Properties

Label 240.2.o.b.239.1
Level $240$
Weight $2$
Character 240.239
Analytic conductor $1.916$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.o (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 240.239
Dual form 240.2.o.b.239.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41421 - 1.00000i) q^{3} +(-1.73205 + 1.41421i) q^{5} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.41421 - 1.00000i) q^{3} +(-1.73205 + 1.41421i) q^{5} +(1.00000 + 2.82843i) q^{9} -4.89898 q^{11} +4.89898i q^{13} +(3.86370 - 0.267949i) q^{15} -3.46410 q^{17} +3.46410i q^{19} +6.00000i q^{23} +(1.00000 - 4.89898i) q^{25} +(1.41421 - 5.00000i) q^{27} -2.82843i q^{29} -3.46410i q^{31} +(6.92820 + 4.89898i) q^{33} -4.89898i q^{37} +(4.89898 - 6.92820i) q^{39} -5.65685i q^{41} -8.48528 q^{43} +(-5.73205 - 3.48477i) q^{45} +6.00000i q^{47} -7.00000 q^{49} +(4.89898 + 3.46410i) q^{51} +10.3923 q^{53} +(8.48528 - 6.92820i) q^{55} +(3.46410 - 4.89898i) q^{57} -4.89898 q^{59} -2.00000 q^{61} +(-6.92820 - 8.48528i) q^{65} +8.48528 q^{67} +(6.00000 - 8.48528i) q^{69} +9.79796 q^{71} +9.79796i q^{73} +(-6.31319 + 5.92820i) q^{75} +10.3923i q^{79} +(-7.00000 + 5.65685i) q^{81} +6.00000i q^{83} +(6.00000 - 4.89898i) q^{85} +(-2.82843 + 4.00000i) q^{87} +5.65685i q^{89} +(-3.46410 + 4.89898i) q^{93} +(-4.89898 - 6.00000i) q^{95} +(-4.89898 - 13.8564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{9} + 8 q^{25} - 32 q^{45} - 56 q^{49} - 16 q^{61} + 48 q^{69} - 56 q^{81} + 48 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.41421 1.00000i −0.816497 0.577350i
\(4\) 0 0
\(5\) −1.73205 + 1.41421i −0.774597 + 0.632456i
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 0 0
\(11\) −4.89898 −1.47710 −0.738549 0.674200i \(-0.764489\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0 0
\(13\) 4.89898i 1.35873i 0.733799 + 0.679366i \(0.237745\pi\)
−0.733799 + 0.679366i \(0.762255\pi\)
\(14\) 0 0
\(15\) 3.86370 0.267949i 0.997604 0.0691842i
\(16\) 0 0
\(17\) −3.46410 −0.840168 −0.420084 0.907485i \(-0.637999\pi\)
−0.420084 + 0.907485i \(0.637999\pi\)
\(18\) 0 0
\(19\) 3.46410i 0.794719i 0.917663 + 0.397360i \(0.130073\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 0 0
\(25\) 1.00000 4.89898i 0.200000 0.979796i
\(26\) 0 0
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0 0
\(29\) 2.82843i 0.525226i −0.964901 0.262613i \(-0.915416\pi\)
0.964901 0.262613i \(-0.0845842\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i −0.950382 0.311086i \(-0.899307\pi\)
0.950382 0.311086i \(-0.100693\pi\)
\(32\) 0 0
\(33\) 6.92820 + 4.89898i 1.20605 + 0.852803i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.89898i 0.805387i −0.915335 0.402694i \(-0.868074\pi\)
0.915335 0.402694i \(-0.131926\pi\)
\(38\) 0 0
\(39\) 4.89898 6.92820i 0.784465 1.10940i
\(40\) 0 0
\(41\) 5.65685i 0.883452i −0.897150 0.441726i \(-0.854366\pi\)
0.897150 0.441726i \(-0.145634\pi\)
\(42\) 0 0
\(43\) −8.48528 −1.29399 −0.646997 0.762493i \(-0.723975\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 0 0
\(45\) −5.73205 3.48477i −0.854484 0.519478i
\(46\) 0 0
\(47\) 6.00000i 0.875190i 0.899172 + 0.437595i \(0.144170\pi\)
−0.899172 + 0.437595i \(0.855830\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 4.89898 + 3.46410i 0.685994 + 0.485071i
\(52\) 0 0
\(53\) 10.3923 1.42749 0.713746 0.700404i \(-0.246997\pi\)
0.713746 + 0.700404i \(0.246997\pi\)
\(54\) 0 0
\(55\) 8.48528 6.92820i 1.14416 0.934199i
