Properties

Label 189.2.p.c.80.1
Level $189$
Weight $2$
Character 189.80
Analytic conductor $1.509$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.50917259820\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 80.1
Root \(-1.93649 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 189.80
Dual form 189.2.p.c.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.93649 + 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-2.00000 - 1.73205i) q^{7} +2.23607i q^{8} +O(q^{10})\) \(q+(-1.93649 + 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-2.00000 - 1.73205i) q^{7} +2.23607i q^{8} +(-3.87298 - 2.23607i) q^{11} -1.73205i q^{13} +(5.80948 + 1.11803i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.87298 - 6.70820i) q^{17} +(-3.00000 + 1.73205i) q^{19} +10.0000 q^{22} +(3.87298 - 2.23607i) q^{23} +(2.50000 - 4.33013i) q^{25} +(1.93649 + 3.35410i) q^{26} +(-7.50000 + 2.59808i) q^{28} +4.47214i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-5.80948 - 3.35410i) q^{32} +17.3205i q^{34} +(-2.50000 - 4.33013i) q^{37} +(3.87298 - 6.70820i) q^{38} -7.74597 q^{41} -7.00000 q^{43} +(-11.6190 + 6.70820i) q^{44} +(-5.00000 + 8.66025i) q^{46} +(3.87298 + 6.70820i) q^{47} +(1.00000 + 6.92820i) q^{49} +11.1803i q^{50} +(-4.50000 - 2.59808i) q^{52} +(-3.87298 - 2.23607i) q^{53} +(3.87298 - 4.47214i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(-3.87298 + 6.70820i) q^{59} +(7.50000 - 4.33013i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(0.500000 - 0.866025i) q^{67} +(-11.6190 - 20.1246i) q^{68} -8.94427i q^{71} +(6.00000 + 3.46410i) q^{73} +(9.68246 + 5.59017i) q^{74} +10.3923i q^{76} +(3.87298 + 11.1803i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(15.0000 - 8.66025i) q^{82} +7.74597 q^{83} +(13.5554 - 7.82624i) q^{86} +(5.00000 - 8.66025i) q^{88} +(7.74597 + 13.4164i) q^{89} +(-3.00000 + 3.46410i) q^{91} -13.4164i q^{92} +(-15.0000 - 8.66025i) q^{94} +1.73205i q^{97} +(-9.68246 - 12.2984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{4} - 8q^{7} + O(q^{10}) \) \( 4q + 6q^{4} - 8q^{7} + 2q^{16} - 12q^{19} + 40q^{22} + 10q^{25} - 30q^{28} - 6q^{31} - 10q^{37} - 28q^{43} - 20q^{46} + 4q^{49} - 18q^{52} - 20q^{58} + 30q^{61} + 52q^{64} + 2q^{67} + 24q^{73} - 22q^{79} + 60q^{82} + 20q^{88} - 12q^{91} - 60q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 2.23607i 0.790569i
\(9\) 0 0
\(10\) 0 0
\(11\) −3.87298 2.23607i −1.16775 0.674200i −0.214600 0.976702i \(-0.568845\pi\)
−0.953149 + 0.302502i \(0.902178\pi\)
\(12\) 0 0
\(13\) 1.73205i 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 5.80948 + 1.11803i 1.55265 + 0.298807i
\(15\) 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
\(22\) 10.0000 2.13201
\(23\) 3.87298 2.23607i 0.807573 0.466252i −0.0385394 0.999257i \(-0.512271\pi\)
0.846112 + 0.533005i \(0.178937\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 1.93649 + 3.35410i 0.379777 + 0.657794i
\(27\) 0 0
\(28\) −7.50000 + 2.59808i −1.41737 + 0.490990i
\(29\) 4.47214i 0.830455i 0.909718 + 0.415227i \(0.136298\pi\)
−0.909718 + 0.415227i \(0.863702\pi\)
\(30\) 0 0
\(31\) −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i \(-0.383046\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −5.80948 3.35410i −1.02698 0.592927i
\(33\) 0 0
\(34\) 17.3205i 2.97044i
\(35\) 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 \(0.968153\pi\)
\(38\) 3.87298 6.70820i 0.628281 1.08821i
\(39\) 0 0
