Properties

Label 570.2.i.h.391.1
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{19})\)
Defining polynomial: \(x^{4} + 19 x^{2} + 361\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(2.17945 - 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.h.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -4.35890 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.17945 + 3.77492i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.67945 + 2.90889i) q^{17} -1.00000 q^{18} +(-2.17945 + 3.77492i) q^{19} -1.00000 q^{20} +(2.17945 - 3.77492i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{26} +1.00000 q^{27} +(2.17945 + 3.77492i) q^{28} +(-4.67945 - 8.10504i) q^{29} +1.00000 q^{30} -10.7178 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.67945 + 2.90889i) q^{34} +(-2.17945 + 3.77492i) q^{35} +(-0.500000 + 0.866025i) q^{36} -7.00000 q^{37} +(2.17945 + 3.77492i) q^{38} -4.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.17945 - 5.50697i) q^{41} +(-2.17945 - 3.77492i) q^{42} +(5.00000 - 8.66025i) q^{43} +(1.50000 + 2.59808i) q^{44} -1.00000 q^{45} +3.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} +12.0000 q^{49} -1.00000 q^{50} +(-1.67945 - 2.90889i) q^{51} +(2.00000 - 3.46410i) q^{52} +(6.53835 + 11.3248i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.50000 + 2.59808i) q^{55} +4.35890 q^{56} +(-2.17945 - 3.77492i) q^{57} -9.35890 q^{58} +(-6.35890 + 11.0139i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-2.67945 - 4.64094i) q^{61} +(-5.35890 + 9.28189i) q^{62} +(2.17945 + 3.77492i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(-1.50000 - 2.59808i) q^{66} +(-5.67945 - 9.83710i) q^{67} +3.35890 q^{68} -3.00000 q^{69} +(2.17945 + 3.77492i) q^{70} +(5.03835 - 8.72668i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-2.32055 + 4.01931i) q^{73} +(-3.50000 + 6.06218i) q^{74} +1.00000 q^{75} +4.35890 q^{76} +13.0767 q^{77} +(-2.00000 + 3.46410i) q^{78} +(2.35890 - 4.08573i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.17945 - 5.50697i) q^{82} -6.00000 q^{83} -4.35890 q^{84} +(1.67945 + 2.90889i) q^{85} +(-5.00000 - 8.66025i) q^{86} +9.35890 q^{87} +3.00000 q^{88} +(-0.179449 - 0.310816i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-8.71780 - 15.0997i) q^{91} +(1.50000 - 2.59808i) q^{92} +(5.35890 - 9.28189i) q^{93} +6.00000 q^{94} +(2.17945 + 3.77492i) q^{95} -1.00000 q^{96} +(7.03835 - 12.1908i) q^{97} +(6.00000 - 10.3923i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} + 2q^{6} - 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} + 4q^{12} + 8q^{13} + 2q^{15} - 2q^{16} + 2q^{17} - 4q^{18} - 4q^{20} - 6q^{22} + 6q^{23} + 2q^{24} - 2q^{25} + 16q^{26} + 4q^{27} - 10q^{29} + 4q^{30} - 8q^{31} + 2q^{32} + 6q^{33} - 2q^{34} - 2q^{36} - 28q^{37} - 16q^{39} - 2q^{40} + 4q^{41} + 20q^{43} + 6q^{44} - 4q^{45} + 12q^{46} + 12q^{47} - 2q^{48} + 48q^{49} - 4q^{50} + 2q^{51} + 8q^{52} + 2q^{54} - 6q^{55} - 20q^{58} - 8q^{59} + 2q^{60} - 2q^{61} - 4q^{62} + 4q^{64} + 16q^{65} - 6q^{66} - 14q^{67} - 4q^{68} - 12q^{69} - 6q^{71} + 2q^{72} - 18q^{73} - 14q^{74} + 4q^{75} - 8q^{78} - 8q^{79} + 2q^{80} - 2q^{81} - 4q^{82} - 24q^{83} - 2q^{85} - 20q^{86} + 20q^{87} + 12q^{88} + 8q^{89} - 2q^{90} + 6q^{92} + 4q^{93} + 24q^{94} - 4q^{96} + 2q^{97} + 24q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −4.35890 −1.64751 −0.823754 0.566947i \(-0.808125\pi\)
−0.823754 + 0.566947i \(0.808125\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) −2.17945 + 3.77492i −0.582482 + 1.00889i
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.67945 + 2.90889i −0.407326 + 0.705510i −0.994589 0.103886i \(-0.966872\pi\)
0.587263 + 0.809396i \(0.300205\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.17945 + 3.77492i −0.500000 + 0.866025i
\(20\) −1.00000 −0.223607
\(21\) 2.17945 3.77492i 0.475595 0.823754i
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) 2.17945 + 3.77492i 0.411877 + 0.713392i
\(29\) −4.67945 8.10504i −0.868952 1.50507i −0.863069 0.505086i \(-0.831461\pi\)
−0.00588307 0.999983i \(-0.501873\pi\)
\(30\) 1.00000 0.182574
\(31\) −10.7178 −1.92497 −0.962487 0.271329i \(-0.912537\pi\)
−0.962487 + 0.271329i \(0.912537\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 1.67945 + 2.90889i 0.288023 + 0.498871i
\(35\) −2.17945 + 3.77492i −0.368394 + 0.638077i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 2.17945 + 3.77492i 0.353553 + 0.612372i
\(39\) −4.00000 −0.640513
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 3.17945 5.50697i 0.496547 0.860044i −0.503445 0.864027i \(-0.667935\pi\)
0.999992 + 0.00398308i \(0.00126786\pi\)
\(42\) −2.17945 3.77492i −0.336296 0.582482i
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) −1.00000 −0.149071
\(46\) 3.00000 0.442326
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 12.0000 1.71429
\(50\) −1.00000 −0.141421
\(51\) −1.67945 2.90889i −0.235170 0.407326i
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 6.53835 + 11.3248i 0.898111 + 1.55557i 0.829906 + 0.557903i \(0.188394\pi\)
0.0682050 + 0.997671i \(0.478273\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −1.50000 + 2.59808i −0.202260 + 0.350325i
\(56\) 4.35890 0.582482
