Properties

Label 1950.2.y.c.199.1
Level $1950$
Weight $2$
Character 1950.199
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 199.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.c.49.1

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 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 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 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 0.559367 0.828920i \(-0.311044\pi\)
−0.438182 + 0.898886i \(0.644378\pi\)
\(12\) 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 −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0.464102 0.267949i 0.106472 0.0614718i −0.445818 0.895123i \(-0.647087\pi\)
0.552291 + 0.833652i \(0.313754\pi\)
\(20\) 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 0.523998 0.851720i \(-0.324440\pi\)
−0.475612 + 0.879655i \(0.657773\pi\)
\(24\) −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 −0.639115 0.769111i \(-0.720699\pi\)
0.985627 + 0.168934i \(0.0540326\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) −0.500000 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 −0.910991 0.412427i \(-0.864681\pi\)
0.812668 + 0.582728i \(0.198015\pi\)
\(38\) 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 0.358614 0.933486i \(-0.383249\pi\)
−0.629115 + 0.777312i \(0.716583\pi\)
\(42\) 1.73205 + 1.00000i 0.267261 + 0.154303i
\(43\) 1.66987 0.964102i 0.254653 0.147024i −0.367240 0.930126i \(-0.619697\pi\)
0.621893 + 0.783102i \(0.286364\pi\)
\(44\) 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 \(0.347845\pi\)
−0.460012 + 0.887913i \(0.652155\pi\)
\(54\) 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 −0.410911 0.911676i \(-0.634789\pi\)
0.584079 + 0.811697i \(0.301456\pi\)
\(60\) 0 0
\(61\) −5.19615 9.00000i −0.665299 1.15233i −0.979204 0.202878i \(-0.934971\pi\)
0.313905 0.949454i \(-0.398363\pi\)
\(62\) 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 −0.970656 0.240471i \(-0.922698\pi\)
0.693582 + 0.720377i \(0.256031\pi\)
\(68\) 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 −0.864864 0.502006i \(-0.832596\pi\)
0.00231747 + 0.999997i \(0.499262\pi\)
\(72\) 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 0.116615 0.993177i \(-0.462795\pi\)
−0.801809 + 0.597581i \(0.796129\pi\)
\(90\) 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 0.611975 0.790877i \(-0.290375\pi\)
−0.990907 + 0.134547i \(0.957042\pi\)
\(98\) 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 −0.454989 0.890497i \(-0.650357\pi\)
0.998688 0.0512163i \(-0.0163098\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) 15.8564i 1.56238i −0.624295 0.781189i \(-0.714613\pi\)
0.624295 0.781189i \(-0.285387\pi\)
\(104\) −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 −0.971557 0.236805i \(-0.923900\pi\)
−0.690858 0.722991i \(-0.742767\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 11.8564i 1.13564i 0.823154 + 0.567819i \(0.192213\pi\)
−0.823154 + 0.567819i \(0.807787\pi\)
\(110\) 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 −0.881118 0.472896i \(-0.843209\pi\)
−0.0310191 + 0.999519i \(0.509875\pi\)
\(114\) 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 0.116044 0.993244i \(-0.462979\pi\)
−0.802153 + 0.597119i \(0.796312\pi\)
\(128\) −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 0.754784 0.655973i \(-0.227741\pi\)
−0.945481 + 0.325676i \(0.894408\pi\)
\(138\) 0.267949 0.0228093
\(139\) 0.464102 + 0.803848i 0.0393646 + 0.0681815i 0.885036 0.465522i \(-0.154133\pi\)
−0.845672 + 0.533703i \(0.820800\pi\)
\(140\) 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 −0.998588 0.0531208i \(-0.983083\pi\)
−0.453290 + 0.891363i \(0.649750\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i −0.906196 0.422857i \(-0.861027\pi\)
0.906196 0.422857i \(-0.138973\pi\)
\(152\) 0.464102 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 \(-0.936061\pi\)
0.979893 0.199522i \(-0.0639388\pi\)
\(158\) −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 −0.823833 0.566833i \(-0.808169\pi\)
