Properties

Label 546.2.l.l.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
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.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.l.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.28078 + 2.21837i) q^{10} +(-0.780776 - 1.35234i) q^{11} -1.00000 q^{12} +(-0.500000 - 3.57071i) q^{13} +1.00000 q^{14} +(-1.28078 - 2.21837i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.06155 - 7.03482i) q^{17} +1.00000 q^{18} +(-0.780776 + 1.35234i) q^{19} +(1.28078 - 2.21837i) q^{20} -1.00000 q^{21} +(-0.780776 + 1.35234i) q^{22} +(-3.56155 - 6.16879i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.56155 q^{25} +(-2.84233 + 2.21837i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-1.06155 - 1.83866i) q^{29} +(-1.28078 + 2.21837i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(0.780776 - 1.35234i) q^{33} -8.12311 q^{34} +(1.28078 - 2.21837i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.28078 + 5.68247i) q^{37} +1.56155 q^{38} +(2.84233 - 2.21837i) q^{39} -2.56155 q^{40} +(-2.62311 - 4.54335i) q^{41} +(0.500000 + 0.866025i) q^{42} +(4.00000 - 6.92820i) q^{43} +1.56155 q^{44} +(1.28078 - 2.21837i) q^{45} +(-3.56155 + 6.16879i) q^{46} -12.6847 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.780776 - 1.35234i) q^{50} +8.12311 q^{51} +(3.34233 + 1.35234i) q^{52} +7.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(2.00000 + 3.46410i) q^{55} +(-0.500000 + 0.866025i) q^{56} -1.56155 q^{57} +(-1.06155 + 1.83866i) q^{58} +(1.56155 - 2.70469i) q^{59} +2.56155 q^{60} +(-2.62311 + 4.54335i) q^{61} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.28078 + 9.14657i) q^{65} -1.56155 q^{66} +(-0.438447 - 0.759413i) q^{67} +(4.06155 + 7.03482i) q^{68} +(3.56155 - 6.16879i) q^{69} -2.56155 q^{70} +(-6.68466 + 11.5782i) q^{71} +(-0.500000 + 0.866025i) q^{72} -6.56155 q^{73} +(3.28078 - 5.68247i) q^{74} +(0.780776 + 1.35234i) q^{75} +(-0.780776 - 1.35234i) q^{76} +1.56155 q^{77} +(-3.34233 - 1.35234i) q^{78} -2.43845 q^{79} +(1.28078 + 2.21837i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.62311 + 4.54335i) q^{82} +3.12311 q^{83} +(0.500000 - 0.866025i) q^{84} +(-10.4039 + 18.0201i) q^{85} -8.00000 q^{86} +(1.06155 - 1.83866i) q^{87} +(-0.780776 - 1.35234i) q^{88} +(-3.78078 - 6.54850i) q^{89} -2.56155 q^{90} +(3.34233 + 1.35234i) q^{91} +7.12311 q^{92} +(6.34233 + 10.9852i) q^{94} +(2.00000 - 3.46410i) q^{95} -1.00000 q^{96} +(4.56155 - 7.90084i) q^{97} +(-0.500000 + 0.866025i) q^{98} +1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 2q^{7} + 4q^{8} - 2q^{9} + q^{10} + q^{11} - 4q^{12} - 2q^{13} + 4q^{14} - q^{15} - 2q^{16} + 8q^{17} + 4q^{18} + q^{19} + q^{20} - 4q^{21} + q^{22} - 6q^{23} + 2q^{24} - 2q^{25} + q^{26} - 4q^{27} - 2q^{28} + 4q^{29} - q^{30} - 2q^{32} - q^{33} - 16q^{34} + q^{35} - 2q^{36} + 9q^{37} - 2q^{38} - q^{39} - 2q^{40} + 6q^{41} + 2q^{42} + 16q^{43} - 2q^{44} + q^{45} - 6q^{46} - 26q^{47} + 2q^{48} - 2q^{49} + q^{50} + 16q^{51} + q^{52} + 28q^{53} + 2q^{54} + 8q^{55} - 2q^{56} + 2q^{57} + 4q^{58} - 2q^{59} + 2q^{60} + 6q^{61} - 2q^{63} + 4q^{64} + q^{65} + 2q^{66} - 10q^{67} + 8q^{68} + 6q^{69} - 2q^{70} - 2q^{71} - 2q^{72} - 18q^{73} + 9q^{74} - q^{75} + q^{76} - 2q^{77} - q^{78} - 18q^{79} + q^{80} - 2q^{81} + 6q^{82} - 4q^{83} + 2q^{84} - 21q^{85} - 32q^{86} - 4q^{87} + q^{88} - 11q^{89} - 2q^{90} + q^{91} + 12q^{92} + 13q^{94} + 8q^{95} - 4q^{96} + 10q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.56155 −1.14556 −0.572781 0.819709i \(-0.694135\pi\)
−0.572781 + 0.819709i \(0.694135\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.28078 + 2.21837i 0.405017 + 0.701510i
\(11\) −0.780776 1.35234i −0.235413 0.407747i 0.723980 0.689821i \(-0.242311\pi\)
−0.959393 + 0.282074i \(0.908978\pi\)
\(12\) −1.00000 −0.288675
\(13\) −0.500000 3.57071i −0.138675 0.990338i
\(14\) 1.00000 0.267261
\(15\) −1.28078 2.21837i −0.330695 0.572781i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.06155 7.03482i 0.985071 1.70619i 0.343452 0.939170i \(-0.388404\pi\)
0.641619 0.767023i \(-0.278263\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.780776 + 1.35234i −0.179122 + 0.310249i −0.941580 0.336789i \(-0.890659\pi\)
0.762458 + 0.647038i \(0.223992\pi\)
\(20\) 1.28078 2.21837i 0.286390 0.496043i
\(21\) −1.00000 −0.218218
\(22\) −0.780776 + 1.35234i −0.166462 + 0.288321i
\(23\) −3.56155 6.16879i −0.742635 1.28628i −0.951292 0.308293i \(-0.900242\pi\)
0.208656 0.977989i \(-0.433091\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 1.56155 0.312311
\(26\) −2.84233 + 2.21837i −0.557427 + 0.435058i
\(27\) −1.00000 −0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −1.06155 1.83866i −0.197125 0.341431i 0.750470 0.660905i \(-0.229827\pi\)
−0.947595 + 0.319474i \(0.896494\pi\)
\(30\) −1.28078 + 2.21837i −0.233837 + 0.405017i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.780776 1.35234i 0.135916 0.235413i
\(34\) −8.12311 −1.39310
\(35\) 1.28078 2.21837i 0.216491 0.374973i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.28078 + 5.68247i 0.539356 + 0.934193i 0.998939 + 0.0460575i \(0.0146657\pi\)
−0.459582 + 0.888135i \(0.652001\pi\)
\(38\) 1.56155 0.253317
\(39\) 2.84233 2.21837i 0.455137 0.355223i
\(40\) −2.56155 −0.405017
\(41\) −2.62311 4.54335i −0.409660 0.709552i 0.585191 0.810895i \(-0.301019\pi\)
−0.994852 + 0.101343i \(0.967686\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) 1.56155 0.235413
