Properties

Label 722.2.e.f.99.1
Level $722$
Weight $2$
Character 722.99
Analytic conductor $5.765$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $6$

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Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 99.1
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 722.99
Dual form 722.2.e.f.423.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.87939 - 0.684040i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.87939 - 0.684040i) q^{9} +(3.00000 + 5.19615i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.868241 - 4.92404i) q^{13} +(0.766044 - 0.642788i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-2.81908 - 1.02606i) q^{17} +2.00000 q^{18} +(0.939693 + 0.342020i) q^{21} +(1.04189 + 5.90885i) q^{22} +(2.29813 + 1.92836i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.868241 + 4.92404i) q^{25} +(2.50000 - 4.33013i) q^{26} +(2.50000 + 4.33013i) q^{27} +(0.939693 - 0.342020i) q^{28} +(-8.45723 + 3.07818i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-4.59627 + 3.85673i) q^{33} +(-2.29813 - 1.92836i) q^{34} +(1.87939 + 0.684040i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(0.766044 + 0.642788i) q^{42} +(6.12836 - 5.14230i) q^{43} +(-1.04189 + 5.90885i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-0.939693 + 0.342020i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(0.520945 - 2.95442i) q^{51} +(3.83022 - 3.21394i) q^{52} +(-2.29813 - 1.92836i) q^{53} +(0.868241 + 4.92404i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(-8.45723 - 3.07818i) q^{59} +(-7.66044 - 6.42788i) q^{61} +(3.06418 - 2.57115i) q^{62} +(0.347296 - 1.96962i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.63816 + 2.05212i) q^{66} +(-4.69846 + 1.71010i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(-4.59627 + 3.85673i) q^{71} +(1.53209 + 1.28558i) q^{72} +(-1.21554 - 6.89365i) q^{73} +(1.87939 + 0.684040i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(4.69846 + 1.71010i) q^{78} +(-1.73648 - 9.84808i) q^{79} +(0.766044 - 0.642788i) q^{81} +(3.00000 - 5.19615i) q^{83} +(0.500000 + 0.866025i) q^{84} +(7.51754 - 2.73616i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-2.08378 + 11.8177i) q^{89} +(-3.83022 - 3.21394i) q^{91} +(0.520945 + 2.95442i) q^{92} +(3.75877 + 1.36808i) q^{93} -1.00000 q^{96} +(9.39693 + 3.42020i) q^{97} +(1.04189 + 5.90885i) q^{98} +(9.19253 + 7.71345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{7} + 3q^{8} + O(q^{10}) \) \( 6q + 3q^{7} + 3q^{8} + 18q^{11} - 3q^{12} + 12q^{18} + 15q^{26} + 15q^{27} + 12q^{31} + 12q^{37} + 30q^{39} + 9q^{46} + 18q^{49} - 15q^{50} + 6q^{56} - 54q^{58} - 3q^{64} - 9q^{68} - 9q^{69} - 30q^{75} + 36q^{77} + 18q^{83} + 3q^{84} - 27q^{87} - 18q^{88} - 6q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 + 0.342020i 0.664463 + 0.241845i
\(3\) 0.173648 + 0.984808i 0.100256 + 0.568579i 0.993010 + 0.118034i \(0.0376592\pi\)
−0.892754 + 0.450545i \(0.851230\pi\)
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(6\) −0.173648 + 0.984808i −0.0708916 + 0.402046i
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) 1.87939 0.684040i 0.626462 0.228013i
\(10\) 0 0
\(11\) 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 0.868241 4.92404i 0.240807 1.36568i −0.589226 0.807968i \(-0.700567\pi\)
0.830033 0.557714i \(-0.188322\pi\)
\(14\) 0.766044 0.642788i 0.204734 0.171792i
\(15\) 0 0
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −2.81908 1.02606i −0.683727 0.248856i −0.0232799 0.999729i \(-0.507411\pi\)
−0.660447 + 0.750873i \(0.729633\pi\)
\(18\) 2.00000 0.471405
\(19\) 0 0
\(20\) 0 0
\(21\) 0.939693 + 0.342020i 0.205058 + 0.0746349i
\(22\) 1.04189 + 5.90885i 0.222131 + 1.25977i
\(23\) 2.29813 + 1.92836i 0.479194 + 0.402091i 0.850135 0.526565i \(-0.176520\pi\)
−0.370941 + 0.928656i \(0.620965\pi\)
\(24\) −0.766044 + 0.642788i −0.156368 + 0.131208i
\(25\) −0.868241 + 4.92404i −0.173648 + 0.984808i
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 2.50000 + 4.33013i 0.481125 + 0.833333i
\(28\) 0.939693 0.342020i 0.177585 0.0646357i
\(29\) −8.45723 + 3.07818i −1.57047 + 0.571604i −0.973104 0.230366i \(-0.926008\pi\)
−0.597365 + 0.801970i \(0.703786\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −0.173648 + 0.984808i −0.0306970 + 0.174091i
\(33\) −4.59627 + 3.85673i −0.800107 + 0.671370i
\(34\) −2.29813 1.92836i −0.394127 0.330711i
\(35\) 0 0
\(36\) 1.87939 + 0.684040i 0.313231 + 0.114007i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(42\) 0.766044 + 0.642788i 0.118203 + 0.0991843i
\(43\) 6.12836 5.14230i 0.934565 0.784194i −0.0420659 0.999115i \(-0.513394\pi\)
0.976631 + 0.214921i \(0.0689495\pi\)
\(44\) −1.04189 + 5.90885i −0.157071 + 0.890792i
