Properties

Label 320.2.j.b.47.7
Level $320$
Weight $2$
Character 320.47
Analytic conductor $2.555$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.7
Root \(1.41323 - 0.0526497i\) of defining polynomial
Character \(\chi\) \(=\) 320.47
Dual form 320.2.j.b.143.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.28110i q^{3} +(-0.841703 - 2.07160i) q^{5} +(1.13975 + 1.13975i) q^{7} +1.35879 q^{9} +O(q^{10})\) \(q+1.28110i q^{3} +(-0.841703 - 2.07160i) q^{5} +(1.13975 + 1.13975i) q^{7} +1.35879 q^{9} +(2.32204 + 2.32204i) q^{11} +1.36502 q^{13} +(2.65392 - 1.07830i) q^{15} +(5.25380 + 5.25380i) q^{17} +(-3.69752 - 3.69752i) q^{19} +(-1.46013 + 1.46013i) q^{21} +(0.911118 - 0.911118i) q^{23} +(-3.58307 + 3.48735i) q^{25} +5.58403i q^{27} +(2.37343 - 2.37343i) q^{29} +0.242577i q^{31} +(-2.97475 + 2.97475i) q^{33} +(1.40178 - 3.32044i) q^{35} -3.34494 q^{37} +1.74872i q^{39} -2.66956i q^{41} -9.04874 q^{43} +(-1.14370 - 2.81488i) q^{45} +(7.87820 - 7.87820i) q^{47} -4.40194i q^{49} +(-6.73063 + 6.73063i) q^{51} +5.80113i q^{53} +(2.85587 - 6.76480i) q^{55} +(4.73688 - 4.73688i) q^{57} +(5.91474 - 5.91474i) q^{59} +(-6.67404 - 6.67404i) q^{61} +(1.54868 + 1.54868i) q^{63} +(-1.14894 - 2.82778i) q^{65} +4.54673 q^{67} +(1.16723 + 1.16723i) q^{69} -15.4389 q^{71} +(1.49307 + 1.49307i) q^{73} +(-4.46763 - 4.59026i) q^{75} +5.29308i q^{77} -10.3024 q^{79} -3.07731 q^{81} +3.26589i q^{83} +(6.46165 - 15.3059i) q^{85} +(3.04060 + 3.04060i) q^{87} -9.77206 q^{89} +(1.55578 + 1.55578i) q^{91} -0.310765 q^{93} +(-4.54758 + 10.7720i) q^{95} +(-1.63587 - 1.63587i) q^{97} +(3.15516 + 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{5} - 2q^{7} - 10q^{9} + O(q^{10}) \) \( 18q - 4q^{5} - 2q^{7} - 10q^{9} + 2q^{11} - 20q^{15} - 6q^{17} - 2q^{19} - 16q^{21} + 2q^{23} + 6q^{25} - 14q^{29} - 8q^{33} + 6q^{35} + 8q^{37} + 44q^{43} - 4q^{45} + 38q^{47} - 8q^{51} + 6q^{55} + 24q^{57} + 10q^{59} + 14q^{61} - 6q^{63} - 12q^{67} + 32q^{69} - 24q^{71} + 14q^{73} - 64q^{75} - 16q^{79} + 2q^{81} - 10q^{85} - 24q^{87} - 12q^{89} + 16q^{93} + 34q^{95} + 18q^{97} + 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.28110i 0.739642i 0.929103 + 0.369821i \(0.120581\pi\)
−0.929103 + 0.369821i \(0.879419\pi\)
\(4\) 0 0
\(5\) −0.841703 2.07160i −0.376421 0.926449i
\(6\) 0 0
\(7\) 1.13975 + 1.13975i 0.430785 + 0.430785i 0.888895 0.458111i \(-0.151474\pi\)
−0.458111 + 0.888895i \(0.651474\pi\)
\(8\) 0 0
\(9\) 1.35879 0.452930
\(10\) 0 0
\(11\) 2.32204 + 2.32204i 0.700120 + 0.700120i 0.964436 0.264316i \(-0.0851462\pi\)
−0.264316 + 0.964436i \(0.585146\pi\)
\(12\) 0 0
\(13\) 1.36502 0.378589 0.189294 0.981920i \(-0.439380\pi\)
0.189294 + 0.981920i \(0.439380\pi\)
\(14\) 0 0
\(15\) 2.65392 1.07830i 0.685240 0.278416i
\(16\) 0 0
\(17\) 5.25380 + 5.25380i 1.27423 + 1.27423i 0.943845 + 0.330389i \(0.107180\pi\)
0.330389 + 0.943845i \(0.392820\pi\)
\(18\) 0 0
\(19\) −3.69752 3.69752i −0.848269 0.848269i 0.141648 0.989917i \(-0.454760\pi\)
−0.989917 + 0.141648i \(0.954760\pi\)
\(20\) 0 0
\(21\) −1.46013 + 1.46013i −0.318626 + 0.318626i
\(22\) 0 0
\(23\) 0.911118 0.911118i 0.189981 0.189981i −0.605707 0.795688i \(-0.707110\pi\)
0.795688 + 0.605707i \(0.207110\pi\)
\(24\) 0 0
\(25\) −3.58307 + 3.48735i −0.716615 + 0.697469i
\(26\) 0 0
\(27\) 5.58403i 1.07465i
\(28\) 0 0
\(29\) 2.37343 2.37343i 0.440736 0.440736i −0.451524 0.892259i \(-0.649119\pi\)
0.892259 + 0.451524i \(0.149119\pi\)
\(30\) 0 0
\(31\) 0.242577i 0.0435681i 0.999763 + 0.0217841i \(0.00693463\pi\)
−0.999763 + 0.0217841i \(0.993065\pi\)
\(32\) 0 0
\(33\) −2.97475 + 2.97475i −0.517838 + 0.517838i
\(34\) 0 0
\(35\) 1.40178 3.32044i 0.236944 0.561256i
\(36\) 0 0
\(37\) −3.34494 −0.549905 −0.274953 0.961458i \(-0.588662\pi\)
−0.274953 + 0.961458i \(0.588662\pi\)
\(38\) 0 0
\(39\) 1.74872i 0.280020i
\(40\) 0 0
\(41\) 2.66956i 0.416915i −0.978031 0.208457i \(-0.933156\pi\)
0.978031 0.208457i \(-0.0668442\pi\)
\(42\) 0 0
\(43\) −9.04874 −1.37992 −0.689960 0.723847i \(-0.742372\pi\)
−0.689960 + 0.723847i \(0.742372\pi\)
\(44\) 0 0
\(45\) −1.14370 2.81488i −0.170492 0.419617i
