Properties

Label 48.4.c.b.47.4
Level $48$
Weight $4$
Character 48.47
Analytic conductor $2.832$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,4,Mod(47,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.47");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 48.c (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: \(2.83209168028\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 47.4
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 48.47
Dual form 48.4.c.b.47.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.89898 + 1.73205i) q^{3} +16.9706i q^{5} -17.3205i q^{7} +(21.0000 + 16.9706i) q^{9} +O(q^{10})\) \(q+(4.89898 + 1.73205i) q^{3} +16.9706i q^{5} -17.3205i q^{7} +(21.0000 + 16.9706i) q^{9} +29.3939 q^{11} -26.0000 q^{13} +(-29.3939 + 83.1384i) q^{15} -67.8823i q^{17} -107.387i q^{19} +(30.0000 - 84.8528i) q^{21} -176.363 q^{23} -163.000 q^{25} +(73.4847 + 119.512i) q^{27} -16.9706i q^{29} -31.1769i q^{31} +(144.000 + 50.9117i) q^{33} +293.939 q^{35} +206.000 q^{37} +(-127.373 - 45.0333i) q^{39} +305.470i q^{41} -93.5307i q^{43} +(-288.000 + 356.382i) q^{45} +117.576 q^{47} +43.0000 q^{49} +(117.576 - 332.554i) q^{51} -50.9117i q^{53} +498.831i q^{55} +(186.000 - 526.087i) q^{57} -558.484 q^{59} +278.000 q^{61} +(293.939 - 363.731i) q^{63} -441.235i q^{65} +890.274i q^{67} +(-864.000 - 305.470i) q^{69} -58.7878 q^{71} -422.000 q^{73} +(-798.534 - 282.324i) q^{75} -509.117i q^{77} -668.572i q^{79} +(153.000 + 712.764i) q^{81} -29.3939 q^{83} +1152.00 q^{85} +(29.3939 - 83.1384i) q^{87} +373.352i q^{89} +450.333i q^{91} +(54.0000 - 152.735i) q^{93} +1822.42 q^{95} -1070.00 q^{97} +(617.271 + 498.831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 84 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 84 q^{9} - 104 q^{13} + 120 q^{21} - 652 q^{25} + 576 q^{33} + 824 q^{37} - 1152 q^{45} + 172 q^{49} + 744 q^{57} + 1112 q^{61} - 3456 q^{69} - 1688 q^{73} + 612 q^{81} + 4608 q^{85} + 216 q^{93} - 4280 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.89898 + 1.73205i 0.942809 + 0.333333i
\(4\) 0 0
\(5\) 16.9706i 1.51789i 0.651153 + 0.758947i \(0.274286\pi\)
−0.651153 + 0.758947i \(0.725714\pi\)
\(6\) 0 0
\(7\) 17.3205i 0.935220i −0.883935 0.467610i \(-0.845115\pi\)
0.883935 0.467610i \(-0.154885\pi\)
\(8\) 0 0
\(9\) 21.0000 + 16.9706i 0.777778 + 0.628539i
\(10\) 0 0
\(11\) 29.3939 0.805690 0.402845 0.915268i \(-0.368021\pi\)
0.402845 + 0.915268i \(0.368021\pi\)
\(12\) 0 0
\(13\) −26.0000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −29.3939 + 83.1384i −0.505964 + 1.43108i
\(16\) 0 0
\(17\) 67.8823i 0.968463i −0.874940 0.484231i \(-0.839099\pi\)
0.874940 0.484231i \(-0.160901\pi\)
\(18\) 0 0
\(19\) 107.387i 1.29665i −0.761365 0.648324i \(-0.775470\pi\)
0.761365 0.648324i \(-0.224530\pi\)
\(20\) 0 0
\(21\) 30.0000 84.8528i 0.311740 0.881733i
\(22\) 0 0
\(23\) −176.363 −1.59888 −0.799441 0.600745i \(-0.794871\pi\)
−0.799441 + 0.600745i \(0.794871\pi\)
\(24\) 0 0
\(25\) −163.000 −1.30400
\(26\) 0 0
\(27\) 73.4847 + 119.512i 0.523783 + 0.851852i
\(28\) 0 0
\(29\) 16.9706i 0.108667i −0.998523 0.0543337i \(-0.982697\pi\)
0.998523 0.0543337i \(-0.0173035\pi\)
\(30\) 0 0
\(31\) 31.1769i 0.180630i −0.995913 0.0903151i \(-0.971213\pi\)
0.995913 0.0903151i \(-0.0287874\pi\)
\(32\) 0 0
\(33\) 144.000 + 50.9117i 0.759612 + 0.268563i
\(34\) 0 0
\(35\) 293.939 1.41956
\(36\) 0 0
\(37\) 206.000 0.915302 0.457651 0.889132i \(-0.348691\pi\)
0.457651 + 0.889132i \(0.348691\pi\)
\(38\) 0 0
\(39\) −127.373 45.0333i −0.522976 0.184900i
\(40\) 0 0
\(41\) 305.470i 1.16357i 0.813342 + 0.581786i \(0.197646\pi\)
−0.813342 + 0.581786i \(0.802354\pi\)
\(42\) 0 0
\(43\) 93.5307i 0.331705i −0.986151 0.165852i \(-0.946962\pi\)
