Properties

Label 722.2.e.f.389.1
Level 722
Weight 2
Character 722.389
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 389.1
Root \(-0.766044 + 0.642788i\)
Character \(\chi\) = 722.389
Dual form 722.2.e.f.245.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +O(q^{10})\) \(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +(3.00000 + 5.19615i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.83022 + 3.21394i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.520945 + 2.95442i) q^{17} +2.00000 q^{18} +(-0.173648 - 0.984808i) q^{21} +(4.59627 - 3.85673i) q^{22} +(-2.81908 + 1.02606i) q^{23} +(0.939693 + 0.342020i) q^{24} +(-3.83022 - 3.21394i) q^{25} +(2.50000 - 4.33013i) q^{26} +(2.50000 + 4.33013i) q^{27} +(-0.173648 + 0.984808i) q^{28} +(1.56283 - 8.86327i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(5.63816 + 2.05212i) q^{33} +(2.81908 - 1.02606i) q^{34} +(-0.347296 - 1.96962i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(-0.939693 + 0.342020i) q^{42} +(-7.51754 - 2.73616i) q^{43} +(-4.59627 - 3.85673i) q^{44} +(1.50000 + 2.59808i) q^{46} +(0.173648 - 0.984808i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(2.29813 + 1.92836i) q^{51} +(-4.69846 - 1.71010i) q^{52} +(2.81908 - 1.02606i) q^{53} +(3.83022 - 3.21394i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(1.56283 + 8.86327i) q^{59} +(9.39693 - 3.42020i) q^{61} +(-3.75877 - 1.36808i) q^{62} +(1.53209 + 1.28558i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.04189 - 5.90885i) q^{66} +(0.868241 - 4.92404i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(5.63816 + 2.05212i) q^{71} +(-1.87939 + 0.684040i) q^{72} +(-5.36231 + 4.49951i) q^{73} +(-0.347296 - 1.96962i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(-0.868241 - 4.92404i) q^{78} +(-7.66044 + 6.42788i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(3.00000 - 5.19615i) q^{83} +(0.500000 + 0.866025i) q^{84} +(-1.38919 + 7.87846i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-9.19253 - 7.71345i) q^{89} +(4.69846 - 1.71010i) q^{91} +(2.29813 - 1.92836i) q^{92} +(-0.694593 - 3.93923i) q^{93} -1.00000 q^{96} +(-1.73648 - 9.84808i) q^{97} +(4.59627 - 3.85673i) q^{98} +(-11.2763 + 4.10424i) 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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 0.984808i −0.122788 0.696364i
\(3\) 0.766044 0.642788i 0.442276 0.371114i −0.394284 0.918989i \(-0.629007\pi\)
0.836560 + 0.547875i \(0.184563\pi\)
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(6\) −0.766044 0.642788i −0.312736 0.262417i
\(7\) 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
\(9\) −0.347296 + 1.96962i −0.115765 + 0.656539i
\(10\) 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
\(13\) 3.83022 + 3.21394i 1.06231 + 0.891386i 0.994334 0.106301i \(-0.0339006\pi\)
0.0679785 + 0.997687i \(0.478345\pi\)
\(14\) −0.939693 0.342020i −0.251143 0.0914087i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) 0.520945 + 2.95442i 0.126348 + 0.716553i 0.980498 + 0.196527i \(0.0629665\pi\)
−0.854151 + 0.520026i \(0.825922\pi\)
\(18\) 2.00000 0.471405
\(19\) 0 0
\(20\) 0 0
\(21\) −0.173648 0.984808i −0.0378931 0.214903i
\(22\) 4.59627 3.85673i 0.979927 0.822257i
\(23\) −2.81908 + 1.02606i −0.587818 + 0.213948i −0.618770 0.785573i \(-0.712369\pi\)
0.0309512 + 0.999521i \(0.490146\pi\)
\(24\) 0.939693 + 0.342020i 0.191814 + 0.0698146i
\(25\) −3.83022 3.21394i −0.766044 0.642788i
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 2.50000 + 4.33013i 0.481125 + 0.833333i
\(28\) −0.173648 + 0.984808i −0.0328164 + 0.186111i
\(29\) 1.56283 8.86327i 0.290211 1.64587i −0.395844 0.918318i \(-0.629548\pi\)
0.686055 0.727550i \(-0.259341\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −0.766044 0.642788i −0.135419 0.113630i
\(33\) 5.63816 + 2.05212i 0.981477 + 0.357228i
\(34\) 2.81908 1.02606i 0.483468 0.175968i
\(35\) 0 0
\(36\) −0.347296 1.96962i −0.0578827 0.328269i
\(37\) 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 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(42\) −0.939693 + 0.342020i −0.144998 + 0.0527749i
\(43\) −7.51754 2.73616i −1.14641 0.417261i −0.302188 0.953248i \(-0.597717\pi\)
−0.844226 + 0.535988i \(0.819939\pi\)
\(44\) −4.59627 3.85673i −0.692913 0.581423i
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(48\) 0.173648 0.984808i 0.0250640 0.142145i
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) −2.50000 + 4.33013i −0.353553 + 0.612372i
