Properties

Label 722.2.e.e.415.1
Level 722
Weight 2
Character 722.415
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 415.1
Root \(0.939693 - 0.342020i\)
Character \(\chi\) = 722.415
Dual form 722.2.e.e.595.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +O(q^{10})\) \(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.69846 + 1.71010i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.29813 + 1.92836i) q^{17} -2.00000 q^{18} +(0.766044 + 0.642788i) q^{21} +(5.63816 - 2.05212i) q^{22} +(0.520945 + 2.95442i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(4.69846 + 1.71010i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(-6.89440 + 5.78509i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.04189 - 5.90885i) q^{33} +(0.520945 + 2.95442i) q^{34} +(-1.53209 - 1.28558i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(0.173648 + 0.984808i) q^{42} +(1.38919 - 7.87846i) q^{43} +(5.63816 + 2.05212i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-0.766044 + 0.642788i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.50000 + 4.33013i) q^{50} +(2.81908 + 1.02606i) q^{51} +(-0.868241 + 4.92404i) q^{52} +(0.520945 + 2.95442i) q^{53} +(-4.69846 + 1.71010i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(-6.89440 - 5.78509i) q^{59} +(-1.73648 - 9.84808i) q^{61} +(0.694593 - 3.93923i) q^{62} +(-1.87939 - 0.684040i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(4.59627 - 3.85673i) q^{66} +(-3.83022 + 3.21394i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} +(1.04189 - 5.90885i) q^{71} +(-0.347296 - 1.96962i) q^{72} +(6.57785 - 2.39414i) q^{73} +(-1.53209 - 1.28558i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(3.83022 + 3.21394i) q^{78} +(-9.39693 + 3.42020i) q^{79} +(0.173648 - 0.984808i) q^{81} +(3.00000 + 5.19615i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(6.12836 - 5.14230i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-11.2763 - 4.10424i) q^{89} +(0.868241 + 4.92404i) q^{91} +(-2.81908 + 1.02606i) q^{92} +(-3.06418 - 2.57115i) q^{93} -1.00000 q^{96} +(7.66044 + 6.42788i) q^{97} +(5.63816 - 2.05212i) q^{98} +(2.08378 + 11.8177i) 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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.766044 + 0.642788i 0.541675 + 0.454519i
\(3\) 0.939693 0.342020i 0.542532 0.197465i −0.0561935 0.998420i \(-0.517896\pi\)
0.598725 + 0.800954i \(0.295674\pi\)
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(6\) 0.939693 + 0.342020i 0.383628 + 0.139629i
\(7\) 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
\(9\) −1.53209 + 1.28558i −0.510696 + 0.428525i
\(10\) 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
\(13\) 4.69846 + 1.71010i 1.30312 + 0.474297i 0.898011 0.439972i \(-0.145012\pi\)
0.405108 + 0.914269i \(0.367234\pi\)
\(14\) −0.173648 + 0.984808i −0.0464094 + 0.263201i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 2.29813 + 1.92836i 0.557379 + 0.467697i 0.877431 0.479703i \(-0.159256\pi\)
−0.320051 + 0.947400i \(0.603700\pi\)
\(18\) −2.00000 −0.471405
\(19\) 0 0
\(20\) 0 0
\(21\) 0.766044 + 0.642788i 0.167165 + 0.140268i
\(22\) 5.63816 2.05212i 1.20206 0.437514i
\(23\) 0.520945 + 2.95442i 0.108624 + 0.616040i 0.989711 + 0.143084i \(0.0457019\pi\)
−0.881086 + 0.472956i \(0.843187\pi\)
\(24\) −0.173648 + 0.984808i −0.0354458 + 0.201023i
\(25\) 4.69846 + 1.71010i 0.939693 + 0.342020i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) −2.50000 + 4.33013i −0.481125 + 0.833333i
\(28\) −0.766044 + 0.642788i −0.144769 + 0.121475i
\(29\) −6.89440 + 5.78509i −1.28026 + 1.07426i −0.287049 + 0.957916i \(0.592674\pi\)
−0.993208 + 0.116348i \(0.962881\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.939693 0.342020i −0.166116 0.0604612i
\(33\) 1.04189 5.90885i 0.181370 1.02860i
\(34\) 0.520945 + 2.95442i 0.0893413 + 0.506679i
\(35\) 0 0
\(36\) −1.53209 1.28558i −0.255348 0.214263i
\(37\) −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 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(42\) 0.173648 + 0.984808i 0.0267945 + 0.151959i
\(43\) 1.38919 7.87846i 0.211849 1.20145i −0.674443 0.738327i \(-0.735616\pi\)
0.886292 0.463127i \(-0.153273\pi\)
\(44\) 5.63816 + 2.05212i 0.849984 + 0.309369i
\(45\) 0 0
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(48\) −0.766044 + 0.642788i −0.110569 + 0.0927784i
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 2.50000 + 4.33013i 0.353553 + 0.612372i
\(51\) 2.81908 + 1.02606i 0.394750 + 0.143677i
