Properties

Label 1950.2.y.b.49.1
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.b.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.09808 - 0.633975i) q^{11} -1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.96410 - 2.86603i) q^{17} -1.00000 q^{18} +(-4.09808 - 2.36603i) q^{19} -2.73205i q^{21} +(-1.09808 - 0.633975i) q^{22} +(3.63397 - 2.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} +1.00000i q^{27} +(-1.36603 - 2.36603i) q^{28} +(-2.23205 - 3.86603i) q^{29} -1.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.633975 + 1.09808i) q^{33} +5.73205i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.76795 + 3.06218i) q^{37} +4.73205i q^{38} +(0.866025 - 3.50000i) q^{39} +(8.13397 - 4.69615i) q^{41} +(-2.36603 + 1.36603i) q^{42} +(8.36603 + 4.83013i) q^{43} +1.26795i q^{44} +(-3.63397 - 2.09808i) q^{46} -2.19615 q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.232051 - 0.401924i) q^{49} +5.73205 q^{51} +(-1.00000 - 3.46410i) q^{52} +6.46410i q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(-2.23205 + 3.86603i) q^{58} +(6.92820 + 4.00000i) q^{59} +(4.59808 - 7.96410i) q^{61} +(-1.26795 + 0.732051i) q^{62} +(1.36603 + 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 - 11.3660i) q^{67} +(4.96410 - 2.86603i) q^{68} +(-2.09808 + 3.63397i) q^{69} +(4.09808 + 2.36603i) q^{71} +(0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(1.76795 - 3.06218i) q^{74} +(4.09808 - 2.36603i) q^{76} +3.46410i q^{77} +(-3.46410 + 1.00000i) q^{78} +2.53590 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.13397 - 4.69615i) q^{82} +0.196152 q^{83} +(2.36603 + 1.36603i) q^{84} -9.66025i q^{86} +(3.86603 + 2.23205i) q^{87} +(1.09808 - 0.633975i) q^{88} +(8.19615 - 4.73205i) q^{89} +(-2.73205 - 9.46410i) q^{91} +4.19615i q^{92} +(0.732051 + 1.26795i) q^{93} +(1.09808 + 1.90192i) q^{94} -1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.232051 + 0.401924i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33} + 2 q^{36} + 14 q^{37} + 36 q^{41} - 6 q^{42} + 30 q^{43} - 18 q^{46} + 12 q^{47} + 6 q^{49} + 16 q^{51} - 4 q^{52} - 2 q^{56} + 12 q^{57} - 2 q^{58} + 8 q^{61} - 12 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 6 q^{68} + 2 q^{69} + 6 q^{71} + 2 q^{72} - 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} - 36 q^{82} - 20 q^{83} + 6 q^{84} + 12 q^{87} - 6 q^{88} + 12 q^{89} - 4 q^{91} - 4 q^{93} - 6 q^{94} + 12 q^{97} + 6 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −1.36603 + 2.36603i −0.516309 + 0.894274i 0.483512 + 0.875338i \(0.339361\pi\)
−0.999821 + 0.0189356i \(0.993972\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 1.09808 0.633975i 0.331082 0.191151i −0.325239 0.945632i \(-0.605445\pi\)
0.656322 + 0.754481i \(0.272111\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 2.73205 0.730171
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.96410 2.86603i −1.20397 0.695113i −0.242536 0.970143i \(-0.577979\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.09808 2.36603i −0.940163 0.542803i −0.0501517 0.998742i \(-0.515970\pi\)
−0.890011 + 0.455938i \(0.849304\pi\)
\(20\) 0 0
\(21\) 2.73205i 0.596182i
\(22\) −1.09808 0.633975i −0.234111 0.135164i
\(23\) 3.63397 2.09808i 0.757736 0.437479i −0.0707462 0.997494i \(-0.522538\pi\)
0.828482 + 0.560015i \(0.189205\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.50000 + 0.866025i 0.686406 + 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) −1.36603 2.36603i −0.258155 0.447137i
\(29\) −2.23205 3.86603i −0.414481 0.717903i 0.580892 0.813980i \(-0.302704\pi\)
−0.995374 + 0.0960774i \(0.969370\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i −0.991319 0.131480i \(-0.958027\pi\)
0.991319 0.131480i \(-0.0419730\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.633975 + 1.09808i −0.110361 + 0.191151i
\(34\) 5.73205i 0.983039i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 1.76795 + 3.06218i 0.290649 + 0.503419i 0.973963 0.226705i \(-0.0727955\pi\)
−0.683314 + 0.730124i \(0.739462\pi\)
\(38\) 4.73205i 0.767640i
\(39\) 0.866025 3.50000i 0.138675 0.560449i
\(40\) 0 0
\(41\) 8.13397 4.69615i 1.27031 0.733416i 0.295267 0.955415i \(-0.404592\pi\)
0.975047 + 0.221999i \(0.0712582\pi\)
\(42\) −2.36603 + 1.36603i −0.365086 + 0.210782i
\(43\) 8.36603 + 4.83013i 1.27581 + 0.736587i 0.976075 0.217436i \(-0.0697693\pi\)
0.299732 + 0.954023i \(0.403103\pi\)
\(44\) 1.26795i 0.191151i
\(45\) 0 0
\(46\) −3.63397 2.09808i −0.535800 0.309344i
\(47\) −2.19615 −0.320342 −0.160171 0.987089i \(-0.551205\pi\)
−0.160171 + 0.987089i \(0.551205\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −0.232051 0.401924i −0.0331501 0.0574177i
\(50\) 0 0
