Properties

Label 462.2.i.g.67.2
Level $462$
Weight $2$
Character 462.67
Analytic conductor $3.689$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.21870000.1
Defining polynomial: \(x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73\)
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 67.2
Root \(0.500000 - 3.05087i\) of defining polynomial
Character \(\chi\) \(=\) 462.67
Dual form 462.2.i.g.331.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.806615 + 1.39710i) q^{5} -1.00000 q^{6} +(-0.806615 - 2.51980i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.806615 + 1.39710i) q^{5} -1.00000 q^{6} +(-0.806615 - 2.51980i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.806615 - 1.39710i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.77890 + 1.95845i) q^{14} +1.61323 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.67103 - 6.35841i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.585515 - 1.01414i) q^{19} -1.61323 q^{20} +(-2.58551 - 0.561349i) q^{21} -1.00000 q^{22} +(-1.77890 - 3.08115i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.19874 - 2.07629i) q^{25} -1.00000 q^{27} +(2.58551 + 0.561349i) q^{28} +10.3975 q^{29} +(-0.806615 - 1.39710i) q^{30} +(-3.17103 + 5.49238i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} -7.34206 q^{34} +(2.86977 - 3.15943i) q^{35} +1.00000 q^{36} +(-1.41449 - 2.44996i) q^{37} +(-0.585515 + 1.01414i) q^{38} +(0.806615 + 1.39710i) q^{40} +4.94457 q^{41} +(0.806615 + 2.51980i) q^{42} -11.5131 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.806615 - 1.39710i) q^{45} +(-1.77890 + 3.08115i) q^{46} +(-3.39213 - 5.87534i) q^{47} -1.00000 q^{48} +(-5.69874 + 4.06501i) q^{49} -2.39749 q^{50} +(-3.67103 - 6.35841i) q^{51} +(-4.00000 + 6.92820i) q^{53} +(0.500000 + 0.866025i) q^{54} +1.61323 q^{55} +(-0.806615 - 2.51980i) q^{56} -1.17103 q^{57} +(-5.19874 - 9.00449i) q^{58} +(-2.19874 + 3.80834i) q^{59} +(-0.806615 + 1.39710i) q^{60} +(5.97764 + 10.3536i) q^{61} +6.34206 q^{62} +(-1.77890 + 1.95845i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(-1.47229 + 2.55007i) q^{67} +(3.67103 + 6.35841i) q^{68} -3.55780 q^{69} +(-4.17103 - 0.905585i) q^{70} +15.5131 q^{71} +(-0.500000 - 0.866025i) q^{72} +(2.55780 - 4.43024i) q^{73} +(-1.41449 + 2.44996i) q^{74} +(-1.19874 - 2.07629i) q^{75} +1.17103 q^{76} +(-2.58551 - 0.561349i) q^{77} +(-2.80661 - 4.86120i) q^{79} +(0.806615 - 1.39710i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.47229 - 4.28212i) q^{82} +5.05543 q^{83} +(1.77890 - 1.95845i) q^{84} +11.8444 q^{85} +(5.75654 + 9.97063i) q^{86} +(5.19874 - 9.00449i) q^{87} +(0.500000 - 0.866025i) q^{88} +(0.386770 + 0.669906i) q^{89} -1.61323 q^{90} +3.55780 q^{92} +(3.17103 + 5.49238i) q^{93} +(-3.39213 + 5.87534i) q^{94} +(0.944570 - 1.63604i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(6.36977 + 2.90275i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} + 3q^{3} - 3q^{4} - 6q^{6} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} + 3q^{3} - 3q^{4} - 6q^{6} + 6q^{8} - 3q^{9} + 3q^{11} + 3q^{12} - 3q^{14} - 3q^{16} - 3q^{17} - 3q^{18} + 9q^{19} - 3q^{21} - 6q^{22} - 3q^{23} + 3q^{24} - 15q^{25} - 6q^{27} + 3q^{28} + 18q^{29} + 6q^{31} - 3q^{32} - 3q^{33} + 6q^{34} - 30q^{35} + 6q^{36} - 21q^{37} + 9q^{38} + 24q^{41} + 6q^{43} + 3q^{44} - 3q^{46} - 3q^{47} - 6q^{48} - 12q^{49} + 30q^{50} + 3q^{51} - 24q^{53} + 3q^{54} + 18q^{57} - 9q^{58} + 9q^{59} + 6q^{61} - 12q^{62} - 3q^{63} + 6q^{64} - 3q^{66} - 6q^{67} - 3q^{68} - 6q^{69} + 18q^{71} - 3q^{72} - 21q^{74} + 15q^{75} - 18q^{76} - 3q^{77} - 12q^{79} - 3q^{81} - 12q^{82} + 36q^{83} + 3q^{84} - 3q^{86} + 9q^{87} + 3q^{88} + 12q^{89} + 6q^{92} - 6q^{93} - 3q^{94} + 3q^{96} + 42q^{97} - 9q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) 0.806615 + 1.39710i 0.360729 + 0.624801i 0.988081 0.153935i \(-0.0491945\pi\)
−0.627352 + 0.778736i \(0.715861\pi\)
\(6\) −1.00000 −0.408248
\(7\) −0.806615 2.51980i −0.304872 0.952393i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.806615 1.39710i 0.255074 0.441801i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.77890 + 1.95845i −0.475431 + 0.523417i
\(15\) 1.61323 0.416534
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.67103 6.35841i 0.890356 1.54214i 0.0509059 0.998703i \(-0.483789\pi\)
0.839450 0.543438i \(-0.182878\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) −0.585515 1.01414i −0.134326 0.232660i 0.791014 0.611799i \(-0.209554\pi\)
−0.925340 + 0.379139i \(0.876220\pi\)
\(20\) −1.61323 −0.360729
\(21\) −2.58551 0.561349i −0.564206 0.122496i
\(22\) −1.00000 −0.213201
\(23\) −1.77890 3.08115i −0.370926 0.642463i 0.618782 0.785563i \(-0.287626\pi\)
−0.989708 + 0.143100i \(0.954293\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 1.19874 2.07629i 0.239749 0.415257i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 2.58551 + 0.561349i 0.488616 + 0.106085i
\(29\) 10.3975 1.93077 0.965383 0.260838i \(-0.0839988\pi\)
0.965383 + 0.260838i \(0.0839988\pi\)
\(30\) −0.806615 1.39710i −0.147267 0.255074i
\(31\) −3.17103 + 5.49238i −0.569534 + 0.986461i 0.427078 + 0.904215i \(0.359543\pi\)
−0.996612 + 0.0822467i \(0.973790\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.500000 0.866025i −0.0870388 0.150756i
\(34\) −7.34206 −1.25915
\(35\) 2.86977 3.15943i 0.485080 0.534040i
\(36\) 1.00000 0.166667
\(37\) −1.41449 2.44996i −0.232540 0.402771i 0.726015 0.687679i \(-0.241370\pi\)
−0.958555 + 0.284908i \(0.908037\pi\)
