Properties

Label 1950.2.bc.d.901.2
Level $1950$
Weight $2$
Character 1950.901
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.bc (of order \(6\), degree \(2\), 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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.901
Dual form 1950.2.bc.d.751.2

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −2.36603 + 1.36603i −0.894274 + 0.516309i −0.875338 0.483512i \(-0.839361\pi\)
−0.0189356 + 0.999821i \(0.506028\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 1.09808 + 0.633975i 0.331082 + 0.191151i 0.656322 0.754481i \(-0.272111\pi\)
−0.325239 + 0.945632i \(0.605445\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.59808 2.50000i 0.720577 0.693375i
\(14\) −2.73205 −0.730171
\(15\) 0 0
\(16\) −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 \(0.588688\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.09808 2.36603i 0.940163 0.542803i 0.0501517 0.998742i \(-0.484030\pi\)
0.890011 + 0.455938i \(0.150696\pi\)
\(20\) 0 0
\(21\) 2.73205i 0.596182i
\(22\) 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 \(0.310795\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.50000 0.866025i 0.686406 0.169842i
\(27\) −1.00000 −0.192450
\(28\) −2.36603 1.36603i −0.447137 0.258155i
\(29\) 2.23205 3.86603i 0.414481 0.717903i −0.580892 0.813980i \(-0.697296\pi\)
0.995374 + 0.0960774i \(0.0306296\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 1.09808 0.633975i 0.191151 0.110361i
\(34\) 5.73205i 0.983039i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −3.06218 1.76795i −0.503419 0.290649i 0.226705 0.973963i \(-0.427205\pi\)
−0.730124 + 0.683314i \(0.760538\pi\)
\(38\) 4.73205 0.767640
\(39\) −0.866025 3.50000i −0.138675 0.560449i
\(40\) 0 0
\(41\) 8.13397 + 4.69615i 1.27031 + 0.733416i 0.975047 0.221999i \(-0.0712582\pi\)
0.295267 + 0.955415i \(0.404592\pi\)
\(42\) −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 \(0.569769\pi\)
\(44\) 1.26795i 0.191151i
\(45\) 0 0
\(46\) −3.63397 + 2.09808i −0.535800 + 0.309344i
\(47\) 2.19615i 0.320342i 0.987089 + 0.160171i \(0.0512045\pi\)
−0.987089 + 0.160171i \(0.948795\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0.232051 0.401924i 0.0331501 0.0574177i
\(50\) 0 0
\(51\) 5.73205 0.802648
\(52\) 3.46410 + 1.00000i 0.480384 + 0.138675i
\(53\) 6.46410 0.887913 0.443956 0.896048i \(-0.353575\pi\)
0.443956 + 0.896048i \(0.353575\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.36603 2.36603i −0.182543 0.316173i
\(57\) 4.73205i 0.626775i
\(58\) 3.86603 2.23205i 0.507634 0.293083i
\(59\) −6.92820 + 4.00000i −0.901975 + 0.520756i −0.877841 0.478953i \(-0.841016\pi\)
−0.0241347 + 0.999709i \(0.507683\pi\)
\(60\) 0 0
\(61\) 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
\(63\) 2.36603 + 1.36603i 0.298091 + 0.172103i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.26795 0.156074
\(67\) 11.3660 + 6.56218i 1.38858 + 0.801698i 0.993155 0.116800i \(-0.0372638\pi\)
0.395426 + 0.918498i \(0.370597\pi\)
\(68\) −2.86603 + 4.96410i −0.347557 + 0.601986i
\(69\) 2.09808 + 3.63397i 0.252579 + 0.437479i
\(70\) 0 0
\(71\) 4.09808 2.36603i 0.486352 0.280796i −0.236708 0.971581i \(-0.576068\pi\)
0.723060 + 0.690785i \(0.242735\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 6.26795i 0.733608i −0.930298 0.366804i \(-0.880452\pi\)
0.930298 0.366804i \(-0.119548\pi\)
\(74\) −1.76795 3.06218i −0.205520 0.355971i
\(75\) 0 0
\(76\) 4.09808 + 2.36603i 0.470082 + 0.271402i
\(77\) −3.46410 −0.394771
\(78\) 1.00000 3.46410i 0.113228 0.392232i
\(79\) −2.53590 −0.285311 −0.142655 0.989772i \(-0.545564\pi\)
−0.142655 + 0.989772i \(0.545564\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.69615 + 8.13397i 0.518603 + 0.898247i
\(83\) 0.196152i 0.0215305i 0.999942 + 0.0107653i \(0.00342676\pi\)
−0.999942 + 0.0107653i \(0.996573\pi\)
\(84\) −2.36603 + 1.36603i −0.258155 + 0.149046i
\(85\) 0 0
\(86\) 9.66025i 1.04169i
\(87\) −2.23205 3.86603i −0.239301 0.414481i
\(88\) −0.633975 + 1.09808i −0.0675819 + 0.117055i
\(89\) −8.19615 4.73205i −0.868790 0.501596i −0.00184433 0.999998i \(-0.500587\pi\)
−0.866946 + 0.498402i \(0.833920\pi\)
\(90\) 0 0
\(91\) −2.73205 + 9.46410i −0.286397 + 0.992107i
\(92\) −4.19615 −0.437479
\(93\) 1.26795 + 0.732051i 0.131480 + 0.0759101i
\(94\) −1.09808 + 1.90192i −0.113258 + 0.196168i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 5.19615 3.00000i 0.527589 0.304604i −0.212445 0.977173i \(-0.568143\pi\)
