Properties

Label 1512.2.s.l.865.2
Level 1512
Weight 2
Character 1512.865
Analytic conductor 12.073
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.l.1297.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.119562 + 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +O(q^{10})\) \(q+(0.119562 + 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +(1.21053 - 2.09671i) q^{11} +0.760877 q^{13} +(-1.71053 + 2.96273i) q^{17} +(-0.590972 - 1.02359i) q^{19} +(-1.09097 - 1.88962i) q^{23} +(2.47141 - 4.28061i) q^{25} +2.89931 q^{29} +(2.32326 - 4.02400i) q^{31} +(0.612725 - 0.157568i) q^{35} +(-2.89248 - 5.00992i) q^{37} -8.54583 q^{41} -3.37756 q^{43} +(2.58414 + 4.47585i) q^{47} +(-5.99028 - 3.62167i) q^{49} +(-1.56238 + 2.70612i) q^{53} +0.578933 q^{55} +(3.11273 - 5.39140i) q^{59} +(-0.681943 - 1.18116i) q^{61} +(0.0909717 + 0.157568i) q^{65} +(7.03379 - 12.1829i) q^{67} +8.02408 q^{71} +(3.91423 - 6.77965i) q^{73} +(-4.48345 - 4.57489i) q^{77} +(-2.27292 - 3.93680i) q^{79} +12.0104 q^{83} -0.818057 q^{85} +(-2.73912 - 4.74430i) q^{89} +(0.540628 - 1.93914i) q^{91} +(0.141315 - 0.244765i) q^{95} +10.3639 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{5} - 4q^{7} + O(q^{10}) \) \( 6q + q^{5} - 4q^{7} - q^{11} + 4q^{13} - 2q^{17} + 5q^{19} + 2q^{23} + 6q^{25} + 2q^{29} - 4q^{31} - 6q^{35} + 8q^{37} - 6q^{43} - 3q^{47} - 12q^{49} + 8q^{53} + 20q^{55} + 9q^{59} + 13q^{61} - 8q^{65} + 16q^{67} - 2q^{71} - 3q^{73} + 7q^{77} + 12q^{79} + 2q^{83} - 22q^{85} - 17q^{89} - 13q^{91} + 28q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.119562 + 0.207087i 0.0534696 + 0.0926120i 0.891521 0.452979i \(-0.149639\pi\)
−0.838052 + 0.545591i \(0.816305\pi\)
\(6\) 0 0
\(7\) 0.710533 2.54856i 0.268556 0.963264i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.21053 2.09671i 0.364990 0.632180i −0.623785 0.781596i \(-0.714406\pi\)
0.988774 + 0.149416i \(0.0477392\pi\)
\(12\) 0 0
\(13\) 0.760877 0.211029 0.105515 0.994418i \(-0.466351\pi\)
0.105515 + 0.994418i \(0.466351\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.71053 + 2.96273i −0.414865 + 0.718568i −0.995414 0.0956576i \(-0.969505\pi\)
0.580549 + 0.814225i \(0.302838\pi\)
\(18\) 0 0
\(19\) −0.590972 1.02359i −0.135578 0.234828i 0.790240 0.612797i \(-0.209956\pi\)
−0.925818 + 0.377969i \(0.876623\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.09097 1.88962i −0.227483 0.394013i 0.729578 0.683897i \(-0.239716\pi\)
−0.957062 + 0.289885i \(0.906383\pi\)
\(24\) 0 0
\(25\) 2.47141 4.28061i 0.494282 0.856122i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.89931 0.538389 0.269194 0.963086i \(-0.413243\pi\)
0.269194 + 0.963086i \(0.413243\pi\)
\(30\) 0 0
\(31\) 2.32326 4.02400i 0.417270 0.722732i −0.578394 0.815757i \(-0.696320\pi\)
0.995664 + 0.0930254i \(0.0296538\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.612725 0.157568i 0.103569 0.0266338i
\(36\) 0 0
\(37\) −2.89248 5.00992i −0.475520 0.823625i 0.524087 0.851665i \(-0.324407\pi\)
−0.999607 + 0.0280398i \(0.991073\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.54583 −1.33463 −0.667317 0.744774i \(-0.732557\pi\)
−0.667317 + 0.744774i \(0.732557\pi\)
\(42\) 0 0
\(43\) −3.37756 −0.515073 −0.257537 0.966269i \(-0.582911\pi\)
−0.257537 + 0.966269i \(0.582911\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.58414 + 4.47585i 0.376935 + 0.652870i 0.990615 0.136685i \(-0.0436447\pi\)
−0.613680 + 0.789555i \(0.710311\pi\)
\(48\) 0 0
\(49\) −5.99028 3.62167i −0.855755 0.517381i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.56238 + 2.70612i −0.214610 + 0.371715i −0.953152 0.302493i \(-0.902181\pi\)
0.738542 + 0.674207i \(0.235515\pi\)
\(54\) 0 0
\(55\) 0.578933 0.0780634
