Properties

Label 570.2.i.h.391.2
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 391.2
Root \(-2.17945 + 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.h.121.2

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 4.35890 1.64751 0.823754 0.566947i \(-0.191875\pi\)
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 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) 2.17945 3.77492i 0.582482 1.00889i
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.67945 4.64094i 0.649862 1.12559i −0.333294 0.942823i \(-0.608160\pi\)
0.983156 0.182771i \(-0.0585066\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.17945 3.77492i 0.500000 0.866025i
\(20\) −1.00000 −0.223607
\(21\) −2.17945 + 3.77492i −0.475595 + 0.823754i
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) −2.17945 3.77492i −0.411877 0.713392i
\(29\) −0.320551 0.555210i −0.0595247 0.103100i 0.834727 0.550663i \(-0.185625\pi\)
−0.894252 + 0.447563i \(0.852292\pi\)
\(30\) 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 −0.943306 0.331923i \(-0.892302\pi\)
0.759107 + 0.650966i \(0.225636\pi\)
\(42\) 2.17945 + 3.77492i 0.336296 + 0.582482i
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) −1.00000 −0.149071
\(46\) 3.00000 0.442326
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 12.0000 1.71429
\(50\) −1.00000 −0.141421
\(51\) 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 −0.829906 0.557903i \(-0.811606\pi\)
−0.0682050 0.997671i \(-0.521727\pi\)
\(54\) 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 −0.670625 0.741797i \(-0.733974\pi\)
0.977727 + 0.209880i \(0.0673072\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) 1.67945 + 2.90889i 0.215031 + 0.372445i 0.953282 0.302081i \(-0.0976813\pi\)
−0.738251 + 0.674526i \(0.764348\pi\)
\(62\) 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 0.774015 0.633167i \(-0.218245\pi\)
−0.935346 + 0.353734i \(0.884912\pi\)
\(68\) −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 −0.217283 + 0.976109i \(0.569720\pi\)
−0.736693 + 0.676227i \(0.763614\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −6.67945 + 11.5691i −0.781770 + 1.35407i 0.149139 + 0.988816i \(0.452350\pi\)
−0.930910 + 0.365250i \(0.880984\pi\)
\(74\) −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 0.247361 + 0.968923i \(0.420437\pi\)
−0.962793 + 0.270241i \(0.912897\pi\)
\(80\) 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 0.997912 0.0645884i \(-0.0205735\pi\)
−0.554891 + 0.831923i \(0.687240\pi\)
\(90\) −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 0.377613 + 0.925963i \(0.376745\pi\)
−0.990714 + 0.135959i \(0.956588\pi\)
\(98\) 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 0.724472 0.689304i \(-0.242084\pi\)
−0.959191 + 0.282759i \(0.908750\pi\)
\(102\) 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 −0.139013 + 0.990291i \(0.544393\pi\)
−0.788111 + 0.615534i \(0.788940\pi\)
\(110\) 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 0.900133 0.435616i \(-0.143469\pi\)
−0.827321 + 0.561730i \(0.810136\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 5.00000 + 8.66025i 0.440225 + 0.762493i
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) −3.00000 −0.261116
\(133\) 9.50000 16.4545i 0.823754 1.42678i
\(134\) −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 −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −1.50000 + 2.59808i −0.127688 + 0.221163i
\(139\) −9.35890 16.2101i −0.793811 1.37492i −0.923591 0.383379i \(-0.874760\pi\)
0.129780 0.991543i \(-0.458573\pi\)
\(140\) −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 0.322470 + 0.946580i \(0.395487\pi\)
−0.980997 + 0.194023i \(0.937846\pi\)
\(150\) 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 −0.948373 0.317156i \(-0.897272\pi\)
0.748852 + 0.662738i \(0.230606\pi\)
\(158\) 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 0.518618 0.855006i \(-0.326447\pi\)
−0.999766 + 0.0216337i \(0.993113\pi\)
\(168\) 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 −0.989016 0.147811i \(-0.952777\pi\)
0.622516 + 0.782607i \(0.286111\pi\)
\(174\) 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 0.976174 0.216990i \(-0.0696239\pi\)
−0.676006 + 0.736896i \(0.736291\pi\)
\(182\) 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 −0.826232 0.563330i \(-0.809520\pi\)
