Properties

Label 390.2.bb.b.121.2
Level $390$
Weight $2$
Character 390.121
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 121.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 390.121
Dual form 390.2.bb.b.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.401924 + 0.232051i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} +(0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(0.232051 + 0.401924i) q^{22} +(-0.133975 + 0.232051i) q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(2.59808 - 2.50000i) q^{26} -1.00000 q^{27} +(1.73205 + 1.00000i) q^{28} +(-1.86603 + 3.23205i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.401924 - 0.232051i) q^{33} +4.00000i q^{34} +(-1.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(1.03590 + 0.598076i) q^{37} -0.535898 q^{38} +(-2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(-1.73205 - 1.00000i) q^{41} +(1.00000 - 1.73205i) q^{42} +(0.964102 + 1.66987i) q^{43} +0.464102i q^{44} +(-0.866025 + 0.500000i) q^{45} +(-0.232051 + 0.133975i) q^{46} +10.4641i q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(-0.866025 - 0.500000i) q^{50} +4.00000 q^{51} +(3.50000 - 0.866025i) q^{52} -12.9282 q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.232051 - 0.401924i) q^{55} +(1.00000 + 1.73205i) q^{56} +0.535898i q^{57} +(-3.23205 + 1.86603i) q^{58} +(-1.33013 + 0.767949i) q^{59} -1.00000i q^{60} +(-5.19615 - 9.00000i) q^{61} +(0.866025 - 1.50000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +(-3.46410 - 1.00000i) q^{65} +0.464102 q^{66} +(3.92820 + 2.26795i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(0.133975 + 0.232051i) q^{69} -2.00000i q^{70} +(-7.26795 + 4.19615i) q^{71} +(0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(0.598076 + 1.03590i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-0.464102 - 0.267949i) q^{76} +0.928203 q^{77} +(-0.866025 - 3.50000i) q^{78} -0.0717968 q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +4.92820i q^{83} +(1.73205 - 1.00000i) q^{84} +(3.46410 - 2.00000i) q^{85} +1.92820i q^{86} +(1.86603 + 3.23205i) q^{87} +(-0.232051 + 0.401924i) q^{88} +(6.46410 + 3.73205i) q^{89} -1.00000 q^{90} +(-1.73205 - 7.00000i) q^{91} -0.267949 q^{92} +(-1.50000 - 0.866025i) q^{93} +(-5.23205 + 9.06218i) q^{94} +(0.267949 + 0.464102i) q^{95} +1.00000i q^{96} +(-6.46410 + 3.73205i) q^{97} +(-2.59808 + 1.50000i) q^{98} -0.464102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + 2q^{10} + 12q^{11} + 4q^{12} + 4q^{13} + 8q^{14} - 2q^{16} + 8q^{17} + 12q^{19} - 6q^{22} - 4q^{23} - 4q^{25} - 4q^{27} - 4q^{29} - 2q^{30} + 12q^{33} - 4q^{35} + 2q^{36} + 18q^{37} - 16q^{38} - 10q^{39} + 4q^{40} + 4q^{42} - 10q^{43} + 6q^{46} + 2q^{48} - 6q^{49} + 16q^{51} + 14q^{52} - 24q^{53} - 6q^{55} + 4q^{56} - 6q^{58} + 12q^{59} - 4q^{64} - 12q^{66} - 12q^{67} - 8q^{68} + 4q^{69} - 36q^{71} - 8q^{74} - 2q^{75} + 12q^{76} - 24q^{77} - 28q^{79} - 2q^{81} - 4q^{82} + 4q^{87} + 6q^{88} + 12q^{89} - 4q^{90} - 8q^{92} - 6q^{93} - 14q^{94} + 8q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 1.73205 1.00000i 0.654654 0.377964i −0.135583 0.990766i \(-0.543291\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 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
\(15\) −0.866025 0.500000i −0.223607 0.129099i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −0.464102 + 0.267949i −0.106472 + 0.0614718i −0.552291 0.833652i \(-0.686246\pi\)
0.445818 + 0.895123i \(0.352913\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 2.00000i 0.436436i
\(22\) 0.232051 + 0.401924i 0.0494734 + 0.0856904i
\(23\) −0.133975 + 0.232051i −0.0279356 + 0.0483859i −0.879655 0.475612i \(-0.842227\pi\)
0.851720 + 0.523998i \(0.175560\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −1.00000 −0.200000
