Properties

Label 1470.2.d.g.1469.13
Level $1470$
Weight $2$
Character 1470.1469
Analytic conductor $11.738$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(1469,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.1469");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.d (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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1469.13
Character \(\chi\) \(=\) 1470.1469
Dual form 1470.2.d.g.1469.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.321854 - 1.70188i) q^{3} +1.00000 q^{4} +(2.20838 + 0.350775i) q^{5} +(-0.321854 + 1.70188i) q^{6} -1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.321854 - 1.70188i) q^{3} +1.00000 q^{4} +(2.20838 + 0.350775i) q^{5} +(-0.321854 + 1.70188i) q^{6} -1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +(-2.20838 - 0.350775i) q^{10} +3.78464i q^{11} +(0.321854 - 1.70188i) q^{12} -6.40306 q^{13} +(1.30776 - 3.64551i) q^{15} +1.00000 q^{16} +5.57902i q^{17} +(2.79282 + 1.09552i) q^{18} +2.10349i q^{19} +(2.20838 + 0.350775i) q^{20} -3.78464i q^{22} +4.70837 q^{23} +(-0.321854 + 1.70188i) q^{24} +(4.75391 + 1.54929i) q^{25} +6.40306 q^{26} +(-2.76332 + 4.40046i) q^{27} +7.55401i q^{29} +(-1.30776 + 3.64551i) q^{30} +3.43184i q^{31} -1.00000 q^{32} +(6.44102 + 1.21810i) q^{33} -5.57902i q^{34} +(-2.79282 - 1.09552i) q^{36} -2.75706i q^{37} -2.10349i q^{38} +(-2.06085 + 10.8973i) q^{39} +(-2.20838 - 0.350775i) q^{40} +8.77986 q^{41} +7.04507i q^{43} +3.78464i q^{44} +(-5.78334 - 3.39897i) q^{45} -4.70837 q^{46} -2.55610i q^{47} +(0.321854 - 1.70188i) q^{48} +(-4.75391 - 1.54929i) q^{50} +(9.49485 + 1.79563i) q^{51} -6.40306 q^{52} +3.08554 q^{53} +(2.76332 - 4.40046i) q^{54} +(-1.32756 + 8.35793i) q^{55} +(3.57990 + 0.677017i) q^{57} -7.55401i q^{58} -12.9727 q^{59} +(1.30776 - 3.64551i) q^{60} -10.3401i q^{61} -3.43184i q^{62} +1.00000 q^{64} +(-14.1404 - 2.24604i) q^{65} +(-6.44102 - 1.21810i) q^{66} +1.48871i q^{67} +5.57902i q^{68} +(1.51541 - 8.01310i) q^{69} +5.06254i q^{71} +(2.79282 + 1.09552i) q^{72} -3.33557 q^{73} +2.75706i q^{74} +(4.16678 - 7.59197i) q^{75} +2.10349i q^{76} +(2.06085 - 10.8973i) q^{78} -7.07694 q^{79} +(2.20838 + 0.350775i) q^{80} +(6.59969 + 6.11916i) q^{81} -8.77986 q^{82} -9.49058i q^{83} +(-1.95698 + 12.3206i) q^{85} -7.04507i q^{86} +(12.8560 + 2.43129i) q^{87} -3.78464i q^{88} +10.6182 q^{89} +(5.78334 + 3.39897i) q^{90} +4.70837 q^{92} +(5.84059 + 1.10455i) q^{93} +2.55610i q^{94} +(-0.737854 + 4.64532i) q^{95} +(-0.321854 + 1.70188i) q^{96} +4.90516 q^{97} +(4.14613 - 10.5698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.321854 1.70188i 0.185822 0.982583i
\(4\) 1.00000 0.500000
\(5\) 2.20838 + 0.350775i 0.987619 + 0.156871i
\(6\) −0.321854 + 1.70188i −0.131396 + 0.694791i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.79282 1.09552i −0.930940 0.365172i
\(10\) −2.20838 0.350775i −0.698352 0.110925i
\(11\) 3.78464i 1.14111i 0.821259 + 0.570556i \(0.193272\pi\)
−0.821259 + 0.570556i \(0.806728\pi\)
\(12\) 0.321854 1.70188i 0.0929111 0.491292i
\(13\) −6.40306 −1.77589 −0.887945 0.459950i \(-0.847868\pi\)
−0.887945 + 0.459950i \(0.847868\pi\)
\(14\) 0 0
\(15\) 1.30776 3.64551i 0.337661 0.941268i
\(16\) 1.00000 0.250000
\(17\) 5.57902i 1.35311i 0.736391 + 0.676556i \(0.236528\pi\)
−0.736391 + 0.676556i \(0.763472\pi\)
\(18\) 2.79282 + 1.09552i 0.658274 + 0.258215i
\(19\) 2.10349i 0.482575i 0.970454 + 0.241287i \(0.0775696\pi\)
−0.970454 + 0.241287i \(0.922430\pi\)
\(20\) 2.20838 + 0.350775i 0.493810 + 0.0784357i
\(21\) 0 0
\(22\) 3.78464i 0.806887i
\(23\) 4.70837 0.981763 0.490882 0.871226i \(-0.336675\pi\)
0.490882 + 0.871226i \(0.336675\pi\)
\(24\) −0.321854 + 1.70188i −0.0656981 + 0.347396i
\(25\) 4.75391 + 1.54929i 0.950783 + 0.309859i
\(26\) 6.40306 1.25574
\(27\) −2.76332 + 4.40046i −0.531801 + 0.846869i
\(28\) 0 0
\(29\) 7.55401i 1.40274i 0.712795 + 0.701372i \(0.247429\pi\)
−0.712795 + 0.701372i \(0.752571\pi\)
\(30\) −1.30776 + 3.64551i −0.238762 + 0.665577i
\(31\) 3.43184i 0.616377i 0.951325 + 0.308188i \(0.0997227\pi\)
−0.951325 + 0.308188i \(0.900277\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.44102 + 1.21810i 1.12124 + 0.212044i
\(34\) 5.57902i 0.956794i
\(35\) 0 0
\(36\) −2.79282 1.09552i −0.465470 0.182586i
\(37\) 2.75706i 0.453259i −0.973981 0.226629i \(-0.927229\pi\)
0.973981 0.226629i \(-0.0727706\pi\)
\(38\) 2.10349i 0.341232i
\(39\) −2.06085 + 10.8973i −0.330000 + 1.74496i
\(40\) −2.20838 0.350775i −0.349176 0.0554624i
\(41\) 8.77986 1.37118 0.685592 0.727986i \(-0.259543\pi\)
0.685592 + 0.727986i \(0.259543\pi\)
\(42\) 0 0
\(43\) 7.04507i 1.07436i 0.843467 + 0.537181i \(0.180511\pi\)
−0.843467 + 0.537181i \(0.819489\pi\)
\(44\) 3.78464i 0.570556i
\(45\) −5.78334 3.39897i −0.862129 0.506689i
\(46\) −4.70837 −0.694211
\(47\) 2.55610i 0.372845i −0.982470 0.186422i \(-0.940311\pi\)
0.982470 0.186422i \(-0.0596893\pi\)
\(48\) 0.321854 1.70188i 0.0464556 0.245646i
\(49\) 0 0
\(50\) −4.75391 1.54929i −0.672305 0.219103i
\(51\) 9.49485 + 1.79563i 1.32955 + 0.251438i
\(52\) −6.40306 −0.887945
\(53\) 3.08554 0.423831 0.211916 0.977288i \(-0.432030\pi\)
0.211916 + 0.977288i \(0.432030\pi\)
\(54\) 2.76332 4.40046i 0.376040 0.598827i
\(55\) −1.32756 + 8.35793i −0.179008 + 1.12698i
\(56\) 0 0
\(57\) 3.57990 + 0.677017i 0.474170 + 0.0896731i
\(58\) 7.55401i 0.991890i
\(59\) −12.9727 −1.68890 −0.844452 0.535631i \(-0.820074\pi\)
−0.844452 + 0.535631i \(0.820074\pi\)
\(60\) 1.30776 3.64551i 0.168830 0.470634i
\(61\) 10.3401i 1.32391i −0.749542 0.661957i \(-0.769726\pi\)
0.749542 0.661957i \(-0.230274\pi\)
\(62\) 3.43184i 0.435844i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −14.1404 2.24604i −1.75390 0.278587i
\(66\) −6.44102 1.21810i −0.792834 0.149938i
\(67\) 1.48871i 0.181875i 0.995857 + 0.0909373i \(0.0289863\pi\)
−0.995857 + 0.0909373i \(0.971014\pi\)
\(68\) 5.57902i 0.676556i
\(69\) 1.51541 8.01310i 0.182433 0.964664i
\(70\) 0 0
\(71\) 5.06254i 0.600812i 0.953811 + 0.300406i \(0.0971222\pi\)
−0.953811 + 0.300406i \(0.902878\pi\)
