Properties

Label 912.2.bb.e.31.3
Level $912$
Weight $2$
Character 912.31
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \(x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 6 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(-1.62241 + 0.606458i\) of defining polynomial
Character \(\chi\) \(=\) 912.31
Dual form 912.2.bb.e.559.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} -3.93569i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} -3.93569i q^{7} +(-0.500000 + 0.866025i) q^{9} -2.20364i q^{11} +(-3.60083 - 2.07894i) q^{13} +(1.33641 - 2.31473i) q^{15} +(-0.571993 - 0.990721i) q^{17} +(-4.24482 - 0.990721i) q^{19} +(-3.40841 + 1.96784i) q^{21} +(3.19243 + 1.84315i) q^{23} +(-1.07199 + 1.85675i) q^{25} +1.00000 q^{27} +(-2.10083 - 1.21292i) q^{29} +3.67282 q^{31} +(-1.90841 + 1.10182i) q^{33} +(9.11007 - 5.25970i) q^{35} -10.0478i q^{37} +4.15788i q^{39} +(8.01847 - 4.62947i) q^{41} +(-0.490764 + 0.283343i) q^{43} -2.67282 q^{45} +(-10.6336 - 6.13932i) q^{47} -8.48963 q^{49} +(-0.571993 + 0.990721i) q^{51} +(4.09159 + 2.36228i) q^{53} +(5.10083 - 2.94497i) q^{55} +(1.26442 + 4.17148i) q^{57} +(-1.33641 - 2.31473i) q^{59} +(-6.41764 + 11.1157i) q^{61} +(3.40841 + 1.96784i) q^{63} -11.1133i q^{65} +(1.73558 - 3.00612i) q^{67} -3.68630i q^{69} +(-6.24482 - 10.8163i) q^{71} +(1.35601 + 2.34868i) q^{73} +2.14399 q^{75} -8.67282 q^{77} +(-3.50924 - 6.07817i) q^{79} +(-0.500000 - 0.866025i) q^{81} -1.98144i q^{83} +(1.52884 - 2.64802i) q^{85} +2.42583i q^{87} +(12.9269 + 7.46334i) q^{89} +(-8.18206 + 14.1717i) q^{91} +(-1.83641 - 3.18076i) q^{93} +(-3.37957 - 11.1496i) q^{95} +(2.91764 - 1.68450i) q^{97} +(1.90841 + 1.10182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{3} - 2q^{5} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{3} - 2q^{5} - 3q^{9} - 3q^{13} - 2q^{15} - 2q^{17} - 4q^{19} - 9q^{21} + 12q^{23} - 5q^{25} + 6q^{27} + 6q^{29} + 2q^{31} + 6q^{35} - 12q^{41} - 33q^{43} + 4q^{45} - 18q^{47} - 8q^{49} - 2q^{51} + 36q^{53} + 12q^{55} - q^{57} + 2q^{59} + 3q^{61} + 9q^{63} + 19q^{67} - 16q^{71} + 11q^{73} + 10q^{75} - 32q^{77} + 9q^{79} - 3q^{81} - 8q^{85} + 6q^{89} + q^{91} - q^{93} - 26q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(-1\)

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 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) 1.33641 + 2.31473i 0.597662 + 1.03518i 0.993165 + 0.116716i \(0.0372367\pi\)
−0.395504 + 0.918464i \(0.629430\pi\)
\(6\) 0 0
\(7\) 3.93569i 1.48755i −0.668430 0.743775i \(-0.733033\pi\)
0.668430 0.743775i \(-0.266967\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.20364i 0.664421i −0.943205 0.332211i \(-0.892205\pi\)
0.943205 0.332211i \(-0.107795\pi\)
\(12\) 0 0
\(13\) −3.60083 2.07894i −0.998691 0.576594i −0.0908300 0.995866i \(-0.528952\pi\)
−0.907861 + 0.419272i \(0.862285\pi\)
\(14\) 0 0
\(15\) 1.33641 2.31473i 0.345060 0.597662i
\(16\) 0 0
\(17\) −0.571993 0.990721i −0.138729 0.240285i 0.788287 0.615308i \(-0.210968\pi\)
−0.927016 + 0.375023i \(0.877635\pi\)
\(18\) 0 0
\(19\) −4.24482 0.990721i −0.973828 0.227287i
\(20\) 0 0
\(21\) −3.40841 + 1.96784i −0.743775 + 0.429419i
\(22\) 0 0
\(23\) 3.19243 + 1.84315i 0.665667 + 0.384323i 0.794433 0.607352i \(-0.207768\pi\)
−0.128766 + 0.991675i \(0.541102\pi\)
\(24\) 0 0
\(25\) −1.07199 + 1.85675i −0.214399 + 0.371349i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.10083 1.21292i −0.390114 0.225233i 0.292095 0.956389i \(-0.405648\pi\)
−0.682210 + 0.731157i \(0.738981\pi\)
\(30\) 0 0
\(31\) 3.67282 0.659659 0.329829 0.944041i \(-0.393009\pi\)
0.329829 + 0.944041i \(0.393009\pi\)
\(32\) 0 0
\(33\) −1.90841 + 1.10182i −0.332211 + 0.191802i
\(34\) 0 0
\(35\) 9.11007 5.25970i 1.53988 0.889051i
\(36\) 0 0
\(37\) 10.0478i 1.65185i −0.563780 0.825925i \(-0.690653\pi\)
0.563780 0.825925i \(-0.309347\pi\)
\(38\) 0 0
\(39\) 4.15788i 0.665794i
\(40\) 0 0
\(41\) 8.01847 4.62947i 1.25227 0.723001i 0.280714 0.959791i \(-0.409429\pi\)
0.971561 + 0.236790i \(0.0760954\pi\)
\(42\) 0 0
\(43\) −0.490764 + 0.283343i −0.0748409 + 0.0432094i −0.536953 0.843612i \(-0.680425\pi\)
0.462113 + 0.886821i \(0.347092\pi\)
\(44\) 0 0
