Properties

Label 1014.2.e.h.529.1
Level $1014$
Weight $2$
Character 1014.529
Analytic conductor $8.097$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.h.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.633975 + 1.09808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.633975 + 1.09808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.866025 - 1.50000i) q^{10} +(0.633975 - 1.09808i) q^{11} -1.00000 q^{12} -1.26795 q^{14} +(-0.866025 + 1.50000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 - 4.50000i) q^{17} +1.00000 q^{18} +(2.36603 + 4.09808i) q^{19} +(0.866025 + 1.50000i) q^{20} +1.26795 q^{21} +(0.633975 + 1.09808i) q^{22} +(4.09808 - 7.09808i) q^{23} +(0.500000 - 0.866025i) q^{24} -2.00000 q^{25} -1.00000 q^{27} +(0.633975 - 1.09808i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.866025 - 1.50000i) q^{30} -9.46410 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.633975 - 1.09808i) q^{33} +5.19615 q^{34} +(-1.09808 - 1.90192i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.50000 - 2.59808i) q^{37} -4.73205 q^{38} -1.73205 q^{40} +(3.23205 - 5.59808i) q^{41} +(-0.633975 + 1.09808i) q^{42} +(2.09808 + 3.63397i) q^{43} -1.26795 q^{44} +(0.866025 + 1.50000i) q^{45} +(4.09808 + 7.09808i) q^{46} +4.73205 q^{47} +(0.500000 + 0.866025i) q^{48} +(2.69615 - 4.66987i) q^{49} +(1.00000 - 1.73205i) q^{50} -5.19615 q^{51} +3.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.09808 + 1.90192i) q^{55} +(0.633975 + 1.09808i) q^{56} +4.73205 q^{57} +(1.50000 + 2.59808i) q^{58} +(-6.92820 - 12.0000i) q^{59} +1.73205 q^{60} +(-7.59808 - 13.1603i) q^{61} +(4.73205 - 8.19615i) q^{62} +(0.633975 - 1.09808i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(3.63397 - 6.29423i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(-4.09808 - 7.09808i) q^{69} +2.19615 q^{70} +(-1.09808 - 1.90192i) q^{71} +(-0.500000 - 0.866025i) q^{72} -12.1244 q^{73} +(1.50000 + 2.59808i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(2.36603 - 4.09808i) q^{76} +1.60770 q^{77} +8.39230 q^{79} +(0.866025 - 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.23205 + 5.59808i) q^{82} -5.66025 q^{83} +(-0.633975 - 1.09808i) q^{84} +(4.50000 + 7.79423i) q^{85} -4.19615 q^{86} +(-1.50000 - 2.59808i) q^{87} +(0.633975 - 1.09808i) q^{88} +(4.73205 - 8.19615i) q^{89} -1.73205 q^{90} -8.19615 q^{92} +(-4.73205 + 8.19615i) q^{93} +(-2.36603 + 4.09808i) q^{94} +(-4.09808 - 7.09808i) q^{95} -1.00000 q^{96} +(3.00000 + 5.19615i) q^{97} +(2.69615 + 4.66987i) q^{98} -1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 6 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 6 q^{7} + 4 q^{8} - 2 q^{9} + 6 q^{11} - 4 q^{12} - 12 q^{14} - 2 q^{16} + 4 q^{18} + 6 q^{19} + 12 q^{21} + 6 q^{22} + 6 q^{23} + 2 q^{24} - 8 q^{25} - 4 q^{27} + 6 q^{28} + 6 q^{29} - 24 q^{31} - 2 q^{32} - 6 q^{33} + 6 q^{35} - 2 q^{36} + 6 q^{37} - 12 q^{38} + 6 q^{41} - 6 q^{42} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 12 q^{47} + 2 q^{48} - 10 q^{49} + 4 q^{50} + 12 q^{53} + 2 q^{54} + 6 q^{55} + 6 q^{56} + 12 q^{57} + 6 q^{58} - 20 q^{61} + 12 q^{62} + 6 q^{63} + 4 q^{64} + 12 q^{66} + 18 q^{67} - 6 q^{69} - 12 q^{70} + 6 q^{71} - 2 q^{72} + 6 q^{74} - 4 q^{75} + 6 q^{76} + 48 q^{77} - 8 q^{79} - 2 q^{81} + 6 q^{82} + 12 q^{83} - 6 q^{84} + 18 q^{85} + 4 q^{86} - 6 q^{87} + 6 q^{88} + 12 q^{89} - 12 q^{92} - 12 q^{93} - 6 q^{94} - 6 q^{95} - 4 q^{96} + 12 q^{97} - 10 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −1.73205 −0.774597 −0.387298 0.921954i \(-0.626592\pi\)
−0.387298 + 0.921954i \(0.626592\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 0.633975 + 1.09808i 0.239620 + 0.415034i 0.960605 0.277916i \(-0.0896439\pi\)
−0.720985 + 0.692950i \(0.756311\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.866025 1.50000i 0.273861 0.474342i
\(11\) 0.633975 1.09808i 0.191151 0.331082i −0.754481 0.656322i \(-0.772111\pi\)
0.945632 + 0.325239i \(0.105445\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.26795 −0.338874
\(15\) −0.866025 + 1.50000i −0.223607 + 0.387298i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.59808 4.50000i −0.630126 1.09141i −0.987526 0.157459i \(-0.949670\pi\)
0.357400 0.933952i \(-0.383663\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.36603 + 4.09808i 0.542803 + 0.940163i 0.998742 + 0.0501517i \(0.0159705\pi\)
−0.455938 + 0.890011i \(0.650696\pi\)
\(20\) 0.866025 + 1.50000i 0.193649 + 0.335410i
\(21\) 1.26795 0.276689
\(22\) 0.633975 + 1.09808i 0.135164 + 0.234111i
\(23\) 4.09808 7.09808i 0.854508 1.48005i −0.0225928 0.999745i \(-0.507192\pi\)
0.877101 0.480306i \(-0.159475\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −2.00000 −0.400000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0.633975 1.09808i 0.119810 0.207517i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) −0.866025 1.50000i −0.158114 0.273861i
\(31\) −9.46410 −1.69980 −0.849901 0.526942i \(-0.823339\pi\)
−0.849901 + 0.526942i \(0.823339\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.633975 1.09808i −0.110361 0.191151i
\(34\) 5.19615 0.891133
\(35\) −1.09808 1.90192i −0.185609 0.321484i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) −4.73205 −0.767640
\(39\) 0 0
\(40\) −1.73205 −0.273861
