Properties

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

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

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

$q$-expansion

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

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 0.401924 0.232051i 0.121185 0.0699660i −0.438182 0.898886i \(-0.644378\pi\)
0.559367 + 0.828920i \(0.311044\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.46410 + 1.00000i −0.960769 + 0.277350i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0.464102 + 0.267949i 0.106472 + 0.0614718i 0.552291 0.833652i \(-0.313754\pi\)
−0.445818 + 0.895123i \(0.647087\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) −0.401924 0.232051i −0.0856904 0.0494734i
\(23\) 0.232051 0.133975i 0.0483859 0.0279356i −0.475612 0.879655i \(-0.657773\pi\)
0.523998 + 0.851720i \(0.324440\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 2.59808 + 2.50000i 0.509525 + 0.490290i
\(27\) 1.00000i 0.192450i
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) 1.86603 + 3.23205i 0.346512 + 0.600177i 0.985627 0.168934i \(-0.0540326\pi\)
−0.639115 + 0.769111i \(0.720699\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.232051 + 0.401924i −0.0403949 + 0.0699660i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −0.598076 1.03590i −0.0983231 0.170301i 0.812668 0.582728i \(-0.198015\pi\)
−0.910991 + 0.412427i \(0.864681\pi\)
\(38\) 0.535898i 0.0869342i
\(39\) 2.50000 2.59808i 0.400320 0.416025i
\(40\) 0 0
\(41\) −1.73205 + 1.00000i −0.270501 + 0.156174i −0.629115 0.777312i \(-0.716583\pi\)
0.358614 + 0.933486i \(0.383249\pi\)
\(42\) 1.73205 1.00000i 0.267261 0.154303i
\(43\) 1.66987 + 0.964102i 0.254653 + 0.147024i 0.621893 0.783102i \(-0.286364\pi\)
−0.367240 + 0.930126i \(0.619697\pi\)
\(44\) 0.464102i 0.0699660i
\(45\) 0 0
\(46\) −0.232051 0.133975i −0.0342140 0.0197535i
\(47\) −10.4641 −1.52635 −0.763173 0.646194i \(-0.776360\pi\)
−0.763173 + 0.646194i \(0.776360\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) 0.866025 3.50000i 0.120096 0.485363i
\(53\) 12.9282i 1.77583i −0.460012 0.887913i \(-0.652155\pi\)
0.460012 0.887913i \(-0.347845\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) −0.535898 −0.0709815
\(58\) 1.86603 3.23205i 0.245021 0.424389i
\(59\) 1.33013 + 0.767949i 0.173168 + 0.0999785i 0.584079 0.811697i \(-0.301456\pi\)
−0.410911 + 0.911676i \(0.634789\pi\)
\(60\) 0 0
\(61\) −5.19615 + 9.00000i −0.665299 + 1.15233i 0.313905 + 0.949454i \(0.398363\pi\)
−0.979204 + 0.202878i \(0.934971\pi\)
\(62\) 1.50000 0.866025i 0.190500 0.109985i
\(63\) −1.00000 1.73205i −0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.464102 0.0571270
\(67\) −2.26795 3.92820i −0.277074 0.479906i 0.693582 0.720377i \(-0.256031\pi\)
−0.970656 + 0.240471i \(0.922698\pi\)
\(68\) 3.46410 2.00000i 0.420084 0.242536i
\(69\) −0.133975 + 0.232051i −0.0161286 + 0.0279356i
\(70\) 0 0
\(71\) −7.26795 4.19615i −0.862547 0.497992i 0.00231747 0.999997i \(-0.499262\pi\)
−0.864864 + 0.502006i \(0.832596\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −0.598076 + 1.03590i −0.0695249 + 0.120421i
\(75\) 0 0
\(76\) −0.464102 + 0.267949i −0.0532361 + 0.0307359i
\(77\) 0.928203i 0.105779i
\(78\) −3.50000 0.866025i −0.396297 0.0980581i
\(79\) 0.0717968 0.00807777 0.00403888 0.999992i \(-0.498714\pi\)
0.00403888 + 0.999992i \(0.498714\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.73205 + 1.00000i 0.191273 + 0.110432i
\(83\) 4.92820 0.540941 0.270470 0.962728i \(-0.412821\pi\)
0.270470 + 0.962728i \(0.412821\pi\)
\(84\) −1.73205 1.00000i −0.188982 0.109109i
\(85\) 0 0
\(86\) 1.92820i 0.207924i
\(87\) −3.23205 1.86603i −0.346512 0.200059i
\(88\) 0.401924 0.232051i 0.0428452 0.0247367i
\(89\) −6.46410 + 3.73205i −0.685193 + 0.395597i −0.801809 0.597581i \(-0.796129\pi\)
0.116615 + 0.993177i \(0.462795\pi\)
\(90\) 0 0
\(91\) −1.73205 + 7.00000i −0.181568 + 0.733799i
\(92\) 0.267949i 0.0279356i
\(93\) −0.866025 1.50000i −0.0898027 0.155543i
\(94\) 5.23205 + 9.06218i 0.539645 + 0.934692i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −3.73205 + 6.46410i −0.378932 + 0.656330i −0.990907 0.134547i \(-0.957042\pi\)
0.611975 + 0.790877i \(0.290375\pi\)
\(98\) 1.50000 2.59808i 0.151523 0.262445i
\(99\) 0.464102i 0.0466440i
\(100\) 0 0
\(101\) 5.46410 + 9.46410i 0.543698 + 0.941713i 0.998688 + 0.0512163i \(0.0163098\pi\)
−0.454989 + 0.890497i \(0.650357\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) 15.8564i 1.56238i 0.624295 + 0.781189i \(0.285387\pi\)