0.740034 + 0.672569i \(0.234809\pi\)
\(98\) 0.401924 0.232051i 0.0406004 0.0234407i
\(99\) 1.26795i 0.127434i
\(100\) 0 0
\(101\) 0.964102 1.66987i 0.0959317 0.166159i −0.814065 0.580773i \(-0.802750\pi\)
0.909997 + 0.414615i \(0.136084\pi\)
\(102\) 4.96410 + 2.86603i 0.491519 + 0.283779i
\(103\) −15.2679 −1.50440 −0.752198 0.658937i \(-0.771006\pi\)
−0.752198 + 0.658937i \(0.771006\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) 0 0
\(106\) 5.59808 + 3.23205i 0.543733 + 0.313925i
\(107\) 5.09808 8.83013i 0.492850 0.853641i −0.507116 0.861878i \(-0.669289\pi\)
0.999966 + 0.00823695i \(0.00262193\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 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
\(112\) 2.73205i 0.258155i
\(113\) −0.669873 1.16025i −0.0630163 0.109148i 0.832796 0.553580i \(-0.186739\pi\)
−0.895812 + 0.444432i \(0.853405\pi\)
\(114\) 2.36603 4.09808i 0.221599 0.383820i
\(115\) 0 0
\(116\) 4.46410 0.414481
\(117\) −3.46410 1.00000i −0.320256 0.0924500i
\(118\) −8.00000 −0.736460
\(119\) −13.5622 7.83013i −1.24324 0.717787i
\(120\) 0 0
\(121\) −4.69615 8.13397i −0.426923 0.739452i
\(122\) 9.19615i 0.832581i
\(123\) 8.13397 4.69615i 0.733416 0.423438i
\(124\) −1.26795 + 0.732051i −0.113865 + 0.0657401i
\(125\) 0 0
\(126\) 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 \(0.0225989\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 9.66025 0.850538
\(130\) 0 0
\(131\) 6.53590 0.571044 0.285522 0.958372i \(-0.407833\pi\)
0.285522 + 0.958372i \(0.407833\pi\)
\(132\) 1.09808 + 0.633975i 0.0955753 + 0.0551804i
\(133\) −6.46410 + 11.1962i −0.560509 + 0.970830i
\(134\) 6.56218 + 11.3660i 0.566886 + 0.981875i
\(135\) 0 0
\(136\) −4.96410 + 2.86603i −0.425668 + 0.245760i
\(137\) 10.3301 5.96410i 0.882562 0.509548i 0.0110599 0.999939i \(-0.496479\pi\)
0.871502 + 0.490391i \(0.163146\pi\)
\(138\) 4.19615i 0.357200i
\(139\) −8.92820 15.4641i −0.757280 1.31165i −0.944233 0.329279i \(-0.893194\pi\)
0.186952 0.982369i \(-0.440139\pi\)
\(140\) 0 0
\(141\) 1.90192 + 1.09808i 0.160171 + 0.0924747i
\(142\) 4.73205 0.397105
\(143\) 4.43782 1.09808i 0.371109 0.0918257i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 3.13397 5.42820i 0.259370 0.449241i
\(147\) −0.232051 0.401924i −0.0191392 0.0331501i
\(148\) 3.53590i 0.290649i
\(149\) 11.4282 6.59808i 0.936235 0.540535i 0.0474568 0.998873i \(-0.484888\pi\)
0.888778 + 0.458338i \(0.151555\pi\)
\(150\) 0 0
\(151\) 6.73205i 0.547847i −0.961752 0.273923i \(-0.911679\pi\)
0.961752 0.273923i \(-0.0883214\pi\)
\(152\) 2.36603 + 4.09808i 0.191910 + 0.332398i
\(153\) 2.86603 4.96410i 0.231704 0.401324i
\(154\) −3.00000 1.73205i −0.241747 0.139573i
\(155\) 0 0
\(156\) 2.59808 2.50000i 0.208013 0.200160i
\(157\) −7.58846 −0.605625 −0.302812 0.953050i \(-0.597926\pi\)
−0.302812 + 0.953050i \(0.597926\pi\)
\(158\) −2.19615 1.26795i −0.174717 0.100873i
\(159\) 3.23205 5.59808i 0.256318 0.443956i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −11.6603 + 6.73205i −0.913302 + 0.527295i −0.881492 0.472199i \(-0.843460\pi\)
−0.0318096 + 0.999494i \(0.510127\pi\)
\(164\) 9.39230i 0.733416i
\(165\) 0 0
\(166\) −0.0980762 + 0.169873i −0.00761219 + 0.0131847i
\(167\) 8.19615 + 4.73205i 0.634237 + 0.366177i 0.782391 0.622787i \(-0.214000\pi\)
−0.148154 + 0.988964i \(0.547333\pi\)
\(168\) −2.73205 −0.210782
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 0 0
\(171\) −4.09808 2.36603i −0.313388 0.180934i
\(172\) −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 \(0.886732\pi\)
\(174\) 4.46410i 0.338423i
\(175\) 0 0
\(176\) −1.09808 + 0.633975i −0.0827706 + 0.0477876i
\(177\) 8.00000i 0.601317i
\(178\) −4.73205 8.19615i −0.354682 0.614328i
\(179\) −8.02628 + 13.9019i −0.599912 + 1.03908i 0.392921 + 0.919572i \(0.371465\pi\)
−0.992833 + 0.119506i \(0.961869\pi\)
\(180\) 0 0
\(181\) −19.1962 −1.42684 −0.713419 0.700737i \(-0.752855\pi\)
−0.713419 + 0.700737i \(0.752855\pi\)
\(182\) −7.09808 + 6.83013i −0.526144 + 0.506283i
\(183\) 9.19615 0.679799
\(184\) −3.63397 2.09808i −0.267900 0.154672i
\(185\) 0 0
\(186\) 0.732051 + 1.26795i 0.0536766 + 0.0929705i
\(187\) 7.26795i 0.531485i
\(188\) −1.90192 + 1.09808i −0.138712 + 0.0800854i
\(189\) 2.36603 1.36603i 0.172103 0.0993637i
\(190\) 0 0
\(191\) 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
\(193\) 10.1603 + 5.86603i 0.731351 + 0.422246i 0.818916 0.573913i \(-0.194575\pi\)