0.986151 0.165852i \(-0.0530375\pi\)
\(44\) 0 0
\(45\) −288.000 + 356.382i −0.954056 + 1.18058i
\(46\) 0 0
\(47\) 117.576 0.364897 0.182448 0.983215i \(-0.441598\pi\)
0.182448 + 0.983215i \(0.441598\pi\)
\(48\) 0 0
\(49\) 43.0000 0.125364
\(50\) 0 0
\(51\) 117.576 332.554i 0.322821 0.913075i
\(52\) 0 0
\(53\) 50.9117i 0.131948i −0.997821 0.0659741i \(-0.978985\pi\)
0.997821 0.0659741i \(-0.0210155\pi\)
\(54\) 0 0
\(55\) 498.831i 1.22295i
\(56\) 0 0
\(57\) 186.000 526.087i 0.432216 1.22249i
\(58\) 0 0
\(59\) −558.484 −1.23235 −0.616173 0.787611i \(-0.711318\pi\)
−0.616173 + 0.787611i \(0.711318\pi\)
\(60\) 0 0
\(61\) 278.000 0.583512 0.291756 0.956493i \(-0.405760\pi\)
0.291756 + 0.956493i \(0.405760\pi\)
\(62\) 0 0
\(63\) 293.939 363.731i 0.587822 0.727393i
\(64\) 0 0
\(65\) 441.235i 0.841976i
\(66\) 0 0
\(67\) 890.274i 1.62335i 0.584111 + 0.811674i \(0.301443\pi\)
−0.584111 + 0.811674i \(0.698557\pi\)
\(68\) 0 0
\(69\) −864.000 305.470i −1.50744 0.532961i
\(70\) 0 0
\(71\) −58.7878 −0.0982651 −0.0491326 0.998792i \(-0.515646\pi\)
−0.0491326 + 0.998792i \(0.515646\pi\)
\(72\) 0 0
\(73\) −422.000 −0.676594 −0.338297 0.941039i \(-0.609851\pi\)
−0.338297 + 0.941039i \(0.609851\pi\)
\(74\) 0 0
\(75\) −798.534 282.324i −1.22942 0.434667i
\(76\) 0 0
\(77\) 509.117i 0.753497i
\(78\) 0 0
\(79\) 668.572i 0.952154i −0.879404 0.476077i \(-0.842058\pi\)
0.879404 0.476077i \(-0.157942\pi\)
\(80\) 0 0
\(81\) 153.000 + 712.764i 0.209877 + 0.977728i
\(82\) 0 0
\(83\) −29.3939 −0.0388723 −0.0194361 0.999811i \(-0.506187\pi\)
−0.0194361 + 0.999811i \(0.506187\pi\)
\(84\) 0 0
\(85\) 1152.00 1.47002
\(86\) 0 0
\(87\) 29.3939 83.1384i 0.0362225 0.102453i
\(88\) 0 0
\(89\) 373.352i 0.444666i 0.974971 + 0.222333i \(0.0713672\pi\)
−0.974971 + 0.222333i \(0.928633\pi\)
\(90\) 0 0
\(91\) 450.333i 0.518766i
\(92\) 0 0
\(93\) 54.0000 152.735i 0.0602101 0.170300i
\(94\) 0 0
\(95\) 1822.42 1.96817
\(96\) 0 0
\(97\) −1070.00 −1.12002 −0.560011 0.828486i \(-0.689203\pi\)
−0.560011 + 0.828486i \(0.689203\pi\)
\(98\) 0 0
\(99\) 617.271 + 498.831i 0.626648 + 0.506408i
\(100\) 0 0
\(101\) 1781.91i 1.75551i 0.479109 + 0.877755i \(0.340960\pi\)
−0.479109 + 0.877755i \(0.659040\pi\)
\(102\) 0 0
\(103\) 17.3205i 0.0165693i −0.999966 0.00828466i \(-0.997363\pi\)
0.999966 0.00828466i \(-0.00263712\pi\)
\(104\) 0 0
\(105\) 1440.00 + 509.117i 1.33838 + 0.473188i
\(106\) 0 0
\(107\) −1381.51 −1.24819 −0.624093 0.781350i \(-0.714531\pi\)
−0.624093 + 0.781350i \(0.714531\pi\)
\(108\) 0 0
\(109\) 358.000 0.314589 0.157294 0.987552i \(-0.449723\pi\)
0.157294 + 0.987552i \(0.449723\pi\)
\(110\) 0 0
\(111\) 1009.19 + 356.802i 0.862955 + 0.305101i
\(112\) 0 0
\(113\) 67.8823i 0.0565117i −0.999601 0.0282559i \(-0.991005\pi\)
0.999601 0.0282559i \(-0.00899532\pi\)
\(114\) 0 0
\(115\) 2992.98i 2.42693i
\(116\) 0 0
\(117\) −546.000 441.235i −0.431433 0.348651i
\(118\) 0 0
\(119\) −1175.76 −0.905725
\(120\) 0 0
\(121\) −467.000 −0.350864
\(122\) 0 0
\(123\) −529.090 + 1496.49i −0.387857 + 1.09703i
\(124\) 0 0
\(125\) 644.881i 0.461440i
\(126\) 0 0
\(127\) 31.1769i 0.0217835i −0.999941 0.0108917i \(-0.996533\pi\)
0.999941 0.0108917i \(-0.00346702\pi\)
\(128\) 0 0
\(129\) 162.000 458.205i 0.110568 0.312734i
\(130\) 0 0
\(131\) 1734.24 1.15665 0.578325 0.815806i \(-0.303707\pi\)
0.578325 + 0.815806i \(0.303707\pi\)
\(132\) 0 0
\(133\) −1860.00 −1.21265
\(134\) 0 0
\(135\) −2028.18 + 1247.08i −1.29302 + 0.795046i
\(136\) 0 0
\(137\) 2274.06i 1.41814i −0.705136 0.709072i \(-0.749114\pi\)
0.705136 0.709072i \(-0.250886\pi\)
\(138\) 0 0
\(139\) 1541.53i 0.940651i 0.882493 + 0.470325i \(0.155863\pi\)
−0.882493 + 0.470325i \(0.844137\pi\)
\(140\) 0 0
\(141\) 576.000 + 203.647i 0.344028 + 0.121632i
\(142\) 0 0
\(143\) −764.241 −0.446916
