Properties

Label 1183.2.e.i.170.7
Level $1183$
Weight $2$
Character 1183.170
Analytic conductor $9.446$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 11 x^{14} + 85 x^{12} + 334 x^{10} + 952 x^{8} + 1050 x^{6} + 853 x^{4} + 93 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 170.7
Root \(1.06275 + 1.84073i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.i.508.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.06275 - 1.84073i) q^{2} +(0.0894272 + 0.154892i) q^{3} +(-1.25885 - 2.18040i) q^{4} +(-1.80301 + 3.12291i) q^{5} +0.380153 q^{6} +(-2.35320 + 1.20931i) q^{7} -1.10038 q^{8} +(1.48401 - 2.57037i) q^{9} +O(q^{10})\) \(q+(1.06275 - 1.84073i) q^{2} +(0.0894272 + 0.154892i) q^{3} +(-1.25885 - 2.18040i) q^{4} +(-1.80301 + 3.12291i) q^{5} +0.380153 q^{6} +(-2.35320 + 1.20931i) q^{7} -1.10038 q^{8} +(1.48401 - 2.57037i) q^{9} +(3.83229 + 6.63772i) q^{10} +(-1.99618 - 3.45748i) q^{11} +(0.225152 - 0.389974i) q^{12} +(-0.274848 + 5.61680i) q^{14} -0.644954 q^{15} +(1.34828 - 2.33529i) q^{16} +(-2.39458 - 4.14753i) q^{17} +(-3.15424 - 5.46330i) q^{18} +(1.57530 - 2.72850i) q^{19} +9.07892 q^{20} +(-0.397753 - 0.256349i) q^{21} -8.48572 q^{22} +(1.08943 - 1.88694i) q^{23} +(-0.0984042 - 0.170441i) q^{24} +(-4.00171 - 6.93117i) q^{25} +1.06740 q^{27} +(5.59912 + 3.60858i) q^{28} -6.57198 q^{29} +(-0.685421 + 1.18718i) q^{30} +(-0.743358 - 1.28753i) q^{31} +(-3.96614 - 6.86956i) q^{32} +(0.357025 - 0.618386i) q^{33} -10.1793 q^{34} +(0.466298 - 9.52925i) q^{35} -7.47259 q^{36} +(-2.48252 + 4.29984i) q^{37} +(-3.34828 - 5.79939i) q^{38} +(1.98401 - 3.43640i) q^{40} -2.11931 q^{41} +(-0.894578 + 0.459722i) q^{42} +1.43145 q^{43} +(-5.02580 + 8.70494i) q^{44} +(5.35136 + 9.26883i) q^{45} +(-2.31557 - 4.01068i) q^{46} +(-0.509464 + 0.882417i) q^{47} +0.482292 q^{48} +(4.07515 - 5.69150i) q^{49} -17.0112 q^{50} +(0.428281 - 0.741804i) q^{51} +(-3.01771 - 5.22682i) q^{53} +(1.13438 - 1.96480i) q^{54} +14.3966 q^{55} +(2.58943 - 1.33070i) q^{56} +0.563498 q^{57} +(-6.98434 + 12.0972i) q^{58} +(2.45161 + 4.24631i) q^{59} +(0.811902 + 1.40626i) q^{60} +(1.01771 - 1.76272i) q^{61} -3.16000 q^{62} +(-0.383795 + 7.84323i) q^{63} -11.4669 q^{64} +(-0.758854 - 1.31437i) q^{66} +(-1.95545 - 3.38694i) q^{67} +(-6.02885 + 10.4423i) q^{68} +0.389698 q^{69} +(-17.0452 - 10.9855i) q^{70} -8.80684 q^{71} +(-1.63297 + 2.82840i) q^{72} +(-1.54439 - 2.67497i) q^{73} +(5.27656 + 9.13927i) q^{74} +(0.715724 - 1.23967i) q^{75} -7.93228 q^{76} +(8.87858 + 5.72217i) q^{77} +(-0.984006 + 1.70435i) q^{79} +(4.86194 + 8.42112i) q^{80} +(-4.35656 - 7.54579i) q^{81} +(-2.25229 + 3.90108i) q^{82} +7.66020 q^{83} +(-0.0582290 + 1.18997i) q^{84} +17.2698 q^{85} +(1.52126 - 2.63491i) q^{86} +(-0.587714 - 1.01795i) q^{87} +(2.19656 + 3.80456i) q^{88} +(6.39960 - 11.0844i) q^{89} +22.7485 q^{90} -5.48572 q^{92} +(0.132953 - 0.230281i) q^{93} +(1.08286 + 1.87557i) q^{94} +(5.68057 + 9.83903i) q^{95} +(0.709362 - 1.22865i) q^{96} +1.35900 q^{97} +(-6.14567 - 13.5499i) q^{98} -11.8494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + 6q^{10} - 18q^{12} - 26q^{14} + 2q^{16} - 8q^{17} - 36q^{22} + 12q^{23} + 32q^{27} - 16q^{29} - 38q^{30} + 56q^{36} - 34q^{38} - 4q^{40} + 16q^{42} - 16q^{43} + 36q^{48} - 40q^{49} - 16q^{51} - 20q^{53} + 24q^{55} + 36q^{56} - 12q^{61} - 44q^{62} - 88q^{64} + 2q^{66} - 2q^{68} + 56q^{69} + 42q^{74} - 8q^{75} + 76q^{77} + 20q^{79} - 24q^{81} + 16q^{82} - 68q^{87} - 4q^{88} + 216q^{90} + 12q^{92} - 26q^{94} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06275 1.84073i 0.751474 1.30159i −0.195634 0.980677i \(-0.562676\pi\)
0.947108 0.320915i \(-0.103990\pi\)
\(3\) 0.0894272 + 0.154892i 0.0516308 + 0.0894272i 0.890686 0.454620i \(-0.150225\pi\)
−0.839055 + 0.544047i \(0.816891\pi\)
\(4\) −1.25885 2.18040i −0.629427 1.09020i
\(5\) −1.80301 + 3.12291i −0.806332 + 1.39661i 0.109056 + 0.994036i \(0.465217\pi\)
−0.915388 + 0.402572i \(0.868116\pi\)
\(6\) 0.380153 0.155197
\(7\) −2.35320 + 1.20931i −0.889428 + 0.457076i
\(8\) −1.10038 −0.389044
\(9\) 1.48401 2.57037i 0.494669 0.856791i
\(10\) 3.83229 + 6.63772i 1.21188 + 2.09903i
\(11\) −1.99618 3.45748i −0.601871 1.04247i −0.992538 0.121939i \(-0.961089\pi\)
0.390667 0.920532i \(-0.372244\pi\)
\(12\) 0.225152 0.389974i 0.0649957 0.112576i
\(13\) 0 0
\(14\) −0.274848 + 5.61680i −0.0734563 + 1.50115i
\(15\) −0.644954 −0.166526
\(16\) 1.34828 2.33529i 0.337070 0.583823i
\(17\) −2.39458 4.14753i −0.580771 1.00592i −0.995388 0.0959284i \(-0.969418\pi\)
0.414618 0.909996i \(-0.363915\pi\)
\(18\) −3.15424 5.46330i −0.743461 1.28771i
\(19\) 1.57530 2.72850i 0.361398 0.625960i −0.626793 0.779186i \(-0.715633\pi\)
0.988191 + 0.153226i \(0.0489662\pi\)
\(20\) 9.07892 2.03011
\(21\) −0.397753 0.256349i −0.0867969 0.0559398i
\(22\) −8.48572 −1.80916
\(23\) 1.08943 1.88694i 0.227161 0.393455i −0.729804 0.683656i \(-0.760389\pi\)
0.956966 + 0.290201i \(0.0937222\pi\)
\(24\) −0.0984042 0.170441i −0.0200867 0.0347911i
\(25\) −4.00171 6.93117i −0.800343 1.38623i
\(26\) 0 0
\(27\) 1.06740 0.205422
\(28\) 5.59912 + 3.60858i 1.05813 + 0.681958i
\(29\) −6.57198 −1.22039 −0.610193 0.792253i \(-0.708908\pi\)
−0.610193 + 0.792253i \(0.708908\pi\)
\(30\) −0.685421 + 1.18718i −0.125140 + 0.216749i
\(31\) −0.743358 1.28753i −0.133511 0.231248i 0.791517 0.611148i \(-0.209292\pi\)
−0.925028 + 0.379900i \(0.875958\pi\)
\(32\) −3.96614 6.86956i −0.701121 1.21438i
\(33\) 0.357025 0.618386i 0.0621502 0.107647i
\(34\) −10.1793 −1.74574
\(35\) 0.466298 9.52925i 0.0788187 1.61074i