\(26\) 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 \(0.279301\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 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
\(35\) −1.00000 1.73205i −0.169031 0.292770i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 1.03590 + 0.598076i 0.170301 + 0.0983231i 0.582728 0.812668i \(-0.301985\pi\)
−0.412427 + 0.910991i \(0.635319\pi\)
\(38\) −0.535898 −0.0869342
\(39\) −2.50000 2.59808i −0.400320 0.416025i
\(40\) 1.00000 0.158114
\(41\) −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 0.930126 0.367240i \(-0.119697\pi\)
−0.783102 + 0.621893i \(0.786364\pi\)
\(44\) 0.464102i 0.0699660i
\(45\) −0.866025 + 0.500000i −0.129099 + 0.0745356i
\(46\) −0.232051 + 0.133975i −0.0342140 + 0.0197535i
\(47\) 10.4641i 1.52635i 0.646194 + 0.763173i \(0.276360\pi\)
−0.646194 + 0.763173i \(0.723640\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 4.00000 0.560112
\(52\) 3.50000 0.866025i 0.485363 0.120096i
\(53\) −12.9282 −1.77583 −0.887913 0.460012i \(-0.847845\pi\)
−0.887913 + 0.460012i \(0.847845\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0.232051 0.401924i 0.0312897 0.0541954i
\(56\) 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 \(0.365211\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −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
\(65\) −3.46410 1.00000i −0.429669 0.124035i
\(66\) 0.464102 0.0571270
\(67\) 3.92820 + 2.26795i 0.479906 + 0.277074i 0.720377 0.693582i \(-0.243969\pi\)
−0.240471 + 0.970656i \(0.577302\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 0.133975 + 0.232051i 0.0161286 + 0.0279356i
\(70\) 2.00000i 0.239046i
\(71\) −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 \(-0.962659\pi\)
0.993127 0.117041i \(-0.0373409\pi\)
\(74\) 0.598076 + 1.03590i 0.0695249 + 0.120421i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) −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 \(0.501286\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) −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 \(0.0871792\pi\)
−0.962728 + 0.270470i \(0.912821\pi\)
\(84\) 1.73205 1.00000i 0.188982 0.109109i
\(85\) 3.46410 2.00000i 0.375735 0.216930i
\(86\) 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 \(0.537205\pi\)
\(90\) −1.00000 −0.105409
\(91\) −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
\(95\) 0.267949 + 0.464102i 0.0274910 + 0.0476158i
\(96\) 1.00000i 0.102062i
\(97\) −6.46410 + 3.73205i −0.656330 + 0.378932i −0.790877 0.611975i \(-0.790375\pi\)
0.134547 + 0.990907i \(0.457042\pi\)
\(98\) −2.59808 + 1.50000i −0.262445 + 0.151523i
\(99\) 0.464102i 0.0466440i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 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 \(-0.214613\pi\)
0.781189 + 0.624295i \(0.214613\pi\)
\(104\) 3.46410 + 1.00000i 0.339683 + 0.0980581i
\(105\) −2.00000 −0.195180
\(106\) −11.1962 6.46410i −1.08747 0.627849i
\(107\) −9.92820 + 17.1962i −0.959796 + 1.66241i −0.236805 + 0.971557i \(0.576100\pi\)
−0.722991 + 0.690858i \(0.757233\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 11.8564i 1.13564i −0.823154 0.567819i \(-0.807787\pi\)
0.823154 0.567819i \(-0.192213\pi\)
\(110\) 0.401924 0.232051i 0.0383219 0.0221252i
\(111\) 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 \(-0.990125\pi\)
0.472896 0.881118i \(-0.343209\pi\)
\(114\) −0.267949 + 0.464102i −0.0250957 + 0.0434671i
\(115\) 0.232051 + 0.133975i 0.0216388 + 0.0124932i
\(116\) −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
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) −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
\(125\) 1.00000i 0.0894427i