\(46\) 0 0
\(47\) 7.87820 7.87820i 1.14915 1.14915i 0.162435 0.986719i \(-0.448065\pi\)
0.986719 0.162435i \(-0.0519348\pi\)
\(48\) 0 0
\(49\) 4.40194i 0.628849i
\(50\) 0 0
\(51\) −6.73063 + 6.73063i −0.942476 + 0.942476i
\(52\) 0 0
\(53\) 5.80113i 0.796846i 0.917202 + 0.398423i \(0.130442\pi\)
−0.917202 + 0.398423i \(0.869558\pi\)
\(54\) 0 0
\(55\) 2.85587 6.76480i 0.385086 0.912165i
\(56\) 0 0
\(57\) 4.73688 4.73688i 0.627415 0.627415i
\(58\) 0 0
\(59\) 5.91474 5.91474i 0.770033 0.770033i −0.208079 0.978112i \(-0.566721\pi\)
0.978112 + 0.208079i \(0.0667210\pi\)
\(60\) 0 0
\(61\) −6.67404 6.67404i −0.854523 0.854523i 0.136163 0.990686i \(-0.456523\pi\)
−0.990686 + 0.136163i \(0.956523\pi\)
\(62\) 0 0
\(63\) 1.54868 + 1.54868i 0.195116 + 0.195116i
\(64\) 0 0
\(65\) −1.14894 2.82778i −0.142509 0.350743i
\(66\) 0 0
\(67\) 4.54673 0.555471 0.277736 0.960658i \(-0.410416\pi\)
0.277736 + 0.960658i \(0.410416\pi\)
\(68\) 0 0
\(69\) 1.16723 + 1.16723i 0.140518 + 0.140518i
\(70\) 0 0
\(71\) −15.4389 −1.83226 −0.916128 0.400885i \(-0.868703\pi\)
−0.916128 + 0.400885i \(0.868703\pi\)
\(72\) 0 0
\(73\) 1.49307 + 1.49307i 0.174750 + 0.174750i 0.789063 0.614313i \(-0.210567\pi\)
−0.614313 + 0.789063i \(0.710567\pi\)
\(74\) 0 0
\(75\) −4.46763 4.59026i −0.515877 0.530038i
\(76\) 0 0
\(77\) 5.29308i 0.603202i
\(78\) 0 0
\(79\) −10.3024 −1.15911 −0.579556 0.814932i \(-0.696774\pi\)
−0.579556 + 0.814932i \(0.696774\pi\)
\(80\) 0 0
\(81\) −3.07731 −0.341924
\(82\) 0 0
\(83\) 3.26589i 0.358478i 0.983806 + 0.179239i \(0.0573636\pi\)
−0.983806 + 0.179239i \(0.942636\pi\)
\(84\) 0 0
\(85\) 6.46165 15.3059i 0.700864 1.66016i
\(86\) 0 0
\(87\) 3.04060 + 3.04060i 0.325986 + 0.325986i
\(88\) 0 0
\(89\) −9.77206 −1.03584 −0.517918 0.855430i \(-0.673293\pi\)
−0.517918 + 0.855430i \(0.673293\pi\)
\(90\) 0 0
\(91\) 1.55578 + 1.55578i 0.163090 + 0.163090i
\(92\) 0 0
\(93\) −0.310765 −0.0322248
\(94\) 0 0
\(95\) −4.54758 + 10.7720i −0.466571 + 1.10518i
\(96\) 0 0
\(97\) −1.63587 1.63587i −0.166097 0.166097i 0.619164 0.785262i \(-0.287472\pi\)
−0.785262 + 0.619164i \(0.787472\pi\)
\(98\) 0 0
\(99\) 3.15516 + 3.15516i 0.317106 + 0.317106i
\(100\) 0 0
\(101\) −6.63953 + 6.63953i −0.660658 + 0.660658i −0.955535 0.294877i \(-0.904721\pi\)
0.294877 + 0.955535i \(0.404721\pi\)
\(102\) 0 0
\(103\) −1.62219 + 1.62219i −0.159839 + 0.159839i −0.782496 0.622656i \(-0.786054\pi\)
0.622656 + 0.782496i \(0.286054\pi\)
\(104\) 0 0
\(105\) 4.25380 + 1.79581i 0.415129 + 0.175253i
\(106\) 0 0
\(107\) 3.65206i 0.353058i −0.984295 0.176529i \(-0.943513\pi\)
0.984295 0.176529i \(-0.0564869\pi\)
\(108\) 0 0
\(109\) −5.20757 + 5.20757i −0.498795 + 0.498795i −0.911063 0.412268i \(-0.864737\pi\)
0.412268 + 0.911063i \(0.364737\pi\)
\(110\) 0 0
\(111\) 4.28519i 0.406733i
\(112\) 0 0
\(113\) −4.27905 + 4.27905i −0.402539 + 0.402539i −0.879127 0.476588i \(-0.841873\pi\)
0.476588 + 0.879127i \(0.341873\pi\)
\(114\) 0 0
\(115\) −2.65437 1.12058i −0.247521 0.104495i
\(116\) 0 0
\(117\) 1.85478 0.171474
\(118\) 0 0
\(119\) 11.9760i 1.09784i
\(120\) 0 0
\(121\) 0.216302i 0.0196639i
\(122\) 0 0
\(123\) 3.41996 0.308367
\(124\) 0 0
\(125\) 10.2403 + 4.48739i 0.915918 + 0.401365i
\(126\) 0 0
\(127\) −7.29257 + 7.29257i −0.647111 + 0.647111i −0.952294 0.305183i \(-0.901282\pi\)
0.305183 + 0.952294i \(0.401282\pi\)
\(128\) 0 0
\(129\) 11.5923i 1.02065i
\(130\) 0 0
\(131\) 11.9793 11.9793i 1.04664 1.04664i 0.0477778 0.998858i \(-0.484786\pi\)
0.998858 0.0477778i \(-0.0152139\pi\)
\(132\) 0 0
\(133\) 8.42848i 0.730842i
\(134\) 0 0
\(135\) 11.5679 4.70010i 0.995606 0.404520i
\(136\) 0 0
\(137\) 4.92762 4.92762i 0.420995 0.420995i −0.464551 0.885546i \(-0.653784\pi\)
0.885546 + 0.464551i \(0.153784\pi\)
\(138\) 0 0
\(139\) 10.3015 10.3015i 0.873761 0.873761i −0.119119 0.992880i \(-0.538007\pi\)
0.992880 + 0.119119i \(0.0380071\pi\)
\(140\) 0 0
\(141\) 10.0927 + 10.0927i 0.849962 + 0.849962i
\(142\) 0 0
\(143\) 3.16963 + 3.16963i 0.265058 + 0.265058i
\(144\) 0 0
\(145\) −6.91454 2.91909i −0.574221 0.242417i
\(146\) 0 0
\(147\) 5.63931 0.465123
