Properties

Label 1950.2.bc.b.901.1
Level $1950$
Weight $2$
Character 1950.901
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 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.901
Dual form 1950.2.bc.b.751.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.401924 + 0.232051i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} -2.00000i q^{21} +(-0.232051 - 0.401924i) q^{22} +(0.133975 - 0.232051i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.59808 - 2.50000i) q^{26} +1.00000 q^{27} +(-1.73205 - 1.00000i) q^{28} +(-1.86603 + 3.23205i) q^{29} -1.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.401924 + 0.232051i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-1.03590 - 0.598076i) q^{37} +0.535898 q^{38} +(-2.50000 - 2.59808i) q^{39} +(-1.73205 - 1.00000i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(-0.964102 - 1.66987i) q^{43} +0.464102i q^{44} +(-0.232051 + 0.133975i) q^{46} -10.4641i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +4.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} +12.9282 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} -0.535898i q^{57} +(3.23205 - 1.86603i) q^{58} +(-1.33013 + 0.767949i) q^{59} +(-5.19615 - 9.00000i) q^{61} +(-0.866025 + 1.50000i) q^{62} +(1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +0.464102 q^{66} +(-3.92820 - 2.26795i) q^{67} +(2.00000 - 3.46410i) q^{68} +(0.133975 + 0.232051i) q^{69} +(-7.26795 + 4.19615i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.00000i q^{73} +(0.598076 + 1.03590i) q^{74} +(-0.464102 - 0.267949i) q^{76} -0.928203 q^{77} +(0.866025 + 3.50000i) q^{78} -0.0717968 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} -4.92820i q^{83} +(1.73205 - 1.00000i) q^{84} +1.92820i q^{86} +(-1.86603 - 3.23205i) q^{87} +(0.232051 - 0.401924i) q^{88} +(6.46410 + 3.73205i) q^{89} +(-1.73205 - 7.00000i) q^{91} +0.267949 q^{92} +(1.50000 + 0.866025i) q^{93} +(-5.23205 + 9.06218i) q^{94} +1.00000i q^{96} +(6.46410 - 3.73205i) q^{97} +(2.59808 - 1.50000i) q^{98} -0.464102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + 12q^{11} - 4q^{12} - 4q^{13} + 8q^{14} - 2q^{16} - 8q^{17} + 12q^{19} + 6q^{22} + 4q^{23} + 4q^{27} - 4q^{29} - 12q^{33} + 2q^{36} - 18q^{37} + 16q^{38} - 10q^{39} - 4q^{42} + 10q^{43} + 6q^{46} - 2q^{48} - 6q^{49} + 16q^{51} - 14q^{52} + 24q^{53} + 4q^{56} + 6q^{58} + 12q^{59} - 4q^{64} - 12q^{66} + 12q^{67} + 8q^{68} + 4q^{69} - 36q^{71} - 8q^{74} + 12q^{76} + 24q^{77} - 28q^{79} - 2q^{81} + 4q^{82} - 4q^{87} - 6q^{88} + 12q^{89} + 8q^{92} + 6q^{93} - 14q^{94} + 12q^{97} + O(q^{100}) \)

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
\(7\) −1.73205 + 1.00000i −0.654654 + 0.377964i −0.790237 0.612801i \(-0.790043\pi\)
0.135583 + 0.990766i \(0.456709\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.401924 + 0.232051i 0.121185 + 0.0699660i 0.559367 0.828920i \(-0.311044\pi\)
−0.438182 + 0.898886i \(0.644378\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −0.464102 + 0.267949i −0.106472 + 0.0614718i −0.552291 0.833652i \(-0.686246\pi\)
0.445818 + 0.895123i \(0.352913\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) −0.232051 0.401924i −0.0494734 0.0856904i
\(23\) 0.133975 0.232051i 0.0279356 0.0483859i −0.851720 0.523998i \(-0.824440\pi\)
0.879655 + 0.475612i \(0.157773\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 2.59808 2.50000i 0.509525 0.490290i
\(27\) 1.00000 0.192450
\(28\) −1.73205 1.00000i −0.327327 0.188982i
\(29\) −1.86603 + 3.23205i −0.346512 + 0.600177i −0.985627 0.168934i \(-0.945967\pi\)
0.639115 + 0.769111i \(0.279301\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −0.401924 + 0.232051i −0.0699660 + 0.0403949i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −1.03590 0.598076i −0.170301 0.0983231i 0.412427 0.910991i \(-0.364681\pi\)
−0.582728 + 0.812668i \(0.698015\pi\)
\(38\) 0.535898 0.0869342
\(39\) −2.50000 2.59808i −0.400320 0.416025i
\(40\) 0 0
\(41\) −1.73205 1.00000i −0.270501 0.156174i 0.358614 0.933486i \(-0.383249\pi\)
−0.629115 + 0.777312i \(0.716583\pi\)
\(42\) −1.00000 + 1.73205i −0.154303 + 0.267261i
\(43\) −0.964102 1.66987i −0.147024 0.254653i 0.783102 0.621893i \(-0.213636\pi\)
−0.930126 + 0.367240i \(0.880303\pi\)
\(44\) 0.464102i 0.0699660i
\(45\) 0 0
\(46\) −0.232051 + 0.133975i −0.0342140 + 0.0197535i
\(47\) 10.4641i 1.52635i −0.646194 0.763173i \(-0.723640\pi\)
0.646194 0.763173i \(-0.276360\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) −3.50000 + 0.866025i −0.485363 + 0.120096i
\(53\) 12.9282 1.77583 0.887913 0.460012i \(-0.152155\pi\)
0.887913 + 0.460012i \(0.152155\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) 0.535898i 0.0709815i
\(58\) 3.23205 1.86603i 0.424389 0.245021i
\(59\) −1.33013 + 0.767949i −0.173168 + 0.0999785i −0.584079 0.811697i \(-0.698544\pi\)
0.410911 + 0.911676i \(0.365211\pi\)
\(60\) 0 0
\(61\) −5.19615 9.00000i −0.665299 1.15233i −0.979204 0.202878i \(-0.934971\pi\)
