Properties

Label 1960.2.q.u.961.1
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.u.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.780776 - 1.35234i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.280776 - 0.486319i) q^{9} +O(q^{10})\) \(q+(-0.780776 - 1.35234i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.280776 - 0.486319i) q^{9} +(-0.780776 - 1.35234i) q^{11} -6.68466 q^{13} -1.56155 q^{15} +(3.78078 + 6.54850i) q^{17} +(-3.56155 + 6.16879i) q^{19} +(-1.56155 + 2.70469i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.56155 q^{27} +0.438447 q^{29} +(3.12311 + 5.40938i) q^{31} +(-1.21922 + 2.11176i) q^{33} +(4.12311 - 7.14143i) q^{37} +(5.21922 + 9.03996i) q^{39} +1.12311 q^{41} -7.12311 q^{43} +(-0.280776 - 0.486319i) q^{45} +(1.21922 - 2.11176i) q^{47} +(5.90388 - 10.2258i) q^{51} +(6.56155 + 11.3649i) q^{53} -1.56155 q^{55} +11.1231 q^{57} +(-2.00000 - 3.46410i) q^{59} +(-3.43845 + 5.95557i) q^{61} +(-3.34233 + 5.78908i) q^{65} +(-1.12311 - 1.94528i) q^{67} +4.87689 q^{69} +(-2.12311 - 3.67733i) q^{73} +(-0.780776 + 1.35234i) q^{75} +(-0.342329 + 0.592932i) q^{79} +(3.50000 + 6.06218i) q^{81} -12.0000 q^{83} +7.56155 q^{85} +(-0.342329 - 0.592932i) q^{87} +(2.56155 - 4.43674i) q^{89} +(4.87689 - 8.44703i) q^{93} +(3.56155 + 6.16879i) q^{95} -1.31534 q^{97} -0.876894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{3} + 2q^{5} - 3q^{9} + O(q^{10}) \) \( 4q + q^{3} + 2q^{5} - 3q^{9} + q^{11} - 2q^{13} + 2q^{15} + 11q^{17} - 6q^{19} + 2q^{23} - 2q^{25} - 14q^{27} + 10q^{29} - 4q^{31} - 9q^{33} + 25q^{39} - 12q^{41} - 12q^{43} + 3q^{45} + 9q^{47} + 3q^{51} + 18q^{53} + 2q^{55} + 28q^{57} - 8q^{59} - 22q^{61} - q^{65} + 12q^{67} + 36q^{69} + 8q^{73} + q^{75} + 11q^{79} + 14q^{81} - 48q^{83} + 22q^{85} + 11q^{87} + 2q^{89} + 36q^{93} + 6q^{95} - 30q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) −0.780776 1.35234i −0.450781 0.780776i 0.547653 0.836705i \(-0.315521\pi\)
−0.998435 + 0.0559290i \(0.982188\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.280776 0.486319i 0.0935921 0.162106i
\(10\) 0 0
\(11\) −0.780776 1.35234i −0.235413 0.407747i 0.723980 0.689821i \(-0.242311\pi\)
−0.959393 + 0.282074i \(0.908978\pi\)
\(12\) 0 0
\(13\) −6.68466 −1.85399 −0.926995 0.375073i \(-0.877618\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −1.56155 −0.403191
\(16\) 0 0
\(17\) 3.78078 + 6.54850i 0.916973 + 1.58824i 0.803987 + 0.594647i \(0.202708\pi\)
0.112986 + 0.993597i \(0.463958\pi\)
\(18\) 0 0
\(19\) −3.56155 + 6.16879i −0.817076 + 1.41522i 0.0907512 + 0.995874i \(0.471073\pi\)
−0.907827 + 0.419344i \(0.862260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.56155 + 2.70469i −0.325606 + 0.563967i −0.981635 0.190769i \(-0.938902\pi\)
0.656029 + 0.754736i \(0.272235\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −5.56155 −1.07032
\(28\) 0 0
\(29\) 0.438447 0.0814176 0.0407088 0.999171i \(-0.487038\pi\)
0.0407088 + 0.999171i \(0.487038\pi\)
\(30\) 0 0
\(31\) 3.12311 + 5.40938i 0.560926 + 0.971553i 0.997416 + 0.0718436i \(0.0228882\pi\)
−0.436490 + 0.899709i \(0.643778\pi\)
\(32\) 0 0
