Properties

Label 722.2.e.e.423.1
Level 722
Weight 2
Character 722.423
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: \(\Q(\zeta_{18})\)
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 423.1
Root \(-0.173648 + 0.984808i\)
Character \(\chi\) = 722.423
Dual form 722.2.e.e.99.1

$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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 0.892754 + 0.450545i \(0.148770\pi\)
−0.993010 + 0.118034i \(0.962341\pi\)
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(6\) −0.173648 0.984808i −0.0708916 0.402046i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i \(-0.106148\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) −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 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −0.868241 4.92404i −0.240807 1.36568i −0.830033 0.557714i \(-0.811678\pi\)
0.589226 0.807968i \(-0.299433\pi\)
\(14\) −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 −0.660447 0.750873i \(-0.729633\pi\)
−0.0232799 + 0.999729i \(0.507411\pi\)
\(18\) −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 −0.370941 0.928656i \(-0.620965\pi\)
0.850135 + 0.526565i \(0.176520\pi\)
\(24\) −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 \(-0.0739923\pi\)
0.597365 + 0.801970i \(0.296214\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 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 \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(42\) 0.766044 0.642788i 0.118203 0.0991843i
\(43\) 6.12836 + 5.14230i 0.934565 + 0.784194i 0.976631 0.214921i \(-0.0689495\pi\)
−0.0420659 + 0.999115i \(0.513394\pi\)
\(44\) −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 \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(48\) 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 \(-0.656164\pi\)
0.786832 + 0.617167i \(0.211720\pi\)
\(54\) 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 \(-0.411872\pi\)
0.827699 + 0.561173i \(0.189650\pi\)
\(60\) 0 0
\(61\) −7.66044 + 6.42788i −0.980819 + 0.823005i −0.984213 0.176989i \(-0.943364\pi\)
0.00339342 + 0.999994i \(0.498920\pi\)
\(62\) 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 \(-0.290091\pi\)
−0.0386729 + 0.999252i \(0.512313\pi\)
\(68\) −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 \(-0.161906\pi\)
−0.327929 + 0.944702i \(0.606351\pi\)
\(72\) −1.53209 + 1.28558i −0.180558 + 0.151506i
\(73\) −1.21554 + 6.89365i −0.142268 + 0.806841i 0.827252 + 0.561830i \(0.189903\pi\)
−0.969520 + 0.245011i \(0.921208\pi\)
\(74\) 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 −0.716522 0.697564i \(-0.754267\pi\)
0.911892 0.410431i \(-0.134622\pi\)
\(80\) 0 0
\(81\) 0.766044 + 0.642788i 0.0851160 + 0.0714208i
\(82\) 0 0
\(83\) 3.00000 + 5.19615i 0.329293 + 0.570352i 0.982372 0.186938i \(-0.0598564\pi\)
−0.653079 + 0.757290i \(0.726523\pi\)
\(84\) −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 0.870406 + 0.492334i \(0.163856\pi\)
−0.649526 + 0.760339i \(0.725033\pi\)
\(90\) 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 \(-0.780605\pi\)
−0.182389 + 0.983226i \(0.558383\pi\)
\(98\) −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 0.593741 + 0.804656i \(0.297650\pi\)
−0.282726 + 0.959201i \(0.591239\pi\)
\(102\) 1.50000 + 2.59808i 0.148522 + 0.257248i
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) 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 \(-0.309929\pi\)
−0.997298 + 0.0734594i \(0.976596\pi\)
\(108\) 0.868241 + 4.92404i 0.0835465 + 0.473816i
\(109\) −8.42649 7.07066i −0.807111 0.677247i 0.142805 0.989751i \(-0.454388\pi\)
−0.949916 + 0.312504i \(0.898832\pi\)
\(110\) 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 \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 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 \(-0.0838382\pi\)
−0.996332 + 0.0855756i \(0.972727\pi\)
\(128\) 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 \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(132\) 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 −0.887898 0.460040i \(-0.847835\pi\)
0.298870 + 0.954294i \(0.403390\pi\)
\(138\) −2.29813 1.92836i −0.195630 0.164153i
\(139\) −0.694593 3.93923i −0.0589146 0.334121i 0.941077 0.338192i \(-0.109815\pi\)
