Properties

Label 1183.2.e.i.508.2
Level $1183$
Weight $2$
Character 1183.508
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 508.2
Root \(-1.06275 + 1.84073i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.i.170.2

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06275 1.84073i −0.751474 1.30159i −0.947108 0.320915i \(-0.896010\pi\)
0.195634 0.980677i \(-0.437324\pi\)
\(3\) 0.0894272 0.154892i 0.0516308 0.0894272i −0.839055 0.544047i \(-0.816891\pi\)
0.890686 + 0.454620i \(0.150225\pi\)
\(4\) −1.25885 + 2.18040i −0.629427 + 1.09020i
\(5\) 1.80301 + 3.12291i 0.806332 + 1.39661i 0.915388 + 0.402572i \(0.131884\pi\)
−0.109056 + 0.994036i \(0.534783\pi\)
\(6\) −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 −0.390667 0.920532i \(-0.627756\pi\)
0.992538 0.121939i \(-0.0389111\pi\)
\(12\) 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 0.414618 + 0.909996i \(0.363915\pi\)
−0.995388 + 0.0959284i \(0.969418\pi\)
\(18\) 3.15424 5.46330i 0.743461 1.28771i
\(19\) −1.57530 2.72850i −0.361398 0.625960i 0.626793 0.779186i \(-0.284367\pi\)
−0.988191 + 0.153226i \(0.951034\pi\)
\(20\) −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 0.956966 0.290201i \(-0.0937222\pi\)
−0.729804 + 0.683656i \(0.760389\pi\)
\(24\) 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 \(-0.790708\pi\)
0.925028 + 0.379900i \(0.124042\pi\)
\(32\) 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 \(-0.0328501\pi\)
−0.586556 + 0.809908i \(0.699517\pi\)
\(38\) −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 \(-0.447079\pi\)
0.165490 + 0.986211i \(0.447079\pi\)
\(42\) −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 \(-0.142990\pi\)
−0.826474 + 0.562974i \(0.809657\pi\)
\(48\) 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 −0.995377 0.0960417i \(-0.969382\pi\)
0.580863 + 0.814001i \(0.302715\pi\)
\(54\) −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 \(-0.936738\pi\)
0.661143 + 0.750260i \(0.270072\pi\)
\(60\) −0.811902 + 1.40626i −0.104816 + 0.181547i
\(61\) 1.01771 + 1.76272i 0.130304 + 0.225693i 0.923794 0.382890i \(-0.125071\pi\)
−0.793490 + 0.608584i \(0.791738\pi\)
\(62\) −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 \(-0.756548\pi\)
0.960398 + 0.278632i \(0.0898810\pi\)
\(68\) −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 \(-0.324966\pi\)
0.522590 + 0.852584i \(0.324966\pi\)
\(72\) 1.63297 + 2.82840i 0.192448 + 0.333330i
\(73\) 1.54439 2.67497i 0.180757 0.313081i −0.761381 0.648304i \(-0.775478\pi\)
0.942139 + 0.335223i \(0.108812\pi\)
\(74\) 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 0.805347 0.592803i \(-0.201979\pi\)
−0.916056 + 0.401049i \(0.868646\pi\)
\(80\) −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 \(-0.638113\pi\)
−0.420408 + 0.907335i \(0.638113\pi\)
\(84\) 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 −0.975476 0.220107i \(-0.929359\pi\)
0.297120 0.954840i \(-0.403974\pi\)
\(90\) 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 \(-0.521979\pi\)
−0.0689930 + 0.997617i \(0.521979\pi\)
\(98\) 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 −0.952757 0.303735i \(-0.901766\pi\)
0.739420 + 0.673244i \(0.235100\pi\)
\(102\) 0.910307 1.57670i 0.0901338 0.156116i
\(103\) −7.21744 12.5010i −0.711155 1.23176i −0.964424 0.264361i \(-0.914839\pi\)
0.253269 0.967396i \(-0.418494\pi\)
\(104\) 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 0.999403 0.0345525i \(-0.0110006\pi\)
−0.529625 + 0.848232i \(0.677667\pi\)
\(108\) −1.34371 + 2.32737i −0.129298 + 0.223951i
\(109\) −3.32428 + 5.75782i −0.318408 + 0.551499i −0.980156 0.198227i \(-0.936482\pi\)
0.661748 + 0.749726i \(0.269815\pi\)
\(110\) −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 −0.895437 0.445188i \(-0.853137\pi\)
0.0621741 0.998065i \(-0.480197\pi\)
\(132\) 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 \(-0.921888\pi\)
0.695412 + 0.718611i \(0.255222\pi\)