\(33\) −1.21922 + 2.11176i −0.212240 + 0.367610i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.12311 7.14143i 0.677834 1.17404i −0.297797 0.954629i \(-0.596252\pi\)
0.975632 0.219414i \(-0.0704147\pi\)
\(38\) 0 0
\(39\) 5.21922 + 9.03996i 0.835745 + 1.44755i
\(40\) 0 0
\(41\) 1.12311 0.175400 0.0876998 0.996147i \(-0.472048\pi\)
0.0876998 + 0.996147i \(0.472048\pi\)
\(42\) 0 0
\(43\) −7.12311 −1.08626 −0.543132 0.839648i \(-0.682762\pi\)
−0.543132 + 0.839648i \(0.682762\pi\)
\(44\) 0 0
\(45\) −0.280776 0.486319i −0.0418557 0.0724962i
\(46\) 0 0
\(47\) 1.21922 2.11176i 0.177842 0.308031i −0.763299 0.646045i \(-0.776422\pi\)
0.941141 + 0.338014i \(0.109755\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 5.90388 10.2258i 0.826709 1.43190i
\(52\) 0 0
\(53\) 6.56155 + 11.3649i 0.901299 + 1.56109i 0.825810 + 0.563948i \(0.190718\pi\)
0.0754885 + 0.997147i \(0.475948\pi\)
\(54\) 0 0
\(55\) −1.56155 −0.210560
\(56\) 0 0
\(57\) 11.1231 1.47329
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) −3.43845 + 5.95557i −0.440248 + 0.762532i −0.997708 0.0676721i \(-0.978443\pi\)
0.557460 + 0.830204i \(0.311776\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.34233 + 5.78908i −0.414565 + 0.718048i
\(66\) 0 0
\(67\) −1.12311 1.94528i −0.137209 0.237653i 0.789230 0.614098i \(-0.210480\pi\)
−0.926439 + 0.376444i \(0.877147\pi\)
\(68\) 0 0
\(69\) 4.87689 0.587109
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −2.12311 3.67733i −0.248491 0.430399i 0.714617 0.699516i \(-0.246601\pi\)
−0.963107 + 0.269118i \(0.913268\pi\)
\(74\) 0 0
\(75\) −0.780776 + 1.35234i −0.0901563 + 0.156155i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.342329 + 0.592932i −0.0385150 + 0.0667100i −0.884640 0.466274i \(-0.845596\pi\)
0.846125 + 0.532984i \(0.178929\pi\)
\(80\) 0 0
\(81\) 3.50000 + 6.06218i 0.388889 + 0.673575i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 7.56155 0.820166
\(86\) 0 0
\(87\) −0.342329 0.592932i −0.0367015 0.0635689i
\(88\) 0 0
\(89\) 2.56155 4.43674i 0.271524 0.470293i −0.697728 0.716363i \(-0.745806\pi\)
0.969252 + 0.246069i \(0.0791390\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 4.87689 8.44703i 0.505710 0.875916i
\(94\) 0 0
\(95\) 3.56155 + 6.16879i 0.365408 + 0.632905i
\(96\) 0 0
\(97\) −1.31534 −0.133553 −0.0667764 0.997768i \(-0.521271\pi\)
−0.0667764 + 0.997768i \(0.521271\pi\)
\(98\) 0 0
\(99\) −0.876894 −0.0881312
\(100\) 0 0
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) −5.90388 + 10.2258i −0.581727 + 1.00758i 0.413548 + 0.910482i \(0.364289\pi\)
−0.995275 + 0.0970980i \(0.969044\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.56155 + 13.0970i −0.731003 + 1.26613i 0.225452 + 0.974254i \(0.427614\pi\)
−0.956455 + 0.291880i \(0.905719\pi\)
\(108\) 0 0
\(109\) 2.21922 + 3.84381i 0.212563 + 0.368170i 0.952516 0.304489i \(-0.0984856\pi\)
−0.739953 + 0.672659i \(0.765152\pi\)
\(110\) 0 0
\(111\) −12.8769 −1.22222
\(112\) 0 0
\(113\) 8.24621 0.775738 0.387869 0.921714i \(-0.373211\pi\)
0.387869 + 0.921714i \(0.373211\pi\)
\(114\) 0 0
\(115\) 1.56155 + 2.70469i 0.145616 + 0.252214i
\(116\) 0 0
