Properties

Label 546.2.p.c.281.9
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 281.9
Root \(-1.25702 + 1.19160i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.0462556 - 1.73143i) q^{3} -1.00000i q^{4} +(1.43062 - 1.43062i) q^{5} +(-1.19160 - 1.25702i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99572 - 0.160177i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.0462556 - 1.73143i) q^{3} -1.00000i q^{4} +(1.43062 - 1.43062i) q^{5} +(-1.19160 - 1.25702i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.99572 - 0.160177i) q^{9} -2.02321i q^{10} +(-3.59738 - 3.59738i) q^{11} +(-1.73143 - 0.0462556i) q^{12} +(2.66989 + 2.42316i) q^{13} +1.00000i q^{14} +(-2.41086 - 2.54321i) q^{15} -1.00000 q^{16} +4.10312 q^{17} +(-2.23156 + 2.00503i) q^{18} +(-4.90374 - 4.90374i) q^{19} +(-1.43062 - 1.43062i) q^{20} +(1.19160 + 1.25702i) q^{21} -5.08746 q^{22} +4.97697 q^{23} +(-1.25702 + 1.19160i) q^{24} +0.906626i q^{25} +(3.60133 - 0.174466i) q^{26} +(-0.415904 + 5.17948i) q^{27} +(0.707107 + 0.707107i) q^{28} +2.59352i q^{29} +(-3.50305 - 0.0935847i) q^{30} +(-1.00229 - 1.00229i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.39501 + 6.06222i) q^{33} +(2.90134 - 2.90134i) q^{34} +2.02321i q^{35} +(-0.160177 + 2.99572i) q^{36} +(8.01932 - 8.01932i) q^{37} -6.93493 q^{38} +(4.31903 - 4.51065i) q^{39} -2.02321 q^{40} +(-0.185417 + 0.185417i) q^{41} +(1.73143 + 0.0462556i) q^{42} +8.21380i q^{43} +(-3.59738 + 3.59738i) q^{44} +(-4.51491 + 4.05660i) q^{45} +(3.51925 - 3.51925i) q^{46} +(2.56188 + 2.56188i) q^{47} +(-0.0462556 + 1.73143i) q^{48} -1.00000i q^{49} +(0.641081 + 0.641081i) q^{50} +(0.189792 - 7.10428i) q^{51} +(2.42316 - 2.66989i) q^{52} -7.36477i q^{53} +(3.36836 + 3.95653i) q^{54} -10.2930 q^{55} +1.00000 q^{56} +(-8.71732 + 8.26367i) q^{57} +(1.83390 + 1.83390i) q^{58} +(-1.33972 - 1.33972i) q^{59} +(-2.54321 + 2.41086i) q^{60} -10.1389 q^{61} -1.41746 q^{62} +(2.23156 - 2.00503i) q^{63} +1.00000i q^{64} +(7.28624 - 0.352981i) q^{65} +(-0.235323 + 8.80859i) q^{66} +(3.13832 + 3.13832i) q^{67} -4.10312i q^{68} +(0.230213 - 8.61729i) q^{69} +(1.43062 + 1.43062i) q^{70} +(9.44085 - 9.44085i) q^{71} +(2.00503 + 2.23156i) q^{72} +(-0.868139 + 0.868139i) q^{73} -11.3410i q^{74} +(1.56976 + 0.0419365i) q^{75} +(-4.90374 + 4.90374i) q^{76} +5.08746 q^{77} +(-0.135495 - 6.24353i) q^{78} +12.6610 q^{79} +(-1.43062 + 1.43062i) q^{80} +(8.94869 + 0.959690i) q^{81} +0.262219i q^{82} +(-0.232559 + 0.232559i) q^{83} +(1.25702 - 1.19160i) q^{84} +(5.87003 - 5.87003i) q^{85} +(5.80804 + 5.80804i) q^{86} +(4.49051 + 0.119965i) q^{87} +5.08746i q^{88} +(3.93141 + 3.93141i) q^{89} +(-0.324071 + 6.06097i) q^{90} +(-3.60133 + 0.174466i) q^{91} -4.97697i q^{92} +(-1.78176 + 1.68904i) q^{93} +3.62305 q^{94} -14.0308 q^{95} +(1.19160 + 1.25702i) q^{96} +(7.65788 + 7.65788i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(10.2005 + 11.3530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.0462556 1.73143i 0.0267057 0.999643i
\(4\) 1.00000i 0.500000i
\(5\) 1.43062 1.43062i 0.639795 0.639795i −0.310710 0.950505i \(-0.600567\pi\)
0.950505 + 0.310710i \(0.100567\pi\)
\(6\) −1.19160 1.25702i −0.486469 0.513175i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.99572 0.160177i −0.998574 0.0533923i
\(10\) 2.02321i 0.639795i
\(11\) −3.59738 3.59738i −1.08465 1.08465i −0.996069 0.0885807i \(-0.971767\pi\)
−0.0885807 0.996069i \(-0.528233\pi\)
\(12\) −1.73143 0.0462556i −0.499822 0.0133528i
\(13\) 2.66989 + 2.42316i 0.740494 + 0.672063i
\(14\) 1.00000i 0.267261i
\(15\) −2.41086 2.54321i −0.622480 0.656653i
\(16\) −1.00000 −0.250000
\(17\) 4.10312 0.995153 0.497577 0.867420i \(-0.334223\pi\)
0.497577 + 0.867420i \(0.334223\pi\)
\(18\) −2.23156 + 2.00503i −0.525983 + 0.472591i
\(19\) −4.90374 4.90374i −1.12499 1.12499i −0.990979 0.134015i \(-0.957213\pi\)
−0.134015 0.990979i \(-0.542787\pi\)
\(20\) −1.43062 1.43062i −0.319897 0.319897i
\(21\) 1.19160 + 1.25702i 0.260029 + 0.274303i
\(22\) −5.08746 −1.08465
\(23\) 4.97697 1.03777 0.518885 0.854844i \(-0.326347\pi\)
0.518885 + 0.854844i \(0.326347\pi\)
\(24\) −1.25702 + 1.19160i −0.256587 + 0.243234i
\(25\) 0.906626i 0.181325i
\(26\) 3.60133 0.174466i 0.706278 0.0342156i
\(27\) −0.415904 + 5.17948i −0.0800408 + 0.996792i
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 2.59352i 0.481605i 0.970574 + 0.240803i \(0.0774107\pi\)
−0.970574 + 0.240803i \(0.922589\pi\)
\(30\) −3.50305 0.0935847i −0.639567 0.0170862i
\(31\) −1.00229 1.00229i −0.180017 0.180017i 0.611346 0.791363i \(-0.290628\pi\)
−0.791363 + 0.611346i \(0.790628\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −6.39501 + 6.06222i −1.11323 + 1.05530i
\(34\) 2.90134 2.90134i 0.497577 0.497577i
\(35\) 2.02321i 0.341985i
\(36\) −0.160177 + 2.99572i −0.0266961 + 0.499287i
\(37\) 8.01932 8.01932i 1.31837 1.31837i 0.403301 0.915067i \(-0.367863\pi\)
0.915067 0.403301i \(-0.132137\pi\)
\(38\) −6.93493 −1.12499
\(39\) 4.31903 4.51065i 0.691599 0.722282i
\(40\) −2.02321 −0.319897
\(41\) −0.185417 + 0.185417i −0.0289573 + 0.0289573i −0.721437 0.692480i \(-0.756518\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(42\) 1.73143 + 0.0462556i 0.267166 + 0.00713739i
\(43\) 8.21380i 1.25259i 0.779585 + 0.626297i \(0.215430\pi\)
−0.779585 + 0.626297i \(0.784570\pi\)
\(44\) −3.59738 + 3.59738i −0.542325 + 0.542325i
\(45\) −4.51491 + 4.05660i −0.673042 + 0.604722i
\(46\) 3.51925 3.51925i 0.518885 0.518885i
\(47\) 2.56188 + 2.56188i 0.373689 + 0.373689i 0.868819 0.495130i \(-0.164880\pi\)
−0.495130 + 0.868819i \(0.664880\pi\)
\(48\) −0.0462556 + 1.73143i −0.00667642 + 0.249911i