−0.0875652 + 0.996159i \(0.527909\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 0.464102 0.0331501
\(197\) −15.4641 8.92820i −1.10177 0.636108i −0.165086 0.986279i \(-0.552790\pi\)
−0.936686 + 0.350171i \(0.886123\pi\)
\(198\) 0.633975 1.09808i 0.0450546 0.0780369i
\(199\) −7.09808 12.2942i −0.503169 0.871515i −0.999993 0.00366345i \(-0.998834\pi\)
0.496824 0.867851i \(-0.334499\pi\)
\(200\) 0 0
\(201\) 11.3660 6.56218i 0.801698 0.462860i
\(202\) 1.66987 0.964102i 0.117492 0.0678340i
\(203\) 12.1962i 0.856002i
\(204\) 2.86603 + 4.96410i 0.200662 + 0.347557i
\(205\) 0 0
\(206\) −13.2224 7.63397i −0.921250 0.531884i
\(207\) 4.19615 0.291653
\(208\) 0.866025 + 3.50000i 0.0600481 + 0.242681i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −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
\(213\) 4.73205i 0.324235i
\(214\) 8.83013 5.09808i 0.603615 0.348497i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −2.00000 3.46410i −0.135769 0.235159i
\(218\) −0.732051 + 1.26795i −0.0495807 + 0.0858764i
\(219\) −5.42820 3.13397i −0.366804 0.211774i
\(220\) 0 0
\(221\) 19.8564 + 5.73205i 1.33569 + 0.385579i
\(222\) −3.53590 −0.237314
\(223\) −23.3205 13.4641i −1.56166 0.901623i −0.997090 0.0762356i \(-0.975710\pi\)
−0.564567 0.825387i \(-0.690957\pi\)
\(224\) 1.36603 2.36603i 0.0912714 0.158087i
\(225\) 0 0
\(226\) 1.33975i 0.0891186i
\(227\) 10.5622 6.09808i 0.701036 0.404744i −0.106697 0.994292i \(-0.534027\pi\)
0.807733 + 0.589548i \(0.200694\pi\)
\(228\) 4.09808 2.36603i 0.271402 0.156694i
\(229\) 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
\(232\) 3.86603 + 2.23205i 0.253817 + 0.146541i
\(233\) −7.85641 −0.514690 −0.257345 0.966320i \(-0.582848\pi\)
−0.257345 + 0.966320i \(0.582848\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) 0 0
\(236\) −6.92820 4.00000i −0.450988 0.260378i
\(237\) −1.26795 + 2.19615i −0.0823622 + 0.142655i
\(238\) −7.83013 13.5622i −0.507552 0.879105i
\(239\) 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 −0.828592 0.559853i \(-0.810857\pi\)
0.0705514 + 0.997508i \(0.477524\pi\)
\(242\) 9.39230i 0.603760i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −4.59808 + 7.96410i −0.294362 + 0.509849i
\(245\) 0 0
\(246\) 9.39230 0.598831
\(247\) 4.73205 16.3923i 0.301093 1.04302i
\(248\) −1.46410 −0.0929705
\(249\) 0.169873 + 0.0980762i 0.0107653 + 0.00621533i
\(250\) 0 0
\(251\) 6.73205 + 11.6603i 0.424923 + 0.735989i 0.996413 0.0846203i \(-0.0269677\pi\)
−0.571490 + 0.820609i \(0.693634\pi\)
\(252\) 2.73205i 0.172103i
\(253\) −4.60770 + 2.66025i −0.289683 + 0.167249i
\(254\) 8.53590 4.92820i 0.535590 0.309223i
\(255\) 0 0
\(256\) −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 \(0.260754\pi\)
\(258\) 8.36603 + 4.83013i 0.520846 + 0.300711i
\(259\) 9.66025 0.600259
\(260\) 0 0
\(261\) −4.46410 −0.276321
\(262\) 5.66025 + 3.26795i 0.349692 + 0.201895i
\(263\) −5.02628 + 8.70577i −0.309934 + 0.536821i −0.978348 0.206969i \(-0.933640\pi\)
0.668414 + 0.743790i \(0.266974\pi\)
\(264\) 0.633975 + 1.09808i 0.0390184 + 0.0675819i
\(265\) 0 0
\(266\) −11.1962 + 6.46410i −0.686480 + 0.396339i
\(267\) −8.19615 + 4.73205i −0.501596 + 0.289597i
\(268\) 13.1244i 0.801698i
\(269\) −2.73205 4.73205i −0.166576 0.288518i 0.770638 0.637273i \(-0.219938\pi\)
−0.937214 + 0.348755i \(0.886604\pi\)
\(270\) 0 0
\(271\) −18.9282 10.9282i −1.14981 0.663841i −0.200966 0.979598i \(-0.564408\pi\)
−0.948840 + 0.315757i \(0.897742\pi\)
\(272\) −5.73205 −0.347557
\(273\) 6.83013 + 7.09808i 0.413378 + 0.429595i
\(274\) 11.9282 0.720609
\(275\) 0 0
\(276\) −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 \(0.778245\pi\)
\(278\) 17.8564i 1.07096i
\(279\) 1.26795 0.732051i 0.0759101 0.0438267i
\(280\) 0 0
\(281\) 12.3205i 0.734980i −0.930027 0.367490i \(-0.880217\pi\)
0.930027 0.367490i \(-0.119783\pi\)
\(282\) 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 \(0.890554\pi\)
\(284\) 4.09808 + 2.36603i 0.243176 + 0.140398i
\(285\) 0 0
\(286\) 4.39230 + 1.26795i 0.259722 + 0.0749754i
\(287\) −25.6603 −1.51468
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) −7.92820 + 13.7321i −0.466365 + 0.807768i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 5.42820 3.13397i 0.317662 0.183402i
\(293\) 26.4282 15.2583i 1.54395 0.891401i 0.545368 0.838196i \(-0.316390\pi\)
0.998584 0.0532048i \(-0.0169436\pi\)
\(294\) 0.464102i 0.0270670i
