Properties

Label 441.2.g.e.79.1
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
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] = [441,2,Mod(67,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (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: \(3.52140272914\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.e.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.849814 - 1.47192i) q^{2} +(-1.64400 + 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} -3.58836 q^{5} +(2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})\) \(q+(-0.849814 - 1.47192i) q^{2} +(-1.64400 + 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} -3.58836 q^{5} +(2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +(3.04944 + 5.28179i) q^{10} -2.81089 q^{11} +(0.310892 - 1.50761i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(5.89926 - 1.95649i) q^{15} +(2.49381 + 4.31941i) q^{16} +(2.05563 + 3.56046i) q^{17} +(-4.68292 - 2.01715i) q^{18} +(0.444368 - 0.769668i) q^{19} +(1.59455 - 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +5.87636 q^{23} +(3.10507 - 1.02980i) q^{24} +7.87636 q^{25} +(-0.849814 + 1.47192i) q^{26} +(-2.97710 + 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-7.89307 - 7.02059i) q^{30} +(3.49381 - 6.05146i) q^{31} +(2.34981 - 4.07000i) q^{32} +(4.62110 - 1.53259i) q^{33} +(3.49381 - 6.05146i) q^{34} +(0.310892 + 2.64802i) q^{36} +(-2.38255 + 4.12669i) q^{37} -1.51052 q^{38} +(1.29418 + 1.15113i) q^{39} +6.77747 q^{40} +(2.70582 + 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +(1.24907 - 2.16345i) q^{44} +(-8.63162 + 6.43292i) q^{45} +(-4.99381 - 8.64953i) q^{46} +(1.33310 + 2.30900i) q^{47} +(-6.45489 - 5.74138i) q^{48} +(-6.69344 - 11.5934i) q^{50} +(-5.32072 - 4.73259i) q^{51} +0.888736 q^{52} +(0.0618219 + 0.107079i) q^{53} +(8.79851 + 0.762918i) q^{54} +10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} -2.88874 q^{58} +(4.43818 - 7.68715i) q^{59} +(-1.11559 + 5.40987i) q^{60} +(-1.93818 - 3.35702i) q^{61} -11.8764 q^{62} +1.98762 q^{64} +(1.79418 + 3.10761i) q^{65} +(-6.18292 - 5.49948i) q^{66} +(-6.15452 + 10.6599i) q^{67} -3.65383 q^{68} +(-9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-4.54325 + 3.38597i) q^{72} +(5.32072 + 9.21576i) q^{73} +8.09888 q^{74} +(-12.9487 + 4.29443i) q^{75} +(0.394926 + 0.684031i) q^{76} +(0.594554 - 2.88318i) q^{78} +(3.54325 + 6.13709i) q^{79} +(-8.94870 - 15.4996i) q^{80} +(2.57234 - 8.62456i) q^{81} +(4.59888 - 7.96550i) q^{82} +(2.05563 - 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +8.85532 q^{86} +(-0.594554 + 2.88318i) q^{87} +5.30903 q^{88} +(-4.80470 + 8.32199i) q^{89} +(16.8040 + 7.23828i) q^{90} +(-2.61126 + 4.52284i) q^{92} +(-2.44437 + 11.8535i) q^{93} +(2.26578 - 3.92445i) q^{94} +(-1.59455 + 2.76185i) q^{95} +(-1.64400 + 7.97225i) q^{96} +(-3.66071 + 6.34053i) q^{97} +(-6.76145 + 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} - 11 q^{12} - 3 q^{13} + 11 q^{15} - 3 q^{16} + 12 q^{17} - 23 q^{18} + 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} - 7 q^{27} - q^{29} - 5 q^{30} + 3 q^{31} + 8 q^{32} + 5 q^{33} + 3 q^{34} - 11 q^{36} + 3 q^{37} + 16 q^{38} + 2 q^{39} + 42 q^{40} + 22 q^{41} + 3 q^{43} - 23 q^{44} - 4 q^{45} - 12 q^{46} + 9 q^{47} - 14 q^{48} - 10 q^{50} + 3 q^{51} + 6 q^{52} + 18 q^{53} + 4 q^{54} - 12 q^{55} + 11 q^{57} - 18 q^{58} + 9 q^{59} + 37 q^{60} + 6 q^{61} - 36 q^{62} - 24 q^{64} + 5 q^{65} - 32 q^{66} + 12 q^{68} - 39 q^{69} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 12 q^{74} - 35 q^{75} + 21 q^{76} + 10 q^{78} - 15 q^{79} - 11 q^{80} + 8 q^{81} - 9 q^{82} + 12 q^{83} - 9 q^{85} + 68 q^{86} - 10 q^{87} - 42 q^{88} + 2 q^{89} + 73 q^{90} - 15 q^{92} - 15 q^{93} - 24 q^{94} - 16 q^{95} + 2 q^{96} - 3 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.849814 1.47192i −0.600909 1.04081i −0.992684 0.120744i \(-0.961472\pi\)
0.391774 0.920061i \(-0.371861\pi\)
\(3\) −1.64400 + 0.545231i −0.949162 + 0.314789i
\(4\) −0.444368 + 0.769668i −0.222184 + 0.384834i
\(5\) −3.58836 −1.60477 −0.802383 0.596810i \(-0.796435\pi\)
−0.802383 + 0.596810i \(0.796435\pi\)
\(6\) 2.19963 + 1.95649i 0.897994 + 0.798733i
\(7\) 0 0
\(8\) −1.88874 −0.667769
\(9\) 2.40545 1.79272i 0.801815 0.597572i
\(10\) 3.04944 + 5.28179i 0.964318 + 1.67025i
\(11\) −2.81089 −0.847516 −0.423758 0.905775i \(-0.639289\pi\)
−0.423758 + 0.905775i \(0.639289\pi\)
\(12\) 0.310892 1.50761i 0.0897469 0.435211i
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 5.89926 1.95649i 1.52318 0.505163i
\(16\) 2.49381 + 4.31941i 0.623453 + 1.07985i
\(17\) 2.05563 + 3.56046i 0.498564 + 0.863538i 0.999999 0.00165734i \(-0.000527549\pi\)
−0.501435 + 0.865196i \(0.667194\pi\)
\(18\) −4.68292 2.01715i −1.10377 0.475447i
\(19\) 0.444368 0.769668i 0.101945 0.176574i −0.810541 0.585682i \(-0.800827\pi\)
0.912486 + 0.409108i \(0.134160\pi\)
\(20\) 1.59455 2.76185i 0.356553 0.617568i
\(21\) 0 0
\(22\) 2.38874 + 4.13741i 0.509280 + 0.882099i