\(51\) 5.73205 0.802648
\(52\) −1.00000 3.46410i −0.138675 0.480384i
\(53\) 6.46410i 0.887913i 0.896048 + 0.443956i \(0.146425\pi\)
−0.896048 + 0.443956i \(0.853575\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.36603 + 2.36603i −0.182543 + 0.316173i
\(57\) 4.73205 0.626775
\(58\) −2.23205 + 3.86603i −0.293083 + 0.507634i
\(59\) 6.92820 + 4.00000i 0.901975 + 0.520756i 0.877841 0.478953i \(-0.158984\pi\)
0.0241347 + 0.999709i \(0.492317\pi\)
\(60\) 0 0
\(61\) 4.59808 7.96410i 0.588723 1.01970i −0.405677 0.914017i \(-0.632964\pi\)
0.994400 0.105682i \(-0.0337026\pi\)
\(62\) −1.26795 + 0.732051i −0.161030 + 0.0929705i
\(63\) 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 −0.918498 0.395426i \(-0.870597\pi\)
0.116800 0.993155i \(-0.462736\pi\)
\(68\) 4.96410 2.86603i 0.601986 0.347557i
\(69\) −2.09808 + 3.63397i −0.252579 + 0.437479i
\(70\) 0 0
\(71\) 4.09808 + 2.36603i 0.486352 + 0.280796i 0.723060 0.690785i \(-0.242735\pi\)
−0.236708 + 0.971581i \(0.576068\pi\)
\(72\) 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
\(75\) 0 0
\(76\) 4.09808 2.36603i 0.470082 0.271402i
\(77\) 3.46410i 0.394771i
\(78\) −3.46410 + 1.00000i −0.392232 + 0.113228i
\(79\) 2.53590 0.285311 0.142655 0.989772i \(-0.454436\pi\)
0.142655 + 0.989772i \(0.454436\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −8.13397 4.69615i −0.898247 0.518603i
\(83\) 0.196152 0.0215305 0.0107653 0.999942i \(-0.496573\pi\)
0.0107653 + 0.999942i \(0.496573\pi\)
\(84\) 2.36603 + 1.36603i 0.258155 + 0.149046i
\(85\) 0 0
\(86\) 9.66025i 1.04169i
\(87\) 3.86603 + 2.23205i 0.414481 + 0.239301i
\(88\) 1.09808 0.633975i 0.117055 0.0675819i
\(89\) 8.19615 4.73205i 0.868790 0.501596i 0.00184433 0.999998i \(-0.499413\pi\)
0.866946 + 0.498402i \(0.166080\pi\)
\(90\) 0 0
\(91\) −2.73205 9.46410i −0.286397 0.992107i
\(92\) 4.19615i 0.437479i
\(93\) 0.732051 + 1.26795i 0.0759101 + 0.131480i
\(94\) 1.09808 + 1.90192i 0.113258 + 0.196168i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i \(-0.734809\pi\)
0.977173 + 0.212445i \(0.0681426\pi\)
\(98\) −0.232051 + 0.401924i −0.0234407 + 0.0406004i
\(99\) 1.26795i 0.127434i
\(100\) 0 0
\(101\) 0.964102 + 1.66987i 0.0959317 + 0.166159i 0.909997 0.414615i \(-0.136084\pi\)
−0.814065 + 0.580773i \(0.802750\pi\)
\(102\) −2.86603 4.96410i −0.283779 0.491519i
\(103\) 15.2679i 1.50440i −0.658937 0.752198i \(-0.728994\pi\)
0.658937 0.752198i \(-0.271006\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) 0 0
\(106\) 5.59808 3.23205i 0.543733 0.313925i
\(107\) 8.83013 5.09808i 0.853641 0.492850i −0.00823695 0.999966i \(-0.502622\pi\)
0.861878 + 0.507116i \(0.169289\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 1.46410i 0.140236i 0.997539 + 0.0701178i \(0.0223375\pi\)
−0.997539 + 0.0701178i \(0.977662\pi\)
\(110\) 0 0
\(111\) −3.06218 1.76795i −0.290649 0.167806i
\(112\) 2.73205 0.258155
\(113\) −1.16025 0.669873i −0.109148 0.0630163i 0.444432 0.895812i \(-0.353405\pi\)
−0.553580 + 0.832796i \(0.686739\pi\)
\(114\) −2.36603 4.09808i −0.221599 0.383820i
\(115\) 0 0
\(116\) 4.46410 0.414481
\(117\) 1.00000 + 3.46410i 0.0924500 + 0.320256i
\(118\) 8.00000i 0.736460i
\(119\) 13.5622 7.83013i 1.24324 0.717787i
\(120\) 0 0
\(121\) −4.69615 + 8.13397i −0.426923 + 0.739452i
\(122\) −9.19615 −0.832581
\(123\) −4.69615 + 8.13397i −0.423438 + 0.733416i
\(124\) 1.26795 + 0.732051i 0.113865 + 0.0657401i
\(125\) 0 0
\(126\) 1.36603 2.36603i 0.121695 0.210782i
\(127\) 8.53590 4.92820i 0.757438 0.437307i −0.0709368 0.997481i \(-0.522599\pi\)
0.828375 + 0.560173i \(0.189266\pi\)
\(128\) −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
\(133\) 11.1962 6.46410i 0.970830 0.560509i
\(134\) −6.56218 + 11.3660i −0.566886 + 0.981875i
\(135\) 0 0
\(136\) −4.96410 2.86603i −0.425668 0.245760i
\(137\) 5.96410 10.3301i 0.509548 0.882562i −0.490391 0.871502i \(-0.663146\pi\)
0.999939 0.0110599i \(-0.00352055\pi\)
\(138\) 4.19615 0.357200
\(139\) 8.92820 15.4641i 0.757280 1.31165i −0.186952 0.982369i \(-0.559861\pi\)
0.944233 0.329279i \(-0.106806\pi\)
\(140\) 0 0
\(141\) 1.90192 1.09808i 0.160171 0.0924747i
\(142\) 4.73205i 0.397105i
\(143\) −1.09808 + 4.43782i −0.0918257 + 0.371109i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 3.13397 + 5.42820i 0.259370 + 0.449241i
\(147\) 0.401924 + 0.232051i 0.0331501 + 0.0191392i
\(148\) −3.53590 −0.290649
\(149\) −11.4282 6.59808i −0.936235 0.540535i −0.0474568 0.998873i \(-0.515112\pi\)
−0.888778 + 0.458338i \(0.848445\pi\)
\(150\) 0 0
\(151\) 6.73205i 0.547847i 0.961752 + 0.273923i \(0.0883214\pi\)
−0.961752 + 0.273923i \(0.911679\pi\)
\(152\) −4.09808 2.36603i −0.332398 0.191910i
\(153\) −4.96410 + 2.86603i −0.401324 + 0.231704i
