Properties

Label 390.2.y.b.139.1
Level $390$
Weight $2$
Character 390.139
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.y (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 139.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 390.139
Dual form 390.2.y.b.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 + 1.86603i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 + 1.86603i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.133975 - 2.23205i) q^{10} +(1.36603 - 2.36603i) q^{11} +1.00000i q^{12} +(1.59808 + 3.23205i) q^{13} +0.732051 q^{14} +(0.133975 + 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.13397 + 1.23205i) q^{17} -1.00000i q^{18} +(2.36603 + 4.09808i) q^{19} +(-1.00000 + 2.00000i) q^{20} -0.732051 q^{21} +(-2.36603 + 1.36603i) q^{22} +(-3.63397 - 2.09808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(0.232051 - 3.59808i) q^{26} +1.00000i q^{27} +(-0.633975 - 0.366025i) q^{28} +(0.232051 - 0.401924i) q^{29} +(1.00000 - 2.00000i) q^{30} +4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.36603 - 1.36603i) q^{33} +2.46410 q^{34} +(-1.46410 - 0.732051i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.13397 + 2.96410i) q^{37} -4.73205i q^{38} +(-0.232051 + 3.59808i) q^{39} +(1.86603 - 1.23205i) q^{40} +(-0.598076 + 1.03590i) q^{41} +(0.633975 + 0.366025i) q^{42} +(5.83013 - 3.36603i) q^{43} +2.73205 q^{44} +(-1.00000 + 2.00000i) q^{45} +(2.09808 + 3.63397i) q^{46} -9.66025i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(4.00000 - 3.00000i) q^{50} -2.46410 q^{51} +(-2.00000 + 3.00000i) q^{52} -4.26795i q^{53} +(0.500000 - 0.866025i) q^{54} +(6.09808 - 0.366025i) q^{55} +(0.366025 + 0.633975i) q^{56} +4.73205i q^{57} +(-0.401924 + 0.232051i) q^{58} +(4.19615 + 7.26795i) q^{59} +(-1.86603 + 1.23205i) q^{60} +(-7.06218 - 12.2321i) q^{61} +(-3.46410 - 2.00000i) q^{62} +(-0.633975 - 0.366025i) q^{63} -1.00000 q^{64} +(-4.06218 + 6.96410i) q^{65} -2.73205 q^{66} +(8.36603 + 4.83013i) q^{67} +(-2.13397 - 1.23205i) q^{68} +(-2.09808 - 3.63397i) q^{69} +(0.901924 + 1.36603i) q^{70} +(-2.36603 - 4.09808i) q^{71} +(0.866025 - 0.500000i) q^{72} -12.6603i q^{73} +(-2.96410 - 5.13397i) q^{74} +(-4.00000 + 3.00000i) q^{75} +(-2.36603 + 4.09808i) q^{76} +2.00000i q^{77} +(2.00000 - 3.00000i) q^{78} -12.0000 q^{79} +(-2.23205 + 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.03590 - 0.598076i) q^{82} -8.73205i q^{83} +(-0.366025 - 0.633975i) q^{84} +(-4.92820 - 2.46410i) q^{85} -6.73205 q^{86} +(0.401924 - 0.232051i) q^{87} +(-2.36603 - 1.36603i) q^{88} +(4.46410 - 7.73205i) q^{89} +(1.86603 - 1.23205i) q^{90} +(-2.19615 - 1.46410i) q^{91} -4.19615i q^{92} +(3.46410 + 2.00000i) q^{93} +(-4.83013 + 8.36603i) q^{94} +(-4.73205 + 9.46410i) q^{95} +1.00000 q^{96} +(-8.66025 + 5.00000i) q^{97} +(5.59808 - 3.23205i) q^{98} +2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{7} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{7} + 2 q^{9} - 4 q^{10} + 2 q^{11} - 4 q^{13} - 4 q^{14} + 4 q^{15} - 2 q^{16} - 12 q^{17} + 6 q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} - 18 q^{23} + 2 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{28} - 6 q^{29} + 4 q^{30} + 16 q^{31} + 6 q^{33} - 4 q^{34} + 8 q^{35} - 2 q^{36} + 24 q^{37} + 6 q^{39} + 4 q^{40} + 8 q^{41} + 6 q^{42} + 6 q^{43} + 4 q^{44} - 4 q^{45} - 2 q^{46} - 6 q^{49} + 16 q^{50} + 4 q^{51} - 8 q^{52} + 2 q^{54} + 14 q^{55} - 2 q^{56} - 12 q^{58} - 4 q^{59} - 4 q^{60} - 4 q^{61} - 6 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{66} + 30 q^{67} - 12 q^{68} + 2 q^{69} + 14 q^{70} - 6 q^{71} + 2 q^{74} - 16 q^{75} - 6 q^{76} + 8 q^{78} - 48 q^{79} - 2 q^{80} - 2 q^{81} + 18 q^{82} + 2 q^{84} + 8 q^{85} - 20 q^{86} + 12 q^{87} - 6 q^{88} + 4 q^{89} + 4 q^{90} + 12 q^{91} - 2 q^{94} - 12 q^{95} + 4 q^{96} + 12 q^{98} + 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.23205 + 1.86603i 0.550990 + 0.834512i
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −0.633975 + 0.366025i −0.239620 + 0.138345i −0.615002 0.788526i \(-0.710845\pi\)
0.375382 + 0.926870i \(0.377511\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −0.133975 2.23205i −0.0423665 0.705836i
\(11\) 1.36603 2.36603i 0.411872 0.713384i −0.583222 0.812313i \(-0.698208\pi\)
0.995094 + 0.0989291i \(0.0315417\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.59808 + 3.23205i 0.443227 + 0.896410i
\(14\) 0.732051 0.195649
\(15\) 0.133975 + 2.23205i 0.0345921 + 0.576313i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.13397 + 1.23205i −0.517565 + 0.298816i −0.735938 0.677049i \(-0.763258\pi\)
0.218373 + 0.975865i \(0.429925\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.36603 + 4.09808i 0.542803 + 0.940163i 0.998742 + 0.0501517i \(0.0159705\pi\)
−0.455938 + 0.890011i \(0.650696\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) −0.732051 −0.159747
\(22\) −2.36603 + 1.36603i −0.504438 + 0.291238i
\(23\) −3.63397 2.09808i −0.757736 0.437479i 0.0707462 0.997494i \(-0.477462\pi\)
−0.828482 + 0.560015i \(0.810795\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −1.96410 + 4.59808i −0.392820 + 0.919615i
\(26\) 0.232051 3.59808i 0.0455089 0.705641i
\(27\) 1.00000i 0.192450i
\(28\) −0.633975 0.366025i −0.119810 0.0691723i
\(29\) 0.232051 0.401924i 0.0430908 0.0746354i −0.843676 0.536853i \(-0.819613\pi\)
0.886766 + 0.462218i \(0.152946\pi\)
\(30\) 1.00000 2.00000i 0.182574 0.365148i
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 2.36603 1.36603i 0.411872 0.237795i
\(34\) 2.46410 0.422590
\(35\) −1.46410 0.732051i −0.247478 0.123739i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 5.13397 + 2.96410i 0.844020 + 0.487295i 0.858629 0.512598i \(-0.171317\pi\)
−0.0146085 + 0.999893i \(0.504650\pi\)
\(38\) 4.73205i 0.767640i
