Properties

Label 980.2.i.h.361.1
Level $980$
Weight $2$
Character 980.361
Analytic conductor $7.825$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 980.361
Dual form 980.2.i.h.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000 q^{13} +1.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} -9.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(1.50000 + 2.59808i) q^{33} +(5.00000 + 8.66025i) q^{37} +(0.500000 - 0.866025i) q^{39} +2.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-1.50000 - 2.59808i) q^{47} +(1.50000 + 2.59808i) q^{51} -3.00000 q^{55} +2.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(4.00000 + 6.92820i) q^{61} +(0.500000 + 0.866025i) q^{65} +(-4.00000 + 6.92820i) q^{67} +6.00000 q^{69} +(7.00000 - 12.1244i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} -3.00000 q^{85} +(-4.50000 + 7.79423i) q^{87} +(6.00000 + 10.3923i) q^{89} +(-4.00000 - 6.92820i) q^{93} +(-1.00000 + 1.73205i) q^{95} -17.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + q^{5} + 2 q^{9} + O(q^{10}) \) \( 2 q + q^{3} + q^{5} + 2 q^{9} - 3 q^{11} + 2 q^{13} + 2 q^{15} - 3 q^{17} + 2 q^{19} + 6 q^{23} - q^{25} + 10 q^{27} - 18 q^{29} + 8 q^{31} + 3 q^{33} + 10 q^{37} + q^{39} + 4 q^{43} - 2 q^{45} - 3 q^{47} + 3 q^{51} - 6 q^{55} + 4 q^{57} + 12 q^{59} + 8 q^{61} + q^{65} - 8 q^{67} + 12 q^{69} + 14 q^{73} + q^{75} - 5 q^{79} - q^{81} + 24 q^{83} - 6 q^{85} - 9 q^{87} + 12 q^{89} - 8 q^{93} - 2 q^{95} - 34 q^{97} - 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.00000 + 8.66025i 0.821995 + 1.42374i 0.904194 + 0.427121i \(0.140472\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 0 0
\(53\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) 0 0
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) 0 0
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) −4.50000 + 7.79423i −0.482451 + 0.835629i
\(88\) 0 0
\(89\) 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i \(0.0527450\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 0 0
\(95\) −1.00000 + 1.73205i −0.102598 + 0.177705i
\(96\) 0 0
\(97\) −17.0000 −1.72609 −0.863044 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) −3.50000 6.06218i −0.344865 0.597324i 0.640464 0.767988i \(-0.278742\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 0 0
\(109\) 9.50000 16.4545i 0.909935 1.57605i 0.0957826 0.995402i \(-0.469465\pi\)
0.814152 0.580651i \(-0.197202\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −3.00000 + 5.19615i −0.279751 + 0.484544i
\(116\) 0 0
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) 1.00000 1.73205i 0.0880451 0.152499i
\(130\) 0 0
\(131\) −9.00000 15.5885i −0.786334 1.36197i −0.928199 0.372084i \(-0.878643\pi\)
0.141865 0.989886i \(-0.454690\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) −1.50000 + 2.59808i −0.125436 + 0.217262i
\(144\) 0 0
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) 9.50000 16.4545i 0.773099 1.33905i −0.162758 0.986666i \(-0.552039\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) −11.0000 + 19.0526i −0.877896 + 1.52056i −0.0242497 + 0.999706i \(0.507720\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 0 0
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 0 0
\(167\) −9.00000 −0.696441 −0.348220 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) 0 0
\(173\) −1.50000 2.59808i −0.114043 0.197528i 0.803354 0.595502i \(-0.203047\pi\)
−0.917397 + 0.397974i \(0.869713\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 10.3923i −0.450988 0.781133i
\(178\) 0 0
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) −5.00000 + 8.66025i −0.367607 + 0.636715i
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.50000 2.59808i −0.108536 0.187990i 0.806641 0.591041i \(-0.201283\pi\)
−0.915177 + 0.403051i \(0.867950\pi\)
\(192\) 0 0
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 0 0
\(201\) 4.00000 + 6.92820i 0.282138 + 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −7.00000 12.1244i −0.473016 0.819288i
\(220\) 0 0
\(221\) −1.50000 + 2.59808i −0.100901 + 0.174766i
\(222\) 0 0
\(223\) −17.0000 −1.13840 −0.569202 0.822198i \(-0.692748\pi\)
−0.569202 + 0.822198i \(0.692748\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) −13.5000 + 23.3827i −0.896026 + 1.55196i −0.0634974 + 0.997982i \(0.520225\pi\)
