Properties

Label 1014.2.e.g.529.2
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: \(x^{4} - x^{2} + 1\)
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 529.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.g.991.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.73205 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.73205 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.86603 + 3.23205i) q^{10} +(-0.633975 + 1.09808i) q^{11} +1.00000 q^{12} -2.73205 q^{14} +(-1.86603 + 3.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} +1.00000 q^{18} +(-2.36603 - 4.09808i) q^{19} +(-1.86603 - 3.23205i) q^{20} -2.73205 q^{21} +(-0.633975 - 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(-0.500000 + 0.866025i) q^{24} +8.92820 q^{25} +1.00000 q^{27} +(1.36603 - 2.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(-1.86603 - 3.23205i) q^{30} +1.46410 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.633975 - 1.09808i) q^{33} -5.73205 q^{34} +(5.09808 + 8.83013i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.76795 + 3.06218i) q^{37} +4.73205 q^{38} +3.73205 q^{40} +(4.69615 - 8.13397i) q^{41} +(1.36603 - 2.36603i) q^{42} +(4.83013 + 8.36603i) q^{43} +1.26795 q^{44} +(-1.86603 - 3.23205i) q^{45} +(-2.09808 - 3.63397i) q^{46} +2.19615 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.232051 + 0.401924i) q^{49} +(-4.46410 + 7.73205i) q^{50} -5.73205 q^{51} -6.46410 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(2.23205 + 3.86603i) q^{58} +(-4.00000 - 6.92820i) q^{59} +3.73205 q^{60} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} +(1.36603 - 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 + 11.3660i) q^{67} +(2.86603 - 4.96410i) q^{68} +(-2.09808 - 3.63397i) q^{69} -10.1962 q^{70} +(-2.36603 - 4.09808i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(-1.76795 - 3.06218i) q^{74} +(-4.46410 + 7.73205i) q^{75} +(-2.36603 + 4.09808i) q^{76} -3.46410 q^{77} -2.53590 q^{79} +(-1.86603 + 3.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.69615 + 8.13397i) q^{82} -0.196152 q^{83} +(1.36603 + 2.36603i) q^{84} +(10.6962 + 18.5263i) q^{85} -9.66025 q^{86} +(2.23205 + 3.86603i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(4.73205 - 8.19615i) q^{89} +3.73205 q^{90} +4.19615 q^{92} +(-0.732051 + 1.26795i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(-8.83013 - 15.2942i) q^{95} +1.00000 q^{96} +(3.00000 + 5.19615i) q^{97} +(-0.232051 - 0.401924i) q^{98} +1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{31} - 2 q^{32} - 6 q^{33} - 16 q^{34} + 10 q^{35} - 2 q^{36} - 14 q^{37} + 12 q^{38} + 8 q^{40} - 2 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - 4 q^{45} + 2 q^{46} - 12 q^{47} - 2 q^{48} + 6 q^{49} - 4 q^{50} - 16 q^{51} - 12 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 12 q^{57} + 2 q^{58} - 16 q^{59} + 8 q^{60} + 8 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 8 q^{68} + 2 q^{69} - 20 q^{70} - 6 q^{71} - 2 q^{72} - 32 q^{73} - 14 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{79} - 4 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} + 2 q^{84} + 22 q^{85} - 4 q^{86} + 2 q^{87} - 6 q^{88} + 12 q^{89} + 8 q^{90} - 4 q^{92} + 4 q^{93} + 6 q^{94} - 18 q^{95} + 4 q^{96} + 12 q^{97} + 6 q^{98} + 12 q^{99} + O(q^{100}) \)

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
\(5\) 3.73205 1.66902 0.834512 0.550990i \(-0.185750\pi\)
0.834512 + 0.550990i \(0.185750\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 1.36603 + 2.36603i 0.516309 + 0.894274i 0.999821 + 0.0189356i \(0.00602775\pi\)
−0.483512 + 0.875338i \(0.660639\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.86603 + 3.23205i −0.590089 + 1.02206i
\(11\) −0.633975 + 1.09808i −0.191151 + 0.331082i −0.945632 0.325239i \(-0.894555\pi\)
0.754481 + 0.656322i \(0.227889\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) −2.73205 −0.730171
\(15\) −1.86603 + 3.23205i −0.481806 + 0.834512i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.86603 + 4.96410i 0.695113 + 1.20397i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.36603 4.09808i −0.542803 0.940163i −0.998742 0.0501517i \(-0.984030\pi\)
0.455938 0.890011i \(-0.349304\pi\)
\(20\) −1.86603 3.23205i −0.417256 0.722709i
\(21\) −2.73205 −0.596182
\(22\) −0.633975 1.09808i −0.135164 0.234111i
\(23\) −2.09808 + 3.63397i −0.437479 + 0.757736i −0.997494 0.0707462i \(-0.977462\pi\)
0.560015 + 0.828482i \(0.310795\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 8.92820 1.78564
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.36603 2.36603i 0.258155 0.447137i
\(29\) 2.23205 3.86603i 0.414481 0.717903i −0.580892 0.813980i \(-0.697296\pi\)
0.995374 + 0.0960774i \(0.0306296\pi\)
\(30\) −1.86603 3.23205i −0.340688 0.590089i
\(31\) 1.46410 0.262960 0.131480 0.991319i \(-0.458027\pi\)
0.131480 + 0.991319i \(0.458027\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.633975 1.09808i −0.110361 0.191151i
\(34\) −5.73205 −0.983039
\(35\) 5.09808 + 8.83013i 0.861732 + 1.49256i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.76795 + 3.06218i −0.290649 + 0.503419i −0.973963 0.226705i \(-0.927205\pi\)
0.683314 + 0.730124i \(0.260538\pi\)
\(38\) 4.73205 0.767640
\(39\) 0 0
\(40\) 3.73205 0.590089
\(41\) 4.69615 8.13397i 0.733416 1.27031i −0.221999 0.975047i \(-0.571258\pi\)
