808i | ||||
\(585\) | 3.25413 | − | 5.86314i | 0.134542 | − | 0.242411i | ||||
\(586\) | −2.89117 | − | 2.89117i | −0.119433 | − | 0.119433i | ||||
\(587\) | −19.4626 | + | 19.4626i | −0.803309 | + | 0.803309i | −0.983611 | − | 0.180303i | \(-0.942292\pi\) |
0.180303 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(588\) | 1.95894 | − | 1.15319i | 0.0807854 | − | 0.0475568i | ||||
\(589\) | −42.1217 | −1.73559 | ||||||||
\(590\) | −5.63841 | − | 5.63841i | −0.232130 | − | 0.232130i | ||||
\(591\) | 16.1066 | − | 9.48163i | 0.662535 | − | 0.390022i | ||||
\(592\) | −5.79440 | + | 1.85066i | −0.238148 | + | 0.0760617i | ||||
\(593\) | 19.0894i | 0.783909i | 0.919985 | + | 0.391954i | \(0.128201\pi\) | ||||
−0.919985 | + | 0.391954i | \(0.871799\pi\) | |||||||
\(594\) | 20.6455 | − | 21.7206i | 0.847097 | − | 0.891206i | ||||
\(595\) | − | 2.58657i | − | 0.106039i | ||||||
\(596\) | −19.4968 | −0.798619 | ||||||||
\(597\) | 2.85245 | − | 11.0173i | 0.116743 | − | 0.450909i | ||||
\(598\) | −13.1218 | + | 13.1218i | −0.536591 | + | 0.536591i | ||||
\(599\) | − | 6.46972i | − | 0.264346i | −0.991227 | − | 0.132173i | \(-0.957805\pi\) | ||
0.991227 | − | 0.132173i | \(-0.0421954\pi\) | |||||||
\(600\) | −1.67676 | − | 0.434124i | −0.0684536 | − | 0.0177230i | ||||
\(601\) | 7.19361 | 0.293433 | 0.146717 | − | 0.989179i | \(-0.453129\pi\) | ||||
0.146717 | + | 0.989179i | \(0.453129\pi\) | |||||||
\(602\) | 21.8393i | 0.890102i | ||||||||
\(603\) | 7.77535 | + | 4.31544i | 0.316637 | + | 0.175738i | ||||
\(604\) | −3.98542 | −0.162165 | ||||||||
\(605\) | 15.7402 | + | 15.7402i | 0.639932 | + | 0.639932i | ||||
\(606\) | 3.90231 | + | 1.01033i | 0.158521 | + | 0.0410419i | ||||
\(607\) | 10.2240 | + | 10.2240i | 0.414978 | + | 0.414978i | 0.883468 | − | 0.468491i | \(-0.155202\pi\) |
−0.468491 | + | 0.883468i | \(0.655202\pi\) | |||||||
\(608\) | 6.04049i | 0.244974i | ||||||||
\(609\) | 3.77125 | + | 0.976398i | 0.152819 | + | 0.0395656i | ||||
\(610\) | −8.82247 | − | 8.82247i | −0.357211 | − | 0.357211i | ||||
\(611\) | 13.3442 | + | 13.3442i | 0.539849 | + | 0.539849i | ||||
\(612\) | −0.895161 | − | 3.12817i | −0.0361847 | − | 0.126449i | ||||
\(613\) | − | 10.1511i | − | 0.409999i | −0.978762 | − | 0.205000i | \(-0.934281\pi\) | ||
0.978762 | − | 0.205000i | \(-0.0657193\pi\) | |||||||
\(614\) | −1.99811 | − | 1.99811i | −0.0806373 | − | 0.0806373i | ||||
\(615\) | 1.23892 | − | 4.78521i | 0.0499580 | − | 0.192958i | ||||
\(616\) | −9.72547 | − | 9.72547i | −0.391850 | − | 0.391850i | ||||
\(617\) | 37.4403 | 1.50729 | 0.753646 | − | 0.657281i | \(-0.228294\pi\) | ||||
0.753646 | + | 0.657281i | \(0.228294\pi\) | |||||||
\(618\) | −3.81592 | − | 6.48214i | −0.153499 | − | 0.260750i | ||||
\(619\) | − | 9.57027i | − | 0.384661i | −0.981330 | − | 0.192331i | \(-0.938395\pi\) | ||
0.981330 | − | 0.192331i | \(-0.0616046\pi\) | |||||||
\(620\) | −6.97322 | −0.280051 | ||||||||
\(621\) | 31.2679 | + | 29.7203i | 1.25474 | + | 1.19264i | ||||
\(622\) | 13.0680i | 0.523981i | ||||||||
\(623\) | −9.27151 | + | 9.27151i | −0.371455 | + | 0.371455i | ||||
\(624\) | −3.74793 | − | 0.970360i | −0.150037 | − | 0.0388455i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 4.73602i | 0.189290i | ||||||||
\(627\) | −58.4125 | − | 15.1233i | −2.33277 | − | 0.603968i | ||||
\(628\) | − | 22.7620i | − | 0.908305i | ||||||
\(629\) | −5.86309 | − | 3.02450i | −0.233777 | − | 0.120595i | ||||
\(630\) | −3.47200 | + | 6.25568i | −0.138328 | + | 0.249232i | ||||
\(631\) | 31.7177 | + | 31.7177i | 1.26266 | + | 1.26266i | 0.949799 | + | 0.312862i | \(0.101288\pi\) |
0.312862 | + | 0.949799i | \(0.398712\pi\) | |||||||
\(632\) | 5.44553 | 0.216612 | ||||||||
\(633\) | −3.45280 | − | 5.86530i | −0.137236 | − | 0.233125i | ||||
\(634\) | −17.6790 | + | 17.6790i | −0.702123 | + | 0.702123i | ||||
\(635\) | −7.50545 | − | 7.50545i | −0.297845 | − | 0.297845i | ||||