\(52\) −0.868241 + 4.92404i −0.120403 + 0.682841i
\(53\) 0.520945 + 2.95442i 0.0715572 + 0.405821i 0.999456 + 0.0329883i \(0.0105024\pi\)
−0.927899 + 0.372833i \(0.878386\pi\)
\(54\) −4.69846 + 1.71010i −0.639380 + 0.232715i
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) −6.89440 5.78509i −0.897574 0.753154i 0.0721404 0.997394i \(-0.477017\pi\)
−0.969715 + 0.244240i \(0.921461\pi\)
\(60\) 0 0
\(61\) −1.73648 9.84808i −0.222334 1.26092i −0.867717 0.497058i \(-0.834413\pi\)
0.645383 0.763859i \(-0.276698\pi\)
\(62\) 0.694593 3.93923i 0.0882134 0.500283i
\(63\) −1.87939 0.684040i −0.236780 0.0861810i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0 0
\(66\) 4.59627 3.85673i 0.565761 0.474730i
\(67\) −3.83022 + 3.21394i −0.467936 + 0.392645i −0.846041 0.533118i \(-0.821020\pi\)
0.378105 + 0.925763i \(0.376576\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) 1.04189 5.90885i 0.123649 0.701251i −0.858451 0.512895i \(-0.828573\pi\)
0.982101 0.188356i \(-0.0603159\pi\)
\(72\) −0.347296 1.96962i −0.0409293 0.232121i
\(73\) 6.57785 2.39414i 0.769879 0.280213i 0.0729331 0.997337i \(-0.476764\pi\)
0.696946 + 0.717124i \(0.254542\pi\)
\(74\) −1.53209 1.28558i −0.178102 0.149445i
\(75\) 5.00000 0.577350
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 3.83022 + 3.21394i 0.433687 + 0.363907i
\(79\) −9.39693 + 3.42020i −1.05724 + 0.384803i −0.811389 0.584506i \(-0.801288\pi\)
−0.245847 + 0.969309i \(0.579066\pi\)
\(80\) 0 0
\(81\) 0.173648 0.984808i 0.0192942 0.109423i
\(82\) 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
\(86\) 6.12836 5.14230i 0.660838 0.554509i
\(87\) −4.50000 + 7.79423i −0.482451 + 0.835629i
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) −11.2763 4.10424i −1.19529 0.435049i −0.333710 0.942676i \(-0.608301\pi\)
−0.861577 + 0.507627i \(0.830523\pi\)
\(90\) 0 0
\(91\) 0.868241 + 4.92404i 0.0910164 + 0.516180i
\(92\) −2.81908 + 1.02606i −0.293909 + 0.106974i
\(93\) −3.06418 2.57115i −0.317740 0.266616i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 7.66044 + 6.42788i 0.777800 + 0.652652i 0.942694 0.333659i \(-0.108284\pi\)
−0.164893 + 0.986311i \(0.552728\pi\)
\(98\) 5.63816 2.05212i 0.569540 0.207296i
\(99\) 2.08378 + 11.8177i 0.209428 + 1.18772i
\(100\) −0.868241 + 4.92404i −0.0868241 + 0.492404i
\(101\) −16.9145 6.15636i −1.68305 0.612581i −0.689329 0.724448i \(-0.742095\pi\)
−0.993723 + 0.111867i \(0.964317\pi\)
\(102\) 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 \(-0.0756043\pi\)
\(104\) −3.83022 + 3.21394i −0.375584 + 0.315153i
\(105\) 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 \(0.976596\pi\)
\(108\) −4.69846 1.71010i −0.452110 0.164555i
\(109\) −1.91013 + 10.8329i −0.182957 + 1.03760i 0.745595 + 0.666400i \(0.232166\pi\)
−0.928552 + 0.371203i \(0.878946\pi\)
\(110\) 0 0
\(111\) −1.87939 + 0.684040i −0.178383 + 0.0649262i
\(112\) −0.766044 0.642788i −0.0723844 0.0607377i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.89440 5.78509i −0.640129 0.537132i
\(117\) −9.39693 + 3.42020i −0.868746 + 0.316198i
\(118\) −1.56283 8.86327i −0.143870 0.815930i
\(119\) −0.520945 + 2.95442i −0.0477549 + 0.270832i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 0 0
\(124\) 3.06418 2.57115i 0.275171 0.230896i
\(125\) 0 0
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) 1.87939 + 0.684040i 0.166768 + 0.0606988i 0.424055 0.905636i \(-0.360606\pi\)
−0.257287 + 0.966335i \(0.582828\pi\)
\(128\) 0.173648 0.984808i 0.0153485 0.0870455i
\(129\) −1.38919 7.87846i −0.122311 0.693660i
\(130\) 0 0
\(131\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) −2.81908 + 1.02606i −0.241734 + 0.0879840i
\(137\) −1.56283 8.86327i −0.133522 0.757240i −0.975878 0.218318i \(-0.929943\pi\)
0.842356 0.538922i \(-0.181168\pi\)
\(138\) −0.520945 + 2.95442i −0.0443457 + 0.251497i
\(139\) 3.75877 + 1.36808i 0.318815 + 0.116039i 0.496470 0.868054i \(-0.334629\pi\)
−0.177656 + 0.984093i \(0.556851\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.59627 3.85673i 0.385710 0.323649i
\(143\) 22.9813 19.2836i 1.92180 1.61258i
\(144\) 1.00000 1.73205i 0.0833333 0.144338i
\(145\) 0 0
\(146\) 6.57785 + 2.39414i 0.544387 + 0.198141i
\(147\) 1.04189 5.90885i 0.0859336 0.487353i
\(148\) −0.347296 1.96962i −0.0285476 0.161901i
\(149\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(150\) 3.83022 + 3.21394i 0.312736 + 0.262417i
\(151\) 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
\(154\) 4.59627 + 3.85673i 0.370378 + 0.310784i