\(38\) −0.585515 + 1.01414i −0.0949831 + 0.164515i
\(39\) 0 0
\(40\) 0.806615 + 1.39710i 0.127537 + 0.220901i
\(41\) 4.94457 0.772212 0.386106 0.922454i \(-0.373820\pi\)
0.386106 + 0.922454i \(0.373820\pi\)
\(42\) 0.806615 + 2.51980i 0.124463 + 0.388813i
\(43\) −11.5131 −1.75573 −0.877865 0.478908i \(-0.841033\pi\)
−0.877865 + 0.478908i \(0.841033\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0.806615 1.39710i 0.120243 0.208267i
\(46\) −1.77890 + 3.08115i −0.262284 + 0.454290i
\(47\) −3.39213 5.87534i −0.494793 0.857007i 0.505189 0.863009i \(-0.331423\pi\)
−0.999982 + 0.00600214i \(0.998089\pi\)
\(48\) −1.00000 −0.144338
\(49\) −5.69874 + 4.06501i −0.814106 + 0.580716i
\(50\) −2.39749 −0.339056
\(51\) −3.67103 6.35841i −0.514047 0.890356i
\(52\) 0 0
\(53\) −4.00000 + 6.92820i −0.549442 + 0.951662i 0.448871 + 0.893597i \(0.351826\pi\)
−0.998313 + 0.0580651i \(0.981507\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 1.61323 0.217528
\(56\) −0.806615 2.51980i −0.107788 0.336722i
\(57\) −1.17103 −0.155107
\(58\) −5.19874 9.00449i −0.682629 1.18235i
\(59\) −2.19874 + 3.80834i −0.286252 + 0.495803i −0.972912 0.231175i \(-0.925743\pi\)
0.686660 + 0.726979i \(0.259076\pi\)
\(60\) −0.806615 + 1.39710i −0.104134 + 0.180365i
\(61\) 5.97764 + 10.3536i 0.765359 + 1.32564i 0.940057 + 0.341019i \(0.110772\pi\)
−0.174698 + 0.984622i \(0.555895\pi\)
\(62\) 6.34206 0.805442
\(63\) −1.77890 + 1.95845i −0.224120 + 0.246741i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) −1.47229 + 2.55007i −0.179868 + 0.311541i −0.941835 0.336075i \(-0.890900\pi\)
0.761967 + 0.647616i \(0.224234\pi\)
\(68\) 3.67103 + 6.35841i 0.445178 + 0.771070i
\(69\) −3.55780 −0.428309
\(70\) −4.17103 0.905585i −0.498533 0.108238i
\(71\) 15.5131 1.84106 0.920532 0.390666i \(-0.127755\pi\)
0.920532 + 0.390666i \(0.127755\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 2.55780 4.43024i 0.299368 0.518520i −0.676624 0.736329i \(-0.736558\pi\)
0.975991 + 0.217809i \(0.0698909\pi\)
\(74\) −1.41449 + 2.44996i −0.164431 + 0.284802i
\(75\) −1.19874 2.07629i −0.138419 0.239749i
\(76\) 1.17103 0.134326
\(77\) −2.58551 0.561349i −0.294647 0.0639717i
\(78\) 0 0
\(79\) −2.80661 4.86120i −0.315769 0.546928i 0.663832 0.747882i \(-0.268929\pi\)
−0.979601 + 0.200954i \(0.935596\pi\)
\(80\) 0.806615 1.39710i 0.0901823 0.156200i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.47229 4.28212i −0.273018 0.472881i
\(83\) 5.05543 0.554906 0.277453 0.960739i \(-0.410510\pi\)
0.277453 + 0.960739i \(0.410510\pi\)
\(84\) 1.77890 1.95845i 0.194094 0.213684i
\(85\) 11.8444 1.28471
\(86\) 5.75654 + 9.97063i 0.620744 + 1.07516i
\(87\) 5.19874 9.00449i 0.557364 0.965383i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 0.386770 + 0.669906i 0.0409976 + 0.0710098i 0.885796 0.464075i \(-0.153613\pi\)
−0.844799 + 0.535085i \(0.820280\pi\)
\(90\) −1.61323 −0.170049
\(91\) 0 0
\(92\) 3.55780 0.370926
\(93\) 3.17103 + 5.49238i 0.328820 + 0.569534i
\(94\) −3.39213 + 5.87534i −0.349871 + 0.605995i
\(95\) 0.944570 1.63604i 0.0969108 0.167855i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 6.36977 + 2.90275i 0.643444 + 0.293222i
\(99\) −1.00000 −0.100504
\(100\) 1.19874 + 2.07629i 0.119874 + 0.207629i
\(101\) −6.81197 + 11.7987i −0.677817 + 1.17401i 0.297820 + 0.954622i \(0.403740\pi\)
−0.975637 + 0.219391i \(0.929593\pi\)
\(102\) −3.67103 + 6.35841i −0.363486 + 0.629576i
\(103\) 6.17103 + 10.6885i 0.608050 + 1.05317i 0.991562 + 0.129637i \(0.0413812\pi\)
−0.383512 + 0.923536i \(0.625285\pi\)
\(104\) 0 0
\(105\) −1.30126 4.06501i −0.126990 0.396704i
\(106\) 8.00000 0.777029
\(107\) 7.86977 + 13.6308i 0.760800 + 1.31774i 0.942439 + 0.334379i \(0.108526\pi\)
−0.181639 + 0.983365i \(0.558140\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −1.97764 + 3.42538i −0.189424 + 0.328092i −0.945058 0.326902i \(-0.893995\pi\)
0.755634 + 0.654994i \(0.227329\pi\)
\(110\) −0.806615 1.39710i −0.0769077 0.133208i
\(111\) −2.82897 −0.268514
\(112\) −1.77890 + 1.95845i −0.168090 + 0.185056i
\(113\) −4.34206 −0.408467 −0.204233 0.978922i \(-0.565470\pi\)
−0.204233 + 0.978922i \(0.565470\pi\)
\(114\) 0.585515 + 1.01414i 0.0548385 + 0.0949831i
\(115\) 2.86977 4.97060i 0.267608 0.463510i
\(116\) −5.19874 + 9.00449i −0.482691 + 0.836046i
\(117\) 0 0
\(118\) 4.39749 0.404822
\(119\) −18.9830 4.12146i −1.74017 0.377813i
\(120\) 1.61323 0.147267
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 5.97764 10.3536i 0.541191 0.937369i
\(123\) 2.47229 4.28212i 0.222918 0.386106i
\(124\) −3.17103 5.49238i −0.284767 0.493231i
\(125\) 11.9339 1.06740
\(126\) 2.58551 + 0.561349i 0.230336 + 0.0500089i
\(127\) −0.442200 −0.0392389 −0.0196195 0.999808i \(-0.506245\pi\)
−0.0196195 + 0.999808i \(0.506245\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −5.75654 + 9.97063i −0.506835 + 0.877865i
\(130\) 0 0
\(131\) 1.17103 + 2.02828i 0.102313 + 0.177212i 0.912637 0.408770i \(-0.134042\pi\)
−0.810324 + 0.585982i \(0.800709\pi\)
\(132\) 1.00000 0.0870388
\(133\) −2.08314 + 2.29340i −0.180632 + 0.198863i
\(134\) 2.94457 0.254372
\(135\) −0.806615 1.39710i −0.0694224 0.120243i
\(136\) 3.67103 6.35841i 0.314788 0.545229i
\(137\) −1.61323 + 2.79420i −0.137828 + 0.238724i −0.926674 0.375866i \(-0.877345\pi\)
0.788847 + 0.614590i \(0.210679\pi\)
\(138\) 1.77890 + 3.08115i 0.151430 + 0.262284i
\(139\) 18.3975 1.56045 0.780227 0.625496i \(-0.215103\pi\)
0.780227 + 0.625496i \(0.215103\pi\)
\(140\) 1.30126 + 4.06501i 0.109976 + 0.343556i
