Properties

Label 567.2.s.e.26.1
Level $567$
Weight $2$
Character 567.26
Analytic conductor $4.528$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-5})\)
Defining polynomial: \(x^{4} - 5 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.1
Root \(-1.93649 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 567.26
Dual form 567.2.s.e.458.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.93649 + 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-0.500000 - 2.59808i) q^{7} +2.23607i q^{8} +O(q^{10})\) \(q+(-1.93649 + 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-0.500000 - 2.59808i) q^{7} +2.23607i q^{8} +4.47214i q^{11} +(1.50000 - 0.866025i) q^{13} +(3.87298 + 4.47214i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.87298 - 6.70820i) q^{17} +(-3.00000 - 1.73205i) q^{19} +(-5.00000 - 8.66025i) q^{22} +4.47214i q^{23} -5.00000 q^{25} +(-1.93649 + 3.35410i) q^{26} +(-7.50000 - 2.59808i) q^{28} +(-3.87298 - 2.23607i) q^{29} +(1.50000 + 0.866025i) q^{31} +(-5.80948 - 3.35410i) q^{32} +(15.0000 + 8.66025i) q^{34} +(-2.50000 + 4.33013i) q^{37} +7.74597 q^{38} +(-3.87298 - 6.70820i) q^{41} +(3.50000 - 6.06218i) q^{43} +(11.6190 + 6.70820i) q^{44} +(-5.00000 - 8.66025i) q^{46} +(-3.87298 - 6.70820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(9.68246 - 5.59017i) q^{50} -5.19615i q^{52} +(3.87298 - 2.23607i) q^{53} +(5.80948 - 1.11803i) q^{56} +10.0000 q^{58} +(3.87298 - 6.70820i) q^{59} +(-7.50000 + 4.33013i) q^{61} -3.87298 q^{62} +13.0000 q^{64} +(0.500000 - 0.866025i) q^{67} -23.2379 q^{68} -8.94427i q^{71} +(6.00000 - 3.46410i) q^{73} -11.1803i q^{74} +(-9.00000 + 5.19615i) q^{76} +(11.6190 - 2.23607i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(15.0000 + 8.66025i) q^{82} +(3.87298 - 6.70820i) q^{83} +15.6525i q^{86} -10.0000 q^{88} +(-7.74597 + 13.4164i) q^{89} +(-3.00000 - 3.46410i) q^{91} +(11.6190 + 6.70820i) q^{92} +(15.0000 + 8.66025i) q^{94} +(1.50000 + 0.866025i) q^{97} +(9.68246 - 12.2984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{4} - 2q^{7} + O(q^{10}) \) \( 4q + 6q^{4} - 2q^{7} + 6q^{13} + 2q^{16} - 12q^{19} - 20q^{22} - 20q^{25} - 30q^{28} + 6q^{31} + 60q^{34} - 10q^{37} + 14q^{43} - 20q^{46} - 26q^{49} + 40q^{58} - 30q^{61} + 52q^{64} + 2q^{67} + 24q^{73} - 36q^{76} - 22q^{79} + 60q^{82} - 40q^{88} - 12q^{91} + 60q^{94} + 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93649 + 1.11803i −1.36931 + 0.790569i −0.990839 0.135045i \(-0.956882\pi\)
−0.378467 + 0.925615i \(0.623549\pi\)
\(3\) 0 0
\(4\) 1.50000 2.59808i 0.750000 1.29904i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 2.23607i 0.790569i
\(9\) 0 0
\(10\) 0 0
\(11\) 4.47214i 1.34840i 0.738549 + 0.674200i \(0.235511\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0 0
\(13\) 1.50000 0.866025i 0.416025 0.240192i −0.277350 0.960769i \(-0.589456\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 3.87298 + 4.47214i 1.03510 + 1.19523i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −3.87298 6.70820i −0.939336 1.62698i −0.766712 0.641991i \(-0.778109\pi\)
−0.172624 0.984988i \(-0.555225\pi\)
\(18\) 0 0
\(19\) −3.00000 1.73205i −0.688247 0.397360i 0.114708 0.993399i \(-0.463407\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −5.00000 8.66025i −1.06600 1.84637i
\(23\) 4.47214i 0.932505i 0.884652 + 0.466252i \(0.154396\pi\)
−0.884652 + 0.466252i \(0.845604\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −1.93649 + 3.35410i −0.379777 + 0.657794i
\(27\) 0 0
\(28\) −7.50000 2.59808i −1.41737 0.490990i
\(29\) −3.87298 2.23607i −0.719195 0.415227i 0.0952614 0.995452i \(-0.469631\pi\)
−0.814456 + 0.580225i \(0.802965\pi\)
\(30\) 0 0
\(31\) 1.50000 + 0.866025i 0.269408 + 0.155543i 0.628619 0.777714i \(-0.283621\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −5.80948 3.35410i −1.02698 0.592927i
\(33\) 0 0
\(34\) 15.0000 + 8.66025i 2.57248 + 1.48522i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.50000 + 4.33013i −0.410997 + 0.711868i −0.994999 0.0998840i \(-0.968153\pi\)
0.584002 + 0.811752i \(0.301486\pi\)
\(38\) 7.74597 1.25656
\(39\) 0 0
\(40\) 0 0
\(41\) −3.87298 6.70820i −0.604858 1.04765i −0.992074 0.125656i \(-0.959896\pi\)
0.387215 0.921989i \(-0.373437\pi\)