\(49\) 1.00000i 0.142857i
\(50\) 0.641081 + 0.641081i 0.0906626 + 0.0906626i
\(51\) 0.189792 7.10428i 0.0265762 0.994798i
\(52\) 2.42316 2.66989i 0.336031 0.370247i
\(53\) 7.36477i 1.01163i −0.862642 0.505814i \(-0.831192\pi\)
0.862642 0.505814i \(-0.168808\pi\)
\(54\) 3.36836 + 3.95653i 0.458375 + 0.538416i
\(55\) −10.2930 −1.38791
\(56\) 1.00000 0.133631
\(57\) −8.71732 + 8.26367i −1.15464 + 1.09455i
\(58\) 1.83390 + 1.83390i 0.240803 + 0.240803i
\(59\) −1.33972 1.33972i −0.174417 0.174417i 0.614500 0.788917i \(-0.289358\pi\)
−0.788917 + 0.614500i \(0.789358\pi\)
\(60\) −2.54321 + 2.41086i −0.328326 + 0.311240i
\(61\) −10.1389 −1.29815 −0.649075 0.760725i \(-0.724844\pi\)
−0.649075 + 0.760725i \(0.724844\pi\)
\(62\) −1.41746 −0.180017
\(63\) 2.23156 2.00503i 0.281150 0.252610i
\(64\) 1.00000i 0.125000i
\(65\) 7.28624 0.352981i 0.903747 0.0437820i
\(66\) −0.235323 + 8.80859i −0.0289663 + 1.08426i
\(67\) 3.13832 + 3.13832i 0.383407 + 0.383407i 0.872328 0.488921i \(-0.162609\pi\)
−0.488921 + 0.872328i \(0.662609\pi\)
\(68\) 4.10312i 0.497577i
\(69\) 0.230213 8.61729i 0.0277143 1.03740i
\(70\) 1.43062 + 1.43062i 0.170992 + 0.170992i
\(71\) 9.44085 9.44085i 1.12042 1.12042i 0.128745 0.991678i \(-0.458905\pi\)
0.991678 0.128745i \(-0.0410947\pi\)
\(72\) 2.00503 + 2.23156i 0.236295 + 0.262991i
\(73\) −0.868139 + 0.868139i −0.101608 + 0.101608i −0.756083 0.654475i \(-0.772890\pi\)
0.654475 + 0.756083i \(0.272890\pi\)
\(74\) 11.3410i 1.31837i
\(75\) 1.56976 + 0.0419365i 0.181261 + 0.00484241i
\(76\) −4.90374 + 4.90374i −0.562497 + 0.562497i
\(77\) 5.08746 0.579770
\(78\) −0.135495 6.24353i −0.0153418 0.706940i
\(79\) 12.6610 1.42448 0.712239 0.701937i \(-0.247681\pi\)
0.712239 + 0.701937i \(0.247681\pi\)
\(80\) −1.43062 + 1.43062i −0.159949 + 0.159949i
\(81\) 8.94869 + 0.959690i 0.994299 + 0.106632i
\(82\) 0.262219i 0.0289573i
\(83\) −0.232559 + 0.232559i −0.0255266 + 0.0255266i −0.719755 0.694228i \(-0.755746\pi\)
0.694228 + 0.719755i \(0.255746\pi\)
\(84\) 1.25702 1.19160i 0.137152 0.130014i
\(85\) 5.87003 5.87003i 0.636694 0.636694i
\(86\) 5.80804 + 5.80804i 0.626297 + 0.626297i
\(87\) 4.49051 + 0.119965i 0.481434 + 0.0128616i
\(88\) 5.08746i 0.542325i
\(89\) 3.93141 + 3.93141i 0.416728 + 0.416728i 0.884074 0.467346i \(-0.154790\pi\)
−0.467346 + 0.884074i \(0.654790\pi\)
\(90\) −0.324071 + 6.06097i −0.0341601 + 0.638882i
\(91\) −3.60133 + 0.174466i −0.377522 + 0.0182890i
\(92\) 4.97697i 0.518885i
\(93\) −1.78176 + 1.68904i −0.184760 + 0.175145i
\(94\) 3.62305 0.373689
\(95\) −14.0308 −1.43953
\(96\) 1.19160 + 1.25702i 0.121617 + 0.128294i
\(97\) 7.65788 + 7.65788i 0.777540 + 0.777540i 0.979412 0.201872i \(-0.0647025\pi\)
−0.201872 + 0.979412i \(0.564702\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 10.2005 + 11.3530i 1.02519 + 1.14101i
\(100\) 0.906626 0.0906626
\(101\) 3.05876 0.304358 0.152179 0.988353i \(-0.451371\pi\)
0.152179 + 0.988353i \(0.451371\pi\)
\(102\) −4.88928 5.15769i −0.484111 0.510687i
\(103\) 8.89812i 0.876758i 0.898790 + 0.438379i \(0.144447\pi\)
−0.898790 + 0.438379i \(0.855553\pi\)
\(104\) −0.174466 3.60133i −0.0171078 0.353139i
\(105\) 3.50305 + 0.0935847i 0.341863 + 0.00913293i
\(106\) −5.20768 5.20768i −0.505814 0.505814i
\(107\) 16.1853i 1.56469i −0.622844 0.782346i \(-0.714023\pi\)
0.622844 0.782346i \(-0.285977\pi\)
\(108\) 5.17948 + 0.415904i 0.498396 + 0.0400204i
\(109\) 1.55437 + 1.55437i 0.148882 + 0.148882i 0.777618 0.628736i \(-0.216428\pi\)
−0.628736 + 0.777618i \(0.716428\pi\)
\(110\) −7.27824 + 7.27824i −0.693953 + 0.693953i
\(111\) −13.5140 14.2559i −1.28269 1.35311i
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 1.67224i 0.157311i −0.996902 0.0786557i \(-0.974937\pi\)
0.996902 0.0786557i \(-0.0250628\pi\)
\(114\) −0.320779 + 12.0074i −0.0300437 + 1.12459i
\(115\) 7.12018 7.12018i 0.663960 0.663960i
\(116\) 2.59352 0.240803
\(117\) −7.61011 7.68676i −0.703555 0.710641i
\(118\) −1.89465 −0.174417
\(119\) −2.90134 + 2.90134i −0.265966 + 0.265966i
\(120\) −0.0935847 + 3.50305i −0.00854308 + 0.319783i
\(121\) 14.8822i 1.35293i
\(122\) −7.16926 + 7.16926i −0.649075 + 0.649075i
\(123\) 0.312461 + 0.329614i 0.0281736 + 0.0297203i
\(124\) −1.00229 + 1.00229i −0.0900085 + 0.0900085i
\(125\) 8.45017 + 8.45017i 0.755806 + 0.755806i
\(126\) 0.160177 2.99572i 0.0142697 0.266880i
\(127\) 19.5094i 1.73118i 0.500754 + 0.865590i \(0.333056\pi\)
−0.500754 + 0.865590i \(0.666944\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 14.2216 + 0.379934i 1.25215 + 0.0334513i
\(130\) 4.90255 5.40174i 0.429982 0.473764i
\(131\) 12.4313i 1.08613i −0.839691 0.543064i \(-0.817264\pi\)
0.839691 0.543064i \(-0.182736\pi\)
\(132\) 6.06222 + 6.39501i 0.527648 + 0.556615i
\(133\) 6.93493 0.601335
\(134\) 4.43825 0.383407
\(135\) 6.81489 + 8.00490i 0.586532 + 0.688952i
\(136\) −2.90134 2.90134i −0.248788 0.248788i
\(137\) 9.19378 + 9.19378i 0.785477 + 0.785477i 0.980749 0.195272i \(-0.0625589\pi\)
−0.195272 + 0.980749i \(0.562559\pi\)
\(138\) −5.93056 6.25613i −0.504843 0.532557i
\(139\) −19.0489 −1.61570 −0.807852 0.589385i \(-0.799370\pi\)
−0.807852 + 0.589385i \(0.799370\pi\)
\(140\) 2.02321 0.170992
\(141\) 4.55423 4.31722i 0.383535 0.363576i
\(142\) 13.3514i 1.12042i
\(143\) −0.887589 18.3216i −0.0742239 1.53213i
\(144\) 2.99572 + 0.160177i 0.249643 + 0.0133481i
\(145\) 3.71036 + 3.71036i 0.308129 + 0.308129i
\(146\) 1.22773i 0.101608i
\(147\) −1.73143 0.0462556i −0.142806 0.00381510i
\(148\) −8.01932 8.01932i −0.659184 0.659184i
\(149\) −4.55291 + 4.55291i −0.372989 + 0.372989i −0.868565 0.495576i \(-0.834957\pi\)
