Properties

Label 2352.2.q.bd.1537.1
Level $2352$
Weight $2$
Character 2352.1537
Analytic conductor $18.781$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1537.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.1537
Dual form 2352.2.q.bd.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.70711 - 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.70711 - 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +2.58579 q^{13} -3.41421 q^{15} +(1.12132 - 1.94218i) q^{17} +(-1.41421 - 2.44949i) q^{19} +(-3.82843 - 6.63103i) q^{23} +(-3.32843 + 5.76500i) q^{25} -1.00000 q^{27} -6.82843 q^{29} +(-0.585786 + 1.01461i) q^{31} +(1.00000 + 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{37} +(1.29289 - 2.23936i) q^{39} +6.24264 q^{41} -5.65685 q^{43} +(-1.70711 + 2.95680i) q^{45} +(-1.41421 - 2.44949i) q^{47} +(-1.12132 - 1.94218i) q^{51} +(1.00000 - 1.73205i) q^{53} +6.82843 q^{55} -2.82843 q^{57} +(-0.585786 + 1.01461i) q^{59} +(-6.12132 - 10.6024i) q^{61} +(-4.41421 - 7.64564i) q^{65} +(-2.82843 + 4.89898i) q^{67} -7.65685 q^{69} -9.31371 q^{71} +(-6.94975 + 12.0373i) q^{73} +(3.32843 + 5.76500i) q^{75} +(6.82843 + 11.8272i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.31371 q^{83} -7.65685 q^{85} +(-3.41421 + 5.91359i) q^{87} +(7.12132 + 12.3345i) q^{89} +(0.585786 + 1.01461i) q^{93} +(-4.82843 + 8.36308i) q^{95} +2.58579 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} - 4q^{5} - 2q^{9} - 4q^{11} + 16q^{13} - 8q^{15} - 4q^{17} - 4q^{23} - 2q^{25} - 4q^{27} - 16q^{29} - 8q^{31} + 4q^{33} + 8q^{37} + 8q^{39} + 8q^{41} - 4q^{45} + 4q^{51} + 4q^{53} + 16q^{55} - 8q^{59} - 16q^{61} - 12q^{65} - 8q^{69} + 8q^{71} - 8q^{73} + 2q^{75} + 16q^{79} - 2q^{81} + 16q^{83} - 8q^{85} - 8q^{87} + 20q^{89} + 8q^{93} - 8q^{95} + 16q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −1.70711 2.95680i −0.763441 1.32232i −0.941067 0.338221i \(-0.890175\pi\)
0.177625 0.984098i \(-0.443158\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) 2.58579 0.717168 0.358584 0.933497i \(-0.383260\pi\)
0.358584 + 0.933497i \(0.383260\pi\)
\(14\) 0 0
\(15\) −3.41421 −0.881546
\(16\) 0 0
\(17\) 1.12132 1.94218i 0.271960 0.471049i −0.697404 0.716679i \(-0.745661\pi\)
0.969364 + 0.245630i \(0.0789948\pi\)
\(18\) 0 0
\(19\) −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i \(-0.271843\pi\)
−0.981399 + 0.191977i \(0.938510\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.82843 6.63103i −0.798282 1.38267i −0.920734 0.390191i \(-0.872409\pi\)
0.122452 0.992474i \(-0.460924\pi\)
\(24\) 0 0
\(25\) −3.32843 + 5.76500i −0.665685 + 1.15300i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) 0 0
\(31\) −0.585786 + 1.01461i −0.105210 + 0.182230i −0.913824 0.406110i \(-0.866885\pi\)
0.808614 + 0.588340i \(0.200218\pi\)
\(32\) 0 0
\(33\) 1.00000 + 1.73205i 0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 0 0
\(39\) 1.29289 2.23936i 0.207029 0.358584i
\(40\) 0 0
\(41\) 6.24264 0.974937 0.487468 0.873141i \(-0.337920\pi\)
0.487468 + 0.873141i \(0.337920\pi\)
\(42\) 0 0
\(43\) −5.65685 −0.862662 −0.431331 0.902194i \(-0.641956\pi\)
−0.431331 + 0.902194i \(0.641956\pi\)
\(44\) 0 0
\(45\) −1.70711 + 2.95680i −0.254480 + 0.440773i
\(46\) 0 0
\(47\) −1.41421 2.44949i −0.206284 0.357295i 0.744257 0.667893i \(-0.232804\pi\)
−0.950541 + 0.310599i \(0.899470\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.12132 1.94218i −0.157016 0.271960i
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) 6.82843 0.920745
\(56\) 0 0
\(57\) −2.82843 −0.374634
\(58\) 0 0
\(59\) −0.585786 + 1.01461i −0.0762629 + 0.132091i −0.901635 0.432498i \(-0.857632\pi\)
0.825372 + 0.564589i \(0.190965\pi\)
\(60\) 0 0
\(61\) −6.12132 10.6024i −0.783755 1.35750i −0.929740 0.368216i \(-0.879969\pi\)
