Properties

Label 1470.2.n.g.79.2
Level $1470$
Weight $2$
Character 1470.79
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.g.949.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.86603 + 1.23205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-0.866025 - 0.500000i) q^{12} +2.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.92820 + 4.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(1.00000 + 2.00000i) q^{20} +2.00000i q^{22} +(-0.500000 - 0.866025i) q^{24} +(4.96410 + 0.598076i) q^{25} +(-1.00000 + 1.73205i) q^{26} +1.00000i q^{27} +6.00000 q^{29} +(-2.23205 - 0.133975i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.73205 - 1.00000i) q^{33} -8.00000 q^{34} +1.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.133975 + 2.23205i) q^{40} +6.00000 q^{41} +8.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(1.23205 - 1.86603i) q^{45} +(3.46410 + 2.00000i) q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(4.00000 - 6.92820i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-1.73205 + 1.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.00000 + 4.00000i) q^{55} -2.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-1.86603 - 1.23205i) q^{60} +(-5.00000 + 8.66025i) q^{61} -6.00000i q^{62} -1.00000 q^{64} +(-0.267949 + 4.46410i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(10.3923 - 6.00000i) q^{67} +(-6.92820 - 4.00000i) q^{68} -14.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-8.66025 + 5.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} +(-4.59808 + 1.96410i) q^{75} -2.00000 q^{76} -2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(-1.23205 + 1.86603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} +16.0000i q^{83} +(-16.0000 + 8.00000i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-5.19615 + 3.00000i) q^{87} +(-1.73205 + 1.00000i) q^{88} +(5.00000 - 8.66025i) q^{89} +(2.00000 - 1.00000i) q^{90} +(5.19615 + 3.00000i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-2.46410 + 3.73205i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000i q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} + 4 q^{10} + 4 q^{11} - 8 q^{15} - 2 q^{16} - 4 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} - 4 q^{26} + 24 q^{29} - 2 q^{30} - 12 q^{31} - 32 q^{34} + 4 q^{36} - 4 q^{39} - 4 q^{40} + 24 q^{41} - 4 q^{44} - 2 q^{45} + 16 q^{50} + 16 q^{51} - 2 q^{54} + 8 q^{55} - 16 q^{59} - 4 q^{60} - 20 q^{61} - 4 q^{64} - 8 q^{65} - 4 q^{66} - 56 q^{71} + 16 q^{74} - 8 q^{75} - 8 q^{76} + 8 q^{79} + 2 q^{80} - 2 q^{81} - 64 q^{85} - 16 q^{86} + 20 q^{89} + 8 q^{90} + 8 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.23205 + 0.133975i 0.998203 + 0.0599153i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.86603 + 1.23205i 0.590089 + 0.389609i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) −2.00000 + 1.00000i −0.516398 + 0.258199i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.92820 + 4.00000i −1.68034 + 0.970143i −0.718900 + 0.695113i \(0.755354\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 4.96410 + 0.598076i 0.992820 + 0.119615i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −2.23205 0.133975i −0.407515 0.0244603i
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) −8.00000 −1.37199
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 6.92820 + 4.00000i 1.13899 + 0.657596i 0.946180 0.323640i \(-0.104907\pi\)
0.192809 + 0.981236i \(0.438240\pi\)
\(38\) −1.73205 + 1.00000i −0.280976 + 0.162221i
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) −0.133975 + 2.23205i −0.0211832 + 0.352918i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) 1.23205 1.86603i 0.183663 0.278171i
\(46\) 0 0
\(47\) 3.46410 + 2.00000i 0.505291 + 0.291730i 0.730896 0.682489i \(-0.239102\pi\)
−0.225605 + 0.974219i \(0.572436\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 4.00000 6.92820i 0.560112 0.970143i
\(52\) −1.73205 + 1.00000i −0.240192 + 0.138675i
\(53\) −1.73205 + 1.00000i −0.237915 + 0.137361i −0.614218 0.789136i \(-0.710529\pi\)
0.376303 + 0.926497i \(0.377195\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 2.00000 + 4.00000i 0.269680 + 0.539360i
\(56\) 0 0
\(57\) 2.00000i 0.264906i
\(58\) 5.19615 + 3.00000i 0.682288 + 0.393919i