\(56\) 0 0
\(57\) 3.46410 4.89898i 0.458831 0.648886i
\(58\) 0 0
\(59\) −4.89898 −0.637793 −0.318896 0.947790i \(-0.603312\pi\)
−0.318896 + 0.947790i \(0.603312\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.92820 8.48528i −0.859338 1.05247i
\(66\) 0 0
\(67\) 8.48528 1.03664 0.518321 0.855186i \(-0.326557\pi\)
0.518321 + 0.855186i \(0.326557\pi\)
\(68\) 0 0
\(69\) 6.00000 8.48528i 0.722315 1.02151i
\(70\) 0 0
\(71\) 9.79796 1.16280 0.581402 0.813617i \(-0.302504\pi\)
0.581402 + 0.813617i \(0.302504\pi\)
\(72\) 0 0
\(73\) 9.79796i 1.14676i 0.819288 + 0.573382i \(0.194369\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) −6.31319 + 5.92820i −0.728985 + 0.684530i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 10.3923i 1.16923i 0.811312 + 0.584613i \(0.198754\pi\)
−0.811312 + 0.584613i \(0.801246\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) 6.00000 4.89898i 0.650791 0.531369i
\(86\) 0 0
\(87\) −2.82843 + 4.00000i −0.303239 + 0.428845i
\(88\) 0 0
\(89\) 5.65685i 0.599625i 0.953998 + 0.299813i \(0.0969242\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.46410 + 4.89898i −0.359211 + 0.508001i
\(94\) 0 0
\(95\) −4.89898 6.00000i −0.502625 0.615587i
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) −4.89898 13.8564i −0.492366 1.39262i
\(100\) 0 0
\(101\) 14.1421i 1.40720i 0.710599 + 0.703598i \(0.248424\pi\)
−0.710599 + 0.703598i \(0.751576\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18.0000i 1.74013i −0.492941 0.870063i \(-0.664078\pi\)
0.492941 0.870063i \(-0.335922\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) −4.89898 + 6.92820i −0.464991 + 0.657596i
\(112\) 0 0
\(113\) −3.46410 −0.325875 −0.162938 0.986636i \(-0.552097\pi\)
−0.162938 + 0.986636i \(0.552097\pi\)
\(114\) 0 0
\(115\) −8.48528 10.3923i −0.791257 0.969087i
\(116\) 0 0
\(117\) −13.8564 + 4.89898i −1.28103 + 0.452911i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 13.0000 1.18182
\(122\) 0 0
\(123\) −5.65685 + 8.00000i −0.510061 + 0.721336i
\(124\) 0 0
\(125\) 5.19615 + 9.89949i 0.464758 + 0.885438i
\(126\) 0 0
\(127\) −16.9706 −1.50589 −0.752947 0.658081i \(-0.771368\pi\)
−0.752947 + 0.658081i \(0.771368\pi\)
\(128\) 0 0
\(129\) 12.0000 + 8.48528i 1.05654 + 0.747087i
\(130\) 0 0
\(131\) 4.89898 0.428026 0.214013 0.976831i \(-0.431347\pi\)
0.214013 + 0.976831i \(0.431347\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 4.62158 + 10.6603i 0.397762 + 0.917489i
\(136\) 0 0
\(137\) −3.46410 −0.295958 −0.147979 0.988990i \(-0.547277\pi\)
−0.147979 + 0.988990i \(0.547277\pi\)
\(138\) 0 0
\(139\) 17.3205i 1.46911i 0.678551 + 0.734553i \(0.262608\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 6.00000 8.48528i 0.505291 0.714590i
\(142\) 0 0
\(143\) 24.0000i 2.00698i
\(144\) 0 0
\(145\) 4.00000 + 4.89898i 0.332182 + 0.406838i
\(146\) 0 0
\(147\) 9.89949 + 7.00000i 0.816497 + 0.577350i
\(148\) 0 0
\(149\) 2.82843i 0.231714i 0.993266 + 0.115857i \(0.0369614\pi\)
−0.993266 + 0.115857i \(0.963039\pi\)
\(150\) 0 0
\(151\) 3.46410i 0.281905i −0.990016 0.140952i \(-0.954984\pi\)
0.990016 0.140952i \(-0.0450164\pi\)
\(152\) 0 0
\(153\) −3.46410 9.79796i −0.280056 0.792118i
\(154\) 0 0
\(155\) 4.89898 + 6.00000i 0.393496 + 0.481932i
\(156\) 0 0
\(157\) 4.89898i 0.390981i 0.980706 + 0.195491i \(0.0626299\pi\)
−0.980706 + 0.195491i \(0.937370\pi\)
\(158\) 0 0
\(159\) −14.6969 10.3923i −1.16554 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.48528 0.664619 0.332309 0.943170i \(-0.392172\pi\)
