Properties

Label 1764.2.e.h.1079.9
Level $1764$
Weight $2$
Character 1764.1079
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + x^{12} - 10 x^{10} + 4 x^{8} - 40 x^{6} + 16 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1079.9
Root \(-0.545545 + 1.30475i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.h.1079.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.545545 - 1.30475i) q^{2} +(-1.40476 - 1.42360i) q^{4} +0.698240i q^{5} +(-2.62381 + 1.05623i) q^{8} +O(q^{10})\) \(q+(0.545545 - 1.30475i) q^{2} +(-1.40476 - 1.42360i) q^{4} +0.698240i q^{5} +(-2.62381 + 1.05623i) q^{8} +(0.911031 + 0.380921i) q^{10} +2.55198 q^{11} -1.88088 q^{13} +(-0.0532920 + 3.99964i) q^{16} +3.97326i q^{17} +7.05819i q^{19} +(0.994017 - 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} -4.02656 q^{23} +4.51246 q^{25} +(-1.02610 + 2.45408i) q^{26} +1.86081i q^{29} -0.941102i q^{31} +(5.18948 + 2.25152i) q^{32} +(5.18413 + 2.16759i) q^{34} -7.49992 q^{37} +(9.20919 + 3.85056i) q^{38} +(-0.737500 - 1.83205i) q^{40} +10.6065i q^{41} -3.97212i q^{43} +(-3.58493 - 3.63301i) q^{44} +(-2.19667 + 5.25366i) q^{46} +8.90438 q^{47} +(2.46175 - 5.88765i) q^{50} +(2.64218 + 2.67762i) q^{52} -0.529774i q^{53} +1.78190i q^{55} +(2.42790 + 1.01516i) q^{58} +13.3007 q^{59} -10.3683 q^{61} +(-1.22791 - 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} -1.31330i q^{65} -2.72300i q^{67} +(5.65635 - 5.58149i) q^{68} +3.51310 q^{71} +2.75071 q^{73} +(-4.09155 + 9.78555i) q^{74} +(10.0481 - 9.91507i) q^{76} +13.5338i q^{79} +(-2.79271 - 0.0372106i) q^{80} +(13.8389 + 5.78632i) q^{82} +17.1516 q^{83} -2.77429 q^{85} +(-5.18264 - 2.16697i) q^{86} +(-6.69592 + 2.69547i) q^{88} +11.8700i q^{89} +(5.65635 + 5.73222i) q^{92} +(4.85774 - 11.6180i) q^{94} -4.92831 q^{95} -10.8682 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{13} - 4q^{16} - 16q^{22} - 24q^{25} + 8q^{34} - 8q^{37} - 52q^{40} + 24q^{46} - 52q^{52} + 12q^{58} - 16q^{61} + 60q^{64} - 8q^{73} - 36q^{76} + 68q^{82} - 16q^{85} - 44q^{88} + 60q^{94} + 88q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.545545 1.30475i 0.385759 0.922600i
\(3\) 0 0
\(4\) −1.40476 1.42360i −0.702381 0.711802i
\(5\) 0.698240i 0.312262i 0.987736 + 0.156131i \(0.0499023\pi\)
−0.987736 + 0.156131i \(0.950098\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.62381 + 1.05623i −0.927657 + 0.373433i
\(9\) 0 0
\(10\) 0.911031 + 0.380921i 0.288093 + 0.120458i
\(11\) 2.55198 0.769452 0.384726 0.923031i \(-0.374296\pi\)
0.384726 + 0.923031i \(0.374296\pi\)
\(12\) 0 0
\(13\) −1.88088 −0.521661 −0.260831 0.965385i \(-0.583996\pi\)
−0.260831 + 0.965385i \(0.583996\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.0532920 + 3.99964i −0.0133230 + 0.999911i
\(17\) 3.97326i 0.963658i 0.876265 + 0.481829i \(0.160027\pi\)
−0.876265 + 0.481829i \(0.839973\pi\)
\(18\) 0 0
\(19\) 7.05819i 1.61926i 0.586941 + 0.809630i \(0.300332\pi\)
−0.586941 + 0.809630i \(0.699668\pi\)
\(20\) 0.994017 0.980861i 0.222269 0.219327i
\(21\) 0 0
\(22\) 1.39222 3.32971i 0.296823 0.709896i
\(23\) −4.02656 −0.839595 −0.419798 0.907618i \(-0.637899\pi\)
−0.419798 + 0.907618i \(0.637899\pi\)
\(24\) 0 0
\(25\) 4.51246 0.902492
\(26\) −1.02610 + 2.45408i −0.201235 + 0.481285i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.86081i 0.345544i 0.984962 + 0.172772i \(0.0552724\pi\)
−0.984962 + 0.172772i \(0.944728\pi\)
\(30\) 0 0
\(31\) 0.941102i 0.169027i −0.996422 0.0845134i \(-0.973066\pi\)
0.996422 0.0845134i \(-0.0269336\pi\)
\(32\) 5.18948 + 2.25152i 0.917378 + 0.398016i
\(33\) 0 0
\(34\) 5.18413 + 2.16759i 0.889071 + 0.371739i
\(35\) 0 0
\(36\) 0 0
\(37\) −7.49992 −1.23298 −0.616490 0.787363i \(-0.711446\pi\)
−0.616490 + 0.787363i \(0.711446\pi\)
\(38\) 9.20919 + 3.85056i 1.49393 + 0.624643i
\(39\) 0 0
\(40\) −0.737500 1.83205i −0.116609 0.289673i
\(41\) 10.6065i 1.65646i 0.560392 + 0.828228i \(0.310651\pi\)
−0.560392 + 0.828228i \(0.689349\pi\)
\(42\) 0 0
\(43\) 3.97212i 0.605743i −0.953031 0.302871i \(-0.902055\pi\)
0.953031 0.302871i \(-0.0979452\pi\)
\(44\) −3.58493 3.63301i −0.540448 0.547697i
\(45\) 0 0
\(46\) −2.19667 + 5.25366i −0.323881 + 0.774610i
\(47\) 8.90438 1.29884 0.649418 0.760431i \(-0.275012\pi\)