\(39\) −0.232051 + 3.59808i −0.0371579 + 0.576153i
\(40\) 1.86603 1.23205i 0.295045 0.194804i
\(41\) −0.598076 + 1.03590i −0.0934038 + 0.161780i −0.908941 0.416924i \(-0.863108\pi\)
0.815538 + 0.578704i \(0.196441\pi\)
\(42\) 0.633975 + 0.366025i 0.0978244 + 0.0564789i
\(43\) 5.83013 3.36603i 0.889086 0.513314i 0.0154426 0.999881i \(-0.495084\pi\)
0.873643 + 0.486567i \(0.161751\pi\)
\(44\) 2.73205 0.411872
\(45\) −1.00000 + 2.00000i −0.149071 + 0.298142i
\(46\) 2.09808 + 3.63397i 0.309344 + 0.535800i
\(47\) 9.66025i 1.40909i −0.709658 0.704546i \(-0.751150\pi\)
0.709658 0.704546i \(-0.248850\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) −3.23205 + 5.59808i −0.461722 + 0.799725i
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) −2.46410 −0.345043
\(52\) −2.00000 + 3.00000i −0.277350 + 0.416025i
\(53\) 4.26795i 0.586248i −0.956074 0.293124i \(-0.905305\pi\)
0.956074 0.293124i \(-0.0946949\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 6.09808 0.366025i 0.822264 0.0493549i
\(56\) 0.366025 + 0.633975i 0.0489122 + 0.0847184i
\(57\) 4.73205i 0.626775i
\(58\) −0.401924 + 0.232051i −0.0527752 + 0.0304698i
\(59\) 4.19615 + 7.26795i 0.546293 + 0.946206i 0.998524 + 0.0543060i \(0.0172946\pi\)
−0.452232 + 0.891900i \(0.649372\pi\)
\(60\) −1.86603 + 1.23205i −0.240903 + 0.159057i
\(61\) −7.06218 12.2321i −0.904219 1.56615i −0.821962 0.569542i \(-0.807120\pi\)
−0.0822573 0.996611i \(-0.526213\pi\)
\(62\) −3.46410 2.00000i −0.439941 0.254000i
\(63\) −0.633975 0.366025i −0.0798733 0.0461149i
\(64\) −1.00000 −0.125000
\(65\) −4.06218 + 6.96410i −0.503851 + 0.863790i
\(66\) −2.73205 −0.336292
\(67\) 8.36603 + 4.83013i 1.02207 + 0.590094i 0.914704 0.404125i \(-0.132424\pi\)
0.107369 + 0.994219i \(0.465757\pi\)
\(68\) −2.13397 1.23205i −0.258782 0.149408i
\(69\) −2.09808 3.63397i −0.252579 0.437479i
\(70\) 0.901924 + 1.36603i 0.107801 + 0.163271i
\(71\) −2.36603 4.09808i −0.280796 0.486352i 0.690785 0.723060i \(-0.257265\pi\)
−0.971581 + 0.236708i \(0.923932\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 12.6603i 1.48177i −0.671632 0.740885i \(-0.734406\pi\)
0.671632 0.740885i \(-0.265594\pi\)
\(74\) −2.96410 5.13397i −0.344570 0.596812i
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) −2.36603 + 4.09808i −0.271402 + 0.470082i
\(77\) 2.00000i 0.227921i
\(78\) 2.00000 3.00000i 0.226455 0.339683i
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) −2.23205 + 0.133975i −0.249551 + 0.0149788i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.03590 0.598076i 0.114396 0.0660465i
\(83\) 8.73205i 0.958467i −0.877687 0.479234i \(-0.840915\pi\)
0.877687 0.479234i \(-0.159085\pi\)
\(84\) −0.366025 0.633975i −0.0399366 0.0691723i
\(85\) −4.92820 2.46410i −0.534539 0.267269i
\(86\) −6.73205 −0.725936
\(87\) 0.401924 0.232051i 0.0430908 0.0248785i
\(88\) −2.36603 1.36603i −0.252219 0.145619i
\(89\) 4.46410 7.73205i 0.473194 0.819596i −0.526335 0.850277i \(-0.676434\pi\)
0.999529 + 0.0306813i \(0.00976769\pi\)
\(90\) 1.86603 1.23205i 0.196696 0.129870i
\(91\) −2.19615 1.46410i −0.230219 0.153480i
\(92\) 4.19615i 0.437479i
\(93\) 3.46410 + 2.00000i 0.359211 + 0.207390i
\(94\) −4.83013 + 8.36603i −0.498190 + 0.862890i
\(95\) −4.73205 + 9.46410i −0.485498 + 0.970996i
\(96\) 1.00000 0.102062
\(97\) −8.66025 + 5.00000i −0.879316 + 0.507673i −0.870433 0.492287i \(-0.836161\pi\)
−0.00888289 + 0.999961i \(0.502828\pi\)
\(98\) 5.59808 3.23205i 0.565491 0.326486i
\(99\) 2.73205 0.274581
\(100\) −4.96410 + 0.598076i −0.496410 + 0.0598076i
\(101\) −0.0358984 + 0.0621778i −0.00357202 + 0.00618692i −0.867806 0.496903i \(-0.834470\pi\)
0.864234 + 0.503090i \(0.167804\pi\)
\(102\) 2.13397 + 1.23205i 0.211295 + 0.121991i
\(103\) 12.7321i 1.25453i −0.778807 0.627263i \(-0.784175\pi\)
0.778807 0.627263i \(-0.215825\pi\)
\(104\) 3.23205 1.59808i 0.316929 0.156704i
\(105\) −0.901924 1.36603i −0.0880187 0.133310i
\(106\) −2.13397 + 3.69615i −0.207270 + 0.359002i
\(107\) −4.09808 2.36603i −0.396176 0.228732i 0.288657 0.957433i \(-0.406791\pi\)
−0.684833 + 0.728700i \(0.740125\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) −5.46410 2.73205i −0.520982 0.260491i
\(111\) 2.96410 + 5.13397i 0.281340 + 0.487295i
\(112\) 0.732051i 0.0691723i
\(113\) −7.79423 + 4.50000i −0.733219 + 0.423324i −0.819599 0.572938i \(-0.805804\pi\)
0.0863794 + 0.996262i \(0.472470\pi\)
\(114\) 2.36603 4.09808i 0.221599 0.383820i
\(115\) −0.562178 9.36603i −0.0524234 0.873386i
\(116\) 0.464102 0.0430908
\(117\) −2.00000 + 3.00000i −0.184900 + 0.277350i
\(118\) 8.39230i 0.772574i
\(119\) 0.901924 1.56218i 0.0826792 0.143205i
\(120\) 2.23205 0.133975i 0.203757 0.0122302i
\(121\) 1.76795 + 3.06218i 0.160723 + 0.278380i
\(122\) 14.1244i 1.27876i
\(123\) −1.03590 + 0.598076i −0.0934038 + 0.0539267i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0.366025 + 0.633975i 0.0326081 + 0.0564789i
\(127\) −3.46410 2.00000i −0.307389 0.177471i 0.338368 0.941014i \(-0.390125\pi\)
−0.645758 + 0.763542i \(0.723458\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 6.73205 0.592724
\(130\) 7.00000 4.00000i 0.613941 0.350823i
\(131\) 13.8564 1.21064 0.605320 0.795982i \(-0.293045\pi\)
0.605320 + 0.795982i \(0.293045\pi\)
\(132\) 2.36603 + 1.36603i 0.205936 + 0.118897i
\(133\) −3.00000 1.73205i −0.260133 0.150188i
\(134\) −4.83013 8.36603i −0.417259 0.722715i
\(135\) −1.86603 + 1.23205i −0.160602 + 0.106038i
\(136\) 1.23205 + 2.13397i 0.105647 + 0.182987i
\(137\) 9.99038 5.76795i 0.853536 0.492789i −0.00830645 0.999966i \(-0.502644\pi\)
0.861842 + 0.507176i \(0.169311\pi\)
\(138\) 4.19615i 0.357200i
\(139\) −7.46410 12.9282i −0.633097 1.09656i −0.986915 0.161242i \(-0.948450\pi\)
0.353818 0.935314i \(-0.384883\pi\)
\(140\) −0.0980762 1.63397i −0.00828895 0.138096i
\(141\) 4.83013 8.36603i 0.406770 0.704546i