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) −1.86603 1.23205i −0.240903 0.159057i
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.267949 + 4.46410i −0.0332350 + 0.553704i
\(66\) −1.00000 1.73205i −0.123091 0.213201i
\(67\) 10.3923 6.00000i 1.26962 0.733017i 0.294706 0.955588i \(-0.404778\pi\)
0.974916 + 0.222571i \(0.0714450\pi\)
\(68\) −6.92820 4.00000i −0.840168 0.485071i
\(69\) 0 0
\(70\) 0 0
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −8.66025 + 5.00000i −1.01361 + 0.585206i −0.912245 0.409644i \(-0.865653\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) −4.59808 + 1.96410i −0.530940 + 0.226795i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 2.00000i 0.226455i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −1.23205 + 1.86603i −0.137747 + 0.208628i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.19615 + 3.00000i 0.573819 + 0.331295i
\(83\) 16.0000i 1.75623i 0.478451 + 0.878114i \(0.341198\pi\)
−0.478451 + 0.878114i \(0.658802\pi\)
\(84\) 0 0
\(85\) −16.0000 + 8.00000i −1.73544 + 0.867722i
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) −5.19615 + 3.00000i −0.557086 + 0.321634i
\(88\) −1.73205 + 1.00000i −0.184637 + 0.106600i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) 2.00000 1.00000i 0.210819 0.105409i
\(91\) 0 0
\(92\) 0 0
\(93\) 5.19615 + 3.00000i 0.538816 + 0.311086i
\(94\) 2.00000 + 3.46410i 0.206284 + 0.357295i
\(95\) −2.46410 + 3.73205i −0.252811 + 0.382900i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 1.96410 + 4.59808i 0.196410 + 0.459808i
\(101\) 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) 6.92820 4.00000i 0.685994 0.396059i
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −10.3923 6.00000i −1.00466 0.580042i −0.0950377 0.995474i \(-0.530297\pi\)
−0.909624 + 0.415432i \(0.863630\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i \(-0.259440\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(110\) −0.267949 + 4.46410i −0.0255480 + 0.425635i
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 1.73205 + 1.00000i 0.160128 + 0.0924500i
\(118\) 8.00000i 0.736460i
\(119\) 0 0
\(120\) −1.00000 2.00000i −0.0912871 0.182574i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −8.66025 + 5.00000i −0.784063 + 0.452679i
\(123\) −5.19615 + 3.00000i −0.468521 + 0.270501i
\(124\) 3.00000 5.19615i 0.269408 0.466628i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 12.0000i 1.06483i −0.846484 0.532414i \(-0.821285\pi\)
0.846484 0.532414i \(-0.178715\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) −2.46410 + 3.73205i −0.216116 + 0.327323i
\(131\) 10.0000 17.3205i 0.873704 1.51330i 0.0155672 0.999879i \(-0.495045\pi\)
0.858137 0.513421i \(-0.171622\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) −0.133975 + 2.23205i −0.0115307 + 0.192104i
\(136\) −4.00000 6.92820i −0.342997 0.594089i
\(137\) 12.1244 7.00000i 1.03585 0.598050i 0.117198 0.993109i \(-0.462609\pi\)
0.918656 + 0.395058i \(0.129276\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) −12.1244 7.00000i −1.01745 0.587427i
\(143\) −3.46410 + 2.00000i −0.289683 + 0.167248i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 13.3923 + 0.803848i 1.11217 + 0.0667559i
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) 8.00000i 0.657596i
\(149\) −9.00000 + 15.5885i −0.737309 + 1.27706i 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) −4.96410 0.598076i −0.405317 0.0488327i
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −1.73205 1.00000i −0.140488 0.0811107i
\(153\) 8.00000i 0.646762i
\(154\) 0 0
\(155\) −6.00000 12.0000i −0.481932 0.963863i
\(156\) 1.00000 1.73205i 0.0800641 0.138675i
\(157\) 8.66025 5.00000i 0.691164 0.399043i −0.112884 0.993608i \(-0.536009\pi\)
0.804048 + 0.594565i \(0.202676\pi\)
\(158\) 3.46410 2.00000i 0.275589 0.159111i
\(159\) 1.00000 1.73205i 0.0793052 0.137361i
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) −3.73205 2.46410i −0.290540 0.191830i
\(166\) −8.00000 + 13.8564i −0.620920 + 1.07547i
\(167\) 8.00000i 0.619059i 0.950890 + 0.309529i \(0.100171\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −17.8564 1.07180i −1.36952 0.0822031i
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) −6.92820 + 4.00000i −0.528271 + 0.304997i
\(173\) 13.8564 + 8.00000i 1.05348 + 0.608229i 0.923622 0.383304i \(-0.125214\pi\)