\(148\) 0 0
\(149\) 15.2040 + 15.2040i 1.24556 + 1.24556i 0.957662 + 0.287896i \(0.0929557\pi\)
0.287896 + 0.957662i \(0.407044\pi\)
\(150\) 0 0
\(151\) 10.7055 0.871204 0.435602 0.900139i \(-0.356536\pi\)
0.435602 + 0.900139i \(0.356536\pi\)
\(152\) 0 0
\(153\) 7.13882 + 7.13882i 0.577139 + 0.577139i
\(154\) 0 0
\(155\) 0.502523 0.204178i 0.0403636 0.0164000i
\(156\) 0 0
\(157\) 2.34588i 0.187222i 0.995609 + 0.0936108i \(0.0298409\pi\)
−0.995609 + 0.0936108i \(0.970159\pi\)
\(158\) 0 0
\(159\) −7.43180 −0.589380
\(160\) 0 0
\(161\) 2.07689 0.163682
\(162\) 0 0
\(163\) 2.73625i 0.214319i −0.994242 0.107160i \(-0.965824\pi\)
0.994242 0.107160i \(-0.0341756\pi\)
\(164\) 0 0
\(165\) 8.66636 + 3.65865i 0.674675 + 0.284825i
\(166\) 0 0
\(167\) −10.1328 10.1328i −0.784097 0.784097i 0.196423 0.980519i \(-0.437068\pi\)
−0.980519 + 0.196423i \(0.937068\pi\)
\(168\) 0 0
\(169\) −11.1367 −0.856670
\(170\) 0 0
\(171\) −5.02415 5.02415i −0.384207 0.384207i
\(172\) 0 0
\(173\) −8.79590 −0.668740 −0.334370 0.942442i \(-0.608523\pi\)
−0.334370 + 0.942442i \(0.608523\pi\)
\(174\) 0 0
\(175\) −8.05851 0.109105i −0.609166 0.00824753i
\(176\) 0 0
\(177\) 7.57735 + 7.57735i 0.569549 + 0.569549i
\(178\) 0 0
\(179\) 6.62071 + 6.62071i 0.494855 + 0.494855i 0.909832 0.414977i \(-0.136210\pi\)
−0.414977 + 0.909832i \(0.636210\pi\)
\(180\) 0 0
\(181\) −5.84339 + 5.84339i −0.434336 + 0.434336i −0.890100 0.455765i \(-0.849366\pi\)
0.455765 + 0.890100i \(0.349366\pi\)
\(182\) 0 0
\(183\) 8.55009 8.55009i 0.632041 0.632041i
\(184\) 0 0
\(185\) 2.81545 + 6.92939i 0.206996 + 0.509459i
\(186\) 0 0
\(187\) 24.3990i 1.78423i
\(188\) 0 0
\(189\) −6.36440 + 6.36440i −0.462942 + 0.462942i
\(190\) 0 0
\(191\) 1.83906i 0.133070i 0.997784 + 0.0665349i \(0.0211944\pi\)
−0.997784 + 0.0665349i \(0.978806\pi\)
\(192\) 0 0
\(193\) 6.18343 6.18343i 0.445093 0.445093i −0.448626 0.893719i \(-0.648087\pi\)
0.893719 + 0.448626i \(0.148087\pi\)
\(194\) 0 0
\(195\) 3.62266 1.47191i 0.259424 0.105405i
\(196\) 0 0
\(197\) 5.55669 0.395898 0.197949 0.980212i \(-0.436572\pi\)
0.197949 + 0.980212i \(0.436572\pi\)
\(198\) 0 0
\(199\) 6.96413i 0.493674i −0.969057 0.246837i \(-0.920609\pi\)
0.969057 0.246837i \(-0.0793912\pi\)
\(200\) 0 0
\(201\) 5.82480i 0.410850i
\(202\) 0 0
\(203\) 5.41024 0.379724
\(204\) 0 0
\(205\) −5.53026 + 2.24697i −0.386250 + 0.156935i
\(206\) 0 0
\(207\) 1.23802 1.23802i 0.0860483 0.0860483i
\(208\) 0 0
\(209\) 17.1715i 1.18778i
\(210\) 0 0
\(211\) −5.43389 + 5.43389i −0.374084 + 0.374084i −0.868962 0.494878i \(-0.835213\pi\)
0.494878 + 0.868962i \(0.335213\pi\)
\(212\) 0 0
\(213\) 19.7787i 1.35521i
\(214\) 0 0
\(215\) 7.61635 + 18.7454i 0.519431 + 1.27843i
\(216\) 0 0
\(217\) −0.276477 + 0.276477i −0.0187685 + 0.0187685i
\(218\) 0 0
\(219\) −1.91276 + 1.91276i −0.129253 + 0.129253i
\(220\) 0 0
\(221\) 7.17155 + 7.17155i 0.482411 + 0.482411i
\(222\) 0 0
\(223\) 8.61776 + 8.61776i 0.577088 + 0.577088i 0.934100 0.357012i \(-0.116204\pi\)
−0.357012 + 0.934100i \(0.616204\pi\)
\(224\) 0 0
\(225\) −4.86865 + 4.73858i −0.324577 + 0.315905i
\(226\) 0 0
\(227\) −6.01977 −0.399546 −0.199773 0.979842i \(-0.564020\pi\)
−0.199773 + 0.979842i \(0.564020\pi\)
\(228\) 0 0
\(229\) 0.568504 + 0.568504i 0.0375678 + 0.0375678i 0.725641 0.688073i \(-0.241543\pi\)
−0.688073 + 0.725641i \(0.741543\pi\)
\(230\) 0 0
\(231\) −6.78094 −0.446153
\(232\) 0 0
\(233\) −12.6979 12.6979i −0.831869 0.831869i 0.155904 0.987772i \(-0.450171\pi\)
−0.987772 + 0.155904i \(0.950171\pi\)
\(234\) 0 0
\(235\) −22.9516 9.68940i −1.49720 0.632067i
\(236\) 0 0
\(237\) 13.1984i 0.857327i
\(238\) 0 0
\(239\) 1.78306 0.115336 0.0576682 0.998336i \(-0.481633\pi\)
0.0576682 + 0.998336i \(0.481633\pi\)
\(240\) 0 0
\(241\) 10.4440 0.672754 0.336377 0.941727i \(-0.390798\pi\)
0.336377 + 0.941727i \(0.390798\pi\)
\(242\) 0 0
\(243\) 12.8098i 0.821747i
\(244\) 0 0
\(245\) −9.11908 + 3.70513i −0.582596 + 0.236712i
\(246\) 0 0
\(247\) −5.04719 5.04719i −0.321145 0.321145i
\(248\) 0 0
\(249\) −4.18392 −0.265145
\(250\) 0 0
\(251\) 12.6497 + 12.6497i 0.798445 + 0.798445i 0.982850 0.184406i \(-0.0590360\pi\)
