Properties

Label 3150.2.bf.c.1601.4
Level 3150
Weight 2
Character 3150.1601
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.bf (of order \(6\), degree \(2\), 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 1601.4
Root \(0.258819 - 0.965926i\)
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.c.1151.4

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.63896 + 0.189469i 0.997433 + 0.0716124i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 4.67303 2.69798i 1.40897 0.813471i 0.413683 0.910421i \(-0.364242\pi\)
0.995289 + 0.0969504i \(0.0309088\pi\)
\(12\) 0 0
\(13\) 2.51764i 0.698267i −0.937073 0.349134i \(-0.886476\pi\)
0.937073 0.349134i \(-0.113524\pi\)
\(14\) 2.19067 + 1.48356i 0.585481 + 0.396499i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.24969 + 3.89658i 0.545630 + 0.945058i 0.998567 + 0.0535160i \(0.0170428\pi\)
−0.452937 + 0.891542i \(0.649624\pi\)
\(18\) 0 0
\(19\) −2.48004 1.43185i −0.568960 0.328489i 0.187774 0.982212i \(-0.439873\pi\)
−0.756734 + 0.653723i \(0.773206\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.39595 1.15042
\(23\) 0.232051 + 0.133975i 0.0483859 + 0.0279356i 0.523998 0.851720i \(-0.324440\pi\)
−0.475612 + 0.879655i \(0.657773\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.25882 2.18034i 0.246875 0.427600i
\(27\) 0 0
\(28\) 1.15539 + 2.38014i 0.218349 + 0.449804i
\(29\) 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 \(0.190574\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.49938i 0.771637i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.25882 + 5.64444i −0.535747 + 0.927940i 0.463380 + 0.886160i \(0.346636\pi\)
−0.999127 + 0.0417807i \(0.986697\pi\)
\(38\) −1.43185 2.48004i −0.232277 0.402316i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.760279 −0.118736 −0.0593678 0.998236i \(-0.518908\pi\)
−0.0593678 + 0.998236i \(0.518908\pi\)
\(42\) 0 0
\(43\) 5.86370 0.894206 0.447103 0.894482i \(-0.352456\pi\)
0.447103 + 0.894482i \(0.352456\pi\)
\(44\) 4.67303 + 2.69798i 0.704486 + 0.406735i
\(45\) 0 0
\(46\) 0.133975 + 0.232051i 0.0197535 + 0.0342140i
\(47\) 3.99768 6.92418i 0.583121 1.01000i −0.411986 0.911190i \(-0.635165\pi\)
0.995107 0.0988053i \(-0.0315021\pi\)
\(48\) 0 0
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 2.18034 1.25882i 0.302359 0.174567i
\(53\) −7.27319 + 4.19918i −0.999050 + 0.576802i −0.907967 0.419042i \(-0.862366\pi\)
−0.0910826 + 0.995843i \(0.529033\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.189469 + 2.63896i −0.0253188 + 0.352646i
\(57\) 0 0
\(58\) 4.44949 7.70674i 0.584247 1.01194i
\(59\) −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 \(0.720342\pi\)
\(62\) 4.82843 0.613211
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.91119 + 8.50643i 0.599997 + 1.03923i 0.992821 + 0.119612i \(0.0381649\pi\)
−0.392824 + 0.919614i \(0.628502\pi\)
\(68\) −2.24969 + 3.89658i −0.272815 + 0.472529i
\(69\) 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
\(73\) −10.0951 + 5.82843i −1.18155 + 0.682166i −0.956372 0.292153i \(-0.905628\pi\)
−0.225174 + 0.974319i \(0.572295\pi\)
\(74\) −5.64444 + 3.25882i −0.656153 + 0.378830i
\(75\) 0 0
\(76\) 2.86370i 0.328489i
\(77\) 12.8431 6.23445i 1.46361 0.710482i
\(78\) 0 0
\(79\) −4.29618 + 7.44120i −0.483358 + 0.837200i −0.999817 0.0191114i \(-0.993916\pi\)
0.516460 + 0.856312i \(0.327250\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.658421 0.380139i −0.0727104 0.0419794i
\(83\) 9.45001 1.03727 0.518636 0.854995i \(-0.326440\pi\)
0.518636 + 0.854995i \(0.326440\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.07812 + 2.93185i 0.547587 + 0.316150i
\(87\) 0 0
\(88\) 2.69798 + 4.67303i 0.287605 + 0.498147i