\(45\) 1.28078 2.21837i 0.190927 0.330695i
\(46\) −3.56155 + 6.16879i −0.525122 + 0.909539i
\(47\) −12.6847 −1.85025 −0.925124 0.379666i \(-0.876039\pi\)
−0.925124 + 0.379666i \(0.876039\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −0.780776 1.35234i −0.110418 0.191250i
\(51\) 8.12311 1.13746
\(52\) 3.34233 + 1.35234i 0.463498 + 0.187536i
\(53\) 7.00000 0.961524 0.480762 0.876851i \(-0.340360\pi\)
0.480762 + 0.876851i \(0.340360\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 2.00000 + 3.46410i 0.269680 + 0.467099i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) −1.56155 −0.206833
\(58\) −1.06155 + 1.83866i −0.139389 + 0.241428i
\(59\) 1.56155 2.70469i 0.203297 0.352120i −0.746292 0.665619i \(-0.768168\pi\)
0.949589 + 0.313498i \(0.101501\pi\)
\(60\) 2.56155 0.330695
\(61\) −2.62311 + 4.54335i −0.335854 + 0.581717i −0.983649 0.180099i \(-0.942358\pi\)
0.647794 + 0.761815i \(0.275692\pi\)
\(62\) 0 0
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) 1.28078 + 9.14657i 0.158861 + 1.13449i
\(66\) −1.56155 −0.192214
\(67\) −0.438447 0.759413i −0.0535648 0.0927770i 0.838000 0.545671i \(-0.183725\pi\)
−0.891565 + 0.452894i \(0.850392\pi\)
\(68\) 4.06155 + 7.03482i 0.492536 + 0.853097i
\(69\) 3.56155 6.16879i 0.428761 0.742635i
\(70\) −2.56155 −0.306164
\(71\) −6.68466 + 11.5782i −0.793323 + 1.37408i 0.130576 + 0.991438i \(0.458317\pi\)
−0.923899 + 0.382637i \(0.875016\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −6.56155 −0.767972 −0.383986 0.923339i \(-0.625449\pi\)
−0.383986 + 0.923339i \(0.625449\pi\)
\(74\) 3.28078 5.68247i 0.381383 0.660574i
\(75\) 0.780776 + 1.35234i 0.0901563 + 0.156155i
\(76\) −0.780776 1.35234i −0.0895612 0.155125i
\(77\) 1.56155 0.177955
\(78\) −3.34233 1.35234i −0.378444 0.153123i
\(79\) −2.43845 −0.274347 −0.137173 0.990547i \(-0.543802\pi\)
−0.137173 + 0.990547i \(0.543802\pi\)
\(80\) 1.28078 + 2.21837i 0.143195 + 0.248021i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.62311 + 4.54335i −0.289674 + 0.501729i
\(83\) 3.12311 0.342805 0.171403 0.985201i \(-0.445170\pi\)
0.171403 + 0.985201i \(0.445170\pi\)
\(84\) 0.500000 0.866025i 0.0545545 0.0944911i
\(85\) −10.4039 + 18.0201i −1.12846 + 1.95455i
\(86\) −8.00000 −0.862662
\(87\) 1.06155 1.83866i 0.113810 0.197125i
\(88\) −0.780776 1.35234i −0.0832310 0.144160i
\(89\) −3.78078 6.54850i −0.400761 0.694139i 0.593056 0.805161i \(-0.297921\pi\)
−0.993818 + 0.111022i \(0.964588\pi\)
\(90\) −2.56155 −0.270011
\(91\) 3.34233 + 1.35234i 0.350371 + 0.141764i
\(92\) 7.12311 0.742635
\(93\) 0 0
\(94\) 6.34233 + 10.9852i 0.654161 + 1.13304i
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) −1.00000 −0.102062
\(97\) 4.56155 7.90084i 0.463156 0.802209i −0.535961 0.844243i \(-0.680050\pi\)
0.999116 + 0.0420341i \(0.0133838\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) 1.56155 0.156942
\(100\) −0.780776 + 1.35234i −0.0780776 + 0.135234i
\(101\) −7.40388 12.8239i −0.736714 1.27603i −0.953967 0.299911i \(-0.903043\pi\)
0.217254 0.976115i \(-0.430290\pi\)
\(102\) −4.06155 7.03482i −0.402154 0.696551i
\(103\) −10.2462 −1.00959 −0.504795 0.863239i \(-0.668432\pi\)
−0.504795 + 0.863239i \(0.668432\pi\)
\(104\) −0.500000 3.57071i −0.0490290 0.350137i
\(105\) 2.56155 0.249982
\(106\) −3.50000 6.06218i −0.339950 0.588811i
\(107\) 7.46543 + 12.9305i 0.721711 + 1.25004i 0.960314 + 0.278923i \(0.0899773\pi\)
−0.238603 + 0.971117i \(0.576689\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.24621 0.406713 0.203357 0.979105i \(-0.434815\pi\)
0.203357 + 0.979105i \(0.434815\pi\)
\(110\) 2.00000 3.46410i 0.190693 0.330289i
\(111\) −3.28078 + 5.68247i −0.311398 + 0.539356i
\(112\) 1.00000 0.0944911
\(113\) 1.28078 2.21837i 0.120485 0.208687i −0.799474 0.600701i \(-0.794888\pi\)
0.919959 + 0.392014i \(0.128222\pi\)
\(114\) 0.780776 + 1.35234i 0.0731264 + 0.126659i
\(115\) 9.12311 + 15.8017i 0.850734 + 1.47351i
\(116\) 2.12311 0.197125
\(117\) 3.34233 + 1.35234i 0.308998 + 0.125024i
\(118\) −3.12311 −0.287505
\(119\) 4.06155 + 7.03482i 0.372322 + 0.644881i
\(120\) −1.28078 2.21837i −0.116918 0.202509i
\(121\) 4.28078 7.41452i 0.389161 0.674047i
\(122\) 5.24621 0.474970
\(123\) 2.62311 4.54335i 0.236517 0.409660i
\(124\) 0 0
\(125\) 8.80776 0.787790
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 10.2462 + 17.7470i 0.909204 + 1.57479i 0.815172 + 0.579219i \(0.196642\pi\)
0.0940321 + 0.995569i \(0.470024\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 8.00000 0.704361
\(130\) 7.28078 5.68247i 0.638566 0.498386i
\(131\) −2.24621 −0.196252 −0.0981262 0.995174i \(-0.531285\pi\)
−0.0981262 + 0.995174i \(0.531285\pi\)
\(132\) 0.780776 + 1.35234i 0.0679579 + 0.117706i
\(133\) −0.780776 1.35234i −0.0677019 0.117263i
\(134\) −0.438447 + 0.759413i −0.0378761 + 0.0656033i
\(135\) 2.56155 0.220463
\(136\) 4.06155 7.03482i 0.348275 0.603230i
\(137\) −8.28078 + 14.3427i −0.707474 + 1.22538i 0.258317 + 0.966060i \(0.416832\pi\)
−0.965791 + 0.259321i \(0.916501\pi\)
\(138\) −7.12311 −0.606359
\(139\) 4.78078 8.28055i 0.405500 0.702347i −0.588879 0.808221i \(-0.700431\pi\)
0.994380 + 0.105874i \(0.0337640\pi\)
\(140\) 1.28078 + 2.21837i 0.108245 + 0.187486i
\(141\) −6.34233 10.9852i −0.534120 0.925124i
\(142\) 13.3693 1.12193
\(143\) −4.43845 + 3.46410i −0.371162 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 2.71922 + 4.70983i 0.225819 + 0.391130i
\(146\) 3.28078 + 5.68247i 0.271519 + 0.470285i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) −6.56155 −0.539356
