Properties

Label 2352.2.q.bb.961.2
Level $2352$
Weight $2$
Character 2352.961
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 961.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.961
Dual form 2352.2.q.bb.1537.2

$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

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

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 −0.177625 0.984098i \(-0.556842\pi\)
0.941067 0.338221i \(-0.109825\pi\)
\(6\) 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 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) −2.58579 −0.717168 −0.358584 0.933497i \(-0.616740\pi\)
−0.358584 + 0.933497i \(0.616740\pi\)
\(14\) 0 0
\(15\) −3.41421 −0.881546
\(16\) 0 0
\(17\) −1.12132 1.94218i −0.271960 0.471049i 0.697404 0.716679i \(-0.254339\pi\)
−0.969364 + 0.245630i \(0.921005\pi\)
\(18\) 0 0
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.82843 + 6.63103i −0.798282 + 1.38267i 0.122452 + 0.992474i \(0.460924\pi\)
−0.920734 + 0.390191i \(0.872409\pi\)
\(24\) 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 \(-0.133115\pi\)
−0.808614 + 0.588340i \(0.799782\pi\)
\(32\) 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 −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 0 0
\(39\) 1.29289 + 2.23936i 0.207029 + 0.358584i
\(40\) 0 0
\(41\) −6.24264 −0.974937 −0.487468 0.873141i \(-0.662080\pi\)
−0.487468 + 0.873141i \(0.662080\pi\)
\(42\) 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 \(-0.767196\pi\)
0.950541 + 0.310599i \(0.100530\pi\)
\(48\) 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 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 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 \(-0.142368\pi\)
−0.825372 + 0.564589i \(0.809035\pi\)
\(60\) 0 0
\(61\) 6.12132 10.6024i 0.783755 1.35750i −0.145985 0.989287i \(-0.546635\pi\)
0.929740 0.368216i \(-0.120031\pi\)
\(62\) 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 0.639906 0.768453i \(-0.278973\pi\)
−0.985453 + 0.169948i \(0.945640\pi\)
\(68\) 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 0.910467 + 0.413583i \(0.135723\pi\)
−0.0970601 + 0.995279i \(0.530944\pi\)
\(74\) 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 −0.170249 0.985401i \(-0.554457\pi\)
0.938507 0.345261i \(-0.112210\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 7.31371 0.802784 0.401392 0.915906i \(-0.368527\pi\)
0.401392 + 0.915906i \(0.368527\pi\)
\(84\) 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 0.190586 + 0.981670i \(0.438961\pi\)
−0.945445 + 0.325783i \(0.894372\pi\)
\(90\) 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 \(-0.541907\pi\)
−0.131273 + 0.991346i \(0.541907\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 1.46447 + 2.53653i 0.145720 + 0.252394i 0.929641 0.368466i \(-0.120117\pi\)
−0.783921 + 0.620860i \(0.786784\pi\)
\(102\) 0 0
\(103\) −2.24264 + 3.88437i −0.220974 + 0.382738i −0.955104 0.296271i \(-0.904257\pi\)
0.734130 + 0.679009i \(0.237590\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.171573 + 0.297173i −0.0165866 + 0.0287288i −0.874200 0.485567i \(-0.838613\pi\)
0.857613 + 0.514296i \(0.171947\pi\)
\(108\) 0 0
\(109\) 2.82843 + 4.89898i 0.270914 + 0.469237i 0.969096 0.246683i \(-0.0793407\pi\)
−0.698182 + 0.715920i \(0.746007\pi\)
\(110\) 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 −0.309207 0.950995i \(-0.600063\pi\)
0.978189 0.207717i \(-0.0666032\pi\)
\(132\) 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 −0.992190 0.124739i \(-0.960191\pi\)
0.388067 0.921631i \(-0.373143\pi\)
\(138\) 0 0
\(139\) −17.6569 −1.49763 −0.748817 0.662776i \(-0.769378\pi\)
−0.748817 + 0.662776i \(0.769378\pi\)
\(140\) 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 0.255958 + 0.966688i \(0.417609\pi\)
