Properties

Label 3024.2.q.i.2881.1
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.1
Root \(0.247934 - 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.i.2305.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.84629 + 3.19787i) q^{5} +(-0.926641 - 2.47817i) q^{7} +O(q^{10})\) \(q+(-1.84629 + 3.19787i) q^{5} +(-0.926641 - 2.47817i) q^{7} +(0.446284 + 0.772987i) q^{11} +(0.598355 + 1.03638i) q^{13} +(0.124991 - 0.216492i) q^{17} +(-1.40414 - 2.43204i) q^{19} +(-1.23886 + 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(-2.07128 + 3.58755i) q^{29} -3.58515 q^{31} +(9.63571 + 1.61215i) q^{35} +(-2.36568 - 4.09747i) q^{37} +(2.39093 + 4.14121i) q^{41} +(4.98928 - 8.64169i) q^{43} -10.1731 q^{47} +(-5.28267 + 4.59275i) q^{49} +(4.94465 - 8.56438i) q^{53} -3.29588 q^{55} +1.81237 q^{59} +10.8041 q^{61} -4.41895 q^{65} -1.02937 q^{67} -4.94533 q^{71} +(-0.915262 + 1.58528i) q^{73} +(1.50205 - 1.82225i) q^{77} +1.79912 q^{79} +(6.16156 - 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(1.20370 + 2.08488i) q^{89} +(2.01387 - 2.44318i) q^{91} +10.3698 q^{95} +(5.52210 - 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{5} + 4q^{7} + O(q^{10}) \) \( 10q - 4q^{5} + 4q^{7} + 4q^{11} - 8q^{13} - 12q^{17} - q^{19} + 3q^{23} - q^{25} - 7q^{29} - 6q^{31} + 5q^{35} - 5q^{41} + 7q^{43} - 54q^{47} - 8q^{49} + 21q^{53} - 4q^{55} - 60q^{59} + 28q^{61} - 22q^{65} - 4q^{67} - 6q^{71} + 15q^{73} - 11q^{77} - 8q^{79} + 9q^{83} - 6q^{85} - 28q^{89} + 4q^{91} + 28q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.84629 + 3.19787i −0.825686 + 1.43013i 0.0757082 + 0.997130i \(0.475878\pi\)
−0.901394 + 0.433000i \(0.857455\pi\)
\(6\) 0 0
\(7\) −0.926641 2.47817i −0.350238 0.936661i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.446284 + 0.772987i 0.134560 + 0.233064i 0.925429 0.378921i \(-0.123705\pi\)
−0.790869 + 0.611985i \(0.790371\pi\)
\(12\) 0 0
\(13\) 0.598355 + 1.03638i 0.165954 + 0.287441i 0.936994 0.349346i \(-0.113596\pi\)
−0.771040 + 0.636787i \(0.780263\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.124991 0.216492i 0.0303149 0.0525069i −0.850470 0.526024i \(-0.823682\pi\)
0.880785 + 0.473517i \(0.157016\pi\)
\(18\) 0 0
\(19\) −1.40414 2.43204i −0.322131 0.557948i 0.658796 0.752321i \(-0.271066\pi\)
−0.980928 + 0.194374i \(0.937733\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.23886 + 2.14576i −0.258320 + 0.447423i −0.965792 0.259318i \(-0.916502\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(24\) 0 0
\(25\) −4.31757 7.47825i −0.863514 1.49565i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.07128 + 3.58755i −0.384626 + 0.666192i −0.991717 0.128440i \(-0.959003\pi\)
0.607091 + 0.794632i \(0.292336\pi\)
\(30\) 0 0
\(31\) −3.58515 −0.643912 −0.321956 0.946755i \(-0.604340\pi\)
−0.321956 + 0.946755i \(0.604340\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 9.63571 + 1.61215i 1.62873 + 0.272502i
\(36\) 0 0
\(37\) −2.36568 4.09747i −0.388915 0.673621i 0.603389 0.797447i \(-0.293817\pi\)
−0.992304 + 0.123826i \(0.960483\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.39093 + 4.14121i 0.373400 + 0.646748i 0.990086 0.140461i \(-0.0448584\pi\)
−0.616686 + 0.787209i \(0.711525\pi\)
\(42\) 0 0
\(43\) 4.98928 8.64169i 0.760859 1.31785i −0.181550 0.983382i \(-0.558111\pi\)
0.942408 0.334464i \(-0.108555\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.1731 −1.48389 −0.741947 0.670459i \(-0.766097\pi\)
−0.741947 + 0.670459i \(0.766097\pi\)
\(48\) 0 0
\(49\) −5.28267 + 4.59275i −0.754667 + 0.656108i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.94465 8.56438i 0.679199 1.17641i −0.296023 0.955181i \(-0.595661\pi\)
0.975222 0.221227i \(-0.0710061\pi\)