\(23\) 5.87636 1.22530 0.612652 0.790352i \(-0.290103\pi\)
0.612652 + 0.790352i \(0.290103\pi\)
\(24\) 3.10507 1.02980i 0.633821 0.210207i
\(25\) 7.87636 1.57527
\(26\) −0.849814 + 1.47192i −0.166662 + 0.288667i
\(27\) −2.97710 + 4.25874i −0.572943 + 0.819595i
\(28\) 0 0
\(29\) 0.849814 1.47192i 0.157807 0.273329i −0.776271 0.630399i \(-0.782891\pi\)
0.934077 + 0.357071i \(0.116224\pi\)
\(30\) −7.89307 7.02059i −1.44107 1.28178i
\(31\) 3.49381 6.05146i 0.627507 1.08687i −0.360544 0.932742i \(-0.617409\pi\)
0.988050 0.154131i \(-0.0492579\pi\)
\(32\) 2.34981 4.07000i 0.415392 0.719481i
\(33\) 4.62110 1.53259i 0.804430 0.266789i
\(34\) 3.49381 6.05146i 0.599183 1.03782i
\(35\) 0 0
\(36\) 0.310892 + 2.64802i 0.0518154 + 0.441337i
\(37\) −2.38255 + 4.12669i −0.391688 + 0.678424i −0.992672 0.120837i \(-0.961442\pi\)
0.600984 + 0.799261i \(0.294775\pi\)
\(38\) −1.51052 −0.245039
\(39\) 1.29418 + 1.15113i 0.207235 + 0.184328i
\(40\) 6.77747 1.07161
\(41\) 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
\(45\) −8.63162 + 6.43292i −1.28673 + 0.958962i
\(46\) −4.99381 8.64953i −0.736297 1.27530i
\(47\) 1.33310 + 2.30900i 0.194453 + 0.336803i 0.946721 0.322055i \(-0.104373\pi\)
−0.752268 + 0.658857i \(0.771040\pi\)
\(48\) −6.45489 5.74138i −0.931683 0.828697i
\(49\) 0 0
\(50\) −6.69344 11.5934i −0.946595 1.63955i
\(51\) −5.32072 4.73259i −0.745050 0.662695i
\(52\) 0.888736 0.123245
\(53\) 0.0618219 + 0.107079i 0.00849190 + 0.0147084i 0.870240 0.492628i \(-0.163964\pi\)
−0.861748 + 0.507336i \(0.830630\pi\)
\(54\) 8.79851 + 0.762918i 1.19733 + 0.103820i
\(55\) 10.0865 1.36006
\(56\) 0 0
\(57\) −0.310892 + 1.50761i −0.0411787 + 0.199688i
\(58\) −2.88874 −0.379310
\(59\) 4.43818 7.68715i 0.577802 1.00078i −0.417929 0.908479i \(-0.637244\pi\)
0.995731 0.0923022i \(-0.0294226\pi\)
\(60\) −1.11559 + 5.40987i −0.144023 + 0.698411i
\(61\) −1.93818 3.35702i −0.248158 0.429823i 0.714857 0.699271i \(-0.246492\pi\)
−0.963015 + 0.269448i \(0.913159\pi\)
\(62\) −11.8764 −1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) 1.79418 + 3.10761i 0.222541 + 0.385452i
\(66\) −6.18292 5.49948i −0.761065 0.676939i
\(67\) −6.15452 + 10.6599i −0.751894 + 1.30232i 0.195010 + 0.980801i \(0.437526\pi\)
−0.946904 + 0.321517i \(0.895807\pi\)
\(68\) −3.65383 −0.443092
\(69\) −9.66071 + 3.20397i −1.16301 + 0.385713i
\(70\) 0 0
\(71\) −2.87636 −0.341361 −0.170680 0.985326i \(-0.554597\pi\)
−0.170680 + 0.985326i \(0.554597\pi\)
\(72\) −4.54325 + 3.38597i −0.535427 + 0.399040i
\(73\) 5.32072 + 9.21576i 0.622744 + 1.07862i 0.988973 + 0.148099i \(0.0473154\pi\)
−0.366229 + 0.930525i \(0.619351\pi\)
\(74\) 8.09888 0.941476
\(75\) −12.9487 + 4.29443i −1.49519 + 0.495879i
\(76\) 0.394926 + 0.684031i 0.0453011 + 0.0784638i
\(77\) 0 0
\(78\) 0.594554 2.88318i 0.0673200 0.326456i
\(79\) 3.54325 + 6.13709i 0.398647 + 0.690477i 0.993559 0.113314i \(-0.0361465\pi\)
−0.594912 + 0.803791i \(0.702813\pi\)
\(80\) −8.94870 15.4996i −1.00049 1.73291i
\(81\) 2.57234 8.62456i 0.285816 0.958285i
\(82\) 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
\(86\) 8.85532 0.954893
\(87\) −0.594554 + 2.88318i −0.0637429 + 0.309109i
\(88\) 5.30903 0.565945
\(89\) −4.80470 + 8.32199i −0.509297 + 0.882129i 0.490645 + 0.871360i \(0.336761\pi\)
−0.999942 + 0.0107692i \(0.996572\pi\)
\(90\) 16.8040 + 7.23828i 1.77130 + 0.762981i
\(91\) 0 0
\(92\) −2.61126 + 4.52284i −0.272243 + 0.471539i
\(93\) −2.44437 + 11.8535i −0.253469 + 1.22915i
\(94\) 2.26578 3.92445i 0.233697 0.404776i
\(95\) −1.59455 + 2.76185i −0.163598 + 0.283360i
\(96\) −1.64400 + 7.97225i −0.167790 + 0.813664i
\(97\) −3.66071 + 6.34053i −0.371688 + 0.643783i −0.989825 0.142287i \(-0.954554\pi\)
0.618137 + 0.786070i \(0.287888\pi\)
\(98\) 0 0
\(99\) −6.76145 + 5.03913i −0.679551 + 0.506452i
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) 3.46472 0.344753 0.172376 0.985031i \(-0.444856\pi\)
0.172376 + 0.985031i \(0.444856\pi\)
\(102\) −2.44437 + 11.8535i −0.242028 + 1.17367i
\(103\) −15.8764 −1.56434 −0.782172 0.623063i \(-0.785888\pi\)
−0.782172 + 0.623063i \(0.785888\pi\)
\(104\) 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 \(-0.750016\pi\)
0.965912 + 0.258869i \(0.0833498\pi\)
\(108\) −1.95489 4.18383i −0.188109 0.402589i
\(109\) 9.43199 + 16.3367i 0.903421 + 1.56477i 0.823023 + 0.568008i \(0.192286\pi\)
0.0803973 + 0.996763i \(0.474381\pi\)
\(110\) −8.57165 14.8465i −0.817275 1.41556i
\(111\) 1.66690 8.08330i 0.158215 0.767233i
\(112\) 0 0
\(113\) 9.27561 + 16.0658i 0.872576 + 1.51135i 0.859322 + 0.511434i \(0.170886\pi\)
0.0132538 + 0.999912i \(0.495781\pi\)
\(114\) 2.48329 0.823583i 0.232581 0.0771356i
\(115\) −21.0865 −1.96633
\(116\) 0.755260 + 1.30815i 0.0701242 + 0.121459i
\(117\) −2.75526 1.18682i −0.254724 0.109722i
\(118\) −15.0865 −1.38883
\(119\) 0 0
\(120\) −11.1421 + 3.69529i −1.01713 + 0.337332i
\(121\) −3.09888 −0.281717
\(122\) −3.29418 + 5.70569i −0.298241 + 0.516569i
\(123\) −7.00364 6.22948i −0.631497 0.561693i
\(124\) 3.10507 + 5.37815i 0.278844 + 0.482972i