\(155\) 0 0
\(156\) 0.868241 + 4.92404i 0.0695149 + 0.394239i
\(157\) −3.82026 + 21.6658i −0.304890 + 1.72912i 0.319132 + 0.947710i \(0.396609\pi\)
−0.624022 + 0.781407i \(0.714503\pi\)
\(158\) −9.39693 3.42020i −0.747579 0.272097i
\(159\) 1.50000 + 2.59808i 0.118958 + 0.206041i
\(160\) 0 0
\(161\) −2.29813 + 1.92836i −0.181118 + 0.151976i
\(162\) 0.766044 0.642788i 0.0601861 0.0505022i
\(163\) −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
\(166\) −1.04189 + 5.90885i −0.0808663 + 0.458615i
\(167\) −2.08378 11.8177i −0.161248 0.914481i −0.952849 0.303443i \(-0.901864\pi\)
0.791602 0.611037i \(-0.209247\pi\)
\(168\) −0.939693 + 0.342020i −0.0724989 + 0.0263874i
\(169\) 9.19253 + 7.71345i 0.707118 + 0.593342i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) −4.59627 3.85673i −0.349448 0.293221i 0.451121 0.892463i \(-0.351024\pi\)
−0.800568 + 0.599242i \(0.795469\pi\)
\(174\) −8.45723 + 3.07818i −0.641141 + 0.233356i
\(175\) 0.868241 + 4.92404i 0.0656328 + 0.372222i
\(176\) −1.04189 + 5.90885i −0.0785353 + 0.445396i
\(177\) −8.45723 3.07818i −0.635685 0.231370i
\(178\) −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
\(181\) −1.53209 + 1.28558i −0.113879 + 0.0955561i −0.697949 0.716147i \(-0.745904\pi\)
0.584070 + 0.811703i \(0.301459\pi\)
\(182\) −2.50000 + 4.33013i −0.185312 + 0.320970i
\(183\) −5.00000 8.66025i −0.369611 0.640184i
\(184\) −2.81908 1.02606i −0.207825 0.0756422i
\(185\) 0 0
\(186\) −0.694593 3.93923i −0.0509300 0.288838i
\(187\) 16.9145 6.15636i 1.23691 0.450198i
\(188\) 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 \(0.465384\pi\)
\(192\) −0.766044 0.642788i −0.0552845 0.0463892i
\(193\) 13.1557 4.78828i 0.946968 0.344668i 0.178054 0.984021i \(-0.443020\pi\)
0.768914 + 0.639353i \(0.220798\pi\)
\(194\) 1.73648 + 9.84808i 0.124672 + 0.707051i
\(195\) 0 0
\(196\) 5.63816 + 2.05212i 0.402725 + 0.146580i
\(197\) 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
\(199\) 8.42649 7.07066i 0.597338 0.501226i −0.293251 0.956036i \(-0.594737\pi\)
0.890589 + 0.454809i \(0.150293\pi\)
\(200\) −3.83022 + 3.21394i −0.270838 + 0.227260i
\(201\) −2.50000 + 4.33013i −0.176336 + 0.305424i
\(202\) −9.00000 15.5885i −0.633238 1.09680i
\(203\) −8.45723 3.07818i −0.593581 0.216046i
\(204\) −0.520945 + 2.95442i −0.0364734 + 0.206851i
\(205\) 0 0
\(206\) 13.1557 4.78828i 0.916601 0.333615i
\(207\) −4.59627 3.85673i −0.319463 0.268061i
\(208\) −5.00000 −0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) −3.83022 3.21394i −0.263683 0.221257i 0.501354 0.865242i \(-0.332835\pi\)
−0.765038 + 0.643985i \(0.777280\pi\)
\(212\) −2.81908 + 1.02606i −0.193615 + 0.0704701i
\(213\) −1.04189 5.90885i −0.0713891 0.404867i
\(214\) 1.56283 8.86327i 0.106833 0.605881i
\(215\) 0 0
\(216\) −2.50000 4.33013i −0.170103 0.294628i
\(217\) 2.00000 3.46410i 0.135769 0.235159i
\(218\) −8.42649 + 7.07066i −0.570714 + 0.478886i
\(219\) 5.36231 4.49951i 0.362351 0.304049i
\(220\) 0 0
\(221\) 7.50000 + 12.9904i 0.504505 + 0.873828i
\(222\) −1.87939 0.684040i −0.126136 0.0459098i
\(223\) −4.51485 + 25.6050i −0.302337 + 1.71464i 0.333445 + 0.942769i \(0.391789\pi\)
−0.635782 + 0.771868i \(0.719322\pi\)
\(224\) −0.173648 0.984808i −0.0116024 0.0658002i
\(225\) −9.39693 + 3.42020i −0.626462 + 0.228013i
\(226\) −4.59627 3.85673i −0.305739 0.256546i
\(227\) 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
\(231\) 5.63816 2.05212i 0.370963 0.135020i
\(232\) −1.56283 8.86327i −0.102605 0.581902i
\(233\) −1.04189 + 5.90885i −0.0682564 + 0.387101i 0.931472 + 0.363812i \(0.118525\pi\)
−0.999729 + 0.0232893i \(0.992586\pi\)
\(234\) −9.39693 3.42020i −0.614296 0.223586i
\(235\) 0 0
\(236\) 4.50000 7.79423i 0.292925 0.507361i
\(237\) −7.66044 + 6.42788i −0.497599 + 0.417535i
\(238\) −2.29813 + 1.92836i −0.148966 + 0.124997i
\(239\) 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
\(241\) 7.51754 + 2.73616i 0.484247 + 0.176252i 0.572596 0.819838i \(-0.305937\pi\)
−0.0883481 + 0.996090i \(0.528159\pi\)
\(242\) 4.34120 24.6202i 0.279063 1.58265i
\(243\) −2.77837 15.7569i −0.178233 1.01081i
\(244\) 9.39693 3.42020i 0.601577 0.218956i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) 4.59627 + 3.85673i 0.291277 + 0.244410i
\(250\) 0 0
\(251\) 1.04189 + 5.90885i 0.0657635 + 0.372963i 0.999872 + 0.0159750i \(0.00508522\pi\)
−0.934109 + 0.356988i \(0.883804\pi\)
\(252\) 0.347296 1.96962i 0.0218776 0.124074i
\(253\) 16.9145 + 6.15636i 1.06340 + 0.387047i