\(42\) 0 0
\(43\) 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i \(-0.654118\pi\)
0.999223 0.0394140i \(-0.0125491\pi\)
\(44\) 11.6190 + 6.70820i 1.75162 + 1.01130i
\(45\) 0 0
\(46\) −5.00000 8.66025i −0.737210 1.27688i
\(47\) −3.87298 6.70820i −0.564933 0.978492i −0.997056 0.0766776i \(-0.975569\pi\)
0.432123 0.901815i \(-0.357765\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 9.68246 5.59017i 1.36931 0.790569i
\(51\) 0 0
\(52\) 5.19615i 0.720577i
\(53\) 3.87298 2.23607i 0.531995 0.307148i −0.209833 0.977737i \(-0.567292\pi\)
0.741829 + 0.670590i \(0.233959\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 5.80948 1.11803i 0.776324 0.149404i
\(57\) 0 0
\(58\) 10.0000 1.31306
\(59\) 3.87298 6.70820i 0.504219 0.873334i −0.495769 0.868455i \(-0.665114\pi\)
0.999988 0.00487911i \(-0.00155308\pi\)
\(60\) 0 0
\(61\) −7.50000 + 4.33013i −0.960277 + 0.554416i −0.896258 0.443533i \(-0.853725\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) −3.87298 −0.491869
\(63\) 0 0
\(64\) 13.0000 1.62500
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 0.866025i 0.0610847 0.105802i −0.833866 0.551967i \(-0.813877\pi\)
0.894951 + 0.446165i \(0.147211\pi\)
\(68\) −23.2379 −2.81801
\(69\) 0 0
\(70\) 0 0
\(71\) 8.94427i 1.06149i −0.847532 0.530745i \(-0.821912\pi\)
0.847532 0.530745i \(-0.178088\pi\)
\(72\) 0 0
\(73\) 6.00000 3.46410i 0.702247 0.405442i −0.105937 0.994373i \(-0.533784\pi\)
0.808184 + 0.588930i \(0.200451\pi\)
\(74\) 11.1803i 1.29969i
\(75\) 0 0
\(76\) −9.00000 + 5.19615i −1.03237 + 0.596040i
\(77\) 11.6190 2.23607i 1.32410 0.254824i
\(78\) 0 0
\(79\) −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 15.0000 + 8.66025i 1.65647 + 0.956365i
\(83\) 3.87298 6.70820i 0.425115 0.736321i −0.571316 0.820730i \(-0.693567\pi\)
0.996431 + 0.0844091i \(0.0269003\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 15.6525i 1.68785i
\(87\) 0 0
\(88\) −10.0000 −1.06600
\(89\) −7.74597 + 13.4164i −0.821071 + 1.42214i 0.0838147 + 0.996481i \(0.473290\pi\)
−0.904886 + 0.425655i \(0.860044\pi\)
\(90\) 0 0
\(91\) −3.00000 3.46410i −0.314485 0.363137i
\(92\) 11.6190 + 6.70820i 1.21136 + 0.699379i
\(93\) 0 0
\(94\) 15.0000 + 8.66025i 1.54713 + 0.893237i
\(95\) 0 0
\(96\) 0 0
\(97\) 1.50000 + 0.866025i 0.152302 + 0.0879316i 0.574214 0.818705i \(-0.305308\pi\)
−0.421912 + 0.906637i \(0.638641\pi\)
\(98\) 9.68246 12.2984i 0.978076 1.24232i
\(99\) 0 0
\(100\) −7.50000 + 12.9904i −0.750000 + 1.29904i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 5.19615i 0.511992i 0.966678 + 0.255996i \(0.0824034\pi\)
−0.966678 + 0.255996i \(0.917597\pi\)
\(104\) 1.93649 + 3.35410i 0.189889 + 0.328897i
\(105\) 0 0
\(106\) −5.00000 + 8.66025i −0.485643 + 0.841158i
\(107\) −3.87298 2.23607i −0.374415 0.216169i 0.300970 0.953634i \(-0.402690\pi\)
−0.675386 + 0.737465i \(0.736023\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) −7.74597 + 4.47214i −0.728679 + 0.420703i −0.817939 0.575305i \(-0.804883\pi\)
0.0892596 + 0.996008i \(0.471550\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −11.6190 + 6.70820i −1.07879 + 0.622841i
\(117\) 0 0
\(118\) 17.3205i 1.59448i
\(119\) −15.4919 + 13.4164i −1.42014 + 1.22988i
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 9.68246 16.7705i 0.876609 1.51833i
\(123\) 0 0
\(124\) 4.50000 2.59808i 0.404112 0.233314i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) −13.5554 + 7.82624i −1.19814 + 0.691748i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −3.00000 + 8.66025i −0.260133 + 0.750939i
\(134\) 2.23607i 0.193167i
\(135\) 0 0
\(136\) 15.0000 8.66025i 1.28624 0.742611i
\(137\) 4.47214i 0.382080i 0.981582 + 0.191040i \(0.0611861\pi\)
−0.981582 + 0.191040i \(0.938814\pi\)
\(138\) 0 0
\(139\) −7.50000 + 4.33013i −0.636142 + 0.367277i −0.783127 0.621862i \(-0.786376\pi\)
0.146985 + 0.989139i \(0.453043\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 10.0000 + 17.3205i 0.839181 + 1.45350i
\(143\) 3.87298 + 6.70820i 0.323875 + 0.560968i
\(144\) 0 0
\(145\) 0 0
\(146\) −7.74597 + 13.4164i −0.641061 + 1.11035i
\(147\) 0 0
\(148\) 7.50000 + 12.9904i 0.616496 + 1.06780i
\(149\) 17.8885i 1.46549i 0.680505 + 0.732743i \(0.261760\pi\)
