Properties

Label 637.2.e.f.508.1
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.f.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-2.20711 - 3.82282i) q^{5} -2.00000 q^{6} -2.82843 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-2.20711 - 3.82282i) q^{5} -2.00000 q^{6} -2.82843 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.12132 + 5.40629i) q^{10} +(2.12132 - 3.67423i) q^{11} -1.00000 q^{13} -6.24264 q^{15} +(2.00000 + 3.46410i) q^{16} +(0.707107 - 1.22474i) q^{17} +(0.707107 - 1.22474i) q^{18} +(-0.621320 - 1.07616i) q^{19} -6.00000 q^{22} +(0.0857864 + 0.148586i) q^{23} +(-2.00000 + 3.46410i) q^{24} +(-7.24264 + 12.5446i) q^{25} +(0.707107 + 1.22474i) q^{26} +5.65685 q^{27} +5.82843 q^{29} +(4.41421 + 7.64564i) q^{30} +(2.62132 - 4.54026i) q^{31} +(-3.00000 - 5.19615i) q^{33} -2.00000 q^{34} +(3.12132 + 5.40629i) q^{37} +(-0.878680 + 1.52192i) q^{38} +(-0.707107 + 1.22474i) q^{39} +(6.24264 + 10.8126i) q^{40} +3.17157 q^{41} -5.00000 q^{43} +(2.20711 - 3.82282i) q^{45} +(0.121320 - 0.210133i) q^{46} +(-2.20711 - 3.82282i) q^{47} +5.65685 q^{48} +20.4853 q^{50} +(-1.00000 - 1.73205i) q^{51} +(2.91421 - 5.04757i) q^{53} +(-4.00000 - 6.92820i) q^{54} -18.7279 q^{55} -1.75736 q^{57} +(-4.12132 - 7.13834i) q^{58} +(-5.82843 + 10.0951i) q^{59} +(-3.00000 - 5.19615i) q^{61} -7.41421 q^{62} +8.00000 q^{64} +(2.20711 + 3.82282i) q^{65} +(-4.24264 + 7.34847i) q^{66} +(-1.24264 + 2.15232i) q^{67} +0.242641 q^{69} +1.07107 q^{71} +(-1.41421 - 2.44949i) q^{72} +(0.378680 - 0.655892i) q^{73} +(4.41421 - 7.64564i) q^{74} +(10.2426 + 17.7408i) q^{75} +2.00000 q^{78} +(0.742641 + 1.28629i) q^{79} +(8.82843 - 15.2913i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-2.24264 - 3.88437i) q^{82} +4.75736 q^{83} -6.24264 q^{85} +(3.53553 + 6.12372i) q^{86} +(4.12132 - 7.13834i) q^{87} +(-6.00000 + 10.3923i) q^{88} +(-2.20711 - 3.82282i) q^{89} -6.24264 q^{90} +(-3.70711 - 6.42090i) q^{93} +(-3.12132 + 5.40629i) q^{94} +(-2.74264 + 4.75039i) q^{95} -13.7279 q^{97} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 6q^{5} - 8q^{6} + 2q^{9} + O(q^{10}) \) \( 4q - 6q^{5} - 8q^{6} + 2q^{9} - 4q^{10} - 4q^{13} - 8q^{15} + 8q^{16} + 6q^{19} - 24q^{22} + 6q^{23} - 8q^{24} - 12q^{25} + 12q^{29} + 12q^{30} + 2q^{31} - 12q^{33} - 8q^{34} + 4q^{37} - 12q^{38} + 8q^{40} + 24q^{41} - 20q^{43} + 6q^{45} - 8q^{46} - 6q^{47} + 48q^{50} - 4q^{51} + 6q^{53} - 16q^{54} - 24q^{55} - 24q^{57} - 8q^{58} - 12q^{59} - 12q^{61} - 24q^{62} + 32q^{64} + 6q^{65} + 12q^{67} - 16q^{69} - 24q^{71} + 10q^{73} + 12q^{74} + 24q^{75} + 8q^{78} - 14q^{79} + 24q^{80} + 10q^{81} + 8q^{82} + 36q^{83} - 8q^{85} + 8q^{87} - 24q^{88} - 6q^{89} - 8q^{90} - 12q^{93} - 4q^{94} + 6q^{95} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(3\) 0.707107 1.22474i 0.408248 0.707107i −0.586445 0.809989i \(-0.699473\pi\)
0.994694 + 0.102882i \(0.0328064\pi\)
\(4\) 0 0
\(5\) −2.20711 3.82282i −0.987048 1.70962i −0.632456 0.774597i \(-0.717953\pi\)
−0.354593 0.935021i \(-0.615380\pi\)
\(6\) −2.00000 −0.816497
\(7\) 0 0
\(8\) −2.82843 −1.00000
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −3.12132 + 5.40629i −0.987048 + 1.70962i
\(11\) 2.12132 3.67423i 0.639602 1.10782i −0.345918 0.938265i \(-0.612432\pi\)
0.985520 0.169559i \(-0.0542342\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −6.24264 −1.61184
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0.707107 1.22474i 0.171499 0.297044i −0.767445 0.641114i \(-0.778472\pi\)
0.938944 + 0.344070i \(0.111806\pi\)
\(18\) 0.707107 1.22474i 0.166667 0.288675i
\(19\) −0.621320 1.07616i −0.142541 0.246888i 0.785912 0.618338i \(-0.212194\pi\)
−0.928453 + 0.371451i \(0.878861\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −6.00000 −1.27920
\(23\) 0.0857864 + 0.148586i 0.0178877 + 0.0309824i 0.874831 0.484429i \(-0.160973\pi\)
−0.856943 + 0.515411i \(0.827639\pi\)
\(24\) −2.00000 + 3.46410i −0.408248 + 0.707107i
\(25\) −7.24264 + 12.5446i −1.44853 + 2.50892i
\(26\) 0.707107 + 1.22474i 0.138675 + 0.240192i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) 5.82843 1.08231 0.541156 0.840922i \(-0.317987\pi\)
0.541156 + 0.840922i \(0.317987\pi\)
\(30\) 4.41421 + 7.64564i 0.805921 + 1.39590i
\(31\) 2.62132 4.54026i 0.470803 0.815455i −0.528639 0.848847i \(-0.677298\pi\)
0.999442 + 0.0333918i \(0.0106309\pi\)
\(32\) 0 0
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 0 0
\(37\) 3.12132 + 5.40629i 0.513142 + 0.888788i 0.999884 + 0.0152420i \(0.00485188\pi\)
−0.486742 + 0.873546i \(0.661815\pi\)
\(38\) −0.878680 + 1.52192i −0.142541 + 0.246888i
\(39\) −0.707107 + 1.22474i −0.113228 + 0.196116i
\(40\) 6.24264 + 10.8126i 0.987048 + 1.70962i
\(41\) 3.17157 0.495316 0.247658 0.968847i \(-0.420339\pi\)
0.247658 + 0.968847i \(0.420339\pi\)
