Properties

Label 2268.2.i.n.2053.8
Level $2268$
Weight $2$
Character 2268.2053
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2053.8
Root \(-0.817131 - 0.735533i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2053
Dual form 2268.2.i.n.865.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.83843 + 3.18426i) q^{5} +(-1.55575 - 2.14001i) q^{7} +O(q^{10})\) \(q+(1.83843 + 3.18426i) q^{5} +(-1.55575 - 2.14001i) q^{7} +(0.301572 - 0.522337i) q^{11} +(2.62851 - 4.55271i) q^{13} +(2.12557 + 3.68159i) q^{17} +(3.68426 - 6.38133i) q^{19} +(0.578891 + 1.00267i) q^{23} +(-4.25969 + 7.37799i) q^{25} +(-3.98826 - 6.90786i) q^{29} +3.15085 q^{31} +(3.95419 - 8.88819i) q^{35} +(0.00266923 - 0.00462323i) q^{37} +(-2.00937 + 3.48033i) q^{41} +(-3.66193 - 6.34264i) q^{43} +12.2173 q^{47} +(-2.15926 + 6.65865i) q^{49} +(-4.64928 - 8.05279i) q^{53} +2.21768 q^{55} +6.61521 q^{59} -1.93850 q^{61} +19.3294 q^{65} +8.63088 q^{67} +1.13815 q^{71} +(-5.33511 - 9.24068i) q^{73} +(-1.58698 + 0.167264i) q^{77} +4.14551 q^{79} +(6.24088 + 10.8095i) q^{83} +(-7.81544 + 13.5367i) q^{85} +(-4.09464 + 7.09212i) q^{89} +(-13.8321 + 1.45787i) q^{91} +27.0931 q^{95} +(6.77935 + 11.7422i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) 0 0
\(5\) 1.83843 + 3.18426i 0.822173 + 1.42405i 0.904061 + 0.427404i \(0.140572\pi\)
−0.0818877 + 0.996642i \(0.526095\pi\)
\(6\) 0 0
\(7\) −1.55575 2.14001i −0.588020 0.808846i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.301572 0.522337i 0.0909273 0.157491i −0.816974 0.576674i \(-0.804350\pi\)
0.907902 + 0.419183i \(0.137684\pi\)
\(12\) 0 0
\(13\) 2.62851 4.55271i 0.729017 1.26269i −0.228282 0.973595i \(-0.573311\pi\)
0.957299 0.289099i \(-0.0933558\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.12557 + 3.68159i 0.515526 + 0.892918i 0.999838 + 0.0180219i \(0.00573685\pi\)
−0.484311 + 0.874896i \(0.660930\pi\)
\(18\) 0 0
\(19\) 3.68426 6.38133i 0.845228 1.46398i −0.0401954 0.999192i \(-0.512798\pi\)
0.885423 0.464786i \(-0.153869\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.578891 + 1.00267i 0.120707 + 0.209071i 0.920047 0.391809i \(-0.128150\pi\)
−0.799340 + 0.600880i \(0.794817\pi\)
\(24\) 0 0
\(25\) −4.25969 + 7.37799i −0.851937 + 1.47560i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.98826 6.90786i −0.740601 1.28276i −0.952222 0.305406i \(-0.901208\pi\)
0.211622 0.977352i \(-0.432126\pi\)
\(30\) 0 0
\(31\) 3.15085 0.565909 0.282954 0.959133i \(-0.408686\pi\)
0.282954 + 0.959133i \(0.408686\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.95419 8.88819i 0.668380 1.50238i
\(36\) 0 0
\(37\) 0.00266923 0.00462323i 0.000438818 0.000760055i −0.865806 0.500380i \(-0.833194\pi\)
0.866245 + 0.499620i \(0.166527\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00937 + 3.48033i −0.313811 + 0.543537i −0.979184 0.202974i \(-0.934939\pi\)
0.665373 + 0.746511i \(0.268272\pi\)
\(42\) 0 0
\(43\) −3.66193 6.34264i −0.558438 0.967244i −0.997627 0.0688488i \(-0.978067\pi\)
0.439189 0.898395i \(-0.355266\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.2173 1.78207 0.891036 0.453933i \(-0.149979\pi\)
0.891036 + 0.453933i \(0.149979\pi\)
\(48\) 0 0
\(49\) −2.15926 + 6.65865i −0.308465 + 0.951236i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.64928 8.05279i −0.638628 1.10614i −0.985734 0.168310i \(-0.946169\pi\)
0.347107 0.937826i \(-0.387164\pi\)
\(54\) 0 0
\(55\) 2.21768 0.299032
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.61521 0.861227 0.430613 0.902537i \(-0.358297\pi\)
0.430613 + 0.902537i \(0.358297\pi\)
\(60\) 0 0
\(61\) −1.93850 −0.248200 −0.124100 0.992270i \(-0.539604\pi\)
−0.124100 + 0.992270i \(0.539604\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 19.3294 2.39751