−0.624295 + 0.781189i \(0.714613\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) 0 0
\(106\) −11.1962 + 6.46410i −1.08747 + 0.627849i
\(107\) −17.1962 + 9.92820i −1.66241 + 0.959796i −0.690858 + 0.722991i \(0.742767\pi\)
−0.971557 + 0.236805i \(0.923900\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 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
\(112\) −2.00000 −0.188982
\(113\) −9.69615 5.59808i −0.912137 0.526623i −0.0310191 0.999519i \(-0.509875\pi\)
−0.881118 + 0.472896i \(0.843209\pi\)
\(114\) 0.267949 + 0.464102i 0.0250957 + 0.0434671i
\(115\) 0 0
\(116\) −3.73205 −0.346512
\(117\) −0.866025 + 3.50000i −0.0800641 + 0.323575i
\(118\) 1.53590i 0.141391i
\(119\) −6.92820 + 4.00000i −0.635107 + 0.366679i
\(120\) 0 0
\(121\) −5.39230 + 9.33975i −0.490210 + 0.849068i
\(122\) 10.3923 0.940875
\(123\) 1.00000 1.73205i 0.0901670 0.156174i
\(124\) −1.50000 0.866025i −0.134704 0.0777714i
\(125\) 0 0
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −7.73205 + 4.46410i −0.686109 + 0.396125i −0.802153 0.597119i \(-0.796312\pi\)
0.116044 + 0.993244i \(0.462979\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −1.92820 −0.169769
\(130\) 0 0
\(131\) −1.33975 −0.117054 −0.0585271 0.998286i \(-0.518640\pi\)
−0.0585271 + 0.998286i \(0.518640\pi\)
\(132\) −0.232051 0.401924i −0.0201974 0.0349830i
\(133\) 0.928203 0.535898i 0.0804854 0.0464683i
\(134\) −2.26795 + 3.92820i −0.195921 + 0.339345i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) −2.23205 + 3.86603i −0.190697 + 0.330297i −0.945481 0.325676i \(-0.894408\pi\)
0.754784 + 0.655973i \(0.227741\pi\)
\(138\) 0.267949 0.0228093
\(139\) 0.464102 0.803848i 0.0393646 0.0681815i −0.845672 0.533703i \(-0.820800\pi\)
0.885036 + 0.465522i \(0.154133\pi\)
\(140\) 0 0
\(141\) 9.06218 5.23205i 0.763173 0.440618i
\(142\) 8.39230i 0.704267i
\(143\) −1.16025 + 1.20577i −0.0970253 + 0.100832i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) −2.59808 1.50000i −0.214286 0.123718i
\(148\) 1.19615 0.0983231
\(149\) −17.7224 10.2321i −1.45188 0.838242i −0.453290 0.891363i \(-0.649750\pi\)
−0.998588 + 0.0531208i \(0.983083\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i 0.906196 + 0.422857i \(0.138973\pi\)
−0.906196 + 0.422857i \(0.861027\pi\)
\(152\) 0.464102 + 0.267949i 0.0376436 + 0.0217335i
\(153\) −3.46410 + 2.00000i −0.280056 + 0.161690i
\(154\) −0.803848 + 0.464102i −0.0647759 + 0.0373984i
\(155\) 0 0
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) 5.00000i 0.399043i 0.979893 + 0.199522i \(0.0639388\pi\)
−0.979893 + 0.199522i \(0.936061\pi\)
\(158\) −0.0358984 0.0621778i −0.00285592 0.00494660i
\(159\) 6.46410 + 11.1962i 0.512637 + 0.887913i
\(160\) 0 0
\(161\) 0.535898i 0.0422347i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −11.5263 + 19.9641i −0.902808 + 1.56371i −0.0789748 + 0.996877i \(0.525165\pi\)
−0.823833 + 0.566833i \(0.808169\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 0 0
\(166\) −2.46410 4.26795i −0.191251 0.331257i
\(167\) −9.16025 15.8660i −0.708842 1.22775i −0.965287 0.261191i \(-0.915885\pi\)
0.256445 0.966559i \(-0.417449\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 0 0
\(171\) 0.464102 0.267949i 0.0354907 0.0204906i
\(172\) −1.66987 + 0.964102i −0.127327 + 0.0735121i
\(173\) 2.53590 + 1.46410i 0.192801 + 0.111314i 0.593293 0.804987i \(-0.297828\pi\)
−0.400492 + 0.916300i \(0.631161\pi\)
\(174\) 3.73205i 0.282926i
\(175\) 0 0
\(176\) −0.401924 0.232051i −0.0302961 0.0174915i
\(177\) −1.53590 −0.115445
\(178\) 6.46410 + 3.73205i 0.484505 + 0.279729i
\(179\) −8.13397 14.0885i −0.607962 1.05302i −0.991576 0.129527i \(-0.958654\pi\)
0.383614 0.923494i \(-0.374679\pi\)
\(180\) 0 0
\(181\) 10.9282 0.812287 0.406143 0.913809i \(-0.366873\pi\)
0.406143 + 0.913809i \(0.366873\pi\)
\(182\) 6.92820 2.00000i 0.513553 0.148250i
\(183\) 10.3923i 0.768221i
\(184\) 0.232051 0.133975i 0.0171070 0.00987674i
\(185\) 0 0
\(186\) −0.866025 + 1.50000i −0.0635001 + 0.109985i
\(187\) −1.85641 −0.135754
\(188\) 5.23205 9.06218i 0.381587 0.660927i
\(189\) 1.73205 + 1.00000i 0.125988 + 0.0727393i
\(190\) 0 0
\(191\) −7.26795 + 12.5885i −0.525890 + 0.910869i 0.473655 + 0.880711i \(0.342934\pi\)
−0.999545 + 0.0301582i \(0.990399\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 11.6603 + 20.1962i 0.839323 + 1.45375i 0.890461 + 0.455059i \(0.150382\pi\)
−0.0511377 + 0.998692i \(0.516285\pi\)
\(194\) 7.46410 0.535891
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −8.19615 14.1962i −0.583952 1.01143i −0.995005 0.0998228i \(-0.968172\pi\)