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(48\) −0.939693 + 0.342020i −0.135633 + 0.0493664i
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) −2.50000 + 4.33013i −0.353553 + 0.612372i
\(51\) 0.520945 2.95442i 0.0729468 0.413702i
\(52\) 3.83022 3.21394i 0.531156 0.445693i
\(53\) −2.29813 1.92836i −0.315673 0.264881i 0.471159 0.882048i \(-0.343836\pi\)
−0.786832 + 0.617167i \(0.788280\pi\)
\(54\) 0.868241 + 4.92404i 0.118153 + 0.670077i
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) −8.45723 3.07818i −1.10104 0.400745i −0.273339 0.961918i \(-0.588128\pi\)
−0.827699 + 0.561173i \(0.810350\pi\)
\(60\) 0 0
\(61\) −7.66044 6.42788i −0.980819 0.823005i 0.00339342 0.999994i \(-0.498920\pi\)
−0.984213 + 0.176989i \(0.943364\pi\)
\(62\) 3.06418 2.57115i 0.389151 0.326536i
\(63\) 0.347296 1.96962i 0.0437552 0.248148i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −5.63816 + 2.05212i −0.694009 + 0.252599i
\(67\) −4.69846 + 1.71010i −0.574009 + 0.208922i −0.612682 0.790330i \(-0.709909\pi\)
0.0386729 + 0.999252i \(0.487687\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) −1.50000 + 2.59808i −0.180579 + 0.312772i
\(70\) 0 0
\(71\) −4.59627 + 3.85673i −0.545476 + 0.457709i −0.873406 0.486993i \(-0.838094\pi\)
0.327929 + 0.944702i \(0.393649\pi\)
\(72\) 1.53209 + 1.28558i 0.180558 + 0.151506i
\(73\) −1.21554 6.89365i −0.142268 0.806841i −0.969520 0.245011i \(-0.921208\pi\)
0.827252 0.561830i \(-0.189903\pi\)
\(74\) 1.87939 + 0.684040i 0.218474 + 0.0795181i
\(75\) −5.00000 −0.577350
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 4.69846 + 1.71010i 0.531996 + 0.193631i
\(79\) −1.73648 9.84808i −0.195369 1.10800i −0.911892 0.410431i \(-0.865378\pi\)
0.716522 0.697564i \(-0.245733\pi\)
\(80\) 0 0
\(81\) 0.766044 0.642788i 0.0851160 0.0714208i
\(82\) 0 0
\(83\) 3.00000 5.19615i 0.329293 0.570352i −0.653079 0.757290i \(-0.726523\pi\)
0.982372 + 0.186938i \(0.0598564\pi\)
\(84\) 0.500000 + 0.866025i 0.0545545 + 0.0944911i
\(85\) 0 0
\(86\) 7.51754 2.73616i 0.810637 0.295048i
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) −2.08378 + 11.8177i −0.220880 + 1.25267i 0.649526 + 0.760339i \(0.274967\pi\)
−0.870406 + 0.492334i \(0.836144\pi\)
\(90\) 0 0
\(91\) −3.83022 3.21394i −0.401516 0.336912i
\(92\) 0.520945 + 2.95442i 0.0543122 + 0.308020i
\(93\) 3.75877 + 1.36808i 0.389766 + 0.141863i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 9.39693 + 3.42020i 0.954113 + 0.347269i 0.771724 0.635958i \(-0.219395\pi\)
0.182389 + 0.983226i \(0.441617\pi\)
\(98\) 1.04189 + 5.90885i 0.105247 + 0.596884i
\(99\) 9.19253 + 7.71345i 0.923884 + 0.775231i
\(100\) −3.83022 + 3.21394i −0.383022 + 0.321394i
\(101\) 3.12567 17.7265i 0.311016 1.76386i −0.282726 0.959201i \(-0.591239\pi\)
0.593741 0.804656i \(-0.297650\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) 4.69846 1.71010i 0.460722 0.167689i
\(105\) 0 0
\(106\) −1.50000 2.59808i −0.145693 0.252347i
\(107\) 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i \(-0.690071\pi\)
0.997298 + 0.0734594i \(0.0234039\pi\)
\(108\) −0.868241 + 4.92404i −0.0835465 + 0.473816i
\(109\) 8.42649 7.07066i 0.807111 0.677247i −0.142805 0.989751i \(-0.545612\pi\)
0.949916 + 0.312504i \(0.101168\pi\)
\(110\) 0 0
\(111\) 0.347296 + 1.96962i 0.0329639 + 0.186948i
\(112\) 0.939693 + 0.342020i 0.0887926 + 0.0323179i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −8.45723 3.07818i −0.785234 0.285802i
\(117\) −1.73648 9.84808i −0.160538 0.910455i
\(118\) −6.89440 5.78509i −0.634681 0.532561i
\(119\) −2.29813 + 1.92836i −0.210670 + 0.176773i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) −5.00000 8.66025i −0.452679 0.784063i
\(123\) 0 0
\(124\) 3.75877 1.36808i 0.337548 0.122857i
\(125\) 0 0
\(126\) 1.00000 1.73205i 0.0890871 0.154303i
\(127\) 0.347296 1.96962i 0.0308176 0.174775i −0.965514 0.260351i \(-0.916162\pi\)
0.996332 + 0.0855756i \(0.0272729\pi\)
\(128\) −0.766044 + 0.642788i −0.0677094 + 0.0568149i
\(129\) 6.12836 + 5.14230i 0.539572 + 0.452754i
\(130\) 0 0
\(131\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) −0.520945 2.95442i −0.0446706 0.253340i
\(137\) −6.89440 5.78509i −0.589028 0.494253i 0.298870 0.954294i \(-0.403390\pi\)
−0.887898 + 0.460040i \(0.847835\pi\)
\(138\) −2.29813 + 1.92836i −0.195630 + 0.164153i
\(139\) −0.694593 + 3.93923i −0.0589146 + 0.334121i −0.999992 0.00407080i \(-0.998704\pi\)
0.941077 + 0.338192i \(0.109815\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.63816 + 2.05212i −0.473144 + 0.172210i
\(143\) 28.1908 10.2606i 2.35743 0.858035i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 0 0
\(146\) 1.21554 6.89365i 0.100599 0.570523i
\(147\) −4.59627 + 3.85673i −0.379094 + 0.318097i
\(148\) 1.53209 + 1.28558i 0.125937 + 0.105674i