0.495576 + 0.868565i \(0.334957\pi\)
\(150\) 1.13964 1.08034i 0.0930515 0.0882091i
\(151\) 12.4782 12.4782i 1.01546 1.01546i 0.0155842 0.999879i \(-0.495039\pi\)
0.999879 0.0155842i \(-0.00496082\pi\)
\(152\) 6.93493i 0.562497i
\(153\) −12.2918 0.657225i −0.993734 0.0531335i
\(154\) 3.59738 3.59738i 0.289885 0.289885i
\(155\) −2.86781 −0.230348
\(156\) −4.51065 4.31903i −0.361141 0.345799i
\(157\) 13.8447 1.10493 0.552466 0.833536i \(-0.313687\pi\)
0.552466 + 0.833536i \(0.313687\pi\)
\(158\) 8.95271 8.95271i 0.712239 0.712239i
\(159\) −12.7516 0.340662i −1.01127 0.0270162i
\(160\) 2.02321i 0.159949i
\(161\) −3.51925 + 3.51925i −0.277356 + 0.277356i
\(162\) 7.00628 5.64907i 0.550465 0.443833i
\(163\) −2.76536 + 2.76536i −0.216600 + 0.216600i −0.807064 0.590464i \(-0.798945\pi\)
0.590464 + 0.807064i \(0.298945\pi\)
\(164\) 0.185417 + 0.185417i 0.0144786 + 0.0144786i
\(165\) −0.476108 + 17.8216i −0.0370650 + 1.38741i
\(166\) 0.328888i 0.0255266i
\(167\) −13.6345 13.6345i −1.05507 1.05507i −0.998392 0.0566794i \(-0.981949\pi\)
−0.0566794 0.998392i \(-0.518051\pi\)
\(168\) 0.0462556 1.73143i 0.00356870 0.133583i
\(169\) 1.25662 + 12.9391i 0.0966630 + 0.995317i
\(170\) 8.30147i 0.636694i
\(171\) 13.9048 + 15.4757i 1.06332 + 1.18346i
\(172\) 8.21380 0.626297
\(173\) −21.9642 −1.66991 −0.834955 0.550318i \(-0.814506\pi\)
−0.834955 + 0.550318i \(0.814506\pi\)
\(174\) 3.26010 3.09044i 0.247148 0.234286i
\(175\) −0.641081 0.641081i −0.0484612 0.0484612i
\(176\) 3.59738 + 3.59738i 0.271162 + 0.271162i
\(177\) −2.38161 + 2.25767i −0.179012 + 0.169697i
\(178\) 5.55985 0.416728
\(179\) −8.56403 −0.640105 −0.320053 0.947400i \(-0.603701\pi\)
−0.320053 + 0.947400i \(0.603701\pi\)
\(180\) 4.05660 + 4.51491i 0.302361 + 0.336521i
\(181\) 0.973124i 0.0723318i −0.999346 0.0361659i \(-0.988486\pi\)
0.999346 0.0361659i \(-0.0115145\pi\)
\(182\) −2.42316 + 2.66989i −0.179616 + 0.197905i
\(183\) −0.468979 + 17.5548i −0.0346679 + 1.29769i
\(184\) −3.51925 3.51925i −0.259442 0.259442i
\(185\) 22.9453i 1.68697i
\(186\) −0.0655652 + 2.45423i −0.00480747 + 0.179953i
\(187\) −14.7605 14.7605i −1.07939 1.07939i
\(188\) 2.56188 2.56188i 0.186844 0.186844i
\(189\) −3.36836 3.95653i −0.245012 0.287796i
\(190\) −9.92128 + 9.92128i −0.719765 + 0.719765i
\(191\) 12.7937i 0.925721i 0.886431 + 0.462860i \(0.153177\pi\)
−0.886431 + 0.462860i \(0.846823\pi\)
\(192\) 1.73143 + 0.0462556i 0.124955 + 0.00333821i
\(193\) 8.73551 8.73551i 0.628796 0.628796i −0.318969 0.947765i \(-0.603337\pi\)
0.947765 + 0.318969i \(0.103337\pi\)
\(194\) 10.8299 0.777540
\(195\) −0.274134 12.6320i −0.0196312 0.904593i
\(196\) −1.00000 −0.0714286
\(197\) −6.29467 + 6.29467i −0.448477 + 0.448477i −0.894848 0.446371i \(-0.852716\pi\)
0.446371 + 0.894848i \(0.352716\pi\)
\(198\) 15.2406 + 0.814893i 1.08310 + 0.0579119i
\(199\) 12.0446i 0.853823i 0.904294 + 0.426911i \(0.140398\pi\)
−0.904294 + 0.426911i \(0.859602\pi\)
\(200\) 0.641081 0.641081i 0.0453313 0.0453313i
\(201\) 5.57895 5.28862i 0.393509 0.373031i
\(202\) 2.16287 2.16287i 0.152179 0.152179i
\(203\) −1.83390 1.83390i −0.128714 0.128714i
\(204\) −7.10428 0.189792i −0.497399 0.0132881i
\(205\) 0.530525i 0.0370534i
\(206\) 6.29192 + 6.29192i 0.438379 + 0.438379i
\(207\) −14.9096 0.797195i −1.03629 0.0554089i
\(208\) −2.66989 2.42316i −0.185124 0.168016i
\(209\) 35.2812i 2.44045i
\(210\) 2.54321 2.41086i 0.175498 0.166365i
\(211\) −23.3032 −1.60426 −0.802129 0.597151i \(-0.796299\pi\)
−0.802129 + 0.597151i \(0.796299\pi\)
\(212\) −7.36477 −0.505814
\(213\) −15.9095 16.7829i −1.09010 1.14994i
\(214\) −11.4447 11.4447i −0.782346 0.782346i
\(215\) 11.7509 + 11.7509i 0.801403 + 0.801403i
\(216\) 3.95653 3.36836i 0.269208 0.229188i
\(217\) 1.41746 0.0962231
\(218\) 2.19822 0.148882
\(219\) 1.46297 + 1.54328i 0.0988582 + 0.104285i
\(220\) 10.2930i 0.693953i
\(221\) 10.9549 + 9.94251i 0.736905 + 0.668805i
\(222\) −19.6362 0.524586i −1.31790 0.0352079i
\(223\) 11.2055 + 11.2055i 0.750374 + 0.750374i 0.974549 0.224175i \(-0.0719686\pi\)
−0.224175 + 0.974549i \(0.571969\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 0.145221 2.71600i 0.00968137 0.181067i
\(226\) −1.18245 1.18245i −0.0786557 0.0786557i
\(227\) 2.20653 2.20653i 0.146452 0.146452i −0.630079 0.776531i \(-0.716977\pi\)
0.776531 + 0.630079i \(0.216977\pi\)
\(228\) 8.26367 + 8.71732i 0.547275 + 0.577318i
\(229\) −17.4293 + 17.4293i −1.15176 + 1.15176i −0.165559 + 0.986200i \(0.552943\pi\)
−0.986200 + 0.165559i \(0.947057\pi\)
\(230\) 10.0694i 0.663960i
\(231\) 0.235323 8.80859i 0.0154831 0.579563i
\(232\) 1.83390 1.83390i 0.120401 0.120401i
\(233\) 7.03391 0.460806 0.230403 0.973095i \(-0.425995\pi\)
0.230403 + 0.973095i \(0.425995\pi\)
\(234\) −10.8165 0.0541977i −0.707098 0.00354301i
\(235\) 7.33018 0.478168
\(236\) −1.33972 + 1.33972i −0.0872084 + 0.0872084i
\(237\) 0.585644 21.9217i 0.0380417 1.42397i
\(238\) 4.10312i 0.265966i
\(239\) 2.66524 2.66524i 0.172400 0.172400i −0.615633 0.788033i \(-0.711100\pi\)
0.788033 + 0.615633i \(0.211100\pi\)
\(240\) 2.41086 + 2.54321i 0.155620 + 0.164163i
\(241\) −1.43539 + 1.43539i −0.0924614 + 0.0924614i −0.751825 0.659363i \(-0.770826\pi\)
0.659363 + 0.751825i \(0.270826\pi\)
\(242\) 10.5233 + 10.5233i 0.676465 + 0.676465i
\(243\) 2.07557 15.4497i 0.133148 0.991096i
\(244\) 10.1389i 0.649075i
\(245\) −1.43062 1.43062i −0.0913993 0.0913993i
\(246\) 0.454015 + 0.0121291i 0.0289470 + 0.000773324i
\(247\) −1.20991 24.9750i −0.0769847 1.58912i
\(248\) 1.41746i 0.0900085i
\(249\) 0.391903 + 0.413417i 0.0248358 + 0.0261992i
\(250\) 11.9503 0.755806
\(251\) 9.15010 0.577549 0.288775 0.957397i \(-0.406752\pi\)