0.411054 0.911611i \(-0.365161\pi\)
\(198\) −0.401924 + 0.232051i −0.0285635 + 0.0164911i
\(199\) −9.46410 + 16.3923i −0.670892 + 1.16202i 0.306759 + 0.951787i \(0.400755\pi\)
−0.977651 + 0.210232i \(0.932578\pi\)
\(200\) 0 0
\(201\) 3.92820 + 2.26795i 0.277074 + 0.159969i
\(202\) 5.46410 9.46410i 0.384453 0.665892i
\(203\) 7.46410 0.523877
\(204\) −2.00000 + 3.46410i −0.140028 + 0.242536i
\(205\) 0 0
\(206\) 13.7321 7.92820i 0.956757 0.552384i
\(207\) 0.267949i 0.0186238i
\(208\) 2.59808 + 2.50000i 0.180144 + 0.173344i
\(209\) 0.248711 0.0172037
\(210\) 0 0
\(211\) −11.6603 20.1962i −0.802725 1.39036i −0.917816 0.397006i \(-0.870049\pi\)
0.115091 0.993355i \(-0.463284\pi\)
\(212\) 11.1962 + 6.46410i 0.768955 + 0.443956i
\(213\) 8.39230 0.575031
\(214\) 17.1962 + 9.92820i 1.17550 + 0.678678i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 3.00000 + 1.73205i 0.203653 + 0.117579i
\(218\) −10.2679 + 5.92820i −0.695433 + 0.401509i
\(219\) 1.73205 1.00000i 0.117041 0.0675737i
\(220\) 0 0
\(221\) 14.0000 + 3.46410i 0.941742 + 0.233021i
\(222\) 1.19615i 0.0802805i
\(223\) 13.7321 + 23.7846i 0.919566 + 1.59274i 0.800075 + 0.599900i \(0.204793\pi\)
0.119491 + 0.992835i \(0.461874\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 0 0
\(226\) 11.1962i 0.744757i
\(227\) −2.19615 + 3.80385i −0.145764 + 0.252470i −0.929658 0.368425i \(-0.879897\pi\)
0.783894 + 0.620895i \(0.213231\pi\)
\(228\) 0.267949 0.464102i 0.0177454 0.0307359i
\(229\) 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
\(232\) 1.86603 + 3.23205i 0.122511 + 0.212195i
\(233\) 18.1244i 1.18737i −0.804699 0.593683i \(-0.797673\pi\)
0.804699 0.593683i \(-0.202327\pi\)
\(234\) 3.46410 1.00000i 0.226455 0.0653720i
\(235\) 0 0
\(236\) −1.33013 + 0.767949i −0.0865839 + 0.0499892i
\(237\) −0.0621778 + 0.0358984i −0.00403888 + 0.00233185i
\(238\) 6.92820 + 4.00000i 0.449089 + 0.259281i
\(239\) 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 0.0461056 0.998937i \(-0.485319\pi\)
−0.842052 + 0.539397i \(0.818652\pi\)
\(242\) 10.7846 0.693261
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −5.19615 9.00000i −0.332650 0.576166i
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −1.87564 0.464102i −0.119344 0.0295301i
\(248\) 1.73205i 0.109985i
\(249\) −4.26795 + 2.46410i −0.270470 + 0.156156i
\(250\) 0 0
\(251\) −6.13397 + 10.6244i −0.387173 + 0.670603i −0.992068 0.125702i \(-0.959882\pi\)
0.604895 + 0.796305i \(0.293215\pi\)
\(252\) 2.00000 0.125988
\(253\) 0.0621778 0.107695i 0.00390909 0.00677074i
\(254\) 7.73205 + 4.46410i 0.485152 + 0.280103i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 19.6244 11.3301i 1.22413 0.706754i 0.258337 0.966055i \(-0.416825\pi\)
0.965797 + 0.259301i \(0.0834921\pi\)
\(258\) 0.964102 + 1.66987i 0.0600223 + 0.103962i
\(259\) −2.39230 −0.148651
\(260\) 0 0
\(261\) 3.73205 0.231008
\(262\) 0.669873 + 1.16025i 0.0413849 + 0.0716807i
\(263\) −15.6962 + 9.06218i −0.967866 + 0.558798i −0.898585 0.438799i \(-0.855404\pi\)
−0.0692812 + 0.997597i \(0.522071\pi\)
\(264\) −0.232051 + 0.401924i −0.0142817 + 0.0247367i
\(265\) 0 0
\(266\) −0.928203 0.535898i −0.0569118 0.0328580i
\(267\) 3.73205 6.46410i 0.228398 0.395597i
\(268\) 4.53590 0.277074
\(269\) 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i \(-0.714120\pi\)
0.988908 + 0.148527i \(0.0474530\pi\)
\(270\) 0 0
\(271\) 7.96410 4.59808i 0.483785 0.279313i −0.238208 0.971214i \(-0.576560\pi\)
0.721992 + 0.691901i \(0.243227\pi\)
\(272\) 4.00000i 0.242536i
\(273\) −2.00000 6.92820i −0.121046 0.419314i
\(274\) 4.46410 0.269686
\(275\) 0 0
\(276\) −0.133975 0.232051i −0.00806432 0.0139678i
\(277\) 8.59808 + 4.96410i 0.516608 + 0.298264i 0.735546 0.677475i \(-0.236926\pi\)
−0.218938 + 0.975739i \(0.570259\pi\)
\(278\) −0.928203 −0.0556699
\(279\) 1.50000 + 0.866025i 0.0898027 + 0.0518476i
\(280\) 0 0
\(281\) 4.92820i 0.293992i 0.989137 + 0.146996i \(0.0469604\pi\)
−0.989137 + 0.146996i \(0.953040\pi\)
\(282\) −9.06218 5.23205i −0.539645 0.311564i
\(283\) 3.40192 1.96410i 0.202223 0.116754i −0.395469 0.918479i \(-0.629418\pi\)
0.597692 + 0.801726i \(0.296085\pi\)
\(284\) 7.26795 4.19615i 0.431273 0.248996i
\(285\) 0 0
\(286\) 1.62436 + 0.401924i 0.0960502 + 0.0237663i
\(287\) 4.00000i 0.236113i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 7.46410i 0.437553i
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) −2.07180 + 3.58846i −0.121036 + 0.209640i −0.920176 0.391504i \(-0.871955\pi\)
