Properties

Label 74.2.c.c.63.3
Level $74$
Weight $2$
Character 74.63
Analytic conductor $0.591$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
Defining polynomial: \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 63.3
Root \(-0.827721 + 1.43366i\) of defining polynomial
Character \(\chi\) \(=\) 74.63
Dual form 74.2.c.c.47.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.52569 - 2.64257i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.629755 + 1.09077i) q^{5} -3.05137 q^{6} +(-1.52569 + 2.64257i) q^{7} +1.00000 q^{8} +(-3.15544 - 5.46539i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.52569 - 2.64257i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.629755 + 1.09077i) q^{5} -3.05137 q^{6} +(-1.52569 + 2.64257i) q^{7} +1.00000 q^{8} +(-3.15544 - 5.46539i) q^{9} +1.25951 q^{10} +5.31088 q^{11} +(1.52569 + 2.64257i) q^{12} +(-1.00000 + 1.73205i) q^{13} +3.05137 q^{14} +(1.92162 + 3.32834i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.55137 - 4.41911i) q^{17} +(-3.15544 + 5.46539i) q^{18} +(-2.39593 + 4.14988i) q^{19} +(-0.629755 - 1.09077i) q^{20} +(4.65544 + 8.06346i) q^{21} +(-2.65544 - 4.59936i) q^{22} +1.74049 q^{23} +(1.52569 - 2.64257i) q^{24} +(1.70682 + 2.95629i) q^{25} +2.00000 q^{26} -10.1027 q^{27} +(-1.52569 - 2.64257i) q^{28} -4.05137 q^{29} +(1.92162 - 3.32834i) q^{30} -0.791864 q^{31} +(-0.500000 + 0.866025i) q^{32} +(8.10275 - 14.0344i) q^{33} +(-2.55137 + 4.41911i) q^{34} +(-1.92162 - 3.32834i) q^{35} +6.31088 q^{36} +(-1.37024 - 5.92642i) q^{37} +4.79186 q^{38} +(3.05137 + 5.28514i) q^{39} +(-0.629755 + 1.09077i) q^{40} +(0.104068 - 0.180251i) q^{41} +(4.65544 - 8.06346i) q^{42} -4.36226 q^{43} +(-2.65544 + 4.59936i) q^{44} +7.94863 q^{45} +(-0.870245 - 1.50731i) q^{46} -3.20814 q^{47} -3.05137 q^{48} +(-1.15544 - 2.00128i) q^{49} +(1.70682 - 2.95629i) q^{50} -15.5704 q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.65544 - 9.79551i) q^{53} +(5.05137 + 8.74924i) q^{54} +(-3.34456 + 5.79294i) q^{55} +(-1.52569 + 2.64257i) q^{56} +(7.31088 + 12.6628i) q^{57} +(2.02569 + 3.50859i) q^{58} +(6.36226 + 11.0198i) q^{59} -3.84324 q^{60} +(-3.02569 + 5.24064i) q^{61} +(0.395932 + 0.685774i) q^{62} +19.2569 q^{63} +1.00000 q^{64} +(-1.25951 - 2.18154i) q^{65} -16.2055 q^{66} +(4.65544 - 8.06346i) q^{67} +5.10275 q^{68} +(2.65544 - 4.59936i) q^{69} +(-1.92162 + 3.32834i) q^{70} +(3.52569 - 6.10667i) q^{71} +(-3.15544 - 5.46539i) q^{72} -3.31088 q^{73} +(-4.44731 + 4.14988i) q^{74} +10.4163 q^{75} +(-2.39593 - 4.14988i) q^{76} +(-8.10275 + 14.0344i) q^{77} +(3.05137 - 5.28514i) q^{78} +(5.70682 - 9.88450i) q^{79} +1.25951 q^{80} +(-5.94731 + 10.3010i) q^{81} -0.208136 q^{82} +(1.78520 + 3.09205i) q^{83} -9.31088 q^{84} +6.42697 q^{85} +(2.18113 + 3.77783i) q^{86} +(-6.18113 + 10.7060i) q^{87} +5.31088 q^{88} +(-1.63642 - 2.83436i) q^{89} +(-3.97431 - 6.88371i) q^{90} +(-3.05137 - 5.28514i) q^{91} +(-0.870245 + 1.50731i) q^{92} +(-1.20814 + 2.09255i) q^{93} +(1.60407 + 2.77833i) q^{94} +(-3.01770 - 5.22681i) q^{95} +(1.52569 + 2.64257i) q^{96} +2.20814 q^{97} +(-1.15544 + 2.00128i) q^{98} +(-16.7582 - 29.0260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 8 q^{11} - 6 q^{13} - 4 q^{15} - 3 q^{16} + 3 q^{17} - 7 q^{18} - 8 q^{19} - q^{20} + 16 q^{21} - 4 q^{22} + 16 q^{23} - 20 q^{25} + 12 q^{26} - 24 q^{27} - 6 q^{29} - 4 q^{30} + 8 q^{31} - 3 q^{32} + 12 q^{33} + 3 q^{34} + 4 q^{35} + 14 q^{36} - 11 q^{37} + 16 q^{38} - q^{40} + 7 q^{41} + 16 q^{42} + 16 q^{43} - 4 q^{44} + 66 q^{45} - 8 q^{46} - 32 q^{47} + 5 q^{49} - 20 q^{50} - 64 q^{51} - 6 q^{52} - 22 q^{53} + 12 q^{54} - 32 q^{55} + 20 q^{57} + 3 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} - 4 q^{62} + 24 q^{63} + 6 q^{64} - 2 q^{65} - 24 q^{66} + 16 q^{67} - 6 q^{68} + 4 q^{69} + 4 q^{70} + 12 q^{71} - 7 q^{72} + 4 q^{73} - 2 q^{74} + 88 q^{75} - 8 q^{76} - 12 q^{77} + 4 q^{79} + 2 q^{80} - 11 q^{81} - 14 q^{82} - 4 q^{83} - 32 q^{84} - 18 q^{85} - 8 q^{86} - 16 q^{87} + 8 q^{88} - 9 q^{89} - 33 q^{90} - 8 q^{92} - 20 q^{93} + 16 q^{94} + 36 q^{95} + 26 q^{97} + 5 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 1.52569 2.64257i 0.880856 1.52569i 0.0304649 0.999536i \(-0.490301\pi\)
0.850391 0.526151i \(-0.176365\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.629755 + 1.09077i −0.281635 + 0.487806i −0.971788 0.235858i \(-0.924210\pi\)
0.690153 + 0.723664i \(0.257543\pi\)
\(6\) −3.05137 −1.24572
\(7\) −1.52569 + 2.64257i −0.576656 + 0.998797i 0.419204 + 0.907892i \(0.362309\pi\)
−0.995860 + 0.0909046i \(0.971024\pi\)
\(8\) 1.00000 0.353553
\(9\) −3.15544 5.46539i −1.05181 1.82180i
\(10\) 1.25951 0.398292
\(11\) 5.31088 1.60129 0.800646 0.599138i \(-0.204490\pi\)
0.800646 + 0.599138i \(0.204490\pi\)
\(12\) 1.52569 + 2.64257i 0.440428 + 0.762844i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 3.05137 0.815514
\(15\) 1.92162 + 3.32834i 0.496160 + 0.859374i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.55137 4.41911i −0.618799 1.07179i −0.989705 0.143121i \(-0.954286\pi\)
0.370906 0.928670i \(-0.379047\pi\)
\(18\) −3.15544 + 5.46539i −0.743745 + 1.28820i
\(19\) −2.39593 + 4.14988i −0.549664 + 0.952047i 0.448633 + 0.893716i \(0.351911\pi\)
−0.998297 + 0.0583306i \(0.981422\pi\)
\(20\) −0.629755 1.09077i −0.140818 0.243903i
\(21\) 4.65544 + 8.06346i 1.01590 + 1.75959i
\(22\) −2.65544 4.59936i −0.566142 0.980587i
\(23\) 1.74049 0.362917 0.181459 0.983399i \(-0.441918\pi\)
0.181459 + 0.983399i \(0.441918\pi\)
\(24\) 1.52569 2.64257i 0.311430 0.539412i
\(25\) 1.70682 + 2.95629i 0.341363 + 0.591259i
\(26\) 2.00000 0.392232
\(27\) −10.1027 −1.94427
\(28\) −1.52569 2.64257i −0.288328 0.499398i