\(51\) 2.29813 + 1.92836i 0.321803 + 0.270025i
\(52\) −4.69846 1.71010i −0.651560 0.237148i
\(53\) 2.81908 1.02606i 0.387230 0.140940i −0.141066 0.990000i \(-0.545053\pi\)
0.528297 + 0.849060i \(0.322831\pi\)
\(54\) 3.83022 3.21394i 0.521227 0.437362i
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) 1.56283 + 8.86327i 0.203464 + 1.15390i 0.899839 + 0.436222i \(0.143684\pi\)
−0.696376 + 0.717678i \(0.745205\pi\)
\(60\) 0 0
\(61\) 9.39693 3.42020i 1.20315 0.437912i 0.338829 0.940848i \(-0.389969\pi\)
0.864324 + 0.502936i \(0.167747\pi\)
\(62\) −3.75877 1.36808i −0.477364 0.173746i
\(63\) 1.53209 + 1.28558i 0.193025 + 0.161967i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) 1.04189 5.90885i 0.128248 0.727329i
\(67\) 0.868241 4.92404i 0.106073 0.601567i −0.884714 0.466134i \(-0.845646\pi\)
0.990787 0.135433i \(-0.0432425\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) −1.50000 + 2.59808i −0.180579 + 0.312772i
\(70\) 0 0
\(71\) 5.63816 + 2.05212i 0.669126 + 0.243542i 0.654172 0.756346i \(-0.273017\pi\)
0.0149545 + 0.999888i \(0.495240\pi\)
\(72\) −1.87939 + 0.684040i −0.221488 + 0.0806149i
\(73\) −5.36231 + 4.49951i −0.627611 + 0.526628i −0.900186 0.435506i \(-0.856569\pi\)
0.272575 + 0.962135i \(0.412125\pi\)
\(74\) −0.347296 1.96962i −0.0403724 0.228963i
\(75\) −5.00000 −0.577350
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) −0.868241 4.92404i −0.0983089 0.557538i
\(79\) −7.66044 + 6.42788i −0.861867 + 0.723193i −0.962369 0.271744i \(-0.912400\pi\)
0.100502 + 0.994937i \(0.467955\pi\)
\(80\) 0 0
\(81\) −0.939693 0.342020i −0.104410 0.0380022i
\(82\) 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
\(86\) −1.38919 + 7.87846i −0.149800 + 0.849556i
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) −9.19253 7.71345i −0.974407 0.817624i 0.00882955 0.999961i \(-0.497189\pi\)
−0.983236 + 0.182337i \(0.941634\pi\)
\(90\) 0 0
\(91\) 4.69846 1.71010i 0.492533 0.179267i
\(92\) 2.29813 1.92836i 0.239597 0.201046i
\(93\) −0.694593 3.93923i −0.0720259 0.408479i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −1.73648 9.84808i −0.176313 0.999921i −0.936617 0.350354i \(-0.886061\pi\)
0.760304 0.649567i \(-0.225050\pi\)
\(98\) 4.59627 3.85673i 0.464293 0.389588i
\(99\) −11.2763 + 4.10424i −1.13331 + 0.412492i
\(100\) 4.69846 + 1.71010i 0.469846 + 0.171010i
\(101\) 13.7888 + 11.5702i 1.37204 + 1.15128i 0.972055 + 0.234753i \(0.0754280\pi\)
0.399982 + 0.916523i \(0.369016\pi\)
\(102\) 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 \(-0.408938\pi\)
\(104\) −0.868241 + 4.92404i −0.0851380 + 0.482842i
\(105\) 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 \(0.0234039\pi\)
\(108\) −3.83022 3.21394i −0.368563 0.309261i
\(109\) −10.3366 3.76222i −0.990069 0.360355i −0.204322 0.978904i \(-0.565499\pi\)
−0.785747 + 0.618548i \(0.787721\pi\)
\(110\) 0 0
\(111\) 1.53209 1.28558i 0.145419 0.122021i
\(112\) −0.173648 0.984808i −0.0164082 0.0930556i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.56283 + 8.86327i 0.145105 + 0.822934i
\(117\) −7.66044 + 6.42788i −0.708208 + 0.594257i
\(118\) 8.45723 3.07818i 0.778551 0.283370i
\(119\) 2.81908 + 1.02606i 0.258424 + 0.0940588i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) −5.00000 8.66025i −0.452679 0.784063i
\(123\) 0 0
\(124\) −0.694593 + 3.93923i −0.0623763 + 0.353753i
\(125\) 0 0
\(126\) 1.00000 1.73205i 0.0890871 0.154303i
\(127\) 1.53209 + 1.28558i 0.135951 + 0.114076i 0.708227 0.705984i \(-0.249495\pi\)
−0.572276 + 0.820061i \(0.693940\pi\)
\(128\) 0.939693 + 0.342020i 0.0830579 + 0.0302306i
\(129\) −7.51754 + 2.73616i −0.661883 + 0.240906i
\(130\) 0 0
\(131\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) −2.29813 + 1.92836i −0.197063 + 0.165356i
\(137\) 8.45723 3.07818i 0.722550 0.262987i 0.0455422 0.998962i \(-0.485498\pi\)
0.677008 + 0.735976i \(0.263276\pi\)
\(138\) 2.81908 + 1.02606i 0.239976 + 0.0873441i
\(139\) −3.06418 2.57115i −0.259900 0.218082i 0.503521 0.863983i \(-0.332038\pi\)
−0.763421 + 0.645901i \(0.776482\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.04189 5.90885i 0.0874334 0.495859i
\(143\) −5.20945 + 29.5442i −0.435636 + 2.47061i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 0 0
\(146\) 5.36231 + 4.49951i 0.443788 + 0.372382i
\(147\) 5.63816 + 2.05212i 0.465027 + 0.169256i
\(148\) −1.87939 + 0.684040i −0.154485 + 0.0562278i
\(149\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(150\) 0.868241 + 4.92404i 0.0708916 + 0.402046i