\(142\) 4.73205i 0.397105i
\(143\) 9.83013 + 0.633975i 0.822037 + 0.0530156i
\(144\) −1.00000 −0.0833333
\(145\) 1.03590 0.0621778i 0.0860267 0.00516359i
\(146\) −6.33013 + 10.9641i −0.523885 + 0.907396i
\(147\) −5.59808 + 3.23205i −0.461722 + 0.266575i
\(148\) 5.92820i 0.487295i
\(149\) 3.03590 + 5.25833i 0.248710 + 0.430779i 0.963168 0.268899i \(-0.0866599\pi\)
−0.714458 + 0.699679i \(0.753327\pi\)
\(150\) 4.96410 0.598076i 0.405317 0.0488327i
\(151\) 19.1244 1.55632 0.778159 0.628067i \(-0.216154\pi\)
0.778159 + 0.628067i \(0.216154\pi\)
\(152\) 4.09808 2.36603i 0.332398 0.191910i
\(153\) −2.13397 1.23205i −0.172522 0.0996054i
\(154\) 1.00000 1.73205i 0.0805823 0.139573i
\(155\) 4.92820 + 7.46410i 0.395843 + 0.599531i
\(156\) −3.23205 + 1.59808i −0.258771 + 0.127948i
\(157\) 11.3923i 0.909205i −0.890694 0.454602i \(-0.849781\pi\)
0.890694 0.454602i \(-0.150219\pi\)
\(158\) 10.3923 + 6.00000i 0.826767 + 0.477334i
\(159\) 2.13397 3.69615i 0.169235 0.293124i
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 3.07180 0.242092
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 5.66025 3.26795i 0.443345 0.255966i −0.261670 0.965157i \(-0.584273\pi\)
0.705016 + 0.709192i \(0.250940\pi\)
\(164\) −1.19615 −0.0934038
\(165\) 5.46410 + 2.73205i 0.425380 + 0.212690i
\(166\) −4.36603 + 7.56218i −0.338869 + 0.586939i
\(167\) −12.0000 6.92820i −0.928588 0.536120i −0.0422232 0.999108i \(-0.513444\pi\)
−0.886365 + 0.462988i \(0.846777\pi\)
\(168\) 0.732051i 0.0564789i
\(169\) −7.89230 + 10.3301i −0.607100 + 0.794625i
\(170\) 3.03590 + 4.59808i 0.232843 + 0.352656i
\(171\) −2.36603 + 4.09808i −0.180934 + 0.313388i
\(172\) 5.83013 + 3.36603i 0.444543 + 0.256657i
\(173\) −19.7321 + 11.3923i −1.50020 + 0.866141i −0.500200 + 0.865910i \(0.666740\pi\)
−1.00000 0.000231036i \(0.999926\pi\)
\(174\) −0.464102 −0.0351835
\(175\) −0.437822 3.63397i −0.0330962 0.274703i
\(176\) 1.36603 + 2.36603i 0.102968 + 0.178346i
\(177\) 8.39230i 0.630804i
\(178\) −7.73205 + 4.46410i −0.579542 + 0.334599i
\(179\) 3.90192 6.75833i 0.291643 0.505141i −0.682555 0.730834i \(-0.739131\pi\)
0.974199 + 0.225693i \(0.0724646\pi\)
\(180\) −2.23205 + 0.133975i −0.166367 + 0.00998588i
\(181\) 8.12436 0.603879 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(182\) 1.16987 + 2.36603i 0.0867168 + 0.175381i
\(183\) 14.1244i 1.04410i
\(184\) −2.09808 + 3.63397i −0.154672 + 0.267900i
\(185\) 0.794229 + 13.2321i 0.0583929 + 0.972840i
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 6.73205i 0.492296i
\(188\) 8.36603 4.83013i 0.610155 0.352273i
\(189\) −0.366025 0.633975i −0.0266244 0.0461149i
\(190\) 8.83013 5.83013i 0.640605 0.422962i
\(191\) 1.26795 + 2.19615i 0.0917456 + 0.158908i 0.908246 0.418437i \(-0.137422\pi\)
−0.816500 + 0.577345i \(0.804089\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 5.76795 + 3.33013i 0.415186 + 0.239708i 0.693016 0.720923i \(-0.256282\pi\)
−0.277830 + 0.960630i \(0.589615\pi\)
\(194\) 10.0000 0.717958
\(195\) −7.00000 + 4.00000i −0.501280 + 0.286446i
\(196\) −6.46410 −0.461722
\(197\) 15.4641 + 8.92820i 1.10177 + 0.636108i 0.936686 0.350171i \(-0.113877\pi\)
0.165086 + 0.986279i \(0.447210\pi\)
\(198\) −2.36603 1.36603i −0.168146 0.0970792i
\(199\) 5.02628 + 8.70577i 0.356304 + 0.617136i 0.987340 0.158617i \(-0.0507036\pi\)
−0.631037 + 0.775753i \(0.717370\pi\)
\(200\) 4.59808 + 1.96410i 0.325133 + 0.138883i
\(201\) 4.83013 + 8.36603i 0.340691 + 0.590094i
\(202\) 0.0621778 0.0358984i 0.00437482 0.00252580i
\(203\) 0.339746i 0.0238455i
\(204\) −1.23205 2.13397i −0.0862608 0.149408i
\(205\) −2.66987 + 0.160254i −0.186472 + 0.0111926i
\(206\) −6.36603 + 11.0263i −0.443542 + 0.768237i
\(207\) 4.19615i 0.291653i
\(208\) −3.59808 0.232051i −0.249482 0.0160898i
\(209\) 12.9282 0.894263
\(210\) 0.0980762 + 1.63397i 0.00676790 + 0.112755i
\(211\) 7.26795 12.5885i 0.500346 0.866625i −0.499654 0.866225i \(-0.666539\pi\)
1.00000 0.000399869i \(-0.000127282\pi\)
\(212\) 3.69615 2.13397i 0.253853 0.146562i
\(213\) 4.73205i 0.324235i
\(214\) 2.36603 + 4.09808i 0.161738 + 0.280139i
\(215\) 13.4641 + 6.73205i 0.918244 + 0.459122i
\(216\) 1.00000 0.0680414
\(217\) −2.53590 + 1.46410i −0.172148 + 0.0993897i
\(218\) 8.66025 + 5.00000i 0.586546 + 0.338643i
\(219\) 6.33013 10.9641i 0.427750 0.740885i
\(220\) 3.36603 + 5.09808i 0.226937 + 0.343712i
\(221\) −7.39230 4.92820i −0.497260 0.331507i
\(222\) 5.92820i 0.397875i
\(223\) 17.6603 + 10.1962i 1.18262 + 0.682785i 0.956619 0.291343i \(-0.0941020\pi\)
0.225999 + 0.974127i \(0.427435\pi\)
\(224\) −0.366025 + 0.633975i −0.0244561 + 0.0423592i
\(225\) −4.96410 + 0.598076i −0.330940 + 0.0398717i
\(226\) 9.00000 0.598671
\(227\) 5.36603 3.09808i 0.356156 0.205627i −0.311237 0.950332i \(-0.600743\pi\)
0.667393 + 0.744706i \(0.267410\pi\)
\(228\) −4.09808 + 2.36603i −0.271402 + 0.156694i
\(229\) 12.7846 0.844831 0.422415 0.906402i \(-0.361182\pi\)
0.422415 + 0.906402i \(0.361182\pi\)
\(230\) −4.19615 + 8.39230i −0.276686 + 0.553372i
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) −0.401924 0.232051i −0.0263876 0.0152349i
\(233\) 8.39230i 0.549798i 0.961473 + 0.274899i \(0.0886444\pi\)
−0.961473 + 0.274899i \(0.911356\pi\)
\(234\) 3.23205 1.59808i 0.211286 0.104470i
\(235\) 18.0263 11.9019i 1.17590 0.776396i
\(236\) −4.19615 + 7.26795i −0.273146 + 0.473103i
\(237\) −10.3923 6.00000i −0.675053 0.389742i
\(238\) −1.56218 + 0.901924i −0.101261 + 0.0584630i
\(239\) −26.5885 −1.71986 −0.859932 0.510408i \(-0.829494\pi\)
−0.859932 + 0.510408i \(0.829494\pi\)
\(240\) −2.00000 1.00000i −0.129099 0.0645497i
\(241\) −5.69615 9.86603i −0.366921 0.635527i 0.622161 0.782889i \(-0.286255\pi\)
−0.989083 + 0.147363i \(0.952922\pi\)
\(242\) 3.53590i 0.227296i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 7.06218 12.2321i 0.452110 0.783077i