\(45\) −2.67282 −0.398441
\(46\) 0 0
\(47\) −10.6336 6.13932i −1.55107 0.895512i −0.998055 0.0623432i \(-0.980143\pi\)
−0.553018 0.833169i \(-0.686524\pi\)
\(48\) 0 0
\(49\) −8.48963 −1.21280
\(50\) 0 0
\(51\) −0.571993 + 0.990721i −0.0800951 + 0.138729i
\(52\) 0 0
\(53\) 4.09159 + 2.36228i 0.562024 + 0.324485i 0.753957 0.656923i \(-0.228142\pi\)
−0.191934 + 0.981408i \(0.561476\pi\)
\(54\) 0 0
\(55\) 5.10083 2.94497i 0.687796 0.397099i
\(56\) 0 0
\(57\) 1.26442 + 4.17148i 0.167476 + 0.552526i
\(58\) 0 0
\(59\) −1.33641 2.31473i −0.173986 0.301353i 0.765824 0.643050i \(-0.222331\pi\)
−0.939810 + 0.341698i \(0.888998\pi\)
\(60\) 0 0
\(61\) −6.41764 + 11.1157i −0.821695 + 1.42322i 0.0827247 + 0.996572i \(0.473638\pi\)
−0.904419 + 0.426645i \(0.859696\pi\)
\(62\) 0 0
\(63\) 3.40841 + 1.96784i 0.429419 + 0.247925i
\(64\) 0 0
\(65\) 11.1133i 1.37843i
\(66\) 0 0
\(67\) 1.73558 3.00612i 0.212035 0.367255i −0.740316 0.672259i \(-0.765324\pi\)
0.952351 + 0.305003i \(0.0986576\pi\)
\(68\) 0 0
\(69\) 3.68630i 0.443778i
\(70\) 0 0
\(71\) −6.24482 10.8163i −0.741123 1.28366i −0.951984 0.306147i \(-0.900960\pi\)
0.210861 0.977516i \(-0.432373\pi\)
\(72\) 0 0
\(73\) 1.35601 + 2.34868i 0.158709 + 0.274893i 0.934404 0.356216i \(-0.115933\pi\)
−0.775694 + 0.631109i \(0.782600\pi\)
\(74\) 0 0
\(75\) 2.14399 0.247566
\(76\) 0 0
\(77\) −8.67282 −0.988360
\(78\) 0 0
\(79\) −3.50924 6.07817i −0.394820 0.683848i 0.598258 0.801303i \(-0.295860\pi\)
−0.993078 + 0.117455i \(0.962526\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 1.98144i 0.217492i −0.994070 0.108746i \(-0.965317\pi\)
0.994070 0.108746i \(-0.0346835\pi\)
\(84\) 0 0
\(85\) 1.52884 2.64802i 0.165826 0.287218i
\(86\) 0 0
\(87\) 2.42583i 0.260076i
\(88\) 0 0
\(89\) 12.9269 + 7.46334i 1.37025 + 0.791112i 0.990959 0.134167i \(-0.0428358\pi\)
0.379287 + 0.925279i \(0.376169\pi\)
\(90\) 0 0
\(91\) −8.18206 + 14.1717i −0.857713 + 1.48560i
\(92\) 0 0
\(93\) −1.83641 3.18076i −0.190427 0.329829i
\(94\) 0 0
\(95\) −3.37957 11.1496i −0.346736 1.14393i
\(96\) 0 0
\(97\) 2.91764 1.68450i 0.296242 0.171035i −0.344512 0.938782i \(-0.611956\pi\)
0.640753 + 0.767747i \(0.278622\pi\)
\(98\) 0 0
\(99\) 1.90841 + 1.10182i 0.191802 + 0.110737i
\(100\) 0 0
\(101\) −5.10083 + 8.83490i −0.507552 + 0.879105i 0.492410 + 0.870363i \(0.336116\pi\)
−0.999962 + 0.00874190i \(0.997217\pi\)
\(102\) 0 0
\(103\) 16.4504 1.62091 0.810455 0.585802i \(-0.199220\pi\)
0.810455 + 0.585802i \(0.199220\pi\)
\(104\) 0 0
\(105\) −9.11007 5.25970i −0.889051 0.513294i
\(106\) 0 0
\(107\) −4.85601 −0.469449 −0.234724 0.972062i \(-0.575419\pi\)
−0.234724 + 0.972062i \(0.575419\pi\)
\(108\) 0 0
\(109\) −12.7345 + 7.35224i −1.21974 + 0.704217i −0.964862 0.262757i \(-0.915368\pi\)
−0.254877 + 0.966973i \(0.582035\pi\)
\(110\) 0 0
\(111\) −8.70166 + 5.02391i −0.825925 + 0.476848i
\(112\) 0 0
\(113\) 14.4823i 1.36238i −0.732107 0.681189i \(-0.761463\pi\)
0.732107 0.681189i \(-0.238537\pi\)
\(114\) 0 0
\(115\) 9.85282i 0.918780i
\(116\) 0 0
\(117\) 3.60083 2.07894i 0.332897 0.192198i
\(118\) 0 0
\(119\) −3.89917 + 2.25119i −0.357436 + 0.206366i
\(120\) 0 0
\(121\) 6.14399 0.558544
\(122\) 0 0
\(123\) −8.01847 4.62947i −0.723001 0.417425i
\(124\) 0 0
\(125\) 7.63362 0.682772
\(126\) 0 0
\(127\) −5.81681 + 10.0750i −0.516158 + 0.894013i 0.483666 + 0.875253i \(0.339305\pi\)
−0.999824 + 0.0187598i \(0.994028\pi\)
\(128\) 0 0
\(129\) 0.490764 + 0.283343i 0.0432094 + 0.0249470i
\(130\) 0 0
\(131\) 10.7160 6.18687i 0.936260 0.540550i 0.0474737 0.998872i \(-0.484883\pi\)
0.888786 + 0.458323i \(0.151550\pi\)
\(132\) 0 0
\(133\) −3.89917 + 16.7063i −0.338101 + 1.44862i
\(134\) 0 0
\(135\) 1.33641 + 2.31473i 0.115020 + 0.199221i
\(136\) 0 0
\(137\) 4.71598 8.16832i 0.402913 0.697866i −0.591163 0.806552i \(-0.701331\pi\)
0.994076 + 0.108686i \(0.0346643\pi\)
\(138\) 0 0
\(139\) 11.8941 + 6.86705i 1.00884 + 0.582456i 0.910853 0.412731i \(-0.135425\pi\)
0.0979905 + 0.995187i \(0.468759\pi\)
\(140\) 0 0
\(141\) 12.2786i 1.03405i
\(142\) 0 0
\(143\) −4.58123 + 7.93492i −0.383102 + 0.663551i
\(144\) 0 0
\(145\) 6.48382i 0.538452i
\(146\) 0 0
\(147\) 4.24482 + 7.35224i 0.350107 + 0.606402i