\(149\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(150\) −4.69846 1.71010i −0.383628 0.139629i
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 5.63816 + 2.05212i 0.454336 + 0.165365i
\(155\) 0 0
\(156\) 3.83022 + 3.21394i 0.306663 + 0.257321i
\(157\) −16.8530 + 14.1413i −1.34501 + 1.12860i −0.364707 + 0.931122i \(0.618831\pi\)
−0.980307 + 0.197478i \(0.936725\pi\)
\(158\) 1.73648 9.84808i 0.138147 0.783471i
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) 0 0
\(161\) 2.81908 1.02606i 0.222174 0.0808649i
\(162\) 0.939693 0.342020i 0.0738292 0.0268716i
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 4.59627 3.85673i 0.356739 0.299340i
\(167\) 9.19253 + 7.71345i 0.711340 + 0.596885i 0.924975 0.380029i \(-0.124086\pi\)
−0.213635 + 0.976914i \(0.568530\pi\)
\(168\) 0.173648 + 0.984808i 0.0133972 + 0.0759796i
\(169\) −11.2763 4.10424i −0.867409 0.315711i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) −5.63816 2.05212i −0.428661 0.156020i 0.118674 0.992933i \(-0.462136\pi\)
−0.547335 + 0.836913i \(0.684358\pi\)
\(174\) −1.56283 8.86327i −0.118478 0.671923i
\(175\) 3.83022 + 3.21394i 0.289538 + 0.242951i
\(176\) −4.59627 + 3.85673i −0.346457 + 0.290712i
\(177\) 1.56283 8.86327i 0.117470 0.666204i
\(178\) −6.00000 + 10.3923i −0.449719 + 0.778936i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) −1.87939 + 0.684040i −0.139694 + 0.0508443i −0.410921 0.911671i \(-0.634793\pi\)
0.271227 + 0.962515i \(0.412571\pi\)
\(182\) −2.50000 4.33013i −0.185312 0.320970i
\(183\) 5.00000 8.66025i 0.369611 0.640184i
\(184\) −0.520945 + 2.95442i −0.0384045 + 0.217803i
\(185\) 0 0
\(186\) 3.06418 + 2.57115i 0.224676 + 0.188526i
\(187\) −3.12567 17.7265i −0.228571 1.29629i
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) −0.939693 0.342020i −0.0678165 0.0246832i
\(193\) 2.43107 + 13.7873i 0.174993 + 0.992432i 0.938152 + 0.346222i \(0.112536\pi\)
−0.763160 + 0.646210i \(0.776353\pi\)
\(194\) 7.66044 + 6.42788i 0.549988 + 0.461495i
\(195\) 0 0
\(196\) −1.04189 + 5.90885i −0.0744206 + 0.422060i
\(197\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(198\) 6.00000 + 10.3923i 0.426401 + 0.738549i
\(199\) −10.3366 + 3.76222i −0.732743 + 0.266697i −0.681326 0.731980i \(-0.738596\pi\)
−0.0514178 + 0.998677i \(0.516374\pi\)
\(200\) −4.69846 + 1.71010i −0.332232 + 0.120922i
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) −1.56283 + 8.86327i −0.109689 + 0.622080i
\(204\) 2.29813 1.92836i 0.160902 0.135012i
\(205\) 0 0
\(206\) −2.43107 13.7873i −0.169381 0.960607i
\(207\) 5.63816 + 2.05212i 0.391879 + 0.142632i
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) −4.69846 1.71010i −0.323456 0.117728i 0.175189 0.984535i \(-0.443946\pi\)
−0.498644 + 0.866807i \(0.666169\pi\)
\(212\) −0.520945 2.95442i −0.0357786 0.202911i
\(213\) −4.59627 3.85673i −0.314931 0.264258i
\(214\) 6.89440 5.78509i 0.471291 0.395461i
\(215\) 0 0
\(216\) −2.50000 + 4.33013i −0.170103 + 0.294628i
\(217\) −2.00000 3.46410i −0.135769 0.235159i
\(218\) 10.3366 3.76222i 0.700084 0.254810i
\(219\) 6.57785 2.39414i 0.444490 0.161781i
\(220\) 0 0
\(221\) −7.50000 + 12.9904i −0.504505 + 0.873828i
\(222\) −0.347296 + 1.96962i −0.0233090 + 0.132192i
\(223\) 19.9172 16.7125i 1.33375 1.11915i 0.350566 0.936538i \(-0.385989\pi\)
0.983185 0.182612i \(-0.0584553\pi\)
\(224\) 0.766044 + 0.642788i 0.0511835 + 0.0429481i
\(225\) 1.73648 + 9.84808i 0.115765 + 0.656539i
\(226\) 5.63816 + 2.05212i 0.375045 + 0.136505i
\(227\) −15.0000 −0.995585 −0.497792 0.867296i \(-0.665856\pi\)
−0.497792 + 0.867296i \(0.665856\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 1.04189 + 5.90885i 0.0685513 + 0.388774i
\(232\) −6.89440 5.78509i −0.452640 0.379810i
\(233\) −4.59627 + 3.85673i −0.301111 + 0.252662i −0.780807 0.624773i \(-0.785192\pi\)
0.479695 + 0.877435i \(0.340747\pi\)
\(234\) 1.73648 9.84808i 0.113517 0.643789i
\(235\) 0 0
\(236\) −4.50000 7.79423i −0.292925 0.507361i
\(237\) 9.39693 3.42020i 0.610396 0.222166i
\(238\) −2.81908 + 1.02606i −0.182734 + 0.0665096i
\(239\) 10.5000 + 18.1865i 0.679189 + 1.17639i 0.975226 + 0.221213i \(0.0710015\pi\)
−0.296037 + 0.955176i \(0.595665\pi\)
\(240\) 0 0
\(241\) 1.38919 7.87846i 0.0894853 0.507496i −0.906813 0.421533i \(-0.861492\pi\)
0.996298 0.0859632i \(-0.0273968\pi\)
\(242\) −19.1511 + 16.0697i −1.23108 + 1.03300i
\(243\) 12.2567 + 10.2846i 0.786268 + 0.659758i
\(244\) −1.73648 9.84808i −0.111167 0.630459i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) 5.63816 + 2.05212i 0.357304 + 0.130048i
\(250\) 0 0
\(251\) 4.59627 + 3.85673i 0.290114 + 0.243434i 0.776215 0.630468i \(-0.217137\pi\)
−0.486101 + 0.873902i \(0.661581\pi\)
\(252\) 1.53209 1.28558i 0.0965125 0.0809836i
\(253\) −3.12567 + 17.7265i −0.196509 + 1.11446i