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.11273 5.39140i 0.405242 0.701900i −0.589107 0.808055i \(-0.700520\pi\)
0.994350 + 0.106155i \(0.0338538\pi\)
\(60\) 0 0
\(61\) −0.681943 1.18116i −0.0873139 0.151232i 0.819061 0.573706i \(-0.194495\pi\)
−0.906375 + 0.422474i \(0.861162\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.0909717 + 0.157568i 0.0112836 + 0.0195438i
\(66\) 0 0
\(67\) 7.03379 12.1829i 0.859314 1.48838i −0.0132695 0.999912i \(-0.504224\pi\)
0.872584 0.488464i \(-0.162443\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.02408 0.952283 0.476141 0.879369i \(-0.342035\pi\)
0.476141 + 0.879369i \(0.342035\pi\)
\(72\) 0 0
\(73\) 3.91423 6.77965i 0.458126 0.793497i −0.540736 0.841192i \(-0.681854\pi\)
0.998862 + 0.0476949i \(0.0151875\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.48345 4.57489i −0.510936 0.521357i
\(78\) 0 0
\(79\) −2.27292 3.93680i −0.255723 0.442925i 0.709369 0.704838i \(-0.248980\pi\)
−0.965092 + 0.261913i \(0.915647\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.0104 1.31831 0.659157 0.752006i \(-0.270913\pi\)
0.659157 + 0.752006i \(0.270913\pi\)
\(84\) 0 0
\(85\) −0.818057 −0.0887307
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.73912 4.74430i −0.290346 0.502895i 0.683545 0.729908i \(-0.260437\pi\)
−0.973892 + 0.227013i \(0.927104\pi\)
\(90\) 0 0
\(91\) 0.540628 1.93914i 0.0566732 0.203277i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.141315 0.244765i 0.0144986 0.0251123i
\(96\) 0 0
\(97\) 10.3639 1.05229 0.526147 0.850394i \(-0.323636\pi\)
0.526147 + 0.850394i \(0.323636\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.06238 + 8.76830i −0.503726 + 0.872479i 0.496265 + 0.868171i \(0.334704\pi\)
−0.999991 + 0.00430755i \(0.998629\pi\)
\(102\) 0 0
\(103\) 1.31806 + 2.28294i 0.129872 + 0.224945i 0.923627 0.383293i \(-0.125210\pi\)
−0.793755 + 0.608238i \(0.791877\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.16991 + 3.75839i 0.209773 + 0.363337i 0.951643 0.307207i \(-0.0993943\pi\)
−0.741870 + 0.670544i \(0.766061\pi\)
\(108\) 0 0
\(109\) 6.46457 11.1970i 0.619194 1.07248i −0.370439 0.928857i \(-0.620793\pi\)
0.989633 0.143619i \(-0.0458738\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −13.1352 −1.23565 −0.617826 0.786315i \(-0.711987\pi\)
−0.617826 + 0.786315i \(0.711987\pi\)
\(114\) 0 0
\(115\) 0.260877 0.451852i 0.0243269 0.0421354i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 6.33530 + 6.46451i 0.580756 + 0.592601i
\(120\) 0 0
\(121\) 2.56922 + 4.45002i 0.233565 + 0.404547i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.37756 0.212655
\(126\) 0 0
\(127\) −3.86156 −0.342658 −0.171329 0.985214i \(-0.554806\pi\)
−0.171329 + 0.985214i \(0.554806\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.25636 12.5684i −0.633991 1.09811i −0.986728 0.162383i \(-0.948082\pi\)
0.352736 0.935723i \(-0.385251\pi\)
\(132\) 0 0
\(133\) −3.02859 + 0.778828i −0.262612 + 0.0675330i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.70370 + 9.87909i −0.487300 + 0.844028i −0.999893 0.0146035i \(-0.995351\pi\)
0.512594 + 0.858631i \(0.328685\pi\)
\(138\) 0 0
\(139\) 1.91874 0.162746 0.0813728 0.996684i \(-0.474070\pi\)
0.0813728 + 0.996684i \(0.474070\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.921067 1.59533i 0.0770235 0.133409i
\(144\) 0 0
\(145\) 0.346647 + 0.600410i 0.0287874 + 0.0498613i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.57730 13.1243i −0.620756 1.07518i −0.989345 0.145589i \(-0.953492\pi\)
0.368589 0.929593i \(-0.379841\pi\)
\(150\) 0 0
\(151\) 5.94966 10.3051i 0.484176 0.838618i −0.515659 0.856794i \(-0.672453\pi\)
0.999835 + 0.0181764i \(0.00578604\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.11109 0.0892449
\(156\) 0 0
\(157\) −1.92395 + 3.33237i −0.153548 + 0.265952i −0.932529 0.361095i \(-0.882403\pi\)