−0.0789748 0.996877i \(-0.525165\pi\)
\(164\) 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 0.256445 + 0.966559i \(0.417449\pi\)
−0.965287 + 0.261191i \(0.915885\pi\)
\(168\) 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 −0.400492 0.916300i \(-0.631161\pi\)
0.593293 + 0.804987i \(0.297828\pi\)
\(174\) 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 0.383614 + 0.923494i \(0.374679\pi\)
−0.991576 + 0.129527i \(0.958654\pi\)
\(180\) 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 −0.999545 0.0301582i \(-0.990399\pi\)
0.473655 0.880711i \(-0.342934\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 11.6603 20.1962i 0.839323 1.45375i −0.0511377 0.998692i \(-0.516285\pi\)
0.890461 0.455059i \(-0.150382\pi\)
\(194\) 7.46410 0.535891
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −8.19615 + 14.1962i −0.583952 + 1.01143i 0.411054 + 0.911611i \(0.365161\pi\)
−0.995005 + 0.0998228i \(0.968172\pi\)
\(198\) −0.401924 0.232051i −0.0285635 0.0164911i
\(199\) −9.46410 16.3923i −0.670892 1.16202i −0.977651 0.210232i \(-0.932578\pi\)
0.306759 0.951787i \(-0.400755\pi\)
\(200\) 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 0.115091 + 0.993355i \(0.463284\pi\)
−0.917816 + 0.397006i \(0.870049\pi\)
\(212\) 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 0.119491 0.992835i \(-0.461874\pi\)
0.800075 0.599900i \(-0.204793\pi\)
\(224\) 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 0.783894 0.620895i \(-0.213231\pi\)
−0.929658 + 0.368425i \(0.879897\pi\)
\(228\) 0.267949 + 0.464102i 0.0177454 + 0.0307359i
\(229\) 19.8564i 1.31215i 0.754696 + 0.656074i \(0.227784\pi\)
−0.754696 + 0.656074i \(0.772216\pi\)
\(230\) 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 \(0.202327\pi\)
−0.804699 + 0.593683i \(0.797673\pi\)
\(234\) 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 \(0.0453717\pi\)
−0.989858 + 0.142057i \(0.954628\pi\)
\(240\) 0 0
\(241\) −12.3564 + 7.13397i −0.795946 + 0.459540i −0.842052 0.539397i \(-0.818652\pi\)
0.0461056 + 0.998937i \(0.485319\pi\)
\(242\) 10.7846 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 0.604895 0.796305i \(-0.293215\pi\)
−0.992068 + 0.125702i \(0.959882\pi\)
\(252\) 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 0.965797 0.259301i \(-0.0834921\pi\)
0.258337 + 0.966055i \(0.416825\pi\)
\(258\) 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 −0.0692812 0.997597i \(-0.522071\pi\)
−0.898585 + 0.438799i \(0.855404\pi\)
\(264\) −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 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) 7.96410 + 4.59808i 0.483785 + 0.279313i 0.721992 0.691901i \(-0.243227\pi\)
−0.238208 + 0.971214i \(0.576560\pi\)
\(272\) 4.00000i 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 −0.218938 0.975739i \(-0.570259\pi\)
0.735546 + 0.677475i \(0.236926\pi\)
\(278\) −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 \(-0.953040\pi\)
0.989137 0.146996i \(-0.0469604\pi\)
\(282\) −9.06218 + 5.23205i −0.539645 + 0.311564i
\(283\) 3.40192 + 1.96410i 0.202223 + 0.116754i 0.597692 0.801726i \(-0.296085\pi\)
−0.395469 + 0.918479i \(0.629418\pi\)
\(284\) 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 0.799141 0.601144i \(-0.205288\pi\)
−0.920176 + 0.391504i \(0.871955\pi\)
\(294\) 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 \(0.290609\pi\)
−0.611393 + 0.791327i \(0.709391\pi\)
\(314\) 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 −0.955962 0.293490i \(-0.905183\pi\)
−0.223812 + 0.974632i \(0.571850\pi\)
\(332\) −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 \(-0.757765\pi\)
0.724145 0.689648i \(-0.242235\pi\)
\(338\) −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 0.120908 0.992664i \(-0.461420\pi\)
0.920126 + 0.391623i \(0.128086\pi\)
\(348\) 3.23205 + 1.86603i 0.173256 + 0.100029i
\(349\) 12.5885 + 7.26795i 0.673845 + 0.389044i 0.797532 0.603277i \(-0.206139\pi\)