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −11.2763 + 4.10424i −0.703397 + 0.256016i −0.668861 0.743388i \(-0.733218\pi\)
−0.0345364 + 0.999403i \(0.510995\pi\)
\(258\) 4.00000 + 6.92820i 0.249029 + 0.431331i
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) 0 0
\(261\) −13.7888 + 11.5702i −0.853505 + 0.716176i
\(262\) 0 0
\(263\) 4.16756 + 23.6354i 0.256983 + 1.45742i 0.790932 + 0.611904i \(0.209596\pi\)
−0.533950 + 0.845516i \(0.679293\pi\)
\(264\) −5.63816 2.05212i −0.347004 0.126299i
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) −4.69846 1.71010i −0.287004 0.104461i
\(269\) −1.04189 5.90885i −0.0635251 0.360269i −0.999956 0.00941580i \(-0.997003\pi\)
0.936431 0.350853i \(-0.114108\pi\)
\(270\) 0 0
\(271\) 8.42649 7.07066i 0.511873 0.429512i −0.349915 0.936782i \(-0.613789\pi\)
0.861788 + 0.507269i \(0.169345\pi\)
\(272\) 0.520945 2.95442i 0.0315869 0.179138i
\(273\) 2.50000 4.33013i 0.151307 0.262071i
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) −28.1908 + 10.2606i −1.69997 + 0.618738i
\(276\) −2.81908 + 1.02606i −0.169689 + 0.0617616i
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 1.38919 7.87846i 0.0831684 0.471671i
\(280\) 0 0
\(281\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(282\) 0 0
\(283\) 20.6732 + 7.52444i 1.22890 + 0.447282i 0.873219 0.487327i \(-0.162028\pi\)
0.355677 + 0.934609i \(0.384250\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 0 0
\(288\) 0.347296 + 1.96962i 0.0204646 + 0.116061i
\(289\) −6.12836 5.14230i −0.360492 0.302488i
\(290\) 0 0
\(291\) −1.73648 + 9.84808i −0.101794 + 0.577305i
\(292\) 3.50000 6.06218i 0.204822 0.354762i
\(293\) 10.5000 + 18.1865i 0.613417 + 1.06247i 0.990660 + 0.136355i \(0.0435386\pi\)
−0.377244 + 0.926114i \(0.623128\pi\)
\(294\) −5.63816 + 2.05212i −0.328824 + 0.119682i
\(295\) 0 0
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) −15.0000 + 25.9808i −0.870388 + 1.50756i
\(298\) 0 0
\(299\) 11.4907 9.64181i 0.664522 0.557601i
\(300\) −3.83022 3.21394i −0.221138 0.185557i
\(301\) −1.38919 7.87846i −0.0800713 0.454107i
\(302\) −9.39693 3.42020i −0.540732 0.196810i
\(303\) 18.0000 1.03407
\(304\) 0 0
\(305\) 0 0
\(306\) −5.63816 2.05212i −0.322312 0.117312i
\(307\) 3.47296 + 19.6962i 0.198212 + 1.12412i 0.907769 + 0.419470i \(0.137784\pi\)
−0.709557 + 0.704649i \(0.751105\pi\)
\(308\) 4.59627 + 3.85673i 0.261897 + 0.219757i
\(309\) 10.7246 8.99903i 0.610102 0.511937i
\(310\) 0 0
\(311\) 10.5000 18.1865i 0.595400 1.03126i −0.398090 0.917346i \(-0.630327\pi\)
0.993490 0.113917i \(-0.0363399\pi\)
\(312\) 2.50000 + 4.33013i 0.141535 + 0.245145i
\(313\) 17.8542 6.49838i 1.00918 0.367310i 0.216060 0.976380i \(-0.430679\pi\)
0.793117 + 0.609070i \(0.208457\pi\)
\(314\) −20.6732 + 7.52444i −1.16666 + 0.424629i
\(315\) 0 0
\(316\) 5.00000 8.66025i 0.281272 0.487177i
\(317\) −1.56283 + 8.86327i −0.0877775 + 0.497811i 0.908945 + 0.416916i \(0.136889\pi\)
−0.996723 + 0.0808951i \(0.974222\pi\)
\(318\) 2.29813 1.92836i 0.128873 0.108137i
\(319\) −41.3664 34.7105i −2.31607 1.94342i
\(320\) 0 0
\(321\) 8.45723 + 3.07818i 0.472037 + 0.171807i
\(322\) 3.00000 0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 23.4923 + 8.55050i 1.30312 + 0.474297i
\(326\) −3.47296 19.6962i −0.192350 1.09087i
\(327\) 8.42649 + 7.07066i 0.465986 + 0.391009i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.500000 + 0.866025i 0.0274825 + 0.0476011i 0.879440 0.476011i \(-0.157918\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 5.63816 2.05212i 0.309434 0.112625i
\(333\) 3.75877 1.36808i 0.205979 0.0749704i
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) 0 0
\(336\) −0.173648 + 0.984808i −0.00947328 + 0.0537257i
\(337\) −3.06418 + 2.57115i −0.166916 + 0.140059i −0.722420 0.691455i \(-0.756970\pi\)
0.555503 + 0.831514i \(0.312526\pi\)
\(338\) −9.19253 7.71345i −0.500008 0.419556i
\(339\) 1.04189 + 5.90885i 0.0565876 + 0.320924i
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 7.51754 + 2.73616i 0.405319 + 0.147524i
\(345\) 0 0
\(346\) −4.59627 3.85673i −0.247097 0.207339i
\(347\) 13.7888 11.5702i 0.740222 0.621120i −0.192676 0.981263i \(-0.561717\pi\)
0.932897 + 0.360143i \(0.117272\pi\)
\(348\) 1.56283 8.86327i 0.0837767 0.475121i
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 2.50000 + 4.33013i 0.133631 + 0.231455i
\(351\) 23.4923 8.55050i 1.25393 0.456392i
\(352\) −5.63816 + 2.05212i −0.300515 + 0.109378i
\(353\) 7.50000 + 12.9904i 0.399185 + 0.691408i 0.993626 0.112731i \(-0.0359599\pi\)
−0.594441 + 0.804139i \(0.702627\pi\)
\(354\) 4.50000 7.79423i 0.239172 0.414259i
\(355\) 0 0
\(356\) −9.19253 + 7.71345i −0.487203 + 0.408812i
\(357\) −2.29813 1.92836i −0.121630 0.102060i
\(358\) 0 0
\(359\) −19.7335 7.18242i −1.04150 0.379074i −0.236049 0.971741i \(-0.575853\pi\)