\(151\) −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
\(154\) −1.04189 5.90885i −0.0839578 0.476148i
\(155\) 0 0
\(156\) −4.69846 + 1.71010i −0.376178 + 0.136918i
\(157\) 20.6732 + 7.52444i 1.64990 + 0.600516i 0.988729 0.149716i \(-0.0478359\pi\)
0.661175 + 0.750232i \(0.270058\pi\)
\(158\) 7.66044 + 6.42788i 0.609432 + 0.511374i
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) 0 0
\(161\) −0.520945 + 2.95442i −0.0410562 + 0.232841i
\(162\) −0.173648 + 0.984808i −0.0136431 + 0.0773738i
\(163\) −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
\(166\) −5.63816 2.05212i −0.437606 0.159275i
\(167\) −11.2763 + 4.10424i −0.872587 + 0.317596i −0.739214 0.673470i \(-0.764803\pi\)
−0.133373 + 0.991066i \(0.542581\pi\)
\(168\) 0.766044 0.642788i 0.0591016 0.0495921i
\(169\) 2.08378 + 11.8177i 0.160291 + 0.909053i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 1.04189 + 5.90885i 0.0792134 + 0.449241i 0.998456 + 0.0555496i \(0.0176911\pi\)
−0.919243 + 0.393692i \(0.871198\pi\)
\(174\) −6.89440 + 5.78509i −0.522663 + 0.438566i
\(175\) −4.69846 + 1.71010i −0.355170 + 0.129271i
\(176\) 5.63816 + 2.05212i 0.424992 + 0.154684i
\(177\) 6.89440 + 5.78509i 0.518215 + 0.434834i
\(178\) −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
\(181\) 0.347296 1.96962i 0.0258143 0.146400i −0.969176 0.246368i \(-0.920763\pi\)
0.994991 + 0.0999676i \(0.0318739\pi\)
\(182\) −2.50000 4.33013i −0.185312 0.320970i
\(183\) 5.00000 8.66025i 0.369611 0.640184i
\(184\) −2.29813 1.92836i −0.169421 0.142161i
\(185\) 0 0
\(186\) −3.75877 + 1.36808i −0.275606 + 0.100313i
\(187\) −13.7888 + 11.5702i −1.00834 + 0.846095i
\(188\) 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 \(0.465384\pi\)
\(192\) 0.173648 + 0.984808i 0.0125320 + 0.0710724i
\(193\) 10.7246 8.99903i 0.771975 0.647764i −0.169239 0.985575i \(-0.554131\pi\)
0.941214 + 0.337811i \(0.109686\pi\)
\(194\) −9.39693 + 3.42020i −0.674660 + 0.245556i
\(195\) 0 0
\(196\) −4.59627 3.85673i −0.328305 0.275480i
\(197\) 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
\(199\) 1.91013 10.8329i 0.135406 0.767923i −0.839171 0.543868i \(-0.816959\pi\)
0.974576 0.224055i \(-0.0719296\pi\)
\(200\) 0.868241 4.92404i 0.0613939 0.348182i
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) −6.89440 5.78509i −0.483892 0.406034i
\(204\) −2.81908 1.02606i −0.197375 0.0718386i
\(205\) 0 0
\(206\) −10.7246 + 8.99903i −0.747220 + 0.626992i
\(207\) −1.04189 5.90885i −0.0724163 0.410693i
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) 0 0
\(211\) 0.868241 + 4.92404i 0.0597722 + 0.338985i 0.999999 0.00156464i \(-0.000498040\pi\)
−0.940227 + 0.340549i \(0.889387\pi\)
\(212\) −2.29813 + 1.92836i −0.157836 + 0.132441i
\(213\) 5.63816 2.05212i 0.386320 0.140609i
\(214\) −8.45723 3.07818i −0.578125 0.210420i
\(215\) 0 0
\(216\) −2.50000 + 4.33013i −0.170103 + 0.294628i
\(217\) −2.00000 3.46410i −0.135769 0.235159i
\(218\) −1.91013 + 10.8329i −0.129370 + 0.733696i
\(219\) −1.21554 + 6.89365i −0.0821384 + 0.465830i
\(220\) 0 0
\(221\) −7.50000 + 12.9904i −0.504505 + 0.873828i
\(222\) −1.53209 1.28558i −0.102827 0.0862822i
\(223\) −24.4320 8.89252i −1.63609 0.595487i −0.649739 0.760157i \(-0.725122\pi\)
−0.986349 + 0.164670i \(0.947344\pi\)
\(224\) −0.939693 + 0.342020i −0.0627859 + 0.0228522i
\(225\) 7.66044 6.42788i 0.510696 0.428525i
\(226\) −1.04189 5.90885i −0.0693054 0.393051i
\(227\) −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
\(231\) 4.59627 3.85673i 0.302412 0.253754i
\(232\) 8.45723 3.07818i 0.555245 0.202093i
\(233\) 5.63816 + 2.05212i 0.369368 + 0.134439i 0.520033 0.854146i \(-0.325919\pi\)
−0.150666 + 0.988585i \(0.548142\pi\)
\(234\) 7.66044 + 6.42788i 0.500779 + 0.420203i
\(235\) 0 0
\(236\) −4.50000 7.79423i −0.292925 0.507361i
\(237\) −1.73648 + 9.84808i −0.112797 + 0.639701i
\(238\) 0.520945 2.95442i 0.0337678 0.191507i
\(239\) 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
\(241\) 6.12836 + 5.14230i 0.394762 + 0.331245i 0.818465 0.574557i \(-0.194825\pi\)
−0.423703 + 0.905801i \(0.639270\pi\)
\(242\) 23.4923 + 8.55050i 1.51014 + 0.549647i
\(243\) −15.0351 + 5.47232i −0.964501 + 0.351050i
\(244\) −7.66044 + 6.42788i −0.490410 + 0.411503i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) −1.04189 5.90885i −0.0660270 0.374458i
\(250\) 0 0
\(251\) −5.63816 + 2.05212i −0.355877 + 0.129529i −0.513771 0.857927i \(-0.671752\pi\)
0.157894 + 0.987456i \(0.449530\pi\)
\(252\) −1.87939 0.684040i −0.118390 0.0430905i