\(54\) 0 0
\(55\) −3.29588 −0.444416
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.81237 0.235951 0.117975 0.993017i \(-0.462360\pi\)
0.117975 + 0.993017i \(0.462360\pi\)
\(60\) 0 0
\(61\) 10.8041 1.38332 0.691662 0.722221i \(-0.256879\pi\)
0.691662 + 0.722221i \(0.256879\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.41895 −0.548103
\(66\) 0 0
\(67\) −1.02937 −0.125757 −0.0628787 0.998021i \(-0.520028\pi\)
−0.0628787 + 0.998021i \(0.520028\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.94533 −0.586903 −0.293451 0.955974i \(-0.594804\pi\)
−0.293451 + 0.955974i \(0.594804\pi\)
\(72\) 0 0
\(73\) −0.915262 + 1.58528i −0.107123 + 0.185543i −0.914604 0.404351i \(-0.867497\pi\)
0.807480 + 0.589894i \(0.200831\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.50205 1.82225i 0.171174 0.207665i
\(78\) 0 0
\(79\) 1.79912 0.202417 0.101209 0.994865i \(-0.467729\pi\)
0.101209 + 0.994865i \(0.467729\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.16156 10.6721i 0.676319 1.17142i −0.299763 0.954014i \(-0.596908\pi\)
0.976082 0.217405i \(-0.0697591\pi\)
\(84\) 0 0
\(85\) 0.461541 + 0.799412i 0.0500611 + 0.0867084i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.20370 + 2.08488i 0.127592 + 0.220997i 0.922743 0.385415i \(-0.125942\pi\)
−0.795151 + 0.606412i \(0.792608\pi\)
\(90\) 0 0
\(91\) 2.01387 2.44318i 0.211111 0.256115i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.3698 1.06392
\(96\) 0 0
\(97\) 5.52210 9.56456i 0.560684 0.971134i −0.436752 0.899582i \(-0.643871\pi\)
0.997437 0.0715522i \(-0.0227952\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.29982 2.25136i −0.129337 0.224018i 0.794083 0.607810i \(-0.207952\pi\)
−0.923420 + 0.383791i \(0.874618\pi\)
\(102\) 0 0
\(103\) 4.85578 8.41045i 0.478454 0.828706i −0.521241 0.853409i \(-0.674531\pi\)
0.999695 + 0.0247032i \(0.00786408\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.45025 9.44012i −0.526896 0.912610i −0.999509 0.0313403i \(-0.990022\pi\)
0.472613 0.881270i \(-0.343311\pi\)
\(108\) 0 0
\(109\) −1.06096 + 1.83764i −0.101622 + 0.176014i −0.912353 0.409404i \(-0.865737\pi\)
0.810731 + 0.585419i \(0.199070\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.91318 13.7060i −0.744409 1.28935i −0.950470 0.310816i \(-0.899398\pi\)
0.206061 0.978539i \(-0.433935\pi\)
\(114\) 0 0
\(115\) −4.57458 7.92341i −0.426582 0.738861i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.652326 0.109140i −0.0597986 0.0100049i
\(120\) 0 0
\(121\) 5.10166 8.83634i 0.463787 0.803303i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 13.4230 1.20059
\(126\) 0 0
\(127\) 1.26946 0.112647 0.0563233 0.998413i \(-0.482062\pi\)
0.0563233 + 0.998413i \(0.482062\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.51444 13.0154i 0.656540 1.13716i −0.324965 0.945726i \(-0.605353\pi\)
0.981505 0.191435i \(-0.0613140\pi\)
\(132\) 0 0
\(133\) −4.72587 + 5.73332i −0.409785 + 0.497142i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.244246 0.423047i −0.0208674 0.0361433i 0.855403 0.517963i \(-0.173309\pi\)
−0.876271 + 0.481819i \(0.839976\pi\)
\(138\) 0 0
\(139\) 4.93487 + 8.54745i 0.418570 + 0.724985i 0.995796 0.0915997i \(-0.0291980\pi\)
−0.577226 + 0.816585i \(0.695865\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.534073 + 0.925042i −0.0446614 + 0.0773559i
\(144\) 0 0
\(145\) −7.64835 13.2473i −0.635161 1.10013i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.5120 18.2073i 0.861175 1.49160i −0.00962096 0.999954i \(-0.503062\pi\)
0.870796 0.491645i \(-0.163604\pi\)
\(150\) 0 0
\(151\) 0.749191 + 1.29764i 0.0609683 + 0.105600i 0.894898 0.446270i \(-0.147248\pi\)
−0.833930 + 0.551870i \(0.813914\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.61922 11.4648i 0.531669 0.920877i