\(89\) 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
\(92\) 0.267949i 0.0279356i
\(93\) 0 0
\(94\) 6.92418 3.99768i 0.714175 0.412329i
\(95\) 0 0
\(96\) 0 0
\(97\) 6.16353i 0.625812i −0.949784 0.312906i \(-0.898698\pi\)
0.949784 0.312906i \(-0.101302\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) 0 0
\(100\) 0 0
\(101\) 7.02458 + 12.1669i 0.698972 + 1.21065i 0.968823 + 0.247753i \(0.0796920\pi\)
−0.269852 + 0.962902i \(0.586975\pi\)
\(102\) 0 0
\(103\) −12.2776 7.08845i −1.20974 0.698446i −0.247040 0.969005i \(-0.579458\pi\)
−0.962703 + 0.270560i \(0.912791\pi\)
\(104\) 2.51764 0.246875
\(105\) 0 0
\(106\) −8.39836 −0.815721
\(107\) −1.42178 0.820863i −0.137448 0.0793559i 0.429699 0.902972i \(-0.358620\pi\)
−0.567147 + 0.823616i \(0.691953\pi\)
\(108\) 0 0
\(109\) 9.94887 + 17.2319i 0.952929 + 1.65052i 0.739039 + 0.673663i \(0.235280\pi\)
0.213890 + 0.976858i \(0.431387\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.48356 + 2.19067i −0.140184 + 0.206999i
\(113\) 5.95867i 0.560545i −0.959921 0.280272i \(-0.909575\pi\)
0.959921 0.280272i \(-0.0904248\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.70674 4.44949i 0.715553 0.413125i
\(117\) 0 0
\(118\) 12.6715i 1.16650i
\(119\) 5.19856 + 10.7091i 0.476551 + 0.981706i
\(120\) 0 0
\(121\) 9.05816 15.6892i 0.823469 1.42629i
\(122\) −1.31079 2.27035i −0.118673 0.205548i
\(123\) 0 0
\(124\) 4.18154 + 2.41421i 0.375513 + 0.216803i
\(125\) 0 0
\(126\) 0 0
\(127\) 14.5103 1.28758 0.643792 0.765200i \(-0.277360\pi\)
0.643792 + 0.765200i \(0.277360\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −7.73325 + 13.3944i −0.675657 + 1.17027i 0.300619 + 0.953744i \(0.402807\pi\)
−0.976276 + 0.216529i \(0.930527\pi\)
\(132\) 0 0
\(133\) −6.27343 4.24849i −0.543975 0.368391i
\(134\) 9.82237i 0.848524i
\(135\) 0 0
\(136\) −3.89658 + 2.24969i −0.334129 + 0.192909i
\(137\) 7.46651 4.31079i 0.637907 0.368296i −0.145901 0.989299i \(-0.546608\pi\)
0.783808 + 0.621004i \(0.213275\pi\)
\(138\) 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
\(142\) 2.38134 4.12460i 0.199838 0.346129i
\(143\) −6.79253 11.7650i −0.568020 0.983839i
\(144\) 0 0
\(145\) 0 0
\(146\) −11.6569 −0.964728
\(147\) 0 0
\(148\) −6.51764 −0.535747
\(149\) 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 \(0.659737\pi\)
\(152\) 1.43185 2.48004i 0.116139 0.201158i
\(153\) 0 0
\(154\) 14.2397 + 1.02236i 1.14747 + 0.0823845i
\(155\) 0 0
\(156\) 0 0
\(157\) −11.9899 + 6.92236i −0.956896 + 0.552464i −0.895216 0.445632i \(-0.852979\pi\)
−0.0616798 + 0.998096i \(0.519646\pi\)
\(158\) −7.44120 + 4.29618i −0.591990 + 0.341786i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.586988 + 0.397520i 0.0462612 + 0.0313289i
\(162\) 0 0
\(163\) −10.3025 + 17.8444i −0.806954 + 1.39768i 0.108010 + 0.994150i \(0.465552\pi\)
−0.914964 + 0.403535i \(0.867781\pi\)
\(164\) −0.380139 0.658421i −0.0296839 0.0514140i
\(165\) 0 0
\(166\) 8.18394 + 4.72500i 0.635197 + 0.366731i
\(167\) 6.84961 0.530038 0.265019 0.964243i \(-0.414622\pi\)
0.265019 + 0.964243i \(0.414622\pi\)
\(168\) 0 0
\(169\) 6.66150 0.512423
\(170\) 0 0
\(171\) 0 0
\(172\) 2.93185 + 5.07812i 0.223552 + 0.387203i
\(173\) −6.37902 + 11.0488i −0.484988 + 0.840024i −0.999851 0.0172486i \(-0.994509\pi\)
0.514863 + 0.857272i \(0.327843\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.39595i 0.406735i
\(177\) 0 0
\(178\) 6.90226 3.98502i 0.517347 0.298690i
\(179\) 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 \(0.601540\pi\)
\(182\) 3.73508 5.51532i 0.276862 0.408822i
\(183\) 0 0
\(184\) −0.133975 + 0.232051i −0.00987674 + 0.0171070i
\(185\) 0 0
\(186\) 0 0
\(187\) 21.0257 + 12.1392i 1.53755 + 0.887707i
\(188\) 7.99536 0.583121
\(189\) 0 0
\(190\) 0 0
