Properties

Label 3150.2.bp.a.899.3
Level 3150
Weight 2
Character 3150.899
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.3
Root \(-0.258819 - 0.965926i\)
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.a.1349.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.189469 + 2.63896i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.189469 + 2.63896i) q^{7} +1.00000 q^{8} +(-4.67303 - 2.69798i) q^{11} +2.51764 q^{13} +(2.19067 - 1.48356i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.89658 - 2.24969i) q^{17} +(2.48004 - 1.43185i) q^{19} +5.39595i q^{22} +(0.133975 + 0.232051i) q^{23} +(-1.25882 - 2.18034i) q^{26} +(-2.38014 - 1.15539i) q^{28} +8.89898i q^{29} +(4.18154 + 2.41421i) q^{31} +(-0.500000 + 0.866025i) q^{32} +4.49938i q^{34} +(5.64444 - 3.25882i) q^{37} +(-2.48004 - 1.43185i) q^{38} +0.760279 q^{41} -5.86370i q^{43} +(4.67303 - 2.69798i) q^{44} +(0.133975 - 0.232051i) q^{46} +(6.92418 - 3.99768i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(-1.25882 + 2.18034i) q^{52} +(4.19918 - 7.27319i) q^{53} +(0.189469 + 2.63896i) q^{56} +(7.70674 - 4.44949i) q^{58} +(-6.33573 + 10.9738i) q^{59} +(-2.27035 + 1.31079i) q^{61} -4.82843i q^{62} +1.00000 q^{64} +(8.50643 + 4.91119i) q^{67} +(3.89658 - 2.24969i) q^{68} -4.76268i q^{71} +(-5.82843 + 10.0951i) q^{73} +(-5.64444 - 3.25882i) q^{74} +2.86370i q^{76} +(6.23445 - 12.8431i) q^{77} +(4.29618 + 7.44120i) q^{79} +(-0.380139 - 0.658421i) q^{82} +9.45001i q^{83} +(-5.07812 + 2.93185i) q^{86} +(-4.67303 - 2.69798i) q^{88} +(3.98502 + 6.90226i) q^{89} +(0.477014 + 6.64394i) q^{91} -0.267949 q^{92} +(-6.92418 - 3.99768i) q^{94} -6.16353 q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 4q^{4} + 8q^{8} + O(q^{10}) \) \( 8q - 4q^{2} - 4q^{4} + 8q^{8} - 24q^{11} + 16q^{13} - 4q^{16} - 24q^{17} + 8q^{23} - 8q^{26} - 4q^{32} - 32q^{41} + 24q^{44} + 8q^{46} - 12q^{47} - 8q^{52} - 4q^{53} - 24q^{59} + 8q^{64} + 48q^{67} + 24q^{68} - 24q^{73} + 4q^{77} + 24q^{79} + 16q^{82} - 24q^{88} - 16q^{89} - 20q^{91} - 16q^{92} + 12q^{94} - 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.189469 + 2.63896i 0.0716124 + 0.997433i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −4.67303 2.69798i −1.40897 0.813471i −0.413683 0.910421i \(-0.635758\pi\)
−0.995289 + 0.0969504i \(0.969091\pi\)
\(12\) 0 0
\(13\) 2.51764 0.698267 0.349134 0.937073i \(-0.386476\pi\)
0.349134 + 0.937073i \(0.386476\pi\)
\(14\) 2.19067 1.48356i 0.585481 0.396499i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.89658 2.24969i −0.945058 0.545630i −0.0535160 0.998567i \(-0.517043\pi\)
−0.891542 + 0.452937i \(0.850376\pi\)
\(18\) 0 0
\(19\) 2.48004 1.43185i 0.568960 0.328489i −0.187774 0.982212i \(-0.560127\pi\)
0.756734 + 0.653723i \(0.226794\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.39595i 1.15042i
\(23\) 0.133975 + 0.232051i 0.0279356 + 0.0483859i 0.879655 0.475612i \(-0.157773\pi\)
−0.851720 + 0.523998i \(0.824440\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.25882 2.18034i −0.246875 0.427600i
\(27\) 0 0
\(28\) −2.38014 1.15539i −0.449804 0.218349i
\(29\) 8.89898i 1.65250i 0.563304 + 0.826250i \(0.309530\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(30\) 0 0
\(31\) 4.18154 + 2.41421i 0.751027 + 0.433606i 0.826065 0.563575i \(-0.190574\pi\)
−0.0750380 + 0.997181i \(0.523908\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 4.49938i 0.771637i
\(35\) 0 0
\(36\) 0 0
\(37\) 5.64444 3.25882i 0.927940 0.535747i 0.0417807 0.999127i \(-0.486697\pi\)
0.886160 + 0.463380i \(0.153364\pi\)
\(38\) −2.48004 1.43185i −0.402316 0.232277i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.760279 0.118736 0.0593678 0.998236i \(-0.481092\pi\)
0.0593678 + 0.998236i \(0.481092\pi\)
\(42\) 0 0
\(43\) 5.86370i 0.894206i −0.894482 0.447103i \(-0.852456\pi\)
0.894482 0.447103i \(-0.147544\pi\)
\(44\) 4.67303 2.69798i 0.704486 0.406735i
\(45\) 0 0
\(46\) 0.133975 0.232051i 0.0197535 0.0342140i
\(47\) 6.92418 3.99768i 1.01000 0.583121i 0.0988053 0.995107i \(-0.468498\pi\)
0.911190 + 0.411986i \(0.135165\pi\)
\(48\) 0 0
\(49\) −6.92820 + 1.00000i −0.989743 + 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.25882 + 2.18034i −0.174567 + 0.302359i
\(53\) 4.19918 7.27319i 0.576802 0.999050i −0.419042 0.907967i \(-0.637634\pi\)