\(156\) 0 0
\(157\) −16.6796 −1.33118 −0.665590 0.746317i \(-0.731820\pi\)
−0.665590 + 0.746317i \(0.731820\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.46555 + 1.08175i 0.509557 + 0.0852537i
\(162\) 0 0
\(163\) 3.34135 + 5.78738i 0.261714 + 0.453303i 0.966698 0.255921i \(-0.0823788\pi\)
−0.704983 + 0.709224i \(0.749046\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.81549 + 15.2689i 0.682163 + 1.18154i 0.974319 + 0.225170i \(0.0722939\pi\)
−0.292156 + 0.956371i \(0.594373\pi\)
\(168\) 0 0
\(169\) 5.78394 10.0181i 0.444919 0.770622i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.88685 0.295511 0.147756 0.989024i \(-0.452795\pi\)
0.147756 + 0.989024i \(0.452795\pi\)
\(174\) 0 0
\(175\) −14.5316 + 17.6293i −1.09848 + 1.33265i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.66758 6.35244i 0.274128 0.474804i −0.695787 0.718248i \(-0.744944\pi\)
0.969915 + 0.243445i \(0.0782775\pi\)
\(180\) 0 0
\(181\) 11.2566 0.836693 0.418346 0.908288i \(-0.362610\pi\)
0.418346 + 0.908288i \(0.362610\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 17.4709 1.28449
\(186\) 0 0
\(187\) 0.223127 0.0163167
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −23.8459 −1.72543 −0.862715 0.505690i \(-0.831238\pi\)
−0.862715 + 0.505690i \(0.831238\pi\)
\(192\) 0 0
\(193\) 5.93456 0.427179 0.213589 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.4682 1.10206 0.551032 0.834484i \(-0.314234\pi\)
0.551032 + 0.834484i \(0.314234\pi\)
\(198\) 0 0
\(199\) −7.74818 + 13.4202i −0.549254 + 0.951336i 0.449072 + 0.893496i \(0.351755\pi\)
−0.998326 + 0.0578402i \(0.981579\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.8099 + 1.80860i 0.758707 + 0.126939i
\(204\) 0 0
\(205\) −17.6574 −1.23325
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.25329 2.17076i 0.0866918 0.150155i
\(210\) 0 0
\(211\) −0.771898 1.33697i −0.0531397 0.0920406i 0.838232 0.545314i \(-0.183590\pi\)
−0.891372 + 0.453273i \(0.850256\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 18.4233 + 31.9101i 1.25646 + 2.17625i
\(216\) 0 0
\(217\) 3.32215 + 8.88461i 0.225522 + 0.603127i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.299157 0.0201235
\(222\) 0 0
\(223\) 2.72171 4.71414i 0.182259 0.315682i −0.760390 0.649466i \(-0.774992\pi\)
0.942649 + 0.333784i \(0.108326\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.03818 + 13.9225i 0.533513 + 0.924072i 0.999234 + 0.0391399i \(0.0124618\pi\)
−0.465721 + 0.884932i \(0.654205\pi\)
\(228\) 0 0
\(229\) 4.98420 8.63289i 0.329365 0.570477i −0.653021 0.757340i \(-0.726499\pi\)
0.982386 + 0.186863i \(0.0598319\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.27045 14.3248i −0.541815 0.938451i −0.998800 0.0489765i \(-0.984404\pi\)
0.456985 0.889474i \(-0.348929\pi\)
\(234\) 0 0
\(235\) 18.7824 32.5321i 1.22523 2.12216i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.0119 19.0732i −0.712303 1.23375i −0.963990 0.265937i \(-0.914319\pi\)
0.251687 0.967809i \(-0.419015\pi\)
\(240\) 0 0
\(241\) −8.36004 14.4800i −0.538517 0.932739i −0.998984 0.0450623i \(-0.985651\pi\)
0.460467 0.887677i \(-0.347682\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.93368 25.3728i −0.315201 1.62101i
\(246\) 0 0
\(247\) 1.68035 2.91045i 0.106918 0.185187i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −8.53099 −0.538471 −0.269236 0.963074i \(-0.586771\pi\)
−0.269236 + 0.963074i \(0.586771\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.55986 + 14.8261i −0.533950 + 0.924828i 0.465264 + 0.885172i \(0.345959\pi\)
−0.999213 + 0.0396557i \(0.987374\pi\)
\(258\) 0 0