0.288775 + 0.957397i \(0.406752\pi\)
\(252\) −2.00503 2.23156i −0.126305 0.140575i
\(253\) −17.9040 17.9040i −1.12562 1.12562i
\(254\) 13.7952 + 13.7952i 0.865590 + 0.865590i
\(255\) −9.89204 10.4351i −0.619463 0.653470i
\(256\) 1.00000 0.0625000
\(257\) −3.54392 −0.221064 −0.110532 0.993873i \(-0.535255\pi\)
−0.110532 + 0.993873i \(0.535255\pi\)
\(258\) 10.3249 9.78757i 0.642799 0.609348i
\(259\) 11.3410i 0.704698i
\(260\) −0.352981 7.28624i −0.0218910 0.451873i
\(261\) 0.415423 7.76947i 0.0257140 0.480918i
\(262\) −8.79026 8.79026i −0.543064 0.543064i
\(263\) 27.6411i 1.70442i 0.523199 + 0.852211i \(0.324739\pi\)
−0.523199 + 0.852211i \(0.675261\pi\)
\(264\) 8.80859 + 0.235323i 0.542131 + 0.0144831i
\(265\) −10.5362 10.5362i −0.647235 0.647235i
\(266\) 4.90374 4.90374i 0.300667 0.300667i
\(267\) 6.98882 6.62512i 0.427709 0.405451i
\(268\) 3.13832 3.13832i 0.191703 0.191703i
\(269\) 20.0051i 1.21973i 0.792504 + 0.609867i \(0.208777\pi\)
−0.792504 + 0.609867i \(0.791223\pi\)
\(270\) 10.4792 + 0.841461i 0.637742 + 0.0512097i
\(271\) −5.17783 + 5.17783i −0.314531 + 0.314531i −0.846662 0.532131i \(-0.821391\pi\)
0.532131 + 0.846662i \(0.321391\pi\)
\(272\) −4.10312 −0.248788
\(273\) 0.135495 + 6.24353i 0.00820052 + 0.377876i
\(274\) 13.0020 0.785477
\(275\) 3.26148 3.26148i 0.196674 0.196674i
\(276\) −8.61729 0.230213i −0.518700 0.0138572i
\(277\) 11.9350i 0.717107i −0.933509 0.358554i \(-0.883270\pi\)
0.933509 0.358554i \(-0.116730\pi\)
\(278\) −13.4696 + 13.4696i −0.807852 + 0.807852i
\(279\) 2.84204 + 3.16313i 0.170149 + 0.189372i
\(280\) 1.43062 1.43062i 0.0854962 0.0854962i
\(281\) −19.4431 19.4431i −1.15988 1.15988i −0.984502 0.175374i \(-0.943887\pi\)
−0.175374 0.984502i \(-0.556113\pi\)
\(282\) 0.167586 6.27306i 0.00997961 0.373555i
\(283\) 10.9224i 0.649272i 0.945839 + 0.324636i \(0.105242\pi\)
−0.945839 + 0.324636i \(0.894758\pi\)
\(284\) −9.44085 9.44085i −0.560211 0.560211i
\(285\) −0.649003 + 24.2934i −0.0384436 + 1.43902i
\(286\) −13.5830 12.3277i −0.803177 0.728953i
\(287\) 0.262219i 0.0154783i
\(288\) 2.23156 2.00503i 0.131496 0.118148i
\(289\) −0.164395 −0.00967032
\(290\) 5.24724 0.308129
\(291\) 13.6133 12.9049i 0.798027 0.756498i
\(292\) 0.868139 + 0.868139i 0.0508040 + 0.0508040i
\(293\) −1.81919 1.81919i −0.106278 0.106278i 0.651968 0.758246i \(-0.273944\pi\)
−0.758246 + 0.651968i \(0.773944\pi\)
\(294\) −1.25702 + 1.19160i −0.0733106 + 0.0694955i
\(295\) −3.83327 −0.223182
\(296\) −11.3410 −0.659184
\(297\) 20.1287 17.1364i 1.16799 0.994353i
\(298\) 6.43879i 0.372989i
\(299\) 13.2880 + 12.0600i 0.768462 + 0.697447i
\(300\) 0.0419365 1.56976i 0.00242121 0.0906303i
\(301\) −5.80804 5.80804i −0.334770 0.334770i
\(302\) 17.6469i 1.01546i
\(303\) 0.141485 5.29604i 0.00812809 0.304250i
\(304\) 4.90374 + 4.90374i 0.281249 + 0.281249i
\(305\) −14.5049 + 14.5049i −0.830549 + 0.830549i
\(306\) −9.15635 + 8.22689i −0.523434 + 0.470300i
\(307\) −9.17766 + 9.17766i −0.523797 + 0.523797i −0.918716 0.394919i \(-0.870773\pi\)
0.394919 + 0.918716i \(0.370773\pi\)
\(308\) 5.08746i 0.289885i
\(309\) 15.4065 + 0.411588i 0.876445 + 0.0234144i
\(310\) −2.02785 + 2.02785i −0.115174 + 0.115174i
\(311\) −2.34596 −0.133027 −0.0665135 0.997786i \(-0.521188\pi\)
−0.0665135 + 0.997786i \(0.521188\pi\)
\(312\) −6.24353 + 0.135495i −0.353470 + 0.00767089i
\(313\) −13.3871 −0.756683 −0.378341 0.925666i \(-0.623505\pi\)
−0.378341 + 0.925666i \(0.623505\pi\)
\(314\) 9.78972 9.78972i 0.552466 0.552466i
\(315\) 0.324071 6.06097i 0.0182593 0.341497i
\(316\) 12.6610i 0.712239i
\(317\) −12.9987 + 12.9987i −0.730081 + 0.730081i −0.970636 0.240555i \(-0.922671\pi\)
0.240555 + 0.970636i \(0.422671\pi\)
\(318\) −9.25763 + 8.77586i −0.519142 + 0.492126i
\(319\) 9.32988 9.32988i 0.522373 0.522373i
\(320\) 1.43062 + 1.43062i 0.0799743 + 0.0799743i
\(321\) −28.0238 0.748661i −1.56413 0.0417862i
\(322\) 4.97697i 0.277356i
\(323\) −20.1206 20.1206i −1.11954 1.11954i
\(324\) 0.959690 8.94869i 0.0533161 0.497149i
\(325\) −2.19690 + 2.42059i −0.121862 + 0.134270i
\(326\) 3.91081i 0.216600i
\(327\) 2.76319 2.61939i 0.152805 0.144853i
\(328\) 0.262219 0.0144786
\(329\) −3.62305 −0.199745
\(330\) 12.2651 + 12.9384i 0.675173 + 0.712238i
\(331\) 0.549427 + 0.549427i 0.0301992 + 0.0301992i 0.722045 0.691846i \(-0.243202\pi\)
−0.691846 + 0.722045i \(0.743202\pi\)
\(332\) 0.232559 + 0.232559i 0.0127633 + 0.0127633i
\(333\) −25.3082 + 22.7391i −1.38688 + 1.24610i
\(334\) −19.2821 −1.05507
\(335\) 8.97951 0.490603
\(336\) −1.19160 1.25702i −0.0650071 0.0685758i
\(337\) 20.1204i 1.09603i −0.836470 0.548013i \(-0.815384\pi\)
0.836470 0.548013i \(-0.184616\pi\)
\(338\) 10.0379 + 8.26078i 0.545990 + 0.449327i
\(339\) −2.89538 0.0773505i −0.157255 0.00420110i
\(340\) −5.87003 5.87003i −0.318347 0.318347i
\(341\) 7.21124i 0.390511i
\(342\) 20.7751 + 1.11082i 1.12339 + 0.0600660i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 5.80804 5.80804i 0.313148 0.313148i
\(345\) −11.9988 12.6575i −0.645991 0.681454i
\(346\) −15.5311 + 15.5311i −0.834955 + 0.834955i
\(347\) 16.4340i 0.882225i −0.897452 0.441113i \(-0.854584\pi\)
0.897452 0.441113i \(-0.145416\pi\)
\(348\) 0.119965 4.49051i 0.00643080 0.240717i
\(349\) 9.67441 9.67441i 0.517859 0.517859i −0.399064 0.916923i \(-0.630665\pi\)
0.916923 + 0.399064i \(0.130665\pi\)
\(350\) −0.906626 −0.0484612
\(351\) −13.6611 + 12.8208i −0.729176 + 0.684326i
\(352\) 5.08746 0.271162
\(353\) −2.54751 + 2.54751i −0.135590 + 0.135590i −0.771645 0.636054i \(-0.780566\pi\)
0.636054 + 0.771645i \(0.280566\pi\)
\(354\) −0.0876382 + 3.28046i −0.00465792 + 0.174354i