\(125\) −10.3214 −0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) −6.38874 11.0656i −0.564690 0.978071i
\(129\) 1.82258 8.83828i 0.160470 0.778167i
\(130\) 3.04944 5.28179i 0.267454 0.463244i
\(131\) 16.0531 1.40256 0.701282 0.712884i \(-0.252611\pi\)
0.701282 + 0.712884i \(0.252611\pi\)
\(132\) −0.873885 + 4.23774i −0.0760619 + 0.368848i
\(133\) 0 0
\(134\) 20.9208 1.80728
\(135\) 10.6829 15.2819i 0.919439 1.31526i
\(136\) −3.88255 6.72477i −0.332926 0.576644i
\(137\) −12.9876 −1.10961 −0.554804 0.831981i \(-0.687207\pi\)
−0.554804 + 0.831981i \(0.687207\pi\)
\(138\) 12.9258 + 11.4970i 1.10032 + 0.978691i
\(139\) −0.555632 0.962383i −0.0471281 0.0816283i 0.841499 0.540259i \(-0.181674\pi\)
−0.888627 + 0.458630i \(0.848340\pi\)
\(140\) 0 0
\(141\) −3.45056 3.06914i −0.290589 0.258468i
\(142\) 2.44437 + 4.23377i 0.205127 + 0.355290i
\(143\) 1.40545 + 2.43430i 0.117529 + 0.203567i
\(144\) 13.7422 + 5.91941i 1.14518 + 0.493284i
\(145\) −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
\(149\) 8.43268 0.690832 0.345416 0.938450i \(-0.387738\pi\)
0.345416 + 0.938450i \(0.387738\pi\)
\(150\) 17.3251 + 15.4100i 1.41458 + 1.25822i
\(151\) −14.8516 −1.20861 −0.604303 0.796755i \(-0.706548\pi\)
−0.604303 + 0.796755i \(0.706548\pi\)
\(152\) −0.839294 + 1.45370i −0.0680757 + 0.117911i
\(153\) 11.3276 + 4.87933i 0.915782 + 0.394470i
\(154\) 0 0
\(155\) −12.5371 + 21.7148i −1.00700 + 1.74418i
\(156\) −1.46108 + 0.484566i −0.116980 + 0.0387964i
\(157\) −1.44437 + 2.50172i −0.115273 + 0.199659i −0.917889 0.396837i \(-0.870108\pi\)
0.802616 + 0.596496i \(0.203441\pi\)
\(158\) 6.02221 10.4308i 0.479101 0.829828i
\(159\) −0.160018 0.142330i −0.0126902 0.0112875i
\(160\) −8.43199 + 14.6046i −0.666607 + 1.15460i
\(161\) 0 0
\(162\) −14.8807 + 3.54299i −1.16914 + 0.278363i
\(163\) 5.15452 8.92788i 0.403733 0.699286i −0.590440 0.807081i \(-0.701046\pi\)
0.994173 + 0.107796i \(0.0343792\pi\)
\(164\) −4.80951 −0.375560
\(165\) −16.5822 + 5.49948i −1.29092 + 0.428134i
\(166\) −6.98762 −0.542345
\(167\) −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
\(171\) −0.310892 2.64802i −0.0237745 0.202499i
\(172\) −2.31522 4.01008i −0.176534 0.305766i
\(173\) 3.30470 + 5.72391i 0.251252 + 0.435181i 0.963871 0.266370i \(-0.0858244\pi\)
−0.712619 + 0.701551i \(0.752491\pi\)
\(174\) 4.74907 1.57503i 0.360026 0.119403i
\(175\) 0 0
\(176\) −7.00983 12.1414i −0.528386 0.915191i
\(177\) −3.10507 + 15.0575i −0.233392 + 1.13179i
\(178\) 16.3324 1.22417
\(179\) 1.92147 + 3.32808i 0.143617 + 0.248752i 0.928856 0.370440i \(-0.120793\pi\)
−0.785239 + 0.619193i \(0.787460\pi\)
\(180\) −1.11559 9.50206i −0.0831515 0.708242i
\(181\) 18.5426 1.37826 0.689129 0.724639i \(-0.257993\pi\)
0.689129 + 0.724639i \(0.257993\pi\)
\(182\) 0 0
\(183\) 5.01671 + 4.46218i 0.370846 + 0.329854i
\(184\) −11.0989 −0.818221
\(185\) 8.54944 14.8081i 0.628567 1.08871i
\(186\) 19.5247 6.47536i 1.43162 0.474796i
\(187\) −5.77816 10.0081i −0.422541 0.731862i
\(188\) −2.36955 −0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) −2.31708 4.01330i −0.167658 0.290392i 0.769938 0.638119i \(-0.220287\pi\)
−0.937596 + 0.347726i \(0.886954\pi\)
\(192\) −3.26764 + 1.08371i −0.235822 + 0.0782102i
\(193\) 12.6483 21.9075i 0.910446 1.57694i 0.0970118 0.995283i \(-0.469072\pi\)
0.813435 0.581656i \(-0.197595\pi\)
\(194\) 12.4437 0.893404
\(195\) −4.64400 4.13066i −0.332563 0.295803i
\(196\) 0 0
\(197\) 10.7207 0.763816 0.381908 0.924200i \(-0.375267\pi\)
0.381908 + 0.924200i \(0.375267\pi\)
\(198\) 13.1632 + 5.67000i 0.935466 + 0.402949i
\(199\) 4.38323 + 7.59199i 0.310719 + 0.538182i 0.978518 0.206160i \(-0.0660968\pi\)
−0.667799 + 0.744342i \(0.732763\pi\)
\(200\) −14.8764 −1.05192
\(201\) 4.30587 20.8805i 0.303713 1.47280i
\(202\) −2.94437 5.09979i −0.207165 0.358820i
\(203\) 0 0
\(204\) 6.00688 1.99218i 0.420566 0.139481i
\(205\) −9.70946 16.8173i −0.678138 1.17457i
\(206\) 13.4920 + 23.3687i 0.940029 + 1.62818i
\(207\) 14.1353 10.5346i 0.982468 0.732208i
\(208\) 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 \(0.951398\pi\)
\(212\) −0.109887 −0.00754705
\(213\) 4.72872 1.56828i 0.324006 0.107457i
\(214\) −9.09888 −0.621987
\(215\) 9.34795 16.1911i 0.637525 1.10423i
\(216\) 5.62296 8.04364i 0.382594 0.547300i
\(217\) 0 0
\(218\) 16.0309 27.7663i 1.08575 1.88057i
\(219\) −13.7720 12.2497i −0.930624 0.827755i
\(220\) −4.48212 + 7.76326i −0.302184 + 0.523399i
\(221\) 2.05563 3.56046i 0.138277 0.239502i
\(222\) −13.3145 + 4.41576i −0.893613 + 0.296367i
\(223\) 2.83379 4.90827i 0.189765 0.328682i −0.755407 0.655256i \(-0.772561\pi\)
0.945172 + 0.326574i \(0.105894\pi\)
\(224\) 0 0
\(225\) 18.9462 14.1201i 1.26308 0.941338i
\(226\) 15.7651 27.3059i 1.04868 1.81636i
\(227\) −11.0989 −0.736659 −0.368329 0.929695i \(-0.620070\pi\)
−0.368329 + 0.929695i \(0.620070\pi\)
\(228\) −1.02221 0.909219i −0.0676976 0.0602145i
\(229\) 19.6428 1.29803 0.649017 0.760774i \(-0.275180\pi\)
0.649017 + 0.760774i \(0.275180\pi\)