0.799141 + 0.601144i \(0.205288\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 0 0
\(296\) −0.598076 1.03590i −0.0347625 0.0602104i
\(297\) 0.232051 + 0.401924i 0.0134650 + 0.0233220i
\(298\) 20.4641i 1.18545i
\(299\) −0.669873 + 0.696152i −0.0387398 + 0.0402595i
\(300\) 0 0
\(301\) 3.33975 1.92820i 0.192500 0.111140i
\(302\) 9.00000 5.19615i 0.517892 0.299005i
\(303\) −9.46410 5.46410i −0.543698 0.313904i
\(304\) 0.535898i 0.0307359i
\(305\) 0 0
\(306\) 3.46410 + 2.00000i 0.198030 + 0.114332i
\(307\) 12.5359 0.715462 0.357731 0.933825i \(-0.383551\pi\)
0.357731 + 0.933825i \(0.383551\pi\)
\(308\) 0.803848 + 0.464102i 0.0458035 + 0.0264446i
\(309\) −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 \(0.569202\pi\)
\(312\) 2.50000 2.59808i 0.141535 0.147087i
\(313\) 28.0000i 1.58265i −0.611393 0.791327i \(-0.709391\pi\)
0.611393 0.791327i \(-0.290609\pi\)
\(314\) 4.33013 2.50000i 0.244363 0.141083i
\(315\) 0 0
\(316\) −0.0358984 + 0.0621778i −0.00201944 + 0.00349778i
\(317\) 21.4641 1.20554 0.602772 0.797913i \(-0.294063\pi\)
0.602772 + 0.797913i \(0.294063\pi\)
\(318\) 6.46410 11.1962i 0.362489 0.627849i
\(319\) 1.50000 + 0.866025i 0.0839839 + 0.0484881i
\(320\) 0 0
\(321\) 9.92820 17.1962i 0.554138 0.959796i
\(322\) −0.464102 + 0.267949i −0.0258634 + 0.0149322i
\(323\) −1.07180 1.85641i −0.0596364 0.103293i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 23.0526 1.27676
\(327\) 5.92820 + 10.2679i 0.327830 + 0.567819i
\(328\) −1.73205 + 1.00000i −0.0956365 + 0.0552158i
\(329\) −10.4641 + 18.1244i −0.576905 + 0.999228i
\(330\) 0 0
\(331\) −21.4641 12.3923i −1.17977 0.681143i −0.223812 0.974632i \(-0.571850\pi\)
−0.955962 + 0.293490i \(0.905183\pi\)
\(332\) −2.46410 + 4.26795i −0.135235 + 0.234234i
\(333\) −1.19615 −0.0655487
\(334\) −9.16025 + 15.8660i −0.501227 + 0.868150i
\(335\) 0 0
\(336\) 1.73205 1.00000i 0.0944911 0.0545545i
\(337\) 25.3205i 1.37930i 0.724145 + 0.689648i \(0.242235\pi\)
−0.724145 + 0.689648i \(0.757765\pi\)
\(338\) −11.5000 6.06218i −0.625518 0.329739i
\(339\) 11.1962 0.608092
\(340\) 0 0
\(341\) 0.401924 + 0.696152i 0.0217654 + 0.0376988i
\(342\) −0.464102 0.267949i −0.0250957 0.0144890i
\(343\) 20.0000 1.07990
\(344\) 1.66987 + 0.964102i 0.0900335 + 0.0519809i
\(345\) 0 0
\(346\) 2.92820i 0.157421i
\(347\) 19.3923 + 11.1962i 1.04103 + 0.601041i 0.920126 0.391623i \(-0.128086\pi\)
0.120908 + 0.992664i \(0.461420\pi\)
\(348\) 3.23205 1.86603i 0.173256 0.100029i
\(349\) 12.5885 7.26795i 0.673845 0.389044i −0.123687 0.992321i \(-0.539472\pi\)
0.797532 + 0.603277i \(0.206139\pi\)
\(350\) 0 0
\(351\) −1.00000 3.46410i −0.0533761 0.184900i
\(352\) 0.464102i 0.0247367i
\(353\) −1.00000 1.73205i −0.0532246 0.0921878i 0.838186 0.545385i \(-0.183617\pi\)
−0.891410 + 0.453197i \(0.850283\pi\)
\(354\) 0.767949 + 1.33013i 0.0408160 + 0.0706955i
\(355\) 0 0
\(356\) 7.46410i 0.395597i
\(357\) 4.00000 6.92820i 0.211702 0.366679i
\(358\) −8.13397 + 14.0885i −0.429894 + 0.744598i
\(359\) 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
\(362\) −5.46410 9.46410i −0.287187 0.497422i
\(363\) 10.7846i 0.566045i
\(364\) −5.19615 5.00000i −0.272352 0.262071i
\(365\) 0 0
\(366\) −9.00000 + 5.19615i −0.470438 + 0.271607i
\(367\) −31.5167 + 18.1962i −1.64516 + 0.949831i −0.666197 + 0.745776i \(0.732079\pi\)
−0.978959 + 0.204056i \(0.934588\pi\)
\(368\) −0.232051 0.133975i −0.0120965 0.00698391i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) −22.3923 12.9282i −1.16255 0.671199i
\(372\) 1.73205 0.0898027
\(373\) −22.3301 12.8923i −1.15621 0.667538i −0.205817 0.978590i \(-0.565985\pi\)
−0.950393 + 0.311052i \(0.899319\pi\)
\(374\) 0.928203 + 1.60770i 0.0479962 + 0.0831319i
\(375\) 0 0
\(376\) −10.4641 −0.539645
\(377\) −9.69615 9.33013i −0.499377 0.480526i
\(378\) 2.00000i 0.102869i
\(379\) 0.124356 0.0717968i 0.00638772 0.00368795i −0.496803 0.867863i \(-0.665493\pi\)
0.503190 + 0.864176i \(0.332159\pi\)
\(380\) 0 0
\(381\) 4.46410 7.73205i 0.228703 0.396125i
\(382\) 14.5359 0.743721
\(383\) 2.30385 3.99038i 0.117721 0.203899i −0.801143 0.598473i \(-0.795774\pi\)
0.918864 + 0.394574i \(0.129108\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 11.6603 20.1962i 0.593491 1.02796i
\(387\) 1.66987 0.964102i 0.0848844 0.0490080i
\(388\) −3.73205 6.46410i −0.189466 0.328165i
\(389\) 20.2679 1.02763 0.513813 0.857902i \(-0.328233\pi\)
0.513813 + 0.857902i \(0.328233\pi\)
\(390\) 0 0
\(391\) −1.07180 −0.0542031
\(392\) 1.50000 + 2.59808i 0.0757614 + 0.131223i
\(393\) 1.16025 0.669873i 0.0585271 0.0337906i
