Properties

Label 570.2.i.h.121.2
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 121.2
Root \(-2.17945 - 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.h.391.2

$q$-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} +(2.67945 + 4.64094i) 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} +(-0.320551 + 0.555210i) q^{29} +1.00000 q^{30} +6.71780 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-2.67945 + 4.64094i) 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} +(-1.17945 - 2.04287i) 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} +(2.67945 - 4.64094i) 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} -0.641101 q^{58} +(2.35890 + 4.08573i) q^{59} +(0.500000 + 0.866025i) q^{60} +(1.67945 - 2.90889i) q^{61} +(3.35890 + 5.81778i) q^{62} +(-2.17945 + 3.77492i) q^{63} +1.00000 q^{64} +4.00000 q^{65} +(-1.50000 + 2.59808i) q^{66} +(-1.32055 + 2.28726i) q^{67} -5.35890 q^{68} -3.00000 q^{69} +(-2.17945 + 3.77492i) q^{70} +(-8.03835 - 13.9228i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.67945 - 11.5691i) 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} +(-6.35890 - 11.0139i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.17945 - 2.04287i) q^{82} -6.00000 q^{83} +4.35890 q^{84} +(-2.67945 + 4.64094i) q^{85} +(-5.00000 + 8.66025i) q^{86} +0.641101 q^{87} +3.00000 q^{88} +(4.17945 - 7.23902i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(8.71780 - 15.0997i) q^{91} +(1.50000 + 2.59808i) q^{92} +(-3.35890 - 5.81778i) q^{93} +6.00000 q^{94} +(-2.17945 + 3.77492i) q^{95} -1.00000 q^{96} +(-6.03835 - 10.4587i) 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 \(-0.191875\pi\)
0.823754 + 0.566947i \(0.191875\pi\)
\(8\) −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
\(17\) 2.67945 + 4.64094i 0.649862 + 1.12559i 0.983156 + 0.182771i \(0.0585066\pi\)
−0.333294 + 0.942823i \(0.608160\pi\)
\(18\) −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
\(29\) −0.320551 + 0.555210i −0.0595247 + 0.103100i −0.894252 0.447563i \(-0.852292\pi\)
0.834727 + 0.550663i \(0.185625\pi\)
\(30\) 1.00000 0.182574
\(31\) 6.71780 1.20655 0.603276 0.797532i \(-0.293862\pi\)
0.603276 + 0.797532i \(0.293862\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) −2.67945 + 4.64094i −0.459522 + 0.795915i
\(35\) 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
\(41\) −1.17945 2.04287i −0.184199 0.319042i 0.759107 0.650966i \(-0.225636\pi\)
−0.943306 + 0.331923i \(0.892302\pi\)
\(42\) 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
\(51\) 2.67945 4.64094i 0.375198 0.649862i
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) −6.53835 + 11.3248i −0.898111 + 1.55557i −0.0682050 + 0.997671i \(0.521727\pi\)
−0.829906 + 0.557903i \(0.811606\pi\)
\(54\) 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
\(58\) −0.641101 −0.0841807
\(59\) 2.35890 + 4.08573i 0.307102 + 0.531917i 0.977727 0.209880i \(-0.0673072\pi\)
−0.670625 + 0.741797i \(0.733974\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 1.67945 2.90889i 0.215031 0.372445i −0.738251 0.674526i \(-0.764348\pi\)
0.953282 + 0.302081i \(0.0976813\pi\)
\(62\) 3.35890 + 5.81778i 0.426581 + 0.738859i
\(63\) −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
\(67\) −1.32055 + 2.28726i −0.161331 + 0.279433i −0.935346 0.353734i \(-0.884912\pi\)
0.774015 + 0.633167i \(0.218245\pi\)
\(68\) −5.35890 −0.649862
\(69\) −3.00000 −0.361158
\(70\) −2.17945 + 3.77492i −0.260494 + 0.451189i
\(71\) −8.03835 13.9228i −0.953976 1.65234i −0.736693 0.676227i \(-0.763614\pi\)
−0.217283 0.976109i \(-0.569720\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −6.67945 11.5691i −0.781770 1.35407i −0.930910 0.365250i \(-0.880984\pi\)
0.149139 0.988816i \(-0.452350\pi\)
\(74\) −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
\(79\) −6.35890 11.0139i −0.715432 1.23916i −0.962793 0.270241i \(-0.912897\pi\)
0.247361 0.968923i \(-0.420437\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.17945 2.04287i 0.130248 0.225597i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 4.35890 0.475595
\(85\) −2.67945 + 4.64094i −0.290627 + 0.503381i
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 0.641101 0.0687332
\(88\) 3.00000 0.319801
\(89\) 4.17945 7.23902i 0.443021 0.767334i −0.554891 0.831923i \(-0.687240\pi\)
0.997912 + 0.0645884i \(0.0205735\pi\)
\(90\) −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
\(93\) −3.35890 5.81778i −0.348302 0.603276i
\(94\) 6.00000 0.618853
\(95\) −2.17945 + 3.77492i −0.223607 + 0.387298i
\(96\) −1.00000 −0.102062
