Properties

Label 1323.2.h.e.802.1
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), degree \(2\), not 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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.e.226.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.69963 q^{2} +0.888736 q^{4} +(1.79418 - 3.10761i) q^{5} +1.88874 q^{8} +O(q^{10})\) \(q-1.69963 q^{2} +0.888736 q^{4} +(1.79418 - 3.10761i) q^{5} +1.88874 q^{8} +(-3.04944 + 5.28179i) q^{10} +(-1.40545 - 2.43430i) q^{11} +(0.500000 + 0.866025i) q^{13} -4.98762 q^{16} +(2.05563 - 3.56046i) q^{17} +(-0.444368 - 0.769668i) q^{19} +(1.59455 - 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +(2.93818 - 5.08907i) q^{23} +(-3.93818 - 6.82112i) q^{25} +(-0.849814 - 1.47192i) q^{26} +(-0.849814 + 1.47192i) q^{29} +6.98762 q^{31} +4.69963 q^{32} +(-3.49381 + 6.05146i) q^{34} +(-2.38255 - 4.12669i) q^{37} +(0.755260 + 1.30815i) q^{38} +(3.38874 - 5.86946i) q^{40} +(2.70582 + 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +(-1.24907 - 2.16345i) q^{44} +(-4.99381 + 8.64953i) q^{46} -2.66621 q^{47} +(6.69344 + 11.5934i) q^{50} +(0.444368 + 0.769668i) q^{52} +(-0.0618219 + 0.107079i) q^{53} -10.0865 q^{55} +(1.44437 - 2.50172i) q^{58} -8.87636 q^{59} -3.87636 q^{61} -11.8764 q^{62} +1.98762 q^{64} +3.58836 q^{65} +12.3090 q^{67} +(1.82691 - 3.16431i) q^{68} +2.87636 q^{71} +(-5.32072 + 9.21576i) q^{73} +(4.04944 + 7.01384i) q^{74} +(-0.394926 - 0.684031i) q^{76} -7.08650 q^{79} +(-8.94870 + 15.4996i) q^{80} +(-4.59888 - 7.96550i) q^{82} +(2.05563 - 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(4.42766 - 7.66893i) q^{86} +(-2.65452 - 4.59776i) q^{88} +(-4.80470 - 8.32199i) q^{89} +(2.61126 - 4.52284i) q^{92} +4.53156 q^{94} -3.18911 q^{95} +(3.66071 - 6.34053i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.69963 −1.20182 −0.600909 0.799317i \(-0.705195\pi\)
−0.600909 + 0.799317i \(0.705195\pi\)
\(3\) 0 0
\(4\) 0.888736 0.444368
\(5\) 1.79418 3.10761i 0.802383 1.38977i −0.115661 0.993289i \(-0.536899\pi\)
0.918044 0.396479i \(-0.129768\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.88874 0.667769
\(9\) 0 0
\(10\) −3.04944 + 5.28179i −0.964318 + 1.67025i
\(11\) −1.40545 2.43430i −0.423758 0.733970i 0.572546 0.819873i \(-0.305956\pi\)
−0.996304 + 0.0859026i \(0.972623\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.98762 −1.24691
\(17\) 2.05563 3.56046i 0.498564 0.863538i −0.501435 0.865196i \(-0.667194\pi\)
0.999999 + 0.00165734i \(0.000527549\pi\)
\(18\) 0 0
\(19\) −0.444368 0.769668i −0.101945 0.176574i 0.810541 0.585682i \(-0.199173\pi\)
−0.912486 + 0.409108i \(0.865840\pi\)
\(20\) 1.59455 2.76185i 0.356553 0.617568i
\(21\) 0 0
\(22\) 2.38874 + 4.13741i 0.509280 + 0.882099i
\(23\) 2.93818 5.08907i 0.612652 1.06115i −0.378139 0.925749i \(-0.623436\pi\)
0.990792 0.135396i \(-0.0432308\pi\)
\(24\) 0 0
\(25\) −3.93818 6.82112i −0.787636 1.36422i
\(26\) −0.849814 1.47192i −0.166662 0.288667i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.849814 + 1.47192i −0.157807 + 0.273329i −0.934077 0.357071i \(-0.883776\pi\)
0.776271 + 0.630399i \(0.217109\pi\)
\(30\) 0 0
\(31\) 6.98762 1.25501 0.627507 0.778611i \(-0.284075\pi\)
0.627507 + 0.778611i \(0.284075\pi\)
\(32\) 4.69963 0.830785
\(33\) 0 0
\(34\) −3.49381 + 6.05146i −0.599183 + 1.03782i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.38255 4.12669i −0.391688 0.678424i 0.600984 0.799261i \(-0.294775\pi\)
−0.992672 + 0.120837i \(0.961442\pi\)
\(38\) 0.755260 + 1.30815i 0.122519 + 0.212210i
\(39\) 0 0
\(40\) 3.38874 5.86946i 0.535806 0.928044i
\(41\) 2.70582 + 4.68661i 0.422578 + 0.731926i 0.996191 0.0872002i \(-0.0277920\pi\)
−0.573613 + 0.819126i \(0.694459\pi\)
\(42\) 0 0
\(43\) −2.60507 + 4.51212i −0.397270 + 0.688092i −0.993388 0.114805i \(-0.963376\pi\)
0.596118 + 0.802897i \(0.296709\pi\)
\(44\) −1.24907 2.16345i −0.188304 0.326153i
\(45\) 0 0
\(46\) −4.99381 + 8.64953i −0.736297 + 1.27530i
\(47\) −2.66621 −0.388906 −0.194453 0.980912i \(-0.562293\pi\)
−0.194453 + 0.980912i \(0.562293\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 6.69344 + 11.5934i 0.946595 + 1.63955i
\(51\) 0 0
\(52\) 0.444368 + 0.769668i 0.0616227 + 0.106734i