\(154\) 3.00000 1.73205i 0.241747 0.139573i
\(155\) 0 0
\(156\) 2.59808 + 2.50000i 0.208013 + 0.200160i
\(157\) 7.58846i 0.605625i 0.953050 + 0.302812i \(0.0979256\pi\)
−0.953050 + 0.302812i \(0.902074\pi\)
\(158\) −1.26795 2.19615i −0.100873 0.174717i
\(159\) −3.23205 5.59808i −0.256318 0.443956i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 6.73205 11.6603i 0.527295 0.913302i −0.472199 0.881492i \(-0.656540\pi\)
0.999494 0.0318096i \(-0.0101270\pi\)
\(164\) 9.39230i 0.733416i
\(165\) 0 0
\(166\) −0.0980762 0.169873i −0.00761219 0.0131847i
\(167\) −4.73205 8.19615i −0.366177 0.634237i 0.622787 0.782391i \(-0.286000\pi\)
−0.988964 + 0.148154i \(0.952667\pi\)
\(168\) 2.73205i 0.210782i
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 0 0
\(171\) −4.09808 + 2.36603i −0.313388 + 0.180934i
\(172\) −8.36603 + 4.83013i −0.637903 + 0.368294i
\(173\) −3.80385 2.19615i −0.289201 0.166970i 0.348380 0.937353i \(-0.386732\pi\)
−0.637582 + 0.770383i \(0.720065\pi\)
\(174\) 4.46410i 0.338423i
\(175\) 0 0
\(176\) −1.09808 0.633975i −0.0827706 0.0477876i
\(177\) −8.00000 −0.601317
\(178\) −8.19615 4.73205i −0.614328 0.354682i
\(179\) 8.02628 + 13.9019i 0.599912 + 1.03908i 0.992833 + 0.119506i \(0.0381312\pi\)
−0.392921 + 0.919572i \(0.628535\pi\)
\(180\) 0 0
\(181\) −19.1962 −1.42684 −0.713419 0.700737i \(-0.752855\pi\)
−0.713419 + 0.700737i \(0.752855\pi\)
\(182\) −6.83013 + 7.09808i −0.506283 + 0.526144i
\(183\) 9.19615i 0.679799i
\(184\) 3.63397 2.09808i 0.267900 0.154672i
\(185\) 0 0
\(186\) 0.732051 1.26795i 0.0536766 0.0929705i
\(187\) −7.26795 −0.531485
\(188\) 1.09808 1.90192i 0.0800854 0.138712i
\(189\) −2.36603 1.36603i −0.172103 0.0993637i
\(190\) 0 0
\(191\) 3.46410 6.00000i 0.250654 0.434145i −0.713052 0.701111i \(-0.752688\pi\)
0.963706 + 0.266966i \(0.0860212\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 5.86603 + 10.1603i 0.422246 + 0.731351i 0.996159 0.0875652i \(-0.0279086\pi\)
−0.573913 + 0.818916i \(0.694575\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 0.464102 0.0331501
\(197\) 8.92820 + 15.4641i 0.636108 + 1.10177i 0.986279 + 0.165086i \(0.0527901\pi\)
−0.350171 + 0.936686i \(0.613877\pi\)
\(198\) −1.09808 + 0.633975i −0.0780369 + 0.0450546i
\(199\) 7.09808 12.2942i 0.503169 0.871515i −0.496824 0.867851i \(-0.665501\pi\)
0.999993 0.00366345i \(-0.00116611\pi\)
\(200\) 0 0
\(201\) 11.3660 + 6.56218i 0.801698 + 0.462860i
\(202\) 0.964102 1.66987i 0.0678340 0.117492i
\(203\) 12.1962 0.856002
\(204\) −2.86603 + 4.96410i −0.200662 + 0.347557i
\(205\) 0 0
\(206\) −13.2224 + 7.63397i −0.921250 + 0.531884i
\(207\) 4.19615i 0.291653i
\(208\) 3.50000 + 0.866025i 0.242681 + 0.0600481i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −8.19615 14.1962i −0.564246 0.977303i −0.997119 0.0758485i \(-0.975833\pi\)
0.432873 0.901455i \(-0.357500\pi\)
\(212\) −5.59808 3.23205i −0.384477 0.221978i
\(213\) −4.73205 −0.324235
\(214\) −8.83013 5.09808i −0.603615 0.348497i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 3.46410 + 2.00000i 0.235159 + 0.135769i
\(218\) 1.26795 0.732051i 0.0858764 0.0495807i
\(219\) 5.42820 3.13397i 0.366804 0.211774i
\(220\) 0 0
\(221\) 19.8564 5.73205i 1.33569 0.385579i
\(222\) 3.53590i 0.237314i
\(223\) −13.4641 23.3205i −0.901623 1.56166i −0.825387 0.564567i \(-0.809043\pi\)
−0.0762356 0.997090i \(-0.524290\pi\)
\(224\) −1.36603 2.36603i −0.0912714 0.158087i
\(225\) 0 0
\(226\) 1.33975i 0.0891186i
\(227\) 6.09808 10.5622i 0.404744 0.701036i −0.589548 0.807733i \(-0.700694\pi\)
0.994292 + 0.106697i \(0.0340275\pi\)
\(228\) −2.36603 + 4.09808i −0.156694 + 0.271402i
\(229\) 11.8564i 0.783493i 0.920073 + 0.391747i \(0.128129\pi\)
−0.920073 + 0.391747i \(0.871871\pi\)
\(230\) 0 0
\(231\) −1.73205 3.00000i −0.113961 0.197386i
\(232\) −2.23205 3.86603i −0.146541 0.253817i
\(233\) 7.85641i 0.514690i −0.966320 0.257345i \(-0.917152\pi\)
0.966320 0.257345i \(-0.0828477\pi\)
\(234\) 2.50000 2.59808i 0.163430 0.169842i
\(235\) 0 0
\(236\) −6.92820 + 4.00000i −0.450988 + 0.260378i
\(237\) −2.19615 + 1.26795i −0.142655 + 0.0823622i
\(238\) −13.5622 7.83013i −0.879105 0.507552i
\(239\) 7.66025i 0.495501i 0.968824 + 0.247750i \(0.0796913\pi\)
−0.968824 + 0.247750i \(0.920309\pi\)
\(240\) 0 0
\(241\) −11.7679 6.79423i −0.758040 0.437655i 0.0705514 0.997508i \(-0.477524\pi\)
−0.828592 + 0.559853i \(0.810857\pi\)
\(242\) 9.39230 0.603760
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 4.59808 + 7.96410i 0.294362 + 0.509849i
\(245\) 0 0
\(246\) 9.39230 0.598831
\(247\) 16.3923 4.73205i 1.04302 0.301093i
\(248\) 1.46410i 0.0929705i
\(249\) −0.169873 + 0.0980762i −0.0107653 + 0.00621533i
\(250\) 0 0