−0.805447 + 0.592667i \(0.798075\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −2.00000 −0.105118
\(363\) −23.4923 8.55050i −1.23303 0.448785i
\(364\) −0.868241 4.92404i −0.0455082 0.258090i
\(365\) 0 0
\(366\) 7.66044 6.42788i 0.400418 0.335990i
\(367\) −4.86215 + 27.5746i −0.253802 + 1.43938i 0.545327 + 0.838224i \(0.316406\pi\)
−0.799129 + 0.601160i \(0.794706\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 0 0
\(370\) 0 0
\(371\) −2.81908 + 1.02606i −0.146359 + 0.0532704i
\(372\) 2.00000 + 3.46410i 0.103695 + 0.179605i
\(373\) −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 3.12567 17.7265i 0.161624 0.916618i
\(375\) 0 0
\(376\) 0 0
\(377\) 7.81417 + 44.3163i 0.402450 + 2.28241i
\(378\) 4.69846 + 1.71010i 0.241663 + 0.0879581i
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 2.81908 + 1.02606i 0.144237 + 0.0524978i
\(383\) 3.12567 + 17.7265i 0.159714 + 0.905784i 0.954348 + 0.298696i \(0.0965515\pi\)
−0.794634 + 0.607088i \(0.792337\pi\)
\(384\) −0.766044 0.642788i −0.0390920 0.0328021i
\(385\) 0 0
\(386\) −2.43107 + 13.7873i −0.123738 + 0.701756i
\(387\) 8.00000 13.8564i 0.406663 0.704361i
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) −16.9145 + 6.15636i −0.857598 + 0.312140i −0.733134 0.680084i \(-0.761943\pi\)
−0.124464 + 0.992224i \(0.539721\pi\)
\(390\) 0 0
\(391\) −4.50000 7.79423i −0.227575 0.394171i
\(392\) −3.00000 + 5.19615i −0.151523 + 0.262445i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 2.08378 + 11.8177i 0.104714 + 0.593861i
\(397\) −18.7939 6.84040i −0.943236 0.343310i −0.175793 0.984427i \(-0.556249\pi\)
−0.767443 + 0.641117i \(0.778471\pi\)
\(398\) −11.0000 −0.551380
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(402\) −0.868241 4.92404i −0.0433039 0.245589i
\(403\) −15.3209 12.8558i −0.763188 0.640391i
\(404\) 13.7888 11.5702i 0.686018 0.575638i
\(405\) 0 0
\(406\) −4.50000 + 7.79423i −0.223331 + 0.386821i
\(407\) 6.00000 + 10.3923i 0.297409 + 0.515127i
\(408\) 2.81908 1.02606i 0.139565 0.0507976i
\(409\) −30.0702 + 10.9446i −1.48687 + 0.541178i −0.952624 0.304149i \(-0.901628\pi\)
−0.534249 + 0.845327i \(0.679406\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) 2.43107 13.7873i 0.119770 0.679252i
\(413\) −6.89440 + 5.78509i −0.339251 + 0.284666i
\(414\) 4.59627 + 3.85673i 0.225894 + 0.189548i
\(415\) 0 0
\(416\) 4.69846 + 1.71010i 0.230361 + 0.0838446i
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 2.95202 + 16.7417i 0.143873 + 0.815942i 0.968265 + 0.249924i \(0.0804056\pi\)
−0.824393 + 0.566018i \(0.808483\pi\)
\(422\) −3.83022 3.21394i −0.186452 0.156452i
\(423\) 0 0
\(424\) 0.520945 2.95442i 0.0252993 0.143479i
\(425\) 7.50000 12.9904i 0.363803 0.630126i
\(426\) −3.00000 5.19615i −0.145350 0.251754i
\(427\) −9.39693 + 3.42020i −0.454749 + 0.165515i
\(428\) 8.45723 3.07818i 0.408796 0.148790i
\(429\) 15.0000 + 25.9808i 0.724207 + 1.25436i
\(430\) 0 0
\(431\) 1.04189 5.90885i 0.0501860 0.284619i −0.949378 0.314135i \(-0.898285\pi\)
0.999564 + 0.0295160i \(0.00939661\pi\)
\(432\) −3.83022 + 3.21394i −0.184282 + 0.154631i
\(433\) 1.53209 + 1.28558i 0.0736275 + 0.0617808i 0.678859 0.734269i \(-0.262475\pi\)
−0.605231 + 0.796050i \(0.706919\pi\)
\(434\) −0.694593 3.93923i −0.0333415 0.189089i
\(435\) 0 0
\(436\) 11.0000 0.526804
\(437\) 0 0
\(438\) 7.00000 0.334473
\(439\) 26.3114 + 9.57656i 1.25577 + 0.457064i 0.882349 0.470596i \(-0.155961\pi\)
0.373425 + 0.927660i \(0.378183\pi\)
\(440\) 0 0
\(441\) 9.19253 + 7.71345i 0.437740 + 0.367307i
\(442\) −11.4907 + 9.64181i −0.546555 + 0.458614i
\(443\) −3.12567 + 17.7265i −0.148505 + 0.842213i 0.815981 + 0.578079i \(0.196197\pi\)
−0.964486 + 0.264134i \(0.914914\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 0 0
\(446\) 24.4320 8.89252i 1.15689 0.421073i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) 9.00000 15.5885i 0.424736 0.735665i −0.571660 0.820491i \(-0.693700\pi\)
0.996396 + 0.0848262i \(0.0270335\pi\)
\(450\) −1.73648 + 9.84808i −0.0818585 + 0.464243i
\(451\) 0 0
\(452\) 4.59627 + 3.85673i 0.216190 + 0.181405i
\(453\) −1.73648 9.84808i −0.0815870 0.462703i
\(454\) −14.0954 5.13030i −0.661529 0.240777i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −20.6732 7.52444i −0.965997 0.351594i
\(459\) −2.60472 14.7721i −0.121578 0.689503i
\(460\) 0 0
\(461\) −9.19253 + 7.71345i −0.428139 + 0.359251i −0.831249 0.555900i \(-0.812374\pi\)
0.403110 + 0.915152i \(0.367929\pi\)
\(462\) −1.04189 + 5.90885i −0.0484731 + 0.274904i
\(463\) 2.00000 3.46410i 0.0929479 0.160990i −0.815802 0.578331i \(-0.803704\pi\)
0.908750 + 0.417340i \(0.137038\pi\)
\(464\) −4.50000 7.79423i −0.208907 0.361838i
\(465\) 0 0
\(466\) −5.63816 + 2.05212i −0.261183 + 0.0950627i