\(141\) −6.78426 −0.571338
\(142\) −7.75654 13.4347i −0.650915 1.12742i
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 8.38677 + 14.5263i 0.696483 + 1.20634i
\(146\) −5.11560 −0.423370
\(147\) 0.671030 + 6.96776i 0.0553456 + 0.574691i
\(148\) 2.82897 0.232540
\(149\) −9.81197 16.9948i −0.803828 1.39227i −0.917079 0.398705i \(-0.869460\pi\)
0.113251 0.993566i \(-0.463874\pi\)
\(150\) −1.19874 + 2.07629i −0.0978771 + 0.169528i
\(151\) 0.165670 0.286949i 0.0134820 0.0233516i −0.859206 0.511630i \(-0.829042\pi\)
0.872688 + 0.488279i \(0.162375\pi\)
\(152\) −0.585515 1.01414i −0.0474915 0.0822577i
\(153\) −7.34206 −0.593570
\(154\) 0.806615 + 2.51980i 0.0649989 + 0.203051i
\(155\) −10.2312 −0.821790
\(156\) 0 0
\(157\) −9.98300 + 17.2911i −0.796730 + 1.37998i 0.125004 + 0.992156i \(0.460106\pi\)
−0.921735 + 0.387821i \(0.873228\pi\)
\(158\) −2.80661 + 4.86120i −0.223282 + 0.386736i
\(159\) 4.00000 + 6.92820i 0.317221 + 0.549442i
\(160\) −1.61323 −0.127537
\(161\) −6.32897 + 6.96776i −0.498793 + 0.549137i
\(162\) 1.00000 0.0785674
\(163\) −10.6433 18.4348i −0.833649 1.44392i −0.895126 0.445814i \(-0.852914\pi\)
0.0614771 0.998108i \(-0.480419\pi\)
\(164\) −2.47229 + 4.28212i −0.193053 + 0.334378i
\(165\) 0.806615 1.39710i 0.0627949 0.108764i
\(166\) −2.52771 4.37813i −0.196189 0.339809i
\(167\) 22.0214 1.70407 0.852035 0.523485i \(-0.175368\pi\)
0.852035 + 0.523485i \(0.175368\pi\)
\(168\) −2.58551 0.561349i −0.199477 0.0433090i
\(169\) −13.0000 −1.00000
\(170\) −5.92221 10.2576i −0.454213 0.786720i
\(171\) −0.585515 + 1.01414i −0.0447754 + 0.0775533i
\(172\) 5.75654 9.97063i 0.438932 0.760253i
\(173\) −0.828970 1.43582i −0.0630254 0.109163i 0.832791 0.553588i \(-0.186742\pi\)
−0.895816 + 0.444424i \(0.853408\pi\)
\(174\) −10.3975 −0.788232
\(175\) −6.19874 1.34583i −0.468581 0.101735i
\(176\) −1.00000 −0.0753778
\(177\) 2.19874 + 3.80834i 0.165268 + 0.286252i
\(178\) 0.386770 0.669906i 0.0289896 0.0502115i
\(179\) −7.53008 + 13.0425i −0.562825 + 0.974841i 0.434423 + 0.900709i \(0.356952\pi\)
−0.997248 + 0.0741327i \(0.976381\pi\)
\(180\) 0.806615 + 1.39710i 0.0601215 + 0.104134i
\(181\) 15.1156 1.12353 0.561767 0.827296i \(-0.310122\pi\)
0.561767 + 0.827296i \(0.310122\pi\)
\(182\) 0 0
\(183\) 11.9553 0.883760
\(184\) −1.77890 3.08115i −0.131142 0.227145i
\(185\) 2.28189 3.95235i 0.167768 0.290582i
\(186\) 3.17103 5.49238i 0.232511 0.402721i
\(187\) −3.67103 6.35841i −0.268452 0.464973i
\(188\) 6.78426 0.494793
\(189\) 0.806615 + 2.51980i 0.0586726 + 0.183288i
\(190\) −1.88914 −0.137053
\(191\) 2.38677 + 4.13401i 0.172701 + 0.299126i 0.939363 0.342924i \(-0.111417\pi\)
−0.766663 + 0.642050i \(0.778084\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −1.55780 + 2.69819i −0.112133 + 0.194220i −0.916630 0.399737i \(-0.869102\pi\)
0.804497 + 0.593957i \(0.202435\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) 0 0
\(196\) −0.671030 6.96776i −0.0479307 0.497697i
\(197\) −4.82897 −0.344050 −0.172025 0.985093i \(-0.555031\pi\)
−0.172025 + 0.985093i \(0.555031\pi\)
\(198\) 0.500000 + 0.866025i 0.0355335 + 0.0615457i
\(199\) −2.94457 + 5.10015i −0.208735 + 0.361540i −0.951316 0.308216i \(-0.900268\pi\)
0.742581 + 0.669756i \(0.233601\pi\)
\(200\) 1.19874 2.07629i 0.0847641 0.146816i
\(201\) 1.47229 + 2.55007i 0.103847 + 0.179868i
\(202\) 13.6239 0.958578
\(203\) −8.38677 26.1996i −0.588636 1.83885i
\(204\) 7.34206 0.514047
\(205\) 3.98836 + 6.90805i 0.278559 + 0.482479i
\(206\) 6.17103 10.6885i 0.429956 0.744706i
\(207\) −1.77890 + 3.08115i −0.123642 + 0.214154i
\(208\) 0 0
\(209\) −1.17103 −0.0810018
\(210\) −2.86977 + 3.15943i −0.198033 + 0.218021i
\(211\) −13.6794 −0.941727 −0.470864 0.882206i \(-0.656058\pi\)
−0.470864 + 0.882206i \(0.656058\pi\)
\(212\) −4.00000 6.92820i −0.274721 0.475831i
\(213\) 7.75654 13.4347i 0.531470 0.920532i
\(214\) 7.86977 13.6308i 0.537967 0.931786i
\(215\) −9.28663 16.0849i −0.633343 1.09698i
\(216\) −1.00000 −0.0680414
\(217\) 16.3975 + 3.56011i 1.11313 + 0.241676i
\(218\) 3.95529 0.267886
\(219\) −2.55780 4.43024i −0.172840 0.299368i
\(220\) −0.806615 + 1.39710i −0.0543820 + 0.0941923i
\(221\) 0 0
\(222\) 1.41449 + 2.44996i 0.0949340 + 0.164431i
\(223\) −5.11560 −0.342566 −0.171283 0.985222i \(-0.554791\pi\)
−0.171283 + 0.985222i \(0.554791\pi\)
\(224\) 2.58551 + 0.561349i 0.172752 + 0.0375067i
\(225\) −2.39749 −0.159833
\(226\) 2.17103 + 3.76033i 0.144415 + 0.250134i
\(227\) 2.64331 4.57836i 0.175443 0.303876i −0.764872 0.644183i \(-0.777198\pi\)
0.940314 + 0.340307i \(0.110531\pi\)
\(228\) 0.585515 1.01414i 0.0387767 0.0671632i
\(229\) 2.44220 + 4.23001i 0.161385 + 0.279527i 0.935366 0.353682i \(-0.115071\pi\)
−0.773981 + 0.633209i \(0.781737\pi\)
\(230\) −5.73955 −0.378455
\(231\) −1.77890 + 1.95845i −0.117043 + 0.128856i
\(232\) 10.3975 0.682629
\(233\) −4.89749 8.48270i −0.320845 0.555720i 0.659817 0.751426i \(-0.270634\pi\)
−0.980663 + 0.195706i \(0.937300\pi\)
\(234\) 0 0
\(235\) 5.47229 9.47828i 0.356973 0.618295i
\(236\) −2.19874 3.80834i −0.143126 0.247902i
\(237\) −5.61323 −0.364618
\(238\) 5.92221 + 18.5005i 0.383880 + 1.19921i
\(239\) −23.9106 −1.54665 −0.773323 0.634012i \(-0.781407\pi\)
−0.773323 + 0.634012i \(0.781407\pi\)
\(240\) −0.806615 1.39710i −0.0520668 0.0901823i
\(241\) −0.944570 + 1.63604i −0.0608451 + 0.105387i −0.894843 0.446380i \(-0.852713\pi\)
0.833998 + 0.551767i \(0.186046\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −11.9553 −0.765359