\(251\) 6.73205 11.6603i 0.424923 0.735989i −0.571490 0.820609i \(-0.693634\pi\)
0.996413 + 0.0846203i \(0.0269677\pi\)
\(252\) −2.73205 −0.172103
\(253\) 2.66025 4.60770i 0.167249 0.289683i
\(254\) −8.53590 4.92820i −0.535590 0.309223i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.08846 + 4.66987i −0.504544 + 0.291299i −0.730588 0.682818i \(-0.760754\pi\)
0.226044 + 0.974117i \(0.427421\pi\)
\(258\) 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
\(263\) 8.70577 5.02628i 0.536821 0.309934i −0.206969 0.978348i \(-0.566360\pi\)
0.743790 + 0.668414i \(0.233026\pi\)
\(264\) −0.633975 + 1.09808i −0.0390184 + 0.0675819i
\(265\) 0 0
\(266\) −11.1962 6.46410i −0.686480 0.396339i
\(267\) −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 \(-0.780062\pi\)
0.937214 + 0.348755i \(0.113396\pi\)
\(270\) 0 0
\(271\) −18.9282 + 10.9282i −1.14981 + 0.663841i −0.948840 0.315757i \(-0.897742\pi\)
−0.200966 + 0.979598i \(0.564408\pi\)
\(272\) 5.73205i 0.347557i
\(273\) 7.09808 + 6.83013i 0.429595 + 0.413378i
\(274\) −11.9282 −0.720609
\(275\) 0 0
\(276\) −2.09808 3.63397i −0.126289 0.218740i
\(277\) −4.96410 2.86603i −0.298264 0.172203i 0.343399 0.939190i \(-0.388422\pi\)
−0.641663 + 0.766987i \(0.721755\pi\)
\(278\) −17.8564 −1.07096
\(279\) −1.26795 0.732051i −0.0759101 0.0438267i
\(280\) 0 0
\(281\) 12.3205i 0.734980i 0.930027 + 0.367490i \(0.119783\pi\)
−0.930027 + 0.367490i \(0.880217\pi\)
\(282\) −1.90192 1.09808i −0.113258 0.0653895i
\(283\) 22.2224 12.8301i 1.32099 0.762672i 0.337100 0.941469i \(-0.390554\pi\)
0.983886 + 0.178797i \(0.0572205\pi\)
\(284\) −4.09808 + 2.36603i −0.243176 + 0.140398i
\(285\) 0 0
\(286\) 4.39230 1.26795i 0.259722 0.0749754i
\(287\) 25.6603i 1.51468i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 7.92820 + 13.7321i 0.466365 + 0.807768i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 3.13397 5.42820i 0.183402 0.317662i
\(293\) −15.2583 + 26.4282i −0.891401 + 1.54395i −0.0532048 + 0.998584i \(0.516944\pi\)
−0.838196 + 0.545368i \(0.816390\pi\)
\(294\) 0.464102i 0.0270670i
\(295\) 0 0
\(296\) 1.76795 + 3.06218i 0.102760 + 0.177985i
\(297\) 0.633975 + 1.09808i 0.0367869 + 0.0637168i
\(298\) 13.1962i 0.764433i
\(299\) −3.63397 + 14.6865i −0.210158 + 0.849344i
\(300\) 0 0
\(301\) −22.8564 + 13.1962i −1.31742 + 0.760614i
\(302\) 5.83013 3.36603i 0.335486 0.193693i
\(303\) −1.66987 0.964102i −0.0959317 0.0553862i
\(304\) 4.73205i 0.271402i
\(305\) 0 0
\(306\) 4.96410 + 2.86603i 0.283779 + 0.163840i
\(307\) 22.5885 1.28919 0.644596 0.764524i \(-0.277026\pi\)
0.644596 + 0.764524i \(0.277026\pi\)
\(308\) −3.00000 1.73205i −0.170941 0.0986928i
\(309\) 7.63397 + 13.2224i 0.434282 + 0.752198i
\(310\) 0 0
\(311\) 1.66025 0.0941444 0.0470722 0.998891i \(-0.485011\pi\)
0.0470722 + 0.998891i \(0.485011\pi\)
\(312\) 0.866025 3.50000i 0.0490290 0.198148i
\(313\) 6.53590i 0.369431i −0.982792 0.184715i \(-0.940864\pi\)
0.982792 0.184715i \(-0.0591363\pi\)
\(314\) 6.57180 3.79423i 0.370868 0.214121i
\(315\) 0 0
\(316\) −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
\(319\) −4.90192 2.83013i −0.274455 0.158457i
\(320\) 0 0
\(321\) −5.09808 + 8.83013i −0.284547 + 0.492850i
\(322\) 9.92820 5.73205i 0.553277 0.319435i
\(323\) 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
\(328\) 8.13397 4.69615i 0.449124 0.259302i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) 17.3205 + 10.0000i 0.952021 + 0.549650i 0.893708 0.448649i \(-0.148095\pi\)
0.0583130 + 0.998298i \(0.481428\pi\)
\(332\) −0.0980762 + 0.169873i −0.00538263 + 0.00932299i
\(333\) 3.53590 0.193766
\(334\) −4.73205 + 8.19615i −0.258926 + 0.448474i
\(335\) 0 0
\(336\) −2.36603 + 1.36603i −0.129077 + 0.0745228i
\(337\) 20.8564i 1.13612i 0.822987 + 0.568060i \(0.192306\pi\)
−0.822987 + 0.568060i \(0.807694\pi\)
\(338\) −11.0000 + 6.92820i −0.598321 + 0.376845i
\(339\) 1.33975 0.0727650
\(340\) 0 0
\(341\) −0.928203 1.60770i −0.0502650 0.0870616i
\(342\) 4.09808 + 2.36603i 0.221599 + 0.127940i
\(343\) −17.8564 −0.964155
\(344\) 8.36603 + 4.83013i 0.451066 + 0.260423i
\(345\) 0 0
\(346\) 4.39230i 0.236132i
\(347\) −28.6865 16.5622i −1.53997 0.889104i −0.998839 0.0481683i \(-0.984662\pi\)
−0.541135 0.840936i \(-0.682005\pi\)
\(348\) −3.86603 + 2.23205i −0.207241 + 0.119650i
\(349\) −13.2679 + 7.66025i −0.710217 + 0.410044i −0.811141 0.584850i \(-0.801153\pi\)
0.100924 + 0.994894i \(0.467820\pi\)
\(350\) 0 0
\(351\) −2.59808 2.50000i −0.138675 0.133440i
\(352\) 1.26795i 0.0675819i
\(353\) −10.8923 18.8660i −0.579739 1.00414i −0.995509 0.0946674i \(-0.969821\pi\)
0.415770 0.909470i \(-0.363512\pi\)
\(354\) 4.00000 + 6.92820i 0.212598 + 0.368230i
\(355\) 0 0
\(356\) 9.46410i 0.501596i
\(357\) −7.83013 + 13.5622i −0.414414 + 0.717787i
