Properties

Label 804.2.q.b.193.1
Level 804
Weight 2
Character 804.193
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 193.1
Character \(\chi\) = 804.193
Dual form 804.2.q.b.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 + 0.755750i) q^{3} +(-3.19644 - 2.05423i) q^{5} +(-0.0504230 + 0.350699i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 + 0.755750i) q^{3} +(-3.19644 - 2.05423i) q^{5} +(-0.0504230 + 0.350699i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.990890 + 0.636806i) q^{11} +(2.04519 + 4.47833i) q^{13} +(-0.540741 - 3.76094i) q^{15} +(2.93464 - 0.861688i) q^{17} +(0.418195 + 2.90861i) q^{19} +(-0.298061 + 0.191552i) q^{21} +(0.101789 + 0.117470i) q^{23} +(3.92029 + 8.58425i) q^{25} +(-0.841254 + 0.540641i) q^{27} +10.1618 q^{29} +(-1.39787 + 3.06091i) q^{31} +(0.167629 + 1.16588i) q^{33} +(0.881590 - 1.01741i) q^{35} +3.68070 q^{37} +(-2.04519 + 4.47833i) q^{39} +(3.40130 - 0.998712i) q^{41} +(3.71322 - 1.09030i) q^{43} +(2.48822 - 2.87156i) q^{45} +(2.23068 + 2.57434i) q^{47} +(6.59600 + 1.93676i) q^{49} +(2.57300 + 1.65357i) q^{51} +(-8.63420 - 2.53523i) q^{53} +(-1.85917 - 4.07102i) q^{55} +(-1.92432 + 2.22079i) q^{57} +(-3.22648 + 7.06500i) q^{59} +(-8.93334 + 5.74111i) q^{61} +(-0.339954 - 0.0998195i) q^{63} +(2.66220 - 18.5160i) q^{65} +(-4.51019 + 6.83068i) q^{67} +(-0.0221208 + 0.153854i) q^{69} +(-9.64253 - 2.83130i) q^{71} +(-1.96622 + 1.26361i) q^{73} +(-3.92029 + 8.58425i) q^{75} +(-0.273291 + 0.315395i) q^{77} +(-3.74200 - 8.19384i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(10.9313 + 7.02512i) q^{83} +(-11.1505 - 3.27408i) q^{85} +(6.65454 + 7.67975i) q^{87} +(-3.15184 + 3.63741i) q^{89} +(-1.67367 + 0.491435i) q^{91} +(-3.22869 + 0.948029i) q^{93} +(4.63821 - 10.1563i) q^{95} +1.62324 q^{97} +(-0.771343 + 0.890177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{6}{11}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.654861 + 0.755750i 0.378084 + 0.436332i
\(4\) 0 0
\(5\) −3.19644 2.05423i −1.42949 0.918678i −0.999877 0.0156645i \(-0.995014\pi\)
−0.429613 0.903013i \(-0.641350\pi\)
\(6\) 0 0
\(7\) −0.0504230 + 0.350699i −0.0190581 + 0.132552i −0.997129 0.0757195i \(-0.975875\pi\)
0.978071 + 0.208271i \(0.0667837\pi\)
\(8\) 0 0
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 0 0
\(11\) 0.990890 + 0.636806i 0.298765 + 0.192004i 0.681431 0.731882i \(-0.261358\pi\)
−0.382667 + 0.923886i \(0.624994\pi\)
\(12\) 0 0
\(13\) 2.04519 + 4.47833i 0.567233 + 1.24207i 0.948258 + 0.317502i \(0.102844\pi\)
−0.381025 + 0.924565i \(0.624429\pi\)
\(14\) 0 0
\(15\) −0.540741 3.76094i −0.139619 0.971070i
\(16\) 0 0
\(17\) 2.93464 0.861688i 0.711755 0.208990i 0.0942403 0.995549i \(-0.469958\pi\)
0.617515 + 0.786559i \(0.288140\pi\)
\(18\) 0 0
\(19\) 0.418195 + 2.90861i 0.0959405 + 0.667281i 0.979866 + 0.199654i \(0.0639819\pi\)
−0.883926 + 0.467627i \(0.845109\pi\)
\(20\) 0 0
\(21\) −0.298061 + 0.191552i −0.0650422 + 0.0418001i
\(22\) 0 0
\(23\) 0.101789 + 0.117470i 0.0212244 + 0.0244943i 0.766263 0.642528i \(-0.222114\pi\)
−0.745038 + 0.667022i \(0.767569\pi\)
\(24\) 0 0
\(25\) 3.92029 + 8.58425i 0.784059 + 1.71685i
\(26\) 0 0
\(27\) −0.841254 + 0.540641i −0.161899 + 0.104046i
\(28\) 0 0
\(29\) 10.1618 1.88699 0.943496 0.331384i \(-0.107515\pi\)
0.943496 + 0.331384i \(0.107515\pi\)
\(30\) 0 0
\(31\) −1.39787 + 3.06091i −0.251065 + 0.549755i −0.992638 0.121116i \(-0.961353\pi\)
0.741573 + 0.670872i \(0.234080\pi\)
\(32\) 0 0
\(33\) 0.167629 + 1.16588i 0.0291804 + 0.202954i
\(34\) 0 0
\(35\) 0.881590 1.01741i 0.149016 0.171973i
\(36\) 0 0
\(37\) 3.68070 0.605103 0.302552 0.953133i \(-0.402162\pi\)
0.302552 + 0.953133i \(0.402162\pi\)
\(38\) 0 0
\(39\) −2.04519 + 4.47833i −0.327492 + 0.717107i
\(40\) 0 0
\(41\) 3.40130 0.998712i 0.531194 0.155973i −0.00512677 0.999987i \(-0.501632\pi\)
0.536321 + 0.844014i \(0.319814\pi\)
\(42\) 0 0
\(43\) 3.71322 1.09030i 0.566261 0.166269i 0.0139431 0.999903i \(-0.495562\pi\)
0.552318 + 0.833634i \(0.313743\pi\)
\(44\) 0 0
\(45\) 2.48822 2.87156i 0.370921 0.428066i
\(46\) 0 0
\(47\) 2.23068 + 2.57434i 0.325378 + 0.375506i 0.894745 0.446577i \(-0.147357\pi\)
−0.569367 + 0.822083i \(0.692812\pi\)
\(48\) 0 0
\(49\) 6.59600 + 1.93676i 0.942286 + 0.276680i
\(50\) 0 0
\(51\) 2.57300 + 1.65357i 0.360292 + 0.231546i
\(52\) 0 0