\(253\) −13.7888 11.5702i −0.866894 0.727411i
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 2.08378 11.8177i 0.129983 0.737167i −0.848241 0.529611i \(-0.822338\pi\)
0.978223 0.207556i \(-0.0665510\pi\)
\(258\) 4.00000 + 6.92820i 0.249029 + 0.431331i
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) 0 0
\(261\) 16.9145 + 6.15636i 1.04698 + 0.381069i
\(262\) 0 0
\(263\) 18.3851 15.4269i 1.13367 0.951264i 0.134458 0.990919i \(-0.457071\pi\)
0.999213 + 0.0396557i \(0.0126261\pi\)
\(264\) 1.04189 + 5.90885i 0.0641238 + 0.363664i
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 0.868241 + 4.92404i 0.0530363 + 0.300784i
\(269\) −4.59627 + 3.85673i −0.280239 + 0.235149i −0.772063 0.635546i \(-0.780775\pi\)
0.491824 + 0.870695i \(0.336331\pi\)
\(270\) 0 0
\(271\) −10.3366 3.76222i −0.627905 0.228539i 0.00841427 0.999965i \(-0.497322\pi\)
−0.636319 + 0.771426i \(0.719544\pi\)
\(272\) 2.29813 + 1.92836i 0.139345 + 0.116924i
\(273\) 2.50000 4.33013i 0.151307 0.262071i
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) 5.20945 29.5442i 0.314141 1.78158i
\(276\) 0.520945 2.95442i 0.0313572 0.177835i
\(277\) −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
\(279\) 6.12836 + 5.14230i 0.366895 + 0.307862i
\(280\) 0 0
\(281\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(282\) 0 0
\(283\) −3.82026 21.6658i −0.227091 1.28790i −0.858647 0.512567i \(-0.828695\pi\)
0.631557 0.775330i \(-0.282416\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 0 0
\(288\) 1.53209 1.28558i 0.0902792 0.0757532i
\(289\) 7.51754 2.73616i 0.442208 0.160951i
\(290\) 0 0
\(291\) −7.66044 6.42788i −0.449063 0.376809i
\(292\) 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 \(0.623128\pi\)
\(294\) 1.04189 5.90885i 0.0607642 0.344611i
\(295\) 0 0
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) −15.0000 + 25.9808i −0.870388 + 1.50756i
\(298\) 0 0
\(299\) −14.0954 5.13030i −0.815157 0.296693i
\(300\) 4.69846 1.71010i 0.271266 0.0987327i
\(301\) −6.12836 + 5.14230i −0.353233 + 0.296397i
\(302\) 1.73648 + 9.84808i 0.0999233 + 0.566693i
\(303\) 18.0000 1.03407
\(304\) 0 0
\(305\) 0 0
\(306\) 1.04189 + 5.90885i 0.0595608 + 0.337786i
\(307\) 15.3209 12.8558i 0.874409 0.733717i −0.0906125 0.995886i \(-0.528882\pi\)
0.965022 + 0.262170i \(0.0844380\pi\)
\(308\) −5.63816 + 2.05212i −0.321264 + 0.116930i
\(309\) −13.1557 4.78828i −0.748401 0.272396i
\(310\) 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
\(313\) −3.29932 + 18.7113i −0.186488 + 1.05763i 0.737540 + 0.675304i \(0.235987\pi\)
−0.924028 + 0.382324i \(0.875124\pi\)
\(314\) 3.82026 21.6658i 0.215590 1.22267i
\(315\) 0 0
\(316\) 5.00000 8.66025i 0.281272 0.487177i
\(317\) −6.89440 5.78509i −0.387228 0.324923i 0.428304 0.903635i \(-0.359111\pi\)
−0.815532 + 0.578712i \(0.803556\pi\)
\(318\) −2.81908 1.02606i −0.158086 0.0575386i
\(319\) 50.7434 18.4691i 2.84109 1.03407i
\(320\) 0 0
\(321\) −1.56283 8.86327i −0.0872289 0.494699i
\(322\) 3.00000 0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −4.34120 24.6202i −0.240807 1.36568i
\(326\) −15.3209 + 12.8558i −0.848546 + 0.712014i
\(327\) −10.3366 + 3.76222i −0.571616 + 0.208051i
\(328\) 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 \(0.824584\pi\)
\(332\) −1.04189 + 5.90885i −0.0571811 + 0.324290i
\(333\) −0.694593 + 3.93923i −0.0380634 + 0.215869i
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) 0 0
\(336\) −0.766044 0.642788i −0.0417912 0.0350669i
\(337\) 3.75877 + 1.36808i 0.204753 + 0.0745241i 0.442361 0.896837i \(-0.354141\pi\)
−0.237608 + 0.971361i \(0.576363\pi\)
\(338\) 11.2763 4.10424i 0.613350 0.223241i
\(339\) 4.59627 3.85673i 0.249635 0.209469i
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) −1.38919 7.87846i −0.0748999 0.424778i
\(345\) 0 0
\(346\) 5.63816 2.05212i 0.303109 0.110323i
\(347\) −16.9145 6.15636i −0.908016 0.330491i −0.154556 0.987984i \(-0.549395\pi\)
−0.753460 + 0.657493i \(0.771617\pi\)
\(348\) 6.89440 + 5.78509i 0.369579 + 0.310113i
\(349\) 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
\(351\) −4.34120 + 24.6202i −0.231716 + 1.31413i
\(352\) 1.04189 5.90885i 0.0555329 0.314943i
\(353\) 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
\(356\) 11.2763 + 4.10424i 0.597643 + 0.217524i
\(357\) 2.81908 1.02606i 0.149201 0.0543049i
\(358\) 0 0
\(359\) 3.64661 + 20.6810i 0.192461 + 1.09150i 0.915989 + 0.401204i \(0.131408\pi\)
−0.723528 + 0.690295i \(0.757481\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −2.00000 −0.105118