\(144\) 0 0
\(145\) 288.000 0.164946
\(146\) 0 0
\(147\) 210.656 + 74.4782i 0.118195 + 0.0417881i
\(148\) 0 0
\(149\) 2358.91i 1.29698i −0.761225 0.648488i \(-0.775402\pi\)
0.761225 0.648488i \(-0.224598\pi\)
\(150\) 0 0
\(151\) 2040.36i 1.09961i −0.835292 0.549807i \(-0.814701\pi\)
0.835292 0.549807i \(-0.185299\pi\)
\(152\) 0 0
\(153\) 1152.00 1425.53i 0.608717 0.753249i
\(154\) 0 0
\(155\) 529.090 0.274178
\(156\) 0 0
\(157\) −106.000 −0.0538836 −0.0269418 0.999637i \(-0.508577\pi\)
−0.0269418 + 0.999637i \(0.508577\pi\)
\(158\) 0 0
\(159\) 88.1816 249.415i 0.0439828 0.124402i
\(160\) 0 0
\(161\) 3054.70i 1.49531i
\(162\) 0 0
\(163\) 79.6743i 0.0382857i −0.999817 0.0191429i \(-0.993906\pi\)
0.999817 0.0191429i \(-0.00609374\pi\)
\(164\) 0 0
\(165\) −864.000 + 2443.76i −0.407650 + 1.15301i
\(166\) 0 0
\(167\) −3115.75 −1.44374 −0.721868 0.692030i \(-0.756716\pi\)
−0.721868 + 0.692030i \(0.756716\pi\)
\(168\) 0 0
\(169\) −1521.00 −0.692308
\(170\) 0 0
\(171\) 1822.42 2255.13i 0.814994 1.00850i
\(172\) 0 0
\(173\) 2223.14i 0.977009i 0.872561 + 0.488504i \(0.162457\pi\)
−0.872561 + 0.488504i \(0.837543\pi\)
\(174\) 0 0
\(175\) 2823.24i 1.21953i
\(176\) 0 0
\(177\) −2736.00 967.322i −1.16187 0.410782i
\(178\) 0 0
\(179\) 2792.42 1.16601 0.583003 0.812470i \(-0.301878\pi\)
0.583003 + 0.812470i \(0.301878\pi\)
\(180\) 0 0
\(181\) 4510.00 1.85208 0.926038 0.377431i \(-0.123192\pi\)
0.926038 + 0.377431i \(0.123192\pi\)
\(182\) 0 0
\(183\) 1361.92 + 481.510i 0.550141 + 0.194504i
\(184\) 0 0
\(185\) 3495.94i 1.38933i
\(186\) 0 0
\(187\) 1995.32i 0.780280i
\(188\) 0 0
\(189\) 2070.00 1272.79i 0.796668 0.489852i
\(190\) 0 0
\(191\) 1881.21 0.712667 0.356334 0.934359i \(-0.384027\pi\)
0.356334 + 0.934359i \(0.384027\pi\)
\(192\) 0 0
\(193\) 4994.00 1.86257 0.931285 0.364292i \(-0.118689\pi\)
0.931285 + 0.364292i \(0.118689\pi\)
\(194\) 0 0
\(195\) 764.241 2161.60i 0.280659 0.793822i
\(196\) 0 0
\(197\) 2155.26i 0.779472i −0.920927 0.389736i \(-0.872566\pi\)
0.920927 0.389736i \(-0.127434\pi\)
\(198\) 0 0
\(199\) 3973.32i 1.41538i 0.706521 + 0.707692i \(0.250264\pi\)
−0.706521 + 0.707692i \(0.749736\pi\)
\(200\) 0 0
\(201\) −1542.00 + 4361.43i −0.541116 + 1.53051i
\(202\) 0 0
\(203\) −293.939 −0.101628
\(204\) 0 0
\(205\) −5184.00 −1.76618
\(206\) 0 0
\(207\) −3703.63 2992.98i −1.24357 1.00496i
\(208\) 0 0
\(209\) 3156.52i 1.04470i
\(210\) 0 0
\(211\) 4908.63i 1.60154i 0.598974 + 0.800768i \(0.295575\pi\)
−0.598974 + 0.800768i \(0.704425\pi\)
\(212\) 0 0
\(213\) −288.000 101.823i −0.0926452 0.0327550i
\(214\) 0 0
\(215\) 1587.27 0.503492
\(216\) 0 0
\(217\) −540.000 −0.168929
\(218\) 0 0
\(219\) −2067.37 730.925i −0.637899 0.225531i
\(220\) 0 0
\(221\) 1764.94i 0.537206i
\(222\) 0 0
\(223\) 4021.82i 1.20772i −0.797091 0.603859i \(-0.793629\pi\)
0.797091 0.603859i \(-0.206371\pi\)
\(224\) 0 0
\(225\) −3423.00 2766.20i −1.01422 0.819615i
\(226\) 0 0
\(227\) −2968.78 −0.868039 −0.434020 0.900903i \(-0.642905\pi\)
−0.434020 + 0.900903i \(0.642905\pi\)
\(228\) 0 0
\(229\) 430.000 0.124084 0.0620419 0.998074i \(-0.480239\pi\)
0.0620419 + 0.998074i \(0.480239\pi\)
\(230\) 0 0
\(231\) 881.816 2494.15i 0.251166 0.710404i
\(232\) 0 0
\(233\) 6346.99i 1.78457i −0.451471 0.892286i \(-0.649101\pi\)
0.451471 0.892286i \(-0.350899\pi\)
\(234\) 0 0
\(235\) 1995.32i 0.553874i
\(236\) 0 0
\(237\) 1158.00 3275.32i 0.317385 0.897700i
\(238\) 0 0
\(239\) −4115.14 −1.11375 −0.556875 0.830596i \(-0.688000\pi\)
−0.556875 + 0.830596i \(0.688000\pi\)
\(240\) 0 0
\(241\) 4690.00 1.25357 0.626783 0.779194i \(-0.284371\pi\)
0.626783 + 0.779194i \(0.284371\pi\)
\(242\) 0 0
\(243\) −484.999 + 3756.82i −0.128036 + 0.991770i
\(244\) 0 0
\(245\) 729.734i 0.190290i
\(246\) 0 0
\(247\) 2792.07i 0.719251i