0.129861 + 0.991532i \(0.458547\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) 6.92820 + 4.00000i 0.520756 + 0.300658i
\(178\) 8.66025 5.00000i 0.649113 0.374766i
\(179\) −1.00000 1.73205i −0.0747435 0.129460i 0.826231 0.563331i \(-0.190480\pi\)
−0.900975 + 0.433872i \(0.857147\pi\)
\(180\) 2.23205 + 0.133975i 0.166367 + 0.00998588i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) 14.9282 + 9.85641i 1.09754 + 0.724657i
\(186\) 3.00000 + 5.19615i 0.219971 + 0.381000i
\(187\) −13.8564 8.00000i −1.01328 0.585018i
\(188\) 4.00000i 0.291730i
\(189\) 0 0
\(190\) −4.00000 + 2.00000i −0.290191 + 0.145095i
\(191\) −7.00000 + 12.1244i −0.506502 + 0.877288i 0.493469 + 0.869763i \(0.335728\pi\)
−0.999972 + 0.00752447i \(0.997605\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 5.00000 8.66025i 0.358979 0.621770i
\(195\) −2.00000 4.00000i −0.143223 0.286446i
\(196\) 0 0
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 1.73205 + 1.00000i 0.123091 + 0.0710669i
\(199\) −13.0000 22.5167i −0.921546 1.59616i −0.797025 0.603947i \(-0.793594\pi\)
−0.124521 0.992217i \(-0.539739\pi\)
\(200\) −0.598076 + 4.96410i −0.0422904 + 0.351015i
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 10.0000i 0.703598i
\(203\) 0 0
\(204\) 8.00000 0.560112
\(205\) 13.3923 + 0.803848i 0.935359 + 0.0561432i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.73205 1.00000i −0.120096 0.0693375i
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) −1.73205 1.00000i −0.118958 0.0686803i
\(213\) 12.1244 7.00000i 0.830747 0.479632i
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −1.07180 + 17.8564i −0.0730959 + 1.21780i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 6.00000i 0.406371i
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) −2.46410 + 3.73205i −0.166130 + 0.251615i
\(221\) −8.00000 13.8564i −0.538138 0.932083i
\(222\) −6.92820 4.00000i −0.464991 0.268462i
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 0 0
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) −3.00000 + 5.19615i −0.199557 + 0.345643i
\(227\) 6.92820 4.00000i 0.459841 0.265489i −0.252136 0.967692i \(-0.581133\pi\)
0.711977 + 0.702202i \(0.247800\pi\)
\(228\) 1.73205 1.00000i 0.114708 0.0662266i
\(229\) 13.0000 22.5167i 0.859064 1.48794i −0.0137585 0.999905i \(-0.504380\pi\)
0.872823 0.488037i \(-0.162287\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) −5.19615 3.00000i −0.340411 0.196537i 0.320043 0.947403i \(-0.396303\pi\)
−0.660454 + 0.750867i \(0.729636\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) 7.46410 + 4.92820i 0.486904 + 0.321481i
\(236\) 4.00000 6.92820i 0.260378 0.450988i
\(237\) 4.00000i 0.259828i
\(238\) 0 0
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0.133975 2.23205i 0.00864802 0.144078i
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 6.06218 3.50000i 0.389692 0.224989i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) −3.46410 2.00000i −0.220416 0.127257i
\(248\) 5.19615 3.00000i 0.329956 0.190500i
\(249\) −8.00000 13.8564i −0.506979 0.878114i
\(250\) 8.52628 + 7.23205i 0.539249 + 0.457395i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 6.00000 10.3923i 0.376473 0.652071i
\(255\) 9.85641 14.9282i 0.617232 0.934840i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.3205 10.0000i −1.08042 0.623783i −0.149413 0.988775i \(-0.547738\pi\)
−0.931011 + 0.364992i \(0.881072\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 0 0
\(260\) −4.00000 + 2.00000i −0.248069 + 0.124035i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 17.3205 10.0000i 1.07006 0.617802i
\(263\) −20.7846 + 12.0000i −1.28163 + 0.739952i −0.977147 0.212565i \(-0.931818\pi\)
−0.304487 + 0.952517i \(0.598485\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) −4.00000 + 2.00000i −0.245718 + 0.122859i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 10.3923 + 6.00000i 0.634811 + 0.366508i
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) −1.23205 + 1.86603i −0.0749802 + 0.113563i
\(271\) −1.00000 + 1.73205i −0.0607457 + 0.105215i −0.894799 0.446469i \(-0.852681\pi\)
0.834053 + 0.551684i \(0.186015\pi\)
\(272\) 8.00000i 0.485071i
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 3.92820 + 9.19615i 0.236880 + 0.554549i