\(467\) −9.00000 15.5885i −0.416470 0.721348i 0.579111 0.815249i \(-0.303400\pi\)
−0.995582 + 0.0939008i \(0.970066\pi\)
\(468\) 5.00000 8.66025i 0.231125 0.400320i
\(469\) −0.868241 + 4.92404i −0.0400916 + 0.227371i
\(470\) 0 0
\(471\) −16.8530 14.1413i −0.776544 0.651598i
\(472\) −1.56283 8.86327i −0.0719352 0.407965i
\(473\) 45.1052 + 16.4170i 2.07394 + 0.754853i
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) −3.00000 −0.137505
\(477\) −5.63816 2.05212i −0.258153 0.0939602i
\(478\) 3.64661 + 20.6810i 0.166792 + 0.945925i
\(479\) 27.5776 + 23.1404i 1.26005 + 1.05731i 0.995676 + 0.0928902i \(0.0296105\pi\)
0.264376 + 0.964420i \(0.414834\pi\)
\(480\) 0 0
\(481\) 1.73648 9.84808i 0.0791768 0.449034i
\(482\) 4.00000 6.92820i 0.182195 0.315571i
\(483\) 1.50000 + 2.59808i 0.0682524 + 0.118217i
\(484\) −23.4923 + 8.55050i −1.06783 + 0.388659i
\(485\) 0 0
\(486\) 8.00000 + 13.8564i 0.362887 + 0.628539i
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) 1.73648 9.84808i 0.0786068 0.445802i
\(489\) 15.3209 12.8558i 0.692835 0.581357i
\(490\) 0 0
\(491\) −6.25133 35.4531i −0.282119 1.59998i −0.715399 0.698716i \(-0.753755\pi\)
0.433280 0.901259i \(-0.357356\pi\)
\(492\) 0 0
\(493\) 27.0000 1.21602
\(494\) 0 0
\(495\) 0 0
\(496\) 3.75877 + 1.36808i 0.168774 + 0.0614286i
\(497\) 1.04189 + 5.90885i 0.0467351 + 0.265048i
\(498\) 4.59627 + 3.85673i 0.205964 + 0.172824i
\(499\) −3.06418 + 2.57115i −0.137171 + 0.115101i −0.708792 0.705418i \(-0.750759\pi\)
0.571620 + 0.820518i \(0.306315\pi\)
\(500\) 0 0
\(501\) −6.00000 + 10.3923i −0.268060 + 0.464294i
\(502\) 3.00000 + 5.19615i 0.133897 + 0.231916i
\(503\) 19.7335 7.18242i 0.879875 0.320248i 0.137716 0.990472i \(-0.456024\pi\)
0.742159 + 0.670223i \(0.233802\pi\)
\(504\) 1.87939 0.684040i 0.0837145 0.0304696i
\(505\) 0 0
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) 2.08378 11.8177i 0.0925438 0.524842i
\(508\) 1.53209 1.28558i 0.0679755 0.0570382i
\(509\) 22.9813 + 19.2836i 1.01863 + 0.854732i 0.989455 0.144843i \(-0.0462676\pi\)
0.0291750 + 0.999574i \(0.490712\pi\)
\(510\) 0 0
\(511\) −6.57785 2.39414i −0.290987 0.105911i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) 1.38919 + 7.87846i 0.0611555 + 0.346830i
\(517\) 0 0
\(518\) 1.53209 1.28558i 0.0673161 0.0564849i
\(519\) 1.04189 5.90885i 0.0457339 0.259370i
\(520\) 0 0
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) −16.9145 + 6.15636i −0.740326 + 0.269457i
\(523\) −10.3366 + 3.76222i −0.451989 + 0.164510i −0.557976 0.829857i \(-0.688422\pi\)
0.105987 + 0.994367i \(0.466200\pi\)
\(524\) 0 0
\(525\) −2.50000 + 4.33013i −0.109109 + 0.188982i
\(526\) −4.16756 + 23.6354i −0.181714 + 1.03055i
\(527\) −9.19253 + 7.71345i −0.400433 + 0.336003i
\(528\) −4.59627 3.85673i −0.200027 0.167842i
\(529\) −2.43107 13.7873i −0.105699 0.599448i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 0 0
\(534\) −11.2763 4.10424i −0.487974 0.177608i
\(535\) 0 0
\(536\) −3.83022 3.21394i −0.165440 0.138821i
\(537\) 0 0
\(538\) 1.04189 5.90885i 0.0449190 0.254748i
\(539\) −18.0000 + 31.1769i −0.775315 + 1.34288i
\(540\) 0 0
\(541\) −1.87939 + 0.684040i −0.0808011 + 0.0294092i −0.382104 0.924119i \(-0.624801\pi\)
0.301303 + 0.953528i \(0.402578\pi\)
\(542\) 10.3366 3.76222i 0.443996 0.161601i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 0 0
\(546\) 3.83022 3.21394i 0.163918 0.137544i
\(547\) 33.7060 + 28.2827i 1.44116 + 1.20928i 0.938726 + 0.344665i \(0.112008\pi\)
0.502437 + 0.864614i \(0.332437\pi\)
\(548\) −1.56283 8.86327i −0.0667609 0.378620i
\(549\) −18.7939 6.84040i −0.802102 0.291941i
\(550\) −30.0000 −1.27920
\(551\) 0 0
\(552\) −3.00000 −0.127688
\(553\) −9.39693 3.42020i −0.399598 0.145442i
\(554\) −1.38919 7.87846i −0.0590208 0.334724i
\(555\) 0 0
\(556\) −3.06418 + 2.57115i −0.129950 + 0.109041i
\(557\) 4.16756 23.6354i 0.176585 1.00146i −0.759713 0.650258i \(-0.774661\pi\)
0.936298 0.351205i \(-0.114228\pi\)
\(558\) 4.00000 6.92820i 0.169334 0.293294i
\(559\) −20.0000 34.6410i −0.845910 1.46516i
\(560\) 0 0
\(561\) 16.9145 6.15636i 0.714129 0.259922i
\(562\) 0 0
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 16.8530 + 14.1413i 0.708383 + 0.594404i
\(567\) −0.173648 0.984808i −0.00729254 0.0413580i
\(568\) −5.63816 2.05212i −0.236572 0.0861051i
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 28.1908 + 10.2606i 1.17872 + 0.429017i
\(573\) 0.520945 + 2.95442i 0.0217628 + 0.123423i
\(574\) 0 0
\(575\) −11.4907 + 9.64181i −0.479194 + 0.402091i
\(576\) −0.347296 + 1.96962i −0.0144707 + 0.0820673i
\(577\) −5.50000 + 9.52628i −0.228968 + 0.396584i −0.957503 0.288425i \(-0.906868\pi\)
0.728535 + 0.685009i \(0.240202\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) −13.1557 + 4.78828i −0.546732 + 0.198994i
\(580\) 0 0
