Properties

Label 1400.2.bh.b.849.2
Level $1400$
Weight $2$
Character 1400.849
Analytic conductor $11.179$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 849.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1400.849
Dual form 1400.2.bh.b.249.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{3} +(-0.866025 + 2.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{3} +(-0.866025 + 2.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(-3.46410 + 2.00000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-0.866025 - 0.500000i) q^{23} +5.00000i q^{27} -9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-1.73205 - 1.00000i) q^{33} +(3.46410 + 2.00000i) q^{37} +1.00000 q^{41} +9.00000i q^{43} +(-5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-8.66025 + 5.00000i) q^{53} +2.00000i q^{57} +(-5.00000 - 8.66025i) q^{59} +(-4.50000 + 7.79423i) q^{61} +(-3.46410 - 4.00000i) q^{63} +(-4.33013 + 2.50000i) q^{67} -1.00000 q^{69} +14.0000 q^{71} +(10.3923 - 6.00000i) q^{73} +(5.19615 - 1.00000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +11.0000i q^{83} +(-7.79423 + 4.50000i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(-3.46410 - 2.00000i) q^{93} +18.0000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{9} - 4 q^{11} - 4 q^{19} + 2 q^{21} - 36 q^{29} - 8 q^{31} + 4 q^{41} - 22 q^{49} - 8 q^{51} - 20 q^{59} - 18 q^{61} - 4 q^{69} + 56 q^{71} + 28 q^{79} - 2 q^{81} - 30 q^{89} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.866025 0.500000i 0.500000 0.288675i −0.228714 0.973494i \(-0.573452\pi\)
0.728714 + 0.684819i \(0.240119\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.866025 + 2.50000i −0.327327 + 0.944911i
\(8\) 0 0
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.46410 + 2.00000i −0.840168 + 0.485071i −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0.500000 + 2.59808i 0.109109 + 0.566947i
\(22\) 0 0
\(23\) −0.866025 0.500000i −0.180579 0.104257i 0.406986 0.913434i \(-0.366580\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.46410 + 2.00000i 0.569495 + 0.328798i 0.756948 0.653476i \(-0.226690\pi\)
−0.187453 + 0.982274i \(0.560023\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.00000 0.156174 0.0780869 0.996947i \(-0.475119\pi\)
0.0780869 + 0.996947i \(0.475119\pi\)
\(42\) 0 0
\(43\) 9.00000i 1.37249i 0.727372 + 0.686244i \(0.240742\pi\)
−0.727372 + 0.686244i \(0.759258\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 0 0
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) −8.66025 + 5.00000i −1.18958 + 0.686803i −0.958211 0.286064i \(-0.907653\pi\)
−0.231367 + 0.972867i \(0.574320\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000i 0.264906i
\(58\) 0 0
\(59\) −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i \(-0.941040\pi\)
0.331949 0.943297i \(-0.392294\pi\)
\(60\) 0 0
\(61\) −4.50000 + 7.79423i −0.576166 + 0.997949i 0.419748 + 0.907641i \(0.362118\pi\)
−0.995914 + 0.0903080i \(0.971215\pi\)
\(62\) 0 0
\(63\) −3.46410 4.00000i −0.436436 0.503953i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.33013 + 2.50000i −0.529009 + 0.305424i −0.740613 0.671932i \(-0.765465\pi\)
0.211604 + 0.977356i \(0.432131\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 0 0
\(73\) 10.3923 6.00000i 1.21633 0.702247i 0.252197 0.967676i \(-0.418847\pi\)
0.964130 + 0.265429i \(0.0855136\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.19615 1.00000i 0.592157 0.113961i
\(78\) 0 0
\(79\) 7.00000 12.1244i 0.787562 1.36410i −0.139895 0.990166i \(-0.544677\pi\)