\(636\) | −6.34149 | − | 10.7724i | −0.251456 | − | 0.427152i | ||||
\(637\) | 2.07432 | − | 2.07432i | 0.0821876 | − | 0.0821876i | ||||
\(638\) | 5.43890i | 0.215328i | ||||||||
\(639\) | 26.7831 | + | 14.8650i | 1.05952 | + | 0.588051i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | − | 5.24179i | − | 0.207038i | −0.994627 | − | 0.103519i | \(-0.966990\pi\) | ||
0.994627 | − | 0.103519i | \(-0.0330103\pi\) | |||||||
\(642\) | 4.65956 | − | 17.9971i | 0.183898 | − | 0.710291i | ||||
\(643\) | −33.1809 | − | 33.1809i | −1.30853 | − | 1.30853i | −0.922478 | − | 0.386049i | \(-0.873839\pi\) |
−0.386049 | − | 0.922478i | \(-0.626161\pi\) | |||||||
\(644\) | 14.0003 | − | 14.0003i | 0.551690 | − | 0.551690i | ||||
\(645\) | 8.04645 | + | 13.6686i | 0.316829 | + | 0.538200i | ||||
\(646\) | −4.63253 | + | 4.63253i | −0.182264 | + | 0.182264i | ||||
\(647\) | −4.39581 | + | 4.39581i | −0.172817 | + | 0.172817i | −0.788216 | − | 0.615399i | \(-0.788995\pi\) |
0.615399 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(648\) | −2.03403 | + | 8.76714i | −0.0799042 | + | 0.344406i | ||||
\(649\) | −32.5176 | − | 32.5176i | −1.27643 | − | 1.27643i | ||||
\(650\) | −2.23522 | −0.0876724 | ||||||||
\(651\) | −7.21956 | + | 27.8849i | −0.282957 | + | 1.09290i | ||||
\(652\) | −7.51726 | + | 7.51726i | −0.294399 | + | 0.294399i | ||||
\(653\) | −13.7401 | + | 13.7401i | −0.537690 | + | 0.537690i | −0.922850 | − | 0.385160i | \(-0.874146\pi\) |
0.385160 | + | 0.922850i | \(0.374146\pi\) | |||||||
\(654\) | 12.7037 | − | 7.47846i | 0.496756 | − | 0.292431i | ||||
\(655\) | −6.84602 | −0.267496 | ||||||||
\(656\) | −2.85384 | −0.111424 | ||||||||
\(657\) | 3.88892 | + | 2.15841i | 0.151721 | + | 0.0842076i | ||||
\(658\) | −14.2376 | − | 14.2376i | −0.555040 | − | 0.555040i | ||||
\(659\) | 6.94050 | 0.270364 | 0.135182 | − | 0.990821i | \(-0.456838\pi\) | ||||
0.135182 | + | 0.990821i | \(0.456838\pi\) | |||||||
\(660\) | −9.67016 | − | 2.50366i | −0.376410 | − | 0.0974548i | ||||
\(661\) | −7.92259 | − | 7.92259i | −0.308153 | − | 0.308153i | 0.536040 | − | 0.844193i | \(-0.319920\pi\) |
−0.844193 | + | 0.536040i | \(0.819920\pi\) | |||||||
\(662\) | 22.8992i | 0.890002i | ||||||||
\(663\) | −2.13015 | − | 3.61851i | −0.0827282 | − | 0.140531i | ||||
\(664\) | 11.4912 | − | 11.4912i | 0.445946 | − | 0.445946i | ||||
\(665\) | 14.4058 | 0.558632 | ||||||||
\(666\) | 10.1202 | + | 15.1849i | 0.392148 | + | 0.588404i | ||||
\(667\) | −7.82958 | −0.303163 | ||||||||
\(668\) | 12.5348 | − | 12.5348i | 0.484986 | − | 0.484986i | ||||
\(669\) | −13.9601 | − | 23.7142i | −0.539729 | − | 0.916843i | ||||
\(670\) | − | 2.96422i | − | 0.114518i | ||||||
\(671\) | −50.8806 | − | 50.8806i | −1.96422 | − | 1.96422i | ||||
\(672\) | 3.99886 | + | 1.03533i | 0.154259 | + | 0.0399386i | ||||
\(673\) | 34.0773 | 1.31358 | 0.656791 | − | 0.754073i | \(-0.271913\pi\) | ||||
0.656791 | + | 0.754073i | \(0.271913\pi\) | |||||||
\(674\) | 8.08858 | + | 8.08858i | 0.311560 | + | 0.311560i | ||||
\(675\) | 0.131812 | + | 5.19448i | 0.00507343 | + | 0.199936i | ||||
\(676\) | 8.00381 | 0.307839 | ||||||||
\(677\) | 6.68405 | 0.256889 | 0.128444 | − | 0.991717i | \(-0.459002\pi\) | ||||
0.128444 | + | 0.991717i | \(0.459002\pi\) | |||||||
\(678\) | −25.4185 | + | 14.9634i | −0.976193 | + | 0.574667i | ||||
\(679\) | 27.2519 | − | 27.2519i | 1.04583 | − | 1.04583i | ||||
\(680\) | −0.766912 | + | 0.766912i | −0.0294097 | + | 0.0294097i | ||||
\(681\) | 1.83155 | − | 7.07419i | 0.0701850 | − | 0.271083i | ||||
\(682\) | −40.2156 | −1.53994 | ||||||||
\(683\) | −20.8898 | − | 20.8898i | −0.799324 | − | 0.799324i | 0.183665 | − | 0.982989i | \(-0.441204\pi\) |
−0.982989 | + | 0.183665i | \(0.941204\pi\) | |||||||
\(684\) | 17.4222 | − | 4.98555i | 0.666154 | − | 0.190627i | ||||
\(685\) | −15.6116 | + | 15.6116i | −0.596490 | + | 0.596490i | ||||
\(686\) | −14.0177 | + | 14.0177i | −0.535198 | + | 0.535198i | ||||