\(254\) 1.00000 + 1.73205i 0.0627456 + 0.108679i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −9.19253 + 7.71345i −0.573414 + 0.481152i −0.882777 0.469792i \(-0.844329\pi\)
0.309362 + 0.950944i \(0.399884\pi\)
\(258\) 4.00000 6.92820i 0.249029 0.431331i
\(259\) −1.00000 1.73205i −0.0621370 0.107624i
\(260\) 0 0
\(261\) 3.12567 17.7265i 0.193474 1.09725i
\(262\) 0 0
\(263\) −22.5526 + 8.20848i −1.39065 + 0.506157i −0.925390 0.379015i \(-0.876263\pi\)
−0.465264 + 0.885172i \(0.654041\pi\)
\(264\) 4.59627 + 3.85673i 0.282881 + 0.237365i
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) −3.83022 3.21394i −0.233968 0.196323i
\(269\) −5.63816 + 2.05212i −0.343764 + 0.125120i −0.508132 0.861279i \(-0.669664\pi\)
0.164368 + 0.986399i \(0.447442\pi\)
\(270\) 0 0
\(271\) 1.91013 10.8329i 0.116032 0.658051i −0.870202 0.492695i \(-0.836012\pi\)
0.986234 0.165356i \(-0.0528772\pi\)
\(272\) −2.81908 1.02606i −0.170932 0.0622141i
\(273\) 2.50000 + 4.33013i 0.151307 + 0.262071i
\(274\) 4.50000 7.79423i 0.271855 0.470867i
\(275\) 22.9813 19.2836i 1.38583 1.16285i
\(276\) −2.29813 + 1.92836i −0.138331 + 0.116074i
\(277\) −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
\(279\) 7.51754 + 2.73616i 0.450063 + 0.163810i
\(280\) 0 0
\(281\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(282\) 0 0
\(283\) −16.8530 14.1413i −1.00181 0.840615i −0.0145720 0.999894i \(-0.504639\pi\)
−0.987234 + 0.159279i \(0.949083\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 0 0
\(288\) 1.87939 0.684040i 0.110744 0.0403075i
\(289\) −1.38919 7.87846i −0.0817168 0.463439i
\(290\) 0 0
\(291\) 9.39693 + 3.42020i 0.550858 + 0.200496i
\(292\) 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 \(0.956461\pi\)
\(294\) 4.59627 3.85673i 0.268060 0.224929i
\(295\) 0 0
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 15.0000 + 25.9808i 0.870388 + 1.50756i
\(298\) 0 0
\(299\) −2.60472 + 14.7721i −0.150635 + 0.854294i
\(300\) 0.868241 + 4.92404i 0.0501279 + 0.284290i
\(301\) 7.51754 2.73616i 0.433304 0.157710i
\(302\) 7.66044 + 6.42788i 0.440809 + 0.369883i
\(303\) −18.0000 −1.03407
\(304\) 0 0
\(305\) 0 0
\(306\) −4.59627 3.85673i −0.262751 0.220474i
\(307\) 18.7939 6.84040i 1.07262 0.390402i 0.255465 0.966818i \(-0.417771\pi\)
0.817157 + 0.576416i \(0.195549\pi\)
\(308\) 1.04189 + 5.90885i 0.0593671 + 0.336688i
\(309\) 2.43107 13.7873i 0.138299 0.784333i
\(310\) 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
\(313\) −14.5548 + 12.2130i −0.822688 + 0.690318i −0.953600 0.301076i \(-0.902654\pi\)
0.130912 + 0.991394i \(0.458210\pi\)
\(314\) −16.8530 + 14.1413i −0.951069 + 0.798041i
\(315\) 0 0
\(316\) −5.00000 8.66025i −0.281272 0.487177i
\(317\) −8.45723 3.07818i −0.475006 0.172888i 0.0934130 0.995627i \(-0.470222\pi\)
−0.568419 + 0.822740i \(0.692445\pi\)
\(318\) −0.520945 + 2.95442i −0.0292131 + 0.165676i
\(319\) 9.37700 + 53.1796i 0.525011 + 2.97749i
\(320\) 0 0
\(321\) −6.89440 5.78509i −0.384808 0.322892i
\(322\) −3.00000 −0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 19.1511 + 16.0697i 1.06231 + 0.891386i
\(326\) −18.7939 + 6.84040i −1.04090 + 0.378855i
\(327\) 1.91013 + 10.8329i 0.105630 + 0.599060i
\(328\) 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 \(0.175416\pi\)
\(332\) −4.59627 + 3.85673i −0.252253 + 0.211665i
\(333\) 3.06418 2.57115i 0.167916 0.140898i
\(334\) 6.00000 10.3923i 0.328305 0.568642i
\(335\) 0 0
\(336\) −0.939693 0.342020i −0.0512644 0.0186587i
\(337\) 0.694593 3.93923i 0.0378369 0.214584i −0.960027 0.279906i \(-0.909697\pi\)
0.997864 + 0.0653228i \(0.0208077\pi\)
\(338\) 2.08378 + 11.8177i 0.113343 + 0.642798i
\(339\) −5.63816 + 2.05212i −0.306223 + 0.111456i
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 6.12836 + 5.14230i 0.330419 + 0.277254i
\(345\) 0 0
\(346\) −1.04189 5.90885i −0.0560123 0.317662i
\(347\) 3.12567 17.7265i 0.167795 0.951611i −0.778341 0.627841i \(-0.783939\pi\)
0.946136 0.323769i \(-0.104950\pi\)
\(348\) −8.45723 3.07818i −0.453355 0.165008i
\(349\) 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
\(351\) −19.1511 + 16.0697i −1.02221 + 0.857737i
\(352\) −4.59627 + 3.85673i −0.244982 + 0.205564i
\(353\) 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
\(356\) 2.08378 11.8177i 0.110440 0.626336i
\(357\) 0.520945 + 2.95442i 0.0275713 + 0.156365i
\(358\) 0 0
\(359\) 16.0869 + 13.4985i 0.849036 + 0.712426i 0.959577 0.281446i \(-0.0908140\pi\)
−0.110541 + 0.993872i \(0.535258\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −2.00000 −0.105118