−0.123687 + 0.992321i \(0.539472\pi\)
\(350\) 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 −0.891410 0.453197i \(-0.850283\pi\)
0.838186 + 0.545385i \(0.183617\pi\)
\(354\) 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 \(0.166482\pi\)
−0.866316 + 0.499496i \(0.833518\pi\)
\(360\) 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 −0.978959 0.204056i \(-0.934588\pi\)
−0.666197 0.745776i \(-0.732079\pi\)
\(368\) −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 −0.950393 0.311052i \(-0.899319\pi\)
−0.205817 + 0.978590i \(0.565985\pi\)
\(374\) 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 0.503190 0.864176i \(-0.332159\pi\)
−0.496803 + 0.867863i \(0.665493\pi\)
\(380\) 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 0.918864 0.394574i \(-0.129108\pi\)
−0.801143 + 0.598473i \(0.795774\pi\)
\(384\) 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 0.977095 0.212806i \(-0.0682602\pi\)
−0.672843 + 0.739786i \(0.734927\pi\)
\(398\) 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 0.992620 0.121265i \(-0.0386950\pi\)
0.391292 + 0.920267i \(0.372028\pi\)
\(402\) 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 −0.411905 0.911227i \(-0.635136\pi\)
0.583193 + 0.812333i \(0.301803\pi\)
\(410\) 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 −0.845722 0.533624i \(-0.820830\pi\)
0.884993 + 0.465605i \(0.154163\pi\)
\(420\) 0 0
\(421\) 16.3923i 0.798912i 0.916752 + 0.399456i \(0.130801\pi\)
−0.916752 + 0.399456i \(0.869199\pi\)
\(422\) −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 0.332858 0.942977i \(-0.391987\pi\)
−0.650213 + 0.759752i \(0.725320\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 13.2679 7.66025i 0.637617 0.368128i −0.146079 0.989273i \(-0.546665\pi\)
0.783696 + 0.621145i \(0.213332\pi\)
\(434\) 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 −0.724123 0.689670i \(-0.757755\pi\)
0.959334 + 0.282274i \(0.0910888\pi\)
\(440\) 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 \(0.0332738\pi\)
−0.994541 + 0.104342i \(0.966726\pi\)
\(444\) −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 0.636982 0.770879i \(-0.280183\pi\)
0.986092 0.166203i \(-0.0531506\pi\)
\(450\) 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 −0.218407 0.975858i \(-0.570086\pi\)
0.954321 0.298783i \(-0.0965807\pi\)
\(458\) −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 −0.363938 0.931423i \(-0.618568\pi\)
0.624667 + 0.780891i \(0.285235\pi\)
\(462\) 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 \(0.0884542\pi\)
−0.961637 + 0.274325i \(0.911546\pi\)
\(468\) −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 0.470753 0.882265i \(-0.343982\pi\)
−0.528687 + 0.848817i \(0.677316\pi\)
\(480\) 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 0.842660 + 0.538446i \(0.180988\pi\)
0.0449775 + 0.998988i \(0.485678\pi\)
\(488\) −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 −0.992559 0.121761i \(-0.961146\pi\)
0.601728 + 0.798701i \(0.294479\pi\)
\(492\) 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 \(0.0974433\pi\)
−0.953508 + 0.301368i \(0.902557\pi\)
\(500\) 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 −0.961414 0.275107i \(-0.911287\pi\)
−0.242457 + 0.970162i \(0.577953\pi\)
\(504\) −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 0.0792726 0.996853i \(-0.474740\pi\)
−0.823664 + 0.567079i \(0.808074\pi\)
\(510\) 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 −0.184496 0.982833i \(-0.559065\pi\)
−0.943407 + 0.331638i \(0.892399\pi\)
\(524\) 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 \(-0.909334\pi\)
0.959708 0.281000i \(-0.0906662\pi\)
\(542\) −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 \(0.0621270\pi\)
−0.981013 + 0.193941i \(0.937873\pi\)
\(548\) −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 0.121315 + 0.992614i \(0.461289\pi\)
−0.920286 + 0.391245i \(0.872044\pi\)
\(558\) 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 0.437637 0.899152i \(-0.355815\pi\)