−0.832529 + 0.553981i \(0.813108\pi\)
\(228\) 0 0
\(229\) −8.00000 13.8564i −0.528655 0.915657i −0.999442 0.0334101i \(-0.989363\pi\)
0.470787 0.882247i \(-0.343970\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.0000 20.7846i −0.786146 1.36165i −0.928312 0.371802i \(-0.878740\pi\)
0.142166 0.989843i \(-0.454593\pi\)
\(234\) 0 0
\(235\) 1.50000 2.59808i 0.0978492 0.169480i
\(236\) 0 0
\(237\) −5.00000 −0.324785
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 + 1.73205i 0.0636285 + 0.110208i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) −1.50000 + 2.59808i −0.0939336 + 0.162698i
\(256\) 0 0
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −9.00000 15.5885i −0.557086 0.964901i
\(262\) 0 0
\(263\) 15.0000 25.9808i 0.924940 1.60204i 0.133281 0.991078i \(-0.457449\pi\)
0.791658 0.610964i \(-0.209218\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 0 0
\(277\) 11.0000 19.0526i 0.660926 1.14476i −0.319447 0.947604i \(-0.603497\pi\)
0.980373 0.197153i \(-0.0631696\pi\)
\(278\) 0 0
\(279\) 16.0000 0.957895
\(280\) 0 0
\(281\) −21.0000 −1.25275 −0.626377 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) 0 0
\(283\) 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i \(-0.727315\pi\)
0.981903 + 0.189383i \(0.0606488\pi\)
\(284\) 0 0
\(285\) 1.00000 + 1.73205i 0.0592349 + 0.102598i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) 0 0
\(293\) 15.0000 0.876309 0.438155 0.898900i \(-0.355632\pi\)
0.438155 + 0.898900i \(0.355632\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 0 0
\(297\) −7.50000 + 12.9904i −0.435194 + 0.753778i
\(298\) 0 0
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 0 0
\(305\) −4.00000 + 6.92820i −0.229039 + 0.396708i
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) 9.00000 15.5885i 0.510343 0.883940i −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) 0 0
\(313\) −6.50000 11.2583i −0.367402 0.636358i 0.621757 0.783210i \(-0.286419\pi\)
−0.989158 + 0.146852i \(0.953086\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 13.5000 23.3827i 0.755855 1.30918i
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) −0.500000 + 0.866025i −0.0277350 + 0.0480384i
\(326\) 0 0
\(327\) −9.50000 16.4545i −0.525351 0.909935i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 0 0
\(333\) −10.0000 + 17.3205i −0.547997 + 0.949158i
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) 12.0000 + 20.7846i 0.649836 + 1.12555i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 3.00000 + 5.19615i 0.161515 + 0.279751i
\(346\) 0 0
\(347\) −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −7.50000 + 12.9904i −0.399185 + 0.691408i −0.993626 0.112731i \(-0.964040\pi\)
0.594441 + 0.804139i \(0.297373\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i \(-0.791675\pi\)
0.923869 + 0.382709i \(0.125009\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) −9.00000 −0.463524
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 10.0000 17.3205i 0.512316 0.887357i
\(382\) 0 0
\(383\) 18.0000 + 31.1769i 0.919757 + 1.59307i 0.799783 + 0.600289i \(0.204948\pi\)
0.119974 + 0.992777i \(0.461719\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 0 0
\(389\) −4.50000 + 7.79423i −0.228159 + 0.395183i −0.957263 0.289220i \(-0.906604\pi\)
0.729103 + 0.684403i \(0.239937\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) 0 0
\(395\) 2.50000 4.33013i 0.125789 0.217872i
\(396\) 0 0
\(397\) 2.50000 + 4.33013i 0.125471 + 0.217323i 0.921917 0.387387i \(-0.126622\pi\)
−0.796446 + 0.604710i \(0.793289\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 0 0
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −30.0000 −1.48704
\(408\) 0 0
\(409\) 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i \(-0.611102\pi\)
0.984803 0.173675i \(-0.0555643\pi\)
\(410\) 0 0
\(411\) 6.00000 + 10.3923i 0.295958 + 0.512615i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 0 0
\(417\) −1.00000 + 1.73205i −0.0489702 + 0.0848189i
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 29.0000 1.41337 0.706687 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) 0 0
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 0 0
\(425\) −1.50000 2.59808i −0.0727607 0.126025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.50000 + 2.59808i 0.0724207 + 0.125436i