\(276\) 0 0
\(277\) 6.92820 4.00000i 0.416275 0.240337i −0.277207 0.960810i \(-0.589409\pi\)
0.693482 + 0.720473i \(0.256075\pi\)
\(278\) 1.73205 + 1.00000i 0.103882 + 0.0599760i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) −3.46410 2.00000i −0.206284 0.119098i
\(283\) 3.46410 2.00000i 0.205919 0.118888i −0.393494 0.919327i \(-0.628734\pi\)
0.599414 + 0.800439i \(0.295400\pi\)
\(284\) −7.00000 12.1244i −0.415374 0.719448i
\(285\) 0.267949 4.46410i 0.0158719 0.264431i
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 23.5000 40.7032i 1.38235 2.39431i
\(290\) 11.1962 + 7.39230i 0.657461 + 0.434091i
\(291\) 5.00000 + 8.66025i 0.293105 + 0.507673i
\(292\) −8.66025 5.00000i −0.506803 0.292603i
\(293\) 16.0000i 0.934730i −0.884064 0.467365i \(-0.845203\pi\)
0.884064 0.467365i \(-0.154797\pi\)
\(294\) 0 0
\(295\) −8.00000 16.0000i −0.465778 0.931556i
\(296\) −4.00000 + 6.92820i −0.232495 + 0.402694i
\(297\) −1.73205 + 1.00000i −0.100504 + 0.0580259i
\(298\) −15.5885 + 9.00000i −0.903015 + 0.521356i
\(299\) 0 0
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) −8.66025 5.00000i −0.497519 0.287242i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) −12.3205 + 18.6603i −0.705470 + 1.06848i
\(306\) −4.00000 + 6.92820i −0.228665 + 0.396059i
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.803848 13.3923i 0.0456555 0.760632i
\(311\) 4.00000 + 6.92820i 0.226819 + 0.392862i 0.956864 0.290537i \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) 1.73205 1.00000i 0.0980581 0.0566139i
\(313\) −8.66025 5.00000i −0.489506 0.282617i 0.234863 0.972028i \(-0.424536\pi\)
−0.724370 + 0.689412i \(0.757869\pi\)
\(314\) 10.0000 0.564333
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) −1.73205 1.00000i −0.0972817 0.0561656i 0.450570 0.892741i \(-0.351221\pi\)
−0.547852 + 0.836576i \(0.684554\pi\)
\(318\) 1.73205 1.00000i 0.0971286 0.0560772i
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) −2.23205 0.133975i −0.124775 0.00748941i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 16.0000i 0.890264i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −1.19615 + 9.92820i −0.0663506 + 0.550718i
\(326\) 0 0
\(327\) 5.19615 + 3.00000i 0.287348 + 0.165900i
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) −2.00000 4.00000i −0.110096 0.220193i
\(331\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) −13.8564 + 8.00000i −0.760469 + 0.439057i
\(333\) 6.92820 4.00000i 0.379663 0.219199i
\(334\) −4.00000 + 6.92820i −0.218870 + 0.379094i
\(335\) 24.0000 12.0000i 1.31126 0.655630i
\(336\) 0 0
\(337\) 32.0000i 1.74315i −0.490261 0.871576i \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 7.79423 + 4.50000i 0.423950 + 0.244768i
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) −14.9282 9.85641i −0.809595 0.534539i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 2.00000i 0.108148i
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 8.00000 + 13.8564i 0.430083 + 0.744925i
\(347\) −3.46410 + 2.00000i −0.185963 + 0.107366i −0.590091 0.807337i \(-0.700908\pi\)
0.404128 + 0.914702i \(0.367575\pi\)
\(348\) −5.19615 3.00000i −0.278543 0.160817i
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) −1.73205 1.00000i −0.0923186 0.0533002i
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 4.00000 + 6.92820i 0.212598 + 0.368230i
\(355\) −31.2487 1.87564i −1.65851 0.0995489i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 2.00000i 0.105703i
\(359\) 7.00000 12.1244i 0.369446 0.639899i −0.620033 0.784576i \(-0.712881\pi\)
0.989479 + 0.144677i \(0.0462142\pi\)
\(360\) 1.86603 + 1.23205i 0.0983482 + 0.0649348i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 19.0526 + 11.0000i 1.00138 + 0.578147i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) −20.0000 + 10.0000i −1.04685 + 0.523424i
\(366\) 5.00000 8.66025i 0.261354 0.452679i
\(367\) 27.7128 16.0000i 1.44660 0.835193i 0.448320 0.893873i \(-0.352022\pi\)
0.998277 + 0.0586798i \(0.0186891\pi\)
\(368\) 0 0
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 8.00000 + 16.0000i 0.415900 + 0.831800i
\(371\) 0 0
\(372\) 6.00000i 0.311086i
\(373\) −31.1769 18.0000i −1.61428 0.932005i −0.988363 0.152115i \(-0.951392\pi\)
−0.625917 0.779890i \(-0.715275\pi\)