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) −4.46410 + 7.73205i −0.396125 + 0.686109i −0.993244 0.116044i \(-0.962979\pi\)
0.597119 + 0.802153i \(0.296312\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 1.92820 0.169769
\(130\) −2.50000 2.59808i −0.219265 0.227866i
\(131\) −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
\(135\) 1.00000i 0.0860663i
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) −3.86603 + 2.23205i −0.330297 + 0.190697i −0.655973 0.754784i \(-0.727741\pi\)
0.325676 + 0.945481i \(0.394408\pi\)
\(138\) 0.267949i 0.0228093i
\(139\) −0.464102 0.803848i −0.0393646 0.0681815i 0.845672 0.533703i \(-0.179200\pi\)
−0.885036 + 0.465522i \(0.845867\pi\)
\(140\) 1.00000 1.73205i 0.0845154 0.146385i
\(141\) 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
\(145\) 3.23205 + 1.86603i 0.268407 + 0.154965i
\(146\) 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 \(0.0169168\pi\)
\(150\) −0.866025 + 0.500000i −0.0707107 + 0.0408248i
\(151\) 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
\(155\) −1.73205 −0.139122
\(156\) 1.00000 3.46410i 0.0800641 0.277350i
\(157\) −5.00000 −0.399043 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(158\) −0.0621778 0.0358984i −0.00494660 0.00285592i
\(159\) −6.46410 + 11.1962i −0.512637 + 0.887913i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 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 \(-0.308169\pi\)
0.996877 0.0789748i \(-0.0251647\pi\)
\(164\) 2.00000i 0.156174i
\(165\) −0.232051 0.401924i −0.0180651 0.0312897i
\(166\) −2.46410 + 4.26795i −0.191251 + 0.331257i
\(167\) 15.8660 + 9.16025i 1.22775 + 0.708842i 0.966559 0.256445i \(-0.0825514\pi\)
0.261191 + 0.965287i \(0.415885\pi\)
\(168\) 2.00000 0.154303
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 4.00000 0.306786
\(171\) 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 0.916300 0.400492i \(-0.131161\pi\)
−0.804987 + 0.593293i \(0.797828\pi\)
\(174\) 3.73205i 0.282926i
\(175\) −1.73205 + 1.00000i −0.130931 + 0.0755929i
\(176\) −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 \(-0.0413460\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) 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
\(185\) 0.598076 1.03590i 0.0439714 0.0761608i
\(186\) −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
\(190\) 0.535898i 0.0388782i
\(191\) −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 0.998692 0.0511377i \(-0.0162847\pi\)
0.455059 + 0.890461i \(0.349618\pi\)
\(194\) −7.46410 −0.535891
\(195\) −2.59808 + 2.50000i −0.186052 + 0.179029i
\(196\) −3.00000 −0.214286
\(197\) 14.1962 + 8.19615i 1.01143 + 0.583952i 0.911611 0.411054i \(-0.134839\pi\)
0.0998228 + 0.995005i \(0.468172\pi\)
\(198\) 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 \(0.599245\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 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
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) 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
\(210\) −1.73205 1.00000i −0.119523 0.0690066i
\(211\) −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
\(215\) 1.66987 0.964102i 0.113884 0.0657512i
\(216\) 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
\(220\) 0.464102 0.0312897
\(221\) 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 \(0.0381263\pi\)
0.599900 + 0.800075i \(0.295207\pi\)
\(224\) −1.00000 + 1.73205i −0.0668153 + 0.115728i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 11.1962i 0.744757i
\(227\) −3.80385 + 2.19615i −0.252470 + 0.145764i −0.620895 0.783894i \(-0.713231\pi\)
0.368425 + 0.929658i \(0.379897\pi\)
\(228\) −0.464102 + 0.267949i −0.0307359 + 0.0177454i
\(229\) 19.8564i 1.31215i −0.754696 0.656074i \(-0.772216\pi\)