\(72\) 2.79282 + 1.09552i 0.329137 + 0.129108i
\(73\) −3.33557 −0.390399 −0.195199 0.980764i \(-0.562535\pi\)
−0.195199 + 0.980764i \(0.562535\pi\)
\(74\) 2.75706i 0.320502i
\(75\) 4.16678 7.59197i 0.481138 0.876645i
\(76\) 2.10349i 0.241287i
\(77\) 0 0
\(78\) 2.06085 10.8973i 0.233345 1.23387i
\(79\) −7.07694 −0.796218 −0.398109 0.917338i \(-0.630333\pi\)
−0.398109 + 0.917338i \(0.630333\pi\)
\(80\) 2.20838 + 0.350775i 0.246905 + 0.0392179i
\(81\) 6.59969 + 6.11916i 0.733299 + 0.679906i
\(82\) −8.77986 −0.969573
\(83\) 9.49058i 1.04173i −0.853640 0.520863i \(-0.825610\pi\)
0.853640 0.520863i \(-0.174390\pi\)
\(84\) 0 0
\(85\) −1.95698 + 12.3206i −0.212265 + 1.33636i
\(86\) 7.04507i 0.759689i
\(87\) 12.8560 + 2.43129i 1.37831 + 0.260661i
\(88\) 3.78464i 0.403444i
\(89\) 10.6182 1.12552 0.562761 0.826620i \(-0.309739\pi\)
0.562761 + 0.826620i \(0.309739\pi\)
\(90\) 5.78334 + 3.39897i 0.609617 + 0.358283i
\(91\) 0 0
\(92\) 4.70837 0.490882
\(93\) 5.84059 + 1.10455i 0.605641 + 0.114537i
\(94\) 2.55610i 0.263641i
\(95\) −0.737854 + 4.64532i −0.0757022 + 0.476600i
\(96\) −0.321854 + 1.70188i −0.0328491 + 0.173698i
\(97\) 4.90516 0.498044 0.249022 0.968498i \(-0.419891\pi\)
0.249022 + 0.968498i \(0.419891\pi\)
\(98\) 0 0
\(99\) 4.14613 10.5698i 0.416702 1.06231i
\(100\) 4.75391 + 1.54929i 0.475391 + 0.154929i
\(101\) −5.63646 −0.560849 −0.280424 0.959876i \(-0.590475\pi\)
−0.280424 + 0.959876i \(0.590475\pi\)
\(102\) −9.49485 1.79563i −0.940130 0.177794i
\(103\) −6.76706 −0.666779 −0.333389 0.942789i \(-0.608192\pi\)
−0.333389 + 0.942789i \(0.608192\pi\)
\(104\) 6.40306 0.627872
\(105\) 0 0
\(106\) −3.08554 −0.299694
\(107\) 9.09162 0.878920 0.439460 0.898262i \(-0.355170\pi\)
0.439460 + 0.898262i \(0.355170\pi\)
\(108\) −2.76332 + 4.40046i −0.265901 + 0.423435i
\(109\) −15.3307 −1.46842 −0.734208 0.678925i \(-0.762446\pi\)
−0.734208 + 0.678925i \(0.762446\pi\)
\(110\) 1.32756 8.35793i 0.126578 0.796897i
\(111\) −4.69220 0.887371i −0.445364 0.0842255i
\(112\) 0 0
\(113\) 2.83057 0.266277 0.133139 0.991097i \(-0.457494\pi\)
0.133139 + 0.991097i \(0.457494\pi\)
\(114\) −3.57990 0.677017i −0.335289 0.0634085i
\(115\) 10.3979 + 1.65158i 0.969608 + 0.154011i
\(116\) 7.55401i 0.701372i
\(117\) 17.8826 + 7.01465i 1.65325 + 0.648505i
\(118\) 12.9727 1.19424
\(119\) 0 0
\(120\) −1.30776 + 3.64551i −0.119381 + 0.332788i
\(121\) −3.32348 −0.302135
\(122\) 10.3401i 0.936148i
\(123\) 2.82583 14.9423i 0.254797 1.34730i
\(124\) 3.43184i 0.308188i
\(125\) 9.95501 + 5.08899i 0.890403 + 0.455173i
\(126\) 0 0
\(127\) 16.6271i 1.47542i 0.675119 + 0.737709i \(0.264092\pi\)
−0.675119 + 0.737709i \(0.735908\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.9899 + 2.26748i 1.05565 + 0.199640i
\(130\) 14.1404 + 2.24604i 1.24020 + 0.196990i
\(131\) −0.210484 −0.0183901 −0.00919504 0.999958i \(-0.502927\pi\)
−0.00919504 + 0.999958i \(0.502927\pi\)
\(132\) 6.44102 + 1.21810i 0.560618 + 0.106022i
\(133\) 0 0
\(134\) 1.48871i 0.128605i
\(135\) −7.64604 + 8.74860i −0.658067 + 0.752960i
\(136\) 5.57902i 0.478397i
\(137\) −3.87172 −0.330784 −0.165392 0.986228i \(-0.552889\pi\)
−0.165392 + 0.986228i \(0.552889\pi\)
\(138\) −1.51541 + 8.01310i −0.129000 + 0.682121i
\(139\) 17.4338i 1.47871i −0.673314 0.739357i \(-0.735130\pi\)
0.673314 0.739357i \(-0.264870\pi\)
\(140\) 0 0
\(141\) −4.35018 0.822689i −0.366351 0.0692829i
\(142\) 5.06254i 0.424839i
\(143\) 24.2333i 2.02649i
\(144\) −2.79282 1.09552i −0.232735 0.0912929i
\(145\) −2.64976 + 16.6821i −0.220051 + 1.38538i
\(146\) 3.33557 0.276053
\(147\) 0 0
\(148\) 2.75706i 0.226629i
\(149\) 8.65775i 0.709270i 0.935005 + 0.354635i \(0.115395\pi\)
−0.935005 + 0.354635i \(0.884605\pi\)
\(150\) −4.16678 + 7.59197i −0.340216 + 0.619881i
\(151\) 16.8301 1.36961 0.684806 0.728726i \(-0.259887\pi\)
0.684806 + 0.728726i \(0.259887\pi\)
\(152\) 2.10349i 0.170616i
\(153\) 6.11191 15.5812i 0.494118 1.25967i
\(154\) 0 0
\(155\) −1.20380 + 7.57882i −0.0966919 + 0.608745i
\(156\) −2.06085 + 10.8973i −0.165000 + 0.872480i
\(157\) 6.23745 0.497802 0.248901 0.968529i \(-0.419931\pi\)
0.248901 + 0.968529i \(0.419931\pi\)
\(158\) 7.07694 0.563011
\(159\) 0.993092 5.25123i 0.0787573 0.416450i
\(160\) −2.20838 0.350775i −0.174588 0.0277312i
\(161\) 0 0
\(162\) −6.59969 6.11916i −0.518521 0.480766i
\(163\) 3.22815i 0.252848i −0.991976 0.126424i \(-0.959650\pi\)
0.991976 0.126424i \(-0.0403500\pi\)
\(164\) 8.77986 0.685592
\(165\) 13.7970 + 4.94938i 1.07409 + 0.385309i
\(166\) 9.49058i 0.736612i
\(167\) 10.9301i 0.845797i 0.906177 + 0.422899i \(0.138987\pi\)
−0.906177 + 0.422899i \(0.861013\pi\)
\(168\) 0 0
\(169\) 27.9992 2.15379
\(170\) 1.95698 12.3206i 0.150094 0.944948i
\(171\) 2.30441 5.87468i 0.176223 0.449248i
\(172\) 7.04507i 0.537181i
\(173\) 4.83283i 0.367434i −0.982979 0.183717i \(-0.941187\pi\)
0.982979 0.183717i \(-0.0588129\pi\)
\(174\) −12.8560 2.43129i −0.974614 0.184315i
\(175\) 0 0
\(176\) 3.78464i 0.285278i
\(177\) −4.17532 + 22.0781i −0.313836 + 1.65949i
\(178\) −10.6182 −0.795864
\(179\) 8.55562i 0.639477i −0.947506 0.319739i \(-0.896405\pi\)
0.947506 0.319739i \(-0.103595\pi\)
\(180\) −5.78334 3.39897i −0.431065 0.253344i
\(181\) 11.2205i 0.834013i 0.908904 + 0.417006i \(0.136921\pi\)
−0.908904 + 0.417006i \(0.863079\pi\)
\(182\) 0 0
\(183\) −17.5976 3.32800i −1.30086 0.246013i
\(184\) −4.70837 −0.347106
\(185\) 0.967110 6.08865i 0.0711033 0.447647i
\(186\) −5.84059 1.10455i −0.428253 0.0809895i
\(187\) −21.1146 −1.54405
\(188\) 2.55610i 0.186422i
\(189\) 0 0
\(190\) 0.737854 4.64532i 0.0535295 0.337007i
\(191\) 2.85343i 0.206467i 0.994657 + 0.103234i \(0.0329189\pi\)
−0.994657 + 0.103234i \(0.967081\pi\)
\(192\) 0.321854 1.70188i 0.0232278 0.122823i
\(193\) 26.7793i 1.92762i 0.266598 + 0.963808i \(0.414100\pi\)
−0.266598 + 0.963808i \(0.585900\pi\)
\(194\) −4.90516 −0.352170
\(195\) −8.37364 + 23.3425i −0.599649 + 1.67159i
\(196\) 0 0
\(197\) 14.7242 1.04905 0.524527 0.851394i \(-0.324242\pi\)
0.524527 + 0.851394i \(0.324242\pi\)
\(198\) −4.14613 + 10.5698i −0.294653 + 0.751164i