\(117\) −1.87689 + 3.25088i −0.173519 + 0.300544i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 4.28078 7.41452i 0.389161 0.674047i
\(122\) 0 0
\(123\) −0.876894 1.51883i −0.0790669 0.136948i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −6.24621 −0.554262 −0.277131 0.960832i \(-0.589384\pi\)
−0.277131 + 0.960832i \(0.589384\pi\)
\(128\) 0 0
\(129\) 5.56155 + 9.63289i 0.489667 + 0.848129i
\(130\) 0 0
\(131\) 7.56155 13.0970i 0.660656 1.14429i −0.319788 0.947489i \(-0.603612\pi\)
0.980444 0.196800i \(-0.0630551\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.78078 + 4.81645i −0.239331 + 0.414534i
\(136\) 0 0
\(137\) 3.68466 + 6.38202i 0.314802 + 0.545252i 0.979395 0.201953i \(-0.0647287\pi\)
−0.664594 + 0.747205i \(0.731395\pi\)
\(138\) 0 0
\(139\) 21.3693 1.81252 0.906261 0.422719i \(-0.138924\pi\)
0.906261 + 0.422719i \(0.138924\pi\)
\(140\) 0 0
\(141\) −3.80776 −0.320672
\(142\) 0 0
\(143\) 5.21922 + 9.03996i 0.436453 + 0.755959i
\(144\) 0 0
\(145\) 0.219224 0.379706i 0.0182055 0.0315329i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.123106 0.213225i 0.0100852 0.0174681i −0.860939 0.508709i \(-0.830123\pi\)
0.871024 + 0.491241i \(0.163456\pi\)
\(150\) 0 0
\(151\) 9.90388 + 17.1540i 0.805966 + 1.39597i 0.915637 + 0.402007i \(0.131687\pi\)
−0.109670 + 0.993968i \(0.534979\pi\)
\(152\) 0 0
\(153\) 4.24621 0.343286
\(154\) 0 0
\(155\) 6.24621 0.501708
\(156\) 0 0
\(157\) 2.12311 + 3.67733i 0.169442 + 0.293483i 0.938224 0.346029i \(-0.112470\pi\)
−0.768782 + 0.639511i \(0.779137\pi\)
\(158\) 0 0
\(159\) 10.2462 17.7470i 0.812577 1.40743i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −9.80776 + 16.9875i −0.768203 + 1.33057i 0.170333 + 0.985387i \(0.445516\pi\)
−0.938536 + 0.345181i \(0.887818\pi\)
\(164\) 0 0
\(165\) 1.21922 + 2.11176i 0.0949164 + 0.164400i
\(166\) 0 0
\(167\) −4.19224 −0.324405 −0.162202 0.986757i \(-0.551860\pi\)
−0.162202 + 0.986757i \(0.551860\pi\)
\(168\) 0 0
\(169\) 31.6847 2.43728
\(170\) 0 0
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 0 0
\(173\) −11.5885 + 20.0719i −0.881060 + 1.52604i −0.0308969 + 0.999523i \(0.509836\pi\)
−0.850163 + 0.526519i \(0.823497\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.12311 + 5.40938i −0.234747 + 0.406594i
\(178\) 0 0
\(179\) 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i \(-0.118904\pi\)
−0.781551 + 0.623841i \(0.785571\pi\)
\(180\) 0 0
\(181\) 5.12311 0.380797 0.190399 0.981707i \(-0.439022\pi\)
0.190399 + 0.981707i \(0.439022\pi\)
\(182\) 0 0
\(183\) 10.7386 0.793823
\(184\) 0 0
\(185\) −4.12311 7.14143i −0.303137 0.525048i
\(186\) 0 0
\(187\) 5.90388 10.2258i 0.431735 0.747786i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.342329 0.592932i 0.0247701 0.0429030i −0.853375 0.521298i \(-0.825448\pi\)
0.878145 + 0.478395i \(0.158781\pi\)
\(192\) 0 0
\(193\) −6.56155 11.3649i −0.472311 0.818066i 0.527187 0.849749i \(-0.323247\pi\)
−0.999498 + 0.0316828i \(0.989913\pi\)
\(194\) 0 0
\(195\) 10.4384 0.747513
\(196\) 0 0
\(197\) −13.1231 −0.934983 −0.467491 0.883998i \(-0.654842\pi\)
−0.467491 + 0.883998i \(0.654842\pi\)
\(198\) 0 0
\(199\) −7.12311 12.3376i −0.504944 0.874588i −0.999984 0.00571778i \(-0.998180\pi\)