\(259\) −7.96211 + 9.65945i −0.494741 + 0.600209i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −10.2763 17.7991i −0.633666 1.09754i −0.986796 0.161967i \(-0.948216\pi\)
0.353130 0.935574i \(-0.385117\pi\)
\(264\) 0 0
\(265\) 18.2585 + 31.6246i 1.12161 + 1.94269i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.92267 + 17.1866i −0.604996 + 1.04788i 0.387057 + 0.922056i \(0.373492\pi\)
−0.992052 + 0.125827i \(0.959842\pi\)
\(270\) 0 0
\(271\) −5.32056 9.21548i −0.323201 0.559801i 0.657946 0.753065i \(-0.271426\pi\)
−0.981147 + 0.193265i \(0.938092\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.85373 6.67485i 0.232388 0.402509i
\(276\) 0 0
\(277\) 12.4407 + 21.5479i 0.747487 + 1.29469i 0.949024 + 0.315205i \(0.102073\pi\)
−0.201536 + 0.979481i \(0.564593\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.83733 11.8426i 0.407881 0.706470i −0.586771 0.809753i \(-0.699601\pi\)
0.994652 + 0.103282i \(0.0329346\pi\)
\(282\) 0 0
\(283\) −6.32179 −0.375791 −0.187896 0.982189i \(-0.560167\pi\)
−0.187896 + 0.982189i \(0.560167\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.04710 9.76255i 0.475005 0.576265i
\(288\) 0 0
\(289\) 8.46875 + 14.6683i 0.498162 + 0.862842i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.31508 + 2.27778i 0.0768277 + 0.133069i 0.901880 0.431987i \(-0.142188\pi\)
−0.825052 + 0.565057i \(0.808854\pi\)
\(294\) 0 0
\(295\) −3.34616 + 5.79573i −0.194821 + 0.337440i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.96511 −0.171477
\(300\) 0 0
\(301\) −26.0389 4.35655i −1.50086 0.251108i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −19.9475 + 34.5501i −1.14219 + 1.97833i
\(306\) 0 0
\(307\) 2.79496 0.159517 0.0797583 0.996814i \(-0.474585\pi\)
0.0797583 + 0.996814i \(0.474585\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.1003 −0.856258 −0.428129 0.903718i \(-0.640827\pi\)
−0.428129 + 0.903718i \(0.640827\pi\)
\(312\) 0 0
\(313\) −25.4785 −1.44013 −0.720064 0.693908i \(-0.755888\pi\)
−0.720064 + 0.693908i \(0.755888\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −32.5209 −1.82656 −0.913278 0.407337i \(-0.866457\pi\)
−0.913278 + 0.407337i \(0.866457\pi\)
\(318\) 0 0
\(319\) −3.69751 −0.207021
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.702021 −0.0390615
\(324\) 0 0
\(325\) 5.16688 8.94931i 0.286607 0.496418i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9.42678 + 25.2106i 0.519715 + 1.38991i
\(330\) 0 0
\(331\) −18.0948 −0.994582 −0.497291 0.867584i \(-0.665672\pi\)
−0.497291 + 0.867584i \(0.665672\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.90051 3.29179i 0.103836 0.179850i
\(336\) 0 0
\(337\) −12.5086 21.6656i −0.681389 1.18020i −0.974557 0.224139i \(-0.928043\pi\)
0.293168 0.956061i \(-0.405290\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.59999 2.77127i −0.0866446 0.150073i
\(342\) 0 0
\(343\) 16.2768 + 8.83553i 0.878863 + 0.477074i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.7489 0.577030 0.288515 0.957475i \(-0.406838\pi\)
0.288515 + 0.957475i \(0.406838\pi\)
\(348\) 0 0
\(349\) −1.64301 + 2.84577i −0.0879482 + 0.152331i −0.906644 0.421897i \(-0.861364\pi\)
0.818695 + 0.574228i \(0.194698\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.40960 + 14.5658i 0.447598 + 0.775262i 0.998229 0.0594866i \(-0.0189463\pi\)
−0.550631 + 0.834748i \(0.685613\pi\)
\(354\) 0 0
\(355\) 9.13051 15.8145i 0.484597 0.839347i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.8921 + 20.5978i 0.627642 + 1.08711i 0.988024 + 0.154303i \(0.0493131\pi\)
−0.360382 + 0.932805i \(0.617354\pi\)
\(360\) 0 0
\(361\) 5.55680 9.62466i 0.292463 0.506561i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.37968 5.85377i −0.176900 0.306401i
\(366\) 0 0