\(199\) 16.4657i 1.16722i −0.812032 0.583612i \(-0.801639\pi\)
0.812032 0.583612i \(-0.198361\pi\)
\(200\) −4.75391 1.54929i −0.336152 0.109552i
\(201\) 2.53361 + 0.479146i 0.178707 + 0.0337964i
\(202\) 5.63646 0.396580
\(203\) 0 0
\(204\) 9.49485 + 1.79563i 0.664773 + 0.125719i
\(205\) 19.3893 + 3.07976i 1.35421 + 0.215100i
\(206\) 6.76706 0.471484
\(207\) −13.1496 5.15809i −0.913963 0.358512i
\(208\) −6.40306 −0.443973
\(209\) −7.96096 −0.550671
\(210\) 0 0
\(211\) −15.8206 −1.08913 −0.544567 0.838717i \(-0.683306\pi\)
−0.544567 + 0.838717i \(0.683306\pi\)
\(212\) 3.08554 0.211916
\(213\) 8.61585 + 1.62940i 0.590348 + 0.111644i
\(214\) −9.09162 −0.621490
\(215\) −2.47124 + 15.5582i −0.168537 + 1.06106i
\(216\) 2.76332 4.40046i 0.188020 0.299413i
\(217\) 0 0
\(218\) 15.3307 1.03833
\(219\) −1.07356 + 5.67675i −0.0725447 + 0.383599i
\(220\) −1.32756 + 8.35793i −0.0895039 + 0.563492i
\(221\) 35.7228i 2.40298i
\(222\) 4.69220 + 0.887371i 0.314920 + 0.0595565i
\(223\) −21.9853 −1.47224 −0.736122 0.676849i \(-0.763345\pi\)
−0.736122 + 0.676849i \(0.763345\pi\)
\(224\) 0 0
\(225\) −11.5796 9.53488i −0.771970 0.635659i
\(226\) −2.83057 −0.188286
\(227\) 27.5101i 1.82591i 0.408063 + 0.912954i \(0.366204\pi\)
−0.408063 + 0.912954i \(0.633796\pi\)
\(228\) 3.57990 + 0.677017i 0.237085 + 0.0448366i
\(229\) 16.1836i 1.06944i −0.845029 0.534720i \(-0.820417\pi\)
0.845029 0.534720i \(-0.179583\pi\)
\(230\) −10.3979 1.65158i −0.685616 0.108902i
\(231\) 0 0
\(232\) 7.55401i 0.495945i
\(233\) 17.8328 1.16827 0.584133 0.811658i \(-0.301435\pi\)
0.584133 + 0.811658i \(0.301435\pi\)
\(234\) −17.8826 7.01465i −1.16902 0.458562i
\(235\) 0.896615 5.64484i 0.0584887 0.368229i
\(236\) −12.9727 −0.844452
\(237\) −2.27774 + 12.0441i −0.147955 + 0.782351i
\(238\) 0 0
\(239\) 18.4508i 1.19348i −0.802433 0.596742i \(-0.796462\pi\)
0.802433 0.596742i \(-0.203538\pi\)
\(240\) 1.30776 3.64551i 0.0844152 0.235317i
\(241\) 13.4629i 0.867223i 0.901100 + 0.433612i \(0.142761\pi\)
−0.901100 + 0.433612i \(0.857239\pi\)
\(242\) 3.32348 0.213641
\(243\) 12.5382 9.26244i 0.804328 0.594186i
\(244\) 10.3401i 0.661957i
\(245\) 0 0
\(246\) −2.82583 + 14.9423i −0.180168 + 0.952687i
\(247\) 13.4688i 0.857000i
\(248\) 3.43184i 0.217922i
\(249\) −16.1519 3.05458i −1.02358 0.193576i
\(250\) −9.95501 5.08899i −0.629610 0.321856i
\(251\) −21.5154 −1.35804 −0.679020 0.734120i \(-0.737595\pi\)
−0.679020 + 0.734120i \(0.737595\pi\)
\(252\) 0 0
\(253\) 17.8195i 1.12030i
\(254\) 16.6271i 1.04328i
\(255\) 20.3384 + 7.29600i 1.27364 + 0.456893i
\(256\) 1.00000 0.0625000
\(257\) 13.2419i 0.826004i −0.910730 0.413002i \(-0.864480\pi\)
0.910730 0.413002i \(-0.135520\pi\)
\(258\) −11.9899 2.26748i −0.746458 0.141167i
\(259\) 0 0
\(260\) −14.1404 2.24604i −0.876951 0.139293i
\(261\) 8.27553 21.0970i 0.512243 1.30587i
\(262\) 0.210484 0.0130038
\(263\) −15.5680 −0.959961 −0.479981 0.877279i \(-0.659356\pi\)
−0.479981 + 0.877279i \(0.659356\pi\)
\(264\) −6.44102 1.21810i −0.396417 0.0749688i
\(265\) 6.81405 + 1.08233i 0.418584 + 0.0664871i
\(266\) 0 0
\(267\) 3.41749 18.0709i 0.209147 1.10592i
\(268\) 1.48871i 0.0909373i
\(269\) 8.37779 0.510803 0.255401 0.966835i \(-0.417792\pi\)
0.255401 + 0.966835i \(0.417792\pi\)
\(270\) 7.64604 8.74860i 0.465323 0.532423i
\(271\) 0.305606i 0.0185642i 0.999957 + 0.00928212i \(0.00295463\pi\)
−0.999957 + 0.00928212i \(0.997045\pi\)
\(272\) 5.57902i 0.338278i
\(273\) 0 0
\(274\) 3.87172 0.233899
\(275\) −5.86351 + 17.9918i −0.353583 + 1.08495i
\(276\) 1.51541 8.01310i 0.0912167 0.482332i
\(277\) 20.9930i 1.26135i 0.776047 + 0.630675i \(0.217222\pi\)
−0.776047 + 0.630675i \(0.782778\pi\)
\(278\) 17.4338i 1.04561i
\(279\) 3.75963 9.58451i 0.225083 0.573810i
\(280\) 0 0
\(281\) 5.67638i 0.338624i −0.985562 0.169312i \(-0.945845\pi\)
0.985562 0.169312i \(-0.0541546\pi\)
\(282\) 4.35018 + 0.822689i 0.259049 + 0.0489904i
\(283\) 15.8411 0.941658 0.470829 0.882224i \(-0.343955\pi\)
0.470829 + 0.882224i \(0.343955\pi\)
\(284\) 5.06254i 0.300406i
\(285\) 7.66832 + 2.75086i 0.454232 + 0.162947i
\(286\) 24.2333i 1.43294i
\(287\) 0 0
\(288\) 2.79282 + 1.09552i 0.164569 + 0.0645539i
\(289\) −14.1255 −0.830911
\(290\) 2.64976 16.6821i 0.155599 0.979609i
\(291\) 1.57875 8.34802i 0.0925477 0.489370i
\(292\) −3.33557 −0.195199
\(293\) 23.2810i 1.36009i 0.733170 + 0.680045i \(0.238040\pi\)
−0.733170 + 0.680045i \(0.761960\pi\)
\(294\) 0 0
\(295\) −28.6487 4.55051i −1.66799 0.264941i
\(296\) 2.75706i 0.160251i
\(297\) −16.6542 10.4582i −0.966372 0.606844i
\(298\) 8.65775i 0.501530i
\(299\) −30.1480 −1.74350
\(300\) 4.16678 7.59197i 0.240569 0.438322i
\(301\) 0 0
\(302\) −16.8301 −0.968462
\(303\) −1.81412 + 9.59260i −0.104218 + 0.551081i
\(304\) 2.10349i 0.120644i
\(305\) 3.62705 22.8349i 0.207684 1.30752i
\(306\) −6.11191 + 15.5812i −0.349394 + 0.890718i
\(307\) −20.2759 −1.15721 −0.578604 0.815608i \(-0.696402\pi\)
−0.578604 + 0.815608i \(0.696402\pi\)
\(308\) 0 0
\(309\) −2.17800 + 11.5168i −0.123902 + 0.655165i
\(310\) 1.20380 7.57882i 0.0683715 0.430448i
\(311\) 11.8199 0.670244 0.335122 0.942175i \(-0.391222\pi\)
0.335122 + 0.942175i \(0.391222\pi\)
\(312\) 2.06085 10.8973i 0.116673 0.616937i
\(313\) −4.00427 −0.226335 −0.113167 0.993576i \(-0.536100\pi\)
−0.113167 + 0.993576i \(0.536100\pi\)
\(314\) −6.23745 −0.351999
\(315\) 0 0
\(316\) −7.07694 −0.398109
\(317\) 0.211278 0.0118665 0.00593327 0.999982i \(-0.498111\pi\)
0.00593327 + 0.999982i \(0.498111\pi\)
\(318\) −0.993092 + 5.25123i −0.0556898 + 0.294474i
\(319\) −28.5892 −1.60069
\(320\) 2.20838 + 0.350775i 0.123452 + 0.0196089i
\(321\) 2.92617 15.4729i 0.163323 0.863612i
\(322\) 0 0
\(323\) −11.7354 −0.652977
\(324\) 6.59969 + 6.11916i 0.366650 + 0.339953i
\(325\) −30.4396 9.92022i −1.68849 0.550275i
\(326\) 3.22815i 0.178790i
\(327\) −4.93424 + 26.0911i −0.272864 + 1.44284i
\(328\) −8.77986 −0.484787
\(329\) 0 0
\(330\) −13.7970 4.94938i −0.759497 0.272454i
\(331\) −4.13421 −0.227237 −0.113618 0.993524i \(-0.536244\pi\)
−0.113618 + 0.993524i \(0.536244\pi\)
\(332\) 9.49058i 0.520863i
