Properties

Label 567.2.s.e.458.1
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 458.1
Root \(-1.93649 - 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 567.458
Dual form 567.2.s.e.26.1

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

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

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 −0.378467 0.925615i \(-0.623549\pi\)
−0.990839 + 0.135045i \(0.956882\pi\)
\(3\) 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 \(-0.764489\pi\)
0.738549 0.674200i \(-0.235511\pi\)
\(12\) 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 \(0.555225\pi\)
−0.766712 + 0.641991i \(0.778109\pi\)
\(18\) 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 \(-0.845604\pi\)
0.884652 0.466252i \(-0.154396\pi\)
\(24\) 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 −0.814456 0.580225i \(-0.802965\pi\)
0.0952614 + 0.995452i \(0.469631\pi\)
\(30\) 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 \(0.373437\pi\)
−0.992074 + 0.125656i \(0.959896\pi\)
\(42\) 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 \(0.357765\pi\)
−0.997056 + 0.0766776i \(0.975569\pi\)
\(48\) 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 0.741829 0.670590i \(-0.233959\pi\)
−0.209833 + 0.977737i \(0.567292\pi\)
\(54\) 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 \(0.00155308\pi\)
−0.495769 + 0.868455i \(0.665114\pi\)
\(60\) 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 \(0.178088\pi\)
−0.847532 + 0.530745i \(0.821912\pi\)
\(72\) 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 0.996431 0.0844091i \(-0.0269003\pi\)
−0.571316 + 0.820730i \(0.693567\pi\)
\(84\) 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 \(-0.860044\pi\)
0.0838147 0.996481i \(-0.473290\pi\)
\(90\) 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 −0.675386 0.737465i \(-0.736023\pi\)
0.300970 + 0.953634i \(0.402690\pi\)
\(108\) 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 0.0892596 0.996008i \(-0.471550\pi\)
−0.817939 + 0.575305i \(0.804883\pi\)
\(114\) 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 \(-0.938814\pi\)
0.981582 0.191040i \(-0.0611861\pi\)
\(138\) 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 \(-0.738240\pi\)
0.680505 0.732743i \(-0.261760\pi\)
\(150\) 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 −0.976067 0.217468i \(-0.930220\pi\)
0.676367 + 0.736565i \(0.263553\pi\)
\(168\) 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 \(-0.632889\pi\)
0.994375 0.105918i \(-0.0337780\pi\)
\(174\) 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 0.181760 0.983343i \(-0.441821\pi\)
−0.760720 + 0.649080i \(0.775154\pi\)
\(180\) 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 0.941645 0.336607i \(-0.109280\pi\)
0.179312 + 0.983792i \(0.442613\pi\)
\(192\) 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 \(0.103222\pi\)
−0.947880 + 0.318626i \(0.896778\pi\)
\(198\) 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 \(-0.219668\pi\)
0.771177 + 0.636621i \(0.219668\pi\)
\(228\) 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 −0.224332 0.974513i \(-0.572020\pi\)
0.731787 + 0.681533i \(0.238687\pi\)
\(234\) 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 0.228100 0.973638i \(-0.426749\pi\)
−0.729145 + 0.684359i \(0.760082\pi\)
\(240\) 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 \(-0.237941\pi\)
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 \(-0.955971\pi\)
0.990449 0.137882i \(-0.0440294\pi\)
\(264\) 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 −0.527217 0.849731i \(-0.676764\pi\)
0.999497 + 0.0317179i \(0.0100978\pi\)
\(270\) 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 −0.884963 0.465661i \(-0.845817\pi\)
−0.0392078 + 0.999231i \(0.512483\pi\)
\(282\) 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 −0.956697 0.291084i \(-0.905984\pi\)
0.730435 + 0.682982i \(0.239317\pi\)
\(294\) 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 0.558397 0.829574i \(-0.311417\pi\)
−0.997631 + 0.0687991i \(0.978083\pi\)