0.332309 + 0.943170i \(0.392172\pi\)
\(164\) 0 0
\(165\) −18.9282 + 1.31268i −1.47356 + 0.102192i
\(166\) 0 0
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 0 0
\(169\) −11.0000 −0.846154
\(170\) 0 0
\(171\) −9.79796 + 3.46410i −0.749269 + 0.264906i
\(172\) 0 0
\(173\) −3.46410 −0.263371 −0.131685 0.991292i \(-0.542039\pi\)
−0.131685 + 0.991292i \(0.542039\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.92820 + 4.89898i 0.520756 + 0.368230i
\(178\) 0 0
\(179\) 24.4949 1.83083 0.915417 0.402506i \(-0.131861\pi\)
0.915417 + 0.402506i \(0.131861\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 2.82843 + 2.00000i 0.209083 + 0.147844i
\(184\) 0 0
\(185\) 6.92820 + 8.48528i 0.509372 + 0.623850i
\(186\) 0 0
\(187\) 16.9706 1.24101
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −19.5959 −1.41791 −0.708955 0.705253i \(-0.750833\pi\)
−0.708955 + 0.705253i \(0.750833\pi\)
\(192\) 0 0
\(193\) 19.5959i 1.41055i −0.708936 0.705273i \(-0.750825\pi\)
0.708936 0.705273i \(-0.249175\pi\)
\(194\) 0 0
\(195\) 1.31268 + 18.9282i 0.0940028 + 1.35548i
\(196\) 0 0
\(197\) 24.2487 1.72765 0.863825 0.503793i \(-0.168062\pi\)
0.863825 + 0.503793i \(0.168062\pi\)
\(198\) 0 0
\(199\) 10.3923i 0.736691i 0.929689 + 0.368345i \(0.120076\pi\)
−0.929689 + 0.368345i \(0.879924\pi\)
\(200\) 0 0
\(201\) −12.0000 8.48528i −0.846415 0.598506i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 8.00000 + 9.79796i 0.558744 + 0.684319i
\(206\) 0 0
\(207\) −16.9706 + 6.00000i −1.17954 + 0.417029i
\(208\) 0 0
\(209\) 16.9706i 1.17388i
\(210\) 0 0
\(211\) 24.2487i 1.66935i −0.550743 0.834675i \(-0.685655\pi\)
0.550743 0.834675i \(-0.314345\pi\)
\(212\) 0 0
\(213\) −13.8564 9.79796i −0.949425 0.671345i
\(214\) 0 0
\(215\) 14.6969 12.0000i 1.00232 0.818393i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 9.79796 13.8564i 0.662085 0.936329i
\(220\) 0 0
\(221\) 16.9706i 1.14156i
\(222\) 0 0
\(223\) 16.9706 1.13643 0.568216 0.822879i \(-0.307634\pi\)
0.568216 + 0.822879i \(0.307634\pi\)
\(224\) 0 0
\(225\) 14.8564 2.07055i 0.990427 0.138037i
\(226\) 0 0
\(227\) 6.00000i 0.398234i 0.979976 + 0.199117i \(0.0638074\pi\)
−0.979976 + 0.199117i \(0.936193\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.46410 −0.226941 −0.113470 0.993541i \(-0.536197\pi\)
−0.113470 + 0.993541i \(0.536197\pi\)
\(234\) 0 0
\(235\) −8.48528 10.3923i −0.553519 0.677919i
\(236\) 0 0
\(237\) 10.3923 14.6969i 0.675053 0.954669i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 15.5563 1.00000i 0.997940 0.0641500i
\(244\) 0 0
\(245\) 12.1244 9.89949i 0.774597 0.632456i
\(246\) 0 0
\(247\) −16.9706 −1.07981
\(248\) 0 0
\(249\) 6.00000 8.48528i 0.380235 0.537733i
\(250\) 0 0
\(251\) 14.6969 0.927663 0.463831 0.885924i \(-0.346474\pi\)
0.463831 + 0.885924i \(0.346474\pi\)
\(252\) 0 0
\(253\) 29.3939i 1.84798i
\(254\) 0 0
\(255\) −13.3843 + 0.928203i −0.838155 + 0.0581263i
\(256\) 0 0
\(257\) −3.46410 −0.216085 −0.108042 0.994146i \(-0.534458\pi\)
−0.108042 + 0.994146i \(0.534458\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 8.00000 2.82843i 0.495188 0.175075i
\(262\) 0 0
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) 0 0
\(265\) −18.0000 + 14.6969i −1.10573 + 0.902826i
\(266\) 0 0
\(267\) 5.65685 8.00000i 0.346194 0.489592i
\(268\) 0 0
\(269\) 19.7990i 1.20717i 0.797300 + 0.603583i \(0.206261\pi\)
−0.797300 + 0.603583i \(0.793739\pi\)