0.754696 0.656074i \(-0.227784\pi\)
\(230\) 0.133975 + 0.232051i 0.00883402 + 0.0153010i
\(231\) 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 \(-0.702327\pi\)
−0.593683 + 0.804699i \(0.702327\pi\)
\(234\) −3.46410 1.00000i −0.226455 0.0653720i
\(235\) 10.4641 0.682603
\(236\) −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 \(-0.0453717\pi\)
\(240\) 0.866025 0.500000i 0.0559017 0.0322749i
\(241\) −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
\(245\) 2.59808 + 1.50000i 0.165985 + 0.0958315i
\(246\) −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
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −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
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 11.3301 19.6244i 0.706754 1.22413i −0.259301 0.965797i \(-0.583492\pi\)
0.966055 0.258337i \(-0.0831745\pi\)
\(258\) 1.66987 + 0.964102i 0.103962 + 0.0600223i
\(259\) 2.39230 0.148651
\(260\) −0.866025 3.50000i −0.0537086 0.217061i
\(261\) 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 \(-0.644596\pi\)
0.997597 0.0692812i \(-0.0220706\pi\)
\(264\) 0.232051 + 0.401924i 0.0142817 + 0.0247367i
\(265\) 12.9282i 0.794173i
\(266\) −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 \(0.952547\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 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
\(275\) −0.401924 0.232051i −0.0242369 0.0139932i
\(276\) −0.133975 + 0.232051i −0.00806432 + 0.0139678i
\(277\) −4.96410 8.59808i −0.298264 0.516608i 0.677475 0.735546i \(-0.263074\pi\)
−0.975739 + 0.218938i \(0.929741\pi\)
\(278\) 0.928203i 0.0556699i
\(279\) −1.50000 + 0.866025i −0.0898027 + 0.0518476i
\(280\) 1.73205 1.00000i 0.103510 0.0597614i
\(281\) 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 −0.918479 0.395469i \(-0.870582\pi\)
0.801726 + 0.597692i \(0.203915\pi\)
\(284\) −7.26795 4.19615i −0.431273 0.248996i
\(285\) 0.535898 0.0317439
\(286\) 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
\(290\) 1.86603 + 3.23205i 0.109577 + 0.189793i
\(291\) 7.46410i 0.437553i
\(292\) 1.73205 1.00000i 0.101361 0.0585206i
\(293\) 3.58846 2.07180i 0.209640 0.121036i −0.391504 0.920176i \(-0.628045\pi\)
0.601144 + 0.799141i \(0.294712\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 0.767949 + 1.33013i 0.0447117 + 0.0774430i
\(296\) −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
\(300\) −1.00000 −0.0577350
\(301\) 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
\(305\) −9.00000 + 5.19615i −0.515339 + 0.297531i
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 12.5359i 0.715462i −0.933825 0.357731i \(-0.883551\pi\)
0.933825 0.357731i \(-0.116449\pi\)
\(308\) 0.464102 + 0.803848i 0.0264446 + 0.0458035i
\(309\) 7.92820 13.7321i 0.451020 0.781189i
\(310\) −1.50000 0.866025i −0.0851943 0.0491869i
\(311\) −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 \(-0.790609\pi\)
−0.791327 + 0.611393i \(0.790609\pi\)
\(314\) −4.33013 2.50000i −0.244363 0.141083i
\(315\) −1.00000 + 1.73205i −0.0563436 + 0.0975900i
\(316\) −0.0358984 0.0621778i −0.00201944 0.00349778i
\(317\) 21.4641i 1.20554i −0.797913 0.602772i \(-0.794063\pi\)
0.797913 0.602772i \(-0.205937\pi\)
\(318\) −11.1962 + 6.46410i −0.627849 + 0.362489i
\(319\) −1.50000 + 0.866025i −0.0839839 + 0.0484881i
\(320\) 1.00000i 0.0559017i
\(321\) 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
\(325\) −1.00000 + 3.46410i −0.0554700 + 0.192154i
\(326\) 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
\(330\) 0.464102i 0.0255480i
\(331\) −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
\(335\) 2.26795 3.92820i 0.123911 0.214621i
\(336\) 1.73205 + 1.00000i 0.0944911 + 0.0545545i