\(97\) −6.03835 10.4587i −0.613101 1.06192i −0.990714 0.135959i \(-0.956588\pi\)
0.377613 0.925963i \(-0.376745\pi\)
\(98\) 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
\(101\) −2.35890 + 4.08573i −0.234719 + 0.406546i −0.959191 0.282759i \(-0.908750\pi\)
0.724472 + 0.689304i \(0.242084\pi\)
\(102\) 5.35890 0.530610
\(103\) −1.64110 −0.161702 −0.0808512 0.996726i \(-0.525764\pi\)
−0.0808512 + 0.996726i \(0.525764\pi\)
\(104\) −2.00000 + 3.46410i −0.196116 + 0.339683i
\(105\) 2.17945 3.77492i 0.212692 0.368394i
\(106\) −13.0767 −1.27012
\(107\) 0.641101 0.0619776 0.0309888 0.999520i \(-0.490134\pi\)
0.0309888 + 0.999520i \(0.490134\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −9.67945 16.7653i −0.927123 1.60582i −0.788111 0.615534i \(-0.788940\pi\)
−0.139013 0.990291i \(-0.544393\pi\)
\(110\) 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
\(113\) −5.35890 −0.504123 −0.252061 0.967711i \(-0.581108\pi\)
−0.252061 + 0.967711i \(0.581108\pi\)
\(114\) 4.35890 0.408248
\(115\) 3.00000 0.279751
\(116\) −0.320551 0.555210i −0.0297624 0.0515499i
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) −2.35890 + 4.08573i −0.217154 + 0.376122i
\(119\) 11.6794 + 20.2294i 1.07065 + 1.85443i
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) −2.00000 −0.181818
\(122\) 3.35890 0.304100
\(123\) −1.17945 + 2.04287i −0.106347 + 0.184199i
\(124\) −3.35890 + 5.81778i −0.301638 + 0.522452i
\(125\) −1.00000 −0.0894427
\(126\) −4.35890 −0.388322
\(127\) 0.820551 1.42124i 0.0728121 0.126114i −0.827321 0.561730i \(-0.810136\pi\)
0.900133 + 0.435616i \(0.143469\pi\)
\(128\) 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
\(134\) −2.64110 −0.228156
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) −2.67945 4.64094i −0.229761 0.397958i
\(137\) −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
\(139\) −9.35890 + 16.2101i −0.793811 + 1.37492i 0.129780 + 0.991543i \(0.458573\pi\)
−0.923591 + 0.383379i \(0.874760\pi\)
\(140\) −4.35890 −0.368394
\(141\) −6.00000 −0.505291
\(142\) 8.03835 13.9228i 0.674563 1.16838i
\(143\) −6.00000 + 10.3923i −0.501745 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) −0.641101 −0.0532405
\(146\) 6.67945 11.5691i 0.552795 0.957469i
\(147\) −6.00000 10.3923i −0.494872 0.857143i
\(148\) 3.50000 6.06218i 0.287698 0.498308i
\(149\) −8.03835 13.9228i −0.658527 1.14060i −0.980997 0.194023i \(-0.937846\pi\)
0.322470 0.946580i \(-0.395487\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 24.0767 1.95933 0.979667 0.200631i \(-0.0642992\pi\)
0.979667 + 0.200631i \(0.0642992\pi\)
\(152\) −2.17945 3.77492i −0.176777 0.306186i
\(153\) −5.35890 −0.433241
\(154\) −6.53835 11.3248i −0.526875 0.912574i
\(155\) 3.35890 + 5.81778i 0.269793 + 0.467296i
\(156\) 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 \(0.897272\pi\)
\(158\) 6.35890 11.0139i 0.505887 0.876222i
\(159\) 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
\(163\) 12.7178 0.996135 0.498067 0.867138i \(-0.334043\pi\)
0.498067 + 0.867138i \(0.334043\pi\)
\(164\) 2.35890 0.184199
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −6.21780 + 10.7695i −0.481148 + 0.833372i −0.999766 0.0216337i \(-0.993113\pi\)
0.518618 + 0.855006i \(0.326447\pi\)
\(168\) 2.17945 + 3.77492i 0.168148 + 0.291241i
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) −5.35890 −0.411009
\(171\) −4.35890 −0.333333
\(172\) −10.0000 −0.762493
\(173\) −4.82055 8.34944i −0.366500 0.634796i 0.622516 0.782607i \(-0.286111\pi\)
−0.989016 + 0.147811i \(0.952777\pi\)
\(174\) 0.320551 + 0.555210i 0.0243009 + 0.0420903i
\(175\) −2.17945 + 3.77492i −0.164751 + 0.285357i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 2.35890 4.08573i 0.177306 0.307102i
\(178\) 8.35890 0.626526
\(179\) −1.71780 −0.128394 −0.0641971 0.997937i \(-0.520449\pi\)
−0.0641971 + 0.997937i \(0.520449\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 4.03835 6.99462i 0.300168 0.519906i −0.676006 0.736896i \(-0.736291\pi\)
0.976174 + 0.216990i \(0.0696239\pi\)
\(182\) 17.4356 1.29241
\(183\) −3.35890 −0.248297
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) 3.35890 5.81778i 0.246286 0.426581i
\(187\) −8.03835 13.9228i −0.587822 1.01814i
\(188\) 3.00000 + 5.19615i 0.218797 + 0.378968i
\(189\) 4.35890 0.317063
\(190\) −4.35890 −0.316228
\(191\) 15.4356 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 1.03835 + 1.79847i 0.0747420 + 0.129457i 0.900974 0.433873i \(-0.142853\pi\)
−0.826232 + 0.563330i \(0.809520\pi\)
\(194\) 6.03835 10.4587i 0.433528 0.750893i
\(195\) −2.00000 3.46410i −0.143223 0.248069i