\(245\) −14.4282 + 0.866025i −0.921784 + 0.0553283i
\(246\) 1.19615 0.0762639
\(247\) −9.46410 + 14.1962i −0.602186 + 0.903280i
\(248\) 4.00000i 0.254000i
\(249\) 4.36603 7.56218i 0.276686 0.479234i
\(250\) 10.5263 + 3.76795i 0.665740 + 0.238306i
\(251\) 7.26795 + 12.5885i 0.458749 + 0.794576i 0.998895 0.0469948i \(-0.0149644\pi\)
−0.540146 + 0.841571i \(0.681631\pi\)
\(252\) 0.732051i 0.0461149i
\(253\) −9.92820 + 5.73205i −0.624181 + 0.360371i
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) −3.03590 4.59808i −0.190115 0.287943i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.59808 + 1.50000i 0.162064 + 0.0935674i 0.578838 0.815442i \(-0.303506\pi\)
−0.416775 + 0.909010i \(0.636840\pi\)
\(258\) −5.83013 3.36603i −0.362968 0.209560i
\(259\) −4.33975 −0.269659
\(260\) −8.06218 0.0358984i −0.499995 0.00222632i
\(261\) 0.464102 0.0287272
\(262\) −12.0000 6.92820i −0.741362 0.428026i
\(263\) 6.16987 + 3.56218i 0.380451 + 0.219653i 0.678014 0.735049i \(-0.262841\pi\)
−0.297564 + 0.954702i \(0.596174\pi\)
\(264\) −1.36603 2.36603i −0.0840731 0.145619i
\(265\) 7.96410 5.25833i 0.489231 0.323017i
\(266\) 1.73205 + 3.00000i 0.106199 + 0.183942i
\(267\) 7.73205 4.46410i 0.473194 0.273199i
\(268\) 9.66025i 0.590094i
\(269\) −8.19615 14.1962i −0.499728 0.865555i 0.500272 0.865868i \(-0.333233\pi\)
−1.00000 0.000313781i \(0.999900\pi\)
\(270\) 2.23205 0.133975i 0.135838 0.00815343i
\(271\) 10.9282 18.9282i 0.663841 1.14981i −0.315757 0.948840i \(-0.602258\pi\)
0.979598 0.200966i \(-0.0644082\pi\)
\(272\) 2.46410i 0.149408i
\(273\) −1.16987 2.36603i −0.0708039 0.143198i
\(274\) −11.5359 −0.696909
\(275\) 8.19615 + 10.9282i 0.494247 + 0.658995i
\(276\) 2.09808 3.63397i 0.126289 0.218740i
\(277\) −19.3301 + 11.1603i −1.16143 + 0.670555i −0.951647 0.307192i \(-0.900610\pi\)
−0.209787 + 0.977747i \(0.567277\pi\)
\(278\) 14.9282i 0.895334i
\(279\) 2.00000 + 3.46410i 0.119737 + 0.207390i
\(280\) −0.732051 + 1.46410i −0.0437484 + 0.0874968i
\(281\) −1.73205 −0.103325 −0.0516627 0.998665i \(-0.516452\pi\)
−0.0516627 + 0.998665i \(0.516452\pi\)
\(282\) −8.36603 + 4.83013i −0.498190 + 0.287630i
\(283\) −8.36603 4.83013i −0.497309 0.287121i 0.230293 0.973121i \(-0.426032\pi\)
−0.727601 + 0.686000i \(0.759365\pi\)
\(284\) 2.36603 4.09808i 0.140398 0.243176i
\(285\) −8.83013 + 5.83013i −0.523052 + 0.345347i
\(286\) −8.19615 5.46410i −0.484649 0.323099i
\(287\) 0.875644i 0.0516877i
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) −5.46410 + 9.46410i −0.321418 + 0.556712i
\(290\) −0.928203 0.464102i −0.0545060 0.0272530i
\(291\) −10.0000 −0.586210
\(292\) 10.9641 6.33013i 0.641626 0.370443i
\(293\) −8.89230 + 5.13397i −0.519494 + 0.299930i −0.736728 0.676190i \(-0.763630\pi\)
0.217234 + 0.976120i \(0.430297\pi\)
\(294\) 6.46410 0.376994
\(295\) −8.39230 + 16.7846i −0.488619 + 0.977238i
\(296\) 2.96410 5.13397i 0.172285 0.298406i
\(297\) 2.36603 + 1.36603i 0.137291 + 0.0792648i
\(298\) 6.07180i 0.351730i
\(299\) 0.973721 15.0981i 0.0563117 0.873144i
\(300\) −4.59808 1.96410i −0.265470 0.113397i
\(301\) −2.46410 + 4.26795i −0.142028 + 0.246001i
\(302\) −16.5622 9.56218i −0.953046 0.550242i
\(303\) −0.0621778 + 0.0358984i −0.00357202 + 0.00206231i
\(304\) −4.73205 −0.271402
\(305\) 14.1244 28.2487i 0.808758 1.61752i
\(306\) 1.23205 + 2.13397i 0.0704317 + 0.121991i
\(307\) 22.7321i 1.29739i −0.761050 0.648693i \(-0.775316\pi\)
0.761050 0.648693i \(-0.224684\pi\)
\(308\) −1.73205 + 1.00000i −0.0986928 + 0.0569803i
\(309\) 6.36603 11.0263i 0.362151 0.627263i
\(310\) −0.535898 8.92820i −0.0304370 0.507088i
\(311\) −21.1244 −1.19785 −0.598926 0.800804i \(-0.704406\pi\)
−0.598926 + 0.800804i \(0.704406\pi\)
\(312\) 3.59808 + 0.232051i 0.203701 + 0.0131373i
\(313\) 14.0000i 0.791327i 0.918396 + 0.395663i \(0.129485\pi\)
−0.918396 + 0.395663i \(0.870515\pi\)
\(314\) −5.69615 + 9.86603i −0.321452 + 0.556772i
\(315\) −0.0980762 1.63397i −0.00552597 0.0920640i
\(316\) −6.00000 10.3923i −0.337526 0.584613i
\(317\) 26.2679i 1.47536i 0.675153 + 0.737678i \(0.264077\pi\)
−0.675153 + 0.737678i \(0.735923\pi\)
\(318\) −3.69615 + 2.13397i −0.207270 + 0.119667i
\(319\) −0.633975 1.09808i −0.0354958 0.0614805i
\(320\) −1.23205 1.86603i −0.0688737 0.104314i
\(321\) −2.36603 4.09808i −0.132059 0.228732i
\(322\) −2.66025 1.53590i −0.148250 0.0855923i
\(323\) −10.0981 5.83013i −0.561872 0.324397i
\(324\) −1.00000 −0.0555556
\(325\) −18.0000 + 1.00000i −0.998460 + 0.0554700i
\(326\) −6.53590 −0.361990
\(327\) −8.66025 5.00000i −0.478913 0.276501i
\(328\) 1.03590 + 0.598076i 0.0571979 + 0.0330232i
\(329\) 3.53590 + 6.12436i 0.194940 + 0.337647i
\(330\) −3.36603 5.09808i −0.185294 0.280640i
\(331\) −6.39230 11.0718i −0.351353 0.608561i 0.635134 0.772402i \(-0.280945\pi\)
−0.986487 + 0.163841i \(0.947612\pi\)
\(332\) 7.56218 4.36603i 0.415028 0.239617i
\(333\) 5.92820i 0.324864i
\(334\) 6.92820 + 12.0000i 0.379094 + 0.656611i
\(335\) 1.29423 + 21.5622i 0.0707113 + 1.17807i
\(336\) 0.366025 0.633975i 0.0199683 0.0345861i
\(337\) 27.0526i 1.47365i −0.676085 0.736823i \(-0.736325\pi\)
0.676085 0.736823i \(-0.263675\pi\)
\(338\) 12.0000 5.00000i 0.652714 0.271964i
\(339\) −9.00000 −0.488813
\(340\) −0.330127 5.50000i −0.0179037 0.298279i
\(341\) 5.46410 9.46410i 0.295898 0.512510i
\(342\) 4.09808 2.36603i 0.221599 0.127940i
\(343\) 9.85641i 0.532196i
\(344\) −3.36603 5.83013i −0.181484 0.314339i
\(345\) 4.19615 8.39230i 0.225913 0.451827i
\(346\) 22.7846 1.22491
\(347\) 10.0981 5.83013i 0.542093 0.312978i −0.203834 0.979006i \(-0.565340\pi\)
0.745927 + 0.666028i \(0.232007\pi\)
\(348\) 0.401924 + 0.232051i 0.0215454 + 0.0124392i
\(349\) −16.4641 + 28.5167i −0.881303 + 1.52646i −0.0314101 + 0.999507i \(0.510000\pi\)
−0.849893 + 0.526955i \(0.823334\pi\)
