Properties

Label 1512.2.s.m.865.1
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.9391935744.3
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 12 x^{5} - 76 x^{4} + 84 x^{3} + 245 x^{2} - 1372 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.1
Root \(2.61033 - 0.431486i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.m.1297.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 - 2.36603i) q^{5} +(-0.931486 + 2.47635i) q^{7} +O(q^{10})\) \(q+(-1.36603 - 2.36603i) q^{5} +(-0.931486 + 2.47635i) q^{7} +(1.17884 - 2.04182i) q^{11} +6.68476 q^{13} +(-2.09808 + 3.63397i) q^{17} +(-1.80056 - 3.11867i) q^{19} +(-3.40784 - 5.90255i) q^{23} +(-1.23205 + 2.13397i) q^{25} +1.00610 q^{29} +(-1.05321 + 1.82421i) q^{31} +(7.13155 - 1.17884i) q^{35} +(2.47941 + 4.29446i) q^{37} +8.91152 q^{41} -2.25127 q^{43} +(-5.85463 - 10.1405i) q^{47} +(-5.26467 - 4.61338i) q^{49} +(4.13989 - 7.17050i) q^{53} -6.44132 q^{55} +(5.91089 - 10.2380i) q^{59} +(-6.00592 - 10.4026i) q^{61} +(-9.13155 - 15.8163i) q^{65} +(3.03262 - 5.25264i) q^{67} +4.89358 q^{71} +(2.28917 - 3.96496i) q^{73} +(3.95818 + 4.82116i) q^{77} +(0.252644 + 0.437591i) q^{79} -11.1900 q^{83} +11.4641 q^{85} +(-4.22900 - 7.32484i) q^{89} +(-6.22676 + 16.5538i) q^{91} +(-4.91923 + 8.52036i) q^{95} +2.25127 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 2q^{7} + O(q^{10}) \) \( 8q - 4q^{5} - 2q^{7} - 2q^{11} - 8q^{13} + 4q^{17} - 6q^{19} + 2q^{23} + 4q^{25} + 16q^{29} - 6q^{31} - 2q^{35} - 16q^{41} - 20q^{47} - 6q^{49} - 10q^{53} + 16q^{55} + 22q^{59} + 2q^{61} - 14q^{65} + 2q^{67} + 44q^{71} - 10q^{73} + 54q^{77} + 8q^{79} - 40q^{83} + 64q^{85} - 16q^{89} - 24q^{91} - 30q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(4\) 0 0
\(5\) −1.36603 2.36603i −0.610905 1.05812i −0.991088 0.133207i \(-0.957472\pi\)
0.380183 0.924911i \(-0.375861\pi\)
\(6\) 0 0
\(7\) −0.931486 + 2.47635i −0.352069 + 0.935974i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.17884 2.04182i 0.355435 0.615631i −0.631758 0.775166i \(-0.717666\pi\)
0.987192 + 0.159535i \(0.0509996\pi\)
\(12\) 0 0
\(13\) 6.68476 1.85402 0.927009 0.375038i \(-0.122370\pi\)
0.927009 + 0.375038i \(0.122370\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.09808 + 3.63397i −0.508858 + 0.881368i 0.491089 + 0.871109i \(0.336599\pi\)
−0.999947 + 0.0102590i \(0.996734\pi\)
\(18\) 0 0
\(19\) −1.80056 3.11867i −0.413078 0.715472i 0.582147 0.813084i \(-0.302213\pi\)
−0.995225 + 0.0976120i \(0.968880\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.40784 5.90255i −0.710584 1.23077i −0.964638 0.263578i \(-0.915097\pi\)
0.254054 0.967190i \(-0.418236\pi\)
\(24\) 0 0
\(25\) −1.23205 + 2.13397i −0.246410 + 0.426795i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.00610 0.186829 0.0934145 0.995627i \(-0.470222\pi\)
0.0934145 + 0.995627i \(0.470222\pi\)
\(30\) 0 0
\(31\) −1.05321 + 1.82421i −0.189162 + 0.327638i −0.944971 0.327154i \(-0.893910\pi\)
0.755809 + 0.654792i \(0.227244\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.13155 1.17884i 1.20545 0.199261i
\(36\) 0 0
\(37\) 2.47941 + 4.29446i 0.407612 + 0.706005i 0.994622 0.103575i \(-0.0330282\pi\)
−0.587010 + 0.809580i \(0.699695\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.91152 1.39175 0.695873 0.718165i \(-0.255018\pi\)
0.695873 + 0.718165i \(0.255018\pi\)
\(42\) 0 0
\(43\) −2.25127 −0.343315 −0.171658 0.985157i \(-0.554912\pi\)
−0.171658 + 0.985157i \(0.554912\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.85463 10.1405i −0.853986 1.47915i −0.877583 0.479426i \(-0.840845\pi\)
0.0235965 0.999722i \(-0.492488\pi\)
\(48\) 0 0
\(49\) −5.26467 4.61338i −0.752095 0.659055i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.13989 7.17050i 0.568658 0.984944i −0.428041 0.903759i \(-0.640796\pi\)