\(245\) −10.2759 4.68281i −0.656504 0.299174i
\(246\) −4.94457 −0.315254
\(247\) 0 0
\(248\) −3.17103 + 5.49238i −0.201361 + 0.348767i
\(249\) 2.52771 4.37813i 0.160187 0.277453i
\(250\) −5.96693 10.3350i −0.377381 0.653644i
\(251\) 0.939830 0.0593215 0.0296608 0.999560i \(-0.490557\pi\)
0.0296608 + 0.999560i \(0.490557\pi\)
\(252\) −0.806615 2.51980i −0.0508120 0.158732i
\(253\) −3.55780 −0.223677
\(254\) 0.221100 + 0.382956i 0.0138730 + 0.0240288i
\(255\) 5.92221 10.2576i 0.370863 0.642354i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.61323 + 9.72240i 0.350144 + 0.606467i 0.986274 0.165115i \(-0.0527994\pi\)
−0.636131 + 0.771581i \(0.719466\pi\)
\(258\) 11.5131 0.716774
\(259\) −5.03246 + 5.54039i −0.312702 + 0.344263i
\(260\) 0 0
\(261\) −5.19874 9.00449i −0.321794 0.557364i
\(262\) 1.17103 2.02828i 0.0723465 0.125308i
\(263\) 0.613230 1.06215i 0.0378134 0.0654947i −0.846499 0.532390i \(-0.821294\pi\)
0.884313 + 0.466895i \(0.154627\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) −12.9058 −0.792799
\(266\) 3.02771 + 0.657356i 0.185641 + 0.0403051i
\(267\) 0.773540 0.0473399
\(268\) −1.47229 2.55007i −0.0899341 0.155770i
\(269\) −4.75119 + 8.22929i −0.289685 + 0.501749i −0.973734 0.227687i \(-0.926884\pi\)
0.684050 + 0.729435i \(0.260217\pi\)
\(270\) −0.806615 + 1.39710i −0.0490890 + 0.0850247i
\(271\) −1.61323 2.79420i −0.0979967 0.169735i 0.812859 0.582461i \(-0.197910\pi\)
−0.910855 + 0.412726i \(0.864577\pi\)
\(272\) −7.34206 −0.445178
\(273\) 0 0
\(274\) 3.22646 0.194918
\(275\) −1.19874 2.07629i −0.0722870 0.125205i
\(276\) 1.77890 3.08115i 0.107077 0.185463i
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) −9.19874 15.9327i −0.551704 0.955579i
\(279\) 6.34206 0.379689
\(280\) 2.86977 3.15943i 0.171502 0.188812i
\(281\) −11.2312 −0.669997 −0.334999 0.942219i \(-0.608736\pi\)
−0.334999 + 0.942219i \(0.608736\pi\)
\(282\) 3.39213 + 5.87534i 0.201998 + 0.349871i
\(283\) 12.7288 22.0470i 0.756650 1.31056i −0.187899 0.982188i \(-0.560168\pi\)
0.944550 0.328369i \(-0.106499\pi\)
\(284\) −7.75654 + 13.4347i −0.460266 + 0.797205i
\(285\) −0.944570 1.63604i −0.0559515 0.0969108i
\(286\) 0 0
\(287\) −3.98836 12.4593i −0.235426 0.735450i
\(288\) 1.00000 0.0589256
\(289\) −18.4529 31.9614i −1.08547 1.88008i
\(290\) 8.38677 14.5263i 0.492488 0.853014i
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) 2.55780 + 4.43024i 0.149684 + 0.259260i
\(293\) 17.9446 1.04833 0.524166 0.851616i \(-0.324377\pi\)
0.524166 + 0.851616i \(0.324377\pi\)
\(294\) 5.69874 4.06501i 0.332358 0.237076i
\(295\) −7.09416 −0.413038
\(296\) −1.41449 2.44996i −0.0822153 0.142401i
\(297\) −0.500000 + 0.866025i −0.0290129 + 0.0502519i
\(298\) −9.81197 + 16.9948i −0.568392 + 0.984485i
\(299\) 0 0
\(300\) 2.39749 0.138419
\(301\) 9.28663 + 29.0106i 0.535272 + 1.67215i
\(302\) −0.331340 −0.0190665
\(303\) 6.81197 + 11.7987i 0.391338 + 0.677817i
\(304\) −0.585515 + 1.01414i −0.0335816 + 0.0581650i
\(305\) −9.64331 + 16.7027i −0.552175 + 0.956394i
\(306\) 3.67103 + 6.35841i 0.209859 + 0.363486i
\(307\) −33.0262 −1.88490 −0.942452 0.334342i \(-0.891486\pi\)
−0.942452 + 0.334342i \(0.891486\pi\)
\(308\) 1.77890 1.95845i 0.101362 0.111593i
\(309\) 12.3421 0.702115
\(310\) 5.11560 + 8.86048i 0.290547 + 0.503241i
\(311\) 0.165670 0.286949i 0.00939429 0.0162714i −0.861290 0.508114i \(-0.830343\pi\)
0.870684 + 0.491842i \(0.163676\pi\)
\(312\) 0 0
\(313\) 7.19874 + 12.4686i 0.406897 + 0.704766i 0.994540 0.104354i \(-0.0332774\pi\)
−0.587643 + 0.809120i \(0.699944\pi\)
\(314\) 19.9660 1.12675
\(315\) −4.17103 0.905585i −0.235011 0.0510239i
\(316\) 5.61323 0.315769
\(317\) −8.76190 15.1761i −0.492118 0.852373i 0.507841 0.861451i \(-0.330444\pi\)
−0.999959 + 0.00907805i \(0.997110\pi\)
\(318\) 4.00000 6.92820i 0.224309 0.388514i
\(319\) 5.19874 9.00449i 0.291074 0.504155i
\(320\) 0.806615 + 1.39710i 0.0450911 + 0.0781002i
\(321\) 15.7395 0.878496
\(322\) 9.19874 + 1.99717i 0.512626 + 0.111298i
\(323\) −8.59777 −0.478393
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −10.6433 + 18.4348i −0.589479 + 1.02101i
\(327\) 1.97764 + 3.42538i 0.109364 + 0.189424i
\(328\) 4.94457 0.273018
\(329\) −12.0685 + 13.2866i −0.665359 + 0.732515i
\(330\) −1.61323 −0.0888054
\(331\) 4.47229 + 7.74622i 0.245819 + 0.425771i 0.962362 0.271772i \(-0.0876098\pi\)
−0.716543 + 0.697543i \(0.754276\pi\)
\(332\) −2.52771 + 4.37813i −0.138726 + 0.240281i
\(333\) −1.41449 + 2.44996i −0.0775133 + 0.134257i
\(334\) −11.0107 19.0711i −0.602480 1.04353i
\(335\) −4.75027 −0.259535
\(336\) 0.806615 + 2.51980i 0.0440045 + 0.137466i
\(337\) −3.33732 −0.181795 −0.0908977 0.995860i \(-0.528974\pi\)
−0.0908977 + 0.995860i \(0.528974\pi\)
\(338\) 6.50000 + 11.2583i 0.353553 + 0.612372i
\(339\) −2.17103 + 3.76033i −0.117914 + 0.204233i
\(340\) −5.92221 + 10.2576i −0.321177 + 0.556295i
\(341\) 3.17103 + 5.49238i 0.171721 + 0.297429i
\(342\) 1.17103 0.0633220
\(343\) 14.8397 + 11.0808i 0.801268 + 0.598306i
\(344\) −11.5131 −0.620744
\(345\) −2.86977 4.97060i −0.154503 0.267608i
\(346\) −0.828970 + 1.43582i −0.0445657 + 0.0771901i
\(347\) 15.2118 26.3477i 0.816614 1.41442i −0.0915491 0.995801i \(-0.529182\pi\)
0.908163 0.418616i \(-0.137485\pi\)
\(348\) 5.19874 + 9.00449i 0.278682 + 0.482691i
\(349\) 17.5238 0.938028 0.469014 0.883191i \(-0.344609\pi\)
0.469014 + 0.883191i \(0.344609\pi\)
\(350\) 1.93385 + 6.04118i 0.103369 + 0.322915i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −2.55780 + 4.43024i −0.136138 + 0.235798i −0.926032 0.377446i \(-0.876802\pi\)
