Properties

Label 3150.2.bp.a.1349.3
Level 3150
Weight 2
Character 3150.1349
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
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 1349.3
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 3150.1349
Dual form 3150.2.bp.a.899.3

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 −0.995289 0.0969504i \(-0.969091\pi\)
−0.413683 + 0.910421i \(0.635758\pi\)
\(12\) 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 −0.891542 0.452937i \(-0.850376\pi\)
−0.0535160 + 0.998567i \(0.517043\pi\)
\(18\) 0 0
\(19\) 2.48004 + 1.43185i 0.568960 + 0.328489i 0.756734 0.653723i \(-0.226794\pi\)
−0.187774 + 0.982212i \(0.560127\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.39595i 1.15042i
\(23\) 0.133975 0.232051i 0.0279356 0.0483859i −0.851720 0.523998i \(-0.824440\pi\)
0.879655 + 0.475612i \(0.157773\pi\)
\(24\) 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 \(-0.690470\pi\)
0.563304 0.826250i \(-0.309530\pi\)
\(30\) 0 0
\(31\) 4.18154 2.41421i 0.751027 0.433606i −0.0750380 0.997181i \(-0.523908\pi\)
0.826065 + 0.563575i \(0.190574\pi\)
\(32\) −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 0.886160 0.463380i \(-0.153364\pi\)
0.0417807 + 0.999127i \(0.486697\pi\)
\(38\) −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 \(0.147544\pi\)
−0.894482 + 0.447103i \(0.852456\pi\)
\(44\) 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 0.911190 0.411986i \(-0.135165\pi\)
0.0988053 + 0.995107i \(0.468498\pi\)
\(48\) 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 0.995843 + 0.0910826i \(0.0290327\pi\)
−0.419042 + 0.907967i \(0.637634\pi\)
\(54\) 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 −0.902040 0.431653i \(-0.857931\pi\)
0.0771977 0.997016i \(-0.475403\pi\)
\(60\) 0 0
\(61\) −2.27035 1.31079i −0.290689 0.167829i 0.347564 0.937656i \(-0.387009\pi\)
−0.638253 + 0.769827i \(0.720342\pi\)
\(62\) 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 0.119612 0.992821i \(-0.461835\pi\)
0.919614 + 0.392824i \(0.128502\pi\)
\(68\) 3.89658 + 2.24969i 0.472529 + 0.272815i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.76268i 0.565226i 0.959234 + 0.282613i \(0.0912013\pi\)
−0.959234 + 0.282613i \(0.908799\pi\)
\(72\) 0 0
\(73\) −5.82843 10.0951i −0.682166 1.18155i −0.974319 0.225174i \(-0.927705\pi\)
0.292153 0.956372i \(-0.405628\pi\)
\(74\) −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 −0.516460 0.856312i \(-0.672750\pi\)
0.999817 + 0.0191114i \(0.00608373\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.380139 + 0.658421i −0.0419794 + 0.0727104i
\(83\) 9.45001i 1.03727i −0.854995 0.518636i \(-0.826440\pi\)
0.854995 0.518636i \(-0.173560\pi\)
\(84\) 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 −0.573763 0.819021i \(-0.694517\pi\)
0.996175 + 0.0873828i \(0.0278503\pi\)
\(90\) 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 −0.968823 0.247753i \(-0.920308\pi\)
0.269852 0.962902i \(-0.413025\pi\)
\(102\) 0 0
\(103\) 7.08845 12.2776i 0.698446 1.20974i −0.270560 0.962703i \(-0.587209\pi\)
0.969005 0.247040i \(-0.0794579\pi\)
\(104\) 2.51764 0.246875
\(105\) 0 0
\(106\) −8.39836 −0.815721
\(107\) 0.820863 1.42178i 0.0793559 0.137448i −0.823616 0.567147i \(-0.808047\pi\)
0.902972 + 0.429699i \(0.141380\pi\)
\(108\) 0 0
\(109\) −9.94887 17.2319i −0.952929 1.65052i −0.739039 0.673663i \(-0.764720\pi\)
−0.213890 0.976858i \(-0.568613\pi\)
\(110\) 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 \(-0.777360\pi\)
0.765200 0.643792i \(-0.222640\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.73325 13.3944i 0.675657 1.17027i −0.300619 0.953744i \(-0.597193\pi\)
0.976276 0.216529i \(-0.0694735\pi\)
\(132\) 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 0.989299 0.145901i \(-0.0466081\pi\)
−0.621004 + 0.783808i \(0.713275\pi\)
\(138\) 0 0
\(139\) 10.2512i 0.869495i −0.900552 0.434748i \(-0.856838\pi\)
0.900552 0.434748i \(-0.143162\pi\)
\(140\) 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 0.789464 0.613797i \(-0.210359\pi\)
−0.136831 + 0.990594i \(0.543692\pi\)
\(150\) 0 0
