Properties

Label 570.2.i.j.391.3
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.29654208.1
Defining polynomial: \(x^{6} + 14 x^{4} + 49 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.3
Root \(0.514306i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.j.121.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +3.84469 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +3.84469 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +5.73549 q^{11} +1.00000 q^{12} +(-2.36774 - 4.10105i) q^{13} +(-1.92234 + 3.32960i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.31315 - 5.73854i) q^{17} +1.00000 q^{18} +(-4.29009 - 0.771459i) q^{19} +1.00000 q^{20} +(-1.92234 + 3.32960i) q^{21} +(-2.86774 + 4.96708i) q^{22} +(2.86774 + 4.96708i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.73549 q^{26} +1.00000 q^{27} +(-1.92234 - 3.32960i) q^{28} +(5.15783 + 8.93363i) q^{29} +1.00000 q^{30} +4.73549 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.86774 + 4.96708i) q^{33} +(3.31315 + 5.73854i) q^{34} +(-1.92234 + 3.32960i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(2.81315 - 3.32960i) q^{38} +4.73549 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.39928 + 7.61978i) q^{41} +(-1.92234 - 3.32960i) q^{42} +(-0.523059 + 0.905965i) q^{43} +(-2.86774 - 4.96708i) q^{44} +1.00000 q^{45} -5.73549 q^{46} +(-0.890804 - 1.54292i) q^{47} +(-0.500000 - 0.866025i) q^{48} +7.78161 q^{49} +1.00000 q^{50} +(3.31315 + 5.73854i) q^{51} +(-2.36774 + 4.10105i) q^{52} +(-2.55460 - 4.42469i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.86774 + 4.96708i) q^{55} +3.84469 q^{56} +(2.81315 - 3.32960i) q^{57} -10.3157 q^{58} +(-3.00000 + 5.19615i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(0.0545981 + 0.0945666i) q^{61} +(-2.36774 + 4.10105i) q^{62} +(-1.92234 - 3.32960i) q^{63} +1.00000 q^{64} +4.73549 q^{65} +(-2.86774 - 4.96708i) q^{66} +(-2.94540 - 5.10159i) q^{67} -6.62629 q^{68} -5.73549 q^{69} +(-1.92234 - 3.32960i) q^{70} +(3.31315 - 5.73854i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(3.05460 - 5.29072i) q^{73} +(0.500000 - 0.866025i) q^{74} +1.00000 q^{75} +(1.47694 + 4.10105i) q^{76} +22.0512 q^{77} +(-2.36774 + 4.10105i) q^{78} +(3.36774 - 5.83311i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.39928 - 7.61978i) q^{82} -16.9420 q^{83} +3.84469 q^{84} +(3.31315 + 5.73854i) q^{85} +(-0.523059 - 0.905965i) q^{86} -10.3157 q^{87} +5.73549 q^{88} +(2.55460 + 4.42469i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-9.10323 - 15.7673i) q^{91} +(2.86774 - 4.96708i) q^{92} +(-2.36774 + 4.10105i) q^{93} +1.78161 q^{94} +(2.81315 - 3.32960i) q^{95} +1.00000 q^{96} +(-4.57766 + 7.92873i) q^{97} +(-3.89080 + 6.73907i) q^{98} +(-2.86774 - 4.96708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + 6q^{8} - 3q^{9} - 3q^{10} + 8q^{11} + 6q^{12} - q^{13} - q^{14} - 3q^{15} - 3q^{16} + 4q^{17} + 6q^{18} - 2q^{19} + 6q^{20} - q^{21} - 4q^{22} + 4q^{23} - 3q^{24} - 3q^{25} + 2q^{26} + 6q^{27} - q^{28} - 6q^{29} + 6q^{30} + 2q^{31} - 3q^{32} - 4q^{33} + 4q^{34} - q^{35} - 3q^{36} - 6q^{37} + q^{38} + 2q^{39} - 3q^{40} - 8q^{41} - q^{42} - 11q^{43} - 4q^{44} + 6q^{45} - 8q^{46} - 3q^{48} + 36q^{49} + 6q^{50} + 4q^{51} - q^{52} - 18q^{53} - 3q^{54} - 4q^{55} + 2q^{56} + q^{57} + 12q^{58} - 18q^{59} - 3q^{60} + 3q^{61} - q^{62} - q^{63} + 6q^{64} + 2q^{65} - 4q^{66} - 15q^{67} - 8q^{68} - 8q^{69} - q^{70} + 4q^{71} - 3q^{72} + 21q^{73} + 3q^{74} + 6q^{75} + q^{76} + 32q^{77} - q^{78} + 7q^{79} - 3q^{80} - 3q^{81} - 8q^{82} + 4q^{83} + 2q^{84} + 4q^{85} - 11q^{86} + 12q^{87} + 8q^{88} + 18q^{89} - 3q^{90} - 15q^{91} + 4q^{92} - q^{93} + q^{95} + 6q^{96} - 38q^{97} - 18q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 3.84469 1.45315 0.726577 0.687085i \(-0.241110\pi\)
0.726577 + 0.687085i \(0.241110\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 5.73549 1.72932 0.864658 0.502362i \(-0.167535\pi\)
0.864658 + 0.502362i \(0.167535\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.36774 4.10105i −0.656694 1.13743i −0.981466 0.191635i \(-0.938621\pi\)
0.324772 0.945792i \(-0.394712\pi\)
\(14\) −1.92234 + 3.32960i −0.513768 + 0.889872i
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.31315 5.73854i 0.803556 1.39180i −0.113705 0.993515i \(-0.536272\pi\)
0.917262 0.398285i \(-0.130395\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.29009 0.771459i −0.984214 0.176985i
\(20\) 1.00000 0.223607
\(21\) −1.92234 + 3.32960i −0.419490 + 0.726577i
\(22\) −2.86774 + 4.96708i −0.611405 + 1.05898i
\(23\) 2.86774 + 4.96708i 0.597966 + 1.03571i 0.993121 + 0.117093i \(0.0373576\pi\)
−0.395155 + 0.918615i \(0.629309\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 4.73549 0.928706
\(27\) 1.00000 0.192450
\(28\) −1.92234 3.32960i −0.363289 0.629234i
\(29\) 5.15783 + 8.93363i 0.957785 + 1.65893i 0.727861 + 0.685724i \(0.240514\pi\)
0.229924 + 0.973209i \(0.426152\pi\)
\(30\) 1.00000 0.182574
\(31\) 4.73549 0.850519 0.425260 0.905071i \(-0.360183\pi\)
0.425260 + 0.905071i \(0.360183\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.86774 + 4.96708i −0.499210 + 0.864658i
\(34\) 3.31315 + 5.73854i 0.568200 + 0.984151i
\(35\) −1.92234 + 3.32960i −0.324935 + 0.562804i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 2.81315 3.32960i 0.456353 0.540132i
\(39\) 4.73549 0.758285
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −4.39928 + 7.61978i −0.687053 + 1.19001i 0.285734 + 0.958309i \(0.407763\pi\)
−0.972787 + 0.231701i \(0.925571\pi\)
\(42\) −1.92234 3.32960i −0.296624 0.513768i