\(41\) 3.23205 5.59808i 0.504762 0.874273i −0.495223 0.868766i \(-0.664914\pi\)
0.999985 0.00550690i \(-0.00175291\pi\)
\(42\) −0.633975 + 1.09808i −0.0978244 + 0.169437i
\(43\) 2.09808 + 3.63397i 0.319954 + 0.554176i 0.980478 0.196629i \(-0.0629993\pi\)
−0.660524 + 0.750805i \(0.729666\pi\)
\(44\) −1.26795 −0.191151
\(45\) 0.866025 + 1.50000i 0.129099 + 0.223607i
\(46\) 4.09808 + 7.09808i 0.604228 + 1.04655i
\(47\) 4.73205 0.690241 0.345120 0.938558i \(-0.387838\pi\)
0.345120 + 0.938558i \(0.387838\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 2.69615 4.66987i 0.385165 0.667125i
\(50\) 1.00000 1.73205i 0.141421 0.244949i
\(51\) −5.19615 −0.727607
\(52\) 0 0
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −1.09808 + 1.90192i −0.148065 + 0.256455i
\(56\) 0.633975 + 1.09808i 0.0847184 + 0.146737i
\(57\) 4.73205 0.626775
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) −6.92820 12.0000i −0.901975 1.56227i −0.824927 0.565240i \(-0.808784\pi\)
−0.0770484 0.997027i \(-0.524550\pi\)
\(60\) 1.73205 0.223607
\(61\) −7.59808 13.1603i −0.972834 1.68500i −0.686905 0.726747i \(-0.741031\pi\)
−0.285929 0.958251i \(-0.592302\pi\)
\(62\) 4.73205 8.19615i 0.600971 1.04091i
\(63\) 0.633975 1.09808i 0.0798733 0.138345i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.26795 0.156074
\(67\) 3.63397 6.29423i 0.443961 0.768962i −0.554019 0.832504i \(-0.686906\pi\)
0.997979 + 0.0635419i \(0.0202397\pi\)
\(68\) −2.59808 + 4.50000i −0.315063 + 0.545705i
\(69\) −4.09808 7.09808i −0.493350 0.854508i
\(70\) 2.19615 0.262490
\(71\) −1.09808 1.90192i −0.130318 0.225717i 0.793481 0.608595i \(-0.208266\pi\)
−0.923799 + 0.382878i \(0.874933\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −12.1244 −1.41905 −0.709524 0.704681i \(-0.751090\pi\)
−0.709524 + 0.704681i \(0.751090\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) −1.00000 + 1.73205i −0.115470 + 0.200000i
\(76\) 2.36603 4.09808i 0.271402 0.470082i
\(77\) 1.60770 0.183214
\(78\) 0 0
\(79\) 8.39230 0.944208 0.472104 0.881543i \(-0.343495\pi\)
0.472104 + 0.881543i \(0.343495\pi\)
\(80\) 0.866025 1.50000i 0.0968246 0.167705i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.23205 + 5.59808i 0.356920 + 0.618204i
\(83\) −5.66025 −0.621294 −0.310647 0.950525i \(-0.600546\pi\)
−0.310647 + 0.950525i \(0.600546\pi\)
\(84\) −0.633975 1.09808i −0.0691723 0.119810i
\(85\) 4.50000 + 7.79423i 0.488094 + 0.845403i
\(86\) −4.19615 −0.452483
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) 0.633975 1.09808i 0.0675819 0.117055i
\(89\) 4.73205 8.19615i 0.501596 0.868790i −0.498402 0.866946i \(-0.666080\pi\)
0.999998 0.00184433i \(-0.000587067\pi\)
\(90\) −1.73205 −0.182574
\(91\) 0 0
\(92\) −8.19615 −0.854508
\(93\) −4.73205 + 8.19615i −0.490691 + 0.849901i
\(94\) −2.36603 + 4.09808i −0.244037 + 0.422684i
\(95\) −4.09808 7.09808i −0.420454 0.728247i
\(96\) −1.00000 −0.102062
\(97\) 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i \(-0.0681426\pi\)
−0.672569 + 0.740034i \(0.734809\pi\)
\(98\) 2.69615 + 4.66987i 0.272353 + 0.471728i
\(99\) −1.26795 −0.127434
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −9.69615 + 16.7942i −0.964803 + 1.67109i −0.254660 + 0.967031i \(0.581964\pi\)
−0.710143 + 0.704058i \(0.751370\pi\)
\(102\) 2.59808 4.50000i 0.257248 0.445566i
\(103\) 6.19615 0.610525 0.305263 0.952268i \(-0.401256\pi\)
0.305263 + 0.952268i \(0.401256\pi\)
\(104\) 0 0
\(105\) −2.19615 −0.214323
\(106\) −1.50000 + 2.59808i −0.145693 + 0.252347i
\(107\) 1.09808 1.90192i 0.106155 0.183866i −0.808054 0.589108i \(-0.799479\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 4.39230 0.420707 0.210353 0.977625i \(-0.432539\pi\)
0.210353 + 0.977625i \(0.432539\pi\)
\(110\) −1.09808 1.90192i −0.104697 0.181341i
\(111\) −1.50000 2.59808i −0.142374 0.246598i
\(112\) −1.26795 −0.119810
\(113\) −0.401924 0.696152i −0.0378098 0.0654885i 0.846501 0.532387i \(-0.178705\pi\)
−0.884311 + 0.466898i \(0.845371\pi\)
\(114\) −2.36603 + 4.09808i −0.221599 + 0.383820i
\(115\) −7.09808 + 12.2942i −0.661899 + 1.14644i
\(116\) −3.00000 −0.278543
\(117\) 0 0
\(118\) 13.8564 1.27559
\(119\) 3.29423 5.70577i 0.301981 0.523047i
\(120\) −0.866025 + 1.50000i −0.0790569 + 0.136931i
\(121\) 4.69615 + 8.13397i 0.426923 + 0.739452i
\(122\) 15.1962 1.37579
\(123\) −3.23205 5.59808i −0.291424 0.504762i
\(124\) 4.73205 + 8.19615i 0.424951 + 0.736036i
\(125\) 12.1244 1.08444
\(126\) 0.633975 + 1.09808i 0.0564789 + 0.0978244i
\(127\) 2.00000 3.46410i 0.177471 0.307389i −0.763542 0.645758i \(-0.776542\pi\)
0.941014 + 0.338368i \(0.109875\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 4.19615 0.369451
\(130\) 0 0
\(131\) −4.39230 −0.383757 −0.191879 0.981419i \(-0.561458\pi\)
−0.191879 + 0.981419i \(0.561458\pi\)
\(132\) −0.633975 + 1.09808i −0.0551804 + 0.0955753i
\(133\) −3.00000 + 5.19615i −0.260133 + 0.450564i
\(134\) 3.63397 + 6.29423i 0.313928 + 0.543739i
\(135\) 1.73205 0.149071
\(136\) −2.59808 4.50000i −0.222783 0.385872i
\(137\) −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i \(-0.292279\pi\)
−0.991694 + 0.128618i \(0.958946\pi\)
\(138\) 8.19615 0.697703
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −1.09808 + 1.90192i −0.0928044 + 0.160742i
\(141\) 2.36603 4.09808i 0.199255 0.345120i
\(142\) 2.19615 0.184297
