Properties

Label 1950.2.bc.d.751.2
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 751.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.d.901.2

$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 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 −0.0189356 0.999821i \(-0.506028\pi\)
−0.875338 + 0.483512i \(0.839361\pi\)
\(8\) 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 −0.325239 0.945632i \(-0.605445\pi\)
0.656322 + 0.754481i \(0.272111\pi\)
\(12\) 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 −0.275029 0.961436i \(-0.588688\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.09808 + 2.36603i 0.940163 + 0.542803i 0.890011 0.455938i \(-0.150696\pi\)
0.0501517 + 0.998742i \(0.484030\pi\)
\(20\) 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 0.560015 0.828482i \(-0.310795\pi\)
−0.997494 + 0.0707462i \(0.977462\pi\)
\(24\) 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 0.995374 0.0960774i \(-0.0306296\pi\)
−0.580892 + 0.813980i \(0.697296\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i −0.991319 0.131480i \(-0.958027\pi\)
0.991319 0.131480i \(-0.0419730\pi\)
\(32\) −0.866025 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 −0.730124 0.683314i \(-0.760538\pi\)
0.226705 + 0.973963i \(0.427205\pi\)
\(38\) 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 0.295267 0.955415i \(-0.404592\pi\)
0.975047 + 0.221999i \(0.0712582\pi\)
\(42\) −1.36603 2.36603i −0.210782 0.365086i
\(43\) 4.83013 8.36603i 0.736587 1.27581i −0.217436 0.976075i \(-0.569769\pi\)
0.954023 0.299732i \(-0.0968974\pi\)
\(44\) 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 \(-0.948795\pi\)
0.987089 0.160171i \(-0.0512045\pi\)
\(48\) 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 −0.0241347 0.999709i \(-0.507683\pi\)
−0.877841 + 0.478953i \(0.841016\pi\)
\(60\) 0 0
\(61\) 4.59808 7.96410i 0.588723 1.01970i −0.405677 0.914017i \(-0.632964\pi\)
0.994400 0.105682i \(-0.0337026\pi\)
\(62\) −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 0.395426 0.918498i \(-0.370597\pi\)
0.993155 + 0.116800i \(0.0372638\pi\)
\(68\) −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 0.723060 0.690785i \(-0.242735\pi\)
−0.236708 + 0.971581i \(0.576068\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 6.26795i 0.733608i 0.930298 + 0.366804i \(0.119548\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(74\) −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 \(-0.996573\pi\)
0.999942 0.0107653i \(-0.00342676\pi\)
\(84\) −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 −0.866946 0.498402i \(-0.833920\pi\)
−0.00184433 + 0.999998i \(0.500587\pi\)
\(90\) 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 0.740034 0.672569i \(-0.234809\pi\)
−0.212445 + 0.977173i \(0.568143\pi\)
\(98\) 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 0.909997 0.414615i \(-0.136084\pi\)
−0.814065 + 0.580773i \(0.802750\pi\)
\(102\) 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 0.999966 0.00823695i \(-0.00262193\pi\)
−0.507116 + 0.861878i \(0.669289\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 1.46410i 0.140236i −0.997539 0.0701178i \(-0.977662\pi\)
0.997539 0.0701178i \(-0.0223375\pi\)
\(110\) 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 −0.895812 0.444432i \(-0.853405\pi\)
0.832796 + 0.553580i \(0.186739\pi\)
\(114\) 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 0.997481 0.0709368i \(-0.0225989\pi\)
−0.560173 + 0.828375i \(0.689266\pi\)
\(128\) −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 0.871502 0.490391i \(-0.163146\pi\)
0.0110599 + 0.999939i \(0.496479\pi\)
\(138\) 4.19615i 0.357200i
\(139\) −8.92820 + 15.4641i −0.757280 + 1.31165i 0.186952 + 0.982369i \(0.440139\pi\)
−0.944233 + 0.329279i \(0.893194\pi\)
\(140\) 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 0.888778 0.458338i \(-0.151555\pi\)
0.0474568 + 0.998873i \(0.484888\pi\)
\(150\) 0 0
\(151\) 6.73205i 0.547847i 0.961752 + 0.273923i \(0.0883214\pi\)