−0.184406 + 0.982850i \(0.559036\pi\)
\(252\) 0 0
\(253\) 4.23130 0.266019
\(254\) 0 0
\(255\) 19.6084 + 8.27800i 1.22792 + 0.518388i
\(256\) 0 0
\(257\) −4.13062 4.13062i −0.257661 0.257661i 0.566441 0.824102i \(-0.308320\pi\)
−0.824102 + 0.566441i \(0.808320\pi\)
\(258\) 0 0
\(259\) −3.81240 3.81240i −0.236891 0.236891i
\(260\) 0 0
\(261\) 3.22500 3.22500i 0.199623 0.199623i
\(262\) 0 0
\(263\) −17.1303 + 17.1303i −1.05630 + 1.05630i −0.0579798 + 0.998318i \(0.518466\pi\)
−0.998318 + 0.0579798i \(0.981534\pi\)
\(264\) 0 0
\(265\) 12.0176 4.88282i 0.738237 0.299949i
\(266\) 0 0
\(267\) 12.5190i 0.766147i
\(268\) 0 0
\(269\) 19.8075 19.8075i 1.20768 1.20768i 0.235910 0.971775i \(-0.424193\pi\)
0.971775 0.235910i \(-0.0758070\pi\)
\(270\) 0 0
\(271\) 27.9542i 1.69810i −0.528316 0.849048i \(-0.677176\pi\)
0.528316 0.849048i \(-0.322824\pi\)
\(272\) 0 0
\(273\) −1.99311 + 1.99311i −0.120628 + 0.120628i
\(274\) 0 0
\(275\) −16.4178 0.222281i −0.990029 0.0134041i
\(276\) 0 0
\(277\) −26.0257 −1.56373 −0.781866 0.623447i \(-0.785732\pi\)
−0.781866 + 0.623447i \(0.785732\pi\)
\(278\) 0 0
\(279\) 0.329612i 0.0197333i
\(280\) 0 0
\(281\) 24.1001i 1.43769i −0.695170 0.718846i \(-0.744671\pi\)
0.695170 0.718846i \(-0.255329\pi\)
\(282\) 0 0
\(283\) −4.73708 −0.281590 −0.140795 0.990039i \(-0.544966\pi\)
−0.140795 + 0.990039i \(0.544966\pi\)
\(284\) 0 0
\(285\) −13.8000 5.82588i −0.817439 0.345096i
\(286\) 0 0
\(287\) 3.04262 3.04262i 0.179600 0.179600i
\(288\) 0 0
\(289\) 38.2049i 2.24734i
\(290\) 0 0
\(291\) 2.09571 2.09571i 0.122852 0.122852i
\(292\) 0 0
\(293\) 3.11001i 0.181689i 0.995865 + 0.0908445i \(0.0289566\pi\)
−0.995865 + 0.0908445i \(0.971043\pi\)
\(294\) 0 0
\(295\) −17.2314 7.27454i −1.00325 0.423540i
\(296\) 0 0
\(297\) −12.9663 + 12.9663i −0.752382 + 0.752382i
\(298\) 0 0
\(299\) 1.24370 1.24370i 0.0719248 0.0719248i
\(300\) 0 0
\(301\) −10.3133 10.3133i −0.594449 0.594449i
\(302\) 0 0
\(303\) −8.50588 8.50588i −0.488650 0.488650i
\(304\) 0 0
\(305\) −8.20840 + 19.4435i −0.470012 + 1.11333i
\(306\) 0 0
\(307\) −14.5670 −0.831382 −0.415691 0.909506i \(-0.636460\pi\)
−0.415691 + 0.909506i \(0.636460\pi\)
\(308\) 0 0
\(309\) −2.07819 2.07819i −0.118224 0.118224i
\(310\) 0 0
\(311\) 14.4572 0.819791 0.409896 0.912132i \(-0.365565\pi\)
0.409896 + 0.912132i \(0.365565\pi\)
\(312\) 0 0
\(313\) 10.1273 + 10.1273i 0.572429 + 0.572429i 0.932807 0.360377i \(-0.117352\pi\)
−0.360377 + 0.932807i \(0.617352\pi\)
\(314\) 0 0
\(315\) 1.90472 4.51178i 0.107319 0.254210i
\(316\) 0 0
\(317\) 13.8750i 0.779295i −0.920964 0.389648i \(-0.872597\pi\)
0.920964 0.389648i \(-0.127403\pi\)
\(318\) 0 0
\(319\) 11.0224 0.617136
\(320\) 0 0
\(321\) 4.67864 0.261136
\(322\) 0 0
\(323\) 38.8520i 2.16179i
\(324\) 0 0
\(325\) −4.89097 + 4.76030i −0.271302 + 0.264054i
\(326\) 0 0
\(327\) −6.67140 6.67140i −0.368930 0.368930i
\(328\) 0 0
\(329\) 17.9584 0.990076
\(330\) 0 0
\(331\) −1.69458 1.69458i −0.0931425 0.0931425i 0.659000 0.752143i \(-0.270980\pi\)
−0.752143 + 0.659000i \(0.770980\pi\)
\(332\) 0 0
\(333\) −4.54508 −0.249069
\(334\) 0 0
\(335\) −3.82699 9.41902i −0.209091 0.514616i
\(336\) 0 0
\(337\) −9.53338 9.53338i −0.519316 0.519316i 0.398048 0.917364i \(-0.369688\pi\)
−0.917364 + 0.398048i \(0.869688\pi\)
\(338\) 0 0
\(339\) −5.48188 5.48188i −0.297735 0.297735i
\(340\) 0 0
\(341\) −0.563273 + 0.563273i −0.0305029 + 0.0305029i
\(342\) 0 0
\(343\) 12.9954 12.9954i 0.701683 0.701683i
\(344\) 0 0
\(345\) 1.43558 3.40050i 0.0772888 0.183077i
\(346\) 0 0
\(347\) 6.67273i 0.358211i 0.983830 + 0.179105i \(0.0573203\pi\)
−0.983830 + 0.179105i \(0.942680\pi\)
\(348\) 0 0
\(349\) −2.02618 + 2.02618i −0.108459 + 0.108459i −0.759254 0.650795i \(-0.774436\pi\)
0.650795 + 0.759254i \(0.274436\pi\)
\(350\) 0 0
\(351\) 7.62233i 0.406850i
\(352\) 0 0
\(353\) −5.36542 + 5.36542i −0.285572 + 0.285572i −0.835327 0.549754i \(-0.814721\pi\)
0.549754 + 0.835327i \(0.314721\pi\)
\(354\) 0 0
\(355\) 12.9949 + 31.9832i 0.689700 + 1.69749i
\(356\) 0 0
\(357\) −15.3425 −0.812009
\(358\) 0 0