\(57\) −2.17945 3.77492i −0.288675 0.500000i
\(58\) −9.35890 −1.22888
\(59\) −6.35890 + 11.0139i −0.827858 + 1.43389i 0.0718571 + 0.997415i \(0.477107\pi\)
−0.899715 + 0.436477i \(0.856226\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −2.67945 4.64094i −0.343068 0.594212i 0.641933 0.766761i \(-0.278133\pi\)
−0.985001 + 0.172549i \(0.944800\pi\)
\(62\) −5.35890 + 9.28189i −0.680581 + 1.17880i
\(63\) 2.17945 + 3.77492i 0.274585 + 0.475595i
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) −5.67945 9.83710i −0.693855 1.20179i −0.970565 0.240839i \(-0.922577\pi\)
0.276710 0.960953i \(-0.410756\pi\)
\(68\) 3.35890 0.407326
\(69\) −3.00000 −0.361158
\(70\) 2.17945 + 3.77492i 0.260494 + 0.451189i
\(71\) 5.03835 8.72668i 0.597942 1.03567i −0.395183 0.918603i \(-0.629319\pi\)
0.993124 0.117063i \(-0.0373480\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −2.32055 + 4.01931i −0.271600 + 0.470425i −0.969272 0.245993i \(-0.920886\pi\)
0.697672 + 0.716418i \(0.254219\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) 1.00000 0.115470
\(76\) 4.35890 0.500000
\(77\) 13.0767 1.49023
\(78\) −2.00000 + 3.46410i −0.226455 + 0.392232i
\(79\) 2.35890 4.08573i 0.265397 0.459681i −0.702271 0.711910i \(-0.747830\pi\)
0.967668 + 0.252229i \(0.0811637\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.17945 5.50697i −0.351111 0.608143i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −4.35890 −0.475595
\(85\) 1.67945 + 2.90889i 0.182162 + 0.315514i
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 9.35890 1.00338
\(88\) 3.00000 0.319801
\(89\) −0.179449 0.310816i −0.0190216 0.0329464i 0.856358 0.516383i \(-0.172722\pi\)
−0.875380 + 0.483436i \(0.839388\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) −8.71780 15.0997i −0.913874 1.58288i
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 5.35890 9.28189i 0.555692 0.962487i
\(94\) 6.00000 0.618853
\(95\) 2.17945 + 3.77492i 0.223607 + 0.387298i
\(96\) −1.00000 −0.102062
\(97\) 7.03835 12.1908i 0.714636 1.23779i −0.248464 0.968641i \(-0.579926\pi\)
0.963100 0.269145i \(-0.0867410\pi\)
\(98\) 6.00000 10.3923i 0.606092 1.04978i
\(99\) 1.50000 + 2.59808i 0.150756 + 0.261116i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 6.35890 + 11.0139i 0.632734 + 1.09593i 0.986990 + 0.160779i \(0.0514007\pi\)
−0.354256 + 0.935148i \(0.615266\pi\)
\(102\) −3.35890 −0.332581
\(103\) −10.3589 −1.02069 −0.510346 0.859969i \(-0.670483\pi\)
−0.510346 + 0.859969i \(0.670483\pi\)
\(104\) −2.00000 3.46410i −0.196116 0.339683i
\(105\) −2.17945 3.77492i −0.212692 0.368394i
\(106\) 13.0767 1.27012
\(107\) 9.35890 0.904759 0.452379 0.891826i \(-0.350575\pi\)
0.452379 + 0.891826i \(0.350575\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −5.32055 + 9.21546i −0.509616 + 0.882681i 0.490322 + 0.871542i \(0.336879\pi\)
−0.999938 + 0.0111398i \(0.996454\pi\)
\(110\) 1.50000 + 2.59808i 0.143019 + 0.247717i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 2.17945 3.77492i 0.205939 0.356696i
\(113\) 3.35890 0.315979 0.157989 0.987441i \(-0.449499\pi\)
0.157989 + 0.987441i \(0.449499\pi\)
\(114\) −4.35890 −0.408248
\(115\) 3.00000 0.279751
\(116\) −4.67945 + 8.10504i −0.434476 + 0.752534i
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) 6.35890 + 11.0139i 0.585384 + 1.01391i
\(119\) 7.32055 12.6796i 0.671074 1.16233i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −2.00000 −0.181818
\(122\) −5.35890 −0.485172
\(123\) 3.17945 + 5.50697i 0.286681 + 0.496547i
\(124\) 5.35890 + 9.28189i 0.481243 + 0.833538i
\(125\) −1.00000 −0.0894427
\(126\) 4.35890 0.388322
\(127\) 5.17945 + 8.97107i 0.459602 + 0.796054i 0.998940 0.0460357i \(-0.0146588\pi\)
−0.539338 + 0.842089i \(0.681325\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 5.00000 + 8.66025i 0.440225 + 0.762493i
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) −3.00000 −0.261116
\(133\) 9.50000 16.4545i 0.823754 1.42678i
\(134\) −11.3589 −0.981259
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 1.67945 2.90889i 0.144012 0.249435i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −1.50000 + 2.59808i −0.127688 + 0.221163i
\(139\) −0.641101 1.11042i −0.0543775 0.0941846i 0.837555 0.546353i \(-0.183984\pi\)
−0.891933 + 0.452168i \(0.850651\pi\)
\(140\) 4.35890 0.368394
\(141\) −6.00000 −0.505291
\(142\) −5.03835 8.72668i −0.422809 0.732326i
\(143\) −6.00000 10.3923i −0.501745 0.869048i
\(144\) 1.00000 0.0833333
\(145\) −9.35890 −0.777214
\(146\) 2.32055 + 4.01931i 0.192050 + 0.332641i
\(147\) −6.00000 + 10.3923i −0.494872 + 0.857143i
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) 5.03835 8.72668i 0.412758 0.714917i −0.582433 0.812879i \(-0.697899\pi\)
0.995190 + 0.0979619i \(0.0312323\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −2.07670 −0.168999 −0.0844996 0.996424i \(-0.526929\pi\)
−0.0844996 + 0.996424i \(0.526929\pi\)
\(152\) 2.17945 3.77492i 0.176777 0.306186i
\(153\) 3.35890 0.271551
\(154\) 6.53835 11.3248i 0.526875 0.912574i
\(155\) −5.35890 + 9.28189i −0.430437 + 0.745539i
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −2.50000 + 4.33013i −0.199522 + 0.345582i −0.948373 0.317156i \(-0.897272\pi\)
0.748852 + 0.662738i \(0.230606\pi\)