\(350\) −1.43782 + 3.36603i −0.0768548 + 0.179922i
\(351\) −3.23205 + 1.59808i −0.172514 + 0.0852990i
\(352\) 2.73205i 0.145619i
\(353\) 20.1340 + 11.6244i 1.07162 + 0.618702i 0.928625 0.371021i \(-0.120992\pi\)
0.142999 + 0.989723i \(0.454325\pi\)
\(354\) 4.19615 7.26795i 0.223023 0.386287i
\(355\) 4.73205 9.46410i 0.251151 0.502302i
\(356\) 8.92820 0.473194
\(357\) 1.56218 0.901924i 0.0826792 0.0477349i
\(358\) −6.75833 + 3.90192i −0.357189 + 0.206223i
\(359\) −33.1244 −1.74824 −0.874118 0.485713i \(-0.838560\pi\)
−0.874118 + 0.485713i \(0.838560\pi\)
\(360\) 2.00000 + 1.00000i 0.105409 + 0.0527046i
\(361\) −1.69615 + 2.93782i −0.0892712 + 0.154622i
\(362\) −7.03590 4.06218i −0.369799 0.213503i
\(363\) 3.53590i 0.185587i
\(364\) 0.169873 2.63397i 0.00890376 0.138058i
\(365\) 23.6244 15.5981i 1.23656 0.816441i
\(366\) −7.06218 + 12.2321i −0.369146 + 0.639380i
\(367\) 16.4378 + 9.49038i 0.858047 + 0.495394i 0.863358 0.504592i \(-0.168357\pi\)
−0.00531057 + 0.999986i \(0.501690\pi\)
\(368\) 3.63397 2.09808i 0.189434 0.109370i
\(369\) −1.19615 −0.0622692
\(370\) 5.92820 11.8564i 0.308193 0.616385i
\(371\) 1.56218 + 2.70577i 0.0811042 + 0.140477i
\(372\) 4.00000i 0.207390i
\(373\) −26.3827 + 15.2321i −1.36604 + 0.788686i −0.990420 0.138087i \(-0.955905\pi\)
−0.375624 + 0.926772i \(0.622571\pi\)
\(374\) 3.36603 5.83013i 0.174053 0.301469i
\(375\) −10.5263 3.76795i −0.543575 0.194576i
\(376\) −9.66025 −0.498190
\(377\) 1.66987 + 0.107695i 0.0860028 + 0.00554658i
\(378\) 0.732051i 0.0376526i
\(379\) −11.1244 + 19.2679i −0.571420 + 0.989728i 0.425001 + 0.905193i \(0.360274\pi\)
−0.996421 + 0.0845351i \(0.973060\pi\)
\(380\) −10.5622 + 0.633975i −0.541828 + 0.0325222i
\(381\) −2.00000 3.46410i −0.102463 0.177471i
\(382\) 2.53590i 0.129748i
\(383\) −11.3205 + 6.53590i −0.578451 + 0.333969i −0.760518 0.649317i \(-0.775055\pi\)
0.182067 + 0.983286i \(0.441721\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −3.73205 + 2.46410i −0.190203 + 0.125582i
\(386\) −3.33013 5.76795i −0.169499 0.293581i
\(387\) 5.83013 + 3.36603i 0.296362 + 0.171105i
\(388\) −8.66025 5.00000i −0.439658 0.253837i
\(389\) 37.9282 1.92304 0.961518 0.274742i \(-0.0885923\pi\)
0.961518 + 0.274742i \(0.0885923\pi\)
\(390\) 8.06218 + 0.0358984i 0.408244 + 0.00181779i
\(391\) 10.3397 0.522903
\(392\) 5.59808 + 3.23205i 0.282746 + 0.163243i
\(393\) 12.0000 + 6.92820i 0.605320 + 0.349482i
\(394\) −8.92820 15.4641i −0.449796 0.779070i
\(395\) −14.7846 22.3923i −0.743894 1.12668i
\(396\) 1.36603 + 2.36603i 0.0686454 + 0.118897i
\(397\) 13.2679 7.66025i 0.665899 0.384457i −0.128622 0.991694i \(-0.541055\pi\)
0.794521 + 0.607237i \(0.207722\pi\)
\(398\) 10.0526i 0.503889i
\(399\) −1.73205 3.00000i −0.0867110 0.150188i
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) −14.5263 + 25.1603i −0.725408 + 1.25644i 0.233398 + 0.972381i \(0.425015\pi\)
−0.958806 + 0.284062i \(0.908318\pi\)
\(402\) 9.66025i 0.481810i
\(403\) 6.39230 + 12.9282i 0.318423 + 0.644000i
\(404\) −0.0717968 −0.00357202
\(405\) −2.23205 + 0.133975i −0.110911 + 0.00665725i
\(406\) 0.169873 0.294229i 0.00843065 0.0146023i
\(407\) 14.0263 8.09808i 0.695257 0.401407i
\(408\) 2.46410i 0.121991i
\(409\) 14.9641 + 25.9186i 0.739927 + 1.28159i 0.952528 + 0.304452i \(0.0984734\pi\)
−0.212600 + 0.977139i \(0.568193\pi\)
\(410\) 2.39230 + 1.19615i 0.118148 + 0.0590738i
\(411\) 11.5359 0.569024
\(412\) 11.0263 6.36603i 0.543226 0.313632i
\(413\) −5.32051 3.07180i −0.261805 0.151153i
\(414\) −2.09808 + 3.63397i −0.103115 + 0.178600i
\(415\) 16.2942 10.7583i 0.799852 0.528106i
\(416\) 3.00000 + 2.00000i 0.147087 + 0.0980581i
\(417\) 14.9282i 0.731037i
\(418\) −11.1962 6.46410i −0.547622 0.316170i
\(419\) −6.73205 + 11.6603i −0.328882 + 0.569641i −0.982290 0.187365i \(-0.940005\pi\)
0.653408 + 0.757006i \(0.273339\pi\)
\(420\) 0.732051 1.46410i 0.0357204 0.0714408i
\(421\) −21.0526 −1.02604 −0.513019 0.858377i \(-0.671473\pi\)
−0.513019 + 0.858377i \(0.671473\pi\)
\(422\) −12.5885 + 7.26795i −0.612797 + 0.353798i
\(423\) 8.36603 4.83013i 0.406770 0.234849i
\(424\) −4.26795 −0.207270
\(425\) −1.47372 12.2321i −0.0714859 0.593342i
\(426\) −2.36603 + 4.09808i −0.114634 + 0.198552i
\(427\) 8.95448 + 5.16987i 0.433338 + 0.250188i
\(428\) 4.73205i 0.228732i
\(429\) 8.19615 + 5.46410i 0.395714 + 0.263809i
\(430\) −8.29423 12.5622i −0.399983 0.605802i
\(431\) 9.09808 15.7583i 0.438239 0.759052i −0.559315 0.828955i \(-0.688936\pi\)
0.997554 + 0.0699032i \(0.0222691\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 21.8205 12.5981i 1.04863 0.605425i 0.126362 0.991984i \(-0.459670\pi\)
0.922265 + 0.386559i \(0.126337\pi\)
\(434\) 2.92820 0.140558
\(435\) 0.928203 + 0.464102i 0.0445039 + 0.0222520i
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 19.8564i 0.949861i
\(438\) −10.9641 + 6.33013i −0.523885 + 0.302465i
\(439\) 10.0981 17.4904i 0.481955 0.834770i −0.517831 0.855483i \(-0.673260\pi\)
0.999785 + 0.0207128i \(0.00659358\pi\)
\(440\) −0.366025 6.09808i −0.0174496 0.290714i
\(441\) −6.46410 −0.307814
\(442\) 3.93782 + 7.96410i 0.187303 + 0.378814i
\(443\) 34.6410i 1.64584i 0.568154 + 0.822922i \(0.307658\pi\)
−0.568154 + 0.822922i \(0.692342\pi\)
\(444\) −2.96410 + 5.13397i −0.140670 + 0.243648i
\(445\) 19.9282 1.19615i 0.944687 0.0567031i
\(446\) −10.1962 17.6603i −0.482802 0.836237i
\(447\) 6.07180i 0.287186i
\(448\) 0.633975 0.366025i 0.0299525 0.0172931i
\(449\) 9.92820 + 17.1962i 0.468541 + 0.811537i 0.999353 0.0359526i \(-0.0114465\pi\)
−0.530813 + 0.847489i \(0.678113\pi\)
\(450\) 4.59808 + 1.96410i 0.216755 + 0.0925886i
\(451\) 1.63397 + 2.83013i 0.0769409 + 0.133265i
\(452\) −7.79423 4.50000i −0.366610 0.211662i
\(453\) 16.5622 + 9.56218i 0.778159 + 0.449270i
\(454\) −6.19615 −0.290800