0.145985 0.989287i \(-0.453365\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.41421 7.64564i −0.547516 0.948325i
\(66\) 0 0
\(67\) −2.82843 + 4.89898i −0.345547 + 0.598506i −0.985453 0.169948i \(-0.945640\pi\)
0.639906 + 0.768453i \(0.278973\pi\)
\(68\) 0 0
\(69\) −7.65685 −0.921777
\(70\) 0 0
\(71\) −9.31371 −1.10533 −0.552667 0.833402i \(-0.686390\pi\)
−0.552667 + 0.833402i \(0.686390\pi\)
\(72\) 0 0
\(73\) −6.94975 + 12.0373i −0.813406 + 1.40886i 0.0970601 + 0.995279i \(0.469056\pi\)
−0.910467 + 0.413583i \(0.864277\pi\)
\(74\) 0 0
\(75\) 3.32843 + 5.76500i 0.384334 + 0.665685i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 6.82843 + 11.8272i 0.768258 + 1.33066i 0.938507 + 0.345261i \(0.112210\pi\)
−0.170249 + 0.985401i \(0.554457\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −7.31371 −0.802784 −0.401392 0.915906i \(-0.631473\pi\)
−0.401392 + 0.915906i \(0.631473\pi\)
\(84\) 0 0
\(85\) −7.65685 −0.830502
\(86\) 0 0
\(87\) −3.41421 + 5.91359i −0.366042 + 0.634004i
\(88\) 0 0
\(89\) 7.12132 + 12.3345i 0.754858 + 1.30745i 0.945445 + 0.325783i \(0.105628\pi\)
−0.190586 + 0.981670i \(0.561039\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.585786 + 1.01461i 0.0607432 + 0.105210i
\(94\) 0 0
\(95\) −4.82843 + 8.36308i −0.495386 + 0.858034i
\(96\) 0 0
\(97\) 2.58579 0.262547 0.131273 0.991346i \(-0.458093\pi\)
0.131273 + 0.991346i \(0.458093\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −1.46447 + 2.53653i −0.145720 + 0.252394i −0.929641 0.368466i \(-0.879883\pi\)
0.783921 + 0.620860i \(0.213216\pi\)
\(102\) 0 0
\(103\) 2.24264 + 3.88437i 0.220974 + 0.382738i 0.955104 0.296271i \(-0.0957431\pi\)
−0.734130 + 0.679009i \(0.762410\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.171573 0.297173i −0.0165866 0.0287288i 0.857613 0.514296i \(-0.171947\pi\)
−0.874200 + 0.485567i \(0.838613\pi\)
\(108\) 0 0
\(109\) 2.82843 4.89898i 0.270914 0.469237i −0.698182 0.715920i \(-0.746007\pi\)
0.969096 + 0.246683i \(0.0793407\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) −5.31371 −0.499872 −0.249936 0.968262i \(-0.580410\pi\)
−0.249936 + 0.968262i \(0.580410\pi\)
\(114\) 0 0
\(115\) −13.0711 + 22.6398i −1.21888 + 2.11117i
\(116\) 0 0
\(117\) −1.29289 2.23936i −0.119528 0.207029i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) 3.12132 5.40629i 0.281440 0.487468i
\(124\) 0 0
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) 1.65685 0.147022 0.0735110 0.997294i \(-0.476580\pi\)
0.0735110 + 0.997294i \(0.476580\pi\)
\(128\) 0 0
\(129\) −2.82843 + 4.89898i −0.249029 + 0.431331i
\(130\) 0 0
\(131\) −7.65685 13.2621i −0.668982 1.15871i −0.978189 0.207717i \(-0.933397\pi\)
0.309207 0.950995i \(-0.399937\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.70711 + 2.95680i 0.146924 + 0.254480i
\(136\) 0 0
\(137\) −7.07107 + 12.2474i −0.604122 + 1.04637i 0.388067 + 0.921631i \(0.373143\pi\)
−0.992190 + 0.124739i \(0.960191\pi\)
\(138\) 0 0
\(139\) 17.6569 1.49763 0.748817 0.662776i \(-0.230622\pi\)
0.748817 + 0.662776i \(0.230622\pi\)
\(140\) 0 0
\(141\) −2.82843 −0.238197
\(142\) 0 0
\(143\) −2.58579 + 4.47871i −0.216234 + 0.374529i
\(144\) 0 0
\(145\) 11.6569 + 20.1903i 0.968049 + 1.67671i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.65685 14.9941i −0.709197 1.22837i −0.965155 0.261678i \(-0.915724\pi\)
0.255958 0.966688i \(-0.417609\pi\)
\(150\) 0 0
\(151\) 6.00000 10.3923i 0.488273 0.845714i −0.511636 0.859202i \(-0.670960\pi\)
0.999909 + 0.0134886i \(0.00429367\pi\)
\(152\) 0 0
\(153\) −2.24264 −0.181307
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −5.87868 + 10.1822i −0.469170 + 0.812626i −0.999379 0.0352411i \(-0.988780\pi\)
0.530209 + 0.847867i \(0.322113\pi\)
\(158\) 0 0