0.927457 0.373930i \(-0.121990\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 11.0000i 1.20741i 0.797209 + 0.603703i \(0.206309\pi\)
−0.797209 + 0.603703i \(0.793691\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −7.79423 + 4.50000i −0.835629 + 0.482451i
\(88\) 0 0
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.46410 2.00000i −0.359211 0.207390i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 18.0000i 1.82762i 0.406138 + 0.913812i \(0.366875\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) 11.2583 + 6.50000i 1.10932 + 0.640464i 0.938652 0.344865i \(-0.112075\pi\)
0.170664 + 0.985329i \(0.445409\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.79423 + 4.50000i 0.753497 + 0.435031i 0.826956 0.562267i \(-0.190071\pi\)
−0.0734594 + 0.997298i \(0.523404\pi\)
\(108\) 0 0
\(109\) −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i \(-0.181917\pi\)
−0.888977 + 0.457951i \(0.848583\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 2.00000i 0.188144i 0.995565 + 0.0940721i \(0.0299884\pi\)
−0.995565 + 0.0940721i \(0.970012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.00000 10.3923i −0.183340 0.952661i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) 0.866025 0.500000i 0.0780869 0.0450835i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 0 0
\(129\) 4.50000 + 7.79423i 0.396203 + 0.686244i
\(130\) 0 0
\(131\) 4.00000 6.92820i 0.349482 0.605320i −0.636676 0.771132i \(-0.719691\pi\)
0.986157 + 0.165812i \(0.0530244\pi\)
\(132\) 0 0
\(133\) −3.46410 4.00000i −0.300376 0.346844i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.3923 + 6.00000i −0.887875 + 0.512615i −0.873247 0.487278i \(-0.837990\pi\)
−0.0146279 + 0.999893i \(0.504656\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.92820 1.00000i −0.571429 0.0824786i
\(148\) 0 0
\(149\) −2.50000 + 4.33013i −0.204808 + 0.354738i −0.950072 0.312032i \(-0.898990\pi\)
0.745264 + 0.666770i \(0.232324\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 8.00000i 0.646762i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.73205 + 1.00000i −0.138233 + 0.0798087i −0.567521 0.823359i \(-0.692098\pi\)
0.429289 + 0.903167i \(0.358764\pi\)
\(158\) 0 0
\(159\) −5.00000 + 8.66025i −0.396526 + 0.686803i
\(160\) 0 0
\(161\) 2.00000 1.73205i 0.157622 0.136505i
\(162\) 0 0
\(163\) 17.3205 + 10.0000i 1.35665 + 0.783260i 0.989170 0.146772i \(-0.0468885\pi\)
0.367477 + 0.930033i \(0.380222\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 17.0000i 1.31550i −0.753237 0.657750i \(-0.771508\pi\)
0.753237 0.657750i \(-0.228492\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) 0 0
\(173\) −13.8564 8.00000i −1.05348 0.608229i −0.129861 0.991532i \(-0.541453\pi\)
−0.923622 + 0.383304i \(0.874786\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.66025 5.00000i −0.650945 0.375823i
\(178\) 0 0
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 9.00000i 0.665299i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.92820 + 4.00000i 0.506640 + 0.292509i
\(188\) 0 0
\(189\) −12.5000 4.33013i −0.909241 0.314970i
\(190\) 0 0
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) −12.1244 + 7.00000i −0.872730 + 0.503871i −0.868255 0.496119i \(-0.834758\pi\)
−0.00447566 + 0.999990i \(0.501425\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 0 0
\(201\) −2.50000 + 4.33013i −0.176336 + 0.305424i
\(202\) 0 0
\(203\) 7.79423 22.5000i 0.547048 1.57919i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.73205 1.00000i 0.120386 0.0695048i