\(358\) 8.02628 13.9019i 0.424202 0.734740i
\(359\) 1.12436i 0.0593412i 0.999560 + 0.0296706i \(0.00944584\pi\)
−0.999560 + 0.0296706i \(0.990554\pi\)
\(360\) 0 0
\(361\) 1.69615 + 2.93782i 0.0892712 + 0.154622i
\(362\) 9.59808 + 16.6244i 0.504464 + 0.873757i
\(363\) 9.39230i 0.492968i
\(364\) 9.56218 + 2.36603i 0.501194 + 0.124013i
\(365\) 0 0
\(366\) 7.96410 4.59808i 0.416290 0.240345i
\(367\) −9.75833 + 5.63397i −0.509381 + 0.294091i −0.732579 0.680682i \(-0.761684\pi\)
0.223198 + 0.974773i \(0.428350\pi\)
\(368\) −3.63397 2.09808i −0.189434 0.109370i
\(369\) 9.39230i 0.488944i
\(370\) 0 0
\(371\) −15.2942 8.83013i −0.794037 0.458437i
\(372\) −1.46410 −0.0759101
\(373\) −11.8923 6.86603i −0.615760 0.355509i 0.159456 0.987205i \(-0.449026\pi\)
−0.775216 + 0.631696i \(0.782359\pi\)
\(374\) 3.63397 + 6.29423i 0.187908 + 0.325467i
\(375\) 0 0
\(376\) −2.19615 −0.113258
\(377\) 15.6244 + 3.86603i 0.804695 + 0.199110i
\(378\) 2.73205i 0.140522i
\(379\) −4.73205 + 2.73205i −0.243069 + 0.140336i −0.616587 0.787287i \(-0.711485\pi\)
0.373517 + 0.927623i \(0.378152\pi\)
\(380\) 0 0
\(381\) −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 \(-0.845243\pi\)
0.846716 + 0.532045i \(0.178576\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 5.86603 10.1603i 0.298573 0.517143i
\(387\) 8.36603 4.83013i 0.425269 0.245529i
\(388\) 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
\(393\) −5.66025 + 3.26795i −0.285522 + 0.164846i
\(394\) 8.92820 15.4641i 0.449796 0.779070i
\(395\) 0 0
\(396\) 1.09808 + 0.633975i 0.0551804 + 0.0318584i
\(397\) 10.1962 17.6603i 0.511730 0.886343i −0.488177 0.872744i \(-0.662338\pi\)
0.999908 0.0135983i \(-0.00432860\pi\)
\(398\) −14.1962 −0.711589
\(399\) −6.46410 + 11.1962i −0.323610 + 0.560509i
\(400\) 0 0
\(401\) 6.99038 4.03590i 0.349083 0.201543i −0.315198 0.949026i \(-0.602071\pi\)
0.664281 + 0.747483i \(0.268738\pi\)
\(402\) 13.1244i 0.654583i
\(403\) 3.80385 + 3.66025i 0.189483 + 0.182330i
\(404\) −1.92820 −0.0959317
\(405\) 0 0
\(406\) −6.09808 10.5622i −0.302642 0.524192i
\(407\) 3.88269 + 2.24167i 0.192458 + 0.111115i
\(408\) 5.73205 0.283779
\(409\) −15.3564 8.86603i −0.759325 0.438397i 0.0697281 0.997566i \(-0.477787\pi\)
−0.829053 + 0.559169i \(0.811120\pi\)
\(410\) 0 0
\(411\) 11.9282i 0.588375i
\(412\) 13.2224 + 7.63397i 0.651422 + 0.376099i
\(413\) −18.9282 + 10.9282i −0.931396 + 0.537742i
\(414\) −3.63397 + 2.09808i −0.178600 + 0.103115i
\(415\) 0 0
\(416\) −1.00000 3.46410i −0.0490290 0.169842i
\(417\) 17.8564i 0.874432i
\(418\) 3.00000 + 5.19615i 0.146735 + 0.254152i
\(419\) −8.73205 15.1244i −0.426589 0.738873i 0.569979 0.821659i \(-0.306951\pi\)
−0.996567 + 0.0827863i \(0.973618\pi\)
\(420\) 0 0
\(421\) 22.7128i 1.10695i 0.832864 + 0.553477i \(0.186699\pi\)
−0.832864 + 0.553477i \(0.813301\pi\)
\(422\) −8.19615 + 14.1962i −0.398982 + 0.691058i
\(423\) −1.09808 + 1.90192i −0.0533903 + 0.0924747i
\(424\) 6.46410i 0.313925i
\(425\) 0 0
\(426\) 2.36603 + 4.09808i 0.114634 + 0.198552i
\(427\) 12.5622 + 21.7583i 0.607926 + 1.05296i
\(428\) 10.1962i 0.492850i
\(429\) −1.26795 4.39230i −0.0612172 0.212062i
\(430\) 0 0
\(431\) −11.3660 + 6.56218i −0.547482 + 0.316089i −0.748106 0.663579i \(-0.769036\pi\)
0.200624 + 0.979668i \(0.435703\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −11.1340 6.42820i −0.535065 0.308920i 0.208012 0.978126i \(-0.433301\pi\)
−0.743076 + 0.669207i \(0.766634\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 0 0
\(436\) −1.26795 0.732051i −0.0607238 0.0350589i
\(437\) −19.8564 −0.949861
\(438\) −5.42820 3.13397i −0.259370 0.149747i
\(439\) 0.169873 + 0.294229i 0.00810760 + 0.0140428i 0.870051 0.492962i \(-0.164086\pi\)
−0.861943 + 0.507005i \(0.830753\pi\)
\(440\) 0 0
\(441\) −0.464102 −0.0221001
\(442\) −14.8923 14.3301i −0.708355 0.681615i
\(443\) 15.6077i 0.741544i −0.928724 0.370772i \(-0.879093\pi\)
0.928724 0.370772i \(-0.120907\pi\)
\(444\) 3.06218 1.76795i 0.145325 0.0839032i
\(445\) 0 0
\(446\) −13.4641 + 23.3205i −0.637544 + 1.10426i
\(447\) 13.1962 0.624157
\(448\) −1.36603 + 2.36603i −0.0645386 + 0.111784i
\(449\) 9.80385 + 5.66025i 0.462672 + 0.267124i 0.713167 0.700994i \(-0.247260\pi\)
−0.250495 + 0.968118i \(0.580593\pi\)
\(450\) 0 0
\(451\) 5.95448 10.3135i 0.280386 0.485642i
\(452\) 1.16025 0.669873i 0.0545738 0.0315082i
\(453\) −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 0.849932 0.526892i \(-0.176643\pi\)
−0.881268 + 0.472617i \(0.843309\pi\)
\(458\) 10.2679 5.92820i 0.479790 0.277007i
\(459\) 2.86603 4.96410i 0.133775 0.231704i
\(460\) 0 0
\(461\) 19.2846 + 11.1340i 0.898174 + 0.518561i 0.876607 0.481207i \(-0.159801\pi\)
