Properties

Label 570.2.i.h.121.1
Level $570$
Weight $2$
Character 570.121
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 121.1
Root \(2.17945 + 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.h.391.1

$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

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

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 −0.443227 0.896410i \(-0.646166\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) −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 0.587263 0.809396i \(-0.300205\pi\)
−0.994589 + 0.103886i \(0.966872\pi\)
\(18\) −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 −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 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 −0.00588307 + 0.999983i \(0.501873\pi\)
−0.863069 + 0.505086i \(0.831461\pi\)
\(30\) 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 0.999992 0.00398308i \(-0.00126786\pi\)
−0.503445 + 0.864027i \(0.667935\pi\)
\(42\) −2.17945 + 3.77492i −0.336296 + 0.582482i
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) 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 −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) −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 0.0682050 0.997671i \(-0.478273\pi\)
0.829906 0.557903i \(-0.188394\pi\)
\(54\) 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 −0.899715 0.436477i \(-0.856226\pi\)
0.0718571 0.997415i \(-0.477107\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −2.67945 + 4.64094i −0.343068 + 0.594212i −0.985001 0.172549i \(-0.944800\pi\)
0.641933 + 0.766761i \(0.278133\pi\)
\(62\) −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 0.276710 + 0.960953i \(0.410756\pi\)
−0.970565 + 0.240839i \(0.922577\pi\)
\(68\) 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 0.993124 + 0.117063i \(0.0373480\pi\)
−0.395183 + 0.918603i \(0.629319\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −2.32055 4.01931i −0.271600 0.470425i 0.697672 0.716418i \(-0.254219\pi\)
−0.969272 + 0.245993i \(0.920886\pi\)
\(74\) −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 0.967668 0.252229i \(-0.0811637\pi\)
−0.702271 + 0.711910i \(0.747830\pi\)
\(80\) 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 −0.875380 0.483436i \(-0.839388\pi\)
0.856358 + 0.516383i \(0.172722\pi\)
\(90\) −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 0.963100 + 0.269145i \(0.0867410\pi\)
−0.248464 + 0.968641i \(0.579926\pi\)
\(98\) 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 −0.354256 0.935148i \(-0.615266\pi\)
0.986990 0.160779i \(-0.0514007\pi\)
\(102\) −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 −0.999938 0.0111398i \(-0.996454\pi\)
0.490322 0.871542i \(-0.336879\pi\)
\(110\) 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 −0.539338 0.842089i \(-0.681325\pi\)
0.998940 + 0.0460357i \(0.0146588\pi\)
\(128\) 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 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) −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 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) −1.50000 2.59808i −0.127688 0.221163i
\(139\) −0.641101 + 1.11042i −0.0543775 + 0.0941846i −0.891933 0.452168i \(-0.850651\pi\)
0.837555 + 0.546353i \(0.183984\pi\)
\(140\) 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 0.995190 0.0979619i \(-0.0312323\pi\)
−0.582433 + 0.812879i \(0.697899\pi\)
\(150\) 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 0.748852 0.662738i \(-0.230606\pi\)
−0.948373 + 0.317156i \(0.897272\pi\)
\(158\) −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 0.00408215 0.999992i \(-0.498701\pi\)
0.863977 0.503531i \(-0.167966\pi\)
\(168\) −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 −0.969193 0.246302i \(-0.920784\pi\)
0.271292 0.962497i \(-0.412549\pi\)
\(174\) 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 0.305574 + 0.952168i \(0.401152\pi\)
−0.977389 + 0.211450i \(0.932182\pi\)
\(182\) −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 −0.865511 0.500891i \(-0.833006\pi\)
−0.00102867 0.999999i \(-0.500327\pi\)
\(194\) −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 0.404426 + 0.914571i \(0.367471\pi\)
−0.994255 + 0.107042i \(0.965862\pi\)
\(200\) 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 −0.999757 0.0220348i \(-0.992986\pi\)
0.480796 0.876833i \(-0.340348\pi\)
\(212\) 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 −0.974472 0.224509i \(-0.927922\pi\)
0.292806 0.956172i \(-0.405411\pi\)
\(224\) −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 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) −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 −0.794393 0.607404i \(-0.792211\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(242\) −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 −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 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 −0.726460 0.687208i \(-0.758836\pi\)
0.958370 + 0.285529i \(0.0921692\pi\)
\(258\) 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 0.964991 0.262284i \(-0.0844756\pi\)
−0.709640 + 0.704565i \(0.751142\pi\)
\(264\) −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 0.810274 0.586051i \(-0.199318\pi\)
−0.912672 + 0.408693i \(0.865985\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 2.35890 + 4.08573i 0.143293 + 0.248191i 0.928735 0.370745i \(-0.120898\pi\)
−0.785442 + 0.618935i \(0.787564\pi\)
\(272\) −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 −0.881636 0.471930i \(-0.843558\pi\)
0.849521 + 0.527555i \(0.176891\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) −4.35890 7.54983i −0.259110 0.448791i 0.706894 0.707319i \(-0.250096\pi\)
−0.966004 + 0.258528i \(0.916762\pi\)
\(284\) −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 0.884763 0.466041i \(-0.154320\pi\)
−0.845985 + 0.533207i \(0.820987\pi\)
\(308\) −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 −0.507206 0.861825i \(-0.669322\pi\)
0.999965 + 0.00834102i \(0.00265506\pi\)
\(314\) 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 0.463401 + 0.886149i \(0.346629\pi\)