0.789894 + 0.613244i \(0.210136\pi\)
\(354\) 2.19874 3.80834i 0.116862 0.202411i
\(355\) 12.5131 + 21.6733i 0.664126 + 1.15030i
\(356\) −0.773540 −0.0409976
\(357\) −13.0608 + 14.3790i −0.691250 + 0.761019i
\(358\) 15.0602 0.795955
\(359\) 15.3421 + 26.5732i 0.809723 + 1.40248i 0.913056 + 0.407834i \(0.133716\pi\)
−0.103333 + 0.994647i \(0.532951\pi\)
\(360\) 0.806615 1.39710i 0.0425123 0.0736335i
\(361\) 8.81434 15.2669i 0.463913 0.803521i
\(362\) −7.55780 13.0905i −0.397229 0.688021i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 8.25264 0.431963
\(366\) −5.97764 10.3536i −0.312456 0.541191i
\(367\) −0.728830 + 1.26237i −0.0380446 + 0.0658952i −0.884421 0.466690i \(-0.845446\pi\)
0.846376 + 0.532586i \(0.178780\pi\)
\(368\) −1.77890 + 3.08115i −0.0927316 + 0.160616i
\(369\) −2.47229 4.28212i −0.128702 0.222918i
\(370\) −4.56378 −0.237260
\(371\) 20.6841 + 4.49079i 1.07387 + 0.233150i
\(372\) −6.34206 −0.328820
\(373\) 17.0932 + 29.6064i 0.885055 + 1.53296i 0.845651 + 0.533736i \(0.179212\pi\)
0.0394037 + 0.999223i \(0.487454\pi\)
\(374\) −3.67103 + 6.35841i −0.189824 + 0.328786i
\(375\) 5.96693 10.3350i 0.308131 0.533698i
\(376\) −3.39213 5.87534i −0.174936 0.302998i
\(377\) 0 0
\(378\) 1.77890 1.95845i 0.0914967 0.100732i
\(379\) −9.28663 −0.477022 −0.238511 0.971140i \(-0.576659\pi\)
−0.238511 + 0.971140i \(0.576659\pi\)
\(380\) 0.944570 + 1.63604i 0.0484554 + 0.0839273i
\(381\) −0.221100 + 0.382956i −0.0113273 + 0.0196195i
\(382\) 2.38677 4.13401i 0.122118 0.211514i
\(383\) 1.81197 + 3.13843i 0.0925876 + 0.160366i 0.908599 0.417669i \(-0.137153\pi\)
−0.816012 + 0.578035i \(0.803820\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −1.30126 4.06501i −0.0663181 0.207172i
\(386\) 3.11560 0.158580
\(387\) 5.75654 + 9.97063i 0.292622 + 0.506835i
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) −3.58016 + 6.20101i −0.181521 + 0.314404i −0.942399 0.334492i \(-0.891435\pi\)
0.760878 + 0.648895i \(0.224769\pi\)
\(390\) 0 0
\(391\) −26.1216 −1.32103
\(392\) −5.69874 + 4.06501i −0.287830 + 0.205314i
\(393\) 2.34206 0.118141
\(394\) 2.41449 + 4.18201i 0.121640 + 0.210687i
\(395\) 4.52771 7.84223i 0.227814 0.394586i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 15.1987 + 26.3250i 0.762803 + 1.32121i 0.941400 + 0.337291i \(0.109511\pi\)
−0.178597 + 0.983922i \(0.557156\pi\)
\(398\) 5.88914 0.295196
\(399\) 0.944570 + 2.95076i 0.0472877 + 0.147723i
\(400\) −2.39749 −0.119874
\(401\) 6.01072 + 10.4109i 0.300161 + 0.519894i 0.976172 0.216997i \(-0.0696263\pi\)
−0.676011 + 0.736891i \(0.736293\pi\)
\(402\) 1.47229 2.55007i 0.0734309 0.127186i
\(403\) 0 0
\(404\) −6.81197 11.7987i −0.338908 0.587007i
\(405\) −1.61323 −0.0801620
\(406\) −18.4961 + 20.3629i −0.917946 + 1.01060i
\(407\) −2.82897 −0.140227
\(408\) −3.67103 6.35841i −0.181743 0.314788i
\(409\) −8.78426 + 15.2148i −0.434354 + 0.752323i −0.997243 0.0742099i \(-0.976357\pi\)
0.562889 + 0.826533i \(0.309690\pi\)
\(410\) 3.98836 6.90805i 0.196971 0.341164i
\(411\) 1.61323 + 2.79420i 0.0795748 + 0.137828i
\(412\) −12.3421 −0.608050
\(413\) 11.3698 + 2.46853i 0.559470 + 0.121468i
\(414\) 3.55780 0.174856
\(415\) 4.07779 + 7.06293i 0.200171 + 0.346706i
\(416\) 0 0
\(417\) 9.19874 15.9327i 0.450464 0.780227i
\(418\) 0.585515 + 1.01414i 0.0286385 + 0.0496033i
\(419\) −27.1710 −1.32739 −0.663696 0.748003i \(-0.731013\pi\)
−0.663696 + 0.748003i \(0.731013\pi\)
\(420\) 4.17103 + 0.905585i 0.203525 + 0.0441880i
\(421\) 23.1710 1.12929 0.564643 0.825335i \(-0.309014\pi\)
0.564643 + 0.825335i \(0.309014\pi\)
\(422\) 6.83969 + 11.8467i 0.332951 + 0.576688i
\(423\) −3.39213 + 5.87534i −0.164931 + 0.285669i
\(424\) −4.00000 + 6.92820i −0.194257 + 0.336463i
\(425\) −8.80126 15.2442i −0.426924 0.739453i
\(426\) −15.5131 −0.751612
\(427\) 21.2673 23.4138i 1.02920 1.13307i
\(428\) −15.7395 −0.760800
\(429\) 0 0
\(430\) −9.28663 + 16.0849i −0.447841 + 0.775683i
\(431\) 8.38677 14.5263i 0.403977 0.699708i −0.590225 0.807239i \(-0.700961\pi\)
0.994202 + 0.107531i \(0.0342944\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 17.3421 0.833406 0.416703 0.909043i \(-0.363185\pi\)
0.416703 + 0.909043i \(0.363185\pi\)
\(434\) −5.11560 15.9807i −0.245557 0.767098i
\(435\) 16.7735 0.804230
\(436\) −1.97764 3.42538i −0.0947120 0.164046i
\(437\) −2.08314 + 3.60811i −0.0996503 + 0.172599i
\(438\) −2.55780 + 4.43024i −0.122216 + 0.211685i
\(439\) −16.5739 28.7068i −0.791028 1.37010i −0.925331 0.379160i \(-0.876213\pi\)
0.134303 0.990940i \(-0.457121\pi\)
\(440\) 1.61323 0.0769077
\(441\) 6.36977 + 2.90275i 0.303323 + 0.138226i
\(442\) 0 0
\(443\) 6.02771 + 10.4403i 0.286385 + 0.496034i 0.972944 0.231040i \(-0.0742129\pi\)
−0.686559 + 0.727074i \(0.740880\pi\)
\(444\) 1.41449 2.44996i 0.0671285 0.116270i
\(445\) −0.623949 + 1.08071i −0.0295780 + 0.0512306i
\(446\) 2.55780 + 4.43024i 0.121115 + 0.209778i
\(447\) −19.6239 −0.928181
\(448\) −0.806615 2.51980i −0.0381090 0.119049i
\(449\) −36.5947 −1.72701 −0.863505 0.504340i \(-0.831736\pi\)
−0.863505 + 0.504340i \(0.831736\pi\)
\(450\) 1.19874 + 2.07629i 0.0565094 + 0.0978771i
\(451\) 2.47229 4.28212i 0.116415 0.201637i
\(452\) 2.17103 3.76033i 0.102117 0.176871i
\(453\) −0.165670 0.286949i −0.00778386 0.0134820i
\(454\) −5.28663 −0.248114
\(455\) 0 0
\(456\) −1.17103 −0.0548385
\(457\) −18.9106 32.7541i −0.884600 1.53217i −0.846172 0.532910i \(-0.821098\pi\)
−0.0384276 0.999261i \(-0.512235\pi\)