0.0215666 + 0.999767i \(0.493135\pi\)
\(462\) −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
\(465\) 0 0
\(466\) −6.80385 + 3.92820i −0.315182 + 0.181971i
\(467\) 18.5885i 0.860171i −0.902788 0.430086i \(-0.858483\pi\)
0.902788 0.430086i \(-0.141517\pi\)
\(468\) −3.50000 0.866025i −0.161788 0.0400320i
\(469\) 35.8564 1.65570
\(470\) 0 0
\(471\) −3.79423 6.57180i −0.174829 0.302812i
\(472\) 6.92820 + 4.00000i 0.318896 + 0.184115i
\(473\) 12.2487 0.563196
\(474\) 2.19615 + 1.26795i 0.100873 + 0.0582388i
\(475\) 0 0
\(476\) 15.6603i 0.717787i
\(477\) 5.59808 + 3.23205i 0.256318 + 0.147985i
\(478\) 6.63397 3.83013i 0.303431 0.175186i
\(479\) −28.9808 + 16.7321i −1.32416 + 0.764507i −0.984390 0.176000i \(-0.943684\pi\)
−0.339775 + 0.940507i \(0.610351\pi\)
\(480\) 0 0
\(481\) −12.3756 3.06218i −0.564281 0.139623i
\(482\) 13.5885i 0.618937i
\(483\) −5.73205 9.92820i −0.260817 0.451749i
\(484\) −4.69615 8.13397i −0.213461 0.369726i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 1.56218 2.70577i 0.0707890 0.122610i −0.828458 0.560051i \(-0.810782\pi\)
0.899247 + 0.437441i \(0.144115\pi\)
\(488\) 4.59808 7.96410i 0.208145 0.360518i
\(489\) 13.4641i 0.608868i
\(490\) 0 0
\(491\) 4.36603 + 7.56218i 0.197036 + 0.341276i 0.947566 0.319560i \(-0.103535\pi\)
−0.750530 + 0.660836i \(0.770202\pi\)
\(492\) −4.69615 8.13397i −0.211719 0.366708i
\(493\) 25.5885i 1.15245i
\(494\) −12.2942 11.8301i −0.553143 0.532263i
\(495\) 0 0
\(496\) −1.26795 + 0.732051i −0.0569326 + 0.0328701i
\(497\) −11.1962 + 6.46410i −0.502216 + 0.289955i
\(498\) 0.169873 + 0.0980762i 0.00761219 + 0.00439490i
\(499\) 32.0000i 1.43252i 0.697835 + 0.716258i \(0.254147\pi\)
−0.697835 + 0.716258i \(0.745853\pi\)
\(500\) 0 0
\(501\) 8.19615 + 4.73205i 0.366177 + 0.211412i
\(502\) −13.4641 −0.600932
\(503\) 35.4904 + 20.4904i 1.58244 + 0.913621i 0.994502 + 0.104713i \(0.0333924\pi\)
0.587935 + 0.808908i \(0.299941\pi\)
\(504\) 1.36603 + 2.36603i 0.0608476 + 0.105391i
\(505\) 0 0
\(506\) −5.32051 −0.236525
\(507\) 6.92820 + 11.0000i 0.307692 + 0.488527i
\(508\) 9.85641i 0.437307i
\(509\) 11.8923 6.86603i 0.527117 0.304331i −0.212725 0.977112i \(-0.568234\pi\)
0.739842 + 0.672781i \(0.234900\pi\)
\(510\) 0 0
\(511\) 8.56218 14.8301i 0.378768 0.656046i
\(512\) 1.00000 0.0441942
\(513\) 2.36603 4.09808i 0.104463 0.180934i
\(514\) 8.08846 + 4.66987i 0.356767 + 0.205979i
\(515\) 0 0
\(516\) 4.83013 8.36603i 0.212634 0.368294i
\(517\) −2.41154 + 1.39230i −0.106060 + 0.0612335i
\(518\) 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
\(523\) 19.4378 11.2224i 0.849957 0.490723i −0.0106796 0.999943i \(-0.503399\pi\)
0.860636 + 0.509220i \(0.170066\pi\)
\(524\) −3.26795 + 5.66025i −0.142761 + 0.247269i
\(525\) 0 0
\(526\) −8.70577 5.02628i −0.379590 0.219156i
\(527\) −4.19615 + 7.26795i −0.182787 + 0.316597i
\(528\) 1.26795 0.0551804
\(529\) −2.69615 + 4.66987i −0.117224 + 0.203038i
\(530\) 0 0
\(531\) 6.92820 4.00000i 0.300658 0.173585i
\(532\) 12.9282i 0.560509i
\(533\) −8.13397 + 32.8731i −0.352322 + 1.42389i
\(534\) 9.46410 0.409552
\(535\) 0 0
\(536\) −6.56218 11.3660i −0.283443 0.490938i
\(537\) −13.9019 8.02628i −0.599912 0.346360i
\(538\) −5.46410 −0.235574
\(539\) −0.509619 0.294229i −0.0219508 0.0126733i
\(540\) 0 0
\(541\) 5.67949i 0.244180i 0.992519 + 0.122090i \(0.0389597\pi\)
−0.992519 + 0.122090i \(0.961040\pi\)
\(542\) 18.9282 + 10.9282i 0.813036 + 0.469407i
\(543\) 16.6244 9.59808i 0.713419 0.411893i
\(544\) 4.96410 2.86603i 0.212834 0.122880i
\(545\) 0 0
\(546\) 2.36603 9.56218i 0.101257 0.409223i
\(547\) 4.19615i 0.179415i −0.995968 0.0897073i \(-0.971407\pi\)
0.995968 0.0897073i \(-0.0285931\pi\)
\(548\) 5.96410 + 10.3301i 0.254774 + 0.441281i
\(549\) −4.59808 7.96410i −0.196241 0.339900i
\(550\) 0 0
\(551\) 21.1244i 0.899928i
\(552\) −2.09808 + 3.63397i −0.0893001 + 0.154672i
\(553\) −3.46410 + 6.00000i −0.147309 + 0.255146i
\(554\) 5.73205i 0.243532i
\(555\) 0 0
\(556\) 8.92820 + 15.4641i 0.378640 + 0.655824i
\(557\) 21.1865 + 36.6962i 0.897702 + 1.55487i 0.830424 + 0.557132i \(0.188098\pi\)
0.0672780 + 0.997734i \(0.478569\pi\)
\(558\) 1.46410i 0.0619804i
\(559\) −33.4641 + 9.66025i −1.41538 + 0.408585i
\(560\) 0 0
\(561\) 6.29423 3.63397i 0.265743 0.153427i
\(562\) 10.6699 6.16025i 0.450081 0.259855i
\(563\) −30.2487 17.4641i −1.27483 0.736024i −0.298938 0.954273i \(-0.596632\pi\)
−0.975893 + 0.218248i \(0.929966\pi\)
\(564\) 2.19615i 0.0924747i
\(565\) 0 0
\(566\) −22.2224 12.8301i −0.934078 0.539290i
\(567\) 2.73205 0.114735
\(568\) 4.09808 + 2.36603i 0.171951 + 0.0992762i
\(569\) −15.3205 26.5359i −0.642269 1.11244i −0.984925 0.172982i \(-0.944660\pi\)
0.342656 0.939461i \(-0.388674\pi\)
\(570\) 0 0
