Properties

Label 567.2.s.e.458.2
Level $567$
Weight $2$
Character 567.458
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 458.2
Root \(1.93649 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 567.458
Dual form 567.2.s.e.26.2

$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

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

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 \(-0.0431180\pi\)
0.378467 + 0.925615i \(0.376451\pi\)
\(3\) 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 0.693375 0.720577i \(-0.256123\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −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 0.172624 0.984988i \(-0.444775\pi\)
0.766712 0.641991i \(-0.221891\pi\)
\(18\) 0 0
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 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 \(-0.530369\pi\)
0.814456 + 0.580225i \(0.197035\pi\)
\(30\) 0 0
\(31\) 1.50000 0.866025i 0.269408 0.155543i −0.359211 0.933257i \(-0.616954\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 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 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) −7.74597 −1.25656
\(39\) 0 0
\(40\) 0 0
\(41\) 3.87298 6.70820i 0.604858 1.04765i −0.387215 0.921989i \(-0.626563\pi\)
0.992074 0.125656i \(-0.0401036\pi\)
\(42\) 0 0
\(43\) 3.50000 + 6.06218i 0.533745 + 0.924473i 0.999223 + 0.0394140i \(0.0125491\pi\)
−0.465478 + 0.885059i \(0.654118\pi\)
\(44\) −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 −0.432123 0.901815i \(-0.642235\pi\)
0.997056 0.0766776i \(-0.0244312\pi\)
\(48\) 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 \(-0.432708\pi\)
−0.741829 + 0.670590i \(0.766041\pi\)
\(54\) 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 −0.999988 0.00487911i \(-0.998447\pi\)
0.495769 0.868455i \(-0.334886\pi\)
\(60\) 0 0
\(61\) −7.50000 4.33013i −0.960277 0.554416i −0.0640184 0.997949i \(-0.520392\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 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 0.894951 0.446165i \(-0.147211\pi\)
−0.833866 + 0.551967i \(0.813877\pi\)
\(68\) 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 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) 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 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 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 \(-0.306433\pi\)
−0.996431 + 0.0844091i \(0.973100\pi\)
\(84\) 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 0.904886 + 0.425655i \(0.139956\pi\)
−0.0838147 + 0.996481i \(0.526710\pi\)
\(90\) 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 −0.421912 0.906637i \(-0.638641\pi\)
0.574214 + 0.818705i \(0.305308\pi\)
\(98\) −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 \(-0.917597\pi\)
0.966678 0.255996i \(-0.0824034\pi\)
\(104\) −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 \(-0.597310\pi\)
0.675386 + 0.737465i \(0.263977\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 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 \(-0.195117\pi\)
−0.0892596 + 0.996008i \(0.528450\pi\)
\(114\) 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 0.146985 0.989139i \(-0.453043\pi\)
−0.783127 + 0.621862i \(0.786376\pi\)
\(140\) 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 −0.895466 0.445130i \(-0.853157\pi\)
−0.0622385 + 0.998061i \(0.519824\pi\)
\(158\) −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 0.999944 + 0.0105623i \(0.00336213\pi\)
−0.490825 + 0.871258i \(0.663305\pi\)
\(164\) 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 \(-0.736447\pi\)
0.976067 + 0.217468i \(0.0697799\pi\)
\(168\) 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 0.405460 + 0.914113i \(0.367111\pi\)
−0.994375 + 0.105918i \(0.966222\pi\)
\(174\) 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 \(-0.224846\pi\)
−0.181760 + 0.983343i \(0.558179\pi\)
\(180\) 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 \(-0.557387\pi\)
−0.941645 + 0.336607i \(0.890720\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) 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 0.992434 0.122782i \(-0.0391815\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 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 −0.328135 0.944631i \(-0.606420\pi\)
0.982142 0.188142i \(-0.0602466\pi\)
\(212\) 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 −0.995025 0.0996209i \(-0.968237\pi\)
−0.411239 + 0.911528i \(0.634904\pi\)
\(224\) 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 \(-0.780332\pi\)
−0.771177 + 0.636621i \(0.780332\pi\)
\(228\) 0 0