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 0 0
\(213\) 12.1244 7.00000i 0.830747 0.479632i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.3923 2.00000i 0.705476 0.135769i
\(218\) 0 0
\(219\) 6.00000 10.3923i 0.405442 0.702247i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.3205 10.0000i 1.14960 0.663723i 0.200812 0.979630i \(-0.435642\pi\)
0.948790 + 0.315906i \(0.102309\pi\)
\(228\) 0 0
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 0 0
\(231\) 4.00000 3.46410i 0.263181 0.227921i
\(232\) 0 0
\(233\) −6.92820 4.00000i −0.453882 0.262049i 0.255586 0.966786i \(-0.417731\pi\)
−0.709468 + 0.704737i \(0.751065\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 14.0000i 0.909398i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 0 0
\(243\) −13.8564 8.00000i −0.888889 0.513200i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 5.50000 + 9.52628i 0.348548 + 0.603703i
\(250\) 0 0
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) 2.00000i 0.125739i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) −8.00000 + 6.92820i −0.497096 + 0.430498i
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 0 0
\(263\) −0.866025 + 0.500000i −0.0534014 + 0.0308313i −0.526463 0.850198i \(-0.676482\pi\)
0.473062 + 0.881029i \(0.343149\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 15.0000i 0.917985i
\(268\) 0 0
\(269\) −10.5000 18.1865i −0.640196 1.10885i −0.985389 0.170321i \(-0.945520\pi\)
0.345192 0.938532i \(-0.387814\pi\)
\(270\) 0 0
\(271\) −11.0000 + 19.0526i −0.668202 + 1.15736i 0.310204 + 0.950670i \(0.399603\pi\)
−0.978406 + 0.206691i \(0.933731\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 24.2487 14.0000i 1.45696 0.841178i 0.458103 0.888899i \(-0.348529\pi\)
0.998861 + 0.0477206i \(0.0151957\pi\)
\(278\) 0 0
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −3.46410 + 2.00000i −0.205919 + 0.118888i −0.599414 0.800439i \(-0.704600\pi\)
0.393494 + 0.919327i \(0.371266\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.866025 + 2.50000i −0.0511199 + 0.147570i
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 9.00000 + 15.5885i 0.527589 + 0.913812i
\(292\) 0 0
\(293\) 12.0000i 0.701047i 0.936554 + 0.350524i \(0.113996\pi\)
−0.936554 + 0.350524i \(0.886004\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 8.66025 5.00000i 0.502519 0.290129i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −22.5000 7.79423i −1.29688 0.449252i
\(302\) 0 0
\(303\) −2.59808 1.50000i −0.149256 0.0861727i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 21.0000i 1.19853i −0.800549 0.599267i \(-0.795459\pi\)
0.800549 0.599267i \(-0.204541\pi\)
\(308\) 0 0
\(309\) 13.0000 0.739544
\(310\) 0 0
\(311\) −13.0000 22.5167i −0.737162 1.27680i −0.953768 0.300544i \(-0.902832\pi\)
0.216606 0.976259i \(-0.430501\pi\)
\(312\) 0 0
\(313\) −13.8564 8.00000i −0.783210 0.452187i 0.0543564 0.998522i \(-0.482689\pi\)
−0.837567 + 0.546335i \(0.816023\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.8564 8.00000i −0.778253 0.449325i 0.0575576 0.998342i \(-0.481669\pi\)
−0.835811 + 0.549017i \(0.815002\pi\)
\(318\) 0 0
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) 9.00000 0.502331
\(322\) 0 0
\(323\) 8.00000i 0.445132i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.866025 0.500000i −0.0478913 0.0276501i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0 0