0.995843 0.0910826i \(-0.0290327\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.189469 + 2.63896i 0.0253188 + 0.352646i
\(57\) 0 0
\(58\) 7.70674 4.44949i 1.01194 0.584247i
\(59\) −6.33573 + 10.9738i −0.824842 + 1.42867i 0.0771977 + 0.997016i \(0.475403\pi\)
−0.902040 + 0.431653i \(0.857931\pi\)
\(60\) 0 0
\(61\) −2.27035 + 1.31079i −0.290689 + 0.167829i −0.638253 0.769827i \(-0.720342\pi\)
0.347564 + 0.937656i \(0.387009\pi\)
\(62\) 4.82843i 0.613211i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.50643 + 4.91119i 1.03923 + 0.599997i 0.919614 0.392824i \(-0.128502\pi\)
0.119612 + 0.992821i \(0.461835\pi\)
\(68\) 3.89658 2.24969i 0.472529 0.272815i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.76268i 0.565226i −0.959234 0.282613i \(-0.908799\pi\)
0.959234 0.282613i \(-0.0912013\pi\)
\(72\) 0 0
\(73\) −5.82843 + 10.0951i −0.682166 + 1.18155i 0.292153 + 0.956372i \(0.405628\pi\)
−0.974319 + 0.225174i \(0.927705\pi\)
\(74\) −5.64444 3.25882i −0.656153 0.378830i
\(75\) 0 0
\(76\) 2.86370i 0.328489i
\(77\) 6.23445 12.8431i 0.710482 1.46361i
\(78\) 0 0
\(79\) 4.29618 + 7.44120i 0.483358 + 0.837200i 0.999817 0.0191114i \(-0.00608373\pi\)
−0.516460 + 0.856312i \(0.672750\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.380139 0.658421i −0.0419794 0.0727104i
\(83\) 9.45001i 1.03727i 0.854995 + 0.518636i \(0.173560\pi\)
−0.854995 + 0.518636i \(0.826440\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −5.07812 + 2.93185i −0.547587 + 0.316150i
\(87\) 0 0
\(88\) −4.67303 2.69798i −0.498147 0.287605i
\(89\) 3.98502 + 6.90226i 0.422412 + 0.731638i 0.996175 0.0873828i \(-0.0278503\pi\)
−0.573763 + 0.819021i \(0.694517\pi\)
\(90\) 0 0
\(91\) 0.477014 + 6.64394i 0.0500046 + 0.696474i
\(92\) −0.267949 −0.0279356
\(93\) 0 0
\(94\) −6.92418 3.99768i −0.714175 0.412329i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.16353 −0.625812 −0.312906 0.949784i \(-0.601302\pi\)
−0.312906 + 0.949784i \(0.601302\pi\)
\(98\) 4.33013 + 5.50000i 0.437409 + 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.02458 + 12.1669i −0.698972 + 1.21065i 0.269852 + 0.962902i \(0.413025\pi\)
−0.968823 + 0.247753i \(0.920308\pi\)
\(102\) 0 0
\(103\) 7.08845 + 12.2776i 0.698446 + 1.20974i 0.969005 + 0.247040i \(0.0794579\pi\)
−0.270560 + 0.962703i \(0.587209\pi\)
\(104\) 2.51764 0.246875
\(105\) 0 0
\(106\) −8.39836 −0.815721
\(107\) 0.820863 + 1.42178i 0.0793559 + 0.137448i 0.902972 0.429699i \(-0.141380\pi\)
−0.823616 + 0.567147i \(0.808047\pi\)
\(108\) 0 0
\(109\) −9.94887 + 17.2319i −0.952929 + 1.65052i −0.213890 + 0.976858i \(0.568613\pi\)
−0.739039 + 0.673663i \(0.764720\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.19067 1.48356i 0.206999 0.140184i
\(113\) −5.95867 −0.560545 −0.280272 0.959921i \(-0.590425\pi\)
−0.280272 + 0.959921i \(0.590425\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −7.70674 4.44949i −0.715553 0.413125i
\(117\) 0 0
\(118\) 12.6715 1.16650
\(119\) 5.19856 10.7091i 0.476551 0.981706i
\(120\) 0 0
\(121\) 9.05816 + 15.6892i 0.823469 + 1.42629i
\(122\) 2.27035 + 1.31079i 0.205548 + 0.118673i
\(123\) 0 0
\(124\) −4.18154 + 2.41421i −0.375513 + 0.216803i
\(125\) 0 0
\(126\) 0 0
\(127\) 14.5103i 1.28758i 0.765200 + 0.643792i \(0.222640\pi\)
−0.765200 + 0.643792i \(0.777360\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.73325 + 13.3944i 0.675657 + 1.17027i 0.976276 + 0.216529i \(0.0694735\pi\)
−0.300619 + 0.953744i \(0.597193\pi\)
\(132\) 0 0
\(133\) 4.24849 + 6.27343i 0.368391 + 0.543975i
\(134\) 9.82237i 0.848524i
\(135\) 0 0
\(136\) −3.89658 2.24969i −0.334129 0.192909i
\(137\) 4.31079 7.46651i 0.368296 0.637907i −0.621004 0.783808i \(-0.713275\pi\)
0.989299 + 0.145901i \(0.0466081\pi\)
\(138\) 0 0
\(139\) 10.2512i 0.869495i 0.900552 + 0.434748i \(0.143162\pi\)
−0.900552 + 0.434748i \(0.856838\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.12460 + 2.38134i −0.346129 + 0.199838i
\(143\) −11.7650 6.79253i −0.983839 0.568020i
\(144\) 0 0
\(145\) 0 0
\(146\) 11.6569 0.964728
\(147\) 0 0
\(148\) 6.51764i 0.535747i
\(149\) 7.96640 4.59940i 0.652633 0.376798i −0.136831 0.990594i \(-0.543692\pi\)
0.789464 + 0.613797i \(0.210359\pi\)
\(150\) 0 0
\(151\) 6.37429 11.0406i 0.518733 0.898471i −0.481030 0.876704i \(-0.659737\pi\)
0.999763 0.0217674i \(-0.00692931\pi\)
\(152\) 2.48004 1.43185i 0.201158 0.116139i
\(153\) 0 0
\(154\) −14.2397 + 1.02236i −1.14747 + 0.0823845i