\(158\) −2.35890 4.08573i −0.187664 0.325043i
\(159\) −13.0767 −1.03705
\(160\) 1.00000 0.0790569
\(161\) −6.53835 11.3248i −0.515294 0.892515i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −4.71780 −0.369526 −0.184763 0.982783i \(-0.559152\pi\)
−0.184763 + 0.982783i \(0.559152\pi\)
\(164\) −6.35890 −0.496547
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 11.2178 + 19.4298i 0.868059 + 1.50352i 0.863977 + 0.503531i \(0.167966\pi\)
0.00408215 + 0.999992i \(0.498701\pi\)
\(168\) −2.17945 + 3.77492i −0.168148 + 0.291241i
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 3.35890 0.257616
\(171\) 4.35890 0.333333
\(172\) −10.0000 −0.762493
\(173\) −9.17945 + 15.8993i −0.697901 + 1.20880i 0.271292 + 0.962497i \(0.412549\pi\)
−0.969193 + 0.246302i \(0.920784\pi\)
\(174\) 4.67945 8.10504i 0.354748 0.614442i
\(175\) 2.17945 + 3.77492i 0.164751 + 0.285357i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −6.35890 11.0139i −0.477964 0.827858i
\(178\) −0.358899 −0.0269006
\(179\) 15.7178 1.17480 0.587402 0.809296i \(-0.300151\pi\)
0.587402 + 0.809296i \(0.300151\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −9.03835 15.6549i −0.671815 1.16362i −0.977389 0.211450i \(-0.932182\pi\)
0.305574 0.952168i \(-0.401152\pi\)
\(182\) −17.4356 −1.29241
\(183\) 5.35890 0.396141
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) −3.50000 + 6.06218i −0.257325 + 0.445700i
\(186\) −5.35890 9.28189i −0.392934 0.680581i
\(187\) 5.03835 8.72668i 0.368441 0.638158i
\(188\) 3.00000 5.19615i 0.218797 0.378968i
\(189\) −4.35890 −0.317063
\(190\) 4.35890 0.316228
\(191\) −19.4356 −1.40631 −0.703155 0.711036i \(-0.748226\pi\)
−0.703155 + 0.711036i \(0.748226\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −12.0383 + 20.8510i −0.866539 + 1.50089i −0.00102867 + 0.999999i \(0.500327\pi\)
−0.865511 + 0.500891i \(0.833006\pi\)
\(194\) −7.03835 12.1908i −0.505324 0.875247i
\(195\) −2.00000 + 3.46410i −0.143223 + 0.248069i
\(196\) −6.00000 10.3923i −0.428571 0.742307i
\(197\) −5.64110 −0.401912 −0.200956 0.979600i \(-0.564405\pi\)
−0.200956 + 0.979600i \(0.564405\pi\)
\(198\) 3.00000 0.213201
\(199\) −8.32055 14.4116i −0.589828 1.02161i −0.994255 0.107042i \(-0.965862\pi\)
0.404426 0.914571i \(-0.367471\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 11.3589 0.801195
\(202\) 12.7178 0.894821
\(203\) 20.3972 + 35.3291i 1.43161 + 2.47961i
\(204\) −1.67945 + 2.90889i −0.117585 + 0.203663i
\(205\) −3.17945 5.50697i −0.222062 0.384623i
\(206\) −5.17945 + 8.97107i −0.360869 + 0.625044i
\(207\) 1.50000 2.59808i 0.104257 0.180579i
\(208\) −4.00000 −0.277350
\(209\) 6.53835 11.3248i 0.452267 0.783349i
\(210\) −4.35890 −0.300793
\(211\) −7.53835 + 13.0568i −0.518961 + 0.898867i 0.480796 + 0.876833i \(0.340348\pi\)
−0.999757 + 0.0220348i \(0.992986\pi\)
\(212\) 6.53835 11.3248i 0.449056 0.777787i
\(213\) 5.03835 + 8.72668i 0.345222 + 0.597942i
\(214\) 4.67945 8.10504i 0.319881 0.554049i
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) −1.00000 −0.0680414
\(217\) 46.7178 3.17141
\(218\) 5.32055 + 9.21546i 0.360353 + 0.624150i
\(219\) −2.32055 4.01931i −0.156808 0.271600i
\(220\) 3.00000 0.202260
\(221\) −13.4356 −0.903776
\(222\) −3.50000 6.06218i −0.234905 0.406867i
\(223\) −10.1794 + 17.6313i −0.681666 + 1.18068i 0.292806 + 0.956172i \(0.405411\pi\)
−0.974472 + 0.224509i \(0.927922\pi\)
\(224\) −2.17945 3.77492i −0.145621 0.252222i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 1.67945 2.90889i 0.111715 0.193497i
\(227\) −3.35890 −0.222938 −0.111469 0.993768i \(-0.535556\pi\)
−0.111469 + 0.993768i \(0.535556\pi\)
\(228\) −2.17945 + 3.77492i −0.144338 + 0.250000i
\(229\) 8.71780 0.576088 0.288044 0.957617i \(-0.406995\pi\)
0.288044 + 0.957617i \(0.406995\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) −6.53835 + 11.3248i −0.430192 + 0.745114i
\(232\) 4.67945 + 8.10504i 0.307221 + 0.532122i
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 6.00000 0.391397
\(236\) 12.7178 0.827858
\(237\) 2.35890 + 4.08573i 0.153227 + 0.265397i
\(238\) −7.32055 12.6796i −0.474521 0.821894i
\(239\) −13.4356 −0.869076 −0.434538 0.900653i \(-0.643088\pi\)
−0.434538 + 0.900653i \(0.643088\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −2.67945 + 4.64094i −0.171534 + 0.297106i
\(245\) 6.00000 10.3923i 0.383326 0.663940i
\(246\) 6.35890 0.405429
\(247\) −17.4356 −1.10940
\(248\) 10.7178 0.680581
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 2.17945 3.77492i 0.137292 0.237797i
\(253\) −4.50000 7.79423i −0.282913 0.490019i
\(254\) 10.3589 0.649975
\(255\) −3.35890 −0.210342
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.71780 + 6.43941i 0.231910 + 0.401680i 0.958370 0.285529i \(-0.0921692\pi\)
−0.726460 + 0.687208i \(0.758836\pi\)
\(258\) 10.0000 0.622573
\(259\) 30.5123 1.89594
\(260\) −2.00000 3.46410i −0.124035 0.214834i
\(261\) −4.67945 + 8.10504i −0.289651 + 0.501690i
\(262\) −1.50000 2.59808i −0.0926703 0.160510i
\(263\) 4.14110 7.17260i 0.255351 0.442281i −0.709640 0.704565i \(-0.751142\pi\)
0.964991 + 0.262284i \(0.0844756\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 13.0767 0.803295
\(266\) −9.50000 16.4545i −0.582482 1.00889i
\(267\) 0.358899 0.0219643