\(270\) 0 0
\(271\) 10.3923i 0.631288i 0.948878 + 0.315644i \(0.102220\pi\)
−0.948878 + 0.315644i \(0.897780\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.89898 + 24.0000i −0.295420 + 1.44725i
\(276\) 0 0
\(277\) 14.6969i 0.883053i 0.897248 + 0.441527i \(0.145563\pi\)
−0.897248 + 0.441527i \(0.854437\pi\)
\(278\) 0 0
\(279\) 9.79796 3.46410i 0.586588 0.207390i
\(280\) 0 0
\(281\) 5.65685i 0.337460i −0.985662 0.168730i \(-0.946033\pi\)
0.985662 0.168730i \(-0.0539665\pi\)
\(282\) 0 0
\(283\) −8.48528 −0.504398 −0.252199 0.967675i \(-0.581154\pi\)
−0.252199 + 0.967675i \(0.581154\pi\)
\(284\) 0 0
\(285\) 0.928203 + 13.3843i 0.0549820 + 0.792815i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −17.3205 −1.01187 −0.505937 0.862570i \(-0.668853\pi\)
−0.505937 + 0.862570i \(0.668853\pi\)
\(294\) 0 0
\(295\) 8.48528 6.92820i 0.494032 0.403376i
\(296\) 0 0
\(297\) −6.92820 + 24.4949i −0.402015 + 1.42134i
\(298\) 0 0
\(299\) −29.3939 −1.69989
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 14.1421 20.0000i 0.812444 1.14897i
\(304\) 0 0
\(305\) 3.46410 2.82843i 0.198354 0.161955i
\(306\) 0 0
\(307\) 8.48528 0.484281 0.242140 0.970241i \(-0.422151\pi\)
0.242140 + 0.970241i \(0.422151\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.79796 −0.555591 −0.277796 0.960640i \(-0.589604\pi\)
−0.277796 + 0.960640i \(0.589604\pi\)
\(312\) 0 0
\(313\) 9.79796i 0.553813i −0.960897 0.276907i \(-0.910691\pi\)
0.960897 0.276907i \(-0.0893093\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.3205 −0.972817 −0.486408 0.873732i \(-0.661693\pi\)
−0.486408 + 0.873732i \(0.661693\pi\)
\(318\) 0 0
\(319\) 13.8564i 0.775810i
\(320\) 0 0
\(321\) −18.0000 + 25.4558i −1.00466 + 1.42081i
\(322\) 0 0
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 24.0000 + 4.89898i 1.33128 + 0.271746i
\(326\) 0 0
\(327\) 2.82843 + 2.00000i 0.156412 + 0.110600i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.3205i 0.952021i 0.879440 + 0.476011i \(0.157918\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 0 0
\(333\) 13.8564 4.89898i 0.759326 0.268462i
\(334\) 0 0
\(335\) −14.6969 + 12.0000i −0.802980 + 0.655630i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 4.89898 + 3.46410i 0.266076 + 0.188144i
\(340\) 0 0
\(341\) 16.9706i 0.919007i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.60770 + 23.1822i 0.0865554 + 1.24809i
\(346\) 0 0
\(347\) 6.00000i 0.322097i 0.986947 + 0.161048i \(0.0514875\pi\)
−0.986947 + 0.161048i \(0.948512\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 24.4949 + 6.92820i 1.30744 + 0.369800i
\(352\) 0 0
\(353\) −31.1769 −1.65938 −0.829690 0.558225i \(-0.811483\pi\)
−0.829690 + 0.558225i \(0.811483\pi\)
\(354\) 0 0
\(355\) −16.9706 + 13.8564i −0.900704 + 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.79796 −0.517116 −0.258558 0.965996i \(-0.583247\pi\)
−0.258558 + 0.965996i \(0.583247\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 0 0
\(363\) −18.3848 13.0000i −0.964951 0.682323i
\(364\) 0 0
\(365\) −13.8564 16.9706i −0.725277 0.888280i
\(366\) 0 0
\(367\) −16.9706 −0.885856 −0.442928 0.896557i \(-0.646060\pi\)
−0.442928 + 0.896557i \(0.646060\pi\)
\(368\) 0 0
\(369\) 16.0000 5.65685i 0.832927 0.294484i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 14.6969i 0.760979i 0.924785 + 0.380489i \(0.124244\pi\)
−0.924785 + 0.380489i \(0.875756\pi\)
\(374\) 0 0
\(375\) 2.55103 19.1962i 0.131734 0.991285i