0.900974 + 0.433873i \(0.142853\pi\)
\(194\) 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 −0.829001 0.559246i \(-0.811091\pi\)
−0.0698209 0.997560i \(-0.522243\pi\)
\(200\) 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 −0.609969 0.792425i \(-0.708818\pi\)
0.991245 + 0.132036i \(0.0421516\pi\)
\(212\) −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 −0.992419 0.122902i \(-0.960780\pi\)
0.602646 + 0.798009i \(0.294113\pi\)
\(224\) 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 −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 6.00000 0.391397
\(236\) −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 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 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 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) −2.17945 + 3.77492i −0.137292 + 0.237797i
\(253\) −4.50000 7.79423i −0.282913 0.490019i
\(254\) 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 −0.876001 0.482310i \(-0.839798\pi\)
0.0203082 0.999794i \(-0.493535\pi\)
\(258\) 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 −0.131242 0.991350i \(-0.541896\pi\)
0.924156 0.382016i \(-0.124770\pi\)
\(264\) −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 −0.772706 0.634764i \(-0.781097\pi\)
0.936075 + 0.351801i \(0.114431\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −6.35890 + 11.0139i −0.386276 + 0.669049i −0.991945 0.126667i \(-0.959572\pi\)
0.605670 + 0.795716i \(0.292905\pi\)
\(272\) 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 0.948792 + 0.315902i \(0.102307\pi\)
−0.200817 + 0.979629i \(0.564360\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) 4.35890 7.54983i 0.259110 0.448791i −0.706894 0.707319i \(-0.749904\pi\)
0.966004 + 0.258528i \(0.0832376\pi\)
\(284\) 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 −0.951713 0.306988i \(-0.900679\pi\)
0.741716 + 0.670714i \(0.234012\pi\)
\(308\) 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 0.507206 0.861825i \(-0.330678\pi\)
−0.999965 + 0.00834102i \(0.997345\pi\)
\(314\) 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 0.948118 0.317919i \(-0.102984\pi\)
−0.749385 + 0.662135i \(0.769651\pi\)
\(318\) 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 −0.0834494 0.996512i \(-0.526594\pi\)
0.904729 0.425987i \(-0.140073\pi\)
\(338\) 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 0.217692 + 0.976018i \(0.430147\pi\)
−0.954102 + 0.299482i \(0.903186\pi\)
\(348\) −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 −0.940248 0.340489i \(-0.889407\pi\)
0.764996 + 0.644034i \(0.222741\pi\)
\(360\) 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 0.899311 0.437310i \(-0.144069\pi\)
−0.828377 + 0.560171i \(0.810735\pi\)
\(368\) −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 −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −6.53835 + 11.3248i −0.333225 + 0.577163i
\(386\) −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 0.997524 + 0.0703264i \(0.0224041\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(390\) 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 −0.249937 0.968262i \(-0.580410\pi\)
0.963508 0.267679i \(-0.0862566\pi\)
\(398\) −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 −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 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 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) 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 −0.961232 0.275742i \(-0.911076\pi\)
0.719416 + 0.694580i \(0.244410\pi\)
\(422\) −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 0.926072 + 0.377346i \(0.123163\pi\)
−0.136245 + 0.990675i \(0.543503\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 3.39725 + 5.88421i 0.163261 + 0.282777i 0.936036 0.351903i \(-0.114465\pi\)
−0.772775 + 0.634680i \(0.781132\pi\)
\(434\) 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 −0.986141 0.165907i \(-0.946945\pi\)
0.636751 + 0.771070i \(0.280278\pi\)
\(440\) 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 0.968820 0.247766i \(-0.0796963\pi\)
−0.698981 + 0.715140i \(0.746363\pi\)
\(444\) −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 −0.995856 0.0909401i \(-0.971013\pi\)
0.576685 + 0.816967i \(0.304346\pi\)