\(367\) −0.344992 0.597544i −0.0180084 0.0311915i 0.856881 0.515515i \(-0.172399\pi\)
−0.874889 + 0.484323i \(0.839066\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −25.8059 4.31757i −1.33978 0.224157i
\(372\) 0 0
\(373\) 1.88006 3.25636i 0.0973457 0.168608i −0.813239 0.581929i \(-0.802298\pi\)
0.910585 + 0.413321i \(0.135631\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.95744 −0.255321
\(378\) 0 0
\(379\) −32.8735 −1.68860 −0.844300 0.535872i \(-0.819983\pi\)
−0.844300 + 0.535872i \(0.819983\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.536335 0.928960i 0.0274055 0.0474676i −0.851997 0.523546i \(-0.824609\pi\)
0.879403 + 0.476078i \(0.157942\pi\)
\(384\) 0 0
\(385\) 3.05410 + 8.16775i 0.155651 + 0.416267i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11.8718 20.5626i −0.601925 1.04256i −0.992529 0.122006i \(-0.961067\pi\)
0.390605 0.920559i \(-0.372266\pi\)
\(390\) 0 0
\(391\) 0.309693 + 0.536405i 0.0156619 + 0.0271271i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.32170 + 5.75336i −0.167133 + 0.289483i
\(396\) 0 0
\(397\) −0.0160489 0.0277975i −0.000805471 0.00139512i 0.865622 0.500697i \(-0.166923\pi\)
−0.866428 + 0.499302i \(0.833590\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.2628 21.2398i 0.612374 1.06066i −0.378465 0.925616i \(-0.623548\pi\)
0.990839 0.135048i \(-0.0431188\pi\)
\(402\) 0 0
\(403\) −2.14519 3.71558i −0.106860 0.185086i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.11153 3.65728i 0.104665 0.181284i
\(408\) 0 0
\(409\) 26.7897 1.32467 0.662333 0.749210i \(-0.269567\pi\)
0.662333 + 0.749210i \(0.269567\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.67942 4.49137i −0.0826388 0.221006i
\(414\) 0 0
\(415\) 22.7520 + 39.4077i 1.11685 + 1.93445i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.5262 18.2320i −0.514240 0.890689i −0.999864 0.0165215i \(-0.994741\pi\)
0.485624 0.874168i \(-0.338593\pi\)
\(420\) 0 0
\(421\) −7.44533 + 12.8957i −0.362863 + 0.628498i −0.988431 0.151672i \(-0.951534\pi\)
0.625568 + 0.780170i \(0.284867\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.15864 −0.104709
\(426\) 0 0
\(427\) −10.0115 26.7744i −0.484492 1.29571i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.95192 + 13.7731i −0.383031 + 0.663428i −0.991494 0.130154i \(-0.958453\pi\)
0.608463 + 0.793582i \(0.291786\pi\)
\(432\) 0 0
\(433\) −16.3658 −0.786490 −0.393245 0.919434i \(-0.628648\pi\)
−0.393245 + 0.919434i \(0.628648\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.95811 0.332851
\(438\) 0 0
\(439\) 15.5447 0.741909 0.370954 0.928651i \(-0.379031\pi\)
0.370954 + 0.928651i \(0.379031\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.79005 0.0850480 0.0425240 0.999095i \(-0.486460\pi\)
0.0425240 + 0.999095i \(0.486460\pi\)
\(444\) 0 0
\(445\) −8.88955 −0.421405
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −13.5666 −0.640250 −0.320125 0.947375i \(-0.603725\pi\)
−0.320125 + 0.947375i \(0.603725\pi\)
\(450\) 0 0
\(451\) −2.13407 + 3.69631i −0.100489 + 0.174053i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.09478 + 10.9509i 0.191966 + 0.513387i
\(456\) 0 0
\(457\) 2.56917 0.120181 0.0600905 0.998193i \(-0.480861\pi\)
0.0600905 + 0.998193i \(0.480861\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −18.0934 + 31.3388i −0.842695 + 1.45959i 0.0449122 + 0.998991i \(0.485699\pi\)
−0.887608 + 0.460600i \(0.847634\pi\)
\(462\) 0 0
\(463\) −8.19224 14.1894i −0.380726 0.659436i 0.610440 0.792062i \(-0.290992\pi\)
−0.991166 + 0.132626i \(0.957659\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.35022 7.53480i −0.201304 0.348669i 0.747645 0.664099i \(-0.231185\pi\)
−0.948949 + 0.315430i \(0.897851\pi\)
\(468\) 0 0