\(196\) −6.00000 + 10.3923i −0.428571 + 0.742307i
\(197\) −14.3589 −1.02303 −0.511515 0.859275i \(-0.670915\pi\)
−0.511515 + 0.859275i \(0.670915\pi\)
\(198\) 3.00000 0.213201
\(199\) −12.6794 + 21.9615i −0.898822 + 1.55681i −0.0698209 + 0.997560i \(0.522243\pi\)
−0.829001 + 0.559246i \(0.811091\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 2.64110 0.186289
\(202\) −4.71780 −0.331943
\(203\) −1.39725 + 2.42010i −0.0980675 + 0.169858i
\(204\) 2.67945 + 4.64094i 0.187599 + 0.324931i
\(205\) 1.17945 2.04287i 0.0823763 0.142680i
\(206\) −0.820551 1.42124i −0.0571705 0.0990221i
\(207\) 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
\(211\) 5.53835 + 9.59270i 0.381276 + 0.660389i 0.991245 0.132036i \(-0.0421516\pi\)
−0.609969 + 0.792425i \(0.708818\pi\)
\(212\) −6.53835 11.3248i −0.449056 0.777787i
\(213\) −8.03835 + 13.9228i −0.550779 + 0.953976i
\(214\) 0.320551 + 0.555210i 0.0219124 + 0.0379534i
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) −1.00000 −0.0680414
\(217\) 29.2822 1.98781
\(218\) 9.67945 16.7653i 0.655575 1.13549i
\(219\) −6.67945 + 11.5691i −0.451355 + 0.781770i
\(220\) 3.00000 0.202260
\(221\) 21.4356 1.44191
\(222\) −3.50000 + 6.06218i −0.234905 + 0.406867i
\(223\) −5.82055 10.0815i −0.389773 0.675106i 0.602646 0.798009i \(-0.294113\pi\)
−0.992419 + 0.122902i \(0.960780\pi\)
\(224\) 2.17945 3.77492i 0.145621 0.252222i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −2.67945 4.64094i −0.178234 0.308711i
\(227\) 5.35890 0.355683 0.177841 0.984059i \(-0.443089\pi\)
0.177841 + 0.984059i \(0.443089\pi\)
\(228\) 2.17945 + 3.77492i 0.144338 + 0.250000i
\(229\) −8.71780 −0.576088 −0.288044 0.957617i \(-0.593005\pi\)
−0.288044 + 0.957617i \(0.593005\pi\)
\(230\) 1.50000 + 2.59808i 0.0989071 + 0.171312i
\(231\) 6.53835 + 11.3248i 0.430192 + 0.745114i
\(232\) 0.320551 0.555210i 0.0210452 0.0364513i
\(233\) −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
\(236\) −4.71780 −0.307102
\(237\) −6.35890 + 11.0139i −0.413055 + 0.715432i
\(238\) −11.6794 + 20.2294i −0.757066 + 1.31128i
\(239\) 21.4356 1.38655 0.693277 0.720671i \(-0.256166\pi\)
0.693277 + 0.720671i \(0.256166\pi\)
\(240\) −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
\(244\) 1.67945 + 2.90889i 0.107516 + 0.186223i
\(245\) 6.00000 + 10.3923i 0.383326 + 0.663940i
\(246\) −2.35890 −0.150398
\(247\) 17.4356 1.10940
\(248\) −6.71780 −0.426581
\(249\) 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
\(254\) 1.64110 0.102972
\(255\) 5.35890 0.335587
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.7178 + 23.7599i −0.855693 + 1.48210i 0.0203082 + 0.999794i \(0.493535\pi\)
−0.876001 + 0.482310i \(0.839798\pi\)
\(258\) 10.0000 0.622573
\(259\) −30.5123 −1.89594
\(260\) −2.00000 + 3.46410i −0.124035 + 0.214834i
\(261\) −0.320551 0.555210i −0.0198416 0.0343666i
\(262\) −1.50000 + 2.59808i −0.0926703 + 0.160510i
\(263\) 12.8589 + 22.2723i 0.792914 + 1.37337i 0.924156 + 0.382016i \(0.124770\pi\)
−0.131242 + 0.991350i \(0.541896\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) −13.0767 −0.803295
\(266\) −9.50000 + 16.4545i −0.582482 + 1.00889i
\(267\) −8.35890 −0.511556
\(268\) −1.32055 2.28726i −0.0806655 0.139717i
\(269\) 2.67945 + 4.64094i 0.163369 + 0.282963i 0.936075 0.351801i \(-0.114431\pi\)
−0.772706 + 0.634764i \(0.781097\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −6.35890 11.0139i −0.386276 0.669049i 0.605670 0.795716i \(-0.292905\pi\)
−0.991945 + 0.126667i \(0.959572\pi\)
\(272\) 2.67945 4.64094i 0.162465 0.281398i
\(273\) −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 \(0.538343\pi\)
\(278\) −18.7178 −1.12262
\(279\) −3.35890 + 5.81778i −0.201092 + 0.348302i
\(280\) −2.17945 3.77492i −0.130247 0.225594i
\(281\) 12.5383 21.7171i 0.747975 1.29553i −0.200817 0.979629i \(-0.564360\pi\)
0.948792 0.315902i \(-0.102307\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 4.35890 + 7.54983i 0.259110 + 0.448791i 0.966004 0.258528i \(-0.0832376\pi\)
−0.706894 + 0.707319i \(0.749904\pi\)
\(284\) 16.0767 0.953976
\(285\) 4.35890 0.258199
\(286\) −12.0000 −0.709575
\(287\) −5.14110 8.90465i −0.303470 0.525625i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −5.85890 + 10.1479i −0.344641 + 0.596936i
\(290\) −0.320551 0.555210i −0.0188234 0.0326030i
\(291\) −6.03835 + 10.4587i −0.353974 + 0.613101i
\(292\) 13.3589 0.781770
\(293\) 14.3589 0.838856 0.419428 0.907789i \(-0.362231\pi\)
0.419428 + 0.907789i \(0.362231\pi\)
\(294\) 6.00000 10.3923i 0.349927 0.606092i
\(295\) −2.35890 + 4.08573i −0.137340 + 0.237881i
\(296\) 7.00000 0.406867
\(297\) −3.00000 −0.174078