\(363\) 4.34120 + 24.6202i 0.227854 + 1.29223i
\(364\) −3.83022 + 3.21394i −0.200758 + 0.168456i
\(365\) 0 0
\(366\) −9.39693 3.42020i −0.491185 0.178777i
\(367\) −21.4492 17.9981i −1.11964 0.939491i −0.121055 0.992646i \(-0.538628\pi\)
−0.998586 + 0.0531551i \(0.983072\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.520945 2.95442i 0.0270461 0.153386i
\(372\) 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 \(0.963641\pi\)
\(374\) 13.7888 + 11.5702i 0.713002 + 0.598280i
\(375\) 0 0
\(376\) 0 0
\(377\) 34.4720 28.9254i 1.77540 1.48974i
\(378\) −0.868241 4.92404i −0.0446575 0.253265i
\(379\) −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
\(382\) −0.520945 2.95442i −0.0266538 0.151161i
\(383\) 13.7888 11.5702i 0.704575 0.591208i −0.218496 0.975838i \(-0.570115\pi\)
0.923071 + 0.384629i \(0.125671\pi\)
\(384\) 0.939693 0.342020i 0.0479535 0.0174536i
\(385\) 0 0
\(386\) −10.7246 8.99903i −0.545869 0.458038i
\(387\) 8.00000 13.8564i 0.406663 0.704361i
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) 3.12567 17.7265i 0.158478 0.898771i −0.797060 0.603901i \(-0.793612\pi\)
0.955537 0.294871i \(-0.0952765\pi\)
\(390\) 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
\(396\) 9.19253 7.71345i 0.461942 0.387616i
\(397\) 3.47296 + 19.6962i 0.174303 + 0.988522i 0.938945 + 0.344067i \(0.111805\pi\)
−0.764642 + 0.644455i \(0.777084\pi\)
\(398\) −11.0000 −0.551380
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(402\) −3.83022 + 3.21394i −0.191034 + 0.160297i
\(403\) 18.7939 6.84040i 0.936188 0.340745i
\(404\) −16.9145 6.15636i −0.841526 0.306290i
\(405\) 0 0
\(406\) −4.50000 + 7.79423i −0.223331 + 0.386821i
\(407\) 6.00000 + 10.3923i 0.297409 + 0.515127i
\(408\) −0.520945 + 2.95442i −0.0257906 + 0.146266i
\(409\) 5.55674 31.5138i 0.274763 1.55826i −0.464950 0.885337i \(-0.653928\pi\)
0.739713 0.672922i \(-0.234961\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) 10.7246 + 8.99903i 0.528364 + 0.443350i
\(413\) 8.45723 + 3.07818i 0.416153 + 0.151467i
\(414\) −5.63816 + 2.05212i −0.277100 + 0.100856i
\(415\) 0 0
\(416\) −0.868241 4.92404i −0.0425690 0.241421i
\(417\) −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
\(421\) 13.0228 10.9274i 0.634690 0.532568i −0.267692 0.963504i \(-0.586261\pi\)
0.902382 + 0.430936i \(0.141817\pi\)
\(422\) 4.69846 1.71010i 0.228718 0.0832464i
\(423\) 0 0
\(424\) 2.29813 + 1.92836i 0.111607 + 0.0936496i
\(425\) 7.50000 12.9904i 0.363803 0.630126i
\(426\) −3.00000 5.19615i −0.145350 0.251754i
\(427\) 1.73648 9.84808i 0.0840342 0.476582i
\(428\) −1.56283 + 8.86327i −0.0755424 + 0.428422i
\(429\) 15.0000 + 25.9808i 0.724207 + 1.25436i
\(430\) 0 0
\(431\) 4.59627 + 3.85673i 0.221394 + 0.185772i 0.746738 0.665118i \(-0.231619\pi\)
−0.525344 + 0.850890i \(0.676063\pi\)
\(432\) 4.69846 + 1.71010i 0.226055 + 0.0822773i
\(433\) −1.87939 + 0.684040i −0.0903175 + 0.0328729i −0.386784 0.922170i \(-0.626414\pi\)
0.296466 + 0.955043i \(0.404192\pi\)
\(434\) −3.06418 + 2.57115i −0.147085 + 0.123419i
\(435\) 0 0
\(436\) 11.0000 0.526804
\(437\) 0 0
\(438\) 7.00000 0.334473
\(439\) −4.86215 27.5746i −0.232058 1.31606i −0.848722 0.528839i \(-0.822628\pi\)
0.616665 0.787226i \(-0.288483\pi\)
\(440\) 0 0
\(441\) −11.2763 + 4.10424i −0.536967 + 0.195440i
\(442\) 14.0954 + 5.13030i 0.670449 + 0.244024i
\(443\) −13.7888 11.5702i −0.655126 0.549716i 0.253496 0.967336i \(-0.418420\pi\)
−0.908621 + 0.417621i \(0.862864\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 0 0
\(446\) −4.51485 + 25.6050i −0.213784 + 1.21243i
\(447\) 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 \(0.0270335\pi\)
\(450\) −7.66044 6.42788i −0.361117 0.303013i
\(451\) 0 0
\(452\) −5.63816 + 2.05212i −0.265197 + 0.0965236i
\(453\) −7.66044 + 6.42788i −0.359919 + 0.302008i
\(454\) 2.60472 + 14.7721i 0.122246 + 0.693290i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 3.82026 + 21.6658i 0.178509 + 1.01237i
\(459\) −11.4907 + 9.64181i −0.536338 + 0.450041i
\(460\) 0 0
\(461\) 11.2763 + 4.10424i 0.525190 + 0.191154i 0.590989 0.806679i \(-0.298737\pi\)
−0.0657993 + 0.997833i \(0.520960\pi\)
\(462\) −4.59627 3.85673i −0.213838 0.179431i
\(463\) 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
\(466\) 1.04189 5.90885i 0.0482646 0.273722i
\(467\) −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
\(469\) −3.83022 3.21394i −0.176863 0.148406i
\(470\) 0 0
\(471\) 20.6732 7.52444i 0.952573 0.346708i