\(53\) −0.0618219 + 0.107079i −0.00849190 + 0.0147084i −0.870240 0.492628i \(-0.836036\pi\)
0.861748 + 0.507336i \(0.169370\pi\)
\(54\) 0 0
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) 0 0
\(58\) 1.44437 2.50172i 0.189655 0.328492i
\(59\) −8.87636 −1.15560 −0.577802 0.816177i \(-0.696089\pi\)
−0.577802 + 0.816177i \(0.696089\pi\)
\(60\) 0 0
\(61\) −3.87636 −0.496317 −0.248158 0.968720i \(-0.579825\pi\)
−0.248158 + 0.968720i \(0.579825\pi\)
\(62\) −11.8764 −1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) 3.58836 0.445082
\(66\) 0 0
\(67\) 12.3090 1.50379 0.751894 0.659284i \(-0.229141\pi\)
0.751894 + 0.659284i \(0.229141\pi\)
\(68\) 1.82691 3.16431i 0.221546 0.383729i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.87636 0.341361 0.170680 0.985326i \(-0.445403\pi\)
0.170680 + 0.985326i \(0.445403\pi\)
\(72\) 0 0
\(73\) −5.32072 + 9.21576i −0.622744 + 1.07862i 0.366229 + 0.930525i \(0.380649\pi\)
−0.988973 + 0.148099i \(0.952685\pi\)
\(74\) 4.04944 + 7.01384i 0.470738 + 0.815342i
\(75\) 0 0
\(76\) −0.394926 0.684031i −0.0453011 0.0784638i
\(77\) 0 0
\(78\) 0 0
\(79\) −7.08650 −0.797294 −0.398647 0.917104i \(-0.630520\pi\)
−0.398647 + 0.917104i \(0.630520\pi\)
\(80\) −8.94870 + 15.4996i −1.00049 + 1.73291i
\(81\) 0 0
\(82\) −4.59888 7.96550i −0.507862 0.879642i
\(83\) 2.05563 3.56046i 0.225635 0.390811i −0.730875 0.682512i \(-0.760888\pi\)
0.956510 + 0.291700i \(0.0942210\pi\)
\(84\) 0 0
\(85\) −7.37636 12.7762i −0.800078 1.38578i
\(86\) 4.42766 7.66893i 0.477447 0.826962i
\(87\) 0 0
\(88\) −2.65452 4.59776i −0.282972 0.490123i
\(89\) −4.80470 8.32199i −0.509297 0.882129i −0.999942 0.0107692i \(-0.996572\pi\)
0.490645 0.871360i \(-0.336761\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.61126 4.52284i 0.272243 0.471539i
\(93\) 0 0
\(94\) 4.53156 0.467395
\(95\) −3.18911 −0.327196
\(96\) 0 0
\(97\) 3.66071 6.34053i 0.371688 0.643783i −0.618137 0.786070i \(-0.712112\pi\)
0.989825 + 0.142287i \(0.0454456\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) −1.73236 3.00054i −0.172376 0.298564i 0.766874 0.641798i \(-0.221811\pi\)
−0.939250 + 0.343233i \(0.888478\pi\)
\(102\) 0 0
\(103\) −7.93818 + 13.7493i −0.782172 + 1.35476i 0.148502 + 0.988912i \(0.452555\pi\)
−0.930674 + 0.365849i \(0.880779\pi\)
\(104\) 0.944368 + 1.63569i 0.0926029 + 0.160393i
\(105\) 0 0
\(106\) 0.105074 0.181994i 0.0102057 0.0176768i
\(107\) −2.67673 4.63623i −0.258769 0.448201i 0.707143 0.707070i \(-0.249984\pi\)
−0.965912 + 0.258869i \(0.916650\pi\)
\(108\) 0 0
\(109\) 9.43199 16.3367i 0.903421 1.56477i 0.0803973 0.996763i \(-0.474381\pi\)
0.823023 0.568008i \(-0.192286\pi\)
\(110\) 17.1433 1.63455
\(111\) 0 0
\(112\) 0 0
\(113\) −9.27561 16.0658i −0.872576 1.51135i −0.859322 0.511434i \(-0.829114\pi\)
−0.0132538 0.999912i \(-0.504219\pi\)
\(114\) 0 0
\(115\) −10.5433 18.2614i −0.983163 1.70289i
\(116\) −0.755260 + 1.30815i −0.0701242 + 0.121459i
\(117\) 0 0
\(118\) 15.0865 1.38883
\(119\) 0 0
\(120\) 0 0
\(121\) 1.54944 2.68371i 0.140858 0.243974i
\(122\) 6.58836 0.596482
\(123\) 0 0
\(124\) 6.21015 0.557688
\(125\) −10.3214 −0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) −12.7775 −1.12938
\(129\) 0 0
\(130\) −6.09888 −0.534908
\(131\) −8.02654 + 13.9024i −0.701282 + 1.21466i 0.266734 + 0.963770i \(0.414055\pi\)
−0.968017 + 0.250886i \(0.919278\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −20.9208 −1.80728
\(135\) 0 0
\(136\) 3.88255 6.72477i 0.332926 0.576644i
\(137\) −6.49381 11.2476i −0.554804 0.960948i −0.997919 0.0644834i \(-0.979460\pi\)
0.443115 0.896465i \(-0.353873\pi\)
\(138\) 0 0
\(139\) 0.555632 + 0.962383i 0.0471281 + 0.0816283i 0.888627 0.458630i \(-0.151660\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.88874 −0.410254
\(143\) 1.40545 2.43430i 0.117529 0.203567i
\(144\) 0 0
\(145\) 3.04944 + 5.28179i 0.253242 + 0.438629i
\(146\) 9.04325 15.6634i 0.748425 1.29631i
\(147\) 0 0
\(148\) −2.11745 3.66754i −0.174054 0.301470i
\(149\) 4.21634 7.30291i 0.345416 0.598278i −0.640013 0.768364i \(-0.721071\pi\)
0.985429 + 0.170086i \(0.0544045\pi\)
\(150\) 0 0
\(151\) 7.42580 + 12.8619i 0.604303 + 1.04668i 0.992161 + 0.124964i \(0.0398816\pi\)
−0.387858 + 0.921719i \(0.626785\pi\)
\(152\) −0.839294 1.45370i −0.0680757 0.117911i
\(153\) 0 0