\(687\) | −21.0151 | − | 35.6985i | −0.801775 | − | 1.36198i | ||||
\(688\) | 6.47528 | − | 6.47528i | 0.246868 | − | 0.246868i | ||||
\(689\) | −11.4068 | − | 11.4068i | −0.434566 | − | 0.434566i | ||||
\(690\) | 3.60415 | − | 13.9207i | 0.137208 | − | 0.529952i | ||||
\(691\) | − | 24.1662i | − | 0.919324i | −0.888094 | − | 0.459662i | \(-0.847971\pi\) | ||
0.888094 | − | 0.459662i | \(-0.152029\pi\) | |||||||
\(692\) | 15.9099i | 0.604802i | ||||||||
\(693\) | −20.0235 | + | 36.0775i | −0.760631 | + | 1.37047i | ||||
\(694\) | 8.21366i | 0.311786i | ||||||||
\(695\) | 3.04969 | − | 3.04969i | 0.115682 | − | 0.115682i | ||||
\(696\) | −0.828666 | − | 1.40767i | −0.0314105 | − | 0.0533574i | ||||
\(697\) | −2.18864 | − | 2.18864i | −0.0829008 | − | 0.0829008i | ||||
\(698\) | 8.18055 | − | 8.18055i | 0.309638 | − | 0.309638i | ||||
\(699\) | 22.5346 | + | 38.2798i | 0.852338 | + | 1.44788i | ||||
\(700\) | 2.38487 | 0.0901395 | ||||||||
\(701\) | 4.73203 | + | 4.73203i | 0.178726 | + | 0.178726i | 0.790800 | − | 0.612074i | \(-0.209665\pi\) |
−0.612074 | + | 0.790800i | \(0.709665\pi\) | |||||||
\(702\) | 0.294627 | + | 11.6108i | 0.0111200 | + | 0.438221i | ||||
\(703\) | 16.8448 | − | 32.6541i | 0.635313 | − | 1.23157i | ||||
\(704\) | 5.76715i | 0.217358i | ||||||||
\(705\) | −14.1566 | − | 3.66523i | −0.533170 | − | 0.138041i | ||||
\(706\) | 12.0058i | 0.451845i | ||||||||
\(707\) | −5.55027 | −0.208739 | ||||||||
\(708\) | 13.3704 | + | 3.46167i | 0.502490 | + | 0.130097i | ||||
\(709\) | −2.36375 | + | 2.36375i | −0.0887727 | + | 0.0887727i | −0.750099 | − | 0.661326i | \(-0.769994\pi\) |
0.661326 | + | 0.750099i | \(0.269994\pi\) | |||||||
\(710\) | − | 10.2106i | − | 0.383196i | ||||||
\(711\) | −4.49449 | − | 15.7062i | −0.168557 | − | 0.589028i | ||||
\(712\) | 5.49796 | 0.206045 | ||||||||
\(713\) | − | 57.8925i | − | 2.16809i | ||||||
\(714\) | 2.27277 | + | 3.86077i | 0.0850561 | + | 0.144486i | ||||
\(715\) | −12.8908 | −0.482090 | ||||||||
\(716\) | 9.10948 | + | 9.10948i | 0.340437 | + | 0.340437i | ||||
\(717\) | 6.75429 | − | 26.0878i | 0.252243 | − | 0.974268i | ||||
\(718\) | 15.6328 | + | 15.6328i | 0.583411 | + | 0.583411i | ||||
\(719\) | − | 20.6295i | − | 0.769349i | −0.923052 | − | 0.384675i | \(-0.874314\pi\) | ||
0.923052 | − | 0.384675i | \(-0.125686\pi\) | |||||||
\(720\) | 2.88423 | − | 0.825355i | 0.107489 | − | 0.0307591i | ||||
\(721\) | 7.32348 | + | 7.32348i | 0.272741 | + | 0.272741i | ||||
\(722\) | −12.3656 | − | 12.3656i | −0.460199 | − | 0.460199i | ||||
\(723\) | 48.9580 | + | 12.6755i | 1.82077 | + | 0.471407i | ||||
\(724\) | − | 4.67113i | − | 0.173601i | ||||||
\(725\) | −0.666860 | − | 0.666860i | −0.0247665 | − | 0.0247665i | ||||
\(726\) | −37.3249 | − | 9.66362i | −1.38526 | − | 0.358651i | ||||
\(727\) | 4.87778 | + | 4.87778i | 0.180907 | + | 0.180907i | 0.791751 | − | 0.610844i | \(-0.209170\pi\) |
−0.610844 | + | 0.791751i | \(0.709170\pi\) | |||||||
\(728\) | 5.33069 | 0.197569 | ||||||||
\(729\) | 26.9653 | − | 1.36939i | 0.998713 | − | 0.0507180i | ||||
\(730\) | − | 1.48258i | − | 0.0548728i | ||||||
\(731\) | 9.93195 | 0.367346 | ||||||||
\(732\) | 20.9207 | + | 5.41650i | 0.773253 | + | 0.200200i | ||||
\(733\) | 27.2107i | 1.00505i | 0.864563 | + | 0.502525i | \(0.167595\pi\) | ||||
−0.864563 | + | 0.502525i | \(0.832405\pi\) | |||||||
\(734\) | −15.4204 | + | 15.4204i | −0.569176 | + | 0.569176i | ||||
\(735\) | −0.569751 | + | 2.20061i | −0.0210156 | + | 0.0811708i | ||||
\(736\) | −8.30212 | −0.306020 | ||||||||
\(737\) | − | 17.0951i | − | 0.629706i | ||||||
\(738\) | 2.35543 | + | 8.23113i | 0.0867045 | + | 0.302992i | ||||
\(739\) | 21.1878i | 0.779406i | 0.920941 | + | 0.389703i | \(0.127422\pi\) | ||||
−0.920941 | + | 0.389703i | \(0.872578\pi\) | |||||||
\(740\) | 2.78864 | − | 5.40587i | 0.102513 | − | 0.198724i | ||||
\(741\) | 20.1531 | − | 11.8638i | 0.740343 | − | 0.435826i | ||||