0.955415 0.295267i \(-0.0954085\pi\)
\(42\) 1.36603 2.36603i 0.210782 0.365086i
\(43\) 4.83013 + 8.36603i 0.736587 + 1.27581i 0.954023 + 0.299732i \(0.0968974\pi\)
−0.217436 + 0.976075i \(0.569769\pi\)
\(44\) 1.26795 0.191151
\(45\) −1.86603 3.23205i −0.278171 0.481806i
\(46\) −2.09808 3.63397i −0.309344 0.535800i
\(47\) 2.19615 0.320342 0.160171 0.987089i \(-0.448795\pi\)
0.160171 + 0.987089i \(0.448795\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −0.232051 + 0.401924i −0.0331501 + 0.0574177i
\(50\) −4.46410 + 7.73205i −0.631319 + 1.09348i
\(51\) −5.73205 −0.802648
\(52\) 0 0
\(53\) −6.46410 −0.887913 −0.443956 0.896048i \(-0.646425\pi\)
−0.443956 + 0.896048i \(0.646425\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −2.36603 + 4.09808i −0.319035 + 0.552584i
\(56\) 1.36603 + 2.36603i 0.182543 + 0.316173i
\(57\) 4.73205 0.626775
\(58\) 2.23205 + 3.86603i 0.293083 + 0.507634i
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 3.73205 0.481806
\(61\) 4.59808 + 7.96410i 0.588723 + 1.01970i 0.994400 + 0.105682i \(0.0337026\pi\)
−0.405677 + 0.914017i \(0.632964\pi\)
\(62\) −0.732051 + 1.26795i −0.0929705 + 0.161030i
\(63\) 1.36603 2.36603i 0.172103 0.298091i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.26795 0.156074
\(67\) −6.56218 + 11.3660i −0.801698 + 1.38858i 0.116800 + 0.993155i \(0.462736\pi\)
−0.918498 + 0.395426i \(0.870597\pi\)
\(68\) 2.86603 4.96410i 0.347557 0.601986i
\(69\) −2.09808 3.63397i −0.252579 0.437479i
\(70\) −10.1962 −1.21867
\(71\) −2.36603 4.09808i −0.280796 0.486352i 0.690785 0.723060i \(-0.257265\pi\)
−0.971581 + 0.236708i \(0.923932\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −6.26795 −0.733608 −0.366804 0.930298i \(-0.619548\pi\)
−0.366804 + 0.930298i \(0.619548\pi\)
\(74\) −1.76795 3.06218i −0.205520 0.355971i
\(75\) −4.46410 + 7.73205i −0.515470 + 0.892820i
\(76\) −2.36603 + 4.09808i −0.271402 + 0.470082i
\(77\) −3.46410 −0.394771
\(78\) 0 0
\(79\) −2.53590 −0.285311 −0.142655 0.989772i \(-0.545564\pi\)
−0.142655 + 0.989772i \(0.545564\pi\)
\(80\) −1.86603 + 3.23205i −0.208628 + 0.361354i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.69615 + 8.13397i 0.518603 + 0.898247i
\(83\) −0.196152 −0.0215305 −0.0107653 0.999942i \(-0.503427\pi\)
−0.0107653 + 0.999942i \(0.503427\pi\)
\(84\) 1.36603 + 2.36603i 0.149046 + 0.258155i
\(85\) 10.6962 + 18.5263i 1.16016 + 2.00946i
\(86\) −9.66025 −1.04169
\(87\) 2.23205 + 3.86603i 0.239301 + 0.414481i
\(88\) −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 \(-0.000587067\pi\)
\(90\) 3.73205 0.393393
\(91\) 0 0
\(92\) 4.19615 0.437479
\(93\) −0.732051 + 1.26795i −0.0759101 + 0.131480i
\(94\) −1.09808 + 1.90192i −0.113258 + 0.196168i
\(95\) −8.83013 15.2942i −0.905952 1.56915i
\(96\) 1.00000 0.102062
\(97\) 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i \(-0.0681426\pi\)
−0.672569 + 0.740034i \(0.734809\pi\)
\(98\) −0.232051 0.401924i −0.0234407 0.0406004i
\(99\) 1.26795 0.127434
\(100\) −4.46410 7.73205i −0.446410 0.773205i
\(101\) −0.964102 + 1.66987i −0.0959317 + 0.166159i −0.909997 0.414615i \(-0.863916\pi\)
0.814065 + 0.580773i \(0.197250\pi\)
\(102\) 2.86603 4.96410i 0.283779 0.491519i
\(103\) −15.2679 −1.50440 −0.752198 0.658937i \(-0.771006\pi\)
−0.752198 + 0.658937i \(0.771006\pi\)
\(104\) 0 0
\(105\) −10.1962 −0.995043
\(106\) 3.23205 5.59808i 0.313925 0.543733i
\(107\) −5.09808 + 8.83013i −0.492850 + 0.853641i −0.999966 0.00823695i \(-0.997378\pi\)
0.507116 + 0.861878i \(0.330711\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 1.46410 0.140236 0.0701178 0.997539i \(-0.477662\pi\)
0.0701178 + 0.997539i \(0.477662\pi\)
\(110\) −2.36603 4.09808i −0.225592 0.390736i
\(111\) −1.76795 3.06218i −0.167806 0.290649i
\(112\) −2.73205 −0.258155
\(113\) 0.669873 + 1.16025i 0.0630163 + 0.109148i 0.895812 0.444432i \(-0.146595\pi\)
−0.832796 + 0.553580i \(0.813261\pi\)
\(114\) −2.36603 + 4.09808i −0.221599 + 0.383820i
\(115\) −7.83013 + 13.5622i −0.730163 + 1.26468i
\(116\) −4.46410 −0.414481
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) −7.83013 + 13.5622i −0.717787 + 1.24324i
\(120\) −1.86603 + 3.23205i −0.170344 + 0.295045i
\(121\) 4.69615 + 8.13397i 0.426923 + 0.739452i
\(122\) −9.19615 −0.832581
\(123\) 4.69615 + 8.13397i 0.423438 + 0.733416i
\(124\) −0.732051 1.26795i −0.0657401 0.113865i
\(125\) 14.6603 1.31125
\(126\) 1.36603 + 2.36603i 0.121695 + 0.210782i
\(127\) 4.92820 8.53590i 0.437307 0.757438i −0.560173 0.828375i \(-0.689266\pi\)
0.997481 + 0.0709368i \(0.0225989\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −9.66025 −0.850538
\(130\) 0 0
\(131\) 6.53590 0.571044 0.285522 0.958372i \(-0.407833\pi\)
0.285522 + 0.958372i \(0.407833\pi\)
\(132\) −0.633975 + 1.09808i −0.0551804 + 0.0955753i
\(133\) 6.46410 11.1962i 0.560509 0.970830i
\(134\) −6.56218 11.3660i −0.566886 0.981875i
\(135\) 3.73205 0.321204
\(136\) 2.86603 + 4.96410i 0.245760 + 0.425668i
\(137\) −5.96410 10.3301i −0.509548 0.882562i −0.999939 0.0110599i \(-0.996479\pi\)
0.490391 0.871502i \(-0.336854\pi\)
\(138\) 4.19615 0.357200
\(139\) −8.92820 15.4641i −0.757280 1.31165i −0.944233 0.329279i \(-0.893194\pi\)
0.186952 0.982369i \(-0.440139\pi\)
\(140\) 5.09808 8.83013i 0.430866 0.746282i
\(141\) −1.09808 + 1.90192i −0.0924747 + 0.160171i
\(142\) 4.73205 0.397105