\(268\) −5.67945 + 9.83710i −0.346928 + 0.600896i
\(269\) −1.67945 + 2.90889i −0.102398 + 0.177358i −0.912672 0.408693i \(-0.865985\pi\)
0.810274 + 0.586051i \(0.199318\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 2.35890 4.08573i 0.143293 0.248191i −0.785442 0.618935i \(-0.787564\pi\)
0.928735 + 0.370745i \(0.120898\pi\)
\(272\) −1.67945 2.90889i −0.101832 0.176377i
\(273\) 17.4356 1.05525
\(274\) −12.0000 −0.724947
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) −1.28220 −0.0769014
\(279\) 5.35890 + 9.28189i 0.320829 + 0.555692i
\(280\) 2.17945 3.77492i 0.130247 0.225594i
\(281\) −0.538348 0.932447i −0.0321152 0.0556251i 0.849521 0.527555i \(-0.176891\pi\)
−0.881636 + 0.471930i \(0.843558\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −4.35890 + 7.54983i −0.259110 + 0.448791i −0.966004 0.258528i \(-0.916762\pi\)
0.706894 + 0.707319i \(0.250096\pi\)
\(284\) −10.0767 −0.597942
\(285\) −4.35890 −0.258199
\(286\) −12.0000 −0.709575
\(287\) −13.8589 + 24.0043i −0.818065 + 1.41693i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 2.85890 + 4.95176i 0.168171 + 0.291280i
\(290\) −4.67945 + 8.10504i −0.274787 + 0.475945i
\(291\) 7.03835 + 12.1908i 0.412595 + 0.714636i
\(292\) 4.64110 0.271600
\(293\) 5.64110 0.329557 0.164778 0.986331i \(-0.447309\pi\)
0.164778 + 0.986331i \(0.447309\pi\)
\(294\) 6.00000 + 10.3923i 0.349927 + 0.606092i
\(295\) 6.35890 + 11.0139i 0.370229 + 0.641256i
\(296\) 7.00000 0.406867
\(297\) −3.00000 −0.174078
\(298\) −5.03835 8.72668i −0.291864 0.505523i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) −21.7945 + 37.7492i −1.25621 + 2.17583i
\(302\) −1.03835 + 1.79847i −0.0597502 + 0.103490i
\(303\) −12.7178 −0.730618
\(304\) −2.17945 3.77492i −0.125000 0.216506i
\(305\) −5.35890 −0.306850
\(306\) 1.67945 2.90889i 0.0960077 0.166290i
\(307\) 0.679449 1.17684i 0.0387782 0.0671659i −0.845985 0.533207i \(-0.820987\pi\)
0.884763 + 0.466041i \(0.154320\pi\)
\(308\) −6.53835 11.3248i −0.372557 0.645288i
\(309\) 5.17945 8.97107i 0.294649 0.510346i
\(310\) 5.35890 + 9.28189i 0.304365 + 0.527176i
\(311\) 1.43560 0.0814052 0.0407026 0.999171i \(-0.487040\pi\)
0.0407026 + 0.999171i \(0.487040\pi\)
\(312\) 4.00000 0.226455
\(313\) 8.71780 + 15.0997i 0.492759 + 0.853484i 0.999965 0.00834102i \(-0.00265506\pi\)
−0.507206 + 0.861825i \(0.669322\pi\)
\(314\) 2.50000 + 4.33013i 0.141083 + 0.244363i
\(315\) 4.35890 0.245596
\(316\) −4.71780 −0.265397
\(317\) −9.53835 16.5209i −0.535727 0.927906i −0.999128 0.0417576i \(-0.986704\pi\)
0.463401 0.886149i \(-0.346629\pi\)
\(318\) −6.53835 + 11.3248i −0.366652 + 0.635061i
\(319\) 14.0383 + 24.3151i 0.785997 + 1.36139i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −4.67945 + 8.10504i −0.261181 + 0.452379i
\(322\) −13.0767 −0.728736
\(323\) −7.32055 12.6796i −0.407326 0.705510i
\(324\) 1.00000 0.0555556
\(325\) 2.00000 3.46410i 0.110940 0.192154i
\(326\) −2.35890 + 4.08573i −0.130647 + 0.226288i
\(327\) −5.32055 9.21546i −0.294227 0.509616i
\(328\) −3.17945 + 5.50697i −0.175556 + 0.304071i
\(329\) −13.0767 22.6495i −0.720942 1.24871i
\(330\) −3.00000 −0.165145
\(331\) 14.3589 0.789236 0.394618 0.918845i \(-0.370877\pi\)
0.394618 + 0.918845i \(0.370877\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 3.50000 + 6.06218i 0.191799 + 0.332205i
\(334\) 22.4356 1.22762
\(335\) −11.3589 −0.620603
\(336\) 2.17945 + 3.77492i 0.118899 + 0.205939i
\(337\) −11.0767 + 19.1854i −0.603386 + 1.04510i 0.388918 + 0.921272i \(0.372849\pi\)
−0.992304 + 0.123823i \(0.960484\pi\)
\(338\) 1.50000 + 2.59808i 0.0815892 + 0.141317i
\(339\) −1.67945 + 2.90889i −0.0912152 + 0.157989i
\(340\) 1.67945 2.90889i 0.0910809 0.157757i
\(341\) 32.1534 1.74120
\(342\) 2.17945 3.77492i 0.117851 0.204124i
\(343\) −21.7945 −1.17679
\(344\) −5.00000 + 8.66025i −0.269582 + 0.466930i
\(345\) −1.50000 + 2.59808i −0.0807573 + 0.139876i
\(346\) 9.17945 + 15.8993i 0.493490 + 0.854750i
\(347\) 3.71780 6.43941i 0.199582 0.345686i −0.748811 0.662784i \(-0.769375\pi\)
0.948393 + 0.317098i \(0.102708\pi\)
\(348\) −4.67945 8.10504i −0.250845 0.434476i
\(349\) 0.0766968 0.00410549 0.00205274 0.999998i \(-0.499347\pi\)
0.00205274 + 0.999998i \(0.499347\pi\)
\(350\) 4.35890 0.232993
\(351\) 2.00000 + 3.46410i 0.106752 + 0.184900i
\(352\) −1.50000 2.59808i −0.0799503 0.138478i
\(353\) −10.0767 −0.536328 −0.268164 0.963373i \(-0.586417\pi\)
−0.268164 + 0.963373i \(0.586417\pi\)
\(354\) −12.7178 −0.675943
\(355\) −5.03835 8.72668i −0.267408 0.463164i
\(356\) −0.179449 + 0.310816i −0.00951080 + 0.0164732i
\(357\) 7.32055 + 12.6796i 0.387445 + 0.671074i
\(358\) 7.85890 13.6120i 0.415356 0.719417i
\(359\) −7.67945 + 13.3012i −0.405306 + 0.702010i −0.994357 0.106085i \(-0.966168\pi\)
0.589051 + 0.808096i \(0.299502\pi\)
\(360\) 1.00000 0.0527046
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) −18.0767 −0.950090
\(363\) 1.00000 1.73205i 0.0524864 0.0909091i
\(364\) −8.71780 + 15.0997i −0.456937 + 0.791438i
\(365\) 2.32055 + 4.01931i 0.121463 + 0.210380i
\(366\) 2.67945 4.64094i 0.140057 0.242586i
\(367\) −7.35890 12.7460i −0.384131 0.665335i 0.607517 0.794307i \(-0.292166\pi\)
−0.991648 + 0.128972i \(0.958832\pi\)
\(368\) −3.00000 −0.156386