\(53\) −8.63420 2.53523i −1.18600 0.348241i −0.371515 0.928427i \(-0.621162\pi\)
−0.814484 + 0.580186i \(0.802980\pi\)
\(54\) 0 0
\(55\) −1.85917 4.07102i −0.250691 0.548937i
\(56\) 0 0
\(57\) −1.92432 + 2.22079i −0.254883 + 0.294150i
\(58\) 0 0
\(59\) −3.22648 + 7.06500i −0.420051 + 0.919784i 0.574786 + 0.818304i \(0.305085\pi\)
−0.994838 + 0.101481i \(0.967642\pi\)
\(60\) 0 0
\(61\) −8.93334 + 5.74111i −1.14380 + 0.735073i −0.968394 0.249424i \(-0.919759\pi\)
−0.175402 + 0.984497i \(0.556122\pi\)
\(62\) 0 0
\(63\) −0.339954 0.0998195i −0.0428302 0.0125761i
\(64\) 0 0
\(65\) 2.66220 18.5160i 0.330205 2.29663i
\(66\) 0 0
\(67\) −4.51019 + 6.83068i −0.551007 + 0.834500i
\(68\) 0 0
\(69\) −0.0221208 + 0.153854i −0.00266303 + 0.0185218i
\(70\) 0 0
\(71\) −9.64253 2.83130i −1.14436 0.336014i −0.346022 0.938226i \(-0.612468\pi\)
−0.798336 + 0.602212i \(0.794286\pi\)
\(72\) 0 0
\(73\) −1.96622 + 1.26361i −0.230128 + 0.147894i −0.650624 0.759400i \(-0.725493\pi\)
0.420496 + 0.907295i \(0.361856\pi\)
\(74\) 0 0
\(75\) −3.92029 + 8.58425i −0.452677 + 0.991223i
\(76\) 0 0
\(77\) −0.273291 + 0.315395i −0.0311444 + 0.0359426i
\(78\) 0 0
\(79\) −3.74200 8.19384i −0.421008 0.921879i −0.994701 0.102808i \(-0.967217\pi\)
0.573693 0.819070i \(-0.305510\pi\)
\(80\) 0 0
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 0 0
\(83\) 10.9313 + 7.02512i 1.19987 + 0.771107i 0.978933 0.204182i \(-0.0654534\pi\)
0.220933 + 0.975289i \(0.429090\pi\)
\(84\) 0 0
\(85\) −11.1505 3.27408i −1.20944 0.355124i
\(86\) 0 0
\(87\) 6.65454 + 7.67975i 0.713442 + 0.823355i
\(88\) 0 0
\(89\) −3.15184 + 3.63741i −0.334094 + 0.385565i −0.897795 0.440414i \(-0.854832\pi\)
0.563701 + 0.825979i \(0.309377\pi\)
\(90\) 0 0
\(91\) −1.67367 + 0.491435i −0.175449 + 0.0515164i
\(92\) 0 0
\(93\) −3.22869 + 0.948029i −0.334800 + 0.0983061i
\(94\) 0 0
\(95\) 4.63821 10.1563i 0.475870 1.04201i
\(96\) 0 0
\(97\) 1.62324 0.164815 0.0824075 0.996599i \(-0.473739\pi\)
0.0824075 + 0.996599i \(0.473739\pi\)
\(98\) 0 0
\(99\) −0.771343 + 0.890177i −0.0775229 + 0.0894662i
\(100\) 0 0
\(101\) −2.15735 15.0047i −0.214665 1.49302i −0.757306 0.653060i \(-0.773485\pi\)
0.542641 0.839965i \(-0.317424\pi\)
\(102\) 0 0
\(103\) 7.65969 16.7724i 0.754731 1.65263i −0.00294037 0.999996i \(-0.500936\pi\)
0.757672 0.652636i \(-0.226337\pi\)
\(104\) 0 0
\(105\) 1.34622 0.131378
\(106\) 0 0
\(107\) −7.38961 + 4.74901i −0.714381 + 0.459105i −0.846678 0.532106i \(-0.821401\pi\)
0.132297 + 0.991210i \(0.457765\pi\)
\(108\) 0 0
\(109\) 0.637789 + 1.39656i 0.0610891 + 0.133766i 0.937714 0.347407i \(-0.112938\pi\)
−0.876625 + 0.481174i \(0.840211\pi\)
\(110\) 0 0
\(111\) 2.41035 + 2.78169i 0.228780 + 0.264026i
\(112\) 0 0
\(113\) −1.84619 + 1.18647i −0.173675 + 0.111614i −0.624590 0.780953i \(-0.714734\pi\)
0.450915 + 0.892567i \(0.351098\pi\)
\(114\) 0 0
\(115\) −0.0840505 0.584584i −0.00783775 0.0545127i
\(116\) 0 0
\(117\) −4.72381 + 1.38704i −0.436717 + 0.128232i
\(118\) 0 0
\(119\) 0.154220 + 1.07263i 0.0141374 + 0.0983274i
\(120\) 0 0
\(121\) −3.99322 8.74394i −0.363020 0.794904i
\(122\) 0 0
\(123\) 2.98216 + 1.91651i 0.268892 + 0.172806i
\(124\) 0 0
\(125\) 2.39930 16.6875i 0.214600 1.49257i
\(126\) 0 0
\(127\) −0.783573 + 5.44987i −0.0695309 + 0.483598i 0.925068 + 0.379802i \(0.124008\pi\)
−0.994599 + 0.103796i \(0.966901\pi\)
\(128\) 0 0
\(129\) 3.25564 + 2.09227i 0.286643 + 0.184214i
\(130\) 0 0
\(131\) 8.56859 + 9.88868i 0.748641 + 0.863978i 0.994436 0.105344i \(-0.0335945\pi\)
−0.245795 + 0.969322i \(0.579049\pi\)
\(132\) 0 0
\(133\) −1.04113 −0.0902778
\(134\) 0 0
\(135\) 3.79961 0.327019
\(136\) 0 0
\(137\) 4.77631 + 5.51215i 0.408068 + 0.470935i 0.922165 0.386797i \(-0.126418\pi\)
−0.514097 + 0.857732i \(0.671873\pi\)
\(138\) 0 0
\(139\) 17.3993 + 11.1818i 1.47579 + 0.948431i 0.997532 + 0.0702105i \(0.0223671\pi\)
0.478256 + 0.878221i \(0.341269\pi\)
\(140\) 0 0
\(141\) −0.484772 + 3.37167i −0.0408252 + 0.283946i
\(142\) 0 0
\(143\) −0.825277 + 5.73993i −0.0690131 + 0.479997i
\(144\) 0 0
\(145\) −32.4814 20.8746i −2.69744 1.73354i
\(146\) 0 0
\(147\) 2.85576 + 6.25324i 0.235539 + 0.515758i
\(148\) 0 0
\(149\) −3.19812 22.2434i −0.262000 1.82225i −0.517775 0.855517i \(-0.673240\pi\)
0.255775 0.966736i \(-0.417669\pi\)
\(150\) 0 0
\(151\) −0.482637 + 0.141715i −0.0392765 + 0.0115326i −0.301312 0.953526i \(-0.597424\pi\)