\(394\) −8.19615 + 14.1962i −0.412916 + 0.715192i
\(395\) 0 0
\(396\) 0.401924 + 0.232051i 0.0201974 + 0.0116610i
\(397\) 6.06218 10.5000i 0.304252 0.526980i −0.672843 0.739786i \(-0.734927\pi\)
0.977095 + 0.212806i \(0.0682602\pi\)
\(398\) 18.9282 0.948785
\(399\) −0.535898 + 0.928203i −0.0268285 + 0.0464683i
\(400\) 0 0
\(401\) 27.7128 16.0000i 1.38391 0.799002i 0.391292 0.920267i \(-0.372028\pi\)
0.992620 + 0.121265i \(0.0386950\pi\)
\(402\) 4.53590i 0.226230i
\(403\) −1.73205 6.00000i −0.0862796 0.298881i
\(404\) −10.9282 −0.543698
\(405\) 0 0
\(406\) −3.73205 6.46410i −0.185219 0.320808i
\(407\) −0.480762 0.277568i −0.0238305 0.0137585i
\(408\) 4.00000 0.198030
\(409\) 3.46410 + 2.00000i 0.171289 + 0.0988936i 0.583193 0.812333i \(-0.301803\pi\)
−0.411905 + 0.911227i \(0.635136\pi\)
\(410\) 0 0
\(411\) 4.46410i 0.220198i
\(412\) −13.7321 7.92820i −0.676530 0.390595i
\(413\) 2.66025 1.53590i 0.130903 0.0755766i
\(414\) −0.232051 + 0.133975i −0.0114047 + 0.00658449i
\(415\) 0 0
\(416\) 0.866025 3.50000i 0.0424604 0.171602i
\(417\) 0.928203i 0.0454543i
\(418\) −0.124356 0.215390i −0.00608243 0.0105351i
\(419\) 0.803848 + 1.39230i 0.0392705 + 0.0680185i 0.884993 0.465605i \(-0.154163\pi\)
−0.845722 + 0.533624i \(0.820830\pi\)
\(420\) 0 0
\(421\) 16.3923i 0.798912i −0.916752 0.399456i \(-0.869199\pi\)
0.916752 0.399456i \(-0.130801\pi\)
\(422\) −11.6603 + 20.1962i −0.567612 + 0.983133i
\(423\) −5.23205 + 9.06218i −0.254391 + 0.440618i
\(424\) 12.9282i 0.627849i
\(425\) 0 0
\(426\) −4.19615 7.26795i −0.203304 0.352133i
\(427\) 10.3923 + 18.0000i 0.502919 + 0.871081i
\(428\) 19.8564i 0.959796i
\(429\) 0.401924 1.62436i 0.0194051 0.0784246i
\(430\) 0 0
\(431\) −6.58846 + 3.80385i −0.317355 + 0.183225i −0.650213 0.759752i \(-0.725320\pi\)
0.332858 + 0.942977i \(0.391987\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 13.2679 + 7.66025i 0.637617 + 0.368128i 0.783696 0.621145i \(-0.213332\pi\)
−0.146079 + 0.989273i \(0.546665\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 0 0
\(436\) 10.2679 + 5.92820i 0.491746 + 0.283909i
\(437\) 0.143594 0.00686901
\(438\) −1.73205 1.00000i −0.0827606 0.0477818i
\(439\) 4.92820 + 8.53590i 0.235210 + 0.407396i 0.959334 0.282274i \(-0.0910888\pi\)
−0.724123 + 0.689670i \(0.757755\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −4.00000 13.8564i −0.190261 0.659082i
\(443\) 4.39230i 0.208685i −0.994541 0.104342i \(-0.966726\pi\)
0.994541 0.104342i \(-0.0332738\pi\)
\(444\) −1.03590 + 0.598076i −0.0491616 + 0.0283834i
\(445\) 0 0
\(446\) 13.7321 23.7846i 0.650231 1.12623i
\(447\) 20.4641 0.967919
\(448\) 1.00000 1.73205i 0.0472456 0.0818317i
\(449\) 34.3923 + 19.8564i 1.62307 + 0.937082i 0.986092 + 0.166203i \(0.0531506\pi\)
0.636982 + 0.770879i \(0.280183\pi\)
\(450\) 0 0
\(451\) −0.464102 + 0.803848i −0.0218537 + 0.0378517i
\(452\) 9.69615 5.59808i 0.456069 0.263311i
\(453\) −5.19615 9.00000i −0.244137 0.422857i
\(454\) 4.39230 0.206141
\(455\) 0 0
\(456\) −0.535898 −0.0250957
\(457\) 15.7321 + 27.2487i 0.735914 + 1.27464i 0.954321 + 0.298783i \(0.0965807\pi\)
−0.218407 + 0.975858i \(0.570086\pi\)
\(458\) −17.1962 + 9.92820i −0.803523 + 0.463914i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) 5.59808 + 3.23205i 0.260728 + 0.150532i 0.624667 0.780891i \(-0.285235\pi\)
−0.363938 + 0.931423i \(0.618568\pi\)
\(462\) 0.464102 0.803848i 0.0215920 0.0373984i
\(463\) −20.9282 −0.972616 −0.486308 0.873787i \(-0.661657\pi\)
−0.486308 + 0.873787i \(0.661657\pi\)
\(464\) 1.86603 3.23205i 0.0866281 0.150044i
\(465\) 0 0
\(466\) −15.6962 + 9.06218i −0.727110 + 0.419797i
\(467\) 11.8564i 0.548649i −0.961637 0.274325i \(-0.911546\pi\)
0.961637 0.274325i \(-0.0884542\pi\)
\(468\) −2.59808 2.50000i −0.120096 0.115563i
\(469\) −9.07180 −0.418897
\(470\) 0 0
\(471\) −2.50000 4.33013i −0.115194 0.199522i
\(472\) 1.33013 + 0.767949i 0.0612241 + 0.0353477i
\(473\) 0.894882 0.0411467
\(474\) 0.0621778 + 0.0358984i 0.00285592 + 0.00164887i
\(475\) 0 0
\(476\) 8.00000i 0.366679i
\(477\) −11.1962 6.46410i −0.512637 0.295971i
\(478\) −3.80385 + 2.19615i −0.173984 + 0.100450i
\(479\) −1.26795 + 0.732051i −0.0579341 + 0.0334483i −0.528687 0.848817i \(-0.677316\pi\)
0.470753 + 0.882265i \(0.343982\pi\)
\(480\) 0 0
\(481\) 3.10770 + 2.99038i 0.141699 + 0.136350i
\(482\) 14.2679i 0.649887i
\(483\) 0.267949 + 0.464102i 0.0121921 + 0.0211174i
\(484\) −5.39230 9.33975i −0.245105 0.424534i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 19.5885 33.9282i 0.887638 1.53743i 0.0449775 0.998988i \(-0.485678\pi\)