\(333\) −6.92820 + 4.00000i −0.379663 + 0.219199i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) 0 0
\(339\) 1.00000 + 1.73205i 0.0543125 + 0.0940721i
\(340\) 0 0
\(341\) −4.00000 + 6.92820i −0.216612 + 0.375183i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.06218 3.50000i 0.325435 0.187890i −0.328378 0.944547i \(-0.606502\pi\)
0.653812 + 0.756657i \(0.273169\pi\)
\(348\) 0 0
\(349\) 19.0000 1.01705 0.508523 0.861048i \(-0.330192\pi\)
0.508523 + 0.861048i \(0.330192\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.1244 7.00000i 0.645314 0.372572i −0.141344 0.989960i \(-0.545142\pi\)
0.786659 + 0.617388i \(0.211809\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −6.92820 8.00000i −0.366679 0.423405i
\(358\) 0 0
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −6.06218 + 3.50000i −0.316443 + 0.182699i −0.649806 0.760100i \(-0.725150\pi\)
0.333363 + 0.942799i \(0.391817\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) 0 0
\(371\) −5.00000 25.9808i −0.259587 1.34885i
\(372\) 0 0
\(373\) 24.2487 + 14.0000i 1.25555 + 0.724893i 0.972206 0.234126i \(-0.0752227\pi\)
0.283344 + 0.959018i \(0.408556\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 30.0000 1.54100 0.770498 0.637442i \(-0.220007\pi\)
0.770498 + 0.637442i \(0.220007\pi\)
\(380\) 0 0
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 0 0
\(383\) −18.1865 10.5000i −0.929288 0.536525i −0.0427020 0.999088i \(-0.513597\pi\)
−0.886586 + 0.462563i \(0.846930\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −15.5885 9.00000i −0.792406 0.457496i
\(388\) 0 0
\(389\) 13.0000 + 22.5167i 0.659126 + 1.14164i 0.980842 + 0.194804i \(0.0624070\pi\)
−0.321716 + 0.946836i \(0.604260\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) 8.00000i 0.403547i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.19615 + 3.00000i 0.260787 + 0.150566i 0.624694 0.780870i \(-0.285224\pi\)
−0.363906 + 0.931436i \(0.618557\pi\)
\(398\) 0 0
\(399\) −5.00000 1.73205i −0.250313 0.0867110i
\(400\) 0 0
\(401\) 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i \(-0.693794\pi\)
0.996371 + 0.0851195i \(0.0271272\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000i 0.396545i
\(408\) 0 0
\(409\) −10.5000 18.1865i −0.519192 0.899266i −0.999751 0.0223042i \(-0.992900\pi\)
0.480560 0.876962i \(-0.340434\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) 0 0
\(413\) 25.9808 5.00000i 1.27843 0.246034i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.73205 1.00000i 0.0848189 0.0489702i
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −15.5885 18.0000i −0.754378 0.871081i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.00000 12.1244i −0.337178 0.584010i 0.646723 0.762725i \(-0.276139\pi\)
−0.983901 + 0.178716i \(0.942806\pi\)
\(432\) 0 0
\(433\) 30.0000i 1.44171i 0.693087 + 0.720854i \(0.256250\pi\)
−0.693087 + 0.720854i \(0.743750\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.73205 1.00000i 0.0828552 0.0478365i
\(438\) 0 0
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) 13.0000 5.19615i 0.619048 0.247436i
\(442\) 0 0
\(443\) 9.52628 + 5.50000i 0.452607 + 0.261313i 0.708931 0.705278i \(-0.249178\pi\)
−0.256323 + 0.966591i \(0.582511\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5.00000i 0.236492i
\(448\) 0 0
\(449\) 41.0000 1.93491 0.967455 0.253044i \(-0.0814317\pi\)
0.967455 + 0.253044i \(0.0814317\pi\)
\(450\) 0 0
\(451\) −1.00000 1.73205i −0.0470882 0.0815591i
\(452\) 0 0