\(369\) −6.35890 −0.331031
\(370\) 3.50000 + 6.06218i 0.181956 + 0.315158i
\(371\) −28.5000 49.3634i −1.47965 2.56282i
\(372\) −10.7178 −0.555692
\(373\) 11.0000 0.569558 0.284779 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(374\) −5.03835 8.72668i −0.260527 0.451246i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) 18.7178 32.4202i 0.964016 1.66972i
\(378\) −2.17945 + 3.77492i −0.112099 + 0.194161i
\(379\) 14.7178 0.756002 0.378001 0.925805i \(-0.376611\pi\)
0.378001 + 0.925805i \(0.376611\pi\)
\(380\) 2.17945 3.77492i 0.111803 0.193649i
\(381\) −10.3589 −0.530702
\(382\) −9.71780 + 16.8317i −0.497206 + 0.861186i
\(383\) −3.00000 + 5.19615i −0.153293 + 0.265511i −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 6.53835 11.3248i 0.333225 0.577163i
\(386\) 12.0383 + 20.8510i 0.612736 + 1.06129i
\(387\) −10.0000 −0.508329
\(388\) −14.0767 −0.714636
\(389\) −2.03835 3.53052i −0.103348 0.179005i 0.809714 0.586825i \(-0.199622\pi\)
−0.913062 + 0.407820i \(0.866289\pi\)
\(390\) 2.00000 + 3.46410i 0.101274 + 0.175412i
\(391\) −10.0767 −0.509600
\(392\) −12.0000 −0.606092
\(393\) 1.50000 + 2.59808i 0.0756650 + 0.131056i
\(394\) −2.82055 + 4.88534i −0.142097 + 0.246120i
\(395\) −2.35890 4.08573i −0.118689 0.205576i
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) −3.21780 + 5.57339i −0.161497 + 0.279720i −0.935406 0.353576i \(-0.884965\pi\)
0.773909 + 0.633297i \(0.218299\pi\)
\(398\) −16.6411 −0.834143
\(399\) 9.50000 + 16.4545i 0.475595 + 0.823754i
\(400\) 1.00000 0.0500000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 5.67945 9.83710i 0.283265 0.490630i
\(403\) −21.4356 37.1275i −1.06778 1.84945i
\(404\) 6.35890 11.0139i 0.316367 0.547964i
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) 40.7945 2.02460
\(407\) 21.0000 1.04093
\(408\) 1.67945 + 2.90889i 0.0831451 + 0.144012i
\(409\) −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) −6.35890 −0.314044
\(411\) 12.0000 0.591916
\(412\) 5.17945 + 8.97107i 0.255173 + 0.441973i
\(413\) 27.7178 48.0086i 1.36390 2.36235i
\(414\) −1.50000 2.59808i −0.0737210 0.127688i
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) 1.28220 0.0627897
\(418\) −6.53835 11.3248i −0.319801 0.553912i
\(419\) 15.7178 0.767865 0.383932 0.923361i \(-0.374570\pi\)
0.383932 + 0.923361i \(0.374570\pi\)
\(420\) −2.17945 + 3.77492i −0.106346 + 0.184197i
\(421\) −18.0383 + 31.2433i −0.879135 + 1.52271i −0.0268440 + 0.999640i \(0.508546\pi\)
−0.852291 + 0.523067i \(0.824788\pi\)
\(422\) 7.53835 + 13.0568i 0.366961 + 0.635595i
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) −6.53835 11.3248i −0.317530 0.549979i
\(425\) 3.35890 0.162931
\(426\) 10.0767 0.488218
\(427\) 11.6794 + 20.2294i 0.565208 + 0.978969i
\(428\) −4.67945 8.10504i −0.226190 0.391772i
\(429\) 12.0000 0.579365
\(430\) −10.0000 −0.482243
\(431\) −5.39725 9.34831i −0.259976 0.450292i 0.706259 0.707954i \(-0.250381\pi\)
−0.966235 + 0.257661i \(0.917048\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −18.3972 31.8650i −0.884115 1.53133i −0.846724 0.532032i \(-0.821429\pi\)
−0.0373910 0.999301i \(-0.511905\pi\)
\(434\) 23.3589 40.4588i 1.12126 1.94208i
\(435\) 4.67945 8.10504i 0.224362 0.388607i
\(436\) 10.6411 0.509616
\(437\) −13.0767 −0.625543
\(438\) −4.64110 −0.221760
\(439\) −11.6794 + 20.2294i −0.557430 + 0.965497i 0.440280 + 0.897860i \(0.354879\pi\)
−0.997710 + 0.0676362i \(0.978454\pi\)
\(440\) 1.50000 2.59808i 0.0715097 0.123858i
\(441\) −6.00000 10.3923i −0.285714 0.494872i
\(442\) −6.71780 + 11.6356i −0.319533 + 0.553447i
\(443\) 1.32055 + 2.28726i 0.0627412 + 0.108671i 0.895690 0.444679i \(-0.146682\pi\)
−0.832949 + 0.553350i \(0.813349\pi\)
\(444\) −7.00000 −0.332205
\(445\) −0.358899 −0.0170134
\(446\) 10.1794 + 17.6313i 0.482011 + 0.834867i
\(447\) 5.03835 + 8.72668i 0.238306 + 0.412758i
\(448\) −4.35890 −0.205939
\(449\) 0.358899 0.0169375 0.00846874 0.999964i \(-0.497304\pi\)
0.00846874 + 0.999964i \(0.497304\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) −9.53835 + 16.5209i −0.449143 + 0.777939i
\(452\) −1.67945 2.90889i −0.0789947 0.136823i
\(453\) 1.03835 1.79847i 0.0487859 0.0844996i
\(454\) −1.67945 + 2.90889i −0.0788205 + 0.136521i
\(455\) −17.4356 −0.817393
\(456\) 2.17945 + 3.77492i 0.102062 + 0.176777i
\(457\) −30.6411 −1.43333 −0.716665 0.697417i \(-0.754332\pi\)
−0.716665 + 0.697417i \(0.754332\pi\)
\(458\) 4.35890 7.54983i 0.203678 0.352781i
\(459\) −1.67945 + 2.90889i −0.0783900 + 0.135775i
\(460\) −1.50000 2.59808i −0.0699379 0.121136i
\(461\) −9.00000 + 15.5885i −0.419172 + 0.726027i −0.995856 0.0909401i \(-0.971013\pi\)
0.576685 + 0.816967i \(0.304346\pi\)
\(462\) 6.53835 + 11.3248i 0.304191 + 0.526875i
\(463\) −17.7945 −0.826980 −0.413490 0.910509i \(-0.635690\pi\)
−0.413490 + 0.910509i \(0.635690\pi\)
\(464\) 9.35890 0.434476
\(465\) −5.35890 9.28189i −0.248513 0.430437i
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) 28.7945 1.33245 0.666225 0.745751i \(-0.267909\pi\)
0.666225 + 0.745751i \(0.267909\pi\)
\(468\) −4.00000 −0.184900
\(469\) 24.7561 + 42.8789i 1.14313 + 1.97996i
\(470\) 3.00000 5.19615i 0.138380 0.239681i
\(471\) −2.50000 4.33013i −0.115194 0.199522i
\(472\) 6.35890 11.0139i 0.292692 0.506957i