\(66\) 0 0
\(67\) 8.63088 1.05443 0.527215 0.849732i \(-0.323236\pi\)
0.527215 + 0.849732i \(0.323236\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.13815 0.135074 0.0675370 0.997717i \(-0.478486\pi\)
0.0675370 + 0.997717i \(0.478486\pi\)
\(72\) 0 0
\(73\) −5.33511 9.24068i −0.624427 1.08154i −0.988651 0.150228i \(-0.951999\pi\)
0.364224 0.931311i \(-0.381334\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.58698 + 0.167264i −0.180853 + 0.0190614i
\(78\) 0 0
\(79\) 4.14551 0.466406 0.233203 0.972428i \(-0.425079\pi\)
0.233203 + 0.972428i \(0.425079\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.24088 + 10.8095i 0.685026 + 1.18650i 0.973429 + 0.228990i \(0.0735423\pi\)
−0.288403 + 0.957509i \(0.593124\pi\)
\(84\) 0 0
\(85\) −7.81544 + 13.5367i −0.847703 + 1.46827i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.09464 + 7.09212i −0.434031 + 0.751764i −0.997216 0.0745672i \(-0.976242\pi\)
0.563185 + 0.826331i \(0.309576\pi\)
\(90\) 0 0
\(91\) −13.8321 + 1.45787i −1.45000 + 0.152827i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 27.0931 2.77969
\(96\) 0 0
\(97\) 6.77935 + 11.7422i 0.688339 + 1.19224i 0.972375 + 0.233425i \(0.0749932\pi\)
−0.284036 + 0.958814i \(0.591673\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.66975 13.2844i 0.763169 1.32185i −0.178041 0.984023i \(-0.556976\pi\)
0.941209 0.337824i \(-0.109691\pi\)
\(102\) 0 0
\(103\) 2.48033 + 4.29606i 0.244394 + 0.423303i 0.961961 0.273186i \(-0.0880775\pi\)
−0.717567 + 0.696490i \(0.754744\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.41399 5.91320i 0.330043 0.571651i −0.652477 0.757808i \(-0.726270\pi\)
0.982520 + 0.186158i \(0.0596035\pi\)
\(108\) 0 0
\(109\) 8.90194 + 15.4186i 0.852651 + 1.47684i 0.878807 + 0.477178i \(0.158340\pi\)
−0.0261554 + 0.999658i \(0.508326\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.63946 + 8.03579i −0.436444 + 0.755943i −0.997412 0.0718940i \(-0.977096\pi\)
0.560968 + 0.827837i \(0.310429\pi\)
\(114\) 0 0
\(115\) −2.12851 + 3.68668i −0.198484 + 0.343785i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.57177 10.2764i 0.419093 0.942035i
\(120\) 0 0
\(121\) 5.31811 + 9.21124i 0.483464 + 0.837385i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.9403 −1.15741
\(126\) 0 0
\(127\) −14.9941 −1.33051 −0.665254 0.746617i \(-0.731677\pi\)
−0.665254 + 0.746617i \(0.731677\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −11.4164 19.7737i −0.997452 1.72764i −0.560508 0.828149i \(-0.689394\pi\)
−0.436944 0.899489i \(-0.643939\pi\)
\(132\) 0 0
\(133\) −19.3879 + 2.04344i −1.68114 + 0.177188i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.762784 + 1.32118i −0.0651690 + 0.112876i −0.896769 0.442499i \(-0.854092\pi\)
0.831600 + 0.555375i \(0.187425\pi\)
\(138\) 0 0
\(139\) −3.31277 + 5.73789i −0.280986 + 0.486681i −0.971628 0.236515i \(-0.923995\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.58537 2.74594i −0.132575 0.229627i
\(144\) 0 0
\(145\) 14.6643 25.3993i 1.21780 2.10930i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.88746 + 15.3935i 0.728089 + 1.26109i 0.957690 + 0.287802i \(0.0929246\pi\)
−0.229601 + 0.973285i \(0.573742\pi\)
\(150\) 0 0
\(151\) −2.31811 + 4.01508i −0.188645 + 0.326743i −0.944799 0.327651i \(-0.893743\pi\)
0.756154 + 0.654394i \(0.227076\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.79262 + 10.0331i 0.465275 + 0.805880i
\(156\) 0 0
\(157\) 3.41320 0.272403 0.136202 0.990681i \(-0.456511\pi\)
0.136202 + 0.990681i \(0.456511\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.24511 2.79874i 0.0981281 0.220571i
\(162\) 0 0
\(163\) 7.55012 13.0772i 0.591371 1.02428i −0.402677 0.915342i \(-0.631920\pi\)