\(230\) 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 \(-0.928183\pi\)
0.681067 + 0.732221i \(0.261516\pi\)
\(234\) 0.594554 + 5.06410i 0.0388672 + 0.331051i
\(235\) −4.78366 8.28554i −0.312052 0.540489i
\(236\) 3.94437 + 6.83185i 0.256756 + 0.444715i
\(237\) −9.17123 8.15747i −0.595735 0.529884i
\(238\) 0 0
\(239\) −5.61126 9.71899i −0.362963 0.628670i 0.625484 0.780237i \(-0.284901\pi\)
−0.988447 + 0.151567i \(0.951568\pi\)
\(240\) 23.1625 + 20.6022i 1.49513 + 1.32986i
\(241\) −6.98624 −0.450023 −0.225012 0.974356i \(-0.572242\pi\)
−0.225012 + 0.974356i \(0.572242\pi\)
\(242\) 2.63348 + 4.56131i 0.169286 + 0.293212i
\(243\) 0.473458 + 15.5813i 0.0303723 + 0.999539i
\(244\) 3.44506 0.220547
\(245\) 0 0
\(246\) −3.21751 + 15.6027i −0.205141 + 0.994792i
\(247\) −0.888736 −0.0565489
\(248\) −6.59888 + 11.4296i −0.419030 + 0.725781i
\(249\) −1.43818 + 6.97418i −0.0911408 + 0.441970i
\(250\) 8.77128 + 15.1923i 0.554745 + 0.960846i
\(251\) 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
\(254\) −8.48762 14.7010i −0.532561 0.922422i
\(255\) 19.0927 + 16.9822i 1.19563 + 1.06347i
\(256\) −8.87085 + 15.3648i −0.554428 + 0.960298i
\(257\) −1.42402 −0.0888277 −0.0444138 0.999013i \(-0.514142\pi\)
−0.0444138 + 0.999013i \(0.514142\pi\)
\(258\) −14.5581 + 4.82819i −0.906348 + 0.300590i
\(259\) 0 0
\(260\) −3.18911 −0.197780
\(261\) −0.594554 5.06410i −0.0368020 0.313460i
\(262\) −13.6421 23.6289i −0.842814 1.45980i
\(263\) 16.2632 1.00283 0.501417 0.865206i \(-0.332812\pi\)
0.501417 + 0.865206i \(0.332812\pi\)
\(264\) −8.72803 + 2.89465i −0.537173 + 0.178153i
\(265\) −0.221840 0.384237i −0.0136275 0.0236035i
\(266\) 0 0
\(267\) 3.36151 16.3010i 0.205721 0.997604i
\(268\) −5.46974 9.47387i −0.334118 0.578709i
\(269\) 9.32691 + 16.1547i 0.568672 + 0.984969i 0.996698 + 0.0812022i \(0.0258759\pi\)
−0.428026 + 0.903767i \(0.640791\pi\)
\(270\) −31.5723 2.73763i −1.92143 0.166607i
\(271\) −1.98143 + 3.43194i −0.120363 + 0.208475i −0.919911 0.392127i \(-0.871739\pi\)
0.799548 + 0.600603i \(0.205073\pi\)
\(272\) −10.2527 + 17.7582i −0.621662 + 1.07675i
\(273\) 0 0
\(274\) 11.0371 + 19.1168i 0.666773 + 1.15489i
\(275\) −22.1396 −1.33507
\(276\) 1.82691 8.85928i 0.109967 0.533266i
\(277\) −2.33379 −0.140224 −0.0701120 0.997539i \(-0.522336\pi\)
−0.0701120 + 0.997539i \(0.522336\pi\)
\(278\) −0.944368 + 1.63569i −0.0566394 + 0.0981024i
\(279\) −2.44437 20.8199i −0.146340 1.24645i
\(280\) 0 0
\(281\) −13.9975 + 24.2443i −0.835018 + 1.44629i 0.0589978 + 0.998258i \(0.481210\pi\)
−0.894016 + 0.448035i \(0.852124\pi\)
\(282\) −1.58520 + 7.68715i −0.0943975 + 0.457763i
\(283\) −5.16002 + 8.93741i −0.306731 + 0.531274i −0.977645 0.210261i \(-0.932569\pi\)
0.670914 + 0.741535i \(0.265902\pi\)
\(284\) 1.27816 2.21384i 0.0758449 0.131367i
\(285\) 1.11559 5.40987i 0.0660821 0.320453i
\(286\) 2.38874 4.13741i 0.141249 0.244650i
\(287\) 0 0
\(288\) −1.64400 14.0027i −0.0968734 0.825117i
\(289\) 0.0487535 0.0844436i 0.00286785 0.00496727i
\(290\) 10.3658 0.608703
\(291\) 2.56113 12.4197i 0.150136 0.728058i
\(292\) −9.45744 −0.553455
\(293\) 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
\(297\) 8.36831 11.9709i 0.485578 0.694620i
\(298\) −7.16621 12.4122i −0.415127 0.719021i
\(299\) −2.93818 5.08907i −0.169919 0.294309i
\(300\) 2.44870 11.8745i 0.141376 0.685575i
\(301\) 0 0
\(302\) 12.6211 + 21.8604i 0.726262 + 1.25792i
\(303\) −5.69599 + 1.88907i −0.327226 + 0.108524i
\(304\) 4.43268 0.254231
\(305\) 6.95489 + 12.0462i 0.398236 + 0.689765i
\(306\) −2.44437 20.8199i −0.139735 1.19019i
\(307\) −11.4437 −0.653125 −0.326563 0.945176i \(-0.605890\pi\)
−0.326563 + 0.945176i \(0.605890\pi\)
\(308\) 0 0
\(309\) 26.1007 8.65628i 1.48482 0.492439i
\(310\) 42.6167 2.42047
\(311\) −5.98143 + 10.3601i −0.339176 + 0.587470i −0.984278 0.176627i \(-0.943481\pi\)
0.645102 + 0.764096i \(0.276815\pi\)
\(312\) −2.44437 2.17417i −0.138385 0.123088i
\(313\) 6.77197 + 11.7294i 0.382774 + 0.662985i 0.991458 0.130429i \(-0.0416353\pi\)
−0.608683 + 0.793413i \(0.708302\pi\)
\(314\) 4.90978 0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) 14.9814 + 25.9486i 0.841441 + 1.45742i 0.888676 + 0.458535i \(0.151626\pi\)
−0.0472355 + 0.998884i \(0.515041\pi\)
\(318\) −0.0735129 + 0.356487i −0.00412240 + 0.0199908i
\(319\) −2.38874 + 4.13741i −0.133744 + 0.231651i
\(320\) −7.13231 −0.398708
\(321\) −1.87271 + 9.08138i −0.104525 + 0.506873i
\(322\) 0 0
\(323\) 3.65383 0.203304
\(324\) 5.49498 + 5.81233i 0.305277 + 0.322907i
\(325\) −3.93818 6.82112i −0.218451 0.378368i
\(326\) −17.5215 −0.970427
\(327\) −24.4134 21.7148i −1.35007 1.20083i
\(328\) −5.11058 8.85178i −0.282184 0.488758i
\(329\) 0 0
\(330\) 22.1866 + 19.7341i 1.22133 + 1.08633i
\(331\) −1.04325 1.80697i −0.0573423 0.0993198i 0.835929 0.548837i \(-0.184929\pi\)
−0.893272 + 0.449517i \(0.851596\pi\)
\(332\) 1.82691 + 3.16431i 0.100265 + 0.173664i
\(333\) 1.66690 + 14.1978i 0.0913454 + 0.778032i
\(334\) −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 \(0.687789\pi\)