\(333\) −3.02041 + 7.69999i −0.165517 + 0.421957i
\(334\) 10.9301i 0.598069i
\(335\) −0.522202 + 3.28764i −0.0285310 + 0.179623i
\(336\) 0 0
\(337\) 1.99207i 0.108515i −0.998527 0.0542576i \(-0.982721\pi\)
0.998527 0.0542576i \(-0.0172792\pi\)
\(338\) −27.9992 −1.52296
\(339\) 0.911028 4.81730i 0.0494803 0.261640i
\(340\) −1.95698 + 12.3206i −0.106132 + 0.668179i
\(341\) −12.9883 −0.703354
\(342\) −2.30441 + 5.87468i −0.124608 + 0.317666i
\(343\) 0 0
\(344\) 7.04507i 0.379844i
\(345\) 6.15740 17.1644i 0.331503 0.924102i
\(346\) 4.83283i 0.259815i
\(347\) 21.4429 1.15111 0.575557 0.817761i \(-0.304785\pi\)
0.575557 + 0.817761i \(0.304785\pi\)
\(348\) 12.8560 + 2.43129i 0.689157 + 0.130331i
\(349\) 17.1982i 0.920598i −0.887764 0.460299i \(-0.847742\pi\)
0.887764 0.460299i \(-0.152258\pi\)
\(350\) 0 0
\(351\) 17.6937 28.1764i 0.944420 1.50395i
\(352\) 3.78464i 0.201722i
\(353\) 3.05545i 0.162625i 0.996689 + 0.0813125i \(0.0259112\pi\)
−0.996689 + 0.0813125i \(0.974089\pi\)
\(354\) 4.17532 22.0781i 0.221916 1.17344i
\(355\) −1.77581 + 11.1800i −0.0942503 + 0.593374i
\(356\) 10.6182 0.562761
\(357\) 0 0
\(358\) 8.55562i 0.452179i
\(359\) 15.3615i 0.810751i −0.914150 0.405375i \(-0.867141\pi\)
0.914150 0.405375i \(-0.132859\pi\)
\(360\) 5.78334 + 3.39897i 0.304809 + 0.179141i
\(361\) 14.5753 0.767122
\(362\) 11.2205i 0.589736i
\(363\) −1.06967 + 5.65618i −0.0561433 + 0.296872i
\(364\) 0 0
\(365\) −7.36621 1.17003i −0.385565 0.0612424i
\(366\) 17.5976 + 3.32800i 0.919844 + 0.173957i
\(367\) −4.12440 −0.215292 −0.107646 0.994189i \(-0.534331\pi\)
−0.107646 + 0.994189i \(0.534331\pi\)
\(368\) 4.70837 0.245441
\(369\) −24.5206 9.61847i −1.27649 0.500718i
\(370\) −0.967110 + 6.08865i −0.0502777 + 0.316534i
\(371\) 0 0
\(372\) 5.84059 + 1.10455i 0.302821 + 0.0572683i
\(373\) 23.8319i 1.23397i −0.786976 0.616983i \(-0.788355\pi\)
0.786976 0.616983i \(-0.211645\pi\)
\(374\) 21.1146 1.09181
\(375\) 11.8649 15.3044i 0.612702 0.790314i
\(376\) 2.55610i 0.131821i
\(377\) 48.3688i 2.49112i
\(378\) 0 0
\(379\) 29.0694 1.49319 0.746596 0.665277i \(-0.231687\pi\)
0.746596 + 0.665277i \(0.231687\pi\)
\(380\) −0.737854 + 4.64532i −0.0378511 + 0.238300i
\(381\) 28.2974 + 5.35150i 1.44972 + 0.274165i
\(382\) 2.85343i 0.145994i
\(383\) 19.4986i 0.996333i −0.867081 0.498166i \(-0.834007\pi\)
0.867081 0.498166i \(-0.165993\pi\)
\(384\) −0.321854 + 1.70188i −0.0164245 + 0.0868489i
\(385\) 0 0
\(386\) 26.7793i 1.36303i
\(387\) 7.71798 19.6756i 0.392327 1.00017i
\(388\) 4.90516 0.249022
\(389\) 6.51453i 0.330300i 0.986268 + 0.165150i \(0.0528108\pi\)
−0.986268 + 0.165150i \(0.947189\pi\)
\(390\) 8.37364 23.3425i 0.424016 1.18199i
\(391\) 26.2681i 1.32844i
\(392\) 0 0
\(393\) −0.0677451 + 0.358220i −0.00341729 + 0.0180698i
\(394\) −14.7242 −0.741793
\(395\) −15.6286 2.48242i −0.786360 0.124904i
\(396\) 4.14613 10.5698i 0.208351 0.531153i
\(397\) 33.0474 1.65860 0.829300 0.558803i \(-0.188739\pi\)
0.829300 + 0.558803i \(0.188739\pi\)
\(398\) 16.4657i 0.825352i
\(399\) 0 0
\(400\) 4.75391 + 1.54929i 0.237696 + 0.0774646i
\(401\) 13.3058i 0.664461i 0.943198 + 0.332230i \(0.107801\pi\)
−0.943198 + 0.332230i \(0.892199\pi\)
\(402\) −2.53361 0.479146i −0.126365 0.0238976i
\(403\) 21.9743i 1.09462i
\(404\) −5.63646 −0.280424
\(405\) 12.4282 + 15.8284i 0.617562 + 0.786522i
\(406\) 0 0
\(407\) 10.4345 0.517218
\(408\) −9.49485 1.79563i −0.470065 0.0888969i
\(409\) 24.4460i 1.20877i −0.796691 0.604387i \(-0.793418\pi\)
0.796691 0.604387i \(-0.206582\pi\)
\(410\) −19.3893 3.07976i −0.957569 0.152098i
\(411\) −1.24613 + 6.58923i −0.0614670 + 0.325023i
\(412\) −6.76706 −0.333389
\(413\) 0 0
\(414\) 13.1496 + 5.15809i 0.646269 + 0.253506i
\(415\) 3.32906 20.9588i 0.163417 1.02883i
\(416\) 6.40306 0.313936
\(417\) −29.6703 5.61112i −1.45296 0.274778i
\(418\) 7.96096 0.389383
\(419\) −27.0524 −1.32160 −0.660799 0.750563i \(-0.729783\pi\)
−0.660799 + 0.750563i \(0.729783\pi\)
\(420\) 0 0
\(421\) 5.39064 0.262724 0.131362 0.991334i \(-0.458065\pi\)
0.131362 + 0.991334i \(0.458065\pi\)
\(422\) 15.8206 0.770134
\(423\) −2.80024 + 7.13872i −0.136152 + 0.347096i
\(424\) −3.08554 −0.149847
\(425\) −8.64354 + 26.5222i −0.419273 + 1.28652i
\(426\) −8.61585 1.62940i −0.417439 0.0789445i
\(427\) 0 0
\(428\) 9.09162 0.439460
\(429\) −41.2422 7.79957i −1.99119 0.376567i
\(430\) 2.47124 15.5582i 0.119174 0.750283i
\(431\) 3.21022i 0.154631i 0.997007 + 0.0773155i \(0.0246349\pi\)
−0.997007 + 0.0773155i \(0.975365\pi\)
\(432\) −2.76332 + 4.40046i −0.132950 + 0.211717i
\(433\) 39.7769 1.91155 0.955777 0.294092i \(-0.0950171\pi\)
0.955777 + 0.294092i \(0.0950171\pi\)
\(434\) 0 0
\(435\) 27.5382 + 9.87879i 1.32036 + 0.473652i
\(436\) −15.3307 −0.734208
\(437\) 9.90403i 0.473774i
\(438\) 1.07356 5.67675i 0.0512969 0.271246i
\(439\) 26.5159i 1.26553i 0.774342 + 0.632767i \(0.218081\pi\)
−0.774342 + 0.632767i \(0.781919\pi\)
\(440\) 1.32756 8.35793i 0.0632888 0.398449i
\(441\) 0 0
\(442\) 35.7228i 1.69916i
\(443\) −21.5549 −1.02410 −0.512052 0.858955i \(-0.671114\pi\)
−0.512052 + 0.858955i \(0.671114\pi\)
\(444\) −4.69220 0.887371i −0.222682 0.0421128i
\(445\) 23.4489 + 3.72459i 1.11159 + 0.176562i
\(446\) 21.9853 1.04103
\(447\) 14.7345 + 2.78653i 0.696917 + 0.131798i
\(448\) 0 0
\(449\) 1.27232i 0.0600445i −0.999549 0.0300222i \(-0.990442\pi\)
0.999549 0.0300222i \(-0.00955781\pi\)
\(450\) 11.5796 + 9.53488i 0.545865 + 0.449479i
\(451\) 33.2286i 1.56467i
\(452\) 2.83057 0.133139
\(453\) 5.41682 28.6428i 0.254504 1.34576i
\(454\) 27.5101i 1.29111i
\(455\) 0 0
\(456\) −3.57990 0.677017i −0.167644 0.0317042i
\(457\) 7.38402i 0.345410i 0.984974 + 0.172705i \(0.0552507\pi\)
−0.984974 + 0.172705i \(0.944749\pi\)
\(458\) 16.1836i 0.756209i
\(459\) −24.5503 15.4166i −1.14591 0.719586i
\(460\) 10.3979 + 1.65158i 0.484804 + 0.0770053i
\(461\) −14.6635 −0.682950 −0.341475 0.939891i \(-0.610926\pi\)
−0.341475 + 0.939891i \(0.610926\pi\)
\(462\) 0 0
\(463\) 27.8566i 1.29460i −0.762233 0.647302i \(-0.775897\pi\)
0.762233 0.647302i \(-0.224103\pi\)
\(464\) 7.55401i 0.350686i