\(455\) 0.0262794 5.90192i 0.00123200 0.276686i
\(456\) 4.73205 0.221599
\(457\) 16.6244 + 9.59808i 0.777655 + 0.448979i 0.835598 0.549341i \(-0.185121\pi\)
−0.0579439 + 0.998320i \(0.518454\pi\)
\(458\) −11.0718 6.39230i −0.517351 0.298693i
\(459\) −1.23205 2.13397i −0.0575072 0.0996054i
\(460\) 7.83013 5.16987i 0.365082 0.241047i
\(461\) −19.9641 34.5788i −0.929821 1.61050i −0.783618 0.621242i \(-0.786628\pi\)
−0.146202 0.989255i \(-0.546705\pi\)
\(462\) 1.73205 1.00000i 0.0805823 0.0465242i
\(463\) 23.6603i 1.09959i 0.835301 + 0.549793i \(0.185293\pi\)
−0.835301 + 0.549793i \(0.814707\pi\)
\(464\) 0.232051 + 0.401924i 0.0107727 + 0.0186588i
\(465\) 0.535898 + 8.92820i 0.0248517 + 0.414036i
\(466\) 4.19615 7.26795i 0.194383 0.336681i
\(467\) 16.0526i 0.742824i 0.928468 + 0.371412i \(0.121126\pi\)
−0.928468 + 0.371412i \(0.878874\pi\)
\(468\) −3.59808 0.232051i −0.166321 0.0107266i
\(469\) −7.07180 −0.326545
\(470\) −21.5622 + 1.29423i −0.994589 + 0.0596983i
\(471\) 5.69615 9.86603i 0.262465 0.454602i
\(472\) 7.26795 4.19615i 0.334534 0.193144i
\(473\) 18.3923i 0.845679i
\(474\) 6.00000 + 10.3923i 0.275589 + 0.477334i
\(475\) −23.4904 + 2.83013i −1.07781 + 0.129855i
\(476\) 1.80385 0.0826792
\(477\) 3.69615 2.13397i 0.169235 0.0977080i
\(478\) 23.0263 + 13.2942i 1.05320 + 0.608064i
\(479\) −8.00000 + 13.8564i −0.365529 + 0.633115i −0.988861 0.148842i \(-0.952445\pi\)
0.623332 + 0.781958i \(0.285779\pi\)
\(480\) 1.23205 + 1.86603i 0.0562352 + 0.0851720i
\(481\) −1.37564 + 21.3301i −0.0627240 + 0.972570i
\(482\) 11.3923i 0.518905i
\(483\) 2.66025 + 1.53590i 0.121046 + 0.0698858i
\(484\) −1.76795 + 3.06218i −0.0803613 + 0.139190i
\(485\) −20.0000 10.0000i −0.908153 0.454077i
\(486\) 1.00000 0.0453609
\(487\) −17.7058 + 10.2224i −0.802325 + 0.463223i −0.844284 0.535897i \(-0.819974\pi\)
0.0419584 + 0.999119i \(0.486640\pi\)
\(488\) −12.2321 + 7.06218i −0.553719 + 0.319690i
\(489\) 6.53590 0.295564
\(490\) 12.9282 + 6.46410i 0.584037 + 0.292018i
\(491\) −16.0981 + 27.8827i −0.726496 + 1.25833i 0.231859 + 0.972749i \(0.425519\pi\)
−0.958355 + 0.285579i \(0.907814\pi\)
\(492\) −1.03590 0.598076i −0.0467019 0.0269634i
\(493\) 1.14359i 0.0515049i
\(494\) 15.2942 7.56218i 0.688120 0.340238i
\(495\) 3.36603 + 5.09808i 0.151292 + 0.229141i
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) 3.00000 + 1.73205i 0.134568 + 0.0776931i
\(498\) −7.56218 + 4.36603i −0.338869 + 0.195646i
\(499\) −19.6077 −0.877761 −0.438880 0.898545i \(-0.644625\pi\)
−0.438880 + 0.898545i \(0.644625\pi\)
\(500\) −7.23205 8.52628i −0.323427 0.381307i
\(501\) −6.92820 12.0000i −0.309529 0.536120i
\(502\) 14.5359i 0.648769i
\(503\) −27.8827 + 16.0981i −1.24323 + 0.717778i −0.969750 0.244101i \(-0.921507\pi\)
−0.273478 + 0.961878i \(0.588174\pi\)
\(504\) −0.366025 + 0.633975i −0.0163041 + 0.0282395i
\(505\) −0.160254 + 0.00961894i −0.00713121 + 0.000428037i
\(506\) 11.4641 0.509641
\(507\) −12.0000 + 5.00000i −0.532939 + 0.222058i
\(508\) 4.00000i 0.177471i
\(509\) 12.3564 21.4019i 0.547688 0.948624i −0.450744 0.892653i \(-0.648841\pi\)
0.998432 0.0559705i \(-0.0178253\pi\)
\(510\) 0.330127 + 5.50000i 0.0146183 + 0.243544i
\(511\) 4.63397 + 8.02628i 0.204995 + 0.355062i
\(512\) 1.00000i 0.0441942i
\(513\) −4.09808 + 2.36603i −0.180934 + 0.104463i
\(514\) −1.50000 2.59808i −0.0661622 0.114596i
\(515\) 23.7583 15.6865i 1.04692 0.691231i
\(516\) 3.36603 + 5.83013i 0.148181 + 0.256657i
\(517\) −22.8564 13.1962i −1.00522 0.580366i
\(518\) 3.75833 + 2.16987i 0.165132 + 0.0953387i
\(519\) −22.7846 −1.00013
\(520\) 6.96410 + 4.06218i 0.305396 + 0.178138i
\(521\) 39.4449 1.72811 0.864055 0.503397i \(-0.167917\pi\)
0.864055 + 0.503397i \(0.167917\pi\)
\(522\) −0.401924 0.232051i −0.0175917 0.0101566i
\(523\) 19.4378 + 11.2224i 0.849957 + 0.490723i 0.860636 0.509220i \(-0.170066\pi\)
−0.0106796 + 0.999943i \(0.503399\pi\)
\(524\) 6.92820 + 12.0000i 0.302660 + 0.524222i
\(525\) 1.43782 3.36603i 0.0627517 0.146905i
\(526\) −3.56218 6.16987i −0.155318 0.269019i
\(527\) −8.53590 + 4.92820i −0.371830 + 0.214676i
\(528\) 2.73205i 0.118897i
\(529\) −2.69615 4.66987i −0.117224 0.203038i
\(530\) −9.52628 + 0.571797i −0.413795 + 0.0248373i
\(531\) −4.19615 + 7.26795i −0.182098 + 0.315402i
\(532\) 3.46410i 0.150188i
\(533\) −4.30385 0.277568i −0.186420 0.0120228i
\(534\) −8.92820 −0.386361
\(535\) −0.633975 10.5622i −0.0274091 0.456643i
\(536\) 4.83013 8.36603i 0.208630 0.361357i
\(537\) 6.75833 3.90192i 0.291643 0.168380i
\(538\) 16.3923i 0.706722i
\(539\) 8.83013 + 15.2942i 0.380340 + 0.658769i
\(540\) −2.00000 1.00000i −0.0860663 0.0430331i
\(541\) 9.19615 0.395373 0.197687 0.980265i \(-0.436657\pi\)
0.197687 + 0.980265i \(0.436657\pi\)
\(542\) −18.9282 + 10.9282i −0.813036 + 0.469407i
\(543\) 7.03590 + 4.06218i 0.301939 + 0.174325i
\(544\) −1.23205 + 2.13397i −0.0528237 + 0.0914934i
\(545\) −12.3205 18.6603i −0.527753 0.799317i
\(546\) −0.169873 + 2.63397i −0.00726989 + 0.112724i
\(547\) 36.1962i 1.54764i 0.633408 + 0.773818i \(0.281655\pi\)
−0.633408 + 0.773818i \(0.718345\pi\)
\(548\) 9.99038 + 5.76795i 0.426768 + 0.246395i
\(549\) 7.06218 12.2321i 0.301406 0.522051i
\(550\) −1.63397 13.5622i −0.0696729 0.578293i
\(551\) 2.19615 0.0935592
\(552\) −3.63397 + 2.09808i −0.154672 + 0.0893001i
\(553\) 7.60770 4.39230i 0.323512 0.186780i
\(554\) 22.3205 0.948308
\(555\) −5.92820 + 11.8564i −0.251638 + 0.503276i
\(556\) 7.46410 12.9282i 0.316548 0.548278i
\(557\) −2.30385 1.33013i −0.0976172 0.0563593i 0.450397 0.892829i \(-0.351283\pi\)
−0.548014 + 0.836469i \(0.684616\pi\)
\(558\) 4.00000i 0.169334i
\(559\) 20.1962 + 13.4641i 0.854206 + 0.569471i
\(560\) 1.36603 0.901924i 0.0577251 0.0381132i
\(561\) −3.36603 + 5.83013i −0.142114 + 0.246148i
\(562\) 1.50000 + 0.866025i 0.0632737 + 0.0365311i