\(155\) 0 0
\(156\) 0 0
\(157\) 6.92236 11.9899i 0.552464 0.956896i −0.445632 0.895216i \(-0.647021\pi\)
0.998096 0.0616798i \(-0.0196457\pi\)
\(158\) 4.29618 7.44120i 0.341786 0.591990i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.586988 + 0.397520i −0.0462612 + 0.0313289i
\(162\) 0 0
\(163\) −17.8444 + 10.3025i −1.39768 + 0.806954i −0.994150 0.108010i \(-0.965552\pi\)
−0.403535 + 0.914964i \(0.632219\pi\)
\(164\) −0.380139 + 0.658421i −0.0296839 + 0.0514140i
\(165\) 0 0
\(166\) 8.18394 4.72500i 0.635197 0.366731i
\(167\) 6.84961i 0.530038i −0.964243 0.265019i \(-0.914622\pi\)
0.964243 0.265019i \(-0.0853783\pi\)
\(168\) 0 0
\(169\) −6.66150 −0.512423
\(170\) 0 0
\(171\) 0 0
\(172\) 5.07812 + 2.93185i 0.387203 + 0.223552i
\(173\) 11.0488 6.37902i 0.840024 0.484988i −0.0172486 0.999851i \(-0.505491\pi\)
0.857272 + 0.514863i \(0.172157\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.39595i 0.406735i
\(177\) 0 0
\(178\) 3.98502 6.90226i 0.298690 0.517347i
\(179\) 16.3390 + 9.43331i 1.22123 + 0.705079i 0.965181 0.261584i \(-0.0842449\pi\)
0.256052 + 0.966663i \(0.417578\pi\)
\(180\) 0 0
\(181\) 25.5498i 1.89910i −0.313615 0.949550i \(-0.601540\pi\)
0.313615 0.949550i \(-0.398460\pi\)
\(182\) 5.51532 3.73508i 0.408822 0.276862i
\(183\) 0 0
\(184\) 0.133975 + 0.232051i 0.00987674 + 0.0171070i
\(185\) 0 0
\(186\) 0 0
\(187\) 12.1392 + 21.0257i 0.887707 + 1.53755i
\(188\) 7.99536i 0.583121i
\(189\) 0 0
\(190\) 0 0
\(191\) −7.00657 + 4.04524i −0.506977 + 0.292704i −0.731590 0.681745i \(-0.761222\pi\)
0.224613 + 0.974448i \(0.427888\pi\)
\(192\) 0 0
\(193\) 12.2343 + 7.06350i 0.880648 + 0.508442i 0.870872 0.491510i \(-0.163555\pi\)
0.00977575 + 0.999952i \(0.496888\pi\)
\(194\) 3.08176 + 5.33777i 0.221258 + 0.383230i
\(195\) 0 0
\(196\) 2.59808 6.50000i 0.185577 0.464286i
\(197\) −14.2738 −1.01697 −0.508483 0.861072i \(-0.669793\pi\)
−0.508483 + 0.861072i \(0.669793\pi\)
\(198\) 0 0
\(199\) −3.06742 1.77098i −0.217444 0.125541i 0.387322 0.921944i \(-0.373400\pi\)
−0.604766 + 0.796403i \(0.706733\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 14.0492 0.988495
\(203\) −23.4840 + 1.68608i −1.64826 + 0.118339i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.08845 12.2776i 0.493876 0.855418i
\(207\) 0 0
\(208\) −1.25882 2.18034i −0.0872834 0.151179i
\(209\) −15.4524 −1.06887
\(210\) 0 0
\(211\) −3.92340 −0.270098 −0.135049 0.990839i \(-0.543119\pi\)
−0.135049 + 0.990839i \(0.543119\pi\)
\(212\) 4.19918 + 7.27319i 0.288401 + 0.499525i
\(213\) 0 0
\(214\) 0.820863 1.42178i 0.0561131 0.0971907i
\(215\) 0 0
\(216\) 0 0
\(217\) −5.57874 + 11.4923i −0.378709 + 0.780150i
\(218\) 19.8977 1.34764
\(219\) 0 0
\(220\) 0 0
\(221\) −9.81017 5.66390i −0.659903 0.380995i
\(222\) 0 0
\(223\) 14.6904 0.983740 0.491870 0.870669i \(-0.336314\pi\)
0.491870 + 0.870669i \(0.336314\pi\)
\(224\) −2.38014 1.15539i −0.159030 0.0771980i
\(225\) 0 0
\(226\) 2.97934 + 5.16036i 0.198182 + 0.343262i
\(227\) 19.7303 + 11.3913i 1.30955 + 0.756068i 0.982021 0.188774i \(-0.0604514\pi\)
0.327527 + 0.944842i \(0.393785\pi\)
\(228\) 0 0
\(229\) 17.5089 10.1087i 1.15702 0.668005i 0.206431 0.978461i \(-0.433815\pi\)
0.950588 + 0.310456i \(0.100482\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.89898i 0.584247i
\(233\) 1.31543 + 2.27840i 0.0861769 + 0.149263i 0.905892 0.423509i \(-0.139202\pi\)
−0.819715 + 0.572771i \(0.805868\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.33573 10.9738i −0.412421 0.714334i
\(237\) 0 0
\(238\) −11.8737 + 0.852491i −0.769656 + 0.0552588i
\(239\) 16.8766i 1.09165i 0.837898 + 0.545827i \(0.183784\pi\)
−0.837898 + 0.545827i \(0.816216\pi\)
\(240\) 0 0
\(241\) −12.5793 7.26268i −0.810306 0.467831i 0.0367560 0.999324i \(-0.488298\pi\)
−0.847062 + 0.531494i \(0.821631\pi\)
\(242\) 9.05816 15.6892i 0.582280 1.00854i
\(243\) 0 0
\(244\) 2.62158i 0.167829i
\(245\) 0 0
\(246\) 0 0
\(247\) 6.24384 3.60488i 0.397286 0.229373i
\(248\) 4.18154 + 2.41421i 0.265528 + 0.153303i
\(249\) 0 0
\(250\) 0 0
\(251\) 15.7243 0.992507 0.496254 0.868178i \(-0.334709\pi\)
0.496254 + 0.868178i \(0.334709\pi\)
\(252\) 0 0
\(253\) 1.44584i 0.0908993i
\(254\) 12.5663 7.25517i 0.788481 0.455230i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 17.0275 9.83083i 1.06215 0.613230i 0.136121 0.990692i \(-0.456536\pi\)
0.926025 + 0.377462i \(0.123203\pi\)