\(191\) 7.00657 + 4.04524i 0.506977 + 0.292704i 0.731590 0.681745i \(-0.238778\pi\)
−0.224613 + 0.974448i \(0.572112\pi\)
\(192\) 0 0
\(193\) −7.06350 12.2343i −0.508442 0.880648i −0.999952 0.00977575i \(-0.996888\pi\)
0.491510 0.870872i \(-0.336445\pi\)
\(194\) 3.08176 5.33777i 0.221258 0.383230i
\(195\) 0 0
\(196\) 2.59808 + 6.50000i 0.185577 + 0.464286i
\(197\) 14.2738i 1.01697i 0.861072 + 0.508483i \(0.169793\pi\)
−0.861072 + 0.508483i \(0.830207\pi\)
\(198\) 0 0
\(199\) 3.06742 1.77098i 0.217444 0.125541i −0.387322 0.921944i \(-0.626600\pi\)
0.604766 + 0.796403i \(0.293267\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 14.0492i 0.988495i
\(203\) 1.68608 23.4840i 0.118339 1.64826i
\(204\) 0 0
\(205\) 0 0
\(206\) −7.08845 12.2776i −0.493876 0.855418i
\(207\) 0 0
\(208\) 2.18034 + 1.25882i 0.151179 + 0.0872834i
\(209\) −15.4524 −1.06887
\(210\) 0 0
\(211\) −3.92340 −0.270098 −0.135049 0.990839i \(-0.543119\pi\)
−0.135049 + 0.990839i \(0.543119\pi\)
\(212\) −7.27319 4.19918i −0.499525 0.288401i
\(213\) 0 0
\(214\) −0.820863 1.42178i −0.0561131 0.0971907i
\(215\) 0 0
\(216\) 0 0
\(217\) 11.4923 5.57874i 0.780150 0.378709i
\(218\) 19.8977i 1.34764i
\(219\) 0 0
\(220\) 0 0
\(221\) 9.81017 5.66390i 0.659903 0.380995i
\(222\) 0 0
\(223\) 14.6904i 0.983740i −0.870669 0.491870i \(-0.836314\pi\)
0.870669 0.491870i \(-0.163686\pi\)
\(224\) −2.38014 + 1.15539i −0.159030 + 0.0771980i
\(225\) 0 0
\(226\) 2.97934 5.16036i 0.198182 0.343262i
\(227\) −11.3913 19.7303i −0.756068 1.30955i −0.944842 0.327527i \(-0.893785\pi\)
0.188774 0.982021i \(-0.439549\pi\)
\(228\) 0 0
\(229\) −17.5089 10.1087i −1.15702 0.668005i −0.206431 0.978461i \(-0.566185\pi\)
−0.950588 + 0.310456i \(0.899518\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.89898 0.584247
\(233\) 2.27840 + 1.31543i 0.149263 + 0.0861769i 0.572771 0.819715i \(-0.305868\pi\)
−0.423509 + 0.905892i \(0.639202\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.33573 10.9738i 0.412421 0.714334i
\(237\) 0 0
\(238\) −0.852491 + 11.8737i −0.0552588 + 0.769656i
\(239\) 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 \(0.488298\pi\)
\(242\) 15.6892 9.05816i 1.00854 0.582280i
\(243\) 0 0
\(244\) 2.62158i 0.167829i
\(245\) 0 0
\(246\) 0 0
\(247\) −3.60488 + 6.24384i −0.229373 + 0.397286i
\(248\) 2.41421 + 4.18154i 0.153303 + 0.265528i
\(249\) 0 0
\(250\) 0 0
\(251\) −15.7243 −0.992507 −0.496254 0.868178i \(-0.665291\pi\)
−0.496254 + 0.868178i \(0.665291\pi\)
\(252\) 0 0
\(253\) 1.44584 0.0908993
\(254\) 12.5663 + 7.25517i 0.788481 + 0.455230i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.83083 17.0275i 0.613230 1.06215i −0.377462 0.926025i \(-0.623203\pi\)
0.990692 0.136121i \(-0.0434636\pi\)
\(258\) 0 0
\(259\) −9.66933 + 14.2780i −0.600823 + 0.887192i
\(260\) 0 0
\(261\) 0 0
\(262\) −13.3944 + 7.73325i −0.827508 + 0.477762i
\(263\) −3.74275 + 2.16088i −0.230788 + 0.133245i −0.610935 0.791680i \(-0.709206\pi\)
0.380148 + 0.924926i \(0.375873\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.30871 6.81601i −0.202870 0.417917i
\(267\) 0 0
\(268\) −4.91119 + 8.50643i −0.299999 + 0.519613i
\(269\) −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 \(0.770351\pi\)
\(272\) −4.49938 −0.272815
\(273\) 0 0
\(274\) 8.62158 0.520849
\(275\) 0 0
\(276\) 0 0
\(277\) 1.50971 + 2.61489i 0.0907097 + 0.157114i 0.907810 0.419382i \(-0.137753\pi\)
−0.817100 + 0.576496i \(0.804420\pi\)
\(278\) −5.12560 + 8.87780i −0.307413 + 0.532455i
\(279\) 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
\(283\) 15.2149 8.78434i 0.904434 0.522175i 0.0257976 0.999667i \(-0.491787\pi\)
0.878636 + 0.477492i \(0.158454\pi\)
\(284\) 4.12460 2.38134i 0.244750 0.141307i
\(285\) 0 0