\(374\) −8.00000 13.8564i −0.413670 0.716498i
\(375\) −10.5263 + 3.76795i −0.543575 + 0.194576i
\(376\) −2.00000 + 3.46410i −0.103142 + 0.178647i
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −4.46410 0.267949i −0.229004 0.0137455i
\(381\) 6.00000 + 10.3923i 0.307389 + 0.532414i
\(382\) −12.1244 + 7.00000i −0.620336 + 0.358151i
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 0 0
\(387\) 6.92820 + 4.00000i 0.352180 + 0.203331i
\(388\) 8.66025 5.00000i 0.439658 0.253837i
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 0.267949 4.46410i 0.0135681 0.226049i
\(391\) 0 0
\(392\) 0 0
\(393\) 20.0000i 1.00887i
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 4.92820 7.46410i 0.247965 0.375560i
\(396\) 1.00000 + 1.73205i 0.0502519 + 0.0870388i
\(397\) 1.73205 + 1.00000i 0.0869291 + 0.0501886i 0.542834 0.839840i \(-0.317351\pi\)
−0.455905 + 0.890028i \(0.650684\pi\)
\(398\) 26.0000i 1.30326i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) −10.3923 + 6.00000i −0.518321 + 0.299253i
\(403\) 10.3923 6.00000i 0.517678 0.298881i
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) −1.00000 2.00000i −0.0496904 0.0993808i
\(406\) 0 0
\(407\) 16.0000i 0.793091i
\(408\) 6.92820 + 4.00000i 0.342997 + 0.198030i
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 11.1962 + 7.39230i 0.552939 + 0.365080i
\(411\) −7.00000 + 12.1244i −0.345285 + 0.598050i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2.14359 + 35.7128i −0.105225 + 1.75307i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) −1.73205 + 1.00000i −0.0848189 + 0.0489702i
\(418\) −3.46410 2.00000i −0.169435 0.0978232i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −6.92820 4.00000i −0.337260 0.194717i
\(423\) 3.46410 2.00000i 0.168430 0.0972433i
\(424\) −1.00000 1.73205i −0.0485643 0.0841158i
\(425\) −36.7846 + 15.7128i −1.78432 + 0.762183i
\(426\) 14.0000 0.678302
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 2.00000 3.46410i 0.0965609 0.167248i
\(430\) −9.85641 + 14.9282i −0.475318 + 0.719902i
\(431\) 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 0 0
\(435\) −12.0000 + 6.00000i −0.575356 + 0.287678i
\(436\) 3.00000 5.19615i 0.143674 0.248851i
\(437\) 0 0
\(438\) 8.66025 5.00000i 0.413803 0.238909i
\(439\) 3.00000 5.19615i 0.143182 0.247999i −0.785511 0.618848i \(-0.787600\pi\)
0.928693 + 0.370849i \(0.120933\pi\)
\(440\) −4.00000 + 2.00000i −0.190693 + 0.0953463i
\(441\) 0 0
\(442\) 16.0000i 0.761042i
\(443\) −31.1769 18.0000i −1.48126 0.855206i −0.481486 0.876454i \(-0.659903\pi\)
−0.999774 + 0.0212481i \(0.993236\pi\)
\(444\) −4.00000 6.92820i −0.189832 0.328798i
\(445\) 12.3205 18.6603i 0.584048 0.884581i
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 18.0000i 0.851371i
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 4.59808 1.96410i 0.216755 0.0925886i
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) −5.19615 + 3.00000i −0.244406 + 0.141108i
\(453\) 6.92820 + 4.00000i 0.325515 + 0.187936i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) 2.00000 0.0936586
\(457\) −24.2487 14.0000i −1.13431 0.654892i −0.189292 0.981921i \(-0.560619\pi\)
−0.945015 + 0.327028i \(0.893953\pi\)
\(458\) 22.5167 13.0000i 1.05213 0.607450i
\(459\) −4.00000 6.92820i −0.186704 0.323381i
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 12.0000i 0.557687i −0.960337 0.278844i \(-0.910049\pi\)
0.960337 0.278844i \(-0.0899511\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 11.1962 + 7.39230i 0.519209 + 0.342810i
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 13.8564 + 8.00000i 0.641198 + 0.370196i 0.785076 0.619400i \(-0.212624\pi\)
−0.143878 + 0.989595i \(0.545957\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 0 0
\(470\) 4.00000 + 8.00000i 0.184506 + 0.369012i
\(471\) −5.00000 + 8.66025i −0.230388 + 0.399043i
\(472\) 6.92820 4.00000i 0.318896 0.184115i
\(473\) −13.8564 + 8.00000i −0.637118 + 0.367840i
\(474\) −2.00000 + 3.46410i −0.0918630 + 0.159111i
\(475\) −6.00000 + 8.00000i −0.275299 + 0.367065i
\(476\) 0 0
\(477\) 2.00000i 0.0915737i
\(478\) 19.0526 + 11.0000i 0.871444 + 0.503128i
\(479\) 4.00000 + 6.92820i 0.182765 + 0.316558i 0.942821 0.333300i \(-0.108162\pi\)
−0.760056 + 0.649857i \(0.774829\pi\)
\(480\) 1.23205 1.86603i 0.0562352 0.0851720i