\(295\) 0 0
\(296\) 1.76795 3.06218i 0.102760 0.177985i
\(297\) −1.09808 0.633975i −0.0637168 0.0367869i
\(298\) 13.1962 0.764433
\(299\) 3.63397 + 14.6865i 0.210158 + 0.849344i
\(300\) 0 0
\(301\) −22.8564 13.1962i −1.31742 0.760614i
\(302\) 3.36603 5.83013i 0.193693 0.335486i
\(303\) −0.964102 1.66987i −0.0553862 0.0959317i
\(304\) 4.73205i 0.271402i
\(305\) 0 0
\(306\) 4.96410 2.86603i 0.283779 0.163840i
\(307\) 22.5885i 1.28919i −0.764524 0.644596i \(-0.777026\pi\)
0.764524 0.644596i \(-0.222974\pi\)
\(308\) −1.73205 3.00000i −0.0986928 0.170941i
\(309\) −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 \(0.485011\pi\)
\(312\) 3.50000 0.866025i 0.198148 0.0490290i
\(313\) −6.53590 −0.369431 −0.184715 0.982792i \(-0.559136\pi\)
−0.184715 + 0.982792i \(0.559136\pi\)
\(314\) −6.57180 3.79423i −0.370868 0.214121i
\(315\) 0 0
\(316\) −1.26795 2.19615i −0.0713277 0.123543i
\(317\) 20.6603i 1.16040i −0.814476 0.580198i \(-0.802975\pi\)
0.814476 0.580198i \(-0.197025\pi\)
\(318\) 5.59808 3.23205i 0.313925 0.181244i
\(319\) 4.90192 2.83013i 0.274455 0.158457i
\(320\) 0 0
\(321\) −5.09808 8.83013i −0.284547 0.492850i
\(322\) 5.73205 9.92820i 0.319435 0.553277i
\(323\) 23.4904 + 13.5622i 1.30704 + 0.754620i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −13.4641 −0.745708
\(327\) 1.26795 + 0.732051i 0.0701178 + 0.0404825i
\(328\) −4.69615 + 8.13397i −0.259302 + 0.449124i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) 17.3205 10.0000i 0.952021 0.549650i 0.0583130 0.998298i \(-0.481428\pi\)
0.893708 + 0.448649i \(0.148095\pi\)
\(332\) −0.169873 + 0.0980762i −0.00932299 + 0.00538263i
\(333\) 3.53590i 0.193766i
\(334\) 4.73205 + 8.19615i 0.258926 + 0.448474i
\(335\) 0 0
\(336\) −2.36603 1.36603i −0.129077 0.0745228i
\(337\) −20.8564 −1.13612 −0.568060 0.822987i \(-0.692306\pi\)
−0.568060 + 0.822987i \(0.692306\pi\)
\(338\) 6.92820 11.0000i 0.376845 0.598321i
\(339\) −1.33975 −0.0727650
\(340\) 0 0
\(341\) −0.928203 + 1.60770i −0.0502650 + 0.0870616i
\(342\) −2.36603 4.09808i −0.127940 0.221599i
\(343\) 17.8564i 0.964155i
\(344\) −8.36603 + 4.83013i −0.451066 + 0.260423i
\(345\) 0 0
\(346\) 4.39230i 0.236132i
\(347\) 16.5622 + 28.6865i 0.889104 + 1.53997i 0.840936 + 0.541135i \(0.182005\pi\)
0.0481683 + 0.998839i \(0.484662\pi\)
\(348\) 2.23205 3.86603i 0.119650 0.207241i
\(349\) 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i \(-0.198847\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(350\) 0 0
\(351\) −2.59808 + 2.50000i −0.138675 + 0.133440i
\(352\) −1.26795 −0.0675819
\(353\) −18.8660 10.8923i −1.00414 0.579739i −0.0946674 0.995509i \(-0.530179\pi\)
−0.909470 + 0.415770i \(0.863512\pi\)
\(354\) −4.00000 + 6.92820i −0.212598 + 0.368230i
\(355\) 0 0
\(356\) 9.46410i 0.501596i
\(357\) −13.5622 + 7.83013i −0.717787 + 0.414414i
\(358\) −13.9019 + 8.02628i −0.734740 + 0.424202i
\(359\) 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
\(362\) −16.6244 9.59808i −0.873757 0.504464i
\(363\) −9.39230 −0.492968
\(364\) −9.56218 + 2.36603i −0.501194 + 0.124013i
\(365\) 0 0
\(366\) 7.96410 + 4.59808i 0.416290 + 0.240345i
\(367\) −5.63397 + 9.75833i −0.294091 + 0.509381i −0.974773 0.223198i \(-0.928350\pi\)
0.680682 + 0.732579i \(0.261684\pi\)
\(368\) −2.09808 3.63397i −0.109370 0.189434i
\(369\) 9.39230i 0.488944i
\(370\) 0 0
\(371\) −15.2942 + 8.83013i −0.794037 + 0.458437i
\(372\) 1.46410i 0.0759101i
\(373\) −6.86603 11.8923i −0.355509 0.615760i 0.631696 0.775216i \(-0.282359\pi\)
−0.987205 + 0.159456i \(0.949026\pi\)
\(374\) −3.63397 + 6.29423i −0.187908 + 0.325467i
\(375\) 0 0
\(376\) −2.19615 −0.113258
\(377\) −3.86603 15.6244i −0.199110 0.804695i
\(378\) 2.73205 0.140522
\(379\) 4.73205 + 2.73205i 0.243069 + 0.140336i 0.616587 0.787287i \(-0.288515\pi\)
−0.373517 + 0.927623i \(0.621848\pi\)
\(380\) 0 0
\(381\) −4.92820 8.53590i −0.252479 0.437307i
\(382\) 6.92820i 0.354478i
\(383\) 1.26795 0.732051i 0.0647892 0.0374060i −0.467255 0.884122i \(-0.654757\pi\)
0.532045 + 0.846716i \(0.321424\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 5.86603 + 10.1603i 0.298573 + 0.517143i
\(387\) 4.83013 8.36603i 0.245529 0.425269i
\(388\) 5.19615 + 3.00000i 0.263795 + 0.152302i
\(389\) −11.7846 −0.597503 −0.298752 0.954331i \(-0.596570\pi\)
−0.298752 + 0.954331i \(0.596570\pi\)
\(390\) 0 0
\(391\) −24.0526 −1.21639
\(392\) 0.401924 + 0.232051i 0.0203002 + 0.0117203i