−0.965155 + 0.261678i \(0.915724\pi\)
\(150\) 0 0
\(151\) 6.00000 + 10.3923i 0.488273 + 0.845714i 0.999909 0.0134886i \(-0.00429367\pi\)
−0.511636 + 0.859202i \(0.670960\pi\)
\(152\) 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 \(-0.0112199\pi\)
−0.530209 + 0.847867i \(0.677887\pi\)
\(158\) 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 −0.997916 0.0645236i \(-0.979447\pi\)
0.554837 + 0.831959i \(0.312781\pi\)
\(164\) 0 0
\(165\) 3.41421 + 5.91359i 0.265796 + 0.460372i
\(166\) 0 0
\(167\) −19.7990 −1.53209 −0.766046 0.642786i \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(168\) 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 −0.117956 0.993019i \(-0.537634\pi\)
0.918957 0.394357i \(-0.129033\pi\)
\(174\) 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 −0.954894 0.296948i \(-0.904031\pi\)
0.220283 0.975436i \(-0.429302\pi\)
\(180\) 0 0
\(181\) 2.58579 0.192200 0.0961000 0.995372i \(-0.469363\pi\)
0.0961000 + 0.995372i \(0.469363\pi\)
\(182\) 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 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) −2.65685 4.60181i −0.191245 0.331245i 0.754418 0.656394i \(-0.227919\pi\)
−0.945663 + 0.325149i \(0.894586\pi\)
\(194\) 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 −0.938857 0.344307i \(-0.888114\pi\)
0.171250 0.985228i \(-0.445219\pi\)
\(200\) 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 \(-0.184844\pi\)
0.836076 + 0.548613i \(0.184844\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) 0 0
\(227\) −11.8995 20.6105i −0.789797 1.36797i −0.926091 0.377300i \(-0.876852\pi\)
0.136294 0.990668i \(-0.456481\pi\)
\(228\) 0 0
\(229\) −0.121320 + 0.210133i −0.00801707 + 0.0138860i −0.870006 0.493041i \(-0.835885\pi\)
0.861989 + 0.506927i \(0.169219\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.07107 5.31925i 0.201192 0.348475i −0.747721 0.664014i \(-0.768852\pi\)
0.948913 + 0.315538i \(0.102185\pi\)
\(234\) 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 −0.999637 0.0269294i \(-0.991427\pi\)
0.476497 0.879176i \(-0.341906\pi\)
\(242\) 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 \(-0.628920\pi\)
−0.394032 + 0.919097i \(0.628920\pi\)
\(252\) 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 −0.235384 0.971902i \(-0.575635\pi\)
0.959384 0.282102i \(-0.0910318\pi\)
\(258\) 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 0.936239 0.351365i \(-0.114282\pi\)
−0.772410 + 0.635124i \(0.780949\pi\)
\(264\) 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 \(-0.314882\pi\)
−0.998320 + 0.0579332i \(0.981549\pi\)
\(270\) 0 0
\(271\) 5.07107 8.78335i 0.308045 0.533550i −0.669889 0.742461i \(-0.733658\pi\)
0.977935 + 0.208911i \(0.0669918\pi\)
\(272\) 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 0.971336 0.237712i \(-0.0763974\pi\)
−0.691532 + 0.722345i \(0.743064\pi\)
\(278\) 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 \(-0.0855130\pi\)
−0.711932 + 0.702248i \(0.752180\pi\)
\(284\) 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 \(-0.660990\pi\)
−0.484476 + 0.874805i \(0.660990\pi\)
\(294\) 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 \(-0.170369\pi\)
0.860151 + 0.510039i \(0.170369\pi\)
\(308\) 0 0
\(309\) 4.48528 0.255159
\(310\) 0 0
\(311\) −3.07107 5.31925i −0.174144 0.301627i 0.765721 0.643173i \(-0.222383\pi\)
−0.939865 + 0.341547i \(0.889049\pi\)
\(312\) 0 0
\(313\) 0.949747 1.64501i 0.0536829 0.0929815i −0.837935 0.545770i \(-0.816237\pi\)
0.891618 + 0.452788i \(0.149571\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) 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 −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 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 0.834808 + 0.550541i \(0.185579\pi\)