\(248\) 0 0
\(249\) −144.000 50.9117i −0.0366491 0.0129574i
\(250\) 0 0
\(251\) −1263.94 −0.317845 −0.158922 0.987291i \(-0.550802\pi\)
−0.158922 + 0.987291i \(0.550802\pi\)
\(252\) 0 0
\(253\) −5184.00 −1.28820
\(254\) 0 0
\(255\) 5643.62 + 1995.32i 1.38595 + 0.490008i
\(256\) 0 0
\(257\) 271.529i 0.0659047i 0.999457 + 0.0329524i \(0.0104910\pi\)
−0.999457 + 0.0329524i \(0.989509\pi\)
\(258\) 0 0
\(259\) 3568.02i 0.856009i
\(260\) 0 0
\(261\) 288.000 356.382i 0.0683017 0.0845191i
\(262\) 0 0
\(263\) 5114.53 1.19915 0.599574 0.800320i \(-0.295337\pi\)
0.599574 + 0.800320i \(0.295337\pi\)
\(264\) 0 0
\(265\) 864.000 0.200283
\(266\) 0 0
\(267\) −646.665 + 1829.05i −0.148222 + 0.419235i
\(268\) 0 0
\(269\) 3173.50i 0.719299i 0.933087 + 0.359649i \(0.117104\pi\)
−0.933087 + 0.359649i \(0.882896\pi\)
\(270\) 0 0
\(271\) 668.572i 0.149863i −0.997189 0.0749314i \(-0.976126\pi\)
0.997189 0.0749314i \(-0.0238738\pi\)
\(272\) 0 0
\(273\) −780.000 + 2206.17i −0.172922 + 0.489098i
\(274\) 0 0
\(275\) −4791.20 −1.05062
\(276\) 0 0
\(277\) −2018.00 −0.437725 −0.218863 0.975756i \(-0.570235\pi\)
−0.218863 + 0.975756i \(0.570235\pi\)
\(278\) 0 0
\(279\) 529.090 654.715i 0.113533 0.140490i
\(280\) 0 0
\(281\) 4717.82i 1.00157i 0.865572 + 0.500785i \(0.166955\pi\)
−0.865572 + 0.500785i \(0.833045\pi\)
\(282\) 0 0
\(283\) 5081.84i 1.06743i −0.845663 0.533717i \(-0.820795\pi\)
0.845663 0.533717i \(-0.179205\pi\)
\(284\) 0 0
\(285\) 8928.00 + 3156.52i 1.85561 + 0.656057i
\(286\) 0 0
\(287\) 5290.90 1.08819
\(288\) 0 0
\(289\) 305.000 0.0620802
\(290\) 0 0
\(291\) −5241.91 1853.29i −1.05597 0.373340i
\(292\) 0 0
\(293\) 424.264i 0.0845931i 0.999105 + 0.0422965i \(0.0134674\pi\)
−0.999105 + 0.0422965i \(0.986533\pi\)
\(294\) 0 0
\(295\) 9477.78i 1.87057i
\(296\) 0 0
\(297\) 2160.00 + 3512.91i 0.422006 + 0.686328i
\(298\) 0 0
\(299\) 4585.44 0.886900
\(300\) 0 0
\(301\) −1620.00 −0.310217
\(302\) 0 0
\(303\) −3086.36 + 8729.54i −0.585170 + 1.65511i
\(304\) 0 0
\(305\) 4717.82i 0.885709i
\(306\) 0 0
\(307\) 3522.99i 0.654944i 0.944861 + 0.327472i \(0.106197\pi\)
−0.944861 + 0.327472i \(0.893803\pi\)
\(308\) 0 0
\(309\) 30.0000 84.8528i 0.00552311 0.0156217i
\(310\) 0 0
\(311\) 9464.83 1.72573 0.862864 0.505437i \(-0.168669\pi\)
0.862864 + 0.505437i \(0.168669\pi\)
\(312\) 0 0
\(313\) −3718.00 −0.671418 −0.335709 0.941966i \(-0.608976\pi\)
−0.335709 + 0.941966i \(0.608976\pi\)
\(314\) 0 0
\(315\) 6172.71 + 4988.31i 1.10410 + 0.892251i
\(316\) 0 0
\(317\) 7212.49i 1.27790i −0.769249 0.638949i \(-0.779369\pi\)
0.769249 0.638949i \(-0.220631\pi\)
\(318\) 0 0
\(319\) 498.831i 0.0875522i
\(320\) 0 0
\(321\) −6768.00 2392.85i −1.17680 0.416062i
\(322\) 0 0
\(323\) −7289.68 −1.25575
\(324\) 0 0
\(325\) 4238.00 0.723329
\(326\) 0 0
\(327\) 1753.83 + 620.074i 0.296597 + 0.104863i
\(328\) 0 0
\(329\) 2036.47i 0.341259i
\(330\) 0 0
\(331\) 1541.53i 0.255982i 0.991775 + 0.127991i \(0.0408528\pi\)
−0.991775 + 0.127991i \(0.959147\pi\)
\(332\) 0 0
\(333\) 4326.00 + 3495.94i 0.711902 + 0.575304i
\(334\) 0 0
\(335\) −15108.5 −2.46407
\(336\) 0 0
\(337\) 2530.00 0.408955 0.204478 0.978871i \(-0.434450\pi\)
0.204478 + 0.978871i \(0.434450\pi\)
\(338\) 0 0
\(339\) 117.576 332.554i 0.0188372 0.0532798i
\(340\) 0 0
\(341\) 916.410i 0.145532i
\(342\) 0 0
\(343\) 6685.72i 1.05246i
\(344\) 0 0
\(345\) 5184.00 14662.6i 0.808977 2.28813i
\(346\) 0 0
\(347\) 5555.44 0.859458 0.429729 0.902958i \(-0.358609\pi\)
0.429729 + 0.902958i \(0.358609\pi\)
\(348\) 0 0
\(349\) −7786.00 −1.19420 −0.597099 0.802168i \(-0.703680\pi\)
−0.597099 + 0.802168i \(0.703680\pi\)
\(350\) 0 0
\(351\) −1910.60 3107.30i −0.290542 0.472522i
\(352\) 0 0
\(353\) 407.294i 0.0614109i 0.999528 + 0.0307054i \(0.00977538\pi\)