0.842660 0.538446i \(-0.180988\pi\)
\(488\) −5.19615 + 9.00000i −0.235219 + 0.407411i
\(489\) 23.0526i 1.04247i
\(490\) 0 0
\(491\) −8.66025 15.0000i −0.390832 0.676941i 0.601728 0.798701i \(-0.294479\pi\)
−0.992559 + 0.121761i \(0.961146\pi\)
\(492\) 1.00000 + 1.73205i 0.0450835 + 0.0780869i
\(493\) 14.9282i 0.672332i
\(494\) 0.535898 + 1.85641i 0.0241112 + 0.0835237i
\(495\) 0 0
\(496\) 1.50000 0.866025i 0.0673520 0.0388857i
\(497\) −14.5359 + 8.39230i −0.652024 + 0.376446i
\(498\) 4.26795 + 2.46410i 0.191251 + 0.110419i
\(499\) 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
\(502\) 12.2679 0.547545
\(503\) −27.0000 15.5885i −1.20387 0.695055i −0.242457 0.970162i \(-0.577953\pi\)
−0.961414 + 0.275107i \(0.911287\pi\)
\(504\) −1.00000 1.73205i −0.0445435 0.0771517i
\(505\) 0 0
\(506\) −0.124356 −0.00552828
\(507\) −6.06218 + 11.5000i −0.269231 + 0.510733i
\(508\) 8.92820i 0.396125i
\(509\) −16.7942 + 9.69615i −0.744391 + 0.429774i −0.823664 0.567079i \(-0.808074\pi\)
0.0792726 + 0.996853i \(0.474740\pi\)
\(510\) 0 0
\(511\) −2.00000 + 3.46410i −0.0884748 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) −0.267949 + 0.464102i −0.0118302 + 0.0204906i
\(514\) −19.6244 11.3301i −0.865593 0.499750i
\(515\) 0 0
\(516\) 0.964102 1.66987i 0.0424422 0.0735121i
\(517\) −4.20577 + 2.42820i −0.184970 + 0.106792i
\(518\) 1.19615 + 2.07180i 0.0525559 + 0.0910295i
\(519\) −2.92820 −0.128534
\(520\) 0 0
\(521\) 17.3205 0.758825 0.379413 0.925228i \(-0.376126\pi\)
0.379413 + 0.925228i \(0.376126\pi\)
\(522\) −1.86603 3.23205i −0.0816737 0.141463i
\(523\) −25.7942 + 14.8923i −1.12790 + 0.651195i −0.943407 0.331638i \(-0.892399\pi\)
−0.184496 + 0.982833i \(0.559065\pi\)
\(524\) 0.669873 1.16025i 0.0292635 0.0506859i
\(525\) 0 0
\(526\) 15.6962 + 9.06218i 0.684385 + 0.395130i
\(527\) 3.46410 6.00000i 0.150899 0.261364i
\(528\) 0.464102 0.0201974
\(529\) −11.4641 + 19.8564i −0.498439 + 0.863322i
\(530\) 0 0
\(531\) 1.33013 0.767949i 0.0577226 0.0333262i
\(532\) 1.07180i 0.0464683i
\(533\) 5.00000 5.19615i 0.216574 0.225070i
\(534\) −7.46410 −0.323003
\(535\) 0 0
\(536\) −2.26795 3.92820i −0.0979605 0.169673i
\(537\) 14.0885 + 8.13397i 0.607962 + 0.351007i
\(538\) −12.0000 −0.517357
\(539\) 1.20577 + 0.696152i 0.0519362 + 0.0299854i
\(540\) 0 0
\(541\) 13.0718i 0.562000i 0.959708 + 0.281000i \(0.0906662\pi\)
−0.959708 + 0.281000i \(0.909334\pi\)
\(542\) −7.96410 4.59808i −0.342087 0.197504i
\(543\) −9.46410 + 5.46410i −0.406143 + 0.234487i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 0 0
\(546\) −5.00000 + 5.19615i −0.213980 + 0.222375i
\(547\) 9.07180i 0.387882i −0.981013 0.193941i \(-0.937873\pi\)
0.981013 0.193941i \(-0.0621270\pi\)
\(548\) −2.23205 3.86603i −0.0953485 0.165148i
\(549\) 5.19615 + 9.00000i 0.221766 + 0.384111i
\(550\) 0 0
\(551\) 2.00000i 0.0852029i
\(552\) −0.133975 + 0.232051i −0.00570234 + 0.00987674i
\(553\) 0.0717968 0.124356i 0.00305311 0.00528814i
\(554\) 9.92820i 0.421809i
\(555\) 0 0
\(556\) 0.464102 + 0.803848i 0.0196823 + 0.0340907i
\(557\) −18.8564 32.6603i −0.798972 1.38386i −0.920286 0.391245i \(-0.872044\pi\)
0.121315 0.992614i \(-0.461289\pi\)
\(558\) 1.73205i 0.0733236i
\(559\) −6.74871 1.66987i −0.285440 0.0706281i
\(560\) 0 0
\(561\) 1.60770 0.928203i 0.0678769 0.0391888i
\(562\) 4.26795 2.46410i 0.180033 0.103942i
\(563\) 34.0526 + 19.6603i 1.43514 + 0.828581i 0.997507 0.0705706i \(-0.0224820\pi\)
0.437637 + 0.899152i \(0.355815\pi\)
\(564\) 10.4641i 0.440618i
\(565\) 0 0
\(566\) −3.40192 1.96410i −0.142994 0.0825573i
\(567\) −2.00000 −0.0839921
\(568\) −7.26795 4.19615i −0.304956 0.176067i
\(569\) −2.66025 4.60770i −0.111524 0.193165i 0.804861 0.593463i \(-0.202240\pi\)
−0.916385 + 0.400299i \(0.868906\pi\)
\(570\) 0 0
\(571\) 45.1769 1.89060 0.945298 0.326209i \(-0.105771\pi\)
0.945298 + 0.326209i \(0.105771\pi\)
\(572\) −0.464102 1.60770i −0.0194051 0.0672211i
\(573\) 14.5359i 0.607246i
\(574\) 3.46410 2.00000i 0.144589 0.0834784i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) −20.1962 11.6603i −0.839323 0.484584i
\(580\) 0 0
\(581\) 4.92820 8.53590i 0.204456 0.354129i
\(582\) −6.46410 + 3.73205i −0.267946 + 0.154698i
\(583\) −3.00000 5.19615i −0.124247 0.215203i
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 4.14359 0.171170
\(587\) 9.19615 + 15.9282i 0.379566 + 0.657427i 0.990999 0.133869i \(-0.0427400\pi\)
−0.611433 + 0.791296i \(0.709407\pi\)
\(588\) 2.59808 1.50000i 0.107143 0.0618590i
\(589\) −0.464102 + 0.803848i −0.0191230 + 0.0331220i