0.778982 + 0.627047i \(0.215736\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.59097 + 1.43777i −0.440630 + 0.113312i
\(162\) 0 0
\(163\) 4.47661 + 7.75372i 0.350635 + 0.607318i 0.986361 0.164597i \(-0.0526323\pi\)
−0.635726 + 0.771915i \(0.719299\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.19562 0.169902 0.0849509 0.996385i \(-0.472927\pi\)
0.0849509 + 0.996385i \(0.472927\pi\)
\(168\) 0 0
\(169\) −12.4211 −0.955467
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.15335 + 12.3900i 0.543859 + 0.941992i 0.998678 + 0.0514079i \(0.0163708\pi\)
−0.454818 + 0.890584i \(0.650296\pi\)
\(174\) 0 0
\(175\) −9.15335 9.34004i −0.691928 0.706041i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.66539 16.7409i 0.722425 1.25128i −0.237600 0.971363i \(-0.576361\pi\)
0.960025 0.279914i \(-0.0903060\pi\)
\(180\) 0 0
\(181\) 1.32614 0.0985710 0.0492855 0.998785i \(-0.484306\pi\)
0.0492855 + 0.998785i \(0.484306\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.691658 1.19799i 0.0508517 0.0880778i
\(186\) 0 0
\(187\) 4.14132 + 7.17297i 0.302843 + 0.524539i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.5172 + 21.6805i 0.905716 + 1.56875i 0.819954 + 0.572430i \(0.193999\pi\)
0.0857621 + 0.996316i \(0.472668\pi\)
\(192\) 0 0
\(193\) −1.97661 + 3.42359i −0.142280 + 0.246436i −0.928355 0.371695i \(-0.878777\pi\)
0.786075 + 0.618131i \(0.212110\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.51135 0.107679 0.0538396 0.998550i \(-0.482854\pi\)
0.0538396 + 0.998550i \(0.482854\pi\)
\(198\) 0 0
\(199\) −13.5241 + 23.4244i −0.958696 + 1.66051i −0.233023 + 0.972471i \(0.574862\pi\)
−0.725673 + 0.688040i \(0.758471\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.06006 7.38906i 0.144588 0.518611i
\(204\) 0 0
\(205\) −1.02175 1.76973i −0.0713624 0.123603i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.86156 −0.197938
\(210\) 0 0
\(211\) −9.42107 −0.648573 −0.324286 0.945959i \(-0.605124\pi\)
−0.324286 + 0.945959i \(0.605124\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.403827 0.699448i −0.0275407 0.0477020i
\(216\) 0 0
\(217\) −8.60464 8.78014i −0.584121 0.596035i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.30150 + 2.25427i −0.0875487 + 0.151639i
\(222\) 0 0
\(223\) 7.03775 0.471283 0.235641 0.971840i \(-0.424281\pi\)
0.235641 + 0.971840i \(0.424281\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.3759 21.4357i 0.821419 1.42274i −0.0832066 0.996532i \(-0.526516\pi\)
0.904626 0.426207i \(-0.140151\pi\)
\(228\) 0 0
\(229\) 13.8542 + 23.9961i 0.915509 + 1.58571i 0.806154 + 0.591706i \(0.201545\pi\)
0.109356 + 0.994003i \(0.465121\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.86389 + 6.69245i 0.253132 + 0.438437i 0.964386 0.264497i \(-0.0852061\pi\)
−0.711255 + 0.702934i \(0.751873\pi\)
\(234\) 0 0
\(235\) −0.617927 + 1.07028i −0.0403091 + 0.0698174i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −27.3880 −1.77158 −0.885790 0.464086i \(-0.846383\pi\)
−0.885790 + 0.464086i \(0.846383\pi\)
\(240\) 0 0
\(241\) −10.6683 + 18.4780i −0.687204 + 1.19027i 0.285535 + 0.958368i \(0.407829\pi\)
−0.972739 + 0.231903i \(0.925505\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.0337917 1.67352i 0.00215887 0.106917i
\(246\) 0 0
\(247\) −0.449657 0.778828i −0.0286110 0.0495556i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.66595 0.294512 0.147256 0.989098i \(-0.452956\pi\)
0.147256 + 0.989098i \(0.452956\pi\)
\(252\) 0 0
\(253\) −5.28263 −0.332116
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.14652 1.98583i −0.0715178 0.123872i 0.828049 0.560656i \(-0.189451\pi\)
−0.899567 + 0.436783i \(0.856118\pi\)
\(258\) 0 0