\(154\) 0 0
\(155\) 12.5371 21.7148i 1.00700 1.74418i
\(156\) 0 0
\(157\) −2.88874 −0.230546 −0.115273 0.993334i \(-0.536774\pi\)
−0.115273 + 0.993334i \(0.536774\pi\)
\(158\) 12.0444 0.958203
\(159\) 0 0
\(160\) 8.43199 14.6046i 0.666607 1.15460i
\(161\) 0 0
\(162\) 0 0
\(163\) 5.15452 + 8.92788i 0.403733 + 0.699286i 0.994173 0.107796i \(-0.0343792\pi\)
−0.590440 + 0.807081i \(0.701046\pi\)
\(164\) 2.40476 + 4.16516i 0.187780 + 0.325245i
\(165\) 0 0
\(166\) −3.49381 + 6.05146i −0.271172 + 0.469684i
\(167\) −6.07598 10.5239i −0.470174 0.814365i 0.529244 0.848469i \(-0.322475\pi\)
−0.999418 + 0.0341045i \(0.989142\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 12.5371 + 21.7148i 0.961549 + 1.66545i
\(171\) 0 0
\(172\) −2.31522 + 4.01008i −0.176534 + 0.305766i
\(173\) −6.60940 −0.502504 −0.251252 0.967922i \(-0.580842\pi\)
−0.251252 + 0.967922i \(0.580842\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 7.00983 + 12.1414i 0.528386 + 0.915191i
\(177\) 0 0
\(178\) 8.16621 + 14.1443i 0.612083 + 1.06016i
\(179\) −1.92147 + 3.32808i −0.143617 + 0.248752i −0.928856 0.370440i \(-0.879207\pi\)
0.785239 + 0.619193i \(0.212540\pi\)
\(180\) 0 0
\(181\) −18.5426 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 5.54944 9.61192i 0.409110 0.708600i
\(185\) −17.0989 −1.25713
\(186\) 0 0
\(187\) −11.5563 −0.845082
\(188\) −2.36955 −0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) −4.63416 −0.335316 −0.167658 0.985845i \(-0.553620\pi\)
−0.167658 + 0.985845i \(0.553620\pi\)
\(192\) 0 0
\(193\) −25.2967 −1.82089 −0.910446 0.413627i \(-0.864262\pi\)
−0.910446 + 0.413627i \(0.864262\pi\)
\(194\) −6.22184 + 10.7765i −0.446702 + 0.773711i
\(195\) 0 0
\(196\) 0 0
\(197\) −10.7207 −0.763816 −0.381908 0.924200i \(-0.624733\pi\)
−0.381908 + 0.924200i \(0.624733\pi\)
\(198\) 0 0
\(199\) −4.38323 + 7.59199i −0.310719 + 0.538182i −0.978518 0.206160i \(-0.933903\pi\)
0.667799 + 0.744342i \(0.267237\pi\)
\(200\) −7.43818 12.8833i −0.525959 0.910987i
\(201\) 0 0
\(202\) 2.94437 + 5.09979i 0.207165 + 0.358820i
\(203\) 0 0
\(204\) 0 0
\(205\) 19.4189 1.35628
\(206\) 13.4920 23.3687i 0.940029 1.62818i
\(207\) 0 0
\(208\) −2.49381 4.31941i −0.172915 0.299497i
\(209\) −1.24907 + 2.16345i −0.0864000 + 0.149649i
\(210\) 0 0
\(211\) −5.26509 9.11941i −0.362464 0.627806i 0.625902 0.779902i \(-0.284731\pi\)
−0.988366 + 0.152096i \(0.951398\pi\)
\(212\) −0.0549434 + 0.0951647i −0.00377353 + 0.00653594i
\(213\) 0 0
\(214\) 4.54944 + 7.87987i 0.310993 + 0.538656i
\(215\) 9.34795 + 16.1911i 0.637525 + 1.10423i
\(216\) 0 0
\(217\) 0 0
\(218\) −16.0309 + 27.7663i −1.08575 + 1.88057i
\(219\) 0 0
\(220\) −8.96424 −0.604369
\(221\) 4.11126 0.276554
\(222\) 0 0
\(223\) −2.83379 + 4.90827i −0.189765 + 0.328682i −0.945172 0.326574i \(-0.894106\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 15.7651 + 27.3059i 1.04868 + 1.81636i
\(227\) 5.54944 + 9.61192i 0.368329 + 0.637965i 0.989304 0.145865i \(-0.0465965\pi\)
−0.620975 + 0.783830i \(0.713263\pi\)
\(228\) 0 0
\(229\) 9.82141 17.0112i 0.649017 1.12413i −0.334341 0.942452i \(-0.608514\pi\)
0.983358 0.181679i \(-0.0581530\pi\)
\(230\) 17.9196 + 31.0377i 1.18158 + 2.04656i
\(231\) 0 0
\(232\) −1.60507 + 2.78007i −0.105378 + 0.182521i
\(233\) 4.48143 + 7.76207i 0.293588 + 0.508510i 0.974656 0.223711i \(-0.0718172\pi\)
−0.681067 + 0.732221i \(0.738484\pi\)
\(234\) 0 0
\(235\) −4.78366 + 8.28554i −0.312052 + 0.540489i
\(236\) −7.88874 −0.513513
\(237\) 0 0
\(238\) 0 0
\(239\) 5.61126 + 9.71899i 0.362963 + 0.628670i 0.988447 0.151567i \(-0.0484320\pi\)
−0.625484 + 0.780237i \(0.715099\pi\)
\(240\) 0 0
\(241\) −3.49312 6.05026i −0.225012 0.389732i 0.731311 0.682044i \(-0.238909\pi\)
−0.956323 + 0.292312i \(0.905575\pi\)
\(242\) −2.63348 + 4.56131i −0.169286 + 0.293212i
\(243\) 0 0
\(244\) −3.44506 −0.220547
\(245\) 0 0
\(246\) 0 0
\(247\) 0.444368 0.769668i 0.0282745 0.0489728i
\(248\) 13.1978 0.838059
\(249\) 0 0
\(250\) 17.5426 1.10949
\(251\) 4.62041 0.291638 0.145819 0.989311i \(-0.453418\pi\)
0.145819 + 0.989311i \(0.453418\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) −16.9752 −1.06512
\(255\) 0 0
\(256\) 17.7417 1.10886
\(257\) 0.712008 1.23323i 0.0444138 0.0769270i −0.842964 0.537970i \(-0.819191\pi\)