\(355\) 27.0126i 1.43368i
\(356\) 3.93141 3.93141i 0.208364 0.208364i
\(357\) 4.88928 + 5.15769i 0.258768 + 0.272974i
\(358\) −6.05568 + 6.05568i −0.320053 + 0.320053i
\(359\) −21.4323 21.4323i −1.13115 1.13115i −0.989986 0.141166i \(-0.954915\pi\)
−0.141166 0.989986i \(-0.545085\pi\)
\(360\) 6.06097 + 0.324071i 0.319441 + 0.0170801i
\(361\) 29.0933i 1.53122i
\(362\) −0.688103 0.688103i −0.0361659 0.0361659i
\(363\) 25.7676 + 0.688386i 1.35245 + 0.0361309i
\(364\) 0.174466 + 3.60133i 0.00914451 + 0.188761i
\(365\) 2.48396i 0.130017i
\(366\) 12.0815 + 12.7447i 0.631509 + 0.666177i
\(367\) −12.2166 −0.637703 −0.318852 0.947805i \(-0.603297\pi\)
−0.318852 + 0.947805i \(0.603297\pi\)
\(368\) −4.97697 −0.259442
\(369\) 0.585157 0.525758i 0.0304621 0.0273699i
\(370\) −16.2248 16.2248i −0.843485 0.843485i
\(371\) 5.20768 + 5.20768i 0.270369 + 0.270369i
\(372\) 1.68904 + 1.78176i 0.0875727 + 0.0923801i
\(373\) 5.78239 0.299401 0.149700 0.988731i \(-0.452169\pi\)
0.149700 + 0.988731i \(0.452169\pi\)
\(374\) −20.8745 −1.07939
\(375\) 15.0218 14.2400i 0.775720 0.735352i
\(376\) 3.62305i 0.186844i
\(377\) −6.28452 + 6.92442i −0.323669 + 0.356626i
\(378\) −5.17948 0.415904i −0.266404 0.0213918i
\(379\) 18.4746 + 18.4746i 0.948977 + 0.948977i 0.998760 0.0497833i \(-0.0158531\pi\)
−0.0497833 + 0.998760i \(0.515853\pi\)
\(380\) 14.0308i 0.719765i
\(381\) 33.7792 + 0.902419i 1.73056 + 0.0462323i
\(382\) 9.04652 + 9.04652i 0.462860 + 0.462860i
\(383\) −22.5886 + 22.5886i −1.15422 + 1.15422i −0.168528 + 0.985697i \(0.553901\pi\)
−0.985697 + 0.168528i \(0.946099\pi\)
\(384\) 1.25702 1.19160i 0.0641468 0.0608086i
\(385\) 7.27824 7.27824i 0.370934 0.370934i
\(386\) 12.3539i 0.628796i
\(387\) 1.31566 24.6063i 0.0668788 1.25081i
\(388\) 7.65788 7.65788i 0.388770 0.388770i
\(389\) 5.36671 0.272103 0.136051 0.990702i \(-0.456559\pi\)
0.136051 + 0.990702i \(0.456559\pi\)
\(390\) −9.12599 8.73830i −0.462112 0.442481i
\(391\) 20.4211 1.03274
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) −21.5240 0.575017i −1.08574 0.0290058i
\(394\) 8.90201i 0.448477i
\(395\) 18.1132 18.1132i 0.911374 0.911374i
\(396\) 11.3530 10.2005i 0.570507 0.512595i
\(397\) 14.5043 14.5043i 0.727949 0.727949i −0.242262 0.970211i \(-0.577889\pi\)
0.970211 + 0.242262i \(0.0778893\pi\)
\(398\) 8.51685 + 8.51685i 0.426911 + 0.426911i
\(399\) 0.320779 12.0074i 0.0160590 0.601120i
\(400\) 0.906626i 0.0453313i
\(401\) 24.1397 + 24.1397i 1.20548 + 1.20548i 0.972476 + 0.233004i \(0.0748554\pi\)
0.233004 + 0.972476i \(0.425145\pi\)
\(402\) 0.205294 7.68454i 0.0102391 0.383270i
\(403\) −0.247298 5.10472i −0.0123188 0.254284i
\(404\) 3.05876i 0.152179i
\(405\) 14.1752 11.4293i 0.704370 0.567924i
\(406\) −2.59352 −0.128714
\(407\) −57.6970 −2.85994
\(408\) −5.15769 + 4.88928i −0.255344 + 0.242055i
\(409\) −11.7934 11.7934i −0.583147 0.583147i 0.352620 0.935767i \(-0.385291\pi\)
−0.935767 + 0.352620i \(0.885291\pi\)
\(410\) 0.375138 + 0.375138i 0.0185267 + 0.0185267i
\(411\) 16.3437 15.4931i 0.806174 0.764220i
\(412\) 8.89812 0.438379
\(413\) 1.89465 0.0932297
\(414\) −11.1064 + 9.97898i −0.545849 + 0.490440i
\(415\) 0.665409i 0.0326636i
\(416\) −3.60133 + 0.174466i −0.176570 + 0.00855391i
\(417\) −0.881117 + 32.9818i −0.0431485 + 1.61513i
\(418\) 24.9476 + 24.9476i 1.22022 + 1.22022i
\(419\) 37.7287i 1.84317i 0.388177 + 0.921585i \(0.373105\pi\)
−0.388177 + 0.921585i \(0.626895\pi\)
\(420\) 0.0935847 3.50305i 0.00456647 0.170931i
\(421\) −2.50345 2.50345i −0.122011 0.122011i 0.643465 0.765476i \(-0.277496\pi\)
−0.765476 + 0.643465i \(0.777496\pi\)
\(422\) −16.4778 + 16.4778i −0.802129 + 0.802129i
\(423\) −7.26432 8.08503i −0.353204 0.393108i
\(424\) −5.20768 + 5.20768i −0.252907 + 0.252907i
\(425\) 3.72000i 0.180446i
\(426\) −23.1170 0.617576i −1.12002 0.0299216i
\(427\) 7.16926 7.16926i 0.346945 0.346945i
\(428\) −16.1853 −0.782346
\(429\) −31.7637 + 0.689325i −1.53357 + 0.0332809i
\(430\) 16.6182 0.801403
\(431\) −3.13738 + 3.13738i −0.151122 + 0.151122i −0.778619 0.627497i \(-0.784080\pi\)
0.627497 + 0.778619i \(0.284080\pi\)
\(432\) 0.415904 5.17948i 0.0200102 0.249198i
\(433\) 32.9365i 1.58283i 0.611280 + 0.791415i \(0.290655\pi\)
−0.611280 + 0.791415i \(0.709345\pi\)
\(434\) 1.00229 1.00229i 0.0481116 0.0481116i
\(435\) 6.59586 6.25261i 0.316247 0.299790i
\(436\) 1.55437 1.55437i 0.0744410 0.0744410i
\(437\) −24.4057 24.4057i −1.16749 1.16749i
\(438\) 2.12574 + 0.0567895i 0.101572 + 0.00271351i
\(439\) 15.3322i 0.731768i 0.930660 + 0.365884i \(0.119233\pi\)
−0.930660 + 0.365884i \(0.880767\pi\)
\(440\) 7.27824 + 7.27824i 0.346977 + 0.346977i
\(441\) −0.160177 + 2.99572i −0.00762747 + 0.142653i
\(442\) 14.7767 0.715856i 0.702855 0.0340498i
\(443\) 26.4837i 1.25828i −0.777292 0.629140i \(-0.783407\pi\)
0.777292 0.629140i \(-0.216593\pi\)
\(444\) −14.2559 + 13.5140i −0.676553 + 0.641345i
\(445\) 11.2487 0.533241
\(446\) 15.8469 0.750374
\(447\) 7.67247 + 8.09366i 0.362895 + 0.382817i
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) 3.73104 + 3.73104i 0.176079 + 0.176079i 0.789644 0.613565i \(-0.210265\pi\)
−0.613565 + 0.789644i \(0.710265\pi\)
\(450\) −1.81781 2.02319i −0.0856926 0.0953740i
\(451\) 1.33403 0.0628170
\(452\) −1.67224 −0.0786557
\(453\) −21.0280 22.1824i −0.987982 1.04222i
\(454\) 3.12050i 0.146452i
\(455\) −4.90255 + 5.40174i −0.229835 + 0.253238i
\(456\) 12.0074 + 0.320779i 0.562296 + 0.0150219i
\(457\) 21.6075 + 21.6075i 1.01075 + 1.01075i 0.999942 + 0.0108124i \(0.00344174\pi\)
0.0108124 + 0.999942i \(0.496558\pi\)
\(458\) 24.6487i 1.15176i
\(459\) −1.70651 + 21.2520i −0.0796529 + 0.991960i