\(469\) 0.953856 + 2.55095i 0.0440450 + 0.117792i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.90655 0.409524
\(474\) 0 0
\(475\) −12.1249 + 21.0010i −0.556330 + 0.963591i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.88370 + 15.3870i 0.405907 + 0.703051i 0.994427 0.105432i \(-0.0336224\pi\)
−0.588520 + 0.808483i \(0.700289\pi\)
\(480\) 0 0
\(481\) 2.83103 4.90349i 0.129084 0.223580i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 20.3908 + 35.3179i 0.925898 + 1.60370i
\(486\) 0 0
\(487\) −8.32763 + 14.4239i −0.377361 + 0.653608i −0.990677 0.136229i \(-0.956502\pi\)
0.613316 + 0.789837i \(0.289835\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3.21021 5.56025i −0.144875 0.250930i 0.784451 0.620190i \(-0.212945\pi\)
−0.929326 + 0.369260i \(0.879611\pi\)
\(492\) 0 0
\(493\) 0.517784 + 0.896827i 0.0233198 + 0.0403911i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.58255 + 12.2554i 0.205555 + 0.549729i
\(498\) 0 0
\(499\) 5.57296 9.65264i 0.249480 0.432112i −0.713902 0.700246i \(-0.753074\pi\)
0.963382 + 0.268134i \(0.0864071\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17.7223 −0.790200 −0.395100 0.918638i \(-0.629290\pi\)
−0.395100 + 0.918638i \(0.629290\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.5411 26.9180i 0.688848 1.19312i −0.283362 0.959013i \(-0.591450\pi\)
0.972211 0.234107i \(-0.0752167\pi\)
\(510\) 0 0
\(511\) 4.77672 + 0.799190i 0.211310 + 0.0353541i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.9303 + 31.0563i 0.790105 + 1.36850i
\(516\) 0 0
\(517\) −4.54008 7.86365i −0.199672 0.345843i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.37986 4.12203i 0.104263 0.180590i −0.809174 0.587570i \(-0.800085\pi\)
0.913437 + 0.406980i \(0.133418\pi\)
\(522\) 0 0
\(523\) −20.1258 34.8588i −0.880038 1.52427i −0.851298 0.524683i \(-0.824184\pi\)
−0.0287402 0.999587i \(-0.509150\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.448113 + 0.776154i −0.0195201 + 0.0338098i
\(528\) 0 0
\(529\) 8.43046 + 14.6020i 0.366542 + 0.634869i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.86125 + 4.95583i −0.123935 + 0.214661i
\(534\) 0 0
\(535\) 40.2510 1.74020
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.90771 2.03376i −0.254463 0.0876003i
\(540\) 0 0
\(541\) 12.0547 + 20.8794i 0.518273 + 0.897675i 0.999775 + 0.0212301i \(0.00675826\pi\)
−0.481502 + 0.876445i \(0.659908\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.91769 6.78564i −0.167815 0.290665i
\(546\) 0 0
\(547\) 6.17751 10.6998i 0.264131 0.457489i −0.703204 0.710988i \(-0.748248\pi\)
0.967336 + 0.253499i \(0.0815814\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11.6334 0.495600
\(552\) 0 0
\(553\) −1.66714 4.45854i −0.0708941 0.189596i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.03845 + 6.99479i −0.171114 + 0.296379i −0.938810 0.344436i \(-0.888070\pi\)
0.767695 + 0.640815i \(0.221403\pi\)
\(558\) 0 0
\(559\) 11.9415 0.505070
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 45.2127 1.90549 0.952744 0.303774i \(-0.0982467\pi\)
0.952744 + 0.303774i \(0.0982467\pi\)
\(564\) 0 0
\(565\) 58.4401 2.45859
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.4299 −0.940309 −0.470155 0.882584i \(-0.655802\pi\)
−0.470155 + 0.882584i \(0.655802\pi\)
\(570\) 0 0
\(571\) 21.8269 0.913426 0.456713 0.889614i \(-0.349027\pi\)
0.456713 + 0.889614i \(0.349027\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 21.3954 0.892251
\(576\) 0 0
\(577\) −16.1022 + 27.8898i −0.670342 + 1.16107i 0.307465 + 0.951559i \(0.400519\pi\)
−0.977807 + 0.209508i \(0.932814\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −32.1569 5.38016i −1.33409 0.223207i
\(582\) 0 0
\(583\) 8.82687 0.365571