\(159\) −1.00000 1.73205i −0.0793052 0.137361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −5.65685 9.79796i −0.443079 0.767435i 0.554837 0.831959i \(-0.312781\pi\)
−0.997916 + 0.0645236i \(0.979447\pi\)
\(164\) 0 0
\(165\) 3.41421 5.91359i 0.265796 0.460372i
\(166\) 0 0
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) −6.31371 −0.485670
\(170\) 0 0
\(171\) −1.41421 + 2.44949i −0.108148 + 0.187317i
\(172\) 0 0
\(173\) −10.5355 18.2481i −0.801002 1.38738i −0.918957 0.394357i \(-0.870967\pi\)
0.117956 0.993019i \(-0.462366\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.585786 + 1.01461i 0.0440304 + 0.0762629i
\(178\) 0 0
\(179\) −9.82843 + 17.0233i −0.734611 + 1.27238i 0.220283 + 0.975436i \(0.429302\pi\)
−0.954894 + 0.296948i \(0.904031\pi\)
\(180\) 0 0
\(181\) −2.58579 −0.192200 −0.0961000 0.995372i \(-0.530637\pi\)
−0.0961000 + 0.995372i \(0.530637\pi\)
\(182\) 0 0
\(183\) −12.2426 −0.905002
\(184\) 0 0
\(185\) 6.82843 11.8272i 0.502036 0.869552i
\(186\) 0 0
\(187\) 2.24264 + 3.88437i 0.163998 + 0.284053i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 0 0
\(193\) −2.65685 + 4.60181i −0.191245 + 0.331245i −0.945663 0.325149i \(-0.894586\pi\)
0.754418 + 0.656394i \(0.227919\pi\)
\(194\) 0 0
\(195\) −8.82843 −0.632217
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 10.8284 18.7554i 0.767607 1.32953i −0.171250 0.985228i \(-0.554781\pi\)
0.938857 0.344307i \(-0.111886\pi\)
\(200\) 0 0
\(201\) 2.82843 + 4.89898i 0.199502 + 0.345547i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −10.6569 18.4582i −0.744307 1.28918i
\(206\) 0 0
\(207\) −3.82843 + 6.63103i −0.266094 + 0.460888i
\(208\) 0 0
\(209\) 5.65685 0.391293
\(210\) 0 0
\(211\) −12.9706 −0.892930 −0.446465 0.894801i \(-0.647317\pi\)
−0.446465 + 0.894801i \(0.647317\pi\)
\(212\) 0 0
\(213\) −4.65685 + 8.06591i −0.319082 + 0.552667i
\(214\) 0 0
\(215\) 9.65685 + 16.7262i 0.658592 + 1.14071i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.94975 + 12.0373i 0.469620 + 0.813406i
\(220\) 0 0
\(221\) 2.89949 5.02207i 0.195041 0.337821i
\(222\) 0 0
\(223\) −24.9706 −1.67215 −0.836076 0.548613i \(-0.815156\pi\)
−0.836076 + 0.548613i \(0.815156\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) 0 0
\(227\) 11.8995 20.6105i 0.789797 1.36797i −0.136294 0.990668i \(-0.543519\pi\)
0.926091 0.377300i \(-0.123148\pi\)
\(228\) 0 0
\(229\) 0.121320 + 0.210133i 0.00801707 + 0.0138860i 0.870006 0.493041i \(-0.164115\pi\)
−0.861989 + 0.506927i \(0.830781\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.07107 + 5.31925i 0.201192 + 0.348475i 0.948913 0.315538i \(-0.102185\pi\)
−0.747721 + 0.664014i \(0.768852\pi\)
\(234\) 0 0
\(235\) −4.82843 + 8.36308i −0.314972 + 0.545547i
\(236\) 0 0
\(237\) 13.6569 0.887108
\(238\) 0 0
\(239\) 15.6569 1.01276 0.506379 0.862311i \(-0.330984\pi\)
0.506379 + 0.862311i \(0.330984\pi\)
\(240\) 0 0
\(241\) 8.12132 14.0665i 0.523140 0.906105i −0.476497 0.879176i \(-0.658094\pi\)
0.999637 0.0269294i \(-0.00857294\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.65685 6.33386i −0.232680 0.403014i
\(248\) 0 0
\(249\) −3.65685 + 6.33386i −0.231744 + 0.401392i
\(250\) 0 0
\(251\) 12.4853 0.788064 0.394032 0.919097i \(-0.371080\pi\)
0.394032 + 0.919097i \(0.371080\pi\)
\(252\) 0 0
\(253\) 15.3137 0.962765
\(254\) 0 0
\(255\) −3.82843 + 6.63103i −0.239745 + 0.415251i
\(256\) 0 0
\(257\) −11.6066 20.1032i −0.724000 1.25400i −0.959384 0.282102i \(-0.908968\pi\)
0.235384 0.971902i \(-0.424365\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.41421 + 5.91359i 0.211335 + 0.366042i
\(262\) 0 0
\(263\) 2.65685 4.60181i 0.163829 0.283760i −0.772410 0.635124i \(-0.780949\pi\)
0.936239 + 0.351365i \(0.114282\pi\)
\(264\) 0 0
\(265\) −6.82843 −0.419467
\(266\) 0 0