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) 2.20711 3.82282i 0.329016 0.569873i
\(46\) 0.121320 0.210133i 0.0178877 0.0309824i
\(47\) −2.20711 3.82282i −0.321940 0.557616i 0.658949 0.752188i \(-0.271001\pi\)
−0.980888 + 0.194572i \(0.937668\pi\)
\(48\) 5.65685 0.816497
\(49\) 0 0
\(50\) 20.4853 2.89706
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) 0 0
\(53\) 2.91421 5.04757i 0.400298 0.693337i −0.593464 0.804861i \(-0.702240\pi\)
0.993762 + 0.111524i \(0.0355733\pi\)
\(54\) −4.00000 6.92820i −0.544331 0.942809i
\(55\) −18.7279 −2.52527
\(56\) 0 0
\(57\) −1.75736 −0.232768
\(58\) −4.12132 7.13834i −0.541156 0.937309i
\(59\) −5.82843 + 10.0951i −0.758797 + 1.31427i 0.184668 + 0.982801i \(0.440879\pi\)
−0.943465 + 0.331473i \(0.892454\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) −7.41421 −0.941606
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) 2.20711 + 3.82282i 0.273758 + 0.474163i
\(66\) −4.24264 + 7.34847i −0.522233 + 0.904534i
\(67\) −1.24264 + 2.15232i −0.151813 + 0.262947i −0.931894 0.362731i \(-0.881844\pi\)
0.780081 + 0.625678i \(0.215178\pi\)
\(68\) 0 0
\(69\) 0.242641 0.0292105
\(70\) 0 0
\(71\) 1.07107 0.127112 0.0635562 0.997978i \(-0.479756\pi\)
0.0635562 + 0.997978i \(0.479756\pi\)
\(72\) −1.41421 2.44949i −0.166667 0.288675i
\(73\) 0.378680 0.655892i 0.0443211 0.0767664i −0.843014 0.537892i \(-0.819221\pi\)
0.887335 + 0.461125i \(0.152554\pi\)
\(74\) 4.41421 7.64564i 0.513142 0.888788i
\(75\) 10.2426 + 17.7408i 1.18272 + 2.04853i
\(76\) 0 0
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 0.742641 + 1.28629i 0.0835536 + 0.144719i 0.904774 0.425892i \(-0.140040\pi\)
−0.821220 + 0.570611i \(0.806706\pi\)
\(80\) 8.82843 15.2913i 0.987048 1.70962i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) −2.24264 3.88437i −0.247658 0.428957i
\(83\) 4.75736 0.522188 0.261094 0.965313i \(-0.415917\pi\)
0.261094 + 0.965313i \(0.415917\pi\)
\(84\) 0 0
\(85\) −6.24264 −0.677109
\(86\) 3.53553 + 6.12372i 0.381246 + 0.660338i
\(87\) 4.12132 7.13834i 0.441852 0.765310i
\(88\) −6.00000 + 10.3923i −0.639602 + 1.10782i
\(89\) −2.20711 3.82282i −0.233953 0.405218i 0.725015 0.688733i \(-0.241833\pi\)
−0.958968 + 0.283515i \(0.908499\pi\)
\(90\) −6.24264 −0.658032
\(91\) 0 0
\(92\) 0 0
\(93\) −3.70711 6.42090i −0.384409 0.665816i
\(94\) −3.12132 + 5.40629i −0.321940 + 0.557616i
\(95\) −2.74264 + 4.75039i −0.281389 + 0.487380i
\(96\) 0 0
\(97\) −13.7279 −1.39386 −0.696930 0.717139i \(-0.745451\pi\)
−0.696930 + 0.717139i \(0.745451\pi\)
\(98\) 0 0
\(99\) 4.24264 0.426401
\(100\) 0 0
\(101\) −0.878680 + 1.52192i −0.0874319 + 0.151436i −0.906425 0.422367i \(-0.861199\pi\)
0.818993 + 0.573803i \(0.194533\pi\)
\(102\) −1.41421 + 2.44949i −0.140028 + 0.242536i
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 2.82843 0.277350
\(105\) 0 0
\(106\) −8.24264 −0.800596
\(107\) −4.07107 7.05130i −0.393565 0.681675i 0.599352 0.800486i \(-0.295425\pi\)
−0.992917 + 0.118811i \(0.962092\pi\)
\(108\) 0 0
\(109\) 4.36396 7.55860i 0.417992 0.723983i −0.577746 0.816217i \(-0.696067\pi\)
0.995737 + 0.0922340i \(0.0294008\pi\)
\(110\) 13.2426 + 22.9369i 1.26264 + 2.18695i
\(111\) 8.82843 0.837957
\(112\) 0 0
\(113\) −20.3137 −1.91095 −0.955476 0.295067i \(-0.904658\pi\)
−0.955476 + 0.295067i \(0.904658\pi\)
\(114\) 1.24264 + 2.15232i 0.116384 + 0.201583i
\(115\) 0.378680 0.655892i 0.0353121 0.0611623i
\(116\) 0 0
\(117\) −0.500000 0.866025i −0.0462250 0.0800641i
\(118\) 16.4853 1.51759
\(119\) 0 0
\(120\) 17.6569 1.61184
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) −4.24264 + 7.34847i −0.384111 + 0.665299i
\(123\) 2.24264 3.88437i 0.202212 0.350242i
\(124\) 0 0
\(125\) 41.8701 3.74497
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −5.65685 9.79796i −0.500000 0.866025i
\(129\) −3.53553 + 6.12372i −0.311286 + 0.539164i
\(130\) 3.12132 5.40629i 0.273758 0.474163i
\(131\) −1.41421 2.44949i −0.123560 0.214013i 0.797609 0.603175i \(-0.206098\pi\)
−0.921169 + 0.389162i \(0.872765\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.51472 0.303625
\(135\) −12.4853 21.6251i −1.07456 1.86120i
\(136\) −2.00000 + 3.46410i −0.171499 + 0.297044i
\(137\) 3.70711 6.42090i 0.316720 0.548574i −0.663082 0.748547i \(-0.730752\pi\)
0.979802 + 0.199972i \(0.0640853\pi\)
\(138\) −0.171573 0.297173i −0.0146053 0.0252970i
\(139\) −2.24264 −0.190218 −0.0951092 0.995467i \(-0.530320\pi\)
−0.0951092 + 0.995467i \(0.530320\pi\)
\(140\) 0 0
\(141\) −6.24264 −0.525725
\(142\) −0.757359 1.31178i −0.0635562 0.110083i
\(143\) −2.12132 + 3.67423i −0.177394 + 0.307255i
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) −12.8640 22.2810i −1.06829 1.85034i
\(146\) −1.07107 −0.0886422
\(147\) 0 0
\(148\) 0 0