0.887378 + 0.461043i \(0.152525\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.18911 0.197780
\(261\) 0 0
\(262\) 13.6421 23.6289i 0.842814 1.45980i
\(263\) 8.13162 + 14.0844i 0.501417 + 0.868480i 0.999999 + 0.00163692i \(0.000521048\pi\)
−0.498582 + 0.866843i \(0.666146\pi\)
\(264\) 0 0
\(265\) 0.221840 + 0.384237i 0.0136275 + 0.0236035i
\(266\) 0 0
\(267\) 0 0
\(268\) 10.9395 0.668235
\(269\) 9.32691 16.1547i 0.568672 0.984969i −0.428026 0.903767i \(-0.640791\pi\)
0.996698 0.0812022i \(-0.0258759\pi\)
\(270\) 0 0
\(271\) 1.98143 + 3.43194i 0.120363 + 0.208475i 0.919911 0.392127i \(-0.128261\pi\)
−0.799548 + 0.600603i \(0.794927\pi\)
\(272\) −10.2527 + 17.7582i −0.621662 + 1.07675i
\(273\) 0 0
\(274\) 11.0371 + 19.1168i 0.666773 + 1.15489i
\(275\) −11.0698 + 19.1734i −0.667534 + 1.15620i
\(276\) 0 0
\(277\) 1.16690 + 2.02112i 0.0701120 + 0.121438i 0.898950 0.438051i \(-0.144331\pi\)
−0.828838 + 0.559488i \(0.810998\pi\)
\(278\) −0.944368 1.63569i −0.0566394 0.0981024i
\(279\) 0 0
\(280\) 0 0
\(281\) 13.9975 24.2443i 0.835018 1.44629i −0.0589978 0.998258i \(-0.518790\pi\)
0.894016 0.448035i \(-0.147876\pi\)
\(282\) 0 0
\(283\) −10.3200 −0.613462 −0.306731 0.951796i \(-0.599235\pi\)
−0.306731 + 0.951796i \(0.599235\pi\)
\(284\) 2.55632 0.151690
\(285\) 0 0
\(286\) −2.38874 + 4.13741i −0.141249 + 0.244650i
\(287\) 0 0
\(288\) 0 0
\(289\) 0.0487535 + 0.0844436i 0.00286785 + 0.00496727i
\(290\) −5.18292 8.97708i −0.304351 0.527152i
\(291\) 0 0
\(292\) −4.72872 + 8.19038i −0.276727 + 0.479306i
\(293\) 15.3480 + 26.5834i 0.896637 + 1.55302i 0.831765 + 0.555127i \(0.187330\pi\)
0.0648718 + 0.997894i \(0.479336\pi\)
\(294\) 0 0
\(295\) −15.9258 + 27.5843i −0.927236 + 1.60602i
\(296\) −4.50000 7.79423i −0.261557 0.453030i
\(297\) 0 0
\(298\) −7.16621 + 12.4122i −0.415127 + 0.719021i
\(299\) 5.87636 0.339838
\(300\) 0 0
\(301\) 0 0
\(302\) −12.6211 21.8604i −0.726262 1.25792i
\(303\) 0 0
\(304\) 2.21634 + 3.83881i 0.127116 + 0.220171i
\(305\) −6.95489 + 12.0462i −0.398236 + 0.689765i
\(306\) 0 0
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −21.3083 + 36.9071i −1.21023 + 2.09618i
\(311\) 11.9629 0.678352 0.339176 0.940723i \(-0.389852\pi\)
0.339176 + 0.940723i \(0.389852\pi\)
\(312\) 0 0
\(313\) 13.5439 0.765549 0.382774 0.923842i \(-0.374969\pi\)
0.382774 + 0.923842i \(0.374969\pi\)
\(314\) 4.90978 0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) 29.9629 1.68288 0.841441 0.540349i \(-0.181708\pi\)
0.841441 + 0.540349i \(0.181708\pi\)
\(318\) 0 0
\(319\) 4.77747 0.267487
\(320\) 3.56615 6.17676i 0.199354 0.345291i
\(321\) 0 0
\(322\) 0 0
\(323\) −3.65383 −0.203304
\(324\) 0 0
\(325\) 3.93818 6.82112i 0.218451 0.378368i
\(326\) −8.76076 15.1741i −0.485214 0.840415i
\(327\) 0 0
\(328\) 5.11058 + 8.85178i 0.282184 + 0.488758i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.08650 0.114685 0.0573423 0.998355i \(-0.481737\pi\)
0.0573423 + 0.998355i \(0.481737\pi\)
\(332\) 1.82691 3.16431i 0.100265 0.173664i
\(333\) 0 0
\(334\) 10.3269 + 17.8867i 0.565064 + 0.978719i
\(335\) 22.0846 38.2517i 1.20661 2.08992i
\(336\) 0 0
\(337\) 8.10439 + 14.0372i 0.441474 + 0.764655i 0.997799 0.0663093i \(-0.0211224\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(338\) −10.1978 + 17.6631i −0.554686 + 0.960743i
\(339\) 0 0
\(340\) −6.55563 11.3547i −0.355529 0.615794i
\(341\) −9.82072 17.0100i −0.531822 0.921143i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.92030 + 8.52220i −0.265285 + 0.459486i
\(345\) 0 0
\(346\) 11.2335 0.603918
\(347\) −11.2670 −0.604842 −0.302421 0.953175i \(-0.597795\pi\)
−0.302421 + 0.953175i \(0.597795\pi\)
\(348\) 0 0
\(349\) −0.0988844 + 0.171273i −0.00529316 + 0.00916803i −0.868660 0.495409i \(-0.835018\pi\)
0.863367 + 0.504577i \(0.168352\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6.60507 11.4403i −0.352052 0.609771i
\(353\) 6.25093 + 10.8269i 0.332703 + 0.576259i 0.983041 0.183386i \(-0.0587059\pi\)
−0.650338 + 0.759645i \(0.725373\pi\)
\(354\) 0 0
\(355\) 5.16071 8.93861i 0.273902 0.474412i
\(356\) −4.27011 7.39605i −0.226315 0.391990i
\(357\) 0 0
\(358\) 3.26578 5.65650i 0.172602 0.298955i
\(359\) 10.0098 + 17.3375i 0.528299 + 0.915040i 0.999456 + 0.0329908i \(0.0105032\pi\)