0.0593789 + 0.998236i \(0.481088\pi\)
\(348\) 0 0
\(349\) 9.89949 0.529908 0.264954 0.964261i \(-0.414643\pi\)
0.264954 + 0.964261i \(0.414643\pi\)
\(350\) 0 0
\(351\) −2.58579 −0.138019
\(352\) 0 0
\(353\) −7.36396 12.7548i −0.391944 0.678867i 0.600762 0.799428i \(-0.294864\pi\)
−0.992706 + 0.120561i \(0.961531\pi\)
\(354\) 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 −0.870518 0.492137i \(-0.836216\pi\)
0.861462 + 0.507822i \(0.169549\pi\)
\(360\) 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 \(-0.139103\pi\)
−0.819537 + 0.573027i \(0.805769\pi\)
\(368\) 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 −0.693894 0.720077i \(-0.744107\pi\)
0.970552 + 0.240892i \(0.0774399\pi\)
\(374\) 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 \(-0.678076\pi\)
0.999358 + 0.0358343i \(0.0114088\pi\)
\(384\) 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 0.998956 0.0456762i \(-0.0145442\pi\)
−0.539035 + 0.842283i \(0.681211\pi\)
\(390\) 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 \(-0.852394\pi\)
0.834551 + 0.550931i \(0.185727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.07107 5.31925i 0.153362 0.265630i −0.779100 0.626900i \(-0.784323\pi\)
0.932461 + 0.361270i \(0.117657\pi\)
\(402\) 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 −0.999411 0.0343258i \(-0.989072\pi\)
0.469978 0.882678i \(-0.344262\pi\)
\(410\) 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 \(-0.199321\pi\)
0.810269 + 0.586059i \(0.199321\pi\)
\(420\) 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 −0.983227 0.182384i \(-0.941618\pi\)
0.333664 0.942692i \(-0.391715\pi\)
\(432\) 0 0
\(433\) 20.2426 0.972799 0.486400 0.873736i \(-0.338310\pi\)
0.486400 + 0.873736i \(0.338310\pi\)
\(434\) 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 \(-0.931235\pi\)
0.674014 + 0.738718i \(0.264569\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.4853 30.2854i 0.830751 1.43890i −0.0666929 0.997774i \(-0.521245\pi\)
0.897444 0.441129i \(-0.145422\pi\)
\(444\) 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 −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) 0 0
\(459\) −1.12132 1.94218i −0.0523388 0.0906534i
\(460\) 0 0
\(461\) 16.5858 0.772477 0.386239 0.922399i \(-0.373774\pi\)
0.386239 + 0.922399i \(0.373774\pi\)
\(462\) 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 \(-0.834814\pi\)
0.863691 + 0.504022i \(0.168147\pi\)
\(468\) 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 \(-0.180181\pi\)
−0.886467 + 0.462792i \(0.846848\pi\)
\(480\) 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 0.992317 + 0.123718i \(0.0394819\pi\)
−0.389016 + 0.921231i \(0.627185\pi\)
\(488\) 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 −0.826554 0.562857i \(-0.809702\pi\)
0.900725 + 0.434389i \(0.143036\pi\)
\(500\) 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 \(-0.794037\pi\)
0.921005 + 0.389552i \(0.127370\pi\)
\(510\) 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 −0.934365 0.356317i \(-0.884032\pi\)
0.158603 0.987343i \(-0.449301\pi\)
\(522\) 0 0
\(523\) 12.8284 22.2195i 0.560948 0.971590i −0.436466 0.899721i \(-0.643770\pi\)
0.997414 0.0718696i \(-0.0228966\pi\)
\(524\) 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 −0.989902 0.141755i \(-0.954725\pi\)
0.617715 + 0.786402i \(0.288059\pi\)
\(542\) 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 −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 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 \(-0.158807\pi\)
−0.853417 + 0.521228i \(0.825474\pi\)
\(564\) 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 −0.639904 0.768455i \(-0.721026\pi\)