\(149\) −3.87868 6.71807i −0.317754 0.550366i 0.662265 0.749270i \(-0.269595\pi\)
−0.980019 + 0.198904i \(0.936262\pi\)
\(150\) 14.4853 25.0892i 1.18272 2.04853i
\(151\) 9.12132 15.7986i 0.742283 1.28567i −0.209171 0.977879i \(-0.567077\pi\)
0.951454 0.307792i \(-0.0995901\pi\)
\(152\) 1.75736 + 3.04384i 0.142541 + 0.246888i
\(153\) 1.41421 0.114332
\(154\) 0 0
\(155\) −23.1421 −1.85882
\(156\) 0 0
\(157\) 6.12132 10.6024i 0.488535 0.846167i −0.511378 0.859356i \(-0.670865\pi\)
0.999913 + 0.0131889i \(0.00419829\pi\)
\(158\) 1.05025 1.81909i 0.0835536 0.144719i
\(159\) −4.12132 7.13834i −0.326842 0.566107i
\(160\) 0 0
\(161\) 0 0
\(162\) −7.07107 −0.555556
\(163\) 4.24264 + 7.34847i 0.332309 + 0.575577i 0.982964 0.183797i \(-0.0588389\pi\)
−0.650655 + 0.759374i \(0.725506\pi\)
\(164\) 0 0
\(165\) −13.2426 + 22.9369i −1.03094 + 1.78564i
\(166\) −3.36396 5.82655i −0.261094 0.452228i
\(167\) −21.3848 −1.65480 −0.827402 0.561610i \(-0.810182\pi\)
−0.827402 + 0.561610i \(0.810182\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 4.41421 + 7.64564i 0.338555 + 0.586394i
\(171\) 0.621320 1.07616i 0.0475136 0.0822959i
\(172\) 0 0
\(173\) 0.363961 + 0.630399i 0.0276714 + 0.0479283i 0.879530 0.475844i \(-0.157857\pi\)
−0.851858 + 0.523773i \(0.824524\pi\)
\(174\) −11.6569 −0.883704
\(175\) 0 0
\(176\) 16.9706 1.27920
\(177\) 8.24264 + 14.2767i 0.619555 + 1.07310i
\(178\) −3.12132 + 5.40629i −0.233953 + 0.405218i
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 0 0
\(181\) 6.72792 0.500083 0.250041 0.968235i \(-0.419556\pi\)
0.250041 + 0.968235i \(0.419556\pi\)
\(182\) 0 0
\(183\) −8.48528 −0.627250
\(184\) −0.242641 0.420266i −0.0178877 0.0309824i
\(185\) 13.7782 23.8645i 1.01299 1.75455i
\(186\) −5.24264 + 9.08052i −0.384409 + 0.665816i
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) 0 0
\(189\) 0 0
\(190\) 7.75736 0.562778
\(191\) −10.4142 18.0379i −0.753546 1.30518i −0.946094 0.323892i \(-0.895008\pi\)
0.192548 0.981288i \(-0.438325\pi\)
\(192\) 5.65685 9.79796i 0.408248 0.707107i
\(193\) −1.24264 + 2.15232i −0.0894472 + 0.154927i −0.907278 0.420532i \(-0.861843\pi\)
0.817830 + 0.575459i \(0.195177\pi\)
\(194\) 9.70711 + 16.8132i 0.696930 + 1.20712i
\(195\) 6.24264 0.447045
\(196\) 0 0
\(197\) 23.6569 1.68548 0.842741 0.538320i \(-0.180941\pi\)
0.842741 + 0.538320i \(0.180941\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) 6.12132 10.6024i 0.433929 0.751587i −0.563279 0.826267i \(-0.690460\pi\)
0.997208 + 0.0746801i \(0.0237936\pi\)
\(200\) 20.4853 35.4815i 1.44853 2.50892i
\(201\) 1.75736 + 3.04384i 0.123955 + 0.214696i
\(202\) 2.48528 0.174864
\(203\) 0 0
\(204\) 0 0
\(205\) −7.00000 12.1244i −0.488901 0.846802i
\(206\) 5.65685 9.79796i 0.394132 0.682656i
\(207\) −0.0857864 + 0.148586i −0.00596257 + 0.0103275i
\(208\) −2.00000 3.46410i −0.138675 0.240192i
\(209\) −5.27208 −0.364677
\(210\) 0 0
\(211\) 17.9706 1.23714 0.618572 0.785728i \(-0.287711\pi\)
0.618572 + 0.785728i \(0.287711\pi\)
\(212\) 0 0
\(213\) 0.757359 1.31178i 0.0518934 0.0898820i
\(214\) −5.75736 + 9.97204i −0.393565 + 0.681675i
\(215\) 11.0355 + 19.1141i 0.752617 + 1.30357i
\(216\) −16.0000 −1.08866
\(217\) 0 0
\(218\) −12.3431 −0.835983
\(219\) −0.535534 0.927572i −0.0361880 0.0626795i
\(220\) 0 0
\(221\) −0.707107 + 1.22474i −0.0475651 + 0.0823853i
\(222\) −6.24264 10.8126i −0.418979 0.725692i
\(223\) 9.24264 0.618933 0.309466 0.950910i \(-0.399850\pi\)
0.309466 + 0.950910i \(0.399850\pi\)
\(224\) 0 0
\(225\) −14.4853 −0.965685
\(226\) 14.3640 + 24.8791i 0.955476 + 1.65493i
\(227\) −10.5858 + 18.3351i −0.702603 + 1.21694i 0.264946 + 0.964263i \(0.414646\pi\)
−0.967550 + 0.252681i \(0.918688\pi\)
\(228\) 0 0
\(229\) 10.7279 + 18.5813i 0.708921 + 1.22789i 0.965258 + 0.261300i \(0.0841511\pi\)
−0.256337 + 0.966588i \(0.582516\pi\)
\(230\) −1.07107 −0.0706241
\(231\) 0 0
\(232\) −16.4853 −1.08231
\(233\) 1.67157 + 2.89525i 0.109508 + 0.189674i 0.915571 0.402156i \(-0.131739\pi\)
−0.806063 + 0.591830i \(0.798406\pi\)
\(234\) −0.707107 + 1.22474i −0.0462250 + 0.0800641i
\(235\) −9.74264 + 16.8747i −0.635540 + 1.10079i
\(236\) 0 0
\(237\) 2.10051 0.136442
\(238\) 0 0
\(239\) 20.4853 1.32508 0.662541 0.749025i \(-0.269478\pi\)
0.662541 + 0.749025i \(0.269478\pi\)
\(240\) −12.4853 21.6251i −0.805921 1.39590i
\(241\) −11.1066 + 19.2372i −0.715439 + 1.23918i 0.247351 + 0.968926i \(0.420440\pi\)
−0.962790 + 0.270251i \(0.912893\pi\)
\(242\) −4.94975 + 8.57321i −0.318182 + 0.551107i
\(243\) 4.94975 + 8.57321i 0.317526 + 0.549972i
\(244\) 0 0
\(245\) 0 0
\(246\) −6.34315 −0.404424
\(247\) 0.621320 + 1.07616i 0.0395337 + 0.0684743i
\(248\) −7.41421 + 12.8418i −0.470803 + 0.815455i
\(249\) 3.36396 5.82655i 0.213182 0.369243i
\(250\) −29.6066 51.2801i −1.87249 3.24324i
\(251\) 19.4142 1.22541 0.612707 0.790310i \(-0.290081\pi\)