0.996699 0.0811851i \(-0.0258705\pi\)
\(54\) 0 0
\(55\) −6.44132 −0.868547
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.91089 10.2380i 0.769533 1.33287i −0.168284 0.985739i \(-0.553822\pi\)
0.937817 0.347131i \(-0.112844\pi\)
\(60\) 0 0
\(61\) −6.00592 10.4026i −0.768979 1.33191i −0.938117 0.346318i \(-0.887432\pi\)
0.169138 0.985592i \(-0.445902\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9.13155 15.8163i −1.13263 1.96177i
\(66\) 0 0
\(67\) 3.03262 5.25264i 0.370493 0.641713i −0.619149 0.785274i \(-0.712522\pi\)
0.989641 + 0.143561i \(0.0458554\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.89358 0.580762 0.290381 0.956911i \(-0.406218\pi\)
0.290381 + 0.956911i \(0.406218\pi\)
\(72\) 0 0
\(73\) 2.28917 3.96496i 0.267927 0.464064i −0.700399 0.713751i \(-0.746995\pi\)
0.968326 + 0.249688i \(0.0803279\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.95818 + 4.82116i 0.451077 + 0.549422i
\(78\) 0 0
\(79\) 0.252644 + 0.437591i 0.0284246 + 0.0492329i 0.879888 0.475182i \(-0.157618\pi\)
−0.851463 + 0.524414i \(0.824284\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −11.1900 −1.22827 −0.614134 0.789202i \(-0.710494\pi\)
−0.614134 + 0.789202i \(0.710494\pi\)
\(84\) 0 0
\(85\) 11.4641 1.24346
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.22900 7.32484i −0.448273 0.776431i 0.550001 0.835164i \(-0.314627\pi\)
−0.998274 + 0.0587326i \(0.981294\pi\)
\(90\) 0 0
\(91\) −6.22676 + 16.5538i −0.652742 + 1.73531i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.91923 + 8.52036i −0.504703 + 0.874171i
\(96\) 0 0
\(97\) 2.25127 0.228582 0.114291 0.993447i \(-0.463540\pi\)
0.114291 + 0.993447i \(0.463540\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.53653 6.12545i 0.351898 0.609505i −0.634684 0.772772i \(-0.718870\pi\)
0.986582 + 0.163267i \(0.0522031\pi\)
\(102\) 0 0
\(103\) −2.87828 4.98532i −0.283605 0.491219i 0.688665 0.725080i \(-0.258197\pi\)
−0.972270 + 0.233861i \(0.924864\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.04245 + 15.6620i 0.874166 + 1.51410i 0.857648 + 0.514237i \(0.171925\pi\)
0.0165180 + 0.999864i \(0.494742\pi\)
\(108\) 0 0
\(109\) 8.00592 13.8667i 0.766828 1.32818i −0.172447 0.985019i \(-0.555167\pi\)
0.939275 0.343166i \(-0.111499\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.84457 −0.267595 −0.133797 0.991009i \(-0.542717\pi\)
−0.133797 + 0.991009i \(0.542717\pi\)
\(114\) 0 0
\(115\) −9.31040 + 16.1261i −0.868199 + 1.50376i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.04468 8.58058i −0.645785 0.786580i
\(120\) 0 0
\(121\) 2.72066 + 4.71232i 0.247333 + 0.428393i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −6.92820 −0.619677
\(126\) 0 0
\(127\) −4.64231 −0.411939 −0.205969 0.978558i \(-0.566035\pi\)
−0.205969 + 0.978558i \(0.566035\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.27692 + 5.67579i 0.286306 + 0.495896i 0.972925 0.231121i \(-0.0742394\pi\)
−0.686619 + 0.727017i \(0.740906\pi\)
\(132\) 0 0
\(133\) 9.40013 1.55384i 0.815095 0.134735i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.78221 + 10.0151i −0.494007 + 0.855646i −0.999976 0.00690610i \(-0.997802\pi\)
0.505969 + 0.862552i \(0.331135\pi\)
\(138\) 0 0
\(139\) −12.5065 −1.06079 −0.530396 0.847750i \(-0.677957\pi\)
−0.530396 + 0.847750i \(0.677957\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.88028 13.6490i 0.658982 1.14139i
\(144\) 0 0
\(145\) −1.37436 2.38047i −0.114135 0.197687i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.36603 5.83013i −0.275756 0.477623i 0.694570 0.719425i \(-0.255595\pi\)
−0.970325 + 0.241803i \(0.922261\pi\)
\(150\) 0 0
\(151\) 2.41089 4.17579i 0.196196 0.339821i −0.751096 0.660193i \(-0.770475\pi\)