−0.999128 + 0.0417576i \(0.986704\pi\)
\(318\) −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 −0.992304 0.123823i \(-0.960484\pi\)
0.388918 0.921272i \(-0.372849\pi\)
\(338\) 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 0.948393 0.317098i \(-0.102708\pi\)
−0.748811 + 0.662784i \(0.769375\pi\)
\(348\) −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 0.589051 0.808096i \(-0.299502\pi\)
−0.994357 + 0.106085i \(0.966168\pi\)
\(360\) 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 −0.991648 0.128972i \(-0.958832\pi\)
0.607517 + 0.794307i \(0.292166\pi\)
\(368\) −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 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) 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 −0.913062 0.407820i \(-0.866289\pi\)
0.809714 + 0.586825i \(0.199622\pi\)
\(390\) 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 0.773909 0.633297i \(-0.218299\pi\)
−0.935406 + 0.353576i \(0.884965\pi\)
\(398\) −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 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 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 −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) −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 −0.852291 0.523067i \(-0.824788\pi\)
−0.0268440 0.999640i \(-0.508546\pi\)
\(422\) 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 −0.966235 0.257661i \(-0.917048\pi\)
0.706259 + 0.707954i \(0.250381\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −18.3972 + 31.8650i −0.884115 + 1.53133i −0.0373910 + 0.999301i \(0.511905\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(434\) 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 −0.997710 0.0676362i \(-0.978454\pi\)
0.440280 0.897860i \(-0.354879\pi\)
\(440\) 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 −0.832949 0.553350i \(-0.813349\pi\)
0.895690 + 0.444679i \(0.146682\pi\)
\(444\) −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 0.576685 0.816967i \(-0.304346\pi\)
−0.995856 + 0.0909401i \(0.971013\pi\)
\(462\) 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 −0.495632 0.868532i \(-0.665064\pi\)
0.999987 0.00503606i \(-0.00160303\pi\)
\(480\) −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 0.645675 0.763612i \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) 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 0.986266 0.165165i \(-0.0528157\pi\)
−0.636170 + 0.771549i \(0.719482\pi\)
\(500\) 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 0.313083 + 0.949726i \(0.398638\pi\)
−0.979028 + 0.203725i \(0.934695\pi\)
\(504\) −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 0.450626 + 0.892713i \(0.351201\pi\)
−0.998425 + 0.0561023i \(0.982133\pi\)
\(510\) −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 −0.0346461 0.999400i \(-0.511030\pi\)
0.882829 0.469695i \(-0.155636\pi\)
\(524\) −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 −0.748842 0.662749i \(-0.769390\pi\)
0.948378 + 0.317142i \(0.102723\pi\)
\(542\) −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 −0.792724 0.609580i \(-0.791338\pi\)
0.924274 + 0.381729i \(0.124671\pi\)
\(548\) −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 −0.726808 0.686841i \(-0.758997\pi\)
0.958226 + 0.286014i \(0.0923303\pi\)
\(558\) 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 0.849588 + 0.527446i \(0.176850\pi\)
0.0319878 + 0.999488i \(0.489816\pi\)
\(588\) 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 −0.935831 0.352449i \(-0.885349\pi\)
0.773145 + 0.634229i \(0.218682\pi\)
\(594\) −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 0.454390 + 0.890803i \(0.349857\pi\)
−0.998653 + 0.0518882i \(0.983476\pi\)
\(600\) −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 0.793697 0.608313i \(-0.208153\pi\)
−0.923663 + 0.383206i \(0.874820\pi\)
\(614\) −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 −0.851215 0.524817i \(-0.824134\pi\)
0.880112 + 0.474765i \(0.157467\pi\)
\(618\) −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 0.0800242 + 0.996793i \(0.474500\pi\)
−0.903260 + 0.429093i \(0.858833\pi\)
\(632\) −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 0.955660 0.294472i \(-0.0951437\pi\)
−0.732850 + 0.680390i \(0.761810\pi\)
\(642\) 4.67945 8.10504i 0.184683 0.319881i
\(643\) 19.7561 + 34.2186i 0.779106 + 1.34945i 0.932457 + 0.361280i \(0.117660\pi\)
−0.153351 + 0.988172i \(0.549007\pi\)
\(644\) −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 −0.161989 0.986793i \(-0.551791\pi\)
0.935582 0.353110i \(-0.114876\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) 8.71780 15.0997i 0.339083 0.587309i −0.645177 0.764033i \(-0.723217\pi\)
0.984261 + 0.176724i \(0.0565499\pi\)
\(662\) 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 0.644493 0.764610i \(-0.277068\pi\)
−0.984418 + 0.175842i \(0.943735\pi\)
\(702\) 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 −0.496849 0.867837i \(-0.665510\pi\)
0.999993 0.00363441i \(-0.00115687\pi\)
\(710\) −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 0.980954 0.194242i \(-0.0622246\pi\)
−0.658695 + 0.752410i \(0.728891\pi\)
\(720\) 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 0.997567 + 0.0697214i \(0.0222110\pi\)
−0.438403 + 0.898779i \(0.644456\pi\)
\(728\) 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 0.976337 0.216255i \(-0.0693843\pi\)
−0.675451 + 0.737405i \(0.736051\pi\)
\(740\) 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 0.771598 0.636111i \(-0.219458\pi\)
−0.936687 + 0.350168i \(0.886124\pi\)
\(744\) −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 −0.995666 0.0930021i \(-0.970354\pi\)
0.578375 + 0.815771i \(0.303687\pi\)
\(752\) −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 −0.819163 0.573561i \(-0.805562\pi\)
−0.0871365 0.996196i \(-0.527772\pi\)
\(758\) 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 −0.889487 0.456961i \(-0.848938\pi\)
0.840483 + 0.541837i \(0.182271\pi\)
\(770\) −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 −0.849438 0.527688i \(-0.823059\pi\)
0.881710 + 0.471791i \(0.156392\pi\)
\(774\) −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