0.994048 0.108942i \(-0.0347464\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.85782 + 4.94988i −0.221144 + 0.383033i −0.955156 0.296104i \(-0.904313\pi\)
0.734011 + 0.679137i \(0.237646\pi\)
\(168\) 0 0
\(169\) −7.31811 12.6753i −0.562931 0.975026i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.89631 0.144174 0.0720871 0.997398i \(-0.477034\pi\)
0.0720871 + 0.997398i \(0.477034\pi\)
\(174\) 0 0
\(175\) 22.4160 2.36259i 1.69449 0.178595i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.29747 + 12.6396i 0.545438 + 0.944727i 0.998579 + 0.0532881i \(0.0169702\pi\)
−0.453141 + 0.891439i \(0.649696\pi\)
\(180\) 0 0
\(181\) 7.89857 0.587096 0.293548 0.955944i \(-0.405164\pi\)
0.293548 + 0.955944i \(0.405164\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.0196288 0.00144314
\(186\) 0 0
\(187\) 2.56405 0.187502
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.47340 −0.613114 −0.306557 0.951852i \(-0.599177\pi\)
−0.306557 + 0.951852i \(0.599177\pi\)
\(192\) 0 0
\(193\) −6.96600 −0.501424 −0.250712 0.968062i \(-0.580665\pi\)
−0.250712 + 0.968062i \(0.580665\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.2371 1.15685 0.578424 0.815736i \(-0.303668\pi\)
0.578424 + 0.815736i \(0.303668\pi\)
\(198\) 0 0
\(199\) −7.35153 12.7332i −0.521136 0.902634i −0.999698 0.0245800i \(-0.992175\pi\)
0.478562 0.878054i \(-0.341158\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.57812 + 19.2818i −0.602066 + 1.35332i
\(204\) 0 0
\(205\) −14.7764 −1.03203
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.22214 3.84886i −0.153709 0.266231i
\(210\) 0 0
\(211\) 8.41053 14.5675i 0.579005 1.00287i −0.416589 0.909095i \(-0.636775\pi\)
0.995594 0.0937708i \(-0.0298921\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 13.4644 23.3211i 0.918266 1.59048i
\(216\) 0 0
\(217\) −4.90194 6.74283i −0.332766 0.457733i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 22.3483 1.50331
\(222\) 0 0
\(223\) 3.45799 + 5.98942i 0.231564 + 0.401081i 0.958269 0.285869i \(-0.0922823\pi\)
−0.726704 + 0.686950i \(0.758949\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.49817 6.05900i 0.232182 0.402150i −0.726268 0.687411i \(-0.758747\pi\)
0.958450 + 0.285261i \(0.0920803\pi\)
\(228\) 0 0
\(229\) 1.41350 + 2.44825i 0.0934066 + 0.161785i 0.908942 0.416922i \(-0.136891\pi\)
−0.815536 + 0.578706i \(0.803558\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.1679 + 19.3434i −0.731635 + 1.26723i 0.224550 + 0.974463i \(0.427909\pi\)
−0.956184 + 0.292766i \(0.905424\pi\)
\(234\) 0 0
\(235\) 22.4606 + 38.9030i 1.46517 + 2.53775i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.954829 1.65381i 0.0617628 0.106976i −0.833491 0.552534i \(-0.813661\pi\)
0.895253 + 0.445557i \(0.146994\pi\)
\(240\) 0 0
\(241\) 9.84352 17.0495i 0.634077 1.09825i −0.352633 0.935762i \(-0.614714\pi\)
0.986710 0.162492i \(-0.0519530\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −25.1725 + 5.36586i −1.60821 + 0.342812i
\(246\) 0 0
\(247\) −19.3682 33.5468i −1.23237 2.13453i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.2990 −0.776306 −0.388153 0.921595i \(-0.626887\pi\)
−0.388153 + 0.921595i \(0.626887\pi\)
\(252\) 0 0
\(253\) 0.698309 0.0439023
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.71210 9.89365i −0.356311 0.617149i 0.631030 0.775758i \(-0.282632\pi\)
−0.987341 + 0.158609i \(0.949299\pi\)
\(258\) 0 0
\(259\) −0.0140464 + 0.00148046i −0.000872802 + 9.19912e-5i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.65544 16.7237i 0.595380 1.03123i −0.398114 0.917336i \(-0.630335\pi\)
0.993493 0.113892i \(-0.0363317\pi\)
\(264\) 0 0