−0.999528 + 0.0307054i \(0.990225\pi\)
\(354\) 0 0
\(355\) 997.661i 0.149156i
\(356\) 0 0
\(357\) −5760.00 2036.47i −0.853926 0.301908i
\(358\) 0 0
\(359\) −8759.38 −1.28775 −0.643875 0.765131i \(-0.722674\pi\)
−0.643875 + 0.765131i \(0.722674\pi\)
\(360\) 0 0
\(361\) −4673.00 −0.681295
\(362\) 0 0
\(363\) −2287.82 808.868i −0.330798 0.116955i
\(364\) 0 0
\(365\) 7161.58i 1.02700i
\(366\) 0 0
\(367\) 12578.2i 1.78903i 0.447037 + 0.894515i \(0.352479\pi\)
−0.447037 + 0.894515i \(0.647521\pi\)
\(368\) 0 0
\(369\) −5184.00 + 6414.87i −0.731350 + 0.905000i
\(370\) 0 0
\(371\) −881.816 −0.123401
\(372\) 0 0
\(373\) −4258.00 −0.591075 −0.295537 0.955331i \(-0.595499\pi\)
−0.295537 + 0.955331i \(0.595499\pi\)
\(374\) 0 0
\(375\) 1116.97 3159.26i 0.153813 0.435049i
\(376\) 0 0
\(377\) 441.235i 0.0602778i
\(378\) 0 0
\(379\) 2726.25i 0.369493i −0.982786 0.184747i \(-0.940854\pi\)
0.982786 0.184747i \(-0.0591465\pi\)
\(380\) 0 0
\(381\) 54.0000 152.735i 0.00726116 0.0205377i
\(382\) 0 0
\(383\) 4232.72 0.564704 0.282352 0.959311i \(-0.408885\pi\)
0.282352 + 0.959311i \(0.408885\pi\)
\(384\) 0 0
\(385\) 8640.00 1.14373
\(386\) 0 0
\(387\) 1587.27 1964.15i 0.208489 0.257993i
\(388\) 0 0
\(389\) 5447.55i 0.710030i 0.934861 + 0.355015i \(0.115524\pi\)
−0.934861 + 0.355015i \(0.884476\pi\)
\(390\) 0 0
\(391\) 11971.9i 1.54846i
\(392\) 0 0
\(393\) 8496.00 + 3003.79i 1.09050 + 0.385550i
\(394\) 0 0
\(395\) 11346.0 1.44527
\(396\) 0 0
\(397\) 13574.0 1.71602 0.858009 0.513634i \(-0.171701\pi\)
0.858009 + 0.513634i \(0.171701\pi\)
\(398\) 0 0
\(399\) −9112.10 3221.61i −1.14330 0.404217i
\(400\) 0 0
\(401\) 11743.6i 1.46247i −0.682128 0.731233i \(-0.738945\pi\)
0.682128 0.731233i \(-0.261055\pi\)
\(402\) 0 0
\(403\) 810.600i 0.100196i
\(404\) 0 0
\(405\) −12096.0 + 2596.50i −1.48409 + 0.318570i
\(406\) 0 0
\(407\) 6055.14 0.737450
\(408\) 0 0
\(409\) 2890.00 0.349392 0.174696 0.984622i \(-0.444106\pi\)
0.174696 + 0.984622i \(0.444106\pi\)
\(410\) 0 0
\(411\) 3938.78 11140.6i 0.472715 1.33704i
\(412\) 0 0
\(413\) 9673.22i 1.15251i
\(414\) 0 0
\(415\) 498.831i 0.0590039i
\(416\) 0 0
\(417\) −2670.00 + 7551.90i −0.313550 + 0.886854i
\(418\) 0 0
\(419\) 8318.47 0.969890 0.484945 0.874545i \(-0.338840\pi\)
0.484945 + 0.874545i \(0.338840\pi\)
\(420\) 0 0
\(421\) 10414.0 1.20558 0.602788 0.797902i \(-0.294057\pi\)
0.602788 + 0.797902i \(0.294057\pi\)
\(422\) 0 0
\(423\) 2469.09 + 1995.32i 0.283809 + 0.229352i
\(424\) 0 0
\(425\) 11064.8i 1.26288i
\(426\) 0 0
\(427\) 4815.10i 0.545712i
\(428\) 0 0
\(429\) −3744.00 1323.70i −0.421357 0.148972i
\(430\) 0 0
\(431\) −13050.9 −1.45856 −0.729279 0.684216i \(-0.760145\pi\)
−0.729279 + 0.684216i \(0.760145\pi\)
\(432\) 0 0
\(433\) −9214.00 −1.02262 −0.511312 0.859395i \(-0.670841\pi\)
−0.511312 + 0.859395i \(0.670841\pi\)
\(434\) 0 0
\(435\) 1410.91 + 498.831i 0.155512 + 0.0549818i
\(436\) 0 0
\(437\) 18939.1i 2.07319i
\(438\) 0 0
\(439\) 7326.57i 0.796534i 0.917270 + 0.398267i \(0.130388\pi\)
−0.917270 + 0.398267i \(0.869612\pi\)
\(440\) 0 0
\(441\) 903.000 + 729.734i 0.0975057 + 0.0787965i
\(442\) 0 0
\(443\) −2204.54 −0.236435 −0.118218 0.992988i \(-0.537718\pi\)
−0.118218 + 0.992988i \(0.537718\pi\)
\(444\) 0 0
\(445\) −6336.00 −0.674956
\(446\) 0 0
\(447\) 4085.75 11556.2i 0.432325 1.22280i
\(448\) 0 0
\(449\) 2851.05i 0.299665i −0.988711 0.149832i \(-0.952127\pi\)
0.988711 0.149832i \(-0.0478734\pi\)
\(450\) 0 0
\(451\) 8978.95i 0.937477i
\(452\) 0 0
\(453\) 3534.00 9995.66i 0.366538 1.03673i
\(454\) 0 0
\(455\) −7642.41 −0.787432
\(456\) 0 0
\(457\) −38.0000 −0.00388964 −0.00194482 0.999998i \(-0.500619\pi\)
−0.00194482 + 0.999998i \(0.500619\pi\)
\(458\) 0 0
\(459\) 8112.71 4988.31i 0.824987 0.507264i
\(460\) 0 0