\(43\) −0.523059 + 0.905965i −0.0797658 + 0.138158i −0.903149 0.429328i \(-0.858751\pi\)
0.823383 + 0.567486i \(0.192084\pi\)
\(44\) −2.86774 4.96708i −0.432329 0.748815i
\(45\) 1.00000 0.149071
\(46\) −5.73549 −0.845652
\(47\) −0.890804 1.54292i −0.129937 0.225058i 0.793715 0.608290i \(-0.208144\pi\)
−0.923652 + 0.383232i \(0.874811\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 7.78161 1.11166
\(50\) 1.00000 0.141421
\(51\) 3.31315 + 5.73854i 0.463933 + 0.803556i
\(52\) −2.36774 + 4.10105i −0.328347 + 0.568714i
\(53\) −2.55460 4.42469i −0.350901 0.607778i 0.635507 0.772095i \(-0.280791\pi\)
−0.986408 + 0.164317i \(0.947458\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −2.86774 + 4.96708i −0.386687 + 0.669761i
\(56\) 3.84469 0.513768
\(57\) 2.81315 3.32960i 0.372610 0.441016i
\(58\) −10.3157 −1.35451
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 0.0545981 + 0.0945666i 0.00699057 + 0.0121080i 0.869500 0.493934i \(-0.164441\pi\)
−0.862509 + 0.506042i \(0.831108\pi\)
\(62\) −2.36774 + 4.10105i −0.300704 + 0.520834i
\(63\) −1.92234 3.32960i −0.242192 0.419490i
\(64\) 1.00000 0.125000
\(65\) 4.73549 0.587365
\(66\) −2.86774 4.96708i −0.352995 0.611405i
\(67\) −2.94540 5.10159i −0.359838 0.623258i 0.628095 0.778136i \(-0.283835\pi\)
−0.987934 + 0.154878i \(0.950501\pi\)
\(68\) −6.62629 −0.803556
\(69\) −5.73549 −0.690472
\(70\) −1.92234 3.32960i −0.229764 0.397963i
\(71\) 3.31315 5.73854i 0.393198 0.681039i −0.599671 0.800246i \(-0.704702\pi\)
0.992869 + 0.119207i \(0.0380353\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 3.05460 5.29072i 0.357514 0.619232i −0.630031 0.776570i \(-0.716958\pi\)
0.987545 + 0.157338i \(0.0502912\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 1.00000 0.115470
\(76\) 1.47694 + 4.10105i 0.169417 + 0.470423i
\(77\) 22.0512 2.51296
\(78\) −2.36774 + 4.10105i −0.268094 + 0.464353i
\(79\) 3.36774 5.83311i 0.378901 0.656276i −0.612002 0.790856i \(-0.709635\pi\)
0.990903 + 0.134581i \(0.0429688\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.39928 7.61978i −0.485820 0.841464i
\(83\) −16.9420 −1.85962 −0.929811 0.368038i \(-0.880030\pi\)
−0.929811 + 0.368038i \(0.880030\pi\)
\(84\) 3.84469 0.419490
\(85\) 3.31315 + 5.73854i 0.359361 + 0.622432i
\(86\) −0.523059 0.905965i −0.0564029 0.0976927i
\(87\) −10.3157 −1.10596
\(88\) 5.73549 0.611405
\(89\) 2.55460 + 4.42469i 0.270787 + 0.469017i 0.969064 0.246811i \(-0.0793828\pi\)
−0.698277 + 0.715828i \(0.746049\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) −9.10323 15.7673i −0.954278 1.65286i
\(92\) 2.86774 4.96708i 0.298983 0.517854i
\(93\) −2.36774 + 4.10105i −0.245524 + 0.425260i
\(94\) 1.78161 0.183759
\(95\) 2.81315 3.32960i 0.288623 0.341609i
\(96\) 1.00000 0.102062
\(97\) −4.57766 + 7.92873i −0.464791 + 0.805041i −0.999192 0.0401898i \(-0.987204\pi\)
0.534401 + 0.845231i \(0.320537\pi\)
\(98\) −3.89080 + 6.73907i −0.393031 + 0.680749i
\(99\) −2.86774 4.96708i −0.288219 0.499210i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 1.84469 + 3.19509i 0.183553 + 0.317923i 0.943088 0.332543i \(-0.107907\pi\)
−0.759535 + 0.650467i \(0.774573\pi\)
\(102\) −6.62629 −0.656101
\(103\) 2.06308 0.203281 0.101641 0.994821i \(-0.467591\pi\)
0.101641 + 0.994821i \(0.467591\pi\)
\(104\) −2.36774 4.10105i −0.232176 0.402141i
\(105\) −1.92234 3.32960i −0.187601 0.324935i
\(106\) 5.10920 0.496249
\(107\) 14.5341 1.40506 0.702530 0.711654i \(-0.252054\pi\)
0.702530 + 0.711654i \(0.252054\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −4.31315 + 7.47059i −0.413125 + 0.715553i −0.995230 0.0975609i \(-0.968896\pi\)
0.582105 + 0.813114i \(0.302229\pi\)
\(110\) −2.86774 4.96708i −0.273429 0.473592i
\(111\) 0.500000 0.866025i 0.0474579 0.0821995i
\(112\) −1.92234 + 3.32960i −0.181644 + 0.314617i
\(113\) −8.53406 −0.802817 −0.401408 0.915899i \(-0.631479\pi\)
−0.401408 + 0.915899i \(0.631479\pi\)
\(114\) 1.47694 + 4.10105i 0.138328 + 0.384099i
\(115\) −5.73549 −0.534837
\(116\) 5.15783 8.93363i 0.478893 0.829467i
\(117\) −2.36774 + 4.10105i −0.218898 + 0.379143i
\(118\) −3.00000 5.19615i −0.276172 0.478345i
\(119\) 12.7380 22.0629i 1.16769 2.02250i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) 21.8958 1.99053
\(122\) −0.109196 −0.00988615
\(123\) −4.39928 7.61978i −0.396670 0.687053i
\(124\) −2.36774 4.10105i −0.212630 0.368286i
\(125\) 1.00000 0.0894427
\(126\) 3.84469 0.342512
\(127\) −2.33621 4.04643i −0.207305 0.359062i 0.743560 0.668669i \(-0.233136\pi\)
−0.950865 + 0.309607i \(0.899802\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −0.523059 0.905965i −0.0460528 0.0797658i
\(130\) −2.36774 + 4.10105i −0.207665 + 0.359686i
\(131\) 6.82163 11.8154i 0.596008 1.03232i −0.397395 0.917647i \(-0.630086\pi\)
0.993404 0.114669i \(-0.0365808\pi\)
\(132\) 5.73549 0.499210
\(133\) −16.4940 2.96602i −1.43021 0.257186i
\(134\) 5.89080 0.508888
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 3.31315 5.73854i 0.284100 0.492076i
\(137\) 6.95388 + 12.0445i 0.594110 + 1.02903i 0.993672 + 0.112323i \(0.0358290\pi\)
−0.399562 + 0.916706i \(0.630838\pi\)
\(138\) 2.86774 4.96708i 0.244119 0.422826i
\(139\) 0.367745 + 0.636953i 0.0311917 + 0.0540256i 0.881200 0.472744i \(-0.156736\pi\)
−0.850008 + 0.526770i \(0.823403\pi\)
\(140\) 3.84469 0.324935
\(141\) 1.78161 0.150038
\(142\) 3.31315 + 5.73854i 0.278033 + 0.481567i
\(143\) −13.5802 23.5216i −1.13563 1.96697i
\(144\) 1.00000 0.0833333
\(145\) −10.3157 −0.856669
\(146\) 3.05460 + 5.29072i 0.252800 + 0.437863i