\(29\) −4.05137 −0.752321 −0.376161 0.926554i \(-0.622756\pi\)
−0.376161 + 0.926554i \(0.622756\pi\)
\(30\) 1.92162 3.32834i 0.350838 0.607669i
\(31\) −0.791864 −0.142223 −0.0711115 0.997468i \(-0.522655\pi\)
−0.0711115 + 0.997468i \(0.522655\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 8.10275 14.0344i 1.41051 2.44307i
\(34\) −2.55137 + 4.41911i −0.437557 + 0.757871i
\(35\) −1.92162 3.32834i −0.324813 0.562592i
\(36\) 6.31088 1.05181
\(37\) −1.37024 5.92642i −0.225267 0.974297i
\(38\) 4.79186 0.777343
\(39\) 3.05137 + 5.28514i 0.488611 + 0.846299i
\(40\) −0.629755 + 1.09077i −0.0995730 + 0.172466i
\(41\) 0.104068 0.180251i 0.0162527 0.0281505i −0.857785 0.514009i \(-0.828160\pi\)
0.874037 + 0.485859i \(0.161493\pi\)
\(42\) 4.65544 8.06346i 0.718350 1.24422i
\(43\) −4.36226 −0.665238 −0.332619 0.943061i \(-0.607932\pi\)
−0.332619 + 0.943061i \(0.607932\pi\)
\(44\) −2.65544 + 4.59936i −0.400323 + 0.693380i
\(45\) 7.94863 1.18491
\(46\) −0.870245 1.50731i −0.128311 0.222240i
\(47\) −3.20814 −0.467955 −0.233977 0.972242i \(-0.575174\pi\)
−0.233977 + 0.972242i \(0.575174\pi\)
\(48\) −3.05137 −0.440428
\(49\) −1.15544 2.00128i −0.165063 0.285898i
\(50\) 1.70682 2.95629i 0.241380 0.418083i
\(51\) −15.5704 −2.18029
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −5.65544 9.79551i −0.776835 1.34552i −0.933757 0.357906i \(-0.883491\pi\)
0.156923 0.987611i \(-0.449843\pi\)
\(54\) 5.05137 + 8.74924i 0.687405 + 1.19062i
\(55\) −3.34456 + 5.79294i −0.450980 + 0.781120i
\(56\) −1.52569 + 2.64257i −0.203879 + 0.353128i
\(57\) 7.31088 + 12.6628i 0.968350 + 1.67723i
\(58\) 2.02569 + 3.50859i 0.265986 + 0.460701i
\(59\) 6.36226 + 11.0198i 0.828296 + 1.43465i 0.899374 + 0.437179i \(0.144022\pi\)
−0.0710788 + 0.997471i \(0.522644\pi\)
\(60\) −3.84324 −0.496160
\(61\) −3.02569 + 5.24064i −0.387400 + 0.670996i −0.992099 0.125458i \(-0.959960\pi\)
0.604699 + 0.796454i \(0.293293\pi\)
\(62\) 0.395932 + 0.685774i 0.0502834 + 0.0870934i
\(63\) 19.2569 2.42614
\(64\) 1.00000 0.125000
\(65\) −1.25951 2.18154i −0.156223 0.270586i
\(66\) −16.2055 −1.99476
\(67\) 4.65544 8.06346i 0.568753 0.985109i −0.427937 0.903809i \(-0.640759\pi\)
0.996690 0.0813001i \(-0.0259072\pi\)
\(68\) 5.10275 0.618799
\(69\) 2.65544 4.59936i 0.319678 0.553698i
\(70\) −1.92162 + 3.32834i −0.229677 + 0.397813i
\(71\) 3.52569 6.10667i 0.418422 0.724728i −0.577359 0.816491i \(-0.695917\pi\)
0.995781 + 0.0917622i \(0.0292500\pi\)
\(72\) −3.15544 5.46539i −0.371872 0.644102i
\(73\) −3.31088 −0.387510 −0.193755 0.981050i \(-0.562067\pi\)
−0.193755 + 0.981050i \(0.562067\pi\)
\(74\) −4.44731 + 4.14988i −0.516989 + 0.482413i
\(75\) 10.4163 1.20277
\(76\) −2.39593 4.14988i −0.274832 0.476023i
\(77\) −8.10275 + 14.0344i −0.923394 + 1.59937i
\(78\) 3.05137 5.28514i 0.345500 0.598424i
\(79\) 5.70682 9.88450i 0.642067 1.11209i −0.342904 0.939371i \(-0.611410\pi\)
0.984971 0.172722i \(-0.0552563\pi\)
\(80\) 1.25951 0.140818
\(81\) −5.94731 + 10.3010i −0.660812 + 1.14456i
\(82\) −0.208136 −0.0229848
\(83\) 1.78520 + 3.09205i 0.195951 + 0.339397i 0.947212 0.320608i \(-0.103887\pi\)
−0.751261 + 0.660005i \(0.770554\pi\)
\(84\) −9.31088 −1.01590
\(85\) 6.42697 0.697102
\(86\) 2.18113 + 3.77783i 0.235197 + 0.407374i
\(87\) −6.18113 + 10.7060i −0.662687 + 1.14781i
\(88\) 5.31088 0.566142
\(89\) −1.63642 2.83436i −0.173460 0.300442i 0.766167 0.642641i \(-0.222162\pi\)
−0.939627 + 0.342199i \(0.888828\pi\)
\(90\) −3.97431 6.88371i −0.418929 0.725607i
\(91\) −3.05137 5.28514i −0.319871 0.554033i
\(92\) −0.870245 + 1.50731i −0.0907293 + 0.157148i
\(93\) −1.20814 + 2.09255i −0.125278 + 0.216988i
\(94\) 1.60407 + 2.77833i 0.165447 + 0.286563i
\(95\) −3.01770 5.22681i −0.309610 0.536260i
\(96\) 1.52569 + 2.64257i 0.155715 + 0.269706i
\(97\) 2.20814 0.224202 0.112101 0.993697i \(-0.464242\pi\)
0.112101 + 0.993697i \(0.464242\pi\)
\(98\) −1.15544 + 2.00128i −0.116717 + 0.202160i
\(99\) −16.7582 29.0260i −1.68426 2.91723i
\(100\) −3.41363 −0.341363
\(101\) 3.36226 0.334557 0.167279 0.985910i \(-0.446502\pi\)
0.167279 + 0.985910i \(0.446502\pi\)
\(102\) 7.78520 + 13.4844i 0.770849 + 1.33515i
\(103\) 17.1541 1.69025 0.845123 0.534572i \(-0.179527\pi\)
0.845123 + 0.534572i \(0.179527\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) −11.7272 −1.14445
\(106\) −5.65544 + 9.79551i −0.549305 + 0.951424i
\(107\) −0.181130 + 0.313726i −0.0175104 + 0.0303290i −0.874648 0.484759i \(-0.838907\pi\)
0.857137 + 0.515088i \(0.172241\pi\)
\(108\) 5.05137 8.74924i 0.486069 0.841896i
\(109\) −0.233823 0.404994i −0.0223962 0.0387914i 0.854610 0.519270i \(-0.173796\pi\)
−0.877006 + 0.480479i \(0.840463\pi\)
\(110\) 6.68912 0.637782
\(111\) −17.7515 5.42090i −1.68490 0.514529i
\(112\) 3.05137 0.288328
\(113\) 0.344558 + 0.596791i 0.0324133 + 0.0561414i 0.881777 0.471667i \(-0.156347\pi\)
−0.849364 + 0.527808i \(0.823014\pi\)
\(114\) 7.31088 12.6628i 0.684727 1.18598i
\(115\) −1.09608 + 1.89847i −0.102210 + 0.177033i
\(116\) 2.02569 3.50859i 0.188080 0.325765i
\(117\) 12.6218 1.16688
\(118\) 6.36226 11.0198i 0.585693 1.01445i
\(119\) 15.5704 1.42734
\(120\) 1.92162 + 3.32834i 0.175419 + 0.303835i
\(121\) 17.2055 1.56414
\(122\) 6.05137 0.547866
\(123\) −0.317551 0.550014i −0.0286326 0.0495931i
\(124\) 0.395932 0.685774i 0.0355557 0.0615843i
\(125\) −10.5971 −0.947830
\(126\) −9.62844 16.6769i −0.857769 1.48570i
\(127\) 7.49201 + 12.9765i 0.664809 + 1.15148i 0.979337 + 0.202234i \(0.0648203\pi\)
−0.314528 + 0.949248i \(0.601846\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −6.65544 + 11.5276i −0.585979 + 1.01495i
\(130\) −1.25951 + 2.18154i −0.110466 + 0.191333i