\(460\) −7.12018 7.12018i −0.331980 0.331980i
\(461\) −7.48400 + 7.48400i −0.348565 + 0.348565i −0.859575 0.511010i \(-0.829271\pi\)
0.511010 + 0.859575i \(0.329271\pi\)
\(462\) −6.06222 6.39501i −0.282040 0.297523i
\(463\) −0.469041 + 0.469041i −0.0217982 + 0.0217982i −0.717922 0.696124i \(-0.754907\pi\)
0.696124 + 0.717922i \(0.254907\pi\)
\(464\) 2.59352i 0.120401i
\(465\) −0.132652 + 4.96542i −0.00615159 + 0.230266i
\(466\) 4.97372 4.97372i 0.230403 0.230403i
\(467\) 32.9039 1.52261 0.761306 0.648393i \(-0.224559\pi\)
0.761306 + 0.648393i \(0.224559\pi\)
\(468\) −7.68676 + 7.61011i −0.355320 + 0.351777i
\(469\) −4.43825 −0.204940
\(470\) 5.18322 5.18322i 0.239084 0.239084i
\(471\) 0.640397 23.9713i 0.0295079 1.10454i
\(472\) 1.89465i 0.0872084i
\(473\) 29.5481 29.5481i 1.35862 1.35862i
\(474\) −15.0869 15.9151i −0.692964 0.731006i
\(475\) 4.44586 4.44586i 0.203990 0.203990i
\(476\) 2.90134 + 2.90134i 0.132983 + 0.132983i
\(477\) −1.17967 + 22.0628i −0.0540132 + 1.01019i
\(478\) 3.76921i 0.172400i
\(479\) −8.56901 8.56901i −0.391528 0.391528i 0.483704 0.875232i \(-0.339291\pi\)
−0.875232 + 0.483704i \(0.839291\pi\)
\(480\) 3.50305 + 0.0935847i 0.159892 + 0.00427154i
\(481\) 40.8428 1.97863i 1.86227 0.0902176i
\(482\) 2.02994i 0.0924614i
\(483\) 5.93056 + 6.25613i 0.269850 + 0.284664i
\(484\) 14.8822 0.676465
\(485\) 21.9111 0.994932
\(486\) −9.45691 12.3922i −0.428974 0.562122i
\(487\) −25.4916 25.4916i −1.15513 1.15513i −0.985509 0.169624i \(-0.945745\pi\)
−0.169624 0.985509i \(-0.554255\pi\)
\(488\) 7.16926 + 7.16926i 0.324537 + 0.324537i
\(489\) 4.66012 + 4.91595i 0.210738 + 0.222307i
\(490\) −2.02321 −0.0913993
\(491\) 42.6747 1.92588 0.962941 0.269712i \(-0.0869287\pi\)
0.962941 + 0.269712i \(0.0869287\pi\)
\(492\) 0.329614 0.312461i 0.0148601 0.0140868i
\(493\) 10.6415i 0.479271i
\(494\) −18.5155 16.8044i −0.833052 0.756067i
\(495\) 30.8349 + 1.64870i 1.38593 + 0.0741035i
\(496\) 1.00229 + 1.00229i 0.0450042 + 0.0450042i
\(497\) 13.3514i 0.598891i
\(498\) 0.569447 + 0.0152129i 0.0255175 + 0.000681706i
\(499\) 21.6317 + 21.6317i 0.968368 + 0.968368i 0.999515 0.0311468i \(-0.00991594\pi\)
−0.0311468 + 0.999515i \(0.509916\pi\)
\(500\) 8.45017 8.45017i 0.377903 0.377903i
\(501\) −24.2380 + 22.9766i −1.08287 + 1.02652i
\(502\) 6.47010 6.47010i 0.288775 0.288775i
\(503\) 9.32655i 0.415850i 0.978145 + 0.207925i \(0.0666710\pi\)
−0.978145 + 0.207925i \(0.933329\pi\)
\(504\) −2.99572 0.160177i −0.133440 0.00713485i
\(505\) 4.37594 4.37594i 0.194727 0.194727i
\(506\) −25.3201 −1.12562
\(507\) 22.4614 1.57725i 0.997544 0.0700479i
\(508\) 19.5094 0.865590
\(509\) 1.25938 1.25938i 0.0558209 0.0558209i −0.678645 0.734466i \(-0.737433\pi\)
0.734466 + 0.678645i \(0.237433\pi\)
\(510\) −14.3734 0.383989i −0.636467 0.0170033i
\(511\) 1.22773i 0.0543117i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 27.4383 23.3593i 1.21143 1.03134i
\(514\) −2.50593 + 2.50593i −0.110532 + 0.110532i
\(515\) 12.7299 + 12.7299i 0.560945 + 0.560945i
\(516\) 0.379934 14.2216i 0.0167257 0.626073i
\(517\) 18.4321i 0.810643i
\(518\) 8.01932 + 8.01932i 0.352349 + 0.352349i
\(519\) −1.01597 + 38.0296i −0.0445961 + 1.66931i
\(520\) −5.40174 4.90255i −0.236882 0.214991i
\(521\) 38.5430i 1.68860i −0.535872 0.844299i \(-0.680017\pi\)
0.535872 0.844299i \(-0.319983\pi\)
\(522\) −5.20010 5.78760i −0.227602 0.253316i
\(523\) 7.07627 0.309424 0.154712 0.987960i \(-0.450555\pi\)
0.154712 + 0.987960i \(0.450555\pi\)
\(524\) −12.4313 −0.543064
\(525\) −1.13964 + 1.08034i −0.0497381 + 0.0471497i
\(526\) 19.5452 + 19.5452i 0.852211 + 0.852211i
\(527\) −4.11253 4.11253i −0.179144 0.179144i
\(528\) 6.39501 6.06222i 0.278307 0.263824i
\(529\) 1.77022 0.0769662
\(530\) −14.9005 −0.647235
\(531\) 3.79884 + 4.22802i 0.164855 + 0.183480i
\(532\) 6.93493i 0.300667i
\(533\) −0.944338 + 0.0457484i −0.0409038 + 0.00198158i
\(534\) 0.257174 9.62650i 0.0111290 0.416580i
\(535\) −23.1551 23.1551i −1.00108 1.00108i
\(536\) 4.43825i 0.191703i
\(537\) −0.396134 + 14.8280i −0.0170944 + 0.639877i
\(538\) 14.1458 + 14.1458i 0.609867 + 0.609867i
\(539\) −3.59738 + 3.59738i −0.154950 + 0.154950i
\(540\) 8.00490 6.81489i 0.344476 0.293266i
\(541\) 6.35434 6.35434i 0.273194 0.273194i −0.557190 0.830385i \(-0.688121\pi\)
0.830385 + 0.557190i \(0.188121\pi\)
\(542\) 7.32256i 0.314531i
\(543\) −1.68490 0.0450124i −0.0723060 0.00193167i
\(544\) −2.90134 + 2.90134i −0.124394 + 0.124394i
\(545\) 4.44745 0.190508
\(546\) 4.51065 + 4.31903i 0.193038 + 0.184837i
\(547\) 10.2100 0.436548 0.218274 0.975888i \(-0.429957\pi\)
0.218274 + 0.975888i \(0.429957\pi\)
\(548\) 9.19378 9.19378i 0.392739 0.392739i
\(549\) 30.3732 + 1.62401i 1.29630 + 0.0693112i
\(550\) 4.61242i 0.196674i
\(551\) 12.7180 12.7180i 0.541803 0.541803i
\(552\) −6.25613 + 5.93056i −0.266279 + 0.252421i
\(553\) −8.95271 + 8.95271i −0.380708 + 0.380708i
\(554\) −8.43935 8.43935i −0.358554 0.358554i
\(555\) −39.7282 1.06135i −1.68637 0.0450517i
\(556\) 19.0489i 0.807852i
\(557\) 1.56817 + 1.56817i 0.0664457 + 0.0664457i 0.739549 0.673103i \(-0.235039\pi\)
−0.673103 + 0.739549i \(0.735039\pi\)
\(558\) 4.24630 + 0.227044i 0.179760 + 0.00961152i
\(559\) −19.9033 + 21.9299i −0.841821 + 0.927538i
\(560\) 2.02321i 0.0854962i
\(561\) −26.2395 + 24.8740i −1.10783 + 1.05018i
\(562\) −27.4966 −1.15988
\(563\) 20.2496 0.853418 0.426709 0.904389i \(-0.359673\pi\)
0.426709 + 0.904389i \(0.359673\pi\)
\(564\) −4.31722 4.55423i −0.181788 0.191767i
\(565\) −2.39235 2.39235i −0.100647 0.100647i
\(566\) 7.72333 + 7.72333i 0.324636 + 0.324636i
\(567\) −7.00628 + 5.64907i −0.294236 + 0.237239i