\(148\) 0 0
\(149\) 8.15322 + 14.1218i 0.667938 + 1.15690i 0.978480 + 0.206343i \(0.0661562\pi\)
−0.310542 + 0.950560i \(0.600510\pi\)
\(150\) 0 0
\(151\) −7.05767 −0.574345 −0.287173 0.957879i \(-0.592715\pi\)
−0.287173 + 0.957879i \(0.592715\pi\)
\(152\) 0 0
\(153\) 1.14399 0.0924858
\(154\) 0 0
\(155\) 4.90841 + 8.50161i 0.394253 + 0.682866i
\(156\) 0 0
\(157\) 5.66246 + 9.80766i 0.451913 + 0.782737i 0.998505 0.0546625i \(-0.0174083\pi\)
−0.546592 + 0.837399i \(0.684075\pi\)
\(158\) 0 0
\(159\) 4.72457i 0.374683i
\(160\) 0 0
\(161\) 7.25405 12.5644i 0.571699 0.990212i
\(162\) 0 0
\(163\) 0.915973i 0.0717445i −0.999356 0.0358723i \(-0.988579\pi\)
0.999356 0.0358723i \(-0.0114209\pi\)
\(164\) 0 0
\(165\) −5.10083 2.94497i −0.397099 0.229265i
\(166\) 0 0
\(167\) 0.192425 0.333290i 0.0148903 0.0257908i −0.858484 0.512840i \(-0.828593\pi\)
0.873375 + 0.487049i \(0.161927\pi\)
\(168\) 0 0
\(169\) 2.14399 + 3.71349i 0.164922 + 0.285653i
\(170\) 0 0
\(171\) 2.98040 3.18076i 0.227917 0.243239i
\(172\) 0 0
\(173\) 9.34960 5.39799i 0.710837 0.410402i −0.100534 0.994934i \(-0.532055\pi\)
0.811371 + 0.584532i \(0.198722\pi\)
\(174\) 0 0
\(175\) 7.30757 + 4.21903i 0.552401 + 0.318929i
\(176\) 0 0
\(177\) −1.33641 + 2.31473i −0.100451 + 0.173986i
\(178\) 0 0
\(179\) 1.03920 0.0776737 0.0388368 0.999246i \(-0.487635\pi\)
0.0388368 + 0.999246i \(0.487635\pi\)
\(180\) 0 0
\(181\) −6.73445 3.88814i −0.500568 0.289003i 0.228380 0.973572i \(-0.426657\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(182\) 0 0
\(183\) 12.8353 0.948811
\(184\) 0 0
\(185\) 23.2580 13.4280i 1.70996 0.987247i
\(186\) 0 0
\(187\) −2.18319 + 1.26047i −0.159651 + 0.0921743i
\(188\) 0 0
\(189\) 3.93569i 0.286279i
\(190\) 0 0
\(191\) 26.2621i 1.90026i 0.311851 + 0.950131i \(0.399051\pi\)
−0.311851 + 0.950131i \(0.600949\pi\)
\(192\) 0 0
\(193\) 8.23445 4.75416i 0.592729 0.342212i −0.173447 0.984843i \(-0.555491\pi\)
0.766176 + 0.642631i \(0.222157\pi\)
\(194\) 0 0
\(195\) −9.62438 + 5.55664i −0.689217 + 0.397919i
\(196\) 0 0
\(197\) 27.9322 1.99008 0.995042 0.0994560i \(-0.0317103\pi\)
0.995042 + 0.0994560i \(0.0317103\pi\)
\(198\) 0 0
\(199\) −6.87562 3.96964i −0.487399 0.281400i 0.236096 0.971730i \(-0.424132\pi\)
−0.723495 + 0.690330i \(0.757466\pi\)
\(200\) 0 0
\(201\) −3.47116 −0.244837
\(202\) 0 0
\(203\) −4.77365 + 8.26821i −0.335045 + 0.580315i
\(204\) 0 0
\(205\) 21.4320 + 12.3737i 1.49687 + 0.864220i
\(206\) 0 0
\(207\) −3.19243 + 1.84315i −0.221889 + 0.128108i
\(208\) 0 0
\(209\) −2.18319 + 9.35403i −0.151014 + 0.647032i
\(210\) 0 0
\(211\) 4.32605 + 7.49293i 0.297817 + 0.515835i 0.975636 0.219394i \(-0.0704081\pi\)
−0.677819 + 0.735229i \(0.737075\pi\)
\(212\) 0 0
\(213\) −6.24482 + 10.8163i −0.427888 + 0.741123i
\(214\) 0 0
\(215\) −1.31173 0.757326i −0.0894590 0.0516492i
\(216\) 0 0
\(217\) 14.4551i 0.981275i
\(218\) 0 0
\(219\) 1.35601 2.34868i 0.0916309 0.158709i
\(220\) 0 0
\(221\) 4.75656i 0.319961i
\(222\) 0 0
\(223\) 7.18206 + 12.4397i 0.480946 + 0.833023i 0.999761 0.0218634i \(-0.00695988\pi\)
−0.518815 + 0.854887i \(0.673627\pi\)
\(224\) 0 0
\(225\) −1.07199 1.85675i −0.0714662 0.123783i
\(226\) 0 0
\(227\) −14.1832 −0.941371 −0.470686 0.882301i \(-0.655993\pi\)
−0.470686 + 0.882301i \(0.655993\pi\)
\(228\) 0 0
\(229\) −16.5473 −1.09348 −0.546738 0.837303i \(-0.684131\pi\)
−0.546738 + 0.837303i \(0.684131\pi\)
\(230\) 0 0
\(231\) 4.33641 + 7.51089i 0.285315 + 0.494180i
\(232\) 0 0
\(233\) 13.1193 + 22.7233i 0.859474 + 1.48865i 0.872431 + 0.488737i \(0.162542\pi\)
−0.0129574 + 0.999916i \(0.504125\pi\)
\(234\) 0 0
\(235\) 32.8187i 2.14085i
\(236\) 0 0
\(237\) −3.50924 + 6.07817i −0.227949 + 0.394820i
\(238\) 0 0
\(239\) 1.26047i 0.0815327i 0.999169 + 0.0407664i \(0.0129799\pi\)
−0.999169 + 0.0407664i \(0.987020\pi\)
\(240\) 0 0
\(241\) −18.1336 10.4695i −1.16809 0.674397i −0.214860 0.976645i \(-0.568930\pi\)
−0.953229 + 0.302248i \(0.902263\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −11.3456 19.6512i −0.724847 1.25547i
\(246\) 0 0
\(247\) 13.2252 + 12.3921i 0.841500 + 0.788493i
\(248\) 0 0
\(249\) −1.71598 + 0.990721i −0.108746 + 0.0627844i
\(250\) 0 0