\(40\) 0 0
\(41\) −7.74597 −1.20972 −0.604858 0.796333i \(-0.706770\pi\)
−0.604858 + 0.796333i \(0.706770\pi\)
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) −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 \(0.0244312\pi\)
−0.432123 + 0.901815i \(0.642235\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 11.1803i 1.58114i
\(51\) 0 0
\(52\) −4.50000 2.59808i −0.624038 0.360288i
\(53\) −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
\(56\) 3.87298 4.47214i 0.517549 0.597614i
\(57\) 0 0
\(58\) −5.00000 8.66025i −0.656532 1.13715i
\(59\) −3.87298 + 6.70820i −0.504219 + 0.873334i 0.495769 + 0.868455i \(0.334886\pi\)
−0.999988 + 0.00487911i \(0.998447\pi\)
\(60\) 0 0
\(61\) 7.50000 4.33013i 0.960277 0.554416i 0.0640184 0.997949i \(-0.479608\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 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 \(0.147211\pi\)
\(68\) −11.6190 20.1246i −1.40900 2.44047i
\(69\) 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 \(0.533784\pi\)
\(74\) 9.68246 + 5.59017i 1.12556 + 0.649844i
\(75\) 0 0
\(76\) 10.3923i 1.19208i
\(77\) 3.87298 + 11.1803i 0.441367 + 1.27412i
\(78\) 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
\(83\) 7.74597 0.850230 0.425115 0.905139i \(-0.360234\pi\)
0.425115 + 0.905139i \(0.360234\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 13.5554 7.82624i 1.46172 0.843925i
\(87\) 0 0
\(88\) 5.00000 8.66025i 0.533002 0.923186i
\(89\) 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
\(92\) 13.4164i 1.39876i
\(93\) 0 0
\(94\) −15.0000 8.66025i −1.54713 0.893237i
\(95\) 0 0
\(96\) 0 0
\(97\) 1.73205i 0.175863i 0.996127 + 0.0879316i \(0.0280257\pi\)
−0.996127 + 0.0879316i \(0.971974\pi\)
\(98\) −9.68246 12.2984i −0.978076 1.24232i
\(99\) 0 0
\(100\) −7.50000 12.9904i −0.750000 1.29904i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −4.50000 + 2.59808i −0.443398 + 0.255996i −0.705038 0.709170i \(-0.749070\pi\)
0.261640 + 0.965166i \(0.415737\pi\)
\(104\) 3.87298 0.379777
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 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
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) 8.94427i 0.841406i −0.907198 0.420703i \(-0.861783\pi\)
0.907198 0.420703i \(-0.138217\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 11.6190 + 6.70820i 1.07879 + 0.622841i
\(117\) 0 0
\(118\) 17.3205i 1.59448i
\(119\) −19.3649 + 6.70820i −1.77518 + 0.614940i
\(120\) 0 0
\(121\) 4.50000 + 7.79423i 0.409091 + 0.708566i
\(122\) −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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 9.00000 + 1.73205i 0.780399 + 0.150188i
\(134\) 2.23607i 0.193167i
\(135\) 0 0
\(136\) 15.0000 + 8.66025i 1.28624 + 0.742611i
\(137\) −3.87298 2.23607i −0.330891 0.191040i 0.325345 0.945595i \(-0.394519\pi\)
−0.656237 + 0.754555i \(0.727853\pi\)
\(138\) 0 0
\(139\) 8.66025i 0.734553i 0.930112 + 0.367277i \(0.119710\pi\)
−0.930112 + 0.367277i \(0.880290\pi\)
\(140\) 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
\(146\) −15.4919 −1.28212
\(147\) 0 0
\(148\) −15.0000 −1.23299
\(149\) 15.4919 8.94427i 1.26915 0.732743i 0.294322 0.955706i \(-0.404906\pi\)
0.974827 + 0.222963i \(0.0715729\pi\)
\(150\) 0 0
\(151\) 6.50000 11.2583i 0.528962 0.916190i −0.470467 0.882418i \(-0.655915\pi\)
0.999430 0.0337724i \(-0.0107521\pi\)
\(152\) −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 \(-0.146843\pi\)