\(298\) 8.03835 13.9228i 0.465649 0.806528i
\(299\) −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
\(302\) 12.0383 + 20.8510i 0.692729 + 1.19984i
\(303\) 4.71780 0.271030
\(304\) 2.17945 3.77492i 0.125000 0.216506i
\(305\) 3.35890 0.192330
\(306\) −2.67945 4.64094i −0.153174 0.265305i
\(307\) −3.67945 6.37299i −0.209997 0.363726i 0.741716 0.670714i \(-0.234012\pi\)
−0.951713 + 0.306988i \(0.900679\pi\)
\(308\) 6.53835 11.3248i 0.372557 0.645288i
\(309\) 0.820551 + 1.42124i 0.0466795 + 0.0808512i
\(310\) −3.35890 + 5.81778i −0.190773 + 0.330428i
\(311\) −33.4356 −1.89596 −0.947979 0.318332i \(-0.896877\pi\)
−0.947979 + 0.318332i \(0.896877\pi\)
\(312\) 4.00000 0.226455
\(313\) −8.71780 + 15.0997i −0.492759 + 0.853484i −0.999965 0.00834102i \(-0.997345\pi\)
0.507206 + 0.861825i \(0.330678\pi\)
\(314\) 2.50000 4.33013i 0.141083 0.244363i
\(315\) −4.35890 −0.245596
\(316\) 12.7178 0.715432
\(317\) 3.53835 6.12860i 0.198733 0.344216i −0.749385 0.662135i \(-0.769651\pi\)
0.948118 + 0.317919i \(0.102984\pi\)
\(318\) 6.53835 + 11.3248i 0.366652 + 0.635061i
\(319\) 0.961652 1.66563i 0.0538422 0.0932573i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) −0.320551 0.555210i −0.0178914 0.0309888i
\(322\) 13.0767 0.728736
\(323\) −11.6794 + 20.2294i −0.649862 + 1.12559i
\(324\) 1.00000 0.0555556
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) 6.35890 + 11.0139i 0.352187 + 0.610005i
\(327\) −9.67945 + 16.7653i −0.535275 + 0.927123i
\(328\) 1.17945 + 2.04287i 0.0651242 + 0.112798i
\(329\) 13.0767 22.6495i 0.720942 1.24871i
\(330\) −3.00000 −0.165145
\(331\) 5.64110 0.310063 0.155031 0.987910i \(-0.450452\pi\)
0.155031 + 0.987910i \(0.450452\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 3.50000 6.06218i 0.191799 0.332205i
\(334\) −12.4356 −0.680446
\(335\) −2.64110 −0.144299
\(336\) −2.17945 + 3.77492i −0.118899 + 0.205939i
\(337\) 15.0767 + 26.1136i 0.821280 + 1.42250i 0.904729 + 0.425987i \(0.140073\pi\)
−0.0834494 + 0.996512i \(0.526594\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) 2.67945 + 4.64094i 0.145528 + 0.252061i
\(340\) −2.67945 4.64094i −0.145314 0.251690i
\(341\) −20.1534 −1.09137
\(342\) −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
\(346\) 4.82055 8.34944i 0.259154 0.448869i
\(347\) −13.7178 23.7599i −0.736410 1.27550i −0.954102 0.299482i \(-0.903186\pi\)
0.217692 0.976018i \(-0.430147\pi\)
\(348\) −0.320551 + 0.555210i −0.0171833 + 0.0297624i
\(349\) −26.0767 −1.39585 −0.697927 0.716169i \(-0.745894\pi\)
−0.697927 + 0.716169i \(0.745894\pi\)
\(350\) −4.35890 −0.232993
\(351\) 2.00000 3.46410i 0.106752 0.184900i
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 16.0767 0.855676 0.427838 0.903855i \(-0.359275\pi\)
0.427838 + 0.903855i \(0.359275\pi\)
\(354\) 4.71780 0.250748
\(355\) 8.03835 13.9228i 0.426631 0.738947i
\(356\) 4.17945 + 7.23902i 0.221510 + 0.383667i
\(357\) 11.6794 20.2294i 0.618142 1.07065i
\(358\) −0.858899 1.48766i −0.0453942 0.0786251i
\(359\) −3.32055 5.75136i −0.175252 0.303545i 0.764996 0.644034i \(-0.222741\pi\)
−0.940248 + 0.340489i \(0.889407\pi\)
\(360\) 1.00000 0.0527046
\(361\) −9.50000 + 16.4545i −0.500000 + 0.866025i
\(362\) 8.07670 0.424502
\(363\) 1.00000 + 1.73205i 0.0524864 + 0.0909091i
\(364\) 8.71780 + 15.0997i 0.456937 + 0.791438i
\(365\) 6.67945 11.5691i 0.349618 0.605557i
\(366\) −1.67945 2.90889i −0.0877862 0.152050i
\(367\) 1.35890 2.35368i 0.0709339 0.122861i −0.828377 0.560171i \(-0.810735\pi\)
0.899311 + 0.437310i \(0.144069\pi\)
\(368\) −3.00000 −0.156386
\(369\) 2.35890 0.122799
\(370\) 3.50000 6.06218i 0.181956 0.315158i
\(371\) −28.5000 + 49.3634i −1.47965 + 2.56282i
\(372\) 6.71780 0.348302
\(373\) 11.0000 0.569558 0.284779 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(374\) 8.03835 13.9228i 0.415653 0.719932i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 1.28220 + 2.22084i 0.0660368 + 0.114379i
\(378\) 2.17945 + 3.77492i 0.112099 + 0.194161i
\(379\) −2.71780 −0.139604 −0.0698020 0.997561i \(-0.522237\pi\)
−0.0698020 + 0.997561i \(0.522237\pi\)
\(380\) −2.17945 3.77492i −0.111803 0.193649i
\(381\) −1.64110 −0.0840762
\(382\) 7.71780 + 13.3676i 0.394877 + 0.683947i
\(383\) −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
\(386\) −1.03835 + 1.79847i −0.0528505 + 0.0915398i
\(387\) −10.0000 −0.508329
\(388\) 12.0767 0.613101
\(389\) 11.0383 19.1190i 0.559666 0.969371i −0.437858 0.899044i \(-0.644263\pi\)
0.997524 0.0703264i \(-0.0224041\pi\)
\(390\) 2.00000 3.46410i 0.101274 0.175412i
\(391\) 16.0767 0.813034
\(392\) −12.0000 −0.606092