0.649418 + 0.760431i \(0.275012\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.46175 5.88765i 0.348144 0.832639i
\(51\) 0 0
\(52\) 2.64218 + 2.67762i 0.366405 + 0.371319i
\(53\) 0.529774i 0.0727701i −0.999338 0.0363850i \(-0.988416\pi\)
0.999338 0.0363850i \(-0.0115843\pi\)
\(54\) 0 0
\(55\) 1.78190i 0.240271i
\(56\) 0 0
\(57\) 0 0
\(58\) 2.42790 + 1.01516i 0.318799 + 0.133297i
\(59\) 13.3007 1.73161 0.865804 0.500383i \(-0.166807\pi\)
0.865804 + 0.500383i \(0.166807\pi\)
\(60\) 0 0
\(61\) −10.3683 −1.32752 −0.663760 0.747946i \(-0.731040\pi\)
−0.663760 + 0.747946i \(0.731040\pi\)
\(62\) −1.22791 0.513413i −0.155944 0.0652036i
\(63\) 0 0
\(64\) 5.76877 5.54268i 0.721096 0.692835i
\(65\) 1.31330i 0.162895i
\(66\) 0 0
\(67\) 2.72300i 0.332667i −0.986070 0.166334i \(-0.946807\pi\)
0.986070 0.166334i \(-0.0531929\pi\)
\(68\) 5.65635 5.58149i 0.685933 0.676855i
\(69\) 0 0
\(70\) 0 0
\(71\) 3.51310 0.416928 0.208464 0.978030i \(-0.433154\pi\)
0.208464 + 0.978030i \(0.433154\pi\)
\(72\) 0 0
\(73\) 2.75071 0.321946 0.160973 0.986959i \(-0.448537\pi\)
0.160973 + 0.986959i \(0.448537\pi\)
\(74\) −4.09155 + 9.78555i −0.475632 + 1.13755i
\(75\) 0 0
\(76\) 10.0481 9.91507i 1.15259 1.13734i
\(77\) 0 0
\(78\) 0 0
\(79\) 13.5338i 1.52267i 0.648358 + 0.761335i \(0.275456\pi\)
−0.648358 + 0.761335i \(0.724544\pi\)
\(80\) −2.79271 0.0372106i −0.312235 0.00416027i
\(81\) 0 0
\(82\) 13.8389 + 5.78632i 1.52825 + 0.638992i
\(83\) 17.1516 1.88264 0.941319 0.337520i \(-0.109588\pi\)
0.941319 + 0.337520i \(0.109588\pi\)
\(84\) 0 0
\(85\) −2.77429 −0.300914
\(86\) −5.18264 2.16697i −0.558858 0.233670i
\(87\) 0 0
\(88\) −6.69592 + 2.69547i −0.713788 + 0.287338i
\(89\) 11.8700i 1.25821i 0.777319 + 0.629107i \(0.216579\pi\)
−0.777319 + 0.629107i \(0.783421\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.65635 + 5.73222i 0.589715 + 0.597625i
\(93\) 0 0
\(94\) 4.85774 11.6180i 0.501038 1.19831i
\(95\) −4.92831 −0.505634
\(96\) 0 0
\(97\) −10.8682 −1.10350 −0.551748 0.834011i \(-0.686039\pi\)
−0.551748 + 0.834011i \(0.686039\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −6.33893 6.42395i −0.633893 0.642395i
\(101\) 10.6065i 1.05539i 0.849435 + 0.527693i \(0.176943\pi\)
−0.849435 + 0.527693i \(0.823057\pi\)
\(102\) 0 0
\(103\) 13.2756i 1.30808i −0.756459 0.654041i \(-0.773072\pi\)
0.756459 0.654041i \(-0.226928\pi\)
\(104\) 4.93507 1.98663i 0.483923 0.194805i
\(105\) 0 0
\(106\) −0.691224 0.289016i −0.0671377 0.0280717i
\(107\) 9.61198 0.929225 0.464613 0.885514i \(-0.346194\pi\)
0.464613 + 0.885514i \(0.346194\pi\)
\(108\) 0 0
\(109\) 14.2241 1.36242 0.681209 0.732089i \(-0.261455\pi\)
0.681209 + 0.732089i \(0.261455\pi\)
\(110\) 2.32494 + 0.972105i 0.221674 + 0.0926866i
\(111\) 0 0
\(112\) 0 0
\(113\) 12.1039i 1.13864i 0.822117 + 0.569319i \(0.192793\pi\)
−0.822117 + 0.569319i \(0.807207\pi\)
\(114\) 0 0
\(115\) 2.81150i 0.262174i
\(116\) 2.64906 2.61400i 0.245959 0.242703i
\(117\) 0 0
\(118\) 7.25615 17.3542i 0.667983 1.59758i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.48738 −0.407944
\(122\) −5.65635 + 13.5280i −0.512102 + 1.22477i
\(123\) 0 0
\(124\) −1.33976 + 1.32202i −0.120314 + 0.118721i
\(125\) 6.64198i 0.594077i
\(126\) 0 0
\(127\) 0.582584i 0.0516960i 0.999666 + 0.0258480i \(0.00822859\pi\)
−0.999666 + 0.0258480i \(0.991771\pi\)
\(128\) −4.08470 10.5506i −0.361040 0.932550i
\(129\) 0 0
\(130\) −1.71354 0.716466i −0.150287 0.0628382i
\(131\) −10.8924 −0.951674 −0.475837 0.879533i \(-0.657855\pi\)
−0.475837 + 0.879533i \(0.657855\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −3.55284 1.48552i −0.306919 0.128329i
\(135\) 0 0
\(136\) −4.19667 10.4251i −0.359861 0.893945i
\(137\) 13.3019i 1.13646i −0.822870 0.568230i \(-0.807628\pi\)
0.822870 0.568230i \(-0.192372\pi\)
\(138\) 0 0
\(139\) 0.840795i 0.0713153i 0.999364 + 0.0356577i \(0.0113526\pi\)
−0.999364 + 0.0356577i \(0.988647\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.91655 4.58373i 0.160834 0.384658i
\(143\) −4.79997 −0.401393
\(144\) 0 0
\(145\) −1.29929 −0.107900
\(146\) 1.50063 3.58899i 0.124193 0.297027i
\(147\) 0 0
\(148\) 10.5356 + 10.6769i 0.866021 + 0.877637i