\(393\) 3.26795 5.66025i 0.164846 0.285522i
\(394\) −8.92820 15.4641i −0.449796 0.779070i
\(395\) 0 0
\(396\) 1.09808 0.633975i 0.0551804 0.0318584i
\(397\) 17.6603 10.1962i 0.886343 0.511730i 0.0135983 0.999908i \(-0.495671\pi\)
0.872744 + 0.488177i \(0.162338\pi\)
\(398\) 14.1962i 0.711589i
\(399\) 6.46410 + 11.1962i 0.323610 + 0.560509i
\(400\) 0 0
\(401\) 6.99038 + 4.03590i 0.349083 + 0.201543i 0.664281 0.747483i \(-0.268738\pi\)
−0.315198 + 0.949026i \(0.602071\pi\)
\(402\) 13.1244 0.654583
\(403\) 3.66025 + 3.80385i 0.182330 + 0.189483i
\(404\) 1.92820 0.0959317
\(405\) 0 0
\(406\) −6.09808 + 10.5622i −0.302642 + 0.524192i
\(407\) −2.24167 3.88269i −0.111115 0.192458i
\(408\) 5.73205i 0.283779i
\(409\) 15.3564 8.86603i 0.759325 0.438397i −0.0697281 0.997566i \(-0.522213\pi\)
0.829053 + 0.559169i \(0.188880\pi\)
\(410\) 0 0
\(411\) 11.9282i 0.588375i
\(412\) −7.63397 13.2224i −0.376099 0.651422i
\(413\) 10.9282 18.9282i 0.537742 0.931396i
\(414\) 3.63397 + 2.09808i 0.178600 + 0.103115i
\(415\) 0 0
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) −17.8564 −0.874432
\(418\) 5.19615 + 3.00000i 0.254152 + 0.146735i
\(419\) 8.73205 15.1244i 0.426589 0.738873i −0.569979 0.821659i \(-0.693049\pi\)
0.996567 + 0.0827863i \(0.0263819\pi\)
\(420\) 0 0
\(421\) 22.7128i 1.10695i −0.832864 0.553477i \(-0.813301\pi\)
0.832864 0.553477i \(-0.186699\pi\)
\(422\) −14.1962 + 8.19615i −0.691058 + 0.398982i
\(423\) 1.90192 1.09808i 0.0924747 0.0533903i
\(424\) 6.46410i 0.313925i
\(425\) 0 0
\(426\) 2.36603 4.09808i 0.114634 0.198552i
\(427\) −21.7583 12.5622i −1.05296 0.607926i
\(428\) 10.1962 0.492850
\(429\) 1.26795 4.39230i 0.0612172 0.212062i
\(430\) 0 0
\(431\) −11.3660 6.56218i −0.547482 0.316089i 0.200624 0.979668i \(-0.435703\pi\)
−0.748106 + 0.663579i \(0.769036\pi\)
\(432\) 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 \(0.933301\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 0 0
\(436\) −1.26795 + 0.732051i −0.0607238 + 0.0350589i
\(437\) 19.8564i 0.949861i
\(438\) −3.13397 5.42820i −0.149747 0.259370i
\(439\) −0.169873 + 0.294229i −0.00810760 + 0.0140428i −0.870051 0.492962i \(-0.835914\pi\)
0.861943 + 0.507005i \(0.169247\pi\)
\(440\) 0 0
\(441\) −0.464102 −0.0221001
\(442\) 14.3301 + 14.8923i 0.681615 + 0.708355i
\(443\) −15.6077 −0.741544 −0.370772 0.928724i \(-0.620907\pi\)
−0.370772 + 0.928724i \(0.620907\pi\)
\(444\) −3.06218 1.76795i −0.145325 0.0839032i
\(445\) 0 0
\(446\) −13.4641 23.3205i −0.637544 1.10426i
\(447\) 13.1962i 0.624157i
\(448\) 2.36603 1.36603i 0.111784 0.0645386i
\(449\) −9.80385 + 5.66025i −0.462672 + 0.267124i −0.713167 0.700994i \(-0.752740\pi\)
0.250495 + 0.968118i \(0.419407\pi\)
\(450\) 0 0
\(451\) 5.95448 + 10.3135i 0.280386 + 0.485642i
\(452\) 0.669873 1.16025i 0.0315082 0.0545738i
\(453\) −5.83013 3.36603i −0.273923 0.158150i
\(454\) 12.1962 0.572394
\(455\) 0 0
\(456\) 4.73205 0.221599
\(457\) 1.16025 + 0.669873i 0.0542744 + 0.0313353i 0.526892 0.849932i \(-0.323357\pi\)
−0.472617 + 0.881268i \(0.656691\pi\)
\(458\) −5.92820 + 10.2679i −0.277007 + 0.479790i
\(459\) −2.86603 4.96410i −0.133775 0.231704i
\(460\) 0 0
\(461\) 19.2846 11.1340i 0.898174 0.518561i 0.0215666 0.999767i \(-0.493135\pi\)
0.876607 + 0.481207i \(0.159801\pi\)
\(462\) −3.00000 + 1.73205i −0.139573 + 0.0805823i
\(463\) 10.0526i 0.467182i 0.972335 + 0.233591i \(0.0750477\pi\)
−0.972335 + 0.233591i \(0.924952\pi\)
\(464\) 2.23205 + 3.86603i 0.103620 + 0.179476i
\(465\) 0 0
\(466\) −6.80385 3.92820i −0.315182 0.181971i
\(467\) 18.5885 0.860171 0.430086 0.902788i \(-0.358483\pi\)
0.430086 + 0.902788i \(0.358483\pi\)
\(468\) −0.866025 3.50000i −0.0400320 0.161788i
\(469\) −35.8564 −1.65570
\(470\) 0 0
\(471\) −3.79423 + 6.57180i −0.174829 + 0.302812i
\(472\) −4.00000 6.92820i −0.184115 0.318896i
\(473\) 12.2487i 0.563196i
\(474\) −2.19615 + 1.26795i −0.100873 + 0.0582388i
\(475\) 0 0
\(476\) 15.6603i 0.717787i
\(477\) −3.23205 5.59808i −0.147985 0.256318i
\(478\) −3.83013 + 6.63397i −0.175186 + 0.303431i
\(479\) 28.9808 + 16.7321i 1.32416 + 0.764507i 0.984390 0.176000i \(-0.0563159\pi\)
0.339775 + 0.940507i \(0.389649\pi\)
\(480\) 0 0
\(481\) −12.3756 + 3.06218i −0.564281 + 0.139623i
\(482\) −13.5885 −0.618937
\(483\) −9.92820 5.73205i −0.451749 0.260817i
\(484\) 4.69615 8.13397i 0.213461 0.369726i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 2.70577 1.56218i 0.122610 0.0707890i −0.437441 0.899247i \(-0.644115\pi\)