0.0622385 + 0.998061i \(0.480176\pi\)
\(158\) 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 \(0.663305\pi\)
\(164\) −11.6190 + 20.1246i −0.907288 + 1.57147i
\(165\) 0 0
\(166\) −15.0000 + 8.66025i −1.16423 + 0.672166i
\(167\) −7.74597 −0.599401 −0.299700 0.954033i \(-0.596887\pi\)
−0.299700 + 0.954033i \(0.596887\pi\)
\(168\) 0 0
\(169\) 10.0000 0.769231
\(170\) 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 \(-0.966222\pi\)
0.405460 0.914113i \(-0.367111\pi\)
\(174\) 0 0
\(175\) −12.5000 + 4.33013i −0.944911 + 0.327327i
\(176\) 4.47214i 0.337100i
\(177\) 0 0
\(178\) −30.0000 17.3205i −2.24860 1.29823i
\(179\) 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 \(\pi\)
\(182\) 1.93649 10.0623i 0.143542 0.745868i
\(183\) 0 0
\(184\) 5.00000 + 8.66025i 0.368605 + 0.638442i
\(185\) 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 \(0.0855996\pi\)
\(194\) −1.93649 3.35410i −0.139032 0.240810i
\(195\) 0 0
\(196\) 19.5000 + 7.79423i 1.39286 + 0.556731i
\(197\) 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 \(0.372515\pi\)
\(200\) 9.68246 + 5.59017i 0.684653 + 0.395285i
\(201\) 0 0
\(202\) 0 0
\(203\) 7.74597 8.94427i 0.543660 0.627765i
\(204\) 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
\(209\) 15.4919 1.07160
\(210\) 0 0
\(211\) −19.0000 −1.30801 −0.654007 0.756489i \(-0.726913\pi\)
−0.654007 + 0.756489i \(0.726913\pi\)
\(212\) −11.6190 + 6.70820i −0.797993 + 0.460721i
\(213\) 0 0
\(214\) −5.00000 + 8.66025i −0.341793 + 0.592003i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.50000 + 4.33013i 0.101827 + 0.293948i
\(218\) 2.23607i 0.151446i
\(219\) 0 0
\(220\) 0 0
\(221\) −11.6190 6.70820i −0.781575 0.451243i
\(222\) 0 0
\(223\) 24.2487i 1.62381i −0.583787 0.811907i \(-0.698430\pi\)
0.583787 0.811907i \(-0.301570\pi\)
\(224\) 5.80948 + 16.7705i 0.388162 + 1.12053i
\(225\) 0 0
\(226\) 10.0000 + 17.3205i 0.665190 + 1.15214i
\(227\) 11.6190 20.1246i 0.771177 1.33572i −0.165742 0.986169i \(-0.553002\pi\)
0.936918 0.349548i \(-0.113665\pi\)
\(228\) 0 0
\(229\) 22.5000 12.9904i 1.48684 0.858429i 0.486954 0.873427i \(-0.338108\pi\)
0.999888 + 0.0149989i \(0.00477447\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) −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
\(238\) 30.0000 34.6410i 1.94461 2.24544i
\(239\) 8.94427i 0.578557i −0.957245 0.289278i \(-0.906585\pi\)
0.957245 0.289278i \(-0.0934153\pi\)
\(240\) 0 0
\(241\) 13.5000 + 7.79423i 0.869611 + 0.502070i 0.867219 0.497927i \(-0.165905\pi\)
0.00239235 + 0.999997i \(0.499238\pi\)
\(242\) −17.4284 10.0623i −1.12034 0.646830i
\(243\) 0 0
\(244\) 25.9808i 1.66325i
\(245\) 0 0
\(246\) 0 0
\(247\) 3.00000 + 5.19615i 0.190885 + 0.330623i
\(248\) 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
\(257\) 11.6190 + 20.1246i 0.724770 + 1.25534i 0.959069 + 0.283174i \(0.0913874\pi\)
−0.234298 + 0.972165i \(0.575279\pi\)
\(258\) 0 0
\(259\) −2.50000 + 12.9904i −0.155342 + 0.807183i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.87298 2.23607i −0.238818 0.137882i 0.375815 0.926695i \(-0.377363\pi\)
−0.614634 + 0.788813i \(0.710696\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −19.3649 + 6.70820i −1.18734 + 0.411306i
\(267\) 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 \(0.316580\pi\)
\(272\) 7.74597 0.469668
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) −19.3649 + 11.1803i −1.16775 + 0.674200i
\(276\) 0 0