\(36\) −7.47259 −1.24543
\(37\) −2.48252 + 4.29984i −0.408123 + 0.706890i −0.994679 0.103019i \(-0.967150\pi\)
0.586556 + 0.809908i \(0.300483\pi\)
\(38\) −3.34828 5.79939i −0.543163 0.940786i
\(39\) 0 0
\(40\) 1.98401 3.43640i 0.313699 0.543342i
\(41\) −2.11931 −0.330981 −0.165490 0.986211i \(-0.552921\pi\)
−0.165490 + 0.986211i \(0.552921\pi\)
\(42\) −0.894578 + 0.459722i −0.138036 + 0.0709367i
\(43\) 1.43145 0.218294 0.109147 0.994026i \(-0.465188\pi\)
0.109147 + 0.994026i \(0.465188\pi\)
\(44\) −5.02580 + 8.70494i −0.757667 + 1.31232i
\(45\) 5.35136 + 9.26883i 0.797734 + 1.38172i
\(46\) −2.31557 4.01068i −0.341412 0.591342i
\(47\) −0.509464 + 0.882417i −0.0743129 + 0.128714i −0.900787 0.434261i \(-0.857010\pi\)
0.826474 + 0.562974i \(0.190343\pi\)
\(48\) 0.482292 0.0696129
\(49\) 4.07515 5.69150i 0.582164 0.813072i
\(50\) −17.0112 −2.40575
\(51\) 0.428281 0.741804i 0.0599713 0.103873i
\(52\) 0 0
\(53\) −3.01771 5.22682i −0.414514 0.717959i 0.580863 0.814001i \(-0.302715\pi\)
−0.995377 + 0.0960417i \(0.969382\pi\)
\(54\) 1.13438 1.96480i 0.154369 0.267376i
\(55\) 14.3966 1.94123
\(56\) 2.58943 1.33070i 0.346027 0.177823i
\(57\) 0.563498 0.0746371
\(58\) −6.98434 + 12.0972i −0.917089 + 1.58844i
\(59\) 2.45161 + 4.24631i 0.319172 + 0.552823i 0.980316 0.197437i \(-0.0632618\pi\)
−0.661143 + 0.750260i \(0.729928\pi\)
\(60\) 0.811902 + 1.40626i 0.104816 + 0.181547i
\(61\) 1.01771 1.76272i 0.130304 0.225693i −0.793490 0.608584i \(-0.791738\pi\)
0.923794 + 0.382890i \(0.125071\pi\)
\(62\) −3.16000 −0.401320
\(63\) −0.383795 + 7.84323i −0.0483537 + 0.988155i
\(64\) −11.4669 −1.43336
\(65\) 0 0
\(66\) −0.758854 1.31437i −0.0934085 0.161788i
\(67\) −1.95545 3.38694i −0.238896 0.413781i 0.721501 0.692413i \(-0.243452\pi\)
−0.960398 + 0.278632i \(0.910119\pi\)
\(68\) −6.02885 + 10.4423i −0.731105 + 1.26631i
\(69\) 0.389698 0.0469141
\(70\) −17.0452 10.9855i −2.03729 1.31302i
\(71\) −8.80684 −1.04518 −0.522590 0.852584i \(-0.675034\pi\)
−0.522590 + 0.852584i \(0.675034\pi\)
\(72\) −1.63297 + 2.82840i −0.192448 + 0.333330i
\(73\) −1.54439 2.67497i −0.180757 0.313081i 0.761381 0.648304i \(-0.224522\pi\)
−0.942139 + 0.335223i \(0.891188\pi\)
\(74\) 5.27656 + 9.13927i 0.613388 + 1.06242i
\(75\) 0.715724 1.23967i 0.0826447 0.143145i
\(76\) −7.93228 −0.909895
\(77\) 8.87858 + 5.72217i 1.01181 + 0.652102i
\(78\) 0 0
\(79\) −0.984006 + 1.70435i −0.110709 + 0.191754i −0.916056 0.401049i \(-0.868646\pi\)
0.805347 + 0.592803i \(0.201979\pi\)
\(80\) 4.86194 + 8.42112i 0.543581 + 0.941510i
\(81\) −4.35656 7.54579i −0.484062 0.838421i
\(82\) −2.25229 + 3.90108i −0.248724 + 0.430802i
\(83\) 7.66020 0.840816 0.420408 0.907335i \(-0.361887\pi\)
0.420408 + 0.907335i \(0.361887\pi\)
\(84\) −0.0582290 + 1.18997i −0.00635330 + 0.129836i
\(85\) 17.2698 1.87318
\(86\) 1.52126 2.63491i 0.164042 0.284129i
\(87\) −0.587714 1.01795i −0.0630095 0.109136i
\(88\) 2.19656 + 3.80456i 0.234154 + 0.405567i
\(89\) 6.39960 11.0844i 0.678356 1.17495i −0.297120 0.954840i \(-0.596026\pi\)
0.975476 0.220107i \(-0.0706406\pi\)
\(90\) 22.7485 2.39791
\(91\) 0 0
\(92\) −5.48572 −0.571926
\(93\) 0.132953 0.230281i 0.0137866 0.0238790i
\(94\) 1.08286 + 1.87557i 0.111689 + 0.193450i
\(95\) 5.68057 + 9.83903i 0.582814 + 1.00946i
\(96\) 0.709362 1.22865i 0.0723989 0.125399i
\(97\) 1.35900 0.137986 0.0689930 0.997617i \(-0.478021\pi\)
0.0689930 + 0.997617i \(0.478021\pi\)
\(98\) −6.14567 13.5499i −0.620806 1.36874i
\(99\) −11.8494 −1.19091
\(100\) −10.0751 + 17.4507i −1.00751 + 1.74507i
\(101\) −2.14400 3.71353i −0.213336 0.369510i 0.739420 0.673244i \(-0.235100\pi\)
−0.952757 + 0.303735i \(0.901766\pi\)
\(102\) −0.910307 1.57670i −0.0901338 0.156116i
\(103\) −7.21744 + 12.5010i −0.711155 + 1.23176i 0.253269 + 0.967396i \(0.418494\pi\)
−0.964424 + 0.264361i \(0.914839\pi\)
\(104\) 0 0
\(105\) 1.51771 0.779948i 0.148113 0.0761151i
\(106\) −12.8282 −1.24599
\(107\) 4.85942 8.41677i 0.469778 0.813680i −0.529625 0.848232i \(-0.677667\pi\)
0.999403 + 0.0345525i \(0.0110006\pi\)
\(108\) −1.34371 2.32737i −0.129298 0.223951i
\(109\) 3.32428 + 5.75782i 0.318408 + 0.551499i 0.980156 0.198227i \(-0.0635185\pi\)
−0.661748 + 0.749726i \(0.730185\pi\)
\(110\) 15.2999 26.5001i 1.45878 2.52669i
\(111\) −0.888018 −0.0842869
\(112\) −0.348694 + 7.12591i −0.0329485 + 0.673335i
\(113\) 17.5434 1.65035 0.825173 0.564880i \(-0.191078\pi\)
0.825173 + 0.564880i \(0.191078\pi\)
\(114\) 0.598855 1.03725i 0.0560879 0.0971471i
\(115\) 3.92850 + 6.80437i 0.366335 + 0.634511i
\(116\) 8.27316 + 14.3295i 0.768144 + 1.33046i
\(117\) 0 0
\(118\) 10.4217 0.959399
\(119\) 10.6506 + 6.86421i 0.976337 + 0.629241i
\(120\) 0.709696 0.0647861
\(121\) −2.46946 + 4.27724i −0.224497 + 0.388840i
\(122\) −2.16313 3.74665i −0.195840 0.339206i
\(123\) −0.189524 0.328265i −0.0170888 0.0295987i
\(124\) −1.87156 + 3.24163i −0.168071 + 0.291107i
\(125\) 10.8304 0.968704
\(126\) 14.0294 + 9.04182i 1.24984 + 0.805510i
\(127\) 19.5143 1.73162 0.865809 0.500375i \(-0.166805\pi\)
0.865809 + 0.500375i \(0.166805\pi\)
\(128\) −4.25407 + 7.36826i −0.376010 + 0.651269i
\(129\) 0.128010 + 0.221720i 0.0112707 + 0.0195214i
\(130\) 0 0
\(131\) −9.53713 + 16.5188i −0.833263 + 1.44325i 0.0621741 + 0.998065i \(0.480197\pi\)
−0.895437 + 0.445188i \(0.853137\pi\)
\(132\) −1.79777 −0.156476
\(133\) −0.407406 + 8.32573i −0.0353266 + 0.721933i
\(134\) −8.31259 −0.718098
\(135\) −1.92455 + 3.33341i −0.165638 + 0.286894i
\(136\) 2.63495 + 4.56387i 0.225945 + 0.391349i