0.560051 + 0.828458i \(0.310782\pi\)
\(488\) −7.96410 + 4.59808i −0.360518 + 0.208145i
\(489\) 13.4641i 0.608868i
\(490\) 0 0
\(491\) 4.36603 7.56218i 0.197036 0.341276i −0.750530 0.660836i \(-0.770202\pi\)
0.947566 + 0.319560i \(0.103535\pi\)
\(492\) 8.13397 + 4.69615i 0.366708 + 0.211719i
\(493\) 25.5885 1.15245
\(494\) 12.2942 11.8301i 0.553143 0.532263i
\(495\) 0 0
\(496\) −1.26795 0.732051i −0.0569326 0.0328701i
\(497\) −6.46410 + 11.1962i −0.289955 + 0.502216i
\(498\) 0.0980762 + 0.169873i 0.00439490 + 0.00761219i
\(499\) 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
\(502\) 13.4641i 0.600932i
\(503\) 20.4904 + 35.4904i 0.913621 + 1.58244i 0.808908 + 0.587935i \(0.200059\pi\)
0.104713 + 0.994502i \(0.466608\pi\)
\(504\) −1.36603 + 2.36603i −0.0608476 + 0.105391i
\(505\) 0 0
\(506\) −5.32051 −0.236525
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 9.85641 0.437307
\(509\) −11.8923 6.86603i −0.527117 0.304331i 0.212725 0.977112i \(-0.431766\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(510\) 0 0
\(511\) 8.56218 + 14.8301i 0.378768 + 0.656046i
\(512\) 1.00000i 0.0441942i
\(513\) −4.09808 + 2.36603i −0.180934 + 0.104463i
\(514\) −8.08846 + 4.66987i −0.356767 + 0.205979i
\(515\) 0 0
\(516\) 4.83013 + 8.36603i 0.212634 + 0.368294i
\(517\) −1.39230 + 2.41154i −0.0612335 + 0.106060i
\(518\) 8.36603 + 4.83013i 0.367582 + 0.212224i
\(519\) −4.39230 −0.192801
\(520\) 0 0
\(521\) 41.4449 1.81573 0.907866 0.419260i \(-0.137710\pi\)
0.907866 + 0.419260i \(0.137710\pi\)
\(522\) −3.86603 2.23205i −0.169211 0.0976942i
\(523\) −11.2224 + 19.4378i −0.490723 + 0.849957i −0.999943 0.0106796i \(-0.996601\pi\)
0.509220 + 0.860636i \(0.329934\pi\)
\(524\) 3.26795 + 5.66025i 0.142761 + 0.247269i
\(525\) 0 0
\(526\) −8.70577 + 5.02628i −0.379590 + 0.219156i
\(527\) −7.26795 + 4.19615i −0.316597 + 0.182787i
\(528\) 1.26795i 0.0551804i
\(529\) 2.69615 + 4.66987i 0.117224 + 0.203038i
\(530\) 0 0
\(531\) 6.92820 + 4.00000i 0.300658 + 0.173585i
\(532\) −12.9282 −0.560509
\(533\) 32.8731 8.13397i 1.42389 0.352322i
\(534\) −9.46410 −0.409552
\(535\) 0 0
\(536\) −6.56218 + 11.3660i −0.283443 + 0.490938i
\(537\) 8.02628 + 13.9019i 0.346360 + 0.599912i
\(538\) 5.46410i 0.235574i
\(539\) 0.509619 0.294229i 0.0219508 0.0126733i
\(540\) 0 0
\(541\) 5.67949i 0.244180i −0.992519 0.122090i \(-0.961040\pi\)
0.992519 0.122090i \(-0.0389597\pi\)
\(542\) −10.9282 18.9282i −0.469407 0.813036i
\(543\) −9.59808 + 16.6244i −0.411893 + 0.713419i
\(544\) −4.96410 2.86603i −0.212834 0.122880i
\(545\) 0 0
\(546\) 2.36603 + 9.56218i 0.101257 + 0.409223i
\(547\) 4.19615 0.179415 0.0897073 0.995968i \(-0.471407\pi\)
0.0897073 + 0.995968i \(0.471407\pi\)
\(548\) 10.3301 + 5.96410i 0.441281 + 0.254774i
\(549\) 4.59808 7.96410i 0.196241 0.339900i
\(550\) 0 0
\(551\) 21.1244i 0.899928i
\(552\) −3.63397 + 2.09808i −0.154672 + 0.0893001i
\(553\) 6.00000 3.46410i 0.255146 0.147309i
\(554\) 5.73205i 0.243532i
\(555\) 0 0
\(556\) 8.92820 15.4641i 0.378640 0.655824i
\(557\) −36.6962 21.1865i −1.55487 0.897702i −0.997734 0.0672780i \(-0.978569\pi\)
−0.557132 0.830424i \(-0.688098\pi\)
\(558\) 1.46410 0.0619804
\(559\) 33.4641 + 9.66025i 1.41538 + 0.408585i
\(560\) 0 0
\(561\) 6.29423 + 3.63397i 0.265743 + 0.153427i
\(562\) 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 \(-0.429966\pi\)
\(564\) 2.19615i 0.0924747i
\(565\) 0 0
\(566\) −22.2224 + 12.8301i −0.934078 + 0.539290i
\(567\) 2.73205i 0.114735i
\(568\) 2.36603 + 4.09808i 0.0992762 + 0.171951i
\(569\) 15.3205 26.5359i 0.642269 1.11244i −0.342656 0.939461i \(-0.611326\pi\)
0.984925 0.172982i \(-0.0553402\pi\)
\(570\) 0 0
\(571\) −14.0526 −0.588081 −0.294041 0.955793i \(-0.595000\pi\)
−0.294041 + 0.955793i \(0.595000\pi\)
\(572\) 3.16987 + 3.29423i 0.132539 + 0.137739i
\(573\) 6.92820 0.289430
\(574\) −22.2224 12.8301i −0.927546 0.535519i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 3.73205i 0.155367i −0.996978 0.0776837i \(-0.975248\pi\)
0.996978 0.0776837i \(-0.0247524\pi\)
\(578\) −13.7321 + 7.92820i −0.571178 + 0.329770i
\(579\) 10.1603 5.86603i 0.422246 0.243784i
\(580\) 0 0
\(581\) −0.267949 0.464102i −0.0111164 0.0192542i
\(582\) 3.00000 5.19615i 0.124354 0.215387i
\(583\) 7.09808 + 4.09808i 0.293972 + 0.169725i
\(584\) 6.26795 0.259370
\(585\) 0 0
\(586\) 30.5167 1.26063
\(587\) 13.8564 + 8.00000i 0.571915 + 0.330195i 0.757914 0.652355i \(-0.226219\pi\)