\(131\) −6.04471 10.4697i −0.528129 0.914746i −0.999462 0.0327906i \(-0.989561\pi\)
0.471334 0.881955i \(-0.343773\pi\)
\(132\) 8.10275 + 14.0344i 0.705254 + 1.22154i
\(133\) −7.31088 12.6628i −0.633934 1.09801i
\(134\) −9.31088 −0.804338
\(135\) 6.36226 11.0198i 0.547576 0.948430i
\(136\) −2.55137 4.41911i −0.218779 0.378936i
\(137\) −16.6865 −1.42562 −0.712811 0.701356i \(-0.752578\pi\)
−0.712811 + 0.701356i \(0.752578\pi\)
\(138\) −5.31088 −0.452093
\(139\) 9.09608 + 15.7549i 0.771520 + 1.33631i 0.936730 + 0.350053i \(0.113836\pi\)
−0.165210 + 0.986258i \(0.552830\pi\)
\(140\) 3.84324 0.324813
\(141\) −4.89461 + 8.47772i −0.412201 + 0.713953i
\(142\) −7.05137 −0.591738
\(143\) −5.31088 + 9.19872i −0.444118 + 0.769236i
\(144\) −3.15544 + 5.46539i −0.262954 + 0.455449i
\(145\) 2.55137 4.41911i 0.211880 0.366987i
\(146\) 1.65544 + 2.86731i 0.137005 + 0.237300i
\(147\) −7.05137 −0.581588
\(148\) 5.81755 + 1.77654i 0.478200 + 0.146031i
\(149\) 13.5324 1.10861 0.554307 0.832312i \(-0.312983\pi\)
0.554307 + 0.832312i \(0.312983\pi\)
\(150\) −5.20814 9.02076i −0.425243 0.736542i
\(151\) −0.610734 + 1.05782i −0.0497008 + 0.0860844i −0.889806 0.456340i \(-0.849160\pi\)
0.840105 + 0.542424i \(0.182493\pi\)
\(152\) −2.39593 + 4.14988i −0.194336 + 0.336599i
\(153\) −16.1014 + 27.8885i −1.30172 + 2.25465i
\(154\) 16.2055 1.30588
\(155\) 0.498680 0.863740i 0.0400550 0.0693772i
\(156\) −6.10275 −0.488611
\(157\) −9.38795 16.2604i −0.749240 1.29772i −0.948188 0.317711i \(-0.897086\pi\)
0.198948 0.980010i \(-0.436248\pi\)
\(158\) −11.4136 −0.908020
\(159\) −34.5137 −2.73712
\(160\) −0.629755 1.09077i −0.0497865 0.0862328i
\(161\) −2.65544 + 4.59936i −0.209278 + 0.362480i
\(162\) 11.8946 0.934529
\(163\) 3.92162 + 6.79244i 0.307165 + 0.532025i 0.977741 0.209816i \(-0.0672863\pi\)
−0.670576 + 0.741841i \(0.733953\pi\)
\(164\) 0.104068 + 0.180251i 0.00812636 + 0.0140753i
\(165\) 10.2055 + 17.6764i 0.794497 + 1.37611i
\(166\) 1.78520 3.09205i 0.138558 0.239990i
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 4.65544 + 8.06346i 0.359175 + 0.622110i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −3.21348 5.56592i −0.246463 0.426886i
\(171\) 30.2409 2.31258
\(172\) 2.18113 3.77783i 0.166310 0.288057i
\(173\) −2.23382 3.86910i −0.169834 0.294162i 0.768527 0.639817i \(-0.220990\pi\)
−0.938362 + 0.345655i \(0.887657\pi\)
\(174\) 12.3623 0.937180
\(175\) −10.4163 −0.787396
\(176\) −2.65544 4.59936i −0.200162 0.346690i
\(177\) 38.8273 2.91844
\(178\) −1.63642 + 2.83436i −0.122655 + 0.212445i
\(179\) −14.1027 −1.05409 −0.527044 0.849838i \(-0.676700\pi\)
−0.527044 + 0.849838i \(0.676700\pi\)
\(180\) −3.97431 + 6.88371i −0.296228 + 0.513082i
\(181\) −6.73250 + 11.6610i −0.500423 + 0.866758i 0.499577 + 0.866270i \(0.333489\pi\)
−1.00000 0.000488579i \(0.999844\pi\)
\(182\) −3.05137 + 5.28514i −0.226183 + 0.391760i
\(183\) 9.23250 + 15.9912i 0.682486 + 1.18210i
\(184\) 1.74049 0.128311
\(185\) 7.32727 + 2.23757i 0.538711 + 0.164510i
\(186\) 2.41627 0.177170
\(187\) −13.5501 23.4694i −0.990878 1.71625i
\(188\) 1.60407 2.77833i 0.116989 0.202630i
\(189\) 15.4136 26.6972i 1.12118 1.94194i
\(190\) −3.01770 + 5.22681i −0.218927 + 0.379193i
\(191\) 9.42697 0.682111 0.341056 0.940043i \(-0.389216\pi\)
0.341056 + 0.940043i \(0.389216\pi\)
\(192\) 1.52569 2.64257i 0.110107 0.190711i
\(193\) 2.48098 0.178585 0.0892924 0.996005i \(-0.471539\pi\)
0.0892924 + 0.996005i \(0.471539\pi\)
\(194\) −1.10407 1.91230i −0.0792675 0.137295i
\(195\) −7.68648 −0.550440
\(196\) 2.31088 0.165063
\(197\) 0.974313 + 1.68756i 0.0694169 + 0.120234i 0.898645 0.438677i \(-0.144553\pi\)
−0.829228 + 0.558911i \(0.811219\pi\)
\(198\) −16.7582 + 29.0260i −1.19095 + 2.06279i
\(199\) −1.98667 −0.140831 −0.0704156 0.997518i \(-0.522433\pi\)
−0.0704156 + 0.997518i \(0.522433\pi\)
\(200\) 1.70682 + 2.95629i 0.120690 + 0.209041i
\(201\) −14.2055 24.6046i −1.00198 1.73548i
\(202\) −1.68113 2.91180i −0.118284 0.204874i
\(203\) 6.18113 10.7060i 0.433830 0.751416i
\(204\) 7.78520 13.4844i 0.545073 0.944094i
\(205\) 0.131075 + 0.227028i 0.00915467 + 0.0158564i
\(206\) −8.57706 14.8559i −0.597592 1.03506i
\(207\) −5.49201 9.51245i −0.381721 0.661161i
\(208\) 2.00000 0.138675
\(209\) −12.7245 + 22.0395i −0.880173 + 1.52450i
\(210\) 5.86358 + 10.1560i 0.404625 + 0.700832i
\(211\) −17.0868 −1.17630 −0.588151 0.808751i \(-0.700144\pi\)
−0.588151 + 0.808751i \(0.700144\pi\)
\(212\) 11.3109 0.776835
\(213\) −10.7582 18.6337i −0.737139 1.27676i
\(214\) 0.362259 0.0247635
\(215\) 2.74716 4.75821i 0.187354 0.324507i
\(216\) −10.1027 −0.687405
\(217\) 1.20814 2.09255i 0.0820136 0.142052i
\(218\) −0.233823 + 0.404994i −0.0158365 + 0.0274297i
\(219\) −5.05137 + 8.74924i −0.341340 + 0.591219i
\(220\) −3.34456 5.79294i −0.225490 0.390560i
\(221\) 10.2055 0.686496
\(222\) 4.18113 + 18.0837i 0.280619 + 1.21370i
\(223\) 1.94599 0.130313 0.0651564 0.997875i \(-0.479245\pi\)
0.0651564 + 0.997875i \(0.479245\pi\)
\(224\) −1.52569 2.64257i −0.101939 0.176564i
\(225\) 10.7715 18.6568i 0.718102 1.24379i
\(226\) 0.344558 0.596791i 0.0229196 0.0396980i
\(227\) −2.29318 + 3.97191i −0.152204 + 0.263625i −0.932037 0.362362i \(-0.881970\pi\)
0.779833 + 0.625987i \(0.215304\pi\)
\(228\) −14.6218 −0.968350
\(229\) 0.817551 1.41604i 0.0540253 0.0935745i −0.837748 0.546057i \(-0.816128\pi\)
0.891773 + 0.452483i \(0.149462\pi\)
\(230\) 2.19216 0.144547
\(231\) 24.7245 + 42.8241i 1.62675 + 2.81762i
\(232\) −4.05137 −0.265986
\(233\) 8.03804 0.526590 0.263295 0.964715i \(-0.415191\pi\)
0.263295 + 0.964715i \(0.415191\pi\)
\(234\) −6.31088 10.9308i −0.412555 0.714567i
\(235\) 2.02034 3.49933i 0.131792 0.228271i
\(236\) −12.7245 −0.828296