\(258\) 0 0
\(259\) 9.66933 + 14.2780i 0.600823 + 0.887192i
\(260\) 0 0
\(261\) 0 0
\(262\) 7.73325 13.3944i 0.477762 0.827508i
\(263\) 2.16088 3.74275i 0.133245 0.230788i −0.791680 0.610935i \(-0.790794\pi\)
0.924926 + 0.380148i \(0.124127\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 3.30871 6.81601i 0.202870 0.417917i
\(267\) 0 0
\(268\) −8.50643 + 4.91119i −0.519613 + 0.299999i
\(269\) −8.79895 + 15.2402i −0.536482 + 0.929214i 0.462608 + 0.886563i \(0.346914\pi\)
−0.999090 + 0.0426509i \(0.986420\pi\)
\(270\) 0 0
\(271\) −9.12436 + 5.26795i −0.554265 + 0.320005i −0.750840 0.660484i \(-0.770351\pi\)
0.196575 + 0.980489i \(0.437018\pi\)
\(272\) 4.49938i 0.272815i
\(273\) 0 0
\(274\) −8.62158 −0.520849
\(275\) 0 0
\(276\) 0 0
\(277\) 2.61489 + 1.50971i 0.157114 + 0.0907097i 0.576496 0.817100i \(-0.304420\pi\)
−0.419382 + 0.907810i \(0.637753\pi\)
\(278\) 8.87780 5.12560i 0.532455 0.307413i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.6880i 0.637591i −0.947824 0.318795i \(-0.896722\pi\)
0.947824 0.318795i \(-0.103278\pi\)
\(282\) 0 0
\(283\) 8.78434 15.2149i 0.522175 0.904434i −0.477492 0.878636i \(-0.658454\pi\)
0.999667 0.0257976i \(-0.00821255\pi\)
\(284\) 4.12460 + 2.38134i 0.244750 + 0.141307i
\(285\) 0 0
\(286\) 13.5851i 0.803301i
\(287\) 0.144049 + 2.00634i 0.00850295 + 0.118431i
\(288\) 0 0
\(289\) 1.62220 + 2.80973i 0.0954235 + 0.165278i
\(290\) 0 0
\(291\) 0 0
\(292\) −5.82843 10.0951i −0.341083 0.590773i
\(293\) 14.6710i 0.857086i −0.903521 0.428543i \(-0.859027\pi\)
0.903521 0.428543i \(-0.140973\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 5.64444 3.25882i 0.328076 0.189415i
\(297\) 0 0
\(298\) −7.96640 4.59940i −0.461481 0.266436i
\(299\) 0.337300 + 0.584220i 0.0195065 + 0.0337863i
\(300\) 0 0
\(301\) 15.4741 1.11099i 0.891911 0.0640363i
\(302\) −12.7486 −0.733599
\(303\) 0 0
\(304\) −2.48004 1.43185i −0.142240 0.0821223i
\(305\) 0 0
\(306\) 0 0
\(307\) 21.2772 1.21435 0.607177 0.794567i \(-0.292302\pi\)
0.607177 + 0.794567i \(0.292302\pi\)
\(308\) 8.00524 + 11.8208i 0.456141 + 0.673550i
\(309\) 0 0
\(310\) 0 0
\(311\) −5.91724 + 10.2490i −0.335536 + 0.581165i −0.983588 0.180431i \(-0.942251\pi\)
0.648052 + 0.761596i \(0.275584\pi\)
\(312\) 0 0
\(313\) −2.25485 3.90551i −0.127452 0.220753i 0.795237 0.606299i \(-0.207346\pi\)
−0.922689 + 0.385546i \(0.874013\pi\)
\(314\) −13.8447 −0.781302
\(315\) 0 0
\(316\) −8.59235 −0.483358
\(317\) 9.19151 + 15.9202i 0.516247 + 0.894165i 0.999822 + 0.0188626i \(0.00600451\pi\)
−0.483576 + 0.875303i \(0.660662\pi\)
\(318\) 0 0
\(319\) 24.0092 41.5852i 1.34426 2.32833i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.637756 + 0.309587i 0.0355408 + 0.0172526i
\(323\) −12.8849 −0.716934
\(324\) 0 0
\(325\) 0 0
\(326\) 17.8444 + 10.3025i 0.988313 + 0.570603i
\(327\) 0 0
\(328\) 0.760279 0.0419794
\(329\) 11.8616 + 17.5152i 0.653952 + 0.965644i
\(330\) 0 0
\(331\) −3.98066 6.89471i −0.218797 0.378967i 0.735643 0.677369i \(-0.236880\pi\)
−0.954440 + 0.298401i \(0.903547\pi\)
\(332\) −8.18394 4.72500i −0.449152 0.259318i
\(333\) 0 0
\(334\) −5.93193 + 3.42480i −0.324581 + 0.187397i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.89417i 0.375549i 0.982212 + 0.187775i \(0.0601275\pi\)
−0.982212 + 0.187775i \(0.939873\pi\)
\(338\) 3.33075 + 5.76903i 0.181169 + 0.313794i
\(339\) 0 0
\(340\) 0 0
\(341\) −13.0270 22.5634i −0.705451 1.22188i
\(342\) 0 0
\(343\) −3.95164 18.0938i −0.213368 0.976972i
\(344\) 5.86370i 0.316150i
\(345\) 0 0
\(346\) −11.0488 6.37902i −0.593986 0.342938i
\(347\) −8.17789 + 14.1645i −0.439012 + 0.760392i −0.997614 0.0690448i \(-0.978005\pi\)
0.558601 + 0.829436i \(0.311338\pi\)
\(348\) 0 0
\(349\) 24.5851i 1.31601i 0.753014 + 0.658004i \(0.228599\pi\)
−0.753014 + 0.658004i \(0.771401\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.67303 2.69798i 0.249073 0.143803i
\(353\) 11.8802 + 6.85906i 0.632321 + 0.365071i 0.781651 0.623717i \(-0.214378\pi\)
−0.149329 + 0.988788i \(0.547711\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.97005 −0.422412
\(357\) 0 0
\(358\) 18.8666i 0.997132i
\(359\) 10.3059 5.95011i 0.543924 0.314035i −0.202744 0.979232i \(-0.564986\pi\)
0.746668 + 0.665197i \(0.231652\pi\)
\(360\) 0 0
\(361\) −5.39960 + 9.35238i −0.284190 + 0.492231i
\(362\) −22.1268 + 12.7749i −1.16296 + 0.671433i
\(363\) 0 0