\(376\) 0 0
\(377\) 13.8564 0.713641
\(378\) 0 0
\(379\) 10.3923i 0.533817i −0.963722 0.266908i \(-0.913998\pi\)
0.963722 0.266908i \(-0.0860021\pi\)
\(380\) 0 0
\(381\) 24.0000 + 16.9706i 1.22956 + 0.869428i
\(382\) 0 0
\(383\) 6.00000i 0.306586i 0.988181 + 0.153293i \(0.0489878\pi\)
−0.988181 + 0.153293i \(0.951012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.48528 24.0000i −0.431331 1.21999i
\(388\) 0 0
\(389\) 2.82843i 0.143407i 0.997426 + 0.0717035i \(0.0228435\pi\)
−0.997426 + 0.0717035i \(0.977156\pi\)
\(390\) 0 0
\(391\) 20.7846i 1.05112i
\(392\) 0 0
\(393\) −6.92820 4.89898i −0.349482 0.247121i
\(394\) 0 0
\(395\) −14.6969 18.0000i −0.739483 0.905678i
\(396\) 0 0
\(397\) 4.89898i 0.245873i 0.992415 + 0.122936i \(0.0392311\pi\)
−0.992415 + 0.122936i \(0.960769\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.6274i 1.12996i 0.825105 + 0.564980i \(0.191116\pi\)
−0.825105 + 0.564980i \(0.808884\pi\)
\(402\) 0 0
\(403\) 16.9706 0.845364
\(404\) 0 0
\(405\) 4.12436 19.6975i 0.204941 0.978774i
\(406\) 0 0
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 4.89898 + 3.46410i 0.241649 + 0.170872i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −8.48528 10.3923i −0.416526 0.510138i
\(416\) 0 0
\(417\) 17.3205 24.4949i 0.848189 1.19952i
\(418\) 0 0
\(419\) −14.6969 −0.717992 −0.358996 0.933339i \(-0.616881\pi\)
−0.358996 + 0.933339i \(0.616881\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 0 0
\(423\) −16.9706 + 6.00000i −0.825137 + 0.291730i
\(424\) 0 0
\(425\) −3.46410 + 16.9706i −0.168034 + 0.823193i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −24.0000 + 33.9411i −1.15873 + 1.63869i
\(430\) 0 0
\(431\) 19.5959 0.943902 0.471951 0.881625i \(-0.343550\pi\)
0.471951 + 0.881625i \(0.343550\pi\)
\(432\) 0 0
\(433\) 19.5959i 0.941720i 0.882208 + 0.470860i \(0.156056\pi\)
−0.882208 + 0.470860i \(0.843944\pi\)
\(434\) 0 0
\(435\) −0.757875 10.9282i −0.0363373 0.523967i
\(436\) 0 0
\(437\) −20.7846 −0.994263
\(438\) 0 0
\(439\) 17.3205i 0.826663i −0.910581 0.413331i \(-0.864365\pi\)
0.910581 0.413331i \(-0.135635\pi\)
\(440\) 0 0
\(441\) −7.00000 19.7990i −0.333333 0.942809i
\(442\) 0 0
\(443\) 30.0000i 1.42534i 0.701498 + 0.712672i \(0.252515\pi\)
−0.701498 + 0.712672i \(0.747485\pi\)
\(444\) 0 0
\(445\) −8.00000 9.79796i −0.379236 0.464468i
\(446\) 0 0
\(447\) 2.82843 4.00000i 0.133780 0.189194i
\(448\) 0 0
\(449\) 22.6274i 1.06785i −0.845531 0.533927i \(-0.820716\pi\)
0.845531 0.533927i \(-0.179284\pi\)
\(450\) 0 0
\(451\) 27.7128i 1.30495i
\(452\) 0 0
\(453\) −3.46410 + 4.89898i −0.162758 + 0.230174i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.79796i 0.458329i −0.973388 0.229165i \(-0.926401\pi\)
0.973388 0.229165i \(-0.0735994\pi\)
\(458\) 0 0
\(459\) −4.89898 + 17.3205i −0.228665 + 0.808452i
\(460\) 0 0
\(461\) 36.7696i 1.71253i −0.516538 0.856264i \(-0.672779\pi\)
0.516538 0.856264i \(-0.327221\pi\)
\(462\) 0 0
\(463\) 16.9706 0.788689 0.394344 0.918963i \(-0.370972\pi\)
0.394344 + 0.918963i \(0.370972\pi\)
\(464\) 0 0
\(465\) −0.928203 13.3843i −0.0430444 0.620680i
\(466\) 0 0
\(467\) 18.0000i 0.832941i −0.909149 0.416470i \(-0.863267\pi\)
0.909149 0.416470i \(-0.136733\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 4.89898 6.92820i 0.225733 0.319235i
\(472\) 0 0
\(473\) 41.5692 1.91135
\(474\) 0 0
\(475\) 16.9706 + 3.46410i 0.778663 + 0.158944i
\(476\) 0 0
\(477\) 10.3923 + 29.3939i 0.475831 + 1.34585i