\(151\) 6.37429 + 11.0406i 0.518733 + 0.898471i 0.999763 + 0.0217674i \(0.00692931\pi\)
−0.481030 + 0.876704i \(0.659737\pi\)
\(152\) 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 0.998096 + 0.0616798i \(0.0196457\pi\)
−0.445632 + 0.895216i \(0.647021\pi\)
\(158\) 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 −0.403535 0.914964i \(-0.632219\pi\)
−0.994150 + 0.108010i \(0.965552\pi\)
\(164\) −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 \(0.0853783\pi\)
−0.964243 + 0.265019i \(0.914622\pi\)
\(168\) 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 0.857272 0.514863i \(-0.172157\pi\)
−0.0172486 + 0.999851i \(0.505491\pi\)
\(174\) 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 0.256052 0.966663i \(-0.417578\pi\)
0.965181 + 0.261584i \(0.0842449\pi\)
\(180\) 0 0
\(181\) 25.5498i 1.89910i 0.313615 + 0.949550i \(0.398460\pi\)
−0.313615 + 0.949550i \(0.601540\pi\)
\(182\) 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 0.224613 0.974448i \(-0.427888\pi\)
−0.731590 + 0.681745i \(0.761222\pi\)
\(192\) 0 0
\(193\) 12.2343 7.06350i 0.880648 0.508442i 0.00977575 0.999952i \(-0.496888\pi\)
0.870872 + 0.491510i \(0.163555\pi\)
\(194\) 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 −0.604766 0.796403i \(-0.706733\pi\)
0.387322 + 0.921944i \(0.373400\pi\)
\(200\) 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 0.327527 0.944842i \(-0.393785\pi\)
0.982021 + 0.188774i \(0.0604514\pi\)
\(228\) 0 0
\(229\) 17.5089 + 10.1087i 1.15702 + 0.668005i 0.950588 0.310456i \(-0.100482\pi\)
0.206431 + 0.978461i \(0.433815\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.89898i 0.584247i
\(233\) 1.31543 2.27840i 0.0861769 0.149263i −0.819715 0.572771i \(-0.805868\pi\)
0.905892 + 0.423509i \(0.139202\pi\)
\(234\) 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 \(-0.816216\pi\)
0.837898 0.545827i \(-0.183784\pi\)
\(240\) 0 0
\(241\) −12.5793 + 7.26268i −0.810306 + 0.467831i −0.847062 0.531494i \(-0.821631\pi\)
0.0367560 + 0.999324i \(0.488298\pi\)
\(242\) 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 0.926025 0.377462i \(-0.123203\pi\)
0.136121 + 0.990692i \(0.456536\pi\)
\(258\) 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 0.924926 0.380148i \(-0.124127\pi\)
−0.791680 + 0.610935i \(0.790794\pi\)
\(264\) 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 −0.999090 0.0426509i \(-0.986420\pi\)
0.462608 0.886563i \(-0.346914\pi\)
\(270\) 0 0
\(271\) −9.12436 5.26795i −0.554265 0.320005i 0.196575 0.980489i \(-0.437018\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(272\) 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 −0.419382 0.907810i \(-0.637753\pi\)
0.576496 + 0.817100i \(0.304420\pi\)
\(278\) 8.87780 + 5.12560i 0.532455 + 0.307413i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.6880i 0.637591i 0.947824 + 0.318795i \(0.103278\pi\)
−0.947824 + 0.318795i \(0.896722\pi\)
\(282\) 0 0
\(283\) 8.78434 + 15.2149i 0.522175 + 0.904434i 0.999667 + 0.0257976i \(0.00821255\pi\)
−0.477492 + 0.878636i \(0.658454\pi\)
\(284\) 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 \(0.140973\pi\)
−0.903521 + 0.428543i \(0.859027\pi\)
\(294\) 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 0.648052 0.761596i \(-0.275584\pi\)
−0.983588 + 0.180431i \(0.942251\pi\)
\(312\) 0 0
\(313\) −2.25485 + 3.90551i −0.127452 + 0.220753i −0.922689 0.385546i \(-0.874013\pi\)
0.795237 + 0.606299i \(0.207346\pi\)
\(314\) −13.8447 −0.781302
\(315\) 0 0
\(316\) −8.59235 −0.483358
\(317\) 9.19151 15.9202i 0.516247 0.894165i −0.483576 0.875303i \(-0.660662\pi\)
0.999822 0.0188626i \(-0.00600451\pi\)
\(318\) 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 −0.954440 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(332\) −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 \(-0.939873\pi\)
0.982212 0.187775i \(-0.0601275\pi\)
\(338\) 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 0.558601 0.829436i \(-0.311338\pi\)
−0.997614 + 0.0690448i \(0.978005\pi\)
\(348\) 0 0
\(349\) 24.5851i 1.31601i −0.753014 0.658004i \(-0.771401\pi\)