\(590\) 0 0
\(591\) 14.1962 + 8.19615i 0.583952 + 0.337145i
\(592\) −0.598076 + 1.03590i −0.0245808 + 0.0425752i
\(593\) 31.1051 1.27733 0.638667 0.769483i \(-0.279486\pi\)
0.638667 + 0.769483i \(0.279486\pi\)
\(594\) 0.232051 0.401924i 0.00952116 0.0164911i
\(595\) 0 0
\(596\) 17.7224 10.2321i 0.725939 0.419121i
\(597\) 18.9282i 0.774680i
\(598\) 0.937822 + 0.232051i 0.0383504 + 0.00948926i
\(599\) −10.3923 −0.424618 −0.212309 0.977203i \(-0.568098\pi\)
−0.212309 + 0.977203i \(0.568098\pi\)
\(600\) 0 0
\(601\) −10.8923 18.8660i −0.444306 0.769561i 0.553697 0.832718i \(-0.313216\pi\)
−0.998004 + 0.0631568i \(0.979883\pi\)
\(602\) −3.33975 1.92820i −0.136118 0.0785877i
\(603\) −4.53590 −0.184716
\(604\) −9.00000 5.19615i −0.366205 0.211428i
\(605\) 0 0
\(606\) 10.9282i 0.443928i
\(607\) 37.3923 + 21.5885i 1.51771 + 0.876248i 0.999783 + 0.0208216i \(0.00662820\pi\)
0.517924 + 0.855427i \(0.326705\pi\)
\(608\) −0.464102 + 0.267949i −0.0188218 + 0.0108668i
\(609\) −6.46410 + 3.73205i −0.261939 + 0.151230i
\(610\) 0 0
\(611\) 36.2487 10.4641i 1.46647 0.423332i
\(612\) 4.00000i 0.161690i
\(613\) 0.473721 + 0.820508i 0.0191334 + 0.0331400i 0.875434 0.483338i \(-0.160576\pi\)
−0.856300 + 0.516478i \(0.827243\pi\)
\(614\) −6.26795 10.8564i −0.252954 0.438129i
\(615\) 0 0
\(616\) 0.928203i 0.0373984i
\(617\) 7.76795 13.4545i 0.312726 0.541657i −0.666226 0.745750i \(-0.732091\pi\)
0.978951 + 0.204093i \(0.0654246\pi\)
\(618\) −7.92820 + 13.7321i −0.318919 + 0.552384i
\(619\) 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
\(622\) 3.80385 + 6.58846i 0.152520 + 0.264173i
\(623\) 14.9282i 0.598086i
\(624\) −3.50000 0.866025i −0.140112 0.0346688i
\(625\) 0 0
\(626\) −24.2487 + 14.0000i −0.969173 + 0.559553i
\(627\) −0.215390 + 0.124356i −0.00860186 + 0.00496629i
\(628\) −4.33013 2.50000i −0.172791 0.0997609i
\(629\) 4.78461i 0.190775i
\(630\) 0 0
\(631\) −21.2487 12.2679i −0.845898 0.488379i 0.0133668 0.999911i \(-0.495745\pi\)
−0.859265 + 0.511531i \(0.829078\pi\)
\(632\) 0.0717968 0.00285592
\(633\) 20.1962 + 11.6603i 0.802725 + 0.463453i
\(634\) −10.7321 18.5885i −0.426224 0.738242i
\(635\) 0 0
\(636\) −12.9282 −0.512637
\(637\) −7.79423 7.50000i −0.308819 0.297161i
\(638\) 1.73205i 0.0685725i
\(639\) −7.26795 + 4.19615i −0.287516 + 0.165997i
\(640\) 0 0
\(641\) −13.9282 + 24.1244i −0.550131 + 0.952855i 0.448134 + 0.893967i \(0.352089\pi\)
−0.998265 + 0.0588882i \(0.981244\pi\)
\(642\) −19.8564 −0.783670
\(643\) −13.7321 + 23.7846i −0.541539 + 0.937973i 0.457277 + 0.889324i \(0.348825\pi\)
−0.998816 + 0.0486490i \(0.984508\pi\)
\(644\) 0.464102 + 0.267949i 0.0182882 + 0.0105587i
\(645\) 0 0
\(646\) −1.07180 + 1.85641i −0.0421693 + 0.0730393i
\(647\) −18.4641 + 10.6603i −0.725899 + 0.419098i −0.816920 0.576751i \(-0.804320\pi\)
0.0910212 + 0.995849i \(0.470987\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 0.712813 0.0279804
\(650\) 0 0
\(651\) −3.46410 −0.135769
\(652\) −11.5263 19.9641i −0.451404 0.781855i
\(653\) −38.3205 + 22.1244i −1.49960 + 0.865793i −1.00000 0.000464739i \(-0.999852\pi\)
−0.499597 + 0.866258i \(0.666519\pi\)
\(654\) 5.92820 10.2679i 0.231811 0.401509i
\(655\) 0 0
\(656\) 1.73205 + 1.00000i 0.0676252 + 0.0390434i
\(657\) −1.00000 + 1.73205i −0.0390137 + 0.0675737i
\(658\) 20.9282 0.815866
\(659\) −1.86603 + 3.23205i −0.0726900 + 0.125903i −0.900079 0.435726i \(-0.856492\pi\)
0.827389 + 0.561629i \(0.189825\pi\)
\(660\) 0 0
\(661\) 37.5167 21.6603i 1.45923 0.842486i 0.460256 0.887786i \(-0.347758\pi\)
0.998973 + 0.0453002i \(0.0144244\pi\)
\(662\) 24.7846i 0.963281i
\(663\) −13.8564 + 4.00000i −0.538138 + 0.155347i
\(664\) 4.92820 0.191251
\(665\) 0 0
\(666\) 0.598076 + 1.03590i 0.0231750 + 0.0401402i
\(667\) 0.866025 + 0.500000i 0.0335326 + 0.0193601i
\(668\) 18.3205 0.708842
\(669\) −23.7846 13.7321i −0.919566 0.530912i
\(670\) 0 0
\(671\) 4.82309i 0.186193i
\(672\) −1.73205 1.00000i −0.0668153 0.0385758i
\(673\) 27.7128 16.0000i 1.06825 0.616755i 0.140548 0.990074i \(-0.455114\pi\)
0.927703 + 0.373319i \(0.121780\pi\)
\(674\) 21.9282 12.6603i 0.844643 0.487655i
\(675\) 0 0
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) 11.6077i 0.446120i −0.974805 0.223060i \(-0.928395\pi\)
0.974805 0.223060i \(-0.0716046\pi\)
\(678\) −5.59808 9.69615i −0.214993 0.372378i
\(679\) 7.46410 + 12.9282i 0.286446 + 0.496139i
\(680\) 0 0
\(681\) 4.39230i 0.168313i
\(682\) 0.401924 0.696152i 0.0153905 0.0266571i
\(683\) 0.392305 0.679492i 0.0150111 0.0260000i −0.858422 0.512944i \(-0.828555\pi\)