\(237\) −17.4136 30.1613i −1.13114 1.95919i
\(238\) −7.78520 13.4844i −0.504639 0.874061i
\(239\) −0.317551 0.550014i −0.0205407 0.0355775i 0.855572 0.517683i \(-0.173205\pi\)
−0.876113 + 0.482106i \(0.839872\pi\)
\(240\) 1.92162 3.32834i 0.124040 0.214844i
\(241\) 3.75819 6.50938i 0.242086 0.419306i −0.719222 0.694780i \(-0.755502\pi\)
0.961308 + 0.275474i \(0.0888349\pi\)
\(242\) −8.60275 14.9004i −0.553006 0.957834i
\(243\) 2.99333 + 5.18461i 0.192022 + 0.332593i
\(244\) −3.02569 5.24064i −0.193700 0.335498i
\(245\) 2.91058 0.185950
\(246\) −0.317551 + 0.550014i −0.0202463 + 0.0350676i
\(247\) −4.79186 8.29975i −0.304899 0.528101i
\(248\) −0.791864 −0.0502834
\(249\) 10.8946 0.690418
\(250\) 5.29853 + 9.17732i 0.335108 + 0.580425i
\(251\) −8.88128 −0.560581 −0.280291 0.959915i \(-0.590431\pi\)
−0.280291 + 0.959915i \(0.590431\pi\)
\(252\) −9.62844 + 16.6769i −0.606534 + 1.05055i
\(253\) 9.24354 0.581136
\(254\) 7.49201 12.9765i 0.470091 0.814221i
\(255\) 9.80554 16.9837i 0.614047 1.06356i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.05005 + 10.4790i 0.377392 + 0.653662i 0.990682 0.136196i \(-0.0434876\pi\)
−0.613290 + 0.789858i \(0.710154\pi\)
\(258\) 13.3109 0.828699
\(259\) 17.7515 + 5.42090i 1.10303 + 0.336838i
\(260\) 2.51902 0.156223
\(261\) 12.7839 + 22.1423i 0.791302 + 1.37058i
\(262\) −6.04471 + 10.4697i −0.373443 + 0.646823i
\(263\) 9.57040 16.5764i 0.590136 1.02215i −0.404078 0.914725i \(-0.632408\pi\)
0.994214 0.107421i \(-0.0342592\pi\)
\(264\) 8.10275 14.0344i 0.498690 0.863756i
\(265\) 14.2462 0.875136
\(266\) −7.31088 + 12.6628i −0.448259 + 0.776408i
\(267\) −9.98667 −0.611174
\(268\) 4.65544 + 8.06346i 0.284376 + 0.492554i
\(269\) −15.7892 −0.962686 −0.481343 0.876532i \(-0.659851\pi\)
−0.481343 + 0.876532i \(0.659851\pi\)
\(270\) −12.7245 −0.774390
\(271\) 9.55005 + 16.5412i 0.580125 + 1.00481i 0.995464 + 0.0951386i \(0.0303294\pi\)
−0.415340 + 0.909666i \(0.636337\pi\)
\(272\) −2.55137 + 4.41911i −0.154700 + 0.267948i
\(273\) −18.6218 −1.12704
\(274\) 8.34324 + 14.4509i 0.504033 + 0.873012i
\(275\) 9.06471 + 15.7005i 0.546622 + 0.946778i
\(276\) 2.65544 + 4.59936i 0.159839 + 0.276849i
\(277\) −8.20015 + 14.2031i −0.492699 + 0.853380i −0.999965 0.00840971i \(-0.997323\pi\)
0.507265 + 0.861790i \(0.330656\pi\)
\(278\) 9.09608 15.7549i 0.545547 0.944915i
\(279\) 2.49868 + 4.32784i 0.149592 + 0.259101i
\(280\) −1.92162 3.32834i −0.114839 0.198906i
\(281\) 2.39725 + 4.15216i 0.143008 + 0.247697i 0.928628 0.371012i \(-0.120989\pi\)
−0.785620 + 0.618709i \(0.787656\pi\)
\(282\) 9.78922 0.582940
\(283\) −12.9730 + 22.4699i −0.771164 + 1.33570i 0.165761 + 0.986166i \(0.446992\pi\)
−0.936925 + 0.349530i \(0.886341\pi\)
\(284\) 3.52569 + 6.10667i 0.209211 + 0.362364i
\(285\) −18.4163 −1.09089
\(286\) 10.6218 0.628078
\(287\) 0.317551 + 0.550014i 0.0187444 + 0.0324663i
\(288\) 6.31088 0.371872
\(289\) −4.51902 + 7.82717i −0.265825 + 0.460422i
\(290\) −5.10275 −0.299644
\(291\) 3.36893 5.83515i 0.197490 0.342063i
\(292\) 1.65544 2.86731i 0.0968774 0.167797i
\(293\) −11.0257 + 19.0971i −0.644128 + 1.11566i 0.340375 + 0.940290i \(0.389446\pi\)
−0.984502 + 0.175372i \(0.943887\pi\)
\(294\) 3.52569 + 6.10667i 0.205622 + 0.356148i
\(295\) −16.0267 −0.933108
\(296\) −1.37024 5.92642i −0.0796439 0.344466i
\(297\) −53.6545 −3.11335
\(298\) −6.76618 11.7194i −0.391954 0.678884i
\(299\) −1.74049 + 3.01462i −0.100655 + 0.174340i
\(300\) −5.20814 + 9.02076i −0.300692 + 0.520814i
\(301\) 6.65544 11.5276i 0.383613 0.664438i
\(302\) 1.22147 0.0702876
\(303\) 5.12976 8.88500i 0.294697 0.510430i
\(304\) 4.79186 0.274832
\(305\) −3.81088 6.60065i −0.218211 0.377952i
\(306\) 32.2029 1.84091
\(307\) −5.74049 −0.327627 −0.163814 0.986491i \(-0.552380\pi\)
−0.163814 + 0.986491i \(0.552380\pi\)
\(308\) −8.10275 14.0344i −0.461697 0.799683i
\(309\) 26.1718 45.3309i 1.48886 2.57879i
\(310\) −0.997361 −0.0566463
\(311\) 5.26618 + 9.12129i 0.298617 + 0.517221i 0.975820 0.218576i \(-0.0701412\pi\)
−0.677202 + 0.735797i \(0.736808\pi\)
\(312\) 3.05137 + 5.28514i 0.172750 + 0.299212i
\(313\) −12.4150 21.5033i −0.701735 1.21544i −0.967857 0.251501i \(-0.919076\pi\)
0.266122 0.963939i \(-0.414257\pi\)
\(314\) −9.38795 + 16.2604i −0.529792 + 0.917627i
\(315\) −12.1271 + 21.0048i −0.683286 + 1.18349i
\(316\) 5.70682 + 9.88450i 0.321034 + 0.556046i
\(317\) 13.1461 + 22.7698i 0.738361 + 1.27888i 0.953233 + 0.302236i \(0.0977331\pi\)
−0.214873 + 0.976642i \(0.568934\pi\)
\(318\) 17.2569 + 29.8898i 0.967717 + 1.67614i
\(319\) −21.5164 −1.20469
\(320\) −0.629755 + 1.09077i −0.0352044 + 0.0609758i
\(321\) 0.552694 + 0.957294i 0.0308484 + 0.0534309i
\(322\) 5.31088 0.295964
\(323\) 24.4517 1.36053
\(324\) −5.94731 10.3010i −0.330406 0.572280i
\(325\) −6.82727 −0.378709
\(326\) 3.92162 6.79244i 0.217198 0.376199i
\(327\) −1.42697 −0.0789114
\(328\) 0.104068 0.180251i 0.00574620 0.00995271i
\(329\) 4.89461 8.47772i 0.269849 0.467392i
\(330\) 10.2055 17.6764i 0.561794 0.973056i
\(331\) −14.8946 25.7982i −0.818682 1.41800i −0.906654 0.421876i \(-0.861372\pi\)
0.0879717 0.996123i \(-0.471961\pi\)
\(332\) −3.57040 −0.195951
\(333\) −28.0664 + 26.1894i −1.53803 + 1.43517i
\(334\) −12.0000 −0.656611
\(335\) 5.86358 + 10.1560i 0.320362 + 0.554882i
\(336\) 4.65544 8.06346i 0.253975 0.439898i
\(337\) 6.36358 11.0220i 0.346646 0.600409i −0.639005 0.769202i \(-0.720654\pi\)
0.985651 + 0.168794i \(0.0539871\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 2.10275 0.114206
\(340\) −3.21348 + 5.56592i −0.174276 + 0.301854i
\(341\) −4.20550 −0.227740
\(342\) −15.1204 26.1894i −0.817620 1.41616i
\(343\) −14.3082 −0.772573
\(344\) −4.36226 −0.235197