0.612707 + 0.790310i \(0.290081\pi\)
\(252\) 0 0
\(253\) 0.727922 0.0457641
\(254\) −1.41421 2.44949i −0.0887357 0.153695i
\(255\) −4.41421 + 7.64564i −0.276429 + 0.478789i
\(256\) 0 0
\(257\) 8.29289 + 14.3637i 0.517296 + 0.895984i 0.999798 + 0.0200887i \(0.00639488\pi\)
−0.482502 + 0.875895i \(0.660272\pi\)
\(258\) 10.0000 0.622573
\(259\) 0 0
\(260\) 0 0
\(261\) 2.91421 + 5.04757i 0.180385 + 0.312436i
\(262\) −2.00000 + 3.46410i −0.123560 + 0.214013i
\(263\) 15.9853 27.6873i 0.985695 1.70727i 0.346887 0.937907i \(-0.387239\pi\)
0.638808 0.769366i \(-0.279428\pi\)
\(264\) 8.48528 + 14.6969i 0.522233 + 0.904534i
\(265\) −25.7279 −1.58045
\(266\) 0 0
\(267\) −6.24264 −0.382043
\(268\) 0 0
\(269\) −7.41421 + 12.8418i −0.452053 + 0.782978i −0.998513 0.0545066i \(-0.982641\pi\)
0.546461 + 0.837485i \(0.315975\pi\)
\(270\) −17.6569 + 30.5826i −1.07456 + 1.86120i
\(271\) −10.0000 17.3205i −0.607457 1.05215i −0.991658 0.128897i \(-0.958856\pi\)
0.384201 0.923249i \(-0.374477\pi\)
\(272\) 5.65685 0.342997
\(273\) 0 0
\(274\) −10.4853 −0.633439
\(275\) 30.7279 + 53.2223i 1.85296 + 3.20943i
\(276\) 0 0
\(277\) −4.74264 + 8.21449i −0.284958 + 0.493561i −0.972599 0.232489i \(-0.925313\pi\)
0.687641 + 0.726051i \(0.258646\pi\)
\(278\) 1.58579 + 2.74666i 0.0951092 + 0.164734i
\(279\) 5.24264 0.313869
\(280\) 0 0
\(281\) −15.5563 −0.928014 −0.464007 0.885832i \(-0.653589\pi\)
−0.464007 + 0.885832i \(0.653589\pi\)
\(282\) 4.41421 + 7.64564i 0.262863 + 0.455291i
\(283\) −4.24264 + 7.34847i −0.252199 + 0.436821i −0.964131 0.265427i \(-0.914487\pi\)
0.711932 + 0.702248i \(0.247820\pi\)
\(284\) 0 0
\(285\) 3.87868 + 6.71807i 0.229753 + 0.397944i
\(286\) 6.00000 0.354787
\(287\) 0 0
\(288\) 0 0
\(289\) 7.50000 + 12.9904i 0.441176 + 0.764140i
\(290\) −18.1924 + 31.5101i −1.06829 + 1.85034i
\(291\) −9.70711 + 16.8132i −0.569041 + 0.985607i
\(292\) 0 0
\(293\) −21.3848 −1.24931 −0.624656 0.780900i \(-0.714761\pi\)
−0.624656 + 0.780900i \(0.714761\pi\)
\(294\) 0 0
\(295\) 51.4558 2.99588
\(296\) −8.82843 15.2913i −0.513142 0.888788i
\(297\) 12.0000 20.7846i 0.696311 1.20605i
\(298\) −5.48528 + 9.50079i −0.317754 + 0.550366i
\(299\) −0.0857864 0.148586i −0.00496116 0.00859298i
\(300\) 0 0
\(301\) 0 0
\(302\) −25.7990 −1.48457
\(303\) 1.24264 + 2.15232i 0.0713878 + 0.123647i
\(304\) 2.48528 4.30463i 0.142541 0.246888i
\(305\) −13.2426 + 22.9369i −0.758271 + 1.31336i
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 4.75736 0.271517 0.135758 0.990742i \(-0.456653\pi\)
0.135758 + 0.990742i \(0.456653\pi\)
\(308\) 0 0
\(309\) 11.3137 0.643614
\(310\) 16.3640 + 28.3432i 0.929411 + 1.60979i
\(311\) 2.29289 3.97141i 0.130018 0.225198i −0.793665 0.608355i \(-0.791830\pi\)
0.923683 + 0.383157i \(0.125163\pi\)
\(312\) 2.00000 3.46410i 0.113228 0.196116i
\(313\) 9.60660 + 16.6391i 0.542997 + 0.940499i 0.998730 + 0.0503822i \(0.0160439\pi\)
−0.455733 + 0.890117i \(0.650623\pi\)
\(314\) −17.3137 −0.977069
\(315\) 0 0
\(316\) 0 0
\(317\) −5.65685 9.79796i −0.317721 0.550308i 0.662291 0.749246i \(-0.269584\pi\)
−0.980012 + 0.198938i \(0.936251\pi\)
\(318\) −5.82843 + 10.0951i −0.326842 + 0.566107i
\(319\) 12.3640 21.4150i 0.692249 1.19901i
\(320\) −17.6569 30.5826i −0.987048 1.70962i
\(321\) −11.5147 −0.642689
\(322\) 0 0
\(323\) −1.75736 −0.0977821
\(324\) 0 0
\(325\) 7.24264 12.5446i 0.401749 0.695850i
\(326\) 6.00000 10.3923i 0.332309 0.575577i
\(327\) −6.17157 10.6895i −0.341289 0.591129i
\(328\) −8.97056 −0.495316
\(329\) 0 0
\(330\) 37.4558 2.06188
\(331\) 9.00000 + 15.5885i 0.494685 + 0.856819i 0.999981 0.00612670i \(-0.00195020\pi\)
−0.505296 + 0.862946i \(0.668617\pi\)
\(332\) 0 0
\(333\) −3.12132 + 5.40629i −0.171047 + 0.296263i
\(334\) 15.1213 + 26.1909i 0.827402 + 1.43310i
\(335\) 10.9706 0.599386
\(336\) 0 0
\(337\) −33.0000 −1.79762 −0.898812 0.438334i \(-0.855569\pi\)
−0.898812 + 0.438334i \(0.855569\pi\)
\(338\) −0.707107 1.22474i −0.0384615 0.0666173i
\(339\) −14.3640 + 24.8791i −0.780143 + 1.35125i
\(340\) 0 0
\(341\) −11.1213 19.2627i −0.602253 1.04313i
\(342\) −1.75736 −0.0950271
\(343\) 0 0
\(344\) 14.1421 0.762493
\(345\) −0.535534 0.927572i −0.0288322 0.0499388i
\(346\) 0.514719 0.891519i 0.0276714 0.0479283i
\(347\) −2.82843 + 4.89898i −0.151838 + 0.262991i −0.931903 0.362707i \(-0.881853\pi\)
0.780065 + 0.625698i \(0.215186\pi\)
\(348\) 0 0
\(349\) −0.272078 −0.0145640 −0.00728200 0.999973i \(-0.502318\pi\)
−0.00728200 + 0.999973i \(0.502318\pi\)
\(350\) 0 0
\(351\) −5.65685 −0.301941
\(352\) 0 0
\(353\) −4.24264 + 7.34847i −0.225813 + 0.391120i −0.956563 0.291526i \(-0.905837\pi\)
0.730750 + 0.682645i \(0.239170\pi\)
\(354\) 11.6569 20.1903i 0.619555 1.07310i
\(355\) −2.36396 4.09450i −0.125466 0.217314i
\(356\) 0 0
\(357\) 0 0
\(358\) −12.7279 −0.672692