\(563\) −6.92820 + 4.00000i −0.291989 + 0.168580i −0.638838 0.769341i \(-0.720585\pi\)
0.346850 + 0.937921i \(0.387251\pi\)
\(564\) 9.66025 0.406770
\(565\) −18.0000 9.00000i −0.757266 0.378633i
\(566\) 4.83013 + 8.36603i 0.203025 + 0.351650i
\(567\) 0.732051i 0.0307432i
\(568\) −4.09808 + 2.36603i −0.171951 + 0.0992762i
\(569\) 22.9282 39.7128i 0.961200 1.66485i 0.241706 0.970350i \(-0.422293\pi\)
0.719494 0.694498i \(-0.244374\pi\)
\(570\) 10.5622 0.633975i 0.442401 0.0265543i
\(571\) −8.33975 −0.349008 −0.174504 0.984657i \(-0.555832\pi\)
−0.174504 + 0.984657i \(0.555832\pi\)
\(572\) 4.36603 + 8.83013i 0.182553 + 0.369206i
\(573\) 2.53590i 0.105939i
\(574\) −0.437822 + 0.758330i −0.0182743 + 0.0316521i
\(575\) 16.7846 12.5885i 0.699967 0.524975i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 27.9808i 1.16485i −0.812883 0.582427i \(-0.802103\pi\)
0.812883 0.582427i \(-0.197897\pi\)
\(578\) 9.46410 5.46410i 0.393655 0.227277i
\(579\) 3.33013 + 5.76795i 0.138395 + 0.239708i
\(580\) 0.571797 + 0.866025i 0.0237426 + 0.0359597i
\(581\) 3.19615 + 5.53590i 0.132599 + 0.229668i
\(582\) 8.66025 + 5.00000i 0.358979 + 0.207257i
\(583\) −10.0981 5.83013i −0.418220 0.241459i
\(584\) −12.6603 −0.523885
\(585\) −8.06218 0.0358984i −0.333330 0.00148422i
\(586\) 10.2679 0.424165
\(587\) −32.7846 18.9282i −1.35317 0.781251i −0.364474 0.931214i \(-0.618751\pi\)
−0.988692 + 0.149963i \(0.952085\pi\)
\(588\) −5.59808 3.23205i −0.230861 0.133288i
\(589\) 9.46410 + 16.3923i 0.389962 + 0.675433i
\(590\) 15.6603 10.3397i 0.644722 0.425681i
\(591\) 8.92820 + 15.4641i 0.367257 + 0.636108i
\(592\) −5.13397 + 2.96410i −0.211005 + 0.121824i
\(593\) 1.39230i 0.0571751i 0.999591 + 0.0285876i \(0.00910094\pi\)
−0.999591 + 0.0285876i \(0.990899\pi\)
\(594\) −1.36603 2.36603i −0.0560487 0.0970792i
\(595\) 4.02628 0.241670i 0.165061 0.00990749i
\(596\) −3.03590 + 5.25833i −0.124355 + 0.215390i
\(597\) 10.0526i 0.411424i
\(598\) −8.39230 + 12.5885i −0.343187 + 0.514780i
\(599\) 32.7846 1.33954 0.669771 0.742567i \(-0.266392\pi\)
0.669771 + 0.742567i \(0.266392\pi\)
\(600\) 3.00000 + 4.00000i 0.122474 + 0.163299i
\(601\) −8.50000 + 14.7224i −0.346722 + 0.600541i −0.985665 0.168714i \(-0.946039\pi\)
0.638943 + 0.769254i \(0.279372\pi\)
\(602\) 4.26795 2.46410i 0.173949 0.100429i
\(603\) 9.66025i 0.393396i
\(604\) 9.56218 + 16.5622i 0.389079 + 0.673905i
\(605\) −3.53590 + 7.07180i −0.143755 + 0.287509i
\(606\) 0.0717968 0.00291654
\(607\) 23.9090 13.8038i 0.970435 0.560281i 0.0710661 0.997472i \(-0.477360\pi\)
0.899369 + 0.437191i \(0.144027\pi\)
\(608\) 4.09808 + 2.36603i 0.166199 + 0.0959550i
\(609\) −0.169873 + 0.294229i −0.00688360 + 0.0119227i
\(610\) −26.3564 + 17.4019i −1.06714 + 0.704583i
\(611\) 31.2224 15.4378i 1.26312 0.624547i
\(612\) 2.46410i 0.0996054i
\(613\) −17.1340 9.89230i −0.692035 0.399546i 0.112339 0.993670i \(-0.464166\pi\)
−0.804374 + 0.594123i \(0.797499\pi\)
\(614\) −11.3660 + 19.6865i −0.458695 + 0.794484i
\(615\) −2.39230 1.19615i −0.0964670 0.0482335i
\(616\) 2.00000 0.0805823
\(617\) 19.6699 11.3564i 0.791879 0.457192i −0.0487445 0.998811i \(-0.515522\pi\)
0.840624 + 0.541620i \(0.182189\pi\)
\(618\) −11.0263 + 6.36603i −0.443542 + 0.256079i
\(619\) −40.1051 −1.61196 −0.805980 0.591942i \(-0.798361\pi\)
−0.805980 + 0.591942i \(0.798361\pi\)
\(620\) −4.00000 + 8.00000i −0.160644 + 0.321288i
\(621\) 2.09808 3.63397i 0.0841929 0.145826i
\(622\) 18.2942 + 10.5622i 0.733532 + 0.423505i
\(623\) 6.53590i 0.261855i
\(624\) −3.00000 2.00000i −0.120096 0.0800641i
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 11.1962 + 6.46410i 0.447131 + 0.258151i
\(628\) 9.86603 5.69615i 0.393697 0.227301i
\(629\) −14.6077 −0.582447
\(630\) −0.732051 + 1.46410i −0.0291656 + 0.0583312i
\(631\) 8.92820 + 15.4641i 0.355426 + 0.615616i 0.987191 0.159544i \(-0.0510024\pi\)
−0.631765 + 0.775160i \(0.717669\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 12.5885 7.26795i 0.500346 0.288875i
\(634\) 13.1340 22.7487i 0.521617 0.903467i
\(635\) −0.535898 8.92820i −0.0212665 0.354305i
\(636\) 4.26795 0.169235
\(637\) −23.2583 1.50000i −0.921529 0.0594322i
\(638\) 1.26795i 0.0501986i
\(639\) 2.36603 4.09808i 0.0935985 0.162117i
\(640\) 0.133975 + 2.23205i 0.00529581 + 0.0882296i
\(641\) 14.5263 + 25.1603i 0.573754 + 0.993770i 0.996176 + 0.0873711i \(0.0278466\pi\)
−0.422422 + 0.906399i \(0.638820\pi\)
\(642\) 4.73205i 0.186759i
\(643\) −28.3923 + 16.3923i −1.11968 + 0.646449i −0.941320 0.337515i \(-0.890414\pi\)
−0.178363 + 0.983965i \(0.557080\pi\)
\(644\) 1.53590 + 2.66025i 0.0605229 + 0.104829i
\(645\) 8.29423 + 12.5622i 0.326585 + 0.494635i
\(646\) 5.83013 + 10.0981i 0.229383 + 0.397303i
\(647\) −9.80385 5.66025i −0.385429 0.222528i 0.294749 0.955575i \(-0.404764\pi\)
−0.680178 + 0.733047i \(0.738097\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 22.9282 0.900011
\(650\) 16.0885 + 8.13397i 0.631041 + 0.319041i
\(651\) −2.92820 −0.114765
\(652\) 5.66025 + 3.26795i 0.221673 + 0.127983i
\(653\) −31.7321 18.3205i −1.24177 0.716937i −0.272317 0.962208i \(-0.587790\pi\)
−0.969455 + 0.245271i \(0.921123\pi\)
\(654\) 5.00000 + 8.66025i 0.195515 + 0.338643i
\(655\) 17.0718 + 25.8564i 0.667050 + 1.01029i
\(656\) −0.598076 1.03590i −0.0233510 0.0404450i
\(657\) 10.9641 6.33013i 0.427750 0.246962i
\(658\) 7.07180i 0.275687i
\(659\) −17.2679 29.9090i −0.672664 1.16509i −0.977146 0.212570i \(-0.931817\pi\)
0.304482 0.952518i \(-0.401517\pi\)
\(660\) 0.366025 + 6.09808i 0.0142475 + 0.237367i
\(661\) −3.25833 + 5.64359i −0.126734 + 0.219510i −0.922410 0.386213i \(-0.873783\pi\)
0.795675 + 0.605724i \(0.207116\pi\)
\(662\) 12.7846i 0.496888i
\(663\) −3.93782 7.96410i −0.152932 0.309300i
\(664\) −8.73205 −0.338869
\(665\) −0.464102 7.73205i −0.0179971 0.299836i