\(481\) −8.00000 + 13.8564i −0.364769 + 0.631798i
\(482\) 10.0000i 0.455488i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) 1.33975 22.3205i 0.0608347 1.01352i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −31.1769 + 18.0000i −1.41276 + 0.815658i −0.995648 0.0931967i \(-0.970291\pi\)
−0.417113 + 0.908855i \(0.636958\pi\)
\(488\) −8.66025 5.00000i −0.392031 0.226339i
\(489\) 0 0
\(490\) 0 0
\(491\) −42.0000 −1.89543 −0.947717 0.319113i \(-0.896615\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) −5.19615 3.00000i −0.234261 0.135250i
\(493\) −41.5692 + 24.0000i −1.87218 + 1.08091i
\(494\) −2.00000 3.46410i −0.0899843 0.155857i
\(495\) 4.46410 + 0.267949i 0.200646 + 0.0120434i
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) 16.0000i 0.716977i
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) 3.76795 + 10.5263i 0.168508 + 0.470750i
\(501\) −4.00000 6.92820i −0.178707 0.309529i
\(502\) 0 0
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) 0 0
\(505\) 10.0000 + 20.0000i 0.444994 + 0.889988i
\(506\) 0 0
\(507\) −7.79423 + 4.50000i −0.346154 + 0.199852i
\(508\) 10.3923 6.00000i 0.461084 0.266207i
\(509\) 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i \(-0.819220\pi\)
0.887336 + 0.461123i \(0.152553\pi\)
\(510\) 16.0000 8.00000i 0.708492 0.354246i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −1.73205 1.00000i −0.0764719 0.0441511i
\(514\) −10.0000 17.3205i −0.441081 0.763975i
\(515\) 0 0
\(516\) 4.00000 6.92820i 0.176090 0.304997i
\(517\) 8.00000i 0.351840i
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) −4.46410 0.267949i −0.195764 0.0117503i
\(521\) 3.00000 + 5.19615i 0.131432 + 0.227648i 0.924229 0.381839i \(-0.124709\pi\)
−0.792797 + 0.609486i \(0.791376\pi\)
\(522\) 5.19615 3.00000i 0.227429 0.131306i
\(523\) 10.3923 + 6.00000i 0.454424 + 0.262362i 0.709697 0.704507i \(-0.248832\pi\)
−0.255273 + 0.966869i \(0.582165\pi\)
\(524\) 20.0000 0.873704
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 41.5692 + 24.0000i 1.81078 + 1.04546i
\(528\) 1.73205 1.00000i 0.0753778 0.0435194i
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) −4.46410 0.267949i −0.193908 0.0116390i
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) −5.00000 + 8.66025i −0.216371 + 0.374766i
\(535\) −22.3923 14.7846i −0.968104 0.639194i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 1.73205 + 1.00000i 0.0747435 + 0.0431532i
\(538\) 14.0000i 0.603583i
\(539\) 0 0
\(540\) −2.00000 + 1.00000i −0.0860663 + 0.0430331i
\(541\) 1.00000 1.73205i 0.0429934 0.0744667i −0.843728 0.536771i \(-0.819644\pi\)
0.886721 + 0.462304i \(0.152977\pi\)
\(542\) −1.73205 + 1.00000i −0.0743980 + 0.0429537i
\(543\) −19.0526 + 11.0000i −0.817624 + 0.472055i
\(544\) 4.00000 6.92820i 0.171499 0.297044i
\(545\) −6.00000 12.0000i −0.257012 0.514024i
\(546\) 0 0
\(547\) 20.0000i 0.855138i −0.903983 0.427569i \(-0.859370\pi\)
0.903983 0.427569i \(-0.140630\pi\)
\(548\) 12.1244 + 7.00000i 0.517927 + 0.299025i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) −1.19615 + 9.92820i −0.0510041 + 0.423340i
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 8.00000 0.339887
\(555\) −17.8564 1.07180i −0.757962 0.0454952i
\(556\) 1.00000 + 1.73205i 0.0424094 + 0.0734553i
\(557\) −5.19615 + 3.00000i −0.220168 + 0.127114i −0.606028 0.795443i \(-0.707238\pi\)
0.385860 + 0.922557i \(0.373905\pi\)
\(558\) −5.19615 3.00000i −0.219971 0.127000i
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 16.0000 0.675521
\(562\) 19.0526 + 11.0000i 0.803684 + 0.464007i
\(563\) 10.3923 6.00000i 0.437983 0.252870i −0.264758 0.964315i \(-0.585292\pi\)
0.702742 + 0.711445i \(0.251959\pi\)
\(564\) −2.00000 3.46410i −0.0842152 0.145865i
\(565\) −0.803848 + 13.3923i −0.0338181 + 0.563418i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 14.0000i 0.587427i
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 2.46410 3.73205i 0.103210 0.156318i
\(571\) 22.0000 + 38.1051i 0.920671 + 1.59465i 0.798379 + 0.602155i \(0.205691\pi\)
0.122292 + 0.992494i \(0.460975\pi\)
\(572\) −3.46410 2.00000i −0.144841 0.0836242i
\(573\) 14.0000i 0.584858i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −15.5885 + 9.00000i −0.648956 + 0.374675i −0.788056 0.615603i \(-0.788912\pi\)
0.139100 + 0.990278i \(0.455579\pi\)