\(147\) −3.89080 + 6.73907i −0.320908 + 0.555829i
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 5.42234 9.39177i 0.444216 0.769404i −0.553782 0.832662i \(-0.686816\pi\)
0.997997 + 0.0632579i \(0.0201491\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −0.936922 −0.0762456 −0.0381228 0.999273i \(-0.512138\pi\)
−0.0381228 + 0.999273i \(0.512138\pi\)
\(152\) −4.29009 0.771459i −0.347972 0.0625736i
\(153\) −6.62629 −0.535704
\(154\) −11.0256 + 19.0969i −0.888466 + 1.53887i
\(155\) −2.36774 + 4.10105i −0.190182 + 0.329405i
\(156\) −2.36774 4.10105i −0.189571 0.328347i
\(157\) −4.34469 + 7.52522i −0.346744 + 0.600578i −0.985669 0.168691i \(-0.946046\pi\)
0.638925 + 0.769269i \(0.279379\pi\)
\(158\) 3.36774 + 5.83311i 0.267923 + 0.464057i
\(159\) 5.10920 0.405186
\(160\) 1.00000 0.0790569
\(161\) 11.0256 + 19.0969i 0.868937 + 1.50504i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −0.206468 −0.0161719 −0.00808593 0.999967i \(-0.502574\pi\)
−0.00808593 + 0.999967i \(0.502574\pi\)
\(164\) 8.79857 0.687053
\(165\) −2.86774 4.96708i −0.223254 0.386687i
\(166\) 8.47098 14.6722i 0.657475 1.13878i
\(167\) −8.86774 15.3594i −0.686207 1.18854i −0.973056 0.230569i \(-0.925941\pi\)
0.286849 0.957976i \(-0.407392\pi\)
\(168\) −1.92234 + 3.32960i −0.148312 + 0.256884i
\(169\) −4.71243 + 8.16217i −0.362495 + 0.627859i
\(170\) −6.62629 −0.508214
\(171\) 1.47694 + 4.10105i 0.112944 + 0.313615i
\(172\) 1.04612 0.0797658
\(173\) −0.709912 + 1.22960i −0.0539736 + 0.0934851i −0.891750 0.452529i \(-0.850522\pi\)
0.837776 + 0.546014i \(0.183855\pi\)
\(174\) 5.15783 8.93363i 0.391014 0.677257i
\(175\) −1.92234 3.32960i −0.145315 0.251694i
\(176\) −2.86774 + 4.96708i −0.216164 + 0.374408i
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −5.10920 −0.382950
\(179\) −17.2065 −1.28607 −0.643036 0.765836i \(-0.722325\pi\)
−0.643036 + 0.765836i \(0.722325\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −8.26703 14.3189i −0.614483 1.06432i −0.990475 0.137693i \(-0.956031\pi\)
0.375992 0.926623i \(-0.377302\pi\)
\(182\) 18.2065 1.34955
\(183\) −0.109196 −0.00807201
\(184\) 2.86774 + 4.96708i 0.211413 + 0.366178i
\(185\) 0.500000 0.866025i 0.0367607 0.0636715i
\(186\) −2.36774 4.10105i −0.173611 0.300704i
\(187\) 19.0025 32.9133i 1.38960 2.40686i
\(188\) −0.890804 + 1.54292i −0.0649685 + 0.112529i
\(189\) 3.84469 0.279660
\(190\) 1.47694 + 4.10105i 0.107149 + 0.297522i
\(191\) −22.4129 −1.62174 −0.810872 0.585224i \(-0.801007\pi\)
−0.810872 + 0.585224i \(0.801007\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 11.5256 19.9629i 0.829629 1.43696i −0.0687002 0.997637i \(-0.521885\pi\)
0.898329 0.439323i \(-0.144781\pi\)
\(194\) −4.57766 7.92873i −0.328657 0.569250i
\(195\) −2.36774 + 4.10105i −0.169558 + 0.293683i
\(196\) −3.89080 6.73907i −0.277915 0.481362i
\(197\) 2.67241 0.190401 0.0952007 0.995458i \(-0.469651\pi\)
0.0952007 + 0.995458i \(0.469651\pi\)
\(198\) 5.73549 0.407603
\(199\) 5.79009 + 10.0287i 0.410448 + 0.710918i 0.994939 0.100483i \(-0.0320388\pi\)
−0.584490 + 0.811401i \(0.698706\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 5.89080 0.415505
\(202\) −3.68937 −0.259583
\(203\) 19.8302 + 34.3470i 1.39181 + 2.41069i
\(204\) 3.31315 5.73854i 0.231967 0.401778i
\(205\) −4.39928 7.61978i −0.307259 0.532189i
\(206\) −1.03154 + 1.78668i −0.0718707 + 0.124484i
\(207\) 2.86774 4.96708i 0.199322 0.345236i
\(208\) 4.73549 0.328347
\(209\) −24.6058 4.42469i −1.70202 0.306062i
\(210\) 3.84469 0.265309
\(211\) −11.6117 + 20.1121i −0.799383 + 1.38457i 0.120635 + 0.992697i \(0.461507\pi\)
−0.920018 + 0.391876i \(0.871826\pi\)
\(212\) −2.55460 + 4.42469i −0.175451 + 0.303889i
\(213\) 3.31315 + 5.73854i 0.227013 + 0.393198i
\(214\) −7.26703 + 12.5869i −0.496764 + 0.860420i
\(215\) −0.523059 0.905965i −0.0356723 0.0617863i
\(216\) 1.00000 0.0680414
\(217\) 18.2065 1.23594
\(218\) −4.31315 7.47059i −0.292123 0.505972i
\(219\) 3.05460 + 5.29072i 0.206411 + 0.357514i
\(220\) 5.73549 0.386687
\(221\) −31.3787 −2.11076
\(222\) 0.500000 + 0.866025i 0.0335578 + 0.0581238i
\(223\) 7.50252 12.9947i 0.502406 0.870192i −0.497590 0.867412i \(-0.665782\pi\)
0.999996 0.00278017i \(-0.000884956\pi\)
\(224\) −1.92234 3.32960i −0.128442 0.222468i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 4.26703 7.39071i 0.283839 0.491623i
\(227\) −20.5341 −1.36289 −0.681447 0.731868i \(-0.738649\pi\)
−0.681447 + 0.731868i \(0.738649\pi\)
\(228\) −4.29009 0.771459i −0.284118 0.0510911i
\(229\) −13.2645 −0.876544 −0.438272 0.898843i \(-0.644409\pi\)
−0.438272 + 0.898843i \(0.644409\pi\)
\(230\) 2.86774 4.96708i 0.189093 0.327520i
\(231\) −11.0256 + 19.0969i −0.725430 + 1.25648i
\(232\) 5.15783 + 8.93363i 0.338628 + 0.586521i
\(233\) −9.42486 + 16.3243i −0.617443 + 1.06944i 0.372507 + 0.928029i \(0.378498\pi\)
−0.989951 + 0.141414i \(0.954835\pi\)
\(234\) −2.36774 4.10105i −0.154784 0.268094i
\(235\) 1.78161 0.116219
\(236\) 6.00000 0.390567
\(237\) 3.36774 + 5.83311i 0.218759 + 0.378901i
\(238\) 12.7380 + 22.0629i 0.825682 + 1.43012i
\(239\) 13.9078 0.899618 0.449809 0.893125i \(-0.351492\pi\)
0.449809 + 0.893125i \(0.351492\pi\)
\(240\) 1.00000 0.0645497
\(241\) 15.1032 + 26.1596i 0.972885 + 1.68509i 0.686745 + 0.726898i \(0.259039\pi\)
0.286139 + 0.958188i \(0.407628\pi\)
\(242\) −10.9479 + 18.9624i −0.703759 + 1.21895i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0.0545981 0.0945666i 0.00349528 0.00605401i
\(245\) −3.89080 + 6.73907i −0.248574 + 0.430543i
\(246\) 8.79857 0.560976
\(247\) 6.99404 + 19.4205i 0.445020 + 1.23570i
\(248\) 4.73549 0.300704