\(286\) 13.5851i 0.803301i
\(287\) −2.00634 0.144049i −0.118431 0.00850295i
\(288\) 0 0
\(289\) −1.62220 + 2.80973i −0.0954235 + 0.165278i
\(290\) 0 0
\(291\) 0 0
\(292\) −10.0951 5.82843i −0.590773 0.341083i
\(293\) −14.6710 −0.857086 −0.428543 0.903521i \(-0.640973\pi\)
−0.428543 + 0.903521i \(0.640973\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −5.64444 3.25882i −0.328076 0.189415i
\(297\) 0 0
\(298\) 4.59940 + 7.96640i 0.266436 + 0.461481i
\(299\) 0.337300 0.584220i 0.0195065 0.0337863i
\(300\) 0 0
\(301\) 15.4741 + 1.11099i 0.891911 + 0.0640363i
\(302\) 12.7486i 0.733599i
\(303\) 0 0
\(304\) 2.48004 1.43185i 0.142240 0.0821223i
\(305\) 0 0
\(306\) 0 0
\(307\) 21.2772i 1.21435i 0.794567 + 0.607177i \(0.207698\pi\)
−0.794567 + 0.607177i \(0.792302\pi\)
\(308\) 11.8208 + 8.00524i 0.673550 + 0.456141i
\(309\) 0 0
\(310\) 0 0
\(311\) 5.91724 + 10.2490i 0.335536 + 0.581165i 0.983588 0.180431i \(-0.0577493\pi\)
−0.648052 + 0.761596i \(0.724416\pi\)
\(312\) 0 0
\(313\) 3.90551 + 2.25485i 0.220753 + 0.127452i 0.606299 0.795237i \(-0.292654\pi\)
−0.385546 + 0.922689i \(0.625987\pi\)
\(314\) −13.8447 −0.781302
\(315\) 0 0
\(316\) −8.59235 −0.483358
\(317\) −15.9202 9.19151i −0.894165 0.516247i −0.0188626 0.999822i \(-0.506005\pi\)
−0.875303 + 0.483576i \(0.839338\pi\)
\(318\) 0 0
\(319\) −24.0092 41.5852i −1.34426 2.32833i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.309587 + 0.637756i 0.0172526 + 0.0355408i
\(323\) 12.8849i 0.716934i
\(324\) 0 0
\(325\) 0 0
\(326\) −17.8444 + 10.3025i −0.988313 + 0.570603i
\(327\) 0 0
\(328\) 0.760279i 0.0419794i
\(329\) 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 \(0.236880\pi\)
\(332\) 4.72500 + 8.18394i 0.259318 + 0.449152i
\(333\) 0 0
\(334\) 5.93193 + 3.42480i 0.324581 + 0.187397i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.89417 0.375549 0.187775 0.982212i \(-0.439873\pi\)
0.187775 + 0.982212i \(0.439873\pi\)
\(338\) 5.76903 + 3.33075i 0.313794 + 0.181169i
\(339\) 0 0
\(340\) 0 0
\(341\) 13.0270 22.5634i 0.705451 1.22188i
\(342\) 0 0
\(343\) 18.0938 + 3.95164i 0.976972 + 0.213368i
\(344\) 5.86370i 0.316150i
\(345\) 0 0
\(346\) −11.0488 + 6.37902i −0.593986 + 0.342938i
\(347\) −14.1645 + 8.17789i −0.760392 + 0.439012i −0.829436 0.558601i \(-0.811338\pi\)
0.0690448 + 0.997614i \(0.478005\pi\)
\(348\) 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
\(352\) −2.69798 + 4.67303i −0.143803 + 0.249073i
\(353\) 6.85906 + 11.8802i 0.365071 + 0.632321i 0.988788 0.149329i \(-0.0477114\pi\)
−0.623717 + 0.781651i \(0.714378\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.97005 0.422412
\(357\) 0 0
\(358\) 18.8666 0.997132
\(359\) 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
\(362\) −12.7749 + 22.1268i −0.671433 + 1.16296i
\(363\) 0 0
\(364\) 5.99233 2.90887i 0.314083 0.152466i
\(365\) 0 0
\(366\) 0 0
\(367\) 10.9026 6.29461i 0.569110 0.328576i −0.187684 0.982230i \(-0.560098\pi\)
0.756794 + 0.653654i \(0.226765\pi\)
\(368\) −0.232051 + 0.133975i −0.0120965 + 0.00698391i
\(369\) 0 0
\(370\) 0 0
\(371\) −19.9893 + 9.70342i −1.03779 + 0.503776i
\(372\) 0 0
\(373\) −13.5868 + 23.5331i −0.703499 + 1.21850i 0.263731 + 0.964596i \(0.415047\pi\)
−0.967230 + 0.253900i \(0.918286\pi\)
\(374\) 12.1392 + 21.0257i 0.627704 + 1.08722i
\(375\) 0 0
\(376\) 6.92418 + 3.99768i 0.357087 + 0.206164i
\(377\) −22.4044 −1.15389
\(378\) 0 0
\(379\) 15.7335 0.808174 0.404087 0.914721i \(-0.367589\pi\)
0.404087 + 0.914721i \(0.367589\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.04524 + 7.00657i 0.206973 + 0.358487i
\(383\) −7.89060 + 13.6669i −0.403191 + 0.698347i −0.994109 0.108384i \(-0.965432\pi\)
0.590918 + 0.806732i \(0.298766\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.1270i 0.719046i