\(465\) 12.5108 + 4.48801i 0.580175 + 0.208126i
\(466\) −17.8328 −0.826089
\(467\) 17.7307i 0.820478i 0.911978 + 0.410239i \(0.134555\pi\)
−0.911978 + 0.410239i \(0.865445\pi\)
\(468\) 17.8826 + 7.01465i 0.826624 + 0.324252i
\(469\) 0 0
\(470\) −0.896615 + 5.64484i −0.0413578 + 0.260377i
\(471\) 2.00754 10.6154i 0.0925028 0.489132i
\(472\) 12.9727 0.597118
\(473\) −26.6630 −1.22597
\(474\) 2.27774 12.0441i 0.104620 0.553205i
\(475\) −3.25893 + 9.99983i −0.149530 + 0.458824i
\(476\) 0 0
\(477\) −8.61736 3.38026i −0.394562 0.154771i
\(478\) 18.4508i 0.843920i
\(479\) −4.63276 −0.211676 −0.105838 0.994383i \(-0.533753\pi\)
−0.105838 + 0.994383i \(0.533753\pi\)
\(480\) −1.30776 + 3.64551i −0.0596906 + 0.166394i
\(481\) 17.6537i 0.804937i
\(482\) 13.4629i 0.613220i
\(483\) 0 0
\(484\) −3.32348 −0.151067
\(485\) 10.8325 + 1.72061i 0.491878 + 0.0781289i
\(486\) −12.5382 + 9.26244i −0.568746 + 0.420153i
\(487\) 43.6309i 1.97711i −0.150876 0.988553i \(-0.548209\pi\)
0.150876 0.988553i \(-0.451791\pi\)
\(488\) 10.3401i 0.468074i
\(489\) −5.49393 1.03899i −0.248444 0.0469848i
\(490\) 0 0
\(491\) 29.4021i 1.32690i 0.748221 + 0.663449i \(0.230908\pi\)
−0.748221 + 0.663449i \(0.769092\pi\)
\(492\) 2.82583 14.9423i 0.127398 0.673651i
\(493\) −42.1440 −1.89807
\(494\) 13.4688i 0.605990i
\(495\) 12.8639 21.8878i 0.578188 0.983785i
\(496\) 3.43184i 0.154094i
\(497\) 0 0
\(498\) 16.1519 + 3.05458i 0.723782 + 0.136879i
\(499\) 21.1826 0.948264 0.474132 0.880454i \(-0.342762\pi\)
0.474132 + 0.880454i \(0.342762\pi\)
\(500\) 9.95501 + 5.08899i 0.445202 + 0.227586i
\(501\) 18.6018 + 3.51790i 0.831067 + 0.157168i
\(502\) 21.5154 0.960279
\(503\) 9.61653i 0.428780i 0.976748 + 0.214390i \(0.0687763\pi\)
−0.976748 + 0.214390i \(0.931224\pi\)
\(504\) 0 0
\(505\) −12.4475 1.97713i −0.553905 0.0879812i
\(506\) 17.8195i 0.792172i
\(507\) 9.01165 47.6514i 0.400221 2.11627i
\(508\) 16.6271i 0.737709i
\(509\) 10.1694 0.450750 0.225375 0.974272i \(-0.427639\pi\)
0.225375 + 0.974272i \(0.427639\pi\)
\(510\) −20.3384 7.29600i −0.900600 0.323072i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −9.25635 5.81263i −0.408678 0.256634i
\(514\) 13.2419i 0.584073i
\(515\) −14.9443 2.37372i −0.658523 0.104599i
\(516\) 11.9899 + 2.26748i 0.527825 + 0.0998202i
\(517\) 9.67389 0.425457
\(518\) 0 0
\(519\) −8.22492 1.55547i −0.361034 0.0682773i
\(520\) 14.1404 + 2.24604i 0.620098 + 0.0984952i
\(521\) −20.3300 −0.890674 −0.445337 0.895363i \(-0.646916\pi\)
−0.445337 + 0.895363i \(0.646916\pi\)
\(522\) −8.27553 + 21.0970i −0.362210 + 0.923390i
\(523\) −41.0473 −1.79487 −0.897436 0.441144i \(-0.854573\pi\)
−0.897436 + 0.441144i \(0.854573\pi\)
\(524\) −0.210484 −0.00919504
\(525\) 0 0
\(526\) 15.5680 0.678795
\(527\) −19.1463 −0.834026
\(528\) 6.44102 + 1.21810i 0.280309 + 0.0530110i
\(529\) −0.831243 −0.0361410
\(530\) −6.81405 1.08233i −0.295984 0.0470135i
\(531\) 36.2305 + 14.2118i 1.57227 + 0.616740i
\(532\) 0 0
\(533\) −56.2180 −2.43507
\(534\) −3.41749 + 18.0709i −0.147889 + 0.782003i
\(535\) 20.0778 + 3.18912i 0.868038 + 0.137877i
\(536\) 1.48871i 0.0643024i
\(537\) −14.5607 2.75366i −0.628340 0.118829i
\(538\) −8.37779 −0.361192
\(539\) 0 0
\(540\) −7.64604 + 8.74860i −0.329033 + 0.376480i
\(541\) −2.37649 −0.102173 −0.0510866 0.998694i \(-0.516268\pi\)
−0.0510866 + 0.998694i \(0.516268\pi\)
\(542\) 0.305606i 0.0131269i
\(543\) 19.0960 + 3.61136i 0.819487 + 0.154978i
\(544\) 5.57902i 0.239199i
\(545\) −33.8561 5.37763i −1.45024 0.230353i
\(546\) 0 0
\(547\) 4.09789i 0.175213i −0.996155 0.0876066i \(-0.972078\pi\)
0.996155 0.0876066i \(-0.0279218\pi\)
\(548\) −3.87172 −0.165392
\(549\) −11.3277 + 28.8780i −0.483456 + 1.23248i
\(550\) 5.86351 17.9918i 0.250021 0.767175i
\(551\) −15.8898 −0.676929
\(552\) −1.51541 + 8.01310i −0.0645000 + 0.341060i
\(553\) 0 0
\(554\) 20.9930i 0.891909i
\(555\) −10.0509 3.60557i −0.426638 0.153048i
\(556\) 17.4338i 0.739357i
\(557\) 37.9488 1.60794 0.803971 0.594669i \(-0.202717\pi\)
0.803971 + 0.594669i \(0.202717\pi\)
\(558\) −3.75963 + 9.58451i −0.159158 + 0.405745i
\(559\) 45.1100i 1.90795i
\(560\) 0 0
\(561\) −6.79580 + 35.9346i −0.286919 + 1.51716i
\(562\) 5.67638i 0.239443i
\(563\) 2.75056i 0.115922i 0.998319 + 0.0579611i \(0.0184599\pi\)
−0.998319 + 0.0579611i \(0.981540\pi\)
\(564\) −4.35018 0.822689i −0.183176 0.0346414i
\(565\) 6.25098 + 0.992893i 0.262981 + 0.0417713i
\(566\) −15.8411 −0.665853
\(567\) 0 0
\(568\) 5.06254i 0.212419i
\(569\) 31.3355i 1.31365i 0.754043 + 0.656825i \(0.228101\pi\)
−0.754043 + 0.656825i \(0.771899\pi\)
\(570\) −7.66832 2.75086i −0.321191 0.115221i
\(571\) −17.2218 −0.720709 −0.360354 0.932816i \(-0.617344\pi\)
−0.360354 + 0.932816i \(0.617344\pi\)
\(572\) 24.2333i 1.01324i
\(573\) 4.85622 + 0.918388i 0.202871 + 0.0383662i
\(574\) 0 0
\(575\) 22.3832 + 7.29464i 0.933443 + 0.304208i
\(576\) −2.79282 1.09552i −0.116368 0.0456465i
\(577\) −17.2429 −0.717829 −0.358915 0.933370i \(-0.616853\pi\)
−0.358915 + 0.933370i \(0.616853\pi\)
\(578\) 14.1255 0.587543
\(579\) 45.5753 + 8.61901i 1.89404 + 0.358194i
\(580\) −2.64976 + 16.6821i −0.110025 + 0.692688i
\(581\) 0 0
\(582\) −1.57875 + 8.34802i −0.0654411 + 0.346037i
\(583\) 11.6776i 0.483639i
\(584\) 3.33557 0.138027
\(585\) 37.0311 + 21.7638i 1.53105 + 0.899823i
\(586\) 23.2810i 0.961729i
\(587\) 14.3325i 0.591567i 0.955255 + 0.295784i \(0.0955807\pi\)
−0.955255 + 0.295784i \(0.904419\pi\)
\(588\) 0 0
\(589\) −7.21885 −0.297448
\(590\) 28.6487 + 4.55051i 1.17945 + 0.187341i
\(591\) 4.73903 25.0588i 0.194938 1.03078i
\(592\) 2.75706i 0.113315i
\(593\) 26.7511i 1.09854i −0.835646 0.549268i \(-0.814907\pi\)
0.835646 0.549268i \(-0.185093\pi\)
\(594\) 16.6542 + 10.4582i 0.683328 + 0.429104i
\(595\) 0 0
\(596\) 8.65775i 0.354635i
\(597\) −28.0228 5.29956i −1.14690 0.216896i
\(598\) 30.1480 1.23284
\(599\) 16.5006i 0.674195i 0.941470 + 0.337097i \(0.109445\pi\)
−0.941470 + 0.337097i \(0.890555\pi\)
\(600\) −4.16678 + 7.59197i −0.170108 + 0.309941i
\(601\) 2.77557i 0.113218i −0.998396 0.0566089i \(-0.981971\pi\)
0.998396 0.0566089i \(-0.0180288\pi\)