0.495040 0.868870i \(-0.335153\pi\)
\(200\) 0 0
\(201\) −1.75379 + 3.03765i −0.123703 + 0.214259i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.561553 0.972638i 0.0392205 0.0679320i
\(206\) 0 0
\(207\) 0.876894 + 1.51883i 0.0609484 + 0.105566i
\(208\) 0 0
\(209\) 11.1231 0.769401
\(210\) 0 0
\(211\) −17.5616 −1.20899 −0.604494 0.796610i \(-0.706624\pi\)
−0.604494 + 0.796610i \(0.706624\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.56155 + 6.16879i −0.242896 + 0.420708i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3.31534 + 5.74234i −0.224030 + 0.388031i
\(220\) 0 0
\(221\) −25.2732 43.7745i −1.70006 2.94459i
\(222\) 0 0
\(223\) −24.6847 −1.65301 −0.826503 0.562932i \(-0.809673\pi\)
−0.826503 + 0.562932i \(0.809673\pi\)
\(224\) 0 0
\(225\) −0.561553 −0.0374369
\(226\) 0 0
\(227\) −5.65767 9.79937i −0.375513 0.650407i 0.614891 0.788612i \(-0.289200\pi\)
−0.990404 + 0.138205i \(0.955867\pi\)
\(228\) 0 0
\(229\) −5.68466 + 9.84612i −0.375653 + 0.650650i −0.990425 0.138055i \(-0.955915\pi\)
0.614772 + 0.788705i \(0.289248\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.43845 9.41967i 0.356285 0.617103i −0.631052 0.775740i \(-0.717377\pi\)
0.987337 + 0.158637i \(0.0507101\pi\)
\(234\) 0 0
\(235\) −1.21922 2.11176i −0.0795334 0.137756i
\(236\) 0 0
\(237\) 1.06913 0.0694475
\(238\) 0 0
\(239\) −18.0540 −1.16781 −0.583907 0.811820i \(-0.698477\pi\)
−0.583907 + 0.811820i \(0.698477\pi\)
\(240\) 0 0
\(241\) 1.00000 + 1.73205i 0.0644157 + 0.111571i 0.896435 0.443176i \(-0.146148\pi\)
−0.832019 + 0.554747i \(0.812815\pi\)
\(242\) 0 0
\(243\) −2.87689 + 4.98293i −0.184553 + 0.319655i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 23.8078 41.2363i 1.51485 2.62380i
\(248\) 0 0
\(249\) 9.36932 + 16.2281i 0.593756 + 1.02842i
\(250\) 0 0
\(251\) −13.3693 −0.843864 −0.421932 0.906628i \(-0.638648\pi\)
−0.421932 + 0.906628i \(0.638648\pi\)
\(252\) 0 0
\(253\) 4.87689 0.306608
\(254\) 0 0
\(255\) −5.90388 10.2258i −0.369715 0.640366i
\(256\) 0 0
\(257\) −9.24621 + 16.0149i −0.576763 + 0.998982i 0.419085 + 0.907947i \(0.362351\pi\)
−0.995848 + 0.0910354i \(0.970982\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.123106 0.213225i 0.00762005 0.0131983i
\(262\) 0 0
\(263\) −4.68466 8.11407i −0.288868 0.500335i 0.684672 0.728852i \(-0.259946\pi\)
−0.973540 + 0.228517i \(0.926612\pi\)
\(264\) 0 0
\(265\) 13.1231 0.806146
\(266\) 0 0
\(267\) −8.00000 −0.489592
\(268\) 0 0
\(269\) 2.12311 + 3.67733i 0.129448 + 0.224211i 0.923463 0.383688i \(-0.125346\pi\)
−0.794015 + 0.607898i \(0.792013\pi\)
\(270\) 0 0
\(271\) −3.12311 + 5.40938i −0.189715 + 0.328596i −0.945155 0.326621i \(-0.894090\pi\)
0.755440 + 0.655218i \(0.227423\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.780776 + 1.35234i −0.0470826 + 0.0815494i
\(276\) 0 0
\(277\) 4.12311 + 7.14143i 0.247733 + 0.429087i 0.962897 0.269871i \(-0.0869810\pi\)
−0.715163 + 0.698958i \(0.753648\pi\)
\(278\) 0 0
\(279\) 3.50758 0.209993
\(280\) 0 0
\(281\) −19.5616 −1.16694 −0.583472 0.812133i \(-0.698306\pi\)
−0.583472 + 0.812133i \(0.698306\pi\)
\(282\) 0 0
\(283\) −2.34233 4.05703i −0.139237 0.241166i 0.787971 0.615712i \(-0.211132\pi\)