\(149\) 5.65685i 0.463428i −0.972784 0.231714i \(-0.925567\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(150\) 0 0
\(151\) 16.9829i 1.38205i −0.722830 0.691026i \(-0.757159\pi\)
0.722830 0.691026i \(-0.242841\pi\)
\(152\) −7.45505 18.5194i −0.604684 1.50212i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.657115 0.0527807
\(156\) 0 0
\(157\) 1.97492 0.157616 0.0788079 0.996890i \(-0.474889\pi\)
0.0788079 + 0.996890i \(0.474889\pi\)
\(158\) 17.6583 + 7.38329i 1.40482 + 0.587383i
\(159\) 0 0
\(160\) −1.57210 + 3.62350i −0.124286 + 0.286463i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.81150i 0.220214i −0.993920 0.110107i \(-0.964881\pi\)
0.993920 0.110107i \(-0.0351194\pi\)
\(164\) 15.0994 14.8996i 1.17907 1.16346i
\(165\) 0 0
\(166\) 9.35699 22.3787i 0.726243 1.73692i
\(167\) −2.40833 −0.186362 −0.0931810 0.995649i \(-0.529704\pi\)
−0.0931810 + 0.995649i \(0.529704\pi\)
\(168\) 0 0
\(169\) −9.46230 −0.727869
\(170\) −1.51350 + 3.61977i −0.116080 + 0.277623i
\(171\) 0 0
\(172\) −5.65472 + 5.57988i −0.431169 + 0.425462i
\(173\) 4.68026i 0.355834i 0.984046 + 0.177917i \(0.0569358\pi\)
−0.984046 + 0.177917i \(0.943064\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.136000 + 10.2070i −0.0102514 + 0.769384i
\(177\) 0 0
\(178\) 15.4874 + 6.47560i 1.16083 + 0.485367i
\(179\) −13.1909 −0.985933 −0.492966 0.870048i \(-0.664087\pi\)
−0.492966 + 0.870048i \(0.664087\pi\)
\(180\) 0 0
\(181\) −17.6801 −1.31415 −0.657075 0.753825i \(-0.728207\pi\)
−0.657075 + 0.753825i \(0.728207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 10.5649 4.25296i 0.778857 0.313532i
\(185\) 5.23675i 0.385013i
\(186\) 0 0
\(187\) 10.1397i 0.741489i
\(188\) −12.5085 12.6763i −0.912278 0.924514i
\(189\) 0 0
\(190\) −2.68862 + 6.43023i −0.195053 + 0.466498i
\(191\) −21.2440 −1.53716 −0.768581 0.639753i \(-0.779037\pi\)
−0.768581 + 0.639753i \(0.779037\pi\)
\(192\) 0 0
\(193\) 4.16763 0.299993 0.149996 0.988687i \(-0.452074\pi\)
0.149996 + 0.988687i \(0.452074\pi\)
\(194\) −5.92908 + 14.1803i −0.425683 + 1.01809i
\(195\) 0 0
\(196\) 0 0
\(197\) 8.04744i 0.573356i −0.958027 0.286678i \(-0.907449\pi\)
0.958027 0.286678i \(-0.0925510\pi\)
\(198\) 0 0
\(199\) 1.52369i 0.108011i −0.998541 0.0540056i \(-0.982801\pi\)
0.998541 0.0540056i \(-0.0171989\pi\)
\(200\) −11.8398 + 4.76618i −0.837203 + 0.337020i
\(201\) 0 0
\(202\) 13.8389 + 5.78632i 0.973698 + 0.407124i
\(203\) 0 0
\(204\) 0 0
\(205\) −7.40588 −0.517249
\(206\) −17.3214 7.24243i −1.20684 0.504604i
\(207\) 0 0
\(208\) 0.100236 7.52284i 0.00695009 0.521615i
\(209\) 18.0124i 1.24594i
\(210\) 0 0
\(211\) 19.2878i 1.32783i 0.747809 + 0.663914i \(0.231106\pi\)
−0.747809 + 0.663914i \(0.768894\pi\)
\(212\) −0.754188 + 0.744206i −0.0517979 + 0.0511123i
\(213\) 0 0
\(214\) 5.24377 12.5413i 0.358457 0.857303i
\(215\) 2.77349 0.189151
\(216\) 0 0
\(217\) 0 0
\(218\) 7.75986 18.5589i 0.525564 1.25697i
\(219\) 0 0
\(220\) 2.53671 2.50314i 0.171025 0.168762i
\(221\) 7.47322i 0.502703i
\(222\) 0 0
\(223\) 18.1390i 1.21468i 0.794443 + 0.607338i \(0.207763\pi\)
−0.794443 + 0.607338i \(0.792237\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 15.7926 + 6.60321i 1.05051 + 0.439239i
\(227\) −9.57818 −0.635726 −0.317863 0.948137i \(-0.602965\pi\)
−0.317863 + 0.948137i \(0.602965\pi\)
\(228\) 0 0
\(229\) −4.84326 −0.320052 −0.160026 0.987113i \(-0.551158\pi\)
−0.160026 + 0.987113i \(0.551158\pi\)
\(230\) −3.66832 1.53380i −0.241882 0.101136i
\(231\) 0 0
\(232\) −1.96544 4.88242i −0.129037 0.320546i
\(233\) 21.6331i 1.41723i 0.705595 + 0.708615i \(0.250680\pi\)
−0.705595 + 0.708615i \(0.749320\pi\)
\(234\) 0 0
\(235\) 6.21739i 0.405578i
\(236\) −18.6844 18.9350i −1.21625 1.23256i
\(237\) 0 0
\(238\) 0 0
\(239\) 20.5549 1.32958 0.664792 0.747028i \(-0.268520\pi\)
0.664792 + 0.747028i \(0.268520\pi\)
\(240\) 0 0
\(241\) −10.7506 −0.692504 −0.346252 0.938142i \(-0.612546\pi\)
−0.346252 + 0.938142i \(0.612546\pi\)
\(242\) −2.44807 + 5.85493i −0.157368 + 0.376369i
\(243\) 0 0
\(244\) 14.5649 + 14.7603i 0.932424 + 0.944930i
\(245\) 0 0
\(246\) 0 0
\(247\) 13.2756i 0.844705i
\(248\) 0.994017 + 2.46927i 0.0631201 + 0.156799i
\(249\) 0 0
\(250\) 8.66615 + 3.62350i 0.548095 + 0.229170i