\(462\) −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 0.815694 0.578484i \(-0.196355\pi\)
−0.908829 + 0.417170i \(0.863022\pi\)
\(480\) −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 −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) −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 −0.453366 0.891325i \(-0.649777\pi\)
0.998593 0.0530363i \(-0.0168899\pi\)
\(500\) 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 0.841196 + 0.540730i \(0.181852\pi\)
0.0476884 + 0.998862i \(0.484815\pi\)
\(504\) 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 0.773978 0.633212i \(-0.218264\pi\)
−0.935367 + 0.353678i \(0.884931\pi\)
\(510\) 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 0.808842 0.588026i \(-0.200095\pi\)
−0.913666 + 0.406465i \(0.866761\pi\)
\(524\) −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 0.996113 + 0.0880894i \(0.0280761\pi\)
−0.421769 + 0.906703i \(0.638591\pi\)
\(542\) 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 −0.634180 0.773186i \(-0.718662\pi\)
−0.352509 0.935809i \(-0.614671\pi\)
\(548\) −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 0.928703 + 0.370825i \(0.120925\pi\)
−0.143208 + 0.989693i \(0.545742\pi\)
\(558\) −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 −0.477926 0.878400i \(-0.658611\pi\)
0.999680 0.0253043i \(-0.00805547\pi\)
\(588\) 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 −0.968577 0.248714i \(-0.919992\pi\)
0.268896 0.963169i \(-0.413341\pi\)
\(594\) −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 −0.960050 0.279827i \(-0.909723\pi\)
0.237688 0.971342i \(-0.423611\pi\)
\(600\) −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 −0.421871 0.906656i \(-0.638627\pi\)
0.996123 0.0879769i \(-0.0280402\pi\)
\(614\) 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 −0.977040 0.213058i \(-0.931658\pi\)
0.304006 0.952670i \(-0.401676\pi\)
\(618\) −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 −0.983192 0.182575i \(-0.941557\pi\)
0.333481 0.942757i \(-0.391777\pi\)
\(632\) 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 −0.429704 0.902970i \(-0.641382\pi\)
0.996847 0.0793499i \(-0.0252844\pi\)
\(642\) 0.320551 + 0.555210i 0.0126511 + 0.0219124i
\(643\) −10.7561 + 18.6302i −0.424181 + 0.734703i −0.996344 0.0854372i \(-0.972771\pi\)
0.572163 + 0.820140i \(0.306105\pi\)
\(644\) 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 0.997213 0.0746062i \(-0.0237700\pi\)
−0.563217 + 0.826309i \(0.690437\pi\)
\(660\) −1.50000 + 2.59808i −0.0583874 + 0.101130i
\(661\) −8.71780 15.0997i −0.339083 0.587309i 0.645177 0.764033i \(-0.276783\pi\)
−0.984261 + 0.176724i \(0.943450\pi\)
\(662\) 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 −0.984418 0.175842i \(-0.943735\pi\)
0.644493 + 0.764610i \(0.277068\pi\)
\(702\) 4.00000 0.150970
\(703\) −15.2561 + 26.4244i −0.575396 + 0.996616i
\(704\) −3.00000 −0.113067
\(705\) −3.00000 + 5.19615i −0.112987 + 0.195698i
\(706\) 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 0.664150 0.747599i \(-0.268794\pi\)
−0.979515 + 0.201371i \(0.935460\pi\)
\(710\) 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 −0.336369 0.941730i \(-0.609199\pi\)
0.983747 0.179561i \(-0.0574677\pi\)
\(720\) 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 −0.994979 0.100086i \(-0.968088\pi\)
0.584167 + 0.811634i \(0.301421\pi\)
\(728\) −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 −0.787159 0.616750i \(-0.788449\pi\)
0.927701 + 0.373325i \(0.121782\pi\)
\(740\) 7.00000 0.257325
\(741\) −8.71780 + 15.0997i −0.320256 + 0.554700i
\(742\) −57.0000 −2.09254
\(743\) −4.50000 + 7.79423i −0.165089 + 0.285943i −0.936687 0.350168i \(-0.886124\pi\)
0.771598 + 0.636111i \(0.219458\pi\)
\(744\) 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 0.876481 + 0.481437i \(0.159885\pi\)
−0.0213037 + 0.999773i \(0.506782\pi\)
\(752\) −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 −0.627029 0.778996i \(-0.715729\pi\)
0.988145 + 0.153525i \(0.0490627\pi\)
\(758\) −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 0.967660 0.252257i \(-0.0811730\pi\)
−0.702291 + 0.711890i \(0.747840\pi\)
\(770\) 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 −0.947036 0.321126i \(-0.895939\pi\)
0.195415 0.980721i \(-0.437395\pi\)
\(774\) −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