\(337\) −25.3205 −1.37930 −0.689648 0.724145i \(-0.742235\pi\)
−0.689648 + 0.724145i \(0.742235\pi\)
\(338\) −6.06218 11.5000i −0.329739 0.625518i
\(339\) −11.1962 −0.608092
\(340\) 3.46410 + 2.00000i 0.187867 + 0.108465i
\(341\) 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
\(345\) 0.232051 0.133975i 0.0124932 0.00721295i
\(346\) 2.92820i 0.157421i
\(347\) −11.1962 19.3923i −0.601041 1.04103i −0.992664 0.120908i \(-0.961420\pi\)
0.391623 0.920126i \(-0.371914\pi\)
\(348\) −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 \(0.793861\pi\)
\(350\) −2.00000 −0.106904
\(351\) −1.00000 + 3.46410i −0.0533761 + 0.184900i
\(352\) −0.464102 −0.0247367
\(353\) −1.73205 1.00000i −0.0921878 0.0532246i 0.453197 0.891410i \(-0.350283\pi\)
−0.545385 + 0.838186i \(0.683617\pi\)
\(354\) −0.767949 + 1.33013i −0.0408160 + 0.0706955i
\(355\) 4.19615 + 7.26795i 0.222709 + 0.385743i
\(356\) 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 \(-0.166482\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) −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
\(365\) −2.00000 −0.104685
\(366\) −9.00000 5.19615i −0.470438 0.271607i
\(367\) −18.1962 + 31.5167i −0.949831 + 1.64516i −0.204056 + 0.978959i \(0.565412\pi\)
−0.745776 + 0.666197i \(0.767921\pi\)
\(368\) −0.133975 0.232051i −0.00698391 0.0120965i
\(369\) 2.00000i 0.104116i
\(370\) 1.03590 0.598076i 0.0538538 0.0310925i
\(371\) −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 \(-0.934015\pi\)
0.311052 0.950393i \(-0.399319\pi\)
\(374\) −0.928203 + 1.60770i −0.0479962 + 0.0831319i
\(375\) 0.866025 + 0.500000i 0.0447214 + 0.0258199i
\(376\) −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 \(0.667841\pi\)
\(380\) −0.267949 + 0.464102i −0.0137455 + 0.0238079i
\(381\) 4.46410 + 7.73205i 0.228703 + 0.396125i
\(382\) 14.5359i 0.743721i
\(383\) −3.99038 + 2.30385i −0.203899 + 0.117721i −0.598473 0.801143i \(-0.704226\pi\)
0.394574 + 0.918864i \(0.370892\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0.928203i 0.0473056i
\(386\) 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 \(0.671767\pi\)
\(390\) −3.50000 + 0.866025i −0.177229 + 0.0438529i
\(391\) −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
\(395\) 0.0717968i 0.00361249i
\(396\) 0.401924 0.232051i 0.0201974 0.0116610i
\(397\) 10.5000 6.06218i 0.526980 0.304252i −0.212806 0.977095i \(-0.568260\pi\)
0.739786 + 0.672843i \(0.234927\pi\)
\(398\) 18.9282i 0.948785i
\(399\) 0.535898 + 0.928203i 0.0268285 + 0.0464683i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 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
\(405\) 0.866025 + 0.500000i 0.0430331 + 0.0248452i
\(406\) −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 \(0.364864\pi\)
\(410\) −1.73205 + 1.00000i −0.0855399 + 0.0493865i
\(411\) 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
\(415\) 4.92820 0.241916
\(416\) 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 \(0.179170\pi\)
\(420\) −1.00000 1.73205i −0.0487950 0.0845154i
\(421\) 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
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) −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
\(430\) 1.92820 0.0929862
\(431\) −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 0.989273 0.146079i \(-0.0466654\pi\)
−0.621145 + 0.783696i \(0.713332\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 3.23205 1.86603i 0.154965 0.0894691i
\(436\) 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 \(0.242245\pi\)
\(440\) 0.401924 + 0.232051i 0.0191610 + 0.0110626i
\(441\) 3.00000 0.142857
\(442\) 13.8564 + 4.00000i 0.659082 + 0.190261i
\(443\) −4.39230 −0.208685 −0.104342 0.994541i \(-0.533274\pi\)
−0.104342 + 0.994541i \(0.533274\pi\)