\(265\) 17.0948 29.6091i 1.05012 1.81887i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −4.00745 6.94110i −0.244338 0.423206i 0.717607 0.696448i \(-0.245237\pi\)
−0.961945 + 0.273242i \(0.911904\pi\)
\(270\) 0 0
\(271\) 2.96658 5.13827i 0.180207 0.312128i −0.761744 0.647878i \(-0.775657\pi\)
0.941951 + 0.335750i \(0.108990\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.56920 + 4.44999i 0.154929 + 0.268344i
\(276\) 0 0
\(277\) 6.02768 10.4402i 0.362168 0.627293i −0.626149 0.779703i \(-0.715370\pi\)
0.988317 + 0.152410i \(0.0487034\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.73700 16.8650i −0.580861 1.00608i −0.995378 0.0960386i \(-0.969383\pi\)
0.414517 0.910042i \(-0.363951\pi\)
\(282\) 0 0
\(283\) −28.7036 −1.70625 −0.853127 0.521704i \(-0.825297\pi\)
−0.853127 + 0.521704i \(0.825297\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.5740 1.11448i 0.624165 0.0657854i
\(288\) 0 0
\(289\) −0.536086 + 0.928529i −0.0315345 + 0.0546193i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −11.3503 + 19.6593i −0.663090 + 1.14851i 0.316709 + 0.948523i \(0.397422\pi\)
−0.979799 + 0.199983i \(0.935911\pi\)
\(294\) 0 0
\(295\) 12.1616 + 21.0646i 0.708077 + 1.22643i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.08648 0.351990
\(300\) 0 0
\(301\) −7.87624 + 17.7041i −0.453979 + 1.02045i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.56381 6.17271i −0.204063 0.353448i
\(306\) 0 0
\(307\) −27.9486 −1.59511 −0.797555 0.603246i \(-0.793874\pi\)
−0.797555 + 0.603246i \(0.793874\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.2982 −0.867479 −0.433739 0.901038i \(-0.642806\pi\)
−0.433739 + 0.901038i \(0.642806\pi\)
\(312\) 0 0
\(313\) 3.34103 0.188846 0.0944230 0.995532i \(-0.469899\pi\)
0.0944230 + 0.995532i \(0.469899\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.01444 −0.506301 −0.253151 0.967427i \(-0.581467\pi\)
−0.253151 + 0.967427i \(0.581467\pi\)
\(318\) 0 0
\(319\) −4.81098 −0.269363
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 31.3246 1.74295
\(324\) 0 0
\(325\) 22.3932 + 38.7862i 1.24215 + 2.15147i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −19.0071 26.1450i −1.04789 1.44142i
\(330\) 0 0
\(331\) 18.2952 1.00559 0.502797 0.864404i \(-0.332304\pi\)
0.502797 + 0.864404i \(0.332304\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 15.8673 + 27.4830i 0.866924 + 1.50156i
\(336\) 0 0
\(337\) −0.868823 + 1.50485i −0.0473278 + 0.0819741i −0.888719 0.458453i \(-0.848404\pi\)
0.841391 + 0.540427i \(0.181737\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.950206 1.64580i 0.0514565 0.0891253i
\(342\) 0 0
\(343\) 17.6088 5.73840i 0.950787 0.309845i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.09272 −0.0586600 −0.0293300 0.999570i \(-0.509337\pi\)
−0.0293300 + 0.999570i \(0.509337\pi\)
\(348\) 0 0
\(349\) −4.70096 8.14231i −0.251637 0.435848i 0.712340 0.701835i \(-0.247636\pi\)
−0.963977 + 0.265987i \(0.914302\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.64549 + 16.7065i −0.513378 + 0.889196i 0.486502 + 0.873680i \(0.338273\pi\)
−0.999880 + 0.0155167i \(0.995061\pi\)
\(354\) 0 0
\(355\) 2.09242 + 3.62418i 0.111054 + 0.192352i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.94976 + 5.10914i −0.155682 + 0.269650i −0.933307 0.359079i \(-0.883091\pi\)
0.777625 + 0.628729i \(0.216424\pi\)
\(360\) 0 0
\(361\) −17.6476 30.5665i −0.928820 1.60876i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 19.6165 33.9768i 1.02677 1.77843i
\(366\) 0 0
\(367\) −5.48300 + 9.49684i −0.286210 + 0.495731i −0.972902 0.231218i \(-0.925729\pi\)
0.686692 + 0.726949i \(0.259062\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.99988 + 22.4776i −0.519168 + 1.16698i
\(372\) 0 0