\(602\) 0 0
\(603\) 1.63090 4.15770i 0.0664155 0.169314i
\(604\) 16.8301 0.684806
\(605\) −7.33952 1.16579i −0.298394 0.0473963i
\(606\) 1.81412 9.59260i 0.0736934 0.389673i
\(607\) −14.8382 −0.602266 −0.301133 0.953582i \(-0.597365\pi\)
−0.301133 + 0.953582i \(0.597365\pi\)
\(608\) 2.10349i 0.0853080i
\(609\) 0 0
\(610\) −3.62705 + 22.8349i −0.146855 + 0.924558i
\(611\) 16.3668i 0.662132i
\(612\) 6.11191 15.5812i 0.247059 0.629833i
\(613\) 8.33176i 0.336517i −0.985743 0.168258i \(-0.946186\pi\)
0.985743 0.168258i \(-0.0538143\pi\)
\(614\) 20.2759 0.818270
\(615\) 11.4819 32.0071i 0.462995 1.29065i
\(616\) 0 0
\(617\) 14.6210 0.588620 0.294310 0.955710i \(-0.404910\pi\)
0.294310 + 0.955710i \(0.404910\pi\)
\(618\) 2.17800 11.5168i 0.0876122 0.463272i
\(619\) 2.57516i 0.103504i 0.998660 + 0.0517522i \(0.0164806\pi\)
−0.998660 + 0.0517522i \(0.983519\pi\)
\(620\) −1.20380 + 7.57882i −0.0483460 + 0.304373i
\(621\) −13.0107 + 20.7190i −0.522103 + 0.831425i
\(622\) −11.8199 −0.473934
\(623\) 0 0
\(624\) −2.06085 + 10.8973i −0.0825000 + 0.436240i
\(625\) 20.1994 + 14.7304i 0.807975 + 0.589216i
\(626\) 4.00427 0.160043
\(627\) −2.56226 + 13.5486i −0.102327 + 0.541080i
\(628\) 6.23745 0.248901
\(629\) 15.3817 0.613309
\(630\) 0 0
\(631\) −3.65345 −0.145442 −0.0727208 0.997352i \(-0.523168\pi\)
−0.0727208 + 0.997352i \(0.523168\pi\)
\(632\) 7.07694 0.281506
\(633\) −5.09191 + 26.9248i −0.202385 + 1.07017i
\(634\) −0.211278 −0.00839092
\(635\) −5.83238 + 36.7190i −0.231451 + 1.45715i
\(636\) 0.993092 5.25123i 0.0393787 0.208225i
\(637\) 0 0
\(638\) 28.5892 1.13186
\(639\) 5.54608 14.1388i 0.219400 0.559320i
\(640\) −2.20838 0.350775i −0.0872940 0.0138656i
\(641\) 45.2701i 1.78806i 0.448005 + 0.894031i \(0.352135\pi\)
−0.448005 + 0.894031i \(0.647865\pi\)
\(642\) −2.92617 + 15.4729i −0.115487 + 0.610666i
\(643\) 27.7814 1.09559 0.547796 0.836612i \(-0.315467\pi\)
0.547796 + 0.836612i \(0.315467\pi\)
\(644\) 0 0
\(645\) 25.6829 + 9.21322i 1.01126 + 0.362770i
\(646\) 11.7354 0.461725
\(647\) 4.09747i 0.161088i 0.996751 + 0.0805441i \(0.0256658\pi\)
−0.996751 + 0.0805441i \(0.974334\pi\)
\(648\) −6.59969 6.11916i −0.259260 0.240383i
\(649\) 49.0970i 1.92723i
\(650\) 30.4396 + 9.92022i 1.19394 + 0.389103i
\(651\) 0 0
\(652\) 3.22815i 0.126424i
\(653\) 30.9842 1.21251 0.606253 0.795272i \(-0.292672\pi\)
0.606253 + 0.795272i \(0.292672\pi\)
\(654\) 4.93424 26.0911i 0.192944 1.02024i
\(655\) −0.464830 0.0738326i −0.0181624 0.00288488i
\(656\) 8.77986 0.342796
\(657\) 9.31564 + 3.65416i 0.363438 + 0.142563i
\(658\) 0 0
\(659\) 35.2668i 1.37380i 0.726752 + 0.686900i \(0.241029\pi\)
−0.726752 + 0.686900i \(0.758971\pi\)
\(660\) 13.7970 + 4.94938i 0.537046 + 0.192654i
\(661\) 21.8678i 0.850560i −0.905062 0.425280i \(-0.860176\pi\)
0.905062 0.425280i \(-0.139824\pi\)
\(662\) 4.13421 0.160681
\(663\) −60.7961 11.4975i −2.36113 0.446527i
\(664\) 9.49058i 0.368306i
\(665\) 0 0
\(666\) 3.02041 7.69999i 0.117038 0.298368i
\(667\) 35.5671i 1.37716i
\(668\) 10.9301i 0.422899i
\(669\) −7.07605 + 37.4164i −0.273576 + 1.44660i
\(670\) 0.522202 3.28764i 0.0201744 0.127013i
\(671\) 39.1335 1.51073
\(672\) 0 0
\(673\) 3.23782i 0.124809i −0.998051 0.0624045i \(-0.980123\pi\)
0.998051 0.0624045i \(-0.0198769\pi\)
\(674\) 1.99207i 0.0767318i
\(675\) −19.9542 + 16.6382i −0.768037 + 0.640405i
\(676\) 27.9992 1.07689
\(677\) 10.5188i 0.404271i −0.979358 0.202136i \(-0.935212\pi\)
0.979358 0.202136i \(-0.0647881\pi\)
\(678\) −0.911028 + 4.81730i −0.0349878 + 0.185007i
\(679\) 0 0
\(680\) 1.95698 12.3206i 0.0750469 0.472474i
\(681\) 46.8190 + 8.85422i 1.79411 + 0.339294i
\(682\) 12.9883 0.497346
\(683\) −46.9660 −1.79710 −0.898552 0.438867i \(-0.855380\pi\)
−0.898552 + 0.438867i \(0.855380\pi\)
\(684\) 2.30441 5.87468i 0.0881113 0.224624i
\(685\) −8.55025 1.35811i −0.326688 0.0518905i
\(686\) 0 0
\(687\) −27.5426 5.20874i −1.05081 0.198726i
\(688\) 7.04507i 0.268591i
\(689\) −19.7569 −0.752678
\(690\) −6.15740 + 17.1644i −0.234408 + 0.653439i
\(691\) 35.7893i 1.36149i −0.732520 0.680745i \(-0.761656\pi\)
0.732520 0.680745i \(-0.238344\pi\)
\(692\) 4.83283i 0.183717i
\(693\) 0 0
\(694\) −21.4429 −0.813961
\(695\) 6.11534 38.5005i 0.231968 1.46041i
\(696\) −12.8560 2.43129i −0.487307 0.0921576i
\(697\) 48.9830i 1.85537i
\(698\) 17.1982i 0.650961i
\(699\) 5.73955 30.3494i 0.217090 1.14792i
\(700\) 0 0
\(701\) 36.5930i 1.38210i −0.722808 0.691049i \(-0.757149\pi\)
0.722808 0.691049i \(-0.242851\pi\)
\(702\) −17.6937 + 28.1764i −0.667806 + 1.06345i
\(703\) 5.79947 0.218731
\(704\) 3.78464i 0.142639i
\(705\) −9.31828 3.34275i −0.350947 0.125895i
\(706\) 3.05545i 0.114993i
\(707\) 0 0
\(708\) −4.17532 + 22.0781i −0.156918 + 0.829744i
\(709\) −23.6152 −0.886888 −0.443444 0.896302i \(-0.646243\pi\)
−0.443444 + 0.896302i \(0.646243\pi\)
\(710\) 1.77581 11.1800i 0.0666450 0.419579i
\(711\) 19.7646 + 7.75290i 0.741231 + 0.290756i
\(712\) −10.6182 −0.397932
\(713\) 16.1584i 0.605136i
\(714\) 0 0
\(715\) 8.50043 53.5164i 0.317898 2.00140i
\(716\) 8.55562i 0.319739i
\(717\) −31.4011 5.93846i −1.17270 0.221776i
\(718\) 15.3615i 0.573287i
\(719\) 28.3294 1.05651 0.528255 0.849086i \(-0.322847\pi\)
0.528255 + 0.849086i \(0.322847\pi\)
\(720\) −5.78334 3.39897i −0.215532 0.126672i
\(721\) 0 0
\(722\) −14.5753 −0.542437
\(723\) 22.9123 + 4.33309i 0.852119 + 0.161149i
\(724\) 11.2205i 0.417006i
\(725\) −11.7034 + 35.9111i −0.434652 + 1.33370i
\(726\) 1.06967 5.65618i 0.0396993 0.209920i
\(727\) 5.04231 0.187009 0.0935045 0.995619i \(-0.470193\pi\)
0.0935045 + 0.995619i \(0.470193\pi\)
\(728\) 0 0
\(729\) −11.7281 24.3198i −0.434375 0.900732i
\(730\) 7.36621 + 1.17003i 0.272636 + 0.0433049i
\(731\) −39.3046 −1.45373
\(732\) −17.5976 3.32800i −0.650428 0.123006i
\(733\) 41.9089 1.54794 0.773969 0.633223i \(-0.218268\pi\)
0.773969 + 0.633223i \(0.218268\pi\)
\(734\) 4.12440 0.152234
\(735\) 0 0
\(736\) −4.70837 −0.173553
\(737\) −5.63422 −0.207539
\(738\) 24.5206 + 9.61847i 0.902615 + 0.354061i
\(739\) 24.0720 0.885502 0.442751 0.896645i \(-0.354003\pi\)