−0.961752 + 0.273923i \(0.911679\pi\)
\(152\) 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 −0.0318096 0.999494i \(-0.510127\pi\)
−0.881492 + 0.472199i \(0.843460\pi\)
\(164\) 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 −0.148154 0.988964i \(-0.547333\pi\)
0.782391 + 0.622787i \(0.214000\pi\)
\(168\) −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 −0.937353 0.348380i \(-0.886732\pi\)
0.770383 + 0.637582i \(0.220065\pi\)
\(174\) 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 −0.992833 0.119506i \(-0.961869\pi\)
0.392921 0.919572i \(-0.371465\pi\)
\(180\) 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 −0.713052 0.701111i \(-0.752688\pi\)
0.963706 + 0.266966i \(0.0860212\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 10.1603 5.86603i 0.731351 0.422246i −0.0875652 0.996159i \(-0.527909\pi\)
0.818916 + 0.573913i \(0.194575\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 0.464102 0.0331501
\(197\) −15.4641 + 8.92820i −1.10177 + 0.636108i −0.936686 0.350171i \(-0.886123\pi\)
−0.165086 + 0.986279i \(0.552790\pi\)
\(198\) 0.633975 + 1.09808i 0.0450546 + 0.0780369i
\(199\) −7.09808 + 12.2942i −0.503169 + 0.871515i 0.496824 + 0.867851i \(0.334499\pi\)
−0.999993 + 0.00366345i \(0.998834\pi\)
\(200\) 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 −0.997119 0.0758485i \(-0.975833\pi\)
0.432873 0.901455i \(-0.357500\pi\)
\(212\) 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 −0.564567 + 0.825387i \(0.690957\pi\)
−0.997090 + 0.0762356i \(0.975710\pi\)
\(224\) 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 0.807733 0.589548i \(-0.200694\pi\)
−0.106697 + 0.994292i \(0.534027\pi\)
\(228\) 4.09808 + 2.36603i 0.271402 + 0.156694i
\(229\) 11.8564i 0.783493i −0.920073 0.391747i \(-0.871871\pi\)
0.920073 0.391747i \(-0.128129\pi\)
\(230\) 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 \(-0.920309\pi\)
0.968824 0.247750i \(-0.0796913\pi\)
\(240\) 0 0
\(241\) −11.7679 6.79423i −0.758040 0.437655i 0.0705514 0.997508i \(-0.477524\pi\)
−0.828592 + 0.559853i \(0.810857\pi\)
\(242\) 9.39230i 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 −0.571490 0.820609i \(-0.693634\pi\)
0.996413 + 0.0846203i \(0.0269677\pi\)
\(252\) 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 0.682818 0.730588i \(-0.260754\pi\)
−0.974117 + 0.226044i \(0.927421\pi\)
\(258\) 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 0.668414 0.743790i \(-0.266974\pi\)
−0.978348 + 0.206969i \(0.933640\pi\)
\(264\) 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 −0.937214 0.348755i \(-0.886604\pi\)
0.770638 + 0.637273i \(0.219938\pi\)
\(270\) 0 0
\(271\) −18.9282 + 10.9282i −1.14981 + 0.663841i −0.948840 0.315757i \(-0.897742\pi\)
−0.200966 + 0.979598i \(0.564408\pi\)
\(272\) −5.73205 −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 −0.766987 0.641663i \(-0.778245\pi\)
0.939190 + 0.343399i \(0.111578\pi\)
\(278\) 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 \(0.119783\pi\)
−0.930027 + 0.367490i \(0.880217\pi\)
\(282\) 1.09808 1.90192i 0.0653895 0.113258i
\(283\) −12.8301 22.2224i −0.762672 1.32099i −0.941469 0.337100i \(-0.890554\pi\)
0.178797 0.983886i \(-0.442780\pi\)
\(284\) 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 0.998584 + 0.0532048i \(0.0169436\pi\)
0.545368 + 0.838196i \(0.316390\pi\)
\(294\) 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 \(0.222974\pi\)
−0.764524 + 0.644596i \(0.777026\pi\)
\(308\) −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 \(0.197025\pi\)
−0.814476 + 0.580198i \(0.802975\pi\)
\(318\) 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 0.893708 0.448649i \(-0.148095\pi\)
0.0583130 + 0.998298i \(0.481428\pi\)
\(332\) −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 0.0481683 0.998839i \(-0.484662\pi\)
0.840936 0.541135i \(-0.182005\pi\)
\(348\) 2.23205 + 3.86603i 0.119650 + 0.207241i