\(571\) −14.0526 −0.588081 −0.294041 0.955793i \(-0.595000\pi\)
−0.294041 + 0.955793i \(0.595000\pi\)
\(572\) −3.29423 3.16987i −0.137739 0.132539i
\(573\) 6.92820i 0.289430i
\(574\) 22.2224 12.8301i 0.927546 0.535519i
\(575\) 0 0
\(576\) 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
\(579\) −10.1603 5.86603i −0.422246 0.243784i
\(580\) 0 0
\(581\) −0.267949 + 0.464102i −0.0111164 + 0.0192542i
\(582\) 5.19615 3.00000i 0.215387 0.124354i
\(583\) 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 0.652355 0.757914i \(-0.273781\pi\)
−0.982550 + 0.185999i \(0.940448\pi\)
\(588\) −0.401924 + 0.232051i −0.0165751 + 0.00956961i
\(589\) −3.46410 + 6.00000i −0.142736 + 0.247226i
\(590\) 0 0
\(591\) −15.4641 8.92820i −0.636108 0.367257i
\(592\) 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
\(595\) 0 0
\(596\) 11.4282 6.59808i 0.468117 0.270268i
\(597\) 14.1962i 0.581010i
\(598\) 14.5359 4.19615i 0.594417 0.171593i
\(599\) 2.53590 0.103614 0.0518070 0.998657i \(-0.483502\pi\)
0.0518070 + 0.998657i \(0.483502\pi\)
\(600\) 0 0
\(601\) −3.96410 6.86603i −0.161699 0.280071i 0.773779 0.633456i \(-0.218364\pi\)
−0.935478 + 0.353385i \(0.885031\pi\)
\(602\) 22.8564 + 13.1962i 0.931558 + 0.537835i
\(603\) −13.1244 −0.534465
\(604\) −5.83013 3.36603i −0.237225 0.136962i
\(605\) 0 0
\(606\) 1.92820i 0.0783279i
\(607\) 35.3205 + 20.3923i 1.43362 + 0.827698i 0.997394 0.0721415i \(-0.0229833\pi\)
0.436221 + 0.899840i \(0.356317\pi\)
\(608\) 4.09808 2.36603i 0.166199 0.0959550i
\(609\) −10.5622 + 6.09808i −0.428001 + 0.247107i
\(610\) 0 0
\(611\) 5.49038 5.70577i 0.222117 0.230831i
\(612\) 5.73205i 0.231704i
\(613\) −4.69615 8.13397i −0.189676 0.328528i 0.755466 0.655187i \(-0.227410\pi\)
−0.945142 + 0.326659i \(0.894077\pi\)
\(614\) −11.2942 19.5622i −0.455798 0.789465i
\(615\) 0 0
\(616\) 3.46410i 0.139573i
\(617\) 6.62436 11.4737i 0.266687 0.461915i −0.701318 0.712849i \(-0.747404\pi\)
0.968004 + 0.250934i \(0.0807378\pi\)
\(618\) 7.63397 13.2224i 0.307083 0.531884i
\(619\) 17.4641i 0.701942i −0.936386 0.350971i \(-0.885852\pi\)
0.936386 0.350971i \(-0.114148\pi\)
\(620\) 0 0
\(621\) 2.09808 + 3.63397i 0.0841929 + 0.145826i
\(622\) −0.830127 1.43782i −0.0332851 0.0576514i
\(623\) 25.8564i 1.03592i
\(624\) −3.46410 + 1.00000i −0.138675 + 0.0400320i
\(625\) 0 0
\(626\) −5.66025 + 3.26795i −0.226229 + 0.130614i
\(627\) 5.19615 3.00000i 0.207514 0.119808i
\(628\) −6.57180 3.79423i −0.262243 0.151406i
\(629\) 20.2679i 0.808136i
\(630\) 0 0
\(631\) 6.67949 + 3.85641i 0.265906 + 0.153521i 0.627026 0.778998i \(-0.284272\pi\)
−0.361119 + 0.932520i \(0.617605\pi\)
\(632\) 2.53590 0.100873
\(633\) 14.1962 + 8.19615i 0.564246 + 0.325768i
\(634\) −10.3301 17.8923i −0.410262 0.710594i
\(635\) 0 0
\(636\) 6.46410 0.256318
\(637\) 1.62436 + 0.401924i 0.0643593 + 0.0159248i
\(638\) 5.66025i 0.224092i
\(639\) 4.09808 2.36603i 0.162117 0.0935985i
\(640\) 0 0
\(641\) −12.9904 + 22.5000i −0.513089 + 0.888697i 0.486796 + 0.873516i \(0.338166\pi\)
−0.999885 + 0.0151806i \(0.995168\pi\)
\(642\) 10.1962 0.402410
\(643\) −6.92820 + 12.0000i −0.273222 + 0.473234i −0.969685 0.244359i \(-0.921423\pi\)
0.696463 + 0.717592i \(0.254756\pi\)
\(644\) −9.92820 5.73205i −0.391226 0.225874i
\(645\) 0 0
\(646\) 13.5622 23.4904i 0.533597 0.924217i
\(647\) 19.2679 11.1244i 0.757501 0.437344i −0.0708966 0.997484i \(-0.522586\pi\)
0.828398 + 0.560140i \(0.189253\pi\)
\(648\) −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
\(653\) 15.1244 8.73205i 0.591862 0.341712i −0.173972 0.984751i \(-0.555660\pi\)
0.765833 + 0.643039i \(0.222327\pi\)
\(654\) −0.732051 + 1.26795i −0.0286255 + 0.0495807i
\(655\) 0 0
\(656\) −8.13397 4.69615i −0.317578 0.183354i
\(657\) −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 \(-0.897303\pi\)
0.748788 + 0.662810i \(0.230636\pi\)
\(660\) 0 0
\(661\) 9.86603 5.69615i 0.383744 0.221555i −0.295702 0.955280i \(-0.595554\pi\)
0.679446 + 0.733726i \(0.262220\pi\)
\(662\) 20.0000i 0.777322i
\(663\) −14.3301 + 14.8923i −0.556536 + 0.578369i
\(664\) 0.196152 0.00761219
\(665\) 0 0
\(666\) −1.76795 3.06218i −0.0685066 0.118657i
\(667\) −16.2224 9.36603i −0.628135 0.362654i
\(668\) 9.46410 0.366177
\(669\) 23.3205 + 13.4641i 0.901623 + 0.520552i
\(670\) 0 0
\(671\) 11.6603i 0.450139i
\(672\) 2.36603 + 1.36603i 0.0912714 + 0.0526956i
\(673\) 24.1865 13.9641i 0.932322 0.538277i 0.0447770 0.998997i \(-0.485742\pi\)
0.887545 + 0.460720i \(0.152409\pi\)
\(674\) 18.0622 10.4282i 0.695729 0.401679i
\(675\) 0 0
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 45.4641i 1.74733i −0.486530 0.873664i \(-0.661738\pi\)
0.486530 0.873664i \(-0.338262\pi\)
\(678\) −0.669873 1.16025i −0.0257263 0.0445593i