0.753014 0.658004i \(-0.228599\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.67303 + 2.69798i 0.249073 + 0.143803i
\(353\) 11.8802 6.85906i 0.632321 0.365071i −0.149329 0.988788i \(-0.547711\pi\)
0.781651 + 0.623717i \(0.214378\pi\)
\(354\) 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 0.746668 0.665197i \(-0.231652\pi\)
−0.202744 + 0.979232i \(0.564986\pi\)
\(360\) 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 0.653654 0.756794i \(-0.273235\pi\)
−0.982230 + 0.187684i \(0.939902\pi\)
\(368\) 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 −0.253900 0.967230i \(-0.581714\pi\)
−0.964596 + 0.263731i \(0.915047\pi\)
\(374\) 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 0.806732 0.590918i \(-0.201234\pi\)
−0.108384 + 0.994109i \(0.534568\pi\)
\(384\) 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 −0.108954 0.994047i \(-0.534750\pi\)
0.806393 + 0.591381i \(0.201417\pi\)
\(390\) 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 −0.167528 + 0.985867i \(0.553578\pi\)
−0.770022 + 0.638017i \(0.779755\pi\)
\(398\) 3.54195i 0.177542i
\(399\) 0 0
\(400\) 0 0
\(401\) 24.4856 + 14.1368i 1.22275 + 0.705957i 0.965504 0.260389i \(-0.0838507\pi\)
0.257249 + 0.966345i \(0.417184\pi\)
\(402\) 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 −0.801949 0.597392i \(-0.796204\pi\)
0.116382 + 0.993204i \(0.462870\pi\)
\(410\) 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 −0.304624 0.952473i \(-0.598531\pi\)
0.672554 + 0.740048i \(0.265197\pi\)
\(432\) 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 0.999986 0.00520362i \(-0.00165637\pi\)
0.495487 + 0.868615i \(0.334990\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 11.3278i 0.538809i
\(443\) −2.04284 + 3.53830i −0.0970582 + 0.168110i −0.910466 0.413584i \(-0.864277\pi\)
0.813408 + 0.581694i \(0.197610\pi\)
\(444\) 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 \(0.155912\pi\)
−0.882422 + 0.470459i \(0.844088\pi\)
\(450\) 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 0.848780 0.528745i \(-0.177337\pi\)
−0.0335168 + 0.999438i \(0.510671\pi\)
\(458\) −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 \(-0.834097\pi\)
0.867222 0.497922i \(-0.165903\pi\)
\(464\) 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 0.223637 0.974672i \(-0.428207\pi\)
−0.732273 + 0.681012i \(0.761540\pi\)
\(468\) 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 0.680620 0.732637i \(-0.261711\pi\)
−0.974792 + 0.223115i \(0.928377\pi\)
\(480\) 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 −0.849388 0.527768i \(-0.823029\pi\)
0.0323665 + 0.999476i \(0.489696\pi\)
\(488\) −2.27035 1.31079i −0.102774 0.0593366i
\(489\) 0 0
\(490\) 0 0
\(491\) 27.3271i 1.23325i −0.787256 0.616627i \(-0.788499\pi\)
0.787256 0.616627i \(-0.211501\pi\)
\(492\) 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 −0.202685 0.979244i \(-0.564967\pi\)
0.949393 0.314092i \(-0.101700\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −7.86214 + 13.6176i −0.350904 + 0.607784i
\(503\) 16.2936i 0.726494i 0.931693 + 0.363247i \(0.118332\pi\)
−0.931693 + 0.363247i \(0.881668\pi\)
\(504\) 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 0.451519 + 0.892261i \(0.350882\pi\)
−0.998481 + 0.0551036i \(0.982451\pi\)
\(510\) 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 0.869112 0.494616i \(-0.164691\pi\)
−0.862906 + 0.505365i \(0.831358\pi\)
\(522\) 0 0
\(523\) −5.64083 + 9.77021i −0.246656 + 0.427222i −0.962596 0.270941i \(-0.912665\pi\)
0.715940 + 0.698162i \(0.245999\pi\)
\(524\) −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 −0.199862 0.979824i \(-0.564049\pi\)
0.948484 0.316826i \(-0.102617\pi\)
\(542\) 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 \(0.273509\pi\)
−0.653002 + 0.757356i \(0.726491\pi\)
\(548\) 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 0.939290 0.343124i \(-0.111485\pi\)
−0.766799 + 0.641887i \(0.778152\pi\)
\(558\) 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 −0.0787491 0.996894i \(-0.525093\pi\)
0.823961 + 0.566646i \(0.191759\pi\)
\(564\) 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 −0.0538334 0.998550i \(-0.517144\pi\)