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −2.59808 + 4.50000i −0.215758 + 0.373705i
\(146\) 6.06218 10.5000i 0.501709 0.868986i
\(147\) −2.69615 4.66987i −0.222375 0.385165i
\(148\) −3.00000 −0.246598
\(149\) 3.06218 + 5.30385i 0.250863 + 0.434508i 0.963764 0.266757i \(-0.0859522\pi\)
−0.712900 + 0.701265i \(0.752619\pi\)
\(150\) −1.00000 1.73205i −0.0816497 0.141421i
\(151\) −10.7321 −0.873362 −0.436681 0.899616i \(-0.643846\pi\)
−0.436681 + 0.899616i \(0.643846\pi\)
\(152\) 2.36603 + 4.09808i 0.191910 + 0.332398i
\(153\) −2.59808 + 4.50000i −0.210042 + 0.363803i
\(154\) −0.803848 + 1.39230i −0.0647759 + 0.112195i
\(155\) 16.3923 1.31666
\(156\) 0 0
\(157\) 7.19615 0.574315 0.287158 0.957883i \(-0.407290\pi\)
0.287158 + 0.957883i \(0.407290\pi\)
\(158\) −4.19615 + 7.26795i −0.333828 + 0.578207i
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) 0.866025 + 1.50000i 0.0684653 + 0.118585i
\(161\) 10.3923 0.819028
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 1.26795 + 2.19615i 0.0993134 + 0.172016i 0.911401 0.411520i \(-0.135002\pi\)
−0.812087 + 0.583536i \(0.801669\pi\)
\(164\) −6.46410 −0.504762
\(165\) 1.09808 + 1.90192i 0.0854851 + 0.148065i
\(166\) 2.83013 4.90192i 0.219660 0.380463i
\(167\) −4.73205 + 8.19615i −0.366177 + 0.634237i −0.988964 0.148154i \(-0.952667\pi\)
0.622787 + 0.782391i \(0.286000\pi\)
\(168\) 1.26795 0.0978244
\(169\) 0 0
\(170\) −9.00000 −0.690268
\(171\) 2.36603 4.09808i 0.180934 0.313388i
\(172\) 2.09808 3.63397i 0.159977 0.277088i
\(173\) 2.19615 + 3.80385i 0.166970 + 0.289201i 0.937353 0.348380i \(-0.113268\pi\)
−0.770383 + 0.637582i \(0.779935\pi\)
\(174\) 3.00000 0.227429
\(175\) −1.26795 2.19615i −0.0958479 0.166014i
\(176\) 0.633975 + 1.09808i 0.0477876 + 0.0827706i
\(177\) −13.8564 −1.04151
\(178\) 4.73205 + 8.19615i 0.354682 + 0.614328i
\(179\) −1.09808 + 1.90192i −0.0820741 + 0.142156i −0.904141 0.427235i \(-0.859488\pi\)
0.822067 + 0.569391i \(0.192821\pi\)
\(180\) 0.866025 1.50000i 0.0645497 0.111803i
\(181\) 19.5885 1.45600 0.727999 0.685578i \(-0.240450\pi\)
0.727999 + 0.685578i \(0.240450\pi\)
\(182\) 0 0
\(183\) −15.1962 −1.12333
\(184\) 4.09808 7.09808i 0.302114 0.523277i
\(185\) −2.59808 + 4.50000i −0.191014 + 0.330847i
\(186\) −4.73205 8.19615i −0.346971 0.600971i
\(187\) −6.58846 −0.481796
\(188\) −2.36603 4.09808i −0.172560 0.298883i
\(189\) −0.633975 1.09808i −0.0461149 0.0798733i
\(190\) 8.19615 0.594611
\(191\) 10.3923 + 18.0000i 0.751961 + 1.30243i 0.946871 + 0.321613i \(0.104225\pi\)
−0.194910 + 0.980821i \(0.562442\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −11.5981 + 20.0885i −0.834848 + 1.44600i 0.0593065 + 0.998240i \(0.481111\pi\)
−0.894154 + 0.447759i \(0.852222\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −5.39230 −0.385165
\(197\) −3.46410 + 6.00000i −0.246807 + 0.427482i −0.962638 0.270791i \(-0.912715\pi\)
0.715831 + 0.698273i \(0.246048\pi\)
\(198\) 0.633975 1.09808i 0.0450546 0.0780369i
\(199\) 11.2942 + 19.5622i 0.800627 + 1.38673i 0.919204 + 0.393781i \(0.128833\pi\)
−0.118578 + 0.992945i \(0.537833\pi\)
\(200\) −2.00000 −0.141421
\(201\) −3.63397 6.29423i −0.256321 0.443961i
\(202\) −9.69615 16.7942i −0.682219 1.18164i
\(203\) 3.80385 0.266978
\(204\) 2.59808 + 4.50000i 0.181902 + 0.315063i
\(205\) −5.59808 + 9.69615i −0.390987 + 0.677209i
\(206\) −3.09808 + 5.36603i −0.215853 + 0.373869i
\(207\) −8.19615 −0.569672
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) 1.09808 1.90192i 0.0757745 0.131245i
\(211\) 12.1962 21.1244i 0.839618 1.45426i −0.0505968 0.998719i \(-0.516112\pi\)
0.890215 0.455541i \(-0.150554\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) −2.19615 −0.150478
\(214\) 1.09808 + 1.90192i 0.0750629 + 0.130013i
\(215\) −3.63397 6.29423i −0.247835 0.429263i
\(216\) −1.00000 −0.0680414
\(217\) −6.00000 10.3923i −0.407307 0.705476i
\(218\) −2.19615 + 3.80385i −0.148742 + 0.257629i
\(219\) −6.06218 + 10.5000i −0.409644 + 0.709524i
\(220\) 2.19615 0.148065
\(221\) 0 0
\(222\) 3.00000 0.201347
\(223\) −2.53590 + 4.39230i −0.169816 + 0.294130i −0.938355 0.345673i \(-0.887651\pi\)
0.768539 + 0.639803i \(0.220984\pi\)
\(224\) 0.633975 1.09808i 0.0423592 0.0733683i
\(225\) 1.00000 + 1.73205i 0.0666667 + 0.115470i
\(226\) 0.803848 0.0534711
\(227\) −10.0981 17.4904i −0.670233 1.16088i −0.977838 0.209363i \(-0.932861\pi\)
0.307605 0.951514i \(-0.400472\pi\)
\(228\) −2.36603 4.09808i −0.156694 0.271402i
\(229\) 7.85641 0.519166 0.259583 0.965721i \(-0.416415\pi\)
0.259583 + 0.965721i \(0.416415\pi\)
\(230\) −7.09808 12.2942i −0.468033 0.810657i
\(231\) 0.803848 1.39230i 0.0528893 0.0916069i
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) −8.19615 −0.534658
\(236\) −6.92820 + 12.0000i −0.450988 + 0.781133i
\(237\) 4.19615 7.26795i 0.272569 0.472104i
\(238\) 3.29423 + 5.70577i 0.213533 + 0.369850i
\(239\) −6.58846 −0.426172 −0.213086 0.977033i \(-0.568351\pi\)
−0.213086 + 0.977033i \(0.568351\pi\)
\(240\) −0.866025 1.50000i −0.0559017 0.0968246i
\(241\) 5.59808 + 9.69615i 0.360604 + 0.624584i 0.988060 0.154068i \(-0.0492373\pi\)
−0.627457 + 0.778652i \(0.715904\pi\)
\(242\) −9.39230 −0.603760
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −7.59808 + 13.1603i −0.486417 + 0.842499i
\(245\) −4.66987 + 8.08846i −0.298347 + 0.516753i