\(387\) 0 0
\(388\) 5.33777 3.08176i 0.270984 0.156453i
\(389\) 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
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 0 0
\(394\) −7.13689 + 12.3615i −0.359552 + 0.622762i
\(395\) 0 0
\(396\) 0 0
\(397\) −32.3557 18.6806i −1.62388 0.937550i −0.985867 0.167528i \(-0.946422\pi\)
−0.638017 0.770022i \(-0.720245\pi\)
\(398\) 3.54195 0.177542
\(399\) 0 0
\(400\) 0 0
\(401\) −24.4856 14.1368i −1.22275 0.705957i −0.257249 0.966345i \(-0.582816\pi\)
−0.965504 + 0.260389i \(0.916149\pi\)
\(402\) 0 0
\(403\) −6.07812 10.5276i −0.302773 0.524417i
\(404\) −7.02458 + 12.1669i −0.349486 + 0.605327i
\(405\) 0 0
\(406\) 13.2022 19.4947i 0.655214 0.967507i
\(407\) 35.1689i 1.74326i
\(408\) 0 0
\(409\) 13.8647 8.00481i 0.685567 0.395812i −0.116382 0.993204i \(-0.537130\pi\)
0.801949 + 0.597392i \(0.203796\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 14.1769i 0.698446i
\(413\) −14.6405 30.1599i −0.720414 1.48407i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.25882 + 2.18034i 0.0617187 + 0.106900i
\(417\) 0 0
\(418\) −13.3822 7.72620i −0.654544 0.377901i
\(419\) −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 \(0.497602\pi\)
\(422\) −3.39776 1.96170i −0.165400 0.0954939i
\(423\) 0 0
\(424\) −4.19918 7.27319i −0.203930 0.353217i
\(425\) 0 0
\(426\) 0 0
\(427\) −5.74301 3.88928i −0.277924 0.188215i
\(428\) 1.64173i 0.0793559i
\(429\) 0 0
\(430\) 0 0
\(431\) −7.63843 + 4.41005i −0.367930 + 0.212425i −0.672554 0.740048i \(-0.734803\pi\)
0.304624 + 0.952473i \(0.401469\pi\)
\(432\) 0 0
\(433\) 9.56388i 0.459611i 0.973237 + 0.229805i \(0.0738089\pi\)
−0.973237 + 0.229805i \(0.926191\pi\)
\(434\) 12.7420 + 0.914836i 0.611636 + 0.0439135i
\(435\) 0 0
\(436\) −9.94887 + 17.2319i −0.476464 + 0.825260i
\(437\) −0.383663 0.664525i −0.0183531 0.0317885i
\(438\) 0 0
\(439\) −31.3336 18.0905i −1.49547 0.863412i −0.495487 0.868615i \(-0.665010\pi\)
−0.999986 + 0.00520362i \(0.998344\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 11.3278 0.538809
\(443\) −3.53830 2.04284i −0.168110 0.0970582i 0.413584 0.910466i \(-0.364277\pi\)
−0.581694 + 0.813408i \(0.697610\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 7.34519 12.7222i 0.347805 0.602415i
\(447\) 0 0
\(448\) −2.63896 0.189469i −0.124679 0.00895155i
\(449\) 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
\(452\) 5.16036 2.97934i 0.242723 0.140136i
\(453\) 0 0
\(454\) 22.7826i 1.06924i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0623 + 17.4283i −0.470693 + 0.815264i −0.999438 0.0335168i \(-0.989329\pi\)
0.528745 + 0.848780i \(0.322663\pi\)
\(458\) −10.1087 17.5089i −0.472351 0.818136i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.909299 0.0423503 0.0211751 0.999776i \(-0.493259\pi\)
0.0211751 + 0.999776i \(0.493259\pi\)
\(462\) 0 0
\(463\) −21.4280 −0.995843 −0.497922 0.867222i \(-0.665903\pi\)
−0.497922 + 0.867222i \(0.665903\pi\)
\(464\) 7.70674 + 4.44949i 0.357777 + 0.206562i
\(465\) 0 0
\(466\) 1.31543 + 2.27840i 0.0609363 + 0.105545i
\(467\) −6.34607 + 10.9917i −0.293661 + 0.508636i −0.974672 0.223637i \(-0.928207\pi\)
0.681012 + 0.732273i \(0.261540\pi\)
\(468\) 0 0
\(469\) 11.3487 + 23.3786i 0.524035 + 1.07952i
\(470\) 0 0
\(471\) 0 0
\(472\) 10.9738 6.33573i 0.505111 0.291626i
\(473\) 27.4013 15.8201i 1.25991 0.727411i
\(474\) 0 0
\(475\) 0 0
\(476\) −6.67511 + 9.85666i −0.305953 + 0.451779i
\(477\) 0 0
\(478\) 8.43828 14.6155i 0.385958 0.668499i
\(479\) −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
\(482\) −14.5254 −0.661612
\(483\) 0 0
\(484\) 18.1163 0.823469
\(485\) 0 0
\(486\) 0 0