−0.680505 + 0.732743i \(0.738240\pi\)
\(150\) 0 0
\(151\) −13.0000 −1.05792 −0.528962 0.848645i \(-0.677419\pi\)
−0.528962 + 0.848645i \(0.677419\pi\)
\(152\) 3.87298 6.70820i 0.314140 0.544107i
\(153\) 0 0
\(154\) −20.0000 + 17.3205i −1.61165 + 1.39573i
\(155\) 0 0
\(156\) 0 0
\(157\) −12.0000 6.92820i −0.957704 0.552931i −0.0622385 0.998061i \(-0.519824\pi\)
−0.895466 + 0.445130i \(0.853157\pi\)
\(158\) 21.3014 + 12.2984i 1.69465 + 0.978406i
\(159\) 0 0
\(160\) 0 0
\(161\) 11.6190 2.23607i 0.915702 0.176227i
\(162\) 0 0
\(163\) 6.50000 11.2583i 0.509119 0.881820i −0.490825 0.871258i \(-0.663305\pi\)
0.999944 0.0105623i \(-0.00336213\pi\)
\(164\) −23.2379 −1.81458
\(165\) 0 0
\(166\) 17.3205i 1.34433i
\(167\) −3.87298 6.70820i −0.299700 0.519096i 0.676367 0.736565i \(-0.263553\pi\)
−0.976067 + 0.217468i \(0.930220\pi\)
\(168\) 0 0
\(169\) −5.00000 + 8.66025i −0.384615 + 0.666173i
\(170\) 0 0
\(171\) 0 0
\(172\) −10.5000 18.1865i −0.800617 1.38671i
\(173\) 7.74597 + 13.4164i 0.588915 + 1.02003i 0.994375 + 0.105918i \(0.0337780\pi\)
−0.405460 + 0.914113i \(0.632889\pi\)
\(174\) 0 0
\(175\) 2.50000 + 12.9904i 0.188982 + 0.981981i
\(176\) −3.87298 + 2.23607i −0.291937 + 0.168550i
\(177\) 0 0
\(178\) 34.6410i 2.59645i
\(179\) −7.74597 + 4.47214i −0.578961 + 0.334263i −0.760720 0.649080i \(-0.775154\pi\)
0.181760 + 0.983343i \(0.441821\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 9.68246 + 3.35410i 0.717712 + 0.248623i
\(183\) 0 0
\(184\) −10.0000 −0.737210
\(185\) 0 0
\(186\) 0 0
\(187\) 30.0000 17.3205i 2.19382 1.26660i
\(188\) −23.2379 −1.69480
\(189\) 0 0
\(190\) 0 0
\(191\) 15.4919 8.94427i 1.12096 0.647185i 0.179312 0.983792i \(-0.442613\pi\)
0.941645 + 0.336607i \(0.109280\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) −3.87298 −0.278064
\(195\) 0 0
\(196\) −3.00000 + 20.7846i −0.214286 + 1.48461i
\(197\) 8.94427i 0.637253i −0.947880 0.318626i \(-0.896778\pi\)
0.947880 0.318626i \(-0.103222\pi\)
\(198\) 0 0
\(199\) 19.5000 11.2583i 1.38232 0.798082i 0.389885 0.920864i \(-0.372515\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 11.1803i 0.790569i
\(201\) 0 0
\(202\) 0 0
\(203\) −3.87298 + 11.1803i −0.271830 + 0.784706i
\(204\) 0 0
\(205\) 0 0
\(206\) −5.80948 10.0623i −0.404765 0.701074i
\(207\) 0 0
\(208\) 1.50000 + 0.866025i 0.104006 + 0.0600481i
\(209\) 7.74597 13.4164i 0.535800 0.928032i
\(210\) 0 0
\(211\) 9.50000 + 16.4545i 0.654007 + 1.13277i 0.982142 + 0.188142i \(0.0602466\pi\)
−0.328135 + 0.944631i \(0.606420\pi\)
\(212\) 13.4164i 0.921443i
\(213\) 0 0
\(214\) 10.0000 0.683586
\(215\) 0 0
\(216\) 0 0
\(217\) 1.50000 4.33013i 0.101827 0.293948i
\(218\) −1.93649 1.11803i −0.131156 0.0757228i
\(219\) 0 0
\(220\) 0 0
\(221\) −11.6190 6.70820i −0.781575 0.451243i
\(222\) 0 0
\(223\) −21.0000 12.1244i −1.40626 0.811907i −0.411239 0.911528i \(-0.634904\pi\)
−0.995025 + 0.0996209i \(0.968237\pi\)
\(224\) −5.80948 + 16.7705i −0.388162 + 1.12053i
\(225\) 0 0
\(226\) 10.0000 17.3205i 0.665190 1.15214i
\(227\) 23.2379 1.54235 0.771177 0.636621i \(-0.219668\pi\)
0.771177 + 0.636621i \(0.219668\pi\)
\(228\) 0 0
\(229\) 25.9808i 1.71686i −0.512933 0.858429i \(-0.671441\pi\)
0.512933 0.858429i \(-0.328559\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.00000 8.66025i 0.328266 0.568574i
\(233\) 7.74597 + 4.47214i 0.507455 + 0.292979i 0.731787 0.681533i \(-0.238687\pi\)
−0.224332 + 0.974513i \(0.572020\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −11.6190 20.1246i −0.756329 1.31000i
\(237\) 0 0
\(238\) 15.0000 43.3013i 0.972306 2.80680i
\(239\) −7.74597 + 4.47214i −0.501045 + 0.289278i −0.729145 0.684359i \(-0.760082\pi\)
0.228100 + 0.973638i \(0.426749\pi\)
\(240\) 0 0
\(241\) 15.5885i 1.00414i 0.864827 + 0.502070i \(0.167428\pi\)
−0.864827 + 0.502070i \(0.832572\pi\)
\(242\) 17.4284 10.0623i 1.12034 0.646830i
\(243\) 0 0
\(244\) 25.9808i 1.66325i
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) −1.93649 + 3.35410i −0.122967 + 0.212986i
\(249\) 0 0
\(250\) 0 0
\(251\) 23.2379 1.46676 0.733382 0.679817i \(-0.237941\pi\)
0.733382 + 0.679817i \(0.237941\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 1.93649 1.11803i 0.121506 0.0701517i
\(255\) 0 0