0.262035 + 0.965058i \(0.415606\pi\)
\(152\) 0 0
\(153\) 0.435275 + 3.02740i 0.0351899 + 0.244751i
\(154\) 0 0
\(155\) 10.7560 6.91246i 0.863943 0.555222i
\(156\) 0 0
\(157\) 10.1380 + 11.6999i 0.809104 + 0.933756i 0.998844 0.0480786i \(-0.0153098\pi\)
−0.189740 + 0.981834i \(0.560764\pi\)
\(158\) 0 0
\(159\) −3.73820 8.18552i −0.296459 0.649154i
\(160\) 0 0
\(161\) −0.0463293 + 0.0297740i −0.00365126 + 0.00234652i
\(162\) 0 0
\(163\) 12.8084 1.00323 0.501616 0.865090i \(-0.332739\pi\)
0.501616 + 0.865090i \(0.332739\pi\)
\(164\) 0 0
\(165\) 1.85917 4.07102i 0.144737 0.316929i
\(166\) 0 0
\(167\) −1.20015 8.34719i −0.0928700 0.645925i −0.982085 0.188436i \(-0.939658\pi\)
0.889215 0.457489i \(-0.151251\pi\)
\(168\) 0 0
\(169\) −7.35950 + 8.49332i −0.566116 + 0.653332i
\(170\) 0 0
\(171\) −2.93852 −0.224714
\(172\) 0 0
\(173\) 2.72820 5.97394i 0.207422 0.454190i −0.777117 0.629356i \(-0.783319\pi\)
0.984539 + 0.175166i \(0.0560461\pi\)
\(174\) 0 0
\(175\) −3.20816 + 0.942002i −0.242514 + 0.0712086i
\(176\) 0 0
\(177\) −7.45226 + 2.18818i −0.560146 + 0.164474i
\(178\) 0 0
\(179\) −1.71515 + 1.97939i −0.128196 + 0.147946i −0.816219 0.577743i \(-0.803934\pi\)
0.688022 + 0.725689i \(0.258479\pi\)
\(180\) 0 0
\(181\) 4.25971 + 4.91597i 0.316622 + 0.365401i 0.891644 0.452736i \(-0.149552\pi\)
−0.575022 + 0.818138i \(0.695007\pi\)
\(182\) 0 0
\(183\) −10.1889 2.99174i −0.753187 0.221156i
\(184\) 0 0
\(185\) −11.7651 7.56099i −0.864989 0.555895i
\(186\) 0 0
\(187\) 3.45664 + 1.01496i 0.252774 + 0.0742212i
\(188\) 0 0
\(189\) −0.147184 0.322288i −0.0107061 0.0234430i
\(190\) 0 0
\(191\) 3.84249 4.43447i 0.278033 0.320867i −0.599508 0.800369i \(-0.704637\pi\)
0.877541 + 0.479502i \(0.159183\pi\)
\(192\) 0 0
\(193\) 9.68025 21.1968i 0.696800 1.52578i −0.147009 0.989135i \(-0.546965\pi\)
0.843809 0.536644i \(-0.180308\pi\)
\(194\) 0 0
\(195\) 15.7368 10.1134i 1.12694 0.724239i
\(196\) 0 0
\(197\) −5.60867 1.64685i −0.399601 0.117334i 0.0757560 0.997126i \(-0.475863\pi\)
−0.475357 + 0.879793i \(0.657681\pi\)
\(198\) 0 0
\(199\) −0.136409 + 0.948747i −0.00966979 + 0.0672549i −0.994085 0.108605i \(-0.965362\pi\)
0.984415 + 0.175860i \(0.0562706\pi\)
\(200\) 0 0
\(201\) −8.11583 + 1.06457i −0.572446 + 0.0750890i
\(202\) 0 0
\(203\) −0.512386 + 3.56372i −0.0359625 + 0.250124i
\(204\) 0 0
\(205\) −12.9236 3.79472i −0.902625 0.265035i
\(206\) 0 0
\(207\) −0.130761 + 0.0840349i −0.00908850 + 0.00584083i
\(208\) 0 0
\(209\) −1.43784 + 3.14842i −0.0994573 + 0.217781i
\(210\) 0 0
\(211\) −7.94880 + 9.17340i −0.547218 + 0.631523i −0.960233 0.279201i \(-0.909930\pi\)
0.413015 + 0.910724i \(0.364476\pi\)
\(212\) 0 0
\(213\) −4.17476 9.14145i −0.286050 0.626362i
\(214\) 0 0
\(215\) −14.1088 4.14272i −0.962212 0.282531i
\(216\) 0 0
\(217\) −1.00297 0.644572i −0.0680863 0.0437564i
\(218\) 0 0
\(219\) −2.24257 0.658478i −0.151539 0.0444958i
\(220\) 0 0
\(221\) 9.86082 + 11.3800i 0.663310 + 0.765501i
\(222\) 0 0
\(223\) −13.9501 + 16.0992i −0.934166 + 1.07809i 0.0626249 + 0.998037i \(0.480053\pi\)
−0.996791 + 0.0800480i \(0.974493\pi\)
\(224\) 0 0
\(225\) −9.05479 + 2.65873i −0.603653 + 0.177248i
\(226\) 0 0
\(227\) 4.47940 1.31527i 0.297308 0.0872975i −0.129677 0.991556i \(-0.541394\pi\)
0.426985 + 0.904259i \(0.359576\pi\)
\(228\) 0 0
\(229\) −0.665416 + 1.45706i −0.0439719 + 0.0962851i −0.930343 0.366690i \(-0.880491\pi\)
0.886371 + 0.462975i \(0.153218\pi\)
\(230\) 0 0
\(231\) −0.417327 −0.0274581
\(232\) 0 0
\(233\) 12.5886 14.5281i 0.824709 0.951764i −0.174752 0.984613i \(-0.555912\pi\)
0.999460 + 0.0328480i \(0.0104577\pi\)
\(234\) 0 0
\(235\) −1.84195 12.8110i −0.120155 0.835699i
\(236\) 0 0
\(237\) 3.74200 8.19384i 0.243069 0.532247i
\(238\) 0 0
\(239\) −12.1902 −0.788519 −0.394259 0.918999i \(-0.628999\pi\)
−0.394259 + 0.918999i \(0.628999\pi\)
\(240\) 0 0
\(241\) 2.56763 1.65012i 0.165396 0.106293i −0.455324 0.890326i \(-0.650477\pi\)
0.620720 + 0.784032i \(0.286840\pi\)
\(242\) 0 0
\(243\) −0.415415 0.909632i −0.0266489 0.0583529i
\(244\) 0 0
\(245\) −17.1052 19.7404i −1.09281 1.26117i
\(246\) 0 0
\(247\) −12.1704 + 7.82147i −0.774387 + 0.497668i
\(248\) 0 0
\(249\) 1.84925 + 12.8618i 0.117191 + 0.815083i
\(250\) 0 0
\(251\) −26.2792 + 7.71628i −1.65873 + 0.487047i −0.971032 0.238950i \(-0.923197\pi\)
−0.687698 + 0.725997i \(0.741379\pi\)