\(149\) 5.71922 9.90599i 0.468537 0.811530i −0.530816 0.847487i \(-0.678115\pi\)
0.999353 + 0.0359569i \(0.0114479\pi\)
\(150\) 0.780776 1.35234i 0.0637501 0.110418i
\(151\) 6.93087 0.564026 0.282013 0.959411i \(-0.408998\pi\)
0.282013 + 0.959411i \(0.408998\pi\)
\(152\) −0.780776 + 1.35234i −0.0633293 + 0.109690i
\(153\) 4.06155 + 7.03482i 0.328357 + 0.568731i
\(154\) −0.780776 1.35234i −0.0629168 0.108975i
\(155\) 0 0
\(156\) 0.500000 + 3.57071i 0.0400320 + 0.285886i
\(157\) −13.6847 −1.09215 −0.546077 0.837735i \(-0.683880\pi\)
−0.546077 + 0.837735i \(0.683880\pi\)
\(158\) 1.21922 + 2.11176i 0.0969962 + 0.168002i
\(159\) 3.50000 + 6.06218i 0.277568 + 0.480762i
\(160\) 1.28078 2.21837i 0.101254 0.175378i
\(161\) 7.12311 0.561379
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 4.24621 7.35465i 0.332589 0.576061i −0.650430 0.759566i \(-0.725411\pi\)
0.983019 + 0.183505i \(0.0587445\pi\)
\(164\) 5.24621 0.409660
\(165\) −2.00000 + 3.46410i −0.155700 + 0.269680i
\(166\) −1.56155 2.70469i −0.121200 0.209925i
\(167\) 10.2462 + 17.7470i 0.792876 + 1.37330i 0.924179 + 0.381959i \(0.124750\pi\)
−0.131304 + 0.991342i \(0.541916\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.5000 + 3.57071i −0.961538 + 0.274670i
\(170\) 20.8078 1.59588
\(171\) −0.780776 1.35234i −0.0597075 0.103416i
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) −2.12311 −0.160952
\(175\) −0.780776 + 1.35234i −0.0590211 + 0.102228i
\(176\) −0.780776 + 1.35234i −0.0588532 + 0.101937i
\(177\) 3.12311 0.234747
\(178\) −3.78078 + 6.54850i −0.283381 + 0.490831i
\(179\) 9.12311 + 15.8017i 0.681893 + 1.18107i 0.974402 + 0.224811i \(0.0721763\pi\)
−0.292510 + 0.956263i \(0.594490\pi\)
\(180\) 1.28078 + 2.21837i 0.0954634 + 0.165348i
\(181\) −3.24621 −0.241289 −0.120644 0.992696i \(-0.538496\pi\)
−0.120644 + 0.992696i \(0.538496\pi\)
\(182\) −0.500000 3.57071i −0.0370625 0.264679i
\(183\) −5.24621 −0.387811
\(184\) −3.56155 6.16879i −0.262561 0.454769i
\(185\) −8.40388 14.5560i −0.617866 1.07017i
\(186\) 0 0
\(187\) −12.6847 −0.927594
\(188\) 6.34233 10.9852i 0.462562 0.801181i
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) −4.00000 −0.290191
\(191\) −1.56155 + 2.70469i −0.112990 + 0.195704i −0.916974 0.398946i \(-0.869376\pi\)
0.803984 + 0.594650i \(0.202709\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 4.06155 + 7.03482i 0.292357 + 0.506377i 0.974367 0.224966i \(-0.0722271\pi\)
−0.682010 + 0.731343i \(0.738894\pi\)
\(194\) −9.12311 −0.655001
\(195\) −7.28078 + 5.68247i −0.521387 + 0.406930i
\(196\) 1.00000 0.0714286
\(197\) −4.21922 7.30791i −0.300607 0.520667i 0.675666 0.737208i \(-0.263856\pi\)
−0.976274 + 0.216541i \(0.930523\pi\)
\(198\) −0.780776 1.35234i −0.0554874 0.0961069i
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 1.56155 0.110418
\(201\) 0.438447 0.759413i 0.0309257 0.0535648i
\(202\) −7.40388 + 12.8239i −0.520935 + 0.902286i
\(203\) 2.12311 0.149013
\(204\) −4.06155 + 7.03482i −0.284366 + 0.492536i
\(205\) 6.71922 + 11.6380i 0.469291 + 0.812836i
\(206\) 5.12311 + 8.87348i 0.356944 + 0.618245i
\(207\) 7.12311 0.495090
\(208\) −2.84233 + 2.21837i −0.197080 + 0.153816i
\(209\) 2.43845 0.168671
\(210\) −1.28078 2.21837i −0.0883820 0.153082i
\(211\) 1.56155 + 2.70469i 0.107502 + 0.186198i 0.914758 0.404003i \(-0.132382\pi\)
−0.807256 + 0.590202i \(0.799048\pi\)
\(212\) −3.50000 + 6.06218i −0.240381 + 0.416352i
\(213\) −13.3693 −0.916050
\(214\) 7.46543 12.9305i 0.510327 0.883912i
\(215\) −10.2462 + 17.7470i −0.698786 + 1.21033i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −2.12311 3.67733i −0.143795 0.249060i
\(219\) −3.28078 5.68247i −0.221694 0.383986i
\(220\) −4.00000 −0.269680
\(221\) −27.1501 10.9852i −1.82631 0.738947i
\(222\) 6.56155 0.440383
\(223\) −13.1231 22.7299i −0.878788 1.52211i −0.852672 0.522447i \(-0.825019\pi\)
−0.0261163 0.999659i \(-0.508314\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −0.780776 + 1.35234i −0.0520518 + 0.0901563i
\(226\) −2.56155 −0.170392
\(227\) 9.56155 16.5611i 0.634623 1.09920i −0.351972 0.936010i \(-0.614489\pi\)
0.986595 0.163188i \(-0.0521778\pi\)
\(228\) 0.780776 1.35234i 0.0517082 0.0895612i
\(229\) −20.0540 −1.32520 −0.662602 0.748972i \(-0.730548\pi\)
−0.662602 + 0.748972i \(0.730548\pi\)
\(230\) 9.12311 15.8017i 0.601560 1.04193i
\(231\) 0.780776 + 1.35234i 0.0513713 + 0.0889777i
\(232\) −1.06155 1.83866i −0.0696944 0.120714i
\(233\) −23.3693 −1.53097 −0.765487 0.643451i \(-0.777502\pi\)
−0.765487 + 0.643451i \(0.777502\pi\)
\(234\) −0.500000 3.57071i −0.0326860 0.233425i
\(235\) 32.4924 2.11957
\(236\) 1.56155 + 2.70469i 0.101648 + 0.176060i
\(237\) −1.21922 2.11176i −0.0791971 0.137173i
\(238\) 4.06155 7.03482i 0.263271 0.455999i
\(239\) −5.36932 −0.347312 −0.173656 0.984806i \(-0.555558\pi\)
−0.173656 + 0.984806i \(0.555558\pi\)
\(240\) −1.28078 + 2.21837i −0.0826738 + 0.143195i
\(241\) 10.4039 18.0201i 0.670173 1.16077i −0.307682 0.951489i \(-0.599553\pi\)
0.977855 0.209284i \(-0.0671134\pi\)
\(242\) −8.56155 −0.550357
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −2.62311 4.54335i −0.167927 0.290858i
\(245\) 1.28078 + 2.21837i 0.0818258 + 0.141726i
\(246\) −5.24621 −0.334486
\(247\) 5.21922 + 2.11176i 0.332091 + 0.134368i
\(248\) 0 0
\(249\) 1.56155 + 2.70469i 0.0989594 + 0.171403i
\(250\) −4.40388 7.62775i −0.278526 0.482421i
\(251\) −13.8078 + 23.9157i −0.871538 + 1.50955i −0.0111332 + 0.999938i \(0.503544\pi\)