\(267\) 14.2426 0.871635
\(268\) 0 0
\(269\) 7.36396 12.7548i 0.448989 0.777671i −0.549332 0.835604i \(-0.685118\pi\)
0.998320 + 0.0579332i \(0.0184510\pi\)
\(270\) 0 0
\(271\) −5.07107 8.78335i −0.308045 0.533550i 0.669889 0.742461i \(-0.266342\pi\)
−0.977935 + 0.208911i \(0.933008\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.65685 11.5300i −0.401423 0.695286i
\(276\) 0 0
\(277\) 4.65685 8.06591i 0.279803 0.484633i −0.691532 0.722345i \(-0.743064\pi\)
0.971336 + 0.237712i \(0.0763974\pi\)
\(278\) 0 0
\(279\) 1.17157 0.0701402
\(280\) 0 0
\(281\) 0.485281 0.0289495 0.0144747 0.999895i \(-0.495392\pi\)
0.0144747 + 0.999895i \(0.495392\pi\)
\(282\) 0 0
\(283\) −4.24264 + 7.34847i −0.252199 + 0.436821i −0.964131 0.265427i \(-0.914487\pi\)
0.711932 + 0.702248i \(0.247820\pi\)
\(284\) 0 0
\(285\) 4.82843 + 8.36308i 0.286011 + 0.495386i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 5.98528 + 10.3668i 0.352075 + 0.609812i
\(290\) 0 0
\(291\) 1.29289 2.23936i 0.0757907 0.131273i
\(292\) 0 0
\(293\) 16.5858 0.968952 0.484476 0.874805i \(-0.339010\pi\)
0.484476 + 0.874805i \(0.339010\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 0 0
\(297\) 1.00000 1.73205i 0.0580259 0.100504i
\(298\) 0 0
\(299\) −9.89949 17.1464i −0.572503 0.991604i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.46447 + 2.53653i 0.0841314 + 0.145720i
\(304\) 0 0
\(305\) −20.8995 + 36.1990i −1.19670 + 2.07275i
\(306\) 0 0
\(307\) −30.1421 −1.72030 −0.860151 0.510039i \(-0.829631\pi\)
−0.860151 + 0.510039i \(0.829631\pi\)
\(308\) 0 0
\(309\) 4.48528 0.255159
\(310\) 0 0
\(311\) 3.07107 5.31925i 0.174144 0.301627i −0.765721 0.643173i \(-0.777617\pi\)
0.939865 + 0.341547i \(0.110951\pi\)
\(312\) 0 0
\(313\) −0.949747 1.64501i −0.0536829 0.0929815i 0.837935 0.545770i \(-0.183763\pi\)
−0.891618 + 0.452788i \(0.850429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i \(-0.257276\pi\)
−0.971589 + 0.236675i \(0.923942\pi\)
\(318\) 0 0
\(319\) 6.82843 11.8272i 0.382319 0.662195i
\(320\) 0 0
\(321\) −0.343146 −0.0191525
\(322\) 0 0
\(323\) −6.34315 −0.352942
\(324\) 0 0
\(325\) −8.60660 + 14.9071i −0.477408 + 0.826896i
\(326\) 0 0
\(327\) −2.82843 4.89898i −0.156412 0.270914i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 0 0
\(333\) 2.00000 3.46410i 0.109599 0.189832i
\(334\) 0 0
\(335\) 19.3137 1.05522
\(336\) 0 0
\(337\) −29.6569 −1.61551 −0.807756 0.589517i \(-0.799318\pi\)
−0.807756 + 0.589517i \(0.799318\pi\)
\(338\) 0 0
\(339\) −2.65685 + 4.60181i −0.144301 + 0.249936i
\(340\) 0 0
\(341\) −1.17157 2.02922i −0.0634442 0.109889i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 13.0711 + 22.6398i 0.703723 + 1.21888i
\(346\) 0 0
\(347\) 16.6569 28.8505i 0.894187 1.54878i 0.0593789 0.998236i \(-0.481088\pi\)
0.834808 0.550541i \(-0.185579\pi\)
\(348\) 0 0
\(349\) −9.89949 −0.529908 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(350\) 0 0
\(351\) −2.58579 −0.138019
\(352\) 0 0
\(353\) 7.36396 12.7548i 0.391944 0.678867i −0.600762 0.799428i \(-0.705136\pi\)
0.992706 + 0.120561i \(0.0384693\pi\)
\(354\) 0 0
\(355\) 15.8995 + 27.5387i 0.843858 + 1.46160i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.171573 0.297173i −0.00905527 0.0156842i 0.861462 0.507822i \(-0.169549\pi\)
−0.870518 + 0.492137i \(0.836216\pi\)
\(360\) 0 0
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 47.4558 2.48395
\(366\) 0 0
\(367\) −1.65685 + 2.86976i −0.0864871 + 0.149800i −0.906024 0.423226i \(-0.860897\pi\)
0.819537 + 0.573027i \(0.194231\pi\)
\(368\) 0 0
\(369\) −3.12132 5.40629i −0.162489 0.281440i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5.34315 + 9.25460i 0.276658 + 0.479185i 0.970552 0.240892i \(-0.0774399\pi\)
−0.693894 + 0.720077i \(0.744107\pi\)
\(374\) 0 0