\(430\) 0 0
\(431\) −7.50000 + 12.9904i −0.361262 + 0.625725i −0.988169 0.153370i \(-0.950987\pi\)
0.626907 + 0.779094i \(0.284321\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) −9.00000 −0.431517
\(436\) 0 0
\(437\) −6.00000 + 10.3923i −0.287019 + 0.497131i
\(438\) 0 0
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.00000 + 5.19615i 0.142534 + 0.246877i 0.928450 0.371457i \(-0.121142\pi\)
−0.785916 + 0.618333i \(0.787808\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 0 0
\(447\) −18.0000 −0.851371
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −9.50000 16.4545i −0.446349 0.773099i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.0000 + 24.2487i 0.654892 + 1.13431i 0.981921 + 0.189292i \(0.0606194\pi\)
−0.327028 + 0.945015i \(0.606047\pi\)
\(458\) 0 0
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 4.00000 6.92820i 0.185496 0.321288i
\(466\) 0 0
\(467\) 7.50000 + 12.9904i 0.347059 + 0.601123i 0.985726 0.168360i \(-0.0538472\pi\)
−0.638667 + 0.769483i \(0.720514\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) 0 0
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 0 0
\(481\) 5.00000 + 8.66025i 0.227980 + 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.50000 14.7224i −0.385965 0.668511i
\(486\) 0 0
\(487\) 5.00000 8.66025i 0.226572 0.392434i −0.730218 0.683214i \(-0.760582\pi\)
0.956790 + 0.290780i \(0.0939149\pi\)
\(488\) 0 0
\(489\) −2.00000 −0.0904431
\(490\) 0 0
\(491\) −15.0000 −0.676941 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 0 0
\(493\) 13.5000 23.3827i 0.608009 1.05310i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) −4.50000 + 7.79423i −0.201045 + 0.348220i
\(502\) 0 0
\(503\) 33.0000 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 0 0
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 5.00000 + 8.66025i 0.220755 + 0.382360i
\(514\) 0 0
\(515\) 3.50000 6.06218i 0.154228 0.267131i
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) 0 0
\(519\) −3.00000 −0.131685
\(520\) 0 0
\(521\) −15.0000 + 25.9808i −0.657162 + 1.13824i 0.324185 + 0.945994i \(0.394910\pi\)
−0.981347 + 0.192244i \(0.938423\pi\)
\(522\) 0 0
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.0000 + 20.7846i 0.522728 + 0.905392i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 24.0000 1.04151
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.5000 + 21.6506i 0.537417 + 0.930834i 0.999042 + 0.0437584i \(0.0139332\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(542\) 0 0
\(543\) −4.00000 + 6.92820i −0.171656 + 0.297318i
\(544\) 0 0
\(545\) 19.0000 0.813871
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 0 0
\(549\) −8.00000 + 13.8564i −0.341432 + 0.591377i
\(550\) 0 0
\(551\) −9.00000 15.5885i −0.383413 0.664091i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 5.00000 + 8.66025i 0.212238 + 0.367607i
\(556\) 0 0
\(557\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 0 0
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) 23.5000 40.7032i 0.978318 1.69450i 0.309797 0.950803i \(-0.399739\pi\)
0.668521 0.743693i \(-0.266928\pi\)
\(578\) 0 0
\(579\) −2.00000 3.46410i −0.0831172 0.143963i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.00000 + 1.73205i −0.0413449 + 0.0716115i
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 0 0
\(593\) −16.5000 28.5788i −0.677574 1.17359i −0.975709 0.219069i \(-0.929698\pi\)
0.298136 0.954524i \(-0.403635\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −10.0000 17.3205i −0.409273 0.708881i
\(598\) 0 0
\(599\) 4.50000 7.79423i 0.183865 0.318464i −0.759328 0.650708i \(-0.774472\pi\)
0.943193 + 0.332244i \(0.107806\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −16.0000 −0.651570
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.50000 2.59808i −0.0606835 0.105107i
\(612\) 0 0
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) −5.00000 + 8.66025i −0.200967 + 0.348085i −0.948840 0.315757i \(-0.897742\pi\)
0.747873 + 0.663842i \(0.231075\pi\)
\(620\) 0 0
\(621\) 15.0000 + 25.9808i 0.601929 + 1.04257i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) 0 0
\(629\) −30.0000 −1.19618
\(630\) 0 0
\(631\) −25.0000 −0.995234 −0.497617 0.867397i \(-0.665792\pi\)
−0.497617 + 0.867397i \(0.665792\pi\)