\(277\) −2.50000 + 4.33013i −0.150210 + 0.260172i −0.931305 0.364241i \(-0.881328\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −9.68246 16.7705i −0.580715 1.00583i
\(279\) 0 0
\(280\) 0 0
\(281\) 17.8885i 1.06714i 0.845756 + 0.533571i \(0.179150\pi\)
−0.845756 + 0.533571i \(0.820850\pi\)
\(282\) 0 0
\(283\) −10.5000 6.06218i −0.624160 0.360359i 0.154327 0.988020i \(-0.450679\pi\)
−0.778487 + 0.627661i \(0.784012\pi\)
\(284\) −23.2379 13.4164i −1.37892 0.796117i
\(285\) 0 0
\(286\) 17.3205i 1.02418i
\(287\) 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
\(292\) 18.0000 10.3923i 1.05337 0.608164i
\(293\) −7.74597 −0.452524 −0.226262 0.974066i \(-0.572651\pi\)
−0.226262 + 0.974066i \(0.572651\pi\)
\(294\) 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
\(301\) 14.0000 + 12.1244i 0.806947 + 0.698836i
\(302\) 29.0689i 1.67273i
\(303\) 0 0
\(304\) −3.00000 1.73205i −0.172062 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 5.19615i 0.296560i 0.988945 + 0.148280i \(0.0473737\pi\)
−0.988945 + 0.148280i \(0.952626\pi\)
\(308\) 34.8569 + 6.70820i 1.98615 + 0.382235i
\(309\) 0 0
\(310\) 0 0
\(311\) 7.74597 13.4164i 0.439233 0.760775i −0.558397 0.829574i \(-0.688583\pi\)
0.997631 + 0.0687991i \(0.0219168\pi\)
\(312\) 0 0
\(313\) 12.0000 6.92820i 0.678280 0.391605i −0.120927 0.992661i \(-0.538587\pi\)
0.799207 + 0.601056i \(0.205253\pi\)
\(314\) −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
\(322\) 25.0000 8.66025i 1.39320 0.482617i
\(323\) 26.8328i 1.49302i
\(324\) 0 0
\(325\) −7.50000 4.33013i −0.416025 0.240192i
\(326\) −25.1744 14.5344i −1.39428 0.804988i
\(327\) 0 0
\(328\) 17.3205i 0.956365i
\(329\) 3.87298 20.1246i 0.213524 1.10951i
\(330\) 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
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) −19.3649 + 11.1803i −1.05331 + 0.608130i
\(339\) 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
\(344\) 15.6525i 0.843925i
\(345\) 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
\(349\) 22.5167i 1.20529i 0.798010 + 0.602645i \(0.205886\pi\)
−0.798010 + 0.602645i \(0.794114\pi\)
\(350\) 19.3649 22.3607i 1.03510 1.19523i
\(351\) 0 0
\(352\) 15.0000 + 25.9808i 0.799503 + 1.38478i
\(353\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 46.4758 2.46321
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) 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
\(364\) 4.50000 + 12.9904i 0.235864 + 0.680881i
\(365\) 0 0
\(366\) 0 0
\(367\) −9.00000 5.19615i −0.469796 0.271237i 0.246358 0.969179i \(-0.420766\pi\)
−0.716154 + 0.697942i \(0.754099\pi\)
\(368\) 3.87298 + 2.23607i 0.201893 + 0.116563i
\(369\) 0 0
\(370\) 0 0
\(371\) 3.87298 + 11.1803i 0.201075 + 0.580454i
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) 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
\(383\) 11.6190 + 20.1246i 0.593701 + 1.02832i 0.993729 + 0.111817i \(0.0356670\pi\)
−0.400028 + 0.916503i \(0.631000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.6525i 0.796690i
\(387\) 0 0
\(388\) 4.50000 + 2.59808i 0.228453 + 0.131897i
\(389\) 7.74597 + 4.47214i 0.392736 + 0.226746i 0.683345 0.730096i \(-0.260525\pi\)
−0.290609 + 0.956842i \(0.593858\pi\)
\(390\) 0 0
\(391\) 34.6410i 1.75187i
\(392\) −15.4919 + 2.23607i −0.782461 + 0.112938i
\(393\) 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 \(0.597987\pi\)
\(398\) −50.3488 −2.52376