\(249\) 8.47098 14.6722i 0.536826 0.929811i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 10.5171 + 18.2161i 0.663833 + 1.14979i 0.979600 + 0.200956i \(0.0644049\pi\)
−0.315767 + 0.948837i \(0.602262\pi\)
\(252\) −1.92234 + 3.32960i −0.121096 + 0.209745i
\(253\) 16.4479 + 28.4886i 1.03407 + 1.79107i
\(254\) 4.67241 0.293173
\(255\) −6.62629 −0.414955
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 1.04612 0.0651285
\(259\) −3.84469 −0.238897
\(260\) −2.36774 4.10105i −0.146841 0.254337i
\(261\) 5.15783 8.93363i 0.319262 0.552978i
\(262\) 6.82163 + 11.8154i 0.421441 + 0.729958i
\(263\) 3.39677 5.88337i 0.209454 0.362784i −0.742089 0.670301i \(-0.766165\pi\)
0.951543 + 0.307517i \(0.0994982\pi\)
\(264\) −2.86774 + 4.96708i −0.176497 + 0.305703i
\(265\) 5.10920 0.313855
\(266\) 10.8157 12.8012i 0.663151 0.784895i
\(267\) −5.10920 −0.312678
\(268\) −2.94540 + 5.10159i −0.179919 + 0.311629i
\(269\) −6.04864 + 10.4765i −0.368792 + 0.638766i −0.989377 0.145373i \(-0.953562\pi\)
0.620585 + 0.784139i \(0.286895\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 0.580175 1.00489i 0.0352431 0.0610429i −0.847866 0.530211i \(-0.822113\pi\)
0.883109 + 0.469168i \(0.155446\pi\)
\(272\) 3.31315 + 5.73854i 0.200889 + 0.347950i
\(273\) 18.2065 1.10191
\(274\) −13.9078 −0.840199
\(275\) −2.86774 4.96708i −0.172932 0.299526i
\(276\) 2.86774 + 4.96708i 0.172618 + 0.298983i
\(277\) 4.83965 0.290786 0.145393 0.989374i \(-0.453555\pi\)
0.145393 + 0.989374i \(0.453555\pi\)
\(278\) −0.735489 −0.0441117
\(279\) −2.36774 4.10105i −0.141753 0.245524i
\(280\) −1.92234 + 3.32960i −0.114882 + 0.198981i
\(281\) −4.66379 8.07793i −0.278219 0.481889i 0.692723 0.721203i \(-0.256411\pi\)
−0.970942 + 0.239314i \(0.923077\pi\)
\(282\) −0.890804 + 1.54292i −0.0530466 + 0.0918794i
\(283\) 4.67241 8.09285i 0.277746 0.481070i −0.693078 0.720862i \(-0.743746\pi\)
0.970824 + 0.239792i \(0.0770793\pi\)
\(284\) −6.62629 −0.393198
\(285\) 1.47694 + 4.10105i 0.0874864 + 0.242925i
\(286\) 27.1604 1.60603
\(287\) −16.9139 + 29.2957i −0.998394 + 1.72927i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −13.4539 23.3028i −0.791405 1.37075i
\(290\) 5.15783 8.93363i 0.302878 0.524601i
\(291\) −4.57766 7.92873i −0.268347 0.464791i
\(292\) −6.10920 −0.357514
\(293\) 3.20143 0.187030 0.0935148 0.995618i \(-0.470190\pi\)
0.0935148 + 0.995618i \(0.470190\pi\)
\(294\) −3.89080 6.73907i −0.226916 0.393031i
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) −1.00000 −0.0581238
\(297\) 5.73549 0.332807
\(298\) 5.42234 + 9.39177i 0.314108 + 0.544051i
\(299\) 13.5802 23.5216i 0.785362 1.36029i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) −2.01100 + 3.48315i −0.115912 + 0.200765i
\(302\) 0.468461 0.811398i 0.0269569 0.0466907i
\(303\) −3.68937 −0.211949
\(304\) 2.81315 3.32960i 0.161345 0.190965i
\(305\) −0.109196 −0.00625255
\(306\) 3.31315 5.73854i 0.189400 0.328050i
\(307\) 14.1117 24.4422i 0.805398 1.39499i −0.110624 0.993862i \(-0.535285\pi\)
0.916022 0.401128i \(-0.131382\pi\)
\(308\) −11.0256 19.0969i −0.628241 1.08814i
\(309\) −1.03154 + 1.78668i −0.0586822 + 0.101641i
\(310\) −2.36774 4.10105i −0.134479 0.232924i
\(311\) −12.8497 −0.728641 −0.364320 0.931274i \(-0.618699\pi\)
−0.364320 + 0.931274i \(0.618699\pi\)
\(312\) 4.73549 0.268094
\(313\) −14.5171 25.1443i −0.820555 1.42124i −0.905270 0.424837i \(-0.860331\pi\)
0.0847148 0.996405i \(-0.473002\pi\)
\(314\) −4.34469 7.52522i −0.245185 0.424673i
\(315\) 3.84469 0.216623
\(316\) −6.73549 −0.378901
\(317\) −2.22701 3.85729i −0.125081 0.216647i 0.796683 0.604397i \(-0.206586\pi\)
−0.921765 + 0.387750i \(0.873253\pi\)
\(318\) −2.55460 + 4.42469i −0.143255 + 0.248124i
\(319\) 29.5827 + 51.2387i 1.65631 + 2.86882i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −7.26703 + 12.5869i −0.405606 + 0.702530i
\(322\) −22.0512 −1.22886
\(323\) −18.6407 + 22.0629i −1.03720 + 1.22761i
\(324\) 1.00000 0.0555556
\(325\) −2.36774 + 4.10105i −0.131339 + 0.227486i
\(326\) 0.103234 0.178807i 0.00571762 0.00990320i
\(327\) −4.31315 7.47059i −0.238518 0.413125i
\(328\) −4.39928 + 7.61978i −0.242910 + 0.420732i
\(329\) −3.42486 5.93203i −0.188819 0.327044i
\(330\) 5.73549 0.315728
\(331\) −11.8447 −0.651043 −0.325521 0.945535i \(-0.605540\pi\)
−0.325521 + 0.945535i \(0.605540\pi\)
\(332\) 8.47098 + 14.6722i 0.464905 + 0.805240i
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) 17.7355 0.970443
\(335\) 5.89080 0.321849
\(336\) −1.92234 3.32960i −0.104872 0.181644i
\(337\) −3.58614 + 6.21137i −0.195349 + 0.338355i −0.947015 0.321189i \(-0.895917\pi\)
0.751666 + 0.659544i \(0.229251\pi\)
\(338\) −4.71243 8.16217i −0.256322 0.443963i
\(339\) 4.26703 7.39071i 0.231753 0.401408i
\(340\) 3.31315 5.73854i 0.179681 0.311216i
\(341\) 27.1604 1.47082
\(342\) −4.29009 0.771459i −0.231981 0.0417157i
\(343\) 3.00504 0.162257
\(344\) −0.523059 + 0.905965i −0.0282015 + 0.0488464i
\(345\) 2.86774 4.96708i 0.154394 0.267419i
\(346\) −0.709912 1.22960i −0.0381651 0.0661039i
\(347\) −11.2065 + 19.4102i −0.601595 + 1.04199i 0.390985 + 0.920397i \(0.372134\pi\)
−0.992580 + 0.121596i \(0.961199\pi\)
\(348\) 5.15783 + 8.93363i 0.276489 + 0.478893i
\(349\) −24.3037 −1.30095 −0.650475 0.759528i \(-0.725430\pi\)
−0.650475 + 0.759528i \(0.725430\pi\)
\(350\) 3.84469 0.205507
\(351\) −2.36774 4.10105i −0.126381 0.218898i
\(352\) −2.86774 4.96708i −0.152851 0.264746i
\(353\) 32.7286 1.74197 0.870984 0.491312i \(-0.163482\pi\)
0.870984 + 0.491312i \(0.163482\pi\)
\(354\) 6.00000 0.318896