\(359\) 7.76117i 0.409619i 0.978802 + 0.204809i \(0.0656574\pi\)
−0.978802 + 0.204809i \(0.934343\pi\)
\(360\) 0 0
\(361\) 8.34326i 0.439119i
\(362\) 0 0
\(363\) 0.277104 0.0145442
\(364\) 0 0
\(365\) 1.83632 4.34976i 0.0961175 0.227677i
\(366\) 0 0
\(367\) 18.0536 18.0536i 0.942389 0.942389i −0.0560392 0.998429i \(-0.517847\pi\)
0.998429 + 0.0560392i \(0.0178472\pi\)
\(368\) 0 0
\(369\) 3.62737i 0.188833i
\(370\) 0 0
\(371\) −6.61183 + 6.61183i −0.343269 + 0.343269i
\(372\) 0 0
\(373\) 4.36197i 0.225854i 0.993603 + 0.112927i \(0.0360226\pi\)
−0.993603 + 0.112927i \(0.963977\pi\)
\(374\) 0 0
\(375\) −5.74879 + 13.1188i −0.296866 + 0.677451i
\(376\) 0 0
\(377\) 3.23979 3.23979i 0.166858 0.166858i
\(378\) 0 0
\(379\) −5.93072 + 5.93072i −0.304641 + 0.304641i −0.842826 0.538186i \(-0.819110\pi\)
0.538186 + 0.842826i \(0.319110\pi\)
\(380\) 0 0
\(381\) −9.34249 9.34249i −0.478630 0.478630i
\(382\) 0 0
\(383\) −19.3340 19.3340i −0.987922 0.987922i 0.0120057 0.999928i \(-0.496178\pi\)
−0.999928 + 0.0120057i \(0.996178\pi\)
\(384\) 0 0
\(385\) 10.9652 4.45520i 0.558836 0.227058i
\(386\) 0 0
\(387\) −12.2954 −0.625008
\(388\) 0 0
\(389\) −6.28607 6.28607i −0.318716 0.318716i 0.529558 0.848274i \(-0.322358\pi\)
−0.848274 + 0.529558i \(0.822358\pi\)
\(390\) 0 0
\(391\) 9.57367 0.484161
\(392\) 0 0
\(393\) 15.3466 + 15.3466i 0.774135 + 0.774135i
\(394\) 0 0
\(395\) 8.67157 + 21.3425i 0.436314 + 1.07386i
\(396\) 0 0
\(397\) 6.58413i 0.330448i 0.986256 + 0.165224i \(0.0528347\pi\)
−0.986256 + 0.165224i \(0.947165\pi\)
\(398\) 0 0
\(399\) 10.7977 0.540561
\(400\) 0 0
\(401\) 19.7951 0.988522 0.494261 0.869313i \(-0.335439\pi\)
0.494261 + 0.869313i \(0.335439\pi\)
\(402\) 0 0
\(403\) 0.331123i 0.0164944i
\(404\) 0 0
\(405\) 2.59018 + 6.37497i 0.128707 + 0.316775i
\(406\) 0 0
\(407\) −7.76707 7.76707i −0.385000 0.385000i
\(408\) 0 0
\(409\) −5.76937 −0.285277 −0.142638 0.989775i \(-0.545559\pi\)
−0.142638 + 0.989775i \(0.545559\pi\)
\(410\) 0 0
\(411\) 6.31276 + 6.31276i 0.311385 + 0.311385i
\(412\) 0 0
\(413\) 13.4826 0.663437
\(414\) 0 0
\(415\) 6.76563 2.74891i 0.332112 0.134939i
\(416\) 0 0
\(417\) 13.1972 + 13.1972i 0.646270 + 0.646270i
\(418\) 0 0
\(419\) 8.68932 + 8.68932i 0.424501 + 0.424501i 0.886750 0.462249i \(-0.152957\pi\)
−0.462249 + 0.886750i \(0.652957\pi\)
\(420\) 0 0
\(421\) 20.1193 20.1193i 0.980555 0.980555i −0.0192594 0.999815i \(-0.506131\pi\)
0.999815 + 0.0192594i \(0.00613083\pi\)
\(422\) 0 0
\(423\) 10.7048 10.7048i 0.520487 0.520487i
\(424\) 0 0
\(425\) −37.1466 0.502930i −1.80187 0.0243957i
\(426\) 0 0
\(427\) 15.2135i 0.736231i
\(428\) 0 0
\(429\) −4.06060 + 4.06060i −0.196048 + 0.196048i
\(430\) 0 0
\(431\) 33.6247i 1.61965i 0.586675 + 0.809823i \(0.300437\pi\)
−0.586675 + 0.809823i \(0.699563\pi\)
\(432\) 0 0
\(433\) 7.46558 7.46558i 0.358773 0.358773i −0.504588 0.863361i \(-0.668355\pi\)
0.863361 + 0.504588i \(0.168355\pi\)
\(434\) 0 0
\(435\) 3.73963 8.85819i 0.179302 0.424718i
\(436\) 0 0
\(437\) −6.73775 −0.322310
\(438\) 0 0
\(439\) 7.91929i 0.377967i 0.981980 + 0.188984i \(0.0605193\pi\)
−0.981980 + 0.188984i \(0.939481\pi\)
\(440\) 0 0
\(441\) 5.98132i 0.284825i
\(442\) 0 0
\(443\) −10.6463 −0.505823 −0.252911 0.967489i \(-0.581388\pi\)
−0.252911 + 0.967489i \(0.581388\pi\)
\(444\) 0 0
\(445\) 8.22517 + 20.2438i 0.389910 + 0.959649i
\(446\) 0 0
\(447\) −19.4778 + 19.4778i −0.921266 + 0.921266i
\(448\) 0 0
\(449\) 6.08115i 0.286987i −0.989651 0.143494i \(-0.954166\pi\)
0.989651 0.143494i \(-0.0458336\pi\)
\(450\) 0 0
\(451\) 6.19880 6.19880i 0.291890 0.291890i
\(452\) 0 0
\(453\) 13.7148i 0.644379i
\(454\) 0 0
\(455\) 1.91346 4.53247i 0.0897042 0.212485i
\(456\) 0 0
\(457\) −0.313815 + 0.313815i −0.0146796 + 0.0146796i −0.714409 0.699729i \(-0.753304\pi\)
0.699729 + 0.714409i \(0.253304\pi\)
\(458\) 0 0
\(459\) −29.3374 + 29.3374i −1.36935 + 1.36935i
\(460\) 0 0
\(461\) 9.90949 + 9.90949i 0.461531 + 0.461531i 0.899157 0.437626i \(-0.144181\pi\)
−0.437626 + 0.899157i \(0.644181\pi\)
\(462\) 0 0
\(463\) 17.3430 + 17.3430i 0.805999 + 0.805999i 0.984026 0.178027i \(-0.0569714\pi\)