\(568\) −13.3514 −0.560211
\(569\) −16.8511 −0.706437 −0.353218 0.935541i \(-0.614913\pi\)
−0.353218 + 0.935541i \(0.614913\pi\)
\(570\) 16.7191 + 17.6370i 0.700287 + 0.738731i
\(571\) 8.55891i 0.358179i −0.983833 0.179090i \(-0.942685\pi\)
0.983833 0.179090i \(-0.0573152\pi\)
\(572\) −18.3216 + 0.887589i −0.766065 + 0.0371120i
\(573\) 22.1515 + 0.591781i 0.925391 + 0.0247220i
\(574\) −0.185417 0.185417i −0.00773916 0.00773916i
\(575\) 4.51225i 0.188174i
\(576\) 0.160177 2.99572i 0.00667404 0.124822i
\(577\) −11.4457 11.4457i −0.476492 0.476492i 0.427516 0.904008i \(-0.359389\pi\)
−0.904008 + 0.427516i \(0.859389\pi\)
\(578\) −0.116245 + 0.116245i −0.00483516 + 0.00483516i
\(579\) −14.7209 15.5290i −0.611779 0.645364i
\(580\) 3.71036 3.71036i 0.154064 0.154064i
\(581\) 0.328888i 0.0136446i
\(582\) 0.500942 18.7512i 0.0207647 0.777263i
\(583\) −26.4938 + 26.4938i −1.09726 + 1.09726i
\(584\) 1.22773 0.0508040
\(585\) −21.8841 0.109653i −0.904795 0.00453360i
\(586\) −2.57273 −0.106278
\(587\) −19.6840 + 19.6840i −0.812445 + 0.812445i −0.985000 0.172555i \(-0.944798\pi\)
0.172555 + 0.985000i \(0.444798\pi\)
\(588\) −0.0462556 + 1.73143i −0.00190755 + 0.0714031i
\(589\) 9.82995i 0.405036i
\(590\) −2.71053 + 2.71053i −0.111591 + 0.111591i
\(591\) 10.6076 + 11.1900i 0.436340 + 0.460294i
\(592\) −8.01932 + 8.01932i −0.329592 + 0.329592i
\(593\) −18.7038 18.7038i −0.768073 0.768073i 0.209694 0.977767i \(-0.432753\pi\)
−0.977767 + 0.209694i \(0.932753\pi\)
\(594\) 2.11590 26.3504i 0.0868163 1.08117i
\(595\) 8.30147i 0.340327i
\(596\) 4.55291 + 4.55291i 0.186495 + 0.186495i
\(597\) 20.8545 + 0.557132i 0.853518 + 0.0228019i
\(598\) 17.9237 0.868312i 0.732955 0.0355079i
\(599\) 6.41962i 0.262299i −0.991363 0.131149i \(-0.958133\pi\)
0.991363 0.131149i \(-0.0418667\pi\)
\(600\) −1.08034 1.13964i −0.0441045 0.0465257i
\(601\) 35.9129 1.46492 0.732459 0.680812i \(-0.238373\pi\)
0.732459 + 0.680812i \(0.238373\pi\)
\(602\) −8.21380 −0.334770
\(603\) −8.89884 9.90421i −0.362389 0.403331i
\(604\) −12.4782 12.4782i −0.507731 0.507731i
\(605\) 21.2909 + 21.2909i 0.865597 + 0.865597i
\(606\) −3.64482 3.84491i −0.148061 0.156189i
\(607\) −3.97978 −0.161534 −0.0807672 0.996733i \(-0.525737\pi\)
−0.0807672 + 0.996733i \(0.525737\pi\)
\(608\) 6.93493 0.281249
\(609\) −3.26010 + 3.09044i −0.132106 + 0.125231i
\(610\) 20.5130i 0.830549i
\(611\) 0.632099 + 13.0478i 0.0255720 + 0.527857i
\(612\) −0.657225 + 12.2918i −0.0265668 + 0.496867i
\(613\) −10.2278 10.2278i −0.413096 0.413096i 0.469720 0.882816i \(-0.344355\pi\)
−0.882816 + 0.469720i \(0.844355\pi\)
\(614\) 12.9792i 0.523797i
\(615\) 0.918568 + 0.0245397i 0.0370402 + 0.000989537i
\(616\) −3.59738 3.59738i −0.144942 0.144942i
\(617\) 28.6473 28.6473i 1.15330 1.15330i 0.167410 0.985887i \(-0.446460\pi\)
0.985887 0.167410i \(-0.0535403\pi\)
\(618\) 11.1851 10.6030i 0.449930 0.426515i
\(619\) −7.15856 + 7.15856i −0.287727 + 0.287727i −0.836181 0.548454i \(-0.815217\pi\)
0.548454 + 0.836181i \(0.315217\pi\)
\(620\) 2.86781i 0.115174i
\(621\) −2.06994 + 25.7781i −0.0830640 + 1.03444i
\(622\) −1.65884 + 1.65884i −0.0665135 + 0.0665135i
\(623\) −5.55985 −0.222751
\(624\) −4.31903 + 4.51065i −0.172900 + 0.180571i
\(625\) 19.6449 0.785796
\(626\) −9.46610 + 9.46610i −0.378341 + 0.378341i
\(627\) 61.0870 + 1.63195i 2.43958 + 0.0651738i
\(628\) 13.8447i 0.552466i
\(629\) 32.9043 32.9043i 1.31198 1.31198i
\(630\) −4.05660 4.51491i −0.161619 0.179878i
\(631\) 30.9238 30.9238i 1.23106 1.23106i 0.267498 0.963558i \(-0.413803\pi\)
0.963558 0.267498i \(-0.0861970\pi\)
\(632\) −8.95271 8.95271i −0.356120 0.356120i
\(633\) −1.07790 + 40.3479i −0.0428428 + 1.60369i
\(634\) 18.3830i 0.730081i
\(635\) 27.9106 + 27.9106i 1.10760 + 1.10760i
\(636\) −0.340662 + 12.7516i −0.0135081 + 0.505634i
\(637\) 2.42316 2.66989i 0.0960090 0.105785i
\(638\) 13.1944i 0.522373i
\(639\) −29.7943 + 26.7699i −1.17865 + 1.05900i
\(640\) 2.02321 0.0799743
\(641\) −19.3831 −0.765585 −0.382792 0.923834i \(-0.625038\pi\)
−0.382792 + 0.923834i \(0.625038\pi\)
\(642\) −20.3452 + 19.2864i −0.802960 + 0.761174i
\(643\) 14.9960 + 14.9960i 0.591384 + 0.591384i 0.938005 0.346621i \(-0.112671\pi\)
−0.346621 + 0.938005i \(0.612671\pi\)
\(644\) 3.51925 + 3.51925i 0.138678 + 0.138678i
\(645\) 20.8894 19.8023i 0.822519 0.779715i
\(646\) −28.4549 −1.11954
\(647\) 17.5674 0.690648 0.345324 0.938484i \(-0.387769\pi\)
0.345324 + 0.938484i \(0.387769\pi\)
\(648\) −5.64907 7.00628i −0.221917 0.275233i
\(649\) 9.63895i 0.378362i
\(650\) 0.158176 + 3.26506i 0.00620416 + 0.128066i
\(651\) 0.0655652 2.45423i 0.00256970 0.0961888i
\(652\) 2.76536 + 2.76536i 0.108300 + 0.108300i
\(653\) 13.2124i 0.517040i 0.966006 + 0.258520i \(0.0832347\pi\)
−0.966006 + 0.258520i \(0.916765\pi\)
\(654\) 0.101680 3.80606i 0.00397599 0.148829i
\(655\) −17.7845 17.7845i −0.694899 0.694899i
\(656\) 0.185417 0.185417i 0.00723932 0.00723932i
\(657\) 2.73976 2.46165i 0.106888 0.0960380i
\(658\) −2.56188 + 2.56188i −0.0998725 + 0.0998725i
\(659\) 25.7020i 1.00121i 0.865677 + 0.500603i \(0.166888\pi\)
−0.865677 + 0.500603i \(0.833112\pi\)
\(660\) 17.8216 + 0.476108i 0.693706 + 0.0185325i
\(661\) 24.0774 24.0774i 0.936502 0.936502i −0.0615994 0.998101i \(-0.519620\pi\)
0.998101 + 0.0615994i \(0.0196201\pi\)
\(662\) 0.777007 0.0301992
\(663\) 17.7215 18.5077i 0.688246 0.718781i
\(664\) 0.328888 0.0127633
\(665\) 9.92128 9.92128i 0.384731 0.384731i
\(666\) −1.81657 + 33.9746i −0.0703907 + 1.31649i
\(667\) 12.9079i 0.499795i
\(668\) −13.6345 + 13.6345i −0.527536 + 0.527536i
\(669\) 19.9199 18.8832i 0.770146 0.730068i
\(670\) 6.34947 6.34947i 0.245302 0.245302i