\(246\) 6.46410 0.412136
\(247\) 0 0
\(248\) −9.46410 −0.600971
\(249\) −2.83013 + 4.90192i −0.179352 + 0.310647i
\(250\) −6.06218 + 10.5000i −0.383406 + 0.664078i
\(251\) −8.19615 14.1962i −0.517337 0.896053i −0.999797 0.0201356i \(-0.993590\pi\)
0.482461 0.875918i \(-0.339743\pi\)
\(252\) −1.26795 −0.0798733
\(253\) −5.19615 9.00000i −0.326679 0.565825i
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) 9.00000 0.563602
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.5981 + 20.0885i −0.723468 + 1.25308i 0.236133 + 0.971721i \(0.424120\pi\)
−0.959601 + 0.281363i \(0.909214\pi\)
\(258\) −2.09808 + 3.63397i −0.130621 + 0.226241i
\(259\) 3.80385 0.236360
\(260\) 0 0
\(261\) −3.00000 −0.185695
\(262\) 2.19615 3.80385i 0.135679 0.235002i
\(263\) −4.09808 + 7.09808i −0.252698 + 0.437686i −0.964268 0.264930i \(-0.914651\pi\)
0.711570 + 0.702616i \(0.247985\pi\)
\(264\) −0.633975 1.09808i −0.0390184 0.0675819i
\(265\) −5.19615 −0.319197
\(266\) −3.00000 5.19615i −0.183942 0.318597i
\(267\) −4.73205 8.19615i −0.289597 0.501596i
\(268\) −7.26795 −0.443961
\(269\) 3.80385 + 6.58846i 0.231925 + 0.401705i 0.958374 0.285514i \(-0.0921644\pi\)
−0.726450 + 0.687220i \(0.758831\pi\)
\(270\) −0.866025 + 1.50000i −0.0527046 + 0.0912871i
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 5.19615 0.315063
\(273\) 0 0
\(274\) 9.00000 0.543710
\(275\) −1.26795 + 2.19615i −0.0764602 + 0.132433i
\(276\) −4.09808 + 7.09808i −0.246675 + 0.427254i
\(277\) −2.40192 4.16025i −0.144318 0.249965i 0.784801 0.619748i \(-0.212765\pi\)
−0.929118 + 0.369783i \(0.879432\pi\)
\(278\) −4.00000 −0.239904
\(279\) 4.73205 + 8.19615i 0.283300 + 0.490691i
\(280\) −1.09808 1.90192i −0.0656226 0.113662i
\(281\) −17.5359 −1.04610 −0.523052 0.852301i \(-0.675207\pi\)
−0.523052 + 0.852301i \(0.675207\pi\)
\(282\) 2.36603 + 4.09808i 0.140895 + 0.244037i
\(283\) 9.90192 17.1506i 0.588608 1.01950i −0.405807 0.913959i \(-0.633009\pi\)
0.994415 0.105541i \(-0.0336573\pi\)
\(284\) −1.09808 + 1.90192i −0.0651588 + 0.112858i
\(285\) −8.19615 −0.485498
\(286\) 0 0
\(287\) 8.19615 0.483804
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −5.00000 + 8.66025i −0.294118 + 0.509427i
\(290\) −2.59808 4.50000i −0.152564 0.264249i
\(291\) 6.00000 0.351726
\(292\) 6.06218 + 10.5000i 0.354762 + 0.614466i
\(293\) 1.33013 + 2.30385i 0.0777069 + 0.134592i 0.902260 0.431192i \(-0.141907\pi\)
−0.824553 + 0.565784i \(0.808574\pi\)
\(294\) 5.39230 0.314486
\(295\) 12.0000 + 20.7846i 0.698667 + 1.21013i
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) −0.633975 + 1.09808i −0.0367869 + 0.0637168i
\(298\) −6.12436 −0.354774
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) −2.66025 + 4.60770i −0.153334 + 0.265583i
\(302\) 5.36603 9.29423i 0.308780 0.534823i
\(303\) 9.69615 + 16.7942i 0.557029 + 0.964803i
\(304\) −4.73205 −0.271402
\(305\) 13.1603 + 22.7942i 0.753554 + 1.30519i
\(306\) −2.59808 4.50000i −0.148522 0.257248i
\(307\) −7.26795 −0.414804 −0.207402 0.978256i \(-0.566501\pi\)
−0.207402 + 0.978256i \(0.566501\pi\)
\(308\) −0.803848 1.39230i −0.0458035 0.0793339i
\(309\) 3.09808 5.36603i 0.176243 0.305263i
\(310\) −8.19615 + 14.1962i −0.465510 + 0.806287i
\(311\) −8.19615 −0.464761 −0.232381 0.972625i \(-0.574651\pi\)
−0.232381 + 0.972625i \(0.574651\pi\)
\(312\) 0 0
\(313\) −3.60770 −0.203919 −0.101959 0.994789i \(-0.532511\pi\)
−0.101959 + 0.994789i \(0.532511\pi\)
\(314\) −3.59808 + 6.23205i −0.203051 + 0.351695i
\(315\) −1.09808 + 1.90192i −0.0618696 + 0.107161i
\(316\) −4.19615 7.26795i −0.236052 0.408854i
\(317\) 18.1244 1.01797 0.508983 0.860777i \(-0.330022\pi\)
0.508983 + 0.860777i \(0.330022\pi\)
\(318\) 1.50000 + 2.59808i 0.0841158 + 0.145693i
\(319\) −1.90192 3.29423i −0.106487 0.184441i
\(320\) −1.73205 −0.0968246
\(321\) −1.09808 1.90192i −0.0612886 0.106155i
\(322\) −5.19615 + 9.00000i −0.289570 + 0.501550i
\(323\) 12.2942 21.2942i 0.684069 1.18484i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −2.53590 −0.140450
\(327\) 2.19615 3.80385i 0.121448 0.210353i
\(328\) 3.23205 5.59808i 0.178460 0.309102i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) −2.19615 −0.120894
\(331\) 6.00000 + 10.3923i 0.329790 + 0.571213i 0.982470 0.186421i \(-0.0596888\pi\)
−0.652680 + 0.757634i \(0.726355\pi\)
\(332\) 2.83013 + 4.90192i 0.155323 + 0.269028i
\(333\) −3.00000 −0.164399
\(334\) −4.73205 8.19615i −0.258926 0.448474i
\(335\) −6.29423 + 10.9019i −0.343890 + 0.595636i
\(336\) −0.633975 + 1.09808i −0.0345861 + 0.0599050i
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) 0 0
\(339\) −0.803848 −0.0436590
\(340\) 4.50000 7.79423i 0.244047 0.422701i
\(341\) −6.00000 + 10.3923i −0.324918 + 0.562775i
\(342\) 2.36603 + 4.09808i 0.127940 + 0.221599i
\(343\) 15.7128 0.848412
\(344\) 2.09808 + 3.63397i 0.113121 + 0.195931i
\(345\) 7.09808 + 12.2942i 0.382148 + 0.661899i
\(346\) −4.39230 −0.236132
\(347\) −9.29423 16.0981i −0.498940 0.864190i 0.501059 0.865413i \(-0.332944\pi\)
−0.999999 + 0.00122316i \(0.999611\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) 4.73205 8.19615i 0.253301 0.438730i −0.711132 0.703059i \(-0.751817\pi\)
0.964433 + 0.264329i \(0.0851504\pi\)
\(350\) 2.53590 0.135549
\(351\) 0 0
\(352\) −1.26795 −0.0675819