\(375\) 2.82843 4.89898i 0.146059 0.252982i
\(376\) 0 0
\(377\) −17.6569 −0.909374
\(378\) 0 0
\(379\) −8.68629 −0.446185 −0.223092 0.974797i \(-0.571615\pi\)
−0.223092 + 0.974797i \(0.571615\pi\)
\(380\) 0 0
\(381\) 0.828427 1.43488i 0.0424416 0.0735110i
\(382\) 0 0
\(383\) −9.17157 15.8856i −0.468645 0.811718i 0.530712 0.847552i \(-0.321924\pi\)
−0.999358 + 0.0358343i \(0.988591\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.82843 + 4.89898i 0.143777 + 0.249029i
\(388\) 0 0
\(389\) 9.07107 15.7116i 0.459921 0.796607i −0.539035 0.842283i \(-0.681211\pi\)
0.998956 + 0.0456762i \(0.0145442\pi\)
\(390\) 0 0
\(391\) −17.1716 −0.868404
\(392\) 0 0
\(393\) −15.3137 −0.772474
\(394\) 0 0
\(395\) 23.3137 40.3805i 1.17304 2.03176i
\(396\) 0 0
\(397\) 1.19239 + 2.06528i 0.0598442 + 0.103653i 0.894395 0.447277i \(-0.147606\pi\)
−0.834551 + 0.550931i \(0.814273\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.07107 + 5.31925i 0.153362 + 0.265630i 0.932461 0.361270i \(-0.117657\pi\)
−0.779100 + 0.626900i \(0.784323\pi\)
\(402\) 0 0
\(403\) −1.51472 + 2.62357i −0.0754535 + 0.130689i
\(404\) 0 0
\(405\) 3.41421 0.169654
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 10.7071 18.5453i 0.529432 0.917004i −0.469978 0.882678i \(-0.655738\pi\)
0.999411 0.0343258i \(-0.0109284\pi\)
\(410\) 0 0
\(411\) 7.07107 + 12.2474i 0.348790 + 0.604122i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 12.4853 + 21.6251i 0.612878 + 1.06154i
\(416\) 0 0
\(417\) 8.82843 15.2913i 0.432330 0.748817i
\(418\) 0 0
\(419\) −33.1716 −1.62054 −0.810269 0.586059i \(-0.800679\pi\)
−0.810269 + 0.586059i \(0.800679\pi\)
\(420\) 0 0
\(421\) 16.6274 0.810371 0.405185 0.914235i \(-0.367207\pi\)
0.405185 + 0.914235i \(0.367207\pi\)
\(422\) 0 0
\(423\) −1.41421 + 2.44949i −0.0687614 + 0.119098i
\(424\) 0 0
\(425\) 7.46447 + 12.9288i 0.362080 + 0.627141i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.58579 + 4.47871i 0.124843 + 0.216234i
\(430\) 0 0
\(431\) −13.4853 + 23.3572i −0.649563 + 1.12508i 0.333664 + 0.942692i \(0.391715\pi\)
−0.983227 + 0.182384i \(0.941618\pi\)
\(432\) 0 0
\(433\) −20.2426 −0.972799 −0.486400 0.873736i \(-0.661690\pi\)
−0.486400 + 0.873736i \(0.661690\pi\)
\(434\) 0 0
\(435\) 23.3137 1.11781
\(436\) 0 0
\(437\) −10.8284 + 18.7554i −0.517994 + 0.897192i
\(438\) 0 0
\(439\) 6.34315 + 10.9867i 0.302742 + 0.524364i 0.976756 0.214354i \(-0.0687647\pi\)
−0.674014 + 0.738718i \(0.735431\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.4853 + 30.2854i 0.830751 + 1.43890i 0.897444 + 0.441129i \(0.145422\pi\)
−0.0666929 + 0.997774i \(0.521245\pi\)
\(444\) 0 0
\(445\) 24.3137 42.1126i 1.15258 1.99633i
\(446\) 0 0
\(447\) −17.3137 −0.818910
\(448\) 0 0
\(449\) −5.31371 −0.250769 −0.125385 0.992108i \(-0.540017\pi\)
−0.125385 + 0.992108i \(0.540017\pi\)
\(450\) 0 0
\(451\) −6.24264 + 10.8126i −0.293954 + 0.509144i
\(452\) 0 0
\(453\) −6.00000 10.3923i −0.281905 0.488273i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) 0 0
\(459\) −1.12132 + 1.94218i −0.0523388 + 0.0906534i
\(460\) 0 0
\(461\) −16.5858 −0.772477 −0.386239 0.922399i \(-0.626226\pi\)
−0.386239 + 0.922399i \(0.626226\pi\)
\(462\) 0 0
\(463\) 26.6274 1.23748 0.618741 0.785595i \(-0.287643\pi\)
0.618741 + 0.785595i \(0.287643\pi\)
\(464\) 0 0
\(465\) 2.00000 3.46410i 0.0927478 0.160644i
\(466\) 0 0
\(467\) 0.100505 + 0.174080i 0.00465082 + 0.00805546i 0.868341 0.495967i \(-0.165186\pi\)
−0.863691 + 0.504022i \(0.831853\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 5.87868 + 10.1822i 0.270875 + 0.469170i
\(472\) 0 0
\(473\) 5.65685 9.79796i 0.260102 0.450511i
\(474\) 0 0
\(475\) 18.8284 0.863907
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) 0.928932 1.60896i 0.0424440 0.0735152i −0.844023 0.536307i \(-0.819819\pi\)