\(373\) 15.9691 + 27.6592i 0.826847 + 1.43214i 0.900500 + 0.434856i \(0.143201\pi\)
−0.0736533 + 0.997284i \(0.523466\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −41.9326 −2.15964
\(378\) 0 0
\(379\) −14.4354 −0.741495 −0.370747 0.928734i \(-0.620898\pi\)
−0.370747 + 0.928734i \(0.620898\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.86006 15.3461i −0.452728 0.784148i 0.545826 0.837898i \(-0.316216\pi\)
−0.998554 + 0.0537502i \(0.982883\pi\)
\(384\) 0 0
\(385\) −3.45016 4.74585i −0.175837 0.241871i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.48751 + 16.4329i −0.481036 + 0.833179i −0.999763 0.0217610i \(-0.993073\pi\)
0.518727 + 0.854940i \(0.326406\pi\)
\(390\) 0 0
\(391\) −2.46095 + 4.26249i −0.124455 + 0.215563i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.62124 + 13.2004i 0.383466 + 0.664183i
\(396\) 0 0
\(397\) −10.5889 + 18.3405i −0.531440 + 0.920482i 0.467886 + 0.883789i \(0.345016\pi\)
−0.999327 + 0.0366930i \(0.988318\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.39038 12.8005i −0.369058 0.639227i 0.620361 0.784317i \(-0.286986\pi\)
−0.989419 + 0.145090i \(0.953653\pi\)
\(402\) 0 0
\(403\) 8.28202 14.3449i 0.412557 0.714570i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.00160993 0.00278847i −7.98011e−5 0.000138219i
\(408\) 0 0
\(409\) −3.73150 −0.184511 −0.0922554 0.995735i \(-0.529408\pi\)
−0.0922554 + 0.995735i \(0.529408\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.2916 14.1566i −0.506418 0.696600i
\(414\) 0 0
\(415\) −22.9469 + 39.7452i −1.12642 + 1.95102i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14.1678 + 24.5393i −0.692142 + 1.19883i 0.278993 + 0.960293i \(0.409999\pi\)
−0.971135 + 0.238532i \(0.923334\pi\)
\(420\) 0 0
\(421\) −8.09776 14.0257i −0.394661 0.683572i 0.598397 0.801200i \(-0.295805\pi\)
−0.993058 + 0.117627i \(0.962471\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −36.2170 −1.75678
\(426\) 0 0
\(427\) 3.01584 + 4.14841i 0.145947 + 0.200756i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13.5528 + 23.4741i 0.652815 + 1.13071i 0.982437 + 0.186595i \(0.0597453\pi\)
−0.329622 + 0.944113i \(0.606921\pi\)
\(432\) 0 0
\(433\) −11.5028 −0.552789 −0.276394 0.961044i \(-0.589140\pi\)
−0.276394 + 0.961044i \(0.589140\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.53115 0.408100
\(438\) 0 0
\(439\) −2.86714 −0.136841 −0.0684205 0.997657i \(-0.521796\pi\)
−0.0684205 + 0.997657i \(0.521796\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8.84301 −0.420144 −0.210072 0.977686i \(-0.567370\pi\)
−0.210072 + 0.977686i \(0.567370\pi\)
\(444\) 0 0
\(445\) −30.1109 −1.42739
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −40.5033 −1.91147 −0.955735 0.294229i \(-0.904937\pi\)
−0.955735 + 0.294229i \(0.904937\pi\)
\(450\) 0 0
\(451\) 1.21194 + 2.09914i 0.0570680 + 0.0988446i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −30.0717 41.3650i −1.40979 1.93922i
\(456\) 0 0
\(457\) 38.8098 1.81545 0.907723 0.419571i \(-0.137819\pi\)
0.907723 + 0.419571i \(0.137819\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.1328 27.9428i −0.751378 1.30142i −0.947155 0.320776i \(-0.896056\pi\)
0.195777 0.980648i \(-0.437277\pi\)
\(462\) 0 0
\(463\) −16.7430 + 28.9997i −0.778112 + 1.34773i 0.154917 + 0.987927i \(0.450489\pi\)
−0.933029 + 0.359802i \(0.882844\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.04280 + 8.73438i −0.233353 + 0.404179i −0.958793 0.284107i \(-0.908303\pi\)
0.725440 + 0.688286i \(0.241636\pi\)
\(468\) 0 0
\(469\) −13.4275 18.4701i −0.620026 0.852872i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.41733 −0.203109
\(474\) 0 0