\(353\) −17.8923 + 30.9904i −0.952311 + 1.64945i −0.211907 + 0.977290i \(0.567967\pi\)
−0.740404 + 0.672162i \(0.765366\pi\)
\(354\) 6.92820 12.0000i 0.368230 0.637793i
\(355\) 1.90192 + 3.29423i 0.100944 + 0.174840i
\(356\) −9.46410 −0.501596
\(357\) −3.29423 5.70577i −0.174349 0.301981i
\(358\) −1.09808 1.90192i −0.0580351 0.100520i
\(359\) 16.0526 0.847222 0.423611 0.905844i \(-0.360762\pi\)
0.423611 + 0.905844i \(0.360762\pi\)
\(360\) 0.866025 + 1.50000i 0.0456435 + 0.0790569i
\(361\) −1.69615 + 2.93782i −0.0892712 + 0.154622i
\(362\) −9.79423 + 16.9641i −0.514773 + 0.891613i
\(363\) 9.39230 0.492968
\(364\) 0 0
\(365\) 21.0000 1.09919
\(366\) 7.59808 13.1603i 0.397158 0.687897i
\(367\) 6.90192 11.9545i 0.360277 0.624019i −0.627729 0.778432i \(-0.716015\pi\)
0.988006 + 0.154413i \(0.0493487\pi\)
\(368\) 4.09808 + 7.09808i 0.213627 + 0.370013i
\(369\) −6.46410 −0.336508
\(370\) −2.59808 4.50000i −0.135068 0.233944i
\(371\) 1.90192 + 3.29423i 0.0987430 + 0.171028i
\(372\) 9.46410 0.490691
\(373\) 13.9904 + 24.2321i 0.724394 + 1.25469i 0.959223 + 0.282651i \(0.0912139\pi\)
−0.234828 + 0.972037i \(0.575453\pi\)
\(374\) 3.29423 5.70577i 0.170341 0.295038i
\(375\) 6.06218 10.5000i 0.313050 0.542218i
\(376\) 4.73205 0.244037
\(377\) 0 0
\(378\) 1.26795 0.0652163
\(379\) 15.1244 26.1962i 0.776886 1.34561i −0.156842 0.987624i \(-0.550131\pi\)
0.933728 0.357982i \(-0.116535\pi\)
\(380\) −4.09808 + 7.09808i −0.210227 + 0.364124i
\(381\) −2.00000 3.46410i −0.102463 0.177471i
\(382\) −20.7846 −1.06343
\(383\) −11.6603 20.1962i −0.595811 1.03198i −0.993432 0.114425i \(-0.963497\pi\)
0.397621 0.917550i \(-0.369836\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −2.78461 −0.141917
\(386\) −11.5981 20.0885i −0.590327 1.02248i
\(387\) 2.09808 3.63397i 0.106651 0.184725i
\(388\) 3.00000 5.19615i 0.152302 0.263795i
\(389\) 7.39230 0.374805 0.187402 0.982283i \(-0.439993\pi\)
0.187402 + 0.982283i \(0.439993\pi\)
\(390\) 0 0
\(391\) −42.5885 −2.15379
\(392\) 2.69615 4.66987i 0.136176 0.235864i
\(393\) −2.19615 + 3.80385i −0.110781 + 0.191879i
\(394\) −3.46410 6.00000i −0.174519 0.302276i
\(395\) −14.5359 −0.731380
\(396\) 0.633975 + 1.09808i 0.0318584 + 0.0551804i
\(397\) 2.19615 + 3.80385i 0.110222 + 0.190910i 0.915860 0.401499i \(-0.131511\pi\)
−0.805638 + 0.592408i \(0.798177\pi\)
\(398\) −22.5885 −1.13226
\(399\) 3.00000 + 5.19615i 0.150188 + 0.260133i
\(400\) 1.00000 1.73205i 0.0500000 0.0866025i
\(401\) 10.5000 18.1865i 0.524345 0.908192i −0.475253 0.879849i \(-0.657644\pi\)
0.999598 0.0283431i \(-0.00902310\pi\)
\(402\) 7.26795 0.362492
\(403\) 0 0
\(404\) 19.3923 0.964803
\(405\) 0.866025 1.50000i 0.0430331 0.0745356i
\(406\) −1.90192 + 3.29423i −0.0943909 + 0.163490i
\(407\) −1.90192 3.29423i −0.0942749 0.163289i
\(408\) −5.19615 −0.257248
\(409\) −10.3301 17.8923i −0.510792 0.884718i −0.999922 0.0125066i \(-0.996019\pi\)
0.489130 0.872211i \(-0.337314\pi\)
\(410\) −5.59808 9.69615i −0.276469 0.478859i
\(411\) −9.00000 −0.443937
\(412\) −3.09808 5.36603i −0.152631 0.264365i
\(413\) 8.78461 15.2154i 0.432262 0.748700i
\(414\) 4.09808 7.09808i 0.201409 0.348851i
\(415\) 9.80385 0.481252
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) 2.19615 3.80385i 0.107289 0.185830i −0.807382 0.590029i \(-0.799116\pi\)
0.914671 + 0.404199i \(0.132450\pi\)
\(420\) 1.09808 + 1.90192i 0.0535806 + 0.0928044i
\(421\) 6.46410 0.315041 0.157521 0.987516i \(-0.449650\pi\)
0.157521 + 0.987516i \(0.449650\pi\)
\(422\) 12.1962 + 21.1244i 0.593699 + 1.02832i
\(423\) −2.36603 4.09808i −0.115040 0.199255i
\(424\) 3.00000 0.145693
\(425\) 5.19615 + 9.00000i 0.252050 + 0.436564i
\(426\) 1.09808 1.90192i 0.0532020 0.0921485i
\(427\) 9.63397 16.6865i 0.466221 0.807518i
\(428\) −2.19615 −0.106155
\(429\) 0 0
\(430\) 7.26795 0.350492
\(431\) 19.0981 33.0788i 0.919922 1.59335i 0.120391 0.992727i \(-0.461585\pi\)
0.799531 0.600625i \(-0.205082\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −3.89230 6.74167i −0.187052 0.323984i 0.757214 0.653167i \(-0.226560\pi\)
−0.944266 + 0.329183i \(0.893227\pi\)
\(434\) 12.0000 0.576018
\(435\) 2.59808 + 4.50000i 0.124568 + 0.215758i
\(436\) −2.19615 3.80385i −0.105177 0.182171i
\(437\) 38.7846 1.85532
\(438\) −6.06218 10.5000i −0.289662 0.501709i
\(439\) 7.29423 12.6340i 0.348135 0.602987i −0.637784 0.770216i \(-0.720149\pi\)
0.985918 + 0.167229i \(0.0534819\pi\)
\(440\) −1.09808 + 1.90192i −0.0523487 + 0.0906707i
\(441\) −5.39230 −0.256776
\(442\) 0 0
\(443\) 16.3923 0.778822 0.389411 0.921064i \(-0.372679\pi\)
0.389411 + 0.921064i \(0.372679\pi\)
\(444\) −1.50000 + 2.59808i −0.0711868 + 0.123299i
\(445\) −8.19615 + 14.1962i −0.388535 + 0.672962i
\(446\) −2.53590 4.39230i −0.120078 0.207982i
\(447\) 6.12436 0.289672
\(448\) 0.633975 + 1.09808i 0.0299525 + 0.0518792i
\(449\) 13.2679 + 22.9808i 0.626153 + 1.08453i 0.988317 + 0.152415i \(0.0487049\pi\)
−0.362163 + 0.932115i \(0.617962\pi\)
\(450\) −2.00000 −0.0942809
\(451\) −4.09808 7.09808i −0.192971 0.334235i
\(452\) −0.401924 + 0.696152i −0.0189049 + 0.0327443i
\(453\) −5.36603 + 9.29423i −0.252118 + 0.436681i
\(454\) 20.1962 0.947852
\(455\) 0 0
\(456\) 4.73205 0.221599
\(457\) −15.9904 + 27.6962i −0.747998 + 1.29557i 0.200782 + 0.979636i \(0.435652\pi\)
−0.948781 + 0.315935i \(0.897682\pi\)