−0.927208 + 0.374547i \(0.877798\pi\)
\(284\) 0 0
\(285\) 5.56155 9.63289i 0.329438 0.570603i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −20.0885 + 34.7944i −1.18168 + 2.04673i
\(290\) 0 0
\(291\) 1.02699 + 1.77879i 0.0602031 + 0.104275i
\(292\) 0 0
\(293\) −32.0540 −1.87261 −0.936307 0.351184i \(-0.885779\pi\)
−0.936307 + 0.351184i \(0.885779\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 4.34233 + 7.52113i 0.251967 + 0.436421i
\(298\) 0 0
\(299\) 10.4384 18.0799i 0.603671 1.04559i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 4.68466 8.11407i 0.269127 0.466141i
\(304\) 0 0
\(305\) 3.43845 + 5.95557i 0.196885 + 0.341015i
\(306\) 0 0
\(307\) 28.6847 1.63712 0.818560 0.574421i \(-0.194773\pi\)
0.818560 + 0.574421i \(0.194773\pi\)
\(308\) 0 0
\(309\) 18.4384 1.04893
\(310\) 0 0
\(311\) −6.43845 11.1517i −0.365091 0.632356i 0.623700 0.781664i \(-0.285629\pi\)
−0.988791 + 0.149308i \(0.952295\pi\)
\(312\) 0 0
\(313\) 13.3423 23.1096i 0.754153 1.30623i −0.191641 0.981465i \(-0.561381\pi\)
0.945794 0.324766i \(-0.105286\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.00000 8.66025i 0.280828 0.486408i −0.690761 0.723083i \(-0.742724\pi\)
0.971589 + 0.236675i \(0.0760576\pi\)
\(318\) 0 0
\(319\) −0.342329 0.592932i −0.0191668 0.0331978i
\(320\) 0 0
\(321\) 23.6155 1.31809
\(322\) 0 0
\(323\) −53.8617 −2.99695
\(324\) 0 0
\(325\) 3.34233 + 5.78908i 0.185399 + 0.321121i
\(326\) 0 0
\(327\) 3.46543 6.00231i 0.191639 0.331928i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.00000 10.3923i 0.329790 0.571213i −0.652680 0.757634i \(-0.726355\pi\)
0.982470 + 0.186421i \(0.0596888\pi\)
\(332\) 0 0
\(333\) −2.31534 4.01029i −0.126880 0.219762i
\(334\) 0 0
\(335\) −2.24621 −0.122724
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) −6.43845 11.1517i −0.349688 0.605678i
\(340\) 0 0
\(341\) 4.87689 8.44703i 0.264099 0.457432i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 2.43845 4.22351i 0.131282 0.227386i
\(346\) 0 0
\(347\) −7.56155 13.0970i −0.405925 0.703083i 0.588503 0.808495i \(-0.299717\pi\)
−0.994429 + 0.105411i \(0.966384\pi\)
\(348\) 0 0
\(349\) 11.7538 0.629166 0.314583 0.949230i \(-0.398135\pi\)
0.314583 + 0.949230i \(0.398135\pi\)
\(350\) 0 0
\(351\) 37.1771 1.98437
\(352\) 0 0
\(353\) −1.09612 1.89853i −0.0583405 0.101049i 0.835380 0.549673i \(-0.185248\pi\)
−0.893721 + 0.448624i \(0.851914\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i \(0.486738\pi\)
−0.886100 + 0.463494i \(0.846596\pi\)
\(360\) 0 0
\(361\) −15.8693 27.4865i −0.835227 1.44666i
\(362\) 0 0
\(363\) −13.3693 −0.701707
\(364\) 0 0
\(365\) −4.24621 −0.222257
\(366\) 0 0
\(367\) 7.46543 + 12.9305i 0.389693 + 0.674967i 0.992408 0.122989i \(-0.0392480\pi\)
−0.602716 + 0.797956i \(0.705915\pi\)
\(368\) 0 0
\(369\) 0.315342 0.546188i 0.0164160 0.0284334i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −7.68466 + 13.3102i −0.397897 + 0.689177i −0.993466 0.114127i \(-0.963593\pi\)
0.595570 + 0.803304i \(0.296926\pi\)
\(374\) 0 0
\(375\) 0.780776 + 1.35234i 0.0403191 + 0.0698348i
\(376\) 0 0
\(377\) −2.93087 −0.150947