\(632\) 0 0
\(633\) 2.50000 4.33013i 0.0993661 0.172107i
\(634\) 0 0
\(635\) 10.0000 + 17.3205i 0.396838 + 0.687343i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 0 0
\(643\) −41.0000 −1.61688 −0.808441 0.588577i \(-0.799688\pi\)
−0.808441 + 0.588577i \(0.799688\pi\)
\(644\) 0 0
\(645\) 2.00000 0.0787499
\(646\) 0 0
\(647\) 24.0000 41.5692i 0.943537 1.63425i 0.184884 0.982760i \(-0.440809\pi\)
0.758654 0.651494i \(-0.225858\pi\)
\(648\) 0 0
\(649\) 18.0000 + 31.1769i 0.706562 + 1.22380i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 0 0
\(655\) 9.00000 15.5885i 0.351659 0.609091i
\(656\) 0 0
\(657\) 28.0000 1.09238
\(658\) 0 0
\(659\) −33.0000 −1.28550 −0.642749 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) 0 0
\(661\) 4.00000 6.92820i 0.155582 0.269476i −0.777689 0.628649i \(-0.783608\pi\)
0.933271 + 0.359174i \(0.116941\pi\)
\(662\) 0 0
\(663\) 1.50000 + 2.59808i 0.0582552 + 0.100901i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −27.0000 46.7654i −1.04544 1.81076i
\(668\) 0 0
\(669\) −8.50000 + 14.7224i −0.328629 + 0.569202i
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 0 0
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 0 0
\(677\) 7.50000 + 12.9904i 0.288248 + 0.499261i 0.973392 0.229147i \(-0.0735938\pi\)
−0.685143 + 0.728408i \(0.740260\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.5000 + 23.3827i 0.517321 + 0.896026i
\(682\) 0 0
\(683\) −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −16.0000 −0.610438
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −14.0000 24.2487i −0.532585 0.922464i −0.999276 0.0380440i \(-0.987887\pi\)
0.466691 0.884420i \(-0.345446\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.00000 1.73205i −0.0379322 0.0657004i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) 3.00000 0.113308 0.0566542 0.998394i \(-0.481957\pi\)
0.0566542 + 0.998394i \(0.481957\pi\)
\(702\) 0 0
\(703\) −10.0000 + 17.3205i −0.377157 + 0.653255i
\(704\) 0 0
\(705\) −1.50000 2.59808i −0.0564933 0.0978492i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.500000 + 0.866025i 0.0187779 + 0.0325243i 0.875262 0.483650i \(-0.160689\pi\)
−0.856484 + 0.516174i \(0.827356\pi\)
\(710\) 0 0
\(711\) 5.00000 8.66025i 0.187515 0.324785i
\(712\) 0 0
\(713\) 48.0000 1.79761
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) 0 0
\(717\) 4.50000 7.79423i 0.168056 0.291081i
\(718\) 0 0
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 5.00000 + 8.66025i 0.185952 + 0.322078i
\(724\) 0 0
\(725\) 4.50000 7.79423i 0.167126 0.289470i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −3.00000 + 5.19615i −0.110959 + 0.192187i
\(732\) 0 0
\(733\) −6.50000 11.2583i −0.240083 0.415836i 0.720655 0.693294i \(-0.243841\pi\)
−0.960738 + 0.277458i \(0.910508\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) 0 0
\(739\) −5.50000 + 9.52628i −0.202321 + 0.350430i −0.949276 0.314445i \(-0.898182\pi\)
0.746955 + 0.664875i \(0.231515\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −26.5000 45.8993i −0.966999 1.67489i −0.704146 0.710055i \(-0.748670\pi\)
−0.262852 0.964836i \(-0.584663\pi\)
\(752\) 0 0
\(753\) −3.00000 + 5.19615i −0.109326 + 0.189358i
\(754\) 0 0
\(755\) 19.0000 0.691481
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 0 0
\(759\) −9.00000 + 15.5885i −0.326679 + 0.565825i
\(760\) 0 0
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) 0 0
\(767\) 6.00000 10.3923i 0.216647 0.375244i
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) 7.50000 12.9904i 0.269756 0.467232i −0.699043 0.715080i \(-0.746390\pi\)
0.968799 + 0.247849i \(0.0797235\pi\)
\(774\) 0 0
\(775\) 4.00000 + 6.92820i 0.143684 + 0.248868i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −45.0000 −1.60817
\(784\) 0 0
\(785\) −22.0000 −0.785214
\(786\) 0 0
\(787\) 2.50000 4.33013i 0.0891154 0.154352i −0.818022 0.575187i \(-0.804929\pi\)
0.907137 + 0.420834i \(0.138263\pi\)
\(788\) 0 0
\(789\) −15.0000 25.9808i −0.534014 0.924940i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 4.00000 + 6.92820i 0.142044 + 0.246028i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.00000 0.106265 0.0531327 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) 0 0
\(801\) −12.0000 + 20.7846i −0.423999 + 0.734388i