\(355\) 3.31315 + 5.73854i 0.175844 + 0.304570i
\(356\) 2.55460 4.42469i 0.135393 0.234508i
\(357\) 12.7380 + 22.0629i 0.674167 + 1.16769i
\(358\) 8.60323 14.9012i 0.454695 0.787555i
\(359\) 0.577657 1.00053i 0.0304876 0.0528060i −0.850379 0.526171i \(-0.823627\pi\)
0.880867 + 0.473365i \(0.156961\pi\)
\(360\) 1.00000 0.0527046
\(361\) 17.8097 + 6.61925i 0.937353 + 0.348382i
\(362\) 16.5341 0.869011
\(363\) −10.9479 + 18.9624i −0.574617 + 0.995265i
\(364\) −9.10323 + 15.7673i −0.477139 + 0.826429i
\(365\) 3.05460 + 5.29072i 0.159885 + 0.276929i
\(366\) 0.0545981 0.0945666i 0.00285389 0.00494308i
\(367\) −13.8387 23.9694i −0.722375 1.25119i −0.960045 0.279845i \(-0.909717\pi\)
0.237670 0.971346i \(-0.423616\pi\)
\(368\) −5.73549 −0.298983
\(369\) 8.79857 0.458035
\(370\) 0.500000 + 0.866025i 0.0259938 + 0.0450225i
\(371\) −9.82163 17.0116i −0.509913 0.883196i
\(372\) 4.73549 0.245524
\(373\) −23.5171 −1.21767 −0.608835 0.793297i \(-0.708363\pi\)
−0.608835 + 0.793297i \(0.708363\pi\)
\(374\) 19.0025 + 32.9133i 0.982597 + 1.70191i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) −0.890804 1.54292i −0.0459397 0.0795699i
\(377\) 24.4249 42.3051i 1.25794 2.17882i
\(378\) −1.92234 + 3.32960i −0.0988746 + 0.171256i
\(379\) 8.29870 0.426276 0.213138 0.977022i \(-0.431632\pi\)
0.213138 + 0.977022i \(0.431632\pi\)
\(380\) −4.29009 0.771459i −0.220077 0.0395750i
\(381\) 4.67241 0.239375
\(382\) 11.2065 19.4102i 0.573373 0.993111i
\(383\) −6.89080 + 11.9352i −0.352104 + 0.609861i −0.986618 0.163050i \(-0.947867\pi\)
0.634514 + 0.772911i \(0.281200\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) −11.0256 + 19.0969i −0.561915 + 0.973266i
\(386\) 11.5256 + 19.9629i 0.586636 + 1.01608i
\(387\) 1.04612 0.0531772
\(388\) 9.15531 0.464791
\(389\) 0.842168 + 1.45868i 0.0426996 + 0.0739579i 0.886585 0.462565i \(-0.153071\pi\)
−0.843886 + 0.536523i \(0.819737\pi\)
\(390\) −2.36774 4.10105i −0.119895 0.207665i
\(391\) 38.0050 1.92200
\(392\) 7.78161 0.393031
\(393\) 6.82163 + 11.8154i 0.344106 + 0.596008i
\(394\) −1.33621 + 2.31438i −0.0673171 + 0.116597i
\(395\) 3.36774 + 5.83311i 0.169450 + 0.293495i
\(396\) −2.86774 + 4.96708i −0.144110 + 0.249605i
\(397\) −7.28161 + 12.6121i −0.365453 + 0.632984i −0.988849 0.148923i \(-0.952419\pi\)
0.623395 + 0.781907i \(0.285753\pi\)
\(398\) −11.5802 −0.580462
\(399\) 10.8157 12.8012i 0.541460 0.640864i
\(400\) 1.00000 0.0500000
\(401\) −10.7816 + 18.6743i −0.538408 + 0.932550i 0.460582 + 0.887617i \(0.347641\pi\)
−0.998990 + 0.0449326i \(0.985693\pi\)
\(402\) −2.94540 + 5.10159i −0.146903 + 0.254444i
\(403\) −11.2124 19.4205i −0.558531 0.967404i
\(404\) 1.84469 3.19509i 0.0917765 0.158962i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) −39.6605 −1.96832
\(407\) −5.73549 −0.284298
\(408\) 3.31315 + 5.73854i 0.164025 + 0.284100i
\(409\) 6.64935 + 11.5170i 0.328789 + 0.569480i 0.982272 0.187462i \(-0.0600261\pi\)
−0.653483 + 0.756942i \(0.726693\pi\)
\(410\) 8.79857 0.434530
\(411\) −13.9078 −0.686019
\(412\) −1.03154 1.78668i −0.0508203 0.0880233i
\(413\) −11.5341 + 19.9776i −0.567554 + 0.983032i
\(414\) 2.86774 + 4.96708i 0.140942 + 0.244119i
\(415\) 8.47098 14.6722i 0.415824 0.720228i
\(416\) −2.36774 + 4.10105i −0.116088 + 0.201071i
\(417\) −0.735489 −0.0360171
\(418\) 16.1348 19.0969i 0.789178 0.934058i
\(419\) −36.9881 −1.80699 −0.903493 0.428603i \(-0.859006\pi\)
−0.903493 + 0.428603i \(0.859006\pi\)
\(420\) −1.92234 + 3.32960i −0.0938007 + 0.162468i
\(421\) 1.68685 2.92172i 0.0822122 0.142396i −0.821988 0.569505i \(-0.807135\pi\)
0.904200 + 0.427110i \(0.140468\pi\)
\(422\) −11.6117 20.1121i −0.565249 0.979041i
\(423\) −0.890804 + 1.54292i −0.0433124 + 0.0750192i
\(424\) −2.55460 4.42469i −0.124062 0.214882i
\(425\) −6.62629 −0.321422
\(426\) −6.62629 −0.321045
\(427\) 0.209912 + 0.363579i 0.0101584 + 0.0175948i
\(428\) −7.26703 12.5869i −0.351265 0.608409i
\(429\) 27.1604 1.31131
\(430\) 1.04612 0.0504483
\(431\) −11.5827 20.0618i −0.557919 0.966344i −0.997670 0.0682240i \(-0.978267\pi\)
0.439751 0.898120i \(-0.355067\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −0.836206 1.44835i −0.0401855 0.0696033i 0.845233 0.534398i \(-0.179462\pi\)
−0.885419 + 0.464794i \(0.846128\pi\)
\(434\) −9.10323 + 15.7673i −0.436969 + 0.756853i
\(435\) 5.15783 8.93363i 0.247299 0.428335i
\(436\) 8.62629 0.413125
\(437\) −8.47098 23.5216i −0.405222 1.12519i
\(438\) −6.10920 −0.291909
\(439\) 13.3703 23.1580i 0.638128 1.10527i −0.347715 0.937600i \(-0.613042\pi\)
0.985843 0.167670i \(-0.0536242\pi\)
\(440\) −2.86774 + 4.96708i −0.136714 + 0.236796i
\(441\) −3.89080 6.73907i −0.185276 0.320908i
\(442\) 15.6894 27.1748i 0.746267 1.29257i
\(443\) −3.04864 5.28039i −0.144845 0.250879i 0.784470 0.620167i \(-0.212935\pi\)
−0.929315 + 0.369288i \(0.879602\pi\)
\(444\) −1.00000 −0.0474579
\(445\) −5.10920 −0.242199
\(446\) 7.50252 + 12.9947i 0.355255 + 0.615319i
\(447\) 5.42234 + 9.39177i 0.256468 + 0.444216i
\(448\) 3.84469 0.181644
\(449\) −5.10920 −0.241118 −0.120559 0.992706i \(-0.538469\pi\)
−0.120559 + 0.992706i \(0.538469\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) −25.2320 + 43.7032i −1.18813 + 2.05790i
\(452\) 4.26703 + 7.39071i 0.200704 + 0.347630i
\(453\) 0.468461 0.811398i 0.0220102 0.0381228i
\(454\) 10.2670 17.7830i 0.481856 0.834598i
\(455\) 18.2065 0.853532
\(456\) 2.81315 3.32960i 0.131738 0.155923i
\(457\) −34.3960 −1.60898 −0.804488 0.593969i \(-0.797560\pi\)
−0.804488 + 0.593969i \(0.797560\pi\)
\(458\) 6.63226 11.4874i 0.309905 0.536771i
\(459\) 3.31315 5.73854i 0.154644 0.267852i