\(475\) 31.3876 + 54.3649i 1.44016 + 2.49443i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.29759 + 7.44365i −0.196362 + 0.340109i −0.947346 0.320211i \(-0.896246\pi\)
0.750984 + 0.660320i \(0.229579\pi\)
\(480\) 0 0
\(481\) −0.0140322 0.0243044i −0.000639812 0.00110819i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −24.9268 + 43.1745i −1.13187 + 1.96045i
\(486\) 0 0
\(487\) −0.298843 0.517612i −0.0135419 0.0234552i 0.859175 0.511682i \(-0.170977\pi\)
−0.872717 + 0.488227i \(0.837644\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.1521 29.7084i 0.774066 1.34072i −0.161253 0.986913i \(-0.551553\pi\)
0.935318 0.353808i \(-0.115113\pi\)
\(492\) 0 0
\(493\) 16.9546 29.3663i 0.763598 1.32259i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.77069 2.43566i −0.0794262 0.109254i
\(498\) 0 0
\(499\) −15.0247 26.0236i −0.672598 1.16497i −0.977165 0.212483i \(-0.931845\pi\)
0.304566 0.952491i \(-0.401488\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.5650 0.827773 0.413887 0.910328i \(-0.364171\pi\)
0.413887 + 0.910328i \(0.364171\pi\)
\(504\) 0 0
\(505\) 56.4013 2.50983
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.50908 + 6.07790i 0.155537 + 0.269398i 0.933254 0.359216i \(-0.116956\pi\)
−0.777717 + 0.628614i \(0.783623\pi\)
\(510\) 0 0
\(511\) −11.4750 + 25.7934i −0.507624 + 1.14103i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.11986 + 15.7961i −0.401869 + 0.696057i
\(516\) 0 0
\(517\) 3.68438 6.38154i 0.162039 0.280660i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.0742 + 26.1092i 0.660411 + 1.14387i 0.980508 + 0.196481i \(0.0629514\pi\)
−0.320096 + 0.947385i \(0.603715\pi\)
\(522\) 0 0
\(523\) −14.1726 + 24.5476i −0.619724 + 1.07339i 0.369812 + 0.929107i \(0.379422\pi\)
−0.989536 + 0.144287i \(0.953911\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.69734 + 11.6001i 0.291741 + 0.505310i
\(528\) 0 0
\(529\) 10.8298 18.7577i 0.470860 0.815553i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.5633 + 18.2962i 0.457547 + 0.792495i
\(534\) 0 0
\(535\) 25.1056 1.08541
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.82689 + 3.13592i 0.121763 + 0.135074i
\(540\) 0 0
\(541\) −14.5245 + 25.1572i −0.624458 + 1.08159i 0.364187 + 0.931326i \(0.381347\pi\)
−0.988645 + 0.150268i \(0.951986\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −32.7313 + 56.6922i −1.40205 + 2.42843i
\(546\) 0 0
\(547\) −8.68455 15.0421i −0.371324 0.643153i 0.618445 0.785828i \(-0.287763\pi\)
−0.989770 + 0.142675i \(0.954430\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −58.7751 −2.50390
\(552\) 0 0
\(553\) −6.44939 8.87141i −0.274256 0.377251i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.5927 + 33.9355i 0.830169 + 1.43789i 0.897904 + 0.440191i \(0.145089\pi\)
−0.0677355 + 0.997703i \(0.521577\pi\)
\(558\) 0 0
\(559\) −38.5016 −1.62844
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 38.4078 1.61870 0.809349 0.587328i \(-0.199820\pi\)
0.809349 + 0.587328i \(0.199820\pi\)
\(564\) 0 0
\(565\) −34.1174 −1.43533
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.08064 0.380680 0.190340 0.981718i \(-0.439041\pi\)
0.190340 + 0.981718i \(0.439041\pi\)
\(570\) 0 0
\(571\) −37.0548 −1.55069 −0.775347 0.631536i \(-0.782425\pi\)
−0.775347 + 0.631536i \(0.782425\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −9.86358 −0.411340
\(576\) 0 0
\(577\) 1.04241 + 1.80550i 0.0433960 + 0.0751641i 0.886908 0.461947i \(-0.152849\pi\)
−0.843512 + 0.537111i \(0.819516\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 13.4232 30.1725i 0.556887 1.25177i
\(582\) 0 0
\(583\) −5.60836 −0.232275
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.75919 + 8.24316i 0.196433 + 0.340232i 0.947369 0.320143i \(-0.103731\pi\)