\(349\) 13.2679 7.66025i 0.710217 0.410044i −0.100924 0.994894i \(-0.532180\pi\)
0.811141 + 0.584850i \(0.198847\pi\)
\(350\) 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 −0.909470 0.415770i \(-0.863512\pi\)
−0.0946674 + 0.995509i \(0.530179\pi\)
\(354\) −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 \(-0.990554\pi\)
0.999560 0.0296706i \(-0.00944584\pi\)
\(360\) 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 0.680682 0.732579i \(-0.261684\pi\)
−0.974773 + 0.223198i \(0.928350\pi\)
\(368\) −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 −0.987205 0.159456i \(-0.949026\pi\)
0.631696 + 0.775216i \(0.282359\pi\)
\(374\) −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 −0.373517 0.927623i \(-0.621848\pi\)
0.616587 + 0.787287i \(0.288515\pi\)
\(380\) 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 0.532045 0.846716i \(-0.321424\pi\)
−0.467255 + 0.884122i \(0.654757\pi\)
\(384\) −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 0.872744 0.488177i \(-0.162338\pi\)
0.0135983 + 0.999908i \(0.495671\pi\)
\(398\) 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 −0.315198 0.949026i \(-0.602071\pi\)
0.664281 + 0.747483i \(0.268738\pi\)
\(402\) 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 0.829053 0.559169i \(-0.188880\pi\)
−0.0697281 + 0.997566i \(0.522213\pi\)
\(410\) 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 0.996567 0.0827863i \(-0.0263819\pi\)
−0.569979 + 0.821659i \(0.693049\pi\)
\(420\) 0 0
\(421\) 22.7128i 1.10695i 0.832864 + 0.553477i \(0.186699\pi\)
−0.832864 + 0.553477i \(0.813301\pi\)
\(422\) −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 −0.748106 0.663579i \(-0.769036\pi\)
0.200624 + 0.979668i \(0.435703\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −6.42820 + 11.1340i −0.308920 + 0.535065i −0.978126 0.208012i \(-0.933301\pi\)
0.669207 + 0.743076i \(0.266634\pi\)
\(434\) 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 0.861943 0.507005i \(-0.169247\pi\)
−0.870051 + 0.492962i \(0.835914\pi\)
\(440\) 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 0.250495 0.968118i \(-0.419407\pi\)
−0.713167 + 0.700994i \(0.752740\pi\)
\(450\) 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 −0.472617 0.881268i \(-0.656691\pi\)
0.526892 + 0.849932i \(0.323357\pi\)
\(458\) −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 0.876607 0.481207i \(-0.159801\pi\)
0.0215666 + 0.999767i \(0.493135\pi\)
\(462\) −3.00000 1.73205i −0.139573 0.0805823i
\(463\) 10.0526i 0.467182i −0.972335 0.233591i \(-0.924952\pi\)
0.972335 0.233591i \(-0.0750477\pi\)
\(464\) 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 0.339775 0.940507i \(-0.389649\pi\)
0.984390 + 0.176000i \(0.0563159\pi\)
\(480\) 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 0.560051 0.828458i \(-0.310782\pi\)
−0.437441 + 0.899247i \(0.644115\pi\)
\(488\) −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 0.947566 0.319560i \(-0.103535\pi\)
−0.750530 + 0.660836i \(0.770202\pi\)
\(492\) 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 \(-0.745853\pi\)
0.697835 0.716258i \(-0.254147\pi\)
\(500\) 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 0.104713 0.994502i \(-0.466608\pi\)
0.808908 0.587935i \(-0.200059\pi\)
\(504\) −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 −0.739842 0.672781i \(-0.765100\pi\)
0.212725 + 0.977112i \(0.431766\pi\)
\(510\) 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 0.509220 0.860636i \(-0.329934\pi\)
−0.999943 + 0.0106796i \(0.996601\pi\)
\(524\) 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 \(0.0389597\pi\)
−0.992519 + 0.122090i \(0.961040\pi\)
\(542\) −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 −0.557132 + 0.830424i \(0.688098\pi\)
−0.997734 + 0.0672780i \(0.978569\pi\)
\(558\) 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 0.218248 + 0.975893i \(0.429966\pi\)
−0.954273 + 0.298938i \(0.903368\pi\)
\(564\) 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 0.984925 + 0.172982i \(0.0553402\pi\)