\(472\) −6.89440 + 5.78509i −0.317340 + 0.266280i
\(473\) −8.33511 47.2708i −0.383249 2.17351i
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) −3.00000 −0.137505
\(477\) 1.04189 + 5.90885i 0.0477048 + 0.270547i
\(478\) 16.0869 13.4985i 0.735799 0.617409i
\(479\) −33.8289 + 12.3127i −1.54568 + 0.562583i −0.967400 0.253253i \(-0.918499\pi\)
−0.578283 + 0.815836i \(0.696277\pi\)
\(480\) 0 0
\(481\) 7.66044 + 6.42788i 0.349286 + 0.293086i
\(482\) 4.00000 6.92820i 0.182195 0.315571i
\(483\) 1.50000 + 2.59808i 0.0682524 + 0.118217i
\(484\) 4.34120 24.6202i 0.197327 1.11910i
\(485\) 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 \(0.181096\pi\)
\(488\) 7.66044 + 6.42788i 0.346772 + 0.290976i
\(489\) −18.7939 6.84040i −0.849887 0.309334i
\(490\) 0 0
\(491\) −27.5776 + 23.1404i −1.24456 + 1.04431i −0.247406 + 0.968912i \(0.579578\pi\)
−0.997154 + 0.0753977i \(0.975977\pi\)
\(492\) 0 0
\(493\) 27.0000 1.21602
\(494\) 0 0
\(495\) 0 0
\(496\) −0.694593 3.93923i −0.0311881 0.176877i
\(497\) 4.59627 3.85673i 0.206171 0.172998i
\(498\) −5.63816 + 2.05212i −0.252652 + 0.0919577i
\(499\) 3.75877 + 1.36808i 0.168266 + 0.0612437i 0.424779 0.905297i \(-0.360352\pi\)
−0.256514 + 0.966541i \(0.582574\pi\)
\(500\) 0 0
\(501\) −6.00000 + 10.3923i −0.268060 + 0.464294i
\(502\) 3.00000 + 5.19615i 0.133897 + 0.231916i
\(503\) −3.64661 + 20.6810i −0.162594 + 0.922119i 0.788916 + 0.614501i \(0.210643\pi\)
−0.951510 + 0.307617i \(0.900468\pi\)
\(504\) −0.347296 + 1.96962i −0.0154698 + 0.0877336i
\(505\) 0 0
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) 9.19253 + 7.71345i 0.408255 + 0.342566i
\(508\) −1.87939 0.684040i −0.0833842 0.0303494i
\(509\) −28.1908 + 10.2606i −1.24953 + 0.454793i −0.880244 0.474521i \(-0.842621\pi\)
−0.369290 + 0.929314i \(0.620399\pi\)
\(510\) 0 0
\(511\) 1.21554 + 6.89365i 0.0537722 + 0.304957i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) 6.12836 5.14230i 0.269786 0.226377i
\(517\) 0 0
\(518\) −1.87939 0.684040i −0.0825754 0.0300550i
\(519\) 4.59627 + 3.85673i 0.201754 + 0.169291i
\(520\) 0 0
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) 3.12567 17.7265i 0.136807 0.775870i
\(523\) 1.91013 10.8329i 0.0835242 0.473689i −0.914141 0.405396i \(-0.867134\pi\)
0.997665 0.0682930i \(-0.0217553\pi\)
\(524\) 0 0
\(525\) −2.50000 + 4.33013i −0.109109 + 0.188982i
\(526\) −18.3851 15.4269i −0.801627 0.672645i
\(527\) 11.2763 + 4.10424i 0.491204 + 0.178784i
\(528\) 5.63816 2.05212i 0.245369 0.0893071i
\(529\) −10.7246 + 8.99903i −0.466288 + 0.391262i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 0 0
\(534\) 2.08378 + 11.8177i 0.0901739 + 0.511402i
\(535\) 0 0
\(536\) 4.69846 1.71010i 0.202943 0.0738651i
\(537\) 0 0
\(538\) 4.59627 + 3.85673i 0.198159 + 0.166275i
\(539\) −18.0000 + 31.1769i −0.775315 + 1.34288i
\(540\) 0 0
\(541\) 0.347296 1.96962i 0.0149314 0.0846804i −0.976431 0.215828i \(-0.930755\pi\)
0.991363 + 0.131147i \(0.0418661\pi\)
\(542\) −1.91013 + 10.8329i −0.0820471 + 0.465312i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 0 0
\(546\) −4.69846 1.71010i −0.201076 0.0731856i
\(547\) −41.3465 + 15.0489i −1.76785 + 0.643444i −0.767852 + 0.640628i \(0.778674\pi\)
−0.999996 + 0.00281615i \(0.999104\pi\)
\(548\) −6.89440 + 5.78509i −0.294514 + 0.247127i
\(549\) 3.47296 + 19.6962i 0.148222 + 0.840611i
\(550\) −30.0000 −1.27920
\(551\) 0 0
\(552\) −3.00000 −0.127688
\(553\) 1.73648 + 9.84808i 0.0738427 + 0.418783i
\(554\) −6.12836 + 5.14230i −0.260369 + 0.218475i
\(555\) 0 0
\(556\) 3.75877 + 1.36808i 0.159407 + 0.0580195i
\(557\) 18.3851 + 15.4269i 0.779000 + 0.653659i 0.942997 0.332802i \(-0.107994\pi\)
−0.163996 + 0.986461i \(0.552439\pi\)
\(558\) 4.00000 6.92820i 0.169334 0.293294i
\(559\) −20.0000 34.6410i −0.845910 1.46516i
\(560\) 0 0
\(561\) −3.12567 + 17.7265i −0.131966 + 0.748415i
\(562\) 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
\(566\) −20.6732 + 7.52444i −0.868961 + 0.316276i
\(567\) −0.766044 + 0.642788i −0.0321708 + 0.0269945i
\(568\) 1.04189 + 5.90885i 0.0437167 + 0.247930i
\(569\) −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 \(0.526673\pi\)
\(572\) −5.20945 29.5442i −0.217818 1.23531i
\(573\) 2.29813 1.92836i 0.0960059 0.0805585i
\(574\) 0 0
\(575\) 14.0954 + 5.13030i 0.587818 + 0.213948i
\(576\) −1.53209 1.28558i −0.0638370 0.0535656i
\(577\) −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
\(579\) 2.43107 13.7873i 0.101032 0.572981i
\(580\) 0 0
\(581\) −3.00000 5.19615i −0.124461 0.215573i