−0.750936 + 0.660374i \(0.770398\pi\)
\(588\) 0 0
\(589\) 11.6085 20.1066i 0.478322 0.828477i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.63267 13.2202i 0.313436 0.542887i −0.665668 0.746248i \(-0.731853\pi\)
0.979104 + 0.203361i \(0.0651865\pi\)
\(594\) 0 0
\(595\) 41.1276 4.33475i 1.68607 0.177707i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20.1195 −0.822059 −0.411030 0.911622i \(-0.634831\pi\)
−0.411030 + 0.911622i \(0.634831\pi\)
\(600\) 0 0
\(601\) −10.1529 17.5854i −0.414146 0.717322i 0.581192 0.813766i \(-0.302586\pi\)
−0.995338 + 0.0964440i \(0.969253\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −19.5540 + 33.8685i −0.794983 + 1.37695i
\(606\) 0 0
\(607\) 1.03649 + 1.79525i 0.0420698 + 0.0728670i 0.886294 0.463124i \(-0.153271\pi\)
−0.844224 + 0.535991i \(0.819938\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 32.1132 55.6217i 1.29916 2.25021i
\(612\) 0 0
\(613\) −1.10053 1.90618i −0.0444502 0.0769900i 0.842944 0.538001i \(-0.180820\pi\)
−0.887395 + 0.461011i \(0.847487\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.1904 + 36.7029i −0.853095 + 1.47760i 0.0253061 + 0.999680i \(0.491944\pi\)
−0.878401 + 0.477924i \(0.841389\pi\)
\(618\) 0 0
\(619\) −6.93536 + 12.0124i −0.278756 + 0.482819i −0.971076 0.238772i \(-0.923255\pi\)
0.692320 + 0.721590i \(0.256589\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 21.5474 2.27105i 0.863280 0.0909876i
\(624\) 0 0
\(625\) −2.49141 4.31525i −0.0996565 0.172610i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.0226945 0.000904889
\(630\) 0 0
\(631\) 45.1845 1.79876 0.899382 0.437163i \(-0.144017\pi\)
0.899382 + 0.437163i \(0.144017\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −27.5656 47.7450i −1.09391 1.89470i
\(636\) 0 0
\(637\) 24.6393 + 27.3328i 0.976244 + 1.08296i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 13.2564 22.9608i 0.523597 0.906896i −0.476026 0.879431i \(-0.657923\pi\)
0.999623 0.0274647i \(-0.00874340\pi\)
\(642\) 0 0
\(643\) 24.3184 42.1207i 0.959024 1.66108i 0.234145 0.972202i \(-0.424771\pi\)
0.724879 0.688876i \(-0.241896\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.7224 18.5717i −0.421540 0.730128i 0.574551 0.818469i \(-0.305177\pi\)
−0.996090 + 0.0883409i \(0.971844\pi\)
\(648\) 0 0
\(649\) 1.99496 3.45537i 0.0783090 0.135635i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.74496 + 3.02235i 0.0682854 + 0.118274i 0.898147 0.439696i \(-0.144914\pi\)
−0.829861 + 0.557970i \(0.811580\pi\)
\(654\) 0 0
\(655\) 41.9765 72.7054i 1.64016 2.84083i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −18.2754 31.6539i −0.711908 1.23306i −0.964140 0.265394i \(-0.914498\pi\)
0.252232 0.967667i \(-0.418835\pi\)
\(660\) 0 0
\(661\) −5.57496 −0.216841 −0.108420 0.994105i \(-0.534579\pi\)
−0.108420 + 0.994105i \(0.534579\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −42.1502 57.9794i −1.63452 2.24835i
\(666\) 0 0
\(667\) 4.61753 7.99780i 0.178792 0.309676i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.584598 + 1.01255i −0.0225682 + 0.0390892i
\(672\) 0 0
\(673\) 1.25661 + 2.17652i 0.0484389 + 0.0838986i 0.889228 0.457464i \(-0.151242\pi\)
−0.840789 + 0.541362i \(0.817909\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31.7213 −1.21915 −0.609574 0.792729i \(-0.708659\pi\)
−0.609574 + 0.792729i \(0.708659\pi\)
\(678\) 0 0
\(679\) 14.5813 32.7758i 0.559581 1.25782i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.4275 + 37.1136i 0.819902 + 1.42011i 0.905754 + 0.423804i \(0.139305\pi\)
−0.0858521 + 0.996308i \(0.527361\pi\)
\(684\) 0 0
\(685\) −5.60932 −0.214321
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −48.8827 −1.86228
\(690\) 0 0