\(256\) 4.50000 7.79423i 0.281250 0.487139i
\(257\) 23.2379 1.44954 0.724770 0.688991i \(-0.241946\pi\)
0.724770 + 0.688991i \(0.241946\pi\)
\(258\) 0 0
\(259\) 12.5000 + 4.33013i 0.776712 + 0.269061i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.47214i 0.275764i 0.990449 + 0.137882i \(0.0440294\pi\)
−0.990449 + 0.137882i \(0.955971\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.87298 20.1246i −0.237468 1.23392i
\(267\) 0 0
\(268\) −1.50000 2.59808i −0.0916271 0.158703i
\(269\) 7.74597 + 13.4164i 0.472280 + 0.818013i 0.999497 0.0317179i \(-0.0100978\pi\)
−0.527217 + 0.849731i \(0.676764\pi\)
\(270\) 0 0
\(271\) 1.50000 + 0.866025i 0.0911185 + 0.0526073i 0.544867 0.838523i \(-0.316580\pi\)
−0.453748 + 0.891130i \(0.649914\pi\)
\(272\) 3.87298 6.70820i 0.234834 0.406745i
\(273\) 0 0
\(274\) −5.00000 8.66025i −0.302061 0.523185i
\(275\) 22.3607i 1.34840i
\(276\) 0 0
\(277\) 5.00000 0.300421 0.150210 0.988654i \(-0.452005\pi\)
0.150210 + 0.988654i \(0.452005\pi\)
\(278\) 9.68246 16.7705i 0.580715 1.00583i
\(279\) 0 0
\(280\) 0 0
\(281\) −15.4919 8.94427i −0.924171 0.533571i −0.0392078 0.999231i \(-0.512483\pi\)
−0.884963 + 0.465661i \(0.845817\pi\)
\(282\) 0 0
\(283\) 10.5000 + 6.06218i 0.624160 + 0.360359i 0.778487 0.627661i \(-0.215988\pi\)
−0.154327 + 0.988020i \(0.549321\pi\)
\(284\) −23.2379 13.4164i −1.37892 0.796117i
\(285\) 0 0
\(286\) −15.0000 8.66025i −0.886969 0.512092i
\(287\) −15.4919 + 13.4164i −0.914460 + 0.791946i
\(288\) 0 0
\(289\) −21.5000 + 37.2391i −1.26471 + 2.19053i
\(290\) 0 0
\(291\) 0 0
\(292\) 20.7846i 1.21633i
\(293\) −3.87298 6.70820i −0.226262 0.391897i 0.730435 0.682982i \(-0.239317\pi\)
−0.956697 + 0.291084i \(0.905984\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −9.68246 5.59017i −0.562781 0.324922i
\(297\) 0 0
\(298\) −20.0000 34.6410i −1.15857 2.00670i
\(299\) 3.87298 + 6.70820i 0.223980 + 0.387945i
\(300\) 0 0
\(301\) −17.5000 6.06218i −1.00868 0.349418i
\(302\) 25.1744 14.5344i 1.44862 0.836363i
\(303\) 0 0
\(304\) 3.46410i 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 5.19615i 0.296560i −0.988945 0.148280i \(-0.952626\pi\)
0.988945 0.148280i \(-0.0473737\pi\)
\(308\) 11.6190 33.5410i 0.662051 1.91118i
\(309\) 0 0
\(310\) 0 0
\(311\) −7.74597 + 13.4164i −0.439233 + 0.760775i −0.997631 0.0687991i \(-0.978083\pi\)
0.558397 + 0.829574i \(0.311417\pi\)
\(312\) 0 0
\(313\) −12.0000 + 6.92820i −0.678280 + 0.391605i −0.799207 0.601056i \(-0.794747\pi\)
0.120927 + 0.992661i \(0.461413\pi\)
\(314\) 30.9839 1.74852
\(315\) 0 0
\(316\) −33.0000 −1.85640
\(317\) 3.87298 2.23607i 0.217528 0.125590i −0.387277 0.921963i \(-0.626584\pi\)
0.604805 + 0.796373i \(0.293251\pi\)
\(318\) 0 0
\(319\) 10.0000 17.3205i 0.559893 0.969762i
\(320\) 0 0
\(321\) 0 0
\(322\) −20.0000 + 17.3205i −1.11456 + 0.965234i
\(323\) 26.8328i 1.49302i
\(324\) 0 0
\(325\) −7.50000 + 4.33013i −0.416025 + 0.240192i
\(326\) 29.0689i 1.60998i
\(327\) 0 0
\(328\) 15.0000 8.66025i 0.828236 0.478183i
\(329\) −15.4919 + 13.4164i −0.854098 + 0.739671i
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −11.6190 20.1246i −0.637673 1.10448i
\(333\) 0 0
\(334\) 15.0000 + 8.66025i 0.820763 + 0.473868i
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000 + 8.66025i 0.272367 + 0.471754i 0.969468 0.245220i \(-0.0788601\pi\)
−0.697100 + 0.716974i \(0.745527\pi\)
\(338\) 22.3607i 1.21626i
\(339\) 0 0
\(340\) 0 0
\(341\) −3.87298 + 6.70820i −0.209734 + 0.363270i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 13.5554 + 7.82624i 0.730860 + 0.421962i
\(345\) 0 0
\(346\) −30.0000 17.3205i −1.61281 0.931156i
\(347\) 7.74597 + 4.47214i 0.415825 + 0.240077i 0.693290 0.720659i \(-0.256161\pi\)
−0.277464 + 0.960736i \(0.589494\pi\)
\(348\) 0 0
\(349\) 19.5000 + 11.2583i 1.04381 + 0.602645i 0.920910 0.389774i \(-0.127447\pi\)
0.122901 + 0.992419i \(0.460780\pi\)
\(350\) −19.3649 22.3607i −1.03510 1.19523i
\(351\) 0 0
\(352\) 15.0000 25.9808i 0.799503 1.38478i
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 23.2379 + 40.2492i 1.23161 + 2.13320i
\(357\) 0 0
\(358\) 10.0000 17.3205i 0.528516 0.915417i
\(359\) −3.87298 2.23607i −0.204408 0.118015i 0.394302 0.918981i \(-0.370986\pi\)
−0.598710 + 0.800966i \(0.704320\pi\)