\(251\) −19.4316 −1.22651 −0.613257 0.789884i \(-0.710141\pi\)
−0.613257 + 0.789884i \(0.710141\pi\)
\(252\) 0 0
\(253\) −10.2757 −0.646028
\(254\) 0.760128 + 0.317826i 0.0476947 + 0.0199422i
\(255\) 0 0
\(256\) −15.9943 0.426298i −0.999645 0.0266436i
\(257\) 8.73670i 0.544980i −0.962159 0.272490i \(-0.912153\pi\)
0.962159 0.272490i \(-0.0878472\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.86962 + 1.84488i −0.115949 + 0.114414i
\(261\) 0 0
\(262\) −5.94230 + 14.2119i −0.367117 + 0.878015i
\(263\) 21.8079 1.34474 0.672368 0.740217i \(-0.265277\pi\)
0.672368 + 0.740217i \(0.265277\pi\)
\(264\) 0 0
\(265\) 0.369910 0.0227234
\(266\) 0 0
\(267\) 0 0
\(268\) −3.87647 + 3.82516i −0.236793 + 0.233659i
\(269\) 14.7040i 0.896519i −0.893904 0.448259i \(-0.852044\pi\)
0.893904 0.448259i \(-0.147956\pi\)
\(270\) 0 0
\(271\) 5.18779i 0.315136i 0.987508 + 0.157568i \(0.0503653\pi\)
−0.987508 + 0.157568i \(0.949635\pi\)
\(272\) −15.8916 0.211743i −0.963573 0.0128388i
\(273\) 0 0
\(274\) −17.3557 7.25680i −1.04850 0.438399i
\(275\) 11.5157 0.694424
\(276\) 0 0
\(277\) 23.7255 1.42553 0.712763 0.701405i \(-0.247444\pi\)
0.712763 + 0.701405i \(0.247444\pi\)
\(278\) 1.09703 + 0.458692i 0.0657955 + 0.0275105i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.12400i 0.246017i 0.992406 + 0.123009i \(0.0392542\pi\)
−0.992406 + 0.123009i \(0.960746\pi\)
\(282\) 0 0
\(283\) 7.05819i 0.419566i −0.977748 0.209783i \(-0.932724\pi\)
0.977748 0.209783i \(-0.0672757\pi\)
\(284\) −4.93507 5.00126i −0.292842 0.296770i
\(285\) 0 0
\(286\) −2.61860 + 6.26277i −0.154841 + 0.370325i
\(287\) 0 0
\(288\) 0 0
\(289\) 1.21317 0.0713628
\(290\) −0.708823 + 1.69526i −0.0416235 + 0.0995489i
\(291\) 0 0
\(292\) −3.86409 3.91592i −0.226129 0.229162i
\(293\) 15.9675i 0.932830i −0.884566 0.466415i \(-0.845545\pi\)
0.884566 0.466415i \(-0.154455\pi\)
\(294\) 0 0
\(295\) 9.28711i 0.540716i
\(296\) 19.6784 7.92162i 1.14378 0.460435i
\(297\) 0 0
\(298\) −7.38080 3.08607i −0.427558 0.178771i
\(299\) 7.57346 0.437984
\(300\) 0 0
\(301\) 0 0
\(302\) −22.1585 9.26495i −1.27508 0.533138i
\(303\) 0 0
\(304\) −28.2302 0.376145i −1.61912 0.0215734i
\(305\) 7.23953i 0.414534i
\(306\) 0 0
\(307\) 5.53450i 0.315871i −0.987449 0.157935i \(-0.949516\pi\)
0.987449 0.157935i \(-0.0504838\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.358486 0.857373i 0.0203606 0.0486955i
\(311\) −10.4888 −0.594766 −0.297383 0.954758i \(-0.596114\pi\)
−0.297383 + 0.954758i \(0.596114\pi\)
\(312\) 0 0
\(313\) −2.26317 −0.127922 −0.0639609 0.997952i \(-0.520373\pi\)
−0.0639609 + 0.997952i \(0.520373\pi\)
\(314\) 1.07741 2.57678i 0.0608017 0.145416i
\(315\) 0 0
\(316\) 19.2668 19.0117i 1.08384 1.06949i
\(317\) 9.50588i 0.533903i 0.963710 + 0.266952i \(0.0860164\pi\)
−0.963710 + 0.266952i \(0.913984\pi\)
\(318\) 0 0
\(319\) 4.74876i 0.265879i
\(320\) 3.87012 + 4.02799i 0.216346 + 0.225171i
\(321\) 0 0
\(322\) 0 0
\(323\) −28.0441 −1.56041
\(324\) 0 0
\(325\) −8.48738 −0.470795
\(326\) −3.66832 1.53380i −0.203169 0.0849494i
\(327\) 0 0
\(328\) −11.2029 27.8294i −0.618574 1.53662i
\(329\) 0 0
\(330\) 0 0
\(331\) 9.94110i 0.546412i −0.961956 0.273206i \(-0.911916\pi\)
0.961956 0.273206i \(-0.0880841\pi\)
\(332\) −24.0940 24.4171i −1.32233 1.34006i
\(333\) 0 0
\(334\) −1.31385 + 3.14227i −0.0718907 + 0.171937i
\(335\) 1.90131 0.103879
\(336\) 0 0
\(337\) 10.6441 0.579822 0.289911 0.957054i \(-0.406374\pi\)
0.289911 + 0.957054i \(0.406374\pi\)
\(338\) −5.16211 + 12.3460i −0.280782 + 0.671532i
\(339\) 0 0
\(340\) 3.89722 + 3.94949i 0.211356 + 0.214191i
\(341\) 2.40168i 0.130058i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.19546 + 10.4221i 0.226204 + 0.561922i
\(345\) 0 0
\(346\) 6.10658 + 2.55329i 0.328292 + 0.137266i
\(347\) −17.5488 −0.942069 −0.471035 0.882115i \(-0.656119\pi\)
−0.471035 + 0.882115i \(0.656119\pi\)
\(348\) 0 0
\(349\) −29.0703 −1.55610 −0.778049 0.628204i \(-0.783790\pi\)
−0.778049 + 0.628204i \(0.783790\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 13.2435 + 5.74584i 0.705879 + 0.306254i
\(353\) 11.2462i 0.598572i 0.954163 + 0.299286i \(0.0967485\pi\)
−0.954163 + 0.299286i \(0.903251\pi\)
\(354\) 0 0
\(355\) 2.45299i 0.130191i