−0.860405 + 0.509611i \(0.829789\pi\)
\(252\) 1.00000 0.0629941
\(253\) −5.56155 + 9.63289i −0.349652 + 0.605615i
\(254\) 10.2462 17.7470i 0.642904 1.11354i
\(255\) −20.8078 −1.30303
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.184658 0.319838i −0.0115187 0.0199509i 0.860209 0.509942i \(-0.170333\pi\)
−0.871727 + 0.489991i \(0.837000\pi\)
\(258\) −4.00000 6.92820i −0.249029 0.431331i
\(259\) −6.56155 −0.407715
\(260\) −8.56155 3.46410i −0.530965 0.214834i
\(261\) 2.12311 0.131417
\(262\) 1.12311 + 1.94528i 0.0693857 + 0.120180i
\(263\) 1.56155 + 2.70469i 0.0962895 + 0.166778i 0.910146 0.414288i \(-0.135969\pi\)
−0.813857 + 0.581066i \(0.802636\pi\)
\(264\) 0.780776 1.35234i 0.0480535 0.0832310i
\(265\) −17.9309 −1.10148
\(266\) −0.780776 + 1.35234i −0.0478725 + 0.0829176i
\(267\) 3.78078 6.54850i 0.231380 0.400761i
\(268\) 0.876894 0.0535648
\(269\) −9.43845 + 16.3479i −0.575472 + 0.996747i 0.420518 + 0.907284i \(0.361848\pi\)
−0.995990 + 0.0894630i \(0.971485\pi\)
\(270\) −1.28078 2.21837i −0.0779456 0.135006i
\(271\) −13.3693 23.1563i −0.812128 1.40665i −0.911372 0.411584i \(-0.864976\pi\)
0.0992436 0.995063i \(-0.468358\pi\)
\(272\) −8.12311 −0.492536
\(273\) 0.500000 + 3.57071i 0.0302614 + 0.216109i
\(274\) 16.5616 1.00052
\(275\) −1.21922 2.11176i −0.0735219 0.127344i
\(276\) 3.56155 + 6.16879i 0.214380 + 0.371318i
\(277\) 7.71922 13.3701i 0.463803 0.803331i −0.535343 0.844634i \(-0.679818\pi\)
0.999147 + 0.0413038i \(0.0131511\pi\)
\(278\) −9.56155 −0.573464
\(279\) 0 0
\(280\) 1.28078 2.21837i 0.0765410 0.132573i
\(281\) −15.9309 −0.950356 −0.475178 0.879890i \(-0.657616\pi\)
−0.475178 + 0.879890i \(0.657616\pi\)
\(282\) −6.34233 + 10.9852i −0.377680 + 0.654161i
\(283\) 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i \(0.0359589\pi\)
−0.399188 + 0.916869i \(0.630708\pi\)
\(284\) −6.68466 11.5782i −0.396662 0.687038i
\(285\) 4.00000 0.236940
\(286\) 5.21922 + 2.11176i 0.308619 + 0.124871i
\(287\) 5.24621 0.309674
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −24.4924 42.4221i −1.44073 2.49542i
\(290\) 2.71922 4.70983i 0.159678 0.276571i
\(291\) 9.12311 0.534806
\(292\) 3.28078 5.68247i 0.191993 0.332541i
\(293\) −10.9654 + 18.9927i −0.640608 + 1.10956i 0.344690 + 0.938717i \(0.387984\pi\)
−0.985297 + 0.170848i \(0.945349\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −4.00000 + 6.92820i −0.232889 + 0.403376i
\(296\) 3.28078 + 5.68247i 0.190691 + 0.330287i
\(297\) 0.780776 + 1.35234i 0.0453052 + 0.0784710i
\(298\) −11.4384 −0.662611
\(299\) −20.2462 + 15.8017i −1.17087 + 0.913835i
\(300\) −1.56155 −0.0901563
\(301\) 4.00000 + 6.92820i 0.230556 + 0.399335i
\(302\) −3.46543 6.00231i −0.199413 0.345394i
\(303\) 7.40388 12.8239i 0.425342 0.736714i
\(304\) 1.56155 0.0895612
\(305\) 6.71922 11.6380i 0.384742 0.666392i
\(306\) 4.06155 7.03482i 0.232184 0.402154i
\(307\) 18.9309 1.08044 0.540221 0.841523i \(-0.318341\pi\)
0.540221 + 0.841523i \(0.318341\pi\)
\(308\) −0.780776 + 1.35234i −0.0444889 + 0.0770570i
\(309\) −5.12311 8.87348i −0.291443 0.504795i
\(310\) 0 0
\(311\) −6.93087 −0.393014 −0.196507 0.980502i \(-0.562960\pi\)
−0.196507 + 0.980502i \(0.562960\pi\)
\(312\) 2.84233 2.21837i 0.160915 0.125590i
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 6.84233 + 11.8513i 0.386135 + 0.668805i
\(315\) 1.28078 + 2.21837i 0.0721636 + 0.124991i
\(316\) 1.21922 2.11176i 0.0685867 0.118796i
\(317\) 16.5616 0.930189 0.465095 0.885261i \(-0.346020\pi\)
0.465095 + 0.885261i \(0.346020\pi\)
\(318\) 3.50000 6.06218i 0.196270 0.339950i
\(319\) −1.65767 + 2.87117i −0.0928117 + 0.160755i
\(320\) −2.56155 −0.143195
\(321\) −7.46543 + 12.9305i −0.416680 + 0.721711i
\(322\) −3.56155 6.16879i −0.198478 0.343773i
\(323\) 6.34233 + 10.9852i 0.352897 + 0.611235i
\(324\) 1.00000 0.0555556
\(325\) −0.780776 5.57586i −0.0433097 0.309293i
\(326\) −8.49242 −0.470352
\(327\) 2.12311 + 3.67733i 0.117408 + 0.203357i
\(328\) −2.62311 4.54335i −0.144837 0.250865i
\(329\) 6.34233 10.9852i 0.349664 0.605636i
\(330\) 4.00000 0.220193
\(331\) 2.68466 4.64996i 0.147562 0.255585i −0.782764 0.622319i \(-0.786191\pi\)
0.930326 + 0.366734i \(0.119524\pi\)
\(332\) −1.56155 + 2.70469i −0.0857013 + 0.148439i
\(333\) −6.56155 −0.359571
\(334\) 10.2462 17.7470i 0.560648 0.971070i
\(335\) 1.12311 + 1.94528i 0.0613618 + 0.106282i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) 19.4924 1.06182 0.530910 0.847428i \(-0.321850\pi\)
0.530910 + 0.847428i \(0.321850\pi\)
\(338\) 9.34233 + 9.03996i 0.508156 + 0.491709i
\(339\) 2.56155 0.139124
\(340\) −10.4039 18.0201i −0.564230 0.977275i
\(341\) 0 0
\(342\) −0.780776 + 1.35234i −0.0422196 + 0.0731264i
\(343\) 1.00000 0.0539949
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) −9.12311 + 15.8017i −0.491171 + 0.850734i
\(346\) −18.0000 −0.967686
\(347\) 11.0270 19.0993i 0.591960 1.02530i −0.402009 0.915636i \(-0.631688\pi\)
0.993968 0.109668i \(-0.0349789\pi\)
\(348\) 1.06155 + 1.83866i 0.0569052 + 0.0985627i
\(349\) 9.00000 + 15.5885i 0.481759 + 0.834431i 0.999781 0.0209364i \(-0.00666475\pi\)
−0.518022 + 0.855367i \(0.673331\pi\)
\(350\) 1.56155 0.0834685
\(351\) 0.500000 + 3.57071i 0.0266880 + 0.190591i
\(352\) 1.56155 0.0832310
\(353\) 6.59612 + 11.4248i 0.351076 + 0.608081i 0.986438 0.164133i \(-0.0524826\pi\)
−0.635362 + 0.772214i \(0.719149\pi\)
\(354\) −1.56155 2.70469i −0.0829956 0.143753i
\(355\) 17.1231 29.6581i 0.908800 1.57409i
\(356\) 7.56155 0.400761