\(363\) −19.1511 16.0697i −1.00517 0.843440i
\(364\) −4.69846 + 1.71010i −0.246266 + 0.0896336i
\(365\) 0 0
\(366\) 1.73648 9.84808i 0.0907674 0.514767i
\(367\) 26.3114 + 9.57656i 1.37344 + 0.499893i 0.920184 0.391486i \(-0.128039\pi\)
0.453260 + 0.891379i \(0.350261\pi\)
\(368\) −1.50000 2.59808i −0.0781929 0.135434i
\(369\) 0 0
\(370\) 0 0
\(371\) −2.29813 + 1.92836i −0.119313 + 0.100116i
\(372\) 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 \(0.630308\pi\)
\(374\) 16.9145 + 6.15636i 0.874626 + 0.318338i
\(375\) 0 0
\(376\) 0 0
\(377\) −42.2862 + 15.3909i −2.17785 + 0.792672i
\(378\) −3.83022 3.21394i −0.197005 0.165307i
\(379\) 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
\(382\) 2.29813 + 1.92836i 0.117583 + 0.0986636i
\(383\) 16.9145 6.15636i 0.864289 0.314575i 0.128437 0.991718i \(-0.459004\pi\)
0.735852 + 0.677142i \(0.236782\pi\)
\(384\) −0.173648 0.984808i −0.00886145 0.0502558i
\(385\) 0 0
\(386\) 13.1557 + 4.78828i 0.669607 + 0.243717i
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) −5.00000 + 8.66025i −0.253837 + 0.439658i
\(389\) 13.7888 11.5702i 0.699120 0.586631i −0.222403 0.974955i \(-0.571390\pi\)
0.921523 + 0.388324i \(0.126946\pi\)
\(390\) 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
\(396\) −11.2763 + 4.10424i −0.566656 + 0.206246i
\(397\) 15.3209 + 12.8558i 0.768933 + 0.645212i 0.940436 0.339972i \(-0.110418\pi\)
−0.171502 + 0.985184i \(0.554862\pi\)
\(398\) 11.0000 0.551380
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(402\) −4.69846 + 1.71010i −0.234338 + 0.0852921i
\(403\) −3.47296 19.6962i −0.173001 0.981135i
\(404\) 3.12567 17.7265i 0.155508 0.881928i
\(405\) 0 0
\(406\) −4.50000 7.79423i −0.223331 0.386821i
\(407\) −6.00000 + 10.3923i −0.297409 + 0.515127i
\(408\) −2.29813 + 1.92836i −0.113775 + 0.0954682i
\(409\) −24.5134 + 20.5692i −1.21211 + 1.01708i −0.212911 + 0.977072i \(0.568295\pi\)
−0.999199 + 0.0400102i \(0.987261\pi\)
\(410\) 0 0
\(411\) −4.50000 7.79423i −0.221969 0.384461i
\(412\) 13.1557 + 4.78828i 0.648135 + 0.235902i
\(413\) 1.56283 8.86327i 0.0769020 0.436133i
\(414\) −1.04189 5.90885i −0.0512061 0.290404i
\(415\) 0 0
\(416\) −3.83022 3.21394i −0.187792 0.157576i
\(417\) 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
\(421\) 15.9748 5.81434i 0.778563 0.283374i 0.0779896 0.996954i \(-0.475150\pi\)
0.700573 + 0.713580i \(0.252928\pi\)
\(422\) −0.868241 4.92404i −0.0422653 0.239698i
\(423\) 0 0
\(424\) −2.81908 1.02606i −0.136907 0.0498299i
\(425\) 7.50000 + 12.9904i 0.363803 + 0.630126i
\(426\) 3.00000 5.19615i 0.145350 0.251754i
\(427\) 7.66044 6.42788i 0.370715 0.311067i
\(428\) 6.89440 5.78509i 0.333253 0.279633i
\(429\) 15.0000 25.9808i 0.724207 1.25436i
\(430\) 0 0
\(431\) 5.63816 + 2.05212i 0.271580 + 0.0988472i 0.474221 0.880406i \(-0.342730\pi\)
−0.202640 + 0.979253i \(0.564952\pi\)
\(432\) 0.868241 4.92404i 0.0417733 0.236908i
\(433\) −0.347296 1.96962i −0.0166900 0.0946537i 0.975325 0.220774i \(-0.0708584\pi\)
−0.992015 + 0.126121i \(0.959747\pi\)
\(434\) 3.75877 1.36808i 0.180427 0.0656700i
\(435\) 0 0
\(436\) −11.0000 −0.526804
\(437\) 0 0
\(438\) 7.00000 0.334473
\(439\) 21.4492 + 17.9981i 1.02372 + 0.859000i 0.990090 0.140434i \(-0.0448499\pi\)
0.0336266 + 0.999434i \(0.489294\pi\)
\(440\) 0 0
\(441\) 2.08378 + 11.8177i 0.0992275 + 0.562747i
\(442\) −2.60472 + 14.7721i −0.123894 + 0.702638i
\(443\) 16.9145 + 6.15636i 0.803631 + 0.292498i 0.710990 0.703202i \(-0.248247\pi\)
0.0926405 + 0.995700i \(0.470469\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) 0 0
\(446\) −19.9172 + 16.7125i −0.943105 + 0.791359i
\(447\) 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 \(0.972967\pi\)
\(450\) −9.39693 3.42020i −0.442975 0.161230i
\(451\) 0 0
\(452\) −1.04189 5.90885i −0.0490063 0.277929i
\(453\) 9.39693 3.42020i 0.441506 0.160695i
\(454\) 11.4907 + 9.64181i 0.539284 + 0.452513i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −16.8530 14.1413i −0.787488 0.660781i
\(459\) −14.0954 + 5.13030i −0.657916 + 0.239462i
\(460\) 0 0
\(461\) −2.08378 + 11.8177i −0.0970512 + 0.550405i 0.897048 + 0.441933i \(0.145707\pi\)
−0.994099 + 0.108472i \(0.965404\pi\)
\(462\) 5.63816 + 2.05212i 0.262311 + 0.0954733i
\(463\) 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
\(466\) −4.59627 + 3.85673i −0.212918 + 0.178659i
\(467\) −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
\(469\) −4.69846 1.71010i −0.216955 0.0789651i
\(470\) 0 0
\(471\) 3.82026 + 21.6658i 0.176028 + 0.998306i