0.313905 0.949454i \(-0.398363\pi\)
\(62\) −0.866025 + 1.50000i −0.109985 + 0.190500i
\(63\) 1.73205 + 1.00000i 0.218218 + 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0.464102 0.0571270
\(67\) −3.92820 2.26795i −0.479906 0.277074i 0.240471 0.970656i \(-0.422698\pi\)
−0.720377 + 0.693582i \(0.756031\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 0.133975 + 0.232051i 0.0161286 + 0.0279356i
\(70\) 0 0
\(71\) −7.26795 + 4.19615i −0.862547 + 0.497992i −0.864864 0.502006i \(-0.832596\pi\)
0.00231747 + 0.999997i \(0.499262\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 0.598076 + 1.03590i 0.0695249 + 0.120421i
\(75\) 0 0
\(76\) −0.464102 0.267949i −0.0532361 0.0307359i
\(77\) −0.928203 −0.105779
\(78\) 0.866025 + 3.50000i 0.0980581 + 0.396297i
\(79\) −0.0717968 −0.00807777 −0.00403888 0.999992i \(-0.501286\pi\)
−0.00403888 + 0.999992i \(0.501286\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.00000 + 1.73205i 0.110432 + 0.191273i
\(83\) 4.92820i 0.540941i −0.962728 0.270470i \(-0.912821\pi\)
0.962728 0.270470i \(-0.0871792\pi\)
\(84\) 1.73205 1.00000i 0.188982 0.109109i
\(85\) 0 0
\(86\) 1.92820i 0.207924i
\(87\) −1.86603 3.23205i −0.200059 0.346512i
\(88\) 0.232051 0.401924i 0.0247367 0.0428452i
\(89\) 6.46410 + 3.73205i 0.685193 + 0.395597i 0.801809 0.597581i \(-0.203871\pi\)
−0.116615 + 0.993177i \(0.537205\pi\)
\(90\) 0 0
\(91\) −1.73205 7.00000i −0.181568 0.733799i
\(92\) 0.267949 0.0279356
\(93\) 1.50000 + 0.866025i 0.155543 + 0.0898027i
\(94\) −5.23205 + 9.06218i −0.539645 + 0.934692i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 6.46410 3.73205i 0.656330 0.378932i −0.134547 0.990907i \(-0.542958\pi\)
0.790877 + 0.611975i \(0.209625\pi\)
\(98\) 2.59808 1.50000i 0.262445 0.151523i
\(99\) 0.464102i 0.0466440i
\(100\) 0 0
\(101\) 5.46410 9.46410i 0.543698 0.941713i −0.454989 0.890497i \(-0.650357\pi\)
0.998688 0.0512163i \(-0.0163098\pi\)
\(102\) −3.46410 2.00000i −0.342997 0.198030i
\(103\) −15.8564 −1.56238 −0.781189 0.624295i \(-0.785387\pi\)
−0.781189 + 0.624295i \(0.785387\pi\)
\(104\) 3.46410 + 1.00000i 0.339683 + 0.0980581i
\(105\) 0 0
\(106\) −11.1962 6.46410i −1.08747 0.627849i
\(107\) 9.92820 17.1962i 0.959796 1.66241i 0.236805 0.971557i \(-0.423900\pi\)
0.722991 0.690858i \(-0.242767\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 11.8564i 1.13564i −0.823154 0.567819i \(-0.807787\pi\)
0.823154 0.567819i \(-0.192213\pi\)
\(110\) 0 0
\(111\) 1.03590 0.598076i 0.0983231 0.0567669i
\(112\) 2.00000i 0.188982i
\(113\) 5.59808 + 9.69615i 0.526623 + 0.912137i 0.999519 + 0.0310191i \(0.00987527\pi\)
−0.472896 + 0.881118i \(0.656791\pi\)
\(114\) −0.267949 + 0.464102i −0.0250957 + 0.0434671i
\(115\) 0 0
\(116\) −3.73205 −0.346512
\(117\) 3.50000 0.866025i 0.323575 0.0800641i
\(118\) 1.53590 0.141391
\(119\) 6.92820 + 4.00000i 0.635107 + 0.366679i
\(120\) 0 0
\(121\) −5.39230 9.33975i −0.490210 0.849068i
\(122\) 10.3923i 0.940875i
\(123\) 1.73205 1.00000i 0.156174 0.0901670i
\(124\) 1.50000 0.866025i 0.134704 0.0777714i
\(125\) 0 0
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) 4.46410 7.73205i 0.396125 0.686109i −0.597119 0.802153i \(-0.703688\pi\)
0.993244 + 0.116044i \(0.0370214\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 1.92820 0.169769
\(130\) 0 0
\(131\) −1.33975 −0.117054 −0.0585271 0.998286i \(-0.518640\pi\)
−0.0585271 + 0.998286i \(0.518640\pi\)
\(132\) −0.401924 0.232051i −0.0349830 0.0201974i
\(133\) 0.535898 0.928203i 0.0464683 0.0804854i
\(134\) 2.26795 + 3.92820i 0.195921 + 0.339345i
\(135\) 0 0
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) 3.86603 2.23205i 0.330297 0.190697i −0.325676 0.945481i \(-0.605592\pi\)
0.655973 + 0.754784i \(0.272259\pi\)
\(138\) 0.267949i 0.0228093i
\(139\) −0.464102 0.803848i −0.0393646 0.0681815i 0.845672 0.533703i \(-0.179200\pi\)
−0.885036 + 0.465522i \(0.845867\pi\)
\(140\) 0 0
\(141\) 9.06218 + 5.23205i 0.763173 + 0.440618i
\(142\) 8.39230 0.704267
\(143\) −1.20577 + 1.16025i −0.100832 + 0.0970253i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) −1.50000 2.59808i −0.123718 0.214286i
\(148\) 1.19615i 0.0983231i
\(149\) 17.7224 10.2321i 1.45188 0.838242i 0.453290 0.891363i \(-0.350250\pi\)
0.998588 + 0.0531208i \(0.0169168\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i −0.906196 0.422857i \(-0.861027\pi\)
0.906196 0.422857i \(-0.138973\pi\)
\(152\) 0.267949 + 0.464102i 0.0217335 + 0.0376436i
\(153\) −2.00000 + 3.46410i −0.161690 + 0.280056i
\(154\) 0.803848 + 0.464102i 0.0647759 + 0.0373984i
\(155\) 0 0
\(156\) 1.00000 3.46410i 0.0800641 0.277350i
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 0.0621778 + 0.0358984i 0.00494660 + 0.00285592i
\(159\) −6.46410 + 11.1962i −0.512637 + 0.887913i
\(160\) 0 0
\(161\) 0.535898i 0.0422347i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −19.9641 + 11.5263i −1.56371 + 0.902808i −0.566833 + 0.823833i \(0.691831\pi\)