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 8.33013 14.4282i 0.691779 1.19820i
\(146\) 3.13397 5.42820i 0.259370 0.449241i
\(147\) −0.232051 0.401924i −0.0191392 0.0331501i
\(148\) 3.53590 0.290649
\(149\) −6.59808 11.4282i −0.540535 0.936235i −0.998873 0.0474568i \(-0.984888\pi\)
0.458338 0.888778i \(-0.348445\pi\)
\(150\) −4.46410 7.73205i −0.364492 0.631319i
\(151\) 6.73205 0.547847 0.273923 0.961752i \(-0.411679\pi\)
0.273923 + 0.961752i \(0.411679\pi\)
\(152\) −2.36603 4.09808i −0.191910 0.332398i
\(153\) 2.86603 4.96410i 0.231704 0.401324i
\(154\) 1.73205 3.00000i 0.139573 0.241747i
\(155\) 5.46410 0.438887
\(156\) 0 0
\(157\) 7.58846 0.605625 0.302812 0.953050i \(-0.402074\pi\)
0.302812 + 0.953050i \(0.402074\pi\)
\(158\) 1.26795 2.19615i 0.100873 0.174717i
\(159\) 3.23205 5.59808i 0.256318 0.443956i
\(160\) −1.86603 3.23205i −0.147522 0.255516i
\(161\) −11.4641 −0.903498
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 6.73205 + 11.6603i 0.527295 + 0.913302i 0.999494 + 0.0318096i \(0.0101270\pi\)
−0.472199 + 0.881492i \(0.656540\pi\)
\(164\) −9.39230 −0.733416
\(165\) −2.36603 4.09808i −0.184195 0.319035i
\(166\) 0.0980762 0.169873i 0.00761219 0.0131847i
\(167\) 4.73205 8.19615i 0.366177 0.634237i −0.622787 0.782391i \(-0.714000\pi\)
0.988964 + 0.148154i \(0.0473331\pi\)
\(168\) −2.73205 −0.210782
\(169\) 0 0
\(170\) −21.3923 −1.64071
\(171\) −2.36603 + 4.09808i −0.180934 + 0.313388i
\(172\) 4.83013 8.36603i 0.368294 0.637903i
\(173\) −2.19615 3.80385i −0.166970 0.289201i 0.770383 0.637582i \(-0.220065\pi\)
−0.937353 + 0.348380i \(0.886732\pi\)
\(174\) −4.46410 −0.338423
\(175\) 12.1962 + 21.1244i 0.921942 + 1.59685i
\(176\) −0.633975 1.09808i −0.0477876 0.0827706i
\(177\) 8.00000 0.601317
\(178\) 4.73205 + 8.19615i 0.354682 + 0.614328i
\(179\) 8.02628 13.9019i 0.599912 1.03908i −0.392921 0.919572i \(-0.628535\pi\)
0.992833 0.119506i \(-0.0381312\pi\)
\(180\) −1.86603 + 3.23205i −0.139085 + 0.240903i
\(181\) 19.1962 1.42684 0.713419 0.700737i \(-0.247145\pi\)
0.713419 + 0.700737i \(0.247145\pi\)
\(182\) 0 0
\(183\) −9.19615 −0.679799
\(184\) −2.09808 + 3.63397i −0.154672 + 0.267900i
\(185\) −6.59808 + 11.4282i −0.485100 + 0.840218i
\(186\) −0.732051 1.26795i −0.0536766 0.0929705i
\(187\) −7.26795 −0.531485
\(188\) −1.09808 1.90192i −0.0800854 0.138712i
\(189\) 1.36603 + 2.36603i 0.0993637 + 0.172103i
\(190\) 17.6603 1.28121
\(191\) 3.46410 + 6.00000i 0.250654 + 0.434145i 0.963706 0.266966i \(-0.0860212\pi\)
−0.713052 + 0.701111i \(0.752688\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 5.86603 10.1603i 0.422246 0.731351i −0.573913 0.818916i \(-0.694575\pi\)
0.996159 + 0.0875652i \(0.0279086\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 0.464102 0.0331501
\(197\) 8.92820 15.4641i 0.636108 1.10177i −0.350171 0.936686i \(-0.613877\pi\)
0.986279 0.165086i \(-0.0527901\pi\)
\(198\) −0.633975 + 1.09808i −0.0450546 + 0.0780369i
\(199\) 7.09808 + 12.2942i 0.503169 + 0.871515i 0.999993 + 0.00366345i \(0.00116611\pi\)
−0.496824 + 0.867851i \(0.665501\pi\)
\(200\) 8.92820 0.631319
\(201\) −6.56218 11.3660i −0.462860 0.801698i
\(202\) −0.964102 1.66987i −0.0678340 0.117492i
\(203\) 12.1962 0.856002
\(204\) 2.86603 + 4.96410i 0.200662 + 0.347557i
\(205\) 17.5263 30.3564i 1.22409 2.12018i
\(206\) 7.63397 13.2224i 0.531884 0.921250i
\(207\) 4.19615 0.291653
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) 5.09808 8.83013i 0.351801 0.609337i
\(211\) −8.19615 + 14.1962i −0.564246 + 0.977303i 0.432873 + 0.901455i \(0.357500\pi\)
−0.997119 + 0.0758485i \(0.975833\pi\)
\(212\) 3.23205 + 5.59808i 0.221978 + 0.384477i
\(213\) 4.73205 0.324235
\(214\) −5.09808 8.83013i −0.348497 0.603615i
\(215\) 18.0263 + 31.2224i 1.22938 + 2.12935i
\(216\) 1.00000 0.0680414
\(217\) 2.00000 + 3.46410i 0.135769 + 0.235159i
\(218\) −0.732051 + 1.26795i −0.0495807 + 0.0858764i
\(219\) 3.13397 5.42820i 0.211774 0.366804i
\(220\) 4.73205 0.319035
\(221\) 0 0
\(222\) 3.53590 0.237314
\(223\) 13.4641 23.3205i 0.901623 1.56166i 0.0762356 0.997090i \(-0.475710\pi\)
0.825387 0.564567i \(-0.190957\pi\)
\(224\) 1.36603 2.36603i 0.0912714 0.158087i
\(225\) −4.46410 7.73205i −0.297607 0.515470i
\(226\) −1.33975 −0.0891186
\(227\) 6.09808 + 10.5622i 0.404744 + 0.701036i 0.994292 0.106697i \(-0.0340275\pi\)
−0.589548 + 0.807733i \(0.700694\pi\)
\(228\) −2.36603 4.09808i −0.156694 0.271402i
\(229\) −11.8564 −0.783493 −0.391747 0.920073i \(-0.628129\pi\)
−0.391747 + 0.920073i \(0.628129\pi\)
\(230\) −7.83013 13.5622i −0.516303 0.894264i
\(231\) 1.73205 3.00000i 0.113961 0.197386i
\(232\) 2.23205 3.86603i 0.146541 0.253817i
\(233\) −7.85641 −0.514690 −0.257345 0.966320i \(-0.582848\pi\)
−0.257345 + 0.966320i \(0.582848\pi\)
\(234\) 0 0
\(235\) 8.19615 0.534658
\(236\) −4.00000 + 6.92820i −0.260378 + 0.450988i
\(237\) 1.26795 2.19615i 0.0823622 0.142655i
\(238\) −7.83013 13.5622i −0.507552 0.879105i
\(239\) 7.66025 0.495501 0.247750 0.968824i \(-0.420309\pi\)
0.247750 + 0.968824i \(0.420309\pi\)
\(240\) −1.86603 3.23205i −0.120451 0.208628i
\(241\) −6.79423 11.7679i −0.437655 0.758040i 0.559853 0.828592i \(-0.310857\pi\)
−0.997508 + 0.0705514i \(0.977524\pi\)
\(242\) −9.39230 −0.603760
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 4.59808 7.96410i 0.294362 0.509849i
\(245\) −0.866025 + 1.50000i −0.0553283 + 0.0958315i