\(742\) | 12.1705 | + | 12.1705i | 0.446794 | + | 0.446794i | ||||
\(743\) | 30.3326 | 1.11279 | 0.556397 | − | 0.830917i | \(-0.312183\pi\) | ||||
0.556397 | + | 0.830917i | \(0.312183\pi\) | |||||||
\(744\) | 10.4084 | − | 6.12722i | 0.381590 | − | 0.224635i | ||||
\(745\) | 13.7863 | − | 13.7863i | 0.505091 | − | 0.505091i | ||||
\(746\) | −13.2322 | − | 13.2322i | −0.484465 | − | 0.484465i | ||||
\(747\) | −42.6277 | − | 23.6590i | −1.55967 | − | 0.865638i | ||||
\(748\) | −4.42290 | + | 4.42290i | −0.161717 | + | 0.161717i | ||||
\(749\) | 25.5974i | 0.935308i | ||||||||
\(750\) | 1.49262 | − | 0.878679i | 0.0545029 | − | 0.0320848i | ||||
\(751\) | 14.3381i | 0.523204i | 0.965176 | + | 0.261602i | \(0.0842508\pi\) | ||||
−0.965176 | + | 0.261602i | \(0.915749\pi\) | |||||||
\(752\) | 8.44283i | 0.307878i | ||||||||
\(753\) | 8.85774 | + | 2.29332i | 0.322794 | + | 0.0835732i | ||||
\(754\) | −1.49058 | − | 1.49058i | −0.0542836 | − | 0.0542836i | ||||
\(755\) | 2.81812 | − | 2.81812i | 0.102562 | − | 0.102562i | ||||
\(756\) | −0.314353 | − | 12.3881i | −0.0114329 | − | 0.450552i | ||||
\(757\) | 23.3542 | − | 23.3542i | 0.848822 | − | 0.848822i | −0.141164 | − | 0.989986i | \(-0.545084\pi\) |
0.989986 | + | 0.141164i | \(0.0450845\pi\) | |||||||
\(758\) | −3.53836 | + | 3.53836i | −0.128519 | + | 0.128519i | ||||
\(759\) | 20.7857 | − | 80.2828i | 0.754472 | − | 2.91408i | ||||
\(760\) | −4.27127 | − | 4.27127i | −0.154935 | − | 0.154935i | ||||
\(761\) | 41.2576 | 1.49559 | 0.747794 | − | 0.663931i | \(-0.231113\pi\) | ||||
0.747794 | + | 0.663931i | \(0.231113\pi\) | |||||||
\(762\) | 17.7977 | + | 4.60792i | 0.644742 | + | 0.166927i | ||||
\(763\) | −14.3526 | + | 14.3526i | −0.519599 | + | 0.519599i | ||||
\(764\) | −2.51857 | + | 2.51857i | −0.0911185 | + | 0.0911185i | ||||
\(765\) | 2.84493 | + | 1.57898i | 0.102858 | + | 0.0570880i | ||||
\(766\) | 10.0042 | 0.361465 | ||||||||
\(767\) | 17.8234 | 0.643567 | ||||||||
\(768\) | −0.878679 | − | 1.49262i | −0.0317066 | − | 0.0538604i | ||||
\(769\) | −6.65238 | − | 6.65238i | −0.239891 | − | 0.239891i | 0.576914 | − | 0.816805i | \(-0.304257\pi\) |
−0.816805 | + | 0.576914i | \(0.804257\pi\) | |||||||
\(770\) | 13.7539 | 0.495656 | ||||||||
\(771\) | −5.67771 | + | 21.9297i | −0.204478 | + | 0.789777i | ||||
\(772\) | 4.71089 | + | 4.71089i | 0.169549 | + | 0.169549i | ||||
\(773\) | − | 24.0960i | − | 0.866674i | −0.901232 | − | 0.433337i | \(-0.857336\pi\) | ||
0.901232 | − | 0.433337i | \(-0.142664\pi\) | |||||||
\(774\) | −24.0206 | − | 13.3318i | −0.863404 | − | 0.479202i | ||||
\(775\) | 4.93081 | − | 4.93081i | 0.177120 | − | 0.177120i | ||||
\(776\) | −16.1603 | −0.580119 | ||||||||
\(777\) | −18.7302 | − | 16.7482i | −0.671940 | − | 0.600839i | ||||
\(778\) | −11.5206 | −0.413034 | ||||||||
\(779\) | 12.1895 | − | 12.1895i | 0.436735 | − | 0.436735i | ||||
\(780\) | 3.33634 | − | 1.96404i | 0.119460 | − | 0.0703239i | ||||
\(781\) | − | 58.8859i | − | 2.10710i | ||||||
\(782\) | −6.36700 | − | 6.36700i | −0.227683 | − | 0.227683i | ||||
\(783\) | −3.37609 | + | 3.55189i | −0.120652 | + | 0.126934i | ||||
\(784\) | 1.31242 | 0.0468720 | ||||||||
\(785\) | 16.0952 | + | 16.0952i | 0.574462 | + | 0.574462i | ||||
\(786\) | 10.2185 | − | 6.01546i | 0.364483 | − | 0.214564i | ||||
\(787\) | −20.9015 | −0.745058 | −0.372529 | − | 0.928021i | \(-0.621509\pi\) | ||||
−0.372529 | + | 0.928021i | \(0.621509\pi\) | |||||||
\(788\) | 10.7908 | 0.384406 | ||||||||
\(789\) | 12.2494 | + | 20.8082i | 0.436090 | + | 0.740791i | ||||
\(790\) | −3.85057 | + | 3.85057i | −0.136997 | + | 0.136997i | ||||
\(791\) | 28.7177 | − | 28.7177i | 1.02108 | − | 1.02108i | ||||
\(792\) | 16.6338 | − | 4.75995i | 0.591057 | − | 0.169137i | ||||
\(793\) | 27.8885 | 0.990349 | ||||||||
\(794\) | 17.0627 | + | 17.0627i | 0.605532 | + | 0.605532i | ||||
\(795\) | 12.1013 | + | 3.13310i | 0.429190 | + | 0.111120i | ||||