\(345\) 3.34456 + 5.79294i 0.180065 + 0.311882i
\(346\) −2.23382 + 3.86910i −0.120091 + 0.208004i
\(347\) 29.5651 1.58714 0.793569 0.608480i \(-0.208220\pi\)
0.793569 + 0.608480i \(0.208220\pi\)
\(348\) −6.18113 10.7060i −0.331343 0.573903i
\(349\) 16.2515 + 28.1485i 0.869924 + 1.50675i 0.862073 + 0.506784i \(0.169166\pi\)
0.00785093 + 0.999969i \(0.497501\pi\)
\(350\) 5.20814 + 9.02076i 0.278387 + 0.482180i
\(351\) 10.1027 17.4985i 0.539245 0.933999i
\(352\) −2.65544 + 4.59936i −0.141536 + 0.245147i
\(353\) −2.05269 3.55537i −0.109254 0.189233i 0.806214 0.591624i \(-0.201513\pi\)
−0.915468 + 0.402390i \(0.868179\pi\)
\(354\) −19.4136 33.6254i −1.03182 1.78717i
\(355\) 4.44064 + 7.69141i 0.235685 + 0.408218i
\(356\) 3.27284 0.173460
\(357\) 23.7556 41.1458i 1.25728 2.17767i
\(358\) 7.05137 + 12.2133i 0.372677 + 0.645495i
\(359\) −28.2055 −1.48863 −0.744315 0.667829i \(-0.767224\pi\)
−0.744315 + 0.667829i \(0.767224\pi\)
\(360\) 7.94863 0.418929
\(361\) −1.98098 3.43116i −0.104262 0.180587i
\(362\) 13.4650 0.707705
\(363\) 26.2502 45.4667i 1.37778 2.38638i
\(364\) 6.10275 0.319871
\(365\) 2.08505 3.61141i 0.109136 0.189030i
\(366\) 9.23250 15.9912i 0.482591 0.835872i
\(367\) 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) −0.870245 1.50731i −0.0453646 0.0785739i
\(369\) −1.31352 −0.0683793
\(370\) −1.72584 7.46439i −0.0897220 0.388055i
\(371\) 34.5137 1.79186
\(372\) −1.20814 2.09255i −0.0626389 0.108494i
\(373\) −18.6785 + 32.3521i −0.967136 + 1.67513i −0.263371 + 0.964695i \(0.584834\pi\)
−0.703765 + 0.710433i \(0.748499\pi\)
\(374\) −13.5501 + 23.4694i −0.700657 + 1.21357i
\(375\) −16.1678 + 28.0034i −0.834901 + 1.44609i
\(376\) −3.20814 −0.165447
\(377\) 4.05137 7.01719i 0.208656 0.361403i
\(378\) −30.8273 −1.58558
\(379\) 2.45397 + 4.25040i 0.126052 + 0.218329i 0.922144 0.386848i \(-0.126436\pi\)
−0.796092 + 0.605176i \(0.793103\pi\)
\(380\) 6.03540 0.309610
\(381\) 45.7219 2.34240
\(382\) −4.71348 8.16399i −0.241163 0.417706i
\(383\) −10.3042 + 17.8474i −0.526521 + 0.911961i 0.473002 + 0.881062i \(0.343171\pi\)
−0.999522 + 0.0308995i \(0.990163\pi\)
\(384\) −3.05137 −0.155715
\(385\) −10.2055 17.6764i −0.520120 0.900875i
\(386\) −1.24049 2.14859i −0.0631393 0.109360i
\(387\) 13.7649 + 23.8414i 0.699707 + 1.21193i
\(388\) −1.10407 + 1.91230i −0.0560506 + 0.0970824i
\(389\) 12.7839 22.1423i 0.648168 1.12266i −0.335392 0.942079i \(-0.608869\pi\)
0.983560 0.180582i \(-0.0577980\pi\)
\(390\) 3.84324 + 6.65668i 0.194610 + 0.337074i
\(391\) −4.44064 7.69141i −0.224573 0.388972i
\(392\) −1.15544 2.00128i −0.0583587 0.101080i
\(393\) −36.8893 −1.86082
\(394\) 0.974313 1.68756i 0.0490852 0.0850180i
\(395\) 7.18780 + 12.4496i 0.361657 + 0.626409i
\(396\) 33.5164 1.68426
\(397\) −30.2923 −1.52033 −0.760163 0.649733i \(-0.774881\pi\)
−0.760163 + 0.649733i \(0.774881\pi\)
\(398\) 0.993334 + 1.72050i 0.0497913 + 0.0862411i
\(399\) −44.6165 −2.23362
\(400\) 1.70682 2.95629i 0.0853408 0.147815i
\(401\) 27.5164 1.37410 0.687051 0.726609i \(-0.258905\pi\)
0.687051 + 0.726609i \(0.258905\pi\)
\(402\) −14.2055 + 24.6046i −0.708506 + 1.22717i
\(403\) 0.791864 1.37155i 0.0394455 0.0683217i
\(404\) −1.68113 + 2.91180i −0.0836393 + 0.144868i
\(405\) −7.49069 12.9743i −0.372216 0.644696i
\(406\) −12.3623 −0.613529
\(407\) −7.27721 31.4745i −0.360718 1.56013i
\(408\) −15.5704 −0.770849
\(409\) −3.62309 6.27537i −0.179150 0.310297i 0.762439 0.647060i \(-0.224001\pi\)
−0.941590 + 0.336762i \(0.890668\pi\)
\(410\) 0.131075 0.227028i 0.00647333 0.0112121i
\(411\) −25.4583 + 44.0951i −1.25577 + 2.17505i
\(412\) −8.57706 + 14.8559i −0.422561 + 0.731898i
\(413\) −38.8273 −1.91056
\(414\) −5.49201 + 9.51245i −0.269918 + 0.467511i
\(415\) −4.49695 −0.220747
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 55.5111 2.71839
\(418\) 25.4490 1.24475
\(419\) 2.28388 + 3.95579i 0.111575 + 0.193253i 0.916405 0.400251i \(-0.131077\pi\)
−0.804831 + 0.593505i \(0.797744\pi\)
\(420\) 5.86358 10.1560i 0.286113 0.495563i
\(421\) 26.8432 1.30826 0.654130 0.756382i \(-0.273035\pi\)
0.654130 + 0.756382i \(0.273035\pi\)
\(422\) 8.54339 + 14.7976i 0.415886 + 0.720335i
\(423\) 10.1231 + 17.5337i 0.492201 + 0.852518i
\(424\) −5.65544 9.79551i −0.274653 0.475712i
\(425\) 8.70946 15.0852i 0.422471 0.731741i
\(426\) −10.7582 + 18.6337i −0.521236 + 0.902807i
\(427\) −9.23250 15.9912i −0.446792 0.773867i
\(428\) −0.181130 0.313726i −0.00875522 0.0151645i
\(429\) 16.2055 + 28.0687i 0.782409 + 1.35517i
\(430\) −5.49431 −0.264959
\(431\) 10.3959 18.0063i 0.500754 0.867332i −0.499245 0.866461i \(-0.666389\pi\)
1.00000 0.000871345i \(-0.000277358\pi\)
\(432\) 5.05137 + 8.74924i 0.243034 + 0.420948i
\(433\) 27.6572 1.32912 0.664559 0.747235i \(-0.268619\pi\)
0.664559 + 0.747235i \(0.268619\pi\)
\(434\) −2.41627 −0.115985
\(435\) −7.78520 13.4844i −0.373272 0.646525i
\(436\) 0.467647 0.0223962
\(437\) −4.17009 + 7.22282i −0.199483 + 0.345514i
\(438\) 10.1027 0.482728
\(439\) 3.46765 6.00614i 0.165502 0.286657i −0.771332 0.636433i \(-0.780409\pi\)
0.936833 + 0.349776i \(0.113742\pi\)
\(440\) −3.34456 + 5.79294i −0.159446 + 0.276168i
\(441\) −7.29186 + 12.6299i −0.347232 + 0.601423i
\(442\) −5.10275 8.83822i −0.242713 0.420391i
\(443\) −19.8653 −0.943829 −0.471915 0.881644i \(-0.656437\pi\)
−0.471915 + 0.881644i \(0.656437\pi\)
\(444\) 13.5704 12.6628i 0.644022 0.600951i
\(445\) 4.12218 0.195410
\(446\) −0.972993 1.68527i −0.0460726 0.0798000i
\(447\) 20.6461 35.7602i 0.976529 1.69140i
\(448\) −1.52569 + 2.64257i −0.0720819 + 0.124850i
\(449\) 13.0691 22.6363i 0.616768 1.06827i −0.373304 0.927709i \(-0.621775\pi\)
0.990072 0.140564i \(-0.0448916\pi\)
\(450\) −21.5430 −1.01555