\(378\) 0 0
\(379\) 32.4924 1.66902 0.834512 0.550990i \(-0.185750\pi\)
0.834512 + 0.550990i \(0.185750\pi\)
\(380\) 0 0
\(381\) 4.87689 + 8.44703i 0.249851 + 0.432754i
\(382\) 0 0
\(383\) −4.87689 + 8.44703i −0.249198 + 0.431623i −0.963303 0.268415i \(-0.913500\pi\)
0.714106 + 0.700038i \(0.246834\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) 0 0
\(389\) −11.1501 19.3125i −0.565332 0.979184i −0.997019 0.0771603i \(-0.975415\pi\)
0.431687 0.902024i \(-0.357919\pi\)
\(390\) 0 0
\(391\) −23.6155 −1.19429
\(392\) 0 0
\(393\) −23.6155 −1.19125
\(394\) 0 0
\(395\) 0.342329 + 0.592932i 0.0172245 + 0.0298336i
\(396\) 0 0
\(397\) −11.5885 + 20.0719i −0.581612 + 1.00738i 0.413676 + 0.910424i \(0.364245\pi\)
−0.995288 + 0.0969578i \(0.969089\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.46543 11.1985i 0.322868 0.559224i −0.658210 0.752834i \(-0.728686\pi\)
0.981079 + 0.193610i \(0.0620195\pi\)
\(402\) 0 0
\(403\) −20.8769 36.1598i −1.03995 1.80125i
\(404\) 0 0
\(405\) 7.00000 0.347833
\(406\) 0 0
\(407\) −12.8769 −0.638284
\(408\) 0 0
\(409\) −9.24621 16.0149i −0.457196 0.791886i 0.541616 0.840626i \(-0.317813\pi\)
−0.998812 + 0.0487399i \(0.984479\pi\)
\(410\) 0 0
\(411\) 5.75379 9.96585i 0.283813 0.491579i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) 0 0
\(417\) −16.6847 28.8987i −0.817051 1.41517i
\(418\) 0 0
\(419\) 18.2462 0.891386 0.445693 0.895186i \(-0.352957\pi\)
0.445693 + 0.895186i \(0.352957\pi\)
\(420\) 0 0
\(421\) 3.56155 0.173579 0.0867897 0.996227i \(-0.472339\pi\)
0.0867897 + 0.996227i \(0.472339\pi\)
\(422\) 0 0
\(423\) −0.684658 1.18586i −0.0332892 0.0576586i
\(424\) 0 0
\(425\) 3.78078 6.54850i 0.183395 0.317649i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 8.15009 14.1164i 0.393490 0.681545i
\(430\) 0 0
\(431\) 11.4654 + 19.8587i 0.552271 + 0.956561i 0.998110 + 0.0614479i \(0.0195718\pi\)
−0.445840 + 0.895113i \(0.647095\pi\)
\(432\) 0 0
\(433\) −19.7538 −0.949307 −0.474653 0.880173i \(-0.657427\pi\)
−0.474653 + 0.880173i \(0.657427\pi\)
\(434\) 0 0
\(435\) −0.684658 −0.0328269
\(436\) 0 0
\(437\) −11.1231 19.2658i −0.532090 0.921607i
\(438\) 0 0
\(439\) 9.56155 16.5611i 0.456348 0.790418i −0.542417 0.840110i \(-0.682491\pi\)
0.998765 + 0.0496917i \(0.0158239\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.80776 16.9875i 0.465981 0.807103i −0.533264 0.845949i \(-0.679035\pi\)
0.999245 + 0.0388461i \(0.0123682\pi\)
\(444\) 0 0
\(445\) −2.56155 4.43674i −0.121429 0.210322i
\(446\) 0 0
\(447\) −0.384472 −0.0181849
\(448\) 0 0
\(449\) −21.3153 −1.00593 −0.502967 0.864306i \(-0.667758\pi\)
−0.502967 + 0.864306i \(0.667758\pi\)
\(450\) 0 0
\(451\) −0.876894 1.51883i −0.0412913 0.0715187i
\(452\) 0 0
\(453\) 15.4654 26.7869i 0.726630 1.25856i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.31534 + 7.47439i −0.201863 + 0.349637i −0.949129 0.314888i \(-0.898033\pi\)
0.747266 + 0.664525i \(0.231366\pi\)
\(458\) 0 0
\(459\) −21.0270 36.4198i −0.981456 1.69993i
\(460\) 0 0
\(461\) −18.8769 −0.879185 −0.439592 0.898197i \(-0.644877\pi\)
−0.439592 + 0.898197i \(0.644877\pi\)
\(462\) 0 0
\(463\) −6.24621 −0.290286 −0.145143 0.989411i \(-0.546364\pi\)