\(137\) 3.21445 + 5.56759i 0.274629 + 0.475672i 0.970042 0.242939i \(-0.0781116\pi\)
−0.695412 + 0.718611i \(0.744778\pi\)
\(138\) 0.414149 0.717328i 0.0352547 0.0610630i
\(139\) −2.42854 −0.205986 −0.102993 0.994682i \(-0.532842\pi\)
−0.102993 + 0.994682i \(0.532842\pi\)
\(140\) −21.3646 + 10.9792i −1.80564 + 0.927913i
\(141\) −0.182240 −0.0153473
\(142\) −9.35942 + 16.2110i −0.785425 + 1.36040i
\(143\) 0 0
\(144\) −4.00171 6.93117i −0.333476 0.577598i
\(145\) 11.8494 20.5237i 0.984036 1.70440i
\(146\) −6.56518 −0.543338
\(147\) 1.24600 + 0.122234i 0.102768 + 0.0100817i
\(148\) 12.5005 1.02753
\(149\) 0.0576764 0.0998984i 0.00472503 0.00818400i −0.863653 0.504086i \(-0.831829\pi\)
0.868378 + 0.495902i \(0.165163\pi\)
\(150\) −1.52126 2.63491i −0.124211 0.215139i
\(151\) −5.90155 10.2218i −0.480262 0.831838i 0.519482 0.854481i \(-0.326125\pi\)
−0.999744 + 0.0226438i \(0.992792\pi\)
\(152\) −1.73343 + 3.00239i −0.140600 + 0.243526i
\(153\) −14.2143 −1.14916
\(154\) 19.9686 10.2619i 1.60912 0.826924i
\(155\) 5.36114 0.430617
\(156\) 0 0
\(157\) 6.57343 + 11.3855i 0.524617 + 0.908663i 0.999589 + 0.0286625i \(0.00912481\pi\)
−0.474972 + 0.880001i \(0.657542\pi\)
\(158\) 2.09149 + 3.62257i 0.166390 + 0.288197i
\(159\) 0.539730 0.934840i 0.0428034 0.0741377i
\(160\) 28.6040 2.26135
\(161\) −0.281749 + 5.75782i −0.0222049 + 0.453780i
\(162\) −18.5197 −1.45504
\(163\) −9.32424 + 16.1501i −0.730331 + 1.26497i 0.226411 + 0.974032i \(0.427301\pi\)
−0.956742 + 0.290938i \(0.906033\pi\)
\(164\) 2.66790 + 4.62094i 0.208328 + 0.360835i
\(165\) 1.28744 + 2.22992i 0.100227 + 0.173599i
\(166\) 8.14084 14.1003i 0.631852 1.09440i
\(167\) 0.972672 0.0752676 0.0376338 0.999292i \(-0.488018\pi\)
0.0376338 + 0.999292i \(0.488018\pi\)
\(168\) 0.437681 + 0.282082i 0.0337678 + 0.0217631i
\(169\) 0 0
\(170\) 18.3534 31.7891i 1.40764 2.43811i
\(171\) −4.67550 8.09821i −0.357545 0.619286i
\(172\) −1.80198 3.12113i −0.137400 0.237984i
\(173\) −1.22855 + 2.12791i −0.0934050 + 0.161782i −0.908942 0.416923i \(-0.863108\pi\)
0.815537 + 0.578705i \(0.196442\pi\)
\(174\) −2.49836 −0.189400
\(175\) 17.7988 + 11.4712i 1.34546 + 0.867138i
\(176\) −10.7656 −0.811491
\(177\) −0.438481 + 0.759471i −0.0329583 + 0.0570854i
\(178\) −13.6023 23.5598i −1.01953 1.76588i
\(179\) −7.23629 12.5336i −0.540866 0.936807i −0.998855 0.0478492i \(-0.984763\pi\)
0.457989 0.888958i \(-0.348570\pi\)
\(180\) 13.4732 23.3362i 1.00423 1.73938i
\(181\) 9.17885 0.682259 0.341129 0.940016i \(-0.389191\pi\)
0.341129 + 0.940016i \(0.389191\pi\)
\(182\) 0 0
\(183\) 0.364043 0.0269108
\(184\) −1.19879 + 2.07636i −0.0883758 + 0.153071i
\(185\) −8.95202 15.5053i −0.658165 1.13998i
\(186\) −0.282590 0.489460i −0.0207205 0.0358889i
\(187\) −9.56002 + 16.5584i −0.699098 + 1.21087i
\(188\) 2.56536 0.187098
\(189\) −2.51182 + 1.29082i −0.182708 + 0.0938935i
\(190\) 24.1480 1.75188
\(191\) −8.79202 + 15.2282i −0.636168 + 1.10188i 0.350098 + 0.936713i \(0.386148\pi\)
−0.986266 + 0.165162i \(0.947185\pi\)
\(192\) −1.02545 1.77613i −0.0740054 0.128181i
\(193\) −9.87791 17.1090i −0.711028 1.23154i −0.964472 0.264186i \(-0.914897\pi\)
0.253444 0.967350i \(-0.418437\pi\)
\(194\) 1.44428 2.50156i 0.103693 0.179601i
\(195\) 0 0
\(196\) −17.5398 1.72068i −1.25284 0.122905i
\(197\) −7.66020 −0.545767 −0.272883 0.962047i \(-0.587977\pi\)
−0.272883 + 0.962047i \(0.587977\pi\)
\(198\) −12.5929 + 21.8115i −0.894935 + 1.55007i
\(199\) 3.27171 + 5.66677i 0.231925 + 0.401706i 0.958375 0.285514i \(-0.0921642\pi\)
−0.726449 + 0.687220i \(0.758831\pi\)
\(200\) 4.40342 + 7.62694i 0.311369 + 0.539306i
\(201\) 0.349741 0.605769i 0.0246688 0.0427277i
\(202\) −9.11412 −0.641267
\(203\) 15.4652 7.94755i 1.08545 0.557809i
\(204\) −2.15657 −0.150990
\(205\) 3.82115 6.61842i 0.266880 0.462250i
\(206\) 15.3406 + 26.5707i 1.06883 + 1.85127i
\(207\) −3.23343 5.60047i −0.224739 0.389259i
\(208\) 0 0
\(209\) −12.5783 −0.870060
\(210\) 0.177265 3.62257i 0.0122324 0.249981i
\(211\) 20.0452 1.37997 0.689983 0.723825i \(-0.257618\pi\)
0.689983 + 0.723825i \(0.257618\pi\)
\(212\) −7.59771 + 13.1596i −0.521813 + 0.903806i
\(213\) −0.787571 1.36411i −0.0539635 0.0934674i
\(214\) −10.3287 17.8898i −0.706052 1.22292i
\(215\) −2.58092 + 4.47028i −0.176017 + 0.304871i
\(216\) −1.17455 −0.0799183
\(217\) 3.30630 + 2.13088i 0.224446 + 0.144654i
\(218\) 14.1314 0.957102
\(219\) 0.276221 0.478429i 0.0186653 0.0323293i
\(220\) −18.1232 31.3902i −1.22186 2.11633i
\(221\) 0 0
\(222\) −0.943736 + 1.63460i −0.0633394 + 0.109707i
\(223\) −27.7139 −1.85586 −0.927931 0.372752i \(-0.878414\pi\)
−0.927931 + 0.372752i \(0.878414\pi\)
\(224\) 17.6406 + 11.3692i 1.17866 + 0.759636i
\(225\) −23.7543 −1.58362
\(226\) 18.6442 32.2927i 1.24019 2.14808i
\(227\) 5.68555 + 9.84766i 0.377363 + 0.653612i 0.990678 0.136227i \(-0.0434976\pi\)
−0.613315 + 0.789839i \(0.710164\pi\)
\(228\) −0.709362 1.22865i −0.0469786 0.0813694i
\(229\) −4.35556 + 7.54406i −0.287824 + 0.498525i −0.973290 0.229579i \(-0.926265\pi\)
0.685466 + 0.728104i \(0.259598\pi\)
\(230\) 16.7000 1.10116
\(231\) −0.0923344 + 1.88694i −0.00607516 + 0.124152i
\(232\) 7.23170 0.474784
\(233\) 1.68228 2.91380i 0.110210 0.190889i −0.805645 0.592399i \(-0.798181\pi\)
0.915855 + 0.401510i \(0.131514\pi\)
\(234\) 0 0
\(235\) −1.83714 3.18202i −0.119842 0.207572i
\(236\) 6.17244 10.6910i 0.401791 0.695923i
\(237\) −0.351987 −0.0228640
\(238\) 23.9540 12.3099i 1.55271 0.797934i
\(239\) 19.8798 1.28592 0.642958 0.765902i \(-0.277707\pi\)
0.642958 + 0.765902i \(0.277707\pi\)
\(240\) −0.869579 + 1.50615i −0.0561311 + 0.0972219i