\(360\) 0 0
\(361\) −3.50000 6.06218i −0.184211 0.319062i
\(362\) 0 0
\(363\) 0 0
\(364\) −13.5000 + 2.59808i −0.707592 + 0.136176i
\(365\) 0 0
\(366\) 0 0
\(367\) 10.3923i 0.542474i −0.962513 0.271237i \(-0.912567\pi\)
0.962513 0.271237i \(-0.0874327\pi\)
\(368\) −3.87298 + 2.23607i −0.201893 + 0.116563i
\(369\) 0 0
\(370\) 0 0
\(371\) −7.74597 8.94427i −0.402151 0.464363i
\(372\) 0 0
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) −38.7298 + 67.0820i −2.00267 + 3.46873i
\(375\) 0 0
\(376\) 15.0000 8.66025i 0.773566 0.446619i
\(377\) −7.74597 −0.398938
\(378\) 0 0
\(379\) 17.0000 0.873231 0.436616 0.899648i \(-0.356177\pi\)
0.436616 + 0.899648i \(0.356177\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −20.0000 + 34.6410i −1.02329 + 1.77239i
\(383\) 23.2379 1.18740 0.593701 0.804686i \(-0.297666\pi\)
0.593701 + 0.804686i \(0.297666\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.6525i 0.796690i
\(387\) 0 0
\(388\) 4.50000 2.59808i 0.228453 0.131897i
\(389\) 8.94427i 0.453493i −0.973954 0.226746i \(-0.927191\pi\)
0.973954 0.226746i \(-0.0728088\pi\)
\(390\) 0 0
\(391\) 30.0000 17.3205i 1.51717 0.875936i
\(392\) −5.80948 14.5344i −0.293423 0.734100i
\(393\) 0 0
\(394\) 10.0000 + 17.3205i 0.503793 + 0.872595i
\(395\) 0 0
\(396\) 0 0
\(397\) −25.5000 14.7224i −1.27981 0.738898i −0.302995 0.952992i \(-0.597987\pi\)
−0.976813 + 0.214094i \(0.931320\pi\)
\(398\) −25.1744 + 43.6033i −1.26188 + 2.18564i
\(399\) 0 0
\(400\) −2.50000 4.33013i −0.125000 0.216506i
\(401\) 22.3607i 1.11664i −0.829626 0.558320i \(-0.811446\pi\)
0.829626 0.558320i \(-0.188554\pi\)
\(402\) 0 0
\(403\) 3.00000 0.149441
\(404\) 0 0
\(405\) 0 0
\(406\) −5.00000 25.9808i −0.248146 1.28940i
\(407\) −19.3649 11.1803i −0.959883 0.554189i
\(408\) 0 0
\(409\) 19.5000 + 11.2583i 0.964213 + 0.556689i 0.897467 0.441081i \(-0.145405\pi\)
0.0667458 + 0.997770i \(0.478738\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 13.5000 + 7.79423i 0.665097 + 0.383994i
\(413\) −19.3649 6.70820i −0.952885 0.330089i
\(414\) 0 0
\(415\) 0 0
\(416\) −11.6190 −0.569666
\(417\) 0 0
\(418\) 34.6410i 1.69435i
\(419\) 7.74597 + 13.4164i 0.378415 + 0.655434i 0.990832 0.135101i \(-0.0431358\pi\)
−0.612417 + 0.790535i \(0.709802\pi\)
\(420\) 0 0
\(421\) 17.0000 29.4449i 0.828529 1.43505i −0.0706626 0.997500i \(-0.522511\pi\)
0.899192 0.437555i \(-0.144155\pi\)
\(422\) −36.7933 21.2426i −1.79107 1.03408i
\(423\) 0 0
\(424\) 5.00000 + 8.66025i 0.242821 + 0.420579i
\(425\) 19.3649 + 33.5410i 0.939336 + 1.62698i
\(426\) 0 0
\(427\) 15.0000 + 17.3205i 0.725901 + 0.838198i
\(428\) −11.6190 + 6.70820i −0.561623 + 0.324253i
\(429\) 0 0
\(430\) 0 0
\(431\) 27.1109 15.6525i 1.30589 0.753953i 0.324479 0.945893i \(-0.394811\pi\)
0.981407 + 0.191940i \(0.0614778\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i 0.927200 + 0.374567i \(0.122209\pi\)
−0.927200 + 0.374567i \(0.877791\pi\)
\(434\) 1.93649 + 10.0623i 0.0929546 + 0.483006i
\(435\) 0 0
\(436\) 3.00000 0.143674
\(437\) 7.74597 13.4164i 0.370540 0.641794i
\(438\) 0 0
\(439\) −3.00000 + 1.73205i −0.143182 + 0.0826663i −0.569880 0.821728i \(-0.693010\pi\)
0.426698 + 0.904394i \(0.359677\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) −30.9839 + 17.8885i −1.47209 + 0.849910i −0.999508 0.0313772i \(-0.990011\pi\)
−0.472580 + 0.881288i \(0.656677\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 54.2218 2.56748
\(447\) 0 0
\(448\) −6.50000 33.7750i −0.307096 1.59572i
\(449\) 8.94427i 0.422106i −0.977475 0.211053i \(-0.932311\pi\)
0.977475 0.211053i \(-0.0676893\pi\)
\(450\) 0 0
\(451\) 30.0000 17.3205i 1.41264 0.815591i
\(452\) 26.8328i 1.26211i
\(453\) 0 0
\(454\) −45.0000 + 25.9808i −2.11195 + 1.21934i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 29.0474 + 50.3115i 1.35729 + 2.35090i
\(459\) 0 0
\(460\) 0 0
\(461\) 3.87298 6.70820i 0.180383 0.312432i −0.761628 0.648014i \(-0.775600\pi\)
0.942011 + 0.335582i \(0.108933\pi\)
\(462\) 0 0
\(463\) −4.00000 6.92820i −0.185896 0.321981i 0.757982 0.652275i \(-0.226185\pi\)
−0.943878 + 0.330294i \(0.892852\pi\)
\(464\) 4.47214i 0.207614i
\(465\) 0 0
\(466\) −20.0000 −0.926482
\(467\) 15.4919 26.8328i 0.716881 1.24167i −0.245348 0.969435i \(-0.578902\pi\)