\(582\) −5.00000 + 8.66025i −0.207257 + 0.358979i
\(583\) 13.7888 + 11.5702i 0.571074 + 0.479188i
\(584\) −6.57785 2.39414i −0.272193 0.0990703i
\(585\) 0 0
\(586\) 16.0869 13.4985i 0.664545 0.557620i
\(587\) −2.08378 11.8177i −0.0860067 0.487768i −0.997135 0.0756451i \(-0.975898\pi\)
0.911128 0.412123i \(-0.135213\pi\)
\(588\) −6.00000 −0.247436
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.53209 1.28558i 0.0629685 0.0528368i
\(593\) 28.1908 10.2606i 1.15766 0.421353i 0.309397 0.950933i \(-0.399873\pi\)
0.848260 + 0.529580i \(0.177651\pi\)
\(594\) 28.1908 + 10.2606i 1.15668 + 0.420998i
\(595\) 0 0
\(596\) 0 0
\(597\) −5.50000 9.52628i −0.225100 0.389885i
\(598\) −2.60472 + 14.7721i −0.106515 + 0.604077i
\(599\) −4.16756 + 23.6354i −0.170282 + 0.965716i 0.773168 + 0.634201i \(0.218671\pi\)
−0.943450 + 0.331515i \(0.892440\pi\)
\(600\) −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 \(-0.0268056\pi\)
\(602\) 6.12836 + 5.14230i 0.249773 + 0.209585i
\(603\) 9.39693 + 3.42020i 0.382672 + 0.139281i
\(604\) 9.39693 3.42020i 0.382356 0.139166i
\(605\) 0 0
\(606\) −3.12567 17.7265i −0.126972 0.720091i
\(607\) −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
\(612\) 5.63816 2.05212i 0.227909 0.0829521i
\(613\) −1.87939 0.684040i −0.0759077 0.0276281i 0.303787 0.952740i \(-0.401749\pi\)
−0.379695 + 0.925112i \(0.623971\pi\)
\(614\) −15.3209 12.8558i −0.618301 0.518816i
\(615\) 0 0
\(616\) 3.00000 + 5.19615i 0.120873 + 0.209359i
\(617\) −1.04189 + 5.90885i −0.0419449 + 0.237881i −0.998571 0.0534364i \(-0.982983\pi\)
0.956626 + 0.291318i \(0.0940937\pi\)
\(618\) −2.43107 + 13.7873i −0.0977922 + 0.554607i
\(619\) 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
\(621\) −11.4907 9.64181i −0.461105 0.386913i
\(622\) −19.7335 7.18242i −0.791243 0.287989i
\(623\) −11.2763 + 4.10424i −0.451776 + 0.164433i
\(624\) 3.83022 3.21394i 0.153332 0.128660i
\(625\) 4.34120 + 24.6202i 0.173648 + 0.984808i
\(626\) 19.0000 0.759393
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) 1.04189 + 5.90885i 0.0415428 + 0.235601i
\(630\) 0 0
\(631\) 15.0351 5.47232i 0.598537 0.217850i −0.0249430 0.999689i \(-0.507940\pi\)
0.623480 + 0.781839i \(0.285718\pi\)
\(632\) −9.39693 3.42020i −0.373790 0.136048i
\(633\) 3.83022 + 3.21394i 0.152238 + 0.127743i
\(634\) −4.50000 + 7.79423i −0.178718 + 0.309548i
\(635\) 0 0
\(636\) −0.520945 + 2.95442i −0.0206568 + 0.117151i
\(637\) −5.20945 + 29.5442i −0.206406 + 1.17059i
\(638\) −27.0000 46.7654i −1.06894 1.85146i
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) 0 0
\(641\) −5.63816 2.05212i −0.222694 0.0810539i 0.228264 0.973599i \(-0.426695\pi\)
−0.450957 + 0.892545i \(0.648917\pi\)
\(642\) −8.45723 + 3.07818i −0.333780 + 0.121486i
\(643\) −16.8530 + 14.1413i −0.664617 + 0.557680i −0.911467 0.411374i \(-0.865049\pi\)
0.246850 + 0.969054i \(0.420605\pi\)
\(644\) −0.520945 2.95442i −0.0205281 0.116421i
\(645\) 0 0
\(646\) 0 0
\(647\) 27.0000 1.06148 0.530740 0.847535i \(-0.321914\pi\)
0.530740 + 0.847535i \(0.321914\pi\)
\(648\) −0.173648 0.984808i −0.00682154 0.0386869i
\(649\) −41.3664 + 34.7105i −1.62377 + 1.36251i
\(650\) −23.4923 + 8.55050i −0.921444 + 0.335378i
\(651\) −3.75877 1.36808i −0.147318 0.0536193i
\(652\) 15.3209 + 12.8558i 0.600012 + 0.503470i
\(653\) −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
\(659\) −34.4720 28.9254i −1.34284 1.12678i −0.980887 0.194578i \(-0.937666\pi\)
−0.361951 0.932197i \(-0.617889\pi\)
\(660\) 0 0
\(661\) 12.2160 4.44626i 0.475147 0.172940i −0.0933352 0.995635i \(-0.529753\pi\)
0.568483 + 0.822695i \(0.307531\pi\)
\(662\) 0.766044 0.642788i 0.0297732 0.0249826i
\(663\) 2.60472 + 14.7721i 0.101159 + 0.573701i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 4.68850 + 26.5898i 0.181539 + 1.02956i
\(668\) 9.19253 7.71345i 0.355670 0.298442i
\(669\) −24.4320 + 8.89252i −0.944596 + 0.343805i
\(670\) 0 0
\(671\) 45.9627 + 38.5673i 1.77437 + 1.48887i
\(672\) −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 \(-0.488883\pi\)
\(674\) 0.694593 3.93923i 0.0267547 0.151734i
\(675\) 4.34120 24.6202i 0.167093 0.947632i
\(676\) −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 \(-0.0519817\pi\)
\(678\) −4.59627 3.85673i −0.176519 0.148117i
\(679\) −9.39693 3.42020i −0.360621 0.131255i
\(680\) 0 0
\(681\) −11.4907 + 9.64181i −0.440323 + 0.369475i
\(682\) −4.16756 23.6354i −0.159584 0.905046i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −2.25743 12.8025i −0.0861889 0.488802i