\(252\) 0 0
\(253\) 0.0260555 + 0.181220i 0.00163810 + 0.0113932i
\(254\) 0 0
\(255\) −4.82764 10.5711i −0.302318 0.661985i
\(256\) 0 0
\(257\) −20.7090 13.3088i −1.29179 0.830182i −0.299496 0.954098i \(-0.596819\pi\)
−0.992293 + 0.123915i \(0.960455\pi\)
\(258\) 0 0
\(259\) −0.185592 + 1.29082i −0.0115321 + 0.0802076i
\(260\) 0 0
\(261\) −1.44617 + 10.0583i −0.0895157 + 0.622595i
\(262\) 0 0
\(263\) −4.65896 2.99413i −0.287284 0.184626i 0.389059 0.921213i \(-0.372800\pi\)
−0.676343 + 0.736587i \(0.736436\pi\)
\(264\) 0 0
\(265\) 22.3908 + 25.8403i 1.37545 + 1.58736i
\(266\) 0 0
\(267\) −4.81299 −0.294550
\(268\) 0 0
\(269\) −16.3292 −0.995609 −0.497804 0.867289i \(-0.665860\pi\)
−0.497804 + 0.867289i \(0.665860\pi\)
\(270\) 0 0
\(271\) −6.16037 7.10945i −0.374216 0.431868i 0.537136 0.843495i \(-0.319506\pi\)
−0.911352 + 0.411627i \(0.864961\pi\)
\(272\) 0 0
\(273\) −1.46743 0.943057i −0.0888126 0.0570764i
\(274\) 0 0
\(275\) −1.58192 + 11.0025i −0.0953935 + 0.663477i
\(276\) 0 0
\(277\) 0.0346367 0.240903i 0.00208112 0.0144745i −0.988754 0.149548i \(-0.952218\pi\)
0.990836 + 0.135074i \(0.0431272\pi\)
\(278\) 0 0
\(279\) −2.83082 1.81925i −0.169477 0.108916i
\(280\) 0 0
\(281\) 2.95729 + 6.47555i 0.176417 + 0.386299i 0.977097 0.212792i \(-0.0682558\pi\)
−0.800681 + 0.599092i \(0.795529\pi\)
\(282\) 0 0
\(283\) −0.805306 5.60103i −0.0478705 0.332947i −0.999657 0.0261857i \(-0.991664\pi\)
0.951787 0.306761i \(-0.0992452\pi\)
\(284\) 0 0
\(285\) 10.7130 3.14561i 0.634582 0.186330i
\(286\) 0 0
\(287\) 0.178744 + 1.24319i 0.0105509 + 0.0733833i
\(288\) 0 0
\(289\) −6.43170 + 4.13340i −0.378335 + 0.243141i
\(290\) 0 0
\(291\) 1.06300 + 1.22676i 0.0623139 + 0.0719141i
\(292\) 0 0
\(293\) −0.531981 1.16488i −0.0310787 0.0680528i 0.893456 0.449151i \(-0.148273\pi\)
−0.924535 + 0.381098i \(0.875546\pi\)
\(294\) 0 0
\(295\) 24.8263 15.9549i 1.44544 0.928931i
\(296\) 0 0
\(297\) −1.17787 −0.0683472
\(298\) 0 0
\(299\) −0.317895 + 0.696093i −0.0183843 + 0.0402561i
\(300\) 0 0
\(301\) 0.195136 + 1.35720i 0.0112475 + 0.0782278i
\(302\) 0 0
\(303\) 9.92704 11.4564i 0.570294 0.658154i
\(304\) 0 0
\(305\) 40.3484 2.31034
\(306\) 0 0
\(307\) −10.3712 + 22.7098i −0.591916 + 1.29611i 0.342362 + 0.939568i \(0.388773\pi\)
−0.934278 + 0.356547i \(0.883954\pi\)
\(308\) 0 0
\(309\) 17.6917 5.19477i 1.00645 0.295520i
\(310\) 0 0
\(311\) 11.9827 3.51845i 0.679478 0.199513i 0.0762587 0.997088i \(-0.475703\pi\)
0.603219 + 0.797575i \(0.293884\pi\)
\(312\) 0 0
\(313\) 9.97368 11.5102i 0.563746 0.650597i −0.400284 0.916391i \(-0.631089\pi\)
0.964030 + 0.265794i \(0.0856340\pi\)
\(314\) 0 0
\(315\) 0.881590 + 1.01741i 0.0496719 + 0.0573245i
\(316\) 0 0
\(317\) 5.74303 + 1.68630i 0.322560 + 0.0947123i 0.439004 0.898485i \(-0.355331\pi\)
−0.116444 + 0.993197i \(0.537149\pi\)
\(318\) 0 0
\(319\) 10.0692 + 6.47108i 0.563767 + 0.362311i
\(320\) 0 0
\(321\) −8.42823 2.47475i −0.470418 0.138127i
\(322\) 0 0
\(323\) 3.73357 + 8.17538i 0.207741 + 0.454890i
\(324\) 0 0
\(325\) −30.4254 + 35.1128i −1.68770 + 1.94771i
\(326\) 0 0
\(327\) −0.637789 + 1.39656i −0.0352698 + 0.0772301i
\(328\) 0 0
\(329\) −1.01530 + 0.652491i −0.0559751 + 0.0359730i
\(330\) 0 0
\(331\) 26.1610 + 7.68156i 1.43794 + 0.422217i 0.905534 0.424273i \(-0.139470\pi\)
0.532404 + 0.846490i \(0.321289\pi\)
\(332\) 0 0
\(333\) −0.523818 + 3.64324i −0.0287051 + 0.199648i
\(334\) 0 0
\(335\) 28.4483 12.5689i 1.55430 0.686712i
\(336\) 0 0
\(337\) 4.21333 29.3044i 0.229515 1.59631i −0.470644 0.882323i \(-0.655978\pi\)
0.700159 0.713987i \(-0.253113\pi\)
\(338\) 0 0
\(339\) −2.10567 0.618281i −0.114364 0.0335804i
\(340\) 0 0
\(341\) −3.33434 + 2.14285i −0.180565 + 0.116042i
\(342\) 0 0
\(343\) −2.04210 + 4.47157i −0.110263 + 0.241442i
\(344\) 0 0
\(345\) 0.386758 0.446342i 0.0208223 0.0240303i
\(346\) 0 0
\(347\) 10.3942 + 22.7601i 0.557990 + 1.22183i 0.952950 + 0.303129i \(0.0980313\pi\)
−0.394960 + 0.918698i \(0.629241\pi\)
\(348\) 0 0
\(349\) 17.8085 + 5.22905i 0.953268 + 0.279905i 0.721147 0.692782i \(-0.243615\pi\)
0.232121 + 0.972687i \(0.425433\pi\)
\(350\) 0 0
\(351\) −4.14169 2.66170i −0.221067 0.142071i
\(352\) 0 0
\(353\) 19.4090 + 5.69900i 1.03304 + 0.303327i 0.753945 0.656937i \(-0.228148\pi\)
0.279092 + 0.960264i \(0.409967\pi\)
\(354\) 0 0
\(355\) 25.0056 + 28.8580i 1.32716 + 1.53162i