−0.185999 + 0.982550i \(0.559552\pi\)
\(588\) 0.232051 0.401924i 0.00956961 0.0165751i
\(589\) 3.46410 + 6.00000i 0.142736 + 0.247226i
\(590\) 0 0
\(591\) −15.4641 + 8.92820i −0.636108 + 0.367257i
\(592\) 3.06218 1.76795i 0.125855 0.0726623i
\(593\) 9.14359i 0.375482i −0.982219 0.187741i \(-0.939883\pi\)
0.982219 0.187741i \(-0.0601166\pi\)
\(594\) −0.633975 1.09808i −0.0260123 0.0450546i
\(595\) 0 0
\(596\) 11.4282 + 6.59808i 0.468117 + 0.270268i
\(597\) −14.1962 −0.581010
\(598\) −4.19615 + 14.5359i −0.171593 + 0.594417i
\(599\) −2.53590 −0.103614 −0.0518070 0.998657i \(-0.516498\pi\)
−0.0518070 + 0.998657i \(0.516498\pi\)
\(600\) 0 0
\(601\) −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
\(603\) 13.1244i 0.534465i
\(604\) 5.83013 3.36603i 0.237225 0.136962i
\(605\) 0 0
\(606\) 1.92820i 0.0783279i
\(607\) −20.3923 35.3205i −0.827698 1.43362i −0.899840 0.436221i \(-0.856317\pi\)
0.0721415 0.997394i \(-0.477017\pi\)
\(608\) −2.36603 + 4.09808i −0.0959550 + 0.166199i
\(609\) 10.5622 + 6.09808i 0.428001 + 0.247107i
\(610\) 0 0
\(611\) 5.49038 + 5.70577i 0.222117 + 0.230831i
\(612\) 5.73205 0.231704
\(613\) −8.13397 4.69615i −0.328528 0.189676i 0.326659 0.945142i \(-0.394077\pi\)
−0.655187 + 0.755466i \(0.727410\pi\)
\(614\) 11.2942 19.5622i 0.455798 0.789465i
\(615\) 0 0
\(616\) 3.46410i 0.139573i
\(617\) 11.4737 6.62436i 0.461915 0.266687i −0.250934 0.968004i \(-0.580738\pi\)
0.712849 + 0.701318i \(0.247404\pi\)
\(618\) −13.2224 + 7.63397i −0.531884 + 0.307083i
\(619\) 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
\(622\) 1.43782 + 0.830127i 0.0576514 + 0.0332851i
\(623\) 25.8564 1.03592
\(624\) 3.46410 + 1.00000i 0.138675 + 0.0400320i
\(625\) 0 0
\(626\) −5.66025 3.26795i −0.226229 0.130614i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −3.79423 6.57180i −0.151406 0.262243i
\(629\) 20.2679i 0.808136i
\(630\) 0 0
\(631\) 6.67949 3.85641i 0.265906 0.153521i −0.361119 0.932520i \(-0.617605\pi\)
0.627026 + 0.778998i \(0.284272\pi\)
\(632\) 2.53590i 0.100873i
\(633\) 8.19615 + 14.1962i 0.325768 + 0.564246i
\(634\) 10.3301 17.8923i 0.410262 0.710594i
\(635\) 0 0
\(636\) 6.46410 0.256318
\(637\) −0.401924 1.62436i −0.0159248 0.0643593i
\(638\) 5.66025 0.224092
\(639\) −4.09808 2.36603i −0.162117 0.0935985i
\(640\) 0 0
\(641\) −12.9904 22.5000i −0.513089 0.888697i −0.999885 0.0151806i \(-0.995168\pi\)
0.486796 0.873516i \(-0.338166\pi\)
\(642\) 10.1962i 0.402410i
\(643\) 12.0000 6.92820i 0.473234 0.273222i −0.244359 0.969685i \(-0.578577\pi\)
0.717592 + 0.696463i \(0.245244\pi\)
\(644\) 9.92820 5.73205i 0.391226 0.225874i
\(645\) 0 0
\(646\) 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 \(0.0225860\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −10.1436 −0.398171
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) −11.6603 6.73205i −0.456651 0.263647i
\(653\) −8.73205 + 15.1244i −0.341712 + 0.591862i −0.984751 0.173972i \(-0.944340\pi\)
0.643039 + 0.765833i \(0.277673\pi\)
\(654\) 0.732051 + 1.26795i 0.0286255 + 0.0495807i
\(655\) 0 0
\(656\) −8.13397 + 4.69615i −0.317578 + 0.183354i
\(657\) −5.42820 + 3.13397i −0.211774 + 0.122268i
\(658\) 6.00000i 0.233904i
\(659\) 5.12436 + 8.87564i 0.199617 + 0.345746i 0.948404 0.317064i \(-0.102697\pi\)
−0.748788 + 0.662810i \(0.769364\pi\)
\(660\) 0 0
\(661\) 9.86603 + 5.69615i 0.383744 + 0.221555i 0.679446 0.733726i \(-0.262220\pi\)
−0.295702 + 0.955280i \(0.595554\pi\)
\(662\) 20.0000 0.777322
\(663\) 14.8923 14.3301i 0.578369 0.556536i
\(664\) −0.196152 −0.00761219
\(665\) 0 0
\(666\) −1.76795 + 3.06218i −0.0685066 + 0.118657i
\(667\) 9.36603 + 16.2224i 0.362654 + 0.628135i
\(668\) 9.46410i 0.366177i
\(669\) −23.3205 + 13.4641i −0.901623 + 0.520552i
\(670\) 0 0
\(671\) 11.6603i 0.450139i
\(672\) −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 \(0.985742\pi\)
\(674\) −18.0622 10.4282i −0.695729 0.401679i
\(675\) 0 0
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 45.4641 1.74733 0.873664 0.486530i \(-0.161738\pi\)
0.873664 + 0.486530i \(0.161738\pi\)
\(678\) −1.16025 0.669873i −0.0445593 0.0257263i
\(679\) −8.19615 + 14.1962i −0.314539 + 0.544798i
\(680\) 0 0
\(681\) 12.1962i 0.467358i
\(682\) −1.60770 + 0.928203i −0.0615618 + 0.0355427i
\(683\) −8.78461 + 5.07180i −0.336134 + 0.194067i −0.658561 0.752527i \(-0.728835\pi\)
0.322427 + 0.946594i \(0.395501\pi\)
\(684\) 4.73205i 0.180934i
\(685\) 0 0