0.985453 + 0.169946i \(0.0543592\pi\)
\(570\) 0 0
\(571\) 11.1716 + 19.3497i 0.467516 + 0.809761i 0.999311 0.0371118i \(-0.0118158\pi\)
−0.531795 + 0.846873i \(0.678482\pi\)
\(572\) 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 −0.966465 0.256799i \(-0.917332\pi\)
0.260837 0.965383i \(-0.416001\pi\)
\(578\) 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 \(-0.656148\pi\)
−0.471115 + 0.882072i \(0.656148\pi\)
\(588\) 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 \(-0.878773\pi\)
0.786082 + 0.618122i \(0.212106\pi\)
\(594\) 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 0.844873 0.534967i \(-0.179676\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(600\) 0 0
\(601\) 15.0711 0.614762 0.307381 0.951587i \(-0.400547\pi\)
0.307381 + 0.951587i \(0.400547\pi\)
\(602\) 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 \(-0.711915\pi\)
0.989913 + 0.141675i \(0.0452487\pi\)
\(608\) 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 0.814819 0.579715i \(-0.196836\pi\)
−0.909458 + 0.415796i \(0.863503\pi\)
\(614\) 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 −0.995217 0.0976926i \(-0.968854\pi\)
0.413004 0.910729i \(-0.364480\pi\)
\(620\) 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 0.952916 0.303235i \(-0.0980668\pi\)
−0.739067 + 0.673632i \(0.764733\pi\)
\(642\) 0 0
\(643\) −34.4264 −1.35764 −0.678822 0.734302i \(-0.737509\pi\)
−0.678822 + 0.734302i \(0.737509\pi\)
\(644\) 0 0
\(645\) 19.3137 0.760477
\(646\) 0 0
\(647\) −13.4142 23.2341i −0.527367 0.913427i −0.999491 0.0318946i \(-0.989846\pi\)
0.472124 0.881532i \(-0.343487\pi\)
\(648\) 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 0.249497 + 0.968376i \(0.419735\pi\)
−0.963386 + 0.268118i \(0.913598\pi\)
\(654\) 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 \(-0.318143\pi\)
−0.998862 + 0.0477040i \(0.984810\pi\)
\(662\) 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 −0.388587 0.921412i \(-0.627037\pi\)
0.992260 0.124180i \(-0.0396301\pi\)
\(678\) 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 0.614413 0.788985i \(-0.289393\pi\)
−0.990487 + 0.137605i \(0.956060\pi\)
\(684\) 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 \(-0.829178\pi\)
0.872479 + 0.488652i \(0.162511\pi\)
\(692\) 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 −0.293229 0.956042i \(-0.594730\pi\)
0.974571 0.224077i \(-0.0719368\pi\)
\(710\) 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 0.148664 + 0.988888i \(0.452503\pi\)
−0.930734 + 0.365697i \(0.880831\pi\)
\(720\) 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 \(-0.425628\pi\)
0.231527 + 0.972829i \(0.425628\pi\)
\(728\) 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 0.115120 0.993352i \(-0.463275\pi\)
0.802708 0.596373i \(-0.203392\pi\)
\(734\) 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 0.905899 0.423493i \(-0.139196\pi\)
−0.819705 + 0.572785i \(0.805863\pi\)
\(740\) 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 −0.714124 0.700020i \(-0.753175\pi\)
0.963297 + 0.268440i \(0.0865079\pi\)
\(752\) 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 \(-0.942340\pi\)
0.647838 + 0.761778i \(0.275673\pi\)
\(762\) 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 \(-0.679868\pi\)
−0.535477 + 0.844550i \(0.679868\pi\)
\(770\) 0 0
\(771\) −23.2132 −0.836003
\(772\) 0 0
\(773\) −4.77817 8.27604i −0.171859 0.297669i 0.767211 0.641395i \(-0.221644\pi\)
−0.939070 + 0.343727i \(0.888311\pi\)
\(774\) 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 \(-0.311683\pi\)
−0.997688 + 0.0679637i \(0.978350\pi\)
\(788\) 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 \(-0.452555\pi\)
0.148502 + 0.988912i \(0.452555\pi\)
\(798\) 0 0
\(799\) −6.34315 −0.224404