\(246\) −9.39230 −0.598831
\(247\) 0 0
\(248\) 1.46410 0.0929705
\(249\) 0.0980762 0.169873i 0.00621533 0.0107653i
\(250\) −7.33013 + 12.6962i −0.463598 + 0.802975i
\(251\) −6.73205 11.6603i −0.424923 0.735989i 0.571490 0.820609i \(-0.306366\pi\)
−0.996413 + 0.0846203i \(0.973032\pi\)
\(252\) −2.73205 −0.172103
\(253\) −2.66025 4.60770i −0.167249 0.289683i
\(254\) 4.92820 + 8.53590i 0.309223 + 0.535590i
\(255\) −21.3923 −1.33964
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.66987 + 8.08846i −0.291299 + 0.504544i −0.974117 0.226044i \(-0.927421\pi\)
0.682818 + 0.730588i \(0.260754\pi\)
\(258\) 4.83013 8.36603i 0.300711 0.520846i
\(259\) −9.66025 −0.600259
\(260\) 0 0
\(261\) −4.46410 −0.276321
\(262\) −3.26795 + 5.66025i −0.201895 + 0.349692i
\(263\) 5.02628 8.70577i 0.309934 0.536821i −0.668414 0.743790i \(-0.733026\pi\)
0.978348 + 0.206969i \(0.0663598\pi\)
\(264\) −0.633975 1.09808i −0.0390184 0.0675819i
\(265\) −24.1244 −1.48195
\(266\) 6.46410 + 11.1962i 0.396339 + 0.686480i
\(267\) 4.73205 + 8.19615i 0.289597 + 0.501596i
\(268\) 13.1244 0.801698
\(269\) −2.73205 4.73205i −0.166576 0.288518i 0.770638 0.637273i \(-0.219938\pi\)
−0.937214 + 0.348755i \(0.886604\pi\)
\(270\) −1.86603 + 3.23205i −0.113563 + 0.196696i
\(271\) 10.9282 18.9282i 0.663841 1.14981i −0.315757 0.948840i \(-0.602258\pi\)
0.979598 0.200966i \(-0.0644082\pi\)
\(272\) −5.73205 −0.347557
\(273\) 0 0
\(274\) 11.9282 0.720609
\(275\) −5.66025 + 9.80385i −0.341326 + 0.591194i
\(276\) −2.09808 + 3.63397i −0.126289 + 0.218740i
\(277\) 2.86603 + 4.96410i 0.172203 + 0.298264i 0.939190 0.343399i \(-0.111578\pi\)
−0.766987 + 0.641663i \(0.778245\pi\)
\(278\) 17.8564 1.07096
\(279\) −0.732051 1.26795i −0.0438267 0.0759101i
\(280\) 5.09808 + 8.83013i 0.304668 + 0.527701i
\(281\) 12.3205 0.734980 0.367490 0.930027i \(-0.380217\pi\)
0.367490 + 0.930027i \(0.380217\pi\)
\(282\) −1.09808 1.90192i −0.0653895 0.113258i
\(283\) −12.8301 + 22.2224i −0.762672 + 1.32099i 0.178797 + 0.983886i \(0.442780\pi\)
−0.941469 + 0.337100i \(0.890554\pi\)
\(284\) −2.36603 + 4.09808i −0.140398 + 0.243176i
\(285\) 17.6603 1.04610
\(286\) 0 0
\(287\) 25.6603 1.51468
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −7.92820 + 13.7321i −0.466365 + 0.807768i
\(290\) 8.33013 + 14.4282i 0.489162 + 0.847253i
\(291\) −6.00000 −0.351726
\(292\) 3.13397 + 5.42820i 0.183402 + 0.317662i
\(293\) −15.2583 26.4282i −0.891401 1.54395i −0.838196 0.545368i \(-0.816390\pi\)
−0.0532048 0.998584i \(-0.516944\pi\)
\(294\) 0.464102 0.0270670
\(295\) −14.9282 25.8564i −0.869154 1.50542i
\(296\) −1.76795 + 3.06218i −0.102760 + 0.177985i
\(297\) −0.633975 + 1.09808i −0.0367869 + 0.0637168i
\(298\) 13.1962 0.764433
\(299\) 0 0
\(300\) 8.92820 0.515470
\(301\) −13.1962 + 22.8564i −0.760614 + 1.31742i
\(302\) −3.36603 + 5.83013i −0.193693 + 0.335486i
\(303\) −0.964102 1.66987i −0.0553862 0.0959317i
\(304\) 4.73205 0.271402
\(305\) 17.1603 + 29.7224i 0.982593 + 1.70190i
\(306\) 2.86603 + 4.96410i 0.163840 + 0.283779i
\(307\) −22.5885 −1.28919 −0.644596 0.764524i \(-0.722974\pi\)
−0.644596 + 0.764524i \(0.722974\pi\)
\(308\) 1.73205 + 3.00000i 0.0986928 + 0.170941i
\(309\) 7.63397 13.2224i 0.434282 0.752198i
\(310\) −2.73205 + 4.73205i −0.155170 + 0.268762i
\(311\) −1.66025 −0.0941444 −0.0470722 0.998891i \(-0.514989\pi\)
−0.0470722 + 0.998891i \(0.514989\pi\)
\(312\) 0 0
\(313\) 6.53590 0.369431 0.184715 0.982792i \(-0.440864\pi\)
0.184715 + 0.982792i \(0.440864\pi\)
\(314\) −3.79423 + 6.57180i −0.214121 + 0.370868i
\(315\) 5.09808 8.83013i 0.287244 0.497521i
\(316\) 1.26795 + 2.19615i 0.0713277 + 0.123543i
\(317\) 20.6603 1.16040 0.580198 0.814476i \(-0.302975\pi\)
0.580198 + 0.814476i \(0.302975\pi\)
\(318\) 3.23205 + 5.59808i 0.181244 + 0.313925i
\(319\) 2.83013 + 4.90192i 0.158457 + 0.274455i
\(320\) 3.73205 0.208628
\(321\) −5.09808 8.83013i −0.284547 0.492850i
\(322\) 5.73205 9.92820i 0.319435 0.553277i
\(323\) 13.5622 23.4904i 0.754620 1.30704i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −13.4641 −0.745708
\(327\) −0.732051 + 1.26795i −0.0404825 + 0.0701178i
\(328\) 4.69615 8.13397i 0.259302 0.449124i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 4.73205 0.260491
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 0.0980762 + 0.169873i 0.00538263 + 0.00932299i
\(333\) 3.53590 0.193766
\(334\) 4.73205 + 8.19615i 0.258926 + 0.448474i
\(335\) −24.4904 + 42.4186i −1.33805 + 2.31757i
\(336\) 1.36603 2.36603i 0.0745228 0.129077i
\(337\) −20.8564 −1.13612 −0.568060 0.822987i \(-0.692306\pi\)
−0.568060 + 0.822987i \(0.692306\pi\)
\(338\) 0 0
\(339\) −1.33975 −0.0727650
\(340\) 10.6962 18.5263i 0.580080 1.00473i
\(341\) −0.928203 + 1.60770i −0.0502650 + 0.0870616i
\(342\) −2.36603 4.09808i −0.127940 0.221599i
\(343\) 17.8564 0.964155
\(344\) 4.83013 + 8.36603i 0.260423 + 0.451066i
\(345\) −7.83013 13.5622i −0.421560 0.730163i
\(346\) 4.39230 0.236132
\(347\) −16.5622 28.6865i −0.889104 1.53997i −0.840936 0.541135i \(-0.817995\pi\)
−0.0481683 0.998839i \(-0.515338\pi\)
\(348\) 2.23205 3.86603i 0.119650 0.207241i
\(349\) −7.66025 + 13.2679i −0.410044 + 0.710217i −0.994894 0.100924i \(-0.967820\pi\)
0.584850 + 0.811141i \(0.301153\pi\)
\(350\) −24.3923 −1.30382
\(351\) 0 0
\(352\) 1.26795 0.0675819
\(353\) 10.8923 18.8660i 0.579739 1.00414i −0.415770 0.909470i \(-0.636488\pi\)