\(259\) −14.8233 + 3.81193i −0.921072 + 0.236862i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.39536 + 4.14888i −0.147704 + 0.255831i −0.930378 0.366600i \(-0.880522\pi\)
0.782675 + 0.622431i \(0.213855\pi\)
\(264\) 0 0
\(265\) −0.747204 −0.0459004
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.49316 + 16.4426i −0.578808 + 1.00253i 0.416808 + 0.908995i \(0.363149\pi\)
−0.995616 + 0.0935310i \(0.970185\pi\)
\(270\) 0 0
\(271\) 14.0579 + 24.3489i 0.853955 + 1.47909i 0.877611 + 0.479373i \(0.159136\pi\)
−0.0236567 + 0.999720i \(0.507531\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.98345 10.3636i −0.360816 0.624951i
\(276\) 0 0
\(277\) 4.08577 7.07676i 0.245490 0.425201i −0.716779 0.697300i \(-0.754384\pi\)
0.962269 + 0.272099i \(0.0877178\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 23.4315 1.39780 0.698902 0.715217i \(-0.253672\pi\)
0.698902 + 0.715217i \(0.253672\pi\)
\(282\) 0 0
\(283\) −1.10752 + 1.91829i −0.0658354 + 0.114030i −0.897064 0.441900i \(-0.854305\pi\)
0.831229 + 0.555930i \(0.187638\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.07210 + 21.7795i −0.358425 + 1.28561i
\(288\) 0 0
\(289\) 2.64815 + 4.58673i 0.155774 + 0.269808i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −22.1866 −1.29615 −0.648077 0.761575i \(-0.724427\pi\)
−0.648077 + 0.761575i \(0.724427\pi\)
\(294\) 0 0
\(295\) 1.48865 0.0866726
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.830095 1.43777i −0.0480056 0.0831482i
\(300\) 0 0
\(301\) −2.39987 + 8.60790i −0.138326 + 0.496151i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.163069 0.282443i 0.00933728 0.0161726i
\(306\) 0 0
\(307\) 16.0183 0.914214 0.457107 0.889412i \(-0.348886\pi\)
0.457107 + 0.889412i \(0.348886\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.35348 5.80840i 0.190159 0.329364i −0.755144 0.655559i \(-0.772433\pi\)
0.945303 + 0.326195i \(0.105766\pi\)
\(312\) 0 0
\(313\) 14.0322 + 24.3044i 0.793144 + 1.37377i 0.924011 + 0.382366i \(0.124891\pi\)
−0.130866 + 0.991400i \(0.541776\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.63323 2.82885i −0.0917316 0.158884i 0.816508 0.577334i \(-0.195907\pi\)
−0.908240 + 0.418450i \(0.862574\pi\)
\(318\) 0 0
\(319\) 3.50972 6.07900i 0.196506 0.340359i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.04351 0.224987
\(324\) 0 0
\(325\) 1.88044 3.25701i 0.104308 0.180667i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13.2431 3.40557i 0.730115 0.187755i
\(330\) 0 0
\(331\) 10.9617 + 18.9862i 0.602509 + 1.04358i 0.992440 + 0.122732i \(0.0391657\pi\)
−0.389931 + 0.920844i \(0.627501\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.36389 0.183789
\(336\) 0 0
\(337\) −14.0733 −0.766624 −0.383312 0.923619i \(-0.625217\pi\)
−0.383312 + 0.923619i \(0.625217\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.62476 9.74238i −0.304598 0.527579i
\(342\) 0 0
\(343\) −13.4863 + 12.6933i −0.728193 + 0.685372i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.50808 4.34412i 0.134641 0.233205i −0.790819 0.612050i \(-0.790345\pi\)
0.925460 + 0.378845i \(0.123679\pi\)
\(348\) 0 0
\(349\) −10.7382 −0.574801 −0.287401 0.957810i \(-0.592791\pi\)
−0.287401 + 0.957810i \(0.592791\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.16307 + 2.01449i −0.0619039 + 0.107221i −0.895316 0.445431i \(-0.853051\pi\)
0.833413 + 0.552651i \(0.186384\pi\)
\(354\) 0 0
\(355\) 0.959372 + 1.66168i 0.0509182 + 0.0881928i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.97141 + 8.61073i 0.262381 + 0.454457i 0.966874 0.255254i \(-0.0821590\pi\)
−0.704493 + 0.709711i \(0.748826\pi\)
\(360\) 0 0
\(361\) 8.80150 15.2447i 0.463237 0.802350i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.87197 0.0979832
\(366\) 0 0
\(367\) −0.464574 + 0.804665i −0.0242505 + 0.0420032i −0.877896 0.478851i \(-0.841053\pi\)