\(356\) 16.8981 16.6745i 0.895599 0.883745i
\(357\) 0 0
\(358\) −7.19622 + 17.2108i −0.380332 + 0.909621i
\(359\) 29.0436 1.53286 0.766431 0.642326i \(-0.222031\pi\)
0.766431 + 0.642326i \(0.222031\pi\)
\(360\) 0 0
\(361\) −30.8180 −1.62200
\(362\) −9.64529 + 23.0682i −0.506945 + 1.21244i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.92065i 0.100532i
\(366\) 0 0
\(367\) 24.0864i 1.25730i 0.777689 + 0.628649i \(0.216392\pi\)
−0.777689 + 0.628649i \(0.783608\pi\)
\(368\) 0.214583 16.1048i 0.0111859 0.839521i
\(369\) 0 0
\(370\) −6.83266 2.85688i −0.355213 0.148522i
\(371\) 0 0
\(372\) 0 0
\(373\) 13.3947 0.693550 0.346775 0.937948i \(-0.387277\pi\)
0.346775 + 0.937948i \(0.387277\pi\)
\(374\) 13.2298 + 5.53167i 0.684097 + 0.286036i
\(375\) 0 0
\(376\) −23.3634 + 9.40504i −1.20488 + 0.485028i
\(377\) 3.49996i 0.180257i
\(378\) 0 0
\(379\) 12.9558i 0.665493i −0.943016 0.332746i \(-0.892025\pi\)
0.943016 0.332746i \(-0.107975\pi\)
\(380\) 6.92310 + 7.01596i 0.355147 + 0.359911i
\(381\) 0 0
\(382\) −11.5896 + 27.7182i −0.592973 + 1.41819i
\(383\) 2.53349 0.129455 0.0647277 0.997903i \(-0.479382\pi\)
0.0647277 + 0.997903i \(0.479382\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.27363 5.43773i 0.115725 0.276773i
\(387\) 0 0
\(388\) 15.2672 + 15.4720i 0.775075 + 0.785471i
\(389\) 15.3047i 0.775979i 0.921664 + 0.387990i \(0.126830\pi\)
−0.921664 + 0.387990i \(0.873170\pi\)
\(390\) 0 0
\(391\) 15.9986i 0.809083i
\(392\) 0 0
\(393\) 0 0
\(394\) −10.4999 4.39024i −0.528978 0.221177i
\(395\) −9.44984 −0.475473
\(396\) 0 0
\(397\) −13.1066 −0.657801 −0.328900 0.944365i \(-0.606678\pi\)
−0.328900 + 0.944365i \(0.606678\pi\)
\(398\) −1.98803 0.831239i −0.0996511 0.0416663i
\(399\) 0 0
\(400\) −0.240478 + 18.0482i −0.0120239 + 0.902412i
\(401\) 1.16046i 0.0579505i −0.999580 0.0289753i \(-0.990776\pi\)
0.999580 0.0289753i \(-0.00922440\pi\)
\(402\) 0 0
\(403\) 1.77010i 0.0881748i
\(404\) 15.0994 14.8996i 0.751225 0.741282i
\(405\) 0 0
\(406\) 0 0
\(407\) −19.1397 −0.948718
\(408\) 0 0
\(409\) −7.18809 −0.355428 −0.177714 0.984082i \(-0.556870\pi\)
−0.177714 + 0.984082i \(0.556870\pi\)
\(410\) −4.04024 + 9.66284i −0.199533 + 0.477214i
\(411\) 0 0
\(412\) −18.8992 + 18.6490i −0.931095 + 0.918771i
\(413\) 0 0
\(414\) 0 0
\(415\) 11.9760i 0.587877i
\(416\) −9.76076 4.23483i −0.478561 0.207630i
\(417\) 0 0
\(418\) 23.5017 + 9.82656i 1.14951 + 0.480633i
\(419\) 16.1127 0.787155 0.393578 0.919291i \(-0.371237\pi\)
0.393578 + 0.919291i \(0.371237\pi\)
\(420\) 0 0
\(421\) 5.49992 0.268050 0.134025 0.990978i \(-0.457210\pi\)
0.134025 + 0.990978i \(0.457210\pi\)
\(422\) 25.1658 + 10.5224i 1.22505 + 0.512221i
\(423\) 0 0
\(424\) 0.559562 + 1.39003i 0.0271747 + 0.0675057i
\(425\) 17.9292i 0.869694i
\(426\) 0 0
\(427\) 0 0
\(428\) −13.5025 13.6836i −0.652670 0.661424i
\(429\) 0 0
\(430\) 1.51307 3.61872i 0.0729665 0.174510i
\(431\) −13.4106 −0.645965 −0.322983 0.946405i \(-0.604686\pi\)
−0.322983 + 0.946405i \(0.604686\pi\)
\(432\) 0 0
\(433\) 31.6801 1.52245 0.761224 0.648489i \(-0.224599\pi\)
0.761224 + 0.648489i \(0.224599\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −19.9814 20.2494i −0.956936 0.969771i
\(437\) 28.4202i 1.35952i
\(438\) 0 0
\(439\) 19.4812i 0.929786i 0.885367 + 0.464893i \(0.153907\pi\)
−0.885367 + 0.464893i \(0.846093\pi\)
\(440\) −1.88209 4.67536i −0.0897250 0.222889i
\(441\) 0 0
\(442\) −9.75071 4.07698i −0.463794 0.193922i
\(443\) 6.88254 0.326999 0.163500 0.986543i \(-0.447722\pi\)
0.163500 + 0.986543i \(0.447722\pi\)
\(444\) 0 0
\(445\) −8.28809 −0.392893
\(446\) 23.6669 + 9.89564i 1.12066 + 0.468572i
\(447\) 0 0
\(448\) 0 0
\(449\) 19.3255i 0.912025i −0.889973 0.456012i \(-0.849277\pi\)
0.889973 0.456012i \(-0.150723\pi\)
\(450\) 0 0
\(451\) 27.0676i 1.27456i
\(452\) 17.2311 17.0031i 0.810484 0.799757i
\(453\) 0 0
\(454\) −5.22533 + 12.4972i −0.245237 + 0.586521i
\(455\) 0 0
\(456\) 0 0
\(457\) 4.83699 0.226265 0.113132 0.993580i \(-0.463912\pi\)
0.113132 + 0.993580i \(0.463912\pi\)
\(458\) −2.64222 + 6.31926i −0.123463 + 0.295279i
\(459\) 0 0
\(460\) −4.00247 + 3.94949i −0.186616 + 0.184146i
\(461\) 26.3490i 1.22720i −0.789618 0.613599i \(-0.789721\pi\)
0.789618 0.613599i \(-0.210279\pi\)