\(473\) −15.0000 + 25.9808i −0.689701 + 1.19460i
\(474\) 4.71780 0.216696
\(475\) 4.35890 0.200000
\(476\) −14.6411 −0.671074
\(477\) 6.53835 11.3248i 0.299370 0.518525i
\(478\) −6.71780 + 11.6356i −0.307265 + 0.532198i
\(479\) 11.0383 + 19.1190i 0.504355 + 0.873569i 0.999987 + 0.00503606i \(0.00160303\pi\)
−0.495632 + 0.868532i \(0.665064\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) −14.0000 24.2487i −0.638345 1.10565i
\(482\) 4.00000 0.182195
\(483\) 13.0767 0.595010
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) −7.03835 12.1908i −0.319595 0.553555i
\(486\) −1.00000 −0.0453609
\(487\) −9.64110 −0.436880 −0.218440 0.975850i \(-0.570097\pi\)
−0.218440 + 0.975850i \(0.570097\pi\)
\(488\) 2.67945 + 4.64094i 0.121293 + 0.210086i
\(489\) 2.35890 4.08573i 0.106673 0.184763i
\(490\) −6.00000 10.3923i −0.271052 0.469476i
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) 3.17945 5.50697i 0.143341 0.248273i
\(493\) 31.4356 1.41579
\(494\) −8.71780 + 15.0997i −0.392232 + 0.679366i
\(495\) 3.00000 0.134840
\(496\) 5.35890 9.28189i 0.240622 0.416769i
\(497\) −21.9617 + 38.0387i −0.985115 + 1.70627i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) 7.82055 13.5456i 0.350096 0.606384i −0.636170 0.771549i \(-0.719482\pi\)
0.986266 + 0.165165i \(0.0528157\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) −22.4356 −1.00235
\(502\) 12.0000 0.535586
\(503\) −14.9356 25.8692i −0.665945 1.15345i −0.979028 0.203725i \(-0.934695\pi\)
0.313083 0.949726i \(-0.398638\pi\)
\(504\) −2.17945 3.77492i −0.0970804 0.168148i
\(505\) 12.7178 0.565935
\(506\) −9.00000 −0.400099
\(507\) −1.50000 2.59808i −0.0666173 0.115385i
\(508\) 5.17945 8.97107i 0.229801 0.398027i
\(509\) −12.3589 21.4062i −0.547799 0.948815i −0.998425 0.0561023i \(-0.982133\pi\)
0.450626 0.892713i \(-0.351201\pi\)
\(510\) −1.67945 + 2.90889i −0.0743673 + 0.128808i
\(511\) 10.1150 17.5198i 0.447463 0.775029i
\(512\) −1.00000 −0.0441942
\(513\) −2.17945 + 3.77492i −0.0962250 + 0.166667i
\(514\) 7.43560 0.327970
\(515\) −5.17945 + 8.97107i −0.228234 + 0.395313i
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 15.2561 26.4244i 0.670317 1.16102i
\(519\) −9.17945 15.8993i −0.402933 0.697901i
\(520\) −4.00000 −0.175412
\(521\) 23.2822 1.02001 0.510006 0.860171i \(-0.329643\pi\)
0.510006 + 0.860171i \(0.329643\pi\)
\(522\) 4.67945 + 8.10504i 0.204814 + 0.354748i
\(523\) 19.3972 + 33.5970i 0.848182 + 1.46910i 0.882829 + 0.469695i \(0.155636\pi\)
−0.0346461 + 0.999400i \(0.511030\pi\)
\(524\) −3.00000 −0.131056
\(525\) −4.35890 −0.190238
\(526\) −4.14110 7.17260i −0.180561 0.312740i
\(527\) 18.0000 31.1769i 0.784092 1.35809i
\(528\) 1.50000 + 2.59808i 0.0652791 + 0.113067i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 6.53835 11.3248i 0.284008 0.491916i
\(531\) 12.7178 0.551905
\(532\) −19.0000 −0.823754
\(533\) 25.4356 1.10174
\(534\) 0.179449 0.310816i 0.00776554 0.0134503i
\(535\) 4.67945 8.10504i 0.202310 0.350412i
\(536\) 5.67945 + 9.83710i 0.245315 + 0.424898i
\(537\) −7.85890 + 13.6120i −0.339137 + 0.587402i
\(538\) 1.67945 + 2.90889i 0.0724062 + 0.125411i
\(539\) −36.0000 −1.55063
\(540\) −1.00000 −0.0430331
\(541\) 4.64110 + 8.03862i 0.199537 + 0.345607i 0.948378 0.317142i \(-0.102723\pi\)
−0.748842 + 0.662749i \(0.769390\pi\)
\(542\) −2.35890 4.08573i −0.101323 0.175497i
\(543\) 18.0767 0.775745
\(544\) −3.35890 −0.144012
\(545\) 5.32055 + 9.21546i 0.227907 + 0.394747i
\(546\) 8.71780 15.0997i 0.373087 0.646206i
\(547\) 3.07670 + 5.32900i 0.131550 + 0.227851i 0.924274 0.381729i \(-0.124671\pi\)
−0.792724 + 0.609580i \(0.791338\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) −2.67945 + 4.64094i −0.114356 + 0.198071i
\(550\) 3.00000 0.127920
\(551\) 40.7945 1.73790
\(552\) 3.00000 0.127688
\(553\) −10.2822 + 17.8093i −0.437244 + 0.757328i
\(554\) −2.00000 + 3.46410i −0.0849719 + 0.147176i
\(555\) −3.50000 6.06218i −0.148567 0.257325i
\(556\) −0.641101 + 1.11042i −0.0271887 + 0.0470923i
\(557\) 5.46165 + 9.45986i 0.231418 + 0.400827i 0.958226 0.286014i \(-0.0923303\pi\)
−0.726808 + 0.686841i \(0.758997\pi\)
\(558\) 10.7178 0.453721
\(559\) 40.0000 1.69182
\(560\) −2.17945 3.77492i −0.0920985 0.159519i
\(561\) 5.03835 + 8.72668i 0.212719 + 0.368441i
\(562\) −1.07670 −0.0454177
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 3.00000 + 5.19615i 0.126323 + 0.218797i
\(565\) 1.67945 2.90889i 0.0706550 0.122378i
\(566\) 4.35890 + 7.54983i 0.183218 + 0.317343i
\(567\) 2.17945 3.77492i 0.0915283 0.158532i
\(568\) −5.03835 + 8.72668i −0.211404 + 0.366163i
\(569\) −37.7945 −1.58443 −0.792214 0.610244i \(-0.791072\pi\)
−0.792214 + 0.610244i \(0.791072\pi\)
\(570\) −2.17945 + 3.77492i −0.0912871 + 0.158114i
\(571\) 34.1534 1.42928 0.714638 0.699495i \(-0.246592\pi\)
0.714638 + 0.699495i \(0.246592\pi\)
\(572\) −6.00000 + 10.3923i −0.250873 + 0.434524i
\(573\) 9.71780 16.8317i 0.405967 0.703155i
\(574\) 13.8589 + 24.0043i 0.578459 + 1.00192i
\(575\) 1.50000 2.59808i 0.0625543 0.108347i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 18.7945 0.782425 0.391213 0.920300i \(-0.372056\pi\)
0.391213 + 0.920300i \(0.372056\pi\)
\(578\) 5.71780 0.237829