−0.471157 + 0.882049i \(0.656163\pi\)
\(360\) 0 0
\(361\) 9.10507 15.7705i 0.479214 0.830024i
\(362\) 31.5155 1.65642
\(363\) 0 0
\(364\) 0 0
\(365\) 19.0927 + 33.0695i 0.999357 + 1.73094i
\(366\) 0 0
\(367\) 15.0364 + 26.0438i 0.784892 + 1.35947i 0.929063 + 0.369921i \(0.120615\pi\)
−0.144171 + 0.989553i \(0.546052\pi\)
\(368\) −14.6545 + 25.3824i −0.763919 + 1.32315i
\(369\) 0 0
\(370\) 29.0617 1.51085
\(371\) 0 0
\(372\) 0 0
\(373\) −3.50619 + 6.07290i −0.181544 + 0.314443i −0.942406 0.334470i \(-0.891443\pi\)
0.760863 + 0.648913i \(0.224776\pi\)
\(374\) 19.6414 1.01564
\(375\) 0 0
\(376\) −5.03576 −0.259700
\(377\) −1.69963 −0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) −2.83427 −0.145395
\(381\) 0 0
\(382\) 7.87636 0.402989
\(383\) −1.60507 + 2.78007i −0.0820155 + 0.142055i −0.904116 0.427288i \(-0.859469\pi\)
0.822100 + 0.569343i \(0.192802\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 42.9949 2.18838
\(387\) 0 0
\(388\) 3.25340 5.63506i 0.165166 0.286077i
\(389\) 2.56801 + 4.44793i 0.130203 + 0.225519i 0.923755 0.382984i \(-0.125104\pi\)
−0.793552 + 0.608503i \(0.791770\pi\)
\(390\) 0 0
\(391\) −12.0796 20.9225i −0.610893 1.05810i
\(392\) 0 0
\(393\) 0 0
\(394\) 18.2212 0.917968
\(395\) −12.7145 + 22.0221i −0.639735 + 1.10805i
\(396\) 0 0
\(397\) 11.4691 + 19.8650i 0.575615 + 0.996995i 0.995975 + 0.0896370i \(0.0285707\pi\)
−0.420359 + 0.907358i \(0.638096\pi\)
\(398\) 7.44987 12.9036i 0.373428 0.646797i
\(399\) 0 0
\(400\) 19.6421 + 34.0212i 0.982107 + 1.70106i
\(401\) −9.10507 + 15.7705i −0.454686 + 0.787539i −0.998670 0.0515566i \(-0.983582\pi\)
0.543984 + 0.839095i \(0.316915\pi\)
\(402\) 0 0
\(403\) 3.49381 + 6.05146i 0.174039 + 0.301445i
\(404\) −1.53961 2.66668i −0.0765985 0.132672i
\(405\) 0 0
\(406\) 0 0
\(407\) −6.69708 + 11.5997i −0.331962 + 0.574975i
\(408\) 0 0
\(409\) 15.3324 0.758139 0.379070 0.925368i \(-0.376244\pi\)
0.379070 + 0.925368i \(0.376244\pi\)
\(410\) −33.0049 −1.63000
\(411\) 0 0
\(412\) −7.05494 + 12.2195i −0.347572 + 0.602013i
\(413\) 0 0
\(414\) 0 0
\(415\) −7.37636 12.7762i −0.362091 0.627160i
\(416\) 2.34981 + 4.07000i 0.115209 + 0.199548i
\(417\) 0 0
\(418\) 2.12296 3.67707i 0.103837 0.179851i
\(419\) −5.28435 9.15276i −0.258157 0.447142i 0.707591 0.706622i \(-0.249782\pi\)
−0.965748 + 0.259481i \(0.916449\pi\)
\(420\) 0 0
\(421\) 18.0858 31.3256i 0.881449 1.52671i 0.0317181 0.999497i \(-0.489902\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(422\) 8.94870 + 15.4996i 0.435616 + 0.754509i
\(423\) 0 0
\(424\) −0.116765 + 0.202243i −0.00567062 + 0.00982181i
\(425\) −32.3818 −1.57075
\(426\) 0 0
\(427\) 0 0
\(428\) −2.37890 4.12038i −0.114989 0.199166i
\(429\) 0 0
\(430\) −15.8880 27.5189i −0.766190 1.32708i
\(431\) 17.5494 30.3965i 0.845327 1.46415i −0.0400101 0.999199i \(-0.512739\pi\)
0.885337 0.464950i \(-0.153928\pi\)
\(432\) 0 0
\(433\) 41.1730 1.97865 0.989324 0.145731i \(-0.0465533\pi\)
0.989324 + 0.145731i \(0.0465533\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 8.38255 14.5190i 0.401451 0.695334i
\(437\) −5.22253 −0.249827
\(438\) 0 0
\(439\) 4.67859 0.223297 0.111648 0.993748i \(-0.464387\pi\)
0.111648 + 0.993748i \(0.464387\pi\)
\(440\) −19.0507 −0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) −30.1730 −1.43356 −0.716781 0.697298i \(-0.754385\pi\)
−0.716781 + 0.697298i \(0.754385\pi\)
\(444\) 0 0
\(445\) −34.4820 −1.63461
\(446\) 4.81639 8.34224i 0.228063 0.395016i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.333792 −0.0157526 −0.00787632 0.999969i \(-0.502507\pi\)
−0.00787632 + 0.999969i \(0.502507\pi\)
\(450\) 0 0
\(451\) 7.60576 13.1736i 0.358141 0.620319i
\(452\) −8.24357 14.2783i −0.387745 0.671594i
\(453\) 0 0
\(454\) −9.43199 16.3367i −0.442665 0.766719i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.3090 −0.903238 −0.451619 0.892211i \(-0.649153\pi\)
−0.451619 + 0.892211i \(0.649153\pi\)
\(458\) −16.6927 + 28.9127i −0.780001 + 1.35100i
\(459\) 0 0
\(460\) −9.37017 16.2296i −0.436886 0.756709i
\(461\) −19.5538 + 33.8681i −0.910710 + 1.57740i −0.0976463 + 0.995221i \(0.531131\pi\)
−0.813064 + 0.582175i \(0.802202\pi\)
\(462\) 0 0
\(463\) −10.9382 18.9455i −0.508340 0.880471i −0.999953 0.00965741i \(-0.996926\pi\)