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) −19.3649 + 11.1803i −0.967038 + 0.558320i −0.898332 0.439317i \(-0.855220\pi\)
−0.0687059 + 0.997637i \(0.521887\pi\)
\(402\) 0 0
\(403\) −1.50000 + 2.59808i −0.0747203 + 0.129419i
\(404\) 0 0
\(405\) 0 0
\(406\) −5.00000 + 25.9808i −0.248146 + 1.28940i
\(407\) 22.3607i 1.10838i
\(408\) 0 0
\(409\) −19.5000 11.2583i −0.964213 0.556689i −0.0667458 0.997770i \(-0.521262\pi\)
−0.897467 + 0.441081i \(0.854595\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.5885i 0.767988i
\(413\) 19.3649 6.70820i 0.952885 0.330089i
\(414\) 0 0
\(415\) 0 0
\(416\) −5.80948 + 10.0623i −0.284833 + 0.493345i
\(417\) 0 0
\(418\) −30.0000 + 17.3205i −1.46735 + 0.847174i
\(419\) 15.4919 0.756830 0.378415 0.925636i \(-0.376469\pi\)
0.378415 + 0.925636i \(0.376469\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 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
\(427\) −22.5000 4.33013i −1.08885 0.209550i
\(428\) 13.4164i 0.648507i
\(429\) 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 \(-0.122209\pi\)
\(434\) −7.74597 6.70820i −0.371818 0.322004i
\(435\) 0 0
\(436\) −1.50000 2.59808i −0.0718370 0.124425i
\(437\) −7.74597 + 13.4164i −0.370540 + 0.641794i
\(438\) 0 0
\(439\) 3.00000 1.73205i 0.143182 0.0826663i −0.426698 0.904394i \(-0.640323\pi\)
0.569880 + 0.821728i \(0.306990\pi\)
\(440\) 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
\(446\) 27.1109 + 46.9574i 1.28374 + 2.22350i
\(447\) 0 0
\(448\) −26.0000 22.5167i −1.22838 1.06381i
\(449\) 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
\(452\) −23.2379 13.4164i −1.09302 0.631055i
\(453\) 0 0
\(454\) 51.9615i 2.43868i
\(455\) 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
\(461\) 7.74597 0.360766 0.180383 0.983596i \(-0.442266\pi\)
0.180383 + 0.983596i \(0.442266\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −3.87298 + 2.23607i −0.179799 + 0.103807i
\(465\) 0 0
\(466\) 10.0000 17.3205i 0.463241 0.802357i
\(467\) −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
\(475\) 17.3205i 0.794719i
\(476\) −11.6190 + 60.3738i −0.532554 + 2.76723i
\(477\) 0 0
\(478\) 10.0000 + 17.3205i 0.457389 + 0.792222i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) −7.50000 + 4.33013i −0.341971 + 0.197437i
\(482\) −34.8569 −1.58769
\(483\) 0 0
\(484\) 27.0000 1.22727
\(485\) 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
\(491\) 22.3607i 1.00912i −0.863376 0.504562i \(-0.831654\pi\)
0.863376 0.504562i \(-0.168346\pi\)
\(492\) 0 0
\(493\) 30.0000 + 17.3205i 1.35113 + 0.780076i
\(494\) −11.6190 6.70820i −0.522761 0.301816i
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) −15.4919 + 17.8885i −0.694908 + 0.802411i
\(498\) 0 0
\(499\) 15.5000 + 26.8468i 0.693875 + 1.20183i 0.970558 + 0.240866i \(0.0774314\pi\)
−0.276683 + 0.960961i \(0.589235\pi\)
\(500\) 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
\(509\) −11.6190 20.1246i −0.515001 0.892008i −0.999848 0.0174091i \(-0.994458\pi\)
0.484848 0.874599i \(-0.338875\pi\)
\(510\) 0 0
\(511\) −6.00000 17.3205i −0.265424 0.766214i
\(512\) 11.1803i 0.494106i
\(513\) 0 0
\(514\) −45.0000 25.9808i −1.98486 1.14596i
\(515\) 0 0
\(516\) 0 0
\(517\) 34.6410i 1.52351i
\(518\) −9.68246 27.9508i −0.425423 1.22809i
\(519\) 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
\(526\) 10.0000 0.436021
\(527\) −11.6190 + 6.70820i −0.506129 + 0.292214i
\(528\) 0 0
\(529\) −1.50000 + 2.59808i −0.0652174 + 0.112960i