\(356\) 0 0
\(357\) −0.709644 + 0.818972i −0.0375583 + 0.0433446i
\(358\) 0 0
\(359\) −32.4753 + 9.53560i −1.71398 + 0.503269i −0.983690 0.179870i \(-0.942432\pi\)
−0.730288 + 0.683139i \(0.760614\pi\)
\(360\) 0 0
\(361\) 9.94524 2.92018i 0.523433 0.153694i
\(362\) 0 0
\(363\) 3.99322 8.74394i 0.209590 0.458938i
\(364\) 0 0
\(365\) 8.88063 0.464833
\(366\) 0 0
\(367\) 17.3088 19.9754i 0.903510 1.04271i −0.0953729 0.995442i \(-0.530404\pi\)
0.998882 0.0472640i \(-0.0150502\pi\)
\(368\) 0 0
\(369\) 0.504491 + 3.50881i 0.0262628 + 0.182661i
\(370\) 0 0
\(371\) 1.32447 2.90018i 0.0687629 0.150570i
\(372\) 0 0
\(373\) −14.2728 −0.739017 −0.369508 0.929227i \(-0.620474\pi\)
−0.369508 + 0.929227i \(0.620474\pi\)
\(374\) 0 0
\(375\) 14.1828 9.11471i 0.732395 0.470682i
\(376\) 0 0
\(377\) 20.7827 + 45.5078i 1.07036 + 2.34377i
\(378\) 0 0
\(379\) −23.2036 26.7784i −1.19189 1.37551i −0.909231 0.416293i \(-0.863329\pi\)
−0.282659 0.959221i \(-0.591216\pi\)
\(380\) 0 0
\(381\) −4.63187 + 2.97672i −0.237298 + 0.152502i
\(382\) 0 0
\(383\) 2.62435 + 18.2527i 0.134098 + 0.932672i 0.940134 + 0.340805i \(0.110700\pi\)
−0.806036 + 0.591867i \(0.798391\pi\)
\(384\) 0 0
\(385\) 1.52145 0.446738i 0.0775403 0.0227679i
\(386\) 0 0
\(387\) 0.550756 + 3.83059i 0.0279965 + 0.194720i
\(388\) 0 0
\(389\) 14.2617 + 31.2288i 0.723098 + 1.58336i 0.809512 + 0.587104i \(0.199732\pi\)
−0.0864137 + 0.996259i \(0.527541\pi\)
\(390\) 0 0
\(391\) 0.399936 + 0.257023i 0.0202256 + 0.0129982i
\(392\) 0 0
\(393\) −1.86213 + 12.9514i −0.0939321 + 0.653312i
\(394\) 0 0
\(395\) −4.87092 + 33.8780i −0.245083 + 1.70459i
\(396\) 0 0
\(397\) 2.48859 + 1.59932i 0.124899 + 0.0802675i 0.601598 0.798799i \(-0.294531\pi\)
−0.476700 + 0.879066i \(0.658167\pi\)
\(398\) 0 0
\(399\) −0.681798 0.786837i −0.0341326 0.0393911i
\(400\) 0 0
\(401\) −31.3647 −1.56628 −0.783140 0.621845i \(-0.786383\pi\)
−0.783140 + 0.621845i \(0.786383\pi\)
\(402\) 0 0
\(403\) −16.5667 −0.825245
\(404\) 0 0
\(405\) 2.48822 + 2.87156i 0.123640 + 0.142689i
\(406\) 0 0
\(407\) 3.64717 + 2.34389i 0.180783 + 0.116182i
\(408\) 0 0
\(409\) 1.55104 10.7877i 0.0766939 0.533418i −0.914865 0.403760i \(-0.867703\pi\)
0.991559 0.129658i \(-0.0413879\pi\)
\(410\) 0 0
\(411\) −1.03799 + 7.21939i −0.0512003 + 0.356106i
\(412\) 0 0
\(413\) −2.31500 1.48776i −0.113914 0.0732080i
\(414\) 0 0
\(415\) −20.5100 44.9107i −1.00680 2.20458i
\(416\) 0 0
\(417\) 2.94344 + 20.4720i 0.144141 + 1.00252i
\(418\) 0 0
\(419\) 8.88773 2.60967i 0.434194 0.127491i −0.0573292 0.998355i \(-0.518258\pi\)
0.491523 + 0.870864i \(0.336440\pi\)
\(420\) 0 0
\(421\) −0.172086 1.19688i −0.00838696 0.0583326i 0.985198 0.171419i \(-0.0548353\pi\)
−0.993585 + 0.113087i \(0.963926\pi\)
\(422\) 0 0
\(423\) −2.86559 + 1.84161i −0.139330 + 0.0895419i
\(424\) 0 0
\(425\) 18.9016 + 21.8136i 0.916862 + 1.05812i
\(426\) 0 0
\(427\) −1.56296 3.42240i −0.0756368 0.165622i
\(428\) 0 0
\(429\) −4.87839 + 3.13515i −0.235531 + 0.151366i
\(430\) 0 0
\(431\) 17.6289 0.849156 0.424578 0.905391i \(-0.360423\pi\)
0.424578 + 0.905391i \(0.360423\pi\)
\(432\) 0 0
\(433\) 11.6413 25.4909i 0.559444 1.22501i −0.392785 0.919630i \(-0.628488\pi\)
0.952230 0.305382i \(-0.0987842\pi\)
\(434\) 0 0
\(435\) −5.49488 38.2178i −0.263460 1.83240i
\(436\) 0 0
\(437\) −0.299108 + 0.345189i −0.0143083 + 0.0165126i
\(438\) 0 0
\(439\) 26.4401 1.26192 0.630959 0.775816i \(-0.282661\pi\)
0.630959 + 0.775816i \(0.282661\pi\)
\(440\) 0 0
\(441\) −2.85576 + 6.25324i −0.135988 + 0.297773i
\(442\) 0 0
\(443\) −0.325591 + 0.0956022i −0.0154693 + 0.00454220i −0.289458 0.957191i \(-0.593475\pi\)
0.273989 + 0.961733i \(0.411657\pi\)
\(444\) 0 0
\(445\) 17.5467 5.15218i 0.831794 0.244237i
\(446\) 0 0
\(447\) 14.7161 16.9833i 0.696049 0.803284i
\(448\) 0 0
\(449\) 5.46323 + 6.30490i 0.257826 + 0.297547i 0.869874 0.493273i \(-0.164200\pi\)
−0.612049 + 0.790820i \(0.709654\pi\)
\(450\) 0 0
\(451\) 4.00630 + 1.17636i 0.188649 + 0.0553925i
\(452\) 0 0
\(453\) −0.423161 0.271949i −0.0198819 0.0127773i
\(454\) 0 0
\(455\) 6.35931 + 1.86726i 0.298129 + 0.0875386i
\(456\) 0 0
\(457\) −6.74236 14.7637i −0.315394 0.690617i 0.683845 0.729628i \(-0.260307\pi\)
−0.999239 + 0.0390106i \(0.987579\pi\)
\(458\) 0 0
\(459\) −2.00291 + 2.31149i −0.0934880 + 0.107891i
\(460\) 0 0