0.886467 + 0.462792i \(0.153152\pi\)
\(480\) 0 0
\(481\) 5.17157 + 8.95743i 0.235803 + 0.408424i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.41421 7.64564i −0.200439 0.347171i
\(486\) 0 0
\(487\) 13.3137 23.0600i 0.603302 1.04495i −0.389016 0.921231i \(-0.627185\pi\)
0.992317 0.123718i \(-0.0394819\pi\)
\(488\) 0 0
\(489\) −11.3137 −0.511624
\(490\) 0 0
\(491\) −5.02944 −0.226975 −0.113488 0.993539i \(-0.536202\pi\)
−0.113488 + 0.993539i \(0.536202\pi\)
\(492\) 0 0
\(493\) −7.65685 + 13.2621i −0.344847 + 0.597293i
\(494\) 0 0
\(495\) −3.41421 5.91359i −0.153457 0.265796i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.65685 + 2.86976i 0.0741710 + 0.128468i 0.900725 0.434389i \(-0.143036\pi\)
−0.826554 + 0.562857i \(0.809702\pi\)
\(500\) 0 0
\(501\) 9.89949 17.1464i 0.442277 0.766046i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) −3.15685 + 5.46783i −0.140201 + 0.242835i
\(508\) 0 0
\(509\) −2.77817 4.81194i −0.123140 0.213285i 0.797864 0.602837i \(-0.205963\pi\)
−0.921005 + 0.389552i \(0.872630\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.41421 + 2.44949i 0.0624391 + 0.108148i
\(514\) 0 0
\(515\) 7.65685 13.2621i 0.337401 0.584396i
\(516\) 0 0
\(517\) 5.65685 0.248788
\(518\) 0 0
\(519\) −21.0711 −0.924917
\(520\) 0 0
\(521\) 17.7071 30.6696i 0.775762 1.34366i −0.158603 0.987343i \(-0.550699\pi\)
0.934365 0.356317i \(-0.115968\pi\)
\(522\) 0 0
\(523\) −12.8284 22.2195i −0.560948 0.971590i −0.997414 0.0718696i \(-0.977103\pi\)
0.436466 0.899721i \(-0.356230\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.31371 + 2.27541i 0.0572260 + 0.0991184i
\(528\) 0 0
\(529\) −17.8137 + 30.8542i −0.774509 + 1.34149i
\(530\) 0 0
\(531\) 1.17157 0.0508419
\(532\) 0 0
\(533\) 16.1421 0.699194
\(534\) 0 0
\(535\) −0.585786 + 1.01461i −0.0253258 + 0.0438655i
\(536\) 0 0
\(537\) 9.82843 + 17.0233i 0.424128 + 0.734611i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −8.65685 14.9941i −0.372187 0.644647i 0.617715 0.786402i \(-0.288059\pi\)
−0.989902 + 0.141755i \(0.954725\pi\)
\(542\) 0 0
\(543\) −1.29289 + 2.23936i −0.0554834 + 0.0961000i
\(544\) 0 0
\(545\) −19.3137 −0.827308
\(546\) 0 0
\(547\) 36.9706 1.58075 0.790374 0.612625i \(-0.209886\pi\)
0.790374 + 0.612625i \(0.209886\pi\)
\(548\) 0 0
\(549\) −6.12132 + 10.6024i −0.261252 + 0.452501i
\(550\) 0 0
\(551\) 9.65685 + 16.7262i 0.411396 + 0.712558i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6.82843 11.8272i −0.289851 0.502036i
\(556\) 0 0
\(557\) −13.0000 + 22.5167i −0.550828 + 0.954062i 0.447387 + 0.894340i \(0.352355\pi\)
−0.998215 + 0.0597213i \(0.980979\pi\)
\(558\) 0 0
\(559\) −14.6274 −0.618674
\(560\) 0 0
\(561\) 4.48528 0.189369
\(562\) 0 0
\(563\) −0.585786 + 1.01461i −0.0246880 + 0.0427608i −0.878105 0.478467i \(-0.841193\pi\)
0.853417 + 0.521228i \(0.174526\pi\)
\(564\) 0 0
\(565\) 9.07107 + 15.7116i 0.381623 + 0.660990i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.24264 + 14.2767i 0.345549 + 0.598509i 0.985453 0.169946i \(-0.0543592\pi\)
−0.639904 + 0.768455i \(0.721026\pi\)
\(570\) 0 0
\(571\) 11.1716 19.3497i 0.467516 0.809761i −0.531795 0.846873i \(-0.678482\pi\)
0.999311 + 0.0371118i \(0.0118158\pi\)
\(572\) 0 0
\(573\) −18.0000 −0.751961
\(574\) 0 0
\(575\) 50.9706 2.12562
\(576\) 0 0
\(577\) 16.9497 29.3578i 0.705627 1.22218i −0.260837 0.965383i \(-0.583999\pi\)
0.966465 0.256799i \(-0.0826680\pi\)
\(578\) 0 0
\(579\) 2.65685 + 4.60181i 0.110415 + 0.191245i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.00000 + 3.46410i 0.0828315 + 0.143468i
\(584\) 0 0
\(585\) −4.41421 + 7.64564i −0.182505 + 0.316108i
\(586\) 0 0
\(587\) 22.8284 0.942230 0.471115 0.882072i \(-0.343852\pi\)
0.471115 + 0.882072i \(0.343852\pi\)