−0.178027 + 0.984026i \(0.556971\pi\)
\(464\) 0 0
\(465\) 0.261571 + 0.643781i 0.0121301 + 0.0298546i
\(466\) 0 0
\(467\) −1.52267 −0.0704606 −0.0352303 0.999379i \(-0.511216\pi\)
−0.0352303 + 0.999379i \(0.511216\pi\)
\(468\) 0 0
\(469\) 5.18213 + 5.18213i 0.239289 + 0.239289i
\(470\) 0 0
\(471\) −3.00530 −0.138477
\(472\) 0 0
\(473\) −21.0115 21.0115i −0.966110 0.966110i
\(474\) 0 0
\(475\) 26.1430 + 0.353952i 1.19952 + 0.0162404i
\(476\) 0 0
\(477\) 7.88252i 0.360916i
\(478\) 0 0
\(479\) 0.507657 0.0231955 0.0115977 0.999933i \(-0.496308\pi\)
0.0115977 + 0.999933i \(0.496308\pi\)
\(480\) 0 0
\(481\) −4.56592 −0.208188
\(482\) 0 0
\(483\) 2.66070i 0.121066i
\(484\) 0 0
\(485\) −2.01195 + 4.76578i −0.0913581 + 0.216403i
\(486\) 0 0
\(487\) 25.9809 + 25.9809i 1.17730 + 1.17730i 0.980428 + 0.196876i \(0.0630798\pi\)
0.196876 + 0.980428i \(0.436920\pi\)
\(488\) 0 0
\(489\) 3.50539 0.158519
\(490\) 0 0
\(491\) 3.28208 + 3.28208i 0.148118 + 0.148118i 0.777277 0.629159i \(-0.216600\pi\)
−0.629159 + 0.777277i \(0.716600\pi\)
\(492\) 0 0
\(493\) 24.9391 1.12320
\(494\) 0 0
\(495\) 3.88053 9.19195i 0.174417 0.413147i
\(496\) 0 0
\(497\) −17.5964 17.5964i −0.789308 0.789308i
\(498\) 0 0
\(499\) −6.73907 6.73907i −0.301682 0.301682i 0.539990 0.841672i \(-0.318428\pi\)
−0.841672 + 0.539990i \(0.818428\pi\)
\(500\) 0 0
\(501\) 12.9810 12.9810i 0.579950 0.579950i
\(502\) 0 0
\(503\) 6.12090 6.12090i 0.272918 0.272918i −0.557356 0.830274i \(-0.688184\pi\)
0.830274 + 0.557356i \(0.188184\pi\)
\(504\) 0 0
\(505\) 19.3430 + 8.16596i 0.860752 + 0.363380i
\(506\) 0 0
\(507\) 14.2672i 0.633629i
\(508\) 0 0
\(509\) −13.8727 + 13.8727i −0.614894 + 0.614894i −0.944217 0.329323i \(-0.893180\pi\)
0.329323 + 0.944217i \(0.393180\pi\)
\(510\) 0 0
\(511\) 3.40344i 0.150559i
\(512\) 0 0
\(513\) 20.6471 20.6471i 0.911590 0.911590i
\(514\) 0 0
\(515\) 4.72594 + 1.99514i 0.208250 + 0.0879162i
\(516\) 0 0
\(517\) 36.5869 1.60909
\(518\) 0 0
\(519\) 11.2684i 0.494628i
\(520\) 0 0
\(521\) 5.87686i 0.257470i 0.991679 + 0.128735i \(0.0410917\pi\)
−0.991679 + 0.128735i \(0.958908\pi\)
\(522\) 0 0
\(523\) 26.0176 1.13767 0.568834 0.822452i \(-0.307395\pi\)
0.568834 + 0.822452i \(0.307395\pi\)
\(524\) 0 0
\(525\) 0.139774 10.3237i 0.00610022 0.450564i
\(526\) 0 0
\(527\) −1.27445 + 1.27445i −0.0555160 + 0.0555160i
\(528\) 0 0
\(529\) 21.3397i 0.927814i
\(530\) 0 0
\(531\) 8.03690 8.03690i 0.348772 0.348772i
\(532\) 0 0
\(533\) 3.64400i 0.157839i
\(534\) 0 0
\(535\) −7.56561 + 3.07394i −0.327090 + 0.132898i
\(536\) 0 0
\(537\) −8.48177 + 8.48177i −0.366016 + 0.366016i
\(538\) 0 0
\(539\) 10.2215 10.2215i 0.440270 0.440270i
\(540\) 0 0
\(541\) −6.57691 6.57691i −0.282764 0.282764i 0.551447 0.834210i \(-0.314076\pi\)
−0.834210 + 0.551447i \(0.814076\pi\)
\(542\) 0 0
\(543\) −7.48594 7.48594i −0.321253 0.321253i
\(544\) 0 0
\(545\) 15.1712 + 6.40479i 0.649865 + 0.274351i
\(546\) 0 0
\(547\) 10.6170 0.453951 0.226976 0.973900i \(-0.427116\pi\)
0.226976 + 0.973900i \(0.427116\pi\)
\(548\) 0 0
\(549\) −9.06863 9.06863i −0.387040 0.387040i
\(550\) 0 0
\(551\) −17.5516 −0.747724
\(552\) 0 0
\(553\) −11.7422 11.7422i −0.499328 0.499328i
\(554\) 0 0
\(555\) −8.87722 + 3.60686i −0.376817 + 0.153103i
\(556\) 0 0
\(557\) 20.9610i 0.888146i 0.895991 + 0.444073i \(0.146467\pi\)
−0.895991 + 0.444073i \(0.853533\pi\)
\(558\) 0 0
\(559\) −12.3517 −0.522422
\(560\) 0 0
\(561\) −31.2575 −1.31969
\(562\) 0 0
\(563\) 16.5598i 0.697911i 0.937139 + 0.348955i \(0.113464\pi\)
−0.937139 + 0.348955i \(0.886536\pi\)
\(564\) 0 0
\(565\) 12.4662 + 5.26280i 0.524456 + 0.221408i
\(566\) 0 0
\(567\) −3.50736 3.50736i −0.147295 0.147295i
\(568\) 0 0
\(569\) 39.6751 1.66327 0.831634 0.555325i \(-0.187406\pi\)
0.831634 + 0.555325i \(0.187406\pi\)
\(570\) 0 0
\(571\) −24.0292 24.0292i −1.00559 1.00559i −0.999984 0.00560819i \(-0.998215\pi\)
−0.00560819 0.999984i \(-0.501785\pi\)
\(572\) 0 0
\(573\) −2.35602 −0.0984240
\(574\) 0 0
\(575\) −0.0872185 + 6.44199i −0.00363726 + 0.268649i
\(576\) 0 0
\(577\) −28.7705 28.7705i −1.19773 1.19773i −0.974844 0.222888i \(-0.928451\pi\)