\(251\) 24.6521 + 14.2329i 1.55603 + 0.898372i 0.997631 + 0.0687973i \(0.0219162\pi\)
0.558396 + 0.829575i \(0.311417\pi\)
\(252\) 0 0
\(253\) 4.06163 7.03494i 0.255352 0.442283i
\(254\) 0 0
\(255\) −3.05767 −0.191479
\(256\) 0 0
\(257\) 10.4764 + 6.04858i 0.653503 + 0.377300i 0.789797 0.613368i \(-0.210186\pi\)
−0.136294 + 0.990668i \(0.543519\pi\)
\(258\) 0 0
\(259\) −39.5450 −2.45721
\(260\) 0 0
\(261\) 2.10083 1.21292i 0.130038 0.0750776i
\(262\) 0 0
\(263\) −1.11930 + 0.646229i −0.0690191 + 0.0398482i −0.534112 0.845413i \(-0.679354\pi\)
0.465093 + 0.885262i \(0.346021\pi\)
\(264\) 0 0
\(265\) 12.6279i 0.775728i
\(266\) 0 0
\(267\) 14.9267i 0.913497i
\(268\) 0 0
\(269\) −24.5420 + 14.1693i −1.49635 + 0.863920i −0.999991 0.00419513i \(-0.998665\pi\)
−0.496363 + 0.868115i \(0.665331\pi\)
\(270\) 0 0
\(271\) −13.2017 + 7.62198i −0.801944 + 0.463002i −0.844150 0.536106i \(-0.819895\pi\)
0.0422066 + 0.999109i \(0.486561\pi\)
\(272\) 0 0
\(273\) 16.3641 0.990402
\(274\) 0 0
\(275\) 4.09159 + 2.36228i 0.246732 + 0.142451i
\(276\) 0 0
\(277\) −15.8353 −0.951450 −0.475725 0.879594i \(-0.657814\pi\)
−0.475725 + 0.879594i \(0.657814\pi\)
\(278\) 0 0
\(279\) −1.83641 + 3.18076i −0.109943 + 0.190427i
\(280\) 0 0
\(281\) −15.8445 9.14784i −0.945205 0.545714i −0.0536166 0.998562i \(-0.517075\pi\)
−0.891588 + 0.452847i \(0.850408\pi\)
\(282\) 0 0
\(283\) −25.4218 + 14.6773i −1.51117 + 0.872474i −0.511254 + 0.859430i \(0.670819\pi\)
−0.999915 + 0.0130439i \(0.995848\pi\)
\(284\) 0 0
\(285\) −7.96608 + 8.50161i −0.471870 + 0.503592i
\(286\) 0 0
\(287\) −18.2201 31.5582i −1.07550 1.86282i
\(288\) 0 0
\(289\) 7.84565 13.5891i 0.461509 0.799356i
\(290\) 0 0
\(291\) −2.91764 1.68450i −0.171035 0.0987472i
\(292\) 0 0
\(293\) 19.6512i 1.14804i −0.818842 0.574019i \(-0.805384\pi\)
0.818842 0.574019i \(-0.194616\pi\)
\(294\) 0 0
\(295\) 3.57199 6.18687i 0.207969 0.360214i
\(296\) 0 0
\(297\) 2.20364i 0.127868i
\(298\) 0 0
\(299\) −7.66359 13.2737i −0.443197 0.767639i
\(300\) 0 0
\(301\) 1.11515 + 1.93150i 0.0642761 + 0.111330i
\(302\) 0 0
\(303\) 10.2017 0.586070
\(304\) 0 0
\(305\) −34.3064 −1.96438
\(306\) 0 0
\(307\) −3.59046 6.21887i −0.204919 0.354929i 0.745188 0.666854i \(-0.232360\pi\)
−0.950107 + 0.311925i \(0.899026\pi\)
\(308\) 0 0
\(309\) −8.22522 14.2465i −0.467916 0.810455i
\(310\) 0 0
\(311\) 29.1868i 1.65503i 0.561444 + 0.827515i \(0.310246\pi\)
−0.561444 + 0.827515i \(0.689754\pi\)
\(312\) 0 0
\(313\) 7.24482 12.5484i 0.409501 0.709277i −0.585333 0.810793i \(-0.699036\pi\)
0.994834 + 0.101516i \(0.0323694\pi\)
\(314\) 0 0
\(315\) 10.5194i 0.592701i
\(316\) 0 0
\(317\) −2.37562 1.37156i −0.133428 0.0770346i 0.431800 0.901969i \(-0.357879\pi\)
−0.565228 + 0.824935i \(0.691212\pi\)
\(318\) 0 0
\(319\) −2.67282 + 4.62947i −0.149649 + 0.259200i
\(320\) 0 0
\(321\) 2.42801 + 4.20543i 0.135518 + 0.234724i
\(322\) 0 0
\(323\) 1.44648 + 4.77212i 0.0804842 + 0.265528i
\(324\) 0 0
\(325\) 7.72013 4.45722i 0.428236 0.247242i
\(326\) 0 0
\(327\) 12.7345 + 7.35224i 0.704217 + 0.406580i
\(328\) 0 0
\(329\) −24.1625 + 41.8506i −1.33212 + 2.30730i
\(330\) 0 0
\(331\) 10.0761 0.553835 0.276918 0.960894i \(-0.410687\pi\)
0.276918 + 0.960894i \(0.410687\pi\)
\(332\) 0 0
\(333\) 8.70166 + 5.02391i 0.476848 + 0.275308i
\(334\) 0 0
\(335\) 9.27781 0.506901
\(336\) 0 0
\(337\) 3.76555 2.17404i 0.205123 0.118428i −0.393920 0.919145i \(-0.628881\pi\)
0.599043 + 0.800717i \(0.295548\pi\)
\(338\) 0 0
\(339\) −12.5420 + 7.24114i −0.681189 + 0.393285i
\(340\) 0 0
\(341\) 8.09357i 0.438291i
\(342\) 0 0
\(343\) 5.86273i 0.316558i
\(344\) 0 0
\(345\) 8.53279 4.92641i 0.459390 0.265229i
\(346\) 0 0
\(347\) 0.542026 0.312939i 0.0290975 0.0167994i −0.485381 0.874303i \(-0.661319\pi\)
0.514478 + 0.857503i \(0.327986\pi\)
\(348\) 0 0
\(349\) 6.79834 0.363907 0.181953 0.983307i \(-0.441758\pi\)
0.181953 + 0.983307i \(0.441758\pi\)
\(350\) 0 0
\(351\) −3.60083 2.07894i −0.192198 0.110966i
\(352\) 0 0
\(353\) 20.0185 1.06548 0.532738 0.846280i \(-0.321163\pi\)
0.532738 + 0.846280i \(0.321163\pi\)
\(354\) 0 0
\(355\) 16.6913 28.9102i 0.885882 1.53439i
\(356\) 0 0
\(357\) 3.89917 + 2.25119i 0.206366 + 0.119145i