\(530\) 0 0
\(531\) 0 0
\(532\) 18.0000 20.7846i 0.780399 0.901127i
\(533\) 13.4164i 0.581129i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.93649 + 1.11803i 0.0836437 + 0.0482917i
\(537\) 0 0
\(538\) 34.6410i 1.49348i
\(539\) 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 \(0.930638\pi\)
\(542\) −1.93649 + 3.35410i −0.0831794 + 0.144071i
\(543\) 0 0
\(544\) −45.0000 + 25.9808i −1.92936 + 1.11392i
\(545\) 0 0
\(546\) 0 0
\(547\) 11.0000 0.470326 0.235163 0.971956i \(-0.424438\pi\)
0.235163 + 0.971956i \(0.424438\pi\)
\(548\) −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
\(553\) −5.50000 + 28.5788i −0.233884 + 1.21530i
\(554\) 11.1803i 0.475007i
\(555\) 0 0
\(556\) 22.5000 + 12.9904i 0.954213 + 0.550915i
\(557\) 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
\(562\) −20.0000 34.6410i −0.843649 1.46124i
\(563\) −3.87298 + 6.70820i −0.163227 + 0.282717i −0.936024 0.351936i \(-0.885524\pi\)
0.772797 + 0.634653i \(0.218857\pi\)
\(564\) 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 \(0.0580014\pi\)
\(572\) 11.6190 + 20.1246i 0.485813 + 0.841452i
\(573\) 0 0
\(574\) −45.0000 8.66025i −1.87826 0.361472i
\(575\) 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 \(0.977883\pi\)
\(578\) 83.2691 + 48.0755i 3.46354 + 1.99968i
\(579\) 0 0
\(580\) 0 0
\(581\) −15.4919 13.4164i −0.642714 0.556606i
\(582\) 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
\(587\) 30.9839 1.27884 0.639421 0.768857i \(-0.279174\pi\)
0.639421 + 0.768857i \(0.279174\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 0 0
\(592\) 2.50000 4.33013i 0.102749 0.177967i
\(593\) −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
\(596\) 53.6656i 2.19823i
\(597\) 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
\(601\) 43.3013i 1.76630i 0.469095 + 0.883148i \(0.344580\pi\)
−0.469095 + 0.883148i \(0.655420\pi\)
\(602\) −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
\(607\) 27.0000 15.5885i 1.09590 0.632716i 0.160756 0.986994i \(-0.448607\pi\)
0.935140 + 0.354278i \(0.115273\pi\)
\(608\) 23.2379 0.942421
\(609\) 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
\(616\) −25.0000 + 8.66025i −1.00728 + 0.348932i
\(617\) 22.3607i 0.900207i −0.892976 0.450104i \(-0.851387\pi\)
0.892976 0.450104i \(-0.148613\pi\)
\(618\) 0 0
\(619\) 4.50000 + 2.59808i 0.180870 + 0.104425i 0.587701 0.809078i \(-0.300033\pi\)
−0.406831 + 0.913503i \(0.633366\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 34.6410i 1.38898i
\(623\) 7.74597 40.2492i 0.310336 1.61255i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −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
\(637\) 12.0000 1.73205i 0.475457 0.0686264i
\(638\) 44.7214i 1.77054i
\(639\) 0 0
\(640\) 0 0
\(641\) −3.87298 2.23607i −0.152974 0.0883194i 0.421559 0.906801i \(-0.361483\pi\)
−0.574533 + 0.818481i \(0.694816\pi\)
\(642\) 0 0
\(643\) 19.0526i 0.751360i 0.926750 + 0.375680i \(0.122591\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) −23.2379 + 26.8328i −0.915702 + 1.05736i
\(645\) 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
\(650\) 19.3649 0.759555
\(651\) 0 0
\(652\) 39.0000 1.52736
\(653\) −19.3649 + 11.1803i −0.757808 + 0.437521i −0.828508 0.559977i \(-0.810810\pi\)
0.0707003 + 0.997498i \(0.477477\pi\)
\(654\) 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
\(659\) 17.8885i 0.696839i 0.937339 + 0.348419i \(0.113281\pi\)
−0.937339 + 0.348419i \(0.886719\pi\)