\(364\) −5.99233 2.90887i −0.314083 0.152466i
\(365\) 0 0
\(366\) 0 0
\(367\) −6.29461 + 10.9026i −0.328576 + 0.569110i −0.982230 0.187684i \(-0.939902\pi\)
0.653654 + 0.756794i \(0.273235\pi\)
\(368\) 0.133975 0.232051i 0.00698391 0.0120965i
\(369\) 0 0
\(370\) 0 0
\(371\) 19.9893 + 9.70342i 1.03779 + 0.503776i
\(372\) 0 0
\(373\) −23.5331 + 13.5868i −1.21850 + 0.703499i −0.964596 0.263731i \(-0.915047\pi\)
−0.253900 + 0.967230i \(0.581714\pi\)
\(374\) 12.1392 21.0257i 0.627704 1.08722i
\(375\) 0 0
\(376\) 6.92418 3.99768i 0.357087 0.206164i
\(377\) 22.4044i 1.15389i
\(378\) 0 0
\(379\) −15.7335 −0.808174 −0.404087 0.914721i \(-0.632411\pi\)
−0.404087 + 0.914721i \(0.632411\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7.00657 + 4.04524i 0.358487 + 0.206973i
\(383\) 13.6669 7.89060i 0.698347 0.403191i −0.108384 0.994109i \(-0.534568\pi\)
0.806732 + 0.590918i \(0.201234\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.1270i 0.719046i
\(387\) 0 0
\(388\) 3.08176 5.33777i 0.156453 0.270984i
\(389\) 13.7556 + 7.94182i 0.697438 + 0.402666i 0.806393 0.591381i \(-0.201417\pi\)
−0.108954 + 0.994047i \(0.534750\pi\)
\(390\) 0 0
\(391\) 1.20560i 0.0609700i
\(392\) −6.92820 + 1.00000i −0.349927 + 0.0505076i
\(393\) 0 0
\(394\) 7.13689 + 12.3615i 0.359552 + 0.622762i
\(395\) 0 0
\(396\) 0 0
\(397\) −18.6806 32.3557i −0.937550 1.62388i −0.770022 0.638017i \(-0.779755\pi\)
−0.167528 0.985867i \(-0.553578\pi\)
\(398\) 3.54195i 0.177542i
\(399\) 0 0
\(400\) 0 0
\(401\) 24.4856 14.1368i 1.22275 0.705957i 0.257249 0.966345i \(-0.417184\pi\)
0.965504 + 0.260389i \(0.0838507\pi\)
\(402\) 0 0
\(403\) 10.5276 + 6.07812i 0.524417 + 0.302773i
\(404\) −7.02458 12.1669i −0.349486 0.605327i
\(405\) 0 0
\(406\) 13.2022 + 19.4947i 0.655214 + 0.967507i
\(407\) −35.1689 −1.74326
\(408\) 0 0
\(409\) −13.8647 8.00481i −0.685567 0.395812i 0.116382 0.993204i \(-0.462870\pi\)
−0.801949 + 0.597392i \(0.796204\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −14.1769 −0.698446
\(413\) −30.1599 14.6405i −1.48407 0.720414i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.25882 + 2.18034i −0.0617187 + 0.106900i
\(417\) 0 0
\(418\) 7.72620 + 13.3822i 0.377901 + 0.654544i
\(419\) −29.5137 −1.44184 −0.720919 0.693020i \(-0.756280\pi\)
−0.720919 + 0.693020i \(0.756280\pi\)
\(420\) 0 0
\(421\) 0.309114 0.0150653 0.00753265 0.999972i \(-0.497602\pi\)
0.00753265 + 0.999972i \(0.497602\pi\)
\(422\) 1.96170 + 3.39776i 0.0954939 + 0.165400i
\(423\) 0 0
\(424\) 4.19918 7.27319i 0.203930 0.353217i
\(425\) 0 0
\(426\) 0 0
\(427\) −3.88928 5.74301i −0.188215 0.277924i
\(428\) −1.64173 −0.0793559
\(429\) 0 0
\(430\) 0 0
\(431\) 7.63843 + 4.41005i 0.367930 + 0.212425i 0.672554 0.740048i \(-0.265197\pi\)
−0.304624 + 0.952473i \(0.598531\pi\)
\(432\) 0 0
\(433\) −9.56388 −0.459611 −0.229805 0.973237i \(-0.573809\pi\)
−0.229805 + 0.973237i \(0.573809\pi\)
\(434\) 12.7420 0.914836i 0.611636 0.0439135i
\(435\) 0 0
\(436\) −9.94887 17.2319i −0.476464 0.825260i
\(437\) 0.664525 + 0.383663i 0.0317885 + 0.0183531i
\(438\) 0 0
\(439\) 31.3336 18.0905i 1.49547 0.863412i 0.495487 0.868615i \(-0.334990\pi\)
0.999986 + 0.00520362i \(0.00165637\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 11.3278i 0.538809i
\(443\) −2.04284 3.53830i −0.0970582 0.168110i 0.813408 0.581694i \(-0.197610\pi\)
−0.910466 + 0.413584i \(0.864277\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −7.34519 12.7222i −0.347805 0.602415i
\(447\) 0 0
\(448\) 0.189469 + 2.63896i 0.00895155 + 0.124679i
\(449\) 19.9377i 0.940918i −0.882422 0.470459i \(-0.844088\pi\)
0.882422 0.470459i \(-0.155912\pi\)
\(450\) 0 0
\(451\) −3.55281 2.05121i −0.167295 0.0965879i
\(452\) 2.97934 5.16036i 0.140136 0.242723i
\(453\) 0 0
\(454\) 22.7826i 1.06924i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.4283 10.0623i 0.815264 0.470693i −0.0335168 0.999438i \(-0.510671\pi\)
0.848780 + 0.528745i \(0.177337\pi\)
\(458\) −17.5089 10.1087i −0.818136 0.472351i
\(459\) 0 0
\(460\) 0 0
\(461\) −0.909299 −0.0423503 −0.0211751 0.999776i \(-0.506741\pi\)
−0.0211751 + 0.999776i \(0.506741\pi\)
\(462\) 0 0
\(463\) 21.4280i 0.995843i 0.867222 + 0.497922i \(0.165903\pi\)
−0.867222 + 0.497922i \(0.834097\pi\)
\(464\) 7.70674 4.44949i 0.357777 0.206562i
\(465\) 0 0
\(466\) 1.31543 2.27840i 0.0609363 0.105545i