−0.999992 + 0.00407080i \(0.998704\pi\)
\(140\) 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 \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(150\) −4.69846 + 1.71010i −0.383628 + 0.139629i
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 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 −0.980307 0.197478i \(-0.936725\pi\)
−0.364707 0.931122i \(-0.618831\pi\)
\(158\) 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 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 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 \(-0.875914\pi\)
0.213635 + 0.976914i \(0.431470\pi\)
\(168\) 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 \(-0.537864\pi\)
0.547335 + 0.836913i \(0.315642\pi\)
\(174\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0 0
\(181\) 1.87939 + 0.684040i 0.139694 + 0.0508443i 0.410921 0.911671i \(-0.365207\pi\)
−0.271227 + 0.962515i \(0.587429\pi\)
\(182\) −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 0.763160 + 0.646210i \(0.223647\pi\)
−0.938152 + 0.346222i \(0.887464\pi\)
\(194\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) −6.00000 + 10.3923i −0.426401 + 0.738549i
\(199\) −10.3366 3.76222i −0.732743 0.266697i −0.0514178 0.998677i \(-0.516374\pi\)
−0.681326 + 0.731980i \(0.738596\pi\)
\(200\) 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 \(-0.556054\pi\)
0.498644 + 0.866807i \(0.333831\pi\)
\(212\) 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 −0.983185 0.182612i \(-0.941545\pi\)
−0.350566 0.936538i \(-0.614011\pi\)
\(224\) −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 \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) 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 0.479695 0.877435i \(-0.340747\pi\)
−0.780807 + 0.624773i \(0.785192\pi\)
\(234\) 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 −0.296037 0.955176i \(-0.595665\pi\)
0.975226 0.221213i \(-0.0710015\pi\)
\(240\) 0 0
\(241\) −1.38919 7.87846i −0.0894853 0.507496i −0.996298 0.0859632i \(-0.972603\pi\)
0.906813 0.421533i \(-0.138508\pi\)
\(242\) 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 −0.486101 0.873902i \(-0.661581\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(252\) 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 \(-0.266782\pi\)
0.0345364 + 0.999403i \(0.489005\pi\)
\(258\) 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 −0.533950 0.845516i \(-0.679293\pi\)
0.790932 0.611904i \(-0.209596\pi\)
\(264\) −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 −0.936431 0.350853i \(-0.885892\pi\)
0.999956 0.00941580i \(-0.00299719\pi\)
\(270\) 0 0
\(271\) 8.42649 + 7.07066i 0.511873 + 0.429512i 0.861788 0.507269i \(-0.169345\pi\)
−0.349915 + 0.936782i \(0.613789\pi\)
\(272\) 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 −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 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 \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(282\) 0 0
\(283\) 20.6732 7.52444i 1.22890 0.447282i 0.355677 0.934609i \(-0.384250\pi\)
0.873219 + 0.487327i \(0.162028\pi\)
\(284\) 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 0.377244 + 0.926114i \(0.376872\pi\)
−0.990660 + 0.136355i \(0.956461\pi\)
\(294\) −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 0.709557 + 0.704649i \(0.248895\pi\)
−0.907769 + 0.419470i \(0.862216\pi\)
\(308\) 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 0.993490 + 0.113917i \(0.0363399\pi\)
−0.398090 + 0.917346i \(0.630327\pi\)
\(312\) −2.50000 + 4.33013i −0.141535 + 0.245145i
\(313\) 17.8542 + 6.49838i 1.00918 + 0.367310i 0.793117 0.609070i \(-0.208457\pi\)
0.216060 + 0.976380i \(0.430679\pi\)
\(314\) 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 0.996723 + 0.0808951i \(0.0257779\pi\)
−0.908945 + 0.416916i \(0.863111\pi\)
\(318\) −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 \(-0.842082\pi\)
0.851957 + 0.523612i \(0.175416\pi\)
\(332\) 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 \(-0.243030\pi\)
−0.555503 + 0.831514i \(0.687474\pi\)
\(338\) 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 0.932897 0.360143i \(-0.117272\pi\)
−0.192676 + 0.981263i \(0.561717\pi\)
\(348\) 1.56283 + 8.86327i 0.0837767 + 0.475121i