\(472\) 8.45723 3.07818i 0.389276 0.141685i
\(473\) −36.7701 30.8538i −1.69069 1.41866i
\(474\) −10.0000 −0.459315
\(475\) 0 0
\(476\) −3.00000 −0.137505
\(477\) −4.59627 3.85673i −0.210449 0.176587i
\(478\) 19.7335 7.18242i 0.902591 0.328516i
\(479\) 6.25133 + 35.4531i 0.285631 + 1.61989i 0.703024 + 0.711166i \(0.251833\pi\)
−0.417393 + 0.908726i \(0.637056\pi\)
\(480\) 0 0
\(481\) −9.39693 3.42020i −0.428463 0.155948i
\(482\) 4.00000 + 6.92820i 0.182195 + 0.315571i
\(483\) −1.50000 + 2.59808i −0.0682524 + 0.118217i
\(484\) 19.1511 16.0697i 0.870505 0.730440i
\(485\) 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 \(0.818904\pi\)
\(488\) 9.39693 + 3.42020i 0.425379 + 0.154825i
\(489\) −3.47296 + 19.6962i −0.157053 + 0.890691i
\(490\) 0 0
\(491\) 33.8289 12.3127i 1.52668 0.555666i 0.563873 0.825861i \(-0.309311\pi\)
0.962805 + 0.270196i \(0.0870885\pi\)
\(492\) 0 0
\(493\) −27.0000 −1.21602
\(494\) 0 0
\(495\) 0 0
\(496\) 3.06418 + 2.57115i 0.137586 + 0.115448i
\(497\) 5.63816 2.05212i 0.252906 0.0920502i
\(498\) 1.04189 + 5.90885i 0.0466882 + 0.264782i
\(499\) −0.694593 + 3.93923i −0.0310942 + 0.176344i −0.996400 0.0847787i \(-0.972982\pi\)
0.965306 + 0.261123i \(0.0840928\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) −3.00000 + 5.19615i −0.133897 + 0.231916i
\(503\) −16.0869 + 13.4985i −0.717281 + 0.601870i −0.926632 0.375970i \(-0.877309\pi\)
0.209351 + 0.977841i \(0.432865\pi\)
\(504\) 1.53209 1.28558i 0.0682447 0.0572641i
\(505\) 0 0
\(506\) 9.00000 + 15.5885i 0.400099 + 0.692991i
\(507\) 11.2763 + 4.10424i 0.500799 + 0.182276i
\(508\) −0.347296 + 1.96962i −0.0154088 + 0.0873876i
\(509\) −5.20945 29.5442i −0.230905 1.30953i −0.851069 0.525053i \(-0.824045\pi\)
0.620165 0.784472i \(-0.287066\pi\)
\(510\) 0 0
\(511\) 5.36231 + 4.49951i 0.237215 + 0.199047i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) 7.51754 2.73616i 0.330941 0.120453i
\(517\) 0 0
\(518\) 0.347296 1.96962i 0.0152593 0.0865399i
\(519\) −5.63816 2.05212i −0.247488 0.0900781i
\(520\) 0 0
\(521\) −18.0000 + 31.1769i −0.788594 + 1.36589i 0.138234 + 0.990400i \(0.455857\pi\)
−0.926828 + 0.375486i \(0.877476\pi\)
\(522\) 13.7888 11.5702i 0.603519 0.506413i
\(523\) −8.42649 + 7.07066i −0.368465 + 0.309179i −0.808154 0.588971i \(-0.799533\pi\)
0.439689 + 0.898150i \(0.355089\pi\)
\(524\) 0 0
\(525\) 2.50000 + 4.33013i 0.109109 + 0.188982i
\(526\) −22.5526 8.20848i −0.983341 0.357907i
\(527\) 2.08378 11.8177i 0.0907708 0.514787i
\(528\) 1.04189 + 5.90885i 0.0453424 + 0.257150i
\(529\) 13.1557 4.78828i 0.571987 0.208186i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) 0 0
\(534\) −9.19253 7.71345i −0.397800 0.333794i
\(535\) 0 0
\(536\) −0.868241 4.92404i −0.0375023 0.212686i
\(537\) 0 0
\(538\) −5.63816 2.05212i −0.243078 0.0884732i
\(539\) −18.0000 31.1769i −0.775315 1.34288i
\(540\) 0 0
\(541\) 1.53209 1.28558i 0.0658696 0.0552712i −0.609258 0.792972i \(-0.708533\pi\)
0.675128 + 0.737701i \(0.264088\pi\)
\(542\) 8.42649 7.07066i 0.361949 0.303711i
\(543\) −1.00000 + 1.73205i −0.0429141 + 0.0743294i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) −0.868241 + 4.92404i −0.0371573 + 0.210729i
\(547\) −7.64052 43.3315i −0.326685 1.85272i −0.497559 0.867430i \(-0.665770\pi\)
0.170874 0.985293i \(-0.445341\pi\)
\(548\) 8.45723 3.07818i 0.361275 0.131493i
\(549\) 15.3209 + 12.8558i 0.653880 + 0.548670i
\(550\) 30.0000 1.27920
\(551\) 0 0
\(552\) −3.00000 −0.127688
\(553\) −7.66044 6.42788i −0.325755 0.273341i
\(554\) −7.51754 + 2.73616i −0.319390 + 0.116248i
\(555\) 0 0
\(556\) −0.694593 + 3.93923i −0.0294573 + 0.167061i
\(557\) −22.5526 8.20848i −0.955585 0.347805i −0.183283 0.983060i \(-0.558673\pi\)
−0.772302 + 0.635256i \(0.780895\pi\)
\(558\) 4.00000 + 6.92820i 0.169334 + 0.293294i
\(559\) 20.0000 34.6410i 0.845910 1.46516i
\(560\) 0 0
\(561\) 13.7888 11.5702i 0.582164 0.488493i
\(562\) 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
\(566\) −3.82026 21.6658i −0.160578 0.910680i
\(567\) 0.939693 0.342020i 0.0394634 0.0143635i
\(568\) 4.59627 + 3.85673i 0.192855 + 0.161825i
\(569\) 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 \(0.526673\pi\)
\(572\) 22.9813 + 19.2836i 0.960898 + 0.806289i
\(573\) 2.81908 1.02606i 0.117769 0.0428643i
\(574\) 0 0
\(575\) −2.60472 + 14.7721i −0.108624 + 0.616040i
\(576\) 1.87939 + 0.684040i 0.0783077 + 0.0285017i
\(577\) −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
\(579\) 10.7246 8.99903i 0.445700 0.373987i