\(478\) 0 0
\(479\) 19.5959 0.895360 0.447680 0.894194i \(-0.352250\pi\)
0.447680 + 0.894194i \(0.352250\pi\)
\(480\) 0 0
\(481\) 24.0000 1.09431
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 33.9411 1.53802 0.769010 0.639237i \(-0.220750\pi\)
0.769010 + 0.639237i \(0.220750\pi\)
\(488\) 0 0
\(489\) −12.0000 8.48528i −0.542659 0.383718i
\(490\) 0 0
\(491\) −24.4949 −1.10544 −0.552720 0.833367i \(-0.686410\pi\)
−0.552720 + 0.833367i \(0.686410\pi\)
\(492\) 0 0
\(493\) 9.79796i 0.441278i
\(494\) 0 0
\(495\) 28.0812 + 17.0718i 1.26216 + 0.767320i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.46410i 0.155074i 0.996989 + 0.0775372i \(0.0247057\pi\)
−0.996989 + 0.0775372i \(0.975294\pi\)
\(500\) 0 0
\(501\) 6.00000 8.48528i 0.268060 0.379094i
\(502\) 0 0
\(503\) 6.00000i 0.267527i 0.991013 + 0.133763i \(0.0427062\pi\)
−0.991013 + 0.133763i \(0.957294\pi\)
\(504\) 0 0
\(505\) −20.0000 24.4949i −0.889988 1.09001i
\(506\) 0 0
\(507\) 15.5563 + 11.0000i 0.690882 + 0.488527i
\(508\) 0 0
\(509\) 36.7696i 1.62978i −0.579614 0.814891i \(-0.696797\pi\)
0.579614 0.814891i \(-0.303203\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 17.3205 + 4.89898i 0.764719 + 0.216295i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 29.3939i 1.29274i
\(518\) 0 0
\(519\) 4.89898 + 3.46410i 0.215041 + 0.152057i
\(520\) 0 0
\(521\) 5.65685i 0.247831i 0.992293 + 0.123916i \(0.0395452\pi\)
−0.992293 + 0.123916i \(0.960455\pi\)
\(522\) 0 0
\(523\) −42.4264 −1.85518 −0.927589 0.373603i \(-0.878122\pi\)
−0.927589 + 0.373603i \(0.878122\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.0000i 0.522728i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) −4.89898 13.8564i −0.212598 0.601317i
\(532\) 0 0
\(533\) 27.7128 1.20038
\(534\) 0 0
\(535\) 25.4558 + 31.1769i 1.10055 + 1.34790i
\(536\) 0 0
\(537\) −34.6410 24.4949i −1.49487 1.05703i
\(538\) 0 0
\(539\) 34.2929 1.47710
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 0 0
\(543\) 14.1421 + 10.0000i 0.606897 + 0.429141i
\(544\) 0 0
\(545\) 3.46410 2.82843i 0.148386 0.121157i
\(546\) 0 0
\(547\) −25.4558 −1.08841 −0.544207 0.838951i \(-0.683169\pi\)
−0.544207 + 0.838951i \(0.683169\pi\)
\(548\) 0 0
\(549\) −2.00000 5.65685i −0.0853579 0.241429i
\(550\) 0 0
\(551\) 9.79796 0.417407
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1.31268 18.9282i −0.0557201 0.803457i
\(556\) 0 0
\(557\) −3.46410 −0.146779 −0.0733893 0.997303i \(-0.523382\pi\)
−0.0733893 + 0.997303i \(0.523382\pi\)
\(558\) 0 0
\(559\) 41.5692i 1.75819i
\(560\) 0 0
\(561\) −24.0000 16.9706i −1.01328 0.716498i
\(562\) 0 0
\(563\) 18.0000i 0.758610i −0.925272 0.379305i \(-0.876163\pi\)
0.925272 0.379305i \(-0.123837\pi\)
\(564\) 0 0
\(565\) 6.00000 4.89898i 0.252422 0.206102i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 28.2843i 1.18574i 0.805299 + 0.592869i \(0.202005\pi\)
−0.805299 + 0.592869i \(0.797995\pi\)
\(570\) 0 0
\(571\) 38.1051i 1.59465i −0.603550 0.797325i \(-0.706248\pi\)
0.603550 0.797325i \(-0.293752\pi\)
\(572\) 0 0
\(573\) 27.7128 + 19.5959i 1.15772 + 0.818631i
\(574\) 0 0
\(575\) 29.3939 + 6.00000i 1.22581 + 0.250217i
\(576\) 0 0
\(577\) 19.5959i 0.815789i 0.913029 + 0.407894i \(0.133737\pi\)
−0.913029 + 0.407894i \(0.866263\pi\)
\(578\) 0 0
\(579\) −19.5959 + 27.7128i −0.814379 + 1.15171i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −50.9117 −2.10855
\(584\) 0 0
\(585\) 17.0718 28.0812i 0.705832 1.16101i