\(461\) 15833.5i 1.59966i −0.600230 0.799828i \(-0.704924\pi\)
0.600230 0.799828i \(-0.295076\pi\)
\(462\) 0 0
\(463\) 11365.7i 1.14084i −0.821353 0.570421i \(-0.806780\pi\)
0.821353 0.570421i \(-0.193220\pi\)
\(464\) 0 0
\(465\) 2592.00 + 916.410i 0.258497 + 0.0913925i
\(466\) 0 0
\(467\) −499.696 −0.0495143 −0.0247571 0.999693i \(-0.507881\pi\)
−0.0247571 + 0.999693i \(0.507881\pi\)
\(468\) 0 0
\(469\) 15420.0 1.51819
\(470\) 0 0
\(471\) −519.292 183.597i −0.0508019 0.0179612i
\(472\) 0 0
\(473\) 2749.23i 0.267251i
\(474\) 0 0
\(475\) 17504.1i 1.69083i
\(476\) 0 0
\(477\) 864.000 1069.15i 0.0829347 0.102626i
\(478\) 0 0
\(479\) 8700.59 0.829937 0.414969 0.909836i \(-0.363793\pi\)
0.414969 + 0.909836i \(0.363793\pi\)
\(480\) 0 0
\(481\) −5356.00 −0.507718
\(482\) 0 0
\(483\) −5290.90 + 14964.9i −0.498435 + 1.40979i
\(484\) 0 0
\(485\) 18158.5i 1.70007i
\(486\) 0 0
\(487\) 4007.97i 0.372933i −0.982461 0.186466i \(-0.940296\pi\)
0.982461 0.186466i \(-0.0597035\pi\)
\(488\) 0 0
\(489\) 138.000 390.323i 0.0127619 0.0360961i
\(490\) 0 0
\(491\) −16901.5 −1.55347 −0.776734 0.629828i \(-0.783125\pi\)
−0.776734 + 0.629828i \(0.783125\pi\)
\(492\) 0 0
\(493\) −1152.00 −0.105240
\(494\) 0 0
\(495\) −8465.44 + 10475.4i −0.768673 + 0.951184i
\(496\) 0 0
\(497\) 1018.23i 0.0918994i
\(498\) 0 0
\(499\) 12439.6i 1.11598i −0.829849 0.557988i \(-0.811573\pi\)
0.829849 0.557988i \(-0.188427\pi\)
\(500\) 0 0
\(501\) −15264.0 5396.64i −1.36117 0.481246i
\(502\) 0 0
\(503\) 12756.9 1.13082 0.565411 0.824809i \(-0.308717\pi\)
0.565411 + 0.824809i \(0.308717\pi\)
\(504\) 0 0
\(505\) −30240.0 −2.66468
\(506\) 0 0
\(507\) −7451.35 2634.45i −0.652714 0.230769i
\(508\) 0 0
\(509\) 5549.37i 0.483245i 0.970370 + 0.241622i \(0.0776796\pi\)
−0.970370 + 0.241622i \(0.922320\pi\)
\(510\) 0 0
\(511\) 7309.25i 0.632764i
\(512\) 0 0
\(513\) 12834.0 7891.31i 1.10455 0.679162i
\(514\) 0 0
\(515\) 293.939 0.0251505
\(516\) 0 0
\(517\) 3456.00 0.293994
\(518\) 0 0
\(519\) −3850.60 + 10891.1i −0.325670 + 0.921133i
\(520\) 0 0
\(521\) 11506.0i 0.967541i −0.875195 0.483770i \(-0.839267\pi\)
0.875195 0.483770i \(-0.160733\pi\)
\(522\) 0 0
\(523\) 17441.8i 1.45827i −0.684371 0.729134i \(-0.739923\pi\)
0.684371 0.729134i \(-0.260077\pi\)
\(524\) 0 0
\(525\) −4890.00 + 13831.0i −0.406509 + 1.14978i
\(526\) 0 0
\(527\) −2116.36 −0.174934
\(528\) 0 0
\(529\) 18937.0 1.55642
\(530\) 0 0
\(531\) −11728.2 9477.78i −0.958491 0.774578i
\(532\) 0 0
\(533\) 7942.22i 0.645433i
\(534\) 0 0
\(535\) 23445.0i 1.89461i
\(536\) 0 0
\(537\) 13680.0 + 4836.61i 1.09932 + 0.388669i
\(538\) 0 0
\(539\) 1263.94 0.101005
\(540\) 0 0
\(541\) −6794.00 −0.539920 −0.269960 0.962871i \(-0.587011\pi\)
−0.269960 + 0.962871i \(0.587011\pi\)
\(542\) 0 0
\(543\) 22094.4 + 7811.55i 1.74615 + 0.617358i
\(544\) 0 0
\(545\) 6075.46i 0.477512i
\(546\) 0 0
\(547\) 3910.97i 0.305706i 0.988249 + 0.152853i \(0.0488461\pi\)
−0.988249 + 0.152853i \(0.951154\pi\)
\(548\) 0 0
\(549\) 5838.00 + 4717.82i 0.453843 + 0.366760i
\(550\) 0 0
\(551\) −1822.42 −0.140903
\(552\) 0 0
\(553\) −11580.0 −0.890473
\(554\) 0 0
\(555\) −6055.14 + 17126.5i −0.463110 + 1.30987i
\(556\) 0 0
\(557\) 22587.8i 1.71827i 0.511749 + 0.859135i \(0.328998\pi\)
−0.511749 + 0.859135i \(0.671002\pi\)
\(558\) 0 0
\(559\) 2431.80i 0.183997i
\(560\) 0 0
\(561\) 3456.00 9775.04i 0.260093 0.735655i
\(562\) 0 0
\(563\) −8729.98 −0.653508 −0.326754 0.945109i \(-0.605955\pi\)
−0.326754 + 0.945109i \(0.605955\pi\)
\(564\) 0 0
\(565\) 1152.00 0.0857788
\(566\) 0 0
\(567\) 12345.4 2650.04i 0.914390 0.196281i
\(568\) 0 0
\(569\) 16122.0i 1.18782i 0.804531 + 0.593911i \(0.202417\pi\)
−0.804531 + 0.593911i \(0.797583\pi\)
\(570\) 0 0
\(571\) 9495.10i 0.695898i 0.937513 + 0.347949i \(0.113122\pi\)