\(458\) −3.92820 + 6.80385i −0.183553 + 0.317923i
\(459\) 2.59808 + 4.50000i 0.121268 + 0.210042i
\(460\) 14.1962 0.661899
\(461\) 15.9904 + 27.6962i 0.744746 + 1.28994i 0.950313 + 0.311295i \(0.100763\pi\)
−0.205567 + 0.978643i \(0.565904\pi\)
\(462\) 0.803848 + 1.39230i 0.0373984 + 0.0647759i
\(463\) 15.8038 0.734467 0.367234 0.930129i \(-0.380305\pi\)
0.367234 + 0.930129i \(0.380305\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 8.19615 14.1962i 0.380087 0.658331i
\(466\) 9.00000 15.5885i 0.416917 0.722121i
\(467\) 5.41154 0.250416 0.125208 0.992130i \(-0.460040\pi\)
0.125208 + 0.992130i \(0.460040\pi\)
\(468\) 0 0
\(469\) 9.21539 0.425527
\(470\) 4.09808 7.09808i 0.189030 0.327410i
\(471\) 3.59808 6.23205i 0.165791 0.287158i
\(472\) −6.92820 12.0000i −0.318896 0.552345i
\(473\) 5.32051 0.244637
\(474\) 4.19615 + 7.26795i 0.192736 + 0.333828i
\(475\) −4.73205 8.19615i −0.217121 0.376065i
\(476\) −6.58846 −0.301981
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) 3.29423 5.70577i 0.150675 0.260976i
\(479\) −0.339746 + 0.588457i −0.0155234 + 0.0268873i −0.873683 0.486496i \(-0.838275\pi\)
0.858159 + 0.513383i \(0.171608\pi\)
\(480\) 1.73205 0.0790569
\(481\) 0 0
\(482\) −11.1962 −0.509971
\(483\) 5.19615 9.00000i 0.236433 0.409514i
\(484\) 4.69615 8.13397i 0.213461 0.369726i
\(485\) −5.19615 9.00000i −0.235945 0.408669i
\(486\) −1.00000 −0.0453609
\(487\) −7.56218 13.0981i −0.342675 0.593530i 0.642254 0.766492i \(-0.278000\pi\)
−0.984929 + 0.172962i \(0.944666\pi\)
\(488\) −7.59808 13.1603i −0.343949 0.595737i
\(489\) 2.53590 0.114677
\(490\) −4.66987 8.08846i −0.210963 0.365399i
\(491\) 15.2942 26.4904i 0.690219 1.19549i −0.281547 0.959547i \(-0.590848\pi\)
0.971766 0.235947i \(-0.0758191\pi\)
\(492\) −3.23205 + 5.59808i −0.145712 + 0.252381i
\(493\) −15.5885 −0.702069
\(494\) 0 0
\(495\) 2.19615 0.0987097
\(496\) 4.73205 8.19615i 0.212475 0.368018i
\(497\) 1.39230 2.41154i 0.0624534 0.108172i
\(498\) −2.83013 4.90192i −0.126821 0.219660i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −6.06218 10.5000i −0.271109 0.469574i
\(501\) 4.73205 + 8.19615i 0.211412 + 0.366177i
\(502\) 16.3923 0.731624
\(503\) −6.29423 10.9019i −0.280646 0.486093i 0.690898 0.722952i \(-0.257215\pi\)
−0.971544 + 0.236859i \(0.923882\pi\)
\(504\) 0.633975 1.09808i 0.0282395 0.0489122i
\(505\) 16.7942 29.0885i 0.747333 1.29442i
\(506\) 10.3923 0.461994
\(507\) 0 0
\(508\) −4.00000 −0.177471
\(509\) 13.3301 23.0885i 0.590847 1.02338i −0.403271 0.915081i \(-0.632127\pi\)
0.994119 0.108297i \(-0.0345398\pi\)
\(510\) −4.50000 + 7.79423i −0.199263 + 0.345134i
\(511\) −7.68653 13.3135i −0.340032 0.588953i
\(512\) 1.00000 0.0441942
\(513\) −2.36603 4.09808i −0.104463 0.180934i
\(514\) −11.5981 20.0885i −0.511569 0.886064i
\(515\) −10.7321 −0.472911
\(516\) −2.09808 3.63397i −0.0923627 0.159977i
\(517\) 3.00000 5.19615i 0.131940 0.228527i
\(518\) −1.90192 + 3.29423i −0.0835657 + 0.144740i
\(519\) 4.39230 0.192801
\(520\) 0 0
\(521\) −29.1962 −1.27911 −0.639553 0.768747i \(-0.720881\pi\)
−0.639553 + 0.768747i \(0.720881\pi\)
\(522\) 1.50000 2.59808i 0.0656532 0.113715i
\(523\) −16.2942 + 28.2224i −0.712497 + 1.23408i 0.251420 + 0.967878i \(0.419102\pi\)
−0.963917 + 0.266203i \(0.914231\pi\)
\(524\) 2.19615 + 3.80385i 0.0959394 + 0.166172i
\(525\) −2.53590 −0.110676
\(526\) −4.09808 7.09808i −0.178685 0.309491i
\(527\) 24.5885 + 42.5885i 1.07109 + 1.85518i
\(528\) 1.26795 0.0551804
\(529\) −22.0885 38.2583i −0.960368 1.66341i
\(530\) 2.59808 4.50000i 0.112853 0.195468i
\(531\) −6.92820 + 12.0000i −0.300658 + 0.520756i
\(532\) 6.00000 0.260133
\(533\) 0 0
\(534\) 9.46410 0.409552
\(535\) −1.90192 + 3.29423i −0.0822273 + 0.142422i
\(536\) 3.63397 6.29423i 0.156964 0.271869i
\(537\) 1.09808 + 1.90192i 0.0473855 + 0.0820741i
\(538\) −7.60770 −0.327991
\(539\) −3.41858 5.92116i −0.147249 0.255042i
\(540\) −0.866025 1.50000i −0.0372678 0.0645497i
\(541\) 10.8564 0.466753 0.233377 0.972386i \(-0.425022\pi\)
0.233377 + 0.972386i \(0.425022\pi\)
\(542\) 0 0
\(543\) 9.79423 16.9641i 0.420311 0.727999i
\(544\) −2.59808 + 4.50000i −0.111392 + 0.192936i
\(545\) −7.60770 −0.325878
\(546\) 0 0
\(547\) 4.19615 0.179415 0.0897073 0.995968i \(-0.471407\pi\)
0.0897073 + 0.995968i \(0.471407\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) −7.59808 + 13.1603i −0.324278 + 0.561666i
\(550\) −1.26795 2.19615i −0.0540655 0.0936443i
\(551\) 14.1962 0.604776
\(552\) −4.09808 7.09808i −0.174426 0.302114i
\(553\) 5.32051 + 9.21539i 0.226251 + 0.391878i
\(554\) 4.80385 0.204096
\(555\) 2.59808 + 4.50000i 0.110282 + 0.191014i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 12.8660 22.2846i 0.545151 0.944229i −0.453446 0.891284i \(-0.649806\pi\)
0.998597 0.0529457i \(-0.0168610\pi\)
\(558\) −9.46410 −0.400647
\(559\) 0 0
\(560\) 2.19615 0.0928044
\(561\) −3.29423 + 5.70577i −0.139082 + 0.240898i
\(562\) 8.76795 15.1865i 0.369854 0.640605i
\(563\) 16.3923 + 28.3923i 0.690853 + 1.19659i 0.971559 + 0.236799i \(0.0760983\pi\)
−0.280705 + 0.959794i \(0.590568\pi\)
\(564\) −4.73205 −0.199255
\(565\) 0.696152 + 1.20577i 0.0292874 + 0.0507272i
\(566\) 9.90192 + 17.1506i 0.416209 + 0.720895i
\(567\) −1.26795 −0.0532489
\(568\) −1.09808 1.90192i −0.0460743 0.0798029i