\(453\) −6.92820 4.00000i −0.325515 0.187936i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.92820 + 4.00000i 0.324088 + 0.187112i 0.653213 0.757174i \(-0.273421\pi\)
−0.329125 + 0.944286i \(0.606754\pi\)
\(458\) 0 0
\(459\) −10.0000 17.3205i −0.466760 0.808452i
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 39.0000i 1.81248i 0.422760 + 0.906242i \(0.361061\pi\)
−0.422760 + 0.906242i \(0.638939\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.06218 3.50000i −0.280524 0.161961i 0.353137 0.935572i \(-0.385115\pi\)
−0.633661 + 0.773611i \(0.718448\pi\)
\(468\) 0 0
\(469\) −2.50000 12.9904i −0.115439 0.599840i
\(470\) 0 0
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) 0 0
\(473\) 15.5885 9.00000i 0.716758 0.413820i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 20.0000i 0.915737i
\(478\) 0 0
\(479\) −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0.866025 2.50000i 0.0394055 0.113754i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.92820 4.00000i 0.313947 0.181257i −0.334744 0.942309i \(-0.608650\pi\)
0.648691 + 0.761052i \(0.275317\pi\)
\(488\) 0 0
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 31.1769 18.0000i 1.40414 0.810679i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −12.1244 + 35.0000i −0.543852 + 1.56996i
\(498\) 0 0
\(499\) −19.0000 + 32.9090i −0.850557 + 1.47321i 0.0301498 + 0.999545i \(0.490402\pi\)
−0.880707 + 0.473662i \(0.842932\pi\)
\(500\) 0 0
\(501\) −8.50000 14.7224i −0.379752 0.657750i
\(502\) 0 0
\(503\) 23.0000i 1.02552i −0.858532 0.512760i \(-0.828623\pi\)
0.858532 0.512760i \(-0.171377\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 11.2583 6.50000i 0.500000 0.288675i
\(508\) 0 0
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) 0 0
\(511\) 6.00000 + 31.1769i 0.265424 + 1.37919i
\(512\) 0 0
\(513\) −8.66025 5.00000i −0.382360 0.220755i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) 0 0
\(521\) 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i \(0.205167\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(522\) 0 0
\(523\) −24.2487 14.0000i −1.06032 0.612177i −0.134801 0.990873i \(-0.543039\pi\)
−0.925521 + 0.378695i \(0.876373\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13.8564 + 8.00000i 0.603595 + 0.348485i
\(528\) 0 0
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) 0 0
\(531\) 20.0000 0.867926
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.3923 + 6.00000i 0.448461 + 0.258919i
\(538\) 0 0
\(539\) −2.00000 + 13.8564i −0.0861461 + 0.596838i
\(540\) 0 0
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) 0 0
\(543\) −21.6506 + 12.5000i −0.929118 + 0.536426i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 35.0000i 1.49649i 0.663421 + 0.748246i \(0.269104\pi\)
−0.663421 + 0.748246i \(0.730896\pi\)
\(548\) 0 0
\(549\) −9.00000 15.5885i −0.384111 0.665299i
\(550\) 0 0
\(551\) 9.00000 15.5885i 0.383413 0.664091i
\(552\) 0 0
\(553\) 24.2487 + 28.0000i 1.03116 + 1.19068i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −25.9808 + 15.0000i −1.10084 + 0.635570i −0.936442 0.350824i \(-0.885902\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 0 0
\(563\) −38.9711 + 22.5000i −1.64244 + 0.948262i −0.662474 + 0.749085i \(0.730494\pi\)
−0.979963 + 0.199177i \(0.936173\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.59808 0.500000i 0.109109 0.0209980i
\(568\) 0 0
\(569\) 23.0000 39.8372i 0.964210 1.67006i 0.252488 0.967600i \(-0.418751\pi\)
0.711722 0.702461i \(-0.247915\pi\)
\(570\) 0 0
\(571\) 13.0000 + 22.5167i 0.544033 + 0.942293i 0.998667 + 0.0516146i \(0.0164367\pi\)