\(580\) 0 0
\(581\) −3.00000 + 5.19615i −0.124461 + 0.215573i
\(582\) 5.00000 + 8.66025i 0.207257 + 0.358979i
\(583\) 16.9145 + 6.15636i 0.700526 + 0.254970i
\(584\) −1.21554 + 6.89365i −0.0502993 + 0.285261i
\(585\) 0 0
\(586\) −19.7335 + 7.18242i −0.815185 + 0.296703i
\(587\) −9.19253 7.71345i −0.379416 0.318368i 0.433057 0.901367i \(-0.357435\pi\)
−0.812473 + 0.582998i \(0.801879\pi\)
\(588\) 6.00000 0.247436
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.87939 0.684040i 0.0772423 0.0281139i
\(593\) −5.20945 29.5442i −0.213926 1.21324i −0.882760 0.469824i \(-0.844317\pi\)
0.668834 0.743412i \(-0.266794\pi\)
\(594\) −5.20945 + 29.5442i −0.213746 + 1.21221i
\(595\) 0 0
\(596\) 0 0
\(597\) 5.50000 9.52628i 0.225100 0.389885i
\(598\) −11.4907 + 9.64181i −0.469888 + 0.394283i
\(599\) 18.3851 15.4269i 0.751193 0.630326i −0.184625 0.982809i \(-0.559107\pi\)
0.935818 + 0.352483i \(0.114663\pi\)
\(600\) −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 \(-0.360139\pi\)
\(602\) 7.51754 + 2.73616i 0.306392 + 0.111518i
\(603\) 1.73648 9.84808i 0.0707150 0.401045i
\(604\) 1.73648 + 9.84808i 0.0706564 + 0.400713i
\(605\) 0 0
\(606\) −13.7888 11.5702i −0.560132 0.470006i
\(607\) 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
\(612\) −1.04189 5.90885i −0.0421159 0.238851i
\(613\) 0.347296 1.96962i 0.0140272 0.0795520i −0.976991 0.213282i \(-0.931585\pi\)
0.991018 + 0.133730i \(0.0426956\pi\)
\(614\) 18.7939 + 6.84040i 0.758458 + 0.276056i
\(615\) 0 0
\(616\) −3.00000 + 5.19615i −0.120873 + 0.209359i
\(617\) −4.59627 + 3.85673i −0.185039 + 0.155266i −0.730602 0.682804i \(-0.760760\pi\)
0.545563 + 0.838070i \(0.316316\pi\)
\(618\) 10.7246 8.99903i 0.431408 0.361994i
\(619\) 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
\(621\) −14.0954 5.13030i −0.565628 0.205872i
\(622\) −3.64661 + 20.6810i −0.146216 + 0.829231i
\(623\) −2.08378 11.8177i −0.0834848 0.473466i
\(624\) −4.69846 + 1.71010i −0.188089 + 0.0684588i
\(625\) 19.1511 + 16.0697i 0.766044 + 0.642788i
\(626\) −19.0000 −0.759393
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −4.59627 3.85673i −0.183265 0.153778i
\(630\) 0 0
\(631\) −2.77837 15.7569i −0.110605 0.627273i −0.988833 0.149030i \(-0.952385\pi\)
0.878227 0.478243i \(-0.158726\pi\)
\(632\) 1.73648 9.84808i 0.0690735 0.391735i
\(633\) −4.69846 1.71010i −0.186747 0.0679704i
\(634\) −4.50000 7.79423i −0.178718 0.309548i
\(635\) 0 0
\(636\) −2.29813 + 1.92836i −0.0911269 + 0.0764646i
\(637\) 22.9813 19.2836i 0.910554 0.764045i
\(638\) −27.0000 + 46.7654i −1.06894 + 1.85146i
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) 0 0
\(641\) −1.04189 + 5.90885i −0.0411521 + 0.233385i −0.998446 0.0557321i \(-0.982251\pi\)
0.957294 + 0.289118i \(0.0933618\pi\)
\(642\) −1.56283 8.86327i −0.0616801 0.349805i
\(643\) 20.6732 7.52444i 0.815273 0.296735i 0.0994728 0.995040i \(-0.468284\pi\)
0.715800 + 0.698305i \(0.246062\pi\)
\(644\) −2.29813 1.92836i −0.0905591 0.0759881i
\(645\) 0 0
\(646\) 0 0
\(647\) 27.0000 1.06148 0.530740 0.847535i \(-0.321914\pi\)
0.530740 + 0.847535i \(0.321914\pi\)
\(648\) 0.766044 + 0.642788i 0.0300931 + 0.0252511i
\(649\) −50.7434 + 18.4691i −1.99185 + 0.724975i
\(650\) 4.34120 + 24.6202i 0.170276 + 0.965683i
\(651\) 0.694593 3.93923i 0.0272232 0.154391i
\(652\) −18.7939 6.84040i −0.736024 0.267891i
\(653\) −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
\(659\) −42.2862 15.3909i −1.64724 0.599545i −0.658953 0.752184i \(-0.729001\pi\)
−0.988282 + 0.152639i \(0.951223\pi\)
\(660\) 0 0
\(661\) 2.25743 + 12.8025i 0.0878037 + 0.497960i 0.996716 + 0.0809729i \(0.0258027\pi\)
−0.908913 + 0.416987i \(0.863086\pi\)
\(662\) −0.939693 + 0.342020i −0.0365222 + 0.0132930i
\(663\) 11.4907 + 9.64181i 0.446261 + 0.374457i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) −20.6832 17.3553i −0.800857 0.671999i
\(668\) 11.2763 4.10424i 0.436294 0.158798i
\(669\) 4.51485 + 25.6050i 0.174554 + 0.989947i
\(670\) 0 0
\(671\) −56.3816 20.5212i −2.17659 0.792212i
\(672\) −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 \(-0.155549\pi\)
\(674\) 3.06418 2.57115i 0.118028 0.0990370i
\(675\) −19.1511 + 16.0697i −0.737127 + 0.618523i
\(676\) −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 \(-0.385315\pi\)
\(678\) −5.63816 2.05212i −0.216532 0.0788112i
\(679\) −1.73648 + 9.84808i −0.0666401 + 0.377935i
\(680\) 0 0
\(681\) 14.0954 5.13030i 0.540136 0.196594i
\(682\) −18.3851 15.4269i −0.704001 0.590727i