0.442751 + 0.896645i \(0.354003\pi\)
\(740\) 0.967110 6.08865i 0.0355517 0.223823i
\(741\) −22.9223 4.33498i −0.842074 0.159250i
\(742\) 0 0
\(743\) 16.7877 0.615880 0.307940 0.951406i \(-0.400360\pi\)
0.307940 + 0.951406i \(0.400360\pi\)
\(744\) −5.84059 1.10455i −0.214127 0.0404948i
\(745\) −3.03692 + 19.1196i −0.111264 + 0.700489i
\(746\) 23.8319i 0.872546i
\(747\) −10.3971 + 26.5055i −0.380409 + 0.969785i
\(748\) −21.1146 −0.772025
\(749\) 0 0
\(750\) −11.8649 + 15.3044i −0.433246 + 0.558836i
\(751\) −44.2677 −1.61535 −0.807675 0.589627i \(-0.799275\pi\)
−0.807675 + 0.589627i \(0.799275\pi\)
\(752\) 2.55610i 0.0932112i
\(753\) −6.92481 + 36.6167i −0.252354 + 1.33439i
\(754\) 48.3688i 1.76149i
\(755\) 37.1672 + 5.90357i 1.35265 + 0.214853i
\(756\) 0 0
\(757\) 41.9657i 1.52527i −0.646829 0.762635i \(-0.723905\pi\)
0.646829 0.762635i \(-0.276095\pi\)
\(758\) −29.0694 −1.05585
\(759\) 30.3267 + 5.73526i 1.10079 + 0.208177i
\(760\) 0.737854 4.64532i 0.0267648 0.168504i
\(761\) 51.0849 1.85183 0.925913 0.377736i \(-0.123297\pi\)
0.925913 + 0.377736i \(0.123297\pi\)
\(762\) −28.2974 5.35150i −1.02511 0.193864i
\(763\) 0 0
\(764\) 2.85343i 0.103234i
\(765\) 18.9629 32.2654i 0.685606 1.16656i
\(766\) 19.4986i 0.704514i
\(767\) 83.0651 2.99931
\(768\) 0.321854 1.70188i 0.0116139 0.0614115i
\(769\) 34.0876i 1.22923i 0.788827 + 0.614616i \(0.210689\pi\)
−0.788827 + 0.614616i \(0.789311\pi\)
\(770\) 0 0
\(771\) −22.5361 4.26194i −0.811618 0.153490i
\(772\) 26.7793i 0.963808i
\(773\) 3.58252i 0.128854i −0.997922 0.0644271i \(-0.979478\pi\)
0.997922 0.0644271i \(-0.0205220\pi\)
\(774\) −7.71798 + 19.6756i −0.277417 + 0.707225i
\(775\) −5.31692 + 16.3147i −0.190990 + 0.586040i
\(776\) −4.90516 −0.176085
\(777\) 0 0
\(778\) 6.51453i 0.233557i
\(779\) 18.4684i 0.661699i
\(780\) −8.37364 + 23.3425i −0.299824 + 0.835794i
\(781\) −19.1599 −0.685594
\(782\) 26.2681i 0.939346i
\(783\) −33.2411 20.8741i −1.18794 0.745981i
\(784\) 0 0
\(785\) 13.7747 + 2.18794i 0.491639 + 0.0780910i
\(786\) 0.0677451 0.358220i 0.00241639 0.0127773i
\(787\) 15.5828 0.555466 0.277733 0.960658i \(-0.410417\pi\)
0.277733 + 0.960658i \(0.410417\pi\)
\(788\) 14.7242 0.524527
\(789\) −5.01060 + 26.4949i −0.178382 + 0.943242i
\(790\) 15.6286 + 2.48242i 0.556041 + 0.0883204i
\(791\) 0 0
\(792\) −4.14613 + 10.5698i −0.147326 + 0.375582i
\(793\) 66.2083i 2.35113i
\(794\) −33.0474 −1.17281
\(795\) 4.03513 11.2484i 0.143111 0.398939i
\(796\) 16.4657i 0.583612i
\(797\) 33.4891i 1.18625i −0.805112 0.593123i \(-0.797895\pi\)
0.805112 0.593123i \(-0.202105\pi\)
\(798\) 0 0
\(799\) 14.2605 0.504501
\(800\) −4.75391 1.54929i −0.168076 0.0547758i
\(801\) −29.6546 11.6323i −1.04779 0.411009i
\(802\) 13.3058i 0.469845i
\(803\) 12.6239i 0.445488i
\(804\) 2.53361 + 0.479146i 0.0893535 + 0.0168982i
\(805\) 0 0
\(806\) 21.9743i 0.774011i
\(807\) 2.69642 14.2580i 0.0949185 0.501906i
\(808\) 5.63646 0.198290
\(809\) 18.8243i 0.661827i −0.943661 0.330914i \(-0.892643\pi\)
0.943661 0.330914i \(-0.107357\pi\)
\(810\) −12.4282 15.8284i −0.436682 0.556155i
\(811\) 9.05687i 0.318030i −0.987276 0.159015i \(-0.949168\pi\)
0.987276 0.159015i \(-0.0508318\pi\)
\(812\) 0 0
\(813\) 0.520106 + 0.0983604i 0.0182409 + 0.00344965i
\(814\) −10.4345 −0.365729
\(815\) 1.13235 7.12898i 0.0396646 0.249717i
\(816\) 9.49485 + 1.79563i 0.332386 + 0.0628596i
\(817\) −14.8193 −0.518460
\(818\) 24.4460i 0.854733i
\(819\) 0 0
\(820\) 19.3893 + 3.07976i 0.677104 + 0.107550i
\(821\) 0.724927i 0.0253001i −0.999920 0.0126501i \(-0.995973\pi\)
0.999920 0.0126501i \(-0.00402675\pi\)
\(822\) 1.24613 6.58923i 0.0434637 0.229826i
\(823\) 7.32363i 0.255286i −0.991820 0.127643i \(-0.959259\pi\)
0.991820 0.127643i \(-0.0407411\pi\)
\(824\) 6.76706 0.235742
\(825\) 28.7328 + 15.7698i 1.00035 + 0.549032i
\(826\) 0 0
\(827\) −24.6605 −0.857529 −0.428764 0.903416i \(-0.641051\pi\)
−0.428764 + 0.903416i \(0.641051\pi\)
\(828\) −13.1496 5.15809i −0.456981 0.179256i
\(829\) 43.1620i 1.49908i 0.661961 + 0.749538i \(0.269724\pi\)
−0.661961 + 0.749538i \(0.730276\pi\)
\(830\) −3.32906 + 20.9588i −0.115553 + 0.727492i
\(831\) 35.7277 + 6.75669i 1.23938 + 0.234387i
\(832\) −6.40306 −0.221986
\(833\) 0 0
\(834\) 29.6703 + 5.61112i 1.02740 + 0.194297i
\(835\) −3.83401 + 24.1379i −0.132682 + 0.835326i
\(836\) −7.96096 −0.275336
\(837\) −15.1017 9.48327i −0.521990 0.327790i
\(838\) 27.0524 0.934511
\(839\) 14.2292 0.491247 0.245623 0.969365i \(-0.421007\pi\)
0.245623 + 0.969365i \(0.421007\pi\)
\(840\) 0 0
\(841\) −28.0630 −0.967691
\(842\) −5.39064 −0.185774
\(843\) −9.66053 1.82696i −0.332726 0.0629239i
\(844\) −15.8206 −0.544567
\(845\) 61.8330 + 9.82143i 2.12712 + 0.337868i
\(846\) 2.80024 7.13872i 0.0962743 0.245434i
\(847\) 0 0
\(848\) 3.08554 0.105958
\(849\) 5.09853 26.9598i 0.174981 0.925258i
\(850\) 8.64354 26.5222i 0.296471 0.909704i
\(851\) 12.9813i 0.444993i
\(852\) 8.61585 + 1.62940i 0.295174 + 0.0558222i
\(853\) −10.7205 −0.367064 −0.183532 0.983014i \(-0.558753\pi\)
−0.183532 + 0.983014i \(0.558753\pi\)
\(854\) 0 0
\(855\) 7.14971 12.1652i 0.244515 0.416042i
\(856\) −9.09162 −0.310745
\(857\) 17.2656i 0.589781i −0.955531 0.294890i \(-0.904717\pi\)
0.955531 0.294890i \(-0.0952831\pi\)
\(858\) 41.2422 + 7.79957i 1.40799 + 0.266273i
\(859\) 6.33253i 0.216063i −0.994147 0.108032i \(-0.965545\pi\)
0.994147 0.108032i \(-0.0344548\pi\)
\(860\) −2.47124 + 15.5582i −0.0842684 + 0.530530i
\(861\) 0 0
\(862\) 3.21022i 0.109341i
\(863\) 4.44663 0.151365 0.0756826 0.997132i \(-0.475886\pi\)
0.0756826 + 0.997132i \(0.475886\pi\)
\(864\) 2.76332 4.40046i 0.0940101 0.149707i
\(865\) 1.69524 10.6727i 0.0576398 0.362884i
\(866\) −39.7769 −1.35167
\(867\) −4.54634 + 24.0400i −0.154402 + 0.816440i
\(868\) 0 0
\(869\) 26.7837i 0.908573i
\(870\) −27.5382 9.87879i −0.933634 0.334922i
\(871\) 9.53229i 0.322989i
\(872\) 15.3307 0.519163
\(873\) −13.6992 5.37368i −0.463649 0.181872i
\(874\) 9.90403i 0.335009i
\(875\) 0 0
\(876\) −1.07356 + 5.67675i −0.0362724 + 0.191800i
\(877\) 40.7210i 1.37505i −0.726161 0.687525i \(-0.758697\pi\)