\(358\) 0 0
\(359\) 14.7882 8.53796i 0.780490 0.450616i −0.0561140 0.998424i \(-0.517871\pi\)
0.836604 + 0.547808i \(0.184538\pi\)
\(360\) 0 0
\(361\) 17.0369 + 8.41086i 0.896681 + 0.442677i
\(362\) 0 0
\(363\) −3.07199 5.32085i −0.161238 0.279272i
\(364\) 0 0
\(365\) −3.62438 + 6.27762i −0.189709 + 0.328586i
\(366\) 0 0
\(367\) 25.5277 + 14.7384i 1.33254 + 0.769340i 0.985688 0.168582i \(-0.0539187\pi\)
0.346848 + 0.937921i \(0.387252\pi\)
\(368\) 0 0
\(369\) 9.25893i 0.482001i
\(370\) 0 0
\(371\) 9.29721 16.1032i 0.482687 0.836038i
\(372\) 0 0
\(373\) 26.6745i 1.38116i −0.723258 0.690578i \(-0.757356\pi\)
0.723258 0.690578i \(-0.242644\pi\)
\(374\) 0 0
\(375\) −3.81681 6.61091i −0.197099 0.341386i
\(376\) 0 0
\(377\) 5.04316 + 8.73500i 0.259736 + 0.449876i
\(378\) 0 0
\(379\) 6.80890 0.349750 0.174875 0.984591i \(-0.444048\pi\)
0.174875 + 0.984591i \(0.444048\pi\)
\(380\) 0 0
\(381\) 11.6336 0.596008
\(382\) 0 0
\(383\) −5.23558 9.06829i −0.267526 0.463368i 0.700697 0.713459i \(-0.252873\pi\)
−0.968222 + 0.250091i \(0.919539\pi\)
\(384\) 0 0
\(385\) −11.5905 20.0753i −0.590705 1.02313i
\(386\) 0 0
\(387\) 0.566686i 0.0288063i
\(388\) 0 0
\(389\) −1.25405 + 2.17208i −0.0635830 + 0.110129i −0.896065 0.443924i \(-0.853586\pi\)
0.832482 + 0.554053i \(0.186919\pi\)
\(390\) 0 0
\(391\) 4.21707i 0.213267i
\(392\) 0 0
\(393\) −10.7160 6.18687i −0.540550 0.312087i
\(394\) 0 0
\(395\) 9.37957 16.2459i 0.471937 0.817419i
\(396\) 0 0
\(397\) −4.54316 7.86898i −0.228014 0.394933i 0.729205 0.684295i \(-0.239890\pi\)
−0.957220 + 0.289363i \(0.906557\pi\)
\(398\) 0 0
\(399\) 16.4176 4.97636i 0.821910 0.249129i
\(400\) 0 0
\(401\) −9.97399 + 5.75848i −0.498077 + 0.287565i −0.727919 0.685663i \(-0.759512\pi\)
0.229842 + 0.973228i \(0.426179\pi\)
\(402\) 0 0
\(403\) −13.2252 7.63558i −0.658795 0.380355i
\(404\) 0 0
\(405\) 1.33641 2.31473i 0.0664068 0.115020i
\(406\) 0 0
\(407\) −22.1417 −1.09752
\(408\) 0 0
\(409\) 16.1664 + 9.33368i 0.799378 + 0.461521i 0.843253 0.537516i \(-0.180637\pi\)
−0.0438759 + 0.999037i \(0.513971\pi\)
\(410\) 0 0
\(411\) −9.43196 −0.465244
\(412\) 0 0
\(413\) −9.11007 + 5.25970i −0.448277 + 0.258813i
\(414\) 0 0
\(415\) 4.58651 2.64802i 0.225143 0.129986i
\(416\) 0 0
\(417\) 13.7341i 0.672562i
\(418\) 0 0
\(419\) 27.2053i 1.32907i −0.747259 0.664533i \(-0.768630\pi\)
0.747259 0.664533i \(-0.231370\pi\)
\(420\) 0 0
\(421\) −1.11930 + 0.646229i −0.0545514 + 0.0314953i −0.527028 0.849848i \(-0.676694\pi\)
0.472476 + 0.881343i \(0.343360\pi\)
\(422\) 0 0
\(423\) 10.6336 6.13932i 0.517024 0.298504i
\(424\) 0 0
\(425\) 2.45269 0.118973
\(426\) 0 0
\(427\) 43.7478 + 25.2578i 2.11711 + 1.22231i
\(428\) 0 0
\(429\) 9.16246 0.442368
\(430\) 0 0
\(431\) 10.6336 18.4180i 0.512203 0.887162i −0.487696 0.873013i \(-0.662163\pi\)
0.999900 0.0141492i \(-0.00450397\pi\)
\(432\) 0 0
\(433\) 33.3890 + 19.2771i 1.60457 + 0.926401i 0.990556 + 0.137108i \(0.0437807\pi\)
0.614017 + 0.789293i \(0.289553\pi\)
\(434\) 0 0
\(435\) −5.61515 + 3.24191i −0.269226 + 0.155438i
\(436\) 0 0
\(437\) −11.7252 10.9866i −0.560893 0.525562i
\(438\) 0 0
\(439\) −12.3692 21.4241i −0.590350 1.02252i −0.994185 0.107684i \(-0.965656\pi\)
0.403835 0.914832i \(-0.367677\pi\)
\(440\) 0 0
\(441\) 4.24482 7.35224i 0.202134 0.350107i
\(442\) 0 0
\(443\) 31.5513 + 18.2161i 1.49905 + 0.865474i 0.999999 0.00110093i \(-0.000350438\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(444\) 0 0
\(445\) 39.8964i 1.89127i
\(446\) 0 0
\(447\) 8.15322 14.1218i 0.385634 0.667938i
\(448\) 0 0
\(449\) 28.9509i 1.36628i −0.730289 0.683138i \(-0.760615\pi\)
0.730289 0.683138i \(-0.239385\pi\)
\(450\) 0 0
\(451\) −10.2017 17.6698i −0.480377 0.832038i
\(452\) 0 0
\(453\) 3.52884 + 6.11213i 0.165799 + 0.287173i
\(454\) 0 0
\(455\) −43.7384 −2.05049
\(456\) 0 0
\(457\) −14.2224 −0.665295 −0.332648 0.943051i \(-0.607942\pi\)
−0.332648 + 0.943051i \(0.607942\pi\)
\(458\) 0 0
\(459\) −0.571993 0.990721i −0.0266984 0.0462429i
\(460\) 0 0
\(461\) −18.1677 31.4674i −0.846156 1.46559i −0.884613 0.466325i \(-0.845578\pi\)
0.0384575 0.999260i \(-0.487756\pi\)
\(462\) 0 0
\(463\) 29.6264i 1.37685i −0.725306 0.688427i \(-0.758302\pi\)