\(467\) −10.9917 + 6.34607i −0.508636 + 0.293661i −0.732273 0.681012i \(-0.761540\pi\)
0.223637 + 0.974672i \(0.428207\pi\)
\(468\) 0 0
\(469\) −11.3487 + 23.3786i −0.524035 + 1.07952i
\(470\) 0 0
\(471\) 0 0
\(472\) −6.33573 + 10.9738i −0.291626 + 0.505111i
\(473\) −15.8201 + 27.4013i −0.727411 + 1.25991i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.67511 + 9.85666i 0.305953 + 0.451779i
\(477\) 0 0
\(478\) 14.6155 8.43828i 0.668499 0.385958i
\(479\) −6.43828 + 11.1514i −0.294172 + 0.509522i −0.974792 0.223115i \(-0.928377\pi\)
0.680620 + 0.732637i \(0.261711\pi\)
\(480\) 0 0
\(481\) 14.2107 8.20453i 0.647950 0.374094i
\(482\) 14.5254i 0.661612i
\(483\) 0 0
\(484\) −18.1163 −0.823469
\(485\) 0 0
\(486\) 0 0
\(487\) −18.0301 10.4097i −0.817022 0.471708i 0.0323665 0.999476i \(-0.489696\pi\)
−0.849388 + 0.527768i \(0.823029\pi\)
\(488\) −2.27035 + 1.31079i −0.102774 + 0.0593366i
\(489\) 0 0
\(490\) 0 0
\(491\) 27.3271i 1.23325i 0.787256 + 0.616627i \(0.211501\pi\)
−0.787256 + 0.616627i \(0.788499\pi\)
\(492\) 0 0
\(493\) 20.0199 34.6755i 0.901653 1.56171i
\(494\) −6.24384 3.60488i −0.280924 0.162191i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) 12.5685 0.902379i 0.563775 0.0404772i
\(498\) 0 0
\(499\) 16.6802 + 28.8909i 0.746708 + 1.29334i 0.949393 + 0.314092i \(0.101700\pi\)
−0.202685 + 0.979244i \(0.564967\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −7.86214 13.6176i −0.350904 0.607784i
\(503\) 16.2936i 0.726494i −0.931693 0.363247i \(-0.881668\pi\)
0.931693 0.363247i \(-0.118332\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1.25214 + 0.722921i −0.0556642 + 0.0321377i
\(507\) 0 0
\(508\) −12.5663 7.25517i −0.557540 0.321896i
\(509\) −12.3400 21.3735i −0.546961 0.947365i −0.998481 0.0551036i \(-0.982451\pi\)
0.451519 0.892261i \(-0.350882\pi\)
\(510\) 0 0
\(511\) −27.7449 13.4683i −1.22736 0.595801i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −17.0275 9.83083i −0.751051 0.433619i
\(515\) 0 0
\(516\) 0 0
\(517\) −43.1426 −1.89741
\(518\) 7.53044 15.5129i 0.330869 0.681597i
\(519\) 0 0
\(520\) 0 0
\(521\) 0.141663 0.245367i 0.00620635 0.0107497i −0.862906 0.505365i \(-0.831358\pi\)
0.869112 + 0.494616i \(0.164691\pi\)
\(522\) 0 0
\(523\) −5.64083 9.77021i −0.246656 0.427222i 0.715940 0.698162i \(-0.245999\pi\)
−0.962596 + 0.270941i \(0.912665\pi\)
\(524\) −15.4665 −0.675657
\(525\) 0 0
\(526\) −4.32175 −0.188437
\(527\) −10.8625 18.8143i −0.473176 0.819565i
\(528\) 0 0
\(529\) 11.4641 19.8564i 0.498439 0.863322i
\(530\) 0 0
\(531\) 0 0
\(532\) −7.55719 + 0.542582i −0.327646 + 0.0235239i
\(533\) 1.91411 0.0829092
\(534\) 0 0
\(535\) 0 0
\(536\) 8.50643 + 4.91119i 0.367422 + 0.212131i
\(537\) 0 0
\(538\) 17.5979 0.758700
\(539\) 35.0737 + 14.0191i 1.51073 + 0.603845i
\(540\) 0 0
\(541\) 17.4125 + 30.1593i 0.748621 + 1.29665i 0.948484 + 0.316826i \(0.102617\pi\)
−0.199862 + 0.979824i \(0.564049\pi\)
\(542\) 9.12436 + 5.26795i 0.391925 + 0.226278i
\(543\) 0 0
\(544\) 3.89658 2.24969i 0.167064 0.0964546i
\(545\) 0 0
\(546\) 0 0
\(547\) 35.4261i 1.51471i −0.653002 0.757356i \(-0.726491\pi\)
0.653002 0.757356i \(-0.273509\pi\)
\(548\) 4.31079 + 7.46651i 0.184148 + 0.318953i
\(549\) 0 0
\(550\) 0 0
\(551\) 12.7420 + 22.0698i 0.542828 + 0.940206i
\(552\) 0 0
\(553\) −18.8230 + 12.7473i −0.800436 + 0.542071i
\(554\) 3.01942i 0.128283i
\(555\) 0 0
\(556\) −8.87780 5.12560i −0.376503 0.217374i
\(557\) 4.07093 7.05105i 0.172491 0.298763i −0.766799 0.641887i \(-0.778152\pi\)
0.939290 + 0.343124i \(0.111485\pi\)
\(558\) 0 0
\(559\) 14.7627i 0.624395i
\(560\) 0 0
\(561\) 0 0
\(562\) −9.25605 + 5.34398i −0.390443 + 0.225422i
\(563\) 17.6821 + 10.2088i 0.745212 + 0.430248i 0.823961 0.566646i \(-0.191759\pi\)
−0.0787491 + 0.996894i \(0.525093\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −17.5687 −0.738467
\(567\) 0 0
\(568\) 4.76268i 0.199838i
\(569\) −22.5542 + 13.0217i −0.945520 + 0.545896i −0.891686 0.452654i \(-0.850477\pi\)
−0.0538334 + 0.998550i \(0.517144\pi\)
\(570\) 0 0
\(571\) 6.18811 10.7181i 0.258964 0.448539i −0.707000 0.707213i \(-0.749952\pi\)
0.965965 + 0.258674i \(0.0832855\pi\)
\(572\) 11.7650 6.79253i 0.491920 0.284010i
\(573\) 0 0
\(574\) 1.66552 1.12792i 0.0695175 0.0470786i
\(575\) 0 0
\(576\) 0 0
\(577\) 13.4753 23.3399i 0.560985 0.971654i −0.436426 0.899740i \(-0.643756\pi\)
0.997411 0.0719139i \(-0.0229107\pi\)