\(666\) 2.96410 5.13397i 0.114857 0.198937i
\(667\) −1.68653 + 0.973721i −0.0653028 + 0.0377026i
\(668\) 13.8564i 0.536120i
\(669\) 10.1962 + 17.6603i 0.394206 + 0.682785i
\(670\) 9.66025 19.3205i 0.373208 0.746416i
\(671\) −38.5885 −1.48969
\(672\) −0.633975 + 0.366025i −0.0244561 + 0.0141197i
\(673\) 11.8923 + 6.86603i 0.458415 + 0.264666i 0.711377 0.702810i \(-0.248072\pi\)
−0.252963 + 0.967476i \(0.581405\pi\)
\(674\) −13.5263 + 23.4282i −0.521013 + 0.902421i
\(675\) −4.59808 1.96410i −0.176980 0.0755983i
\(676\) −12.8923 1.66987i −0.495858 0.0642259i
\(677\) 20.6410i 0.793299i 0.917970 + 0.396649i \(0.129827\pi\)
−0.917970 + 0.396649i \(0.870173\pi\)
\(678\) 7.79423 + 4.50000i 0.299336 + 0.172821i
\(679\) 3.66025 6.33975i 0.140468 0.243297i
\(680\) −2.46410 + 4.92820i −0.0944940 + 0.188988i
\(681\) 6.19615 0.237437
\(682\) −9.46410 + 5.46410i −0.362399 + 0.209231i
\(683\) 11.3205 6.53590i 0.433167 0.250089i −0.267528 0.963550i \(-0.586207\pi\)
0.700695 + 0.713461i \(0.252873\pi\)
\(684\) −4.73205 −0.180934
\(685\) 23.0718 + 11.5359i 0.881528 + 0.440764i
\(686\) −4.92820 + 8.53590i −0.188160 + 0.325902i
\(687\) 11.0718 + 6.39230i 0.422415 + 0.243882i
\(688\) 6.73205i 0.256657i
\(689\) 13.7942 6.82051i 0.525518 0.259841i
\(690\) −7.83013 + 5.16987i −0.298088 + 0.196814i
\(691\) −4.70577 + 8.15064i −0.179016 + 0.310065i −0.941544 0.336891i \(-0.890625\pi\)
0.762528 + 0.646955i \(0.223958\pi\)
\(692\) −19.7321 11.3923i −0.750100 0.433070i
\(693\) −1.73205 + 1.00000i −0.0657952 + 0.0379869i
\(694\) −11.6603 −0.442617
\(695\) 14.9282 29.8564i 0.566259 1.13252i
\(696\) −0.232051 0.401924i −0.00879586 0.0152349i
\(697\) 2.94744i 0.111642i
\(698\) 28.5167 16.4641i 1.07937 0.623175i
\(699\) −4.19615 + 7.26795i −0.158713 + 0.274899i
\(700\) 2.92820 2.19615i 0.110676 0.0830068i
\(701\) −6.53590 −0.246857 −0.123429 0.992353i \(-0.539389\pi\)
−0.123429 + 0.992353i \(0.539389\pi\)
\(702\) 3.59808 + 0.232051i 0.135801 + 0.00875819i
\(703\) 28.0526i 1.05802i
\(704\) −1.36603 + 2.36603i −0.0514840 + 0.0891729i
\(705\) 21.5622 1.29423i 0.812079 0.0487435i
\(706\) −11.6244 20.1340i −0.437488 0.757752i
\(707\) 0.0525589i 0.00197668i
\(708\) −7.26795 + 4.19615i −0.273146 + 0.157701i
\(709\) −0.526279 0.911543i −0.0197648 0.0342337i 0.855974 0.517019i \(-0.172958\pi\)
−0.875739 + 0.482785i \(0.839625\pi\)
\(710\) −8.83013 + 5.83013i −0.331389 + 0.218801i
\(711\) −6.00000 10.3923i −0.225018 0.389742i
\(712\) −7.73205 4.46410i −0.289771 0.167299i
\(713\) −14.5359 8.39230i −0.544374 0.314294i
\(714\) −1.80385 −0.0675073
\(715\) 10.9282 + 19.1244i 0.408692 + 0.715210i
\(716\) 7.80385 0.291643
\(717\) −23.0263 13.2942i −0.859932 0.496482i
\(718\) 28.6865 + 16.5622i 1.07057 + 0.618095i
\(719\) −5.80385 10.0526i −0.216447 0.374897i 0.737272 0.675596i \(-0.236114\pi\)
−0.953719 + 0.300699i \(0.902780\pi\)
\(720\) −1.23205 1.86603i −0.0459158 0.0695427i
\(721\) 4.66025 + 8.07180i 0.173557 + 0.300609i
\(722\) 2.93782 1.69615i 0.109334 0.0631243i
\(723\) 11.3923i 0.423684i
\(724\) 4.06218 + 7.03590i 0.150970 + 0.261487i
\(725\) 1.39230 + 1.85641i 0.0517089 + 0.0689452i
\(726\) 1.76795 3.06218i 0.0656147 0.113648i
\(727\) 16.7321i 0.620557i −0.950646 0.310279i \(-0.899578\pi\)
0.950646 0.310279i \(-0.100422\pi\)
\(728\) −1.46410 + 2.19615i −0.0542632 + 0.0813948i
\(729\) −1.00000 −0.0370370
\(730\) −28.2583 + 1.69615i −1.04589 + 0.0627774i
\(731\) −8.29423 + 14.3660i −0.306773 + 0.531347i
\(732\) 12.2321 7.06218i 0.452110 0.261026i
\(733\) 24.6077i 0.908906i −0.890771 0.454453i \(-0.849835\pi\)
0.890771 0.454453i \(-0.150165\pi\)
\(734\) −9.49038 16.4378i −0.350296 0.606731i
\(735\) −12.9282 6.46410i −0.476864 0.238432i
\(736\) −4.19615 −0.154672
\(737\) 22.8564 13.1962i 0.841927 0.486087i
\(738\) 1.03590 + 0.598076i 0.0381319 + 0.0220155i
\(739\) 14.9282 25.8564i 0.549143 0.951143i −0.449191 0.893436i \(-0.648288\pi\)
0.998334 0.0577074i \(-0.0183790\pi\)
\(740\) −11.0622 + 7.30385i −0.406654 + 0.268495i
\(741\) −15.2942 + 7.56218i −0.561848 + 0.277804i
\(742\) 3.12436i 0.114699i
\(743\) −12.5885 7.26795i −0.461826 0.266635i 0.250986 0.967991i \(-0.419245\pi\)
−0.712812 + 0.701356i \(0.752579\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) −6.07180 + 12.1436i −0.222453 + 0.444907i
\(746\) 30.4641 1.11537
\(747\) 7.56218 4.36603i 0.276686 0.159745i
\(748\) −5.83013 + 3.36603i −0.213171 + 0.123074i
\(749\) 3.46410 0.126576
\(750\) 7.23205 + 8.52628i 0.264077 + 0.311336i
\(751\) 1.02628 1.77757i 0.0374495 0.0648644i −0.846693 0.532081i \(-0.821410\pi\)
0.884143 + 0.467217i \(0.154743\pi\)
\(752\) 8.36603 + 4.83013i 0.305078 + 0.176137i
\(753\) 14.5359i 0.529718i
\(754\) −1.39230 0.928203i −0.0507048 0.0338032i
\(755\) 23.5622 + 35.6865i 0.857515 + 1.29877i
\(756\) 0.366025 0.633975i 0.0133122 0.0230574i
\(757\) −31.2679 18.0526i −1.13645 0.656131i −0.190903 0.981609i \(-0.561142\pi\)
−0.945550 + 0.325477i \(0.894475\pi\)
\(758\) 19.2679 11.1244i 0.699843 0.404055i
\(759\) −11.4641 −0.416121
\(760\) 9.46410 + 4.73205i 0.343299 + 0.171650i
\(761\) −18.4641 31.9808i −0.669323 1.15930i −0.978094 0.208165i \(-0.933251\pi\)
0.308771 0.951137i \(-0.400082\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 6.33975 3.66025i 0.229514 0.132510i
\(764\) −1.26795 + 2.19615i −0.0458728 + 0.0794540i
\(765\) −0.330127 5.50000i −0.0119358 0.198853i
\(766\) 13.0718 0.472303
\(767\) −16.7846 + 25.1769i −0.606057 + 0.909086i
\(768\) 1.00000i 0.0360844i
\(769\) 19.2679 33.3731i 0.694820 1.20346i −0.275421 0.961324i \(-0.588817\pi\)
0.970241 0.242140i \(-0.0778493\pi\)
\(770\) 4.46410 0.267949i 0.160875 0.00965622i
\(771\) 1.50000 + 2.59808i 0.0540212 + 0.0935674i
\(772\) 6.66025i 0.239708i
\(773\) 24.8038 14.3205i 0.892132 0.515073i 0.0174930 0.999847i \(-0.494432\pi\)
0.874639 +