\(393\) 1.50000 2.59808i 0.0756650 0.131056i
\(394\) −7.17945 12.4352i −0.361695 0.626475i
\(395\) 6.35890 11.0139i 0.319951 0.554171i
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 14.2178 + 24.6259i 0.713571 + 1.23594i 0.963508 + 0.267679i \(0.0862566\pi\)
−0.249937 + 0.968262i \(0.580410\pi\)
\(398\) −25.3589 −1.27113
\(399\) 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 \(0.684957\pi\)
\(402\) 1.32055 + 2.28726i 0.0658631 + 0.114078i
\(403\) 13.4356 23.2711i 0.669275 1.15922i
\(404\) −2.35890 4.08573i −0.117360 0.203273i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) −2.79449 −0.138688
\(407\) 21.0000 1.04093
\(408\) −2.67945 + 4.64094i −0.132653 + 0.229761i
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 2.35890 0.116498
\(411\) 12.0000 0.591916
\(412\) 0.820551 1.42124i 0.0404256 0.0700192i
\(413\) 10.2822 + 17.8093i 0.505954 + 0.876338i
\(414\) −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
\(417\) 18.7178 0.916615
\(418\) 6.53835 11.3248i 0.319801 0.553912i
\(419\) −1.71780 −0.0839199 −0.0419600 0.999119i \(-0.513360\pi\)
−0.0419600 + 0.999119i \(0.513360\pi\)
\(420\) 2.17945 + 3.77492i 0.106346 + 0.184197i
\(421\) −4.96165 8.59383i −0.241816 0.418838i 0.719416 0.694580i \(-0.244410\pi\)
−0.961232 + 0.275742i \(0.911076\pi\)
\(422\) −5.53835 + 9.59270i −0.269603 + 0.466965i
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 6.53835 11.3248i 0.317530 0.549979i
\(425\) −5.35890 −0.259945
\(426\) −16.0767 −0.778919
\(427\) 7.32055 12.6796i 0.354266 0.613607i
\(428\) −0.320551 + 0.555210i −0.0154944 + 0.0268371i
\(429\) 12.0000 0.579365
\(430\) −10.0000 −0.482243
\(431\) 16.3972 28.4009i 0.789828 1.36802i −0.136245 0.990675i \(-0.543503\pi\)
0.926072 0.377346i \(-0.123163\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 3.39725 5.88421i 0.163261 0.282777i −0.772775 0.634680i \(-0.781132\pi\)
0.936036 + 0.351903i \(0.114465\pi\)
\(434\) 14.6411 + 25.3591i 0.702795 + 1.21728i
\(435\) 0.320551 + 0.555210i 0.0153692 + 0.0266203i
\(436\) 19.3589 0.927123
\(437\) 13.0767 0.625543
\(438\) −13.3589 −0.638313
\(439\) −7.32055 12.6796i −0.349391 0.605163i 0.636751 0.771070i \(-0.280278\pi\)
−0.986141 + 0.165907i \(0.946945\pi\)
\(440\) 1.50000 + 2.59808i 0.0715097 + 0.123858i
\(441\) −6.00000 + 10.3923i −0.285714 + 0.494872i
\(442\) 10.7178 + 18.5638i 0.509794 + 0.882989i
\(443\) 5.67945 9.83710i 0.269839 0.467374i −0.698981 0.715140i \(-0.746363\pi\)
0.968820 + 0.247766i \(0.0796963\pi\)
\(444\) −7.00000 −0.332205
\(445\) 8.35890 0.396250
\(446\) 5.82055 10.0815i 0.275611 0.477372i
\(447\) −8.03835 + 13.9228i −0.380201 + 0.658527i
\(448\) 4.35890 0.205939
\(449\) −8.35890 −0.394481 −0.197240 0.980355i \(-0.563198\pi\)
−0.197240 + 0.980355i \(0.563198\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) 3.53835 + 6.12860i 0.166614 + 0.288584i
\(452\) 2.67945 4.64094i 0.126031 0.218292i
\(453\) −12.0383 20.8510i −0.565611 0.979667i
\(454\) 2.67945 + 4.64094i 0.125753 + 0.217810i
\(455\) 17.4356 0.817393
\(456\) −2.17945 + 3.77492i −0.102062 + 0.176777i
\(457\) −39.3589 −1.84113 −0.920566 0.390587i \(-0.872272\pi\)
−0.920566 + 0.390587i \(0.872272\pi\)
\(458\) −4.35890 7.54983i −0.203678 0.352781i
\(459\) 2.67945 + 4.64094i 0.125066 + 0.216621i
\(460\) −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
\(463\) 25.7945 1.19877 0.599386 0.800460i \(-0.295412\pi\)
0.599386 + 0.800460i \(0.295412\pi\)
\(464\) 0.641101 0.0297624
\(465\) 3.35890 5.81778i 0.155765 0.269793i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −14.7945 −0.684608 −0.342304 0.939589i \(-0.611207\pi\)
−0.342304 + 0.939589i \(0.611207\pi\)
\(468\) −4.00000 −0.184900
\(469\) −5.75615 + 9.96994i −0.265794 + 0.460369i
\(470\) 3.00000 + 5.19615i 0.138380 + 0.239681i
\(471\) −2.50000 + 4.33013i −0.115194 + 0.199522i
\(472\) −2.35890 4.08573i −0.108577 0.188061i
\(473\) −15.0000 25.9808i −0.689701 1.19460i
\(474\) −12.7178 −0.584148
\(475\) −4.35890 −0.200000
\(476\) −23.3589 −1.07065
\(477\) −6.53835 11.3248i −0.299370 0.518525i
\(478\) 10.7178 + 18.5638i 0.490221 + 0.849087i
\(479\) −2.03835 + 3.53052i −0.0931345 + 0.161314i −0.908829 0.417170i \(-0.863022\pi\)
0.815694 + 0.578484i \(0.196355\pi\)
\(480\) −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
\(485\) 6.03835 10.4587i 0.274187 0.474906i
\(486\) −1.00000 −0.0453609
\(487\) −18.3589 −0.831921 −0.415961 0.909383i \(-0.636555\pi\)
−0.415961 + 0.909383i \(0.636555\pi\)
\(488\) −1.67945 + 2.90889i −0.0760251 + 0.131679i
\(489\) −6.35890 11.0139i −0.287559 0.498067i