−0.145143 + 0.989411i \(0.546364\pi\)
\(464\) 0 0
\(465\) −4.87689 8.44703i −0.226161 0.391722i
\(466\) 0 0
\(467\) 12.7808 22.1370i 0.591424 1.02438i −0.402617 0.915368i \(-0.631899\pi\)
0.994041 0.109008i \(-0.0347673\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.31534 5.74234i 0.152763 0.264593i
\(472\) 0 0
\(473\) 5.56155 + 9.63289i 0.255720 + 0.442921i
\(474\) 0 0
\(475\) 7.12311 0.326831
\(476\) 0 0
\(477\) 7.36932 0.337418
\(478\) 0 0
\(479\) 8.68466 + 15.0423i 0.396812 + 0.687299i 0.993331 0.115300i \(-0.0367831\pi\)
−0.596518 + 0.802599i \(0.703450\pi\)
\(480\) 0 0
\(481\) −27.5616 + 47.7380i −1.25670 + 2.17667i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.657671 + 1.13912i −0.0298633 + 0.0517247i
\(486\) 0 0
\(487\) −1.56155 2.70469i −0.0707607 0.122561i 0.828474 0.560027i \(-0.189209\pi\)
−0.899235 + 0.437466i \(0.855876\pi\)
\(488\) 0 0
\(489\) 30.6307 1.38517
\(490\) 0 0
\(491\) −3.31534 −0.149619 −0.0748096 0.997198i \(-0.523835\pi\)
−0.0748096 + 0.997198i \(0.523835\pi\)
\(492\) 0 0
\(493\) 1.65767 + 2.87117i 0.0746577 + 0.129311i
\(494\) 0 0
\(495\) −0.438447 + 0.759413i −0.0197067 + 0.0341331i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0.0961180 0.166481i 0.00430283 0.00745272i −0.863866 0.503722i \(-0.831964\pi\)
0.868169 + 0.496269i \(0.165297\pi\)
\(500\) 0 0
\(501\) 3.27320 + 5.66935i 0.146236 + 0.253288i
\(502\) 0 0
\(503\) 29.1771 1.30094 0.650471 0.759531i \(-0.274572\pi\)
0.650471 + 0.759531i \(0.274572\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −24.7386 42.8486i −1.09868 1.90297i
\(508\) 0 0
\(509\) 16.3693 28.3525i 0.725557 1.25670i −0.233187 0.972432i \(-0.574915\pi\)
0.958744 0.284270i \(-0.0917512\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 19.8078 34.3081i 0.874534 1.51474i
\(514\) 0 0
\(515\) 5.90388 + 10.2258i 0.260156 + 0.450604i
\(516\) 0 0
\(517\) −3.80776 −0.167465
\(518\) 0 0
\(519\) 36.1922 1.58866
\(520\) 0 0
\(521\) −6.12311 10.6055i −0.268258 0.464637i 0.700154 0.713992i \(-0.253115\pi\)
−0.968412 + 0.249355i \(0.919781\pi\)
\(522\) 0 0
\(523\) −6.00000 + 10.3923i −0.262362 + 0.454424i −0.966869 0.255273i \(-0.917835\pi\)
0.704507 + 0.709697i \(0.251168\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.6155 + 40.9033i −1.02871 + 1.78178i
\(528\) 0 0
\(529\) 6.62311 + 11.4716i 0.287961 + 0.498763i
\(530\) 0 0
\(531\) −2.24621 −0.0974773
\(532\) 0 0
\(533\) −7.50758 −0.325189
\(534\) 0 0
\(535\) 7.56155 + 13.0970i 0.326914 + 0.566232i
\(536\) 0 0
\(537\) 3.12311 5.40938i 0.134772 0.233432i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −20.7116 + 35.8736i −0.890463 + 1.54233i −0.0511422 + 0.998691i \(0.516286\pi\)
−0.839321 + 0.543636i \(0.817047\pi\)
\(542\) 0 0
\(543\) −4.00000 6.92820i −0.171656 0.297318i
\(544\) 0 0
\(545\) 4.43845 0.190122
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 0 0
\(549\) 1.93087 + 3.34436i 0.0824075 + 0.142734i
\(550\) 0 0
\(551\) −1.56155 + 2.70469i −0.0665244 + 0.115224i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6.43845 + 11.1517i −0.273297 + 0.473364i
\(556\) 0 0