\(444\) 1.03590 + 0.598076i 0.0491616 + 0.0283834i
\(445\) 3.73205 6.46410i 0.176916 0.306428i
\(446\) 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 \(0.946849\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −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
\(455\) −7.00000 + 1.73205i −0.328165 + 0.0811998i
\(456\) −0.535898 −0.0250957
\(457\) −27.2487 15.7321i −1.27464 0.735914i −0.298783 0.954321i \(-0.596581\pi\)
−0.975858 + 0.218407i \(0.929914\pi\)
\(458\) 9.92820 17.1962i 0.463914 0.803523i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0.267949i 0.0124932i
\(461\) 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 \(-0.838343\pi\)
0.873787 0.486308i \(-0.161657\pi\)
\(464\) −1.86603 3.23205i −0.0866281 0.150044i
\(465\) −0.866025 + 1.50000i −0.0401610 + 0.0695608i
\(466\) −15.6962 9.06218i −0.727110 0.419797i
\(467\) 11.8564 0.548649 0.274325 0.961637i \(-0.411546\pi\)
0.274325 + 0.961637i \(0.411546\pi\)
\(468\) −2.50000 2.59808i −0.115563 0.120096i
\(469\) 9.07180 0.418897
\(470\) 9.06218 + 5.23205i 0.418007 + 0.241337i
\(471\) −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
\(475\) 0.464102 0.267949i 0.0212944 0.0122944i
\(476\) 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 \(0.656018\pi\)
\(480\) 1.00000 0.0456435
\(481\) 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
\(485\) 3.73205 + 6.46410i 0.169464 + 0.293520i
\(486\) 1.00000i 0.0453609i
\(487\) 33.9282 19.5885i 1.53743 0.887638i 0.538446 0.842660i \(-0.319012\pi\)
0.998988 0.0449775i \(-0.0143216\pi\)
\(488\) 9.00000 5.19615i 0.407411 0.235219i
\(489\) 23.0526i 1.04247i
\(490\) 1.50000 + 2.59808i 0.0677631 + 0.117369i
\(491\) −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
\(495\) −0.464102 −0.0208598
\(496\) 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 \(-0.0974433\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 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 \(-0.922047\pi\)
0.275107 0.961414i \(-0.411287\pi\)
\(504\) 1.00000 1.73205i 0.0445435 0.0771517i
\(505\) −9.46410 5.46410i −0.421147 0.243149i
\(506\) −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 \(0.525260\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) −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
\(515\) 15.8564i 0.698717i
\(516\) 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
\(520\) 1.00000 3.46410i 0.0438529 0.151911i
\(521\) 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 \(-0.607601\pi\)
0.982833 0.184496i \(-0.0590653\pi\)
\(524\) −0.669873 1.16025i −0.0292635 0.0506859i
\(525\) 2.00000i 0.0872872i
\(526\) 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
\(530\) −6.46410 + 11.1962i −0.280783 + 0.486330i
\(531\) 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
\(535\) 17.1962 + 9.92820i 0.743455 + 0.429234i
\(536\) −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
\(540\) −0.866025 + 0.500000i −0.0372678 + 0.0215166i
\(541\) 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
\(545\) −11.8564 −0.507873
\(546\) −5.00000 5.19615i −0.213980 0.222375i
\(547\) 9.07180 0.387882 0.193941 0.981013i \(-0.437873\pi\)
0.193941 + 0.981013i \(0.437873\pi\)
\(548\) −3.86603 2.23205i −0.165148 0.0953485i
\(549\) −5.19615 + 9.00000i −0.221766 + 0.384111i
\(550\) −0.232051 0.401924i −0.00989468 0.0171381i
\(551\) 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
\(555\) −0.598076 1.03590i −0.0253869 0.0439714i
\(556\) 0.464102 0.803848i 0.0196823 0.0340907i
\(557\) 32.6603 + 18.8564i 1.38386 + 0.798972i 0.992614 0.121315i \(-0.0387111\pi\)
0.391245 + 0.920286i \(0.372044\pi\)
\(558\) −1.73205 −0.0733236
\(559\) 6.74871 1.66987i 0.285440 0.0706281i
\(560\) 2.00000 0.0845154