\(462\) 0 0
\(463\) 38.1024i 1.77077i −0.464858 0.885385i \(-0.653895\pi\)
0.464858 0.885385i \(-0.346105\pi\)
\(464\) −7.44258 0.0991663i −0.345513 0.00460368i
\(465\) 0 0
\(466\) 28.2258 + 11.8018i 1.30754 + 0.546709i
\(467\) −6.38439 −0.295435 −0.147717 0.989030i \(-0.547193\pi\)
−0.147717 + 0.989030i \(0.547193\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.11216 + 3.39187i 0.374186 + 0.156455i
\(471\) 0 0
\(472\) −34.8986 + 14.0486i −1.60634 + 0.646639i
\(473\) 10.1368i 0.466090i
\(474\) 0 0
\(475\) 31.8498i 1.46137i
\(476\) 0 0
\(477\) 0 0
\(478\) 11.2136 26.8190i 0.512899 1.22667i
\(479\) 21.0410 0.961387 0.480693 0.876889i \(-0.340385\pi\)
0.480693 + 0.876889i \(0.340385\pi\)
\(480\) 0 0
\(481\) 14.1064 0.643198
\(482\) −5.86491 + 14.0268i −0.267139 + 0.638904i
\(483\) 0 0
\(484\) 6.30370 + 6.38825i 0.286532 + 0.290375i
\(485\) 7.58860i 0.344581i
\(486\) 0 0
\(487\) 15.7836i 0.715224i 0.933870 + 0.357612i \(0.116409\pi\)
−0.933870 + 0.357612i \(0.883591\pi\)
\(488\) 27.2044 10.9512i 1.23148 0.495739i
\(489\) 0 0
\(490\) 0 0
\(491\) 18.8204 0.849351 0.424675 0.905346i \(-0.360388\pi\)
0.424675 + 0.905346i \(0.360388\pi\)
\(492\) 0 0
\(493\) −7.39349 −0.332986
\(494\) −17.3214 7.24243i −0.779325 0.325852i
\(495\) 0 0
\(496\) 3.76407 + 0.0501532i 0.169012 + 0.00225194i
\(497\) 0 0
\(498\) 0 0
\(499\) 8.05889i 0.360766i 0.983596 + 0.180383i \(0.0577337\pi\)
−0.983596 + 0.180383i \(0.942266\pi\)
\(500\) 9.45555 9.33040i 0.422865 0.417268i
\(501\) 0 0
\(502\) −10.6008 + 25.3535i −0.473138 + 1.13158i
\(503\) −0.823898 −0.0367358 −0.0183679 0.999831i \(-0.505847\pi\)
−0.0183679 + 0.999831i \(0.505847\pi\)
\(504\) 0 0
\(505\) −7.40588 −0.329557
\(506\) −5.60586 + 13.4073i −0.249211 + 0.596025i
\(507\) 0 0
\(508\) 0.829368 0.818391i 0.0367973 0.0363102i
\(509\) 39.1011i 1.73313i −0.499067 0.866563i \(-0.666324\pi\)
0.499067 0.866563i \(-0.333676\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −9.28184 + 20.6361i −0.410203 + 0.911994i
\(513\) 0 0
\(514\) −11.3992 4.76626i −0.502799 0.210231i
\(515\) 9.26954 0.408465
\(516\) 0 0
\(517\) 22.7238 0.999392
\(518\) 0 0
\(519\) 0 0
\(520\) 1.38715 + 3.44586i 0.0608304 + 0.151111i
\(521\) 0.523131i 0.0229188i −0.999934 0.0114594i \(-0.996352\pi\)
0.999934 0.0114594i \(-0.00364772\pi\)
\(522\) 0 0
\(523\) 37.5317i 1.64115i −0.571542 0.820573i \(-0.693655\pi\)
0.571542 0.820573i \(-0.306345\pi\)
\(524\) 15.3012 + 15.5065i 0.668438 + 0.677403i
\(525\) 0 0
\(526\) 11.8972 28.4540i 0.518743 1.24065i
\(527\) 3.73925 0.162884
\(528\) 0 0
\(529\) −6.78683 −0.295080
\(530\) 0.201802 0.482641i 0.00876573 0.0209646i
\(531\) 0 0
\(532\) 0 0
\(533\) 19.9495i 0.864109i
\(534\) 0 0
\(535\) 6.71147i 0.290162i
\(536\) 2.87610 + 7.14463i 0.124229 + 0.308601i
\(537\) 0 0
\(538\) −19.1851 8.02169i −0.827128 0.345840i
\(539\) 0 0
\(540\) 0 0
\(541\) 22.3541 0.961076 0.480538 0.876974i \(-0.340441\pi\)
0.480538 + 0.876974i \(0.340441\pi\)
\(542\) 6.76878 + 2.83017i 0.290744 + 0.121566i
\(543\) 0 0
\(544\) −8.94588 + 20.6192i −0.383552 + 0.884039i
\(545\) 9.93181i 0.425432i
\(546\) 0 0
\(547\) 8.09960i 0.346314i 0.984894 + 0.173157i \(0.0553968\pi\)
−0.984894 + 0.173157i \(0.944603\pi\)
\(548\) −18.9367 + 18.6860i −0.808934 + 0.798227i
\(549\) 0 0
\(550\) 6.28235 15.0252i 0.267880 0.640676i
\(551\) −13.1340 −0.559525
\(552\) 0 0
\(553\) 0 0
\(554\) 12.9433 30.9559i 0.549909 1.31519i
\(555\) 0 0
\(556\) 1.19696 1.18112i 0.0507624 0.0500905i
\(557\) 31.5924i 1.33861i 0.742986 + 0.669307i \(0.233409\pi\)
−0.742986 + 0.669307i \(0.766591\pi\)
\(558\) 0 0
\(559\) 7.47107i 0.315992i
\(560\) 0 0
\(561\) 0 0
\(562\) 5.38080 + 2.24983i 0.226975 + 0.0949032i
\(563\) −8.35892 −0.352286 −0.176143 0.984365i \(-0.556362\pi\)
−0.176143 + 0.984365i \(0.556362\pi\)
\(564\) 0 0
\(565\) −8.45141 −0.355554
\(566\) −9.20919 3.85056i −0.387091 0.161851i
\(567\) 0 0
\(568\) −9.21771 + 3.71063i −0.386766 + 0.155695i
\(569\) 13.0294i 0.546220i 0.961983 + 0.273110i \(0.0880524\pi\)
−0.961983 + 0.273110i \(0.911948\pi\)
\(570\) 0 0
\(571\) 14.3864i 0.602052i 0.953616 + 0.301026i \(0.0973290\pi\)
−0.953616 + 0.301026i \(0.902671\pi\)
\(572\) 6.74281 + 6.83325i 0.281931 + 0.285712i