−0.937513 + 0.347949i \(0.886878\pi\)
\(572\) 0 0
\(573\) 9216.00 + 3258.35i 0.671909 + 0.237556i
\(574\) 0 0
\(575\) 28747.2 2.08494
\(576\) 0 0
\(577\) −8974.00 −0.647474 −0.323737 0.946147i \(-0.604939\pi\)
−0.323737 + 0.946147i \(0.604939\pi\)
\(578\) 0 0
\(579\) 24465.5 + 8649.86i 1.75605 + 0.620857i
\(580\) 0 0
\(581\) 509.117i 0.0363541i
\(582\) 0 0
\(583\) 1496.49i 0.106309i
\(584\) 0 0
\(585\) 7488.00 9265.93i 0.529215 0.654870i
\(586\) 0 0
\(587\) −4908.78 −0.345157 −0.172578 0.984996i \(-0.555210\pi\)
−0.172578 + 0.984996i \(0.555210\pi\)
\(588\) 0 0
\(589\) −3348.00 −0.234214
\(590\) 0 0
\(591\) 3733.02 10558.6i 0.259824 0.734893i
\(592\) 0 0
\(593\) 14730.4i 1.02008i 0.860151 + 0.510040i \(0.170369\pi\)
−0.860151 + 0.510040i \(0.829631\pi\)
\(594\) 0 0
\(595\) 19953.2i 1.37479i
\(596\) 0 0
\(597\) −6882.00 + 19465.2i −0.471795 + 1.33444i
\(598\) 0 0
\(599\) −10052.7 −0.685714 −0.342857 0.939388i \(-0.611395\pi\)
−0.342857 + 0.939388i \(0.611395\pi\)
\(600\) 0 0
\(601\) 23690.0 1.60788 0.803939 0.594711i \(-0.202734\pi\)
0.803939 + 0.594711i \(0.202734\pi\)
\(602\) 0 0
\(603\) −15108.5 + 18695.8i −1.02034 + 1.26260i
\(604\) 0 0
\(605\) 7925.25i 0.532574i
\(606\) 0 0
\(607\) 22589.4i 1.51050i −0.655435 0.755252i \(-0.727515\pi\)
0.655435 0.755252i \(-0.272485\pi\)
\(608\) 0 0
\(609\) −1440.00 509.117i −0.0958157 0.0338760i
\(610\) 0 0
\(611\) −3056.96 −0.202408
\(612\) 0 0
\(613\) 9422.00 0.620801 0.310400 0.950606i \(-0.399537\pi\)
0.310400 + 0.950606i \(0.399537\pi\)
\(614\) 0 0
\(615\) −25396.3 8978.95i −1.66517 0.588726i
\(616\) 0 0
\(617\) 984.293i 0.0642239i 0.999484 + 0.0321119i \(0.0102233\pi\)
−0.999484 + 0.0321119i \(0.989777\pi\)
\(618\) 0 0
\(619\) 12238.7i 0.794691i 0.917669 + 0.397345i \(0.130069\pi\)
−0.917669 + 0.397345i \(0.869931\pi\)
\(620\) 0 0
\(621\) −12960.0 21077.4i −0.837467 1.36201i
\(622\) 0 0
\(623\) 6466.65 0.415860
\(624\) 0 0
\(625\) −9431.00 −0.603584
\(626\) 0 0
\(627\) 5467.26 15463.7i 0.348232 0.984948i
\(628\) 0 0
\(629\) 13983.7i 0.886436i
\(630\) 0 0
\(631\) 13922.2i 0.878344i 0.898403 + 0.439172i \(0.144728\pi\)
−0.898403 + 0.439172i \(0.855272\pi\)
\(632\) 0 0
\(633\) −8502.00 + 24047.3i −0.533845 + 1.50994i
\(634\) 0 0
\(635\) 529.090 0.0330650
\(636\) 0 0
\(637\) −1118.00 −0.0695397
\(638\) 0 0
\(639\) −1234.54 997.661i −0.0764284 0.0617635i
\(640\) 0 0
\(641\) 16427.5i 1.01224i −0.862462 0.506121i \(-0.831079\pi\)
0.862462 0.506121i \(-0.168921\pi\)
\(642\) 0 0
\(643\) 1465.31i 0.0898700i −0.998990 0.0449350i \(-0.985692\pi\)
0.998990 0.0449350i \(-0.0143081\pi\)
\(644\) 0 0
\(645\) 7776.00 + 2749.23i 0.474697 + 0.167831i
\(646\) 0 0
\(647\) −12286.6 −0.746581 −0.373290 0.927715i \(-0.621770\pi\)
−0.373290 + 0.927715i \(0.621770\pi\)
\(648\) 0 0
\(649\) −16416.0 −0.992888
\(650\) 0 0
\(651\) −2645.45 935.307i −0.159268 0.0563097i
\(652\) 0 0
\(653\) 8502.25i 0.509523i −0.967004 0.254762i \(-0.918003\pi\)
0.967004 0.254762i \(-0.0819970\pi\)
\(654\) 0 0
\(655\) 29431.0i 1.75567i
\(656\) 0 0
\(657\) −8862.00 7161.58i −0.526240 0.425266i
\(658\) 0 0
\(659\) 17136.6 1.01297 0.506486 0.862248i \(-0.330944\pi\)
0.506486 + 0.862248i \(0.330944\pi\)
\(660\) 0 0
\(661\) −10018.0 −0.589493 −0.294747 0.955575i \(-0.595235\pi\)
−0.294747 + 0.955575i \(0.595235\pi\)
\(662\) 0 0
\(663\) −3056.96 + 8646.40i −0.179069 + 0.506483i
\(664\) 0 0
\(665\) 31565.2i 1.84067i
\(666\) 0 0
\(667\) 2992.98i 0.173746i
\(668\) 0 0
\(669\) 6966.00 19702.8i 0.402573 1.13865i
\(670\) 0 0
\(671\) 8171.50 0.470130
\(672\) 0 0
\(673\) 1682.00 0.0963393 0.0481696 0.998839i \(-0.484661\pi\)
0.0481696 + 0.998839i \(0.484661\pi\)
\(674\) 0 0
\(675\) −11978.0 19480.4i −0.683013 1.11081i
\(676\) 0 0
\(677\) 9113.19i 0.517354i 0.965964 + 0.258677i \(0.0832865\pi\)