\(490\) −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 \(0.943243\pi\)
\(492\) −1.17945 2.04287i −0.0531737 0.0920995i
\(493\) −3.43560 −0.154731
\(494\) 8.71780 + 15.0997i 0.392232 + 0.679366i
\(495\) 3.00000 0.134840
\(496\) −3.35890 5.81778i −0.150819 0.261226i
\(497\) −35.0383 60.6882i −1.57168 2.72224i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 12.1794 + 21.0954i 0.545227 + 0.944361i 0.998593 + 0.0530363i \(0.0168899\pi\)
−0.453366 + 0.891325i \(0.649777\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 12.4356 0.555581
\(502\) 12.0000 0.535586
\(503\) 19.9356 34.5295i 0.888884 1.53959i 0.0476884 0.998862i \(-0.484815\pi\)
0.841196 0.540730i \(-0.181852\pi\)
\(504\) 2.17945 3.77492i 0.0970804 0.168148i
\(505\) −4.71780 −0.209939
\(506\) −9.00000 −0.400099
\(507\) −1.50000 + 2.59808i −0.0666173 + 0.115385i
\(508\) 0.820551 + 1.42124i 0.0364060 + 0.0630571i
\(509\) −3.64110 + 6.30657i −0.161389 + 0.279534i −0.935367 0.353678i \(-0.884931\pi\)
0.773978 + 0.633212i \(0.218264\pi\)
\(510\) 2.67945 + 4.64094i 0.118648 + 0.205504i
\(511\) −29.1150 50.4287i −1.28797 2.23084i
\(512\) −1.00000 −0.0441942
\(513\) 2.17945 + 3.77492i 0.0962250 + 0.166667i
\(514\) −27.4356 −1.21013
\(515\) −0.820551 1.42124i −0.0361578 0.0626271i
\(516\) 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
\(519\) −4.82055 + 8.34944i −0.211599 + 0.366500i
\(520\) −4.00000 −0.175412
\(521\) 40.7178 1.78388 0.891940 0.452155i \(-0.149344\pi\)
0.891940 + 0.452155i \(0.149344\pi\)
\(522\) 0.320551 0.555210i 0.0140301 0.0243009i
\(523\) −2.39725 + 4.15215i −0.104824 + 0.181561i −0.913666 0.406465i \(-0.866761\pi\)
0.808842 + 0.588026i \(0.200095\pi\)
\(524\) −3.00000 −0.131056
\(525\) 4.35890 0.190238
\(526\) −12.8589 + 22.2723i −0.560675 + 0.971117i
\(527\) 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
\(531\) −4.71780 −0.204735
\(532\) −19.0000 −0.823754
\(533\) −9.43560 −0.408701
\(534\) −4.17945 7.23902i −0.180862 0.313263i
\(535\) 0.320551 + 0.555210i 0.0138586 + 0.0240038i
\(536\) 1.32055 2.28726i 0.0570391 0.0987946i
\(537\) 0.858899 + 1.48766i 0.0370642 + 0.0641971i
\(538\) −2.67945 + 4.64094i −0.115519 + 0.200085i
\(539\) −36.0000 −1.55063
\(540\) −1.00000 −0.0430331
\(541\) 13.3589 23.1383i 0.574344 0.994793i −0.421769 0.906703i \(-0.638591\pi\)
0.996113 0.0880894i \(-0.0280761\pi\)
\(542\) 6.35890 11.0139i 0.273138 0.473089i
\(543\) −8.07670 −0.346604
\(544\) 5.35890 0.229761
\(545\) 9.67945 16.7653i 0.414622 0.718146i
\(546\) −8.71780 15.0997i −0.373087 0.646206i
\(547\) −23.0767 + 39.9700i −0.986688 + 1.70899i −0.352509 + 0.935809i \(0.614671\pi\)
−0.634180 + 0.773186i \(0.718662\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) 1.67945 + 2.90889i 0.0716772 + 0.124148i
\(550\) 3.00000 0.127920
\(551\) −2.79449 −0.119049
\(552\) 3.00000 0.127688
\(553\) −27.7178 48.0086i −1.17868 2.04153i
\(554\) −2.00000 3.46410i −0.0849719 0.147176i
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) −9.35890 16.2101i −0.396906 0.687461i
\(557\) 18.5383 32.1094i 0.785495 1.36052i −0.143208 0.989693i \(-0.545742\pi\)
0.928703 0.370825i \(-0.120925\pi\)
\(558\) −6.71780 −0.284387
\(559\) 40.0000 1.69182
\(560\) 2.17945 3.77492i 0.0920985 0.159519i
\(561\) −8.03835 + 13.9228i −0.339379 + 0.587822i
\(562\) 25.0767 1.05780
\(563\) 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
\(565\) −2.67945 4.64094i −0.112725 0.195246i
\(566\) −4.35890 + 7.54983i −0.183218 + 0.317343i
\(567\) −2.17945 3.77492i −0.0915283 0.158532i
\(568\) 8.03835 + 13.9228i 0.337282 + 0.584189i
\(569\) 5.79449 0.242918 0.121459 0.992596i \(-0.461243\pi\)
0.121459 + 0.992596i \(0.461243\pi\)
\(570\) 2.17945 + 3.77492i 0.0912871 + 0.158114i
\(571\) −18.1534 −0.759696 −0.379848 0.925049i \(-0.624024\pi\)
−0.379848 + 0.925049i \(0.624024\pi\)
\(572\) −6.00000 10.3923i −0.250873 0.434524i
\(573\) −7.71780 13.3676i −0.322416 0.558440i
\(574\) 5.14110 8.90465i 0.214585 0.371673i
\(575\) 1.50000 + 2.59808i 0.0625543 + 0.108347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −24.7945 −1.03221 −0.516104 0.856526i \(-0.672618\pi\)
−0.516104 + 0.856526i \(0.672618\pi\)
\(578\) −11.7178 −0.487396
\(579\) 1.03835 1.79847i 0.0431523 0.0747420i
\(580\) 0.320551 0.555210i 0.0133101 0.0230538i
\(581\) −26.1534 −1.08503
\(582\) −12.0767 −0.500595
\(583\) 19.6150 33.9743i 0.812372 1.40707i
\(584\) 6.67945 + 11.5691i 0.276398 + 0.478735i
\(585\) −2.00000 + 3.46410i −0.0826898 + 0.143223i
\(586\) 7.17945 + 12.4352i 0.296580 + 0.513692i
\(587\) 12.6411 + 21.8950i 0.521754 + 0.903705i 0.999680 + 0.0253043i \(0.00805547\pi\)