\(312\) 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 0.604805 0.796373i \(-0.293251\pi\)
−0.387277 + 0.921963i \(0.626584\pi\)
\(318\) 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 −0.277464 0.960736i \(-0.589494\pi\)
0.693290 + 0.720659i \(0.256161\pi\)
\(348\) 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 −0.598710 0.800966i \(-0.704320\pi\)
0.394302 + 0.918981i \(0.370986\pi\)
\(360\) 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 \(-0.297666\pi\)
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 \(0.0728088\pi\)
−0.973954 + 0.226746i \(0.927191\pi\)
\(390\) 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 \(0.188554\pi\)
−0.829626 + 0.558320i \(0.811446\pi\)
\(402\) 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 −0.612417 0.790535i \(-0.709802\pi\)
0.990832 + 0.135101i \(0.0431358\pi\)
\(420\) 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 0.981407 0.191940i \(-0.0614778\pi\)
0.324479 + 0.945893i \(0.394811\pi\)
\(432\) 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 −0.472580 0.881288i \(-0.656677\pi\)
−0.999508 + 0.0313772i \(0.990011\pi\)
\(444\) 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 \(0.0676893\pi\)
−0.977475 + 0.211053i \(0.932311\pi\)
\(450\) 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 0.942011 0.335582i \(-0.108933\pi\)
−0.761628 + 0.648014i \(0.775600\pi\)
\(462\) 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 \(0.0877643\pi\)
−0.245348 + 0.969435i \(0.578902\pi\)
\(468\) 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 −0.00527540 0.999986i \(-0.501679\pi\)
−0.868651 + 0.495424i \(0.835013\pi\)
\(492\) 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 −0.938307 0.345804i \(-0.887606\pi\)
0.768628 + 0.639696i \(0.220940\pi\)
\(522\) 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 −0.330265 0.943888i \(-0.607138\pi\)
−0.982564 + 0.185926i \(0.940471\pi\)
\(558\) 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 0.936024 0.351936i \(-0.114476\pi\)
−0.772797 + 0.634653i \(0.781143\pi\)
\(564\) 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 0.788248 0.615358i \(-0.210989\pi\)
−0.138792 + 0.990322i \(0.544322\pi\)
\(570\) 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 \(0.0541590\pi\)
−0.346140 + 0.938183i \(0.612508\pi\)
\(588\) 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 \(0.0528187\pi\)
−0.350087 + 0.936717i \(0.613848\pi\)
\(594\) 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 −0.333336 0.942808i \(-0.608174\pi\)
0.649828 + 0.760082i \(0.274841\pi\)
\(600\) 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 0.0566871 0.998392i \(-0.481946\pi\)
−0.836289 + 0.548288i \(0.815280\pi\)
\(618\) 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 \(-0.971850\pi\)
0.996092 0.0883194i \(-0.0281496\pi\)
\(642\) 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 −0.672630 0.739979i \(-0.734835\pi\)
0.977156 + 0.212525i \(0.0681688\pi\)
\(648\) 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 \(0.144143\pi\)
−0.899208 + 0.437521i \(0.855857\pi\)
\(654\) 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 −0.770409 0.637549i \(-0.779948\pi\)
0.166929 + 0.985969i \(0.446615\pi\)
\(660\) 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 \(0.369674\pi\)
−0.993490 + 0.113921i \(0.963659\pi\)
\(678\) 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 −0.228269 0.973598i \(-0.573307\pi\)
−0.957295 + 0.289112i \(0.906640\pi\)
\(684\) 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 \(0.0540248\pi\)
−0.985631 + 0.168910i \(0.945975\pi\)
\(702\) 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 0.684666 0.728857i \(-0.259948\pi\)
−0.973542 + 0.228509i \(0.926615\pi\)
\(720\) 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 0.906647 0.421891i \(-0.138633\pi\)
0.0879552 + 0.996124i \(0.471967\pi\)
\(744\) 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 \(0.354793\pi\)
−0.997728 + 0.0673675i \(0.978540\pi\)
\(774\) 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