\(569\) −4.39230 + 7.60770i −0.184135 + 0.318931i −0.943285 0.331985i \(-0.892282\pi\)
0.759150 + 0.650916i \(0.225615\pi\)
\(570\) 4.09808 7.09808i 0.171650 0.297306i
\(571\) −24.1962 −1.01258 −0.506289 0.862364i \(-0.668983\pi\)
−0.506289 + 0.862364i \(0.668983\pi\)
\(572\) 0 0
\(573\) 20.7846 0.868290
\(574\) −4.09808 + 7.09808i −0.171050 + 0.296268i
\(575\) −8.19615 + 14.1962i −0.341803 + 0.592020i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 19.7321 0.821456 0.410728 0.911758i \(-0.365275\pi\)
0.410728 + 0.911758i \(0.365275\pi\)
\(578\) −5.00000 8.66025i −0.207973 0.360219i
\(579\) 11.5981 + 20.0885i 0.482000 + 0.834848i
\(580\) 5.19615 0.215758
\(581\) −3.58846 6.21539i −0.148874 0.257858i
\(582\) −3.00000 + 5.19615i −0.124354 + 0.215387i
\(583\) 1.90192 3.29423i 0.0787696 0.136433i
\(584\) −12.1244 −0.501709
\(585\) 0 0
\(586\) −2.66025 −0.109894
\(587\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(588\) −2.69615 + 4.66987i −0.111187 + 0.192582i
\(589\) −22.3923 38.7846i −0.922659 1.59809i
\(590\) −24.0000 −0.988064
\(591\) 3.46410 + 6.00000i 0.142494 + 0.246807i
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) 19.1436 0.786133 0.393067 0.919510i \(-0.371414\pi\)
0.393067 + 0.919510i \(0.371414\pi\)
\(594\) −0.633975 1.09808i −0.0260123 0.0450546i
\(595\) −5.70577 + 9.88269i −0.233914 + 0.405151i
\(596\) 3.06218 5.30385i 0.125432 0.217254i
\(597\) 22.5885 0.924484
\(598\) 0 0
\(599\) 16.3923 0.669771 0.334886 0.942259i \(-0.391302\pi\)
0.334886 + 0.942259i \(0.391302\pi\)
\(600\) −1.00000 + 1.73205i −0.0408248 + 0.0707107i
\(601\) 9.89230 17.1340i 0.403516 0.698909i −0.590632 0.806941i \(-0.701121\pi\)
0.994147 + 0.108032i \(0.0344548\pi\)
\(602\) −2.66025 4.60770i −0.108424 0.187796i
\(603\) −7.26795 −0.295974
\(604\) 5.36603 + 9.29423i 0.218340 + 0.378177i
\(605\) −8.13397 14.0885i −0.330693 0.572777i
\(606\) −19.3923 −0.787759
\(607\) 3.60770 + 6.24871i 0.146432 + 0.253627i 0.929906 0.367797i \(-0.119888\pi\)
−0.783474 + 0.621424i \(0.786554\pi\)
\(608\) 2.36603 4.09808i 0.0959550 0.166199i
\(609\) 1.90192 3.29423i 0.0770698 0.133489i
\(610\) −26.3205 −1.06569
\(611\) 0 0
\(612\) 5.19615 0.210042
\(613\) −6.57180 + 11.3827i −0.265432 + 0.459742i −0.967677 0.252194i \(-0.918848\pi\)
0.702244 + 0.711936i \(0.252181\pi\)
\(614\) 3.63397 6.29423i 0.146655 0.254014i
\(615\) 5.59808 + 9.69615i 0.225736 + 0.390987i
\(616\) 1.60770 0.0647759
\(617\) 15.6962 + 27.1865i 0.631903 + 1.09449i 0.987162 + 0.159721i \(0.0510594\pi\)
−0.355259 + 0.934768i \(0.615607\pi\)
\(618\) 3.09808 + 5.36603i 0.124623 + 0.215853i
\(619\) 28.3923 1.14118 0.570592 0.821234i \(-0.306714\pi\)
0.570592 + 0.821234i \(0.306714\pi\)
\(620\) −8.19615 14.1962i −0.329165 0.570131i
\(621\) −4.09808 + 7.09808i −0.164450 + 0.284836i
\(622\) 4.09808 7.09808i 0.164318 0.284607i
\(623\) 12.0000 0.480770
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 1.80385 3.12436i 0.0720962 0.124874i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −3.59808 6.23205i −0.143579 0.248686i
\(629\) −15.5885 −0.621552
\(630\) −1.09808 1.90192i −0.0437484 0.0757745i
\(631\) −0.928203 1.60770i −0.0369512 0.0640013i 0.846958 0.531659i \(-0.178431\pi\)
−0.883910 + 0.467658i \(0.845098\pi\)
\(632\) 8.39230 0.333828
\(633\) −12.1962 21.1244i −0.484754 0.839618i
\(634\) −9.06218 + 15.6962i −0.359905 + 0.623374i
\(635\) −3.46410 + 6.00000i −0.137469 + 0.238103i
\(636\) −3.00000 −0.118958
\(637\) 0 0
\(638\) 3.80385 0.150596
\(639\) −1.09808 + 1.90192i −0.0434392 + 0.0752389i
\(640\) 0.866025 1.50000i 0.0342327 0.0592927i
\(641\) 20.5981 + 35.6769i 0.813575 + 1.40915i 0.910347 + 0.413847i \(0.135815\pi\)
−0.0967715 + 0.995307i \(0.530852\pi\)
\(642\) 2.19615 0.0866752
\(643\) 13.8564 + 24.0000i 0.546443 + 0.946468i 0.998515 + 0.0544858i \(0.0173519\pi\)
−0.452071 + 0.891982i \(0.649315\pi\)
\(644\) −5.19615 9.00000i −0.204757 0.354650i
\(645\) −7.26795 −0.286175
\(646\) 12.2942 + 21.2942i 0.483710 + 0.837810i
\(647\) 24.5885 42.5885i 0.966672 1.67433i 0.261618 0.965172i \(-0.415744\pi\)
0.705054 0.709153i \(-0.250923\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −17.5692 −0.689652
\(650\) 0 0
\(651\) −12.0000 −0.470317
\(652\) 1.26795 2.19615i 0.0496567 0.0860080i
\(653\) −6.58846 + 11.4115i −0.257826 + 0.446568i −0.965659 0.259812i \(-0.916340\pi\)
0.707833 + 0.706380i \(0.249673\pi\)
\(654\) 2.19615 + 3.80385i 0.0858764 + 0.148742i
\(655\) 7.60770 0.297257
\(656\) 3.23205 + 5.59808i 0.126190 + 0.218568i
\(657\) 6.06218 + 10.5000i 0.236508 + 0.409644i
\(658\) −6.00000 −0.233904
\(659\) 18.5885 + 32.1962i 0.724103 + 1.25418i 0.959342 + 0.282246i \(0.0910796\pi\)
−0.235238 + 0.971938i \(0.575587\pi\)
\(660\) 1.09808 1.90192i 0.0427426 0.0740323i
\(661\) 4.50000 7.79423i 0.175030 0.303160i −0.765142 0.643862i \(-0.777331\pi\)
0.940172 + 0.340701i \(0.110665\pi\)
\(662\) −12.0000 −0.466393
\(663\) 0 0
\(664\) −5.66025 −0.219660
\(665\) 5.19615 9.00000i 0.201498 0.349005i
\(666\) 1.50000 2.59808i 0.0581238 0.100673i
\(667\) −12.2942 21.2942i −0.476034 0.824516i
\(668\) 9.46410 0.366177
\(669\) 2.53590 + 4.39230i 0.0980435 + 0.169816i
\(670\) −6.29423 10.9019i −0.243167 0.421178i
\(671\) −19.2679 −0.743831
\(672\) −0.633975 1.09808i −0.0244561 0.0423592i
\(673\) −0.500000 + 0.866025i −0.0192736 + 0.0333828i −0.875501 0.483216i \(-0.839469\pi\)