\(687\) −16.8530 + 14.1413i −0.642981 + 0.539525i
\(688\) −7.51754 + 2.73616i −0.286604 + 0.104315i
\(689\) 14.0954 + 5.13030i 0.536992 + 0.195449i
\(690\) 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
\(693\) −2.08378 + 11.8177i −0.0791562 + 0.448917i
\(694\) −3.12567 + 17.7265i −0.118649 + 0.672890i
\(695\) 0 0
\(696\) 4.50000 7.79423i 0.170572 0.295439i
\(697\) 0 0
\(698\) −9.39693 3.42020i −0.355679 0.129457i
\(699\) 5.63816 2.05212i 0.213255 0.0776183i
\(700\) 3.83022 3.21394i 0.144769 0.121475i
\(701\) 2.08378 + 11.8177i 0.0787032 + 0.446348i 0.998539 + 0.0540435i \(0.0172110\pi\)
−0.919835 + 0.392305i \(0.871678\pi\)
\(702\) 25.0000 0.943564
\(703\) 0 0
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) 11.4907 9.64181i 0.432457 0.362874i
\(707\) 16.9145 6.15636i 0.636134 0.231534i
\(708\) −8.45723 3.07818i −0.317842 0.115685i
\(709\) −7.66044 6.42788i −0.287694 0.241404i 0.487506 0.873119i \(-0.337907\pi\)
−0.775200 + 0.631716i \(0.782351\pi\)
\(710\) 0 0
\(711\) −10.0000 17.3205i −0.375029 0.649570i
\(712\) 2.08378 11.8177i 0.0780929 0.442887i
\(713\) −2.08378 + 11.8177i −0.0780381 + 0.442576i
\(714\) −1.50000 2.59808i −0.0561361 0.0972306i
\(715\) 0 0
\(716\) 0 0
\(717\) 19.7335 + 7.18242i 0.736963 + 0.268233i
\(718\) 19.7335 7.18242i 0.736449 0.268046i
\(719\) 29.8757 25.0687i 1.11418 0.934905i 0.115881 0.993263i \(-0.463031\pi\)
0.998296 + 0.0583577i \(0.0185864\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 8.00000 0.297523
\(724\) 0.347296 + 1.96962i 0.0129072 + 0.0732002i
\(725\) −34.4720 + 28.9254i −1.28026 + 1.07426i
\(726\) 23.4923 8.55050i 0.871882 0.317339i
\(727\) 34.7686 + 12.6547i 1.28950 + 0.469339i 0.893562 0.448940i \(-0.148198\pi\)
0.395935 + 0.918279i \(0.370421\pi\)
\(728\) 3.83022 + 3.21394i 0.141957 + 0.119116i
\(729\) −6.50000 + 11.2583i −0.240741 + 0.416975i
\(730\) 0 0
\(731\) 4.16756 23.6354i 0.154143 0.874186i
\(732\) −1.73648 + 9.84808i −0.0641822 + 0.363995i
\(733\) −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
\(736\) 2.81908 + 1.02606i 0.103913 + 0.0378211i
\(737\) 28.1908 10.2606i 1.03842 0.377954i
\(738\) 0 0
\(739\) −2.77837 15.7569i −0.102204 0.579628i −0.992300 0.123855i \(-0.960474\pi\)
0.890096 0.455773i \(-0.150637\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.00000 −0.110133
\(743\) −6.25133 35.4531i −0.229339 1.30065i −0.854214 0.519922i \(-0.825961\pi\)
0.624874 0.780725i \(-0.285150\pi\)
\(744\) 3.06418 2.57115i 0.112338 0.0942629i
\(745\) 0 0
\(746\) 21.6129 + 7.86646i 0.791306 + 0.288012i
\(747\) 9.19253 + 7.71345i 0.336337 + 0.282220i
\(748\) 9.00000 15.5885i 0.329073 0.569970i
\(749\) −4.50000 7.79423i −0.164426 0.284795i
\(750\) 0 0
\(751\) −6.94593 + 39.3923i −0.253460 + 1.43745i 0.546533 + 0.837437i \(0.315947\pi\)
−0.799994 + 0.600008i \(0.795164\pi\)
\(752\) 0 0
\(753\) −3.00000 + 5.19615i −0.109326 + 0.189358i
\(754\) −34.4720 28.9254i −1.25540 1.05340i
\(755\) 0 0
\(756\) −4.69846 + 1.71010i −0.170881 + 0.0621958i
\(757\) 1.53209 1.28558i 0.0556847 0.0467250i −0.614521 0.788901i \(-0.710651\pi\)
0.670205 + 0.742176i \(0.266206\pi\)
\(758\) 1.21554 + 6.89365i 0.0441503 + 0.250389i
\(759\) −18.0000 −0.653359
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) −0.347296 1.96962i −0.0125812 0.0713516i
\(763\) −8.42649 + 7.07066i −0.305059 + 0.255975i
\(764\) −2.81908 + 1.02606i −0.101991 + 0.0371216i
\(765\) 0 0
\(766\) −13.7888 11.5702i −0.498210 0.418047i
\(767\) −22.5000 + 38.9711i −0.812428 + 1.40717i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 0.868241 4.92404i 0.0313096 0.177565i −0.965143 0.261724i \(-0.915709\pi\)
0.996452 + 0.0841584i \(0.0268202\pi\)
\(770\) 0 0
\(771\) −6.00000 10.3923i −0.216085 0.374270i
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 39.0683 + 32.7822i 1.40519 + 1.17909i 0.958740 + 0.284283i \(0.0917554\pi\)
0.446447 + 0.894810i \(0.352689\pi\)
\(774\) −15.0351 5.47232i −0.540425 0.196699i
\(775\) −18.7939 + 6.84040i −0.675095 + 0.245715i
\(776\) 7.66044 6.42788i 0.274994 0.230747i
\(777\) −0.347296 1.96962i −0.0124592 0.0706596i
\(778\) −18.0000 −0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) 6.25133 + 35.4531i 0.223690 + 1.26861i
\(782\) −6.89440 + 5.78509i −0.246543 + 0.206874i
\(783\) 42.2862 15.3909i 1.51118 0.550026i
\(784\) 5.63816 + 2.05212i 0.201363 + 0.0732900i
\(785\) 0 0
\(786\) 0 0
\(787\) 15.5000 + 26.8468i 0.552515 + 0.956985i 0.998092 + 0.0617409i \(0.0196653\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)