\(671\) 36.4733 + 36.4733i 1.40804 + 1.40804i
\(672\) −1.73143 0.0462556i −0.0667915 0.00178435i
\(673\) 18.7017i 0.720898i 0.932779 + 0.360449i \(0.117377\pi\)
−0.932779 + 0.360449i \(0.882623\pi\)
\(674\) −14.2273 14.2273i −0.548013 0.548013i
\(675\) −4.69585 0.377070i −0.180743 0.0145134i
\(676\) 12.9391 1.25662i 0.497659 0.0483315i
\(677\) 23.9791i 0.921593i −0.887506 0.460797i \(-0.847564\pi\)
0.887506 0.460797i \(-0.152436\pi\)
\(678\) −2.10203 + 1.99264i −0.0807282 + 0.0765271i
\(679\) −10.8299 −0.415613
\(680\) −8.30147 −0.318347
\(681\) −3.71839 3.92252i −0.142489 0.150311i
\(682\) 5.09912 + 5.09912i 0.195255 + 0.195255i
\(683\) −23.6663 23.6663i −0.905564 0.905564i 0.0903464 0.995910i \(-0.471203\pi\)
−0.995910 + 0.0903464i \(0.971203\pi\)
\(684\) 15.4757 13.9048i 0.591728 0.531662i
\(685\) 26.3057 1.00509
\(686\) 1.00000 0.0381802
\(687\) 29.3714 + 30.9838i 1.12059 + 1.18211i
\(688\) 8.21380i 0.313148i
\(689\) 17.8460 19.6631i 0.679878 0.749105i
\(690\) −17.4346 0.465768i −0.663723 0.0177315i
\(691\) 3.19271 + 3.19271i 0.121456 + 0.121456i 0.765222 0.643766i \(-0.222629\pi\)
−0.643766 + 0.765222i \(0.722629\pi\)
\(692\) 21.9642i 0.834955i
\(693\) −15.2406 0.814893i −0.578943 0.0309552i
\(694\) −11.6206 11.6206i −0.441113 0.441113i
\(695\) −27.2518 + 27.2518i −1.03372 + 1.03372i
\(696\) −3.09044 3.26010i −0.117143 0.123574i
\(697\) −0.760789 + 0.760789i −0.0288169 + 0.0288169i
\(698\) 13.6817i 0.517859i
\(699\) 0.325357 12.1787i 0.0123061 0.460642i
\(700\) −0.641081 + 0.641081i −0.0242306 + 0.0242306i
\(701\) −24.7374 −0.934318 −0.467159 0.884173i \(-0.654722\pi\)
−0.467159 + 0.884173i \(0.654722\pi\)
\(702\) −0.594164 + 18.7256i −0.0224253 + 0.706751i
\(703\) −78.6493 −2.96631
\(704\) 3.59738 3.59738i 0.135581 0.135581i
\(705\) 0.339062 12.6917i 0.0127698 0.477998i
\(706\) 3.60273i 0.135590i
\(707\) −2.16287 + 2.16287i −0.0813431 + 0.0813431i
\(708\) 2.25767 + 2.38161i 0.0848483 + 0.0895062i
\(709\) 12.7061 12.7061i 0.477187 0.477187i −0.427044 0.904231i \(-0.640445\pi\)
0.904231 + 0.427044i \(0.140445\pi\)
\(710\) −19.1008 19.1008i −0.716840 0.716840i
\(711\) −37.9289 2.02801i −1.42245 0.0760562i
\(712\) 5.55985i 0.208364i
\(713\) −4.98838 4.98838i −0.186816 0.186816i
\(714\) 7.10428 + 0.189792i 0.265871 + 0.00710280i
\(715\) −27.4811 24.9415i −1.02774 0.932760i
\(716\) 8.56403i 0.320053i
\(717\) −4.49140 4.73796i −0.167734 0.176942i
\(718\) −30.3098 −1.13115
\(719\) 19.2223 0.716870 0.358435 0.933555i \(-0.383310\pi\)
0.358435 + 0.933555i \(0.383310\pi\)
\(720\) 4.51491 4.05660i 0.168261 0.151181i
\(721\) −6.29192 6.29192i −0.234323 0.234323i
\(722\) 20.5720 + 20.5720i 0.765612 + 0.765612i
\(723\) 2.41888 + 2.55167i 0.0899592 + 0.0948977i
\(724\) −0.973124 −0.0361659
\(725\) −2.35136 −0.0873272
\(726\) 18.7072 17.7337i 0.694289 0.658158i
\(727\) 49.4631i 1.83448i −0.398330 0.917242i \(-0.630410\pi\)
0.398330 0.917242i \(-0.369590\pi\)
\(728\) 2.66989 + 2.42316i 0.0989527 + 0.0898082i
\(729\) −26.6540 4.30834i −0.987187 0.159568i
\(730\) 1.75643 + 1.75643i 0.0650083 + 0.0650083i
\(731\) 33.7022i 1.24652i
\(732\) 17.5548 + 0.468979i 0.648843 + 0.0173340i
\(733\) −7.14061 7.14061i −0.263744 0.263744i 0.562829 0.826573i \(-0.309713\pi\)
−0.826573 + 0.562829i \(0.809713\pi\)
\(734\) −8.63847 + 8.63847i −0.318852 + 0.318852i
\(735\) −2.54321 + 2.41086i −0.0938075 + 0.0889258i
\(736\) −3.51925 + 3.51925i −0.129721 + 0.129721i
\(737\) 22.5794i 0.831724i
\(738\) 0.0420015 0.785536i 0.00154610 0.0289160i
\(739\) −23.2049 + 23.2049i −0.853607 + 0.853607i −0.990575 0.136968i \(-0.956264\pi\)
0.136968 + 0.990575i \(0.456264\pi\)
\(740\) −22.9453 −0.843485
\(741\) −43.2984 + 0.939648i −1.59061 + 0.0345188i
\(742\) 7.36477 0.270369
\(743\) 15.5087 15.5087i 0.568959 0.568959i −0.362878 0.931837i \(-0.618206\pi\)
0.931837 + 0.362878i \(0.118206\pi\)
\(744\) 2.45423 + 0.0655652i 0.0899764 + 0.00240374i
\(745\) 13.0270i 0.477273i
\(746\) 4.08877 4.08877i 0.149700 0.149700i
\(747\) 0.733932 0.659431i 0.0268532 0.0241273i
\(748\) −14.7605 + 14.7605i −0.539696 + 0.539696i
\(749\) 11.4447 + 11.4447i 0.418182 + 0.418182i
\(750\) 0.552770 20.6912i 0.0201843 0.755536i
\(751\) 15.4920i 0.565311i 0.959221 + 0.282656i \(0.0912154\pi\)
−0.959221 + 0.282656i \(0.908785\pi\)
\(752\) −2.56188 2.56188i −0.0934222 0.0934222i
\(753\) 0.423243 15.8428i 0.0154238 0.577343i
\(754\) 0.452482 + 9.34013i 0.0164784 + 0.340147i
\(755\) 35.7033i 1.29938i
\(756\) −3.95653 + 3.36836i −0.143898 + 0.122506i
\(757\) 3.34900 0.121721 0.0608607 0.998146i \(-0.480615\pi\)
0.0608607 + 0.998146i \(0.480615\pi\)
\(758\) 26.1270 0.948977
\(759\) −31.8278 + 30.1715i −1.15528 + 1.09515i
\(760\) 9.92128 + 9.92128i 0.359883 + 0.359883i
\(761\) −34.2779 34.2779i −1.24257 1.24257i −0.958930 0.283642i \(-0.908457\pi\)
−0.283642 0.958930i \(-0.591543\pi\)
\(762\) 24.5236 23.2474i 0.888397 0.842165i
\(763\) −2.19822 −0.0795807
\(764\) 12.7937 0.462860
\(765\) −18.5252 + 16.6447i −0.669780 + 0.601791i
\(766\) 31.9451i 1.15422i
\(767\) −0.330552 6.82326i −0.0119356 0.246374i
\(768\) 0.0462556 1.73143i 0.00166910 0.0624777i
\(769\) −26.5941 26.5941i −0.959007 0.959007i 0.0401857 0.999192i \(-0.487205\pi\)
−0.999192 + 0.0401857i \(0.987205\pi\)
\(770\) 10.2930i 0.370934i
\(771\) −0.163926 + 6.13606i −0.00590365 + 0.220985i
\(772\) −8.73551 8.73551i −0.314398 0.314398i
\(773\) −33.0906 + 33.0906i −1.19018 + 1.19018i −0.213170 + 0.977015i \(0.568379\pi\)
−0.977015 + 0.213170i \(0.931621\pi\)
\(774\) −16.4689 18.3296i −0.591964 0.658843i
\(775\) 0.908704 0.908704i 0.0326416 0.0326416i
\(776\) 10.8299i 0.388770i