\(579\) −12.0383 20.8510i −0.500297 0.866539i
\(580\) 4.67945 + 8.10504i 0.194304 + 0.336544i
\(581\) 26.1534 1.08503
\(582\) 14.0767 0.583498
\(583\) −19.6150 33.9743i −0.812372 1.40707i
\(584\) 2.32055 4.01931i 0.0960251 0.166320i
\(585\) −2.00000 3.46410i −0.0826898 0.143223i
\(586\) 2.82055 4.88534i 0.116516 0.201811i
\(587\) 21.3589 36.9947i 0.881576 1.52693i 0.0319878 0.999488i \(-0.489816\pi\)
0.849588 0.527446i \(-0.176850\pi\)
\(588\) 12.0000 0.494872
\(589\) 23.3589 40.4588i 0.962487 1.66708i
\(590\) 12.7178 0.523583
\(591\) 2.82055 4.88534i 0.116022 0.200956i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −3.96165 6.86178i −0.162686 0.281780i 0.773145 0.634229i \(-0.218682\pi\)
−0.935831 + 0.352449i \(0.885349\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) −7.32055 12.6796i −0.300113 0.519812i
\(596\) −10.0767 −0.412758
\(597\) 16.6411 0.681075
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) −13.3206 23.0719i −0.544263 0.942691i −0.998653 0.0518882i \(-0.983476\pi\)
0.454390 0.890803i \(-0.349857\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 5.71780 0.233234 0.116617 0.993177i \(-0.462795\pi\)
0.116617 + 0.993177i \(0.462795\pi\)
\(602\) 21.7945 + 37.7492i 0.888277 + 1.53854i
\(603\) −5.67945 + 9.83710i −0.231285 + 0.400597i
\(604\) 1.03835 + 1.79847i 0.0422498 + 0.0731788i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) −6.35890 + 11.0139i −0.258313 + 0.447411i
\(607\) −35.7945 −1.45285 −0.726427 0.687244i \(-0.758820\pi\)
−0.726427 + 0.687244i \(0.758820\pi\)
\(608\) −4.35890 −0.176777
\(609\) −40.7945 −1.65308
\(610\) −2.67945 + 4.64094i −0.108488 + 0.187906i
\(611\) −12.0000 + 20.7846i −0.485468 + 0.840855i
\(612\) −1.67945 2.90889i −0.0678877 0.117585i
\(613\) −3.21780 + 5.57339i −0.129966 + 0.225107i −0.923663 0.383206i \(-0.874820\pi\)
0.793697 + 0.608313i \(0.208153\pi\)
\(614\) −0.679449 1.17684i −0.0274203 0.0474934i
\(615\) 6.35890 0.256416
\(616\) −13.0767 −0.526875
\(617\) 0.717798 + 1.24326i 0.0288975 + 0.0500519i 0.880112 0.474765i \(-0.157467\pi\)
−0.851215 + 0.524817i \(0.824134\pi\)
\(618\) −5.17945 8.97107i −0.208348 0.360869i
\(619\) −3.64110 −0.146348 −0.0731741 0.997319i \(-0.523313\pi\)
−0.0731741 + 0.997319i \(0.523313\pi\)
\(620\) 10.7178 0.430437
\(621\) 1.50000 + 2.59808i 0.0601929 + 0.104257i
\(622\) 0.717798 1.24326i 0.0287811 0.0498503i
\(623\) 0.782202 + 1.35481i 0.0313383 + 0.0542795i
\(624\) 2.00000 3.46410i 0.0800641 0.138675i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 17.4356 0.696867
\(627\) 6.53835 + 11.3248i 0.261116 + 0.452267i
\(628\) 5.00000 0.199522
\(629\) 11.7561 20.3622i 0.468748 0.811896i
\(630\) 2.17945 3.77492i 0.0868313 0.150396i
\(631\) −20.6794 35.8179i −0.823236 1.42589i −0.903260 0.429093i \(-0.858833\pi\)
0.0800242 0.996793i \(-0.474500\pi\)
\(632\) −2.35890 + 4.08573i −0.0938320 + 0.162522i
\(633\) −7.53835 13.0568i −0.299622 0.518961i
\(634\) −19.0767 −0.757632
\(635\) 10.3589 0.411080
\(636\) 6.53835 + 11.3248i 0.259262 + 0.449056i
\(637\) 24.0000 + 41.5692i 0.950915 + 1.64703i
\(638\) 28.0767 1.11157
\(639\) −10.0767 −0.398628
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 5.64110 9.77067i 0.222810 0.385918i −0.732850 0.680390i \(-0.761810\pi\)
0.955660 + 0.294472i \(0.0951437\pi\)
\(642\) 4.67945 + 8.10504i 0.184683 + 0.319881i
\(643\) 19.7561 34.2186i 0.779106 1.34945i −0.153351 0.988172i \(-0.549007\pi\)
0.932457 0.361280i \(-0.117660\pi\)
\(644\) −6.53835 + 11.3248i −0.257647 + 0.446258i
\(645\) 10.0000 0.393750
\(646\) −14.6411 −0.576046
\(647\) −17.1534 −0.674369 −0.337185 0.941438i \(-0.609475\pi\)
−0.337185 + 0.941438i \(0.609475\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 19.0767 33.0418i 0.748826 1.29700i
\(650\) −2.00000 3.46410i −0.0784465 0.135873i
\(651\) −23.3589 + 40.4588i −0.915507 + 1.58571i
\(652\) 2.35890 + 4.08573i 0.0923816 + 0.160010i
\(653\) −25.0767 −0.981327 −0.490663 0.871349i \(-0.663246\pi\)
−0.490663 + 0.871349i \(0.663246\pi\)
\(654\) −10.6411 −0.416100
\(655\) −1.50000 2.59808i −0.0586098 0.101515i
\(656\) 3.17945 + 5.50697i 0.124137 + 0.215011i
\(657\) 4.64110 0.181067
\(658\) −26.1534 −1.01957
\(659\) 19.8589 + 34.3966i 0.773593 + 1.33990i 0.935582 + 0.353110i \(0.114876\pi\)
−0.161989 + 0.986793i \(0.551791\pi\)
\(660\) −1.50000 + 2.59808i −0.0583874 + 0.101130i
\(661\) 8.71780 + 15.0997i 0.339083 + 0.587309i 0.984261 0.176724i \(-0.0565499\pi\)
−0.645177 + 0.764033i \(0.723217\pi\)
\(662\) 7.17945 12.4352i 0.279037 0.483307i
\(663\) 6.71780 11.6356i 0.260898 0.451888i
\(664\) 6.00000 0.232845
\(665\) −9.50000 16.4545i −0.368394 0.638077i
\(666\) 7.00000 0.271244
\(667\) 14.0383 24.3151i 0.543567 0.941486i
\(668\) 11.2178 19.4298i 0.434030 0.751761i
\(669\) −10.1794 17.6313i −0.393560 0.681666i
\(670\) −5.67945 + 9.83710i −0.219416 + 0.380040i
\(671\) 8.03835 + 13.9228i 0.310317 + 0.537485i
\(672\) 4.35890 0.168148
\(673\) −21.2822 −0.820369 −0.410184 0.912003i \(-0.634536\pi\)
−0.410184 + 0.912003i \(0.634536\pi\)
\(674\) 11.0767 + 19.1854i 0.426658 + 0.738994i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 3.00000 0.115385
\(677\) 7.07670 0.271980 0.135990 0.990710i \(-0.456579\pi\)
0.135990 + 0.990710i \(0.456579\pi\)