\(458\) 2.44220 4.23001i 0.114117 0.197656i
\(459\) −3.67103 + 6.35841i −0.171349 + 0.296785i
\(460\) 2.86977 + 4.97060i 0.133804 + 0.231755i
\(461\) 34.9707 1.62875 0.814375 0.580339i \(-0.197080\pi\)
0.814375 + 0.580339i \(0.197080\pi\)
\(462\) 2.58551 + 0.561349i 0.120289 + 0.0261163i
\(463\) 7.56852 0.351739 0.175869 0.984413i \(-0.443726\pi\)
0.175869 + 0.984413i \(0.443726\pi\)
\(464\) −5.19874 9.00449i −0.241346 0.418023i
\(465\) −5.11560 + 8.86048i −0.237230 + 0.410895i
\(466\) −4.89749 + 8.48270i −0.226872 + 0.392954i
\(467\) 7.31434 + 12.6688i 0.338468 + 0.586243i 0.984145 0.177368i \(-0.0567581\pi\)
−0.645677 + 0.763610i \(0.723425\pi\)
\(468\) 0 0
\(469\) 7.61323 + 1.65293i 0.351546 + 0.0763253i
\(470\) −10.9446 −0.504835
\(471\) 9.98300 + 17.2911i 0.459993 + 0.796730i
\(472\) −2.19874 + 3.80834i −0.101205 + 0.175293i
\(473\) −5.75654 + 9.97063i −0.264686 + 0.458450i
\(474\) 2.80661 + 4.86120i 0.128912 + 0.223282i
\(475\) −2.80753 −0.128818
\(476\) 13.0608 14.3790i 0.598640 0.659062i
\(477\) 8.00000 0.366295
\(478\) 11.9553 + 20.7072i 0.546822 + 0.947124i
\(479\) 0.613230 1.06215i 0.0280192 0.0485307i −0.851676 0.524069i \(-0.824413\pi\)
0.879695 + 0.475538i \(0.157747\pi\)
\(480\) −0.806615 + 1.39710i −0.0368168 + 0.0637685i
\(481\) 0 0
\(482\) 1.88914 0.0860480
\(483\) 2.86977 + 8.96493i 0.130579 + 0.407918i
\(484\) 1.00000 0.0454545
\(485\) 5.64630 + 9.77969i 0.256385 + 0.444073i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −15.3528 + 26.5918i −0.695701 + 1.20499i 0.274243 + 0.961660i \(0.411573\pi\)
−0.969944 + 0.243329i \(0.921761\pi\)
\(488\) 5.97764 + 10.3536i 0.270595 + 0.468685i
\(489\) −21.2866 −0.962615
\(490\) 1.08253 + 11.2406i 0.0489035 + 0.507799i
\(491\) 30.9446 1.39651 0.698254 0.715850i \(-0.253960\pi\)
0.698254 + 0.715850i \(0.253960\pi\)
\(492\) 2.47229 + 4.28212i 0.111459 + 0.193053i
\(493\) 38.1695 66.1115i 1.71907 2.97751i
\(494\) 0 0
\(495\) −0.806615 1.39710i −0.0362546 0.0627949i
\(496\) 6.34206 0.284767
\(497\) −12.5131 39.0898i −0.561289 1.75342i
\(498\) −5.05543 −0.226539
\(499\) 5.17103 + 8.95649i 0.231487 + 0.400947i 0.958246 0.285945i \(-0.0923076\pi\)
−0.726759 + 0.686893i \(0.758974\pi\)
\(500\) −5.96693 + 10.3350i −0.266849 + 0.462196i
\(501\) 11.0107 19.0711i 0.491923 0.852035i
\(502\) −0.469915 0.813917i −0.0209733 0.0363269i
\(503\) 4.66268 0.207899 0.103949 0.994583i \(-0.466852\pi\)
0.103949 + 0.994583i \(0.466852\pi\)
\(504\) −1.77890 + 1.95845i −0.0792385 + 0.0872362i
\(505\) −21.9786 −0.978033
\(506\) 1.77890 + 3.08115i 0.0790817 + 0.136974i
\(507\) −6.50000 + 11.2583i −0.288675 + 0.500000i
\(508\) 0.221100 0.382956i 0.00980973 0.0169909i
\(509\) −12.7950 22.1616i −0.567127 0.982294i −0.996848 0.0793318i \(-0.974721\pi\)
0.429721 0.902962i \(-0.358612\pi\)
\(510\) −11.8444 −0.524480
\(511\) −13.2265 2.87164i −0.585104 0.127034i
\(512\) 1.00000 0.0441942
\(513\) 0.585515 + 1.01414i 0.0258511 + 0.0447754i
\(514\) 5.61323 9.72240i 0.247589 0.428837i
\(515\) −9.95529 + 17.2431i −0.438682 + 0.759820i
\(516\) −5.75654 9.97063i −0.253418 0.438932i
\(517\) −6.78426 −0.298371
\(518\) 7.31434 + 1.58804i 0.321374 + 0.0697745i
\(519\) −1.65794 −0.0727755
\(520\) 0 0
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) −5.19874 + 9.00449i −0.227543 + 0.394116i
\(523\) −15.1817 26.2956i −0.663852 1.14982i −0.979595 0.200980i \(-0.935587\pi\)
0.315744 0.948844i \(-0.397746\pi\)
\(524\) −2.34206 −0.102313
\(525\) −4.26489 + 4.69536i −0.186135 + 0.204922i
\(526\) −1.22646 −0.0534762
\(527\) 23.2819 + 40.3254i 1.01418 + 1.75660i
\(528\) −0.500000 + 0.866025i −0.0217597 + 0.0376889i
\(529\) 5.17103 8.95649i 0.224827 0.389412i
\(530\) 6.45292 + 11.1768i 0.280297 + 0.485488i
\(531\) 4.39749 0.190835
\(532\) −0.944570 2.95076i −0.0409523 0.127932i
\(533\) 0 0
\(534\) −0.386770 0.669906i −0.0167372 0.0289896i
\(535\) −12.6958 + 21.9897i −0.548885 + 0.950697i
\(536\) −1.47229 + 2.55007i −0.0635930 + 0.110146i
\(537\) 7.53008 + 13.0425i 0.324947 + 0.562825i
\(538\) 9.50237 0.409676
\(539\) 0.671030 + 6.96776i 0.0289033 + 0.300123i
\(540\) 1.61323 0.0694224
\(541\) −0.806615 1.39710i −0.0346791 0.0600659i 0.848165 0.529732i \(-0.177708\pi\)
−0.882844 + 0.469666i \(0.844374\pi\)
\(542\) −1.61323 + 2.79420i −0.0692942 + 0.120021i
\(543\) 7.55780 13.0905i 0.324336 0.561767i
\(544\) 3.67103 + 6.35841i 0.157394 + 0.272615i
\(545\) −6.38079 −0.273323
\(546\) 0 0
\(547\) 15.7348 0.672772 0.336386 0.941724i \(-0.390795\pi\)
0.336386 + 0.941724i \(0.390795\pi\)
\(548\) −1.61323 2.79420i −0.0689138 0.119362i
\(549\) 5.97764 10.3536i 0.255120 0.441880i
\(550\) −1.19874 + 2.07629i −0.0511146 + 0.0885332i
\(551\) −6.08788 10.5445i −0.259353 0.449212i
\(552\) −3.55780 −0.151430
\(553\) −9.98537 + 10.9932i −0.424621 + 0.467479i
\(554\) −16.0000 −0.679775
\(555\) −2.28189 3.95235i −0.0968608 0.167768i
\(556\) −9.19874 + 15.9327i −0.390114 + 0.675697i
\(557\) −5.64094 + 9.77040i −0.239015 + 0.413985i −0.960432 0.278515i \(-0.910158\pi\)
0.721417 + 0.692501i \(0.243491\pi\)
\(558\) −3.17103 5.49238i −0.134240 0.232511i
\(559\) 0 0
\(560\) −4.17103 0.905585i −0.176258 0.0382680i
\(561\) −7.34206 −0.309982
\(562\) 5.61560 + 9.72650i 0.236880 + 0.410288i
\(563\) −10.4529 + 18.1050i −0.440538 + 0.763034i −0.997729 0.0673499i \(-0.978546\pi\)
0.557191 + 0.830384i \(0.311879\pi\)
\(564\) 3.39213 5.87534i 0.142834 0.247396i
\(565\) −3.50237 6.06628i −0.147346 0.255210i
\(566\) −25.4577 −1.07007