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.72304 + 16.8408i −0.401313 + 0.695094i −0.993885 0.110424i \(-0.964779\pi\)
0.592572 + 0.805518i \(0.298113\pi\)
\(588\) 0 0
\(589\) 5.03404 + 8.71921i 0.207424 + 0.359269i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.4202 + 24.9766i 0.592168 + 1.02566i 0.993940 + 0.109925i \(0.0350611\pi\)
−0.401772 + 0.915740i \(0.631606\pi\)
\(594\) 0 0
\(595\) 1.55340 1.88455i 0.0636831 0.0772589i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −46.9989 −1.92032 −0.960161 0.279447i \(-0.909849\pi\)
−0.960161 + 0.279447i \(0.909849\pi\)
\(600\) 0 0
\(601\) −7.80843 + 13.5246i −0.318512 + 0.551680i −0.980178 0.198119i \(-0.936517\pi\)
0.661665 + 0.749799i \(0.269850\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 18.8383 + 32.6289i 0.765885 + 1.32655i
\(606\) 0 0
\(607\) −14.3266 + 24.8144i −0.581500 + 1.00719i 0.413802 + 0.910367i \(0.364200\pi\)
−0.995302 + 0.0968200i \(0.969133\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.08711 10.5432i −0.246258 0.426531i
\(612\) 0 0
\(613\) 14.6734 25.4151i 0.592653 1.02651i −0.401220 0.915982i \(-0.631414\pi\)
0.993873 0.110524i \(-0.0352529\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.06401 3.57497i −0.0830938 0.143923i 0.821484 0.570232i \(-0.193147\pi\)
−0.904577 + 0.426310i \(0.859813\pi\)
\(618\) 0 0
\(619\) 11.3565 + 19.6700i 0.456456 + 0.790605i 0.998771 0.0495708i \(-0.0157853\pi\)
−0.542315 + 0.840175i \(0.682452\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.05128 4.91492i 0.162311 0.196912i
\(624\) 0 0
\(625\) −3.19498 + 5.53387i −0.127799 + 0.221355i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.18276 −0.0471597
\(630\) 0 0
\(631\) 38.6411 1.53828 0.769138 0.639082i \(-0.220686\pi\)
0.769138 + 0.639082i \(0.220686\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.34380 + 4.05958i −0.0930107 + 0.161099i
\(636\) 0 0
\(637\) −7.92076 2.72677i −0.313832 0.108038i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −14.2363 24.6580i −0.562301 0.973933i −0.997295 0.0735002i \(-0.976583\pi\)
0.434995 0.900433i \(-0.356750\pi\)
\(642\) 0 0
\(643\) 8.52125 + 14.7592i 0.336045 + 0.582048i 0.983685 0.179899i \(-0.0575771\pi\)
−0.647640 + 0.761947i \(0.724244\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.68809 2.92386i 0.0663657 0.114949i −0.830933 0.556372i \(-0.812193\pi\)
0.897299 + 0.441423i \(0.145526\pi\)
\(648\) 0 0
\(649\) 0.808833 + 1.40094i 0.0317495 + 0.0549917i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.17255 + 15.8873i −0.358950 + 0.621719i −0.987786 0.155819i \(-0.950198\pi\)
0.628836 + 0.777538i \(0.283532\pi\)
\(654\) 0 0
\(655\) 27.7477 + 48.0604i 1.08419 + 1.87787i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13.9248 + 24.1184i −0.542432 + 0.939519i 0.456332 + 0.889810i \(0.349163\pi\)
−0.998764 + 0.0497098i \(0.984170\pi\)
\(660\) 0 0
\(661\) 39.0141 1.51747 0.758737 0.651397i \(-0.225817\pi\)
0.758737 + 0.651397i \(0.225817\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.60906 25.6981i −0.372624 0.996529i
\(666\) 0 0
\(667\) −5.13203 8.88894i −0.198713 0.344181i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.82170 + 8.35143i 0.186140 + 0.322404i
\(672\) 0 0
\(673\) 24.6154 42.6352i 0.948856 1.64347i 0.201014 0.979588i \(-0.435576\pi\)
0.747841 0.663878i \(-0.231090\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23.3915 0.899010 0.449505 0.893278i \(-0.351600\pi\)
0.449505 + 0.893278i \(0.351600\pi\)
\(678\) 0 0
\(679\) −28.8196 4.82180i −1.10600 0.185044i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −15.1632 + 26.2634i −0.580204 + 1.00494i 0.415251 + 0.909707i \(0.363694\pi\)
−0.995455 + 0.0952356i \(0.969640\pi\)
\(684\) 0 0
\(685\) 1.80380 0.0689196