0.995509 0.0946674i \(-0.0301788\pi\)
\(354\) −4.00000 + 6.92820i −0.212598 + 0.368230i
\(355\) −8.83013 15.2942i −0.468654 0.811733i
\(356\) −9.46410 −0.501596
\(357\) −7.83013 13.5622i −0.414414 0.717787i
\(358\) 8.02628 + 13.9019i 0.424202 + 0.734740i
\(359\) −1.12436 −0.0593412 −0.0296706 0.999560i \(-0.509446\pi\)
−0.0296706 + 0.999560i \(0.509446\pi\)
\(360\) −1.86603 3.23205i −0.0983482 0.170344i
\(361\) −1.69615 + 2.93782i −0.0892712 + 0.154622i
\(362\) −9.59808 + 16.6244i −0.504464 + 0.873757i
\(363\) −9.39230 −0.492968
\(364\) 0 0
\(365\) −23.3923 −1.22441
\(366\) 4.59808 7.96410i 0.240345 0.416290i
\(367\) 5.63397 9.75833i 0.294091 0.509381i −0.680682 0.732579i \(-0.738316\pi\)
0.974773 + 0.223198i \(0.0716498\pi\)
\(368\) −2.09808 3.63397i −0.109370 0.189434i
\(369\) −9.39230 −0.488944
\(370\) −6.59808 11.4282i −0.343018 0.594124i
\(371\) −8.83013 15.2942i −0.458437 0.794037i
\(372\) 1.46410 0.0759101
\(373\) 6.86603 + 11.8923i 0.355509 + 0.615760i 0.987205 0.159456i \(-0.0509741\pi\)
−0.631696 + 0.775216i \(0.717641\pi\)
\(374\) 3.63397 6.29423i 0.187908 0.325467i
\(375\) −7.33013 + 12.6962i −0.378526 + 0.655626i
\(376\) 2.19615 0.113258
\(377\) 0 0
\(378\) −2.73205 −0.140522
\(379\) 2.73205 4.73205i 0.140336 0.243069i −0.787287 0.616587i \(-0.788515\pi\)
0.927623 + 0.373517i \(0.121848\pi\)
\(380\) −8.83013 + 15.2942i −0.452976 + 0.784577i
\(381\) 4.92820 + 8.53590i 0.252479 + 0.437307i
\(382\) −6.92820 −0.354478
\(383\) 0.732051 + 1.26795i 0.0374060 + 0.0647892i 0.884122 0.467255i \(-0.154757\pi\)
−0.846716 + 0.532045i \(0.821424\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) −12.9282 −0.658882
\(386\) 5.86603 + 10.1603i 0.298573 + 0.517143i
\(387\) 4.83013 8.36603i 0.245529 0.425269i
\(388\) 3.00000 5.19615i 0.152302 0.263795i
\(389\) 11.7846 0.597503 0.298752 0.954331i \(-0.403430\pi\)
0.298752 + 0.954331i \(0.403430\pi\)
\(390\) 0 0
\(391\) −24.0526 −1.21639
\(392\) −0.232051 + 0.401924i −0.0117203 + 0.0203002i
\(393\) −3.26795 + 5.66025i −0.164846 + 0.285522i
\(394\) 8.92820 + 15.4641i 0.449796 + 0.779070i
\(395\) −9.46410 −0.476191
\(396\) −0.633975 1.09808i −0.0318584 0.0551804i
\(397\) −10.1962 17.6603i −0.511730 0.886343i −0.999908 0.0135983i \(-0.995671\pi\)
0.488177 0.872744i \(-0.337662\pi\)
\(398\) −14.1962 −0.711589
\(399\) 6.46410 + 11.1962i 0.323610 + 0.560509i
\(400\) −4.46410 + 7.73205i −0.223205 + 0.386603i
\(401\) −4.03590 + 6.99038i −0.201543 + 0.349083i −0.949026 0.315198i \(-0.897929\pi\)
0.747483 + 0.664281i \(0.231262\pi\)
\(402\) 13.1244 0.654583
\(403\) 0 0
\(404\) 1.92820 0.0959317
\(405\) −1.86603 + 3.23205i −0.0927235 + 0.160602i
\(406\) −6.09808 + 10.5622i −0.302642 + 0.524192i
\(407\) −2.24167 3.88269i −0.111115 0.192458i
\(408\) −5.73205 −0.283779
\(409\) −8.86603 15.3564i −0.438397 0.759325i 0.559169 0.829053i \(-0.311120\pi\)
−0.997566 + 0.0697281i \(0.977787\pi\)
\(410\) 17.5263 + 30.3564i 0.865561 + 1.49920i
\(411\) 11.9282 0.588375
\(412\) 7.63397 + 13.2224i 0.376099 + 0.651422i
\(413\) 10.9282 18.9282i 0.537742 0.931396i
\(414\) −2.09808 + 3.63397i −0.103115 + 0.178600i
\(415\) −0.732051 −0.0359350
\(416\) 0 0
\(417\) 17.8564 0.874432
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) 8.73205 15.1244i 0.426589 0.738873i −0.569979 0.821659i \(-0.693049\pi\)
0.996567 + 0.0827863i \(0.0263819\pi\)
\(420\) 5.09808 + 8.83013i 0.248761 + 0.430866i
\(421\) −22.7128 −1.10695 −0.553477 0.832864i \(-0.686699\pi\)
−0.553477 + 0.832864i \(0.686699\pi\)
\(422\) −8.19615 14.1962i −0.398982 0.691058i
\(423\) −1.09808 1.90192i −0.0533903 0.0924747i
\(424\) −6.46410 −0.313925
\(425\) 25.5885 + 44.3205i 1.24122 + 2.14986i
\(426\) −2.36603 + 4.09808i −0.114634 + 0.198552i
\(427\) −12.5622 + 21.7583i −0.607926 + 1.05296i
\(428\) 10.1962 0.492850
\(429\) 0 0
\(430\) −36.0526 −1.73861
\(431\) −6.56218 + 11.3660i −0.316089 + 0.547482i −0.979668 0.200624i \(-0.935703\pi\)
0.663579 + 0.748106i \(0.269036\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −6.42820 11.1340i −0.308920 0.535065i 0.669207 0.743076i \(-0.266634\pi\)
−0.978126 + 0.208012i \(0.933301\pi\)
\(434\) −4.00000 −0.192006
\(435\) 8.33013 + 14.4282i 0.399399 + 0.691779i
\(436\) −0.732051 1.26795i −0.0350589 0.0607238i
\(437\) 19.8564 0.949861
\(438\) 3.13397 + 5.42820i 0.149747 + 0.259370i
\(439\) 0.169873 0.294229i 0.00810760 0.0140428i −0.861943 0.507005i \(-0.830753\pi\)
0.870051 + 0.492962i \(0.164086\pi\)
\(440\) −2.36603 + 4.09808i −0.112796 + 0.195368i
\(441\) 0.464102 0.0221001
\(442\) 0 0
\(443\) 15.6077 0.741544 0.370772 0.928724i \(-0.379093\pi\)
0.370772 + 0.928724i \(0.379093\pi\)
\(444\) −1.76795 + 3.06218i −0.0839032 + 0.145325i
\(445\) 17.6603 30.5885i 0.837176 1.45003i
\(446\) 13.4641 + 23.3205i 0.637544 + 1.10426i
\(447\) 13.1962 0.624157
\(448\) 1.36603 + 2.36603i 0.0645386 + 0.111784i
\(449\) −5.66025 9.80385i −0.267124 0.462672i 0.700994 0.713167i \(-0.252740\pi\)
−0.968118 + 0.250495i \(0.919407\pi\)
\(450\) 8.92820 0.420880
\(451\) 5.95448 + 10.3135i 0.280386 + 0.485642i
\(452\) 0.669873 1.16025i 0.0315082 0.0545738i
\(453\) −3.36603 + 5.83013i −0.158150 + 0.273923i
\(454\) −12.1962 −0.572394
\(455\) 0 0
\(456\) 4.73205 0.221599
\(457\) −0.669873 + 1.16025i −0.0313353 + 0.0542744i −0.881268 0.472617i \(-0.843309\pi\)
0.849932 + 0.526892i \(0.176643\pi\)