\(359\) 4.05025 + 7.01524i 0.213764 + 0.370250i 0.952890 0.303317i \(-0.0980943\pi\)
−0.739125 + 0.673568i \(0.764761\pi\)
\(360\) −6.24264 + 10.8126i −0.329016 + 0.569873i
\(361\) 8.72792 15.1172i 0.459364 0.795642i
\(362\) −4.75736 8.23999i −0.250041 0.433084i
\(363\) −9.89949 −0.519589
\(364\) 0 0
\(365\) −3.34315 −0.174988
\(366\) 6.00000 + 10.3923i 0.313625 + 0.543214i
\(367\) −0.878680 + 1.52192i −0.0458667 + 0.0794435i −0.888047 0.459752i \(-0.847938\pi\)
0.842181 + 0.539196i \(0.181272\pi\)
\(368\) −0.343146 + 0.594346i −0.0178877 + 0.0309824i
\(369\) 1.58579 + 2.74666i 0.0825527 + 0.142986i
\(370\) −38.9706 −2.02598
\(371\) 0 0
\(372\) 0 0
\(373\) 4.24264 + 7.34847i 0.219676 + 0.380489i 0.954709 0.297542i \(-0.0961668\pi\)
−0.735033 + 0.678031i \(0.762833\pi\)
\(374\) −4.24264 + 7.34847i −0.219382 + 0.379980i
\(375\) 29.6066 51.2801i 1.52888 2.64809i
\(376\) 6.24264 + 10.8126i 0.321940 + 0.557616i
\(377\) −5.82843 −0.300179
\(378\) 0 0
\(379\) 32.2426 1.65619 0.828097 0.560585i \(-0.189424\pi\)
0.828097 + 0.560585i \(0.189424\pi\)
\(380\) 0 0
\(381\) 1.41421 2.44949i 0.0724524 0.125491i
\(382\) −14.7279 + 25.5095i −0.753546 + 1.30518i
\(383\) 1.75736 + 3.04384i 0.0897969 + 0.155533i 0.907425 0.420214i \(-0.138045\pi\)
−0.817628 + 0.575746i \(0.804712\pi\)
\(384\) −16.0000 −0.816497
\(385\) 0 0
\(386\) 3.51472 0.178894
\(387\) −2.50000 4.33013i −0.127082 0.220113i
\(388\) 0 0
\(389\) −9.17157 + 15.8856i −0.465017 + 0.805433i −0.999202 0.0399341i \(-0.987285\pi\)
0.534185 + 0.845368i \(0.320619\pi\)
\(390\) −4.41421 7.64564i −0.223522 0.387152i
\(391\) 0.242641 0.0122709
\(392\) 0 0
\(393\) −4.00000 −0.201773
\(394\) −16.7279 28.9736i −0.842741 1.45967i
\(395\) 3.27817 5.67796i 0.164943 0.285689i
\(396\) 0 0
\(397\) −12.1066 20.9692i −0.607613 1.05242i −0.991633 0.129092i \(-0.958794\pi\)
0.384020 0.923325i \(-0.374539\pi\)
\(398\) −17.3137 −0.867858
\(399\) 0 0
\(400\) −57.9411 −2.89706
\(401\) −8.82843 15.2913i −0.440871 0.763610i 0.556884 0.830590i \(-0.311997\pi\)
−0.997754 + 0.0669802i \(0.978664\pi\)
\(402\) 2.48528 4.30463i 0.123955 0.214696i
\(403\) −2.62132 + 4.54026i −0.130577 + 0.226166i
\(404\) 0 0
\(405\) −22.0711 −1.09672
\(406\) 0 0
\(407\) 26.4853 1.31283
\(408\) 2.82843 + 4.89898i 0.140028 + 0.242536i
\(409\) 2.62132 4.54026i 0.129616 0.224501i −0.793912 0.608033i \(-0.791959\pi\)
0.923528 + 0.383531i \(0.125292\pi\)
\(410\) −9.89949 + 17.1464i −0.488901 + 0.846802i
\(411\) −5.24264 9.08052i −0.258600 0.447909i
\(412\) 0 0
\(413\) 0 0
\(414\) 0.242641 0.0119251
\(415\) −10.5000 18.1865i −0.515425 0.892742i
\(416\) 0 0
\(417\) −1.58579 + 2.74666i −0.0776563 + 0.134505i
\(418\) 3.72792 + 6.45695i 0.182339 + 0.315820i
\(419\) 32.8701 1.60581 0.802904 0.596109i \(-0.203287\pi\)
0.802904 + 0.596109i \(0.203287\pi\)
\(420\) 0 0
\(421\) −18.7279 −0.912743 −0.456372 0.889789i \(-0.650851\pi\)
−0.456372 + 0.889789i \(0.650851\pi\)
\(422\) −12.7071 22.0094i −0.618572 1.07140i
\(423\) 2.20711 3.82282i 0.107313 0.185872i
\(424\) −8.24264 + 14.2767i −0.400298 + 0.693337i
\(425\) 10.2426 + 17.7408i 0.496841 + 0.860554i
\(426\) −2.14214 −0.103787
\(427\) 0 0
\(428\) 0 0
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 15.6066 27.0314i 0.752617 1.30357i
\(431\) 11.8284 20.4874i 0.569755 0.986845i −0.426835 0.904330i \(-0.640371\pi\)
0.996590 0.0825154i \(-0.0262953\pi\)
\(432\) 11.3137 + 19.5959i 0.544331 + 0.942809i
\(433\) 8.97056 0.431098 0.215549 0.976493i \(-0.430846\pi\)
0.215549 + 0.976493i \(0.430846\pi\)
\(434\) 0 0
\(435\) −36.3848 −1.74452
\(436\) 0 0
\(437\) 0.106602 0.184640i 0.00509945 0.00883251i
\(438\) −0.757359 + 1.31178i −0.0361880 + 0.0626795i
\(439\) 8.75736 + 15.1682i 0.417966 + 0.723938i 0.995735 0.0922622i \(-0.0294098\pi\)
−0.577769 + 0.816200i \(0.696076\pi\)
\(440\) 52.9706 2.52527
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) 13.1569 + 22.7883i 0.625101 + 1.08271i 0.988521 + 0.151081i \(0.0482756\pi\)
−0.363420 + 0.931625i \(0.618391\pi\)
\(444\) 0 0
\(445\) −9.74264 + 16.8747i −0.461845 + 0.799940i
\(446\) −6.53553 11.3199i −0.309466 0.536012i
\(447\) −10.9706 −0.518890
\(448\) 0 0
\(449\) 26.8284 1.26611 0.633056 0.774106i \(-0.281800\pi\)
0.633056 + 0.774106i \(0.281800\pi\)
\(450\) 10.2426 + 17.7408i 0.482843 + 0.836308i
\(451\) 6.72792 11.6531i 0.316805 0.548723i
\(452\) 0 0
\(453\) −12.8995 22.3426i −0.606071 1.04975i
\(454\) 29.9411 1.40521
\(455\) 0 0
\(456\) 4.97056 0.232768
\(457\) −17.6066 30.4955i −0.823602 1.42652i −0.902983 0.429676i \(-0.858628\pi\)
0.0793809 0.996844i \(-0.474706\pi\)
\(458\) 15.1716 26.2779i 0.708921 1.22789i
\(459\) 4.00000 6.92820i 0.186704 0.323381i
\(460\) 0 0
\(461\) 3.17157 0.147715 0.0738574 0.997269i \(-0.476469\pi\)
0.0738574 + 0.997269i \(0.476469\pi\)