\(567\) 2.58551 + 0.561349i 0.108581 + 0.0235744i
\(568\) 15.5131 0.650915
\(569\) 3.91686 + 6.78419i 0.164203 + 0.284408i 0.936372 0.351009i \(-0.114161\pi\)
−0.772169 + 0.635417i \(0.780828\pi\)
\(570\) −0.944570 + 1.63604i −0.0395637 + 0.0685263i
\(571\) −1.19874 + 2.07629i −0.0501659 + 0.0868899i −0.890018 0.455926i \(-0.849308\pi\)
0.839852 + 0.542815i \(0.182642\pi\)
\(572\) 0 0
\(573\) 4.77354 0.199418
\(574\) −8.79590 + 9.68368i −0.367134 + 0.404189i
\(575\) −8.52979 −0.355717
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −12.8143 + 22.1951i −0.533468 + 0.923994i 0.465768 + 0.884907i \(0.345778\pi\)
−0.999236 + 0.0390869i \(0.987555\pi\)
\(578\) −18.4529 + 31.9614i −0.767540 + 1.32942i
\(579\) 1.55780 + 2.69819i 0.0647400 + 0.112133i
\(580\) −16.7735 −0.696483
\(581\) −4.07779 12.7387i −0.169175 0.528488i
\(582\) −7.00000 −0.290159
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) 2.55780 4.43024i 0.105843 0.183325i
\(585\) 0 0
\(586\) −8.97229 15.5405i −0.370642 0.641970i
\(587\) 5.79972 0.239380 0.119690 0.992811i \(-0.461810\pi\)
0.119690 + 0.992811i \(0.461810\pi\)
\(588\) −6.36977 2.90275i −0.262685 0.119707i
\(589\) 7.42674 0.306014
\(590\) 3.54708 + 6.14372i 0.146031 + 0.252933i
\(591\) −2.41449 + 4.18201i −0.0993186 + 0.172025i
\(592\) −1.41449 + 2.44996i −0.0581350 + 0.100693i
\(593\) −15.5962 27.0135i −0.640461 1.10931i −0.985330 0.170660i \(-0.945410\pi\)
0.344869 0.938651i \(-0.387923\pi\)
\(594\) 1.00000 0.0410305
\(595\) −9.55389 29.8455i −0.391671 1.22355i
\(596\) 19.6239 0.803828
\(597\) 2.94457 + 5.10015i 0.120513 + 0.208735i
\(598\) 0 0
\(599\) 15.6463 27.1002i 0.639291 1.10728i −0.346298 0.938125i \(-0.612561\pi\)
0.985589 0.169159i \(-0.0541053\pi\)
\(600\) −1.19874 2.07629i −0.0489385 0.0847641i
\(601\) −22.1203 −0.902307 −0.451154 0.892446i \(-0.648987\pi\)
−0.451154 + 0.892446i \(0.648987\pi\)
\(602\) 20.4806 22.5478i 0.834728 0.918979i
\(603\) 2.94457 0.119912
\(604\) 0.165670 + 0.286949i 0.00674102 + 0.0116758i
\(605\) 0.806615 1.39710i 0.0327936 0.0568001i
\(606\) 6.81197 11.7987i 0.276718 0.479289i
\(607\) 10.3090 + 17.8557i 0.418429 + 0.724740i 0.995782 0.0917548i \(-0.0292476\pi\)
−0.577353 + 0.816495i \(0.695914\pi\)
\(608\) 1.17103 0.0474915
\(609\) −26.8829 5.83662i −1.08935 0.236512i
\(610\) 19.2866 0.780893
\(611\) 0 0
\(612\) 3.67103 6.35841i 0.148393 0.257023i
\(613\) 7.87750 13.6442i 0.318169 0.551086i −0.661937 0.749560i \(-0.730265\pi\)
0.980106 + 0.198474i \(0.0635986\pi\)
\(614\) 16.5131 + 28.6015i 0.666414 + 1.15426i
\(615\) 7.97673 0.321653
\(616\) −2.58551 0.561349i −0.104173 0.0226174i
\(617\) 34.2526 1.37896 0.689480 0.724305i \(-0.257839\pi\)
0.689480 + 0.724305i \(0.257839\pi\)
\(618\) −6.17103 10.6885i −0.248235 0.429956i
\(619\) 10.9854 19.0272i 0.441539 0.764769i −0.556264 0.831005i \(-0.687766\pi\)
0.997804 + 0.0662365i \(0.0210992\pi\)
\(620\) 5.11560 8.86048i 0.205447 0.355845i
\(621\) 1.77890 + 3.08115i 0.0713848 + 0.123642i
\(622\) −0.331340 −0.0132855
\(623\) 1.37605 1.51494i 0.0551303 0.0606947i
\(624\) 0 0
\(625\) 3.63230 + 6.29133i 0.145292 + 0.251653i
\(626\) 7.19874 12.4686i 0.287720 0.498345i
\(627\) −0.585515 + 1.01414i −0.0233832 + 0.0405009i
\(628\) −9.98300 17.2911i −0.398365 0.689989i
\(629\) −20.7705 −0.828173
\(630\) 1.30126 + 4.06501i 0.0518433 + 0.161954i
\(631\) −27.5685 −1.09749 −0.548743 0.835991i \(-0.684893\pi\)
−0.548743 + 0.835991i \(0.684893\pi\)
\(632\) −2.80661 4.86120i −0.111641 0.193368i
\(633\) −6.83969 + 11.8467i −0.271853 + 0.470864i
\(634\) −8.76190 + 15.1761i −0.347980 + 0.602718i
\(635\) −0.356685 0.617797i −0.0141546 0.0245165i
\(636\) −8.00000 −0.317221
\(637\) 0 0
\(638\) −10.3975 −0.411641
\(639\) −7.75654 13.4347i −0.306844 0.531470i
\(640\) 0.806615 1.39710i 0.0318843 0.0552251i
\(641\) −2.82897 + 4.89992i −0.111738 + 0.193535i −0.916471 0.400101i \(-0.868975\pi\)
0.804733 + 0.593636i \(0.202308\pi\)
\(642\) −7.86977 13.6308i −0.310595 0.537967i
\(643\) 17.4791 0.689308 0.344654 0.938730i \(-0.387996\pi\)
0.344654 + 0.938730i \(0.387996\pi\)
\(644\) −2.86977 8.96493i −0.113085 0.353268i
\(645\) −18.5733 −0.731321
\(646\) 4.29889 + 7.44589i 0.169137 + 0.292955i
\(647\) 4.41984 7.65540i 0.173762 0.300965i −0.765970 0.642876i \(-0.777741\pi\)
0.939732 + 0.341912i \(0.111074\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 2.19874 + 3.80834i 0.0863083 + 0.149490i
\(650\) 0 0
\(651\) 11.2819 12.4206i 0.442172 0.486801i
\(652\) 21.2866 0.833649
\(653\) 12.3751 + 21.4344i 0.484276 + 0.838791i 0.999837 0.0180618i \(-0.00574958\pi\)
−0.515560 + 0.856853i \(0.672416\pi\)
\(654\) 1.97764 3.42538i 0.0773320 0.133943i
\(655\) −1.88914 + 3.27209i −0.0738148 + 0.127851i
\(656\) −2.47229 4.28212i −0.0965265 0.167189i
\(657\) −5.11560 −0.199579
\(658\) 17.5408 + 3.80834i 0.683812 + 0.148464i
\(659\) 5.62869 0.219263 0.109631 0.993972i \(-0.465033\pi\)
0.109631 + 0.993972i \(0.465033\pi\)
\(660\) 0.806615 + 1.39710i 0.0313974 + 0.0543820i
\(661\) 6.70111 11.6067i 0.260643 0.451447i −0.705770 0.708441i \(-0.749399\pi\)
0.966413 + 0.256994i \(0.0827321\pi\)
\(662\) 4.47229 7.74622i 0.173820 0.301066i
\(663\) 0 0
\(664\) 5.05543 0.196189
\(665\) −4.88440 1.06047i −0.189409 0.0411231i
\(666\) 2.82897 0.109620
\(667\) −18.4961 32.0362i −0.716172 1.24045i
\(668\) −11.0107 + 19.0711i −0.426018 + 0.737884i
\(669\) −2.55780 + 4.43024i −0.0988903 + 0.171283i
\(670\) 2.37513 + 4.11385i 0.0917594 + 0.158932i
\(671\) 11.9553 0.461529