\(573\) 0 0
\(574\) 0 0
\(575\) −18.1697 −0.757728
\(576\) 0 0
\(577\) 25.7616 1.07247 0.536235 0.844069i \(-0.319846\pi\)
0.536235 + 0.844069i \(0.319846\pi\)
\(578\) 0.661838 1.58288i 0.0275288 0.0658393i
\(579\) 0 0
\(580\) 1.82520 + 1.84968i 0.0757871 + 0.0768037i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.35197i 0.0559931i
\(584\) −7.21734 + 2.90537i −0.298656 + 0.120225i
\(585\) 0 0
\(586\) −20.8336 8.71098i −0.860629 0.359847i
\(587\) −33.3927 −1.37826 −0.689131 0.724637i \(-0.742008\pi\)
−0.689131 + 0.724637i \(0.742008\pi\)
\(588\) 0 0
\(589\) 6.64247 0.273698
\(590\) 12.1174 + 5.06654i 0.498865 + 0.208586i
\(591\) 0 0
\(592\) 0.399686 29.9970i 0.0164270 1.23287i
\(593\) 29.5496i 1.21346i 0.794909 + 0.606729i \(0.207519\pi\)
−0.794909 + 0.606729i \(0.792481\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8.05312 + 7.94653i −0.329868 + 0.325503i
\(597\) 0 0
\(598\) 4.13166 9.88149i 0.168956 0.404084i
\(599\) 5.99928 0.245124 0.122562 0.992461i \(-0.460889\pi\)
0.122562 + 0.992461i \(0.460889\pi\)
\(600\) 0 0
\(601\) 5.44843 0.222246 0.111123 0.993807i \(-0.464555\pi\)
0.111123 + 0.993807i \(0.464555\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −24.1770 + 23.8570i −0.983746 + 0.970726i
\(605\) 3.13327i 0.127386i
\(606\) 0 0
\(607\) 4.34699i 0.176439i 0.996101 + 0.0882195i \(0.0281177\pi\)
−0.996101 + 0.0882195i \(0.971882\pi\)
\(608\) −15.8916 + 36.6283i −0.644491 + 1.48547i
\(609\) 0 0
\(610\) −9.44580 3.94949i −0.382449 0.159910i
\(611\) −16.7480 −0.677553
\(612\) 0 0
\(613\) −14.9621 −0.604312 −0.302156 0.953258i \(-0.597706\pi\)
−0.302156 + 0.953258i \(0.597706\pi\)
\(614\) −7.22116 3.01932i −0.291422 0.121850i
\(615\) 0 0
\(616\) 0 0
\(617\) 21.4967i 0.865425i 0.901532 + 0.432713i \(0.142443\pi\)
−0.901532 + 0.432713i \(0.857557\pi\)
\(618\) 0 0
\(619\) 14.3864i 0.578238i −0.957293 0.289119i \(-0.906638\pi\)
0.957293 0.289119i \(-0.0933623\pi\)
\(620\) −0.923089 0.935471i −0.0370722 0.0375694i
\(621\) 0 0
\(622\) −5.72212 + 13.6853i −0.229436 + 0.548731i
\(623\) 0 0
\(624\) 0 0
\(625\) 17.9246 0.716984
\(626\) −1.23466 + 2.95288i −0.0493470 + 0.118021i
\(627\) 0 0
\(628\) −2.77429 2.81150i −0.110706 0.112191i
\(629\) 29.7992i 1.18817i
\(630\) 0 0
\(631\) 15.8983i 0.632900i 0.948609 + 0.316450i \(0.102491\pi\)
−0.948609 + 0.316450i \(0.897509\pi\)
\(632\) −14.2948 35.5101i −0.568615 1.41252i
\(633\) 0 0
\(634\) 12.4028 + 5.18588i 0.492579 + 0.205958i
\(635\) −0.406784 −0.0161427
\(636\) 0 0
\(637\) 0 0
\(638\) 6.19596 + 2.59066i 0.245300 + 0.102565i
\(639\) 0 0
\(640\) 7.36685 2.85210i 0.291200 0.112739i
\(641\) 1.56599i 0.0618528i 0.999522 + 0.0309264i \(0.00984576\pi\)
−0.999522 + 0.0309264i \(0.990154\pi\)
\(642\) 0 0
\(643\) 33.5314i 1.32235i −0.750232 0.661174i \(-0.770058\pi\)
0.750232 0.661174i \(-0.229942\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −15.2993 + 36.5906i −0.601943 + 1.43964i
\(647\) −17.3184 −0.680857 −0.340429 0.940270i \(-0.610572\pi\)
−0.340429 + 0.940270i \(0.610572\pi\)
\(648\) 0 0
\(649\) 33.9433 1.33239
\(650\) −4.63025 + 11.0739i −0.181613 + 0.434356i
\(651\) 0 0
\(652\) −4.00247 + 3.94949i −0.156749 + 0.154674i
\(653\) 27.0948i 1.06030i −0.847904 0.530150i \(-0.822136\pi\)
0.847904 0.530150i \(-0.177864\pi\)
\(654\) 0 0
\(655\) 7.60552i 0.297172i
\(656\) −42.4222 0.565241i −1.65631 0.0220690i
\(657\) 0 0
\(658\) 0 0
\(659\) 10.9749 0.427521 0.213761 0.976886i \(-0.431429\pi\)
0.213761 + 0.976886i \(0.431429\pi\)
\(660\) 0 0
\(661\) −2.88072 −0.112047 −0.0560235 0.998429i \(-0.517842\pi\)
−0.0560235 + 0.998429i \(0.517842\pi\)
\(662\) −12.9707 5.42332i −0.504120 0.210783i
\(663\) 0 0
\(664\) −45.0027 + 18.1160i −1.74644 + 0.703038i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.49266i 0.290117i
\(668\) 3.38312 + 3.42850i 0.130897 + 0.132653i
\(669\) 0 0
\(670\) 1.03725 2.48074i 0.0400724 0.0958392i
\(671\) −26.4596 −1.02146
\(672\) 0 0
\(673\) 9.09255 0.350492 0.175246 0.984525i \(-0.443928\pi\)
0.175246 + 0.984525i \(0.443928\pi\)
\(674\) 5.80685 13.8880i 0.223671 0.534944i
\(675\) 0 0
\(676\) 13.2923 + 13.4706i 0.511241 + 0.518099i
\(677\) 15.9675i 0.613680i −0.951761 0.306840i \(-0.900728\pi\)