\(660\) 0 0
\(661\) −24.0000 13.8564i −0.933492 0.538952i −0.0455776 0.998961i \(-0.514513\pi\)
−0.887914 + 0.460009i \(0.847846\pi\)
\(662\) −7.74597 4.47214i −0.301056 0.173814i
\(663\) 0 0
\(664\) 17.3205i 0.672166i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.0000 + 17.3205i 0.387202 + 0.670653i
\(668\) −11.6190 + 20.1246i −0.449551 + 0.778645i
\(669\) 0 0
\(670\) 0 0
\(671\) −38.7298 −1.49515
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 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 \(0.0363411\pi\)
−0.398086 + 0.917348i \(0.630326\pi\)
\(678\) 0 0
\(679\) 3.00000 3.46410i 0.115129 0.132940i
\(680\) 0 0
\(681\) 0 0
\(682\) −15.0000 8.66025i −0.574380 0.331618i
\(683\) 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
\(686\) −1.93649 + 41.3673i −0.0739356 + 1.57941i
\(687\) 0 0
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) −3.87298 + 6.70820i −0.147549 + 0.255562i
\(690\) 0 0
\(691\) −28.5000 + 16.4545i −1.08419 + 0.625958i −0.932024 0.362397i \(-0.881959\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) −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
\(698\) −25.1744 43.6033i −0.952865 1.65041i
\(699\) 0 0
\(700\) −7.50000 + 38.9711i −0.283473 + 1.47297i
\(701\) 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
\(704\) −50.3488 29.0689i −1.89759 1.09557i
\(705\) 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
\(713\) −7.74597 −0.290089
\(714\) 0 0
\(715\) 0 0
\(716\) 23.2379 13.4164i 0.868441 0.501395i
\(717\) 0 0
\(718\) −5.00000 + 8.66025i −0.186598 + 0.323198i
\(719\) 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
\(722\) 15.6525i 0.582525i
\(723\) 0 0
\(724\) 0 0
\(725\) 19.3649 + 11.1803i 0.719195 + 0.415227i
\(726\) 0 0
\(727\) 19.0526i 0.706620i −0.935506 0.353310i \(-0.885056\pi\)
0.935506 0.353310i \(-0.114944\pi\)
\(728\) −7.74597 6.70820i −0.287085 0.248623i
\(729\) 0 0
\(730\) 0 0
\(731\) −27.1109 + 46.9574i −1.00273 + 1.73678i
\(732\) 0 0
\(733\) 31.5000 18.1865i 1.16348 0.671735i 0.211344 0.977412i \(-0.432216\pi\)
0.952135 + 0.305677i \(0.0988827\pi\)
\(734\) 23.2379 0.857727
\(735\) 0 0
\(736\) −30.0000 −1.10581
\(737\) −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
\(742\) −20.0000 17.3205i −0.734223 0.635856i
\(743\) 31.3050i 1.14847i 0.818691 + 0.574234i \(0.194700\pi\)
−0.818691 + 0.574234i \(0.805300\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.87298 + 2.23607i 0.141800 + 0.0818683i
\(747\) 0 0
\(748\) 103.923i 3.79980i
\(749\) −11.6190 2.23607i −0.424547 0.0817041i
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) −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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 0 0
\(763\) −2.50000 + 0.866025i −0.0905061 + 0.0313522i
\(764\) 53.6656i 1.94155i
\(765\) 0 0
\(766\) −45.0000 25.9808i −1.62592 0.938723i
\(767\) 11.6190 + 6.70820i 0.419536 + 0.242219i
\(768\) 0 0
\(769\) 34.6410i 1.24919i 0.780950 + 0.624593i \(0.214735\pi\)
−0.780950 + 0.624593i \(0.785265\pi\)
\(770\) 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
\(776\) −3.87298 −0.139032
\(777\) 0 0
\(778\) −20.0000 −0.717035
\(779\) 23.2379 13.4164i 0.832584 0.480693i
\(780\) 0 0
\(781\) −20.0000 + 34.6410i −0.715656 + 1.23955i
\(782\) 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 \(-0.223050\pi\)
−0.176209 + 0.984353i \(0.556383\pi\)
\(788\) −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