0.491613 0.870814i \(-0.336407\pi\)
\(464\) 4.23855 7.34138i 0.196770 0.340815i
\(465\) 0 0
\(466\) −7.61677 13.1926i −0.352840 0.611137i
\(467\) 6.16002 + 10.6695i 0.285052 + 0.493724i 0.972622 0.232394i \(-0.0746559\pi\)
−0.687570 + 0.726118i \(0.741323\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.13045 14.0823i 0.375029 0.649570i
\(471\) 0 0
\(472\) −16.7651 −0.771676
\(473\) 14.6452 0.673385
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) −9.53706 16.5187i −0.436215 0.755547i
\(479\) −6.74474 11.6822i −0.308175 0.533775i 0.669788 0.742552i \(-0.266385\pi\)
−0.977963 + 0.208777i \(0.933052\pi\)
\(480\) 0 0
\(481\) 2.38255 4.12669i 0.108635 0.188161i
\(482\) 5.93701 + 10.2832i 0.270423 + 0.468387i
\(483\) 0 0
\(484\) 1.37704 2.38511i 0.0625929 0.108414i
\(485\) −13.1359 22.7521i −0.596473 1.03312i
\(486\) 0 0
\(487\) −3.77197 + 6.53324i −0.170924 + 0.296050i −0.938743 0.344617i \(-0.888009\pi\)
0.767819 + 0.640667i \(0.221342\pi\)
\(488\) −7.32141 −0.331425
\(489\) 0 0
\(490\) 0 0
\(491\) −8.06979 13.9773i −0.364185 0.630786i 0.624460 0.781057i \(-0.285319\pi\)
−0.988645 + 0.150270i \(0.951986\pi\)
\(492\) 0 0
\(493\) 3.49381 + 6.05146i 0.157353 + 0.272544i
\(494\) −0.755260 + 1.30815i −0.0339808 + 0.0588564i
\(495\) 0 0
\(496\) −34.8516 −1.56488
\(497\) 0 0
\(498\) 0 0
\(499\) 15.4327 26.7302i 0.690862 1.19661i −0.280694 0.959797i \(-0.590565\pi\)
0.971556 0.236810i \(-0.0761019\pi\)
\(500\) −9.17301 −0.410229
\(501\) 0 0
\(502\) −7.85297 −0.350495
\(503\) 24.6304 1.09822 0.549109 0.835751i \(-0.314967\pi\)
0.549109 + 0.835751i \(0.314967\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) 28.0741 1.24805
\(507\) 0 0
\(508\) 8.87636 0.393825
\(509\) −6.79487 + 11.7691i −0.301177 + 0.521654i −0.976403 0.215957i \(-0.930713\pi\)
0.675226 + 0.737611i \(0.264046\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −4.59937 −0.203265
\(513\) 0 0
\(514\) −1.21015 + 2.09604i −0.0533774 + 0.0924523i
\(515\) 28.4851 + 49.3376i 1.25520 + 2.17407i
\(516\) 0 0
\(517\) 3.74721 + 6.49036i 0.164802 + 0.285446i
\(518\) 0 0
\(519\) 0 0
\(520\) 6.77747 0.297212
\(521\) 19.5865 33.9248i 0.858100 1.48627i −0.0156383 0.999878i \(-0.504978\pi\)
0.873739 0.486396i \(-0.161689\pi\)
\(522\) 0 0
\(523\) 9.56182 + 16.5616i 0.418109 + 0.724187i 0.995749 0.0921051i \(-0.0293596\pi\)
−0.577640 + 0.816292i \(0.696026\pi\)
\(524\) −7.13348 + 12.3555i −0.311627 + 0.539754i
\(525\) 0 0
\(526\) −13.8207 23.9382i −0.602612 1.04375i
\(527\) 14.3640 24.8791i 0.625705 1.08375i
\(528\) 0 0
\(529\) −5.76578 9.98663i −0.250686 0.434201i
\(530\) −0.377045 0.653061i −0.0163778 0.0283671i
\(531\) 0 0
\(532\) 0 0
\(533\) −2.70582 + 4.68661i −0.117202 + 0.203000i
\(534\) 0 0
\(535\) −19.2101 −0.830527
\(536\) 23.2485 1.00418
\(537\) 0 0
\(538\) −15.8523 + 27.4570i −0.683441 + 1.18375i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.26509 2.19120i −0.0543906 0.0942072i 0.837548 0.546363i \(-0.183988\pi\)
−0.891939 + 0.452156i \(0.850655\pi\)
\(542\) −3.36769 5.83302i −0.144655 0.250550i
\(543\) 0 0
\(544\) 9.66071 16.7328i 0.414199 0.717414i
\(545\) −33.8454 58.6220i −1.44978 2.51109i
\(546\) 0 0
\(547\) −8.92580 + 15.4599i −0.381640 + 0.661019i −0.991297 0.131646i \(-0.957974\pi\)
0.609657 + 0.792665i \(0.291307\pi\)
\(548\) −5.77128 9.99615i −0.246537 0.427015i
\(549\) 0 0
\(550\) 18.8145 32.5877i 0.802254 1.38955i
\(551\) 1.51052 0.0643503
\(552\) 0 0
\(553\) 0 0
\(554\) −1.98329 3.43516i −0.0842619 0.145946i
\(555\) 0 0
\(556\) 0.493810 + 0.855304i 0.0209422 + 0.0362730i
\(557\) 20.6804 35.8195i 0.876255 1.51772i 0.0208360 0.999783i \(-0.493367\pi\)
0.855419 0.517936i \(-0.173299\pi\)
\(558\) 0 0
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 0 0
\(562\) −23.7905 + 41.2063i −1.00354 + 1.73818i
\(563\) −20.7366 −0.873944 −0.436972 0.899475i \(-0.643949\pi\)
−0.436972 + 0.899475i \(0.643949\pi\)
\(564\) 0 0
\(565\) −66.5685 −2.80056
\(566\) 17.5402 0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) 0.268329 0.0112489 0.00562446 0.999984i \(-0.498210\pi\)
0.00562446 + 0.999984i \(0.498210\pi\)
\(570\) 0 0
\(571\) 35.9367 1.50391 0.751953 0.659217i \(-0.229112\pi\)
0.751953 + 0.659217i \(0.229112\pi\)
\(572\) 1.24907 2.16345i 0.0522263 0.0904585i