0.951761 0.306840i \(-0.0992717\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 7.27922 2.93028i 0.279145 0.112371i
\(681\) 0 0
\(682\) −3.13359 1.31022i −0.119991 0.0501710i
\(683\) 44.5539 1.70481 0.852404 0.522885i \(-0.175144\pi\)
0.852404 + 0.522885i \(0.175144\pi\)
\(684\) 0 0
\(685\) 9.28793 0.354874
\(686\) 0 0
\(687\) 0 0
\(688\) 15.8871 + 0.211682i 0.605689 + 0.00807031i
\(689\) 0.996440i 0.0379613i
\(690\) 0 0
\(691\) 13.9926i 0.532304i 0.963931 + 0.266152i \(0.0857523\pi\)
−0.963931 + 0.266152i \(0.914248\pi\)
\(692\) 6.66283 6.57465i 0.253283 0.249931i
\(693\) 0 0
\(694\) −9.57366 + 22.8969i −0.363411 + 0.869153i
\(695\) −0.587077 −0.0222691
\(696\) 0 0
\(697\) −42.1424 −1.59626
\(698\) −15.8592 + 37.9296i −0.600278 + 1.43566i
\(699\) 0 0
\(700\) 0 0
\(701\) 14.4059i 0.544104i −0.962283 0.272052i \(-0.912298\pi\)
0.962283 0.272052i \(-0.0877022\pi\)
\(702\) 0 0
\(703\) 52.9359i 1.99651i
\(704\) 14.7218 14.1448i 0.554849 0.533103i
\(705\) 0 0
\(706\) 14.6735 + 6.13528i 0.552243 + 0.230904i
\(707\) 0 0
\(708\) 0 0
\(709\) −44.1878 −1.65951 −0.829753 0.558130i \(-0.811519\pi\)
−0.829753 + 0.558130i \(0.811519\pi\)
\(710\) 3.20054 + 1.33821i 0.120114 + 0.0502223i
\(711\) 0 0
\(712\) −12.5374 31.1446i −0.469858 1.16719i
\(713\) 3.78940i 0.141914i
\(714\) 0 0
\(715\) 3.35153i 0.125340i
\(716\) 18.5300 + 18.7786i 0.692500 + 0.701789i
\(717\) 0 0
\(718\) 15.8446 37.8947i 0.591315 1.41422i
\(719\) 12.1366 0.452619 0.226309 0.974055i \(-0.427334\pi\)
0.226309 + 0.974055i \(0.427334\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −16.8126 + 40.2099i −0.625701 + 1.49646i
\(723\) 0 0
\(724\) 24.8363 + 25.1694i 0.923034 + 0.935415i
\(725\) 8.39684i 0.311851i
\(726\) 0 0
\(727\) 27.8081i 1.03134i −0.856786 0.515672i \(-0.827542\pi\)
0.856786 0.515672i \(-0.172458\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.50598 + 1.04780i 0.0927505 + 0.0387809i
\(731\) 15.7823 0.583729
\(732\) 0 0
\(733\) 39.6626 1.46497 0.732486 0.680782i \(-0.238360\pi\)
0.732486 + 0.680782i \(0.238360\pi\)
\(734\) 31.4268 + 13.1402i 1.15998 + 0.485014i
\(735\) 0 0
\(736\) −20.8957 9.06587i −0.770227 0.334173i
\(737\) 6.94905i 0.255971i
\(738\) 0 0
\(739\) 32.6564i 1.20129i −0.799517 0.600643i \(-0.794911\pi\)
0.799517 0.600643i \(-0.205089\pi\)
\(740\) −7.45505 + 7.35638i −0.274053 + 0.270426i
\(741\) 0 0
\(742\) 0 0
\(743\) −33.8538 −1.24198 −0.620988 0.783820i \(-0.713268\pi\)
−0.620988 + 0.783820i \(0.713268\pi\)
\(744\) 0 0
\(745\) 3.94984 0.144711
\(746\) 7.30740 17.4767i 0.267543 0.639869i
\(747\) 0 0
\(748\) 14.4349 14.2439i 0.527793 0.520807i
\(749\) 0 0
\(750\) 0 0
\(751\) 29.7617i 1.08602i −0.839726 0.543010i \(-0.817285\pi\)
0.839726 0.543010i \(-0.182715\pi\)
\(752\) −0.474532 + 35.6143i −0.0173044 + 1.29872i
\(753\) 0 0
\(754\) −4.56658 1.90938i −0.166305 0.0695357i
\(755\) 11.8582 0.431563
\(756\) 0 0
\(757\) 21.4183 0.778460 0.389230 0.921141i \(-0.372741\pi\)
0.389230 + 0.921141i \(0.372741\pi\)
\(758\) −16.9041 7.06795i −0.613983 0.256720i
\(759\) 0 0
\(760\) 12.9310 5.20541i 0.469055 0.188820i
\(761\) 43.7901i 1.58739i −0.608315 0.793696i \(-0.708154\pi\)
0.608315 0.793696i \(-0.291846\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 29.8427 + 30.2430i 1.07967 + 1.09415i
\(765\) 0 0
\(766\) 1.38213 3.30558i 0.0499385 0.119436i
\(767\) −25.0170 −0.903313
\(768\) 0 0
\(769\) 53.6687 1.93534 0.967672 0.252212i \(-0.0811581\pi\)
0.967672 + 0.252212i \(0.0811581\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.85452 5.93305i −0.210709 0.213535i
\(773\) 43.5231i 1.56542i 0.622389 + 0.782708i \(0.286162\pi\)
−0.622389 + 0.782708i \(0.713838\pi\)
\(774\) 0 0
\(775\) 4.24668i 0.152545i
\(776\) 28.5161 11.4793i 1.02367 0.412082i
\(777\) 0 0
\(778\) 19.9689 + 8.34941i 0.715918 + 0.299341i
\(779\) −74.8626 −2.68223
\(780\) 0 0
\(781\) 8.96537 0.320806
\(782\) −20.8742 8.72795i −0.746460 0.312111i
\(783\) 0 0
\(784\) 0 0
\(785\) 1.37897i 0.0492175i
\(786\) 0 0
\(787\) 11.3049i 0.402975i −0.979491 0.201488i \(-0.935422\pi\)
0.979491 0.201488i \(-0.0645776\pi\)
\(788\) −11.4564 + 11.3047i −0.408116 + 0.402714i
\(789\) 0 0
\(790\) −5.15531 + 12.3297i −0.183418 + 0.438671i
\(791\) 0 0
\(792\) 0 0
\(793\) 19.5014