\(686\) 8.92820 15.4641i 0.340880 0.590422i
\(687\) 10.2679 + 5.92820i 0.391747 + 0.226175i
\(688\) −9.66025 −0.368294
\(689\) 16.7942 16.1603i 0.639809 0.615657i
\(690\) 0 0
\(691\) −37.8109 21.8301i −1.43839 0.830457i −0.440656 0.897676i \(-0.645254\pi\)
−0.997738 + 0.0672190i \(0.978587\pi\)
\(692\) 2.19615 3.80385i 0.0834852 0.144601i
\(693\) 1.73205 + 3.00000i 0.0657952 + 0.113961i
\(694\) 33.1244i 1.25738i
\(695\) 0 0
\(696\) 3.86603 2.23205i 0.146541 0.0846057i
\(697\) 53.8372i 2.03923i
\(698\) 7.66025 + 13.2679i 0.289945 + 0.502199i
\(699\) −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 \(0.480027\pi\)
\(702\) −3.50000 + 0.866025i −0.132099 + 0.0326860i
\(703\) −16.7321 −0.631061
\(704\) −1.09808 0.633975i −0.0413853 0.0238938i
\(705\) 0 0
\(706\) −10.8923 18.8660i −0.409937 0.710032i
\(707\) 5.26795i 0.198122i
\(708\) −6.92820 + 4.00000i −0.260378 + 0.150329i
\(709\) −11.3827 + 6.57180i −0.427486 + 0.246809i −0.698275 0.715830i \(-0.746049\pi\)
0.270789 + 0.962639i \(0.412715\pi\)
\(710\) 0 0
\(711\) 1.26795 + 2.19615i 0.0475518 + 0.0823622i
\(712\) 4.73205 8.19615i 0.177341 0.307164i
\(713\) −5.32051 3.07180i −0.199255 0.115040i
\(714\) −15.6603 −0.586070
\(715\) 0 0
\(716\) −16.0526 −0.599912
\(717\) 6.63397 + 3.83013i 0.247750 + 0.143039i
\(718\) −0.562178 + 0.973721i −0.0209803 + 0.0363389i
\(719\) −14.7321 25.5167i −0.549413 0.951611i −0.998315 0.0580299i \(-0.981518\pi\)
0.448902 0.893581i \(-0.351815\pi\)
\(720\) 0 0
\(721\) 36.1244 20.8564i 1.34534 0.776733i
\(722\) 2.93782 1.69615i 0.109334 0.0631243i
\(723\) 13.5885i 0.505360i
\(724\) −9.59808 16.6244i −0.356710 0.617839i
\(725\) 0 0
\(726\) −8.13397 4.69615i −0.301880 0.174291i
\(727\) −30.9808 −1.14901 −0.574506 0.818500i \(-0.694806\pi\)
−0.574506 + 0.818500i \(0.694806\pi\)
\(728\) −9.46410 2.73205i −0.350763 0.101257i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −27.6865 + 47.9545i −1.02402 + 1.77366i
\(732\) 4.59808 + 7.96410i 0.169950 + 0.294362i
\(733\) 19.0000i 0.701781i −0.936416 0.350891i \(-0.885879\pi\)
0.936416 0.350891i \(-0.114121\pi\)
\(734\) −9.75833 + 5.63397i −0.360187 + 0.207954i
\(735\) 0 0
\(736\) 4.19615i 0.154672i
\(737\) 8.32051 + 14.4115i 0.306490 + 0.530856i
\(738\) 4.69615 8.13397i 0.172868 0.299416i
\(739\) 2.53590 + 1.46410i 0.0932845 + 0.0538578i 0.545917 0.837840i \(-0.316182\pi\)
−0.452632 + 0.891697i \(0.649515\pi\)
\(740\) 0 0
\(741\) −11.8301 12.2942i −0.434591 0.451640i
\(742\) −17.6603 −0.648328
\(743\) −41.9090 24.1962i −1.53749 0.887671i −0.998985 0.0450491i \(-0.985656\pi\)
−0.538506 0.842622i \(-0.681011\pi\)
\(744\) −0.732051 + 1.26795i −0.0268383 + 0.0464853i
\(745\) 0 0
\(746\) 13.7321i 0.502766i
\(747\) 0.169873 0.0980762i 0.00621533 0.00358842i
\(748\) −6.29423 + 3.63397i −0.230140 + 0.132871i
\(749\) 27.8564i 1.01785i
\(750\) 0 0
\(751\) −24.9545 + 43.2224i −0.910602 + 1.57721i −0.0973862 + 0.995247i \(0.531048\pi\)
−0.813216 + 0.581962i \(0.802285\pi\)
\(752\) −1.90192 1.09808i −0.0693560 0.0400427i
\(753\) 13.4641 0.490659
\(754\) 4.46410 15.4641i 0.162573 0.563169i
\(755\) 0 0
\(756\) 2.36603 + 1.36603i 0.0860515 + 0.0496819i
\(757\) 10.4641 18.1244i 0.380324 0.658741i −0.610784 0.791797i \(-0.709146\pi\)
0.991109 + 0.133056i \(0.0424791\pi\)
\(758\) 2.73205 + 4.73205i 0.0992326 + 0.171876i
\(759\) 5.32051i 0.193122i
\(760\) 0 0
\(761\) −9.80385 + 5.66025i −0.355389 + 0.205184i −0.667056 0.745007i \(-0.732446\pi\)
0.311667 + 0.950191i \(0.399113\pi\)
\(762\) 9.85641i 0.357060i
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) −3.46410 + 6.00000i −0.125327 + 0.217072i
\(765\) 0 0
\(766\) 1.46410 0.0529001
\(767\) −8.00000 + 27.7128i −0.288863 + 1.00065i
\(768\) −1.00000 −0.0360844
\(769\) 37.9808 + 21.9282i 1.36962 + 0.790751i 0.990879 0.134751i \(-0.0430235\pi\)
0.378742 + 0.925502i \(0.376357\pi\)
\(770\) 0 0
\(771\) 4.66987 + 8.08846i 0.168181 + 0.291299i
\(772\) 11.7321i 0.422246i
\(773\) 42.3731 24.4641i 1.52405 0.879913i 0.524459 0.851436i \(-0.324268\pi\)
0.999594 0.0284768i \(-0.00906566\pi\)
\(774\) 8.36603 4.83013i 0.300711 0.173615i
\(775\) 0 0
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) 4.83013 8.36603i 0.173280 0.300129i
\(778\) −10.2058 5.89230i −0.365895 0.211249i
\(779\) 44.4449 1.59240
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −20.8301 12.0263i −0.744884 0.430059i
\(783\) −2.23205 + 3.86603i −0.0797670 + 0.138160i
\(784\) 0.232051