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 11.8346 0.450863
\(690\) 0 0
\(691\) 4.11330 0.156477 0.0782387 0.996935i \(-0.475070\pi\)
0.0782387 + 0.996935i \(0.475070\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −36.4448 −1.38243
\(696\) 0 0
\(697\) 1.19538 0.0452784
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −29.1835 −1.10225 −0.551123 0.834424i \(-0.685800\pi\)
−0.551123 + 0.834424i \(0.685800\pi\)
\(702\) 0 0
\(703\) −6.64347 + 11.5068i −0.250563 + 0.433988i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.37478 + 5.30738i −0.164531 + 0.199605i
\(708\) 0 0
\(709\) −42.4617 −1.59468 −0.797342 0.603528i \(-0.793761\pi\)
−0.797342 + 0.603528i \(0.793761\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.44149 7.69288i 0.166335 0.288101i
\(714\) 0 0
\(715\) −1.97211 3.41579i −0.0737526 0.127743i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5.57126 9.64970i −0.207773 0.359873i 0.743240 0.669025i \(-0.233288\pi\)
−0.951013 + 0.309152i \(0.899955\pi\)
\(720\) 0 0
\(721\) −25.3421 4.23997i −0.943789 0.157905i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 35.7715 1.32852
\(726\) 0 0
\(727\) 14.3410 24.8393i 0.531878 0.921239i −0.467430 0.884030i \(-0.654820\pi\)
0.999308 0.0372089i \(-0.0118467\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.24724 2.16028i −0.0461307 0.0799007i
\(732\) 0 0
\(733\) 12.5264 21.6964i 0.462674 0.801375i −0.536419 0.843952i \(-0.680223\pi\)
0.999093 + 0.0425768i \(0.0135567\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.459391 0.795689i −0.0169219 0.0293096i
\(738\) 0 0
\(739\) −13.7608 + 23.8344i −0.506198 + 0.876761i 0.493776 + 0.869589i \(0.335616\pi\)
−0.999974 + 0.00717223i \(0.997717\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.00608 12.1349i −0.257028 0.445186i 0.708416 0.705795i \(-0.249410\pi\)
−0.965444 + 0.260609i \(0.916077\pi\)
\(744\) 0 0
\(745\) 38.8163 + 67.2318i 1.42212 + 2.46318i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.3438 + 22.2543i −0.670268 + 0.813153i
\(750\) 0 0
\(751\) −26.1297 + 45.2580i −0.953486 + 1.65149i −0.215692 + 0.976461i \(0.569201\pi\)
−0.737795 + 0.675025i \(0.764133\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.53289 −0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.62550 + 14.9398i −0.312674 + 0.541568i −0.978940 0.204146i \(-0.934558\pi\)
0.666266 + 0.745714i \(0.267891\pi\)
\(762\) 0 0
\(763\) 5.53713 + 0.926414i 0.200457 + 0.0335384i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.08444 + 1.87831i 0.0391570 + 0.0678218i
\(768\) 0 0
\(769\) −10.6727 18.4856i −0.384867 0.666609i 0.606884 0.794790i \(-0.292419\pi\)
−0.991751 + 0.128182i \(0.959086\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.57357 11.3858i 0.236435 0.409517i −0.723254 0.690582i \(-0.757354\pi\)
0.959689 + 0.281065i \(0.0906877\pi\)
\(774\) 0 0
\(775\) 15.4791 + 26.8106i 0.556027 + 0.963066i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.71439 11.6297i 0.240568 0.416676i
\(780\) 0 0
\(781\) −2.20702 3.82268i −0.0789735 0.136786i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 30.7954 53.3393i 1.09914 1.90376i
\(786\) 0 0
\(787\) 28.1301 1.00273 0.501364 0.865236i \(-0.332832\pi\)
0.501364 + 0.865236i \(0.332832\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −26.6332 + 32.3108i −0.946968 + 1.14884i
\(792\) 0 0
\(793\) 6.46470 + 11.1972i 0.229568 + 0.397624i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.8683 22.2885i −0.455817 0.789499i 0.542917 0.839786i \(-0.317320\pi\)
−0.998735 + 0.0502873i \(0.983986\pi\)
\(798\) 0 0
\(799\) −1.27155 + 2.20238i −0.0449841 + 0.0779147i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.63387 −0.0576580