\(138\) −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 \(-0.168171\pi\)
−0.868378 + 0.495902i \(0.834837\pi\)
\(150\) 1.52126 2.63491i 0.124211 0.215139i
\(151\) 5.90155 10.2218i 0.480262 0.831838i −0.519482 0.854481i \(-0.673875\pi\)
0.999744 + 0.0226438i \(0.00720835\pi\)
\(152\) −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 −0.474972 0.880001i \(-0.657542\pi\)
0.999589 0.0286625i \(-0.00912481\pi\)
\(158\) −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 0.956742 + 0.290938i \(0.0939673\pi\)
−0.226411 + 0.974032i \(0.572699\pi\)
\(164\) −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 \(-0.511982\pi\)
−0.0376338 + 0.999292i \(0.511982\pi\)
\(168\) 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 0.815537 0.578705i \(-0.196442\pi\)
−0.908942 + 0.416923i \(0.863108\pi\)
\(174\) 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 0.457989 + 0.888958i \(0.348570\pi\)
−0.998855 + 0.0478492i \(0.984763\pi\)
\(180\) −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 −0.986266 0.165162i \(-0.947185\pi\)
0.350098 0.936713i \(-0.386148\pi\)
\(192\) −1.02545 + 1.77613i −0.0740054 + 0.128181i
\(193\) 9.87791 17.1090i 0.711028 1.23154i −0.253444 0.967350i \(-0.581563\pi\)
0.964472 0.264186i \(-0.0851033\pi\)
\(194\) 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 \(-0.412023\pi\)
0.272883 + 0.962047i \(0.412023\pi\)
\(198\) −12.5929 21.8115i −0.894935 1.55007i
\(199\) 3.27171 5.66677i 0.231925 0.401706i −0.726449 0.687220i \(-0.758831\pi\)
0.958375 + 0.285514i \(0.0921642\pi\)
\(200\) −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 \(-0.121586\pi\)
0.927931 + 0.372752i \(0.121586\pi\)
\(224\) 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 \(-0.956502\pi\)
0.613315 + 0.789839i \(0.289836\pi\)
\(228\) 0.709362 1.22865i 0.0469786 0.0813694i
\(229\) 4.35556 + 7.54406i 0.287824 + 0.498525i 0.973290 0.229579i \(-0.0737349\pi\)
−0.685466 + 0.728104i \(0.740402\pi\)
\(230\) 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 0.915855 0.401510i \(-0.131514\pi\)
−0.805645 + 0.592399i \(0.798181\pi\)
\(234\) 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 \(-0.722293\pi\)
−0.642958 + 0.765902i \(0.722293\pi\)
\(240\) 0.869579 + 1.50615i 0.0561311 + 0.0972219i
\(241\) 9.43595 16.3435i 0.607823 1.05278i −0.383776 0.923426i \(-0.625376\pi\)
0.991599 0.129354i \(-0.0412902\pi\)
\(242\) −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 −0.982371 0.186944i \(-0.940142\pi\)
0.329287 0.944230i \(-0.393192\pi\)
\(258\) −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 −0.729395 0.684093i \(-0.760198\pi\)
0.957139 + 0.289628i \(0.0935316\pi\)
\(264\) −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 0.275529 + 0.961293i \(0.411147\pi\)
−0.970268 + 0.242032i \(0.922186\pi\)
\(270\) 4.09060 7.08513i 0.248946 0.431187i
\(271\) 2.08316 + 3.60814i 0.126543 + 0.219179i 0.922335 0.386391i \(-0.126278\pi\)
−0.795792 + 0.605570i \(0.792945\pi\)
\(272\) −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 −0.877462 0.479646i \(-0.840765\pi\)
0.854116 + 0.520082i \(0.174099\pi\)
\(278\) 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 \(-0.384511\pi\)
0.354912 + 0.934900i \(0.384511\pi\)
\(282\) −0.193674 0.335454i −0.0115331 0.0199760i
\(283\) 7.95202 13.7733i 0.472698 0.818738i −0.526813 0.849981i \(-0.676613\pi\)
0.999512 + 0.0312434i \(0.00994670\pi\)
\(284\) −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 \(-0.436949\pi\)
0.196789 + 0.980446i \(0.436949\pi\)
\(294\) −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 \(-0.637969\pi\)
−0.419998 + 0.907525i \(0.637969\pi\)
\(308\) 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 0.0985808 + 0.995129i \(0.468570\pi\)
−0.911097 + 0.412191i \(0.864764\pi\)
\(312\) 0 0
\(313\) 16.4125 + 28.4274i 0.927692 + 1.60681i 0.787174 + 0.616732i \(0.211544\pi\)
0.140518 + 0.990078i \(0.455123\pi\)
\(314\) −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 \(-0.261121\pi\)