0.947292 + 0.320372i \(0.103808\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.75483 0.462239
\(156\) 0 0
\(157\) −10.5538 + 18.2798i −0.842288 + 1.45889i 0.0456678 + 0.998957i \(0.485458\pi\)
−0.887956 + 0.459929i \(0.847875\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 17.7912 2.94087i 1.40214 0.231773i
\(162\) 0 0
\(163\) 6.36297 + 11.0210i 0.498387 + 0.863231i 0.999998 0.00186211i \(-0.000592727\pi\)
−0.501612 + 0.865093i \(0.667259\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.4535 −0.963683 −0.481841 0.876258i \(-0.660032\pi\)
−0.481841 + 0.876258i \(0.660032\pi\)
\(168\) 0 0
\(169\) 31.6860 2.43739
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.81282 16.9963i −0.746055 1.29220i −0.949700 0.313160i \(-0.898612\pi\)
0.203646 0.979045i \(-0.434721\pi\)
\(174\) 0 0
\(175\) −4.13684 5.03876i −0.312716 0.380895i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.50305 + 11.2636i −0.486061 + 0.841882i −0.999872 0.0160213i \(-0.994900\pi\)
0.513811 + 0.857904i \(0.328233\pi\)
\(180\) 0 0
\(181\) 15.7684 1.17206 0.586028 0.810291i \(-0.300691\pi\)
0.586028 + 0.810291i \(0.300691\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.77387 11.7327i 0.498025 0.862604i
\(186\) 0 0
\(187\) 4.94660 + 8.56777i 0.361732 + 0.626537i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.47244 + 4.28239i 0.178900 + 0.309863i 0.941504 0.337002i \(-0.109413\pi\)
−0.762604 + 0.646865i \(0.776080\pi\)
\(192\) 0 0
\(193\) −4.92620 + 8.53243i −0.354596 + 0.614178i −0.987049 0.160421i \(-0.948715\pi\)
0.632453 + 0.774599i \(0.282048\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 27.0955 1.93047 0.965236 0.261380i \(-0.0841775\pi\)
0.965236 + 0.261380i \(0.0841775\pi\)
\(198\) 0 0
\(199\) 13.7441 23.8054i 0.974292 1.68752i 0.292038 0.956407i \(-0.405667\pi\)
0.682253 0.731116i \(-0.261000\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.937173 + 2.49147i −0.0657767 + 0.174867i
\(204\) 0 0
\(205\) −12.1734 21.0849i −0.850225 1.47263i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.49033 −0.587288
\(210\) 0 0
\(211\) 1.66636 0.114717 0.0573584 0.998354i \(-0.481732\pi\)
0.0573584 + 0.998354i \(0.481732\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.07529 + 5.32656i 0.209733 + 0.363269i
\(216\) 0 0
\(217\) −3.53634 4.30734i −0.240062 0.292401i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −14.0251 + 24.2922i −0.943433 + 1.63407i
\(222\) 0 0
\(223\) 5.19005 0.347551 0.173776 0.984785i \(-0.444403\pi\)
0.173776 + 0.984785i \(0.444403\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.05016 + 1.81892i −0.0697013 + 0.120726i −0.898770 0.438421i \(-0.855538\pi\)
0.829069 + 0.559147i \(0.188871\pi\)
\(228\) 0 0
\(229\) 12.6316 + 21.8785i 0.834716 + 1.44577i 0.894261 + 0.447546i \(0.147702\pi\)
−0.0595446 + 0.998226i \(0.518965\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.9862 + 19.0286i 0.719729 + 1.24661i 0.961107 + 0.276176i \(0.0890673\pi\)
−0.241378 + 0.970431i \(0.577599\pi\)
\(234\) 0 0
\(235\) −15.9952 + 27.7044i −1.04341 + 1.80724i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 21.3038 1.37803 0.689015 0.724747i \(-0.258043\pi\)
0.689015 + 0.724747i \(0.258043\pi\)
\(240\) 0 0
\(241\) 6.17866 10.7017i 0.398002 0.689360i −0.595477 0.803372i \(-0.703037\pi\)
0.993479 + 0.114012i \(0.0363703\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.72371 + 18.7583i −0.237899 + 1.19843i
\(246\) 0 0
\(247\) −12.0363 20.8476i −0.765854 1.32650i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.35158 0.0853110 0.0426555 0.999090i \(-0.486418\pi\)
0.0426555 + 0.999090i \(0.486418\pi\)
\(252\) 0 0
\(253\) −16.0692 −1.01026
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.59502 + 9.69087i 0.349008 + 0.604500i 0.986074 0.166310i \(-0.0531853\pi\)