\(458\) 5.92820 10.2679i 0.277007 0.479790i
\(459\) 2.86603 + 4.96410i 0.133775 + 0.231704i
\(460\) 15.6603 0.730163
\(461\) −11.1340 19.2846i −0.518561 0.898174i −0.999767 0.0215666i \(-0.993135\pi\)
0.481207 0.876607i \(-0.340199\pi\)
\(462\) 1.73205 + 3.00000i 0.0805823 + 0.139573i
\(463\) 10.0526 0.467182 0.233591 0.972335i \(-0.424952\pi\)
0.233591 + 0.972335i \(0.424952\pi\)
\(464\) 2.23205 + 3.86603i 0.103620 + 0.179476i
\(465\) −2.73205 + 4.73205i −0.126696 + 0.219444i
\(466\) 3.92820 6.80385i 0.181971 0.315182i
\(467\) 18.5885 0.860171 0.430086 0.902788i \(-0.358483\pi\)
0.430086 + 0.902788i \(0.358483\pi\)
\(468\) 0 0
\(469\) −35.8564 −1.65570
\(470\) −4.09808 + 7.09808i −0.189030 + 0.327410i
\(471\) −3.79423 + 6.57180i −0.174829 + 0.302812i
\(472\) −4.00000 6.92820i −0.184115 0.318896i
\(473\) −12.2487 −0.563196
\(474\) 1.26795 + 2.19615i 0.0582388 + 0.100873i
\(475\) −21.1244 36.5885i −0.969252 1.67879i
\(476\) 15.6603 0.717787
\(477\) 3.23205 + 5.59808i 0.147985 + 0.256318i
\(478\) −3.83013 + 6.63397i −0.175186 + 0.303431i
\(479\) −16.7321 + 28.9808i −0.764507 + 1.32416i 0.176000 + 0.984390i \(0.443684\pi\)
−0.940507 + 0.339775i \(0.889649\pi\)
\(480\) 3.73205 0.170344
\(481\) 0 0
\(482\) 13.5885 0.618937
\(483\) 5.73205 9.92820i 0.260817 0.451749i
\(484\) 4.69615 8.13397i 0.213461 0.369726i
\(485\) 11.1962 + 19.3923i 0.508391 + 0.880559i
\(486\) 1.00000 0.0453609
\(487\) 1.56218 + 2.70577i 0.0707890 + 0.122610i 0.899247 0.437441i \(-0.144115\pi\)
−0.828458 + 0.560051i \(0.810782\pi\)
\(488\) 4.59808 + 7.96410i 0.208145 + 0.360518i
\(489\) −13.4641 −0.608868
\(490\) −0.866025 1.50000i −0.0391230 0.0677631i
\(491\) −4.36603 + 7.56218i −0.197036 + 0.341276i −0.947566 0.319560i \(-0.896465\pi\)
0.750530 + 0.660836i \(0.229798\pi\)
\(492\) 4.69615 8.13397i 0.211719 0.366708i
\(493\) 25.5885 1.15245
\(494\) 0 0
\(495\) 4.73205 0.212690
\(496\) −0.732051 + 1.26795i −0.0328701 + 0.0569326i
\(497\) 6.46410 11.1962i 0.289955 0.502216i
\(498\) 0.0980762 + 0.169873i 0.00439490 + 0.00761219i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) −7.33013 12.6962i −0.327813 0.567789i
\(501\) 4.73205 + 8.19615i 0.211412 + 0.366177i
\(502\) 13.4641 0.600932
\(503\) −20.4904 35.4904i −0.913621 1.58244i −0.808908 0.587935i \(-0.799941\pi\)
−0.104713 0.994502i \(-0.533392\pi\)
\(504\) 1.36603 2.36603i 0.0608476 0.105391i
\(505\) −3.59808 + 6.23205i −0.160112 + 0.277323i
\(506\) 5.32051 0.236525
\(507\) 0 0
\(508\) −9.85641 −0.437307
\(509\) −6.86603 + 11.8923i −0.304331 + 0.527117i −0.977112 0.212725i \(-0.931766\pi\)
0.672781 + 0.739842i \(0.265100\pi\)
\(510\) 10.6962 18.5263i 0.473634 0.820357i
\(511\) −8.56218 14.8301i −0.378768 0.656046i
\(512\) 1.00000 0.0441942
\(513\) −2.36603 4.09808i −0.104463 0.180934i
\(514\) −4.66987 8.08846i −0.205979 0.356767i
\(515\) −56.9808 −2.51087
\(516\) 4.83013 + 8.36603i 0.212634 + 0.368294i
\(517\) −1.39230 + 2.41154i −0.0612335 + 0.106060i
\(518\) 4.83013 8.36603i 0.212224 0.367582i
\(519\) 4.39230 0.192801
\(520\) 0 0
\(521\) 41.4449 1.81573 0.907866 0.419260i \(-0.137710\pi\)
0.907866 + 0.419260i \(0.137710\pi\)
\(522\) 2.23205 3.86603i 0.0976942 0.169211i
\(523\) 11.2224 19.4378i 0.490723 0.849957i −0.509220 0.860636i \(-0.670066\pi\)
0.999943 + 0.0106796i \(0.00339949\pi\)
\(524\) −3.26795 5.66025i −0.142761 0.247269i
\(525\) −24.3923 −1.06457
\(526\) 5.02628 + 8.70577i 0.219156 + 0.379590i
\(527\) 4.19615 + 7.26795i 0.182787 + 0.316597i
\(528\) 1.26795 0.0551804
\(529\) 2.69615 + 4.66987i 0.117224 + 0.203038i
\(530\) 12.0622 20.8923i 0.523948 0.907504i
\(531\) −4.00000 + 6.92820i −0.173585 + 0.300658i
\(532\) −12.9282 −0.560509
\(533\) 0 0
\(534\) −9.46410 −0.409552
\(535\) −19.0263 + 32.9545i −0.822578 + 1.42475i
\(536\) −6.56218 + 11.3660i −0.283443 + 0.490938i
\(537\) 8.02628 + 13.9019i 0.346360 + 0.599912i
\(538\) 5.46410 0.235574
\(539\) −0.294229 0.509619i −0.0126733 0.0219508i
\(540\) −1.86603 3.23205i −0.0803009 0.139085i
\(541\) 5.67949 0.244180 0.122090 0.992519i \(-0.461040\pi\)
0.122090 + 0.992519i \(0.461040\pi\)
\(542\) 10.9282 + 18.9282i 0.469407 + 0.813036i
\(543\) −9.59808 + 16.6244i −0.411893 + 0.713419i
\(544\) 2.86603 4.96410i 0.122880 0.212834i
\(545\) 5.46410 0.234056
\(546\) 0 0
\(547\) −4.19615 −0.179415 −0.0897073 0.995968i \(-0.528593\pi\)
−0.0897073 + 0.995968i \(0.528593\pi\)
\(548\) −5.96410 + 10.3301i −0.254774 + 0.441281i
\(549\) 4.59808 7.96410i 0.196241 0.339900i
\(550\) −5.66025 9.80385i −0.241354 0.418037i
\(551\) −21.1244 −0.899928
\(552\) −2.09808 3.63397i −0.0893001 0.154672i
\(553\) −3.46410 6.00000i −0.147309 0.255146i
\(554\) −5.73205 −0.243532
\(555\) −6.59808 11.4282i −0.280073 0.485100i
\(556\) −8.92820 + 15.4641i −0.378640 + 0.655824i
\(557\) −21.1865 + 36.6962i −0.897702 + 1.55487i −0.0672780 + 0.997734i \(0.521431\pi\)
−0.830424 + 0.557132i \(0.811902\pi\)
\(558\) 1.46410 0.0619804
\(559\) 0 0
\(560\) −10.1962 −0.430866
\(561\) 3.63397 6.29423i 0.153427 0.265743i
\(562\) −6.16025 + 10.6699i −0.259855 + 0.450081i
\(563\) −17.4641 30.2487i −0.736024 1.27483i −0.954273 0.298938i \(-0.903368\pi\)
0.218248 0.975893i \(-0.429966\pi\)
\(564\) 2.19615 0.0924747
\(565\) 2.50000 + 4.33013i 0.105176 + 0.182170i
\(566\) −12.8301 22.2224i −0.539290 0.934078i
\(567\) −2.73205 −0.114735
\(568\) −2.36603 4.09808i −0.0992762 0.171951i