0.853645 + 0.520855i \(0.174387\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.78659 + 5.90461i 0.300425 + 0.306552i
\(372\) 0 0
\(373\) 15.1352 + 26.2149i 0.783669 + 1.35735i 0.929791 + 0.368088i \(0.119988\pi\)
−0.146122 + 0.989267i \(0.546679\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.20602 0.113616
\(378\) 0 0
\(379\) −28.5757 −1.46783 −0.733917 0.679240i \(-0.762310\pi\)
−0.733917 + 0.679240i \(0.762310\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 11.8107 + 20.4567i 0.603497 + 1.04529i 0.992287 + 0.123961i \(0.0395597\pi\)
−0.388790 + 0.921326i \(0.627107\pi\)
\(384\) 0 0
\(385\) 0.411351 1.47544i 0.0209644 0.0751956i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.23749 14.2677i 0.417657 0.723404i −0.578046 0.816004i \(-0.696185\pi\)
0.995703 + 0.0926005i \(0.0295180\pi\)
\(390\) 0 0
\(391\) 7.46457 0.377500
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.543507 0.941382i 0.0273468 0.0473660i
\(396\) 0 0
\(397\) 6.41586 + 11.1126i 0.322003 + 0.557726i 0.980901 0.194507i \(-0.0623105\pi\)
−0.658898 + 0.752232i \(0.728977\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.8187 27.3989i −0.789950 1.36823i −0.925997 0.377532i \(-0.876773\pi\)
0.136046 0.990702i \(-0.456560\pi\)
\(402\) 0 0
\(403\) 1.76771 3.06177i 0.0880561 0.152518i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14.0058 −0.694240
\(408\) 0 0
\(409\) −12.0144 + 20.8095i −0.594072 + 1.02896i 0.399605 + 0.916687i \(0.369147\pi\)
−0.993677 + 0.112275i \(0.964186\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −11.5286 11.7637i −0.567285 0.578855i
\(414\) 0 0
\(415\) 1.43598 + 2.48720i 0.0704897 + 0.122092i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.72777 −0.0844073 −0.0422036 0.999109i \(-0.513438\pi\)
−0.0422036 + 0.999109i \(0.513438\pi\)
\(420\) 0 0
\(421\) −20.0949 −0.979367 −0.489683 0.871900i \(-0.662888\pi\)
−0.489683 + 0.871900i \(0.662888\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.45486 + 14.6442i 0.410121 + 0.710350i
\(426\) 0 0
\(427\) −3.49480 + 0.898718i −0.169125 + 0.0434920i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.4246 + 18.0560i −0.502137 + 0.869727i 0.497860 + 0.867257i \(0.334119\pi\)
−0.999997 + 0.00246928i \(0.999214\pi\)
\(432\) 0 0
\(433\) 10.2255 0.491404 0.245702 0.969345i \(-0.420982\pi\)
0.245702 + 0.969345i \(0.420982\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.28947 + 2.23342i −0.0616836 + 0.106839i
\(438\) 0 0
\(439\) 3.55718 + 6.16122i 0.169775 + 0.294059i 0.938341 0.345712i \(-0.112363\pi\)
−0.768566 + 0.639771i \(0.779029\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.22094 9.04293i −0.248054 0.429642i 0.714932 0.699194i \(-0.246458\pi\)
−0.962986 + 0.269552i \(0.913124\pi\)
\(444\) 0 0
\(445\) 0.654988 1.13447i 0.0310494 0.0537792i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 41.3502 1.95144 0.975719 0.219028i \(-0.0702885\pi\)
0.975719 + 0.219028i \(0.0702885\pi\)
\(450\) 0 0
\(451\) −10.3450 + 17.9181i −0.487128 + 0.843730i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.466208 0.119889i 0.0218562 0.00562051i
\(456\) 0 0
\(457\) 6.87592 + 11.9095i 0.321642 + 0.557101i 0.980827 0.194880i \(-0.0624318\pi\)
−0.659185 + 0.751981i \(0.729099\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.54583 0.304870 0.152435 0.988314i \(-0.451289\pi\)
0.152435 + 0.988314i \(0.451289\pi\)
\(462\) 0 0
\(463\) −0.228720 −0.0106295 −0.00531475 0.999986i \(-0.501692\pi\)
−0.00531475 + 0.999986i \(0.501692\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.3788 30.1010i −0.804195 1.39291i −0.916833 0.399271i \(-0.869263\pi\)
0.112638 0.993636i \(-0.464070\pi\)
\(468\) 0 0
\(469\) −26.0510 26.5824i −1.20292 1.22746i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.08865 + 7.08175i −0.187996 + 0.325619i