\(451\) 0.552694 0.957294i 0.0260253 0.0450772i
\(452\) −0.689115 −0.0324133
\(453\) 1.86358 + 3.22781i 0.0875586 + 0.151656i
\(454\) 4.58637 0.215249
\(455\) 7.68648 0.360348
\(456\) 7.31088 + 12.6628i 0.342364 + 0.592991i
\(457\) 10.3432 17.9150i 0.483836 0.838029i −0.515991 0.856594i \(-0.672576\pi\)
0.999828 + 0.0185648i \(0.00590969\pi\)
\(458\) −1.63510 −0.0764033
\(459\) 25.7759 + 44.6452i 1.20312 + 2.08386i
\(460\) −1.09608 1.89847i −0.0511051 0.0885166i
\(461\) −11.1027 19.2305i −0.517107 0.895655i −0.999803 0.0198669i \(-0.993676\pi\)
0.482696 0.875788i \(-0.339658\pi\)
\(462\) 24.7245 42.8241i 1.15029 1.99236i
\(463\) −11.0961 + 19.2190i −0.515679 + 0.893182i 0.484156 + 0.874982i \(0.339127\pi\)
−0.999834 + 0.0181998i \(0.994207\pi\)
\(464\) 2.02569 + 3.50859i 0.0940402 + 0.162882i
\(465\) −1.52166 2.63559i −0.0705653 0.122223i
\(466\) −4.01902 6.96115i −0.186178 0.322469i
\(467\) −11.8920 −0.550295 −0.275147 0.961402i \(-0.588727\pi\)
−0.275147 + 0.961402i \(0.588727\pi\)
\(468\) −6.31088 + 10.9308i −0.291721 + 0.505275i
\(469\) 14.2055 + 24.6046i 0.655949 + 1.13614i
\(470\) −4.04068 −0.186383
\(471\) −57.2923 −2.63989
\(472\) 6.36226 + 11.0198i 0.292847 + 0.507225i
\(473\) −23.1675 −1.06524
\(474\) −17.4136 + 30.1613i −0.799835 + 1.38535i
\(475\) −16.3577 −0.750541
\(476\) −7.78520 + 13.4844i −0.356834 + 0.618055i
\(477\) −35.6908 + 61.8184i −1.63417 + 2.83047i
\(478\) −0.317551 + 0.550014i −0.0145244 + 0.0251571i
\(479\) −16.5678 28.6962i −0.757000 1.31116i −0.944374 0.328874i \(-0.893331\pi\)
0.187374 0.982289i \(-0.440002\pi\)
\(480\) −3.84324 −0.175419
\(481\) 11.6351 + 3.55308i 0.530515 + 0.162007i
\(482\) −7.51638 −0.342362
\(483\) 8.10275 + 14.0344i 0.368688 + 0.638586i
\(484\) −8.60275 + 14.9004i −0.391034 + 0.677291i
\(485\) −1.39059 + 2.40856i −0.0631432 + 0.109367i
\(486\) 2.99333 5.18461i 0.135780 0.235179i
\(487\) 19.6377 0.889871 0.444935 0.895563i \(-0.353227\pi\)
0.444935 + 0.895563i \(0.353227\pi\)
\(488\) −3.02569 + 5.24064i −0.136966 + 0.237233i
\(489\) 23.9327 1.08227
\(490\) −1.45529 2.52064i −0.0657434 0.113871i
\(491\) −5.31088 −0.239677 −0.119838 0.992793i \(-0.538238\pi\)
−0.119838 + 0.992793i \(0.538238\pi\)
\(492\) 0.635102 0.0286326
\(493\) 10.3366 + 17.9035i 0.465536 + 0.806332i
\(494\) −4.79186 + 8.29975i −0.215596 + 0.373423i
\(495\) 42.2142 1.89739
\(496\) 0.395932 + 0.685774i 0.0177779 + 0.0307922i
\(497\) 10.7582 + 18.6337i 0.482571 + 0.835837i
\(498\) −5.44731 9.43501i −0.244100 0.422793i
\(499\) −11.1878 + 19.3778i −0.500835 + 0.867471i 0.499165 + 0.866507i \(0.333640\pi\)
−1.00000 0.000963882i \(0.999693\pi\)
\(500\) 5.29853 9.17732i 0.236957 0.410422i
\(501\) −18.3082 31.7108i −0.817952 1.41673i
\(502\) 4.44064 + 7.69141i 0.198195 + 0.343285i
\(503\) −11.8636 20.5483i −0.528971 0.916204i −0.999429 0.0337822i \(-0.989245\pi\)
0.470458 0.882422i \(-0.344089\pi\)
\(504\) 19.2569 0.857769
\(505\) −2.11740 + 3.66744i −0.0942231 + 0.163199i
\(506\) −4.62177 8.00514i −0.205463 0.355872i
\(507\) 27.4624 1.21965
\(508\) −14.9840 −0.664809
\(509\) 3.62976 + 6.28692i 0.160886 + 0.278663i 0.935187 0.354155i \(-0.115231\pi\)
−0.774301 + 0.632818i \(0.781898\pi\)
\(510\) −19.6111 −0.868393
\(511\) 5.05137 8.74924i 0.223460 0.387043i
\(512\) 1.00000 0.0441942
\(513\) 24.2055 41.9252i 1.06870 1.85104i
\(514\) 6.05005 10.4790i 0.266856 0.462209i
\(515\) −10.8029 + 18.7112i −0.476033 + 0.824513i
\(516\) −6.65544 11.5276i −0.292990 0.507473i
\(517\) −17.0380 −0.749332
\(518\) −4.18113 18.0837i −0.183708 0.794553i
\(519\) −13.6325 −0.598399
\(520\) −1.25951 2.18154i −0.0552332 0.0956667i
\(521\) −1.03367 + 1.79037i −0.0452860 + 0.0784377i −0.887780 0.460268i \(-0.847753\pi\)
0.842494 + 0.538706i \(0.181087\pi\)
\(522\) 12.7839 22.1423i 0.559535 0.969143i
\(523\) 18.6125 32.2377i 0.813866 1.40966i −0.0962729 0.995355i \(-0.530692\pi\)
0.910139 0.414303i \(-0.135975\pi\)
\(524\) 12.0894 0.528129
\(525\) −15.8920 + 27.5257i −0.693583 + 1.20132i
\(526\) −19.1408 −0.834578
\(527\) 2.02034 + 3.49933i 0.0880074 + 0.152433i
\(528\) −16.2055 −0.705254
\(529\) −19.9707 −0.868291
\(530\) −7.12309 12.3376i −0.309407 0.535909i
\(531\) 40.1515 69.5444i 1.74243 3.01797i
\(532\) 14.6218 0.633934
\(533\) 0.208136 + 0.360503i 0.00901538 + 0.0156151i
\(534\) 4.99333 + 8.64871i 0.216083 + 0.374266i
\(535\) −0.228135 0.395141i −0.00986312 0.0170834i
\(536\) 4.65544 8.06346i 0.201084 0.348289i
\(537\) −21.5164 + 37.2675i −0.928500 + 1.60821i
\(538\) 7.89461 + 13.6739i 0.340361 + 0.589522i
\(539\) −6.13642 10.6286i −0.264314 0.457806i
\(540\) 6.36226 + 11.0198i 0.273788 + 0.474215i
\(541\) −1.74313 −0.0749430 −0.0374715 0.999298i \(-0.511930\pi\)
−0.0374715 + 0.999298i \(0.511930\pi\)
\(542\) 9.55005 16.5412i 0.410210 0.710505i
\(543\) 20.5434 + 35.5822i 0.881601 + 1.52698i
\(544\) 5.10275 0.218779
\(545\) 0.589006 0.0252302
\(546\) 9.31088 + 16.1269i 0.398469 + 0.690169i
\(547\) 31.6191 1.35194 0.675968 0.736931i \(-0.263726\pi\)
0.675968 + 0.736931i \(0.263726\pi\)
\(548\) 8.34324 14.4509i 0.356405 0.617312i
\(549\) 38.1895 1.62989
\(550\) 9.06471 15.7005i 0.386520 0.669473i
\(551\) 9.70682 16.8127i 0.413524 0.716245i
\(552\) 2.65544 4.59936i 0.113023 0.195762i
\(553\) 17.4136 + 30.1613i 0.740503 + 1.28259i
\(554\) 16.4003 0.696782
\(555\) 17.0921 15.9490i 0.725517 0.676996i
\(556\) −18.1922 −0.771520
\(557\) 11.3702 + 19.6938i 0.481773 + 0.834455i 0.999781 0.0209207i \(-0.00665974\pi\)
−0.518008 + 0.855376i \(0.673326\pi\)
\(558\) 2.49868 4.32784i 0.105778 0.183212i
\(559\) 4.36226 7.55565i 0.184504 0.319570i
\(560\) −1.92162 + 3.32834i −0.0812032 + 0.140648i
\(561\) −82.6926 −3.49128