−0.637066 + 0.770810i \(0.719852\pi\)
\(258\) 0 0
\(259\) −12.9441 + 2.13966i −0.804310 + 0.132952i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.93540 + 12.0125i −0.427655 + 0.740720i −0.996664 0.0816108i \(-0.973994\pi\)
0.569009 + 0.822331i \(0.307327\pi\)
\(264\) 0 0
\(265\) −22.6208 −1.38958
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.9115 + 22.3634i −0.787230 + 1.36352i 0.140429 + 0.990091i \(0.455152\pi\)
−0.927658 + 0.373431i \(0.878181\pi\)
\(270\) 0 0
\(271\) −12.0895 20.9397i −0.734388 1.27200i −0.954991 0.296633i \(-0.904136\pi\)
0.220604 0.975364i \(-0.429197\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.90479 + 5.03124i 0.175165 + 0.303395i
\(276\) 0 0
\(277\) 6.03653 10.4556i 0.362700 0.628215i −0.625704 0.780060i \(-0.715188\pi\)
0.988404 + 0.151846i \(0.0485217\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.6554 −0.635648 −0.317824 0.948150i \(-0.602952\pi\)
−0.317824 + 0.948150i \(0.602952\pi\)
\(282\) 0 0
\(283\) −1.23205 + 2.13397i −0.0732378 + 0.126852i −0.900319 0.435231i \(-0.856667\pi\)
0.827081 + 0.562083i \(0.190000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.30096 + 22.0681i −0.489990 + 1.30264i
\(288\) 0 0
\(289\) −0.303848 0.526279i −0.0178734 0.0309576i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.38047 −0.314330 −0.157165 0.987572i \(-0.550236\pi\)
−0.157165 + 0.987572i \(0.550236\pi\)
\(294\) 0 0
\(295\) −32.2977 −1.88045
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −22.7806 39.4572i −1.31744 2.28187i
\(300\) 0 0
\(301\) 2.09703 5.57494i 0.120871 0.321334i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −16.4085 + 28.4203i −0.939546 + 1.62734i
\(306\) 0 0
\(307\) 18.3083 1.04491 0.522455 0.852667i \(-0.325016\pi\)
0.522455 + 0.852667i \(0.325016\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00063 + 1.73314i −0.0567405 + 0.0982775i −0.893000 0.450056i \(-0.851404\pi\)
0.836260 + 0.548333i \(0.184737\pi\)
\(312\) 0 0
\(313\) 2.04401 + 3.54032i 0.115534 + 0.200111i 0.917993 0.396596i \(-0.129809\pi\)
−0.802459 + 0.596707i \(0.796475\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.88639 8.46347i −0.274447 0.475356i 0.695549 0.718479i \(-0.255161\pi\)
−0.969995 + 0.243123i \(0.921828\pi\)
\(318\) 0 0
\(319\) 1.18604 2.05428i 0.0664055 0.115018i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.1109 0.840792
\(324\) 0 0
\(325\) −8.23596 + 14.2651i −0.456849 + 0.791286i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 30.5650 5.05239i 1.68511 0.278547i
\(330\) 0 0
\(331\) 16.8369 + 29.1624i 0.925440 + 1.60291i 0.790852 + 0.612008i \(0.209638\pi\)
0.134588 + 0.990902i \(0.457029\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −16.5705 −0.905344
\(336\) 0 0
\(337\) 24.7790 1.34980 0.674898 0.737911i \(-0.264188\pi\)
0.674898 + 0.737911i \(0.264188\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.48313 + 4.30091i 0.134469 + 0.232908i
\(342\) 0 0
\(343\) 16.3283 8.73988i 0.881647 0.471909i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.53590 + 14.7846i −0.458231 + 0.793679i −0.998868 0.0475768i \(-0.984850\pi\)
0.540637 + 0.841256i \(0.318183\pi\)
\(348\) 0 0
\(349\) −11.0714 −0.592640 −0.296320 0.955089i \(-0.595759\pi\)
−0.296320 + 0.955089i \(0.595759\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −10.0670 + 17.4365i −0.535810 + 0.928050i 0.463314 + 0.886194i \(0.346660\pi\)
−0.999124 + 0.0418556i \(0.986673\pi\)
\(354\) 0 0
\(355\) −6.68476 11.5783i −0.354790 0.614515i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.04245 15.6620i −0.477242 0.826607i 0.522418 0.852690i \(-0.325030\pi\)
−0.999660 + 0.0260822i \(0.991697\pi\)
\(360\) 0 0
\(361\) 3.01594 5.22375i 0.158733 0.274934i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.5083 −0.654713