−0.996877 + 0.0789748i \(0.974835\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 0 0
\(166\) −2.46410 + 4.26795i −0.191251 + 0.331257i
\(167\) −15.8660 9.16025i −1.22775 0.708842i −0.261191 0.965287i \(-0.584115\pi\)
−0.966559 + 0.256445i \(0.917449\pi\)
\(168\) −2.00000 −0.154303
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) 0.464102 + 0.267949i 0.0354907 + 0.0204906i
\(172\) 0.964102 1.66987i 0.0735121 0.127327i
\(173\) −1.46410 2.53590i −0.111314 0.192801i 0.804987 0.593293i \(-0.202172\pi\)
−0.916300 + 0.400492i \(0.868839\pi\)
\(174\) 3.73205i 0.282926i
\(175\) 0 0
\(176\) −0.401924 + 0.232051i −0.0302961 + 0.0174915i
\(177\) 1.53590i 0.115445i
\(178\) −3.73205 6.46410i −0.279729 0.484505i
\(179\) 8.13397 14.0885i 0.607962 1.05302i −0.383614 0.923494i \(-0.625321\pi\)
0.991576 0.129527i \(-0.0413460\pi\)
\(180\) 0 0
\(181\) 10.9282 0.812287 0.406143 0.913809i \(-0.366873\pi\)
0.406143 + 0.913809i \(0.366873\pi\)
\(182\) −2.00000 + 6.92820i −0.148250 + 0.513553i
\(183\) 10.3923 0.768221
\(184\) −0.232051 0.133975i −0.0171070 0.00987674i
\(185\) 0 0
\(186\) −0.866025 1.50000i −0.0635001 0.109985i
\(187\) 1.85641i 0.135754i
\(188\) 9.06218 5.23205i 0.660927 0.381587i
\(189\) −1.73205 + 1.00000i −0.125988 + 0.0727393i
\(190\) 0 0
\(191\) −7.26795 12.5885i −0.525890 0.910869i −0.999545 0.0301582i \(-0.990399\pi\)
0.473655 0.880711i \(-0.342934\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −20.1962 11.6603i −1.45375 0.839323i −0.455059 0.890461i \(-0.650382\pi\)
−0.998692 + 0.0511377i \(0.983715\pi\)
\(194\) −7.46410 −0.535891
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −14.1962 8.19615i −1.01143 0.583952i −0.0998228 0.995005i \(-0.531828\pi\)
−0.911611 + 0.411054i \(0.865161\pi\)
\(198\) −0.232051 + 0.401924i −0.0164911 + 0.0285635i
\(199\) 9.46410 + 16.3923i 0.670892 + 1.16202i 0.977651 + 0.210232i \(0.0674221\pi\)
−0.306759 + 0.951787i \(0.599245\pi\)
\(200\) 0 0
\(201\) 3.92820 2.26795i 0.277074 0.159969i
\(202\) −9.46410 + 5.46410i −0.665892 + 0.384453i
\(203\) 7.46410i 0.523877i
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) 13.7321 + 7.92820i 0.956757 + 0.552384i
\(207\) −0.267949 −0.0186238
\(208\) −2.50000 2.59808i −0.173344 0.180144i
\(209\) −0.248711 −0.0172037
\(210\) 0 0
\(211\) −11.6603 + 20.1962i −0.802725 + 1.39036i 0.115091 + 0.993355i \(0.463284\pi\)
−0.917816 + 0.397006i \(0.870049\pi\)
\(212\) 6.46410 + 11.1962i 0.443956 + 0.768955i
\(213\) 8.39230i 0.575031i
\(214\) −17.1962 + 9.92820i −1.17550 + 0.678678i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 1.73205 + 3.00000i 0.117579 + 0.203653i
\(218\) −5.92820 + 10.2679i −0.401509 + 0.695433i
\(219\) −1.73205 1.00000i −0.117041 0.0675737i
\(220\) 0 0
\(221\) 14.0000 3.46410i 0.941742 0.233021i
\(222\) −1.19615 −0.0802805
\(223\) −23.7846 13.7321i −1.59274 0.919566i −0.992835 0.119491i \(-0.961874\pi\)
−0.599900 0.800075i \(-0.704793\pi\)
\(224\) −1.00000 + 1.73205i −0.0668153 + 0.115728i
\(225\) 0 0
\(226\) 11.1962i 0.744757i
\(227\) 3.80385 2.19615i 0.252470 0.145764i −0.368425 0.929658i \(-0.620103\pi\)
0.620895 + 0.783894i \(0.286769\pi\)
\(228\) 0.464102 0.267949i 0.0307359 0.0177454i
\(229\) 19.8564i 1.31215i −0.754696 0.656074i \(-0.772216\pi\)
0.754696 0.656074i \(-0.227784\pi\)
\(230\) 0 0
\(231\) 0.464102 0.803848i 0.0305356 0.0528893i
\(232\) 3.23205 + 1.86603i 0.212195 + 0.122511i
\(233\) 18.1244 1.18737 0.593683 0.804699i \(-0.297673\pi\)
0.593683 + 0.804699i \(0.297673\pi\)
\(234\) −3.46410 1.00000i −0.226455 0.0653720i
\(235\) 0 0
\(236\) −1.33013 0.767949i −0.0865839 0.0499892i
\(237\) 0.0358984 0.0621778i 0.00233185 0.00403888i
\(238\) −4.00000 6.92820i −0.259281 0.449089i
\(239\) 4.39230i 0.284115i −0.989858 0.142057i \(-0.954628\pi\)
0.989858 0.142057i \(-0.0453717\pi\)
\(240\) 0 0
\(241\) −12.3564 + 7.13397i −0.795946 + 0.459540i −0.842052 0.539397i \(-0.818652\pi\)
0.0461056 + 0.998937i \(0.485319\pi\)
\(242\) 10.7846i 0.693261i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 5.19615 9.00000i 0.332650 0.576166i
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −0.464102 1.87564i −0.0295301 0.119344i
\(248\) −1.73205 −0.109985
\(249\) 4.26795 + 2.46410i 0.270470 + 0.156156i
\(250\) 0 0
\(251\) −6.13397 10.6244i −0.387173 0.670603i 0.604895 0.796305i \(-0.293215\pi\)
−0.992068 + 0.125702i \(0.959882\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 0.107695 0.0621778i 0.00677074 0.00390909i
\(254\) −7.73205 + 4.46410i −0.485152 + 0.280103i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.3301 + 19.6244i −0.706754 + 1.22413i 0.259301 + 0.965797i \(0.416508\pi\)
−0.966055 + 0.258337i \(0.916825\pi\)
\(258\) −1.66987 0.964102i −0.103962 0.0600223i
\(259\) 2.39230 0.148651
\(260\) 0 0
\(261\) 3.73205 0.231008
\(262\) 1.16025 + 0.669873i 0.0716807 + 0.0413849i
\(263\) −9.06218 + 15.6962i −0.558798 + 0.967866i 0.438799 + 0.898585i \(0.355404\pi\)
−0.997597 + 0.0692812i \(0.977929\pi\)