\(474\) 0 0
\(475\) −5.84213 −0.268055
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.4721 + 21.6023i −0.569865 + 0.987035i 0.426714 + 0.904387i \(0.359671\pi\)
−0.996579 + 0.0826481i \(0.973662\pi\)
\(480\) 0 0
\(481\) −2.20082 3.81193i −0.100349 0.173809i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.23912 + 2.14622i 0.0562657 + 0.0974550i
\(486\) 0 0
\(487\) 3.88207 6.72395i 0.175914 0.304691i −0.764564 0.644548i \(-0.777045\pi\)
0.940477 + 0.339857i \(0.110379\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −24.6224 −1.11120 −0.555598 0.831451i \(-0.687510\pi\)
−0.555598 + 0.831451i \(0.687510\pi\)
\(492\) 0 0
\(493\) −4.95937 + 8.58988i −0.223359 + 0.386869i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.70137 20.4498i 0.255742 0.917300i
\(498\) 0 0
\(499\) −12.3811 21.4447i −0.554255 0.959998i −0.997961 0.0638259i \(-0.979670\pi\)
0.443706 0.896173i \(-0.353664\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.01367 0.134373 0.0671865 0.997740i \(-0.478598\pi\)
0.0671865 + 0.997740i \(0.478598\pi\)
\(504\) 0 0
\(505\) −2.42107 −0.107736
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.7323 + 30.7132i 0.785970 + 1.36134i 0.928418 + 0.371537i \(0.121169\pi\)
−0.142448 + 0.989802i \(0.545497\pi\)
\(510\) 0 0
\(511\) −14.4971 14.7928i −0.641315 0.654395i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.315178 + 0.545904i −0.0138884 + 0.0240554i
\(516\) 0 0
\(517\) 12.5127 0.550309
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.48276 + 6.03232i −0.152582 + 0.264281i −0.932176 0.362005i \(-0.882092\pi\)
0.779594 + 0.626286i \(0.215426\pi\)
\(522\) 0 0
\(523\) 16.6940 + 28.9148i 0.729977 + 1.26436i 0.956892 + 0.290443i \(0.0938025\pi\)
−0.226916 + 0.973914i \(0.572864\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.94802 + 13.7664i 0.346221 + 0.599673i
\(528\) 0 0
\(529\) 9.11956 15.7955i 0.396503 0.686763i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.50232 −0.281647
\(534\) 0 0
\(535\) −0.518875 + 0.898718i −0.0224329 + 0.0388549i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −14.8450 + 8.17571i −0.639420 + 0.352153i
\(540\) 0 0
\(541\) 4.10752 + 7.11444i 0.176596 + 0.305874i 0.940713 0.339205i \(-0.110158\pi\)
−0.764116 + 0.645079i \(0.776825\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.09166 0.132432
\(546\) 0 0
\(547\) −8.50232 −0.363533 −0.181767 0.983342i \(-0.558182\pi\)
−0.181767 + 0.983342i \(0.558182\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.71341 2.96772i −0.0729938 0.126429i
\(552\) 0 0
\(553\) −11.6482 + 2.99542i −0.495330 + 0.127378i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.83009 13.5621i 0.331772 0.574646i −0.651088 0.759003i \(-0.725687\pi\)
0.982859 + 0.184357i \(0.0590203\pi\)
\(558\) 0 0
\(559\) −2.56991 −0.108695
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 21.2443 36.7963i 0.895342 1.55078i 0.0619602 0.998079i \(-0.480265\pi\)
0.833381 0.552698i \(-0.186402\pi\)
\(564\) 0 0
\(565\) −1.57046 2.72012i −0.0660698 0.114436i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.422701 0.732140i −0.0177206 0.0306929i 0.857029 0.515268i \(-0.172308\pi\)
−0.874750 + 0.484575i \(0.838974\pi\)
\(570\) 0 0
\(571\) 14.8353 25.6955i 0.620838 1.07532i −0.368492 0.929631i \(-0.620126\pi\)
0.989330 0.145692i \(-0.0465408\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10.7850 −0.449764
\(576\) 0 0
\(577\) 6.04871 10.4767i 0.251811 0.436150i −0.712213 0.701963i \(-0.752307\pi\)
0.964024 + 0.265813i \(0.0856405\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.53379 30.6092i 0.354041 1.26988i
\(582\) 0 0
\(583\) 3.78263 + 6.55171i 0.156661 + 0.271344i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.9338 −0.575109 −0.287555 0.957764i \(-0.592842\pi\)