\(679\) 8.19615 + 14.1962i 0.314539 + 0.544798i
\(680\) 0 0
\(681\) 12.1962i 0.467358i
\(682\) −0.928203 + 1.60770i −0.0355427 + 0.0615618i
\(683\) 5.07180 8.78461i 0.194067 0.336134i −0.752527 0.658561i \(-0.771165\pi\)
0.946594 + 0.322427i \(0.104499\pi\)
\(684\) 4.73205i 0.180934i
\(685\) 0 0
\(686\) 8.92820 + 15.4641i 0.340880 + 0.590422i
\(687\) −5.92820 10.2679i −0.226175 0.391747i
\(688\) 9.66025i 0.368294i
\(689\) −16.7942 16.1603i −0.639809 0.615657i
\(690\) 0 0
\(691\) −37.8109 + 21.8301i −1.43839 + 0.830457i −0.997738 0.0672190i \(-0.978587\pi\)
−0.440656 + 0.897676i \(0.645254\pi\)
\(692\) 3.80385 2.19615i 0.144601 0.0834852i
\(693\) 3.00000 + 1.73205i 0.113961 + 0.0657952i
\(694\) 33.1244i 1.25738i
\(695\) 0 0
\(696\) 3.86603 + 2.23205i 0.146541 + 0.0846057i
\(697\) −53.8372 −2.03923
\(698\) 13.2679 + 7.66025i 0.502199 + 0.289945i
\(699\) 3.92820 + 6.80385i 0.148578 + 0.257345i
\(700\) 0 0
\(701\) 3.32051 0.125414 0.0627069 0.998032i \(-0.480027\pi\)
0.0627069 + 0.998032i \(0.480027\pi\)
\(702\) −0.866025 + 3.50000i −0.0326860 + 0.132099i
\(703\) 16.7321i 0.631061i
\(704\) 1.09808 0.633975i 0.0413853 0.0238938i
\(705\) 0 0
\(706\) −10.8923 + 18.8660i −0.409937 + 0.710032i
\(707\) −5.26795 −0.198122
\(708\) 4.00000 6.92820i 0.150329 0.260378i
\(709\) 11.3827 + 6.57180i 0.427486 + 0.246809i 0.698275 0.715830i \(-0.253951\pi\)
−0.270789 + 0.962639i \(0.587285\pi\)
\(710\) 0 0
\(711\) 1.26795 2.19615i 0.0475518 0.0823622i
\(712\) 8.19615 4.73205i 0.307164 0.177341i
\(713\) −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
\(718\) 0.973721 0.562178i 0.0363389 0.0209803i
\(719\) 14.7321 25.5167i 0.549413 0.951611i −0.448902 0.893581i \(-0.648185\pi\)
0.998315 0.0580299i \(-0.0184819\pi\)
\(720\) 0 0
\(721\) 36.1244 + 20.8564i 1.34534 + 0.776733i
\(722\) 1.69615 2.93782i 0.0631243 0.109334i
\(723\) 13.5885 0.505360
\(724\) 9.59808 16.6244i 0.356710 0.617839i
\(725\) 0 0
\(726\) −8.13397 + 4.69615i −0.301880 + 0.174291i
\(727\) 30.9808i 1.14901i 0.818500 + 0.574506i \(0.194806\pi\)
−0.818500 + 0.574506i \(0.805194\pi\)
\(728\) −2.73205 9.46410i −0.101257 0.350763i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −27.6865 47.9545i −1.02402 1.77366i
\(732\) −7.96410 4.59808i −0.294362 0.169950i
\(733\) −19.0000 −0.701781 −0.350891 0.936416i \(-0.614121\pi\)
−0.350891 + 0.936416i \(0.614121\pi\)
\(734\) 9.75833 + 5.63397i 0.360187 + 0.207954i
\(735\) 0 0
\(736\) 4.19615i 0.154672i
\(737\) −14.4115 8.32051i −0.530856 0.306490i
\(738\) −8.13397 + 4.69615i −0.299416 + 0.172868i
\(739\) −2.53590 + 1.46410i −0.0932845 + 0.0538578i −0.545917 0.837840i \(-0.683818\pi\)
0.452632 + 0.891697i \(0.350485\pi\)
\(740\) 0 0
\(741\) −11.8301 + 12.2942i −0.434591 + 0.451640i
\(742\) 17.6603i 0.648328i
\(743\) −24.1962 41.9090i −0.887671 1.53749i −0.842622 0.538506i \(-0.818989\pi\)
−0.0450491 0.998985i \(-0.514344\pi\)
\(744\) 0.732051 + 1.26795i 0.0268383 + 0.0464853i
\(745\) 0 0
\(746\) 13.7321i 0.502766i
\(747\) 0.0980762 0.169873i 0.00358842 0.00621533i
\(748\) 3.63397 6.29423i 0.132871 0.230140i
\(749\) 27.8564i 1.01785i
\(750\) 0 0
\(751\) −24.9545 43.2224i −0.910602 1.57721i −0.813216 0.581962i \(-0.802285\pi\)
−0.0973862 0.995247i \(-0.531048\pi\)
\(752\) 1.09808 + 1.90192i 0.0400427 + 0.0693560i
\(753\) 13.4641i 0.490659i
\(754\) −4.46410 15.4641i −0.162573 0.563169i
\(755\) 0 0
\(756\) 2.36603 1.36603i 0.0860515 0.0496819i
\(757\) 18.1244 10.4641i 0.658741 0.380324i −0.133056 0.991109i \(-0.542479\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(758\) 4.73205 + 2.73205i 0.171876 + 0.0992326i
\(759\) 5.32051i 0.193122i
\(760\) 0 0
\(761\) −9.80385 5.66025i −0.355389 0.205184i 0.311667 0.950191i \(-0.399113\pi\)
−0.667056 + 0.745007i \(0.732446\pi\)
\(762\) 9.85641 0.357060
\(763\) −3.46410 2.00000i −0.125409 0.0724049i
\(764\) 3.46410 + 6.00000i 0.125327 + 0.217072i
\(765\) 0 0
\(766\) 1.46410 0.0529001
\(767\) −27.7128 + 8.00000i −1.00065 + 0.288863i
\(768\) 1.00000i 0.0360844i
\(769\) −37.9808 + 21.9282i −1.36962 + 0.790751i −0.990879 0.134751i \(-0.956977\pi\)
−0.378742 + 0.925502i \(0.623643\pi\)
\(770\) 0 0
\(771\) 4.66987 8.08846i 0.168181 0.291299i
\(772\) −11.7321 −0.422246
\(773\) −24.4641 + 42.3731i −0.879913 + 1.52405i −0.0284768 + 0.999594i \(0.509066\pi\)
−0.851436 + 0.524459i \(0.824268\pi\)
\(774\) −8.36603 4.83013i −0.300711 0.173615i
\(775\) 0 0
\(776\) 3.00000 5.19615i 0.107694 0.186531i
\(777\) 8.36603 4.83013i 0.300129 0.173280i
\(778\) −5.89230 10.2058i −0.211249 0.365895i
\(779\) −44.4449 −1.59240
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 12.0263 + 20.8301i 0.430059 + 0.744884i
\(783\) 3.86603 2.23205i 0.138160