\(461\) 1.21962 2.67060i 0.0568034 0.124382i −0.879102 0.476634i \(-0.841857\pi\)
0.935905 + 0.352252i \(0.114584\pi\)
\(462\) 0 0
\(463\) −12.0853 + 7.76675i −0.561652 + 0.360952i −0.790454 0.612521i \(-0.790155\pi\)
0.228802 + 0.973473i \(0.426519\pi\)
\(464\) 0 0
\(465\) 12.2678 + 3.60214i 0.568904 + 0.167045i
\(466\) 0 0
\(467\) 3.48857 24.2635i 0.161432 1.12278i −0.734506 0.678602i \(-0.762586\pi\)
0.895938 0.444180i \(-0.146505\pi\)
\(468\) 0 0
\(469\) −2.16810 1.92614i −0.100113 0.0889411i
\(470\) 0 0
\(471\) −2.20321 + 15.3236i −0.101518 + 0.706076i
\(472\) 0 0
\(473\) 4.37371 + 1.28424i 0.201103 + 0.0590492i
\(474\) 0 0
\(475\) −23.3288 + 14.9925i −1.07040 + 0.687903i
\(476\) 0 0
\(477\) 3.73820 8.18552i 0.171160 0.374789i
\(478\) 0 0
\(479\) −26.7115 + 30.8267i −1.22048 + 1.40851i −0.336045 + 0.941846i \(0.609089\pi\)
−0.884435 + 0.466663i \(0.845456\pi\)
\(480\) 0 0
\(481\) 7.52772 + 16.4834i 0.343234 + 0.751578i
\(482\) 0 0
\(483\) −0.0528410 0.0155155i −0.00240435 0.000705980i
\(484\) 0 0
\(485\) −5.18858 3.33450i −0.235601 0.151412i
\(486\) 0 0
\(487\) −0.262833 0.0771748i −0.0119101 0.00349712i 0.275772 0.961223i \(-0.411066\pi\)
−0.287682 + 0.957726i \(0.592885\pi\)
\(488\) 0 0
\(489\) 8.38772 + 9.67995i 0.379306 + 0.437742i
\(490\) 0 0
\(491\) −8.01760 + 9.25281i −0.361829 + 0.417573i −0.907252 0.420588i \(-0.861824\pi\)
0.545422 + 0.838161i \(0.316369\pi\)
\(492\) 0 0
\(493\) 29.8211 8.75627i 1.34308 0.394363i
\(494\) 0 0
\(495\) 4.29418 1.26088i 0.193009 0.0566725i
\(496\) 0 0
\(497\) 1.47914 3.23887i 0.0663486 0.145283i
\(498\) 0 0
\(499\) −19.5844 −0.876718 −0.438359 0.898800i \(-0.644440\pi\)
−0.438359 + 0.898800i \(0.644440\pi\)
\(500\) 0 0
\(501\) 5.52246 6.37326i 0.246725 0.284736i
\(502\) 0 0
\(503\) −4.56388 31.7425i −0.203494 1.41533i −0.793814 0.608160i \(-0.791908\pi\)
0.590321 0.807169i \(-0.299001\pi\)
\(504\) 0 0
\(505\) −23.9272 + 52.3933i −1.06475 + 2.33147i
\(506\) 0 0
\(507\) −11.2383 −0.499109
\(508\) 0 0
\(509\) −6.22712 + 4.00193i −0.276012 + 0.177382i −0.671322 0.741165i \(-0.734273\pi\)
0.395310 + 0.918548i \(0.370637\pi\)
\(510\) 0 0
\(511\) −0.344005 0.753266i −0.0152179 0.0333225i
\(512\) 0 0
\(513\) −1.92432 2.22079i −0.0849609 0.0980501i
\(514\) 0 0
\(515\) −58.9380 + 37.8771i −2.59712 + 1.66907i
\(516\) 0 0
\(517\) 0.571001 + 3.97140i 0.0251126 + 0.174662i
\(518\) 0 0
\(519\) 6.30139 1.85026i 0.276600 0.0812172i
\(520\) 0 0
\(521\) −0.426051 2.96325i −0.0186656 0.129822i 0.978358 0.206920i \(-0.0663439\pi\)
−0.997024 + 0.0770974i \(0.975435\pi\)
\(522\) 0 0
\(523\) −9.87342 21.6198i −0.431735 0.945367i −0.993042 0.117760i \(-0.962429\pi\)
0.561307 0.827607i \(-0.310299\pi\)
\(524\) 0 0
\(525\) −2.81282 1.80769i −0.122761 0.0788940i
\(526\) 0 0
\(527\) −1.46470 + 10.1872i −0.0638032 + 0.443761i
\(528\) 0 0
\(529\) 3.26980 22.7420i 0.142165 0.988782i
\(530\) 0 0
\(531\) −6.53391 4.19909i −0.283548 0.182225i
\(532\) 0 0
\(533\) 11.4289 + 13.1896i 0.495039 + 0.571306i
\(534\) 0 0
\(535\) 33.3760 1.44297
\(536\) 0 0
\(537\) −2.61910 −0.113023
\(538\) 0 0
\(539\) 5.30257 + 6.11950i 0.228398 + 0.263585i
\(540\) 0 0
\(541\) −14.9170 9.58656i −0.641331 0.412158i 0.179158 0.983820i \(-0.442663\pi\)
−0.820489 + 0.571662i \(0.806299\pi\)
\(542\) 0 0
\(543\) −0.925724 + 6.43855i −0.0397266 + 0.276305i
\(544\) 0 0
\(545\) 0.830203 5.77419i 0.0355620 0.247339i
\(546\) 0 0
\(547\) −34.1543 21.9496i −1.46033 0.938498i −0.998676 0.0514381i \(-0.983620\pi\)
−0.461655 0.887060i \(-0.652744\pi\)
\(548\) 0 0
\(549\) −4.41132 9.65945i −0.188271 0.412255i
\(550\) 0 0
\(551\) 4.24960 + 29.5566i 0.181039 + 1.25915i
\(552\) 0 0
\(553\) 3.06226 0.899160i 0.130220 0.0382362i
\(554\) 0 0
\(555\) −1.99031 13.8429i −0.0844838 0.587598i
\(556\) 0 0
\(557\) −19.6051 + 12.5994i −0.830693 + 0.533854i −0.885498 0.464643i \(-0.846183\pi\)
0.0548052 + 0.998497i \(0.482546\pi\)
\(558\) 0 0
\(559\) 12.4770 + 14.3992i 0.527719 + 0.609021i
\(560\) 0 0
\(561\) 1.49656 + 3.27701i 0.0631848 + 0.138355i
\(562\) 0 0
\(563\) 10.6220 6.82634i 0.447664 0.287696i −0.297321 0.954778i \(-0.596093\pi\)
0.744985 + 0.667082i \(0.232457\pi\)
\(564\) 0 0
\(565\) 8.33850 0.350803
\(566\) 0 0
\(567\) 0.147184 0.322288i 0.00618114 0.0135348i
\(568\) 0 0
\(569\) −6.32134 43.9659i −0.265004 1.84314i −0.493682 0.869643i \(-0.664349\pi\)
0.228678 0.973502i \(-0.426560\pi\)