0.725306 0.688427i \(-0.241698\pi\)
\(464\) 0 0
\(465\) 4.90841 8.50161i 0.227622 0.394253i
\(466\) 0 0
\(467\) 30.4879i 1.41081i 0.708803 + 0.705407i \(0.249236\pi\)
−0.708803 + 0.705407i \(0.750764\pi\)
\(468\) 0 0
\(469\) −11.8311 6.83071i −0.546311 0.315413i
\(470\) 0 0
\(471\) 5.66246 9.80766i 0.260912 0.451913i
\(472\) 0 0
\(473\) 0.624385 + 1.08147i 0.0287092 + 0.0497259i
\(474\) 0 0
\(475\) 6.38993 6.81950i 0.293190 0.312900i
\(476\) 0 0
\(477\) −4.09159 + 2.36228i −0.187341 + 0.108162i
\(478\) 0 0
\(479\) −20.5882 11.8866i −0.940699 0.543113i −0.0505196 0.998723i \(-0.516088\pi\)
−0.890179 + 0.455610i \(0.849421\pi\)
\(480\) 0 0
\(481\) −20.8888 + 36.1805i −0.952447 + 1.64969i
\(482\) 0 0
\(483\) −14.5081 −0.660142
\(484\) 0 0
\(485\) 7.79834 + 4.50237i 0.354104 + 0.204442i
\(486\) 0 0
\(487\) −10.2880 −0.466193 −0.233096 0.972454i \(-0.574886\pi\)
−0.233096 + 0.972454i \(0.574886\pi\)
\(488\) 0 0
\(489\) −0.793256 + 0.457986i −0.0358723 + 0.0207109i
\(490\) 0 0
\(491\) 28.5513 16.4841i 1.28850 0.743916i 0.310114 0.950699i \(-0.399633\pi\)
0.978387 + 0.206783i \(0.0662996\pi\)
\(492\) 0 0
\(493\) 2.77512i 0.124985i
\(494\) 0 0
\(495\) 5.88993i 0.264733i
\(496\) 0 0
\(497\) −42.5697 + 24.5776i −1.90951 + 1.10246i
\(498\) 0 0
\(499\) −14.2067 + 8.20227i −0.635981 + 0.367184i −0.783065 0.621940i \(-0.786345\pi\)
0.147084 + 0.989124i \(0.453011\pi\)
\(500\) 0 0
\(501\) −0.384851 −0.0171939
\(502\) 0 0
\(503\) −12.8521 7.42014i −0.573045 0.330848i 0.185320 0.982678i \(-0.440668\pi\)
−0.758365 + 0.651831i \(0.774001\pi\)
\(504\) 0 0
\(505\) −27.2672 −1.21338
\(506\) 0 0
\(507\) 2.14399 3.71349i 0.0952178 0.164922i
\(508\) 0 0
\(509\) 24.8168 + 14.3280i 1.09999 + 0.635077i 0.936217 0.351422i \(-0.114302\pi\)
0.163769 + 0.986499i \(0.447635\pi\)
\(510\) 0 0
\(511\) 9.24369 5.33684i 0.408917 0.236088i
\(512\) 0 0
\(513\) −4.24482 0.990721i −0.187413 0.0437414i
\(514\) 0 0
\(515\) 21.9846 + 38.0784i 0.968755 + 1.67793i
\(516\) 0 0
\(517\) −13.5288 + 23.4326i −0.594998 + 1.03057i
\(518\) 0 0
\(519\) −9.34960 5.39799i −0.410402 0.236946i
\(520\) 0 0
\(521\) 0.911178i 0.0399194i −0.999801 0.0199597i \(-0.993646\pi\)
0.999801 0.0199597i \(-0.00635380\pi\)
\(522\) 0 0
\(523\) 5.12043 8.86885i 0.223901 0.387808i −0.732088 0.681210i \(-0.761454\pi\)
0.955989 + 0.293402i \(0.0947875\pi\)
\(524\) 0 0
\(525\) 8.43806i 0.368267i
\(526\) 0 0
\(527\) −2.10083 3.63875i −0.0915136 0.158506i
\(528\) 0 0
\(529\) −4.70561 8.15036i −0.204592 0.354364i
\(530\) 0 0
\(531\) 2.67282 0.115991
\(532\) 0 0
\(533\) −38.4975 −1.66751
\(534\) 0 0
\(535\) −6.48963 11.2404i −0.280571 0.485964i
\(536\) 0 0
\(537\) −0.519602 0.899976i −0.0224225 0.0388368i
\(538\) 0 0
\(539\) 18.7081i 0.805813i
\(540\) 0 0
\(541\) 19.6233 33.9885i 0.843670 1.46128i −0.0431020 0.999071i \(-0.513724\pi\)
0.886772 0.462208i \(-0.152943\pi\)
\(542\) 0 0
\(543\) 7.77627i 0.333712i
\(544\) 0 0
\(545\) −34.0369 19.6512i −1.45798 0.841767i
\(546\) 0 0
\(547\) 5.81794 10.0770i 0.248757 0.430860i −0.714424 0.699713i \(-0.753311\pi\)
0.963181 + 0.268853i \(0.0866446\pi\)
\(548\) 0 0
\(549\) −6.41764 11.1157i −0.273898 0.474406i
\(550\) 0 0
\(551\) 7.71598 + 7.22994i 0.328712 + 0.308006i
\(552\) 0 0
\(553\) −23.9218 + 13.8113i −1.01726 + 0.587314i
\(554\) 0 0
\(555\) −23.2580 13.4280i −0.987247 0.569988i
\(556\) 0 0
\(557\) −0.514319 + 0.890827i −0.0217924 + 0.0377455i −0.876716 0.481008i \(-0.840271\pi\)
0.854924 + 0.518754i \(0.173604\pi\)
\(558\) 0 0
\(559\) 2.35621 0.0996572
\(560\) 0 0
\(561\) 2.18319 + 1.26047i 0.0921743 + 0.0532169i
\(562\) 0 0
\(563\) 4.29588 0.181050 0.0905249 0.995894i \(-0.471146\pi\)
0.0905249 + 0.995894i \(0.471146\pi\)
\(564\) 0 0
\(565\) 33.5226 19.3543i 1.41031 0.814241i
\(566\) 0 0
\(567\) −3.40841 + 1.96784i −0.143140 + 0.0826417i
\(568\) 0 0
\(569\) 25.9992i 1.08995i 0.838454 + 0.544973i \(0.183460\pi\)
−0.838454 + 0.544973i \(0.816540\pi\)
\(570\) 0 0
\(571\) 35.2310i 1.47437i −0.675691 0.737185i \(-0.736154\pi\)
0.675691 0.737185i \(-0.263846\pi\)
\(572\) 0 0
\(573\) 22.7437 13.1311i 0.950131 0.548558i
\(574\) 0 0
\(575\) −6.84452 + 3.95168i −0.285436 + 0.164797i
\(576\) 0 0