−0.287555 + 0.957764i \(0.592842\pi\)
\(588\) 0 0
\(589\) −5.49192 −0.226291
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6.77743 11.7389i −0.278316 0.482057i 0.692651 0.721273i \(-0.256443\pi\)
−0.970966 + 0.239216i \(0.923109\pi\)
\(594\) 0 0
\(595\) −0.581257 + 2.08486i −0.0238292 + 0.0854711i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20.3960 + 35.3270i −0.833360 + 1.44342i 0.0619992 + 0.998076i \(0.480252\pi\)
−0.895359 + 0.445345i \(0.853081\pi\)
\(600\) 0 0
\(601\) 30.2164 1.23255 0.616277 0.787530i \(-0.288640\pi\)
0.616277 + 0.787530i \(0.288640\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.614360 + 1.06410i −0.0249773 + 0.0432619i
\(606\) 0 0
\(607\) 4.10752 + 7.11444i 0.166719 + 0.288766i 0.937264 0.348619i \(-0.113349\pi\)
−0.770545 + 0.637385i \(0.780016\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.96621 + 3.40557i 0.0795443 + 0.137775i
\(612\) 0 0
\(613\) 17.0224 29.4837i 0.687530 1.19084i −0.285105 0.958496i \(-0.592028\pi\)
0.972635 0.232340i \(-0.0746383\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.9064 1.52606 0.763028 0.646365i \(-0.223712\pi\)
0.763028 + 0.646365i \(0.223712\pi\)
\(618\) 0 0
\(619\) 20.0293 34.6917i 0.805045 1.39438i −0.111216 0.993796i \(-0.535475\pi\)
0.916261 0.400582i \(-0.131192\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14.0374 + 3.60983i −0.562395 + 0.144625i
\(624\) 0 0
\(625\) −12.0728 20.9107i −0.482911 0.836427i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 19.7907 0.789107
\(630\) 0 0
\(631\) 3.44514 0.137149 0.0685745 0.997646i \(-0.478155\pi\)
0.0685745 + 0.997646i \(0.478155\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.461695 0.799679i −0.0183218 0.0317343i
\(636\) 0 0
\(637\) −4.55787 2.75564i −0.180589 0.109183i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8.47537 + 14.6798i −0.334757 + 0.579816i −0.983438 0.181244i \(-0.941988\pi\)
0.648681 + 0.761060i \(0.275321\pi\)
\(642\) 0 0
\(643\) 32.8090 1.29386 0.646931 0.762549i \(-0.276052\pi\)
0.646931 + 0.762549i \(0.276052\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −13.5374 + 23.4474i −0.532208 + 0.921812i 0.467084 + 0.884213i \(0.345304\pi\)
−0.999293 + 0.0375994i \(0.988029\pi\)
\(648\) 0 0
\(649\) −7.53611 13.0529i −0.295818 0.512372i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 15.9487 + 27.6240i 0.624121 + 1.08101i 0.988710 + 0.149841i \(0.0478762\pi\)
−0.364589 + 0.931169i \(0.618790\pi\)
\(654\) 0 0
\(655\) 1.73517 3.00539i 0.0677985 0.117430i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −33.9852 −1.32388 −0.661938 0.749559i \(-0.730266\pi\)
−0.661938 + 0.749559i \(0.730266\pi\)
\(660\) 0 0
\(661\) −7.58414 + 13.1361i −0.294989 + 0.510935i −0.974982 0.222283i \(-0.928649\pi\)
0.679994 + 0.733218i \(0.261983\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.523388 0.534063i −0.0202961 0.0207101i
\(666\) 0 0
\(667\) −3.16307 5.47860i −0.122475 0.212132i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.30206 −0.127475
\(672\) 0 0
\(673\) 17.7324 0.683535 0.341767 0.939785i \(-0.388975\pi\)
0.341767 + 0.939785i \(0.388975\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.67154 + 2.89519i 0.0642425 + 0.111271i 0.896358 0.443332i \(-0.146204\pi\)
−0.832115 + 0.554603i \(0.812870\pi\)
\(678\) 0 0
\(679\) 7.36389 26.4130i 0.282600 1.01364i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23.7427 41.1235i 0.908489 1.57355i 0.0923244 0.995729i \(-0.470570\pi\)
0.816164 0.577820i \(-0.196096\pi\)
\(684\) 0 0
\(685\) −2.72777 −0.104223
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.18878 + 2.05903i −0.0452889 + 0.0784427i
\(690\) 0 0
\(691\) 3.67674 + 6.36830i 0.139870 + 0.242262i 0.927447 0.373954i \(-0.121998\pi\)