\(357\) −4.06155 + 7.03482i −0.214960 + 0.372322i
\(358\) 9.12311 15.8017i 0.482171 0.835145i
\(359\) −18.2462 −0.962998 −0.481499 0.876447i \(-0.659908\pi\)
−0.481499 + 0.876447i \(0.659908\pi\)
\(360\) 1.28078 2.21837i 0.0675028 0.116918i
\(361\) 8.28078 + 14.3427i 0.435830 + 0.754880i
\(362\) 1.62311 + 2.81130i 0.0853085 + 0.147759i
\(363\) 8.56155 0.449365
\(364\) −2.84233 + 2.21837i −0.148979 + 0.116274i
\(365\) 16.8078 0.879759
\(366\) 2.62311 + 4.54335i 0.137112 + 0.237485i
\(367\) 13.8078 + 23.9157i 0.720759 + 1.24839i 0.960696 + 0.277603i \(0.0895401\pi\)
−0.239936 + 0.970789i \(0.577127\pi\)
\(368\) −3.56155 + 6.16879i −0.185659 + 0.321570i
\(369\) 5.24621 0.273107
\(370\) −8.40388 + 14.5560i −0.436897 + 0.756728i
\(371\) −3.50000 + 6.06218i −0.181711 + 0.314733i
\(372\) 0 0
\(373\) 15.9654 27.6529i 0.826659 1.43182i −0.0739860 0.997259i \(-0.523572\pi\)
0.900645 0.434556i \(-0.143095\pi\)
\(374\) 6.34233 + 10.9852i 0.327954 + 0.568033i
\(375\) 4.40388 + 7.62775i 0.227415 + 0.393895i
\(376\) −12.6847 −0.654161
\(377\) −6.03457 + 4.70983i −0.310796 + 0.242569i
\(378\) −1.00000 −0.0514344
\(379\) 1.80776 + 3.13114i 0.0928586 + 0.160836i 0.908713 0.417422i \(-0.137066\pi\)
−0.815854 + 0.578258i \(0.803733\pi\)
\(380\) 2.00000 + 3.46410i 0.102598 + 0.177705i
\(381\) −10.2462 + 17.7470i −0.524929 + 0.909204i
\(382\) 3.12311 0.159792
\(383\) −3.90388 + 6.76172i −0.199479 + 0.345508i −0.948360 0.317197i \(-0.897258\pi\)
0.748881 + 0.662705i \(0.230592\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −4.00000 −0.203859
\(386\) 4.06155 7.03482i 0.206728 0.358063i
\(387\) 4.00000 + 6.92820i 0.203331 + 0.352180i
\(388\) 4.56155 + 7.90084i 0.231578 + 0.401104i
\(389\) −17.6847 −0.896648 −0.448324 0.893871i \(-0.647979\pi\)
−0.448324 + 0.893871i \(0.647979\pi\)
\(390\) 8.56155 + 3.46410i 0.433531 + 0.175412i
\(391\) −57.8617 −2.92619
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) −1.12311 1.94528i −0.0566532 0.0981262i
\(394\) −4.21922 + 7.30791i −0.212561 + 0.368167i
\(395\) 6.24621 0.314281
\(396\) −0.780776 + 1.35234i −0.0392355 + 0.0679579i
\(397\) 0.465435 0.806157i 0.0233595 0.0404598i −0.854109 0.520093i \(-0.825897\pi\)
0.877469 + 0.479634i \(0.159230\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0.780776 1.35234i 0.0390877 0.0677019i
\(400\) −0.780776 1.35234i −0.0390388 0.0676172i
\(401\) −9.40388 16.2880i −0.469607 0.813384i 0.529789 0.848130i \(-0.322271\pi\)
−0.999396 + 0.0347457i \(0.988938\pi\)
\(402\) −0.876894 −0.0437355
\(403\) 0 0
\(404\) 14.8078 0.736714
\(405\) 1.28078 + 2.21837i 0.0636423 + 0.110232i
\(406\) −1.06155 1.83866i −0.0526840 0.0912513i
\(407\) 5.12311 8.87348i 0.253943 0.439842i
\(408\) 8.12311 0.402154
\(409\) 3.71922 6.44188i 0.183904 0.318531i −0.759303 0.650737i \(-0.774460\pi\)
0.943207 + 0.332207i \(0.107793\pi\)
\(410\) 6.71922 11.6380i 0.331839 0.574762i
\(411\) −16.5616 −0.816921
\(412\) 5.12311 8.87348i 0.252397 0.437165i
\(413\) 1.56155 + 2.70469i 0.0768390 + 0.133089i
\(414\) −3.56155 6.16879i −0.175041 0.303180i
\(415\) −8.00000 −0.392705
\(416\) 3.34233 + 1.35234i 0.163871 + 0.0663041i
\(417\) 9.56155 0.468231
\(418\) −1.21922 2.11176i −0.0596342 0.103289i
\(419\) 0.684658 + 1.18586i 0.0334478 + 0.0579332i 0.882265 0.470754i \(-0.156018\pi\)
−0.848817 + 0.528687i \(0.822685\pi\)
\(420\) −1.28078 + 2.21837i −0.0624955 + 0.108245i
\(421\) 31.3002 1.52548 0.762739 0.646707i \(-0.223854\pi\)
0.762739 + 0.646707i \(0.223854\pi\)
\(422\) 1.56155 2.70469i 0.0760152 0.131662i
\(423\) 6.34233 10.9852i 0.308375 0.534120i
\(424\) 7.00000 0.339950
\(425\) 6.34233 10.9852i 0.307648 0.532862i
\(426\) 6.68466 + 11.5782i 0.323873 + 0.560964i
\(427\) −2.62311 4.54335i −0.126941 0.219868i
\(428\) −14.9309 −0.721711
\(429\) −5.21922 2.11176i −0.251986 0.101957i
\(430\) 20.4924 0.988232
\(431\) 2.68466 + 4.64996i 0.129315 + 0.223981i 0.923412 0.383811i \(-0.125389\pi\)
−0.794096 + 0.607792i \(0.792055\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 16.8423 29.1718i 0.809391 1.40191i −0.103896 0.994588i \(-0.533131\pi\)
0.913287 0.407318i \(-0.133536\pi\)
\(434\) 0 0
\(435\) −2.71922 + 4.70983i −0.130377 + 0.225819i
\(436\) −2.12311 + 3.67733i −0.101678 + 0.176112i
\(437\) 11.1231 0.532090
\(438\) −3.28078 + 5.68247i −0.156762 + 0.271519i
\(439\) 4.87689 + 8.44703i 0.232761 + 0.403155i 0.958620 0.284690i \(-0.0918905\pi\)
−0.725858 + 0.687844i \(0.758557\pi\)
\(440\) 2.00000 + 3.46410i 0.0953463 + 0.165145i
\(441\) 1.00000 0.0476190
\(442\) 4.06155 + 29.0053i 0.193188 + 1.37964i
\(443\) 10.0540 0.477679 0.238839 0.971059i \(-0.423233\pi\)
0.238839 + 0.971059i \(0.423233\pi\)
\(444\) −3.28078 5.68247i −0.155699 0.269678i
\(445\) 9.68466 + 16.7743i 0.459097 + 0.795179i
\(446\) −13.1231 + 22.7299i −0.621397 + 1.07629i
\(447\) 11.4384 0.541020
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 15.6847 27.1666i 0.740205 1.28207i −0.212197 0.977227i \(-0.568062\pi\)
0.952402 0.304845i \(-0.0986048\pi\)
\(450\) 1.56155 0.0736123
\(451\) −4.09612 + 7.09468i −0.192879 + 0.334076i
\(452\) 1.28078 + 2.21837i 0.0602427 + 0.104343i
\(453\) 3.46543 + 6.00231i 0.162820 + 0.282013i
\(454\) −19.1231 −0.897492
\(455\) −8.56155 3.46410i −0.401372 0.162400i
\(456\) −1.56155 −0.0731264
\(457\) −0.0345652 0.0598686i −0.00161689 0.00280054i 0.865216 0.501400i \(-0.167181\pi\)
−0.866833 + 0.498599i \(0.833848\pi\)
\(458\) 10.0270 + 17.3673i 0.468530 + 0.811518i
\(459\) −4.06155 + 7.03482i −0.189577 + 0.328357i