\(796\) | 4.64611 | − | 4.64611i | 0.164677 | − | 0.164677i | ||||
\(797\) | 10.8270 | − | 10.8270i | 0.383511 | − | 0.383511i | −0.488854 | − | 0.872366i | \(-0.662585\pi\) |
0.872366 | + | 0.488854i | \(0.162585\pi\) | |||||||
\(798\) | −21.5024 | + | 12.6580i | −0.761176 | + | 0.448090i | ||||
\(799\) | −6.47491 | + | 6.47491i | −0.229066 | + | 0.229066i | ||||
\(800\) | −0.707107 | − | 0.707107i | −0.0250000 | − | 0.0250000i | ||||
\(801\) | −4.53776 | − | 15.8574i | −0.160334 | − | 0.560293i | ||||
\(802\) | 3.18941i | 0.112622i | ||||||||
\(803\) | − | 8.55027i | − | 0.301733i | ||||||
\(804\) | 2.60459 | + | 4.42446i | 0.0918570 | + | 0.156039i | ||||
\(805\) | 19.7994i | 0.697839i | ||||||||
\(806\) | 11.0214 | − | 11.0214i | 0.388213 | − | 0.388213i | ||||
\(807\) | −15.0953 | + | 8.88631i | −0.531379 | + | 0.312813i | ||||
\(808\) | 1.64564 | + | 1.64564i | 0.0578935 | + | 0.0578935i | ||||
\(809\) | 29.1906 | − | 29.1906i | 1.02629 | − | 1.02629i | 0.0266408 | − | 0.999645i | \(-0.491519\pi\) |
0.999645 | − | 0.0266408i | \(-0.00848104\pi\) | |||||||
\(810\) | −4.76103 | − | 7.63758i | −0.167285 | − | 0.268357i | ||||
\(811\) | −52.5079 | −1.84380 | −0.921902 | − | 0.387424i | \(-0.873365\pi\) | ||||
−0.921902 | + | 0.387424i | \(0.873365\pi\) | |||||||
\(812\) | 1.59037 | + | 1.59037i | 0.0558111 | + | 0.0558111i | ||||
\(813\) | −25.7371 | − | 43.7199i | −0.902639 | − | 1.53332i | ||||
\(814\) | 16.0825 | − | 31.1765i | 0.563693 | − | 1.09274i | ||||
\(815\) | − | 10.6310i | − | 0.372388i | ||||||
\(816\) | 0.470841 | − | 1.81858i | 0.0164827 | − | 0.0636630i | ||||
\(817\) | 55.3154i | 1.93524i | ||||||||
\(818\) | 0.950746 | 0.0332420 | ||||||||
\(819\) | −4.39971 | − | 15.3749i | −0.153738 | − | 0.537244i | ||||
\(820\) | 2.01797 | − | 2.01797i | 0.0704705 | − | 0.0704705i | ||||
\(821\) | 16.4066i | 0.572593i | 0.958141 | + | 0.286297i | \(0.0924242\pi\) | ||||
−0.958141 | + | 0.286297i | \(0.907576\pi\) | |||||||
\(822\) | 9.58466 | − | 37.0199i | 0.334303 | − | 1.29122i | ||||
\(823\) | −39.0832 | −1.36235 | −0.681177 | − | 0.732118i | \(-0.738532\pi\) | ||||
−0.681177 | + | 0.732118i | \(0.738532\pi\) | |||||||
\(824\) | − | 4.34279i | − | 0.151288i | ||||||
\(825\) | 8.60819 | − | 5.06748i | 0.299699 | − | 0.176427i | ||||
\(826\) | −19.0167 | −0.661676 | ||||||||
\(827\) | 13.5649 | + | 13.5649i | 0.471699 | + | 0.471699i | 0.902464 | − | 0.430765i | \(-0.141756\pi\) |
−0.430765 | + | 0.902464i | \(0.641756\pi\) | |||||||
\(828\) | 6.85219 | + | 23.9452i | 0.238130 | + | 0.832155i | ||||
\(829\) | −23.0222 | − | 23.0222i | −0.799595 | − | 0.799595i | 0.183437 | − | 0.983032i | \(-0.441278\pi\) |
−0.983032 | + | 0.183437i | \(0.941278\pi\) | |||||||
\(830\) | 16.2511i | 0.564082i | ||||||||
\(831\) | −7.31116 | + | 28.2387i | −0.253621 | + | 0.979590i | ||||
\(832\) | −1.58054 | − | 1.58054i | −0.0547953 | − | 0.0547953i | ||||
\(833\) | 1.00651 | + | 1.00651i | 0.0348734 | + | 0.0348734i | ||||
\(834\) | −1.87234 | + | 7.23175i | −0.0648339 | + | 0.250415i | ||||
\(835\) | 17.7269i | 0.613465i | ||||||||
\(836\) | −24.6331 | − | 24.6331i | −0.851954 | − | 0.851954i | ||||
\(837\) | −26.2629 | − | 24.9631i | −0.907780 | − | 0.862849i | ||||
\(838\) | 6.21524 | + | 6.21524i | 0.214702 | + | 0.214702i | ||||
\(839\) | 27.1461 | 0.937188 | 0.468594 | − | 0.883414i | \(-0.344761\pi\) | ||||
0.468594 | + | 0.883414i | \(0.344761\pi\) | |||||||
\(840\) | −3.55970 | + | 2.09553i | −0.122821 | + | 0.0723027i | ||||
\(841\) | 28.1106i | 0.969331i | ||||||||
\(842\) | −32.2872 | −1.11269 | ||||||||
\(843\) | −2.17925 | + | 8.41718i | −0.0750575 | + | 0.289903i | ||||
\(844\) | − | 3.92953i | − | 0.135260i | ||||||
\(845\) | −5.65955 | + | 5.65955i | −0.194694 | + | 0.194694i | ||||
\(846\) | 24.3511 | − | 6.96833i | 0.837207 | − | 0.239576i | ||||
\(847\) | 53.0873 | 1.82410 | ||||||||
\(848\) | − | 7.21707i | − | 0.247835i | ||||||