\(229\) 25.9808i 1.71686i 0.512933 + 0.858429i \(0.328559\pi\)
−0.512933 + 0.858429i \(0.671441\pi\)
\(230\) 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 \(-0.761313\pi\)
0.224332 + 0.974513i \(0.427980\pi\)
\(234\) 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 \(-0.239918\pi\)
−0.228100 + 0.973638i \(0.573251\pi\)
\(240\) 0 0
\(241\) 15.5885i 1.00414i −0.864827 0.502070i \(-0.832572\pi\)
0.864827 0.502070i \(-0.167428\pi\)
\(242\) −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 \(-0.762059\pi\)
−0.733382 + 0.679817i \(0.762059\pi\)
\(252\) 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 \(-0.758054\pi\)
−0.724770 + 0.688991i \(0.758054\pi\)
\(258\) 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 \(-0.989902\pi\)
0.527217 + 0.849731i \(0.323236\pi\)
\(270\) 0 0
\(271\) 1.50000 0.866025i 0.0911185 0.0526073i −0.453748 0.891130i \(-0.649914\pi\)
0.544867 + 0.838523i \(0.316580\pi\)
\(272\) −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 \(-0.487517\pi\)
0.884963 + 0.465661i \(0.154183\pi\)
\(282\) 0 0
\(283\) 10.5000 6.06218i 0.624160 0.360359i −0.154327 0.988020i \(-0.549321\pi\)
0.778487 + 0.627661i \(0.215988\pi\)
\(284\) 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 \(-0.760683\pi\)
0.956697 + 0.291084i \(0.0940161\pi\)
\(294\) 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 \(0.0473737\pi\)
−0.988945 + 0.148280i \(0.952626\pi\)
\(308\) −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 \(-0.0219168\pi\)
−0.558397 + 0.829574i \(0.688583\pi\)
\(312\) 0 0
\(313\) −12.0000 6.92820i −0.678280 0.391605i 0.120927 0.992661i \(-0.461413\pi\)
−0.799207 + 0.601056i \(0.794747\pi\)
\(314\) −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 \(-0.373416\pi\)
−0.604805 + 0.796373i \(0.706749\pi\)
\(318\) 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 −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 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 −0.697100 0.716974i \(-0.745527\pi\)
0.969468 + 0.245220i \(0.0788601\pi\)
\(338\) 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 \(-0.743839\pi\)
0.277464 + 0.960736i \(0.410506\pi\)
\(348\) 0 0
\(349\) 19.5000 11.2583i 1.04381 0.602645i 0.122901 0.992419i \(-0.460780\pi\)
0.920910 + 0.389774i \(0.127447\pi\)
\(350\) 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 \(-0.629014\pi\)
0.598710 + 0.800966i \(0.295680\pi\)
\(360\) 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 \(0.0874327\pi\)
−0.962513 + 0.271237i \(0.912567\pi\)
\(368\) 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 \(-0.702334\pi\)
−0.593701 + 0.804686i \(0.702334\pi\)
\(384\) 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 −0.976813 0.214094i \(-0.931320\pi\)
−0.302995 + 0.952992i \(0.597987\pi\)
\(398\) 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 0.0667458 0.997770i \(-0.478738\pi\)
0.897467 + 0.441081i \(0.145405\pi\)
\(410\) 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 \(-0.956864\pi\)
0.612417 + 0.790535i \(0.290198\pi\)
\(420\) 0 0
\(421\) 17.0000 + 29.4449i 0.828529 + 1.43505i 0.899192 + 0.437555i \(0.144155\pi\)
−0.0706626 + 0.997500i \(0.522511\pi\)
\(422\) 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 \(-0.605189\pi\)
−0.981407 + 0.191940i \(0.938522\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i −0.927200 0.374567i \(-0.877791\pi\)
0.927200 0.374567i \(-0.122209\pi\)
\(434\) −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 0.426698 0.904394i \(-0.359677\pi\)
−0.569880 + 0.821728i \(0.693010\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) 30.9839 + 17.8885i 1.47209 + 0.849910i 0.999508 0.0313772i \(-0.00998932\pi\)
0.472580 + 0.881288i \(0.343323\pi\)
\(444\) 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 −0.965512 0.260358i \(-0.916159\pi\)
0.708233 + 0.705979i \(0.249493\pi\)
\(458\) −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 \(-0.224400\pi\)
−0.942011 + 0.335582i \(0.891067\pi\)
\(462\) 0 0
\(463\) −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i \(-0.892852\pi\)
0.757982 + 0.652275i \(0.226185\pi\)
\(464\) 4.47214i 0.207614i
\(465\) 0 0
\(466\) −20.0000 −0.926482
\(467\) −15.4919 26.8328i −0.716881 1.24167i −0.962229 0.272240i \(-0.912236\pi\)
0.245348 0.969435i \(-0.421098\pi\)
\(468\) 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 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) 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 \(-0.164987\pi\)
0.00527540 + 0.999986i \(0.498321\pi\)
\(492\) 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 \(-0.326653\pi\)
0.518063 + 0.855342i \(0.326653\pi\)