\(586\) 0 0
\(587\) 18.0000i 0.742940i −0.928445 0.371470i \(-0.878854\pi\)
0.928445 0.371470i \(-0.121146\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) −34.2929 24.2487i −1.41062 0.997459i
\(592\) 0 0
\(593\) 24.2487 0.995775 0.497888 0.867242i \(-0.334109\pi\)
0.497888 + 0.867242i \(0.334109\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10.3923 14.6969i 0.425329 0.601506i
\(598\) 0 0
\(599\) 9.79796 0.400334 0.200167 0.979762i \(-0.435852\pi\)
0.200167 + 0.979762i \(0.435852\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 8.48528 + 24.0000i 0.345547 + 0.977356i
\(604\) 0 0
\(605\) −22.5167 + 18.3848i −0.915432 + 0.747447i
\(606\) 0 0
\(607\) 16.9706 0.688814 0.344407 0.938820i \(-0.388080\pi\)
0.344407 + 0.938820i \(0.388080\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −29.3939 −1.18915
\(612\) 0 0
\(613\) 14.6969i 0.593604i 0.954939 + 0.296802i \(0.0959201\pi\)
−0.954939 + 0.296802i \(0.904080\pi\)
\(614\) 0 0
\(615\) −1.51575 21.8564i −0.0611209 0.881335i
\(616\) 0 0
\(617\) 24.2487 0.976216 0.488108 0.872783i \(-0.337687\pi\)
0.488108 + 0.872783i \(0.337687\pi\)
\(618\) 0 0
\(619\) 10.3923i 0.417702i −0.977947 0.208851i \(-0.933028\pi\)
0.977947 0.208851i \(-0.0669724\pi\)
\(620\) 0 0
\(621\) 30.0000 + 8.48528i 1.20386 + 0.340503i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) 0 0
\(627\) −16.9706 + 24.0000i −0.677739 + 0.958468i
\(628\) 0 0
\(629\) 16.9706i 0.676661i
\(630\) 0 0
\(631\) 38.1051i 1.51694i 0.651707 + 0.758470i \(0.274053\pi\)
−0.651707 + 0.758470i \(0.725947\pi\)
\(632\) 0 0
\(633\) −24.2487 + 34.2929i −0.963800 + 1.36302i
\(634\) 0 0
\(635\) 29.3939 24.0000i 1.16646 0.952411i
\(636\) 0 0
\(637\) 34.2929i 1.35873i
\(638\) 0 0
\(639\) 9.79796 + 27.7128i 0.387601 + 1.09630i
\(640\) 0 0
\(641\) 22.6274i 0.893729i −0.894602 0.446865i \(-0.852541\pi\)
0.894602 0.446865i \(-0.147459\pi\)
\(642\) 0 0
\(643\) 8.48528 0.334627 0.167313 0.985904i \(-0.446491\pi\)
0.167313 + 0.985904i \(0.446491\pi\)
\(644\) 0 0
\(645\) −32.7846 + 2.27362i −1.29089 + 0.0895239i
\(646\) 0 0
\(647\) 42.0000i 1.65119i −0.564263 0.825595i \(-0.690840\pi\)
0.564263 0.825595i \(-0.309160\pi\)
\(648\) 0 0
\(649\) 24.0000 0.942082
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.1769 −1.22005 −0.610023 0.792383i \(-0.708840\pi\)
−0.610023 + 0.792383i \(0.708840\pi\)
\(654\) 0 0
\(655\) −8.48528 + 6.92820i −0.331547 + 0.270707i
\(656\) 0 0
\(657\) −27.7128 + 9.79796i −1.08118 + 0.382255i
\(658\) 0 0
\(659\) −14.6969 −0.572511 −0.286256 0.958153i \(-0.592411\pi\)
−0.286256 + 0.958153i \(0.592411\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 0 0
\(663\) −16.9706 + 24.0000i −0.659082 + 0.932083i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 16.9706 0.657103
\(668\) 0 0
\(669\) −24.0000 16.9706i −0.927894 0.656120i
\(670\) 0 0
\(671\) 9.79796 0.378246
\(672\) 0 0
\(673\) 39.1918i 1.51073i 0.655302 + 0.755367i \(0.272541\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) −23.0807 11.9282i −0.888376 0.459117i
\(676\) 0 0
\(677\) 10.3923 0.399409 0.199704 0.979856i \(-0.436002\pi\)
0.199704 + 0.979856i \(0.436002\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6.00000 8.48528i 0.229920 0.325157i
\(682\) 0 0
\(683\) 6.00000i 0.229584i 0.993390 + 0.114792i \(0.0366201\pi\)
−0.993390 + 0.114792i \(0.963380\pi\)
\(684\) 0 0
\(685\) 6.00000 4.89898i 0.229248 0.187180i
\(686\) 0 0
\(687\) 14.1421 + 10.0000i 0.539556 + 0.381524i