\(581\) −3.00000 5.19615i −0.124461 0.215573i
\(582\) −5.00000 + 8.66025i −0.207257 + 0.358979i
\(583\) 3.12567 17.7265i 0.129452 0.734158i
\(584\) 5.36231 4.49951i 0.221894 0.186191i
\(585\) 0 0
\(586\) 3.64661 + 20.6810i 0.150640 + 0.854323i
\(587\) 11.2763 + 4.10424i 0.465423 + 0.169400i 0.564078 0.825722i \(-0.309232\pi\)
−0.0986548 + 0.995122i \(0.531454\pi\)
\(588\) −6.00000 −0.247436
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.347296 + 1.96962i 0.0142738 + 0.0809507i
\(593\) −22.9813 19.2836i −0.943730 0.791884i 0.0345003 0.999405i \(-0.489016\pi\)
−0.978231 + 0.207521i \(0.933460\pi\)
\(594\) −22.9813 + 19.2836i −0.942936 + 0.791217i
\(595\) 0 0
\(596\) 0 0
\(597\) −5.50000 9.52628i −0.225100 0.389885i
\(598\) 14.0954 5.13030i 0.576403 0.209794i
\(599\) 22.5526 8.20848i 0.921475 0.335390i 0.162650 0.986684i \(-0.447996\pi\)
0.758825 + 0.651294i \(0.225774\pi\)
\(600\) −2.50000 4.33013i −0.102062 0.176777i
\(601\) 14.0000 24.2487i 0.571072 0.989126i −0.425384 0.905013i \(-0.639861\pi\)
0.996456 0.0841128i \(-0.0268056\pi\)
\(602\) 1.38919 7.87846i 0.0566190 0.321102i
\(603\) −7.66044 + 6.42788i −0.311957 + 0.261763i
\(604\) −7.66044 6.42788i −0.311699 0.261547i
\(605\) 0 0
\(606\) 16.9145 + 6.15636i 0.687103 + 0.250085i
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) −9.00000 −0.364698
\(610\) 0 0
\(611\) 0 0
\(612\) −4.59627 3.85673i −0.185793 0.155899i
\(613\) 1.53209 1.28558i 0.0618805 0.0519239i −0.611323 0.791381i \(-0.709362\pi\)
0.673203 + 0.739457i \(0.264918\pi\)
\(614\) −3.47296 + 19.6962i −0.140157 + 0.794872i
\(615\) 0 0
\(616\) 3.00000 + 5.19615i 0.120873 + 0.209359i
\(617\) 5.63816 2.05212i 0.226984 0.0826153i −0.226025 0.974122i \(-0.572573\pi\)
0.453008 + 0.891506i \(0.350351\pi\)
\(618\) 13.1557 4.78828i 0.529200 0.192613i
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) 0 0
\(621\) −2.60472 + 14.7721i −0.104524 + 0.592785i
\(622\) 16.0869 13.4985i 0.645027 0.541242i
\(623\) 9.19253 + 7.71345i 0.368291 + 0.309033i
\(624\) 0.868241 + 4.92404i 0.0347575 + 0.197119i
\(625\) −23.4923 8.55050i −0.939693 0.342020i
\(626\) 19.0000 0.759393
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −5.63816 2.05212i −0.224808 0.0818234i
\(630\) 0 0
\(631\) −12.2567 10.2846i −0.487932 0.409424i 0.365352 0.930869i \(-0.380948\pi\)
−0.853284 + 0.521446i \(0.825393\pi\)
\(632\) 7.66044 6.42788i 0.304716 0.255687i
\(633\) 0.868241 4.92404i 0.0345095 0.195713i
\(634\) −4.50000 + 7.79423i −0.178718 + 0.309548i
\(635\) 0 0
\(636\) 2.81908 1.02606i 0.111784 0.0406859i
\(637\) 28.1908 10.2606i 1.11696 0.406540i
\(638\) −27.0000 46.7654i −1.06894 1.85146i
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) 0 0
\(641\) 4.59627 3.85673i 0.181542 0.152332i −0.547488 0.836813i \(-0.684416\pi\)
0.729030 + 0.684482i \(0.239971\pi\)
\(642\) 6.89440 + 5.78509i 0.272100 + 0.228319i
\(643\) −3.82026 21.6658i −0.150656 0.854415i −0.962650 0.270748i \(-0.912729\pi\)
0.811994 0.583666i \(-0.198382\pi\)
\(644\) 2.81908 + 1.02606i 0.111087 + 0.0404324i
\(645\) 0 0
\(646\) 0 0
\(647\) 27.0000 1.06148 0.530740 0.847535i \(-0.321914\pi\)
0.530740 + 0.847535i \(0.321914\pi\)
\(648\) 0.939693 + 0.342020i 0.0369146 + 0.0134358i
\(649\) −9.37700 53.1796i −0.368080 2.08748i
\(650\) 19.1511 + 16.0697i 0.751168 + 0.630305i
\(651\) 3.06418 2.57115i 0.120095 0.100771i
\(652\) 3.47296 19.6962i 0.136012 0.771361i
\(653\) −12.0000 + 20.7846i −0.469596 + 0.813365i −0.999396 0.0347583i \(-0.988934\pi\)
0.529799 + 0.848123i \(0.322267\pi\)
\(654\) 5.50000 + 9.52628i 0.215067 + 0.372507i
\(655\) 0 0
\(656\) 0 0
\(657\) −7.00000 12.1244i −0.273096 0.473016i
\(658\) 0 0
\(659\) −7.81417 + 44.3163i −0.304397 + 1.72632i 0.321934 + 0.946762i \(0.395667\pi\)
−0.626330 + 0.779558i \(0.715444\pi\)
\(660\) 0 0
\(661\) −9.95858 8.35624i −0.387344 0.325020i 0.428234 0.903668i \(-0.359136\pi\)
−0.815577 + 0.578648i \(0.803580\pi\)
\(662\) 0.173648 + 0.984808i 0.00674903 + 0.0382756i
\(663\) −14.0954 5.13030i −0.547420 0.199244i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) −25.3717 9.23454i −0.982396 0.357563i
\(668\) 2.08378 + 11.8177i 0.0806238 + 0.457240i
\(669\) 19.9172 + 16.7125i 0.770042 + 0.646142i
\(670\) 0 0
\(671\) 10.4189 59.0885i 0.402217 2.28108i
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) −22.0000 38.1051i −0.848038 1.46884i −0.882957 0.469454i \(-0.844451\pi\)
0.0349191 0.999390i \(-0.488883\pi\)
\(674\) −3.75877 + 1.36808i −0.144782 + 0.0526965i
\(675\) −23.4923 + 8.55050i −0.904220 + 0.329109i
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i \(-0.614685\pi\)
0.986695 0.162581i \(-0.0519817\pi\)
\(678\) −1.04189 + 5.90885i −0.0400135 + 0.226928i
\(679\) 7.66044 6.42788i 0.293981 0.246679i
\(680\) 0 0