\(504\) 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 \(-0.327792\pi\)
0.515001 + 0.857190i \(0.327792\pi\)
\(510\) 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 \(-0.779060\pi\)
0.938307 + 0.345804i \(0.112394\pi\)
\(522\) 0 0
\(523\) −16.5000 + 9.52628i −0.721495 + 0.416555i −0.815303 0.579035i \(-0.803429\pi\)
0.0938079 + 0.995590i \(0.470096\pi\)
\(524\) 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 0.675399 0.737453i \(-0.263972\pi\)
−0.976352 + 0.216186i \(0.930638\pi\)
\(542\) 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 0.724157 0.689635i \(-0.242229\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(548\) −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 \(-0.0595286\pi\)
0.330265 + 0.943888i \(0.392862\pi\)
\(558\) 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 \(-0.218857\pi\)
−0.936024 + 0.351936i \(0.885524\pi\)
\(564\) 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 \(-0.455678\pi\)
−0.788248 + 0.615358i \(0.789011\pi\)
\(570\) 0 0
\(571\) 8.00000 + 13.8564i 0.334790 + 0.579873i 0.983444 0.181210i \(-0.0580014\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) −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 −0.438667 0.898650i \(-0.644549\pi\)
−0.997587 + 0.0694283i \(0.977883\pi\)
\(578\) 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 −0.985560 0.169326i \(-0.945841\pi\)
0.346140 0.938183i \(-0.387492\pi\)
\(588\) 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 −0.986264 0.165174i \(-0.947181\pi\)
0.350087 0.936717i \(-0.386152\pi\)
\(594\) 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 \(-0.725159\pi\)
0.333336 + 0.942808i \(0.391826\pi\)
\(600\) 0 0
\(601\) 37.5000 21.6506i 1.52966 0.883148i 0.530281 0.847822i \(-0.322086\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) −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 \(0.218060\pi\)
−0.774384 + 0.632716i \(0.781940\pi\)
\(608\) −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 −0.999178 0.0405396i \(-0.987092\pi\)
0.534697 + 0.845044i \(0.320426\pi\)
\(614\) −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 \(-0.184720\pi\)
−0.0566871 + 0.998392i \(0.518054\pi\)
\(618\) 0 0
\(619\) 5.19615i 0.208851i −0.994533 0.104425i \(-0.966700\pi\)
0.994533 0.104425i \(-0.0333004\pi\)
\(620\) 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 0.138027 0.990429i \(-0.455924\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) −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 \(-0.931831\pi\)
0.672630 + 0.739979i \(0.265165\pi\)
\(648\) 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 \(-0.553385\pi\)
0.770409 + 0.637549i \(0.220052\pi\)
\(660\) 0 0
\(661\) 24.0000 13.8564i 0.933492 0.538952i 0.0455776 0.998961i \(-0.485487\pi\)
0.887914 + 0.460009i \(0.152154\pi\)
\(662\) 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 0.846108 0.533011i \(-0.178940\pi\)
−0.884655 + 0.466246i \(0.845606\pi\)
\(674\) 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 −0.398086 0.917348i \(-0.630326\pi\)
0.993490 0.113921i \(-0.0363411\pi\)
\(678\) 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 \(-0.0933600\pi\)
0.228269 + 0.973598i \(0.426693\pi\)
\(684\) 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 0.932024 0.362397i \(-0.118041\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) −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 −0.950628 0.310334i \(-0.899559\pi\)
0.744071 + 0.668101i \(0.232892\pi\)
\(710\) 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 \(-0.0733852\pi\)
−0.684666 + 0.728857i \(0.740052\pi\)
\(720\) 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 −0.773729 0.633517i \(-0.781611\pi\)
0.161778 + 0.986827i \(0.448277\pi\)
\(728\) −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 \(0.234451\pi\)
−0.740792 + 0.671735i \(0.765549\pi\)
\(734\) −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 −0.996235 0.0866983i \(-0.972368\pi\)
0.573200 + 0.819415i \(0.305702\pi\)
\(740\) 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 \(-0.528033\pi\)
−0.906647 + 0.421891i \(0.861367\pi\)
\(744\) 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 −0.150439 0.988619i \(-0.548069\pi\)
−0.931389 + 0.364026i \(0.881402\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10.5000 + 18.1865i −0.377903 + 0.654548i
\(773\) 15.4919 26.8328i 0.557206 0.965109i −0.440522 0.897742i \(-0.645207\pi\)
0.997728 0.0673675i \(-0.0214600\pi\)
\(774\) 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 −0.764370 0.644778i \(-0.776950\pi\)
0.176209 + 0.984353i \(0.443617\pi\)
\(788\) 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 0.461302i