\(460\) −18.2462 −0.850734
\(461\) 15.5270 26.8935i 0.723164 1.25256i −0.236561 0.971617i \(-0.576020\pi\)
0.959725 0.280940i \(-0.0906462\pi\)
\(462\) 0.780776 1.35234i 0.0363250 0.0629168i
\(463\) 24.6847 1.14719 0.573597 0.819138i \(-0.305548\pi\)
0.573597 + 0.819138i \(0.305548\pi\)
\(464\) −1.06155 + 1.83866i −0.0492814 + 0.0853578i
\(465\) 0 0
\(466\) 11.6847 + 20.2384i 0.541281 + 0.937527i
\(467\) 28.9848 1.34126 0.670629 0.741793i \(-0.266024\pi\)
0.670629 + 0.741793i \(0.266024\pi\)
\(468\) −2.84233 + 2.21837i −0.131387 + 0.102544i
\(469\) 0.876894 0.0404912
\(470\) −16.2462 28.1393i −0.749382 1.29797i
\(471\) −6.84233 11.8513i −0.315278 0.546077i
\(472\) 1.56155 2.70469i 0.0718763 0.124493i
\(473\) −12.4924 −0.574402
\(474\) −1.21922 + 2.11176i −0.0560008 + 0.0969962i
\(475\) −1.21922 + 2.11176i −0.0559418 + 0.0968941i
\(476\) −8.12311 −0.372322
\(477\) −3.50000 + 6.06218i −0.160254 + 0.277568i
\(478\) 2.68466 + 4.64996i 0.122793 + 0.212684i
\(479\) −13.4654 23.3228i −0.615251 1.06565i −0.990340 0.138658i \(-0.955721\pi\)
0.375089 0.926989i \(-0.377612\pi\)
\(480\) 2.56155 0.116918
\(481\) 18.6501 14.5560i 0.850371 0.663694i
\(482\) −20.8078 −0.947768
\(483\) 3.56155 + 6.16879i 0.162056 + 0.280690i
\(484\) 4.28078 + 7.41452i 0.194581 + 0.337024i
\(485\) −11.6847 + 20.2384i −0.530573 + 0.918979i
\(486\) −1.00000 −0.0453609
\(487\) −5.65767 + 9.79937i −0.256374 + 0.444052i −0.965268 0.261263i \(-0.915861\pi\)
0.708894 + 0.705315i \(0.249194\pi\)
\(488\) −2.62311 + 4.54335i −0.118742 + 0.205668i
\(489\) 8.49242 0.384041
\(490\) 1.28078 2.21837i 0.0578596 0.100216i
\(491\) −8.24621 14.2829i −0.372146 0.644576i 0.617749 0.786375i \(-0.288045\pi\)
−0.989895 + 0.141799i \(0.954711\pi\)
\(492\) 2.62311 + 4.54335i 0.118259 + 0.204830i
\(493\) −17.2462 −0.776730
\(494\) −0.780776 5.57586i −0.0351288 0.250870i
\(495\) −4.00000 −0.179787
\(496\) 0 0
\(497\) −6.68466 11.5782i −0.299848 0.519352i
\(498\) 1.56155 2.70469i 0.0699749 0.121200i
\(499\) 13.7538 0.615704 0.307852 0.951434i \(-0.400390\pi\)
0.307852 + 0.951434i \(0.400390\pi\)
\(500\) −4.40388 + 7.62775i −0.196948 + 0.341123i
\(501\) −10.2462 + 17.7470i −0.457767 + 0.792876i
\(502\) 27.6155 1.23254
\(503\) −2.24621 + 3.89055i −0.100154 + 0.173471i −0.911748 0.410750i \(-0.865267\pi\)
0.811594 + 0.584222i \(0.198600\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 18.9654 + 32.8491i 0.843951 + 1.46177i
\(506\) 11.1231 0.494482
\(507\) −9.34233 9.03996i −0.414907 0.401479i
\(508\) −20.4924 −0.909204
\(509\) 10.5961 + 18.3530i 0.469665 + 0.813483i 0.999398 0.0346809i \(-0.0110415\pi\)
−0.529734 + 0.848164i \(0.677708\pi\)
\(510\) 10.4039 + 18.0201i 0.460692 + 0.797941i
\(511\) 3.28078 5.68247i 0.145133 0.251378i
\(512\) 1.00000 0.0441942
\(513\) 0.780776 1.35234i 0.0344721 0.0597075i
\(514\) −0.184658 + 0.319838i −0.00814493 + 0.0141074i
\(515\) 26.2462 1.15655
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) 9.90388 + 17.1540i 0.435572 + 0.754433i
\(518\) 3.28078 + 5.68247i 0.144149 + 0.249673i
\(519\) 18.0000 0.790112
\(520\) 1.28078 + 9.14657i 0.0561658 + 0.401104i
\(521\) 34.1231 1.49496 0.747480 0.664284i \(-0.231263\pi\)
0.747480 + 0.664284i \(0.231263\pi\)
\(522\) −1.06155 1.83866i −0.0464629 0.0804761i
\(523\) −1.90388 3.29762i −0.0832509 0.144195i 0.821394 0.570362i \(-0.193197\pi\)
−0.904645 + 0.426167i \(0.859864\pi\)
\(524\) 1.12311 1.94528i 0.0490631 0.0849798i
\(525\) −1.56155 −0.0681518
\(526\) 1.56155 2.70469i 0.0680869 0.117930i
\(527\) 0 0
\(528\) −1.56155 −0.0679579
\(529\) −13.8693 + 24.0224i −0.603014 + 1.04445i
\(530\) 8.96543 + 15.5286i 0.389434 + 0.674519i
\(531\) 1.56155 + 2.70469i 0.0677656 + 0.117373i
\(532\) 1.56155 0.0677019
\(533\) −14.9115 + 11.6380i −0.645887 + 0.504099i
\(534\) −7.56155 −0.327220
\(535\) −19.1231 33.1222i −0.826764 1.43200i
\(536\) −0.438447 0.759413i −0.0189380 0.0328016i
\(537\) −9.12311 + 15.8017i −0.393691 + 0.681893i
\(538\) 18.8769 0.813841
\(539\) −0.780776 + 1.35234i −0.0336304 + 0.0582496i
\(540\) −1.28078 + 2.21837i −0.0551158 + 0.0954634i
\(541\) −26.1771 −1.12544 −0.562720 0.826647i \(-0.690245\pi\)
−0.562720 + 0.826647i \(0.690245\pi\)
\(542\) −13.3693 + 23.1563i −0.574261 + 0.994650i
\(543\) −1.62311 2.81130i −0.0696541 0.120644i
\(544\) 4.06155 + 7.03482i 0.174138 + 0.301615i
\(545\) −10.8769 −0.465915
\(546\) 2.84233 2.21837i 0.121640 0.0949375i
\(547\) 7.61553 0.325616 0.162808 0.986658i \(-0.447945\pi\)
0.162808 + 0.986658i \(0.447945\pi\)
\(548\) −8.28078 14.3427i −0.353737 0.612691i
\(549\) −2.62311 4.54335i −0.111951 0.193906i
\(550\) −1.21922 + 2.11176i −0.0519879 + 0.0900456i
\(551\) 3.31534 0.141238
\(552\) 3.56155 6.16879i 0.151590 0.262561i
\(553\) 1.21922 2.11176i 0.0518467 0.0898011i
\(554\) −15.4384 −0.655917
\(555\) 8.40388 14.5560i 0.356725 0.617866i
\(556\) 4.78078 + 8.28055i 0.202750 + 0.351173i
\(557\) −1.93845 3.35749i −0.0821346 0.142261i 0.822032 0.569441i \(-0.192840\pi\)
−0.904167 + 0.427180i \(0.859507\pi\)
\(558\) 0 0
\(559\) −26.7386 10.8188i −1.13092 0.457585i
\(560\) −2.56155 −0.108245
\(561\) −6.34233 10.9852i −0.267773 0.463797i
\(562\) 7.96543 + 13.7965i 0.336002 + 0.581972i
\(563\) 11.1231 19.2658i 0.468783 0.811956i −0.530580 0.847635i \(-0.678026\pi\)
0.999363 + 0.0356787i \(0.0113593\pi\)
\(564\) 12.6847 0.534120
\(565\) −3.28078 + 5.68247i −0.138023 + 0.239063i
\(566\) 10.0000 17.3205i 0.420331 0.728035i
\(567\) 1.00000 0.0419961