\(578\) 40.7032 23.5000i 1.69303 0.977471i
\(579\) 0 0
\(580\) 6.00000 + 12.0000i 0.249136 + 0.498273i
\(581\) 0 0
\(582\) 10.0000i 0.414513i
\(583\) −3.46410 2.00000i −0.143468 0.0828315i
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) 3.73205 + 2.46410i 0.154301 + 0.101878i
\(586\) 8.00000 13.8564i 0.330477 0.572403i
\(587\) 4.00000i 0.165098i −0.996587 0.0825488i \(-0.973694\pi\)
0.996587 0.0825488i \(-0.0263060\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 1.07180 17.8564i 0.0441252 0.735137i
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) −6.92820 + 4.00000i −0.284747 + 0.164399i
\(593\) 27.7128 + 16.0000i 1.13803 + 0.657041i 0.945942 0.324337i \(-0.105141\pi\)
0.192087 + 0.981378i \(0.438474\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 22.5167 + 13.0000i 0.921546 + 0.532055i
\(598\) 0 0
\(599\) 7.00000 + 12.1244i 0.286012 + 0.495388i 0.972854 0.231419i \(-0.0743369\pi\)
−0.686842 + 0.726807i \(0.741004\pi\)
\(600\) −1.96410 4.59808i −0.0801841 0.187716i
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 8.62436 13.0622i 0.350630 0.531053i
\(606\) −5.00000 8.66025i −0.203111 0.351799i
\(607\) −13.8564 8.00000i −0.562414 0.324710i 0.191700 0.981454i \(-0.438600\pi\)
−0.754114 + 0.656744i \(0.771933\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) −20.0000 + 10.0000i −0.809776 + 0.404888i
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) −6.92820 + 4.00000i −0.280056 + 0.161690i
\(613\) 27.7128 16.0000i 1.11931 0.646234i 0.178085 0.984015i \(-0.443010\pi\)
0.941225 + 0.337781i \(0.109676\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) −12.0000 + 6.00000i −0.483887 + 0.241943i
\(616\) 0 0
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 0 0
\(619\) −9.00000 15.5885i −0.361741 0.626553i 0.626507 0.779416i \(-0.284484\pi\)
−0.988247 + 0.152863i \(0.951151\pi\)
\(620\) 7.39230 11.1962i 0.296882 0.449648i
\(621\) 0 0
\(622\) 8.00000i 0.320771i
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) 3.46410 2.00000i 0.138343 0.0798723i
\(628\) 8.66025 + 5.00000i 0.345582 + 0.199522i
\(629\) −64.0000 −2.55185
\(630\) 0 0
\(631\) 12.0000 0.477712 0.238856 0.971055i \(-0.423228\pi\)
0.238856 + 0.971055i \(0.423228\pi\)
\(632\) 3.46410 + 2.00000i 0.137795 + 0.0795557i
\(633\) 6.92820 4.00000i 0.275371 0.158986i
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) 1.60770 26.7846i 0.0637994 1.06291i
\(636\) 2.00000 0.0793052
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) −7.00000 + 12.1244i −0.276916 + 0.479632i
\(640\) −1.86603 1.23205i −0.0737611 0.0487011i
\(641\) −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 10.3923 + 6.00000i 0.410152 + 0.236801i
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) −8.00000 16.0000i −0.315000 0.629999i
\(646\) 8.00000 13.8564i 0.314756 0.545173i
\(647\) −13.8564 + 8.00000i −0.544752 + 0.314512i −0.747002 0.664821i \(-0.768508\pi\)
0.202251 + 0.979334i \(0.435174\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 8.00000 13.8564i 0.314027 0.543912i
\(650\) −6.00000 + 8.00000i −0.235339 + 0.313786i
\(651\) 0 0
\(652\) 0 0
\(653\) 12.1244 + 7.00000i 0.474463 + 0.273931i 0.718106 0.695934i \(-0.245009\pi\)
−0.243643 + 0.969865i \(0.578343\pi\)
\(654\) 3.00000 + 5.19615i 0.117309 + 0.203186i
\(655\) 24.6410 37.3205i 0.962804 1.45823i
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 10.0000i 0.390137i
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0.267949 4.46410i 0.0104299 0.173765i
\(661\) −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i \(-0.228968\pi\)
−0.946729 + 0.322031i \(0.895634\pi\)
\(662\) 0 0
\(663\) 13.8564 + 8.00000i 0.538138 + 0.310694i
\(664\) −16.0000 −0.620920
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) 0 0
\(668\) −6.92820 + 4.00000i −0.268060 + 0.154765i
\(669\) 8.00000 + 13.8564i 0.309298 + 0.535720i
\(670\) 26.7846 + 1.60770i 1.03478 + 0.0621107i
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) 12.0000i 0.462566i 0.972887 + 0.231283i \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) 16.0000 27.7128i 0.616297 1.06746i
\(675\) −0.598076 + 4.96410i −0.0230200 + 0.191068i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) −8.00000 16.0000i −0.306786 0.613572i
\(681\) −4.00000 + 6.92820i −0.153280 + 0.265489i