\(561\) 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 \(0.144185\pi\)
−0.0705706 + 0.997507i \(0.522482\pi\)
\(564\) 10.4641i 0.440618i
\(565\) −9.69615 + 5.59808i −0.407920 + 0.235513i
\(566\) −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 \(0.131094\pi\)
\(570\) 0.464102 + 0.267949i 0.0194391 + 0.0112232i
\(571\) 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
\(575\) 0.133975 0.232051i 0.00558713 0.00967719i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 10.0000i 0.416305i 0.978096 + 0.208153i \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) 0.866025 0.500000i 0.0360219 0.0207973i
\(579\) 20.1962 11.6603i 0.839323 0.484584i
\(580\) 3.73205i 0.154965i
\(581\) 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
\(585\) 0.866025 + 3.50000i 0.0358057 + 0.144707i
\(586\) 4.14359 0.171170
\(587\) −15.9282 9.19615i −0.657427 0.379566i 0.133869 0.990999i \(-0.457260\pi\)
−0.791296 + 0.611433i \(0.790593\pi\)
\(588\) −1.50000 + 2.59808i −0.0618590 + 0.107143i
\(589\) 0.464102 + 0.803848i 0.0191230 + 0.0331220i
\(590\) 1.53590i 0.0632319i
\(591\) 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 \(0.220514\pi\)
−0.769483 + 0.638667i \(0.779486\pi\)
\(594\) −0.232051 0.401924i −0.00952116 0.0164911i
\(595\) 4.00000 6.92820i 0.163984 0.284029i
\(596\) 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 \(0.431902\pi\)
\(600\) −0.866025 0.500000i −0.0353553 0.0204124i
\(601\) −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
\(605\) −9.33975 + 5.39230i −0.379715 + 0.219228i
\(606\) 10.9282i 0.443928i
\(607\) −21.5885 37.3923i −0.876248 1.51771i −0.855427 0.517924i \(-0.826705\pi\)
−0.0208216 0.999783i \(-0.506628\pi\)
\(608\) 0.267949 0.464102i 0.0108668 0.0188218i
\(609\) 6.46410 + 3.73205i 0.261939 + 0.151230i
\(610\) −10.3923 −0.420772
\(611\) 36.2487 + 10.4641i 1.46647 + 0.423332i
\(612\) 4.00000 0.161690
\(613\) 0.820508 + 0.473721i 0.0331400 + 0.0191334i 0.516478 0.856300i \(-0.327243\pi\)
−0.483338 + 0.875434i \(0.660576\pi\)
\(614\) 6.26795 10.8564i 0.252954 0.438129i
\(615\) 1.00000 + 1.73205i 0.0403239 + 0.0698430i
\(616\) 0.928203i 0.0373984i
\(617\) 13.4545 7.76795i 0.541657 0.312726i −0.204093 0.978951i \(-0.565425\pi\)
0.745750 + 0.666226i \(0.232091\pi\)
\(618\) 13.7321 7.92820i 0.552384 0.318919i
\(619\) 24.2487i 0.974638i −0.873224 0.487319i \(-0.837975\pi\)
0.873224 0.487319i \(-0.162025\pi\)
\(620\) −0.866025 1.50000i −0.0347804 0.0602414i
\(621\) 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
\(625\) 1.00000 0.0400000
\(626\) −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
\(630\) −1.73205 + 1.00000i −0.0690066 + 0.0398410i
\(631\) −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
\(635\) 7.73205 + 4.46410i 0.306837 + 0.177152i
\(636\) −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
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −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 0.0486490 0.998816i \(-0.484508\pi\)
0.889324 + 0.457277i \(0.151175\pi\)
\(644\) −0.464102 + 0.267949i −0.0182882 + 0.0105587i
\(645\) 1.92820i 0.0759229i
\(646\) −1.07180 1.85641i −0.0421693 0.0730393i
\(647\) −10.6603 + 18.4641i −0.419098 + 0.725899i −0.995849 0.0910212i \(-0.970987\pi\)
0.576751 + 0.816920i \(0.304320\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −0.712813 −0.0279804
\(650\) −2.59808 + 2.50000i −0.101905 + 0.0980581i
\(651\) −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 \(-0.500148\pi\)
0.866258 0.499597i \(-0.166519\pi\)
\(654\) −5.92820 10.2679i −0.231811 0.401509i
\(655\) 1.33975i 0.0523482i
\(656\) 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 \(0.810175\pi\)
\(660\) 0.232051 0.401924i 0.00903257 0.0156449i