\(264\) 0.232051 + 0.401924i 0.0142817 + 0.0247367i
\(265\) 0 0
\(266\) −0.928203 + 0.535898i −0.0569118 + 0.0328580i
\(267\) −6.46410 + 3.73205i −0.395597 + 0.228398i
\(268\) 4.53590i 0.277074i
\(269\) −6.00000 10.3923i −0.365826 0.633630i 0.623082 0.782157i \(-0.285880\pi\)
−0.988908 + 0.148527i \(0.952547\pi\)
\(270\) 0 0
\(271\) 7.96410 + 4.59808i 0.483785 + 0.279313i 0.721992 0.691901i \(-0.243227\pi\)
−0.238208 + 0.971214i \(0.576560\pi\)
\(272\) 4.00000 0.242536
\(273\) 6.92820 + 2.00000i 0.419314 + 0.121046i
\(274\) −4.46410 −0.269686
\(275\) 0 0
\(276\) −0.133975 + 0.232051i −0.00806432 + 0.0139678i
\(277\) 4.96410 + 8.59808i 0.298264 + 0.516608i 0.975739 0.218938i \(-0.0702591\pi\)
−0.677475 + 0.735546i \(0.736926\pi\)
\(278\) 0.928203i 0.0556699i
\(279\) −1.50000 + 0.866025i −0.0898027 + 0.0518476i
\(280\) 0 0
\(281\) 4.92820i 0.293992i −0.989137 0.146996i \(-0.953040\pi\)
0.989137 0.146996i \(-0.0469604\pi\)
\(282\) −5.23205 9.06218i −0.311564 0.539645i
\(283\) 1.96410 3.40192i 0.116754 0.202223i −0.801726 0.597692i \(-0.796085\pi\)
0.918479 + 0.395469i \(0.129418\pi\)
\(284\) −7.26795 4.19615i −0.431273 0.248996i
\(285\) 0 0
\(286\) 1.62436 0.401924i 0.0960502 0.0237663i
\(287\) 4.00000 0.236113
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 7.46410i 0.437553i
\(292\) −1.73205 + 1.00000i −0.101361 + 0.0585206i
\(293\) −3.58846 + 2.07180i −0.209640 + 0.121036i −0.601144 0.799141i \(-0.705288\pi\)
0.391504 + 0.920176i \(0.371955\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 0 0
\(296\) −0.598076 + 1.03590i −0.0347625 + 0.0602104i
\(297\) 0.401924 + 0.232051i 0.0233220 + 0.0134650i
\(298\) −20.4641 −1.18545
\(299\) 0.669873 + 0.696152i 0.0387398 + 0.0402595i
\(300\) 0 0
\(301\) 3.33975 + 1.92820i 0.192500 + 0.111140i
\(302\) −5.19615 + 9.00000i −0.299005 + 0.517892i
\(303\) 5.46410 + 9.46410i 0.313904 + 0.543698i
\(304\) 0.535898i 0.0307359i
\(305\) 0 0
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 12.5359i 0.715462i 0.933825 + 0.357731i \(0.116449\pi\)
−0.933825 + 0.357731i \(0.883551\pi\)
\(308\) −0.464102 0.803848i −0.0264446 0.0458035i
\(309\) 7.92820 13.7321i 0.451020 0.781189i
\(310\) 0 0
\(311\) −7.60770 −0.431393 −0.215696 0.976460i \(-0.569202\pi\)
−0.215696 + 0.976460i \(0.569202\pi\)
\(312\) −2.59808 + 2.50000i −0.147087 + 0.141535i
\(313\) 28.0000 1.58265 0.791327 0.611393i \(-0.209391\pi\)
0.791327 + 0.611393i \(0.209391\pi\)
\(314\) −4.33013 2.50000i −0.244363 0.141083i
\(315\) 0 0
\(316\) −0.0358984 0.0621778i −0.00201944 0.00349778i
\(317\) 21.4641i 1.20554i 0.797913 + 0.602772i \(0.205937\pi\)
−0.797913 + 0.602772i \(0.794063\pi\)
\(318\) 11.1962 6.46410i 0.627849 0.362489i
\(319\) −1.50000 + 0.866025i −0.0839839 + 0.0484881i
\(320\) 0 0
\(321\) 9.92820 + 17.1962i 0.554138 + 0.959796i
\(322\) 0.267949 0.464102i 0.0149322 0.0258634i
\(323\) 1.85641 + 1.07180i 0.103293 + 0.0596364i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 23.0526 1.27676
\(327\) 10.2679 + 5.92820i 0.567819 + 0.327830i
\(328\) −1.00000 + 1.73205i −0.0552158 + 0.0956365i
\(329\) 10.4641 + 18.1244i 0.576905 + 0.999228i
\(330\) 0 0
\(331\) −21.4641 + 12.3923i −1.17977 + 0.681143i −0.955962 0.293490i \(-0.905183\pi\)
−0.223812 + 0.974632i \(0.571850\pi\)
\(332\) 4.26795 2.46410i 0.234234 0.135235i
\(333\) 1.19615i 0.0655487i
\(334\) 9.16025 + 15.8660i 0.501227 + 0.868150i
\(335\) 0 0
\(336\) 1.73205 + 1.00000i 0.0944911 + 0.0545545i
\(337\) 25.3205 1.37930 0.689648 0.724145i \(-0.257765\pi\)
0.689648 + 0.724145i \(0.257765\pi\)
\(338\) 6.06218 + 11.5000i 0.329739 + 0.625518i
\(339\) −11.1962 −0.608092
\(340\) 0 0
\(341\) 0.401924 0.696152i 0.0217654 0.0376988i
\(342\) −0.267949 0.464102i −0.0144890 0.0250957i
\(343\) 20.0000i 1.07990i
\(344\) −1.66987 + 0.964102i −0.0900335 + 0.0519809i
\(345\) 0 0
\(346\) 2.92820i 0.157421i
\(347\) 11.1962 + 19.3923i 0.601041 + 1.04103i 0.992664 + 0.120908i \(0.0385805\pi\)
−0.391623 + 0.920126i \(0.628086\pi\)
\(348\) 1.86603 3.23205i 0.100029 0.173256i
\(349\) −12.5885 7.26795i −0.673845 0.389044i 0.123687 0.992321i \(-0.460528\pi\)
−0.797532 + 0.603277i \(0.793861\pi\)
\(350\) 0 0
\(351\) −1.00000 + 3.46410i −0.0533761 + 0.184900i
\(352\) 0.464102 0.0247367
\(353\) 1.73205 + 1.00000i 0.0921878 + 0.0532246i 0.545385 0.838186i \(-0.316383\pi\)
−0.453197 + 0.891410i \(0.649717\pi\)
\(354\) −0.767949 + 1.33013i −0.0408160 + 0.0706955i
\(355\) 0 0
\(356\) 7.46410i 0.395597i
\(357\) −6.92820 + 4.00000i −0.366679 + 0.211702i
\(358\) −14.0885 + 8.13397i −0.744598 + 0.429894i
\(359\) 18.9282i 0.998992i −0.866316 0.499496i \(-0.833518\pi\)
0.866316 0.499496i \(-0.166482\pi\)
\(360\) 0 0
\(361\) −9.35641 + 16.2058i −0.492442 + 0.852935i
\(362\) −9.46410 5.46410i −0.497422 0.287187i
\(363\) 10.7846 0.566045
\(364\) 5.19615 5.00000i 0.272352 0.262071i
\(365\) 0 0
\(366\) −9.00000 5.19615i −0.470438 0.271607i