\(573\) 0 0
\(574\) 0 0
\(575\) −46.2843 −1.93019
\(576\) 0 0
\(577\) 2.71565 4.70364i 0.113054 0.195815i −0.803946 0.594702i \(-0.797270\pi\)
0.917000 + 0.398887i \(0.130603\pi\)
\(578\) −0.0828628 0.143523i −0.00344664 0.00596976i
\(579\) 0 0
\(580\) 2.71015 + 4.69412i 0.112533 + 0.194913i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.347550 0.0143940
\(584\) −10.0494 + 17.4061i −0.415849 + 0.720271i
\(585\) 0 0
\(586\) −26.0858 45.1820i −1.07760 1.86645i
\(587\) −17.5822 + 30.4532i −0.725694 + 1.25694i 0.232994 + 0.972478i \(0.425148\pi\)
−0.958688 + 0.284461i \(0.908185\pi\)
\(588\) 0 0
\(589\) −3.10507 5.37815i −0.127942 0.221603i
\(590\) 27.0679 46.8830i 1.11437 1.93014i
\(591\) 0 0
\(592\) 11.8832 + 20.5824i 0.488398 + 0.845930i
\(593\) 16.7534 + 29.0177i 0.687980 + 1.19162i 0.972490 + 0.232943i \(0.0748355\pi\)
−0.284511 + 0.958673i \(0.591831\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.74721 6.49036i 0.153492 0.265856i
\(597\) 0 0
\(598\) −9.98762 −0.408424
\(599\) −6.24729 −0.255257 −0.127629 0.991822i \(-0.540737\pi\)
−0.127629 + 0.991822i \(0.540737\pi\)
\(600\) 0 0
\(601\) 11.2040 19.4058i 0.457019 0.791580i −0.541783 0.840519i \(-0.682250\pi\)
0.998802 + 0.0489384i \(0.0155838\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 6.59957 + 11.4308i 0.268533 + 0.465112i
\(605\) −5.55996 9.63014i −0.226045 0.391521i
\(606\) 0 0
\(607\) 7.47524 12.9475i 0.303411 0.525523i −0.673496 0.739191i \(-0.735208\pi\)
0.976906 + 0.213669i \(0.0685413\pi\)
\(608\) −2.08836 3.61715i −0.0846943 0.146695i
\(609\) 0 0
\(610\) 11.8207 20.4741i 0.478607 0.828972i
\(611\) −1.33310 2.30900i −0.0539316 0.0934123i
\(612\) 0 0
\(613\) −17.5989 + 30.4822i −0.710812 + 1.23116i 0.253740 + 0.967272i \(0.418339\pi\)
−0.964553 + 0.263891i \(0.914994\pi\)
\(614\) −19.4500 −0.784938
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00619 1.74277i −0.0405077 0.0701614i 0.845061 0.534670i \(-0.179564\pi\)
−0.885568 + 0.464509i \(0.846231\pi\)
\(618\) 0 0
\(619\) 19.6909 + 34.1056i 0.791444 + 1.37082i 0.925073 + 0.379789i \(0.124004\pi\)
−0.133629 + 0.991031i \(0.542663\pi\)
\(620\) 11.1421 19.2987i 0.447479 0.775056i
\(621\) 0 0
\(622\) −20.3324 −0.815256
\(623\) 0 0
\(624\) 0 0
\(625\) 1.17240 2.03065i 0.0468959 0.0812261i
\(626\) −23.0197 −0.920051
\(627\) 0 0
\(628\) −2.56732 −0.102447
\(629\) −19.5906 −0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) −13.3845 −0.532408
\(633\) 0 0
\(634\) −50.9257 −2.02252
\(635\) 17.9196 31.0377i 0.711118 1.23169i
\(636\) 0 0
\(637\) 0 0
\(638\) −8.11993 −0.321471
\(639\) 0 0
\(640\) −22.9251 + 39.7075i −0.906195 + 1.56957i
\(641\) −7.49312 12.9785i −0.295961 0.512619i 0.679247 0.733909i \(-0.262306\pi\)
−0.975208 + 0.221291i \(0.928973\pi\)
\(642\) 0 0
\(643\) −5.32691 9.22649i −0.210073 0.363857i 0.741664 0.670771i \(-0.234037\pi\)
−0.951737 + 0.306914i \(0.900703\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.21015 0.244335
\(647\) −1.06478 + 1.84424i −0.0418606 + 0.0725047i −0.886197 0.463309i \(-0.846662\pi\)
0.844336 + 0.535814i \(0.179995\pi\)
\(648\) 0 0
\(649\) 12.4752 + 21.6078i 0.489696 + 0.848178i
\(650\) −6.69344 + 11.5934i −0.262538 + 0.454730i
\(651\) 0 0
\(652\) 4.58100 + 7.93453i 0.179406 + 0.310740i
\(653\) 5.58582 9.67492i 0.218590 0.378609i −0.735787 0.677213i \(-0.763188\pi\)
0.954377 + 0.298604i \(0.0965210\pi\)
\(654\) 0 0
\(655\) 28.8022 + 49.8868i 1.12539 + 1.94924i
\(656\) −13.4956 23.3751i −0.526914 0.912642i
\(657\) 0 0
\(658\) 0 0
\(659\) −5.65452 + 9.79391i −0.220269 + 0.381517i −0.954890 0.296961i \(-0.904027\pi\)
0.734621 + 0.678478i \(0.237360\pi\)
\(660\) 0 0
\(661\) −32.3570 −1.25854 −0.629271 0.777186i \(-0.716646\pi\)
−0.629271 + 0.777186i \(0.716646\pi\)
\(662\) −3.54628 −0.137830
\(663\) 0 0
\(664\) 3.88255 6.72477i 0.150672 0.260972i
\(665\) 0 0
\(666\) 0 0
\(667\) 4.99381 + 8.64953i 0.193361 + 0.334911i
\(668\) −5.39995 9.35298i −0.208930 0.361878i
\(669\) 0 0
\(670\) −37.5357 + 65.0137i −1.45013 + 2.51170i
\(671\) 5.44801 + 9.43623i 0.210318 + 0.364282i
\(672\) 0 0
\(673\) 12.0803 20.9237i 0.465662 0.806550i −0.533569 0.845756i \(-0.679150\pi\)
0.999231 + 0.0392063i \(0.0124830\pi\)
\(674\) −13.7744 23.8580i −0.530572 0.918977i