−0.965964 + 0.258677i \(0.916714\pi\)
\(678\) 0 0
\(679\) 18532.9i 1.04747i
\(680\) 0 0
\(681\) −14544.0 5142.08i −0.818395 0.289346i
\(682\) 0 0
\(683\) −23250.6 −1.30257 −0.651287 0.758832i \(-0.725771\pi\)
−0.651287 + 0.758832i \(0.725771\pi\)
\(684\) 0 0
\(685\) 38592.0 2.15259
\(686\) 0 0
\(687\) 2106.56 + 744.782i 0.116987 + 0.0413613i
\(688\) 0 0
\(689\) 1323.70i 0.0731917i
\(690\) 0 0
\(691\) 25222.1i 1.38856i 0.719705 + 0.694280i \(0.244277\pi\)
−0.719705 + 0.694280i \(0.755723\pi\)
\(692\) 0 0
\(693\) 8640.00 10691.5i 0.473602 0.586053i
\(694\) 0 0
\(695\) −26160.6 −1.42781
\(696\) 0 0
\(697\) 20736.0 1.12688
\(698\) 0 0
\(699\) 10993.3 31093.8i 0.594857 1.68251i
\(700\) 0 0
\(701\) 16410.5i 0.884190i 0.896968 + 0.442095i \(0.145765\pi\)
−0.896968 + 0.442095i \(0.854235\pi\)
\(702\) 0 0
\(703\) 22121.8i 1.18682i
\(704\) 0 0
\(705\) −3456.00 + 9775.04i −0.184625 + 0.522198i
\(706\) 0 0
\(707\) 30863.6 1.64179
\(708\) 0 0
\(709\) −27602.0 −1.46208 −0.731040 0.682334i \(-0.760965\pi\)
−0.731040 + 0.682334i \(0.760965\pi\)
\(710\) 0 0
\(711\) 11346.0 14040.0i 0.598466 0.740564i
\(712\) 0 0
\(713\) 5498.46i 0.288806i
\(714\) 0 0
\(715\) 12969.6i 0.678371i
\(716\) 0 0
\(717\) −20160.0 7127.64i −1.05005 0.371250i
\(718\) 0 0
\(719\) −31627.8 −1.64050 −0.820249 0.572006i \(-0.806165\pi\)
−0.820249 + 0.572006i \(0.806165\pi\)
\(720\) 0 0
\(721\) −300.000 −0.0154960
\(722\) 0 0
\(723\) 22976.2 + 8123.32i 1.18187 + 0.417855i
\(724\) 0 0
\(725\) 2766.20i 0.141702i
\(726\) 0 0
\(727\) 27279.8i 1.39168i 0.718197 + 0.695840i \(0.244968\pi\)
−0.718197 + 0.695840i \(0.755032\pi\)
\(728\) 0 0
\(729\) −8883.00 + 17564.5i −0.451303 + 0.892371i
\(730\) 0 0
\(731\) −6349.08 −0.321244
\(732\) 0 0
\(733\) −15914.0 −0.801906 −0.400953 0.916099i \(-0.631321\pi\)
−0.400953 + 0.916099i \(0.631321\pi\)
\(734\) 0 0
\(735\) −1263.94 + 3574.95i −0.0634299 + 0.179407i
\(736\) 0 0
\(737\) 26168.6i 1.30791i
\(738\) 0 0
\(739\) 2275.91i 0.113289i 0.998394 + 0.0566447i \(0.0180402\pi\)
−0.998394 + 0.0566447i \(0.981960\pi\)
\(740\) 0 0
\(741\) −4836.00 + 13678.3i −0.239750 + 0.678116i
\(742\) 0 0
\(743\) 8641.80 0.426698 0.213349 0.976976i \(-0.431563\pi\)
0.213349 + 0.976976i \(0.431563\pi\)
\(744\) 0 0
\(745\) 40032.0 1.96867
\(746\) 0 0
\(747\) −617.271 498.831i −0.0302340 0.0244327i
\(748\) 0 0
\(749\) 23928.5i 1.16733i
\(750\) 0 0
\(751\) 16631.2i 0.808095i −0.914738 0.404048i \(-0.867603\pi\)
0.914738 0.404048i \(-0.132397\pi\)
\(752\) 0 0
\(753\) −6192.00 2189.20i −0.299667 0.105948i
\(754\) 0 0
\(755\) 34626.0 1.66910
\(756\) 0 0
\(757\) 11422.0 0.548401 0.274201 0.961673i \(-0.411587\pi\)
0.274201 + 0.961673i \(0.411587\pi\)
\(758\) 0 0
\(759\) −25396.3 8978.95i −1.21453 0.429401i
\(760\) 0 0
\(761\) 12660.0i 0.603057i −0.953457 0.301528i \(-0.902503\pi\)
0.953457 0.301528i \(-0.0974968\pi\)
\(762\) 0 0
\(763\) 6200.74i 0.294210i
\(764\) 0 0
\(765\) 24192.0 + 19550.1i 1.14335 + 0.923967i
\(766\) 0 0
\(767\) 14520.6 0.683582
\(768\) 0 0
\(769\) 18818.0 0.882437 0.441219 0.897400i \(-0.354546\pi\)
0.441219 + 0.897400i \(0.354546\pi\)
\(770\) 0 0
\(771\) −470.302 + 1330.22i −0.0219682 + 0.0621356i
\(772\) 0 0
\(773\) 1917.67i 0.0892289i 0.999004 + 0.0446144i \(0.0142059\pi\)
−0.999004 + 0.0446144i \(0.985794\pi\)
\(774\) 0 0
\(775\) 5081.84i 0.235542i
\(776\) 0 0
\(777\) 6180.00 17479.7i 0.285336 0.807053i
\(778\) 0 0
\(779\) 32803.6 1.50874
\(780\) 0 0
\(781\) −1728.00 −0.0791712
\(782\) 0 0
\(783\) 2028.18 1247.08i 0.0925685 0.0569181i
\(784\) 0 0
\(785\) 1798.88i 0.0817895i
\(786\) 0 0
\(787\) 19845.8i 0.898892i 0.893308 + 0.449446i \(0.148379\pi\)
−0.893308 + 0.449446i \(0.851621\pi\)
\(788\) 0 0
\(789\) 25056.0 + 8858.63i 1.13057 + 0.399716i
\(790\) 0 0