\(487\) −10.4097 18.0301i −0.471708 0.817022i 0.527768 0.849388i \(-0.323029\pi\)
−0.999476 + 0.0323665i \(0.989696\pi\)
\(488\) 1.31079 2.27035i 0.0593366 0.102774i
\(489\) 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
\(493\) 34.6755 20.0199i 1.56171 0.901653i
\(494\) −6.24384 + 3.60488i −0.280924 + 0.162191i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) 0.902379 12.5685i 0.0404772 0.563775i
\(498\) 0 0
\(499\) −16.6802 + 28.8909i −0.746708 + 1.29334i 0.202685 + 0.979244i \(0.435033\pi\)
−0.949393 + 0.314092i \(0.898300\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −13.6176 7.86214i −0.607784 0.350904i
\(503\) −16.2936 −0.726494 −0.363247 0.931693i \(-0.618332\pi\)
−0.363247 + 0.931693i \(0.618332\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1.25214 + 0.722921i 0.0556642 + 0.0321377i
\(507\) 0 0
\(508\) 7.25517 + 12.5663i 0.321896 + 0.557540i
\(509\) −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
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 17.0275 9.83083i 0.751051 0.433619i
\(515\) 0 0
\(516\) 0 0
\(517\) 43.1426i 1.89741i
\(518\) −15.5129 + 7.53044i −0.681597 + 0.330869i
\(519\) 0 0
\(520\) 0 0
\(521\) −0.141663 0.245367i −0.00620635 0.0107497i 0.862906 0.505365i \(-0.168642\pi\)
−0.869112 + 0.494616i \(0.835309\pi\)
\(522\) 0 0
\(523\) 9.77021 + 5.64083i 0.427222 + 0.246656i 0.698162 0.715940i \(-0.254001\pi\)
−0.270941 + 0.962596i \(0.587335\pi\)
\(524\) −15.4665 −0.675657
\(525\) 0 0
\(526\) −4.32175 −0.188437
\(527\) 18.8143 + 10.8625i 0.819565 + 0.473176i
\(528\) 0 0
\(529\) −11.4641 19.8564i −0.498439 0.863322i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.542582 7.55719i 0.0235239 0.327646i
\(533\) 1.91411i 0.0829092i
\(534\) 0 0
\(535\) 0 0
\(536\) −8.50643 + 4.91119i −0.367422 + 0.212131i
\(537\) 0 0
\(538\) 17.5979i 0.758700i
\(539\) 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 \(-0.102617\pi\)
\(542\) −5.26795 9.12436i −0.226278 0.391925i
\(543\) 0 0
\(544\) −3.89658 2.24969i −0.167064 0.0964546i
\(545\) 0 0
\(546\) 0 0
\(547\) −35.4261 −1.51471 −0.757356 0.653002i \(-0.773509\pi\)
−0.757356 + 0.653002i \(0.773509\pi\)
\(548\) 7.46651 + 4.31079i 0.318953 + 0.184148i
\(549\) 0 0
\(550\) 0 0
\(551\) −12.7420 + 22.0698i −0.542828 + 0.940206i
\(552\) 0 0
\(553\) −12.7473 + 18.8230i −0.542071 + 0.800436i
\(554\) 3.01942i 0.128283i
\(555\) 0 0
\(556\) −8.87780 + 5.12560i −0.376503 + 0.217374i
\(557\) 7.05105 4.07093i 0.298763 0.172491i −0.343124 0.939290i \(-0.611485\pi\)
0.641887 + 0.766799i \(0.278152\pi\)
\(558\) 0 0
\(559\) 14.7627i 0.624395i
\(560\) 0 0
\(561\) 0 0
\(562\) 5.34398 9.25605i 0.225422 0.390443i
\(563\) 10.2088 + 17.6821i 0.430248 + 0.745212i 0.996894 0.0787491i \(-0.0250926\pi\)
−0.566646 + 0.823961i \(0.691759\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 17.5687 0.738467
\(567\) 0 0
\(568\) 4.76268 0.199838
\(569\) −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 \(0.749952\pi\)
\(572\) 6.79253 11.7650i 0.284010 0.491920i
\(573\) 0 0
\(574\) −1.66552 1.12792i −0.0695175 0.0470786i
\(575\) 0 0
\(576\) 0 0
\(577\) −23.3399 + 13.4753i −0.971654 + 0.560985i −0.899740 0.436426i \(-0.856244\pi\)
−0.0719139 + 0.997411i \(0.522911\pi\)
\(578\) −2.80973 + 1.62220i −0.116869 + 0.0674746i
\(579\) 0 0
\(580\) 0 0
\(581\) 24.9382 + 1.79048i 1.03461 + 0.0742816i
\(582\) 0 0
\(583\) −22.6586 + 39.2458i −0.938422 + 1.62539i
\(584\) −5.82843 10.0951i −0.241182 0.417740i
\(585\) 0 0
\(586\) −12.7054 7.33548i −0.524856 0.303026i
\(587\) −35.3511 −1.45910 −0.729548 0.683930i \(-0.760269\pi\)
−0.729548 + 0.683930i \(0.760269\pi\)
\(588\) 0 0
\(589\) −13.8272 −0.569739
\(590\) 0 0
\(591\) 0 0
\(592\) −3.25882 5.64444i −0.133937 0.231985i