\(570\) 0 0
\(571\) 5.84462 6.74505i 0.244590 0.282271i −0.620159 0.784476i \(-0.712932\pi\)
0.864749 + 0.502204i \(0.167478\pi\)
\(572\) 0 0
\(573\) 5.86764 0.245124
\(574\) 0 0
\(575\) −0.609353 + 1.33430i −0.0254118 + 0.0556441i
\(576\) 0 0
\(577\) −42.8229 + 12.5739i −1.78274 + 0.523459i −0.995633 0.0933579i \(-0.970240\pi\)
−0.787106 + 0.616817i \(0.788422\pi\)
\(578\) 0 0
\(579\) 22.3587 6.56510i 0.929195 0.272836i
\(580\) 0 0
\(581\) −3.01489 + 3.47937i −0.125079 + 0.144349i
\(582\) 0 0
\(583\) −6.94110 8.01045i −0.287471 0.331759i
\(584\) 0 0
\(585\) 17.9487 + 5.27020i 0.742086 + 0.217896i
\(586\) 0 0
\(587\) −12.2014 7.84136i −0.503606 0.323648i 0.264051 0.964509i \(-0.414941\pi\)
−0.767657 + 0.640861i \(0.778578\pi\)
\(588\) 0 0
\(589\) −9.48758 2.78580i −0.390929 0.114787i
\(590\) 0 0
\(591\) −2.42829 5.31721i −0.0998865 0.218721i
\(592\) 0 0
\(593\) 9.23657 10.6596i 0.379301 0.437736i −0.533713 0.845666i \(-0.679204\pi\)
0.913013 + 0.407930i \(0.133749\pi\)
\(594\) 0 0
\(595\) 1.71046 3.74538i 0.0701220 0.153546i
\(596\) 0 0
\(597\) −0.806344 + 0.518206i −0.0330015 + 0.0212088i
\(598\) 0 0
\(599\) 31.6690 + 9.29886i 1.29396 + 0.379941i 0.855030 0.518579i \(-0.173539\pi\)
0.438931 + 0.898521i \(0.355357\pi\)
\(600\) 0 0
\(601\) 1.84726 12.8480i 0.0753515 0.524081i −0.916830 0.399278i \(-0.869261\pi\)
0.992181 0.124803i \(-0.0398300\pi\)
\(602\) 0 0
\(603\) −6.11929 5.43639i −0.249197 0.221387i
\(604\) 0 0
\(605\) −5.19794 + 36.1524i −0.211326 + 1.46981i
\(606\) 0 0
\(607\) 36.0732 + 10.5920i 1.46417 + 0.429918i 0.914198 0.405268i \(-0.132822\pi\)
0.549968 + 0.835186i \(0.314640\pi\)
\(608\) 0 0
\(609\) −3.02883 + 1.94651i −0.122734 + 0.0788765i
\(610\) 0 0
\(611\) −6.96660 + 15.2547i −0.281838 + 0.617140i
\(612\) 0 0
\(613\) 22.4269 25.8820i 0.905813 1.04536i −0.0929514 0.995671i \(-0.529630\pi\)
0.998765 0.0496934i \(-0.0158244\pi\)
\(614\) 0 0
\(615\) −5.59532 12.2520i −0.225625 0.494050i
\(616\) 0 0
\(617\) 12.2630 + 3.60074i 0.493689 + 0.144960i 0.519094 0.854717i \(-0.326269\pi\)
−0.0254051 + 0.999677i \(0.508088\pi\)
\(618\) 0 0
\(619\) 23.7216 + 15.2450i 0.953453 + 0.612747i 0.922179 0.386764i \(-0.126407\pi\)
0.0312738 + 0.999511i \(0.490044\pi\)
\(620\) 0 0
\(621\) −0.149139 0.0437913i −0.00598476 0.00175728i
\(622\) 0 0
\(623\) −1.11671 1.28876i −0.0447402 0.0516329i
\(624\) 0 0
\(625\) −11.0493 + 12.7516i −0.441971 + 0.510062i
\(626\) 0 0
\(627\) −3.32100 + 0.975134i −0.132628 + 0.0389431i
\(628\) 0 0
\(629\) 10.8015 3.17162i 0.430685 0.126461i
\(630\) 0 0
\(631\) −0.481429 + 1.05418i −0.0191654 + 0.0419663i −0.918973 0.394321i \(-0.870980\pi\)
0.899807 + 0.436288i \(0.143707\pi\)
\(632\) 0 0
\(633\) −12.1381 −0.482448
\(634\) 0 0
\(635\) 13.6999 15.8105i 0.543664 0.627422i
\(636\) 0 0
\(637\) 4.81659 + 33.5001i 0.190840 + 1.32732i
\(638\) 0 0
\(639\) 4.17476 9.14145i 0.165151 0.361630i
\(640\) 0 0
\(641\) −24.6079 −0.971952 −0.485976 0.873972i \(-0.661536\pi\)
−0.485976 + 0.873972i \(0.661536\pi\)
\(642\) 0 0
\(643\) 40.1111 25.7779i 1.58183 1.01658i 0.606703 0.794928i \(-0.292492\pi\)
0.975126 0.221651i \(-0.0711447\pi\)
\(644\) 0 0
\(645\) −6.10844 13.3756i −0.240520 0.526665i
\(646\) 0 0
\(647\) 24.7607 + 28.5754i 0.973444 + 1.12341i 0.992333 + 0.123592i \(0.0394416\pi\)
−0.0188892 + 0.999822i \(0.506013\pi\)
\(648\) 0 0
\(649\) −7.69612 + 4.94600i −0.302099 + 0.194147i
\(650\) 0 0
\(651\) −0.169673 1.18010i −0.00665001 0.0462519i
\(652\) 0 0
\(653\) −15.3387 + 4.50386i −0.600251 + 0.176250i −0.567721 0.823221i \(-0.692175\pi\)
−0.0325305 + 0.999471i \(0.510357\pi\)
\(654\) 0 0
\(655\) −7.07538 49.2103i −0.276458 1.92281i
\(656\) 0 0
\(657\) −0.970927 2.12603i −0.0378795 0.0829445i
\(658\) 0 0
\(659\) −6.47946 4.16409i −0.252404 0.162210i 0.408321 0.912839i \(-0.366115\pi\)
−0.660725 + 0.750628i \(0.729751\pi\)
\(660\) 0 0
\(661\) −1.89605 + 13.1873i −0.0737477 + 0.512926i 0.919146 + 0.393918i \(0.128881\pi\)
−0.992893 + 0.119008i \(0.962028\pi\)
\(662\) 0 0
\(663\) −2.14296 + 14.9046i −0.0832257 + 0.578847i
\(664\) 0 0
\(665\) 3.32792 + 2.13873i 0.129051 + 0.0829362i
\(666\) 0 0
\(667\) 1.03435 + 1.19371i 0.0400503 + 0.0462205i
\(668\) 0 0
\(669\) −21.3024 −0.823597
\(670\) 0 0
\(671\) −12.5079 −0.482863
\(672\) 0 0
\(673\) 8.51241 + 9.82384i 0.328129 + 0.378681i 0.895712 0.444635i \(-0.146667\pi\)