−0.222888 0.974844i \(-0.571549\pi\)
\(578\) 0 0
\(579\) 7.92157 + 7.92157i 0.329209 + 0.329209i
\(580\) 0 0
\(581\) −3.72230 + 3.72230i −0.154427 + 0.154427i
\(582\) 0 0
\(583\) −13.4704 + 13.4704i −0.557888 + 0.557888i
\(584\) 0 0
\(585\) −1.56117 3.84237i −0.0645466 0.158862i
\(586\) 0 0
\(587\) 33.4854i 1.38209i −0.722811 0.691046i \(-0.757150\pi\)
0.722811 0.691046i \(-0.242850\pi\)
\(588\) 0 0
\(589\) 0.896933 0.896933i 0.0369575 0.0369575i
\(590\) 0 0
\(591\) 7.11866i 0.292822i
\(592\) 0 0
\(593\) 11.5298 11.5298i 0.473472 0.473472i −0.429564 0.903036i \(-0.641333\pi\)
0.903036 + 0.429564i \(0.141333\pi\)
\(594\) 0 0
\(595\) 24.8096 10.0803i 1.01709 0.413250i
\(596\) 0 0
\(597\) 8.92172 0.365142
\(598\) 0 0
\(599\) 20.0148i 0.817781i −0.912583 0.408891i \(-0.865916\pi\)
0.912583 0.408891i \(-0.134084\pi\)
\(600\) 0 0
\(601\) 27.5924i 1.12552i 0.826621 + 0.562759i \(0.190260\pi\)
−0.826621 + 0.562759i \(0.809740\pi\)
\(602\) 0 0
\(603\) 6.17806 0.251590
\(604\) 0 0
\(605\) −0.448093 + 0.182062i −0.0182176 + 0.00740188i
\(606\) 0 0
\(607\) −30.4850 + 30.4850i −1.23735 + 1.23735i −0.276265 + 0.961081i \(0.589097\pi\)
−0.961081 + 0.276265i \(0.910903\pi\)
\(608\) 0 0
\(609\) 6.93104i 0.280860i
\(610\) 0 0
\(611\) 10.7539 10.7539i 0.435057 0.435057i
\(612\) 0 0
\(613\) 20.2657i 0.818523i 0.912417 + 0.409261i \(0.134214\pi\)
−0.912417 + 0.409261i \(0.865786\pi\)
\(614\) 0 0
\(615\) −2.87859 7.08480i −0.116076 0.285687i
\(616\) 0 0
\(617\) −1.61302 + 1.61302i −0.0649378 + 0.0649378i −0.738830 0.673892i \(-0.764621\pi\)
0.673892 + 0.738830i \(0.264621\pi\)
\(618\) 0 0
\(619\) −2.46756 + 2.46756i −0.0991797 + 0.0991797i −0.754956 0.655776i \(-0.772342\pi\)
0.655776 + 0.754956i \(0.272342\pi\)
\(620\) 0 0
\(621\) 5.08771 + 5.08771i 0.204163 + 0.204163i
\(622\) 0 0
\(623\) −11.1377 11.1377i −0.446222 0.446222i
\(624\) 0 0
\(625\) 0.676829 24.9908i 0.0270732 0.999633i
\(626\) 0 0
\(627\) 21.9984 0.878531
\(628\) 0 0
\(629\) −17.5737 17.5737i −0.700708 0.700708i
\(630\) 0 0
\(631\) 29.9602 1.19270 0.596348 0.802726i \(-0.296618\pi\)
0.596348 + 0.802726i \(0.296618\pi\)
\(632\) 0 0
\(633\) −6.96133 6.96133i −0.276688 0.276688i
\(634\) 0 0
\(635\) 21.2455 + 8.96913i 0.843101 + 0.355929i
\(636\) 0 0
\(637\) 6.00875i 0.238075i
\(638\) 0 0
\(639\) −20.9782 −0.829885
\(640\) 0 0
\(641\) −37.3386 −1.47478 −0.737392 0.675465i \(-0.763943\pi\)
−0.737392 + 0.675465i \(0.763943\pi\)
\(642\) 0 0
\(643\) 24.5635i 0.968691i 0.874877 + 0.484345i \(0.160942\pi\)
−0.874877 + 0.484345i \(0.839058\pi\)
\(644\) 0 0
\(645\) −24.0147 + 9.75728i −0.945577 + 0.384193i
\(646\) 0 0
\(647\) 23.1347 + 23.1347i 0.909519 + 0.909519i 0.996233 0.0867142i \(-0.0276367\pi\)
−0.0867142 + 0.996233i \(0.527637\pi\)
\(648\) 0 0
\(649\) 27.4685 1.07823
\(650\) 0 0
\(651\) −0.354194 0.354194i −0.0138820 0.0138820i
\(652\) 0 0
\(653\) −50.8060 −1.98819 −0.994097 0.108496i \(-0.965397\pi\)
−0.994097 + 0.108496i \(0.965397\pi\)
\(654\) 0 0
\(655\) −34.8993 14.7333i −1.36363 0.575679i
\(656\) 0 0
\(657\) 2.02877 + 2.02877i 0.0791497 + 0.0791497i
\(658\) 0 0
\(659\) −9.97780 9.97780i −0.388680 0.388680i 0.485537 0.874216i \(-0.338624\pi\)
−0.874216 + 0.485537i \(0.838624\pi\)
\(660\) 0 0
\(661\) −5.09643 + 5.09643i −0.198228 + 0.198228i −0.799240 0.601012i \(-0.794764\pi\)
0.601012 + 0.799240i \(0.294764\pi\)
\(662\) 0 0
\(663\) −9.18745 + 9.18745i −0.356811 + 0.356811i
\(664\) 0 0
\(665\) −17.4605 + 7.09428i −0.677088 + 0.275104i
\(666\) 0 0
\(667\) 4.32496i 0.167463i
\(668\) 0 0
\(669\) −11.0402 + 11.0402i −0.426838 + 0.426838i
\(670\) 0 0
\(671\) 30.9947i 1.19654i
\(672\) 0 0
\(673\) −31.6322 + 31.6322i −1.21933 + 1.21933i −0.251464 + 0.967867i \(0.580912\pi\)
−0.967867 + 0.251464i \(0.919088\pi\)
\(674\) 0 0
\(675\) −19.4735 20.0080i −0.749534 0.770108i
\(676\) 0 0
\(677\) 25.6600 0.986196 0.493098 0.869974i \(-0.335864\pi\)
0.493098 + 0.869974i \(0.335864\pi\)
\(678\) 0 0
\(679\) 3.72896i 0.143104i
\(680\) 0 0
\(681\) 7.71190i 0.295521i
\(682\) 0 0
\(683\) −12.3536 −0.472698 −0.236349 0.971668i \(-0.575951\pi\)