−0.477926 + 0.878400i \(0.658611\pi\)
\(588\) 12.0000 0.494872
\(589\) 14.6411 + 25.3591i 0.603276 + 1.04490i
\(590\) −4.71780 −0.194229
\(591\) 7.17945 + 12.4352i 0.295323 + 0.511515i
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) −17.0383 + 29.5113i −0.699681 + 1.21188i 0.268896 + 0.963169i \(0.413341\pi\)
−0.968577 + 0.248714i \(0.919992\pi\)
\(594\) −1.50000 2.59808i −0.0615457 0.106600i
\(595\) −11.6794 + 20.2294i −0.478811 + 0.829325i
\(596\) 16.0767 0.658527
\(597\) 25.3589 1.03787
\(598\) 6.00000 10.3923i 0.245358 0.424973i
\(599\) −17.6794 + 30.6217i −0.722363 + 1.25117i 0.237688 + 0.971342i \(0.423611\pi\)
−0.960050 + 0.279827i \(0.909723\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −11.7178 −0.477979 −0.238989 0.971022i \(-0.576816\pi\)
−0.238989 + 0.971022i \(0.576816\pi\)
\(602\) −21.7945 + 37.7492i −0.888277 + 1.53854i
\(603\) −1.32055 2.28726i −0.0537770 0.0931445i
\(604\) −12.0383 + 20.8510i −0.489833 + 0.848416i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) 2.35890 + 4.08573i 0.0958237 + 0.165972i
\(607\) 7.79449 0.316369 0.158184 0.987410i \(-0.449436\pi\)
0.158184 + 0.987410i \(0.449436\pi\)
\(608\) 4.35890 0.176777
\(609\) 2.79449 0.113239
\(610\) 1.67945 + 2.90889i 0.0679989 + 0.117778i
\(611\) −12.0000 20.7846i −0.485468 0.840855i
\(612\) 2.67945 4.64094i 0.108310 0.187599i
\(613\) 14.2178 + 24.6259i 0.574251 + 0.994633i 0.996123 + 0.0879769i \(0.0280402\pi\)
−0.421871 + 0.906656i \(0.638627\pi\)
\(614\) 3.67945 6.37299i 0.148490 0.257193i
\(615\) −2.35890 −0.0951200
\(616\) 13.0767 0.526875
\(617\) −16.7178 + 28.9561i −0.673033 + 1.16573i 0.304006 + 0.952670i \(0.401676\pi\)
−0.977040 + 0.213058i \(0.931658\pi\)
\(618\) −0.820551 + 1.42124i −0.0330074 + 0.0571705i
\(619\) −12.3589 −0.496746 −0.248373 0.968664i \(-0.579896\pi\)
−0.248373 + 0.968664i \(0.579896\pi\)
\(620\) −6.71780 −0.269793
\(621\) 1.50000 2.59808i 0.0601929 0.104257i
\(622\) −16.7178 28.9561i −0.670323 1.16103i
\(623\) 18.2178 31.5542i 0.729881 1.26419i
\(624\) 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
\(629\) −18.7561 32.4866i −0.747857 1.29533i
\(630\) −2.17945 3.77492i −0.0868313 0.150396i
\(631\) −16.3206 + 28.2680i −0.649711 + 1.12533i 0.333481 + 0.942757i \(0.391777\pi\)
−0.983192 + 0.182575i \(0.941557\pi\)
\(632\) 6.35890 + 11.0139i 0.252943 + 0.438111i
\(633\) 5.53835 9.59270i 0.220130 0.381276i
\(634\) 7.07670 0.281052
\(635\) 1.64110 0.0651251
\(636\) −6.53835 + 11.3248i −0.259262 + 0.449056i
\(637\) 24.0000 41.5692i 0.950915 1.64703i
\(638\) 1.92330 0.0761443
\(639\) 16.0767 0.635984
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 14.3589 + 24.8703i 0.567142 + 0.982319i 0.996847 + 0.0793499i \(0.0252844\pi\)
−0.429704 + 0.902970i \(0.641382\pi\)
\(642\) 0.320551 0.555210i 0.0126511 0.0219124i
\(643\) −10.7561 18.6302i −0.424181 0.734703i 0.572163 0.820140i \(-0.306105\pi\)
−0.996344 + 0.0854372i \(0.972771\pi\)
\(644\) 6.53835 + 11.3248i 0.257647 + 0.446258i
\(645\) 10.0000 0.393750
\(646\) −23.3589 −0.919044
\(647\) 35.1534 1.38202 0.691011 0.722844i \(-0.257165\pi\)
0.691011 + 0.722844i \(0.257165\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −7.07670 12.2572i −0.277785 0.481137i
\(650\) −2.00000 + 3.46410i −0.0784465 + 0.135873i
\(651\) −14.6411 25.3591i −0.573830 0.993903i
\(652\) −6.35890 + 11.0139i −0.249034 + 0.431339i
\(653\) 1.07670 0.0421344 0.0210672 0.999778i \(-0.493294\pi\)
0.0210672 + 0.999778i \(0.493294\pi\)
\(654\) −19.3589 −0.756993
\(655\) −1.50000 + 2.59808i −0.0586098 + 0.101515i
\(656\) −1.17945 + 2.04287i −0.0460498 + 0.0797605i
\(657\) 13.3589 0.521180
\(658\) 26.1534 1.01957
\(659\) 11.1411 19.2970i 0.433996 0.751703i −0.563217 0.826309i \(-0.690437\pi\)
0.997213 + 0.0746062i \(0.0237700\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) −8.71780 + 15.0997i −0.339083 + 0.587309i −0.984261 0.176724i \(-0.943450\pi\)
0.645177 + 0.764033i \(0.276783\pi\)
\(662\) 2.82055 + 4.88534i 0.109624 + 0.189874i
\(663\) −10.7178 18.5638i −0.416245 0.720957i
\(664\) 6.00000 0.232845
\(665\) −9.50000 + 16.4545i −0.368394 + 0.638077i
\(666\) 7.00000 0.271244
\(667\) 0.961652 + 1.66563i 0.0372353 + 0.0644934i
\(668\) −6.21780 10.7695i −0.240574 0.416686i
\(669\) −5.82055 + 10.0815i −0.225035 + 0.389773i
\(670\) −1.32055 2.28726i −0.0510173 0.0883646i
\(671\) −5.03835 + 8.72668i −0.194503 + 0.336890i
\(672\) −4.35890 −0.168148
\(673\) −38.7178 −1.49246 −0.746231 0.665687i \(-0.768138\pi\)
−0.746231 + 0.665687i \(0.768138\pi\)
\(674\) −15.0767 + 26.1136i −0.580733 + 1.00586i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 3.00000 0.115385