−0.787577 + 0.616216i \(0.788665\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.229408 + 0.397347i 0.00870195 + 0.0150722i
\(696\) 0 0
\(697\) 14.6179 25.3190i 0.553693 0.959025i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 45.1729 1.70616 0.853079 0.521782i \(-0.174733\pi\)
0.853079 + 0.521782i \(0.174733\pi\)
\(702\) 0 0
\(703\) −3.41874 + 5.92144i −0.128940 + 0.223331i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18.7495 + 19.1319i 0.705149 + 0.719531i
\(708\) 0 0
\(709\) −19.9246 34.5105i −0.748285 1.29607i −0.948644 0.316346i \(-0.897544\pi\)
0.200359 0.979723i \(-0.435789\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.1384 −0.379687
\(714\) 0 0
\(715\) 0.440497 0.0164737
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −20.4211 35.3703i −0.761577 1.31909i −0.942037 0.335508i \(-0.891092\pi\)
0.180460 0.983582i \(-0.442241\pi\)
\(720\) 0 0
\(721\) 6.75473 1.73704i 0.251559 0.0646906i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.16539 12.4108i 0.266116 0.460926i
\(726\) 0 0
\(727\) −6.42898 −0.238438 −0.119219 0.992868i \(-0.538039\pi\)
−0.119219 + 0.992868i \(0.538039\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.77743 10.0068i 0.213686 0.370115i
\(732\) 0 0
\(733\) 11.0773 + 19.1864i 0.409149 + 0.708667i 0.994795 0.101900i \(-0.0324922\pi\)
−0.585645 + 0.810567i \(0.699159\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −17.0293 29.4956i −0.627282 1.08648i
\(738\) 0 0
\(739\) 9.62081 16.6637i 0.353907 0.612985i −0.633023 0.774133i \(-0.718186\pi\)
0.986930 + 0.161148i \(0.0515196\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30.8616 −1.13220 −0.566100 0.824336i \(-0.691549\pi\)
−0.566100 + 0.824336i \(0.691549\pi\)
\(744\) 0 0
\(745\) 1.81191 3.13832i 0.0663832 0.114979i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 11.1202 2.85967i 0.406325 0.104490i
\(750\) 0 0
\(751\) −2.12476 3.68020i −0.0775337 0.134292i 0.824652 0.565641i \(-0.191371\pi\)
−0.902185 + 0.431349i \(0.858038\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.84540 0.103555
\(756\) 0 0
\(757\) 2.69578 0.0979798 0.0489899 0.998799i \(-0.484400\pi\)
0.0489899 + 0.998799i \(0.484400\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 19.5064 + 33.7862i 0.707108 + 1.22475i 0.965925 + 0.258821i \(0.0833339\pi\)
−0.258817 + 0.965926i \(0.583333\pi\)
\(762\) 0 0
\(763\) −23.9428 24.4312i −0.866788 0.884467i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.36840 4.10219i 0.0855180 0.148121i
\(768\) 0 0
\(769\) −32.0930 −1.15730 −0.578652 0.815574i \(-0.696421\pi\)
−0.578652 + 0.815574i \(0.696421\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.3873 + 21.4554i −0.445539 + 0.771697i −0.998090 0.0617828i \(-0.980321\pi\)
0.552550 + 0.833480i \(0.313655\pi\)
\(774\) 0 0
\(775\) −11.4834 19.8899i −0.412498 0.714467i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.05034 + 8.74745i 0.180947 + 0.313410i
\(780\) 0 0
\(781\) 9.71341 16.8241i 0.347573 0.602014i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.920120 −0.0328405
\(786\) 0 0
\(787\) −4.03543 + 6.98956i −0.143847 + 0.249151i −0.928942 0.370224i \(-0.879281\pi\)
0.785095 + 0.619375i \(0.212614\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.33297 + 33.4757i −0.331842 + 1.19026i
\(792\) 0 0
\(793\) −0.518875 0.898718i −0.0184258 0.0319144i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 32.6342 1.15596 0.577982 0.816050i \(-0.303840\pi\)
0.577982 + 0.816050i \(0.303840\pi\)
\(798\) 0 0
\(799\) −17.6810 −0.625509
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −9.47661 16.4140i −0.334422 0.579237i
\(804\) 0 0
\(805\) −0.966208 0.985915i −0.0340544 0.0347489i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) <