\(366\) 0 0
\(367\) 2.60441 4.51097i 0.135949 0.235471i −0.790010 0.613093i \(-0.789925\pi\)
0.925960 + 0.377622i \(0.123258\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 13.9005 + 16.9311i 0.721676 + 0.879017i
\(372\) 0 0
\(373\) −10.3299 17.8919i −0.534862 0.926408i −0.999170 0.0407341i \(-0.987030\pi\)
0.464308 0.885674i \(-0.346303\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.72557 0.346385
\(378\) 0 0
\(379\) −27.9829 −1.43738 −0.718691 0.695329i \(-0.755259\pi\)
−0.718691 + 0.695329i \(0.755259\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.11424 + 14.0543i 0.414618 + 0.718140i 0.995388 0.0959276i \(-0.0305817\pi\)
−0.580770 + 0.814068i \(0.697248\pi\)
\(384\) 0 0
\(385\) 6.00000 15.9510i 0.305788 0.812938i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.72434 8.18280i 0.239534 0.414884i −0.721047 0.692886i \(-0.756339\pi\)
0.960581 + 0.278002i \(0.0896721\pi\)
\(390\) 0 0
\(391\) 28.5996 1.44635
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.690235 1.19552i 0.0347295 0.0601532i
\(396\) 0 0
\(397\) 8.64823 + 14.9792i 0.434042 + 0.751783i 0.997217 0.0745546i \(-0.0237535\pi\)
−0.563175 + 0.826338i \(0.690420\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.46347 4.26686i −0.123020 0.213077i 0.797937 0.602740i \(-0.205925\pi\)
−0.920957 + 0.389664i \(0.872591\pi\)
\(402\) 0 0
\(403\) −7.04044 + 12.1944i −0.350709 + 0.607447i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.6913 0.579518
\(408\) 0 0
\(409\) 2.63374 4.56178i 0.130230 0.225565i −0.793535 0.608525i \(-0.791762\pi\)
0.923765 + 0.382959i \(0.125095\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 19.8469 + 24.1740i 0.976603 + 1.18952i
\(414\) 0 0
\(415\) 15.2859 + 26.4759i 0.750355 + 1.29965i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.06569 −0.198622 −0.0993110 0.995056i \(-0.531664\pi\)
−0.0993110 + 0.995056i \(0.531664\pi\)
\(420\) 0 0
\(421\) −17.9479 −0.874725 −0.437363 0.899285i \(-0.644087\pi\)
−0.437363 + 0.899285i \(0.644087\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.16987 8.95448i −0.250776 0.434356i
\(426\) 0 0
\(427\) 31.3548 5.18294i 1.51737 0.250820i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −17.4892 + 30.2922i −0.842427 + 1.45913i 0.0454101 + 0.998968i \(0.485541\pi\)
−0.887837 + 0.460158i \(0.847793\pi\)
\(432\) 0 0
\(433\) −16.6314 −0.799252 −0.399626 0.916678i \(-0.630860\pi\)
−0.399626 + 0.916678i \(0.630860\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.2721 + 21.2559i −0.587053 + 1.01681i
\(438\) 0 0
\(439\) 10.1550 + 17.5889i 0.484670 + 0.839473i 0.999845 0.0176119i \(-0.00560632\pi\)
−0.515175 + 0.857085i \(0.672273\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.65739 + 14.9950i 0.411325 + 0.712436i 0.995035 0.0995265i \(-0.0317328\pi\)
−0.583710 + 0.811962i \(0.698399\pi\)
\(444\) 0 0
\(445\) −11.5538 + 20.0118i −0.547704 + 0.948652i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −8.85030 −0.417672 −0.208836 0.977951i \(-0.566967\pi\)
−0.208836 + 0.977951i \(0.566967\pi\)
\(450\) 0 0
\(451\) 10.5053 18.1957i 0.494675 0.856802i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 47.6727 7.88028i 2.23493 0.369433i
\(456\) 0 0
\(457\) −3.51668 6.09107i −0.164503 0.284928i 0.771975 0.635652i \(-0.219269\pi\)
−0.936479 + 0.350724i \(0.885935\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.0452 0.514426 0.257213 0.966355i \(-0.417196\pi\)
0.257213 + 0.966355i \(0.417196\pi\)
\(462\) 0 0
\(463\) 2.49597 0.115998 0.0579989 0.998317i \(-0.481528\pi\)
0.0579989 + 0.998317i \(0.481528\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.66135 15.0019i −0.400799 0.694205i 0.593023 0.805185i \(-0.297934\pi\)
−0.993823 + 0.110981i \(0.964601\pi\)