\(672\) 1.77890 1.95845i 0.0686226 0.0755487i
\(673\) −29.0262 −1.11888 −0.559438 0.828872i \(-0.688983\pi\)
−0.559438 + 0.828872i \(0.688983\pi\)
\(674\) 1.66866 + 2.89020i 0.0642744 + 0.111326i
\(675\) −1.19874 + 2.07629i −0.0461397 + 0.0799163i
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) 10.1540 + 17.5873i 0.390251 + 0.675935i 0.992482 0.122387i \(-0.0390548\pi\)
−0.602231 + 0.798322i \(0.705721\pi\)
\(678\) 4.34206 0.166756
\(679\) −5.64630 17.6386i −0.216685 0.676906i
\(680\) 11.8444 0.454213
\(681\) −2.64331 4.57836i −0.101292 0.175443i
\(682\) 3.17103 5.49238i 0.121425 0.210314i
\(683\) 5.36977 9.30072i 0.205469 0.355882i −0.744813 0.667273i \(-0.767461\pi\)
0.950282 + 0.311391i \(0.100795\pi\)
\(684\) −0.585515 1.01414i −0.0223877 0.0387767i
\(685\) −5.20502 −0.198874
\(686\) 2.17639 18.3919i 0.0830949 0.702207i
\(687\) 4.88440 0.186351
\(688\) 5.75654 + 9.97063i 0.219466 + 0.380127i
\(689\) 0 0
\(690\) −2.86977 + 4.97060i −0.109250 + 0.189227i
\(691\) −2.98537 5.17082i −0.113569 0.196707i 0.803638 0.595119i \(-0.202895\pi\)
−0.917207 + 0.398411i \(0.869562\pi\)
\(692\) 1.65794 0.0630254
\(693\) 0.806615 + 2.51980i 0.0306408 + 0.0957191i
\(694\) −30.4237 −1.15487
\(695\) 14.8397 + 25.7031i 0.562902 + 0.974974i
\(696\) 5.19874 9.00449i 0.197058 0.341314i
\(697\) 18.1517 31.4396i 0.687543 1.19086i
\(698\) −8.76190 15.1761i −0.331643 0.574422i
\(699\) −9.79498 −0.370480
\(700\) 4.26489 4.69536i 0.161198 0.177468i
\(701\) −5.28189 −0.199494 −0.0997471 0.995013i \(-0.531803\pi\)
−0.0997471 + 0.995013i \(0.531803\pi\)
\(702\) 0 0
\(703\) −1.65640 + 2.86898i −0.0624725 + 0.108205i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −5.47229 9.47828i −0.206098 0.356973i
\(706\) 5.11560 0.192528
\(707\) 35.2249 + 7.64779i 1.32477 + 0.287625i
\(708\) −4.39749 −0.165268
\(709\) −19.6564 34.0459i −0.738212 1.27862i −0.953300 0.302026i \(-0.902337\pi\)
0.215088 0.976595i \(-0.430996\pi\)
\(710\) 12.5131 21.6733i 0.469608 0.813385i
\(711\) −2.80661 + 4.86120i −0.105256 + 0.182309i
\(712\) 0.386770 + 0.669906i 0.0144948 + 0.0251058i
\(713\) 22.5638 0.845020
\(714\) 18.9830 + 4.12146i 0.710421 + 0.154242i
\(715\) 0 0
\(716\) −7.53008 13.0425i −0.281412 0.487421i
\(717\) −11.9553 + 20.7072i −0.446478 + 0.773323i
\(718\) 15.3421 26.5732i 0.572561 0.991704i
\(719\) 17.6788 + 30.6205i 0.659306 + 1.14195i 0.980795 + 0.195039i \(0.0624833\pi\)
−0.321489 + 0.946913i \(0.604183\pi\)
\(720\) −1.61323 −0.0601215
\(721\) 21.9553 24.1713i 0.817658 0.900185i
\(722\) −17.6287 −0.656072
\(723\) 0.944570 + 1.63604i 0.0351289 + 0.0608451i
\(724\) −7.55780 + 13.0905i −0.280883 + 0.486504i
\(725\) 12.4639 21.5882i 0.462899 0.801765i
\(726\) 0.500000 + 0.866025i 0.0185567 + 0.0321412i
\(727\) −40.2312 −1.49209 −0.746046 0.665894i \(-0.768050\pi\)
−0.746046 + 0.665894i \(0.768050\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −4.12632 7.14699i −0.152722 0.264522i
\(731\) −42.2649 + 73.2049i −1.56322 + 2.70758i
\(732\) −5.97764 + 10.3536i −0.220940 + 0.382679i
\(733\) −14.3644 24.8799i −0.530562 0.918960i −0.999364 0.0356568i \(-0.988648\pi\)
0.468802 0.883303i \(-0.344686\pi\)
\(734\) 1.45766 0.0538032
\(735\) −9.19339 + 6.55780i −0.339103 + 0.241888i
\(736\) 3.55780 0.131142
\(737\) 1.47229 + 2.55007i 0.0542323 + 0.0939331i
\(738\) −2.47229 + 4.28212i −0.0910061 + 0.157627i
\(739\) 8.17103 14.1526i 0.300576 0.520613i −0.675690 0.737186i \(-0.736154\pi\)
0.976267 + 0.216572i \(0.0694877\pi\)
\(740\) 2.28189 + 3.95235i 0.0838839 + 0.145291i
\(741\) 0 0
\(742\) −6.45292 20.1584i −0.236894 0.740037i
\(743\) 45.3897 1.66519 0.832593 0.553885i \(-0.186855\pi\)
0.832593 + 0.553885i \(0.186855\pi\)
\(744\) 3.17103 + 5.49238i 0.116256 + 0.201361i
\(745\) 15.8290 27.4166i 0.579929 1.00447i
\(746\) 17.0932 29.6064i 0.625828 1.08397i
\(747\) −2.52771 4.37813i −0.0924843 0.160187i
\(748\) 7.34206 0.268452
\(749\) 27.9991 30.8251i 1.02306 1.12632i
\(750\) −11.9339 −0.435763
\(751\) 13.8999 + 24.0753i 0.507213 + 0.878519i 0.999965 + 0.00834907i \(0.00265762\pi\)
−0.492752 + 0.870170i \(0.664009\pi\)
\(752\) −3.39213 + 5.87534i −0.123698 + 0.214252i
\(753\) 0.469915 0.813917i 0.0171247 0.0296608i
\(754\) 0 0
\(755\) 0.534528 0.0194535
\(756\) −2.58551 0.561349i −0.0940343 0.0204161i
\(757\) 19.0816 0.693533 0.346766 0.937952i \(-0.387280\pi\)
0.346766 + 0.937952i \(0.387280\pi\)
\(758\) 4.64331 + 8.04246i 0.168653 + 0.292115i
\(759\) −1.77890 + 3.08115i −0.0645700 + 0.111838i
\(760\) 0.944570 1.63604i 0.0342632 0.0593455i
\(761\) −23.6093 40.8925i −0.855837 1.48235i −0.875866 0.482554i \(-0.839709\pi\)
0.0200287 0.999799i \(-0.493624\pi\)
\(762\) 0.442200 0.0160192
\(763\) 10.2265 + 2.22030i 0.370223 + 0.0803802i
\(764\) −4.77354 −0.172701
\(765\) −5.92221 10.2576i −0.214118 0.370863i
\(766\) 1.81197 3.13843i 0.0654693 0.113396i
\(767\) 0 0
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −9.56852 −0.345050 −0.172525 0.985005i \(-0.555192\pi\)
−0.172525 + 0.985005i \(0.555192\pi\)
\(770\) −2.86977 + 3.15943i −0.103419 + 0.113858i
\(771\) 11.2265 0.404311
\(772\) −1.55780 2.69819i −0.0560664 0.0971099i
\(773\) −7.97764 + 13.8177i −0.286936 + 0.496988i −0.973077 0.230481i \(-0.925970\pi\)
0.686141 + 0.727469i \(0.259303\pi\)
\(774\) 5.75654 9.97063i 0.206915 0.358387i
\(775\) 7.60251 + 13.1679i 0.273090 + 0.473006i
\(776\) 7.00000 0.251285
\(777\) 2.28189 + 7.12843i 0.0818623 + 0.255731i
\(778\) 7.16031 0.256710
\(779\) −2.89512 5.01449i −0.103728 0.179663i
\(780\) 0 0
\(781\)