\(338\) −20.3955 −1.10937
\(339\) −24.0087 21.3548i −1.30397 1.15983i
\(340\) 13.1113 0.711058
\(341\) −9.82072 + 17.0100i −0.531822 + 0.921143i
\(342\) −3.63348 + 2.70793i −0.196476 + 0.146428i
\(343\) 0 0
\(344\) 4.92030 8.52220i 0.265285 0.459486i
\(345\) 34.6661 11.4970i 1.86636 0.618979i
\(346\) 5.61677 9.72852i 0.301959 0.523009i
\(347\) −5.63348 + 9.75747i −0.302421 + 0.523808i −0.976684 0.214683i \(-0.931128\pi\)
0.674263 + 0.738491i \(0.264461\pi\)
\(348\) −1.95489 1.73880i −0.104793 0.0932095i
\(349\) 0.0988844 0.171273i 0.00529316 0.00916803i −0.863367 0.504577i \(-0.831648\pi\)
0.868660 + 0.495409i \(0.164982\pi\)
\(350\) 0 0
\(351\) 5.17673 + 0.448873i 0.276313 + 0.0239591i
\(352\) −6.60507 + 11.4403i −0.352052 + 0.609771i
\(353\) −12.5019 −0.665407 −0.332703 0.943032i \(-0.607961\pi\)
−0.332703 + 0.943032i \(0.607961\pi\)
\(354\) 24.8022 8.22563i 1.31822 0.437187i
\(355\) 10.3214 0.547804
\(356\) −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 0.471157 + 0.882049i \(0.343837\pi\)
−0.999456 + 0.0329908i \(0.989497\pi\)
\(360\) 16.3028 12.1501i 0.859235 0.640365i
\(361\) 9.10507 + 15.7705i 0.479214 + 0.830024i
\(362\) −15.7577 27.2932i −0.828208 1.43450i
\(363\) 5.09455 1.68961i 0.267395 0.0886814i
\(364\) 0 0
\(365\) −19.0927 33.0695i −0.999357 1.73094i
\(366\) 2.30470 11.1762i 0.120469 0.584191i
\(367\) 30.0727 1.56978 0.784892 0.619632i \(-0.212718\pi\)
0.784892 + 0.619632i \(0.212718\pi\)
\(368\) 14.6545 + 25.3824i 0.763919 + 1.32315i
\(369\) 14.9105 + 6.42264i 0.776208 + 0.334349i
\(370\) −29.0617 −1.51085
\(371\) 0 0
\(372\) −8.03706 7.14867i −0.416702 0.370641i
\(373\) 7.01238 0.363087 0.181544 0.983383i \(-0.441891\pi\)
0.181544 + 0.983383i \(0.441891\pi\)
\(374\) −9.82072 + 17.0100i −0.507818 + 0.879566i
\(375\) 16.9684 5.62755i 0.876242 0.290606i
\(376\) −2.51788 4.36110i −0.129850 0.224906i
\(377\) −1.69963 −0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) −1.41714 2.45455i −0.0726976 0.125916i
\(381\) −16.4196 + 5.44556i −0.841202 + 0.278985i
\(382\) −3.93818 + 6.82112i −0.201495 + 0.348999i
\(383\) 3.21015 0.164031 0.0820155 0.996631i \(-0.473864\pi\)
0.0820155 + 0.996631i \(0.473864\pi\)
\(384\) 16.5364 + 14.7085i 0.843868 + 0.750590i
\(385\) 0 0
\(386\) −42.9949 −2.18838
\(387\) 1.82258 + 15.5238i 0.0926471 + 0.789120i
\(388\) −3.25340 5.63506i −0.165166 0.286077i
\(389\) 5.13602 0.260407 0.130203 0.991487i \(-0.458437\pi\)
0.130203 + 0.991487i \(0.458437\pi\)
\(390\) −2.13348 + 10.3459i −0.108033 + 0.523885i
\(391\) 12.0796 + 20.9225i 0.610893 + 1.05810i
\(392\) 0 0
\(393\) −26.3912 + 8.75264i −1.33126 + 0.441512i
\(394\) −9.11058 15.7800i −0.458984 0.794984i
\(395\) −12.7145 22.0221i −0.639735 1.10805i
\(396\) −0.873885 7.44330i −0.0439144 0.374040i
\(397\) −11.4691 + 19.8650i −0.575615 + 0.996995i 0.420359 + 0.907358i \(0.361904\pi\)
−0.995975 + 0.0896370i \(0.971429\pi\)
\(398\) 7.44987 12.9036i 0.373428 0.646797i
\(399\) 0 0
\(400\) 19.6421 + 34.0212i 0.982107 + 1.70106i
\(401\) −18.2101 −0.909371 −0.454686 0.890652i \(-0.650248\pi\)
−0.454686 + 0.890652i \(0.650248\pi\)
\(402\) −34.3937 + 11.4067i −1.71540 + 0.568912i
\(403\) −6.98762 −0.348078
\(404\) −1.53961 + 2.66668i −0.0765985 + 0.132672i
\(405\) −9.23050 + 30.9481i −0.458667 + 1.53782i
\(406\) 0 0
\(407\) 6.69708 11.5997i 0.331962 0.574975i
\(408\) 10.0494 + 8.93861i 0.497522 + 0.442527i
\(409\) 7.66621 13.2783i 0.379070 0.656568i −0.611858 0.790968i \(-0.709577\pi\)
0.990927 + 0.134400i \(0.0429108\pi\)
\(410\) −16.5025 + 28.5831i −0.814999 + 1.41162i
\(411\) 21.3516 7.08125i 1.05320 0.349293i
\(412\) 7.05494 12.2195i 0.347572 0.602013i
\(413\) 0 0
\(414\) −27.5185 11.8535i −1.35246 0.582568i
\(415\) −7.37636 + 12.7762i −0.362091 + 0.627160i
\(416\) −4.69963 −0.230418
\(417\) 1.43818 + 1.27921i 0.0704279 + 0.0626430i
\(418\) 4.24591 0.207674
\(419\) −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
\(423\) 7.34610 + 3.16431i 0.357179 + 0.153854i
\(424\) −0.116765 0.202243i −0.00567062 0.00982181i
\(425\) 16.1909 + 28.0434i 0.785374 + 1.36031i
\(426\) −6.32691 5.62755i −0.306540 0.272656i
\(427\) 0 0
\(428\) 2.37890 + 4.12038i 0.114989 + 0.199166i
\(429\) −3.63781 3.23569i −0.175635 0.156221i
\(430\) −31.7761 −1.53238
\(431\) −17.5494 30.3965i −0.845327 1.46415i −0.885337 0.464950i \(-0.846072\pi\)
0.0400101 0.999199i \(-0.487261\pi\)
\(432\) −25.8196 2.23881i −1.24224 0.107715i
\(433\) −41.1730 −1.97865 −0.989324 0.145731i \(-0.953447\pi\)
−0.989324 + 0.145731i \(0.953447\pi\)
\(434\) 0 0
\(435\) 2.13348 10.3459i 0.102292 0.496047i
\(436\) −16.7651 −0.802902
\(437\) 2.61126 4.52284i 0.124914 0.216357i
\(438\) −6.32691 + 30.6812i −0.302312 + 1.46600i
\(439\) 2.33929 + 4.05178i 0.111648 + 0.193381i 0.916435 0.400184i \(-0.131054\pi\)
−0.804787 + 0.593564i \(0.797720\pi\)
\(440\) −19.0507 −0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) −15.0865 26.1306i −0.716781 1.24150i −0.962268 0.272102i \(-0.912281\pi\)
0.245487 0.969400i \(-0.421052\pi\)