\(241\) −9.43595 16.3435i −0.607823 1.05278i −0.991599 0.129354i \(-0.958710\pi\)
0.383776 0.923426i \(-0.374624\pi\)
\(242\) 5.24882 + 9.09123i 0.337407 + 0.584406i
\(243\) 2.38030 4.12280i 0.152696 0.264477i
\(244\) −5.12458 −0.328068
\(245\) 10.4265 + 22.9882i 0.666125 + 1.46866i
\(246\) −0.805663 −0.0513672
\(247\) 0 0
\(248\) 0.817978 + 1.41678i 0.0519417 + 0.0899656i
\(249\) 0.685030 + 1.18651i 0.0434120 + 0.0751918i
\(250\) 11.5100 19.9359i 0.727956 1.26086i
\(251\) −9.79601 −0.618319 −0.309159 0.951010i \(-0.600048\pi\)
−0.309159 + 0.951010i \(0.600048\pi\)
\(252\) 17.5845 9.03666i 1.10772 0.569256i
\(253\) −8.69877 −0.546887
\(254\) 20.7388 35.9206i 1.30127 2.25386i
\(255\) 1.54439 + 2.67497i 0.0967136 + 0.167513i
\(256\) −2.42488 4.20002i −0.151555 0.262501i
\(257\) −10.4697 + 18.1341i −0.653083 + 1.13117i 0.329287 + 0.944230i \(0.393192\pi\)
−0.982371 + 0.186944i \(0.940142\pi\)
\(258\) 0.544170 0.0338785
\(259\) 0.642031 13.1205i 0.0398939 0.815271i
\(260\) 0 0
\(261\) −9.75285 + 16.8924i −0.603686 + 1.04562i
\(262\) 20.2711 + 35.1105i 1.25235 + 2.16914i
\(263\) 3.69340 + 6.39715i 0.227745 + 0.394465i 0.957139 0.289628i \(-0.0935316\pi\)
−0.729395 + 0.684093i \(0.760198\pi\)
\(264\) −0.392865 + 0.680462i −0.0241792 + 0.0418795i
\(265\) 21.7639 1.33694
\(266\) 14.8924 + 9.59806i 0.913114 + 0.588495i
\(267\) 2.28919 0.140096
\(268\) −4.92326 + 8.52733i −0.300736 + 0.520890i
\(269\) −11.3946 19.7360i −0.694740 1.20332i −0.970268 0.242032i \(-0.922186\pi\)
0.275529 0.961293i \(-0.411147\pi\)
\(270\) 4.09060 + 7.08513i 0.248946 + 0.431187i
\(271\) −2.08316 + 3.60814i −0.126543 + 0.219179i −0.922335 0.386391i \(-0.873722\pi\)
0.795792 + 0.605570i \(0.207055\pi\)
\(272\) −12.9143 −0.783042
\(273\) 0 0
\(274\) 13.6646 0.825507
\(275\) −15.9763 + 27.6717i −0.963406 + 1.66867i
\(276\) −0.490572 0.849696i −0.0295290 0.0511457i
\(277\) −0.388551 0.672989i −0.0233457 0.0404360i 0.854116 0.520082i \(-0.174099\pi\)
−0.877462 + 0.479646i \(0.840765\pi\)
\(278\) −2.58092 + 4.47028i −0.154793 + 0.268110i
\(279\) −4.41259 −0.264175
\(280\) −0.513106 + 10.4858i −0.0306639 + 0.626648i
\(281\) −11.8988 −0.709824 −0.354912 0.934900i \(-0.615489\pi\)
−0.354912 + 0.934900i \(0.615489\pi\)
\(282\) −0.193674 + 0.335454i −0.0115331 + 0.0199760i
\(283\) 7.95202 + 13.7733i 0.472698 + 0.818738i 0.999512 0.0312434i \(-0.00994670\pi\)
−0.526813 + 0.849981i \(0.676613\pi\)
\(284\) 11.0865 + 19.2024i 0.657864 + 1.13945i
\(285\) −1.01599 + 1.75975i −0.0601823 + 0.104239i
\(286\) 0 0
\(287\) 4.98717 2.56290i 0.294383 0.151283i
\(288\) −23.5431 −1.38729
\(289\) −2.96801 + 5.14075i −0.174589 + 0.302397i
\(290\) −25.1857 43.6229i −1.47896 2.56163i
\(291\) 0.121532 + 0.210500i 0.00712433 + 0.0123397i
\(292\) −3.88833 + 6.73478i −0.227547 + 0.394123i
\(293\) −6.73698 −0.393579 −0.196789 0.980446i \(-0.563051\pi\)
−0.196789 + 0.980446i \(0.563051\pi\)
\(294\) 1.54918 2.16364i 0.0903500 0.126186i
\(295\) −17.6811 −1.02944
\(296\) 2.73172 4.73148i 0.158778 0.275011i
\(297\) −2.13073 3.69054i −0.123638 0.214147i
\(298\) −0.122591 0.212333i −0.00710148 0.0123001i
\(299\) 0 0
\(300\) −3.60397 −0.208075
\(301\) −3.36849 + 1.73106i −0.194157 + 0.0997768i
\(302\) −25.0874 −1.44362
\(303\) 0.383465 0.664180i 0.0220295 0.0381562i
\(304\) −4.24789 7.35756i −0.243633 0.421985i
\(305\) 3.66988 + 6.35642i 0.210137 + 0.363968i
\(306\) −15.1061 + 26.1646i −0.863561 + 1.49573i
\(307\) 14.7179 0.839996 0.419998 0.907525i \(-0.362031\pi\)
0.419998 + 0.907525i \(0.362031\pi\)
\(308\) 1.29978 26.5622i 0.0740617 1.51352i
\(309\) −2.58174 −0.146870
\(310\) 5.69752 9.86840i 0.323597 0.560487i
\(311\) −14.3289 24.8184i −0.812517 1.40732i −0.911097 0.412191i \(-0.864764\pi\)
0.0985808 0.995129i \(-0.468570\pi\)
\(312\) 0 0
\(313\) 16.4125 28.4274i 0.927692 1.60681i 0.140518 0.990078i \(-0.455123\pi\)
0.787174 0.616732i \(-0.211544\pi\)
\(314\) 27.9435 1.57694
\(315\) −23.8017 15.3400i −1.34108 0.864312i
\(316\) 4.95488 0.278734
\(317\) 5.20605 9.01715i 0.292401 0.506453i −0.681976 0.731375i \(-0.738879\pi\)
0.974377 + 0.224921i \(0.0722125\pi\)
\(318\) −1.14719 1.98699i −0.0643313 0.111425i
\(319\) 13.1188 + 22.7225i 0.734515 + 1.27222i
\(320\) 20.6749 35.8100i 1.15576 2.00184i
\(321\) 1.73826 0.0970201
\(322\) 10.2992 + 6.63772i 0.573949 + 0.369905i
\(323\) −15.0887 −0.839558
\(324\) −10.9686 + 18.9981i −0.609364 + 1.05545i
\(325\) 0 0
\(326\) 19.8186 + 34.3268i 1.09765 + 1.90118i
\(327\) −0.594562 + 1.02981i −0.0328793 + 0.0569487i
\(328\) 2.33205 0.128766
\(329\) 0.131758 2.69261i 0.00726406 0.148448i
\(330\) 5.47290 0.301273
\(331\) −2.23007 + 3.86260i −0.122576 + 0.212308i −0.920783 0.390076i \(-0.872449\pi\)
0.798207 + 0.602383i \(0.205782\pi\)
\(332\) −9.64307 16.7023i −0.529232 0.916657i
\(333\) 7.36813 + 12.7620i 0.403771 + 0.699352i
\(334\) 1.03370 1.79043i 0.0565617 0.0979677i
\(335\) 14.1028 0.770519
\(336\) −1.13493 + 0.583240i −0.0619156 + 0.0318183i
\(337\) −10.7949 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(338\) 0 0
\(339\) 1.56886 + 2.71734i 0.0852087 + 0.147586i
\(340\) −21.7402 37.6551i −1.17903 2.04214i
\(341\) −2.96775 + 5.14030i −0.160713 + 0.278363i
\(342\) −19.8755 −1.07474
\(343\) −2.70687 + 18.3214i −0.146157 + 0.989261i
\(344\) −1.57514 −0.0849259
\(345\) −0.702630 + 1.21699i −0.0378283 + 0.0655206i
\(346\) 2.61127 + 4.52286i 0.140383 + 0.243150i
\(347\) 2.03516 + 3.52499i 0.109253 + 0.189232i 0.915468 0.402391i \(-0.131821\pi\)
−0.806215 + 0.591623i \(0.798487\pi\)