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) −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 −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) −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 −0.805447 0.592667i \(-0.798075\pi\)
−0.236049 + 0.971741i \(0.575853\pi\)
\(360\) 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 −0.799129 0.601160i \(-0.794706\pi\)
0.545327 0.838224i \(-0.316406\pi\)
\(368\) −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 0.993484 + 0.113975i \(0.0363585\pi\)
−0.398036 + 0.917370i \(0.630308\pi\)
\(374\) −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 \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(380\) 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 0.794634 + 0.607088i \(0.207663\pi\)
−0.954348 + 0.298696i \(0.903449\pi\)
\(384\) −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 −0.124464 0.992224i \(-0.539721\pi\)
−0.733134 + 0.680084i \(0.761943\pi\)
\(390\) 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 −0.767443 0.641117i \(-0.778471\pi\)
−0.175793 + 0.984427i \(0.556249\pi\)
\(398\) 11.0000 0.551380
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(402\) 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 \(-0.0983721\pi\)
0.534249 + 0.845327i \(0.320594\pi\)
\(410\) 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 0.824393 + 0.566018i \(0.191517\pi\)
−0.968265 + 0.249924i \(0.919594\pi\)
\(422\) −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 \(-0.101715\pi\)
−0.999564 + 0.0295160i \(0.990603\pi\)
\(432\) 3.83022 + 3.21394i 0.184282 + 0.154631i
\(433\) −1.53209 + 1.28558i −0.0736275 + 0.0617808i −0.678859 0.734269i \(-0.737525\pi\)
0.605231 + 0.796050i \(0.293081\pi\)
\(434\) −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 \(-0.844039\pi\)
−0.373425 + 0.927660i \(0.621817\pi\)
\(440\) 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 −0.964486 0.264134i \(-0.914914\pi\)
0.815981 0.578079i \(-0.196197\pi\)
\(444\) −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 \(-0.306300\pi\)
−0.996396 + 0.0848262i \(0.972967\pi\)
\(450\) 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 0.403110 0.915152i \(-0.367929\pi\)
−0.831249 + 0.555900i \(0.812374\pi\)
\(462\) −1.04189 5.90885i −0.0484731 0.274904i
\(463\) 2.00000 + 3.46410i 0.0929479 + 0.160990i 0.908750 0.417340i \(-0.137038\pi\)
−0.815802 + 0.578331i \(0.803704\pi\)
\(464\) 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 −0.995582 0.0939008i \(-0.970066\pi\)
0.579111 + 0.815249i \(0.303400\pi\)
\(468\) −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 0.264376 0.964420i \(-0.414834\pi\)
0.995676 0.0928902i \(-0.0296105\pi\)
\(480\) 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 \(-0.152238\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) −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 0.433280 + 0.901259i \(0.357356\pi\)
−0.715399 + 0.698716i \(0.753755\pi\)
\(492\) 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 0.571620 0.820518i \(-0.306315\pi\)
−0.708792 + 0.705418i \(0.750759\pi\)
\(500\) 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 0.742159 0.670223i \(-0.233802\pi\)
0.137716 + 0.990472i \(0.456024\pi\)
\(504\) −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 \(-0.953732\pi\)
−0.0291750 + 0.999574i \(0.509288\pi\)
\(510\) 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 0.138234 + 0.990400i \(0.455857\pi\)
−0.926828 + 0.375486i \(0.877476\pi\)
\(522\) −16.9145 6.15636i −0.740326 0.269457i
\(523\) 10.3366 + 3.76222i 0.451989 + 0.164510i 0.557976 0.829857i \(-0.311578\pi\)
−0.105987 + 0.994367i \(0.533800\pi\)
\(524\) 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 0.301303 0.953528i \(-0.402578\pi\)
−0.382104 + 0.924119i \(0.624801\pi\)
\(542\) −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 −0.502437 + 0.864614i \(0.667563\pi\)
−0.938726 + 0.344665i \(0.887992\pi\)
\(548\) −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 0.936298 + 0.351205i \(0.114228\pi\)
−0.759713 + 0.650258i \(0.774661\pi\)
\(558\) 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 \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 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 \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 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 0.728535 0.685009i \(-0.240202\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 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 −0.0986548 0.995122i \(-0.531454\pi\)