0.873433 + 0.486944i \(0.161888\pi\)
\(684\) 0.535898i 0.0204906i
\(685\) 0 0
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 9.92820 + 17.1962i 0.378785 + 0.656074i
\(688\) 1.92820i 0.0735121i
\(689\) 12.9282 + 44.7846i 0.492525 + 1.70616i
\(690\) 0 0
\(691\) −30.4641 + 17.5885i −1.15891 + 0.669096i −0.951042 0.309061i \(-0.899985\pi\)
−0.207867 + 0.978157i \(0.566652\pi\)
\(692\) −2.53590 + 1.46410i −0.0964004 + 0.0556568i
\(693\) −0.803848 0.464102i −0.0305356 0.0176298i
\(694\) 22.3923i 0.850000i
\(695\) 0 0
\(696\) −3.23205 1.86603i −0.122511 0.0707315i
\(697\) 8.00000 0.303022
\(698\) −12.5885 7.26795i −0.476480 0.275096i
\(699\) 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 \(0.522453\pi\)
\(702\) −2.50000 + 2.59808i −0.0943564 + 0.0980581i
\(703\) 0.641016i 0.0241764i
\(704\) 0.401924 0.232051i 0.0151481 0.00874574i
\(705\) 0 0
\(706\) −1.00000 + 1.73205i −0.0376355 + 0.0651866i
\(707\) 21.8564 0.821995
\(708\) 0.767949 1.33013i 0.0288613 0.0499892i
\(709\) −7.85641 4.53590i −0.295054 0.170349i 0.345165 0.938542i \(-0.387823\pi\)
−0.640219 + 0.768193i \(0.721156\pi\)
\(710\) 0 0
\(711\) 0.0358984 0.0621778i 0.00134629 0.00233185i
\(712\) −6.46410 + 3.73205i −0.242252 + 0.139865i
\(713\) 0.232051 + 0.401924i 0.00869037 + 0.0150522i
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) 16.2679 0.607962
\(717\) 2.19615 + 3.80385i 0.0820168 + 0.142057i
\(718\) −16.3923 + 9.46410i −0.611755 + 0.353197i
\(719\) 17.3205 30.0000i 0.645946 1.11881i −0.338136 0.941097i \(-0.609796\pi\)
0.984082 0.177714i \(-0.0568702\pi\)
\(720\) 0 0
\(721\) 27.4641 + 15.8564i 1.02282 + 0.590523i
\(722\) −9.35641 + 16.2058i −0.348209 + 0.603116i
\(723\) 14.2679 0.530631
\(724\) −5.46410 + 9.46410i −0.203072 + 0.351731i
\(725\) 0 0
\(726\) −9.33975 + 5.39230i −0.346630 + 0.200127i
\(727\) 23.7128i 0.879460i −0.898130 0.439730i \(-0.855074\pi\)
0.898130 0.439730i \(-0.144926\pi\)
\(728\) −1.73205 + 7.00000i −0.0641941 + 0.259437i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −3.85641 6.67949i −0.142634 0.247050i
\(732\) 9.00000 + 5.19615i 0.332650 + 0.192055i
\(733\) 37.0718 1.36928 0.684639 0.728882i \(-0.259960\pi\)
0.684639 + 0.728882i \(0.259960\pi\)
\(734\) 31.5167 + 18.1962i 1.16330 + 0.671632i
\(735\) 0 0
\(736\) 0.267949i 0.00987674i
\(737\) −1.82309 1.05256i −0.0671542 0.0387715i
\(738\) 1.73205 1.00000i 0.0637577 0.0368105i
\(739\) 13.2679 7.66025i 0.488069 0.281787i −0.235704 0.971825i \(-0.575740\pi\)
0.723773 + 0.690038i \(0.242406\pi\)
\(740\) 0 0
\(741\) 1.85641 0.535898i 0.0681968 0.0196867i
\(742\) 25.8564i 0.949219i
\(743\) 16.7679 + 29.0429i 0.615156 + 1.06548i 0.990357 + 0.138539i \(0.0442405\pi\)
−0.375201 + 0.926944i \(0.622426\pi\)
\(744\) −0.866025 1.50000i −0.0317500 0.0549927i
\(745\) 0 0
\(746\) 25.7846i 0.944042i
\(747\) 2.46410 4.26795i 0.0901568 0.156156i
\(748\) 0.928203 1.60770i 0.0339385 0.0587832i
\(749\) 39.7128i 1.45107i
\(750\) 0 0
\(751\) −13.9641 24.1865i −0.509557 0.882579i −0.999939 0.0110712i \(-0.996476\pi\)
0.490381 0.871508i \(-0.336857\pi\)
\(752\) 5.23205 + 9.06218i 0.190793 + 0.330464i
\(753\) 12.2679i 0.447069i
\(754\) −3.23205 + 13.0622i −0.117704 + 0.475696i
\(755\) 0 0
\(756\) −1.73205 + 1.00000i −0.0629941 + 0.0363696i
\(757\) 15.5885 9.00000i 0.566572 0.327111i −0.189207 0.981937i \(-0.560592\pi\)
0.755779 + 0.654827i \(0.227258\pi\)
\(758\) −0.124356 0.0717968i −0.00451680 0.00260778i
\(759\) 0.124356i 0.00451382i
\(760\) 0 0
\(761\) −16.3923 9.46410i −0.594221 0.343073i 0.172544 0.985002i \(-0.444801\pi\)
−0.766765 + 0.641928i \(0.778135\pi\)
\(762\) −8.92820 −0.323435
\(763\) −20.5359 11.8564i −0.743449 0.429231i
\(764\) −7.26795 12.5885i −0.262945 0.455434i
\(765\) 0 0
\(766\) −4.60770 −0.166483
\(767\) −5.37564 1.33013i −0.194103 0.0480281i
\(768\) 1.00000i 0.0360844i
\(769\) 16.9641 9.79423i 0.611741 0.353189i −0.161905 0.986806i \(-0.551764\pi\)
0.773647 + 0.633617i \(0.218431\pi\)
\(770\) 0 0
\(771\) −11.3301 + 19.6244i −0.408045 + 0.706754i
\(772\) −23.3205 −0.839323
\(773\) −13.8564 + 24.0000i −0.498380 + 0.863220i −0.999998 0.00186926i \(-0.999405\pi\)
0.501618 + 0.865089i \(0.332738\pi\)
\(774\) −1.66987 0.964102i −0.0600223 0.0346539i
\(775\) 0 0
\(776\) −3.73205 + 6.46410i −0.133973 + 0.232048i
\(777\) 2.07180 1.19615i 0.0743253 0.0429117i
\(778\) −10.1340 17.5526i −0.363321 0.629290i
\(779\) −1.07180 −0.0384011
\(780\) 0 0
\(781\) −3.89488 −0.139370
\(782\) 0.535898 + 0.928203i 0.0191637 + 0.0331925i
\(783\) −3.23205 + 1.86603i −0.115504 +