−0.236349 + 0.971668i \(0.575951\pi\)
\(684\) 0 0
\(685\) −14.3557 6.06048i −0.548501 0.231559i
\(686\) 0 0
\(687\) −0.728309 + 0.728309i −0.0277867 + 0.0277867i
\(688\) 0 0
\(689\) 7.91866i 0.301677i
\(690\) 0 0
\(691\) −22.5426 + 22.5426i −0.857561 + 0.857561i −0.991050 0.133489i \(-0.957382\pi\)
0.133489 + 0.991050i \(0.457382\pi\)
\(692\) 0 0
\(693\) 7.19219i 0.273209i
\(694\) 0 0
\(695\) −30.0114 12.6698i −1.13840 0.480593i
\(696\) 0 0
\(697\) 14.0253 14.0253i 0.531247 0.531247i
\(698\) 0 0
\(699\) 16.2673 16.2673i 0.615285 0.615285i
\(700\) 0 0
\(701\) 26.9530 + 26.9530i 1.01800 + 1.01800i 0.999835 + 0.0181663i \(0.00578284\pi\)
0.0181663 + 0.999835i \(0.494217\pi\)
\(702\) 0 0
\(703\) 12.3680 + 12.3680i 0.466467 + 0.466467i
\(704\) 0 0
\(705\) 12.4131 29.4032i 0.467503 1.10739i
\(706\) 0 0
\(707\) −15.1348 −0.569203
\(708\) 0 0
\(709\) −7.78615 7.78615i −0.292415 0.292415i 0.545619 0.838034i \(-0.316295\pi\)
−0.838034 + 0.545619i \(0.816295\pi\)
\(710\) 0 0
\(711\) −13.9988 −0.524997
\(712\) 0 0
\(713\) 0.221016 + 0.221016i 0.00827713 + 0.00827713i
\(714\) 0 0
\(715\) 3.89833 9.23410i 0.145789 0.345336i
\(716\) 0 0
\(717\) 2.28427i 0.0853076i
\(718\) 0 0
\(719\) 20.6777 0.771150 0.385575 0.922677i \(-0.374003\pi\)
0.385575 + 0.922677i \(0.374003\pi\)
\(720\) 0 0
\(721\) −3.69779 −0.137713
\(722\) 0 0
\(723\) 13.3797i 0.497597i
\(724\) 0 0
\(725\) −0.227201 + 16.7812i −0.00843805 + 0.623237i
\(726\) 0 0
\(727\) −20.4994 20.4994i −0.760280 0.760280i 0.216093 0.976373i \(-0.430669\pi\)
−0.976373 + 0.216093i \(0.930669\pi\)
\(728\) 0 0
\(729\) −25.6425 −0.949722
\(730\) 0 0
\(731\) −47.5403 47.5403i −1.75834 1.75834i
\(732\) 0 0
\(733\) 10.7306 0.396344 0.198172 0.980167i \(-0.436500\pi\)
0.198172 + 0.980167i \(0.436500\pi\)
\(734\) 0 0
\(735\) −4.74663 11.6824i −0.175082 0.430912i
\(736\) 0 0
\(737\) 10.5577 + 10.5577i 0.388897 + 0.388897i
\(738\) 0 0
\(739\) 2.93837 + 2.93837i 0.108090 + 0.108090i 0.759083 0.650994i \(-0.225648\pi\)
−0.650994 + 0.759083i \(0.725648\pi\)
\(740\) 0 0
\(741\) 6.46594 6.46594i 0.237532 0.237532i
\(742\) 0 0
\(743\) 0.223404 0.223404i 0.00819590 0.00819590i −0.702997 0.711193i \(-0.748155\pi\)
0.711193 + 0.702997i \(0.248155\pi\)
\(744\) 0 0
\(745\) 18.6994 44.2938i 0.685091 1.62280i
\(746\) 0 0
\(747\) 4.43766i 0.162366i
\(748\) 0 0
\(749\) 4.16243 4.16243i 0.152092 0.152092i
\(750\) 0 0
\(751\) 39.9939i 1.45940i 0.683769 + 0.729699i \(0.260340\pi\)
−0.683769 + 0.729699i \(0.739660\pi\)
\(752\) 0 0
\(753\) −16.2055 + 16.2055i −0.590563 + 0.590563i
\(754\) 0 0
\(755\) −9.01088 22.1776i −0.327939 0.807126i
\(756\) 0 0
\(757\) 32.9120 1.19621 0.598103 0.801419i \(-0.295921\pi\)
0.598103 + 0.801419i \(0.295921\pi\)
\(758\) 0 0
\(759\) 5.42070i 0.196759i
\(760\) 0 0
\(761\) 33.9591i 1.23102i 0.788130 + 0.615509i \(0.211049\pi\)
−0.788130 + 0.615509i \(0.788951\pi\)
\(762\) 0 0
\(763\) −11.8707 −0.429747
\(764\) 0 0
\(765\) 8.78003 20.7976i 0.317443 0.751937i
\(766\) 0 0
\(767\) 8.07375 8.07375i 0.291526 0.291526i
\(768\) 0 0
\(769\) 40.2535i 1.45158i −0.687917 0.725789i \(-0.741475\pi\)
0.687917 0.725789i \(-0.258525\pi\)
\(770\) 0 0
\(771\) 5.29172 5.29172i 0.190577 0.190577i
\(772\) 0 0
\(773\) 9.47175i 0.340675i −0.985386 0.170338i \(-0.945514\pi\)
0.985386 0.170338i \(-0.0544858\pi\)
\(774\) 0 0
\(775\) −0.845950 0.869172i −0.0303874 0.0312216i
\(776\) 0 0
\(777\) 4.88405 4.88405i 0.175214 0.175214i
\(778\) 0 0
\(779\) −9.87073 + 9.87073i −0.353656 + 0.353656i
\(780\) 0 0
\(781\) −35.8496 35.8496i −1.28280 1.28280i
\(782\) 0 0
\(783\) 13.2533 + 13.2533i 0.473636 + 0.473636i
\(784\) 0 0
\(785\) 4.85973 1.97453i 0.173451 0.0704741i
\(786\) 0 0
\(787\) 48.1367 1.71589 0.857945 0.513742i \(-0.171741\pi\)
0.857945 + 0.513742i \(0.171741\pi\)
\(788\) 0 0
\(789\) −21.9455 21.9455i −0.781282 0.781282i
\(790\) 0 0
\(791\) −9.75409 −0.346815
\(792\) 0 0
\(793\) −9.11021 9.11021i −0.323513 0.323513i
\(794\) 0 0
\(795\) 6.25537 + 15.3957i 0.221855 + 0.546031i
\(796\) 0 0
\(797\) 33.8962i 1.20066i −0.799751 0.600332i \(-0.795035\pi\)
0.799751 0.600332i \(-0.204965\pi\)