\(577\) 9.51037 0.395922 0.197961 0.980210i \(-0.436568\pi\)
0.197961 + 0.980210i \(0.436568\pi\)
\(578\) 0 0
\(579\) −8.23445 4.75416i −0.342212 0.197576i
\(580\) 0 0
\(581\) −7.79834 −0.323530
\(582\) 0 0
\(583\) 5.20561 9.01639i 0.215594 0.373421i
\(584\) 0 0
\(585\) 9.62438 + 5.55664i 0.397919 + 0.229739i
\(586\) 0 0
\(587\) −9.84452 + 5.68373i −0.406327 + 0.234593i −0.689210 0.724561i \(-0.742042\pi\)
0.282884 + 0.959154i \(0.408709\pi\)
\(588\) 0 0
\(589\) −15.5905 3.63875i −0.642394 0.149932i
\(590\) 0 0
\(591\) −13.9661 24.1900i −0.574488 0.995042i
\(592\) 0 0
\(593\) 12.9269 22.3900i 0.530843 0.919447i −0.468509 0.883459i \(-0.655209\pi\)
0.999352 0.0359886i \(-0.0114580\pi\)
\(594\) 0 0
\(595\) −10.4218 6.01702i −0.427252 0.246674i
\(596\) 0 0
\(597\) 7.93928i 0.324933i
\(598\) 0 0
\(599\) −2.56276 + 4.43883i −0.104711 + 0.181366i −0.913620 0.406569i \(-0.866725\pi\)
0.808909 + 0.587934i \(0.200059\pi\)
\(600\) 0 0
\(601\) 12.7822i 0.521398i 0.965420 + 0.260699i \(0.0839530\pi\)
−0.965420 + 0.260699i \(0.916047\pi\)
\(602\) 0 0
\(603\) 1.73558 + 3.00612i 0.0706783 + 0.122418i
\(604\) 0 0
\(605\) 8.21090 + 14.2217i 0.333820 + 0.578194i
\(606\) 0 0
\(607\) −31.7882 −1.29024 −0.645121 0.764080i \(-0.723193\pi\)
−0.645121 + 0.764080i \(0.723193\pi\)
\(608\) 0 0
\(609\) 9.54731 0.386876
\(610\) 0 0
\(611\) 25.5266 + 44.2133i 1.03269 + 1.78868i
\(612\) 0 0
\(613\) −21.1664 36.6613i −0.854903 1.48074i −0.876735 0.480974i \(-0.840283\pi\)
0.0218315 0.999762i \(-0.493050\pi\)
\(614\) 0 0
\(615\) 24.7475i 0.997915i
\(616\) 0 0
\(617\) −10.1717 + 17.6179i −0.409497 + 0.709270i −0.994833 0.101521i \(-0.967629\pi\)
0.585336 + 0.810791i \(0.300962\pi\)
\(618\) 0 0
\(619\) 13.1402i 0.528150i −0.964502 0.264075i \(-0.914933\pi\)
0.964502 0.264075i \(-0.0850667\pi\)
\(620\) 0 0
\(621\) 3.19243 + 1.84315i 0.128108 + 0.0739630i
\(622\) 0 0
\(623\) 29.3734 50.8761i 1.17682 2.03831i
\(624\) 0 0
\(625\) 15.5616 + 26.9535i 0.622465 + 1.07814i
\(626\) 0 0
\(627\) 9.19243 2.78632i 0.367110 0.111275i
\(628\) 0 0
\(629\) −9.95458 + 5.74728i −0.396915 + 0.229159i
\(630\) 0 0
\(631\) 3.57312 + 2.06294i 0.142244 + 0.0821245i 0.569433 0.822038i \(-0.307163\pi\)
−0.427189 + 0.904162i \(0.640496\pi\)
\(632\) 0 0
\(633\) 4.32605 7.49293i 0.171945 0.297817i
\(634\) 0 0
\(635\) −31.0946 −1.23395
\(636\) 0 0
\(637\) 30.5697 + 17.6494i 1.21122 + 0.699296i
\(638\) 0 0
\(639\) 12.4896 0.494082
\(640\) 0 0
\(641\) 31.9714 18.4587i 1.26279 0.729074i 0.289179 0.957275i \(-0.406618\pi\)
0.973614 + 0.228201i \(0.0732844\pi\)
\(642\) 0 0
\(643\) 6.62854 3.82699i 0.261404 0.150922i −0.363571 0.931567i \(-0.618443\pi\)
0.624975 + 0.780645i \(0.285109\pi\)
\(644\) 0 0
\(645\) 1.51465i 0.0596394i
\(646\) 0 0
\(647\) 26.5387i 1.04335i 0.853146 + 0.521673i \(0.174692\pi\)
−0.853146 + 0.521673i \(0.825308\pi\)
\(648\) 0 0
\(649\) −5.10083 + 2.94497i −0.200225 + 0.115600i
\(650\) 0 0
\(651\) −12.5185 + 7.22754i −0.490638 + 0.283270i
\(652\) 0 0
\(653\) −2.23860 −0.0876033 −0.0438017 0.999040i \(-0.513947\pi\)
−0.0438017 + 0.999040i \(0.513947\pi\)
\(654\) 0 0
\(655\) 28.6419 + 16.5364i 1.11913 + 0.646132i
\(656\) 0 0
\(657\) −2.71203 −0.105806
\(658\) 0 0
\(659\) 3.43724 5.95348i 0.133896 0.231915i −0.791279 0.611455i \(-0.790585\pi\)
0.925175 + 0.379540i \(0.123918\pi\)
\(660\) 0 0
\(661\) 32.2386 + 18.6130i 1.25394 + 0.723960i 0.971889 0.235440i \(-0.0756531\pi\)
0.282047 + 0.959400i \(0.408986\pi\)
\(662\) 0 0
\(663\) 4.11930 2.37828i 0.159980 0.0923647i
\(664\) 0 0
\(665\) −43.8815 + 13.3009i −1.70165 + 0.515788i
\(666\) 0 0
\(667\) −4.47116 7.74428i −0.173124 0.299860i
\(668\) 0 0
\(669\) 7.18206 12.4397i 0.277674 0.480946i
\(670\) 0 0
\(671\) 24.4949 + 14.1421i 0.945616 + 0.545952i
\(672\) 0 0
\(673\) 40.4406i 1.55887i −0.626482 0.779436i \(-0.715506\pi\)
0.626482 0.779436i \(-0.284494\pi\)
\(674\) 0 0
\(675\) −1.07199 + 1.85675i −0.0412610 + 0.0714662i
\(676\) 0 0
\(677\) 14.1650i 0.544405i −0.962240 0.272202i \(-0.912248\pi\)
0.962240 0.272202i \(-0.0877520\pi\)
\(678\) 0 0
\(679\) −6.62967 11.4829i −0.254423 0.440674i
\(680\) 0 0
\(681\) 7.09159 + 12.2830i 0.271751 + 0.470686i
\(682\) 0 0