0.997507 + 0.0705706i \(0.0224820\pi\)
\(564\) 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 −0.916385 0.400299i \(-0.868906\pi\)
0.804861 + 0.593463i \(0.202240\pi\)
\(570\) 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 −0.611433 0.791296i \(-0.709407\pi\)
0.990999 + 0.133869i \(0.0427400\pi\)
\(588\) 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 −0.998004 0.0631568i \(-0.979883\pi\)
0.553697 + 0.832718i \(0.313216\pi\)
\(602\) −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 0.517924 0.855427i \(-0.326705\pi\)
0.999783 0.0208216i \(-0.00662820\pi\)
\(608\) −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 −0.856300 0.516478i \(-0.827243\pi\)
0.875434 + 0.483338i \(0.160576\pi\)
\(614\) −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 0.978951 0.204093i \(-0.0654246\pi\)
−0.666226 + 0.745750i \(0.732091\pi\)
\(618\) −7.92820 13.7321i −0.318919 0.552384i
\(619\) 24.2487i 0.974638i 0.873224 + 0.487319i \(0.162025\pi\)
−0.873224 + 0.487319i \(0.837975\pi\)
\(620\) 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 −0.859265 0.511531i \(-0.829078\pi\)
0.0133668 + 0.999911i \(0.495745\pi\)
\(632\) 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 −0.998265 0.0588882i \(-0.981244\pi\)
0.448134 0.893967i \(-0.352089\pi\)
\(642\) −19.8564 −0.783670
\(643\) −13.7321 23.7846i −0.541539 0.937973i −0.998816 0.0486490i \(-0.984508\pi\)
0.457277 0.889324i \(-0.348825\pi\)
\(644\) 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 0.0910212 0.995849i \(-0.470987\pi\)
−0.816920 + 0.576751i \(0.804320\pi\)
\(648\) −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 −0.499597 0.866258i \(-0.666519\pi\)
−1.00000 0.000464739i \(0.999852\pi\)
\(654\) 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 0.827389 0.561629i \(-0.189825\pi\)
−0.900079 + 0.435726i \(0.856492\pi\)
\(660\) 0 0
\(661\) 37.5167 + 21.6603i 1.45923 + 0.842486i 0.998973 0.0453002i \(-0.0144244\pi\)
0.460256 + 0.887786i \(0.347758\pi\)
\(662\) 24.7846i 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 0.927703 0.373319i \(-0.121780\pi\)
0.140548 + 0.990074i \(0.455114\pi\)
\(674\) 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 \(0.0716046\pi\)
−0.974805 + 0.223060i \(0.928395\pi\)
\(678\) −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 0.873433 0.486944i \(-0.161888\pi\)
−0.858422 + 0.512944i \(0.828555\pi\)
\(684\) 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 −0.207867 0.978157i \(-0.566652\pi\)
−0.951042 + 0.309061i \(0.899985\pi\)
\(692\) −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 −0.640219 0.768193i \(-0.721156\pi\)
0.345165 + 0.938542i \(0.387823\pi\)
\(710\) 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 0.984082 + 0.177714i \(0.0568702\pi\)
−0.338136 + 0.941097i \(0.609796\pi\)
\(720\) 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 \(0.144926\pi\)
−0.898130 + 0.439730i \(0.855074\pi\)
\(728\) −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 0.723773 0.690038i \(-0.242406\pi\)
−0.235704 + 0.971825i \(0.575740\pi\)
\(740\) 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 −0.375201 0.926944i \(-0.622426\pi\)
0.990357 0.138539i \(-0.0442405\pi\)
\(744\) −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 0.490381 + 0.871508i \(0.336857\pi\)
−0.999939 + 0.0110712i \(0.996476\pi\)
\(752\) 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 0.755779 0.654827i \(-0.227258\pi\)
−0.189207 + 0.981937i \(0.560592\pi\)
\(758\) −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 −0.766765 0.641928i \(-0.778135\pi\)
0.172544 + 0.985002i \(0.444801\pi\)
\(762\) −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 0.773647 0.633617i \(-0.218431\pi\)
−0.161905 + 0.986806i \(0.551764\pi\)
\(770\) 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 0.501618 0.865089i \(-0.332738\pi\)
−0.999998 + 0.00186926i \(0.999405\pi\)
\(774\) −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 0.0666863i