\(691\) −14.7637 −0.561639 −0.280820 0.959761i \(-0.590606\pi\)
−0.280820 + 0.959761i \(0.590606\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.3613 −0.924075
\(696\) 0 0
\(697\) −17.0842 −0.647111
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19.8352 0.749167 0.374583 0.927193i \(-0.377786\pi\)
0.374583 + 0.927193i \(0.377786\pi\)
\(702\) 0 0
\(703\) −0.0196683 0.0340664i −0.000741802 0.00128484i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −40.3609 + 4.25394i −1.51793 + 0.159986i
\(708\) 0 0
\(709\) 10.2058 0.383288 0.191644 0.981464i \(-0.438618\pi\)
0.191644 + 0.981464i \(0.438618\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.82400 + 3.15926i 0.0683092 + 0.118315i
\(714\) 0 0
\(715\) 5.82919 10.0965i 0.217999 0.377586i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.2769 28.1924i 0.607025 1.05140i −0.384703 0.923040i \(-0.625696\pi\)
0.991728 0.128358i \(-0.0409706\pi\)
\(720\) 0 0
\(721\) 5.33481 11.9915i 0.198679 0.446588i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 67.9549 2.52378
\(726\) 0 0
\(727\) −7.65095 13.2518i −0.283758 0.491483i 0.688549 0.725190i \(-0.258248\pi\)
−0.972307 + 0.233706i \(0.924915\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 15.5673 26.9634i 0.575779 0.997279i
\(732\) 0 0
\(733\) 4.34677 + 7.52882i 0.160552 + 0.278083i 0.935067 0.354472i \(-0.115339\pi\)
−0.774515 + 0.632555i \(0.782006\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.60283 4.50823i 0.0958764 0.166063i
\(738\) 0 0
\(739\) −6.61922 11.4648i −0.243492 0.421740i 0.718215 0.695822i \(-0.244960\pi\)
−0.961707 + 0.274081i \(0.911626\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.7693 18.6530i 0.395089 0.684314i −0.598024 0.801478i \(-0.704047\pi\)
0.993112 + 0.117165i \(0.0373805\pi\)
\(744\) 0 0
\(745\) −32.6780 + 56.6000i −1.19723 + 2.07366i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −17.9656 + 1.89353i −0.656449 + 0.0691881i
\(750\) 0 0
\(751\) −19.8241 34.3364i −0.723393 1.25295i −0.959632 0.281258i \(-0.909248\pi\)
0.236239 0.971695i \(-0.424085\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −17.0468 −0.620395
\(756\) 0 0
\(757\) 13.0719 0.475108 0.237554 0.971374i \(-0.423654\pi\)
0.237554 + 0.971374i \(0.423654\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.17145 15.8854i −0.332465 0.575846i 0.650530 0.759481i \(-0.274547\pi\)
−0.982995 + 0.183635i \(0.941214\pi\)
\(762\) 0 0
\(763\) 19.1467 43.0378i 0.693157 1.55807i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 17.3881 30.1171i 0.627849 1.08747i
\(768\) 0 0
\(769\) 7.46351 12.9272i 0.269141 0.466166i −0.699499 0.714633i \(-0.746594\pi\)
0.968640 + 0.248467i \(0.0799269\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 14.7818 + 25.6029i 0.531666 + 0.920873i 0.999317 + 0.0369592i \(0.0117672\pi\)
−0.467651 + 0.883913i \(0.654900\pi\)
\(774\) 0 0
\(775\) −13.4216 + 23.2469i −0.482118 + 0.835054i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 14.8061 + 25.6449i 0.530483 + 0.918824i
\(780\) 0 0
\(781\) 0.343235 0.594500i 0.0122819 0.0212729i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.27495 + 10.8685i 0.223962 + 0.387914i
\(786\) 0 0
\(787\) −9.32859 −0.332528 −0.166264 0.986081i \(-0.553170\pi\)
−0.166264 + 0.986081i \(0.553170\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24.4145 2.57323i 0.868080 0.0914935i
\(792\) 0 0
\(793\) −5.09537 + 8.82545i −0.180942 + 0.313401i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11.9334 + 20.6692i −0.422701 + 0.732140i −0.996203 0.0870647i \(-0.972251\pi\)
0.573502 + 0.819204i \(0.305585\pi\)
\(798\) 0 0
\(799\) 25.9686 + 44.9790i 0.918705 + 1.59124i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0