\(588\) 0 0
\(589\) 3.31371 0.136539
\(590\) 0 0
\(591\) 1.00000 1.73205i 0.0411345 0.0712470i
\(592\) 0 0
\(593\) 3.46447 + 6.00063i 0.142269 + 0.246416i 0.928351 0.371706i \(-0.121227\pi\)
−0.786082 + 0.618122i \(0.787894\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −10.8284 18.7554i −0.443178 0.767607i
\(598\) 0 0
\(599\) −1.00000 + 1.73205i −0.0408589 + 0.0707697i −0.885732 0.464198i \(-0.846343\pi\)
0.844873 + 0.534967i \(0.179676\pi\)
\(600\) 0 0
\(601\) −15.0711 −0.614762 −0.307381 0.951587i \(-0.599453\pi\)
−0.307381 + 0.951587i \(0.599453\pi\)
\(602\) 0 0
\(603\) 5.65685 0.230365
\(604\) 0 0
\(605\) 11.9497 20.6976i 0.485826 0.841476i
\(606\) 0 0
\(607\) −9.17157 15.8856i −0.372263 0.644778i 0.617651 0.786453i \(-0.288085\pi\)
−0.989913 + 0.141675i \(0.954751\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.65685 6.33386i −0.147940 0.256240i
\(612\) 0 0
\(613\) −2.34315 + 4.05845i −0.0946388 + 0.163919i −0.909458 0.415796i \(-0.863503\pi\)
0.814819 + 0.579715i \(0.196836\pi\)
\(614\) 0 0
\(615\) −21.3137 −0.859452
\(616\) 0 0
\(617\) −24.4853 −0.985740 −0.492870 0.870103i \(-0.664052\pi\)
−0.492870 + 0.870103i \(0.664052\pi\)
\(618\) 0 0
\(619\) 14.4853 25.0892i 0.582213 1.00842i −0.413004 0.910729i \(-0.635520\pi\)
0.995217 0.0976926i \(-0.0311462\pi\)
\(620\) 0 0
\(621\) 3.82843 + 6.63103i 0.153629 + 0.266094i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 6.98528 + 12.0989i 0.279411 + 0.483954i
\(626\) 0 0
\(627\) 2.82843 4.89898i 0.112956 0.195646i
\(628\) 0 0
\(629\) 8.97056 0.357680
\(630\) 0 0
\(631\) −23.3137 −0.928104 −0.464052 0.885808i \(-0.653605\pi\)
−0.464052 + 0.885808i \(0.653605\pi\)
\(632\) 0 0
\(633\) −6.48528 + 11.2328i −0.257767 + 0.446465i
\(634\) 0 0
\(635\) −2.82843 4.89898i −0.112243 0.194410i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 4.65685 + 8.06591i 0.184222 + 0.319082i
\(640\) 0 0
\(641\) 5.41421 9.37769i 0.213849 0.370397i −0.739067 0.673632i \(-0.764733\pi\)
0.952916 + 0.303235i \(0.0980668\pi\)
\(642\) 0 0
\(643\) 34.4264 1.35764 0.678822 0.734302i \(-0.262491\pi\)
0.678822 + 0.734302i \(0.262491\pi\)
\(644\) 0 0
\(645\) 19.3137 0.760477
\(646\) 0 0
\(647\) 13.4142 23.2341i 0.527367 0.913427i −0.472124 0.881532i \(-0.656513\pi\)
0.999491 0.0318946i \(-0.0101541\pi\)
\(648\) 0 0
\(649\) −1.17157 2.02922i −0.0459883 0.0796540i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −18.2426 31.5972i −0.713890 1.23649i −0.963386 0.268118i \(-0.913598\pi\)
0.249497 0.968376i \(-0.419735\pi\)
\(654\) 0 0
\(655\) −26.1421 + 45.2795i −1.02146 + 1.76922i
\(656\) 0 0
\(657\) 13.8995 0.542271
\(658\) 0 0
\(659\) −9.31371 −0.362811 −0.181405 0.983408i \(-0.558065\pi\)
−0.181405 + 0.983408i \(0.558065\pi\)
\(660\) 0 0
\(661\) 11.7782 20.4004i 0.458118 0.793483i −0.540744 0.841187i \(-0.681857\pi\)
0.998862 + 0.0477040i \(0.0151904\pi\)
\(662\) 0 0
\(663\) −2.89949 5.02207i −0.112607 0.195041i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 26.1421 + 45.2795i 1.01223 + 1.75323i
\(668\) 0 0
\(669\) −12.4853 + 21.6251i −0.482709 + 0.836076i
\(670\) 0 0
\(671\) 24.4853 0.945244
\(672\) 0 0
\(673\) 23.3137 0.898677 0.449339 0.893361i \(-0.351660\pi\)
0.449339 + 0.893361i \(0.351660\pi\)
\(674\) 0 0
\(675\) 3.32843 5.76500i 0.128111 0.221895i
\(676\) 0 0
\(677\) −15.7071 27.2055i −0.603673 1.04559i −0.992260 0.124180i \(-0.960370\pi\)
0.388587 0.921412i \(-0.372963\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −11.8995 20.6105i −0.455990 0.789797i
\(682\) 0 0
\(683\) −9.82843 + 17.0233i −0.376074 + 0.651380i −0.990487 0.137605i \(-0.956060\pi\)
0.614413 + 0.788985i \(0.289393\pi\)
\(684\) 0 0
\(685\) 48.2843 1.84485
\(686\) 0 0
\(687\) 0.242641 0.00925732
\(688\) 0 0