0.564078 + 0.825722i \(0.309232\pi\)
\(588\) 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 −0.978231 0.207521i \(-0.933460\pi\)
0.0345003 + 0.999405i \(0.489016\pi\)
\(594\) −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 \(-0.552004\pi\)
−0.758825 + 0.651294i \(0.774226\pi\)
\(600\) −2.50000 + 4.33013i −0.102062 + 0.176777i
\(601\) −14.0000 24.2487i −0.571072 0.989126i −0.996456 0.0841128i \(-0.973194\pi\)
0.425384 0.905013i \(-0.360139\pi\)
\(602\) −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 \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 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 0.673203 0.739457i \(-0.264918\pi\)
−0.611323 + 0.791381i \(0.709362\pi\)
\(614\) −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 0.453008 0.891506i \(-0.350351\pi\)
−0.226025 + 0.974122i \(0.572573\pi\)
\(618\) −13.1557 4.78828i −0.529200 0.192613i
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 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 −0.853284 0.521446i \(-0.825393\pi\)
0.365352 + 0.930869i \(0.380948\pi\)
\(632\) 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 \(-0.315584\pi\)
−0.729030 + 0.684482i \(0.760029\pi\)
\(642\) −6.89440 + 5.78509i −0.272100 + 0.228319i
\(643\) −3.82026 + 21.6658i −0.150656 + 0.854415i 0.811994 + 0.583666i \(0.198382\pi\)
−0.962650 + 0.270748i \(0.912729\pi\)
\(644\) 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 0.529799 0.848123i \(-0.322267\pi\)
−0.999396 + 0.0347583i \(0.988934\pi\)
\(654\) −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 0.626330 + 0.779558i \(0.284556\pi\)
−0.321934 + 0.946762i \(0.604333\pi\)
\(660\) 0 0
\(661\) 9.95858 8.35624i 0.387344 0.325020i −0.428234 0.903668i \(-0.640864\pi\)
0.815577 + 0.578648i \(0.196420\pi\)
\(662\) 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 −0.0349191 0.999390i \(-0.511117\pi\)
0.882957 0.469454i \(-0.155549\pi\)
\(674\) −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 −0.986695 0.162581i \(-0.948018\pi\)
0.352549 0.935793i \(-0.385315\pi\)
\(678\) 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 \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 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 0.945319 0.326146i \(-0.105750\pi\)
−0.755110 + 0.655598i \(0.772417\pi\)
\(692\) 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 −0.546072 0.837738i \(-0.683878\pi\)
0.120172 + 0.992753i \(0.461655\pi\)
\(702\) −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 −0.999897 0.0143670i \(-0.995427\pi\)
0.934682 0.355485i \(-0.115684\pi\)
\(710\) 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 −0.549687 0.835371i \(-0.685253\pi\)
0.802251 0.596988i \(-0.203636\pi\)
\(720\) 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 −0.0579875 0.998317i \(-0.518468\pi\)
−0.993220 + 0.116249i \(0.962913\pi\)
\(728\) 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 0.403128 + 0.915144i \(0.367923\pi\)
−0.994102 + 0.108453i \(0.965410\pi\)
\(734\) 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 −0.0503375 0.998732i \(-0.516030\pi\)
0.603412 + 0.797430i \(0.293807\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.00000 −0.110133
\(743\) −33.8289 + 12.3127i −1.24106 + 0.451710i −0.877373 0.479810i \(-0.840706\pi\)
−0.363691 + 0.931520i \(0.618483\pi\)
\(744\) −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 \(-0.649281\pi\)
−0.919619 + 0.392811i \(0.871503\pi\)
\(752\) 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 −0.977846 0.209327i \(-0.932873\pi\)
0.990468 + 0.137740i \(0.0439838\pi\)
\(758\) −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 0.255912 0.966700i \(-0.417624\pi\)
−0.425343 + 0.905032i \(0.639846\pi\)
\(770\) 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 −0.551704 0.834040i \(-0.686022\pi\)
0.233174 0.972435i \(-0.425089\pi\)
\(774\) −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
\(785\) 0 0
\(786\) 0 0
\(787\) −15.5000 + 26.8468i −0.552515 + 0.956985i 0.445577 + 0.895244i \(0.352999\pi\)
−0.998092 + 0.0617409i \(0.980335\pi\)
\(788\)