\(682\) 10.3923 6.00000i 0.397942 0.229752i
\(683\) 24.2487 14.0000i 0.927851 0.535695i 0.0417198 0.999129i \(-0.486716\pi\)
0.886131 + 0.463434i \(0.153383\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 28.0000 14.0000i 1.06983 0.534913i
\(686\) 0 0
\(687\) 26.0000i 0.991962i
\(688\) −6.92820 4.00000i −0.264135 0.152499i
\(689\) −2.00000 3.46410i −0.0761939 0.131972i
\(690\) 0 0
\(691\) 7.00000 12.1244i 0.266293 0.461232i −0.701609 0.712562i \(-0.747535\pi\)
0.967901 + 0.251330i \(0.0808679\pi\)
\(692\) 16.0000i 0.608229i
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 4.46410 + 0.267949i 0.169333 + 0.0101639i
\(696\) −3.00000 5.19615i −0.113715 0.196960i
\(697\) −41.5692 + 24.0000i −1.57455 + 0.909065i
\(698\) −15.5885 9.00000i −0.590032 0.340655i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −1.73205 1.00000i −0.0653720 0.0377426i
\(703\) −13.8564 + 8.00000i −0.522604 + 0.301726i
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) −8.92820 0.535898i −0.336256 0.0201831i
\(706\) 0 0
\(707\) 0 0
\(708\) 8.00000i 0.300658i
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) −26.1244 17.2487i −0.980430 0.647333i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) 8.66025 + 5.00000i 0.324557 + 0.187383i
\(713\) 0 0
\(714\) 0 0
\(715\) −8.00000 + 4.00000i −0.299183 + 0.149592i
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) −19.0526 + 11.0000i −0.711531 + 0.410803i
\(718\) 12.1244 7.00000i 0.452477 0.261238i
\(719\) −10.0000 + 17.3205i −0.372937 + 0.645946i −0.990016 0.140955i \(-0.954983\pi\)
0.617079 + 0.786901i \(0.288316\pi\)
\(720\) 1.00000 + 2.00000i 0.0372678 + 0.0745356i
\(721\) 0 0
\(722\) 15.0000i 0.558242i
\(723\) −8.66025 5.00000i −0.322078 0.185952i
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) 29.7846 + 3.58846i 1.10617 + 0.133272i
\(726\) −3.50000 + 6.06218i −0.129897 + 0.224989i
\(727\) 16.0000i 0.593407i −0.954970 0.296704i \(-0.904113\pi\)
0.954970 0.296704i \(-0.0958873\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −22.3205 1.33975i −0.826119 0.0495862i
\(731\) −32.0000 55.4256i −1.18356 2.04999i
\(732\) 8.66025 5.00000i 0.320092 0.184805i
\(733\) 25.9808 + 15.0000i 0.959621 + 0.554038i 0.896056 0.443940i \(-0.146420\pi\)
0.0635649 + 0.997978i \(0.479753\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 0 0
\(737\) 20.7846 + 12.0000i 0.765611 + 0.442026i
\(738\) 5.19615 3.00000i 0.191273 0.110432i
\(739\) 10.0000 + 17.3205i 0.367856 + 0.637145i 0.989230 0.146369i \(-0.0467586\pi\)
−0.621374 + 0.783514i \(0.713425\pi\)
\(740\) −1.07180 + 17.8564i −0.0394000 + 0.656415i
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) −3.00000 + 5.19615i −0.109985 + 0.190500i
\(745\) −22.1769 + 33.5885i −0.812499 + 1.23059i
\(746\) −18.0000 31.1769i −0.659027 1.14147i
\(747\) 13.8564 + 8.00000i 0.506979 + 0.292705i
\(748\) 16.0000i 0.585018i
\(749\) 0 0
\(750\) −11.0000 2.00000i −0.401663 0.0730297i
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) −3.46410 + 2.00000i −0.126323 + 0.0729325i
\(753\) 0 0
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) −8.00000 16.0000i −0.291150 0.582300i
\(756\) 0 0
\(757\) 4.00000i 0.145382i 0.997354 + 0.0726912i \(0.0231588\pi\)
−0.997354 + 0.0726912i \(0.976841\pi\)
\(758\) 24.2487 + 14.0000i 0.880753 + 0.508503i
\(759\) 0 0
\(760\) −3.73205 2.46410i −0.135376 0.0893824i
\(761\) −3.00000 + 5.19615i −0.108750 + 0.188360i −0.915264 0.402854i \(-0.868018\pi\)
0.806514 + 0.591215i \(0.201351\pi\)
\(762\) 12.0000i 0.434714i
\(763\) 0 0
\(764\) −14.0000 −0.506502
\(765\) −1.07180 + 17.8564i −0.0387509 + 0.645600i
\(766\) 0 0
\(767\) 13.8564 8.00000i 0.500326 0.288863i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 42.0000 1.51456 0.757279 0.653091i \(-0.226528\pi\)
0.757279 + 0.653091i \(0.226528\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) 0 0
\(773\) −27.7128 + 16.0000i −0.996761 + 0.575480i −0.907288 0.420509i \(-0.861851\pi\)
−0.0894724 + 0.995989i \(0.528518\pi\)
\(774\) 4.00000 + 6.92820i 0.143777 + 0.249029i
\(775\) −11.7846 27.5885i −0.423316 0.991007i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 2.46410 3.73205i 0.0882290 0.133629i
\(781\) −14.0000 24.2487i −0.500959 0.867687i
\(782\) 0 0
\(783\) 6.00000i 0.214423i