\(681\) −2.60472 14.7721i −0.0998132 0.566069i
\(682\) 22.5526 + 8.20848i 0.863585 + 0.314319i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 12.2160 + 4.44626i 0.466409 + 0.169759i
\(687\) −3.82026 21.6658i −0.145752 0.826601i
\(688\) 6.12836 + 5.14230i 0.233641 + 0.196048i
\(689\) −11.4907 + 9.64181i −0.437760 + 0.367324i
\(690\) 0 0
\(691\) 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i \(-0.772417\pi\)
0.945319 + 0.326146i \(0.105750\pi\)
\(692\) −3.00000 5.19615i −0.114043 0.197528i
\(693\) 11.2763 4.10424i 0.428352 0.155907i
\(694\) 16.9145 6.15636i 0.642064 0.233692i
\(695\) 0 0
\(696\) 4.50000 7.79423i 0.170572 0.295439i
\(697\) 0 0
\(698\) 7.66044 6.42788i 0.289952 0.243299i
\(699\) −4.59627 3.85673i −0.173847 0.145875i
\(700\) 0.868241 + 4.92404i 0.0328164 + 0.186111i
\(701\) −11.2763 4.10424i −0.425900 0.155015i 0.120172 0.992753i \(-0.461655\pi\)
−0.546072 + 0.837738i \(0.683878\pi\)
\(702\) 25.0000 0.943564
\(703\) 0 0
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) 2.60472 + 14.7721i 0.0980300 + 0.555956i
\(707\) −13.7888 11.5702i −0.518581 0.435141i
\(708\) 6.89440 5.78509i 0.259107 0.217417i
\(709\) −1.73648 + 9.84808i −0.0652149 + 0.369852i 0.934682 + 0.355485i \(0.115684\pi\)
−0.999897 + 0.0143670i \(0.995427\pi\)
\(710\) 0 0
\(711\) −10.0000 17.3205i −0.375029 0.649570i
\(712\) −11.2763 + 4.10424i −0.422598 + 0.153813i
\(713\) 11.2763 4.10424i 0.422301 0.153705i
\(714\) −1.50000 2.59808i −0.0561361 0.0972306i
\(715\) 0 0
\(716\) 0 0
\(717\) −16.0869 + 13.4985i −0.600778 + 0.504112i
\(718\) −16.0869 13.4985i −0.600359 0.503761i
\(719\) 6.77228 + 38.4075i 0.252563 + 1.43236i 0.802251 + 0.596988i \(0.203636\pi\)
−0.549687 + 0.835371i \(0.685253\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 8.00000 0.297523
\(724\) −1.87939 0.684040i −0.0698468 0.0254222i
\(725\) −7.81417 44.3163i −0.290211 1.64587i
\(726\) −19.1511 16.0697i −0.710764 0.596402i
\(727\) −28.3436 + 23.7831i −1.05121 + 0.882068i −0.993220 0.116249i \(-0.962913\pi\)
−0.0579875 + 0.998317i \(0.518468\pi\)
\(728\) 0.868241 4.92404i 0.0321791 0.182497i
\(729\) −6.50000 + 11.2583i −0.240741 + 0.416975i
\(730\) 0 0
\(731\) −22.5526 + 8.20848i −0.834139 + 0.303602i
\(732\) 9.39693 3.42020i 0.347320 0.126414i
\(733\) −16.0000 27.7128i −0.590973 1.02360i −0.994102 0.108453i \(-0.965410\pi\)
0.403128 0.915144i \(-0.367923\pi\)
\(734\) −14.0000 + 24.2487i −0.516749 + 0.895036i
\(735\) 0 0
\(736\) −2.29813 + 1.92836i −0.0847103 + 0.0710804i
\(737\) −22.9813 19.2836i −0.846528 0.710322i
\(738\) 0 0
\(739\) 15.0351 + 5.47232i 0.553074 + 0.201303i 0.603412 0.797430i \(-0.293807\pi\)
−0.0503375 + 0.998732i \(0.516030\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.00000 −0.110133
\(743\) 33.8289 + 12.3127i 1.24106 + 0.451710i 0.877373 0.479810i \(-0.159294\pi\)
0.363691 + 0.931520i \(0.381517\pi\)
\(744\) 0.694593 + 3.93923i 0.0254650 + 0.144419i
\(745\) 0 0
\(746\) −17.6190 + 14.7841i −0.645078 + 0.541285i
\(747\) 2.08378 11.8177i 0.0762415 0.432387i
\(748\) 9.00000 15.5885i 0.329073 0.569970i
\(749\) −4.50000 7.79423i −0.164426 0.284795i
\(750\) 0 0
\(751\) 37.5877 13.6808i 1.37159 0.499220i 0.451975 0.892030i \(-0.350719\pi\)
0.919619 + 0.392811i \(0.128497\pi\)
\(752\) 0 0
\(753\) −3.00000 + 5.19615i −0.109326 + 0.189358i
\(754\) −7.81417 + 44.3163i −0.284575 + 1.61391i
\(755\) 0 0
\(756\) 3.83022 + 3.21394i 0.139304 + 0.116890i
\(757\) 0.347296 + 1.96962i 0.0126227 + 0.0715869i 0.990468 0.137740i \(-0.0439838\pi\)
−0.977846 + 0.209327i \(0.932873\pi\)
\(758\) −6.57785 2.39414i −0.238918 0.0869591i
\(759\) −18.0000 −0.653359
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 1.87939 + 0.684040i 0.0680829 + 0.0247802i
\(763\) −1.91013 10.8329i −0.0691513 0.392177i
\(764\) 2.29813 + 1.92836i 0.0831435 + 0.0697657i
\(765\) 0 0
\(766\) −3.12567 + 17.7265i −0.112935 + 0.640486i
\(767\) −22.5000 + 38.9711i −0.812428 + 1.40717i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −4.69846 + 1.71010i −0.169431 + 0.0616678i −0.425343 0.905032i \(-0.639846\pi\)
0.255912 + 0.966700i \(0.417624\pi\)
\(770\) 0 0
\(771\) −6.00000 10.3923i −0.216085 0.374270i
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 8.85606 50.2252i 0.318530 1.80647i −0.233174 0.972435i \(-0.574911\pi\)
0.551704 0.834040i \(-0.313978\pi\)
\(774\) 12.2567 10.2846i 0.440558 0.369672i
\(775\) 15.3209 + 12.8558i 0.550343 + 0.461792i
\(776\) 1.73648 + 9.84808i 0.0623361 + 0.353525i
\(777\) 1.87939 + 0.684040i 0.0674226 + 0.0245398i
\(778\) −18.0000 −0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) −33.8289 12.3127i −1.21049 0.440584i
\(782\) −1.56283 8.86327i −0.0558868 0.316950i
\(783\) −34.4720 28.9254i −1.23193 1.03371i
\(784\) −4.59627 + 3.85673i −0.164152 + 0.137740i