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 9.95858 + 8.35624i 0.380220 + 0.319043i
\(687\) −20.6732 + 7.52444i −0.788733 + 0.287075i
\(688\) 1.38919 + 7.87846i 0.0529622 + 0.300364i
\(689\) −2.60472 + 14.7721i −0.0992320 + 0.562773i
\(690\) 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
\(693\) −9.19253 + 7.71345i −0.349195 + 0.293010i
\(694\) 13.7888 11.5702i 0.523416 0.439198i
\(695\) 0 0
\(696\) −4.50000 7.79423i −0.170572 0.295439i
\(697\) 0 0
\(698\) −1.73648 + 9.84808i −0.0657268 + 0.372755i
\(699\) 1.04189 + 5.90885i 0.0394079 + 0.223493i
\(700\) −4.69846 + 1.71010i −0.177585 + 0.0646357i
\(701\) 9.19253 + 7.71345i 0.347197 + 0.291333i 0.799663 0.600448i \(-0.205011\pi\)
−0.452466 + 0.891782i \(0.649456\pi\)
\(702\) −25.0000 −0.943564
\(703\) 0 0
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) 14.0954 5.13030i 0.530487 0.193081i
\(707\) −3.12567 17.7265i −0.117553 0.666675i
\(708\) 1.56283 8.86327i 0.0587349 0.333102i
\(709\) 9.39693 + 3.42020i 0.352909 + 0.128448i 0.512391 0.858753i \(-0.328760\pi\)
−0.159482 + 0.987201i \(0.550982\pi\)
\(710\) 0 0
\(711\) 10.0000 17.3205i 0.375029 0.649570i
\(712\) 9.19253 7.71345i 0.344505 0.289074i
\(713\) 9.19253 7.71345i 0.344263 0.288871i
\(714\) −1.50000 + 2.59808i −0.0561361 + 0.0972306i
\(715\) 0 0
\(716\) 0 0
\(717\) 3.64661 20.6810i 0.136185 0.772345i
\(718\) 3.64661 + 20.6810i 0.136090 + 0.771807i
\(719\) −36.6480 + 13.3388i −1.36674 + 0.497453i −0.918132 0.396276i \(-0.870302\pi\)
−0.448609 + 0.893728i \(0.648080\pi\)
\(720\) 0 0
\(721\) 14.0000 0.521387
\(722\) 0 0
\(723\) 8.00000 0.297523
\(724\) −1.53209 1.28558i −0.0569396 0.0477780i
\(725\) −42.2862 + 15.3909i −1.57047 + 0.571604i
\(726\) −4.34120 24.6202i −0.161117 0.913741i
\(727\) −6.42498 + 36.4379i −0.238289 + 1.35141i 0.597285 + 0.802029i \(0.296246\pi\)
−0.835574 + 0.549377i \(0.814865\pi\)
\(728\) −4.69846 1.71010i −0.174137 0.0633805i
\(729\) −6.50000 11.2583i −0.240741 0.416975i
\(730\) 0 0
\(731\) 18.3851 15.4269i 0.679996 0.570585i
\(732\) 7.66044 6.42788i 0.283138 0.237581i
\(733\) −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
\(736\) 0.520945 2.95442i 0.0192023 0.108901i
\(737\) 5.20945 + 29.5442i 0.191892 + 1.08828i
\(738\) 0 0
\(739\) −12.2567 10.2846i −0.450870 0.378325i 0.388888 0.921285i \(-0.372859\pi\)
−0.839759 + 0.542960i \(0.817304\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.00000 −0.110133
\(743\) 27.5776 + 23.1404i 1.01172 + 0.848937i 0.988565 0.150795i \(-0.0481832\pi\)
0.0231589 + 0.999732i \(0.492628\pi\)
\(744\) 3.75877 1.36808i 0.137803 0.0501563i
\(745\) 0 0
\(746\) −3.99391 + 22.6506i −0.146227 + 0.829297i
\(747\) −11.2763 4.10424i −0.412579 0.150166i
\(748\) 9.00000 + 15.5885i 0.329073 + 0.569970i
\(749\) 4.50000 7.79423i 0.164426 0.284795i
\(750\) 0 0
\(751\) 30.6418 25.7115i 1.11813 0.938226i 0.119626 0.992819i \(-0.461831\pi\)
0.998509 + 0.0545929i \(0.0173861\pi\)
\(752\) 0 0
\(753\) 3.00000 + 5.19615i 0.109326 + 0.189358i
\(754\) −42.2862 15.3909i −1.53997 0.560504i
\(755\) 0 0
\(756\) −0.868241 4.92404i −0.0315776 0.179086i
\(757\) −1.87939 + 0.684040i −0.0683074 + 0.0248619i −0.375948 0.926641i \(-0.622683\pi\)
0.307640 + 0.951503i \(0.400461\pi\)
\(758\) 5.36231 + 4.49951i 0.194768 + 0.163430i
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 1.53209 + 1.28558i 0.0555017 + 0.0465715i
\(763\) −10.3366 + 3.76222i −0.374211 + 0.136202i
\(764\) 0.520945 + 2.95442i 0.0188471 + 0.106887i
\(765\) 0 0
\(766\) 16.9145 + 6.15636i 0.611145 + 0.222438i
\(767\) −22.5000 38.9711i −0.812428 1.40717i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 3.83022 3.21394i 0.138121 0.115898i −0.571109 0.820874i \(-0.693487\pi\)
0.709231 + 0.704976i \(0.249042\pi\)
\(770\) 0 0
\(771\) −6.00000 + 10.3923i −0.216085 + 0.374270i
\(772\) 7.00000 + 12.1244i 0.251936 + 0.436365i
\(773\) 47.9243 + 17.4430i 1.72372 + 0.627382i 0.998152 0.0607702i \(-0.0193557\pi\)
0.725566 + 0.688152i \(0.241578\pi\)
\(774\) −2.77837 + 15.7569i −0.0998665 + 0.566371i
\(775\) −3.47296 19.6962i −0.124753 0.707507i
\(776\) −9.39693 + 3.42020i −0.337330 + 0.122778i
\(777\) −1.53209 1.28558i −0.0549634 0.0461198i
\(778\) 18.0000 0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) −27.5776 23.1404i −0.986804 0.828027i
\(782\) −8.45723 + 3.07818i −0.302430 + 0.110076i
\(783\) −7.81417 44.3163i −0.279256 1.58374i
\(784\) −1.04189 + 5.90885i −0.0372103 + 0.211030i
\(785\) 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 \(0.980335\pi\)
\(788\)