0.962229 0.272240i \(-0.0877643\pi\)
\(468\) 0 0
\(469\) −2.50000 0.866025i −0.115439 0.0399893i
\(470\) 0 0
\(471\) 0 0
\(472\) 15.0000 + 8.66025i 0.690431 + 0.398621i
\(473\) 27.1109 + 15.6525i 1.24656 + 0.719702i
\(474\) 0 0
\(475\) 15.0000 + 8.66025i 0.688247 + 0.397360i
\(476\) 11.6190 + 60.3738i 0.532554 + 2.76723i
\(477\) 0 0
\(478\) 10.0000 17.3205i 0.457389 0.792222i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 8.66025i 0.394874i
\(482\) −17.4284 30.1869i −0.793843 1.37498i
\(483\) 0 0
\(484\) −13.5000 + 23.3827i −0.613636 + 1.06285i
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0000 + 34.6410i 0.906287 + 1.56973i 0.819181 + 0.573535i \(0.194428\pi\)
0.0871056 + 0.996199i \(0.472238\pi\)
\(488\) −9.68246 16.7705i −0.438304 0.759165i
\(489\) 0 0
\(490\) 0 0
\(491\) −19.3649 + 11.1803i −0.873926 + 0.504562i −0.868651 0.495424i \(-0.835013\pi\)
−0.00527540 + 0.999986i \(0.501679\pi\)
\(492\) 0 0
\(493\) 34.6410i 1.56015i
\(494\) 11.6190 6.70820i 0.522761 0.301816i
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) −23.2379 + 4.47214i −1.04236 + 0.200603i
\(498\) 0 0
\(499\) −31.0000 −1.38775 −0.693875 0.720095i \(-0.744098\pi\)
−0.693875 + 0.720095i \(0.744098\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −45.0000 + 25.9808i −2.00845 + 1.15958i
\(503\) −23.2379 −1.03613 −0.518063 0.855342i \(-0.673347\pi\)
−0.518063 + 0.855342i \(0.673347\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 38.7298 22.3607i 1.72175 0.994053i
\(507\) 0 0
\(508\) −1.50000 + 2.59808i −0.0665517 + 0.115271i
\(509\) −23.2379 −1.03000 −0.515001 0.857190i \(-0.672208\pi\)
−0.515001 + 0.857190i \(0.672208\pi\)
\(510\) 0 0
\(511\) −12.0000 13.8564i −0.530849 0.612971i
\(512\) 11.1803i 0.494106i
\(513\) 0 0
\(514\) −45.0000 + 25.9808i −1.98486 + 1.14596i
\(515\) 0 0
\(516\) 0 0
\(517\) 30.0000 17.3205i 1.31940 0.761755i
\(518\) −29.0474 + 5.59017i −1.27627 + 0.245618i
\(519\) 0 0
\(520\) 0 0
\(521\) −3.87298 6.70820i −0.169678 0.293892i 0.768628 0.639696i \(-0.220940\pi\)
−0.938307 + 0.345804i \(0.887606\pi\)
\(522\) 0 0
\(523\) −16.5000 9.52628i −0.721495 0.416555i 0.0938079 0.995590i \(-0.470096\pi\)
−0.815303 + 0.579035i \(0.803429\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −5.00000 8.66025i −0.218010 0.377605i
\(527\) 13.4164i 0.584428i
\(528\) 0 0
\(529\) 3.00000 0.130435
\(530\) 0 0
\(531\) 0 0
\(532\) 18.0000 + 20.7846i 0.780399 + 0.901127i
\(533\) −11.6190 6.70820i −0.503273 0.290565i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.93649 + 1.11803i 0.0836437 + 0.0482917i
\(537\) 0 0
\(538\) −30.0000 17.3205i −1.29339 0.746740i
\(539\) −11.6190 29.0689i −0.500464 1.25209i
\(540\) 0 0
\(541\) −7.00000 + 12.1244i −0.300954 + 0.521267i −0.976352 0.216186i \(-0.930638\pi\)
0.675399 + 0.737453i \(0.263972\pi\)
\(542\) −3.87298 −0.166359
\(543\) 0 0
\(544\) 51.9615i 2.22783i
\(545\) 0 0
\(546\) 0 0
\(547\) −5.50000 + 9.52628i −0.235163 + 0.407314i −0.959320 0.282321i \(-0.908896\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(548\) 11.6190 + 6.70820i 0.496337 + 0.286560i
\(549\) 0 0
\(550\) 25.0000 + 43.3013i 1.06600 + 1.84637i
\(551\) 7.74597 + 13.4164i 0.329989 + 0.571558i
\(552\) 0 0
\(553\) −22.0000 + 19.0526i −0.935535 + 0.810197i
\(554\) −9.68246 + 5.59017i −0.411368 + 0.237504i
\(555\) 0 0
\(556\) 25.9808i 1.10183i
\(557\) −30.9839 + 17.8885i −1.31283 + 0.757962i −0.982564 0.185926i \(-0.940471\pi\)
−0.330265 + 0.943888i \(0.607138\pi\)
\(558\) 0 0
\(559\) 12.1244i 0.512806i
\(560\) 0 0
\(561\) 0 0
\(562\) 40.0000 1.68730
\(563\) 3.87298 6.70820i 0.163227 0.282717i −0.772797 0.634653i \(-0.781143\pi\)
0.936024 + 0.351936i \(0.114476\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −27.1109 −1.13956
\(567\) 0 0
\(568\) 20.0000 0.839181
\(569\) 15.4919 8.94427i 0.649456 0.374963i −0.138792 0.990322i \(-0.544322\pi\)
0.788248 + 0.615358i \(0.210989\pi\)
\(570\) 0 0
\(571\) 8.00000 13.8564i 0.334790 0.579873i −0.648655 0.761083i \(-0.724668\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) 23.2379 0.971625
\(573\) 0 0
\(574\) 15.0000 43.3013i 0.626088 1.80736i
\(575\) 22.3607i 0.932505i
\(576\) 0 0