\(677\) −19.0767 −0.733177 −0.366589 0.930383i \(-0.619474\pi\)
−0.366589 + 0.930383i \(0.619474\pi\)
\(678\) −2.67945 + 4.64094i −0.102904 + 0.178234i
\(679\) −26.3206 45.5885i −1.01009 1.74953i
\(680\) 2.67945 4.64094i 0.102752 0.177972i
\(681\) −2.67945 4.64094i −0.102677 0.177841i
\(682\) −10.0767 17.4534i −0.385857 0.668323i
\(683\) 20.7945 0.795679 0.397840 0.917455i \(-0.369760\pi\)
0.397840 + 0.917455i \(0.369760\pi\)
\(684\) 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
\(691\) 40.3589 1.53532 0.767662 0.640854i \(-0.221420\pi\)
0.767662 + 0.640854i \(0.221420\pi\)
\(692\) 9.64110 0.366500
\(693\) 6.53835 11.3248i 0.248371 0.430192i
\(694\) 13.7178 23.7599i 0.520720 0.901914i
\(695\) −18.7178 −0.710007
\(696\) −0.641101 −0.0243009
\(697\) 6.32055 10.9475i 0.239408 0.414667i
\(698\) −13.0383 22.5831i −0.493509 0.854782i
\(699\) −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
\(706\) 8.03835 + 13.9228i 0.302527 + 0.523993i
\(707\) −10.2822 + 17.8093i −0.386702 + 0.669788i
\(708\) 2.35890 + 4.08573i 0.0886529 + 0.153551i
\(709\) −8.39725 + 14.5445i −0.315365 + 0.546229i −0.979515 0.201371i \(-0.935460\pi\)
0.664150 + 0.747599i \(0.268794\pi\)
\(710\) 16.0767 0.603348
\(711\) 12.7178 0.476955
\(712\) −4.17945 + 7.23902i −0.156631 + 0.271294i
\(713\) 10.0767 17.4534i 0.377375 0.653633i
\(714\) 23.3589 0.874185
\(715\) −12.0000 −0.448775
\(716\) 0.858899 1.48766i 0.0320986 0.0555963i
\(717\) −10.7178 18.5638i −0.400263 0.693277i
\(718\) 3.32055 5.75136i 0.123922 0.214639i
\(719\) 17.3589 + 30.0665i 0.647378 + 1.12129i 0.983747 + 0.179561i \(0.0574677\pi\)
−0.336369 + 0.941730i \(0.609199\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −7.15339 −0.266406
\(722\) −19.0000 −0.707107
\(723\) −4.00000 −0.148762
\(724\) 4.03835 + 6.99462i 0.150084 + 0.259953i
\(725\) −0.320551 0.555210i −0.0119049 0.0206200i
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) −11.0767 19.1854i −0.410812 0.711547i 0.584167 0.811634i \(-0.301421\pi\)
−0.994979 + 0.100086i \(0.968088\pi\)
\(728\) −8.71780 + 15.0997i −0.323103 + 0.559631i
\(729\) 1.00000 0.0370370
\(730\) 13.3589 0.494435
\(731\) −26.7945 + 46.4094i −0.991030 + 1.71651i
\(732\) 1.67945 2.90889i 0.0620742 0.107516i
\(733\) 44.4356 1.64127 0.820633 0.571455i \(-0.193621\pi\)
0.820633 + 0.571455i \(0.193621\pi\)
\(734\) 2.71780 0.100316
\(735\) 6.00000 10.3923i 0.221313 0.383326i
\(736\) −1.50000 2.59808i −0.0552907 0.0957664i
\(737\) 3.96165 6.86178i 0.145929 0.252757i
\(738\) 1.17945 + 2.04287i 0.0434161 + 0.0751990i
\(739\) 3.82055 + 6.61739i 0.140541 + 0.243425i 0.927701 0.373325i \(-0.121782\pi\)
−0.787159 + 0.616750i \(0.788449\pi\)
\(740\) 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 \(0.886124\pi\)
\(744\) 3.35890 + 5.81778i 0.123143 + 0.213290i
\(745\) 8.03835 13.9228i 0.294502 0.510093i
\(746\) 5.50000 + 9.52628i 0.201369 + 0.348782i
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 16.0767 0.587822
\(749\) 2.79449 0.102109
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 23.4356 40.5916i 0.855177 1.48121i −0.0213037 0.999773i \(-0.506782\pi\)
0.876481 0.481437i \(-0.159885\pi\)
\(752\) −6.00000 −0.218797
\(753\) −12.0000 −0.437304
\(754\) −1.28220 + 2.22084i −0.0466950 + 0.0808782i
\(755\) 12.0383 + 20.8510i 0.438120 + 0.758847i
\(756\) −2.17945 + 3.77492i −0.0792658 + 0.137292i
\(757\) 9.93560 + 17.2090i 0.361115 + 0.625470i 0.988145 0.153525i \(-0.0490627\pi\)
−0.627029 + 0.778996i \(0.715729\pi\)
\(758\) −1.35890 2.35368i −0.0493574 0.0854896i
\(759\) 9.00000 0.326679
\(760\) 2.17945 3.77492i 0.0790569 0.136931i
\(761\) 19.0767 0.691530 0.345765 0.938321i \(-0.387619\pi\)
0.345765 + 0.938321i \(0.387619\pi\)
\(762\) −0.820551 1.42124i −0.0297254 0.0514859i
\(763\) −42.1917 73.0782i −1.52744 2.64561i
\(764\) −7.71780 + 13.3676i −0.279220 + 0.483623i
\(765\) −2.67945 4.64094i −0.0968757 0.167794i
\(766\) 3.00000 5.19615i 0.108394 0.187745i
\(767\) 18.8712 0.681399
\(768\) 1.00000 0.0360844
\(769\) 7.35890 12.7460i 0.265369 0.459632i −0.702291 0.711890i \(-0.747840\pi\)
0.967660 + 0.252257i \(0.0811730\pi\)
\(770\) 6.53835 11.3248i 0.235626 0.408116i
\(771\) 27.4356 0.988069
\(772\) −2.07670 −0.0747420
\(773\) −20.8972 + 36.1951i −0.751622 + 1.30185i 0.195415 + 0.980721i \(0.437395\pi\)
−0.947036 + 0.321126i \(0.895939\pi\)
\(774\) −5.00000 8.66025i −0.179721 0.311286i
\(775\) −3.35890 + 5.81778i −0.120655 + 0.208981i
\(776\) 6.03835 + 10.4587i 0.216764 + 0.375446i
\(777\) 15.2561 + 26.4244i 0.547311 + 0.947971i
\(778\) 22.0767