−0.974377 + 0.224921i \(0.927788\pi\)
\(318\) 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 \(-0.127551\pi\)
−0.798207 + 0.602383i \(0.794218\pi\)
\(332\) 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 −0.806215 0.591623i \(-0.798487\pi\)
0.915468 + 0.402391i \(0.131821\pi\)
\(348\) −1.47969 2.56290i −0.0793198 0.137386i
\(349\) −23.8727 −1.27788 −0.638938 0.769258i \(-0.720626\pi\)
−0.638938 + 0.769258i \(0.720626\pi\)
\(350\) 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 −0.276311 0.961068i \(-0.589112\pi\)
0.970465 0.241242i \(-0.0775548\pi\)
\(354\) 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 −0.992184 0.124786i \(-0.960176\pi\)
0.388024 0.921649i \(-0.373158\pi\)
\(360\) −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 −0.525582 0.850743i \(-0.676153\pi\)
0.999556 + 0.0297964i \(0.00948589\pi\)
\(368\) −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 0.994981 0.100060i \(-0.0319034\pi\)
−0.584145 + 0.811649i \(0.698570\pi\)
\(374\) 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 \(-0.752689\pi\)
−0.713055 + 0.701108i \(0.752689\pi\)
\(380\) 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 −0.977741 0.209815i \(-0.932714\pi\)
0.307165 0.951656i \(-0.400620\pi\)
\(384\) 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 −0.345127 0.938556i \(-0.612164\pi\)
0.985377 0.170389i \(-0.0545026\pi\)
\(390\) 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 \(-0.289308\pi\)
−0.990450 + 0.137871i \(0.955974\pi\)
\(398\) −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 \(-0.209267\pi\)
−0.924999 + 0.379970i \(0.875934\pi\)
\(402\) −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 \(-0.859847\pi\)
0.821424 + 0.570319i \(0.193180\pi\)
\(410\) 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 \(-0.367333\pi\)
0.404822 + 0.914395i \(0.367333\pi\)
\(422\) −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 \(-0.668479\pi\)
0.999984 + 0.00569505i \(0.00181280\pi\)
\(432\) 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 0.660192 0.751097i \(-0.270475\pi\)
−0.980565 + 0.196195i \(0.937142\pi\)
\(440\) 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 0.921510 + 0.388354i \(0.126956\pi\)
−0.124430 + 0.992228i \(0.539710\pi\)
\(444\) −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 \(-0.801833\pi\)
−0.812388 + 0.583117i \(0.801833\pi\)
\(450\) 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 \(-0.268761\pi\)
−0.979495 + 0.201471i \(0.935428\pi\)
\(458\) 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 \(-0.489925\pi\)
0.0316476 + 0.999499i \(0.489925\pi\)
\(462\) −3.37522 + 2.17530i −0.157030 + 0.101204i
\(463\) −2.49836 −0.116109 −0.0580543 0.998313i \(-0.518490\pi\)
−0.0580543 + 0.998313i \(0.518490\pi\)
\(464\) −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 0.991794 + 0.127849i \(0.0408072\pi\)
−0.385176 + 0.922843i \(0.625859\pi\)
\(468\) 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 −0.453843 0.891082i \(-0.649947\pi\)
0.998621 0.0525011i \(-0.0167193\pi\)
\(480\) 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 \(-0.756171\pi\)
0.960727 + 0.277496i \(0.0895045\pi\)
\(488\) 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 \(-0.262068\pi\)
−0.975042 + 0.222020i \(0.928735\pi\)
\(500\) 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 −0.990721 0.135909i \(-0.956604\pi\)
0.377660 0.925944i \(-0.376729\pi\)
\(510\) 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 −0.984618 0.174721i \(-0.944098\pi\)
0.643622 + 0.765344i \(0.277431\pi\)
\(522\) −20.7296 + 35.9047i −0.907310 + 1.57151i
\(523\) −13.6169 23.5852i −0.595425 1.03131i −0.993487 0.113948i \(-0.963650\pi\)
0.398061 0.917359i \(-0.369683\pi\)
\(524\) 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 −0.999720 0.0236453i \(-0.992473\pi\)
0.479383 0.877606i \(-0.340861\pi\)
\(542\) 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 \(-0.676550\pi\)
0.999518 + 0.0310455i \(0.00988367\pi\)