\(577\) −34.5000 + 19.9186i −1.43625 + 0.829222i −0.997587 0.0694283i \(-0.977883\pi\)
−0.438667 + 0.898650i \(0.644549\pi\)
\(578\) 96.1509i 3.99935i
\(579\) 0 0
\(580\) 0 0
\(581\) −19.3649 6.70820i −0.803392 0.278303i
\(582\) 0 0
\(583\) 10.0000 + 17.3205i 0.414158 + 0.717342i
\(584\) 7.74597 + 13.4164i 0.320530 + 0.555175i
\(585\) 0 0
\(586\) 15.0000 + 8.66025i 0.619644 + 0.357752i
\(587\) 15.4919 26.8328i 0.639421 1.10751i −0.346140 0.938183i \(-0.612508\pi\)
0.985560 0.169326i \(-0.0541590\pi\)
\(588\) 0 0
\(589\) −3.00000 5.19615i −0.123613 0.214104i
\(590\) 0 0
\(591\) 0 0
\(592\) −5.00000 −0.205499
\(593\) 15.4919 26.8328i 0.636177 1.10189i −0.350087 0.936717i \(-0.613848\pi\)
0.986264 0.165174i \(-0.0528187\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 46.4758 + 26.8328i 1.90372 + 1.09911i
\(597\) 0 0
\(598\) −15.0000 8.66025i −0.613396 0.354144i
\(599\) 7.74597 + 4.47214i 0.316492 + 0.182727i 0.649828 0.760082i \(-0.274841\pi\)
−0.333336 + 0.942808i \(0.608174\pi\)
\(600\) 0 0
\(601\) 37.5000 + 21.6506i 1.52966 + 0.883148i 0.999376 + 0.0353259i \(0.0112469\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 40.6663 7.82624i 1.65744 0.318974i
\(603\) 0 0
\(604\) −19.5000 + 33.7750i −0.793444 + 1.37428i
\(605\) 0 0
\(606\) 0 0
\(607\) 31.1769i 1.26543i −0.774384 0.632716i \(-0.781940\pi\)
0.774384 0.632716i \(-0.218060\pi\)
\(608\) 11.6190 + 20.1246i 0.471211 + 0.816161i
\(609\) 0 0
\(610\) 0 0
\(611\) −11.6190 6.70820i −0.470052 0.271385i
\(612\) 0 0
\(613\) −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) 5.80948 + 10.0623i 0.234451 + 0.406082i
\(615\) 0 0
\(616\) 5.00000 + 25.9808i 0.201456 + 1.04679i
\(617\) −19.3649 + 11.1803i −0.779602 + 0.450104i −0.836289 0.548288i \(-0.815280\pi\)
0.0566871 + 0.998392i \(0.481946\pi\)
\(618\) 0 0
\(619\) 5.19615i 0.208851i 0.994533 + 0.104425i \(0.0333004\pi\)
−0.994533 + 0.104425i \(0.966700\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 34.6410i 1.38898i
\(623\) 38.7298 + 13.4164i 1.55168 + 0.537517i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 15.4919 26.8328i 0.619182 1.07246i
\(627\) 0 0
\(628\) −36.0000 + 20.7846i −1.43656 + 0.829396i
\(629\) 38.7298 1.54426
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 21.3014 12.2984i 0.847325 0.489203i
\(633\) 0 0
\(634\) −5.00000 + 8.66025i −0.198575 + 0.343943i
\(635\) 0 0
\(636\) 0 0
\(637\) −7.50000 + 9.52628i −0.297161 + 0.377445i
\(638\) 44.7214i 1.77054i
\(639\) 0 0
\(640\) 0 0
\(641\) 4.47214i 0.176639i 0.996092 + 0.0883194i \(0.0281496\pi\)
−0.996092 + 0.0883194i \(0.971850\pi\)
\(642\) 0 0
\(643\) −16.5000 + 9.52628i −0.650696 + 0.375680i −0.788723 0.614749i \(-0.789257\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) 11.6190 33.5410i 0.457851 1.32170i
\(645\) 0 0
\(646\) −30.0000 51.9615i −1.18033 2.04440i
\(647\) 7.74597 + 13.4164i 0.304525 + 0.527453i 0.977156 0.212525i \(-0.0681688\pi\)
−0.672630 + 0.739979i \(0.734835\pi\)
\(648\) 0 0
\(649\) 30.0000 + 17.3205i 1.17760 + 0.679889i
\(650\) 9.68246 16.7705i 0.379777 0.657794i
\(651\) 0 0
\(652\) −19.5000 33.7750i −0.763679 1.32273i
\(653\) 22.3607i 0.875041i −0.899208 0.437521i \(-0.855857\pi\)
0.899208 0.437521i \(-0.144143\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.87298 6.70820i 0.151215 0.261911i
\(657\) 0 0
\(658\) 15.0000 43.3013i 0.584761 1.68806i
\(659\) −15.4919 8.94427i −0.603480 0.348419i 0.166929 0.985969i \(-0.446615\pi\)
−0.770409 + 0.637549i \(0.779948\pi\)
\(660\) 0 0
\(661\) 24.0000 + 13.8564i 0.933492 + 0.538952i 0.887914 0.460009i \(-0.152154\pi\)
0.0455776 + 0.998961i \(0.485487\pi\)
\(662\) −7.74597 4.47214i −0.301056 0.173814i
\(663\) 0 0
\(664\) 15.0000 + 8.66025i 0.582113 + 0.336083i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.0000 17.3205i 0.387202 0.670653i
\(668\) −23.2379 −0.899101
\(669\) 0 0
\(670\) 0 0
\(671\) −19.3649 33.5410i −0.747574 1.29484i
\(672\) 0 0
\(673\) −1.00000 + 1.73205i −0.0385472 + 0.0667657i −0.884655 0.466246i \(-0.845606\pi\)
0.846108 + 0.533011i \(0.178940\pi\)
\(674\) −19.3649 11.1803i −0.745909 0.430651i
\(675\) 0 0
\(676\) 15.0000 + 25.9808i 0.576923 + 0.999260i
\(677\) −15.4919 26.8328i −0.595403 1.03127i −0.993490 0.113921i \(-0.963659\pi\)