\(562\) 2.39725 4.15216i 0.101122 0.175148i
\(563\) −13.4676 −0.567594 −0.283797 0.958884i \(-0.591594\pi\)
−0.283797 + 0.958884i \(0.591594\pi\)
\(564\) −4.89461 8.47772i −0.206100 0.356976i
\(565\) −0.867948 −0.0365148
\(566\) 25.9460 1.09059
\(567\) −18.1475 31.4323i −0.762122 1.32003i
\(568\) 3.52569 6.10667i 0.147935 0.256230i
\(569\) −41.8627 −1.75497 −0.877487 0.479600i \(-0.840782\pi\)
−0.877487 + 0.479600i \(0.840782\pi\)
\(570\) 9.20814 + 15.9490i 0.385686 + 0.668028i
\(571\) −14.2502 24.6821i −0.596353 1.03291i −0.993354 0.115095i \(-0.963283\pi\)
0.397002 0.917818i \(-0.370051\pi\)
\(572\) −5.31088 9.19872i −0.222059 0.384618i
\(573\) 14.3826 24.9114i 0.600842 1.04069i
\(574\) 0.317551 0.550014i 0.0132543 0.0229571i
\(575\) 2.97070 + 5.14540i 0.123887 + 0.214578i
\(576\) −3.15544 5.46539i −0.131477 0.227724i
\(577\) −12.1675 21.0747i −0.506538 0.877349i −0.999971 0.00756570i \(-0.997592\pi\)
0.493434 0.869783i \(-0.335742\pi\)
\(578\) 9.03804 0.375933
\(579\) 3.78520 6.55615i 0.157307 0.272464i
\(580\) 2.55137 + 4.41911i 0.105940 + 0.183494i
\(581\) −10.8946 −0.451985
\(582\) −6.73785 −0.279293
\(583\) −30.0354 52.0228i −1.24394 2.15457i
\(584\) −3.31088 −0.137005
\(585\) −7.94863 + 13.7674i −0.328635 + 0.569213i
\(586\) 22.0514 0.910934
\(587\) −22.5230 + 39.0111i −0.929626 + 1.61016i −0.145678 + 0.989332i \(0.546536\pi\)
−0.783948 + 0.620827i \(0.786797\pi\)
\(588\) 3.52569 6.10667i 0.145397 0.251835i
\(589\) 1.89725 3.28614i 0.0781749 0.135403i
\(590\) 8.01333 + 13.8795i 0.329904 + 0.571410i
\(591\) 5.94599 0.244585
\(592\) −4.44731 + 4.14988i −0.182783 + 0.170559i
\(593\) 6.93265 0.284690 0.142345 0.989817i \(-0.454536\pi\)
0.142345 + 0.989817i \(0.454536\pi\)
\(594\) 26.8273 + 46.4662i 1.10074 + 1.90653i
\(595\) −9.80554 + 16.9837i −0.401988 + 0.696263i
\(596\) −6.76618 + 11.7194i −0.277153 + 0.480044i
\(597\) −3.03103 + 5.24990i −0.124052 + 0.214864i
\(598\) 3.48098 0.142348
\(599\) 16.7582 29.0260i 0.684721 1.18597i −0.288803 0.957388i \(-0.593257\pi\)
0.973524 0.228583i \(-0.0734093\pi\)
\(600\) 10.4163 0.425243
\(601\) −4.08637 7.07779i −0.166686 0.288709i 0.770566 0.637360i \(-0.219973\pi\)
−0.937253 + 0.348650i \(0.886640\pi\)
\(602\) −13.3109 −0.542511
\(603\) −58.7599 −2.39289
\(604\) −0.610734 1.05782i −0.0248504 0.0430422i
\(605\) −10.8353 + 18.7672i −0.440516 + 0.762995i
\(606\) −10.2595 −0.416764
\(607\) 21.2772 + 36.8532i 0.863615 + 1.49583i 0.868415 + 0.495837i \(0.165139\pi\)
−0.00480007 + 0.999988i \(0.501528\pi\)
\(608\) −2.39593 4.14988i −0.0971679 0.168300i
\(609\) −18.8609 32.6681i −0.764284 1.32378i
\(610\) −3.81088 + 6.60065i −0.154298 + 0.267252i
\(611\) 3.20814 5.55666i 0.129787 0.224798i
\(612\) −16.1014 27.8885i −0.650862 1.12733i
\(613\) −20.1461 34.8941i −0.813695 1.40936i −0.910261 0.414034i \(-0.864119\pi\)
0.0965665 0.995327i \(-0.469214\pi\)
\(614\) 2.87024 + 4.97141i 0.115834 + 0.200630i
\(615\) 0.799917 0.0322558
\(616\) −8.10275 + 14.0344i −0.326469 + 0.565461i
\(617\) 10.5501 + 18.2732i 0.424729 + 0.735653i 0.996395 0.0848339i \(-0.0270360\pi\)
−0.571666 + 0.820487i \(0.693703\pi\)
\(618\) −52.3436 −2.10557
\(619\) 47.9140 1.92583 0.962914 0.269808i \(-0.0869604\pi\)
0.962914 + 0.269808i \(0.0869604\pi\)
\(620\) 0.498680 + 0.863740i 0.0200275 + 0.0346886i
\(621\) −17.5837 −0.705611
\(622\) 5.26618 9.12129i 0.211154 0.365730i
\(623\) 9.98667 0.400107
\(624\) 3.05137 5.28514i 0.122153 0.211575i
\(625\) −1.86053 + 3.22253i −0.0744212 + 0.128901i
\(626\) −12.4150 + 21.5033i −0.496201 + 0.859446i
\(627\) 38.8273 + 67.2508i 1.55061 + 2.68574i
\(628\) 18.7759 0.749240
\(629\) −22.6935 + 21.1758i −0.904848 + 0.844333i
\(630\) 24.2542 0.966312
\(631\) 15.5053 + 26.8560i 0.617258 + 1.06912i 0.989984 + 0.141181i \(0.0450899\pi\)
−0.372726 + 0.927942i \(0.621577\pi\)
\(632\) 5.70682 9.88450i 0.227005 0.393184i
\(633\) −26.0691 + 45.1530i −1.03615 + 1.79467i
\(634\) 13.1461 22.7698i 0.522100 0.904303i
\(635\) −18.8725 −0.748934
\(636\) 17.2569 29.8898i 0.684279 1.18521i
\(637\) 4.62177 0.183121
\(638\) 10.7582 + 18.6337i 0.425921 + 0.737717i
\(639\) −44.5004 −1.76041
\(640\) 1.25951 0.0497865
\(641\) 16.3096 + 28.2490i 0.644189 + 1.11577i 0.984488 + 0.175451i \(0.0561384\pi\)
−0.340299 + 0.940317i \(0.610528\pi\)
\(642\) 0.552694 0.957294i 0.0218131 0.0377814i
\(643\) 18.1701 0.716559 0.358279 0.933614i \(-0.383364\pi\)
0.358279 + 0.933614i \(0.383364\pi\)
\(644\) −2.65544 4.59936i −0.104639 0.181240i
\(645\) −8.38260 14.5191i −0.330065 0.571689i
\(646\) −12.2258 21.1758i −0.481019 0.833150i
\(647\) 13.0067 22.5282i 0.511345 0.885675i −0.488569 0.872525i \(-0.662481\pi\)
0.999914 0.0131498i \(-0.00418582\pi\)
\(648\) −5.94731 + 10.3010i −0.233632 + 0.404663i
\(649\) 33.7892 + 58.5247i 1.32634 + 2.29729i
\(650\) 3.41363 + 5.91259i 0.133894 + 0.231911i
\(651\) −3.68648 6.38516i −0.144484 0.250254i
\(652\) −7.84324 −0.307165
\(653\) 3.62976 6.28692i 0.142043 0.246026i −0.786223 0.617943i \(-0.787966\pi\)
0.928266 + 0.371917i \(0.121299\pi\)
\(654\) 0.713483 + 1.23579i 0.0278994 + 0.0483231i
\(655\) 15.2267 0.594958
\(656\) −0.208136 −0.00812636
\(657\) 10.4473 + 18.0953i 0.407588 + 0.705964i
\(658\) −9.78922 −0.381624
\(659\) −3.06471 + 5.30823i −0.119384 + 0.206779i −0.919524 0.393034i \(-0.871425\pi\)
0.800140 + 0.599814i \(0.204759\pi\)
\(660\) −20.4110 −0.794497
\(661\) 16.9406 29.3420i 0.658915 1.14127i −0.321982 0.946746i \(-0.604349\pi\)
0.980897 0.194528i \(-0.0623175\pi\)
\(662\) −14.8946 + 25.7982i −0.578896 + 1.00268i
\(663\) 15.5704 26.9687i 0.604704 1.04738i
\(664\) 1.78520 + 3.09205i 0.0692791 + 0.119995i
\(665\) 18.4163 0.714152
\(666\) 36.7139 + 11.2116i 1.42263 + 0.434439i