\(593\) 14.7057 25.4711i 0.603893 1.04597i −0.388333 0.921519i \(-0.626949\pi\)
0.992225 0.124454i \(-0.0397178\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.19881i 0.376798i
\(597\) 0 0
\(598\) 0.584220 0.337300i 0.0238905 0.0137932i
\(599\) −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 \(-0.246992\pi\)
\(602\) 12.8454 + 8.69918i 0.523541 + 0.354552i
\(603\) 0 0
\(604\) −6.37429 + 11.0406i −0.259366 + 0.449236i
\(605\) 0 0
\(606\) 0 0
\(607\) −28.2475 16.3087i −1.14653 0.661950i −0.198492 0.980103i \(-0.563604\pi\)
−0.948040 + 0.318153i \(0.896938\pi\)
\(608\) 2.86370 0.116139
\(609\) 0 0
\(610\) 0 0
\(611\) −17.4326 10.0647i −0.705247 0.407174i
\(612\) 0 0
\(613\) −7.99843 13.8537i −0.323054 0.559545i 0.658063 0.752963i \(-0.271376\pi\)
−0.981117 + 0.193418i \(0.938043\pi\)
\(614\) −10.6386 + 18.4266i −0.429339 + 0.743636i
\(615\) 0 0
\(616\) 6.23445 + 12.8431i 0.251193 + 0.517464i
\(617\) 25.1429i 1.01221i −0.862471 0.506107i \(-0.831084\pi\)
0.862471 0.506107i \(-0.168916\pi\)
\(618\) 0 0
\(619\) 32.3379 18.6703i 1.29977 0.750423i 0.319406 0.947618i \(-0.396517\pi\)
0.980364 + 0.197195i \(0.0631832\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.8345i 0.474519i
\(623\) 11.8241 17.4597i 0.473722 0.699510i
\(624\) 0 0
\(625\) 0 0
\(626\) 2.25485 + 3.90551i 0.0901219 + 0.156096i
\(627\) 0 0
\(628\) −11.9899 6.92236i −0.478448 0.276232i
\(629\) −29.3253 −1.16928
\(630\) 0 0
\(631\) 49.5015 1.97062 0.985311 0.170767i \(-0.0546245\pi\)
0.985311 + 0.170767i \(0.0546245\pi\)
\(632\) −7.44120 4.29618i −0.295995 0.170893i
\(633\) 0 0
\(634\) −9.19151 15.9202i −0.365041 0.632270i
\(635\) 0 0
\(636\) 0 0
\(637\) 2.51764 17.4427i 0.0997525 0.691105i
\(638\) 48.0185i 1.90107i
\(639\) 0 0
\(640\) 0 0
\(641\) 31.4439 18.1542i 1.24196 0.717046i 0.272467 0.962165i \(-0.412160\pi\)
0.969493 + 0.245119i \(0.0788271\pi\)
\(642\) 0 0
\(643\) 10.2653i 0.404824i 0.979300 + 0.202412i \(0.0648780\pi\)
−0.979300 + 0.202412i \(0.935122\pi\)
\(644\) −0.0507680 + 0.707107i −0.00200054 + 0.0278639i
\(645\) 0 0
\(646\) 6.44244 11.1586i 0.253474 0.439031i
\(647\) −10.9108 18.8980i −0.428946 0.742956i 0.567834 0.823143i \(-0.307782\pi\)
−0.996780 + 0.0801869i \(0.974448\pi\)
\(648\) 0 0
\(649\) −59.2142 34.1873i −2.32436 1.34197i
\(650\) 0 0
\(651\) 0 0
\(652\) −20.6050 −0.806954
\(653\) 40.9556 + 23.6457i 1.60272 + 0.925329i 0.990941 + 0.134297i \(0.0428776\pi\)
0.611775 + 0.791032i \(0.290456\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.380139 0.658421i 0.0148419 0.0257070i
\(657\) 0 0
\(658\) 19.0301 9.23779i 0.741869 0.360127i
\(659\) 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 \(0.343468\pi\)
\(662\) −6.89471 + 3.98066i −0.267970 + 0.154713i
\(663\) 0 0
\(664\) 9.45001i 0.366731i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.19224 2.06502i 0.0461636 0.0799577i
\(668\) 3.42480 + 5.93193i 0.132510 + 0.229513i
\(669\) 0 0
\(670\) 0 0
\(671\) −14.1459 −0.546097
\(672\) 0 0
\(673\) 2.02242 0.0779587 0.0389794 0.999240i \(-0.487589\pi\)
0.0389794 + 0.999240i \(0.487589\pi\)
\(674\) 5.97053 + 3.44709i 0.229976 + 0.132777i
\(675\) 0 0
\(676\) 3.33075 + 5.76903i 0.128106 + 0.221886i
\(677\) 11.4413 19.8169i 0.439725 0.761626i −0.557943 0.829879i \(-0.688409\pi\)
0.997668 + 0.0682532i \(0.0217426\pi\)
\(678\) 0 0
\(679\) 1.16780 16.2653i 0.0448159 0.624205i
\(680\) 0 0
\(681\) 0 0
\(682\) 22.5634 13.0270i 0.863997 0.498829i
\(683\) 27.1977 15.7026i 1.04069 0.600844i 0.120663 0.992694i \(-0.461498\pi\)
0.920029 + 0.391850i \(0.128165\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 13.6938 + 12.4691i 0.522834 + 0.476073i
\(687\) 0 0
\(688\) −2.93185 + 5.07812i −0.111776 + 0.193601i