\(460\) 2.86774 + 4.96708i 0.133709 + 0.231591i
\(461\) 5.73549 9.93416i 0.267128 0.462680i −0.700991 0.713170i \(-0.747259\pi\)
0.968119 + 0.250491i \(0.0805919\pi\)
\(462\) −11.0256 19.0969i −0.512956 0.888466i
\(463\) 1.93692 0.0900164 0.0450082 0.998987i \(-0.485669\pi\)
0.0450082 + 0.998987i \(0.485669\pi\)
\(464\) −10.3157 −0.478893
\(465\) −2.36774 4.10105i −0.109802 0.190182i
\(466\) −9.42486 16.3243i −0.436598 0.756210i
\(467\) −9.78664 −0.452872 −0.226436 0.974026i \(-0.572707\pi\)
−0.226436 + 0.974026i \(0.572707\pi\)
\(468\) 4.73549 0.218898
\(469\) −11.3241 19.6140i −0.522900 0.905690i
\(470\) −0.890804 + 1.54292i −0.0410897 + 0.0711695i
\(471\) −4.34469 7.52522i −0.200193 0.346744i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) −6.73549 −0.309371
\(475\) 1.47694 + 4.10105i 0.0677667 + 0.188169i
\(476\) −25.4760 −1.16769
\(477\) −2.55460 + 4.42469i −0.116967 + 0.202593i
\(478\) −6.95388 + 12.0445i −0.318063 + 0.550902i
\(479\) −13.2040 22.8699i −0.603304 1.04495i −0.992317 0.123721i \(-0.960517\pi\)
0.389013 0.921232i \(-0.372816\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 2.36774 + 4.10105i 0.107960 + 0.186992i
\(482\) −30.2065 −1.37587
\(483\) −22.0512 −1.00336
\(484\) −10.9479 18.9624i −0.497633 0.861925i
\(485\) −4.57766 7.92873i −0.207861 0.360025i
\(486\) 1.00000 0.0453609
\(487\) 39.3377 1.78256 0.891280 0.453454i \(-0.149808\pi\)
0.891280 + 0.453454i \(0.149808\pi\)
\(488\) 0.0545981 + 0.0945666i 0.00247154 + 0.00428083i
\(489\) 0.103234 0.178807i 0.00466841 0.00808593i
\(490\) −3.89080 6.73907i −0.175769 0.304440i
\(491\) −5.33872 + 9.24694i −0.240933 + 0.417309i −0.960980 0.276617i \(-0.910787\pi\)
0.720047 + 0.693925i \(0.244120\pi\)
\(492\) −4.39928 + 7.61978i −0.198335 + 0.343526i
\(493\) 68.3546 3.07854
\(494\) −20.3157 3.65323i −0.914045 0.164367i
\(495\) 5.73549 0.257791
\(496\) −2.36774 + 4.10105i −0.106315 + 0.184143i
\(497\) 12.7380 22.0629i 0.571378 0.989655i
\(498\) 8.47098 + 14.6722i 0.379594 + 0.657475i
\(499\) −12.7670 + 22.1131i −0.571531 + 0.989920i 0.424878 + 0.905250i \(0.360317\pi\)
−0.996409 + 0.0846697i \(0.973016\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 17.7355 0.792363
\(502\) −21.0342 −0.938802
\(503\) 11.3387 + 19.6392i 0.505569 + 0.875671i 0.999979 + 0.00644217i \(0.00205062\pi\)
−0.494411 + 0.869229i \(0.664616\pi\)
\(504\) −1.92234 3.32960i −0.0856280 0.148312i
\(505\) −3.68937 −0.164175
\(506\) −32.8958 −1.46240
\(507\) −4.71243 8.16217i −0.209286 0.362495i
\(508\) −2.33621 + 4.04643i −0.103652 + 0.179531i
\(509\) −12.3618 21.4112i −0.547926 0.949036i −0.998416 0.0562549i \(-0.982084\pi\)
0.450490 0.892781i \(-0.351249\pi\)
\(510\) 3.31315 5.73854i 0.146709 0.254107i
\(511\) 11.7440 20.3412i 0.519523 0.899840i
\(512\) 1.00000 0.0441942
\(513\) −4.29009 0.771459i −0.189412 0.0340607i
\(514\) 6.00000 0.264649
\(515\) −1.03154 + 1.78668i −0.0454550 + 0.0787304i
\(516\) −0.523059 + 0.905965i −0.0230264 + 0.0398829i
\(517\) −5.10920 8.84939i −0.224702 0.389196i
\(518\) 1.92234 3.32960i 0.0844629 0.146294i
\(519\) −0.709912 1.22960i −0.0311617 0.0539736i
\(520\) 4.73549 0.207665
\(521\) 21.1604 0.927052 0.463526 0.886083i \(-0.346584\pi\)
0.463526 + 0.886083i \(0.346584\pi\)
\(522\) 5.15783 + 8.93363i 0.225752 + 0.391014i
\(523\) 3.11768 + 5.39997i 0.136326 + 0.236124i 0.926103 0.377270i \(-0.123137\pi\)
−0.789777 + 0.613394i \(0.789804\pi\)
\(524\) −13.6433 −0.596008
\(525\) 3.84469 0.167796
\(526\) 3.39677 + 5.88337i 0.148106 + 0.256527i
\(527\) 15.6894 27.1748i 0.683440 1.18375i
\(528\) −2.86774 4.96708i −0.124803 0.216164i
\(529\) −4.94792 + 8.57005i −0.215127 + 0.372611i
\(530\) −2.55460 + 4.42469i −0.110965 + 0.192196i
\(531\) 6.00000 0.260378
\(532\) 5.67837 + 15.7673i 0.246189 + 0.683598i
\(533\) 41.6655 1.80473
\(534\) 2.55460 4.42469i 0.110548 0.191475i
\(535\) −7.26703 + 12.5869i −0.314181 + 0.544178i
\(536\) −2.94540 5.10159i −0.127222 0.220355i
\(537\) 8.60323 14.9012i 0.371257 0.643036i
\(538\) −6.04864 10.4765i −0.260775 0.451676i
\(539\) 44.6313 1.92241
\(540\) 1.00000 0.0430331
\(541\) −20.2636 35.0976i −0.871200 1.50896i −0.860757 0.509016i \(-0.830009\pi\)
−0.0104427 0.999945i \(-0.503324\pi\)
\(542\) 0.580175 + 1.00489i 0.0249207 + 0.0431638i
\(543\) 16.5341 0.709544
\(544\) −6.62629 −0.284100
\(545\) −4.31315 7.47059i −0.184755 0.320005i
\(546\) −9.10323 + 15.7673i −0.389582 + 0.674777i
\(547\) 0.632255 + 1.09510i 0.0270333 + 0.0468230i 0.879226 0.476406i \(-0.158061\pi\)
−0.852192 + 0.523229i \(0.824727\pi\)
\(548\) 6.95388 12.0445i 0.297055 0.514515i
\(549\) 0.0545981 0.0945666i 0.00233019 0.00403601i
\(550\) 5.73549 0.244562
\(551\) −15.2356 42.3051i −0.649060 1.80226i
\(552\) −5.73549 −0.244119
\(553\) 12.9479 22.4265i 0.550602 0.953670i
\(554\) −2.41982 + 4.19126i −0.102809 + 0.178070i
\(555\) 0.500000 + 0.866025i 0.0212238 + 0.0367607i
\(556\) 0.367745 0.636953i 0.0155959 0.0270128i
\(557\) 10.3362 + 17.9028i 0.437959 + 0.758567i 0.997532 0.0702137i \(-0.0223681\pi\)
−0.559573 + 0.828781i \(0.689035\pi\)
\(558\) 4.73549 0.200469
\(559\) 4.95388 0.209527
\(560\) −1.92234 3.32960i −0.0812338 0.140701i
\(561\) 19.0025 + 32.9133i 0.802287 + 1.38960i
\(562\) 9.32759 0.393461
\(563\) 9.03419 0.380746 0.190373 0.981712i \(-0.439030\pi\)
0.190373 + 0.981712i \(0.439030\pi\)
\(564\) −0.890804 1.54292i −0.0375096 0.0649685i
\(565\) 4.26703 7.39071i 0.179515 0.310930i
\(566\) 4.67241 + 8.09285i 0.196396 + 0.340168i
\(567\) −1.92234 + 3.32960i −0.0807308 + 0.139830i
\(568\) 3.31315 5.73854i 0.139017 0.240784i