\(348\) −1.47969 + 2.56290i −0.0793198 + 0.137386i
\(349\) 23.8727 1.27788 0.638938 0.769258i \(-0.279374\pi\)
0.638938 + 0.769258i \(0.279374\pi\)
\(350\) 40.0309 20.5718i 2.13974 1.09961i
\(351\) 0 0
\(352\) −15.8343 + 27.4257i −0.843969 + 1.46180i
\(353\) −13.0420 22.5894i −0.694154 1.20231i −0.970465 0.241242i \(-0.922445\pi\)
0.276311 0.961068i \(-0.410888\pi\)
\(354\) 0.931987 + 1.61425i 0.0495346 + 0.0857964i
\(355\) 15.8788 27.5030i 0.842762 1.45971i
\(356\) −32.2246 −1.70790
\(357\) −0.110763 + 2.26354i −0.00586217 + 0.119799i
\(358\) −30.7613 −1.62579
\(359\) 11.4472 19.8271i 0.604160 1.04644i −0.388024 0.921649i \(-0.626842\pi\)
0.992184 0.124786i \(-0.0398244\pi\)
\(360\) −5.88855 10.1993i −0.310354 0.537549i
\(361\) 4.53687 + 7.85809i 0.238783 + 0.413584i
\(362\) 9.75478 16.8958i 0.512700 0.888022i
\(363\) −0.883349 −0.0463638
\(364\) 0 0
\(365\) 11.1382 0.583002
\(366\) 0.386885 0.670104i 0.0202228 0.0350269i
\(367\) 9.08003 + 15.7271i 0.473974 + 0.820946i 0.999556 0.0297964i \(-0.00948589\pi\)
−0.525582 + 0.850743i \(0.676153\pi\)
\(368\) −2.93771 5.08826i −0.153139 0.265244i
\(369\) −3.14507 + 5.44742i −0.163726 + 0.283581i
\(370\) −38.0548 −1.97838
\(371\) 13.4221 + 8.65045i 0.696842 + 0.449109i
\(372\) −0.669473 −0.0347105
\(373\) 7.93457 13.7431i 0.410836 0.711590i −0.584145 0.811649i \(-0.698570\pi\)
0.994981 + 0.100060i \(0.0319034\pi\)
\(374\) 20.3197 + 35.1948i 1.05071 + 1.81988i
\(375\) 0.968536 + 1.67755i 0.0500150 + 0.0866285i
\(376\) 0.560605 0.970997i 0.0289110 0.0500754i
\(377\) 0 0
\(378\) −0.293375 + 5.99540i −0.0150896 + 0.308370i
\(379\) 27.7634 1.42611 0.713055 0.701108i \(-0.247311\pi\)
0.713055 + 0.701108i \(0.247311\pi\)
\(380\) 14.3020 24.7718i 0.733678 1.27077i
\(381\) 1.74511 + 3.02262i 0.0894048 + 0.154854i
\(382\) 18.6873 + 32.3674i 0.956128 + 1.65606i
\(383\) 13.1234 22.7304i 0.670576 1.16147i −0.307165 0.951656i \(-0.599380\pi\)
0.977741 0.209815i \(-0.0672863\pi\)
\(384\) −1.52172 −0.0776548
\(385\) −33.8780 + 17.4099i −1.72658 + 0.887289i
\(386\) −41.9908 −2.13728
\(387\) 2.12428 3.67936i 0.107983 0.187032i
\(388\) −1.71079 2.96317i −0.0868521 0.150432i
\(389\) 12.6277 + 21.8718i 0.640250 + 1.10895i 0.985377 + 0.170389i \(0.0545026\pi\)
−0.345127 + 0.938556i \(0.612164\pi\)
\(390\) 0 0
\(391\) −10.4349 −0.527714
\(392\) −4.48422 + 6.26283i −0.226487 + 0.316321i
\(393\) −3.41151 −0.172088
\(394\) −8.14084 + 14.1003i −0.410129 + 0.710365i
\(395\) −3.54835 6.14592i −0.178537 0.309235i
\(396\) 14.9166 + 25.8363i 0.749588 + 1.29833i
\(397\) 7.48827 12.9701i 0.375826 0.650949i −0.614625 0.788820i \(-0.710692\pi\)
0.990450 + 0.137871i \(0.0440258\pi\)
\(398\) 13.9080 0.697143
\(399\) −1.32603 + 0.681443i −0.0663843 + 0.0341148i
\(400\) −21.5817 −1.07909
\(401\) 2.67204 4.62811i 0.133435 0.231117i −0.791563 0.611087i \(-0.790733\pi\)
0.924999 + 0.379970i \(0.124066\pi\)
\(402\) −0.743371 1.28756i −0.0370760 0.0642175i
\(403\) 0 0
\(404\) −5.39798 + 9.34957i −0.268559 + 0.465159i
\(405\) 31.4198 1.56126
\(406\) 1.80630 36.9135i 0.0896451 1.83199i
\(407\) 19.8222 0.982549
\(408\) −0.471273 + 0.816269i −0.0233315 + 0.0404113i
\(409\) 1.68259 + 2.91433i 0.0831985 + 0.144104i 0.904622 0.426214i \(-0.140153\pi\)
−0.821424 + 0.570319i \(0.806820\pi\)
\(410\) −8.12181 14.0674i −0.401107 0.694739i
\(411\) −0.574919 + 0.995789i −0.0283587 + 0.0491186i
\(412\) 36.3428 1.79048
\(413\) −10.9042 7.02769i −0.536562 0.345810i
\(414\) −13.7453 −0.675542
\(415\) −13.8114 + 23.9221i −0.677977 + 1.17429i
\(416\) 0 0
\(417\) −0.217178 0.376163i −0.0106352 0.0184208i
\(418\) −13.3675 + 23.1533i −0.653828 + 1.13246i
\(419\) −28.8639 −1.41010 −0.705048 0.709160i \(-0.749074\pi\)
−0.705048 + 0.709160i \(0.749074\pi\)
\(420\) −3.61117 2.32737i −0.176207 0.113564i
\(421\) −16.6125 −0.809644 −0.404822 0.914395i \(-0.632667\pi\)
−0.404822 + 0.914395i \(0.632667\pi\)
\(422\) 21.3029 36.8977i 1.03701 1.79615i
\(423\) 1.51209 + 2.61902i 0.0735205 + 0.127341i
\(424\) 3.32064 + 5.75151i 0.161264 + 0.279318i
\(425\) −19.1648 + 33.1945i −0.929631 + 1.61017i
\(426\) −3.34795 −0.162209
\(427\) −0.263201 + 5.37877i −0.0127372 + 0.260297i
\(428\) −24.4692 −1.18276
\(429\) 0 0
\(430\) 5.48572 + 9.50154i 0.264545 + 0.458205i
\(431\) −10.2777 17.8015i −0.495060 0.857469i 0.504924 0.863164i \(-0.331521\pi\)
−0.999984 + 0.00569505i \(0.998187\pi\)
\(432\) 1.43916 2.49270i 0.0692417 0.119930i
\(433\) 19.4092 0.932748 0.466374 0.884588i \(-0.345560\pi\)
0.466374 + 0.884588i \(0.345560\pi\)
\(434\) 7.43613 3.82141i 0.356945 0.183434i
\(435\) 4.23862 0.203226
\(436\) 8.36956 14.4965i 0.400829 0.694257i
\(437\) −3.43235 5.94500i −0.164191 0.284388i
\(438\) −0.587106 1.01690i −0.0280530 0.0485892i
\(439\) −6.71256 + 11.6265i −0.320373 + 0.554902i −0.980565 0.196195i \(-0.937142\pi\)
0.660192 + 0.751097i \(0.270475\pi\)
\(440\) −15.8417 −0.755225
\(441\) −8.58174 18.9209i −0.408654 0.900994i
\(442\) 0 0
\(443\) 16.7766 29.0579i 0.797080 1.38058i −0.124430 0.992228i \(-0.539710\pi\)
0.921510 0.388354i \(-0.126956\pi\)
\(444\) 1.11788 + 1.93623i 0.0530524 + 0.0918895i
\(445\) 23.0771 + 39.9707i 1.09396 + 1.89479i
\(446\) −29.4528 + 51.0138i −1.39463 + 2.41557i
\(447\) 0.0206313 0.000975829
\(448\) 26.9839 13.8670i 1.27487 0.655153i
\(449\) 34.4284 1.62478 0.812388 0.583117i \(-0.198167\pi\)
0.812388 + 0.583117i \(0.198167\pi\)
\(450\) −25.2447 + 43.7251i −1.19005 + 2.06122i
\(451\) 4.23052 + 7.32748i 0.199208 + 0.345038i
\(452\) −22.0846 38.2517i −1.03877 1.79921i
\(453\) 1.05552 1.82821i 0.0495926 0.0858969i