\(568\) −6.68466 + 11.5782i −0.280482 + 0.485809i
\(569\) 11.0000 + 19.0526i 0.461144 + 0.798725i 0.999018 0.0443003i \(-0.0141058\pi\)
−0.537874 + 0.843025i \(0.680772\pi\)
\(570\) −2.00000 3.46410i −0.0837708 0.145095i
\(571\) −12.8769 −0.538881 −0.269441 0.963017i \(-0.586839\pi\)
−0.269441 + 0.963017i \(0.586839\pi\)
\(572\) −0.780776 5.57586i −0.0326459 0.233138i
\(573\) −3.12311 −0.130470
\(574\) −2.62311 4.54335i −0.109486 0.189636i
\(575\) −5.56155 9.63289i −0.231933 0.401719i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −31.4384 −1.30880 −0.654400 0.756149i \(-0.727079\pi\)
−0.654400 + 0.756149i \(0.727079\pi\)
\(578\) −24.4924 + 42.4221i −1.01875 + 1.76453i
\(579\) −4.06155 + 7.03482i −0.168792 + 0.292357i
\(580\) −5.43845 −0.225819
\(581\) −1.56155 + 2.70469i −0.0647841 + 0.112209i
\(582\) −4.56155 7.90084i −0.189082 0.327500i
\(583\) −5.46543 9.46641i −0.226355 0.392059i
\(584\) −6.56155 −0.271519
\(585\) −8.56155 3.46410i −0.353977 0.143223i
\(586\) 21.9309 0.905956
\(587\) 7.12311 + 12.3376i 0.294002 + 0.509226i 0.974752 0.223289i \(-0.0716794\pi\)
−0.680750 + 0.732516i \(0.738346\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) 0 0
\(590\) 8.00000 0.329355
\(591\) 4.21922 7.30791i 0.173556 0.300607i
\(592\) 3.28078 5.68247i 0.134839 0.233548i
\(593\) 31.9848 1.31346 0.656730 0.754126i \(-0.271939\pi\)
0.656730 + 0.754126i \(0.271939\pi\)
\(594\) 0.780776 1.35234i 0.0320356 0.0554874i
\(595\) −10.4039 18.0201i −0.426518 0.738750i
\(596\) 5.71922 + 9.90599i 0.234269 + 0.405765i
\(597\) 16.0000 0.654836
\(598\) 23.8078 + 9.63289i 0.973572 + 0.393918i
\(599\) −33.8617 −1.38355 −0.691777 0.722112i \(-0.743172\pi\)
−0.691777 + 0.722112i \(0.743172\pi\)
\(600\) 0.780776 + 1.35234i 0.0318751 + 0.0552092i
\(601\) 12.6501 + 21.9106i 0.516008 + 0.893752i 0.999827 + 0.0185842i \(0.00591589\pi\)
−0.483819 + 0.875168i \(0.660751\pi\)
\(602\) 4.00000 6.92820i 0.163028 0.282372i
\(603\) 0.876894 0.0357099
\(604\) −3.46543 + 6.00231i −0.141007 + 0.244230i
\(605\) −10.9654 + 18.9927i −0.445808 + 0.772163i
\(606\) −14.8078 −0.601524
\(607\) −8.49242 + 14.7093i −0.344697 + 0.597032i −0.985299 0.170841i \(-0.945352\pi\)
0.640602 + 0.767873i \(0.278685\pi\)
\(608\) −0.780776 1.35234i −0.0316647 0.0548448i
\(609\) 1.06155 + 1.83866i 0.0430163 + 0.0745064i
\(610\) −13.4384 −0.544107
\(611\) 6.34233 + 45.2933i 0.256583 + 1.83237i
\(612\) −8.12311 −0.328357
\(613\) −8.71922 15.1021i −0.352166 0.609970i 0.634463 0.772954i \(-0.281221\pi\)
−0.986629 + 0.162984i \(0.947888\pi\)
\(614\) −9.46543 16.3946i −0.381994 0.661633i
\(615\) −6.71922 + 11.6380i −0.270945 + 0.469291i
\(616\) 1.56155 0.0629168
\(617\) 11.0885 19.2059i 0.446408 0.773201i −0.551741 0.834015i \(-0.686036\pi\)
0.998149 + 0.0608143i \(0.0193697\pi\)
\(618\) −5.12311 + 8.87348i −0.206082 + 0.356944i
\(619\) 30.9309 1.24322 0.621608 0.783328i \(-0.286480\pi\)
0.621608 + 0.783328i \(0.286480\pi\)
\(620\) 0 0
\(621\) 3.56155 + 6.16879i 0.142920 + 0.247545i
\(622\) 3.46543 + 6.00231i 0.138951 + 0.240671i
\(623\) 7.56155 0.302947
\(624\) −3.34233 1.35234i −0.133800 0.0541371i
\(625\) −30.3693 −1.21477
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 1.21922 + 2.11176i 0.0486911 + 0.0843355i
\(628\) 6.84233 11.8513i 0.273039 0.472917i
\(629\) 53.3002 2.12522
\(630\) 1.28078 2.21837i 0.0510274 0.0883820i
\(631\) 19.4654 33.7151i 0.774907 1.34218i −0.159940 0.987127i \(-0.551130\pi\)
0.934847 0.355051i \(-0.115537\pi\)
\(632\) −2.43845 −0.0969962
\(633\) −1.56155 + 2.70469i −0.0620662 + 0.107502i
\(634\) −8.28078 14.3427i −0.328872 0.569622i
\(635\) −26.2462 45.4598i −1.04155 1.80402i
\(636\) −7.00000 −0.277568
\(637\) −2.84233 + 2.21837i −0.112617 + 0.0878950i
\(638\) 3.31534 0.131256
\(639\) −6.68466 11.5782i −0.264441 0.458025i
\(640\) 1.28078 + 2.21837i 0.0506271 + 0.0876888i
\(641\) −6.28078 + 10.8786i −0.248076 + 0.429680i −0.962992 0.269530i \(-0.913132\pi\)
0.714916 + 0.699210i \(0.246465\pi\)
\(642\) 14.9309 0.589274
\(643\) −17.6577 + 30.5840i −0.696351 + 1.20611i 0.273373 + 0.961908i \(0.411861\pi\)
−0.969723 + 0.244206i \(0.921473\pi\)
\(644\) −3.56155 + 6.16879i −0.140345 + 0.243084i
\(645\) −20.4924 −0.806888
\(646\) 6.34233 10.9852i 0.249536 0.432208i
\(647\) 23.0270 + 39.8839i 0.905284 + 1.56800i 0.820535 + 0.571596i \(0.193676\pi\)
0.0847492 + 0.996402i \(0.472991\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −4.87689 −0.191435
\(650\) −4.43845 + 3.46410i −0.174090 + 0.135873i
\(651\) 0 0
\(652\) 4.24621 + 7.35465i 0.166294 + 0.288030i
\(653\) −8.21922 14.2361i −0.321643 0.557102i 0.659184 0.751982i \(-0.270902\pi\)
−0.980827 + 0.194879i \(0.937568\pi\)
\(654\) 2.12311 3.67733i 0.0830200 0.143795i
\(655\) 5.75379 0.224819
\(656\) −2.62311 + 4.54335i −0.102415 + 0.177388i
\(657\) 3.28078 5.68247i 0.127995 0.221694i
\(658\) −12.6847 −0.494499
\(659\) −15.4654 + 26.7869i −0.602448 + 1.04347i 0.390001 + 0.920814i \(0.372475\pi\)
−0.992449 + 0.122656i \(0.960859\pi\)
\(660\) −2.00000 3.46410i −0.0778499 0.134840i
\(661\) −8.52699 14.7692i −0.331661 0.574454i 0.651176 0.758926i \(-0.274276\pi\)
−0.982838 + 0.184472i \(0.940942\pi\)
\(662\) −5.36932 −0.208684
\(663\) −4.06155 29.0053i −0.157738 1.12647i
\(664\) 3.12311 0.121200
\(665\) 2.00000 + 3.46410i 0.0775567 + 0.134332i
\(666\) 3.28078 + 5.68247i 0.127128 + 0.220191i
\(667\) −7.56155 + 13.0970i −0.292784 + 0.507118i
\(668\) −20.4924 −0.792876
\(669\) 13.1231 22.7299i 0.507369 0.878788i
\(670\) 1.12311 1.94528i 0.0433894 0.0751526i