\(468\) 0 0
\(469\) 10.1826 + 12.4026i 0.470187 + 0.572699i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.65389 + 4.59668i −0.122026 + 0.211356i
\(474\) 0 0
\(475\) 8.87355 0.407146
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.44966 + 12.9032i −0.340384 + 0.589562i −0.984504 0.175363i \(-0.943890\pi\)
0.644120 + 0.764924i \(0.277224\pi\)
\(480\) 0 0
\(481\) 16.5742 + 28.7074i 0.755720 + 1.30895i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.07529 5.32656i −0.139642 0.241867i
\(486\) 0 0
\(487\) 16.0637 27.8231i 0.727914 1.26078i −0.229849 0.973226i \(-0.573823\pi\)
0.957763 0.287558i \(-0.0928435\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −26.3099 −1.18735 −0.593675 0.804705i \(-0.702324\pi\)
−0.593675 + 0.804705i \(0.702324\pi\)
\(492\) 0 0
\(493\) −2.11088 + 3.65616i −0.0950695 + 0.164665i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.55831 + 12.1183i −0.204468 + 0.543578i
\(498\) 0 0
\(499\) 2.94132 + 5.09451i 0.131671 + 0.228062i 0.924321 0.381616i \(-0.124632\pi\)
−0.792650 + 0.609678i \(0.791299\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 33.7798 1.50617 0.753083 0.657926i \(-0.228566\pi\)
0.753083 + 0.657926i \(0.228566\pi\)
\(504\) 0 0
\(505\) −19.3240 −0.859905
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.5902 28.7350i −0.735347 1.27366i −0.954571 0.297983i \(-0.903686\pi\)
0.219224 0.975674i \(-0.429647\pi\)
\(510\) 0 0
\(511\) 7.68632 + 9.36211i 0.340023 + 0.414155i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.86360 + 13.6202i −0.346512 + 0.600176i
\(516\) 0 0
\(517\) −27.6068 −1.21414
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20.8642 36.1379i 0.914079 1.58323i 0.105834 0.994384i \(-0.466249\pi\)
0.808245 0.588847i \(-0.200418\pi\)
\(522\) 0 0
\(523\) 14.9319 + 25.8629i 0.652928 + 1.13090i 0.982409 + 0.186742i \(0.0597928\pi\)
−0.329481 + 0.944162i \(0.606874\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.41942 7.65466i −0.192513 0.333442i
\(528\) 0 0
\(529\) −11.7268 + 20.3114i −0.509859 + 0.883102i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 59.5714 2.58032
\(534\) 0 0
\(535\) 24.7044 42.7893i 1.06807 1.84994i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −15.6259 + 5.31103i −0.673055 + 0.228762i
\(540\) 0 0
\(541\) −11.8903 20.5946i −0.511204 0.885431i −0.999916 0.0129859i \(-0.995866\pi\)
0.488712 0.872445i \(-0.337467\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −43.7451 −1.87384
\(546\) 0 0
\(547\) −8.03499 −0.343552 −0.171776 0.985136i \(-0.554950\pi\)
−0.171776 + 0.985136i \(0.554950\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.81156 3.13771i −0.0771749 0.133671i
\(552\) 0 0
\(553\) −1.31897 + 0.218025i −0.0560881 + 0.00927135i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.38397 16.2535i 0.397611 0.688683i −0.595819 0.803119i \(-0.703173\pi\)
0.993431 + 0.114435i \(0.0365059\pi\)
\(558\) 0 0
\(559\) −15.0492 −0.636513
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13.0335 22.5746i 0.549296 0.951408i −0.449027 0.893518i \(-0.648229\pi\)
0.998323 0.0578898i \(-0.0184372\pi\)
\(564\) 0 0
\(565\) 3.88576 + 6.73033i 0.163475 + 0.283147i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.04792 8.74326i −0.211620 0.366536i 0.740602 0.671944i \(-0.234541\pi\)
−0.952222 + 0.305408i \(0.901207\pi\)
\(570\) 0 0
\(571\) 9.50983 16.4715i 0.397974 0.689311i −0.595502 0.803354i \(-0.703047\pi\)
0.993476 + 0.114043i \(0.0363801\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16.7945 0.700380
\(576\) 0 0
\(577\) 0.960818 1.66419i 0.0399994 0.0692810i −0.845333 0.534240i \(-0.820598\pi\)
0.885332 + 0.464959i \(0.153931\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10.4234 27.7105i 0.432435 1.14963i
\(582\) 0 0