\(454\) 24.1691 1.13431
\(455\) 0 0
\(456\) −0.620064 −0.0290371
\(457\) 6.73967 11.6735i 0.315269 0.546061i −0.664226 0.747532i \(-0.731239\pi\)
0.979495 + 0.201471i \(0.0645720\pi\)
\(458\) 9.25771 + 16.0348i 0.432584 + 0.749258i
\(459\) −2.55598 4.42710i −0.119303 0.206639i
\(460\) 9.89082 17.1314i 0.461162 0.798756i
\(461\) −1.35900 −0.0632951 −0.0316476 0.999499i \(-0.510075\pi\)
−0.0316476 + 0.999499i \(0.510075\pi\)
\(462\) 3.37522 + 2.17530i 0.157030 + 0.101204i
\(463\) 2.49836 0.116109 0.0580543 0.998313i \(-0.481510\pi\)
0.0580543 + 0.998313i \(0.481510\pi\)
\(464\) −8.86088 + 15.3475i −0.411356 + 0.712489i
\(465\) 0.479431 + 0.830399i 0.0222331 + 0.0385088i
\(466\) −3.57567 6.19325i −0.165640 0.286897i
\(467\) 13.1091 22.7056i 0.606617 1.05069i −0.385176 0.922843i \(-0.625859\pi\)
0.991794 0.127849i \(-0.0408072\pi\)
\(468\) 0 0
\(469\) 8.69744 + 5.60542i 0.401610 + 0.258834i
\(470\) −7.80965 −0.360232
\(471\) −1.17569 + 2.03635i −0.0541728 + 0.0938301i
\(472\) −2.69771 4.67257i −0.124172 0.215072i
\(473\) −2.85743 4.94921i −0.131385 0.227565i
\(474\) −0.374073 + 0.647913i −0.0171817 + 0.0297596i
\(475\) −25.2156 −1.15697
\(476\) 1.55919 31.8635i 0.0714653 1.46046i
\(477\) −17.9132 −0.820188
\(478\) 21.1271 36.5933i 0.966332 1.67374i
\(479\) −11.9230 20.6513i −0.544778 0.943583i −0.998621 0.0525011i \(-0.983281\pi\)
0.453843 0.891082i \(-0.350053\pi\)
\(480\) 2.55798 + 4.43055i 0.116755 + 0.202226i
\(481\) 0 0
\(482\) −40.1120 −1.82705
\(483\) −0.917038 + 0.471265i −0.0417267 + 0.0214433i
\(484\) 12.4348 0.565217
\(485\) −2.45030 + 4.24405i −0.111263 + 0.192712i
\(486\) −5.05930 8.76296i −0.229494 0.397496i
\(487\) −5.29733 9.17524i −0.240045 0.415770i 0.720682 0.693266i \(-0.243829\pi\)
−0.960727 + 0.277496i \(0.910496\pi\)
\(488\) −1.11987 + 1.93967i −0.0506941 + 0.0878047i
\(489\) −3.33536 −0.150830
\(490\) 53.3957 + 5.23820i 2.41217 + 0.236638i
\(491\) −19.7704 −0.892224 −0.446112 0.894977i \(-0.647192\pi\)
−0.446112 + 0.894977i \(0.647192\pi\)
\(492\) −0.477166 + 0.826476i −0.0215123 + 0.0372604i
\(493\) 15.7371 + 27.2575i 0.708764 + 1.22762i
\(494\) 0 0
\(495\) 21.3646 37.0045i 0.960266 1.66323i
\(496\) −4.00902 −0.180010
\(497\) 20.7243 10.6502i 0.929612 0.477726i
\(498\) 2.91205 0.130492
\(499\) 6.59530 11.4234i 0.295246 0.511381i −0.679796 0.733401i \(-0.737932\pi\)
0.975042 + 0.222020i \(0.0712650\pi\)
\(500\) −13.6339 23.6147i −0.609728 1.05608i
\(501\) 0.0869833 + 0.150660i 0.00388613 + 0.00673097i
\(502\) −10.4107 + 18.0318i −0.464651 + 0.804798i
\(503\) 37.9046 1.69008 0.845040 0.534703i \(-0.179576\pi\)
0.845040 + 0.534703i \(0.179576\pi\)
\(504\) 0.422322 8.63056i 0.0188117 0.384436i
\(505\) 15.4627 0.688080
\(506\) −9.24457 + 16.0121i −0.410971 + 0.711823i
\(507\) 0 0
\(508\) −24.5657 42.5490i −1.08993 1.88781i
\(509\) 13.8313 23.9565i 0.613062 1.06185i −0.377660 0.925944i \(-0.623271\pi\)
0.990721 0.135909i \(-0.0433956\pi\)
\(510\) 6.56518 0.290711
\(511\) 6.86913 + 4.42710i 0.303872 + 0.195843i
\(512\) −27.3244 −1.20758
\(513\) 1.68148 2.91241i 0.0742392 0.128586i
\(514\) 22.2533 + 38.5438i 0.981551 + 1.70010i
\(515\) −26.0263 45.0788i −1.14685 1.98641i
\(516\) 0.322293 0.558227i 0.0141881 0.0245746i
\(517\) 4.06792 0.178907
\(518\) −23.4690 15.1256i −1.03117 0.664580i
\(519\) −0.439464 −0.0192903
\(520\) 0 0
\(521\) −7.78339 13.4812i −0.340996 0.590623i 0.643622 0.765344i \(-0.277431\pi\)
−0.984618 + 0.174721i \(0.944098\pi\)
\(522\) 20.7296 + 35.9047i 0.907310 + 1.57151i
\(523\) −13.6169 + 23.5852i −0.595425 + 1.03131i 0.398061 + 0.917359i \(0.369683\pi\)
−0.993487 + 0.113948i \(0.963650\pi\)
\(524\) 48.0234 2.09791
\(525\) −0.185101 + 3.78273i −0.00807849 + 0.165092i
\(526\) 15.7005 0.684577
\(527\) −3.56006 + 6.16620i −0.155079 + 0.268604i
\(528\) −0.962741 1.66752i −0.0418979 0.0725694i
\(529\) 9.12630 + 15.8072i 0.396796 + 0.687270i
\(530\) 23.1294 40.0614i 1.00468 1.74015i
\(531\) 14.5528 0.631538
\(532\) 18.6663 9.59258i 0.809286 0.415891i
\(533\) 0 0
\(534\) 2.43283 4.21378i 0.105279 0.182348i
\(535\) 17.5232 + 30.3511i 0.757594 + 1.31219i
\(536\) 2.15175 + 3.72693i 0.0929413 + 0.160979i
\(537\) 1.29424 2.24169i 0.0558507 0.0967362i
\(538\) −48.4381 −2.08832
\(539\) −27.8130 2.72850i −1.19799 0.117525i
\(540\) 9.69089 0.417029
\(541\) 12.1027 20.9626i 0.520338 0.901251i −0.479383 0.877606i \(-0.659139\pi\)
0.999720 0.0236453i \(-0.00752724\pi\)
\(542\) 4.42774 + 7.66907i 0.190188 + 0.329415i
\(543\) 0.820839 + 1.42174i 0.0352256 + 0.0610125i
\(544\) −18.9945 + 32.8994i −0.814381 + 1.41055i
\(545\) −23.9749 −1.02697
\(546\) 0 0
\(547\) −22.2177 −0.949960 −0.474980 0.879997i \(-0.657545\pi\)
−0.474980 + 0.879997i \(0.657545\pi\)
\(548\) 8.09305 14.0176i 0.345718 0.598801i
\(549\) −3.02057 5.23178i −0.128915 0.223287i
\(550\) 33.9574 + 58.8160i 1.44795 + 2.50792i
\(551\) −10.3528 + 17.9316i −0.441045 + 0.763913i
\(552\) −0.428817 −0.0182517
\(553\) 0.254485 5.20065i 0.0108218 0.221154i
\(554\) −1.65172 −0.0701749
\(555\) 1.60111 2.77320i 0.0679632 0.117716i
\(556\) 3.05718 + 5.29519i 0.129653 + 0.224566i
\(557\) −11.1602 19.3300i −0.472873 0.819040i 0.526645 0.850085i \(-0.323450\pi\)
−0.999518 + 0.0310455i \(0.990116\pi\)
\(558\) −4.68946 + 8.12238i −0.198521 + 0.343848i
\(559\) 0 0
\(560\) −21.6249 13.9370i −0.913818 0.588948i
\(561\) −3.41970 −0.144380
\(562\) −12.6454 + 21.9025i −0.533415 + 0.923901i
\(563\) −13.3519 23.1262i −0.562717 0.974655i −0.997258 0.0740027i \(-0.976423\pi\)
0.434541 0.900652i \(-0.356911\pi\)
\(564\) 0.229413 + 0.397355i 0.00966004 + 0.0167317i