\(849\) | −5.87747 | + | 22.7012i | −0.201714 | + | 0.779104i | ||||
\(850\) | − | 1.08458i | − | 0.0372007i | ||||||
\(851\) | 44.8802 | + | 23.1517i | 1.53847 | + | 0.793629i | ||||
\(852\) | 8.97181 | + | 15.2405i | 0.307369 | + | 0.522132i | ||||
\(853\) | −6.09664 | − | 6.09664i | −0.208745 | − | 0.208745i | 0.594989 | − | 0.803734i | \(-0.297156\pi\) |
−0.803734 | + | 0.594989i | \(0.797156\pi\) | |||||||
\(854\) | −29.7556 | −1.01822 | ||||||||
\(855\) | −8.79403 | + | 15.8447i | −0.300749 | + | 0.541876i | ||||
\(856\) | 7.58956 | − | 7.58956i | 0.259406 | − | 0.259406i | ||||
\(857\) | −14.1481 | − | 14.1481i | −0.483291 | − | 0.483291i | 0.422890 | − | 0.906181i | \(-0.361016\pi\) |
−0.906181 | + | 0.422890i | \(0.861016\pi\) | |||||||
\(858\) | 19.2412 | − | 11.3269i | 0.656882 | − | 0.386694i | ||||
\(859\) | −36.0754 | + | 36.0754i | −1.23088 | + | 1.23088i | −0.267248 | + | 0.963628i | \(0.586114\pi\) |
−0.963628 | + | 0.267248i | \(0.913886\pi\) | |||||||
\(860\) | 9.15744i | 0.312266i | ||||||||
\(861\) | −5.98031 | − | 10.1588i | −0.203808 | − | 0.346212i | ||||
\(862\) | − | 30.0600i | − | 1.02385i | ||||||
\(863\) | − | 20.6159i | − | 0.701775i | −0.936418 | − | 0.350887i | \(-0.885880\pi\) | ||
0.936418 | − | 0.350887i | \(-0.114120\pi\) | |||||||
\(864\) | −3.57985 | + | 3.76626i | −0.121789 | + | 0.128131i | ||||
\(865\) | −11.2500 | − | 11.2500i | −0.382510 | − | 0.382510i | ||||
\(866\) | −14.8428 | + | 14.8428i | −0.504379 | + | 0.504379i | ||||
\(867\) | −23.6188 | + | 13.9039i | −0.802137 | + | 0.472203i | ||||
\(868\) | −11.7593 | + | 11.7593i | −0.399137 | + | 0.399137i | ||||
\(869\) | −22.2068 | + | 22.2068i | −0.753316 | + | 0.753316i | ||||
\(870\) | 1.58133 | + | 0.409414i | 0.0536119 | + | 0.0138804i | ||||
\(871\) | 4.68505 | + | 4.68505i | 0.158747 | + | 0.158747i | ||||
\(872\) | 8.51102 | 0.288220 | ||||||||
\(873\) | 13.3379 | + | 46.6099i | 0.451421 | + | 1.57751i | ||||
\(874\) | 35.4606 | − | 35.4606i | 1.19947 | − | 1.19947i | ||||
\(875\) | −1.68635 | + | 1.68635i | −0.0570092 | + | 0.0570092i | ||||
\(876\) | 1.30271 | + | 2.21293i | 0.0440146 | + | 0.0747681i | ||||
\(877\) | 21.2420 | 0.717291 | 0.358645 | − | 0.933474i | \(-0.383239\pi\) | ||||
0.358645 | + | 0.933474i | \(0.383239\pi\) | |||||||
\(878\) | −2.11256 | −0.0712955 | ||||||||
\(879\) | −6.10293 | + | 3.59268i | −0.205847 | + | 0.121178i | ||||
\(880\) | −4.07799 | − | 4.07799i | −0.137469 | − | 0.137469i | ||||
\(881\) | −8.09375 | −0.272685 | −0.136343 | − | 0.990662i | \(-0.543535\pi\) | ||||
−0.136343 | + | 0.990662i | \(0.543535\pi\) | |||||||
\(882\) | −1.08321 | − | 3.78531i | −0.0364735 | − | 0.127458i | ||||
\(883\) | 38.6040 | + | 38.6040i | 1.29913 | + | 1.29913i | 0.928969 | + | 0.370158i | \(0.120697\pi\) |
0.370158 | + | 0.928969i | \(0.379303\pi\) | |||||||
\(884\) | − | 2.42426i | − | 0.0815369i | ||||||
\(885\) | −11.9021 | + | 7.00652i | −0.400083 | + | 0.235521i | ||||
\(886\) | 3.58752 | − | 3.58752i | 0.120525 | − | 0.120525i | ||||
\(887\) | −47.1547 | −1.58330 | −0.791649 | − | 0.610976i | \(-0.790777\pi\) | ||||
−0.791649 | + | 0.610976i | \(0.790777\pi\) | |||||||
\(888\) | 0.587635 | + | 10.5193i | 0.0197197 | + | 0.353003i | ||||
\(889\) | −25.3137 | −0.848994 | ||||||||
\(890\) | −3.88764 | + | 3.88764i | −0.130314 | + | 0.130314i | ||||
\(891\) | −27.4576 | − | 44.0471i | −0.919863 | − | 1.47563i | ||||
\(892\) | − | 15.8876i | − | 0.531956i | ||||||
\(893\) | −36.0616 | − | 36.0616i | −1.20676 | − | 1.20676i | ||||
\(894\) | −8.46401 | + | 32.6915i | −0.283079 | + | 1.09337i | ||||
\(895\) | −12.8828 | −0.430623 | ||||||||
\(896\) | 1.68635 | + | 1.68635i | 0.0563372 | + | 0.0563372i | ||||
\(897\) | 16.3057 | + | 27.6987i | 0.544431 | + | 0.924831i | ||||
\(898\) | −5.15494 | −0.172022 | ||||||||
\(899\) | 6.57631 | 0.219332 | ||||||||
\(900\) | −1.45585 | + | 2.62307i | −0.0485282 | + | 0.0874358i | ||||