\(462\) 0 0
\(463\) 4.24264 0.197172 0.0985861 0.995129i \(-0.468568\pi\)
0.0985861 + 0.995129i \(0.468568\pi\)
\(464\) 11.6569 + 20.1903i 0.541156 + 0.937309i
\(465\) −16.3640 + 28.3432i −0.758861 + 1.31438i
\(466\) 2.36396 4.09450i 0.109508 0.189674i
\(467\) −7.94975 13.7694i −0.367870 0.637170i 0.621362 0.783524i \(-0.286580\pi\)
−0.989232 + 0.146353i \(0.953246\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 27.5563 1.27108
\(471\) −8.65685 14.9941i −0.398887 0.690892i
\(472\) 16.4853 28.5533i 0.758797 1.31427i
\(473\) −10.6066 + 18.3712i −0.487692 + 0.844707i
\(474\) −1.48528 2.57258i −0.0682212 0.118163i
\(475\) 18.0000 0.825897
\(476\) 0 0
\(477\) 5.82843 0.266865
\(478\) −14.4853 25.0892i −0.662541 1.14756i
\(479\) −18.1066 + 31.3616i −0.827312 + 1.43295i 0.0728279 + 0.997345i \(0.476798\pi\)
−0.900140 + 0.435601i \(0.856536\pi\)
\(480\) 0 0
\(481\) −3.12132 5.40629i −0.142320 0.246505i
\(482\) 31.4142 1.43088
\(483\) 0 0
\(484\) 0 0
\(485\) 30.2990 + 52.4794i 1.37581 + 2.38297i
\(486\) 7.00000 12.1244i 0.317526 0.549972i
\(487\) −19.7279 + 34.1698i −0.893957 + 1.54838i −0.0588679 + 0.998266i \(0.518749\pi\)
−0.835090 + 0.550114i \(0.814584\pi\)
\(488\) 8.48528 + 14.6969i 0.384111 + 0.665299i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −28.6274 −1.29194 −0.645969 0.763364i \(-0.723546\pi\)
−0.645969 + 0.763364i \(0.723546\pi\)
\(492\) 0 0
\(493\) 4.12132 7.13834i 0.185615 0.321494i
\(494\) 0.878680 1.52192i 0.0395337 0.0684743i
\(495\) −9.36396 16.2189i −0.420879 0.728983i
\(496\) 20.9706 0.941606
\(497\) 0 0
\(498\) −9.51472 −0.426365
\(499\) 19.3640 + 33.5394i 0.866850 + 1.50143i 0.865198 + 0.501430i \(0.167192\pi\)
0.00165145 + 0.999999i \(0.499474\pi\)
\(500\) 0 0
\(501\) −15.1213 + 26.1909i −0.675571 + 1.17012i
\(502\) −13.7279 23.7775i −0.612707 1.06124i
\(503\) 16.6274 0.741380 0.370690 0.928757i \(-0.379121\pi\)
0.370690 + 0.928757i \(0.379121\pi\)
\(504\) 0 0
\(505\) 7.75736 0.345198
\(506\) −0.514719 0.891519i −0.0228820 0.0396328i
\(507\) 0.707107 1.22474i 0.0314037 0.0543928i
\(508\) 0 0
\(509\) 12.4497 + 21.5636i 0.551825 + 0.955790i 0.998143 + 0.0609149i \(0.0194018\pi\)
−0.446318 + 0.894875i \(0.647265\pi\)
\(510\) 12.4853 0.552858
\(511\) 0 0
\(512\) −22.6274 −1.00000
\(513\) −3.51472 6.08767i −0.155179 0.268777i
\(514\) 11.7279 20.3134i 0.517296 0.895984i
\(515\) 17.6569 30.5826i 0.778054 1.34763i
\(516\) 0 0
\(517\) −18.7279 −0.823653
\(518\) 0 0
\(519\) 1.02944 0.0451873
\(520\) −6.24264 10.8126i −0.273758 0.474163i
\(521\) 8.82843 15.2913i 0.386780 0.669923i −0.605234 0.796048i \(-0.706920\pi\)
0.992014 + 0.126124i \(0.0402538\pi\)
\(522\) 4.12132 7.13834i 0.180385 0.312436i
\(523\) 1.48528 + 2.57258i 0.0649468 + 0.112491i 0.896670 0.442699i \(-0.145979\pi\)
−0.831724 + 0.555190i \(0.812646\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −45.2132 −1.97139
\(527\) −3.70711 6.42090i −0.161484 0.279699i
\(528\) 12.0000 20.7846i 0.522233 0.904534i
\(529\) 11.4853 19.8931i 0.499360 0.864917i
\(530\) 18.1924 + 31.5101i 0.790227 + 1.36871i
\(531\) −11.6569 −0.505864
\(532\) 0 0
\(533\) −3.17157 −0.137376
\(534\) 4.41421 + 7.64564i 0.191022 + 0.330859i
\(535\) −17.9706 + 31.1259i −0.776935 + 1.34569i
\(536\) 3.51472 6.08767i 0.151813 0.262947i
\(537\) −6.36396 11.0227i −0.274625 0.475665i
\(538\) 20.9706 0.904105
\(539\) 0 0
\(540\) 0 0
\(541\) −17.6066 30.4955i −0.756967 1.31111i −0.944391 0.328826i \(-0.893347\pi\)
0.187424 0.982279i \(-0.439986\pi\)
\(542\) −14.1421 + 24.4949i −0.607457 + 1.05215i
\(543\) 4.75736 8.23999i 0.204158 0.353612i
\(544\) 0 0
\(545\) −38.5269 −1.65031
\(546\) 0 0
\(547\) 18.5147 0.791632 0.395816 0.918330i \(-0.370462\pi\)
0.395816 + 0.918330i \(0.370462\pi\)
\(548\) 0 0
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 43.4558 75.2677i 1.85296 3.20943i
\(551\) −3.62132 6.27231i −0.154273 0.267209i
\(552\) −0.686292 −0.0292105
\(553\) 0 0
\(554\) 13.4142 0.569915
\(555\) −19.4853 33.7495i −0.827104 1.43259i
\(556\) 0 0
\(557\) −6.00000 + 10.3923i −0.254228 + 0.440336i −0.964686 0.263404i \(-0.915155\pi\)
0.710457 + 0.703740i \(0.248488\pi\)
\(558\) −3.70711 6.42090i −0.156934 0.271818i
\(559\) 5.00000 0.211477
\(560\) 0 0
\(561\) −8.48528 −0.358249
\(562\) 11.0000 + 19.0526i 0.464007 + 0.803684i
\(563\) 8.82843 15.2913i 0.372074 0.644451i −0.617811 0.786327i \(-0.711980\pi\)
0.989884 + 0.141876i \(0.0453135\pi\)
\(564\) 0 0
\(565\) 44.8345 + 77.6557i 1.88620 + 3.26700i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) −3.02944 −0.127112
\(569\) 11.5711 + 20.0417i 0.485084 + 0.840191i 0.999853 0.0171383i \(-0.00545554\pi\)
−0.514769 + 0.857329i \(0.672122\pi\)
\(570\) 5.48528 9.50079i 0.229753 0.397944i
\(571\) 4.22792 7.32298i 0.176933 0.306457i −0.763896 0.645340i \(-0.776716\pi\)