\(683\) −23.8952 −0.914325 −0.457163 0.889383i \(-0.651134\pi\)
−0.457163 + 0.889383i \(0.651134\pi\)
\(684\) 0 0
\(685\) 25.2100 0.963223
\(686\) 0 0
\(687\) 8.27365 + 14.3304i 0.315660 + 0.546738i
\(688\) 0 0
\(689\) −9.82209 17.0124i −0.374192 0.648119i
\(690\) 0 0
\(691\) 19.0166i 0.723427i 0.932289 + 0.361714i \(0.117808\pi\)
−0.932289 + 0.361714i \(0.882192\pi\)
\(692\) 0 0
\(693\) 4.33641 7.51089i 0.164727 0.285315i
\(694\) 0 0
\(695\) 36.7088i 1.39245i
\(696\) 0 0
\(697\) −9.17302 5.29605i −0.347453 0.200602i
\(698\) 0 0
\(699\) 13.1193 22.7233i 0.496218 0.859474i
\(700\) 0 0
\(701\) 14.2109 + 24.6140i 0.536738 + 0.929658i 0.999077 + 0.0429544i \(0.0136770\pi\)
−0.462339 + 0.886703i \(0.652990\pi\)
\(702\) 0 0
\(703\) −9.95458 + 42.6511i −0.375444 + 1.60862i
\(704\) 0 0
\(705\) −28.4218 + 16.4093i −1.07043 + 0.618011i
\(706\) 0 0
\(707\) 34.7714 + 20.0753i 1.30771 + 0.755008i
\(708\) 0 0
\(709\) 13.8681 24.0202i 0.520826 0.902098i −0.478880 0.877880i \(-0.658957\pi\)
0.999707 0.0242175i \(-0.00770943\pi\)
\(710\) 0 0
\(711\) 7.01847 0.263213
\(712\) 0 0
\(713\) 11.7252 + 6.76956i 0.439113 + 0.253522i
\(714\) 0 0
\(715\) −24.4896 −0.915860
\(716\) 0 0
\(717\) 1.09159 0.630233i 0.0407664 0.0235365i
\(718\) 0 0
\(719\) −0.844517 + 0.487582i −0.0314952 + 0.0181837i −0.515665 0.856790i \(-0.672455\pi\)
0.484170 + 0.874974i \(0.339122\pi\)
\(720\) 0 0
\(721\) 64.7438i 2.41118i
\(722\) 0 0
\(723\) 20.9389i 0.778726i
\(724\) 0 0
\(725\) 4.50415 2.60047i 0.167280 0.0965792i
\(726\) 0 0
\(727\) 22.6924 13.1015i 0.841615 0.485907i −0.0161975 0.999869i \(-0.505156\pi\)
0.857813 + 0.513962i \(0.171823\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.561428 + 0.324141i 0.0207652 + 0.0119888i
\(732\) 0 0
\(733\) 27.2751 1.00743 0.503715 0.863870i \(-0.331966\pi\)
0.503715 + 0.863870i \(0.331966\pi\)
\(734\) 0 0
\(735\) −11.3456 + 19.6512i −0.418491 + 0.724847i
\(736\) 0 0
\(737\) −6.62438 3.82459i −0.244012 0.140881i
\(738\) 0 0
\(739\) −21.2908 + 12.2922i −0.783195 + 0.452178i −0.837561 0.546343i \(-0.816019\pi\)
0.0543667 + 0.998521i \(0.482686\pi\)
\(740\) 0 0
\(741\) 4.11930 17.6494i 0.151326 0.648368i
\(742\) 0 0
\(743\) 24.1101 + 41.7599i 0.884513 + 1.53202i 0.846271 + 0.532752i \(0.178842\pi\)
0.0382412 + 0.999269i \(0.487824\pi\)
\(744\) 0 0
\(745\) −21.7921 + 37.7451i −0.798402 + 1.38287i
\(746\) 0 0
\(747\) 1.71598 + 0.990721i 0.0627844 + 0.0362486i
\(748\) 0 0
\(749\) 19.1118i 0.698328i
\(750\) 0 0
\(751\) −16.2437 + 28.1349i −0.592741 + 1.02666i 0.401121 + 0.916025i \(0.368621\pi\)
−0.993861 + 0.110632i \(0.964713\pi\)
\(752\) 0 0
\(753\) 28.4658i 1.03735i
\(754\) 0 0
\(755\) −9.43196 16.3366i −0.343264 0.594551i
\(756\) 0 0
\(757\) −11.5801 20.0573i −0.420886 0.728996i 0.575141 0.818055i \(-0.304947\pi\)
−0.996026 + 0.0890590i \(0.971614\pi\)
\(758\) 0 0
\(759\) −8.12325 −0.294855
\(760\) 0 0
\(761\) −18.5496 −0.672421 −0.336211 0.941787i \(-0.609145\pi\)
−0.336211 + 0.941787i \(0.609145\pi\)
\(762\) 0 0
\(763\) 28.9361 + 50.1188i 1.04756 + 1.81442i
\(764\) 0 0
\(765\) 1.52884 + 2.64802i 0.0552752 + 0.0957395i
\(766\) 0 0
\(767\) 11.1133i 0.401277i
\(768\) 0 0
\(769\) −18.8249 + 32.6057i −0.678844 + 1.17579i 0.296486 + 0.955037i \(0.404185\pi\)
−0.975329 + 0.220755i \(0.929148\pi\)
\(770\) 0 0
\(771\) 12.0972i 0.435668i
\(772\) 0 0
\(773\) −0.981529 0.566686i −0.0353031 0.0203823i 0.482245 0.876037i \(-0.339822\pi\)
−0.517548 + 0.855654i \(0.673155\pi\)
\(774\) 0 0
\(775\) −3.93724 + 6.81950i −0.141430 + 0.244964i
\(776\) 0 0
\(777\) 19.7725 + 34.2470i 0.709335 + 1.22860i
\(778\) 0 0
\(779\) −38.6235 + 11.7072i −1.38383 + 0.419453i
\(780\) 0 0
\(781\) −23.8353 + 13.7613i −0.852893 + 0.492418i
\(782\) 0 0
\(783\) −2.10083 1.21292i −0.0750776 0.0433460i
\(784\) 0 0
\(785\) −15.1348 + 26.2142i −0.540182 + 0.935623i
\(786\) 0 0
\(787\) 13.9687 0.497930 0.248965 0.968512i \(-0.419910\pi\)
0.248965 + 0.968512i \(0.419910\pi\)
\(788\) 0 0
\(789\) 1.11930 + 0.646229i 0.0398482 + 0.0230064i
\(790\) 0 0
\(791\) −56.9977 −2.02661
\(792\) 0 0
\(793\) 46.2177 26.6838i 1.64124 0.947569i
\(794\) 0 0
\(795\) 10.9361 6.31397i 0.387864 0.223933i
\(796\) 0 0