\(444\) 5.48074 + 4.87492i 0.260104 + 0.231353i
\(445\) 17.2410 29.8623i 0.817303 1.41561i
\(446\) −9.63279 −0.456126
\(447\) −13.8633 + 4.59776i −0.655711 + 0.217466i
\(448\) 0 0
\(449\) 0.333792 0.0157526 0.00787632 0.999969i \(-0.497493\pi\)
0.00787632 + 0.999969i \(0.497493\pi\)
\(450\) −36.8843 15.8878i −1.73874 0.748959i
\(451\) −7.60576 13.1736i −0.358141 0.620319i
\(452\) −16.4871 −0.775490
\(453\) 24.4160 8.09755i 1.14716 0.380456i
\(454\) 9.43199 + 16.3367i 0.442665 + 0.766719i
\(455\) 0 0
\(456\) 0.587193 2.84748i 0.0274979 0.133346i
\(457\) 9.65452 + 16.7221i 0.451619 + 0.782227i 0.998487 0.0549917i \(-0.0175132\pi\)
−0.546868 + 0.837219i \(0.684180\pi\)
\(458\) −16.6927 28.9127i −0.780001 1.35100i
\(459\) −21.2829 1.84544i −0.993401 0.0861376i
\(460\) 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 \(-0.336407\pi\)
\(464\) 8.47710 0.393539
\(465\) 8.77128 42.5347i 0.406758 1.97250i
\(466\) 15.2335 0.705680
\(467\) 6.16002 10.6695i 0.285052 0.493724i −0.687570 0.726118i \(-0.741323\pi\)
0.972622 + 0.232394i \(0.0746559\pi\)
\(468\) 2.13781 1.59325i 0.0988201 0.0736480i
\(469\) 0 0
\(470\) −8.13045 + 14.0823i −0.375029 + 0.649570i
\(471\) 1.01052 4.90033i 0.0465623 0.225795i
\(472\) −8.38255 + 14.5190i −0.385838 + 0.668291i
\(473\) 7.32258 12.6831i 0.336693 0.583169i
\(474\) −4.21331 + 20.4317i −0.193524 + 0.938457i
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 0 0
\(477\) 0.340671 + 0.146743i 0.0155983 + 0.00671890i
\(478\) −9.53706 + 16.5187i −0.436215 + 0.755547i
\(479\) 13.4895 0.616350 0.308175 0.951330i \(-0.400282\pi\)
0.308175 + 0.951330i \(0.400282\pi\)
\(480\) 5.89926 28.6073i 0.269263 1.30574i
\(481\) 4.76509 0.217269
\(482\) 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
\(486\) 22.5320 13.9381i 1.02207 0.632244i
\(487\) −3.77197 6.53324i −0.170924 0.296050i 0.767819 0.640667i \(-0.221342\pi\)
−0.938743 + 0.344617i \(0.888009\pi\)
\(488\) 3.66071 + 6.34053i 0.165712 + 0.287022i
\(489\) −3.60624 + 17.4878i −0.163080 + 0.790826i
\(490\) 0 0
\(491\) 8.06979 + 13.9773i 0.364185 + 0.630786i 0.988645 0.150270i \(-0.0480143\pi\)
−0.624460 + 0.781057i \(0.714681\pi\)
\(492\) 7.90682 2.62230i 0.356467 0.118222i
\(493\) 6.98762 0.314707
\(494\) 0.755260 + 1.30815i 0.0339808 + 0.0588564i
\(495\) 24.2625 18.0822i 1.09052 0.812736i
\(496\) 34.8516 1.56488
\(497\) 0 0
\(498\) 11.4876 3.80987i 0.514773 0.170724i
\(499\) −30.8654 −1.38172 −0.690862 0.722987i \(-0.742769\pi\)
−0.690862 + 0.722987i \(0.742769\pi\)
\(500\) 4.58650 7.94406i 0.205115 0.355269i
\(501\) 15.7269 + 13.9885i 0.702624 + 0.624958i
\(502\) −3.92649 6.80088i −0.175248 0.303538i
\(503\) 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
\(506\) 14.0371 + 24.3129i 0.624024 + 1.08084i
\(507\) −4.19777 + 20.3563i −0.186429 + 0.904055i
\(508\) −4.43818 + 7.68715i −0.196912 + 0.341062i
\(509\) 13.5897 0.602355 0.301177 0.953568i \(-0.402620\pi\)
0.301177 + 0.953568i \(0.402620\pi\)
\(510\) 8.77128 42.5347i 0.388399 1.88347i
\(511\) 0 0
\(512\) 4.59937 0.203265
\(513\) 1.95489 + 4.18383i 0.0863104 + 0.184720i
\(514\) 1.21015 + 2.09604i 0.0533774 + 0.0924523i
\(515\) 56.9701 2.51040
\(516\) 5.99264 + 5.33023i 0.263811 + 0.234650i
\(517\) −3.74721 6.49036i −0.164802 0.285446i
\(518\) 0 0
\(519\) −8.55377 7.60826i −0.375469 0.333966i
\(520\) −3.38874 5.86946i −0.148606 0.257393i
\(521\) 19.5865 + 33.9248i 0.858100 + 1.48627i 0.873739 + 0.486396i \(0.161689\pi\)
−0.0156383 + 0.999878i \(0.504978\pi\)
\(522\) −6.94870 + 5.17868i −0.304136 + 0.226665i
\(523\) −9.56182 + 16.5616i −0.418109 + 0.724187i −0.995749 0.0921051i \(-0.970640\pi\)
0.577640 + 0.816292i \(0.303974\pi\)
\(524\) −7.13348 + 12.3555i −0.311627 + 0.539754i
\(525\) 0 0
\(526\) −13.8207 23.9382i −0.602612 1.04375i
\(527\) 28.7280 1.25141
\(528\) 18.1440 + 16.1384i 0.789616 + 0.702334i
\(529\) 11.5316 0.501372
\(530\) −0.377045 + 0.653061i −0.0163778 + 0.0283671i
\(531\) −3.10507 26.4474i −0.134749 1.14772i
\(532\) 0 0
\(533\) 2.70582 4.68661i 0.117202 0.203000i
\(534\) −26.8504 + 8.90494i −1.16193 + 0.385354i
\(535\) −9.60507 + 16.6365i −0.415264 + 0.719258i
\(536\) 11.6243 20.1338i 0.502091 0.869648i
\(537\) −4.97346 4.42371i −0.214621 0.190897i
\(538\) 15.8523 27.4570i 0.683441 1.18375i
\(539\) 0 0
\(540\) 7.01485 + 15.0131i 0.301871 + 0.646061i
\(541\) −1.26509 + 2.19120i −0.0543906 + 0.0942072i −0.891939 0.452156i \(-0.850655\pi\)
0.837548 + 0.546363i \(0.183988\pi\)
\(542\) 6.73539 0.289310
\(543\) −30.4839 + 10.1100i −1.30819 + 0.433861i
\(544\) 19.3214 0.828399
\(545\) −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
\(549\) −10.6804 4.60054i −0.455827 0.196346i
\(550\) 18.8145 + 32.5877i 0.802254 + 1.38955i
\(551\) −0.755260 1.30815i −0.0321752 0.0557290i
\(552\) 18.2465 6.05146i 0.776624 0.257567i
\(553\) 0 0
\(554\) 1.98329 + 3.43516i 0.0842619 + 0.145946i
\(555\) −5.98143 + 29.0058i −0.253898 + 1.23123i
\(556\) 0.987620 0.0418844
\(557\) −20.6804 35.8195i −0.876255 1.51772i −0.855419 0.517936i \(-0.826701\pi\)