\(901\) | 5.53486 | − | 5.53486i | 0.184393 | − | 0.184393i | ||||
\(902\) | 11.6379 | − | 11.6379i | 0.387501 | − | 0.387501i | ||||
\(903\) | 36.6193 | + | 9.48094i | 1.21861 | + | 0.315506i | ||||
\(904\) | −17.0294 | −0.566391 | ||||||||
\(905\) | 3.30299 | + | 3.30299i | 0.109795 | + | 0.109795i | ||||
\(906\) | −1.73017 | + | 6.68261i | −0.0574809 | + | 0.222015i | ||||
\(907\) | −25.8953 | + | 25.8953i | −0.859840 | + | 0.859840i | −0.991319 | − | 0.131479i | \(-0.958027\pi\) |
0.131479 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(908\) | 2.98325 | − | 2.98325i | 0.0990026 | − | 0.0990026i | ||||
\(909\) | 3.38817 | − | 6.10465i | 0.112379 | − | 0.202478i | ||||
\(910\) | −3.76937 | + | 3.76937i | −0.124953 | + | 0.124953i | ||||
\(911\) | 0.380958 | + | 0.380958i | 0.0126217 | + | 0.0126217i | 0.713389 | − | 0.700768i | \(-0.247159\pi\) |
−0.700768 | + | 0.713389i | \(0.747159\pi\) | |||||||
\(912\) | 10.1285 | + | 2.62232i | 0.335388 | + | 0.0868337i | ||||
\(913\) | 93.7223i | 3.10176i | ||||||||
\(914\) | 20.4534i | 0.676539i | ||||||||
\(915\) | −18.6232 | + | 10.9632i | −0.615665 | + | 0.362431i | ||||
\(916\) | − | 23.9167i | − | 0.790229i | ||||||
\(917\) | −11.5448 | + | 11.5448i | −0.381244 | + | 0.381244i | ||||
\(918\) | −5.63381 | + | 0.142960i | −0.185944 | + | 0.00471838i | ||||
\(919\) | 28.6235 | + | 28.6235i | 0.944201 | + | 0.944201i | 0.998523 | − | 0.0543226i | \(-0.0172999\pi\) |
−0.0543226 | + | 0.998523i | \(0.517300\pi\) | |||||||
\(920\) | 5.87049 | − | 5.87049i | 0.193544 | − | 0.193544i | ||||
\(921\) | −4.21779 | + | 2.48294i | −0.138981 | + | 0.0818156i | ||||
\(922\) | −4.92734 | −0.162273 | ||||||||
\(923\) | 16.1382 | + | 16.1382i | 0.531194 | + | 0.531194i | ||||
\(924\) | −20.5294 | + | 12.0853i | −0.675367 | + | 0.397576i | ||||
\(925\) | 1.85066 | + | 5.79440i | 0.0608493 | + | 0.190519i | ||||
\(926\) | − | 19.5845i | − | 0.643586i | ||||||
\(927\) | −12.5256 | + | 3.58434i | −0.411395 | + | 0.117725i | ||||
\(928\) | − | 0.943082i | − | 0.0309582i | ||||||
\(929\) | 55.7240 | 1.82825 | 0.914123 | − | 0.405436i | \(-0.132880\pi\) | ||||
0.914123 | + | 0.405436i | \(0.132880\pi\) | |||||||
\(930\) | −3.02724 | + | 11.6924i | −0.0992671 | + | 0.383410i | ||||
\(931\) | −5.60569 | + | 5.60569i | −0.183719 | + | 0.183719i | ||||
\(932\) | 25.6460i | 0.840063i | ||||||||
\(933\) | 21.9120 | + | 5.67315i | 0.717367 | + | 0.185730i | ||||
\(934\) | −5.72028 | −0.187173 | ||||||||
\(935\) | − | 6.25492i | − | 0.204558i | ||||||
\(936\) | −3.25413 | + | 5.86314i | −0.106365 | + | 0.191643i | ||||
\(937\) | 28.5848 | 0.933823 | 0.466912 | − | 0.884304i | \(-0.345367\pi\) | ||||
0.466912 | + | 0.884304i | \(0.345367\pi\) | |||||||
\(938\) | −4.99872 | − | 4.99872i | −0.163214 | − | 0.163214i | ||||
\(939\) | 7.94119 | + | 2.05602i | 0.259151 | + | 0.0670957i | ||||
\(940\) | −5.96998 | − | 5.96998i | −0.194719 | − | 0.194719i | ||||
\(941\) | − | 42.0849i | − | 1.37193i | −0.727635 | − | 0.685965i | \(-0.759380\pi\) | ||
0.727635 | − | 0.685965i | \(-0.240620\pi\) | |||||||
\(942\) | −38.1666 | − | 9.88154i | −1.24353 | − | 0.321958i | ||||
\(943\) | 16.7534 | + | 16.7534i | 0.545567 | + | 0.545567i | ||||
\(944\) | 5.63841 | + | 5.63841i | 0.183515 | + | 0.183515i | ||||
\(945\) | 8.98202 | + | 8.53746i | 0.292185 | + | 0.277723i | ||||
\(946\) | 52.8123i | 1.71708i | ||||||||
\(947\) | 26.2598 | + | 26.2598i | 0.853329 | + | 0.853329i | 0.990542 | − | 0.137212i | \(-0.0438143\pi\) |
−0.137212 | + | 0.990542i | \(0.543814\pi\) | |||||||
\(948\) | 2.36403 | − | 9.13087i | 0.0767803 | − | 0.296557i | ||||
\(949\) | 2.34327 | + | 2.34327i | 0.0760659 | + | 0.0760659i | ||||
\(950\) | 6.04049 | 0.195980 | ||||||||
\(951\) | 21.9686 | + | 37.3184i | 0.712382 | + | 1.21013i | ||||
\(952\) | 2.58657i | 0.0838312i | ||||||||
\(953\) | 26.0414 | 0.843562 | 0.421781 | − | 0.906698i | \(-0.361405\pi\) | ||||