\(667\) −7.05137 −0.273030
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 2.96897 5.14240i 0.114787 0.198817i
\(670\) 5.86358 10.1560i 0.226530 0.392361i
\(671\) −16.0691 + 27.8325i −0.620340 + 1.07446i
\(672\) −9.31088 −0.359175
\(673\) 12.8229 22.2099i 0.494286 0.856129i −0.505692 0.862714i \(-0.668763\pi\)
0.999978 + 0.00658502i \(0.00209609\pi\)
\(674\) −12.7272 −0.490232
\(675\) −17.2435 29.8667i −0.663704 1.14957i
\(676\) −9.00000 −0.346154
\(677\) 10.7759 0.414151 0.207076 0.978325i \(-0.433605\pi\)
0.207076 + 0.978325i \(0.433605\pi\)
\(678\) −1.05137 1.82103i −0.0403778 0.0699364i
\(679\) −3.36893 + 5.83515i −0.129287 + 0.223932i
\(680\) 6.42697 0.246463
\(681\) 6.99736 + 12.1198i 0.268139 + 0.464431i
\(682\) 2.10275 + 3.64207i 0.0805184 + 0.139462i
\(683\) 15.2458 + 26.4066i 0.583366 + 1.01042i 0.995077 + 0.0991047i \(0.0315979\pi\)
−0.411711 + 0.911314i \(0.635069\pi\)
\(684\) −15.1204 + 26.1894i −0.578145 + 1.00138i
\(685\) 10.5084 18.2011i 0.401505 0.695427i
\(686\) 7.15412 + 12.3913i 0.273146 + 0.473102i
\(687\) −2.49465 4.32087i −0.0951770 0.164851i
\(688\) 2.18113 + 3.77783i 0.0831548 + 0.144028i
\(689\) 22.6218 0.861821
\(690\) 3.34456 5.79294i 0.127325 0.220534i
\(691\) −4.49868 7.79194i −0.171138 0.296419i 0.767680 0.640833i \(-0.221411\pi\)
−0.938818 + 0.344414i \(0.888078\pi\)
\(692\) 4.46765 0.169834
\(693\) 102.271 3.88495
\(694\) −14.7826 25.6041i −0.561138 0.971920i
\(695\) −22.9132 −0.869148
\(696\) −6.18113 + 10.7060i −0.234295 + 0.405811i
\(697\) −1.06207 −0.0402287
\(698\) 16.2515 28.1485i 0.615129 1.06544i
\(699\) 12.2635 21.2411i 0.463850 0.803411i
\(700\) 5.20814 9.02076i 0.196849 0.340953i
\(701\) −17.3756 30.0954i −0.656267 1.13669i −0.981575 0.191080i \(-0.938801\pi\)
0.325308 0.945608i \(-0.394532\pi\)
\(702\) −20.2055 −0.762607
\(703\) 27.8769 + 8.51295i 1.05140 + 0.321072i
\(704\) 5.31088 0.200162
\(705\) −6.16482 10.6778i −0.232180 0.402148i
\(706\) −2.05269 + 3.55537i −0.0772542 + 0.133808i
\(707\) −5.12976 + 8.88500i −0.192924 + 0.334155i
\(708\) −19.4136 + 33.6254i −0.729609 + 1.26372i
\(709\) 39.9947 1.50203 0.751017 0.660283i \(-0.229564\pi\)
0.751017 + 0.660283i \(0.229564\pi\)
\(710\) 4.44064 7.69141i 0.166654 0.288654i
\(711\) −72.0301 −2.70134
\(712\) −1.63642 2.83436i −0.0613275 0.106222i
\(713\) −1.37823 −0.0516151
\(714\) −47.5111 −1.77806
\(715\) −6.68912 11.5859i −0.250159 0.433288i
\(716\) 7.05137 12.2133i 0.263522 0.456434i
\(717\) −1.93793 −0.0723734
\(718\) 14.1027 + 24.4267i 0.526310 + 0.911595i
\(719\) −1.50535 2.60734i −0.0561399 0.0972372i 0.836590 0.547830i \(-0.184546\pi\)
−0.892730 + 0.450593i \(0.851213\pi\)
\(720\) −3.97431 6.88371i −0.148114 0.256541i
\(721\) −26.1718 + 45.3309i −0.974690 + 1.68821i
\(722\) −1.98098 + 3.43116i −0.0737244 + 0.127694i
\(723\) −11.4676 19.8625i −0.426486 0.738696i
\(724\) −6.73250 11.6610i −0.250212 0.433379i
\(725\) −6.91495 11.9770i −0.256815 0.444816i
\(726\) −52.5004 −1.94847
\(727\) −26.7112 + 46.2651i −0.990663 + 1.71588i −0.377264 + 0.926106i \(0.623135\pi\)
−0.613399 + 0.789773i \(0.710198\pi\)
\(728\) −3.05137 5.28514i −0.113091 0.195880i
\(729\) −17.4163 −0.645047
\(730\) −4.17009 −0.154342
\(731\) 11.1298 + 19.2773i 0.411649 + 0.712997i
\(732\) −18.4650 −0.682486
\(733\) −2.82991 + 4.90154i −0.104525 + 0.181043i −0.913544 0.406740i \(-0.866666\pi\)
0.809019 + 0.587782i \(0.199999\pi\)
\(734\) −4.00000 −0.147643
\(735\) 4.44064 7.69141i 0.163795 0.283702i
\(736\) −0.870245 + 1.50731i −0.0320776 + 0.0555601i
\(737\) 24.7245 42.8241i 0.910739 1.57745i
\(738\) 0.656762 + 1.13755i 0.0241757 + 0.0418736i
\(739\) 2.21883 0.0816209 0.0408105 0.999167i \(-0.487006\pi\)
0.0408105 + 0.999167i \(0.487006\pi\)
\(740\) −5.60143 + 5.22681i −0.205913 + 0.192141i
\(741\) −29.2435 −1.07429
\(742\) −17.2569 29.8898i −0.633520 1.09729i
\(743\) −3.43397 + 5.94782i −0.125980 + 0.218204i −0.922116 0.386914i \(-0.873541\pi\)
0.796135 + 0.605119i \(0.206874\pi\)
\(744\) −1.20814 + 2.09255i −0.0442924 + 0.0767167i
\(745\) −8.52207 + 14.7607i −0.312225 + 0.540789i
\(746\) 37.3570 1.36774
\(747\) 11.2662 19.5136i 0.412208 0.713965i
\(748\) 27.1001 0.990878
\(749\) −0.552694 0.957294i −0.0201950 0.0349788i
\(750\) 32.3356 1.18073
\(751\) −3.80256 −0.138757 −0.0693786 0.997590i \(-0.522102\pi\)
−0.0693786 + 0.997590i \(0.522102\pi\)
\(752\) 1.60407 + 2.77833i 0.0584943 + 0.101315i
\(753\) −13.5501 + 23.4694i −0.493791 + 0.855272i
\(754\) −8.10275 −0.295085
\(755\) −0.769226 1.33234i −0.0279950 0.0484888i
\(756\) 15.4136 + 26.6972i 0.560588 + 0.970968i
\(757\) 1.59608 + 2.76450i 0.0580106 + 0.100477i 0.893572 0.448919i \(-0.148191\pi\)
−0.835562 + 0.549397i \(0.814858\pi\)
\(758\) 2.45397 4.25040i 0.0891323 0.154382i
\(759\) 14.1027 24.4267i 0.511897 0.886632i
\(760\) −3.01770 5.22681i −0.109464 0.189596i
\(761\) −19.0297 32.9604i −0.689827 1.19481i −0.971894 0.235420i \(-0.924353\pi\)
0.282067 0.959395i \(-0.408980\pi\)
\(762\) −22.8609 39.5963i −0.828164 1.43442i
\(763\) 1.42697 0.0516596
\(764\) −4.71348 + 8.16399i −0.170528 + 0.295363i
\(765\) −20.2799 35.1259i −0.733222 1.26998i
\(766\) 20.6084 0.744613
\(767\) −25.4490 −0.918911
\(768\) 1.52569 + 2.64257i 0.0550535 + 0.0953554i
\(769\) −2.76520 −0.0997156 −0.0498578 0.998756i \(-0.515877\pi\)
−0.0498578 + 0.998756i \(0.515877\pi\)
\(770\) −10.2055 + 17.6764i −0.367781 + 0.637015i
\(771\) 36.9220 1.32971
\(772\) −1.24049 + 2.14859i −0.0446462 + 0.0773295i
\(773\) −14.4527 + 25.0327i −0.519826 + 0.900365i 0.479909 + 0.877318i \(0.340670\pi\)
−0.999734 + 0.0230462i \(0.992664\pi\)
\(774\) 13.7649 23.8414i 0.494768 0.856963i
\(775\) −1.35157 2.34098i −0.0485497 0.0840905i
\(776\) 2.20814