−0.891686 + 0.452654i \(0.850477\pi\)
\(570\) 0 0
\(571\) 6.18811 + 10.7181i 0.258964 + 0.448539i 0.965965 0.258674i \(-0.0832855\pi\)
−0.707000 + 0.707213i \(0.749952\pi\)
\(572\) 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 0.997411 + 0.0719139i \(0.0229107\pi\)
−0.436426 + 0.899740i \(0.643756\pi\)
\(578\) 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 \(-0.739731\pi\)
0.683930 0.729548i \(-0.260269\pi\)
\(588\) 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 −0.124454 0.992225i \(-0.539718\pi\)
−0.921519 + 0.388333i \(0.873051\pi\)
\(594\) 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 −0.932182 0.361990i \(-0.882097\pi\)
−0.152598 + 0.988288i \(0.548764\pi\)
\(600\) 0 0
\(601\) 34.3407i 1.40078i −0.713758 0.700392i \(-0.753008\pi\)
0.713758 0.700392i \(-0.246992\pi\)
\(602\) −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 0.318153 + 0.948040i \(0.396938\pi\)
−0.980103 + 0.198492i \(0.936396\pi\)
\(608\) 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 −0.193418 0.981117i \(-0.561957\pi\)
0.752963 + 0.658063i \(0.228624\pi\)
\(614\) −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 −0.980364 0.197195i \(-0.936817\pi\)
−0.319406 + 0.947618i \(0.603483\pi\)
\(620\) 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 −0.969493 0.245119i \(-0.921173\pi\)
−0.272467 + 0.962165i \(0.587840\pi\)
\(642\) 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 −0.0801869 0.996780i \(-0.525552\pi\)
0.823143 + 0.567834i \(0.192218\pi\)
\(648\) 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 0.134297 0.990941i \(-0.457122\pi\)
0.791032 0.611775i \(-0.209544\pi\)
\(654\) 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 \(0.0222291\pi\)
−0.997563 + 0.0697782i \(0.977771\pi\)
\(660\) 0 0
\(661\) −1.41761 + 0.818459i −0.0551388 + 0.0318344i −0.527316 0.849669i \(-0.676802\pi\)
0.472177 + 0.881504i \(0.343468\pi\)
\(662\) −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 \(0.0124107\pi\)
−0.999240 + 0.0389794i \(0.987589\pi\)
\(674\) 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 0.829879 0.557943i \(-0.188409\pi\)
−0.0682532 + 0.997668i \(0.521743\pi\)
\(678\) 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 −0.992694 0.120663i \(-0.961498\pi\)
0.391850 0.920029i \(-0.371835\pi\)
\(684\) 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 0.940684 0.339283i \(-0.110184\pi\)
0.176515 + 0.984298i \(0.443518\pi\)
\(692\) 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 \(0.0637205\pi\)
−0.980030 + 0.198849i \(0.936280\pi\)
\(702\) 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 −0.689398 0.724382i \(-0.742125\pi\)
0.972033 + 0.234845i \(0.0754584\pi\)
\(710\) 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 −0.998716 0.0506506i \(-0.983871\pi\)
0.543223 + 0.839589i \(0.317204\pi\)
\(720\) 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 −0.0753789 0.997155i \(-0.524017\pi\)
0.901251 0.433297i \(-0.142650\pi\)
\(734\) 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 0.598161 0.801376i \(-0.295898\pi\)
−0.993092 + 0.117334i \(0.962565\pi\)
\(740\) 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 −0.876708 0.481023i \(-0.840265\pi\)
0.854932 + 0.518740i \(0.173599\pi\)
\(752\) −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 \(-0.837474\pi\)
0.872456 0.488693i \(-0.162526\pi\)
\(758\) 7.86673 13.6256i 0.285732 0.494903i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.939574 + 1.62739i −0.0340595 + 0.0589928i −0.882553 0.470213i \(-0.844177\pi\)
0.848493 + 0.529206i \(0.177510\pi\)
\(762\) 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 \(0.366492\pi\)
−0.407239 + 0.913322i \(0.633508\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.2343 7.06350i −0.440324 0.254221i
\(773\) −42.1499 + 24.3353i −1.51603 + 0.875279i −0.516204 + 0.856466i \(0.672655\pi\)
−0.999823 + 0.0188128i \(0.994011\pi\)
\(774\) 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 0.701540 0.712630i \(-0.252496\pi\)
−0.967926 + 0.251236i \(0.919163\pi\)
\(788\) 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
\(795\) 0 0
\(796\) 3.06742 +