\(569\) 25.7405 1.07910 0.539549 0.841954i \(-0.318595\pi\)
0.539549 + 0.841954i \(0.318595\pi\)
\(570\) −4.29009 0.771459i −0.179692 0.0323129i
\(571\) 15.5513 0.650801 0.325401 0.945576i \(-0.394501\pi\)
0.325401 + 0.945576i \(0.394501\pi\)
\(572\) −13.5802 + 23.5216i −0.567816 + 0.983486i
\(573\) 11.2065 19.4102i 0.468157 0.810872i
\(574\) −16.9139 29.2957i −0.705971 1.22278i
\(575\) 2.86774 4.96708i 0.119593 0.207142i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −38.3157 −1.59510 −0.797551 0.603252i \(-0.793872\pi\)
−0.797551 + 0.603252i \(0.793872\pi\)
\(578\) 26.9078 1.11922
\(579\) 11.5256 + 19.9629i 0.478987 + 0.829629i
\(580\) 5.15783 + 8.93363i 0.214167 + 0.370949i
\(581\) −65.1365 −2.70232
\(582\) 9.15531 0.379500
\(583\) −14.6519 25.3778i −0.606818 1.05104i
\(584\) 3.05460 5.29072i 0.126400 0.218932i
\(585\) −2.36774 4.10105i −0.0978942 0.169558i
\(586\) −1.60072 + 2.77252i −0.0661250 + 0.114532i
\(587\) −15.3618 + 26.6074i −0.634049 + 1.09820i 0.352667 + 0.935749i \(0.385275\pi\)
−0.986716 + 0.162456i \(0.948059\pi\)
\(588\) 7.78161 0.320908
\(589\) −20.3157 3.65323i −0.837092 0.150529i
\(590\) 6.00000 0.247016
\(591\) −1.33621 + 2.31438i −0.0549642 + 0.0952007i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) −5.98556 10.3673i −0.245797 0.425734i 0.716558 0.697527i \(-0.245716\pi\)
−0.962356 + 0.271794i \(0.912383\pi\)
\(594\) −2.86774 + 4.96708i −0.117665 + 0.203802i
\(595\) 12.7380 + 22.0629i 0.522207 + 0.904490i
\(596\) −10.8447 −0.444216
\(597\) −11.5802 −0.473945
\(598\) 13.5802 + 23.5216i 0.555335 + 0.961868i
\(599\) 4.33011 + 7.49996i 0.176923 + 0.306440i 0.940825 0.338892i \(-0.110052\pi\)
−0.763902 + 0.645332i \(0.776719\pi\)
\(600\) 1.00000 0.0408248
\(601\) −44.3787 −1.81025 −0.905123 0.425149i \(-0.860222\pi\)
−0.905123 + 0.425149i \(0.860222\pi\)
\(602\) −2.01100 3.48315i −0.0819622 0.141963i
\(603\) −2.94540 + 5.10159i −0.119946 + 0.207753i
\(604\) 0.468461 + 0.811398i 0.0190614 + 0.0330153i
\(605\) −10.9479 + 18.9624i −0.445096 + 0.770929i
\(606\) 1.84469 3.19509i 0.0749352 0.129792i
\(607\) −24.6944 −1.00232 −0.501158 0.865356i \(-0.667092\pi\)
−0.501158 + 0.865356i \(0.667092\pi\)
\(608\) 1.47694 + 4.10105i 0.0598979 + 0.166320i
\(609\) −39.6605 −1.60712
\(610\) 0.0545981 0.0945666i 0.00221061 0.00382889i
\(611\) −4.21839 + 7.30647i −0.170658 + 0.295588i
\(612\) 3.31315 + 5.73854i 0.133926 + 0.231967i
\(613\) 9.18341 15.9061i 0.370914 0.642443i −0.618792 0.785555i \(-0.712378\pi\)
0.989706 + 0.143112i \(0.0457110\pi\)
\(614\) 14.1117 + 24.4422i 0.569502 + 0.986407i
\(615\) 8.79857 0.354792
\(616\) 22.0512 0.888466
\(617\) 6.00000 + 10.3923i 0.241551 + 0.418378i 0.961156 0.276005i \(-0.0890106\pi\)
−0.719605 + 0.694383i \(0.755677\pi\)
\(618\) −1.03154 1.78668i −0.0414946 0.0718707i
\(619\) 8.46594 0.340275 0.170137 0.985420i \(-0.445579\pi\)
0.170137 + 0.985420i \(0.445579\pi\)
\(620\) 4.73549 0.190182
\(621\) 2.86774 + 4.96708i 0.115079 + 0.199322i
\(622\) 6.42486 11.1282i 0.257613 0.446200i
\(623\) 9.82163 + 17.0116i 0.393495 + 0.681554i
\(624\) −2.36774 + 4.10105i −0.0947856 + 0.164174i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 29.0342 1.16044
\(627\) 16.1348 19.0969i 0.644361 0.762655i
\(628\) 8.68937 0.346744
\(629\) −3.31315 + 5.73854i −0.132104 + 0.228811i
\(630\) −1.92234 + 3.32960i −0.0765880 + 0.132654i
\(631\) −10.2611 17.7727i −0.408487 0.707520i 0.586234 0.810142i \(-0.300610\pi\)
−0.994720 + 0.102622i \(0.967277\pi\)
\(632\) 3.36774 5.83311i 0.133962 0.232028i
\(633\) −11.6117 20.1121i −0.461524 0.799383i
\(634\) 4.45402 0.176892
\(635\) 4.67241 0.185419
\(636\) −2.55460 4.42469i −0.101296 0.175451i
\(637\) −18.4249 31.9128i −0.730020 1.26443i
\(638\) −59.1654 −2.34238
\(639\) −6.62629 −0.262132
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −14.1434 + 24.4971i −0.558630 + 0.967576i 0.438981 + 0.898496i \(0.355340\pi\)
−0.997611 + 0.0690797i \(0.977994\pi\)
\(642\) −7.26703 12.5869i −0.286807 0.496764i
\(643\) 15.4795 26.8112i 0.610450 1.05733i −0.380714 0.924693i \(-0.624322\pi\)
0.991165 0.132638i \(-0.0423448\pi\)
\(644\) 11.0256 19.0969i 0.434469 0.752522i
\(645\) 1.04612 0.0411909
\(646\) −9.78664 27.1748i −0.385050 1.06918i
\(647\) −33.0220 −1.29823 −0.649114 0.760691i \(-0.724860\pi\)
−0.649114 + 0.760691i \(0.724860\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −17.2065 + 29.8025i −0.675413 + 1.16985i
\(650\) −2.36774 4.10105i −0.0928706 0.160857i
\(651\) −9.10323 + 15.7673i −0.356784 + 0.617968i
\(652\) 0.103234 + 0.178807i 0.00404297 + 0.00700262i
\(653\) 33.1193 1.29606 0.648029 0.761616i \(-0.275594\pi\)
0.648029 + 0.761616i \(0.275594\pi\)
\(654\) 8.62629 0.337315
\(655\) 6.82163 + 11.8154i 0.266543 + 0.461666i
\(656\) −4.39928 7.61978i −0.171763 0.297503i
\(657\) −6.10920 −0.238342
\(658\) 6.84972 0.267030
\(659\) 6.55712 + 11.3573i 0.255429 + 0.442416i 0.965012 0.262206i \(-0.0844500\pi\)
−0.709583 + 0.704622i \(0.751117\pi\)
\(660\) −2.86774 + 4.96708i −0.111627 + 0.193343i
\(661\) −3.17227 5.49454i −0.123387 0.213713i 0.797714 0.603036i \(-0.206042\pi\)
−0.921101 + 0.389323i \(0.872709\pi\)
\(662\) 5.92234 10.2578i 0.230178 0.398681i
\(663\) 15.6894 27.1748i 0.609325 1.05538i
\(664\) −16.9420 −0.657475
\(665\) 10.8157 12.8012i 0.419413 0.496411i
\(666\) −1.00000 −0.0387492
\(667\) −29.5827 + 51.2387i −1.14545 + 1.98397i
\(668\) −8.86774 + 15.3594i −0.343103 + 0.594272i
\(669\) 7.50252 + 12.9947i 0.290064 + 0.502406i
\(670\) −2.94540 + 5.10159i −0.113791 + 0.197091i
\(671\) 0.313147 + 0.542386i 0.0120889 + 0.0209386i