\(367\) 18.1962 31.5167i 0.949831 1.64516i 0.204056 0.978959i \(-0.434588\pi\)
0.745776 0.666197i \(-0.232079\pi\)
\(368\) 0.133975 + 0.232051i 0.00698391 + 0.0120965i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) −22.3923 + 12.9282i −1.16255 + 0.671199i
\(372\) 1.73205i 0.0898027i
\(373\) 12.8923 + 22.3301i 0.667538 + 1.15621i 0.978590 + 0.205817i \(0.0659853\pi\)
−0.311052 + 0.950393i \(0.600681\pi\)
\(374\) −0.928203 + 1.60770i −0.0479962 + 0.0831319i
\(375\) 0 0
\(376\) −10.4641 −0.539645
\(377\) −9.33013 9.69615i −0.480526 0.499377i
\(378\) 2.00000 0.102869
\(379\) −0.124356 0.0717968i −0.00638772 0.00368795i 0.496803 0.867863i \(-0.334507\pi\)
−0.503190 + 0.864176i \(0.667841\pi\)
\(380\) 0 0
\(381\) 4.46410 + 7.73205i 0.228703 + 0.396125i
\(382\) 14.5359i 0.743721i
\(383\) 3.99038 2.30385i 0.203899 0.117721i −0.394574 0.918864i \(-0.629108\pi\)
0.598473 + 0.801143i \(0.295774\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 11.6603 + 20.1962i 0.593491 + 1.02796i
\(387\) −0.964102 + 1.66987i −0.0490080 + 0.0848844i
\(388\) 6.46410 + 3.73205i 0.328165 + 0.189466i
\(389\) −20.2679 −1.02763 −0.513813 0.857902i \(-0.671767\pi\)
−0.513813 + 0.857902i \(0.671767\pi\)
\(390\) 0 0
\(391\) −1.07180 −0.0542031
\(392\) 2.59808 + 1.50000i 0.131223 + 0.0757614i
\(393\) 0.669873 1.16025i 0.0337906 0.0585271i
\(394\) 8.19615 + 14.1962i 0.412916 + 0.715192i
\(395\) 0 0
\(396\) 0.401924 0.232051i 0.0201974 0.0116610i
\(397\) −10.5000 + 6.06218i −0.526980 + 0.304252i −0.739786 0.672843i \(-0.765073\pi\)
0.212806 + 0.977095i \(0.431740\pi\)
\(398\) 18.9282i 0.948785i
\(399\) 0.535898 + 0.928203i 0.0268285 + 0.0464683i
\(400\) 0 0
\(401\) 27.7128 + 16.0000i 1.38391 + 0.799002i 0.992620 0.121265i \(-0.0386950\pi\)
0.391292 + 0.920267i \(0.372028\pi\)
\(402\) −4.53590 −0.226230
\(403\) 6.00000 + 1.73205i 0.298881 + 0.0862796i
\(404\) 10.9282 0.543698
\(405\) 0 0
\(406\) −3.73205 + 6.46410i −0.185219 + 0.320808i
\(407\) −0.277568 0.480762i −0.0137585 0.0238305i
\(408\) 4.00000i 0.198030i
\(409\) −3.46410 + 2.00000i −0.171289 + 0.0988936i −0.583193 0.812333i \(-0.698197\pi\)
0.411905 + 0.911227i \(0.364864\pi\)
\(410\) 0 0
\(411\) 4.46410i 0.220198i
\(412\) −7.92820 13.7321i −0.390595 0.676530i
\(413\) 1.53590 2.66025i 0.0755766 0.130903i
\(414\) 0.232051 + 0.133975i 0.0114047 + 0.00658449i
\(415\) 0 0
\(416\) 0.866025 + 3.50000i 0.0424604 + 0.171602i
\(417\) 0.928203 0.0454543
\(418\) 0.215390 + 0.124356i 0.0105351 + 0.00608243i
\(419\) −0.803848 + 1.39230i −0.0392705 + 0.0680185i −0.884993 0.465605i \(-0.845837\pi\)
0.845722 + 0.533624i \(0.179170\pi\)
\(420\) 0 0
\(421\) 16.3923i 0.798912i 0.916752 + 0.399456i \(0.130801\pi\)
−0.916752 + 0.399456i \(0.869199\pi\)
\(422\) 20.1962 11.6603i 0.983133 0.567612i
\(423\) −9.06218 + 5.23205i −0.440618 + 0.254391i
\(424\) 12.9282i 0.627849i
\(425\) 0 0
\(426\) −4.19615 + 7.26795i −0.203304 + 0.352133i
\(427\) 18.0000 + 10.3923i 0.871081 + 0.502919i
\(428\) 19.8564 0.959796
\(429\) −0.401924 1.62436i −0.0194051 0.0784246i
\(430\) 0 0
\(431\) −6.58846 3.80385i −0.317355 0.183225i 0.332858 0.942977i \(-0.391987\pi\)
−0.650213 + 0.759752i \(0.725320\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −7.66025 13.2679i −0.368128 0.637617i 0.621145 0.783696i \(-0.286668\pi\)
−0.989273 + 0.146079i \(0.953335\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 0 0
\(436\) 10.2679 5.92820i 0.491746 0.283909i
\(437\) 0.143594i 0.00686901i
\(438\) 1.00000 + 1.73205i 0.0477818 + 0.0827606i
\(439\) −4.92820 + 8.53590i −0.235210 + 0.407396i −0.959334 0.282274i \(-0.908911\pi\)
0.724123 + 0.689670i \(0.242245\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −13.8564 4.00000i −0.659082 0.190261i
\(443\) 4.39230 0.208685 0.104342 0.994541i \(-0.466726\pi\)
0.104342 + 0.994541i \(0.466726\pi\)
\(444\) 1.03590 + 0.598076i 0.0491616 + 0.0283834i
\(445\) 0 0
\(446\) 13.7321 + 23.7846i 0.650231 + 1.12623i
\(447\) 20.4641i 0.967919i
\(448\) 1.73205 1.00000i 0.0818317 0.0472456i
\(449\) −34.3923 + 19.8564i −1.62307 + 0.937082i −0.636982 + 0.770879i \(0.719817\pi\)
−0.986092 + 0.166203i \(0.946849\pi\)
\(450\) 0 0
\(451\) −0.464102 0.803848i −0.0218537 0.0378517i
\(452\) −5.59808 + 9.69615i −0.263311 + 0.456069i
\(453\) 9.00000 + 5.19615i 0.422857 + 0.244137i
\(454\) −4.39230 −0.206141
\(455\) 0 0
\(456\) −0.535898 −0.0250957
\(457\) 27.2487 + 15.7321i 1.27464 + 0.735914i 0.975858 0.218407i \(-0.0700859\pi\)
0.298783 + 0.954321i \(0.403419\pi\)
\(458\) −9.92820 + 17.1962i −0.463914 + 0.803523i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 5.59808 3.23205i 0.260728 0.150532i −0.363938 0.931423i \(-0.618568\pi\)
0.624667 + 0.780891i \(0.285235\pi\)
\(462\) −0.803848 + 0.464102i −0.0373984 + 0.0215920i
\(463\) 20.9282i 0.972616i 0.873787 + 0.486308i \(0.161657\pi\)
−0.873787 + 0.486308i \(0.838343\pi\)
\(464\) −1.86603 3.23205i −0.0866281 0.150044i
\(465\) 0 0
\(466\) −15.6962 9.06218i −0.727110 0.419797i