\(569\) −15.3205 + 26.5359i −0.642269 + 1.11244i 0.342656 + 0.939461i \(0.388674\pi\)
−0.984925 + 0.172982i \(0.944660\pi\)
\(570\) −8.83013 + 15.2942i −0.369853 + 0.640605i
\(571\) 14.0526 0.588081 0.294041 0.955793i \(-0.405000\pi\)
0.294041 + 0.955793i \(0.405000\pi\)
\(572\) 0 0
\(573\) −6.92820 −0.289430
\(574\) −12.8301 + 22.2224i −0.535519 + 0.927546i
\(575\) −18.7321 + 32.4449i −0.781181 + 1.35304i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 3.73205 0.155367 0.0776837 0.996978i \(-0.475248\pi\)
0.0776837 + 0.996978i \(0.475248\pi\)
\(578\) −7.92820 13.7321i −0.329770 0.571178i
\(579\) 5.86603 + 10.1603i 0.243784 + 0.422246i
\(580\) −16.6603 −0.691779
\(581\) −0.267949 0.464102i −0.0111164 0.0192542i
\(582\) 3.00000 5.19615i 0.124354 0.215387i
\(583\) 4.09808 7.09808i 0.169725 0.293972i
\(584\) −6.26795 −0.259370
\(585\) 0 0
\(586\) 30.5167 1.26063
\(587\) −8.00000 + 13.8564i −0.330195 + 0.571915i −0.982550 0.185999i \(-0.940448\pi\)
0.652355 + 0.757914i \(0.273781\pi\)
\(588\) −0.232051 + 0.401924i −0.00956961 + 0.0165751i
\(589\) −3.46410 6.00000i −0.142736 0.247226i
\(590\) 29.8564 1.22917
\(591\) 8.92820 + 15.4641i 0.367257 + 0.636108i
\(592\) −1.76795 3.06218i −0.0726623 0.125855i
\(593\) −9.14359 −0.375482 −0.187741 0.982219i \(-0.560117\pi\)
−0.187741 + 0.982219i \(0.560117\pi\)
\(594\) −0.633975 1.09808i −0.0260123 0.0450546i
\(595\) −29.2224 + 50.6147i −1.19800 + 2.07500i
\(596\) −6.59808 + 11.4282i −0.270268 + 0.468117i
\(597\) −14.1962 −0.581010
\(598\) 0 0
\(599\) −2.53590 −0.103614 −0.0518070 0.998657i \(-0.516498\pi\)
−0.0518070 + 0.998657i \(0.516498\pi\)
\(600\) −4.46410 + 7.73205i −0.182246 + 0.315660i
\(601\) −3.96410 + 6.86603i −0.161699 + 0.280071i −0.935478 0.353385i \(-0.885031\pi\)
0.773779 + 0.633456i \(0.218364\pi\)
\(602\) −13.1962 22.8564i −0.537835 0.931558i
\(603\) 13.1244 0.534465
\(604\) −3.36603 5.83013i −0.136962 0.237225i
\(605\) 17.5263 + 30.3564i 0.712545 + 1.23416i
\(606\) 1.92820 0.0783279
\(607\) 20.3923 + 35.3205i 0.827698 + 1.43362i 0.899840 + 0.436221i \(0.143683\pi\)
−0.0721415 + 0.997394i \(0.522983\pi\)
\(608\) −2.36603 + 4.09808i −0.0959550 + 0.166199i
\(609\) −6.09808 + 10.5622i −0.247107 + 0.428001i
\(610\) −34.3205 −1.38960
\(611\) 0 0
\(612\) −5.73205 −0.231704
\(613\) 4.69615 8.13397i 0.189676 0.328528i −0.755466 0.655187i \(-0.772590\pi\)
0.945142 + 0.326659i \(0.105923\pi\)
\(614\) 11.2942 19.5622i 0.455798 0.789465i
\(615\) 17.5263 + 30.3564i 0.706728 + 1.22409i
\(616\) −3.46410 −0.139573
\(617\) 6.62436 + 11.4737i 0.266687 + 0.461915i 0.968004 0.250934i \(-0.0807378\pi\)
−0.701318 + 0.712849i \(0.747404\pi\)
\(618\) 7.63397 + 13.2224i 0.307083 + 0.531884i
\(619\) 17.4641 0.701942 0.350971 0.936386i \(-0.385852\pi\)
0.350971 + 0.936386i \(0.385852\pi\)
\(620\) −2.73205 4.73205i −0.109722 0.190044i
\(621\) −2.09808 + 3.63397i −0.0841929 + 0.145826i
\(622\) 0.830127 1.43782i 0.0332851 0.0576514i
\(623\) 25.8564 1.03592
\(624\) 0 0
\(625\) 10.0718 0.402872
\(626\) −3.26795 + 5.66025i −0.130614 + 0.226229i
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) −3.79423 6.57180i −0.151406 0.262243i
\(629\) −20.2679 −0.808136
\(630\) 5.09808 + 8.83013i 0.203112 + 0.351801i
\(631\) 3.85641 + 6.67949i 0.153521 + 0.265906i 0.932520 0.361119i \(-0.117605\pi\)
−0.778998 + 0.627026i \(0.784272\pi\)
\(632\) −2.53590 −0.100873
\(633\) −8.19615 14.1962i −0.325768 0.564246i
\(634\) −10.3301 + 17.8923i −0.410262 + 0.710594i
\(635\) 18.3923 31.8564i 0.729876 1.26418i
\(636\) −6.46410 −0.256318
\(637\) 0 0
\(638\) −5.66025 −0.224092
\(639\) −2.36603 + 4.09808i −0.0935985 + 0.162117i
\(640\) −1.86603 + 3.23205i −0.0737611 + 0.127758i
\(641\) 12.9904 + 22.5000i 0.513089 + 0.888697i 0.999885 + 0.0151806i \(0.00483233\pi\)
−0.486796 + 0.873516i \(0.661834\pi\)
\(642\) 10.1962 0.402410
\(643\) 6.92820 + 12.0000i 0.273222 + 0.473234i 0.969685 0.244359i \(-0.0785774\pi\)
−0.696463 + 0.717592i \(0.745244\pi\)
\(644\) 5.73205 + 9.92820i 0.225874 + 0.391226i
\(645\) −36.0526 −1.41957
\(646\) 13.5622 + 23.4904i 0.533597 + 0.924217i
\(647\) 11.1244 19.2679i 0.437344 0.757501i −0.560140 0.828398i \(-0.689253\pi\)
0.997484 + 0.0708966i \(0.0225860\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 10.1436 0.398171
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 6.73205 11.6603i 0.263647 0.456651i
\(653\) 8.73205 15.1244i 0.341712 0.591862i −0.643039 0.765833i \(-0.722327\pi\)
0.984751 + 0.173972i \(0.0556601\pi\)
\(654\) −0.732051 1.26795i −0.0286255 0.0495807i
\(655\) 24.3923 0.953086
\(656\) 4.69615 + 8.13397i 0.183354 + 0.317578i
\(657\) 3.13397 + 5.42820i 0.122268 + 0.211774i
\(658\) −6.00000 −0.233904
\(659\) 5.12436 + 8.87564i 0.199617 + 0.345746i 0.948404 0.317064i \(-0.102697\pi\)
−0.748788 + 0.662810i \(0.769364\pi\)
\(660\) −2.36603 + 4.09808i −0.0920974 + 0.159517i
\(661\) −5.69615 + 9.86603i −0.221555 + 0.383744i −0.955280 0.295702i \(-0.904446\pi\)
0.733726 + 0.679446i \(0.237780\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) −0.196152 −0.00761219
\(665\) 24.1244 41.7846i 0.935502 1.62034i
\(666\) −1.76795 + 3.06218i −0.0685066 + 0.118657i
\(667\) 9.36603 + 16.2224i 0.362654 + 0.628135i
\(668\) −9.46410 −0.366177
\(669\) 13.4641 + 23.3205i 0.520552 + 0.901623i
\(670\) −24.4904 42.4186i −0.946146 1.63877i