\(689\) 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 \(0.443518\pi\)
\(692\) −12.7580 −0.484988
\(693\) 0 0
\(694\) −16.3558 −0.620857
\(695\) 0 0
\(696\) 0 0
\(697\) −1.71039 2.96248i −0.0647857 0.112212i
\(698\) −12.2925 + 21.2913i −0.465279 + 0.805887i
\(699\) 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
\(703\) 16.1640 9.33229i 0.609637 0.351974i
\(704\) −4.67303 + 2.69798i −0.176122 + 0.101684i
\(705\) 0 0
\(706\) 13.7181i 0.516288i
\(707\) 16.2323 + 33.4390i 0.610479 + 1.25760i
\(708\) 0 0
\(709\) −7.52572 + 13.0349i −0.282634 + 0.489537i −0.972033 0.234845i \(-0.924542\pi\)
0.689398 + 0.724382i \(0.257875\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.90226 + 3.98502i 0.258673 + 0.149345i
\(713\) 1.29377 0.0484522
\(714\) 0 0
\(715\) 0 0
\(716\) 16.3390 + 9.43331i 0.610616 + 0.352539i
\(717\) 0 0
\(718\) 5.95011 + 10.3059i 0.222056 + 0.384613i
\(719\) −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
\(722\) 10.7992i 0.401905i
\(723\) 0 0
\(724\) −22.1268 + 12.7749i −0.822335 + 0.474775i
\(725\) 0 0
\(726\) 0 0
\(727\) 43.7349i 1.62204i 0.585020 + 0.811019i \(0.301087\pi\)
−0.585020 + 0.811019i \(0.698913\pi\)
\(728\) 6.64394 + 0.477014i 0.246241 + 0.0176793i
\(729\) 0 0
\(730\) 0 0
\(731\) 13.1915 + 22.8484i 0.487906 + 0.845077i
\(732\) 0 0
\(733\) −38.7280 22.3596i −1.43045 0.825872i −0.433297 0.901251i \(-0.642650\pi\)
−0.997155 + 0.0753789i \(0.975983\pi\)
\(734\) 12.5892 0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) 45.9003 + 26.5005i 1.69076 + 0.976160i
\(738\) 0 0
\(739\) 10.7360 + 18.5954i 0.394932 + 0.684042i 0.993092 0.117334i \(-0.0374348\pi\)
−0.598161 + 0.801376i \(0.704102\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −22.1629 1.59123i −0.813626 0.0584157i
\(743\) 29.5637i 1.08459i 0.840190 + 0.542293i \(0.182444\pi\)
−0.840190 + 0.542293i \(0.817556\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −23.5331 + 13.5868i −0.861607 + 0.497449i
\(747\) 0 0
\(748\) 24.2784i 0.887707i
\(749\) −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 \(0.173599\pi\)
\(752\) 3.99768 + 6.92418i 0.145780 + 0.252499i
\(753\) 0 0
\(754\) −19.4028 11.2022i −0.706608 0.407960i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.8915 0.977386 0.488693 0.872456i \(-0.337474\pi\)
0.488693 + 0.872456i \(0.337474\pi\)
\(758\) 13.6256 + 7.86673i 0.494903 + 0.285732i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.939574 1.62739i 0.0340595 0.0589928i −0.848493 0.529206i \(-0.822490\pi\)
0.882553 + 0.470213i \(0.155823\pi\)
\(762\) 0 0
\(763\) 22.9897 + 47.3594i 0.832284 + 1.71452i
\(764\) 8.09049i 0.292704i
\(765\) 0 0
\(766\) −13.6669 + 7.89060i −0.493806 + 0.285099i
\(767\) −27.6281 + 15.9511i −0.997592 + 0.575960i
\(768\) 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
\(772\) 7.06350 12.2343i 0.254221 0.440324i
\(773\) −24.3353 42.1499i −0.875279 1.51603i −0.856466 0.516204i \(-0.827345\pi\)
−0.0188128 0.999823i \(-0.505989\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 6.16353 0.221258
\(777\) 0 0
\(778\) 15.8836 0.569456
\(779\) 1.88552 + 1.08861i 0.0675558 + 0.0390034i
\(780\) 0 0
\(781\) −12.8496 22.2562i −0.459795 0.796388i
\(782\) −0.602802 + 1.04408i −0.0215562 + 0.0373364i
\(783\) 0 0
\(784\) −4.33013 + 5.50000i −0.154647 + 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) 12.9437 7.47307i 0.461395 0.266386i −0.251236 0.967926i \(-0.580837\pi\)
0.712630 + 0.701540i \(0.247504\pi\)
\(788\) −12.3615 + 7.13689i −0.440359 + 0.254241i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.12898 15.7247i 0.0401420 0.559105i
\(792\) 0 0
\(793\) −3.30009 + 5.71593i −0.117190 + 0.202979i
\(794\) −18.6806 32.3557i −0.662948 1.14826i
\(795\) 0 0
\(796\) 3.06742 + 1.77098i 0.108722 +