−0.454634 + 0.890678i \(0.650230\pi\)
\(572\) 0 0
\(573\) 18.0000i 0.751961i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.73205 + 1.00000i −0.0721062 + 0.0416305i −0.535620 0.844459i \(-0.679922\pi\)
0.463513 + 0.886090i \(0.346589\pi\)
\(578\) 0 0
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) 0 0
\(581\) −27.5000 9.52628i −1.14089 0.395217i
\(582\) 0 0
\(583\) 17.3205 + 10.0000i 0.717342 + 0.414158i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) −9.00000 15.5885i −0.370211 0.641223i
\(592\) 0 0
\(593\) −15.5885 9.00000i −0.640141 0.369586i 0.144528 0.989501i \(-0.453834\pi\)
−0.784669 + 0.619915i \(0.787167\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3.46410 2.00000i −0.141776 0.0818546i
\(598\) 0 0
\(599\) 2.00000 + 3.46410i 0.0817178 + 0.141539i 0.903988 0.427558i \(-0.140626\pi\)
−0.822270 + 0.569097i \(0.807293\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 10.0000i 0.407231i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 23.3827 + 13.5000i 0.949074 + 0.547948i 0.892793 0.450467i \(-0.148742\pi\)
0.0562808 + 0.998415i \(0.482076\pi\)
\(608\) 0 0
\(609\) −4.50000 23.3827i −0.182349 0.947514i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −17.3205 + 10.0000i −0.699569 + 0.403896i −0.807187 0.590296i \(-0.799011\pi\)
0.107618 + 0.994192i \(0.465678\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) 0 0
\(619\) −17.0000 29.4449i −0.683288 1.18349i −0.973972 0.226670i \(-0.927216\pi\)
0.290684 0.956819i \(-0.406117\pi\)
\(620\) 0 0
\(621\) 2.50000 4.33013i 0.100322 0.173762i
\(622\) 0 0
\(623\) −25.9808 30.0000i −1.04090 1.20192i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.46410 2.00000i 0.138343 0.0798723i
\(628\) 0 0
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −2.00000 −0.0796187 −0.0398094 0.999207i \(-0.512675\pi\)
−0.0398094 + 0.999207i \(0.512675\pi\)
\(632\) 0 0
\(633\) 1.73205 1.00000i 0.0688428 0.0397464i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −14.0000 + 24.2487i −0.553831 + 0.959264i
\(640\) 0 0
\(641\) 9.50000 + 16.4545i 0.375227 + 0.649913i 0.990361 0.138510i \(-0.0442313\pi\)
−0.615134 + 0.788423i \(0.710898\pi\)
\(642\) 0 0
\(643\) 4.00000i 0.157745i −0.996885 0.0788723i \(-0.974868\pi\)
0.996885 0.0788723i \(-0.0251319\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −19.9186 + 11.5000i −0.783080 + 0.452112i −0.837521 0.546405i \(-0.815996\pi\)
0.0544405 + 0.998517i \(0.482662\pi\)
\(648\) 0 0
\(649\) −10.0000 + 17.3205i −0.392534 + 0.679889i
\(650\) 0 0
\(651\) 8.00000 6.92820i 0.313545 0.271538i
\(652\) 0 0
\(653\) −31.1769 18.0000i −1.22005 0.704394i −0.255119 0.966910i \(-0.582115\pi\)
−0.964928 + 0.262515i \(0.915448\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 24.0000i 0.936329i
\(658\) 0 0
\(659\) −2.00000 −0.0779089 −0.0389545 0.999241i \(-0.512403\pi\)
−0.0389545 + 0.999241i \(0.512403\pi\)
\(660\) 0 0
\(661\) 1.50000 + 2.59808i 0.0583432 + 0.101053i 0.893722 0.448622i \(-0.148085\pi\)
−0.835379 + 0.549675i \(0.814752\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.79423 + 4.50000i 0.301794 + 0.174241i
\(668\) 0 0
\(669\) −2.00000 3.46410i −0.0773245 0.133930i
\(670\) 0 0
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 24.0000i 0.925132i 0.886585 + 0.462566i \(0.153071\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −20.7846 12.0000i −0.798817 0.461197i 0.0442400 0.999021i \(-0.485913\pi\)
−0.843057 + 0.537823i \(0.819247\pi\)