\(565\) −31.6310 + 54.7865i −1.33073 + 2.30489i
\(566\) 33.8039 1.42088
\(567\) 19.3771 + 12.4884i 0.813760 + 0.524462i
\(568\) 9.69090 0.406621
\(569\) −3.30510 + 5.72461i −0.138557 + 0.239988i −0.926951 0.375183i \(-0.877580\pi\)
0.788393 + 0.615171i \(0.210913\pi\)
\(570\) 2.15949 + 3.74034i 0.0904509 + 0.156666i
\(571\) 21.0643 + 36.4844i 0.881513 + 1.52683i 0.849659 + 0.527333i \(0.176808\pi\)
0.0318546 + 0.999493i \(0.489859\pi\)
\(572\) 0 0
\(573\) −3.14498 −0.131383
\(574\) 0.582489 11.9037i 0.0243126 0.496853i
\(575\) −17.4383 −0.727227
\(576\) −17.0169 + 29.4741i −0.709037 + 1.22809i
\(577\) 7.94195 + 13.7559i 0.330628 + 0.572664i 0.982635 0.185549i \(-0.0594063\pi\)
−0.652007 + 0.758213i \(0.726073\pi\)
\(578\) 6.30848 + 10.9266i 0.262398 + 0.454487i
\(579\) 1.76671 3.06003i 0.0734219 0.127170i
\(580\) −59.6665 −2.47752
\(581\) −18.0260 + 9.26354i −0.747845 + 0.384316i
\(582\) 0.516630 0.0214150
\(583\) −12.0478 + 20.8674i −0.498968 + 0.864238i
\(584\) 1.69942 + 2.94349i 0.0703226 + 0.121802i
\(585\) 0 0
\(586\) −7.15969 + 12.4010i −0.295764 + 0.512279i
\(587\) −18.5676 −0.766366 −0.383183 0.923672i \(-0.625172\pi\)
−0.383183 + 0.923672i \(0.625172\pi\)
\(588\) −1.30201 2.87065i −0.0536940 0.118384i
\(589\) −4.68404 −0.193003
\(590\) −18.7905 + 32.5462i −0.773594 + 1.33990i
\(591\) −0.685030 1.18651i −0.0281784 0.0488064i
\(592\) 6.69426 + 11.5948i 0.275132 + 0.476543i
\(593\) −10.3050 + 17.8487i −0.423175 + 0.732960i −0.996248 0.0865442i \(-0.972418\pi\)
0.573073 + 0.819504i \(0.305751\pi\)
\(594\) −9.05770 −0.371642
\(595\) −40.6394 + 20.8845i −1.66605 + 0.856183i
\(596\) −0.290425 −0.0118963
\(597\) −0.585159 + 1.01353i −0.0239490 + 0.0414809i
\(598\) 0 0
\(599\) 6.80224 + 11.7818i 0.277932 + 0.481393i 0.970871 0.239604i \(-0.0770176\pi\)
−0.692939 + 0.720997i \(0.743684\pi\)
\(600\) −0.787571 + 1.36411i −0.0321524 + 0.0556897i
\(601\) −12.1503 −0.495621 −0.247810 0.968809i \(-0.579711\pi\)
−0.247810 + 0.968809i \(0.579711\pi\)
\(602\) −0.393431 + 8.04015i −0.0160351 + 0.327692i
\(603\) −11.6076 −0.472698
\(604\) −14.8584 + 25.7355i −0.604579 + 1.04716i
\(605\) −8.90496 15.4238i −0.362038 0.627068i
\(606\) −0.815050 1.41171i −0.0331092 0.0573467i
\(607\) −17.6166 + 30.5128i −0.715035 + 1.23848i 0.247911 + 0.968783i \(0.420256\pi\)
−0.962946 + 0.269695i \(0.913077\pi\)
\(608\) −24.9914 −1.01354
\(609\) 2.61403 + 1.68472i 0.105926 + 0.0682682i
\(610\) 15.6006 0.631650
\(611\) 0 0
\(612\) 17.8937 + 30.9928i 0.723310 + 1.25281i
\(613\) 15.0310 + 26.0345i 0.607097 + 1.05152i 0.991716 + 0.128448i \(0.0409996\pi\)
−0.384619 + 0.923075i \(0.625667\pi\)
\(614\) 15.6414 27.0917i 0.631236 1.09333i
\(615\) 1.36686 0.0551170
\(616\) −9.76984 6.29658i −0.393638 0.253697i
\(617\) 7.01712 0.282499 0.141249 0.989974i \(-0.454888\pi\)
0.141249 + 0.989974i \(0.454888\pi\)
\(618\) −2.74373 + 4.75228i −0.110369 + 0.191165i
\(619\) 21.9241 + 37.9736i 0.881203 + 1.52629i 0.850004 + 0.526776i \(0.176599\pi\)
0.0311993 + 0.999513i \(0.490067\pi\)
\(620\) −6.74889 11.6894i −0.271042 0.469458i
\(621\) 1.16286 2.01413i 0.0466640 0.0808244i
\(622\) −60.9118 −2.44234
\(623\) −1.65507 + 33.8230i −0.0663091 + 1.35509i
\(624\) 0 0
\(625\) 0.481145 0.833367i 0.0192458 0.0333347i
\(626\) −34.8847 60.4221i −1.39427 2.41495i
\(627\) −1.12484 1.94829i −0.0449219 0.0778070i
\(628\) 16.5500 28.6654i 0.660416 1.14387i
\(629\) 23.7783 0.948103
\(630\) −53.5320 + 27.5100i −2.13276 + 1.09602i
\(631\) −23.4936 −0.935267 −0.467634 0.883922i \(-0.654893\pi\)
−0.467634 + 0.883922i \(0.654893\pi\)
\(632\) 1.08278 1.87544i 0.0430708 0.0746008i
\(633\) 1.79258 + 3.10485i 0.0712488 + 0.123407i
\(634\) −11.0654 19.1659i −0.439464 0.761173i
\(635\) −35.1846 + 60.9415i −1.39626 + 2.41839i
\(636\) −2.71777 −0.107766
\(637\) 0 0
\(638\) 55.7680 2.20788
\(639\) −13.0694 + 22.6369i −0.517017 + 0.895500i
\(640\) −15.3403 26.5702i −0.606378 1.05028i
\(641\) −3.70233 6.41262i −0.146233 0.253283i 0.783599 0.621267i \(-0.213382\pi\)
−0.929832 + 0.367983i \(0.880048\pi\)
\(642\) 1.84732 3.19966i 0.0729081 0.126281i
\(643\) 39.9607 1.57590 0.787948 0.615742i \(-0.211144\pi\)
0.787948 + 0.615742i \(0.211144\pi\)
\(644\) 12.9090 6.63393i 0.508687 0.261413i
\(645\) −0.923218 −0.0363517
\(646\) −16.0354 + 27.7742i −0.630906 + 1.09276i
\(647\) −13.6234 23.5964i −0.535591 0.927670i −0.999134 0.0415963i \(-0.986756\pi\)
0.463544 0.886074i \(-0.346578\pi\)
\(648\) 4.79389 + 8.30326i 0.188322 + 0.326183i
\(649\) 9.78770 16.9528i 0.384201 0.665456i
\(650\) 0 0
\(651\) −0.0343844 + 0.702679i −0.00134763 + 0.0275402i
\(652\) 46.9514 1.83876
\(653\) −9.57255 + 16.5801i −0.374603 + 0.648831i −0.990267 0.139177i \(-0.955554\pi\)
0.615665 + 0.788008i \(0.288888\pi\)
\(654\) 1.26373 + 2.18885i 0.0494159 + 0.0855909i
\(655\) −34.3911 59.5672i −1.34377 2.32748i
\(656\) −2.85743 + 4.94921i −0.111564 + 0.193234i
\(657\) −9.16755 −0.357660
\(658\) −4.81633 3.10409i −0.187760 0.121010i
\(659\) 41.5725 1.61943 0.809717 0.586820i \(-0.199620\pi\)
0.809717 + 0.586820i \(0.199620\pi\)
\(660\) 3.24141 5.61428i 0.126172 0.218536i
\(661\) −17.1023 29.6221i −0.665203 1.15217i −0.979230 0.202752i \(-0.935012\pi\)
0.314027 0.949414i \(-0.398322\pi\)
\(662\) 4.74000 + 8.20992i 0.184225 + 0.319088i
\(663\) 0 0
\(664\) −8.42915 −0.327115
\(665\) −25.2660 16.2837i −0.979772 0.631455i
\(666\) 31.3218 1.21369
\(667\) −7.15969 + 12.4010i −0.277224 + 0.480167i
\(668\) −1.22445 2.12081i −0.0473755 0.0820567i
\(669\) −2.47838 4.29268i −0.0958197 0.165965i