\(671\) −11.6603 −0.450139
\(672\) 1.36603 + 2.36603i 0.0526956 + 0.0912714i
\(673\) −13.9641 + 24.1865i −0.538277 + 0.932322i 0.460720 + 0.887545i \(0.347591\pi\)
−0.998997 + 0.0447770i \(0.985742\pi\)
\(674\) 10.4282 18.0622i 0.401679 0.695729i
\(675\) 8.92820 0.343647
\(676\) 0 0
\(677\) −45.4641 −1.74733 −0.873664 0.486530i \(-0.838262\pi\)
−0.873664 + 0.486530i \(0.838262\pi\)
\(678\) 0.669873 1.16025i 0.0257263 0.0445593i
\(679\) −8.19615 + 14.1962i −0.314539 + 0.544798i
\(680\) 10.6962 + 18.5263i 0.410179 + 0.710450i
\(681\) −12.1962 −0.467358
\(682\) −0.928203 1.60770i −0.0355427 0.0615618i
\(683\) 5.07180 + 8.78461i 0.194067 + 0.336134i 0.946594 0.322427i \(-0.104499\pi\)
−0.752527 + 0.658561i \(0.771165\pi\)
\(684\) 4.73205 0.180934
\(685\) −22.2583 38.5526i −0.850447 1.47302i
\(686\) −8.92820 + 15.4641i −0.340880 + 0.590422i
\(687\) 5.92820 10.2679i 0.226175 0.391747i
\(688\) −9.66025 −0.368294
\(689\) 0 0
\(690\) 15.6603 0.596176
\(691\) −21.8301 + 37.8109i −0.830457 + 1.43839i 0.0672190 + 0.997738i \(0.478587\pi\)
−0.897676 + 0.440656i \(0.854746\pi\)
\(692\) −2.19615 + 3.80385i −0.0834852 + 0.144601i
\(693\) 1.73205 + 3.00000i 0.0657952 + 0.113961i
\(694\) 33.1244 1.25738
\(695\) −33.3205 57.7128i −1.26392 2.18917i
\(696\) 2.23205 + 3.86603i 0.0846057 + 0.146541i
\(697\) 53.8372 2.03923
\(698\) −7.66025 13.2679i −0.289945 0.502199i
\(699\) 3.92820 6.80385i 0.148578 0.257345i
\(700\) 12.1962 21.1244i 0.460971 0.798426i
\(701\) −3.32051 −0.125414 −0.0627069 0.998032i \(-0.519973\pi\)
−0.0627069 + 0.998032i \(0.519973\pi\)
\(702\) 0 0
\(703\) 16.7321 0.631061
\(704\) −0.633975 + 1.09808i −0.0238938 + 0.0413853i
\(705\) −4.09808 + 7.09808i −0.154342 + 0.267329i
\(706\) 10.8923 + 18.8660i 0.409937 + 0.710032i
\(707\) −5.26795 −0.198122
\(708\) −4.00000 6.92820i −0.150329 0.260378i
\(709\) −6.57180 11.3827i −0.246809 0.427486i 0.715830 0.698275i \(-0.246049\pi\)
−0.962639 + 0.270789i \(0.912715\pi\)
\(710\) 17.6603 0.662778
\(711\) 1.26795 + 2.19615i 0.0475518 + 0.0823622i
\(712\) 4.73205 8.19615i 0.177341 0.307164i
\(713\) −3.07180 + 5.32051i −0.115040 + 0.199255i
\(714\) 15.6603 0.586070
\(715\) 0 0
\(716\) −16.0526 −0.599912
\(717\) −3.83013 + 6.63397i −0.143039 + 0.247750i
\(718\) 0.562178 0.973721i 0.0209803 0.0363389i
\(719\) 14.7321 + 25.5167i 0.549413 + 0.951611i 0.998315 + 0.0580299i \(0.0184819\pi\)
−0.448902 + 0.893581i \(0.648185\pi\)
\(720\) 3.73205 0.139085
\(721\) −20.8564 36.1244i −0.776733 1.34534i
\(722\) −1.69615 2.93782i −0.0631243 0.109334i
\(723\) 13.5885 0.505360
\(724\) −9.59808 16.6244i −0.356710 0.617839i
\(725\) 19.9282 34.5167i 0.740115 1.28192i
\(726\) 4.69615 8.13397i 0.174291 0.301880i
\(727\) −30.9808 −1.14901 −0.574506 0.818500i \(-0.694806\pi\)
−0.574506 + 0.818500i \(0.694806\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 11.6962 20.2583i 0.432894 0.749794i
\(731\) −27.6865 + 47.9545i −1.02402 + 1.77366i
\(732\) 4.59808 + 7.96410i 0.169950 + 0.294362i
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 5.63397 + 9.75833i 0.207954 + 0.360187i
\(735\) −0.866025 1.50000i −0.0319438 0.0553283i
\(736\) 4.19615 0.154672
\(737\) −8.32051 14.4115i −0.306490 0.530856i
\(738\) 4.69615 8.13397i 0.172868 0.299416i
\(739\) −1.46410 + 2.53590i −0.0538578 + 0.0932845i −0.891697 0.452632i \(-0.850485\pi\)
0.837840 + 0.545917i \(0.183818\pi\)
\(740\) 13.1962 0.485100
\(741\) 0 0
\(742\) 17.6603 0.648328
\(743\) 24.1962 41.9090i 0.887671 1.53749i 0.0450491 0.998985i \(-0.485656\pi\)
0.842622 0.538506i \(-0.181011\pi\)
\(744\) −0.732051 + 1.26795i −0.0268383 + 0.0464853i
\(745\) −24.6244 42.6506i −0.902167 1.56260i
\(746\) −13.7321 −0.502766
\(747\) 0.0980762 + 0.169873i 0.00358842 + 0.00621533i
\(748\) 3.63397 + 6.29423i 0.132871 + 0.230140i
\(749\) −27.8564 −1.01785
\(750\) −7.33013 12.6962i −0.267658 0.463598i
\(751\) 24.9545 43.2224i 0.910602 1.57721i 0.0973862 0.995247i \(-0.468952\pi\)
0.813216 0.581962i \(-0.197715\pi\)
\(752\) −1.09808 + 1.90192i −0.0400427 + 0.0693560i
\(753\) 13.4641 0.490659
\(754\) 0 0
\(755\) 25.1244 0.914369
\(756\) 1.36603 2.36603i 0.0496819 0.0860515i
\(757\) −10.4641 + 18.1244i −0.380324 + 0.658741i −0.991109 0.133056i \(-0.957521\pi\)
0.610784 + 0.791797i \(0.290854\pi\)
\(758\) 2.73205 + 4.73205i 0.0992326 + 0.171876i
\(759\) 5.32051 0.193122
\(760\) −8.83013 15.2942i −0.320302 0.554780i
\(761\) −5.66025 9.80385i −0.205184 0.355389i 0.745007 0.667056i \(-0.232446\pi\)
−0.950191 + 0.311667i \(0.899113\pi\)
\(762\) −9.85641 −0.357060
\(763\) 2.00000 + 3.46410i 0.0724049 + 0.125409i
\(764\) 3.46410 6.00000i 0.125327 0.217072i
\(765\) 10.6962 18.5263i 0.386720 0.669819i
\(766\) −1.46410 −0.0529001
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 21.9282 37.9808i 0.790751 1.36962i −0.134751 0.990879i \(-0.543023\pi\)
0.925502 0.378742i \(-0.123643\pi\)
\(770\) 6.46410 11.1962i 0.232950 0.403481i
\(771\) −4.66987 8.08846i −0.168181 0.291299i
\(772\) −11.7321 −0.422246
\(773\) 24.4641 + 42.3731i 0.879913 + 1.52405i 0.851436 + 0.524459i \(0.175732\pi\)
0.0284768 + 0.999594i \(0.490934\pi\)
\(774\) 4.83013 + 8.36603i 0.173615 + 0.300711i
\(775\) 13.0718 0.469553
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) 4.83013 8.36603i 0.173280 0.300129i
\(778\) −5.89230 + 10.2058i −0.211249 + 0.365895i
\(779\) −44.4449 −1.59240
\(780\) 0