\(678\) 0 0
\(679\) −45.0000 15.5885i −1.72694 0.598230i
\(680\) 0 0
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) 0 0
\(683\) 7.79423 4.50000i 0.298238 0.172188i −0.343413 0.939184i \(-0.611583\pi\)
0.641651 + 0.766997i \(0.278250\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i \(0.566655\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(692\) 0 0
\(693\) −3.46410 + 10.0000i −0.131590 + 0.379869i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.46410 + 2.00000i −0.131212 + 0.0757554i
\(698\) 0 0
\(699\) −8.00000 −0.302588
\(700\) 0 0
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) −6.92820 + 4.00000i −0.261302 + 0.150863i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 7.79423 1.50000i 0.293132 0.0564133i
\(708\) 0 0
\(709\) 10.5000 18.1865i 0.394336 0.683010i −0.598680 0.800988i \(-0.704308\pi\)
0.993016 + 0.117978i \(0.0376414\pi\)
\(710\) 0 0
\(711\) 14.0000 + 24.2487i 0.525041 + 0.909398i
\(712\) 0 0
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 20.7846 12.0000i 0.776215 0.448148i
\(718\) 0 0
\(719\) −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i \(0.453064\pi\)
−0.930087 + 0.367338i \(0.880269\pi\)
\(720\) 0 0
\(721\) −26.0000 + 22.5167i −0.968291 + 0.838564i
\(722\) 0 0
\(723\) 19.0526 + 11.0000i 0.708572 + 0.409094i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 31.0000i 1.14973i 0.818250 + 0.574863i \(0.194945\pi\)
−0.818250 + 0.574863i \(0.805055\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) −18.0000 31.1769i −0.665754 1.15312i
\(732\) 0 0
\(733\) 22.5167 + 13.0000i 0.831672 + 0.480166i 0.854425 0.519575i \(-0.173910\pi\)
−0.0227529 + 0.999741i \(0.507243\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.66025 + 5.00000i 0.319005 + 0.184177i
\(738\) 0 0
\(739\) 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i \(-0.107785\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27.0000i 0.990534i 0.868741 + 0.495267i \(0.164930\pi\)
−0.868741 + 0.495267i \(0.835070\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −19.0526 11.0000i −0.697097 0.402469i
\(748\) 0 0
\(749\) −18.0000 + 15.5885i −0.657706 + 0.569590i
\(750\) 0 0
\(751\) −6.00000 + 10.3923i −0.218943 + 0.379221i −0.954485 0.298259i \(-0.903594\pi\)
0.735542 + 0.677479i \(0.236928\pi\)
\(752\) 0 0
\(753\) 6.92820 4.00000i 0.252478 0.145768i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 24.0000i 0.872295i 0.899875 + 0.436147i \(0.143657\pi\)
−0.899875 + 0.436147i \(0.856343\pi\)
\(758\) 0 0
\(759\) 1.00000 + 1.73205i 0.0362977 + 0.0628695i
\(760\) 0 0
\(761\) 3.00000 5.19615i 0.108750 0.188360i −0.806514 0.591215i \(-0.798649\pi\)
0.915264 + 0.402854i \(0.131982\pi\)
\(762\) 0 0
\(763\) 2.59808 0.500000i 0.0940567 0.0181012i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −3.46410 + 10.0000i −0.124274 + 0.358748i
\(778\) 0 0
\(779\) −1.00000 + 1.73205i −0.0358287 + 0.0620572i
\(780\) 0 0
\(781\) −14.0000 24.2487i −0.500959 0.867687i
\(782\) 0 0
\(783\) 45.0000i 1.60817i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −38.9711 + 22.5000i −1.38917 + 0.802038i −0.993222 0.116234i \(-0.962918\pi\)
−0.395949 + 0.918272i \(0.629584\pi\)
\(788\) 0 0
\(789\) −0.500000 + 0.866025i −0.0178005 + 0.0308313i
\(790\) 0 0
\(791\) −5.00000 1.73205i −0.177780 0.0615846i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.00000i 0.283375i −0.989911 0.141687i \(-0.954747\pi\)
0.989911 0.141687i \(-0.0452527\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\)