\(578\) 1.62220 2.80973i 0.0674746 0.116869i
\(579\) 0 0
\(580\) 0 0
\(581\) −24.9382 + 1.79048i −1.03461 + 0.0742816i
\(582\) 0 0
\(583\) −39.2458 + 22.6586i −1.62539 + 0.938422i
\(584\) −5.82843 + 10.0951i −0.241182 + 0.417740i
\(585\) 0 0
\(586\) −12.7054 + 7.33548i −0.524856 + 0.303026i
\(587\) 35.3511i 1.45910i 0.683930 + 0.729548i \(0.260269\pi\)
−0.683930 + 0.729548i \(0.739731\pi\)
\(588\) 0 0
\(589\) 13.8272 0.569739
\(590\) 0 0
\(591\) 0 0
\(592\) −5.64444 3.25882i −0.231985 0.133937i
\(593\) −25.4711 + 14.7057i −1.04597 + 0.603893i −0.921519 0.388333i \(-0.873051\pi\)
−0.124454 + 0.992225i \(0.539718\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.19881i 0.376798i
\(597\) 0 0
\(598\) 0.337300 0.584220i 0.0137932 0.0238905i
\(599\) −26.5494 15.3283i −1.08478 0.626298i −0.152598 0.988288i \(-0.548764\pi\)
−0.932182 + 0.361990i \(0.882097\pi\)
\(600\) 0 0
\(601\) 34.3407i 1.40078i 0.713758 + 0.700392i \(0.246992\pi\)
−0.713758 + 0.700392i \(0.753008\pi\)
\(602\) −8.69918 12.8454i −0.354552 0.523541i
\(603\) 0 0
\(604\) 6.37429 + 11.0406i 0.259366 + 0.449236i
\(605\) 0 0
\(606\) 0 0
\(607\) −16.3087 28.2475i −0.661950 1.14653i −0.980103 0.198492i \(-0.936396\pi\)
0.318153 0.948040i \(-0.396938\pi\)
\(608\) 2.86370i 0.116139i
\(609\) 0 0
\(610\) 0 0
\(611\) 17.4326 10.0647i 0.705247 0.407174i
\(612\) 0 0
\(613\) 13.8537 + 7.99843i 0.559545 + 0.323054i 0.752963 0.658063i \(-0.228624\pi\)
−0.193418 + 0.981117i \(0.561957\pi\)
\(614\) −10.6386 18.4266i −0.429339 0.743636i
\(615\) 0 0
\(616\) 6.23445 12.8431i 0.251193 0.517464i
\(617\) 25.1429 1.01221 0.506107 0.862471i \(-0.331084\pi\)
0.506107 + 0.862471i \(0.331084\pi\)
\(618\) 0 0
\(619\) −32.3379 18.6703i −1.29977 0.750423i −0.319406 0.947618i \(-0.603483\pi\)
−0.980364 + 0.197195i \(0.936817\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.8345 0.474519
\(623\) −17.4597 + 11.8241i −0.699510 + 0.473722i
\(624\) 0 0
\(625\) 0 0
\(626\) −2.25485 + 3.90551i −0.0901219 + 0.156096i
\(627\) 0 0
\(628\) 6.92236 + 11.9899i 0.276232 + 0.478448i
\(629\) −29.3253 −1.16928
\(630\) 0 0
\(631\) 49.5015 1.97062 0.985311 0.170767i \(-0.0546245\pi\)
0.985311 + 0.170767i \(0.0546245\pi\)
\(632\) 4.29618 + 7.44120i 0.170893 + 0.295995i
\(633\) 0 0
\(634\) 9.19151 15.9202i 0.365041 0.632270i
\(635\) 0 0
\(636\) 0 0
\(637\) −17.4427 + 2.51764i −0.691105 + 0.0997525i
\(638\) −48.0185 −1.90107
\(639\) 0 0
\(640\) 0 0
\(641\) −31.4439 18.1542i −1.24196 0.717046i −0.272467 0.962165i \(-0.587840\pi\)
−0.969493 + 0.245119i \(0.921173\pi\)
\(642\) 0 0
\(643\) −10.2653 −0.404824 −0.202412 0.979300i \(-0.564878\pi\)
−0.202412 + 0.979300i \(0.564878\pi\)
\(644\) −0.0507680 0.707107i −0.00200054 0.0278639i
\(645\) 0 0
\(646\) 6.44244 + 11.1586i 0.253474 + 0.439031i
\(647\) 18.8980 + 10.9108i 0.742956 + 0.428946i 0.823143 0.567834i \(-0.192218\pi\)
−0.0801869 + 0.996780i \(0.525552\pi\)
\(648\) 0 0
\(649\) 59.2142 34.1873i 2.32436 1.34197i
\(650\) 0 0
\(651\) 0 0
\(652\) 20.6050i 0.806954i
\(653\) 23.6457 + 40.9556i 0.925329 + 1.60272i 0.791032 + 0.611775i \(0.209544\pi\)
0.134297 + 0.990941i \(0.457122\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.380139 0.658421i −0.0148419 0.0257070i
\(657\) 0 0
\(658\) 9.23779 19.0301i 0.360127 0.741869i
\(659\) 3.58255i 0.139556i −0.997563 0.0697782i \(-0.977771\pi\)
0.997563 0.0697782i \(-0.0222291\pi\)
\(660\) 0 0
\(661\) −1.41761 0.818459i −0.0551388 0.0318344i 0.472177 0.881504i \(-0.343468\pi\)
−0.527316 + 0.849669i \(0.676802\pi\)
\(662\) −3.98066 + 6.89471i −0.154713 + 0.267970i
\(663\) 0 0
\(664\) 9.45001i 0.366731i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.06502 + 1.19224i −0.0799577 + 0.0461636i
\(668\) 5.93193 + 3.42480i 0.229513 + 0.132510i
\(669\) 0 0
\(670\) 0 0
\(671\) 14.1459 0.546097
\(672\) 0 0
\(673\) 2.02242i 0.0779587i −0.999240 0.0389794i \(-0.987589\pi\)
0.999240 0.0389794i \(-0.0124107\pi\)
\(674\) 5.97053 3.44709i 0.229976 0.132777i
\(675\) 0 0
\(676\) 3.33075 5.76903i 0.128106 0.221886i
\(677\) 19.8169 11.4413i 0.761626 0.439725i −0.0682532 0.997668i \(-0.521743\pi\)
0.829879 + 0.557943i \(0.188409\pi\)
\(678\) 0 0
\(679\) −1.16780 16.2653i −0.0448159 0.624205i
\(680\) 0 0
\(681\) 0 0
\(682\) −13.0270 + 22.5634i −0.498829 + 0.863997i
\(683\) −15.7026 + 27.1977i −0.600844 + 1.04069i 0.391850 + 0.920029i \(0.371835\pi\)
