Properties

Label 441.2.g.d.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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Newspace parameters

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

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
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
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.d.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.849814 - 1.47192i) q^{2} +(1.64400 - 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} +3.58836 q^{5} +(-2.19963 - 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})\) \(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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 2q^{3} - 3q^{4} + 10q^{5} - q^{6} - 12q^{8} + 8q^{9} + O(q^{10}) \) \( 6q + q^{2} - 2q^{3} - 3q^{4} + 10q^{5} - q^{6} - 12q^{8} + 8q^{9} - 4q^{11} + 11q^{12} + 3q^{13} + 11q^{15} - 3q^{16} - 12q^{17} - 23q^{18} - 3q^{19} - 16q^{20} + 15q^{22} + 12q^{25} - q^{26} + 7q^{27} - q^{29} - 5q^{30} - 3q^{31} + 8q^{32} - 5q^{33} - 3q^{34} - 11q^{36} + 3q^{37} - 16q^{38} + 2q^{39} - 42q^{40} - 22q^{41} + 3q^{43} - 23q^{44} + 4q^{45} - 12q^{46} - 9q^{47} + 14q^{48} - 10q^{50} + 3q^{51} - 6q^{52} + 18q^{53} - 4q^{54} + 12q^{55} + 11q^{57} - 18q^{58} - 9q^{59} + 37q^{60} - 6q^{61} + 36q^{62} - 24q^{64} + 5q^{65} + 32q^{66} - 12q^{68} + 39q^{69} + 18q^{71} + 9q^{72} + 3q^{73} + 12q^{74} + 35q^{75} - 21q^{76} + 10q^{78} - 15q^{79} + 11q^{80} + 8q^{81} + 9q^{82} - 12q^{83} - 9q^{85} + 68q^{86} + 10q^{87} - 42q^{88} - 2q^{89} - 73q^{90} - 15q^{92} - 15q^{93} + 24q^{94} - 16q^{95} - 2q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