−0.0208360 0.999783i \(-0.506633\pi\)
\(558\) −28.5679 + 21.2909i −1.20938 + 0.901317i
\(559\) 5.21015 0.220366
\(560\) 0 0
\(561\) 14.9560 + 13.3028i 0.631442 + 0.561644i
\(562\) 47.5809 2.00708
\(563\) 10.3683 17.9584i 0.436972 0.756858i −0.560482 0.828166i \(-0.689384\pi\)
0.997454 + 0.0713087i \(0.0227175\pi\)
\(564\) 3.89554 1.29195i 0.164032 0.0544011i
\(565\) −33.2843 57.6501i −1.40028 2.42536i
\(566\) 17.5402 0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) 0.134164 + 0.232379i 0.00562446 + 0.00974185i 0.868824 0.495121i \(-0.164876\pi\)
−0.863199 + 0.504863i \(0.831543\pi\)
\(570\) −8.91095 + 2.95531i −0.373239 + 0.123785i
\(571\) −17.9684 + 31.1221i −0.751953 + 1.30242i 0.194923 + 0.980819i \(0.437554\pi\)
−0.946875 + 0.321601i \(0.895779\pi\)
\(572\) −2.49814 −0.104453
\(573\) 5.99745 + 5.33451i 0.250547 + 0.222852i
\(574\) 0 0
\(575\) 46.2843 1.93019
\(576\) 4.78111 3.56324i 0.199213 0.148468i
\(577\) −2.71565 4.70364i −0.113054 0.195815i 0.803946 0.594702i \(-0.202730\pi\)
−0.917000 + 0.398887i \(0.869397\pi\)
\(578\) −0.165726 −0.00689328
\(579\) −8.84913 + 42.9122i −0.367757 + 1.78337i
\(580\) −2.71015 4.69412i −0.112533 0.194913i
\(581\) 0 0
\(582\) −20.4574 + 6.78468i −0.847985 + 0.281234i
\(583\) −0.173775 0.300987i −0.00719702 0.0124656i
\(584\) −10.0494 17.4061i −0.415849 0.720271i
\(585\) 9.88688 + 4.25874i 0.408772 + 0.176077i
\(586\) 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
\(590\) 54.1359 2.22874
\(591\) −17.6247 + 5.84524i −0.724985 + 0.240441i
\(592\) −23.7665 −0.976796
\(593\) 16.7534 29.0177i 0.687980 1.19162i −0.284511 0.958673i \(-0.591831\pi\)
0.972490 0.232943i \(-0.0748355\pi\)
\(594\) −24.7317 2.14448i −1.01475 0.0879891i
\(595\) 0 0
\(596\) −3.74721 + 6.49036i −0.153492 + 0.265856i
\(597\) −11.3454 10.0913i −0.464337 0.413010i
\(598\) −4.99381 + 8.64953i −0.204212 + 0.353706i
\(599\) −3.12364 + 5.41031i −0.127629 + 0.221059i −0.922757 0.385381i \(-0.874070\pi\)
0.795129 + 0.606441i \(0.207403\pi\)
\(600\) 24.4567 8.11105i 0.998439 0.331132i
\(601\) −11.2040 + 19.4058i −0.457019 + 0.791580i −0.998802 0.0489384i \(-0.984416\pi\)
0.541783 + 0.840519i \(0.317750\pi\)
\(602\) 0 0
\(603\) 4.30587 + 36.6752i 0.175349 + 1.49353i
\(604\) 6.59957 11.4308i 0.268533 0.465112i
\(605\) 11.1199 0.452089
\(606\) 7.62110 + 6.77868i 0.309586 + 0.275365i
\(607\) 14.9505 0.606821 0.303411 0.952860i \(-0.401875\pi\)
0.303411 + 0.952860i \(0.401875\pi\)
\(608\) −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
\(612\) −8.78909 + 6.55027i −0.355278 + 0.264779i
\(613\) −17.5989 30.4822i −0.710812 1.23116i −0.964553 0.263891i \(-0.914994\pi\)
0.253740 0.967272i \(-0.418339\pi\)
\(614\) 9.72500 + 16.8442i 0.392469 + 0.679776i
\(615\) 25.1316 + 22.3536i 1.01340 + 0.901386i
\(616\) 0 0
\(617\) 1.00619 + 1.74277i 0.0405077 + 0.0701614i 0.885568 0.464509i \(-0.153769\pi\)
−0.845061 + 0.534670i \(0.820436\pi\)
\(618\) −34.9221 31.0619i −1.40477 1.24949i
\(619\) 39.3818 1.58289 0.791444 0.611242i \(-0.209330\pi\)
0.791444 + 0.611242i \(0.209330\pi\)
\(620\) −11.1421 19.2987i −0.447479 0.775056i
\(621\) −17.4945 + 25.0259i −0.702030 + 1.00425i
\(622\) 20.3324 0.815256
\(623\) 0 0
\(624\) −1.74474 + 8.46079i −0.0698455 + 0.338703i
\(625\) −2.34479 −0.0937918
\(626\) 11.5098 19.9356i 0.460025 0.796787i
\(627\) 0.873885 4.23774i 0.0348996 0.169239i
\(628\) −1.28366 2.22337i −0.0512237 0.0887220i
\(629\) −19.5906 −0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) −6.69227 11.5913i −0.266204 0.461079i
\(633\) 13.6280 + 12.1216i 0.541663 + 0.481789i
\(634\) 25.4629 44.1030i 1.01126 1.75155i
\(635\) −35.8392 −1.42224
\(636\) 0.180653 0.0599137i 0.00716337 0.00237573i
\(637\) 0 0
\(638\) 8.11993 0.321471
\(639\) −6.91892 + 5.15649i −0.273708 + 0.203988i
\(640\) 22.9251 + 39.7075i 0.906195 + 1.56957i
\(641\) −14.9862 −0.591921 −0.295961 0.955200i \(-0.595640\pi\)
−0.295961 + 0.955200i \(0.595640\pi\)
\(642\) 14.9585 4.96099i 0.590366 0.195795i
\(643\) 5.32691 + 9.22649i 0.210073 + 0.363857i 0.951737 0.306914i \(-0.0992965\pi\)
−0.741664 + 0.670771i \(0.765963\pi\)
\(644\) 0 0
\(645\) −6.54009 + 31.7150i −0.257516 + 1.24878i
\(646\) −3.10507 5.37815i −0.122168 0.211600i
\(647\) −1.06478 1.84424i −0.0418606 0.0725047i 0.844336 0.535814i \(-0.179995\pi\)
−0.886197 + 0.463309i \(0.846662\pi\)
\(648\) −4.85848 + 16.2895i −0.190859 + 0.639913i
\(649\) −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
\(653\) 11.1716 0.437180 0.218590 0.975817i \(-0.429854\pi\)
0.218590 + 0.975817i \(0.429854\pi\)
\(654\) −11.2156 + 54.3882i −0.438567 + 2.12675i
\(655\) −57.6043 −2.25079
\(656\) −13.4956 + 23.3751i −0.526914 + 0.912642i
\(657\) 29.3200 + 12.6295i 1.14388 + 0.492723i
\(658\) 0 0
\(659\) 5.65452 9.79391i 0.220269 0.381517i −0.734621 0.678478i \(-0.762640\pi\)
0.954890 + 0.296961i \(0.0959733\pi\)
\(660\) 3.13582 15.2066i 0.122062 0.591914i
\(661\) −16.1785 + 28.0220i −0.629271 + 1.08993i 0.358427 + 0.933558i \(0.383313\pi\)
−0.987698 + 0.156372i \(0.950020\pi\)