\(675\) 0 0
\(676\) 5.33242 9.23601i 0.205093 0.355231i
\(677\) 25.0741 0.963677 0.481838 0.876260i \(-0.339969\pi\)
0.481838 + 0.876260i \(0.339969\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −13.9320 24.1309i −0.534267 0.925378i
\(681\) 0 0
\(682\) 16.6916 + 28.9107i 0.639154 + 1.10705i
\(683\) −23.8392 + 41.2907i −0.912182 + 1.57995i −0.101207 + 0.994865i \(0.532271\pi\)
−0.810975 + 0.585081i \(0.801063\pi\)
\(684\) 0 0
\(685\) −46.6043 −1.78066
\(686\) 0 0
\(687\) 0 0
\(688\) 12.9931 22.5047i 0.495358 0.857985i
\(689\) −0.123644 −0.00471046
\(690\) 0 0
\(691\) 24.6800 0.938870 0.469435 0.882967i \(-0.344458\pi\)
0.469435 + 0.882967i \(0.344458\pi\)
\(692\) −5.87402 −0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) 3.98762 0.151259
\(696\) 0 0
\(697\) 22.2487 0.842728
\(698\) 0.168067 0.291100i 0.00636142 0.0110183i
\(699\) 0 0
\(700\) 0 0
\(701\) 29.6784 1.12094 0.560469 0.828175i \(-0.310621\pi\)
0.560469 + 0.828175i \(0.310621\pi\)
\(702\) 0 0
\(703\) −2.11745 + 3.66754i −0.0798613 + 0.138324i
\(704\) −2.79349 4.83847i −0.105284 0.182357i
\(705\) 0 0
\(706\) −10.6243 18.4018i −0.399849 0.692559i
\(707\) 0 0
\(708\) 0 0
\(709\) −29.2581 −1.09881 −0.549406 0.835555i \(-0.685146\pi\)
−0.549406 + 0.835555i \(0.685146\pi\)
\(710\) −8.77128 + 15.1923i −0.329180 + 0.570157i
\(711\) 0 0
\(712\) −9.07481 15.7180i −0.340093 0.589058i
\(713\) 20.5309 35.5605i 0.768887 1.33175i
\(714\) 0 0
\(715\) −5.04325 8.73517i −0.188607 0.326677i
\(716\) −1.70768 + 2.95778i −0.0638189 + 0.110538i
\(717\) 0 0
\(718\) −17.0130 29.4674i −0.634919 1.09971i
\(719\) −0.537063 0.930220i −0.0200291 0.0346913i 0.855837 0.517245i \(-0.173043\pi\)
−0.875866 + 0.482554i \(0.839709\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.4752 + 26.8039i −0.575929 + 0.997538i
\(723\) 0 0
\(724\) −16.4794 −0.612454
\(725\) 13.3869 0.497176
\(726\) 0 0
\(727\) 12.7163 22.0253i 0.471623 0.816875i −0.527850 0.849338i \(-0.677002\pi\)
0.999473 + 0.0324628i \(0.0103350\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −32.4505 56.2059i −1.20105 2.08027i
\(731\) 10.7101 + 18.5505i 0.396129 + 0.686116i
\(732\) 0 0
\(733\) −5.69777 + 9.86883i −0.210452 + 0.364513i −0.951856 0.306545i \(-0.900827\pi\)
0.741404 + 0.671059i \(0.234160\pi\)
\(734\) −25.5562 44.2647i −0.943298 1.63384i
\(735\) 0 0
\(736\) 13.8083 23.9168i 0.508982 0.881583i
\(737\) −17.2997 29.9639i −0.637242 1.10374i
\(738\) 0 0
\(739\) 14.9697 25.9283i 0.550671 0.953790i −0.447556 0.894256i \(-0.647705\pi\)
0.998226 0.0595336i \(-0.0189613\pi\)
\(740\) −15.1964 −0.558630
\(741\) 0 0
\(742\) 0 0
\(743\) −9.50069 16.4557i −0.348546 0.603700i 0.637445 0.770496i \(-0.279991\pi\)
−0.985991 + 0.166796i \(0.946658\pi\)
\(744\) 0 0
\(745\) −15.1298 26.2055i −0.554311 0.960096i
\(746\) 5.95922 10.3217i 0.218183 0.377903i
\(747\) 0 0
\(748\) −10.2705 −0.375527
\(749\) 0 0
\(750\) 0 0
\(751\) −0.0130684 + 0.0226352i −0.000476873 + 0.000825969i −0.866264 0.499587i \(-0.833485\pi\)
0.865787 + 0.500413i \(0.166818\pi\)
\(752\) 13.2980 0.484929
\(753\) 0 0
\(754\) 2.88874 0.105202
\(755\) 53.2929 1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) 32.4189 1.17751
\(759\) 0 0
\(760\) −6.02338 −0.218491
\(761\) 7.32141 12.6811i 0.265401 0.459688i −0.702268 0.711913i \(-0.747829\pi\)
0.967669 + 0.252225i \(0.0811623\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4.11855 −0.149004
\(765\) 0 0
\(766\) 2.72803 4.72509i 0.0985677 0.170724i
\(767\) −4.43818 7.68715i −0.160253 0.277567i
\(768\) 0 0
\(769\) 24.5672 + 42.5517i 0.885918 + 1.53445i 0.844658 + 0.535306i \(0.179804\pi\)
0.0412592 + 0.999148i \(0.486863\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −22.4820 −0.809146
\(773\) −6.22067 + 10.7745i −0.223742 + 0.387532i −0.955941 0.293558i \(-0.905161\pi\)
0.732199 + 0.681090i \(0.238494\pi\)
\(774\) 0 0
\(775\) −27.5185 47.6634i −0.988493 1.71212i
\(776\) 6.91411 11.9756i 0.248202 0.429898i
\(777\) 0 0
\(778\) −4.36467 7.55982i −0.156481 0.271033i
\(779\) 2.40476 4.16516i 0.0861594 0.149232i
\(780\) 0 0
\(781\) −4.04256 7.00193i −0.144654 0.250549i
\(782\) 20.5309 + 35.5605i 0.734183 + 1.27164i
\(783\) 0 0
\(784\) 0 0
\(785\) −5.18292 + 8.97708i −0.184986 + 0.320406i
\(786\) 0 0
\(787\) 32.9133