0.398086 0.917348i \(-0.369674\pi\)
\(678\) 0 0
\(679\) 1.50000 4.33013i 0.0575647 0.166175i
\(680\) 0 0
\(681\) 0 0
\(682\) 17.3205i 0.663237i
\(683\) −30.9839 + 17.8885i −1.18556 + 0.684486i −0.957295 0.289112i \(-0.906640\pi\)
−0.228269 + 0.973598i \(0.573307\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −36.7933 19.0066i −1.40478 0.725675i
\(687\) 0 0
\(688\) 7.00000 0.266872
\(689\) 3.87298 6.70820i 0.147549 0.255562i
\(690\) 0 0
\(691\) 28.5000 16.4545i 1.08419 0.625958i 0.152167 0.988355i \(-0.451375\pi\)
0.932024 + 0.362397i \(0.118041\pi\)
\(692\) 46.4758 1.76674
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) 0 0
\(696\) 0 0
\(697\) −30.0000 + 51.9615i −1.13633 + 1.96818i
\(698\) −50.3488 −1.90573
\(699\) 0 0
\(700\) 37.5000 + 12.9904i 1.41737 + 0.490990i
\(701\) 8.94427i 0.337820i −0.985631 0.168910i \(-0.945975\pi\)
0.985631 0.168910i \(-0.0540248\pi\)
\(702\) 0 0
\(703\) 15.0000 8.66025i 0.565736 0.326628i
\(704\) 58.1378i 2.19115i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −5.50000 9.52628i −0.206557 0.357767i 0.744071 0.668101i \(-0.232892\pi\)
−0.950628 + 0.310334i \(0.899559\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −30.0000 17.3205i −1.12430 0.649113i
\(713\) −3.87298 + 6.70820i −0.145044 + 0.251224i
\(714\) 0 0
\(715\) 0 0
\(716\) 26.8328i 1.00279i
\(717\) 0 0
\(718\) 10.0000 0.373197
\(719\) −7.74597 + 13.4164i −0.288876 + 0.500348i −0.973542 0.228509i \(-0.926615\pi\)
0.684666 + 0.728857i \(0.259948\pi\)
\(720\) 0 0
\(721\) 13.5000 2.59808i 0.502766 0.0967574i
\(722\) 13.5554 + 7.82624i 0.504481 + 0.291262i
\(723\) 0 0
\(724\) 0 0
\(725\) 19.3649 + 11.1803i 0.719195 + 0.415227i
\(726\) 0 0
\(727\) −16.5000 9.52628i −0.611951 0.353310i 0.161778 0.986827i \(-0.448277\pi\)
−0.773729 + 0.633517i \(0.781611\pi\)
\(728\) 7.74597 6.70820i 0.287085 0.248623i
\(729\) 0 0
\(730\) 0 0
\(731\) −54.2218 −2.00546
\(732\) 0 0
\(733\) 36.3731i 1.34347i −0.740792 0.671735i \(-0.765549\pi\)
0.740792 0.671735i \(-0.234451\pi\)
\(734\) 11.6190 + 20.1246i 0.428863 + 0.742813i
\(735\) 0 0
\(736\) 15.0000 25.9808i 0.552907 0.957664i
\(737\) 3.87298 + 2.23607i 0.142663 + 0.0823666i
\(738\) 0 0
\(739\) −11.5000 19.9186i −0.423034 0.732717i 0.573200 0.819415i \(-0.305702\pi\)
−0.996235 + 0.0866983i \(0.972368\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 25.0000 + 8.66025i 0.917779 + 0.317928i
\(743\) 27.1109 15.6525i 0.994602 0.574234i 0.0879552 0.996124i \(-0.471967\pi\)
0.906647 + 0.421891i \(0.138633\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −3.87298 + 2.23607i −0.141800 + 0.0818683i
\(747\) 0 0
\(748\) 103.923i 3.79980i
\(749\) −3.87298 + 11.1803i −0.141516 + 0.408521i
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 3.87298 6.70820i 0.141233 0.244623i
\(753\) 0 0
\(754\) 15.0000 8.66025i 0.546268 0.315388i
\(755\) 0 0
\(756\) 0 0
\(757\) −25.0000 −0.908640 −0.454320 0.890838i \(-0.650118\pi\)
−0.454320 + 0.890838i \(0.650118\pi\)
\(758\) −32.9204 + 19.0066i −1.19572 + 0.690350i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 2.00000 1.73205i 0.0724049 0.0627044i
\(764\) 53.6656i 1.94155i
\(765\) 0 0
\(766\) −45.0000 + 25.9808i −1.62592 + 0.938723i
\(767\) 13.4164i 0.484438i
\(768\) 0 0
\(769\) −30.0000 + 17.3205i −1.08183 + 0.624593i −0.931389 0.364026i \(-0.881402\pi\)
−0.150439 + 0.988619i \(0.548069\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10.5000 18.1865i −0.377903 0.654548i
\(773\) −15.4919 26.8328i −0.557206 0.965109i −0.997728 0.0673675i \(-0.978540\pi\)
0.440522 0.897742i \(-0.354793\pi\)
\(774\) 0 0
\(775\) −7.50000 4.33013i −0.269408 0.155543i
\(776\) −1.93649 + 3.35410i −0.0695160 + 0.120405i
\(777\) 0 0
\(778\) 10.0000 + 17.3205i 0.358517 + 0.620970i
\(779\) 26.8328i 0.961385i
\(780\) 0 0
\(781\) 40.0000 1.43131
\(782\) −38.7298 + 67.0820i −1.38498 + 2.39885i
\(783\) 0 0
\(784\) −5.50000 4.33013i −0.196429 0.154647i
\(785\) 0 0
\(786\) 0 0
\(787\) −16.5000 9.52628i −0.588161 0.339575i 0.176209 0.984353i \(-0.443617\pi\)
−0.764370 + 0.644778i \(0.776950\pi\)
\(788\) −23.2379 13.4164i −0.827816 0.477940i
\(789\) 0 0
\(790\) 0 0
\(791\) 15.4919 + 17.8885i 0.550830 + 0.636043i
\(792\) 0 0
\(793\) −7.50000 + 12.9904i −0.266333