\(678\) 1.67945 + 2.90889i 0.0644989 + 0.111715i
\(679\) −30.6794 + 53.1384i −1.17737 + 2.03926i
\(680\) −1.67945 2.90889i −0.0644039 0.111551i
\(681\) 1.67945 2.90889i 0.0643566 0.111469i
\(682\) 16.0767 27.8457i 0.615609 1.06627i
\(683\) −22.7945 −0.872207 −0.436104 0.899896i \(-0.643642\pi\)
−0.436104 + 0.899896i \(0.643642\pi\)
\(684\) −2.17945 3.77492i −0.0833333 0.144338i
\(685\) −12.0000 −0.458496
\(686\) −10.8972 + 18.8746i −0.416059 + 0.720635i
\(687\) −4.35890 + 7.54983i −0.166302 + 0.288044i
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) −26.1534 + 45.2990i −0.996365 + 1.72575i
\(690\) 1.50000 + 2.59808i 0.0571040 + 0.0989071i
\(691\) 31.6411 1.20368 0.601842 0.798615i \(-0.294434\pi\)
0.601842 + 0.798615i \(0.294434\pi\)
\(692\) 18.3589 0.697901
\(693\) −6.53835 11.3248i −0.248371 0.430192i
\(694\) −3.71780 6.43941i −0.141126 0.244437i
\(695\) −1.28220 −0.0486367
\(696\) −9.35890 −0.354748
\(697\) 10.6794 + 18.4973i 0.404513 + 0.700637i
\(698\) 0.0383484 0.0664214i 0.00145151 0.00251409i
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) 2.17945 3.77492i 0.0823754 0.142678i
\(701\) −9.00000 + 15.5885i −0.339925 + 0.588768i −0.984418 0.175842i \(-0.943735\pi\)
0.644493 + 0.764610i \(0.277068\pi\)
\(702\) 4.00000 0.150970
\(703\) 15.2561 26.4244i 0.575396 0.996616i
\(704\) −3.00000 −0.113067
\(705\) −3.00000 + 5.19615i −0.112987 + 0.195698i
\(706\) −5.03835 + 8.72668i −0.189621 + 0.328433i
\(707\) −27.7178 48.0086i −1.04244 1.80555i
\(708\) −6.35890 + 11.0139i −0.238982 + 0.413929i
\(709\) 13.3972 + 23.2047i 0.503144 + 0.871471i 0.999993 + 0.00363441i \(0.00115687\pi\)
−0.496849 + 0.867837i \(0.665510\pi\)
\(710\) −10.0767 −0.378172
\(711\) −4.71780 −0.176931
\(712\) 0.179449 + 0.310816i 0.00672515 + 0.0116483i
\(713\) −16.0767 27.8457i −0.602077 1.04283i
\(714\) 14.6411 0.547929
\(715\) −12.0000 −0.448775
\(716\) −7.85890 13.6120i −0.293701 0.508705i
\(717\) 6.71780 11.6356i 0.250881 0.434538i
\(718\) 7.67945 + 13.3012i 0.286595 + 0.496396i
\(719\) 8.64110 14.9668i 0.322259 0.558168i −0.658695 0.752410i \(-0.728891\pi\)
0.980954 + 0.194242i \(0.0622246\pi\)
\(720\) 0.500000 0.866025i 0.0186339 0.0322749i
\(721\) 45.1534 1.68160
\(722\) −19.0000 −0.707107
\(723\) −4.00000 −0.148762
\(724\) −9.03835 + 15.6549i −0.335908 + 0.581809i
\(725\) −4.67945 + 8.10504i −0.173790 + 0.301014i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 15.0767 26.1136i 0.559164 0.968500i −0.438403 0.898779i \(-0.644456\pi\)
0.997567 0.0697214i \(-0.0222110\pi\)
\(728\) 8.71780 + 15.0997i 0.323103 + 0.559631i
\(729\) 1.00000 0.0370370
\(730\) 4.64110 0.171775
\(731\) 16.7945 + 29.0889i 0.621167 + 1.07589i
\(732\) −2.67945 4.64094i −0.0990353 0.171534i
\(733\) 9.56440 0.353269 0.176635 0.984276i \(-0.443479\pi\)
0.176635 + 0.984276i \(0.443479\pi\)
\(734\) −14.7178 −0.543244
\(735\) 6.00000 + 10.3923i 0.221313 + 0.383326i
\(736\) −1.50000 + 2.59808i −0.0552907 + 0.0957664i
\(737\) 17.0383 + 29.5113i 0.627616 + 1.08706i
\(738\) −3.17945 + 5.50697i −0.117037 + 0.202714i
\(739\) 8.17945 14.1672i 0.300886 0.521150i −0.675451 0.737405i \(-0.736051\pi\)
0.976337 + 0.216255i \(0.0693843\pi\)
\(740\) 7.00000 0.257325
\(741\) 8.71780 15.0997i 0.320256 0.554700i
\(742\) −57.0000 −2.09254
\(743\) −4.50000 + 7.79423i −0.165089 + 0.285943i −0.936687 0.350168i \(-0.886124\pi\)
0.771598 + 0.636111i \(0.219458\pi\)
\(744\) −5.35890 + 9.28189i −0.196467 + 0.340290i
\(745\) −5.03835 8.72668i −0.184591 0.319721i
\(746\) 5.50000 9.52628i 0.201369 0.348782i
\(747\) 3.00000 + 5.19615i 0.109764 + 0.190117i
\(748\) −10.0767 −0.368441
\(749\) −40.7945 −1.49060
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) −11.4356 19.8070i −0.417291 0.722769i 0.578375 0.815771i \(-0.303687\pi\)
−0.995666 + 0.0930021i \(0.970354\pi\)
\(752\) −6.00000 −0.218797
\(753\) −12.0000 −0.437304
\(754\) −18.7178 32.4202i −0.681662 1.18067i
\(755\) −1.03835 + 1.79847i −0.0377894 + 0.0654531i
\(756\) 2.17945 + 3.77492i 0.0792658 + 0.137292i
\(757\) −24.9356 + 43.1897i −0.906300 + 1.56976i −0.0871365 + 0.996196i \(0.527772\pi\)
−0.819163 + 0.573561i \(0.805562\pi\)
\(758\) 7.35890 12.7460i 0.267287 0.462955i
\(759\) 9.00000 0.326679
\(760\) −2.17945 3.77492i −0.0790569 0.136931i
\(761\) −7.07670 −0.256530 −0.128265 0.991740i \(-0.540941\pi\)
−0.128265 + 0.991740i \(0.540941\pi\)
\(762\) −5.17945 + 8.97107i −0.187632 + 0.324988i
\(763\) 23.1917 40.1693i 0.839597 1.45423i
\(764\) 9.71780 + 16.8317i 0.351578 + 0.608950i
\(765\) 1.67945 2.90889i 0.0607206 0.105171i
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) −50.8712 −1.83685
\(768\) 1.00000 0.0360844
\(769\) −1.35890 2.35368i −0.0490031 0.0848759i 0.840483 0.541837i \(-0.182271\pi\)
−0.889487 + 0.456961i \(0.848938\pi\)
\(770\) −6.53835 11.3248i −0.235626 0.408116i
\(771\) −7.43560 −0.267786
\(772\) 24.0767 0.866539
\(773\) 0.897247 + 1.55408i 0.0322717 + 0.0558963i 0.881710 0.471791i \(-0.156392\pi\)
−0.849438 + 0.527688i \(0.823059\pi\)
\(774\) −5.00000 + 8.66025i −0.179721 + 0.311286i
\(775\) 5.35890 + 9.28189i 0.192497 + 0.333415i
\(776\) −7.03835 + 12.1908i −0.252662 + 0.437623i
\(777\) −15.2561 + 26.4244i −0.547311 + 0.947971i
\(778\) −4.07670