0.856228 + 0.516599i \(0.172802\pi\)
\(674\) 15.5000 26.8468i 0.597038 1.03410i
\(675\) 2.00000 0.0769800
\(676\) 0 0
\(677\) −16.3923 −0.630007 −0.315004 0.949090i \(-0.602006\pi\)
−0.315004 + 0.949090i \(0.602006\pi\)
\(678\) 0.401924 0.696152i 0.0154358 0.0267356i
\(679\) −3.80385 + 6.58846i −0.145978 + 0.252842i
\(680\) 4.50000 + 7.79423i 0.172567 + 0.298895i
\(681\) −20.1962 −0.773918
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) −13.8564 24.0000i −0.530201 0.918334i −0.999379 0.0352311i \(-0.988783\pi\)
0.469179 0.883103i \(-0.344550\pi\)
\(684\) −4.73205 −0.180934
\(685\) 7.79423 + 13.5000i 0.297802 + 0.515808i
\(686\) −7.85641 + 13.6077i −0.299959 + 0.519544i
\(687\) 3.92820 6.80385i 0.149870 0.259583i
\(688\) −4.19615 −0.159977
\(689\) 0 0
\(690\) −14.1962 −0.540438
\(691\) 12.7583 22.0981i 0.485350 0.840650i −0.514509 0.857485i \(-0.672026\pi\)
0.999858 + 0.0168348i \(0.00535894\pi\)
\(692\) 2.19615 3.80385i 0.0834852 0.144601i
\(693\) −0.803848 1.39230i −0.0305356 0.0528893i
\(694\) 18.5885 0.705608
\(695\) −3.46410 6.00000i −0.131401 0.227593i
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) −33.5885 −1.27225
\(698\) 4.73205 + 8.19615i 0.179111 + 0.310229i
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) −1.26795 + 2.19615i −0.0479240 + 0.0830068i
\(701\) −16.3923 −0.619129 −0.309564 0.950878i \(-0.600183\pi\)
−0.309564 + 0.950878i \(0.600183\pi\)
\(702\) 0 0
\(703\) 14.1962 0.535418
\(704\) 0.633975 1.09808i 0.0238938 0.0413853i
\(705\) −4.09808 + 7.09808i −0.154342 + 0.267329i
\(706\) −17.8923 30.9904i −0.673386 1.16634i
\(707\) −24.5885 −0.924744
\(708\) 6.92820 + 12.0000i 0.260378 + 0.450988i
\(709\) −22.6244 39.1865i −0.849676 1.47168i −0.881498 0.472188i \(-0.843464\pi\)
0.0318226 0.999494i \(-0.489869\pi\)
\(710\) −3.80385 −0.142756
\(711\) −4.19615 7.26795i −0.157368 0.272569i
\(712\) 4.73205 8.19615i 0.177341 0.307164i
\(713\) −38.7846 + 67.1769i −1.45250 + 2.51580i
\(714\) 6.58846 0.246567
\(715\) 0 0
\(716\) 2.19615 0.0820741
\(717\) −3.29423 + 5.70577i −0.123025 + 0.213086i
\(718\) −8.02628 + 13.9019i −0.299538 + 0.518815i
\(719\) −15.8038 27.3731i −0.589384 1.02084i −0.994313 0.106495i \(-0.966037\pi\)
0.404929 0.914348i \(-0.367296\pi\)
\(720\) −1.73205 −0.0645497
\(721\) 3.92820 + 6.80385i 0.146294 + 0.253389i
\(722\) −1.69615 2.93782i −0.0631243 0.109334i
\(723\) 11.1962 0.416389
\(724\) −9.79423 16.9641i −0.364000 0.630466i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) −4.69615 + 8.13397i −0.174291 + 0.301880i
\(727\) −13.8038 −0.511956 −0.255978 0.966683i \(-0.582398\pi\)
−0.255978 + 0.966683i \(0.582398\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −10.5000 + 18.1865i −0.388622 + 0.673114i
\(731\) 10.9019 18.8827i 0.403222 0.698401i
\(732\) 7.59808 + 13.1603i 0.280833 + 0.486417i
\(733\) −20.3205 −0.750555 −0.375278 0.926912i \(-0.622453\pi\)
−0.375278 + 0.926912i \(0.622453\pi\)
\(734\) 6.90192 + 11.9545i 0.254755 + 0.441248i
\(735\) 4.66987 + 8.08846i 0.172251 + 0.298347i
\(736\) −8.19615 −0.302114
\(737\) −4.60770 7.98076i −0.169727 0.293975i
\(738\) 3.23205 5.59808i 0.118973 0.206068i
\(739\) −2.53590 + 4.39230i −0.0932845 + 0.161574i −0.908891 0.417033i \(-0.863070\pi\)
0.815607 + 0.578607i \(0.196403\pi\)
\(740\) 5.19615 0.191014
\(741\) 0 0
\(742\) −3.80385 −0.139644
\(743\) −8.19615 + 14.1962i −0.300688 + 0.520806i −0.976292 0.216458i \(-0.930550\pi\)
0.675604 + 0.737264i \(0.263883\pi\)
\(744\) −4.73205 + 8.19615i −0.173485 + 0.300486i
\(745\) −5.30385 9.18653i −0.194318 0.336569i
\(746\) −27.9808 −1.02445
\(747\) 2.83013 + 4.90192i 0.103549 + 0.179352i
\(748\) 3.29423 + 5.70577i 0.120449 + 0.208624i
\(749\) 2.78461 0.101747
\(750\) 6.06218 + 10.5000i 0.221359 + 0.383406i
\(751\) −13.4904 + 23.3660i −0.492271 + 0.852638i −0.999960 0.00890181i \(-0.997166\pi\)
0.507689 + 0.861540i \(0.330500\pi\)
\(752\) −2.36603 + 4.09808i −0.0862801 + 0.149441i
\(753\) −16.3923 −0.597369
\(754\) 0 0
\(755\) 18.5885 0.676503
\(756\) −0.633975 + 1.09808i −0.0230574 + 0.0399366i
\(757\) 11.3923 19.7321i 0.414060 0.717174i −0.581269 0.813712i \(-0.697444\pi\)
0.995329 + 0.0965379i \(0.0307769\pi\)
\(758\) 15.1244 + 26.1962i 0.549341 + 0.951487i
\(759\) −10.3923 −0.377217
\(760\) −4.09808 7.09808i −0.148653 0.257474i
\(761\) 8.19615 + 14.1962i 0.297110 + 0.514610i 0.975474 0.220117i \(-0.0706438\pi\)
−0.678363 + 0.734727i \(0.737310\pi\)
\(762\) 4.00000 0.144905
\(763\) 2.78461 + 4.82309i 0.100810 + 0.174607i
\(764\) 10.3923 18.0000i 0.375980 0.651217i
\(765\) 4.50000 7.79423i 0.162698 0.281801i
\(766\) 23.3205 0.842604
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −10.8564 + 18.8038i −0.391492 + 0.678084i −0.992647 0.121049i \(-0.961374\pi\)
0.601155 + 0.799133i \(0.294708\pi\)
\(770\) 1.39230 2.41154i 0.0501752 0.0869060i
\(771\) 11.5981 + 20.0885i 0.417695 + 0.723468i
\(772\) 23.1962 0.834848
\(773\) −4.60770 7.98076i −0.165727 0.287048i 0.771186 0.636610i \(-0.219664\pi\)
−0.936913 + 0.349562i \(0.886330\pi\)
\(774\) 2.09808 + 3.63397i 0.0754138 + 0.130621i
\(775\) 18.9282 0.679921
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) 1.90192 3.29423i 0.0682311 0.118180i
\(778\) −3.69615 + 6.40192i −0.132513 + 0.229520i
\(779\) 30.5885 1.09595