\(558\) −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 0.434541 + 0.900652i \(0.356911\pi\)
−0.997258 + 0.0740027i \(0.976423\pi\)
\(564\) −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 0.788393 0.615171i \(-0.210913\pi\)
−0.926951 + 0.375183i \(0.877580\pi\)
\(570\) −2.15949 + 3.74034i −0.0904509 + 0.156666i
\(571\) 21.0643 36.4844i 0.881513 1.52683i 0.0318546 0.999493i \(-0.489859\pi\)
0.849659 0.527333i \(-0.176808\pi\)
\(572\) 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 \(-0.940594\pi\)
0.652007 + 0.758213i \(0.273927\pi\)
\(578\) −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 \(-0.374828\pi\)
0.383183 + 0.923672i \(0.374828\pi\)
\(588\) −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 \(-0.0275824\pi\)
−0.573073 + 0.819504i \(0.694249\pi\)
\(594\) −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 −0.692939 0.720997i \(-0.743684\pi\)
0.970871 + 0.239604i \(0.0770176\pi\)
\(600\) 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 −0.962946 0.269695i \(-0.913077\pi\)
0.247911 0.968783i \(-0.420256\pi\)
\(608\) −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 0.384619 + 0.923075i \(0.374333\pi\)
−0.991716 + 0.128448i \(0.959000\pi\)
\(614\) 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 \(-0.545112\pi\)
−0.141249 + 0.989974i \(0.545112\pi\)
\(618\) 2.74373 + 4.75228i 0.110369 + 0.191165i
\(619\) −21.9241 + 37.9736i −0.881203 + 1.52629i −0.0311993 + 0.999513i \(0.509933\pi\)
−0.850004 + 0.526776i \(0.823401\pi\)
\(620\) −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 \(-0.345107\pi\)
0.467634 + 0.883922i \(0.345107\pi\)
\(632\) −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 −0.929832 0.367983i \(-0.880048\pi\)
0.783599 + 0.621267i \(0.213382\pi\)
\(642\) −1.84732 3.19966i −0.0729081 0.126281i
\(643\) −39.9607 −1.57590 −0.787948 0.615742i \(-0.788856\pi\)
−0.787948 + 0.615742i \(0.788856\pi\)
\(644\) −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 0.463544 + 0.886074i \(0.346578\pi\)
−0.999134 + 0.0415963i \(0.986756\pi\)
\(648\) −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 0.615665 0.788008i \(-0.288888\pi\)
−0.990267 + 0.139177i \(0.955554\pi\)
\(654\) 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 −0.314027 0.949414i \(-0.601678\pi\)
0.979230 0.202752i \(-0.0649885\pi\)
\(662\) 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 0.756603 0.653874i \(-0.226857\pi\)
−0.944573 + 0.328301i \(0.893524\pi\)
\(678\) −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 \(-0.738924\pi\)
0.974345 + 0.225058i \(0.0722572\pi\)
\(684\) 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 0.914540 + 0.404496i \(0.132553\pi\)
−0.106967 + 0.994263i \(0.534114\pi\)
\(692\) 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 \(-0.254857\pi\)
−0.969762 + 0.244052i \(0.921523\pi\)
\(710\) 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 −0.984663 0.174465i \(-0.944180\pi\)
0.341240 0.939976i \(-0.389153\pi\)
\(720\) −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 −0.943814 0.330477i \(-0.892790\pi\)
0.185706 0.982605i \(-0.440543\pi\)
\(734\) −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 \(-0.837586\pi\)
0.859268 + 0.511526i \(0.170920\pi\)
\(740\) −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 \(-0.597598\pi\)
−0.301832 + 0.953361i \(0.597598\pi\)
\(744\) −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 0.539675 0.841874i \(-0.318547\pi\)
−0.998921 + 0.0464350i \(0.985214\pi\)
\(752\) −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 −0.967948 0.251151i \(-0.919191\pi\)
0.266471 0.963843i \(-0.414142\pi\)
\(762\) −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 \(-0.274009\pi\)
0.651811 + 0.758381i \(0.274009\pi\)
\(770\) −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 −0.458030 0.888937i \(-0.651445\pi\)
0.998857 0.0478033i \(-0.0152221\pi\)
\(774\) 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
\(781\) 17.5800