\(467\) −11.8564 −0.548649 −0.274325 0.961637i \(-0.588454\pi\)
−0.274325 + 0.961637i \(0.588454\pi\)
\(468\) 2.50000 + 2.59808i 0.115563 + 0.120096i
\(469\) 9.07180 0.418897
\(470\) 0 0
\(471\) −2.50000 + 4.33013i −0.115194 + 0.199522i
\(472\) 0.767949 + 1.33013i 0.0353477 + 0.0612241i
\(473\) 0.894882i 0.0411467i
\(474\) −0.0621778 + 0.0358984i −0.00285592 + 0.00164887i
\(475\) 0 0
\(476\) 8.00000i 0.366679i
\(477\) −6.46410 11.1962i −0.295971 0.512637i
\(478\) −2.19615 + 3.80385i −0.100450 + 0.173984i
\(479\) 1.26795 + 0.732051i 0.0579341 + 0.0334483i 0.528687 0.848817i \(-0.322684\pi\)
−0.470753 + 0.882265i \(0.656018\pi\)
\(480\) 0 0
\(481\) 3.10770 2.99038i 0.141699 0.136350i
\(482\) 14.2679 0.649887
\(483\) −0.464102 0.267949i −0.0211174 0.0121921i
\(484\) 5.39230 9.33975i 0.245105 0.424534i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −33.9282 + 19.5885i −1.53743 + 0.887638i −0.538446 + 0.842660i \(0.680988\pi\)
−0.998988 + 0.0449775i \(0.985678\pi\)
\(488\) −9.00000 + 5.19615i −0.407411 + 0.235219i
\(489\) 23.0526i 1.04247i
\(490\) 0 0
\(491\) −8.66025 + 15.0000i −0.390832 + 0.676941i −0.992559 0.121761i \(-0.961146\pi\)
0.601728 + 0.798701i \(0.294479\pi\)
\(492\) 1.73205 + 1.00000i 0.0780869 + 0.0450835i
\(493\) 14.9282 0.672332
\(494\) −0.535898 + 1.85641i −0.0241112 + 0.0835237i
\(495\) 0 0
\(496\) 1.50000 + 0.866025i 0.0673520 + 0.0388857i
\(497\) 8.39230 14.5359i 0.376446 0.652024i
\(498\) −2.46410 4.26795i −0.110419 0.191251i
\(499\) 13.4641i 0.602736i −0.953508 0.301368i \(-0.902557\pi\)
0.953508 0.301368i \(-0.0974433\pi\)
\(500\) 0 0
\(501\) 15.8660 9.16025i 0.708842 0.409250i
\(502\) 12.2679i 0.547545i
\(503\) 15.5885 + 27.0000i 0.695055 + 1.20387i 0.970162 + 0.242457i \(0.0779533\pi\)
−0.275107 + 0.961414i \(0.588713\pi\)
\(504\) 1.00000 1.73205i 0.0445435 0.0771517i
\(505\) 0 0
\(506\) −0.124356 −0.00552828
\(507\) 11.5000 6.06218i 0.510733 0.269231i
\(508\) 8.92820 0.396125
\(509\) 16.7942 + 9.69615i 0.744391 + 0.429774i 0.823664 0.567079i \(-0.191926\pi\)
−0.0792726 + 0.996853i \(0.525260\pi\)
\(510\) 0 0
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) −0.464102 + 0.267949i −0.0204906 + 0.0118302i
\(514\) 19.6244 11.3301i 0.865593 0.499750i
\(515\) 0 0
\(516\) 0.964102 + 1.66987i 0.0424422 + 0.0735121i
\(517\) 2.42820 4.20577i 0.106792 0.184970i
\(518\) −2.07180 1.19615i −0.0910295 0.0525559i
\(519\) 2.92820 0.128534
\(520\) 0 0
\(521\) 17.3205 0.758825 0.379413 0.925228i \(-0.376126\pi\)
0.379413 + 0.925228i \(0.376126\pi\)
\(522\) −3.23205 1.86603i −0.141463 0.0816737i
\(523\) −14.8923 + 25.7942i −0.651195 + 1.12790i 0.331638 + 0.943407i \(0.392399\pi\)
−0.982833 + 0.184496i \(0.940935\pi\)
\(524\) −0.669873 1.16025i −0.0292635 0.0506859i
\(525\) 0 0
\(526\) 15.6962 9.06218i 0.684385 0.395130i
\(527\) −6.00000 + 3.46410i −0.261364 + 0.150899i
\(528\) 0.464102i 0.0201974i
\(529\) 11.4641 + 19.8564i 0.498439 + 0.863322i
\(530\) 0 0
\(531\) 1.33013 + 0.767949i 0.0577226 + 0.0333262i
\(532\) 1.07180 0.0464683
\(533\) 5.19615 5.00000i 0.225070 0.216574i
\(534\) 7.46410 0.323003
\(535\) 0 0
\(536\) −2.26795 + 3.92820i −0.0979605 + 0.169673i
\(537\) 8.13397 + 14.0885i 0.351007 + 0.607962i
\(538\) 12.0000i 0.517357i
\(539\) −1.20577 + 0.696152i −0.0519362 + 0.0299854i
\(540\) 0 0
\(541\) 13.0718i 0.562000i −0.959708 0.281000i \(-0.909334\pi\)
0.959708 0.281000i \(-0.0906662\pi\)
\(542\) −4.59808 7.96410i −0.197504 0.342087i
\(543\) −5.46410 + 9.46410i −0.234487 + 0.406143i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 0 0
\(546\) −5.00000 5.19615i −0.213980 0.222375i
\(547\) −9.07180 −0.387882 −0.193941 0.981013i \(-0.562127\pi\)
−0.193941 + 0.981013i \(0.562127\pi\)
\(548\) 3.86603 + 2.23205i 0.165148 + 0.0953485i
\(549\) −5.19615 + 9.00000i −0.221766 + 0.384111i
\(550\) 0 0
\(551\) 2.00000i 0.0852029i
\(552\) 0.232051 0.133975i 0.00987674 0.00570234i
\(553\) 0.124356 0.0717968i 0.00528814 0.00305311i
\(554\) 9.92820i 0.421809i
\(555\) 0 0
\(556\) 0.464102 0.803848i 0.0196823 0.0340907i
\(557\) −32.6603 18.8564i −1.38386 0.798972i −0.391245 0.920286i \(-0.627956\pi\)
−0.992614 + 0.121315i \(0.961289\pi\)
\(558\) 1.73205 0.0733236
\(559\) 6.74871 1.66987i 0.285440 0.0706281i
\(560\) 0 0
\(561\) 1.60770 + 0.928203i 0.0678769 + 0.0391888i
\(562\) −2.46410 + 4.26795i −0.103942 + 0.180033i
\(563\) −19.6603 34.0526i −0.828581 1.43514i −0.899152 0.437637i \(-0.855815\pi\)
0.0705706 0.997507i \(-0.477518\pi\)
\(564\) 10.4641i 0.440618i
\(565\) 0 0
\(566\) −3.40192 + 1.96410i −0.142994 + 0.0825573i
\(567\) 2.00000i 0.0839921i
\(568\) 4.19615 + 7.26795i 0.176067 + 0.304956i
\(569\) 2.66025 4.60770i 0.111524 0.193165i −0.804861 0.593463i \(-0.797760\pi\)
0.916385 + 0.400299i \(0.131094\pi\)
\(570\) 0 0
\(571\) 45.1769 1.89060 0.945298 0.326209i \(-0.105771\pi\)
0.945298 + 0.326209i \(0.105771\pi\)
\(572\) −1.60770 0.464102i −0.0672211 0.0194051i
\(573\) 14.5359 0.607246