\(688\) 0 0
\(689\) 50.9117i 1.93958i
\(690\) 0 0
\(691\) 31.1769i 1.18603i 0.805193 + 0.593013i \(0.202062\pi\)
−0.805193 + 0.593013i \(0.797938\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.4949 30.0000i −0.929144 1.13796i
\(696\) 0 0
\(697\) 19.5959i 0.742248i
\(698\) 0 0
\(699\) 4.89898 + 3.46410i 0.185296 + 0.131024i
\(700\) 0 0
\(701\) 19.7990i 0.747798i 0.927470 + 0.373899i \(0.121979\pi\)
−0.927470 + 0.373899i \(0.878021\pi\)
\(702\) 0 0
\(703\) 16.9706 0.640057
\(704\) 0 0
\(705\) 1.60770 + 23.1822i 0.0605493 + 0.873093i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 0 0
\(711\) −29.3939 + 10.3923i −1.10236 + 0.389742i
\(712\) 0 0
\(713\) 20.7846 0.778390
\(714\) 0 0
\(715\) 33.9411 + 41.5692i 1.26933 + 1.55460i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −19.5959 −0.730804 −0.365402 0.930850i \(-0.619069\pi\)
−0.365402 + 0.930850i \(0.619069\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −14.1421 10.0000i −0.525952 0.371904i
\(724\) 0 0
\(725\) −13.8564 2.82843i −0.514614 0.105045i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 29.3939 1.08717
\(732\) 0 0
\(733\) 44.0908i 1.62853i 0.580492 + 0.814266i \(0.302860\pi\)
−0.580492 + 0.814266i \(0.697140\pi\)
\(734\) 0 0
\(735\) −27.0459 + 1.87564i −0.997604 + 0.0691842i
\(736\) 0 0
\(737\) −41.5692 −1.53122
\(738\) 0 0
\(739\) 24.2487i 0.892003i −0.895032 0.446002i \(-0.852848\pi\)
0.895032 0.446002i \(-0.147152\pi\)
\(740\) 0 0
\(741\) 24.0000 + 16.9706i 0.881662 + 0.623429i
\(742\) 0 0
\(743\) 6.00000i 0.220119i 0.993925 + 0.110059i \(0.0351041\pi\)
−0.993925 + 0.110059i \(0.964896\pi\)
\(744\) 0 0
\(745\) −4.00000 4.89898i −0.146549 0.179485i
\(746\) 0 0
\(747\) −16.9706 + 6.00000i −0.620920 + 0.219529i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 31.1769i 1.13766i −0.822455 0.568831i \(-0.807396\pi\)
0.822455 0.568831i \(-0.192604\pi\)
\(752\) 0 0
\(753\) −20.7846 14.6969i −0.757433 0.535586i
\(754\) 0 0
\(755\) 4.89898 + 6.00000i 0.178292 + 0.218362i
\(756\) 0 0
\(757\) 14.6969i 0.534169i 0.963673 + 0.267085i \(0.0860603\pi\)
−0.963673 + 0.267085i \(0.913940\pi\)
\(758\) 0 0
\(759\) −29.3939 + 41.5692i −1.06693 + 1.50887i
\(760\) 0 0
\(761\) 39.5980i 1.43543i 0.696339 + 0.717713i \(0.254811\pi\)
−0.696339 + 0.717713i \(0.745189\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 19.8564 + 12.0716i 0.717910 + 0.436449i
\(766\) 0 0
\(767\) 24.0000i 0.866590i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 4.89898 + 3.46410i 0.176432 + 0.124757i
\(772\) 0 0
\(773\) 24.2487 0.872166 0.436083 0.899907i \(-0.356365\pi\)
0.436083 + 0.899907i \(0.356365\pi\)
\(774\) 0 0
\(775\) −16.9706 3.46410i −0.609601 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19.5959 0.702097
\(780\) 0 0
\(781\) −48.0000 −1.71758
\(782\) 0 0
\(783\) −14.1421 4.00000i −0.505399 0.142948i
\(784\) 0 0
\(785\) −6.92820 8.48528i −0.247278 0.302853i
\(786\) 0 0
\(787\) −25.4558 −0.907403 −0.453701 0.891154i \(-0.649897\pi\)
−0.453701 + 0.891154i \(0.649897\pi\)
\(788\) 0 0
\(789\) 6.00000 8.48528i 0.213606 0.302084i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 9.79796i 0.347936i
\(794\) 0 0
\(795\) 40.1528 2.78461i 1.42407 0.0987599i
\(796\) 0 0
\(797\) −17.3205 −0.613524 −0.306762 0.951786i \(-0.599246\pi\)
−0.306762 + 0.951786i \(0.599246\pi\)
\(798\) 0 0
\(799\) 20.7846i 0.735307i
\(800\) 0 0
\(801\) −16.0000 + 5.65685i −0.565332 + 0.199875i
\(802\) 0