\(670\) 14.9877 25.9595i 0.579025 1.00290i
\(671\) −8.12611 −0.313705
\(672\) −0.183456 + 3.74910i −0.00707697 + 0.144625i
\(673\) 21.4308 0.826098 0.413049 0.910709i \(-0.364464\pi\)
0.413049 + 0.910709i \(0.364464\pi\)
\(674\) −11.4722 + 19.8704i −0.441893 + 0.765381i
\(675\) −4.27145 7.39837i −0.164408 0.284763i
\(676\) 0 0
\(677\) −4.89083 + 8.47117i −0.187970 + 0.325573i −0.944573 0.328301i \(-0.893524\pi\)
0.756603 + 0.653874i \(0.226857\pi\)
\(678\) 6.66919 0.256129
\(679\) −3.19802 + 1.64346i −0.122729 + 0.0630700i
\(680\) −19.0034 −0.728748
\(681\) −1.01688 + 1.76130i −0.0389671 + 0.0674930i
\(682\) 6.30793 + 10.9256i 0.241543 + 0.418365i
\(683\) −7.63818 13.2297i −0.292267 0.506221i 0.682079 0.731279i \(-0.261076\pi\)
−0.974345 + 0.225058i \(0.927743\pi\)
\(684\) −11.7716 + 20.3889i −0.450097 + 0.779590i
\(685\) −23.1828 −0.885769
\(686\) 30.8480 + 24.4536i 1.17778 + 0.933642i
\(687\) −1.55802 −0.0594423
\(688\) 1.92999 3.34285i 0.0735803 0.127445i
\(689\) 0 0
\(690\) 1.49343 + 2.58670i 0.0568540 + 0.0984741i
\(691\) −21.2286 + 36.7690i −0.807573 + 1.39876i 0.106967 + 0.994263i \(0.465886\pi\)
−0.914540 + 0.404496i \(0.867447\pi\)
\(692\) 6.18627 0.235167
\(693\) 27.8840 14.3295i 1.05922 0.544334i
\(694\) 8.65141 0.328403
\(695\) 4.37869 7.58412i 0.166093 0.287682i
\(696\) 0.646710 + 1.12013i 0.0245135 + 0.0424586i
\(697\) 5.07486 + 8.78991i 0.192224 + 0.332942i
\(698\) 25.3706 43.9432i 0.960291 1.66327i
\(699\) 0.601767 0.0227609
\(700\) 2.60565 53.2489i 0.0984842 2.01262i
\(701\) −2.79985 −0.105749 −0.0528744 0.998601i \(-0.516838\pi\)
−0.0528744 + 0.998601i \(0.516838\pi\)
\(702\) 0 0
\(703\) 7.82141 + 13.5471i 0.294990 + 0.510937i
\(704\) 22.8899 + 39.6465i 0.862696 + 1.49423i
\(705\) 0.328581 0.569118i 0.0123751 0.0214342i
\(706\) −55.4412 −2.08656
\(707\) 9.53608 + 6.14592i 0.358641 + 0.231141i
\(708\) 2.20793 0.0829793
\(709\) 7.28319 12.6149i 0.273526 0.473761i −0.696236 0.717813i \(-0.745143\pi\)
0.969762 + 0.244052i \(0.0784767\pi\)
\(710\) −33.7503 58.4573i −1.26663 2.19386i
\(711\) 2.92054 + 5.05852i 0.109529 + 0.189709i
\(712\) −7.04201 + 12.1971i −0.263910 + 0.457106i
\(713\) −3.23934 −0.121314
\(714\) 4.04885 + 2.60945i 0.151524 + 0.0976562i
\(715\) 0 0
\(716\) −18.2189 + 31.5560i −0.680871 + 1.17930i
\(717\) 1.77779 + 3.07923i 0.0663928 + 0.114996i
\(718\) −24.3309 42.1423i −0.908021 1.57274i
\(719\) −17.2529 + 29.8828i −0.643423 + 1.11444i 0.341240 + 0.939976i \(0.389153\pi\)
−0.984663 + 0.174465i \(0.944180\pi\)
\(720\) 28.8606 1.07557
\(721\) 1.86658 38.1454i 0.0695152 1.42061i
\(722\) 19.2861 0.717756
\(723\) 1.68766 2.92311i 0.0627648 0.108712i
\(724\) −11.5548 20.0136i −0.429432 0.743798i
\(725\) 26.2992 + 45.5515i 0.976727 + 1.69174i
\(726\) −0.938775 + 1.62601i −0.0348412 + 0.0603467i
\(727\) 35.7571 1.32616 0.663078 0.748550i \(-0.269250\pi\)
0.663078 + 0.748550i \(0.269250\pi\)
\(728\) 0 0
\(729\) −25.2879 −0.936590
\(730\) 11.8371 20.5025i 0.438111 0.758830i
\(731\) −3.42771 5.93698i −0.126779 0.219587i
\(732\) −0.458277 0.793759i −0.0169384 0.0293382i
\(733\) 20.5250 35.5504i 0.758108 1.31308i −0.185706 0.982605i \(-0.559457\pi\)
0.943814 0.330477i \(-0.107210\pi\)
\(734\) 38.5990 1.42472
\(735\) −2.62828 + 3.67075i −0.0969456 + 0.135398i
\(736\) −17.2833 −0.637071
\(737\) −7.80686 + 13.5219i −0.287570 + 0.498085i
\(738\) 6.68481 + 11.5784i 0.246071 + 0.426208i
\(739\) 0.363205 + 0.629089i 0.0133607 + 0.0231414i 0.872628 0.488385i \(-0.162414\pi\)
−0.859268 + 0.511526i \(0.829080\pi\)
\(740\) −22.5386 + 39.0379i −0.828534 + 1.43506i
\(741\) 0 0
\(742\) 30.1874 15.5133i 1.10822 0.569510i
\(743\) 16.4547 0.603664 0.301832 0.953361i \(-0.402402\pi\)
0.301832 + 0.953361i \(0.402402\pi\)
\(744\) −0.146299 + 0.253397i −0.00536358 + 0.00929000i
\(745\) 0.207983 + 0.360236i 0.00761989 + 0.0131980i
\(746\) −16.8648 29.2108i −0.617466 1.06948i
\(747\) 11.3678 19.6896i 0.415925 0.720404i
\(748\) 48.1387 1.76012
\(749\) −1.25675 + 25.6829i −0.0459206 + 0.938433i
\(750\) 4.11723 0.150340
\(751\) −12.5854 + 21.7985i −0.459247 + 0.795439i −0.998921 0.0464350i \(-0.985214\pi\)
0.539675 + 0.841874i \(0.318547\pi\)
\(752\) 1.37380 + 2.37949i 0.0500974 + 0.0867712i
\(753\) −0.876030 1.51733i −0.0319243 0.0552945i
\(754\) 0 0
\(755\) 42.5623 1.54900
\(756\) 5.97652 + 3.85182i 0.217364 + 0.140089i
\(757\) 44.0743 1.60191 0.800953 0.598727i \(-0.204327\pi\)
0.800953 + 0.598727i \(0.204327\pi\)
\(758\) 29.5054 51.1049i 1.07168 1.85621i
\(759\) −0.777906 1.34737i −0.0282362 0.0489066i
\(760\) −6.25080 10.8267i −0.226740 0.392726i
\(761\) 19.3511 33.5171i 0.701477 1.21499i −0.266471 0.963843i \(-0.585858\pi\)
0.967948 0.251151i \(-0.0808090\pi\)
\(762\) 7.41844 0.268742
\(763\) −14.7857 9.52925i −0.535278 0.344982i
\(764\) 44.2715 1.60169
\(765\) 25.6285 44.3899i 0.926601 1.60492i
\(766\) −27.8937 48.3133i −1.00784 1.74563i
\(767\) 0 0
\(768\) 0.433701 0.751191i 0.0156498 0.0271063i
\(769\) −36.1506 −1.30362 −0.651811 0.758381i \(-0.725991\pi\)
−0.651811 + 0.758381i \(0.725991\pi\)
\(770\) −3.95687 + 80.8625i −0.142596 + 2.91408i
\(771\) −3.74511 −0.134877
\(772\) −24.8697 + 43.0756i −0.895080 + 1.55032i
\(773\) −15.0366 26.0441i −0.540827 0.936740i −0.998857 0.0478033i \(-0.984778\pi\)
0.458030 0.888937i \(-0.348555\pi\)
\(774\) −4.51513 7.82043i −0.162293 0.281100i
\(775\) −5.94941 + 10.3047i −0.213709 + 0.370155i
\(776\) −1.49543 −0.0536827
\(777\) 2.08969 1.07389i 0.0749671 0.0385255i
\(778\) 53.6801 1.92453
\(779\) −3.33855 + 5.78253i −0.119616 + 0.207181i
\(780\) 0 0