\(574\) −3.46410 2.00000i −0.144589 0.0834784i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 10.0000i 0.416305i −0.978096 0.208153i \(-0.933255\pi\)
0.978096 0.208153i \(-0.0667451\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) 20.1962 11.6603i 0.839323 0.484584i
\(580\) 0 0
\(581\) 4.92820 + 8.53590i 0.204456 + 0.354129i
\(582\) 3.73205 6.46410i 0.154698 0.267946i
\(583\) 5.19615 + 3.00000i 0.215203 + 0.124247i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) 4.14359 0.171170
\(587\) 15.9282 + 9.19615i 0.657427 + 0.379566i 0.791296 0.611433i \(-0.209407\pi\)
−0.133869 + 0.990999i \(0.542740\pi\)
\(588\) 1.50000 2.59808i 0.0618590 0.107143i
\(589\) 0.464102 + 0.803848i 0.0191230 + 0.0331220i
\(590\) 0 0
\(591\) 14.1962 8.19615i 0.583952 0.337145i
\(592\) 1.03590 0.598076i 0.0425752 0.0245808i
\(593\) 31.1051i 1.27733i −0.769483 0.638667i \(-0.779486\pi\)
0.769483 0.638667i \(-0.220514\pi\)
\(594\) −0.232051 0.401924i −0.00952116 0.0164911i
\(595\) 0 0
\(596\) 17.7224 + 10.2321i 0.725939 + 0.419121i
\(597\) −18.9282 −0.774680
\(598\) −0.232051 0.937822i −0.00948926 0.0383504i
\(599\) 10.3923 0.424618 0.212309 0.977203i \(-0.431902\pi\)
0.212309 + 0.977203i \(0.431902\pi\)
\(600\) 0 0
\(601\) −10.8923 + 18.8660i −0.444306 + 0.769561i −0.998004 0.0631568i \(-0.979883\pi\)
0.553697 + 0.832718i \(0.313216\pi\)
\(602\) −1.92820 3.33975i −0.0785877 0.136118i
\(603\) 4.53590i 0.184716i
\(604\) 9.00000 5.19615i 0.366205 0.211428i
\(605\) 0 0
\(606\) 10.9282i 0.443928i
\(607\) 21.5885 + 37.3923i 0.876248 + 1.51771i 0.855427 + 0.517924i \(0.173295\pi\)
0.0208216 + 0.999783i \(0.493372\pi\)
\(608\) −0.267949 + 0.464102i −0.0108668 + 0.0188218i
\(609\) 6.46410 + 3.73205i 0.261939 + 0.151230i
\(610\) 0 0
\(611\) 36.2487 + 10.4641i 1.46647 + 0.423332i
\(612\) −4.00000 −0.161690
\(613\) −0.820508 0.473721i −0.0331400 0.0191334i 0.483338 0.875434i \(-0.339424\pi\)
−0.516478 + 0.856300i \(0.672757\pi\)
\(614\) 6.26795 10.8564i 0.252954 0.438129i
\(615\) 0 0
\(616\) 0.928203i 0.0373984i
\(617\) −13.4545 + 7.76795i −0.541657 + 0.312726i −0.745750 0.666226i \(-0.767909\pi\)
0.204093 + 0.978951i \(0.434575\pi\)
\(618\) −13.7321 + 7.92820i −0.552384 + 0.318919i
\(619\) 24.2487i 0.974638i −0.873224 0.487319i \(-0.837975\pi\)
0.873224 0.487319i \(-0.162025\pi\)
\(620\) 0 0
\(621\) 0.133975 0.232051i 0.00537622 0.00931188i
\(622\) 6.58846 + 3.80385i 0.264173 + 0.152520i
\(623\) −14.9282 −0.598086
\(624\) 3.50000 0.866025i 0.140112 0.0346688i
\(625\) 0 0
\(626\) −24.2487 14.0000i −0.969173 0.559553i
\(627\) 0.124356 0.215390i 0.00496629 0.00860186i
\(628\) 2.50000 + 4.33013i 0.0997609 + 0.172791i
\(629\) 4.78461i 0.190775i
\(630\) 0 0
\(631\) −21.2487 + 12.2679i −0.845898 + 0.488379i −0.859265 0.511531i \(-0.829078\pi\)
0.0133668 + 0.999911i \(0.495745\pi\)
\(632\) 0.0717968i 0.00285592i
\(633\) −11.6603 20.1962i −0.463453 0.802725i
\(634\) 10.7321 18.5885i 0.426224 0.738242i
\(635\) 0 0
\(636\) −12.9282 −0.512637
\(637\) −7.50000 7.79423i −0.297161 0.308819i
\(638\) 1.73205 0.0685725
\(639\) 7.26795 + 4.19615i 0.287516 + 0.165997i
\(640\) 0 0
\(641\) −13.9282 24.1244i −0.550131 0.952855i −0.998265 0.0588882i \(-0.981244\pi\)
0.448134 0.893967i \(-0.352089\pi\)
\(642\) 19.8564i 0.783670i
\(643\) −23.7846 + 13.7321i −0.937973 + 0.541539i −0.889324 0.457277i \(-0.848825\pi\)
−0.0486490 + 0.998816i \(0.515492\pi\)
\(644\) −0.464102 + 0.267949i −0.0182882 + 0.0105587i
\(645\) 0 0
\(646\) −1.07180 1.85641i −0.0421693 0.0730393i
\(647\) 10.6603 18.4641i 0.419098 0.725899i −0.576751 0.816920i \(-0.695680\pi\)
0.995849 + 0.0910212i \(0.0290131\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −0.712813 −0.0279804
\(650\) 0 0
\(651\) −3.46410 −0.135769
\(652\) −19.9641 11.5263i −0.781855 0.451404i
\(653\) −22.1244 + 38.3205i −0.865793 + 1.49960i 0.000464739 1.00000i \(0.499852\pi\)
−0.866258 + 0.499597i \(0.833481\pi\)
\(654\) −5.92820 10.2679i −0.231811 0.401509i
\(655\) 0 0
\(656\) 1.73205 1.00000i 0.0676252 0.0390434i
\(657\) 1.73205 1.00000i 0.0675737 0.0390137i
\(658\) 20.9282i 0.815866i
\(659\) 1.86603 + 3.23205i 0.0726900 + 0.125903i 0.900079 0.435726i \(-0.143508\pi\)
−0.827389 + 0.561629i \(0.810175\pi\)
\(660\) 0 0
\(661\) 37.5167 + 21.6603i 1.45923 + 0.842486i 0.998973 0.0453002i \(-0.0144244\pi\)
0.460256 + 0.887786i \(0.347758\pi\)
\(662\) 24.7846 0.963281
\(663\) −4.00000 + 13.8564i −0.155347 + 0.538138i
\(664\) −4.92820 −0.191251
\(665\) 0 0
\(666\) 0.598076 1.03590i 0.0231750 0.0401402i
\(667\) 0.500000 + 0.866025i 0.0193601 + 0.0335326i
\(668\) 18.3205i 0.708842i
\(669\) 23.7846 13.7321i 0.919566 0.530912i
\(670\) 0 0
\(671\) 4.82309i 0.186193i
\(672\) −1.00000 1.73205i −0.0385758 0.0668153i
\(673\) 16.0000 27.7128i 0.616755 1.06825i −0.373319 0.927703i \(-0.621780\pi\)
0.990074 0.140548i \(-0.0448863\pi\)
\(674\) −21.9282 12.6603i −0.844643 0.487655i
\(675\) 0 0
\(676\) 0.500000 12.9904i 0.0192308 0.499630i