\(583\) −9.76056 16.9058i −0.404241 0.700166i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.1471 −0.418817 −0.209409 0.977828i \(-0.567154\pi\)
−0.209409 + 0.977828i \(0.567154\pi\)
\(588\) 0 0
\(589\) 7.58547 0.312554
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.85177 4.93941i −0.117108 0.202837i 0.801512 0.597978i \(-0.204029\pi\)
−0.918620 + 0.395141i \(0.870696\pi\)
\(594\) 0 0
\(595\) −10.6787 + 28.3892i −0.437782 + 1.16384i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16.3833 + 28.3768i −0.669405 + 1.15944i 0.308666 + 0.951171i \(0.400118\pi\)
−0.978071 + 0.208273i \(0.933216\pi\)
\(600\) 0 0
\(601\) −33.3712 −1.36124 −0.680619 0.732638i \(-0.738289\pi\)
−0.680619 + 0.732638i \(0.738289\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.43298 12.8743i 0.302194 0.523415i
\(606\) 0 0
\(607\) −15.5037 26.8532i −0.629277 1.08994i −0.987697 0.156379i \(-0.950018\pi\)
0.358420 0.933560i \(-0.383315\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −39.1368 67.7870i −1.58331 2.74237i
\(612\) 0 0
\(613\) −0.394215 + 0.682800i −0.0159222 + 0.0275780i −0.873877 0.486148i \(-0.838402\pi\)
0.857955 + 0.513726i \(0.171735\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.534638 −0.0215237 −0.0107619 0.999942i \(-0.503426\pi\)
−0.0107619 + 0.999942i \(0.503426\pi\)
\(618\) 0 0
\(619\) 10.8238 18.7474i 0.435045 0.753520i −0.562254 0.826964i \(-0.690066\pi\)
0.997299 + 0.0734444i \(0.0233992\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 22.0782 3.64951i 0.884543 0.146215i
\(624\) 0 0
\(625\) 15.6244 + 27.0622i 0.624974 + 1.08249i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −20.8079 −0.829667
\(630\) 0 0
\(631\) −19.7378 −0.785749 −0.392874 0.919592i \(-0.628519\pi\)
−0.392874 + 0.919592i \(0.628519\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.34152 + 10.9838i 0.251656 + 0.435880i
\(636\) 0 0
\(637\) −35.1930 30.8394i −1.39440 1.22190i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −15.6580 + 27.1205i −0.618455 + 1.07119i 0.371313 + 0.928508i \(0.378908\pi\)
−0.989768 + 0.142687i \(0.954426\pi\)
\(642\) 0 0
\(643\) 14.2846 0.563331 0.281665 0.959513i \(-0.409113\pi\)
0.281665 + 0.959513i \(0.409113\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.10642 + 1.91637i −0.0434977 + 0.0753402i −0.886955 0.461857i \(-0.847183\pi\)
0.843457 + 0.537197i \(0.180517\pi\)
\(648\) 0 0
\(649\) −13.9360 24.1379i −0.547037 0.947496i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.1578 + 31.4503i 0.710571 + 1.23074i 0.964643 + 0.263560i \(0.0848966\pi\)
−0.254072 + 0.967185i \(0.581770\pi\)
\(654\) 0 0
\(655\) 8.95271 15.5065i 0.349811 0.605891i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.37474 0.287279 0.143640 0.989630i \(-0.454119\pi\)
0.143640 + 0.989630i \(0.454119\pi\)
\(660\) 0 0
\(661\) −17.0943 + 29.6082i −0.664890 + 1.15162i 0.314425 + 0.949282i \(0.398188\pi\)
−0.979315 + 0.202342i \(0.935145\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.5172 20.1184i −0.640511 0.780157i
\(666\) 0 0
\(667\) −3.42865 5.93859i −0.132758 0.229943i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −28.3201 −1.09329
\(672\) 0 0
\(673\) 22.7219 0.875866 0.437933 0.899008i \(-0.355711\pi\)
0.437933 + 0.899008i \(0.355711\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21.7606 37.6904i −0.836326 1.44856i −0.892946 0.450164i \(-0.851365\pi\)
0.0566194 0.998396i \(-0.481968\pi\)
\(678\) 0 0
\(679\) −2.09703 + 5.57494i −0.0804765 + 0.213947i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.71875 + 13.3693i −0.295350 + 0.511561i −0.975066 0.221914i \(-0.928769\pi\)
0.679716 + 0.733475i \(0.262103\pi\)
\(684\) 0 0
\(685\) 31.5946 1.20717
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 27.6742 47.9331i 1.05430 1.82611i