\(671\) 8.19224 0.316258
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 9.62311 + 16.6677i 0.370943 + 0.642493i 0.989711 0.143081i \(-0.0457010\pi\)
−0.618767 + 0.785574i \(0.712368\pi\)
\(674\) −9.74621 16.8809i −0.375410 0.650229i
\(675\) −1.56155 −0.0601042
\(676\) 3.15767 12.6107i 0.121449 0.485026i
\(677\) 24.7386 0.950783 0.475391 0.879774i \(-0.342306\pi\)
0.475391 + 0.879774i \(0.342306\pi\)
\(678\) −1.28078 2.21837i −0.0491879 0.0851960i
\(679\) 4.56155 + 7.90084i 0.175056 + 0.303206i
\(680\) −10.4039 + 18.0201i −0.398971 + 0.691037i
\(681\) 19.1231 0.732799
\(682\) 0 0
\(683\) −3.75379 + 6.50175i −0.143635 + 0.248783i −0.928863 0.370424i \(-0.879212\pi\)
0.785228 + 0.619207i \(0.212546\pi\)
\(684\) 1.56155 0.0597075
\(685\) 21.2116 36.7396i 0.810455 1.40375i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −10.0270 17.3673i −0.382553 0.662602i
\(688\) −8.00000 −0.304997
\(689\) −3.50000 24.9950i −0.133339 0.952234i
\(690\) 18.2462 0.694621
\(691\) −16.4924 28.5657i −0.627401 1.08669i −0.988071 0.153997i \(-0.950785\pi\)
0.360670 0.932694i \(-0.382548\pi\)
\(692\) 9.00000 + 15.5885i 0.342129 + 0.592584i
\(693\) −0.780776 + 1.35234i −0.0296592 + 0.0513713i
\(694\) −22.0540 −0.837157
\(695\) −12.2462 + 21.2111i −0.464525 + 0.804581i
\(696\) 1.06155 1.83866i 0.0402381 0.0696944i
\(697\) −42.6155 −1.61418
\(698\) 9.00000 15.5885i 0.340655 0.590032i
\(699\) −11.6847 20.2384i −0.441954 0.765487i
\(700\) −0.780776 1.35234i −0.0295106 0.0511138i
\(701\) 14.3002 0.540111 0.270055 0.962845i \(-0.412958\pi\)
0.270055 + 0.962845i \(0.412958\pi\)
\(702\) 2.84233 2.21837i 0.107277 0.0837270i
\(703\) −10.2462 −0.386443
\(704\) −0.780776 1.35234i −0.0294266 0.0509684i
\(705\) 16.2462 + 28.1393i 0.611868 + 1.05979i
\(706\) 6.59612 11.4248i 0.248248 0.429978i
\(707\) 14.8078 0.556903
\(708\) −1.56155 + 2.70469i −0.0586867 + 0.101648i
\(709\) −7.65009 + 13.2504i −0.287305 + 0.497627i −0.973166 0.230106i \(-0.926093\pi\)
0.685860 + 0.727733i \(0.259426\pi\)
\(710\) −34.2462 −1.28524
\(711\) 1.21922 2.11176i 0.0457245 0.0791971i
\(712\) −3.78078 6.54850i −0.141691 0.245415i
\(713\) 0 0
\(714\) 8.12311 0.304000
\(715\) 11.3693 8.87348i 0.425188 0.331849i
\(716\) −18.2462 −0.681893
\(717\) −2.68466 4.64996i −0.100260 0.173656i
\(718\) 9.12311 + 15.8017i 0.340471 + 0.589714i
\(719\) 9.90388 17.1540i 0.369352 0.639737i −0.620112 0.784513i \(-0.712913\pi\)
0.989464 + 0.144776i \(0.0462462\pi\)
\(720\) −2.56155 −0.0954634
\(721\) 5.12311 8.87348i 0.190794 0.330466i
\(722\) 8.28078 14.3427i 0.308179 0.533781i
\(723\) 20.8078 0.773849
\(724\) 1.62311 2.81130i 0.0603222 0.104481i
\(725\) −1.65767 2.87117i −0.0615643 0.106633i
\(726\) −4.28078 7.41452i −0.158875 0.275179i
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 3.34233 + 1.35234i 0.123875 + 0.0501212i
\(729\) 1.00000 0.0370370
\(730\) −8.40388 14.5560i −0.311042 0.538740i
\(731\) −32.4924 56.2785i −1.20178 2.08154i
\(732\) 2.62311 4.54335i 0.0969528 0.167927i
\(733\) 28.8617 1.06603 0.533016 0.846105i \(-0.321058\pi\)
0.533016 + 0.846105i \(0.321058\pi\)
\(734\) 13.8078 23.9157i 0.509654 0.882746i
\(735\) −1.28078 + 2.21837i −0.0472421 + 0.0818258i
\(736\) 7.12311 0.262561
\(737\) −0.684658 + 1.18586i −0.0252197 + 0.0436818i
\(738\) −2.62311 4.54335i −0.0965579 0.167243i
\(739\) 4.68466 + 8.11407i 0.172328 + 0.298481i 0.939233 0.343279i \(-0.111538\pi\)
−0.766905 + 0.641760i \(0.778204\pi\)
\(740\) 16.8078 0.617866
\(741\) 0.780776 + 5.57586i 0.0286825 + 0.204834i
\(742\) 7.00000 0.256978
\(743\) −14.2462 24.6752i −0.522643 0.905244i −0.999653 0.0263461i \(-0.991613\pi\)
0.477010 0.878898i \(-0.341721\pi\)
\(744\) 0 0
\(745\) −14.6501 + 25.3747i −0.536738 + 0.929657i
\(746\) −31.9309 −1.16907
\(747\) −1.56155 + 2.70469i −0.0571342 + 0.0989594i
\(748\) 6.34233 10.9852i 0.231899 0.401660i
\(749\) −14.9309 −0.545562
\(750\) 4.40388 7.62775i 0.160807 0.278526i
\(751\) 10.0961 + 17.4870i 0.368413 + 0.638109i 0.989318 0.145777i \(-0.0465681\pi\)
−0.620905 + 0.783886i \(0.713235\pi\)
\(752\) 6.34233 + 10.9852i 0.231281 + 0.400590i
\(753\) −27.6155 −1.00637
\(754\) 7.09612 + 2.87117i 0.258425 + 0.104562i
\(755\) −17.7538 −0.646127
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) −1.63068 2.82443i −0.0592682 0.102656i 0.834869 0.550449i \(-0.185543\pi\)
−0.894137 + 0.447793i \(0.852210\pi\)
\(758\) 1.80776 3.13114i 0.0656609 0.113728i
\(759\) −11.1231 −0.403743
\(760\) 2.00000 3.46410i 0.0725476 0.125656i
\(761\) 7.49242 12.9773i 0.271600 0.470425i −0.697672 0.716418i \(-0.745781\pi\)
0.969272 + 0.245993i \(0.0791139\pi\)
\(762\) 20.4924 0.742362
\(763\) −2.12311 + 3.67733i −0.0768616 + 0.133128i
\(764\) −1.56155 2.70469i −0.0564950 0.0978522i
\(765\) −10.4039 18.0201i −0.376153 0.651516i
\(766\) 7.80776 0.282106
\(767\) −10.4384 4.22351i −0.376910 0.152502i
\(768\) −1.00000 −0.0360844
\(769\) −6.56155 11.3649i −0.236616 0.409830i 0.723125 0.690717i \(-0.242705\pi\)
−0.959741 + 0.280887i \(0.909372\pi\)
\(770\) 2.00000 + 3.46410i 0.0720750 + 0.124838i
\(771\) 0.184658 0.319838i 0.00665031 0.0115187i
\(772\) −8.12311 −0.292357
\(773\) 14.3693 24.8884i 0.516828 0.895173i −0.482981 0.875631i \(-0.660446\pi\)
0.999809 0.0195420i \(-0.00622081\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) 0 0
\(776\) 4.56155 7.90084i 0.163750 0.283624i
\(777\) −3.28078 5.68247i −0.117697 0.203858i
\(778\) 8.84233 + 15.3154i 0.317013 + 0.549082i
\(779\) 8.19224 0.293517