−0.342656 + 0.939461i \(0.611326\pi\)
\(570\) 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 \(0.0247524\pi\)
−0.996978 + 0.0776837i \(0.975248\pi\)
\(578\) −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 −0.185999 0.982550i \(-0.559552\pi\)
0.757914 + 0.652355i \(0.226219\pi\)
\(588\) 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 \(0.0601166\pi\)
−0.982219 + 0.187741i \(0.939883\pi\)
\(594\) −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 0.773779 0.633456i \(-0.218364\pi\)
−0.935478 + 0.353385i \(0.885031\pi\)
\(602\) −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 0.0721415 + 0.997394i \(0.477017\pi\)
−0.899840 + 0.436221i \(0.856317\pi\)
\(608\) −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 −0.655187 0.755466i \(-0.727410\pi\)
0.326659 + 0.945142i \(0.394077\pi\)
\(614\) 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 0.712849 0.701318i \(-0.247404\pi\)
−0.250934 + 0.968004i \(0.580738\pi\)
\(618\) −13.2224 7.63397i −0.531884 0.307083i
\(619\) 17.4641i 0.701942i 0.936386 + 0.350971i \(0.114148\pi\)
−0.936386 + 0.350971i \(0.885852\pi\)
\(620\) 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 0.627026 0.778998i \(-0.284272\pi\)
−0.361119 + 0.932520i \(0.617605\pi\)
\(632\) 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 0.486796 + 0.873516i \(0.338166\pi\)
−0.999885 + 0.0151806i \(0.995168\pi\)
\(642\) 10.1962i 0.402410i
\(643\) 12.0000 + 6.92820i 0.473234 + 0.273222i 0.717592 0.696463i \(-0.245244\pi\)
−0.244359 + 0.969685i \(0.578577\pi\)
\(644\) 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 0.997484 0.0708966i \(-0.0225860\pi\)
−0.560140 + 0.828398i \(0.689253\pi\)
\(648\) −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 0.643039 0.765833i \(-0.277673\pi\)
−0.984751 + 0.173972i \(0.944340\pi\)
\(654\) 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 −0.748788 0.662810i \(-0.769364\pi\)
0.948404 + 0.317064i \(0.102697\pi\)
\(660\) 0 0
\(661\) 9.86603 5.69615i 0.383744 0.221555i −0.295702 0.955280i \(-0.595554\pi\)
0.679446 + 0.733726i \(0.262220\pi\)
\(662\) 20.0000 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 −0.998997 0.0447770i \(-0.985742\pi\)
0.460720 0.887545i \(-0.347591\pi\)
\(674\) −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 0.322427 0.946594i \(-0.395501\pi\)
−0.658561 + 0.752527i \(0.728835\pi\)
\(684\) 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 −0.997738 0.0672190i \(-0.978587\pi\)
−0.440656 + 0.897676i \(0.645254\pi\)
\(692\) 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 0.270789 0.962639i \(-0.412715\pi\)
−0.698275 + 0.715830i \(0.746049\pi\)
\(710\) 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 0.448902 + 0.893581i \(0.351815\pi\)
−0.998315 + 0.0580299i \(0.981518\pi\)
\(720\) 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 \(0.114121\pi\)
−0.936416 + 0.350891i \(0.885879\pi\)
\(734\) −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 −0.452632 0.891697i \(-0.649515\pi\)
0.545917 + 0.837840i \(0.316182\pi\)
\(740\) 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 −0.538506 + 0.842622i \(0.681011\pi\)
−0.998985 + 0.0450491i \(0.985656\pi\)
\(744\) −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 −0.813216 0.581962i \(-0.802285\pi\)
−0.0973862 0.995247i \(-0.531048\pi\)
\(752\) −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 0.991109 0.133056i \(-0.0424791\pi\)
−0.610784 + 0.791797i \(0.709146\pi\)
\(758\) 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 0.311667 0.950191i \(-0.399113\pi\)
−0.667056 + 0.745007i \(0.732446\pi\)
\(762\) 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 0.378742 0.925502i \(-0.376357\pi\)
0.990879 + 0.134751i \(0.0430235\pi\)
\(770\) 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 0.999594 + 0.0284768i \(0.00906566\pi\)
0.524459 + 0.851436i \(0.324268\pi\)
\(774\) 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