0.940829 + 0.338883i \(0.110049\pi\)
\(572\) 0 0
\(573\) −29.4558 −1.23054
\(574\) 0 0
\(575\) −2.48528 −0.103643
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) −13.4853 + 23.3572i −0.561400 + 0.972373i 0.435975 + 0.899959i \(0.356404\pi\)
−0.997375 + 0.0724139i \(0.976930\pi\)
\(578\) 10.6066 18.3712i 0.441176 0.764140i
\(579\) 1.75736 + 3.04384i 0.0730334 + 0.126497i
\(580\) 0 0
\(581\) 0 0
\(582\) 27.4558 1.13808
\(583\) −12.3640 21.4150i −0.512063 0.886919i
\(584\) −1.07107 + 1.85514i −0.0443211 + 0.0767664i
\(585\) −2.20711 + 3.82282i −0.0912526 + 0.158054i
\(586\) 15.1213 + 26.1909i 0.624656 + 1.08194i
\(587\) 24.5563 1.01355 0.506775 0.862079i \(-0.330838\pi\)
0.506775 + 0.862079i \(0.330838\pi\)
\(588\) 0 0
\(589\) −6.51472 −0.268434
\(590\) −36.3848 63.0203i −1.49794 2.59450i
\(591\) 16.7279 28.9736i 0.688095 1.19182i
\(592\) −12.4853 + 21.6251i −0.513142 + 0.888788i
\(593\) −15.2782 26.4626i −0.627399 1.08669i −0.988072 0.153995i \(-0.950786\pi\)
0.360672 0.932693i \(-0.382547\pi\)
\(594\) −33.9411 −1.39262
\(595\) 0 0
\(596\) 0 0
\(597\) −8.65685 14.9941i −0.354301 0.613668i
\(598\) −0.121320 + 0.210133i −0.00496116 + 0.00859298i
\(599\) −5.39949 + 9.35220i −0.220617 + 0.382121i −0.954996 0.296620i \(-0.904141\pi\)
0.734378 + 0.678740i \(0.237474\pi\)
\(600\) −28.9706 50.1785i −1.18272 2.04853i
\(601\) −5.02944 −0.205155 −0.102578 0.994725i \(-0.532709\pi\)
−0.102578 + 0.994725i \(0.532709\pi\)
\(602\) 0 0
\(603\) −2.48528 −0.101208
\(604\) 0 0
\(605\) −15.4497 + 26.7597i −0.628122 + 1.08794i
\(606\) 1.75736 3.04384i 0.0713878 0.123647i
\(607\) 0.636039 + 1.10165i 0.0258160 + 0.0447147i 0.878645 0.477476i \(-0.158448\pi\)
−0.852829 + 0.522191i \(0.825115\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 37.4558 1.51654
\(611\) 2.20711 + 3.82282i 0.0892900 + 0.154655i
\(612\) 0 0
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) −3.36396 5.82655i −0.135758 0.235140i
\(615\) −19.7990 −0.798372
\(616\) 0 0
\(617\) 23.6569 0.952389 0.476195 0.879340i \(-0.342016\pi\)
0.476195 + 0.879340i \(0.342016\pi\)
\(618\) −8.00000 13.8564i −0.321807 0.557386i
\(619\) 16.4853 28.5533i 0.662599 1.14766i −0.317331 0.948315i \(-0.602787\pi\)
0.979930 0.199341i \(-0.0638801\pi\)
\(620\) 0 0
\(621\) 0.485281 + 0.840532i 0.0194737 + 0.0337294i
\(622\) −6.48528 −0.260036
\(623\) 0 0
\(624\) −5.65685 −0.226455
\(625\) −56.1985 97.3386i −2.24794 3.89355i
\(626\) 13.5858 23.5313i 0.542997 0.940499i
\(627\) −3.72792 + 6.45695i −0.148879 + 0.257866i
\(628\) 0 0
\(629\) 8.82843 0.352012
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −2.10051 3.63818i −0.0835536 0.144719i
\(633\) 12.7071 22.0094i 0.505062 0.874793i
\(634\) −8.00000 + 13.8564i −0.317721 + 0.550308i
\(635\) −4.41421 7.64564i −0.175173 0.303408i
\(636\) 0 0
\(637\) 0 0
\(638\) −34.9706 −1.38450
\(639\) 0.535534 + 0.927572i 0.0211854 + 0.0366942i
\(640\) −24.9706 + 43.2503i −0.987048 + 1.70962i
\(641\) −13.3284 + 23.0855i −0.526441 + 0.911823i 0.473084 + 0.881017i \(0.343141\pi\)
−0.999525 + 0.0308057i \(0.990193\pi\)
\(642\) 8.14214 + 14.1026i 0.321344 + 0.556585i
\(643\) 4.48528 0.176882 0.0884411 0.996081i \(-0.471811\pi\)
0.0884411 + 0.996081i \(0.471811\pi\)
\(644\) 0 0
\(645\) 31.2132 1.22902
\(646\) 1.24264 + 2.15232i 0.0488910 + 0.0846818i
\(647\) 25.2635 43.7576i 0.993209 1.72029i 0.395847 0.918316i \(-0.370451\pi\)
0.597362 0.801972i \(-0.296216\pi\)
\(648\) −7.07107 + 12.2474i −0.277778 + 0.481125i
\(649\) 24.7279 + 42.8300i 0.970656 + 1.68123i
\(650\) −20.4853 −0.803499
\(651\) 0 0
\(652\) 0 0
\(653\) 2.65685 + 4.60181i 0.103971 + 0.180083i 0.913317 0.407249i \(-0.133512\pi\)
−0.809346 + 0.587331i \(0.800179\pi\)
\(654\) −8.72792 + 15.1172i −0.341289 + 0.591129i
\(655\) −6.24264 + 10.8126i −0.243920 + 0.422482i
\(656\) 6.34315 + 10.9867i 0.247658 + 0.428957i
\(657\) 0.757359 0.0295474
\(658\) 0 0
\(659\) −26.6569 −1.03840 −0.519202 0.854652i \(-0.673771\pi\)
−0.519202 + 0.854652i \(0.673771\pi\)
\(660\) 0 0
\(661\) 9.62132 16.6646i 0.374226 0.648178i −0.615985 0.787758i \(-0.711242\pi\)
0.990211 + 0.139580i \(0.0445751\pi\)
\(662\) 12.7279 22.0454i 0.494685 0.856819i
\(663\) 1.00000 + 1.73205i 0.0388368 + 0.0672673i
\(664\) −13.4558 −0.522188
\(665\) 0 0
\(666\) 8.82843 0.342095
\(667\) 0.500000 + 0.866025i 0.0193601 + 0.0335326i
\(668\) 0 0
\(669\) 6.53553 11.3199i 0.252678 0.437652i
\(670\) −7.75736 13.4361i −0.299693 0.519083i
\(671\) −25.4558 −0.982712
\(672\) 0 0
\(673\) 40.9411 1.57816 0.789082 0.614288i \(-0.210557\pi\)
0.789082 + 0.614288i \(0.210557\pi\)
\(674\) 23.3345 + 40.4166i 0.898812 + 1.55679i
\(675\) −40.9706 + 70.9631i −1.57696 + 2.73137i
\(676\) 0 0
\(677\) −14.6777 25.4225i −0.564109 0.977065i −0.997132 0.0756822i \(-0.975887\pi\)