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 \(-0.203565\pi\)
0.802383 + 0.596810i \(0.203565\pi\)
\(6\) −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 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 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 0.501435 0.865196i \(-0.332806\pi\)
−0.999999 + 0.00165734i \(0.999472\pi\)
\(18\) −4.68292 2.01715i −1.10377 0.475447i
\(19\) −0.444368 + 0.769668i −0.101945 + 0.176574i −0.912486 0.409108i \(-0.865840\pi\)
0.810541 + 0.585682i \(0.199173\pi\)
\(20\) −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 \(0.382591\pi\)
−0.988050 + 0.154131i \(0.950742\pi\)
\(32\) 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 0.573613 0.819126i \(-0.305541\pi\)
−0.996191 + 0.0872002i \(0.972208\pi\)
\(42\) 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 0.752268 0.658857i \(-0.228960\pi\)
−0.946721 + 0.322055i \(0.895627\pi\)
\(48\) 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 \(0.362756\pi\)
−0.995731 + 0.0923022i \(0.970577\pi\)
\(60\) −1.11559 + 5.40987i −0.144023 + 0.698411i
\(61\) 1.93818 + 3.35702i 0.248158 + 0.429823i 0.963015 0.269448i \(-0.0868414\pi\)
−0.714857 + 0.699271i \(0.753508\pi\)
\(62\) 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 \(-0.952685\pi\)
0.366229 0.930525i \(-0.380649\pi\)
\(74\) 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 −0.956510 0.291700i \(-0.905779\pi\)
0.730875 + 0.682512i \(0.239112\pi\)
\(84\) 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 \(-0.663239\pi\)
0.999942 0.0107692i \(-0.00342802\pi\)
\(90\) −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 −0.618137 0.786070i \(-0.712112\pi\)
0.989825 + 0.142287i \(0.0454456\pi\)
\(98\) 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 \(-0.555144\pi\)
−0.172376 + 0.985031i \(0.555144\pi\)
\(102\) −2.44437 + 11.8535i −0.242028 + 1.17367i
\(103\) 15.8764 1.56434 0.782172 0.623063i \(-0.214112\pi\)
0.782172 + 0.623063i \(0.214112\pi\)
\(104\) −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 \(-0.747389\pi\)
−0.701282 + 0.712884i \(0.747389\pi\)
\(132\) 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 0.888627 0.458630i \(-0.151660\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(140\) 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 −0.802616 0.596496i \(-0.796559\pi\)
0.917889 + 0.396837i \(0.129892\pi\)
\(158\) 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 0.999418 0.0341045i \(-0.0108579\pi\)
−0.529244 + 0.848469i \(0.677525\pi\)
\(168\) 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 0.712619 0.701551i \(-0.247509\pi\)
−0.963871 + 0.266370i \(0.914176\pi\)
\(174\) −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 \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(182\) 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 0.667799 0.744342i \(-0.267237\pi\)
−0.978518 + 0.206160i \(0.933903\pi\)
\(200\) −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 −0.945172 0.326574i \(-0.894106\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(224\) 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 \(-0.379930\pi\)
0.368329 + 0.929695i \(0.379930\pi\)
\(228\) −1.02221 0.909219i −0.0676976 0.0602145i
\(229\) −19.6428 −1.29803 −0.649017 0.760774i \(-0.724820\pi\)
−0.649017 + 0.760774i \(0.724820\pi\)
\(230\) −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 \(-0.427758\pi\)
0.225012 + 0.974356i \(0.427758\pi\)
\(242\) 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 \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(252\) 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 \(-0.485858\pi\)
0.0444138 + 0.999013i \(0.485858\pi\)
\(258\) 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 \(-0.974124\pi\)
0.428026 0.903767i \(-0.359209\pi\)
\(270\) −31.5723 2.73763i −1.92143 0.166607i
\(271\) 1.98143 3.43194i 0.120363 0.208475i −0.799548 0.600603i \(-0.794927\pi\)
0.919911 + 0.392127i \(0.128261\pi\)
\(272\) 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 −0.670914 0.741535i \(-0.734098\pi\)
0.977645 + 0.210261i \(0.0674314\pi\)
\(284\) 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 \(-0.812670\pi\)
−0.0648718 0.997894i \(-0.520664\pi\)
\(294\) 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 \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 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 −0.645102 0.764096i \(-0.723185\pi\)
0.984278 + 0.176627i \(0.0565185\pi\)
\(312\) −2.44437 2.17417i −0.138385 0.123088i
\(313\) −6.77197 11.7294i −0.382774 0.662985i 0.608683 0.793413i \(-0.291698\pi\)
−0.991458 + 0.130429i \(0.958365\pi\)
\(314\) −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 −0.868660 0.495409i \(-0.835018\pi\)
0.863367 + 0.504577i \(0.168352\pi\)
\(350\) 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 \(-0.392039\pi\)
0.332703 + 0.943032i \(0.392039\pi\)
\(354\) 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 \(-0.787282\pi\)
−0.784892 + 0.619632i \(0.787282\pi\)
\(368\) 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 \(-0.526136\pi\)
−0.0820155 + 0.996631i \(0.526136\pi\)
\(384\) −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 \(-0.638096\pi\)
0.995975 0.0896370i \(-0.0285707\pi\)
\(398\) −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 −0.990927 0.134400i \(-0.957089\pi\)
0.611858 + 0.790968i \(0.290423\pi\)
\(410\) −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 0.965748 0.259481i \(-0.0835513\pi\)
−0.707591 + 0.706622i \(0.750218\pi\)
\(420\) 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 \(-0.0465533\pi\)
0.989324 + 0.145731i \(0.0465533\pi\)
\(434\) 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 0.804787 0.593564i \(-0.202280\pi\)
−0.916435 + 0.400184i \(0.868946\pi\)
\(440\) 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 \(-0.468869\pi\)
0.813064 0.582175i \(-0.197798\pi\)
\(462\) 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 −0.972622 0.232394i \(-0.925344\pi\)
0.687570 + 0.726118i \(0.258677\pi\)
\(468\) −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 \(-0.599718\pi\)
−0.308175 + 0.951330i \(0.599718\pi\)
\(480\) 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 \(-0.685033\pi\)
−0.549109 + 0.835751i \(0.685033\pi\)
\(504\) 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 \(-0.597380\pi\)
−0.301177 + 0.953568i \(0.597380\pi\)
\(510\) −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 \(-0.838311\pi\)
0.0156383 0.999878i \(-0.495022\pi\)
\(522\) −6.94870 + 5.17868i −0.304136 + 0.226665i
\(523\) 9.56182 16.5616i 0.418109 0.724187i −0.577640 0.816292i \(-0.696026\pi\)
0.995749 + 0.0921051i \(0.0293596\pi\)
\(524\) 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 −0.997454 0.0713087i \(-0.977282\pi\)
0.560482 + 0.828166i \(0.310616\pi\)
\(564\) 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 0.917000 0.398887i \(-0.130603\pi\)
−0.803946 + 0.594702i \(0.797270\pi\)
\(578\) −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 \(-0.574852\pi\)
0.958688 0.284461i \(-0.0918145\pi\)
\(588\) 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 \(0.408169\pi\)
−0.972490 + 0.232943i \(0.925164\pi\)
\(594\) 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 −0.541783 0.840519i \(-0.682250\pi\)
0.998802 + 0.0489384i \(0.0155838\pi\)
\(602\) 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 \(-0.598125\pi\)
−0.303411 + 0.952860i \(0.598125\pi\)
\(608\) 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 \(-0.790670\pi\)
−0.791444 + 0.611242i \(0.790670\pi\)
\(620\) −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 0.741664 0.670771i \(-0.234037\pi\)
−0.951737 + 0.306914i \(0.900703\pi\)
\(644\) 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 0.886197 0.463309i \(-0.153338\pi\)
−0.844336 + 0.535814i \(0.820005\pi\)
\(648\) −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 \(-0.616687\pi\)
0.987698 0.156372i \(-0.0499798\pi\)
\(662\) −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 0.999783 0.0208457i \(-0.00663587\pi\)
−0.517944 + 0.855414i \(0.673303\pi\)
\(678\) 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 0.529954 0.848026i \(-0.322209\pi\)
−0.999389 + 0.0349408i \(0.988876\pi\)
\(692\) 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 −0.855837 0.517245i \(-0.826957\pi\)
0.875866 + 0.482554i \(0.160291\pi\)
\(720\) 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 −0.527850 0.849338i \(-0.677002\pi\)
0.999473 + 0.0324628i \(0.0103350\pi\)
\(728\) 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 \(-0.432506\pi\)
0.210452 + 0.977604i \(0.432506\pi\)
\(734\) 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 \(-0.414496\pi\)
0.265401 + 0.964138i \(0.414496\pi\)
\(762\) −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 \(0.179804\pi\)
0.0412592 + 0.999148i \(0.486863\pi\)
\(770\) 0 0
\(771\) 2.34108 0.776418i 0.0843118 0.0279620i
\(772\) 11.2410 + 19.4700i 0.404573 + 0.700741i
\(773\) 6.22067 + 10.7745i 0.223742 + 0.387532i 0.955941 0.293558i \(-0.0948394\pi\)
−0.732199 + 0.681090i \(0.761506\pi\)
\(774\) 21.3010 15.8751i 0.765648 0.570617i
\(775\) −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
\(779\) 4.80951 0.172319
\(780\) −5.24288 + 1.73880i −0.187725 + 0.0622590i