\(677\) −11.6077 −0.446120 −0.223060 0.974805i \(-0.571605\pi\)
−0.223060 + 0.974805i \(0.571605\pi\)
\(678\) 9.69615 + 5.59808i 0.372378 + 0.214993i
\(679\) −7.46410 + 12.9282i −0.286446 + 0.496139i
\(680\) 0 0
\(681\) 4.39230i 0.168313i
\(682\) −0.696152 + 0.401924i −0.0266571 + 0.0153905i
\(683\) 0.679492 0.392305i 0.0260000 0.0150111i −0.486944 0.873433i \(-0.661888\pi\)
0.512944 + 0.858422i \(0.328555\pi\)
\(684\) 0.535898i 0.0204906i
\(685\) 0 0
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) 17.1962 + 9.92820i 0.656074 + 0.378785i
\(688\) 1.92820 0.0735121
\(689\) −12.9282 + 44.7846i −0.492525 + 1.70616i
\(690\) 0 0
\(691\) −30.4641 17.5885i −1.15891 0.669096i −0.207867 0.978157i \(-0.566652\pi\)
−0.951042 + 0.309061i \(0.899985\pi\)
\(692\) 1.46410 2.53590i 0.0556568 0.0964004i
\(693\) 0.464102 + 0.803848i 0.0176298 + 0.0305356i
\(694\) 22.3923i 0.850000i
\(695\) 0 0
\(696\) −3.23205 + 1.86603i −0.122511 + 0.0707315i
\(697\) 8.00000i 0.303022i
\(698\) 7.26795 + 12.5885i 0.275096 + 0.476480i
\(699\) −9.06218 + 15.6962i −0.342763 + 0.593683i
\(700\) 0 0
\(701\) −3.73205 −0.140958 −0.0704788 0.997513i \(-0.522453\pi\)
−0.0704788 + 0.997513i \(0.522453\pi\)
\(702\) 2.59808 2.50000i 0.0980581 0.0943564i
\(703\) 0.641016 0.0241764
\(704\) −0.401924 0.232051i −0.0151481 0.00874574i
\(705\) 0 0
\(706\) −1.00000 1.73205i −0.0376355 0.0651866i
\(707\) 21.8564i 0.821995i
\(708\) 1.33013 0.767949i 0.0499892 0.0288613i
\(709\) 7.85641 4.53590i 0.295054 0.170349i −0.345165 0.938542i \(-0.612177\pi\)
0.640219 + 0.768193i \(0.278844\pi\)
\(710\) 0 0
\(711\) 0.0358984 + 0.0621778i 0.00134629 + 0.00233185i
\(712\) 3.73205 6.46410i 0.139865 0.242252i
\(713\) −0.401924 0.232051i −0.0150522 0.00869037i
\(714\) 8.00000 0.299392
\(715\) 0 0
\(716\) 16.2679 0.607962
\(717\) 3.80385 + 2.19615i 0.142057 + 0.0820168i
\(718\) −9.46410 + 16.3923i −0.353197 + 0.611755i
\(719\) −17.3205 30.0000i −0.645946 1.11881i −0.984082 0.177714i \(-0.943130\pi\)
0.338136 0.941097i \(-0.390204\pi\)
\(720\) 0 0
\(721\) 27.4641 15.8564i 1.02282 0.590523i
\(722\) 16.2058 9.35641i 0.603116 0.348209i
\(723\) 14.2679i 0.530631i
\(724\) 5.46410 + 9.46410i 0.203072 + 0.351731i
\(725\) 0 0
\(726\) −9.33975 5.39230i −0.346630 0.200127i
\(727\) −23.7128 −0.879460 −0.439730 0.898130i \(-0.644926\pi\)
−0.439730 + 0.898130i \(0.644926\pi\)
\(728\) −7.00000 + 1.73205i −0.259437 + 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −3.85641 + 6.67949i −0.142634 + 0.247050i
\(732\) 5.19615 + 9.00000i 0.192055 + 0.332650i
\(733\) 37.0718i 1.36928i −0.728882 0.684639i \(-0.759960\pi\)
0.728882 0.684639i \(-0.240040\pi\)
\(734\) −31.5167 + 18.1962i −1.16330 + 0.671632i
\(735\) 0 0
\(736\) 0.267949i 0.00987674i
\(737\) −1.05256 1.82309i −0.0387715 0.0671542i
\(738\) 1.00000 1.73205i 0.0368105 0.0637577i
\(739\) −13.2679 7.66025i −0.488069 0.281787i 0.235704 0.971825i \(-0.424260\pi\)
−0.723773 + 0.690038i \(0.757594\pi\)
\(740\) 0 0
\(741\) 1.85641 + 0.535898i 0.0681968 + 0.0196867i
\(742\) 25.8564 0.949219
\(743\) −29.0429 16.7679i −1.06548 0.615156i −0.138539 0.990357i \(-0.544240\pi\)
−0.926944 + 0.375201i \(0.877574\pi\)
\(744\) 0.866025 1.50000i 0.0317500 0.0549927i
\(745\) 0 0
\(746\) 25.7846i 0.944042i
\(747\) −4.26795 + 2.46410i −0.156156 + 0.0901568i
\(748\) 1.60770 0.928203i 0.0587832 0.0339385i
\(749\) 39.7128i 1.45107i
\(750\) 0 0
\(751\) −13.9641 + 24.1865i −0.509557 + 0.882579i 0.490381 + 0.871508i \(0.336857\pi\)
−0.999939 + 0.0110712i \(0.996476\pi\)
\(752\) 9.06218 + 5.23205i 0.330464 + 0.190793i
\(753\) 12.2679 0.447069
\(754\) 3.23205 + 13.0622i 0.117704 + 0.475696i
\(755\) 0 0
\(756\) −1.73205 1.00000i −0.0629941 0.0363696i
\(757\) −9.00000 + 15.5885i −0.327111 + 0.566572i −0.981937 0.189207i \(-0.939408\pi\)
0.654827 + 0.755779i \(0.272742\pi\)
\(758\) 0.0717968 + 0.124356i 0.00260778 + 0.00451680i
\(759\) 0.124356i 0.00451382i
\(760\) 0 0
\(761\) −16.3923 + 9.46410i −0.594221 + 0.343073i −0.766765 0.641928i \(-0.778135\pi\)
0.172544 + 0.985002i \(0.444801\pi\)
\(762\) 8.92820i 0.323435i
\(763\) 11.8564 + 20.5359i 0.429231 + 0.743449i
\(764\) 7.26795 12.5885i 0.262945 0.455434i
\(765\) 0 0
\(766\) −4.60770 −0.166483
\(767\) −1.33013 5.37564i −0.0480281 0.194103i
\(768\) 1.00000 0.0360844
\(769\) −16.9641 9.79423i −0.611741 0.353189i 0.161905 0.986806i \(-0.448236\pi\)
−0.773647 + 0.633617i \(0.781569\pi\)
\(770\) 0 0
\(771\) −11.3301 19.6244i −0.408045 0.706754i
\(772\) 23.3205i 0.839323i
\(773\) −24.0000 + 13.8564i −0.863220 + 0.498380i −0.865089 0.501618i \(-0.832738\pi\)
0.00186926 + 0.999998i \(0.499405\pi\)
\(774\) 1.66987 0.964102i 0.0600223 0.0346539i
\(775\) 0 0
\(776\) −3.73205 6.46410i −0.133973 0.232048i
\(777\) −1.19615 + 2.07180i −0.0429117 + 0.0743253i
\(778\) 17.5526 + 10.1340i 0.629290 + 0.363321i
\(779\) 1.07180 0.0384011
\(780\) 0 0
\(781\) −3.89488 −0.139370
\(782\) 0.928203 + 0.535898i 0.0331925 + 0.0191637i
\(783\) −1.86603