\(661\) 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
\(665\) 0.928203 + 0.535898i 0.0359942 + 0.0207812i
\(666\) 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
\(670\) 3.92820 2.26795i 0.151760 0.0876185i
\(671\) 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 \(0.378220\pi\)
−0.990074 + 0.140548i \(0.955114\pi\)
\(674\) −21.9282 12.6603i −0.844643 0.487655i
\(675\) 1.00000 0.0384900
\(676\) 0.500000 12.9904i 0.0192308 0.499630i
\(677\) 11.6077 0.446120 0.223060 0.974805i \(-0.428395\pi\)
0.223060 + 0.974805i \(0.428395\pi\)
\(678\) −9.69615 5.59808i −0.372378 0.214993i
\(679\) −7.46410 + 12.9282i −0.286446 + 0.496139i
\(680\) 2.00000 + 3.46410i 0.0766965 + 0.132842i
\(681\) 4.39230i 0.168313i
\(682\) 0.696152 0.401924i 0.0266571 0.0153905i
\(683\) −0.679492 + 0.392305i −0.0260000 + 0.0150111i −0.512944 0.858422i \(-0.671445\pi\)
0.486944 + 0.873433i \(0.338112\pi\)
\(684\) 0.535898i 0.0204906i
\(685\) 2.23205 + 3.86603i 0.0852823 + 0.147713i
\(686\) −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
\(690\) 0.267949 0.0102007
\(691\) −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
\(695\) −0.803848 + 0.464102i −0.0304917 + 0.0176044i
\(696\) −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
\(700\) −1.73205 1.00000i −0.0654654 0.0377964i
\(701\) −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
\(705\) 5.23205 9.06218i 0.197050 0.341301i
\(706\) −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 \(0.278844\pi\)
\(710\) 8.39230i 0.314958i
\(711\) 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
\(715\) −1.16025 1.20577i −0.0433910 0.0450933i
\(716\) 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 \(-0.390204\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 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
\(725\) 1.86603 3.23205i 0.0693024 0.120035i
\(726\) −9.33975 5.39230i −0.346630 0.200127i
\(727\) 23.7128 0.879460 0.439730 0.898130i \(-0.355074\pi\)
0.439730 + 0.898130i \(0.355074\pi\)
\(728\) 7.00000 1.73205i 0.259437 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) −1.73205 1.00000i −0.0641061 0.0370117i
\(731\) −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 \(0.240040\pi\)
−0.728882 + 0.684639i \(0.759960\pi\)
\(734\) −31.5167 + 18.1962i −1.16330 + 0.671632i
\(735\) 2.59808 1.50000i 0.0958315 0.0553283i
\(736\) 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 \(0.757594\pi\)
\(740\) 1.19615 0.0439714
\(741\) 1.85641 + 0.535898i 0.0681968 + 0.0196867i
\(742\) −25.8564 −0.949219
\(743\) 29.0429 + 16.7679i 1.06548 + 0.615156i 0.926944 0.375201i \(-0.122426\pi\)
0.138539 + 0.990357i \(0.455760\pi\)
\(744\) 0.866025 1.50000i 0.0317500 0.0549927i
\(745\) −10.2321 17.7224i −0.374873 0.649300i
\(746\) 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
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) −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
\(755\) −10.3923 −0.378215
\(756\) −1.73205 1.00000i −0.0629941 0.0363696i
\(757\) 9.00000 15.5885i 0.327111 0.566572i −0.654827 0.755779i \(-0.727258\pi\)
0.981937 + 0.189207i \(0.0605917\pi\)
\(758\) −0.0717968 0.124356i −0.00260778 0.00451680i
\(759\) 0.124356i 0.00451382i
\(760\) −0.464102 + 0.267949i −0.0168347 + 0.00971954i
\(761\) −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
\(765\) −3.46410 2.00000i −0.125245 0.0723102i
\(766\) −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 \(0.781569\pi\)
\(770\) 0.464102 0.803848i 0.0167251 0.0289687i
\(771\) −11.3301 19.6244i −0.408045 0.706754i
\(772\) 23.3205i 0.839323i
\(773\) 24.0000 13.8564i 0.863220 0.498380i −0.00186926 0.999998i \(-0.500595\pi\)
0.865089 + 0.501618i \(0.167262\pi\)
\(774\) 1.66987 0.964102i 0.0600223 0.0346539i
\(775\) 1.73205i