\(672\) 3.84469 0.148312
\(673\) 32.2987 1.24502 0.622512 0.782610i \(-0.286112\pi\)
0.622512 + 0.782610i \(0.286112\pi\)
\(674\) −3.58614 6.21137i −0.138133 0.239253i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 9.42486 0.362495
\(677\) 1.54598 0.0594169 0.0297084 0.999559i \(-0.490542\pi\)
0.0297084 + 0.999559i \(0.490542\pi\)
\(678\) 4.26703 + 7.39071i 0.163874 + 0.283839i
\(679\) −17.5997 + 30.4835i −0.675413 + 1.16985i
\(680\) 3.31315 + 5.73854i 0.127053 + 0.220063i
\(681\) 10.2670 17.7830i 0.393433 0.681447i
\(682\) −13.5802 + 23.5216i −0.520012 + 0.900687i
\(683\) −14.5341 −0.556130 −0.278065 0.960562i \(-0.589693\pi\)
−0.278065 + 0.960562i \(0.589693\pi\)
\(684\) 2.81315 3.32960i 0.107563 0.127310i
\(685\) −13.9078 −0.531388
\(686\) −1.50252 + 2.60244i −0.0573664 + 0.0993615i
\(687\) 6.63226 11.4874i 0.253036 0.438272i
\(688\) −0.523059 0.905965i −0.0199414 0.0345396i
\(689\) −12.0973 + 20.9531i −0.460869 + 0.798249i
\(690\) 2.86774 + 4.96708i 0.109173 + 0.189093i
\(691\) 8.48794 0.322896 0.161448 0.986881i \(-0.448384\pi\)
0.161448 + 0.986881i \(0.448384\pi\)
\(692\) 1.41982 0.0539736
\(693\) −11.0256 19.0969i −0.418827 0.725430i
\(694\) −11.2065 19.4102i −0.425392 0.736800i
\(695\) −0.735489 −0.0278987
\(696\) −10.3157 −0.391014
\(697\) 29.1509 + 50.4909i 1.10417 + 1.91248i
\(698\) 12.1519 21.0477i 0.459955 0.796666i
\(699\) −9.42486 16.3243i −0.356481 0.617443i
\(700\) −1.92234 + 3.32960i −0.0726577 + 0.125847i
\(701\) 9.29870 16.1058i 0.351207 0.608309i −0.635254 0.772303i \(-0.719105\pi\)
0.986461 + 0.163994i \(0.0524379\pi\)
\(702\) 4.73549 0.178730
\(703\) 4.29009 + 0.771459i 0.161804 + 0.0290961i
\(704\) 5.73549 0.216164
\(705\) −0.890804 + 1.54292i −0.0335496 + 0.0581096i
\(706\) −16.3643 + 28.3438i −0.615879 + 1.06673i
\(707\) 7.09224 + 12.2841i 0.266731 + 0.461992i
\(708\) −3.00000 + 5.19615i −0.112747 + 0.195283i
\(709\) −3.96236 6.86301i −0.148810 0.257746i 0.781978 0.623306i \(-0.214211\pi\)
−0.930788 + 0.365560i \(0.880877\pi\)
\(710\) −6.62629 −0.248680
\(711\) −6.73549 −0.252601
\(712\) 2.55460 + 4.42469i 0.0957376 + 0.165822i
\(713\) 13.5802 + 23.5216i 0.508582 + 0.880889i
\(714\) −25.4760 −0.953416
\(715\) 27.1604 1.01574
\(716\) 8.60323 + 14.9012i 0.321518 + 0.556885i
\(717\) −6.95388 + 12.0445i −0.259697 + 0.449809i
\(718\) 0.577657 + 1.00053i 0.0215580 + 0.0373395i
\(719\) 14.8328 25.6911i 0.553169 0.958116i −0.444875 0.895593i \(-0.646752\pi\)
0.998043 0.0625235i \(-0.0199148\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 7.93189 0.295399
\(722\) −14.6373 + 12.1140i −0.544744 + 0.450837i
\(723\) −30.2065 −1.12339
\(724\) −8.26703 + 14.3189i −0.307242 + 0.532158i
\(725\) 5.15783 8.93363i 0.191557 0.331787i
\(726\) −10.9479 18.9624i −0.406315 0.703759i
\(727\) 7.25855 12.5722i 0.269205 0.466276i −0.699452 0.714680i \(-0.746573\pi\)
0.968657 + 0.248403i \(0.0799059\pi\)
\(728\) −9.10323 15.7673i −0.337388 0.584374i
\(729\) 1.00000 0.0370370
\(730\) −6.10920 −0.226111
\(731\) 3.46594 + 6.00319i 0.128193 + 0.222036i
\(732\) 0.0545981 + 0.0945666i 0.00201800 + 0.00349528i
\(733\) 25.7355 0.950562 0.475281 0.879834i \(-0.342346\pi\)
0.475281 + 0.879834i \(0.342346\pi\)
\(734\) 27.6774 1.02159
\(735\) −3.89080 6.73907i −0.143514 0.248574i
\(736\) 2.86774 4.96708i 0.105706 0.183089i
\(737\) −16.8933 29.2601i −0.622274 1.07781i
\(738\) −4.39928 + 7.61978i −0.161940 + 0.280488i
\(739\) 2.23297 3.86762i 0.0821412 0.142273i −0.822028 0.569447i \(-0.807157\pi\)
0.904169 + 0.427174i \(0.140491\pi\)
\(740\) −1.00000 −0.0367607
\(741\) −20.3157 3.65323i −0.746315 0.134205i
\(742\) 19.6433 0.721127
\(743\) −5.04002 + 8.72957i −0.184900 + 0.320257i −0.943543 0.331250i \(-0.892530\pi\)
0.758643 + 0.651507i \(0.225863\pi\)
\(744\) −2.36774 + 4.10105i −0.0868057 + 0.150352i
\(745\) 5.42234 + 9.39177i 0.198659 + 0.344088i
\(746\) 11.7585 20.3664i 0.430511 0.745667i
\(747\) 8.47098 + 14.6722i 0.309937 + 0.536826i
\(748\) −38.0050 −1.38960
\(749\) 55.8789 2.04177
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 1.94792 + 3.37390i 0.0710806 + 0.123115i 0.899375 0.437178i \(-0.144022\pi\)
−0.828295 + 0.560293i \(0.810689\pi\)
\(752\) 1.78161 0.0649685
\(753\) −21.0342 −0.766529
\(754\) 24.4249 + 42.3051i 0.889501 + 1.54066i
\(755\) 0.468461 0.811398i 0.0170490 0.0295298i
\(756\) −1.92234 3.32960i −0.0699149 0.121096i
\(757\) −18.2866 + 31.6734i −0.664639 + 1.15119i 0.314744 + 0.949177i \(0.398081\pi\)
−0.979383 + 0.202012i \(0.935252\pi\)
\(758\) −4.14935 + 7.18689i −0.150711 + 0.261040i
\(759\) −32.8958 −1.19404
\(760\) 2.81315 3.32960i 0.102044 0.120777i
\(761\) 29.9589 1.08601 0.543005 0.839729i \(-0.317286\pi\)
0.543005 + 0.839729i \(0.317286\pi\)
\(762\) −2.33621 + 4.04643i −0.0846318 + 0.146587i
\(763\) −16.5827 + 28.7221i −0.600334 + 1.03981i
\(764\) 11.2065 + 19.4102i 0.405436 + 0.702235i
\(765\) 3.31315 5.73854i 0.119787 0.207477i
\(766\) −6.89080 11.9352i −0.248975 0.431237i
\(767\) 28.4129 1.02593
\(768\) 1.00000 0.0360844
\(769\) 24.9940 + 43.2909i 0.901308 + 1.56111i 0.825798 + 0.563966i \(0.190725\pi\)
0.0755103 + 0.997145i \(0.475941\pi\)
\(770\) −11.0256 19.0969i −0.397334 0.688203i
\(771\) 6.00000 0.216085
\(772\) −23.0512 −0.829629
\(773\) 14.3532 + 24.8604i 0.516247 + 0.894167i 0.999822 + 0.0188637i \(0.00600486\pi\)
−0.483575 + 0.875303i \(0.660662\pi\)
\(774\) −0.523059 + 0.905965i −0.0188010 + 0.0325642i
\(775\) −2.36774 4.10105i −0.0850519 0.147314i
\(776\) −4.57766 + 7.92873i −0.164328 + 0.284625i
\(777\) 1.92234 3.32960i 0.0689637 0.119449i