−0.567583 + 0.823316i \(0.692121\pi\)
\(674\) 0 0
\(675\) −7.93896 5.10206i −0.305571 0.196378i
\(676\) 0 0
\(677\) −0.361503 + 2.51431i −0.0138937 + 0.0966327i −0.995588 0.0938288i \(-0.970089\pi\)
0.981695 + 0.190462i \(0.0609985\pi\)
\(678\) 0 0
\(679\) −0.0818485 + 0.569269i −0.00314106 + 0.0218465i
\(680\) 0 0
\(681\) 3.92740 + 2.52398i 0.150498 + 0.0967193i
\(682\) 0 0
\(683\) −8.28073 18.1323i −0.316853 0.693812i 0.682458 0.730925i \(-0.260911\pi\)
−0.999311 + 0.0371131i \(0.988184\pi\)
\(684\) 0 0
\(685\) −3.94396 27.4309i −0.150691 1.04808i
\(686\) 0 0
\(687\) −1.53693 + 0.451282i −0.0586374 + 0.0172175i
\(688\) 0 0
\(689\) −6.30495 43.8519i −0.240199 1.67062i
\(690\) 0 0
\(691\) −33.6260 + 21.6101i −1.27919 + 0.822089i −0.990788 0.135419i \(-0.956762\pi\)
−0.288407 + 0.957508i \(0.593125\pi\)
\(692\) 0 0
\(693\) −0.273291 0.315395i −0.0103815 0.0119809i
\(694\) 0 0
\(695\) −32.6457 71.4841i −1.23832 2.71155i
\(696\) 0 0
\(697\) 9.12102 5.86172i 0.345483 0.222029i
\(698\) 0 0
\(699\) 19.2234 0.727095
\(700\) 0 0
\(701\) 0.768533 1.68285i 0.0290271 0.0635604i −0.894563 0.446942i \(-0.852513\pi\)
0.923590 + 0.383381i \(0.125240\pi\)
\(702\) 0 0
\(703\) 1.53925 + 10.7057i 0.0580539 + 0.403774i
\(704\) 0 0
\(705\) 8.47571 9.78149i 0.319214 0.368392i
\(706\) 0 0
\(707\) 5.37092 0.201994
\(708\) 0 0
\(709\) 11.7210 25.6655i 0.440193 0.963888i −0.551370 0.834261i \(-0.685895\pi\)
0.991563 0.129627i \(-0.0413779\pi\)
\(710\) 0 0
\(711\) 8.64298 2.53781i 0.324137 0.0951752i
\(712\) 0 0
\(713\) −0.501854 + 0.147358i −0.0187946 + 0.00551858i
\(714\) 0 0
\(715\) 14.4290 16.6520i 0.539616 0.622750i
\(716\) 0 0
\(717\) −7.98289 9.21274i −0.298126 0.344056i
\(718\) 0 0
\(719\) −27.3864 8.04136i −1.02134 0.299892i −0.272154 0.962254i \(-0.587736\pi\)
−0.749184 + 0.662361i \(0.769554\pi\)
\(720\) 0 0
\(721\) 5.49584 + 3.53196i 0.204676 + 0.131537i
\(722\) 0 0
\(723\) 2.92852 + 0.859891i 0.108913 + 0.0319797i
\(724\) 0 0
\(725\) 39.8371 + 87.2311i 1.47951 + 3.23968i
\(726\) 0 0
\(727\) −21.6009 + 24.9287i −0.801131 + 0.924555i −0.998443 0.0557859i \(-0.982234\pi\)
0.197311 + 0.980341i \(0.436779\pi\)
\(728\) 0 0
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) 0 0
\(731\) 9.95747 6.39928i 0.368290 0.236686i
\(732\) 0 0
\(733\) −13.6055 3.99494i −0.502531 0.147557i 0.0206350 0.999787i \(-0.493431\pi\)
−0.523166 + 0.852231i \(0.675249\pi\)
\(734\) 0 0
\(735\) 3.71731 25.8544i 0.137115 0.953656i
\(736\) 0 0
\(737\) −8.81892 + 3.89634i −0.324849 + 0.143523i
\(738\) 0 0
\(739\) 0.500901 3.48385i 0.0184260 0.128155i −0.978532 0.206094i \(-0.933925\pi\)
0.996958 + 0.0779387i \(0.0248338\pi\)
\(740\) 0 0
\(741\) −13.8810 4.07584i −0.509932 0.149730i
\(742\) 0 0
\(743\) 18.6088 11.9592i 0.682691 0.438739i −0.152790 0.988259i \(-0.548826\pi\)
0.835481 + 0.549520i \(0.185189\pi\)
\(744\) 0 0
\(745\) −35.4704 + 77.6694i −1.29954 + 2.84559i
\(746\) 0 0
\(747\) −8.50930 + 9.82026i −0.311339 + 0.359304i
\(748\) 0 0
\(749\) −1.29287 2.83099i −0.0472405 0.103442i
\(750\) 0 0
\(751\) −41.9740 12.3247i −1.53165 0.449734i −0.596096 0.802913i \(-0.703282\pi\)
−0.935556 + 0.353179i \(0.885101\pi\)
\(752\) 0 0
\(753\) −23.0408 14.8074i −0.839653 0.539613i
\(754\) 0 0
\(755\) 1.83383 + 0.538462i 0.0667401 + 0.0195967i
\(756\) 0 0
\(757\) 15.3995 + 17.7720i 0.559705 + 0.645934i 0.963117 0.269084i \(-0.0867211\pi\)
−0.403411 + 0.915019i \(0.632176\pi\)
\(758\) 0 0
\(759\) −0.119894 + 0.138365i −0.00435188 + 0.00502234i
\(760\) 0 0
\(761\) −34.9472 + 10.2614i −1.26683 + 0.371976i −0.845034 0.534712i \(-0.820420\pi\)
−0.421801 + 0.906689i \(0.638602\pi\)
\(762\) 0 0
\(763\) −0.521933 + 0.153253i −0.0188952 + 0.00554814i
\(764\) 0 0
\(765\) 4.82764 10.5711i 0.174544 0.382197i
\(766\) 0 0
\(767\) −38.2382 −1.38070
\(768\) 0 0
\(769\) −0.204041 + 0.235476i −0.00735792 + 0.00849150i −0.759417 0.650605i \(-0.774516\pi\)
0.752059 + 0.659096i \(0.229061\pi\)
\(770\) 0 0
\(771\) −3.50333 24.3662i −0.126169 0.877528i
\(772\) 0 0
\(773\) 21.4537 46.9770i 0.771635 1.68964i 0.0486139 0.998818i \(-0.484520\pi\)
0.723021 0.690826i \(-0.242753\pi\)
\(774\) 0 0
\(775\) −31.7557 −1.14070
\(776\) 0 0
\(777\) −1.09707 + 0.705046i −0.0393573 + 0.0252934i
\(778\) 0 0
\(779\) 4.32727 + 9.47541i 0.155041 + 0.339492i
\(780\) 0 0
\(781\) −7.75170 8.94594i −0.277378