\(690\) 0 0
\(691\) 0.726764 + 1.25879i 0.0276474 + 0.0478867i 0.879518 0.475866i \(-0.157865\pi\)
−0.851871 + 0.523752i \(0.824532\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17.0843 + 29.5908i 0.648043 + 1.12244i
\(696\) 0 0
\(697\) −18.6971 + 32.3843i −0.708202 + 1.22664i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.25700 −0.0474762 −0.0237381 0.999718i \(-0.507557\pi\)
−0.0237381 + 0.999718i \(0.507557\pi\)
\(702\) 0 0
\(703\) 8.92866 15.4649i 0.336751 0.583270i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.8746 + 14.4635i 0.446589 + 0.543955i
\(708\) 0 0
\(709\) −0.971298 1.68234i −0.0364779 0.0631815i 0.847210 0.531258i \(-0.178281\pi\)
−0.883688 + 0.468076i \(0.844947\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 14.3567 0.537661
\(714\) 0 0
\(715\) −43.0587 −1.61030
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −19.7817 34.2629i −0.737733 1.27779i −0.953514 0.301349i \(-0.902563\pi\)
0.215781 0.976442i \(-0.430770\pi\)
\(720\) 0 0
\(721\) 15.0265 2.48388i 0.559616 0.0925044i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.23957 + 2.14700i −0.0460366 + 0.0797377i
\(726\) 0 0
\(727\) 11.6317 0.431397 0.215699 0.976460i \(-0.430797\pi\)
0.215699 + 0.976460i \(0.430797\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.72334 8.18106i 0.174699 0.302587i
\(732\) 0 0
\(733\) 0.636397 + 1.10227i 0.0235058 + 0.0407133i 0.877539 0.479505i \(-0.159184\pi\)
−0.854033 + 0.520219i \(0.825850\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.14995 12.3841i −0.263372 0.456174i
\(738\) 0 0
\(739\) −0.279341 + 0.483833i −0.0102757 + 0.0177981i −0.871118 0.491075i \(-0.836604\pi\)
0.860842 + 0.508873i \(0.169938\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13.2067 −0.484508 −0.242254 0.970213i \(-0.577887\pi\)
−0.242254 + 0.970213i \(0.577887\pi\)
\(744\) 0 0
\(745\) −9.19615 + 15.9282i −0.336921 + 0.583564i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −47.2075 + 7.80339i −1.72493 + 0.285130i
\(750\) 0 0
\(751\) −20.6281 35.7289i −0.752729 1.30377i −0.946495 0.322718i \(-0.895404\pi\)
0.193766 0.981048i \(-0.437930\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13.1734 −0.479428
\(756\) 0 0
\(757\) 41.7615 1.51785 0.758923 0.651181i \(-0.225726\pi\)
0.758923 + 0.651181i \(0.225726\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 25.3695 + 43.9413i 0.919644 + 1.59287i 0.799955 + 0.600059i \(0.204856\pi\)
0.119689 + 0.992811i \(0.461810\pi\)
\(762\) 0 0
\(763\) 26.8814 + 32.7421i 0.973170 + 1.18534i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 39.5129 68.4384i 1.42673 2.47117i
\(768\) 0 0
\(769\) 4.16070 0.150039 0.0750193 0.997182i \(-0.476098\pi\)
0.0750193 + 0.997182i \(0.476098\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10.0926 17.4809i 0.363006 0.628744i −0.625448 0.780266i \(-0.715084\pi\)
0.988454 + 0.151521i \(0.0484172\pi\)
\(774\) 0 0
\(775\) −2.59521 4.49504i −0.0932227 0.161467i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16.0458 27.7921i −0.574899 0.995755i
\(780\) 0 0
\(781\) 5.76877 9.99180i 0.206423 0.357535i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 57.6672 2.05823
\(786\) 0 0
\(787\) −14.0902 + 24.4049i −0.502261 + 0.869941i 0.497736 + 0.867329i \(0.334165\pi\)
−0.999997 + 0.00261235i \(0.999168\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.64968 7.04417i 0.0942118 0.250462i
\(792\) 0 0
\(793\) −40.1481 69.5386i −1.42570 2.46939i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.44006 −0.157275 −0.0786374 0.996903i \(-0.525057\pi\)
−0.0786374 + 0.996903i \(0.525057\pi\)
\(798\) 0 0
\(799\) 49.1339 1.73823
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.39715 9.34814i −0.190461 0.329889i
\(804\) 0 0