\(689\) 2.58579 4.47871i 0.0985106 0.170625i
\(690\) 0 0
\(691\) −0.343146 0.594346i −0.0130539 0.0226100i 0.859425 0.511262i \(-0.170822\pi\)
−0.872479 + 0.488652i \(0.837489\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −30.1421 52.2077i −1.14336 1.98035i
\(696\) 0 0
\(697\) 7.00000 12.1244i 0.265144 0.459243i
\(698\) 0 0
\(699\) 6.14214 0.232317
\(700\) 0 0
\(701\) −17.1716 −0.648561 −0.324281 0.945961i \(-0.605122\pi\)
−0.324281 + 0.945961i \(0.605122\pi\)
\(702\) 0 0
\(703\) 5.65685 9.79796i 0.213352 0.369537i
\(704\) 0 0
\(705\) 4.82843 + 8.36308i 0.181849 + 0.314972i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 18.1421 + 31.4231i 0.681342 + 1.18012i 0.974571 + 0.224077i \(0.0719368\pi\)
−0.293229 + 0.956042i \(0.594730\pi\)
\(710\) 0 0
\(711\) 6.82843 11.8272i 0.256086 0.443554i
\(712\) 0 0
\(713\) 8.97056 0.335950
\(714\) 0 0
\(715\) 17.6569 0.660329
\(716\) 0 0
\(717\) 7.82843 13.5592i 0.292358 0.506379i
\(718\) 0 0
\(719\) 20.9706 + 36.3221i 0.782070 + 1.35459i 0.930734 + 0.365697i \(0.119169\pi\)
−0.148664 + 0.988888i \(0.547497\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −8.12132 14.0665i −0.302035 0.523140i
\(724\) 0 0
\(725\) 22.7279 39.3659i 0.844094 1.46201i
\(726\) 0 0
\(727\) −12.4853 −0.463053 −0.231527 0.972829i \(-0.574372\pi\)
−0.231527 + 0.972829i \(0.574372\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −6.34315 + 10.9867i −0.234610 + 0.406356i
\(732\) 0 0
\(733\) −24.8492 43.0402i −0.917828 1.58972i −0.802708 0.596373i \(-0.796608\pi\)
−0.115120 0.993352i \(-0.536725\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.65685 9.79796i −0.208373 0.360912i
\(738\) 0 0
\(739\) 2.34315 4.05845i 0.0861940 0.149292i −0.819705 0.572785i \(-0.805863\pi\)
0.905899 + 0.423493i \(0.139196\pi\)
\(740\) 0 0
\(741\) −7.31371 −0.268676
\(742\) 0 0
\(743\) 50.9706 1.86993 0.934964 0.354742i \(-0.115431\pi\)
0.934964 + 0.354742i \(0.115431\pi\)
\(744\) 0 0
\(745\) −29.5563 + 51.1931i −1.08286 + 1.87557i
\(746\) 0 0
\(747\) 3.65685 + 6.33386i 0.133797 + 0.231744i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 6.82843 + 11.8272i 0.249173 + 0.431580i 0.963297 0.268440i \(-0.0865079\pi\)
−0.714124 + 0.700020i \(0.753175\pi\)
\(752\) 0 0
\(753\) 6.24264 10.8126i 0.227494 0.394032i
\(754\) 0 0
\(755\) −40.9706 −1.49107
\(756\) 0 0
\(757\) 26.3431 0.957458 0.478729 0.877963i \(-0.341098\pi\)
0.478729 + 0.877963i \(0.341098\pi\)
\(758\) 0 0
\(759\) 7.65685 13.2621i 0.277926 0.481382i
\(760\) 0 0
\(761\) 9.26346 + 16.0448i 0.335800 + 0.581623i 0.983638 0.180155i \(-0.0576600\pi\)
−0.647838 + 0.761778i \(0.724327\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3.82843 + 6.63103i 0.138417 + 0.239745i
\(766\) 0 0
\(767\) −1.51472 + 2.62357i −0.0546933 + 0.0947316i
\(768\) 0 0
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) −23.2132 −0.836003
\(772\) 0 0
\(773\) 4.77817 8.27604i 0.171859 0.297669i −0.767211 0.641395i \(-0.778356\pi\)
0.939070 + 0.343727i \(0.111689\pi\)
\(774\) 0 0
\(775\) −3.89949 6.75412i −0.140074 0.242615i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.82843 15.2913i −0.316311 0.547867i
\(780\) 0 0
\(781\) 9.31371 16.1318i 0.333271 0.577242i
\(782\) 0 0
\(783\) 6.82843 0.244028
\(784\) 0 0
\(785\) 40.1421 1.43273
\(786\) 0 0
\(787\) 12.3431 21.3790i 0.439986 0.762077i −0.557702 0.830041i \(-0.688317\pi\)
0.997688 + 0.0679637i \(0.0216502\pi\)
\(788\) 0 0
\(789\) −2.65685 4.60181i −0.0945865 0.163829i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −15.8284 27.4156i −0.562084 0.973558i
\(794\) 0 0
\(795\) −3.41421 + 5.91359i −0.121090 + 0.209733i
\(796\) 0 0
\(797\) −8.38478 −0.297004 −0.148502 0.988912i \(-0.547445\pi\)
−0.148502 + 0.988912i \(0.547445\pi\)
\(798\) 0 0
\(799\) −6.34315 −0.224404