\(662\) −1.77314 + 3.07117i −0.0689151 + 0.119364i
\(663\) −1.43818 + 6.97418i −0.0558542 + 0.270855i
\(664\) −3.88255 + 6.72477i −0.150672 + 0.260972i
\(665\) 0 0
\(666\) 19.4814 14.5190i 0.754890 0.562600i
\(667\) 4.99381 8.64953i 0.193361 0.334911i
\(668\) 10.7999 0.417860
\(669\) −1.98260 + 9.61425i −0.0766518 + 0.371708i
\(670\) −75.0714 −2.90026
\(671\) 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
\(675\) −23.4487 + 33.5434i −0.902541 + 1.29108i
\(676\) 5.33242 + 9.23601i 0.205093 + 0.355231i
\(677\) −12.5371 21.7148i −0.481838 0.834569i 0.517944 0.855414i \(-0.326697\pi\)
−0.999783 + 0.0208457i \(0.993364\pi\)
\(678\) −11.0297 + 53.4865i −0.423593 + 2.05414i
\(679\) 0 0
\(680\) 13.9320 + 24.1309i 0.534267 + 0.925378i
\(681\) 18.2465 6.05146i 0.699208 0.231892i
\(682\) 33.3832 1.27831
\(683\) 23.8392 + 41.2907i 0.912182 + 1.57995i 0.810975 + 0.585081i \(0.198937\pi\)
0.101207 + 0.994865i \(0.467729\pi\)
\(684\) 2.17625 + 0.937411i 0.0832109 + 0.0358428i
\(685\) 46.6043 1.78066
\(686\) 0 0
\(687\) −32.2927 + 10.7099i −1.23204 + 0.408607i
\(688\) −25.9862 −0.990716
\(689\) 0.0618219 0.107079i 0.00235523 0.00407937i
\(690\) −46.3825 41.2555i −1.76575 1.57057i
\(691\) 12.3400 + 21.3735i 0.469435 + 0.813085i 0.999389 0.0349408i \(-0.0111243\pi\)
−0.529954 + 0.848026i \(0.677791\pi\)
\(692\) −5.87402 −0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) 1.99381 + 3.45338i 0.0756295 + 0.130994i
\(696\) 1.12296 5.44556i 0.0425655 0.206413i
\(697\) −11.1243 + 19.2679i −0.421364 + 0.729824i
\(698\) −0.336134 −0.0127228
\(699\) 3.13533 15.2042i 0.118589 0.575076i
\(700\) 0 0
\(701\) −29.6784 −1.12094 −0.560469 0.828175i \(-0.689379\pi\)
−0.560469 + 0.828175i \(0.689379\pi\)
\(702\) −3.73855 8.00119i −0.141102 0.301986i
\(703\) 2.11745 + 3.66754i 0.0798613 + 0.138324i
\(704\) −5.58699 −0.210567
\(705\) 12.3819 + 11.0132i 0.466328 + 0.414781i
\(706\) 10.6243 + 18.4018i 0.399849 + 0.692559i
\(707\) 0 0
\(708\) −10.2095 9.08094i −0.383695 0.341282i
\(709\) 14.6291 + 25.3383i 0.549406 + 0.951599i 0.998315 + 0.0580220i \(0.0184794\pi\)
−0.448909 + 0.893577i \(0.648187\pi\)
\(710\) −8.77128 15.1923i −0.329180 0.570157i
\(711\) 19.5252 + 8.41040i 0.732251 + 0.315415i
\(712\) 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
\(716\) −3.41535 −0.127638
\(717\) 14.5240 + 12.9186i 0.542408 + 0.482452i
\(718\) 34.0260 1.26984
\(719\) −0.537063 + 0.930220i −0.0200291 + 0.0346913i −0.875866 0.482554i \(-0.839709\pi\)
0.855837 + 0.517245i \(0.173043\pi\)
\(720\) −49.3120 21.2410i −1.83775 0.791605i
\(721\) 0 0
\(722\) 15.4752 26.8039i 0.575929 0.997538i
\(723\) 11.4854 3.80912i 0.427145 0.141663i
\(724\) −8.23972 + 14.2716i −0.306227 + 0.530400i
\(725\) 6.69344 11.5934i 0.248588 0.430567i
\(726\) −6.81639 6.06293i −0.252980 0.225016i
\(727\) −12.7163 + 22.0253i −0.471623 + 0.816875i −0.999473 0.0324628i \(-0.989665\pi\)
0.527850 + 0.849338i \(0.322998\pi\)
\(728\) 0 0
\(729\) −9.27375 25.3574i −0.343472 0.939163i
\(730\) −32.4505 + 56.2059i −1.20105 + 2.08027i
\(731\) −21.4203 −0.792258
\(732\) −5.66366 + 1.87835i −0.209335 + 0.0694259i
\(733\) −11.3955 −0.420904 −0.210452 0.977604i \(-0.567494\pi\)
−0.210452 + 0.977604i \(0.567494\pi\)
\(734\) −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
\(738\) −3.21751 27.4051i −0.118438 1.00879i
\(739\) 14.9697 + 25.9283i 0.550671 + 0.953790i 0.998226 + 0.0595336i \(0.0189613\pi\)
−0.447556 + 0.894256i \(0.647705\pi\)
\(740\) 7.59820 + 13.1605i 0.279315 + 0.483788i
\(741\) 1.46108 0.484566i 0.0536740 0.0178010i
\(742\) 0 0
\(743\) 9.50069 + 16.4557i 0.348546 + 0.603700i 0.985991 0.166796i \(-0.0533420\pi\)
−0.637445 + 0.770496i \(0.720009\pi\)
\(744\) 4.61677 22.3881i 0.169259 0.820789i
\(745\) −30.2595 −1.10862
\(746\) −5.95922 10.3217i −0.218183 0.377903i
\(747\) −1.43818 12.2497i −0.0526202 0.448191i
\(748\) 10.2705 0.375527
\(749\) 0 0
\(750\) −22.7033 20.1937i −0.829006 0.737370i
\(751\) 0.0261368 0.000953747 0.000476873 1.00000i \(-0.499848\pi\)
0.000476873 1.00000i \(0.499848\pi\)
\(752\) −6.64902 + 11.5164i −0.242465 + 0.419961i
\(753\) −7.59593 + 2.51919i −0.276811 + 0.0918044i
\(754\) 1.44437 + 2.50172i 0.0526008 + 0.0911072i
\(755\) 53.2929 1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) 16.2095 + 28.0756i 0.588754 + 1.01975i
\(759\) 27.1552 9.00602i 0.985672 0.326898i
\(760\) 3.01169 5.21640i 0.109246 0.189219i
\(761\) −14.6428 −0.530802 −0.265401 0.964138i \(-0.585504\pi\)
−0.265401 + 0.964138i \(0.585504\pi\)
\(762\) 21.9691 + 19.5407i 0.795855 + 0.707883i
\(763\) 0 0
\(764\) 4.11855 0.149004
\(765\) −40.6476 17.5088i −1.46962 0.633032i
\(766\) −2.72803 4.72509i −0.0985677 0.170724i
\(767\) −8.87636 −0.320507
\(768\) 6.20630 30.0963i 0.223951 1.08601i
\(769\) −24.5672 42.5517i −0.885918 1.53445i −0.844658 0.535306i \(-0.820196\pi\)
−0.0412592 0.999148i \(-0.513137\pi\)
\(770\) 0 0
\(771\) 2.34108 0.776418i 0.0843118 0.0279620i
\(772\) 11.2410 + 19.4700i 0.404573 + 0.700741i
\(773\) −6.22067