0.421781 | + | 0.906698i | \(0.361405\pi\) | |||||||
\(954\) | −20.8157 | + | 5.95664i | −0.673933 | + | 0.192853i | ||||
\(955\) | − | 3.56179i | − | 0.115257i | ||||||
\(956\) | 11.0015 | − | 11.0015i | 0.355813 | − | 0.355813i | ||||
\(957\) | 9.11975 | + | 2.36115i | 0.294800 | + | 0.0763253i | ||||
\(958\) | −5.70788 | −0.184413 | ||||||||
\(959\) | 52.6535i | 1.70027i | ||||||||
\(960\) | 1.67676 | + | 0.434124i | 0.0541173 | + | 0.0140113i | ||||
\(961\) | 17.6258i | 0.568573i | ||||||||
\(962\) | 4.13663 | + | 12.9517i | 0.133370 | + | 0.417581i | ||||
\(963\) | −28.1541 | − | 15.6260i | −0.907254 | − | 0.503540i | ||||
\(964\) | 20.6461 | + | 20.6461i | 0.664965 | + | 0.664965i | ||||
\(965\) | −6.66221 | −0.214464 | ||||||||
\(966\) | −17.3974 | − | 29.5531i | −0.559751 | − | 0.950855i | ||||
\(967\) | 2.52912 | − | 2.52912i | 0.0813311 | − | 0.0813311i | −0.665271 | − | 0.746602i | \(-0.731684\pi\) |
0.746602 | + | 0.665271i | \(0.231684\pi\) | |||||||
\(968\) | −15.7402 | − | 15.7402i | −0.505911 | − | 0.505911i | ||||
\(969\) | 5.75656 | + | 9.77874i | 0.184927 | + | 0.314138i | ||||
\(970\) | 11.4270 | − | 11.4270i | 0.366900 | − | 0.366900i | ||||
\(971\) | 55.6668i | 1.78643i | 0.449628 | + | 0.893216i | \(0.351556\pi\) | ||||
−0.449628 | + | 0.893216i | \(0.648444\pi\) | |||||||
\(972\) | 13.8174 | + | 7.21661i | 0.443193 | + | 0.231473i | ||||
\(973\) | − | 10.2857i | − | 0.329746i | ||||||
\(974\) | − | 7.78760i | − | 0.249531i | ||||||
\(975\) | −0.970360 | + | 3.74793i | −0.0310764 | + | 0.120030i | ||||
\(976\) | 8.82247 | + | 8.82247i | 0.282400 | + | 0.282400i | ||||
\(977\) | 13.3819 | − | 13.3819i | 0.428126 | − | 0.428126i | −0.459864 | − | 0.887990i | \(-0.652102\pi\) |
0.887990 | + | 0.459864i | \(0.152102\pi\) | |||||||
\(978\) | 9.34125 | + | 15.8681i | 0.298700 | + | 0.507406i | ||||
\(979\) | −22.4206 | + | 22.4206i | −0.716567 | + | 0.716567i | ||||
\(980\) | −0.928018 | + | 0.928018i | −0.0296444 | + | 0.0296444i | ||||
\(981\) | −7.02461 | − | 24.5478i | −0.224279 | − | 0.783750i | ||||
\(982\) | 10.3432 | + | 10.3432i | 0.330066 | + | 0.330066i | ||||
\(983\) | −21.6640 | −0.690975 | −0.345488 | − | 0.938423i | \(-0.612286\pi\) | ||||
−0.345488 | + | 0.938423i | \(0.612286\pi\) | |||||||
\(984\) | −1.23892 | + | 4.78521i | −0.0394953 | + | 0.152547i | ||||
\(985\) | −7.63023 | + | 7.63023i | −0.243119 | + | 0.243119i | ||||
\(986\) | 0.723261 | − | 0.723261i | 0.0230333 | − | 0.0230333i | ||||
\(987\) | −30.0540 | + | 17.6922i | −0.956629 | + | 0.563150i | ||||
\(988\) | 13.5018 | 0.429550 | ||||||||
\(989\) | −76.0261 | −2.41749 | ||||||||
\(990\) | −8.39609 | + | 15.1277i | −0.266845 | + | 0.480789i | ||||
\(991\) | 8.58660 | + | 8.58660i | 0.272762 | + | 0.272762i | 0.830211 | − | 0.557449i | \(-0.188220\pi\) |
−0.557449 | + | 0.830211i | \(0.688220\pi\) | |||||||
\(992\) | 6.97322 | 0.221400 | ||||||||
\(993\) | 38.3965 | + | 9.94108i | 1.21848 | + | 0.315471i | ||||
\(994\) | −17.2186 | − | 17.2186i | −0.546142 | − | 0.546142i | ||||
\(995\) | 6.57059i | 0.208302i | ||||||||
\(996\) | −14.2795 | − | 24.2567i | −0.452462 | − | 0.768603i | ||||
\(997\) | −13.9394 | + | 13.9394i | −0.441465 | + | 0.441465i | −0.892504 | − | 0.451039i | \(-0.851053\pi\) |
0.451039 | + | 0.892504i | \(0.351053\pi\) | |||||||
\(998\) | −4.94303 | −0.156469 | ||||||||
\(999\) | 29.8550 | − | 10.3770i | 0.944569 | − | 0.328313i |
(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 | 1110.2.u.e.401.20 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.401.4 | yes | 40 | |
37.6 | odd | 4 | inner | 1110.2.u.e.191.4 | ✓ | 40 | |
111.80 | even | 4 | inner | 1110.2.u.e.191.20 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.4 | ✓ | 40 | 37.6 | odd | 4 | inner | |
1110.2.u.e.191.20 | yes | 40 | 111.80 | even | 4 | inner | |
1110.2.u.e.401.4 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.401.20 | yes | 40 | 1.1 | even | 1 | trivial |