0.433023 0.901383i \(-0.357447\pi\)
\(678\) 40.6274 1.56029
\(679\) 0 0
\(680\) 17.6569 0.677109
\(681\) 14.9706 + 25.9298i 0.573673 + 0.993631i
\(682\) −15.7279 + 27.2416i −0.602253 + 1.04313i
\(683\) 13.4142 23.2341i 0.513281 0.889028i −0.486601 0.873624i \(-0.661763\pi\)
0.999881 0.0154036i \(-0.00490332\pi\)
\(684\) 0 0
\(685\) −32.7279 −1.25047
\(686\) 0 0
\(687\) 30.3431 1.15766
\(688\) −10.0000 17.3205i −0.381246 0.660338i
\(689\) −2.91421 + 5.04757i −0.111023 + 0.192297i
\(690\) −0.757359 + 1.31178i −0.0288322 + 0.0499388i
\(691\) 15.3492 + 26.5857i 0.583913 + 1.01137i 0.995010 + 0.0997750i \(0.0318123\pi\)
−0.411097 + 0.911591i \(0.634854\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 8.00000 0.303676
\(695\) 4.94975 + 8.57321i 0.187755 + 0.325201i
\(696\) −11.6569 + 20.1903i −0.441852 + 0.765310i
\(697\) 2.24264 3.88437i 0.0849461 0.147131i
\(698\) 0.192388 + 0.333226i 0.00728200 + 0.0126128i
\(699\) 4.72792 0.178826
\(700\) 0 0
\(701\) 28.7990 1.08772 0.543861 0.839175i \(-0.316962\pi\)
0.543861 + 0.839175i \(0.316962\pi\)
\(702\) 4.00000 + 6.92820i 0.150970 + 0.261488i
\(703\) 3.87868 6.71807i 0.146287 0.253377i
\(704\) 16.9706 29.3939i 0.639602 1.10782i
\(705\) 13.7782 + 23.8645i 0.518916 + 0.898789i
\(706\) 12.0000 0.451626
\(707\) 0 0
\(708\) 0 0
\(709\) 12.3640 + 21.4150i 0.464338 + 0.804258i 0.999171 0.0407002i \(-0.0129589\pi\)
−0.534833 + 0.844958i \(0.679626\pi\)
\(710\) −3.34315 + 5.79050i −0.125466 + 0.217314i
\(711\) −0.742641 + 1.28629i −0.0278512 + 0.0482397i
\(712\) 6.24264 + 10.8126i 0.233953 + 0.405218i
\(713\) 0.899495 0.0336864
\(714\) 0 0
\(715\) 18.7279 0.700385
\(716\) 0 0
\(717\) 14.4853 25.0892i 0.540963 0.936975i
\(718\) 5.72792 9.92105i 0.213764 0.370250i
\(719\) 5.12132 + 8.87039i 0.190993 + 0.330810i 0.945580 0.325391i \(-0.105496\pi\)
−0.754587 + 0.656201i \(0.772163\pi\)
\(720\) 17.6569 0.658032
\(721\) 0 0
\(722\) −24.6863 −0.918729
\(723\) 15.7071 + 27.2055i 0.584154 + 1.01178i
\(724\) 0 0
\(725\) −42.2132 + 73.1154i −1.56776 + 2.71544i
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) 42.0000 1.55769 0.778847 0.627214i \(-0.215805\pi\)
0.778847 + 0.627214i \(0.215805\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 2.36396 + 4.09450i 0.0874941 + 0.151544i
\(731\) −3.53553 + 6.12372i −0.130766 + 0.226494i
\(732\) 0 0
\(733\) −21.3492 36.9780i −0.788552 1.36581i −0.926854 0.375422i \(-0.877498\pi\)
0.138302 0.990390i \(-0.455836\pi\)
\(734\) 2.48528 0.0917334
\(735\) 0 0
\(736\) 0 0
\(737\) 5.27208 + 9.13151i 0.194199 + 0.336363i
\(738\) 2.24264 3.88437i 0.0825527 0.142986i
\(739\) −20.8492 + 36.1119i −0.766952 + 1.32840i 0.172257 + 0.985052i \(0.444894\pi\)
−0.939208 + 0.343347i \(0.888439\pi\)
\(740\) 0 0
\(741\) 1.75736 0.0645582
\(742\) 0 0
\(743\) −18.3431 −0.672945 −0.336472 0.941693i \(-0.609234\pi\)
−0.336472 + 0.941693i \(0.609234\pi\)
\(744\) 10.4853 + 18.1610i 0.384409 + 0.665816i
\(745\) −17.1213 + 29.6550i −0.627277 + 1.08648i
\(746\) 6.00000 10.3923i 0.219676 0.380489i
\(747\) 2.37868 + 4.11999i 0.0870313 + 0.150743i
\(748\) 0 0
\(749\) 0 0
\(750\) −83.7401 −3.05776
\(751\) 0.742641 + 1.28629i 0.0270993 + 0.0469374i 0.879257 0.476348i \(-0.158040\pi\)
−0.852158 + 0.523285i \(0.824706\pi\)
\(752\) 8.82843 15.2913i 0.321940 0.557616i
\(753\) 13.7279 23.7775i 0.500273 0.866499i
\(754\) 4.12132 + 7.13834i 0.150090 + 0.259963i
\(755\) −80.5269 −2.93067
\(756\) 0 0
\(757\) 4.51472 0.164090 0.0820451 0.996629i \(-0.473855\pi\)
0.0820451 + 0.996629i \(0.473855\pi\)
\(758\) −22.7990 39.4890i −0.828097 1.43431i
\(759\) 0.514719 0.891519i 0.0186831 0.0323601i
\(760\) 7.75736 13.4361i 0.281389 0.487380i
\(761\) −21.6213 37.4492i −0.783772 1.35753i −0.929730 0.368243i \(-0.879960\pi\)
0.145958 0.989291i \(-0.453374\pi\)
\(762\) −4.00000 −0.144905
\(763\) 0 0
\(764\) 0 0
\(765\) −3.12132 5.40629i −0.112852 0.195465i
\(766\) 2.48528 4.30463i 0.0897969 0.155533i
\(767\) 5.82843 10.0951i 0.210452 0.364514i
\(768\) 0 0
\(769\) 9.78680 0.352921 0.176460 0.984308i \(-0.443535\pi\)
0.176460 + 0.984308i \(0.443535\pi\)
\(770\) 0 0
\(771\) 23.4558 0.844742
\(772\) 0 0
\(773\) 13.5858 23.5313i 0.488647 0.846361i −0.511268 0.859421i \(-0.670824\pi\)
0.999915 + 0.0130603i \(0.00415735\pi\)
\(774\) −3.53553 + 6.12372i −0.127082 + 0.220113i
\(775\) 37.9706 + 65.7669i 1.36394 + 2.36242i
\(776\) 38.8284 1.39386
\(777\) 0 0
\(778\) 25.9411 0.930034
\(779\) −1.97056 3.41311i −0.0706027 0.122288i
\(780\) 0 0
\(781\) 2.27208 3.93535i 0.0813013 0.140818i
\(782\) −0.171573 0.297173i −0.00613543 0.0106269i
\(783\) 32.9706 1.17827
\(784\) 0 0
\(785\) −54.0416 −1.92883
\(786\) 2.82843 + 4.89898i 0.100887 + 0.174741i
\(787\) 16.6213 28.7890i 0.592486 1.02622i −0.401410 0.915898i \(-0.631480\pi\)
0.993896 0.110318i \(-0.0351868\pi\)