−0.992694 + 0.120663i \(0.961498\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −13.6938 + 12.4691i −0.522834 + 0.476073i
\(687\) 0 0
\(688\) −5.07812 + 2.93185i −0.193601 + 0.111776i
\(689\) 10.5720 18.3113i 0.402762 0.697604i
\(690\) 0 0
\(691\) 29.3677 16.9554i 1.11720 0.645015i 0.176515 0.984298i \(-0.443518\pi\)
0.940684 + 0.339283i \(0.110184\pi\)
\(692\) 12.7580i 0.484988i
\(693\) 0 0
\(694\) 16.3558 0.620857
\(695\) 0 0
\(696\) 0 0
\(697\) −2.96248 1.71039i −0.112212 0.0647857i
\(698\) 21.2913 12.2925i 0.805887 0.465279i
\(699\) 0 0
\(700\) 0 0
\(701\) 10.5296i 0.397699i −0.980030 0.198849i \(-0.936280\pi\)
0.980030 0.198849i \(-0.0637205\pi\)
\(702\) 0 0
\(703\) 9.33229 16.1640i 0.351974 0.609637i
\(704\) −4.67303 2.69798i −0.176122 0.101684i
\(705\) 0 0
\(706\) 13.7181i 0.516288i
\(707\) −33.4390 16.2323i −1.25760 0.610479i
\(708\) 0 0
\(709\) 7.52572 + 13.0349i 0.282634 + 0.489537i 0.972033 0.234845i \(-0.0754584\pi\)
−0.689398 + 0.724382i \(0.742125\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.98502 + 6.90226i 0.149345 + 0.258673i
\(713\) 1.29377i 0.0484522i
\(714\) 0 0
\(715\) 0 0
\(716\) −16.3390 + 9.43331i −0.610616 + 0.352539i
\(717\) 0 0
\(718\) −10.3059 5.95011i −0.384613 0.222056i
\(719\) −12.2137 21.1547i −0.455494 0.788938i 0.543223 0.839589i \(-0.317204\pi\)
−0.998716 + 0.0506506i \(0.983871\pi\)
\(720\) 0 0
\(721\) −31.0569 + 21.0323i −1.15662 + 0.783285i
\(722\) 10.7992 0.401905
\(723\) 0 0
\(724\) 22.1268 + 12.7749i 0.822335 + 0.474775i
\(725\) 0 0
\(726\) 0 0
\(727\) 43.7349 1.62204 0.811019 0.585020i \(-0.198913\pi\)
0.811019 + 0.585020i \(0.198913\pi\)
\(728\) 0.477014 + 6.64394i 0.0176793 + 0.246241i
\(729\) 0 0
\(730\) 0 0
\(731\) −13.1915 + 22.8484i −0.487906 + 0.845077i
\(732\) 0 0
\(733\) 22.3596 + 38.7280i 0.825872 + 1.43045i 0.901251 + 0.433297i \(0.142650\pi\)
−0.0753789 + 0.997155i \(0.524017\pi\)
\(734\) 12.5892 0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) −26.5005 45.9003i −0.976160 1.69076i
\(738\) 0 0
\(739\) −10.7360 + 18.5954i −0.394932 + 0.684042i −0.993092 0.117334i \(-0.962565\pi\)
0.598161 + 0.801376i \(0.295898\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.59123 22.1629i −0.0584157 0.813626i
\(743\) 29.5637 1.08459 0.542293 0.840190i \(-0.317556\pi\)
0.542293 + 0.840190i \(0.317556\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 23.5331 + 13.5868i 0.861607 + 0.497449i
\(747\) 0 0
\(748\) −24.2784 −0.887707
\(749\) −3.59648 + 2.43561i −0.131413 + 0.0889951i
\(750\) 0 0
\(751\) −0.596750 1.03360i −0.0217757 0.0377166i 0.854932 0.518740i \(-0.173599\pi\)
−0.876708 + 0.481023i \(0.840265\pi\)
\(752\) −6.92418 3.99768i −0.252499 0.145780i
\(753\) 0 0
\(754\) 19.4028 11.2022i 0.706608 0.407960i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.8915i 0.977386i 0.872456 + 0.488693i \(0.162526\pi\)
−0.872456 + 0.488693i \(0.837474\pi\)
\(758\) 7.86673 + 13.6256i 0.285732 + 0.494903i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.939574 1.62739i −0.0340595 0.0589928i 0.848493 0.529206i \(-0.177510\pi\)
−0.882553 + 0.470213i \(0.844177\pi\)
\(762\) 0 0
\(763\) −47.3594 22.9897i −1.71452 0.832284i
\(764\) 8.09049i 0.292704i
\(765\) 0 0
\(766\) −13.6669 7.89060i −0.493806 0.285099i
\(767\) −15.9511 + 27.6281i −0.575960 + 0.997592i
\(768\) 0 0
\(769\) 50.6544i 1.82664i −0.407239 0.913322i \(-0.633508\pi\)
0.407239 0.913322i \(-0.366492\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.2343 + 7.06350i −0.440324 + 0.254221i
\(773\) −42.1499 24.3353i −1.51603 0.875279i −0.999823 0.0188128i \(-0.994011\pi\)
−0.516204 0.856466i \(-0.672655\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −6.16353 −0.221258
\(777\) 0 0
\(778\) 15.8836i 0.569456i
\(779\) 1.88552 1.08861i 0.0675558 0.0390034i
\(780\) 0 0
\(781\) −12.8496 + 22.2562i −0.459795 + 0.796388i
\(782\) −1.04408 + 0.602802i −0.0373364 + 0.0215562i
\(783\) 0 0
\(784\) 4.33013 + 5.50000i 0.154647 + 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −7.47307 + 12.9437i −0.266386 + 0.461395i −0.967926 0.251236i \(-0.919163\pi\)
0.701540 + 0.712630i \(0.252496\pi\)
\(788\) 7.13689 12.3615i 0.254241 0.440359i
\(789\) 0 0
\(790\) 0 0
\(791\) −1.12898 15.7247i −0.0401420 0.559105i
\(792\) 0 0
\(793\) −5.71593 + 3.30009i −0.202979 + 0.117190i
\(794\) −18.6806 + 32.3557i −0.662948 + 1.14826i