0.726161 0.687525i \(-0.241303\pi\)
\(878\) 26.5159i 0.894868i
\(879\) 39.6215 + 7.49307i 1.33640 + 0.252735i
\(880\) −1.32756 + 8.35793i −0.0447520 + 0.281746i
\(881\) 16.0602 0.541081 0.270540 0.962709i \(-0.412798\pi\)
0.270540 + 0.962709i \(0.412798\pi\)
\(882\) 0 0
\(883\) 18.9924i 0.639145i 0.947562 + 0.319572i \(0.103539\pi\)
−0.947562 + 0.319572i \(0.896461\pi\)
\(884\) 35.7228i 1.20149i
\(885\) −16.9651 + 47.2922i −0.570277 + 1.58971i
\(886\) 21.5549 0.724151
\(887\) 32.7978i 1.10124i −0.834755 0.550621i \(-0.814391\pi\)
0.834755 0.550621i \(-0.185609\pi\)
\(888\) 4.69220 + 0.887371i 0.157460 + 0.0297782i
\(889\) 0 0
\(890\) −23.4489 3.72459i −0.786010 0.124848i
\(891\) −23.1588 + 24.9774i −0.775848 + 0.836776i
\(892\) −21.9853 −0.736122
\(893\) 5.37673 0.179925
\(894\) −14.7345 2.78653i −0.492795 0.0931954i
\(895\) 3.00110 18.8941i 0.100316 0.631560i
\(896\) 0 0
\(897\) −9.70324 + 51.3084i −0.323982 + 1.71314i
\(898\) 1.27232i 0.0424578i
\(899\) −25.9241 −0.864619
\(900\) −11.5796 9.53488i −0.385985 0.317829i
\(901\) 17.2143i 0.573491i
\(902\) 33.2286i 1.10639i
\(903\) 0 0
\(904\) −2.83057 −0.0941432
\(905\) −3.93587 + 24.7791i −0.130833 + 0.823687i
\(906\) −5.41682 + 28.6428i −0.179962 + 0.951594i
\(907\) 57.7453i 1.91740i −0.284420 0.958700i \(-0.591801\pi\)
0.284420 0.958700i \(-0.408199\pi\)
\(908\) 27.5101i 0.912954i
\(909\) 15.7416 + 6.17483i 0.522117 + 0.204806i
\(910\) 0 0
\(911\) 29.3826i 0.973490i 0.873544 + 0.486745i \(0.161816\pi\)
−0.873544 + 0.486745i \(0.838184\pi\)
\(912\) 3.57990 + 0.677017i 0.118542 + 0.0224183i
\(913\) 35.9184 1.18873
\(914\) 7.38402i 0.244242i
\(915\) −37.6950 13.5223i −1.24616 0.447034i
\(916\) 16.1836i 0.534720i
\(917\) 0 0
\(918\) 24.5503 + 15.4166i 0.810280 + 0.508824i
\(919\) 42.6061 1.40545 0.702723 0.711464i \(-0.251967\pi\)
0.702723 + 0.711464i \(0.251967\pi\)
\(920\) −10.3979 1.65158i −0.342808 0.0544510i
\(921\) −6.52588 + 34.5073i −0.215035 + 1.13705i
\(922\) 14.6635 0.482918
\(923\) 32.4157i 1.06698i
\(924\) 0 0
\(925\) 4.27150 13.1068i 0.140446 0.430950i
\(926\) 27.8566i 0.915424i
\(927\) 18.8992 + 7.41342i 0.620731 + 0.243489i
\(928\) 7.55401i 0.247972i
\(929\) −26.5385 −0.870700 −0.435350 0.900261i \(-0.643375\pi\)
−0.435350 + 0.900261i \(0.643375\pi\)
\(930\) −12.5108 4.48801i −0.410246 0.147168i
\(931\) 0 0
\(932\) 17.8328 0.584133
\(933\) 3.80427 20.1161i 0.124546 0.658571i
\(934\) 17.7307i 0.580165i
\(935\) −46.6291 7.40647i −1.52493 0.242218i
\(936\) −17.8826 7.01465i −0.584511 0.229281i
\(937\) 33.5524 1.09611 0.548054 0.836443i \(-0.315369\pi\)
0.548054 + 0.836443i \(0.315369\pi\)
\(938\) 0 0
\(939\) −1.28879 + 6.81481i −0.0420581 + 0.222393i
\(940\) 0.896615 5.64484i 0.0292444 0.184114i
\(941\) 14.9463 0.487237 0.243618 0.969871i \(-0.421666\pi\)
0.243618 + 0.969871i \(0.421666\pi\)
\(942\) −2.00754 + 10.6154i −0.0654093 + 0.345869i
\(943\) 41.3388 1.34618
\(944\) −12.9727 −0.422226
\(945\) 0 0
\(946\) 26.6630 0.866890
\(947\) 21.5510 0.700312 0.350156 0.936691i \(-0.386129\pi\)
0.350156 + 0.936691i \(0.386129\pi\)
\(948\) −2.27774 + 12.0441i −0.0739775 + 0.391175i
\(949\) 21.3578 0.693305
\(950\) 3.25893 9.99983i 0.105734 0.324437i
\(951\) 0.0680006 0.359571i 0.00220507 0.0116599i
\(952\) 0 0
\(953\) −0.489212 −0.0158471 −0.00792356 0.999969i \(-0.502522\pi\)
−0.00792356 + 0.999969i \(0.502522\pi\)
\(954\) 8.61736 + 3.38026i 0.278997 + 0.109440i
\(955\) −1.00091 + 6.30148i −0.0323888 + 0.203911i
\(956\) 18.4508i 0.596742i
\(957\) −9.20153 + 48.6555i −0.297443 + 1.57281i
\(958\) 4.63276 0.149678
\(959\) 0 0
\(960\) 1.30776 3.64551i 0.0422076 0.117658i
\(961\) 19.2225 0.620080
\(962\) 17.6537i 0.569177i
\(963\) −25.3913 9.96001i −0.818222 0.320957i
\(964\) 13.4629i 0.433612i
\(965\) −9.39351 + 59.1389i −0.302388 + 1.90375i
\(966\) 0 0
\(967\) 44.7126i 1.43786i −0.695083 0.718930i \(-0.744632\pi\)
0.695083 0.718930i \(-0.255368\pi\)
\(968\) 3.32348 0.106821
\(969\) −3.77709 + 19.9724i −0.121338 + 0.641605i
\(970\) −10.8325 1.72061i −0.347810 0.0552455i
\(971\) 8.30533 0.266531 0.133265 0.991080i \(-0.457454\pi\)
0.133265 + 0.991080i \(0.457454\pi\)
\(972\) 12.5382 9.26244i 0.402164 0.297093i
\(973\) 0 0
\(974\) 43.6309i 1.39802i
\(975\) −26.6802 + 48.6118i −0.854449 + 1.55682i
\(976\) 10.3401i 0.330978i
\(977\) 11.6472 0.372625 0.186313 0.982490i \(-0.440346\pi\)
0.186313 + 0.982490i \(0.440346\pi\)
\(978\) 5.49393 + 1.03899i 0.175677 + 0.0332233i
\(979\) 40.1859i 1.28435i
\(980\) 0 0
\(981\) 42.8159 + 16.7950i 1.36701 + 0.536224i
\(982\) 29.4021i 0.938259i
\(983\) 18.4536i 0.588577i 0.955717 + 0.294289i \(0.0950827\pi\)
−0.955717 + 0.294289i \(0.904917\pi\)
\(984\) −2.82583 + 14.9423i −0.0900842 + 0.476343i
\(985\) 32.5166 + 5.16488i 1.03607 + 0.164567i
\(986\) 42.1440 1.34214
\(987\) 0 0
\(988\) 13.4688i 0.428500i
\(989\) 33.1708i 1.05477i
\(990\) −12.8639 + 21.8878i −0.408841 + 0.695641i
\(991\) −51.2911 −1.62932 −0.814658 0.579942i \(-0.803075\pi\)
−0.814658 + 0.579942i \(0.803075\pi\)
\(992\) 3.43184i 0.108961i
\(993\) −1.33061 + 7.03594i −0.0422256 + 0.223279i
\(994\) 0 0
\(995\) 5.77577 36.3626i 0.183104 1.15277i
\(996\) −16.1519 3.05458i −0.511791 0.0967880i
\(997\) −17.6179 −0.557964 −0.278982 0.960296i \(-0.589997\pi\)
−0.278982 + 0.960296i \(0.589997\pi\)
\(998\) −21.1826 −0.670524
\(999\) 12.1324 + 7.61865i 0.383851 + 0.241043i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 1470.2.d.g.1469.13 yes 24
3.2 odd 2 1470.2.d.h.1469.14 yes 24
5.4 even 2 1470.2.d.h.1469.12 yes 24
7.6 odd 2 inner 1470.2.d.g.1469.12 yes 24
15.14 odd 2 inner 1470.2.d.g.1469.11 24
21.20 even 2 1470.2.d.h.1469.11 yes 24
35.34 odd 2 1470.2.d.h.1469.13 yes 24
105.104 even 2 inner 1470.2.d.g.1469.14 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.d.g.1469.11 24 15.14 odd 2 inner
1470.2.d.g.1469.12 yes 24 7.6 odd 2 inner
1470.2.d.g.1469.13 yes 24 1.1 even 1 trivial
1470.2.d.g.1469.14 yes 24 105.104 even 2 inner
1470.2.d.h.1469.11 yes 24 21.20 even 2
1470.2.d.h.1469.12 yes 24 5.4 even 2
1470.2.d.h.1469.13 yes 24 35.34 odd 2
1470.2.d.h.1469.14 yes 24 3.2 odd 2