\(557\) 8.80776 + 15.2555i 0.373197 + 0.646396i 0.990055 0.140678i \(-0.0449282\pi\)
−0.616858 + 0.787074i \(0.711595\pi\)
\(558\) 0 0
\(559\) 47.6155 2.01392
\(560\) 0 0
\(561\) −18.4384 −0.778472
\(562\) 0 0
\(563\) −3.75379 6.50175i −0.158203 0.274016i 0.776017 0.630711i \(-0.217237\pi\)
−0.934221 + 0.356695i \(0.883903\pi\)
\(564\) 0 0
\(565\) 4.12311 7.14143i 0.173460 0.300442i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.49242 + 16.4414i −0.397943 + 0.689258i −0.993472 0.114076i \(-0.963609\pi\)
0.595529 + 0.803334i \(0.296943\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 0 0
\(573\) −1.06913 −0.0446636
\(574\) 0 0
\(575\) 3.12311 0.130243
\(576\) 0 0
\(577\) −1.78078 3.08440i −0.0741347 0.128405i 0.826575 0.562827i \(-0.190286\pi\)
−0.900710 + 0.434422i \(0.856953\pi\)
\(578\) 0 0
\(579\) −10.2462 + 17.7470i −0.425818 + 0.737538i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 10.2462 17.7470i 0.424355 0.735004i
\(584\) 0 0
\(585\) 1.87689 + 3.25088i 0.0776000 + 0.134407i
\(586\) 0 0
\(587\) −10.2462 −0.422906 −0.211453 0.977388i \(-0.567820\pi\)
−0.211453 + 0.977388i \(0.567820\pi\)
\(588\) 0 0
\(589\) −44.4924 −1.83328
\(590\) 0 0
\(591\) 10.2462 + 17.7470i 0.421473 + 0.730012i
\(592\) 0 0
\(593\) 18.7116 32.4095i 0.768395 1.33090i −0.170038 0.985438i \(-0.554389\pi\)
0.938433 0.345462i \(-0.112278\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −11.1231 + 19.2658i −0.455238 + 0.788496i
\(598\) 0 0
\(599\) 23.4654 + 40.6433i 0.958772 + 1.66064i 0.725491 + 0.688232i \(0.241613\pi\)
0.233281 + 0.972409i \(0.425054\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −1.26137 −0.0513668
\(604\) 0 0
\(605\) −4.28078 7.41452i −0.174038 0.301443i
\(606\) 0 0
\(607\) −4.34233 + 7.52113i −0.176250 + 0.305273i −0.940593 0.339536i \(-0.889730\pi\)
0.764343 + 0.644809i \(0.223063\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.15009 + 14.1164i −0.329717 + 0.571087i
\(612\) 0 0
\(613\) −8.36932 14.4961i −0.338034 0.585491i 0.646029 0.763313i \(-0.276428\pi\)
−0.984063 + 0.177821i \(0.943095\pi\)
\(614\) 0 0
\(615\) −1.75379 −0.0707196
\(616\) 0 0
\(617\) −15.7538 −0.634224 −0.317112 0.948388i \(-0.602713\pi\)
−0.317112 + 0.948388i \(0.602713\pi\)
\(618\) 0 0
\(619\) 5.31534 + 9.20644i 0.213642 + 0.370038i 0.952852 0.303437i \(-0.0981342\pi\)
−0.739210 + 0.673475i \(0.764801\pi\)
\(620\) 0 0
\(621\) 8.68466 15.0423i 0.348503 0.603625i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −8.68466 15.0423i −0.346832 0.600730i
\(628\) 0 0
\(629\) 62.3542 2.48622
\(630\) 0 0
\(631\) −27.4233 −1.09170 −0.545852 0.837882i \(-0.683794\pi\)
−0.545852 + 0.837882i \(0.683794\pi\)
\(632\) 0 0
\(633\) 13.7116 + 23.7493i 0.544989 + 0.943949i
\(634\) 0 0
\(635\) −3.12311 + 5.40938i −0.123937 + 0.214665i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 11.4924 + 19.9055i 0.453923 + 0.786218i 0.998626 0.0524112i \(-0.0166906\pi\)
−0.544702 + 0.838630i \(0.683357\pi\)
\(642\) 0 0
\(643\) 30.0540 1.18521 0.592607 0.805492i \(-0.298099\pi\)
0.592607 + 0.805492i \(0.298099\pi\)
\(644\) 0 0
\(645\) 11.1231 0.437972
\(646\) 0 0
\(647\) 4.00000 + 6.92820i 0.157256 + 0.272376i 0.933878 0.357591i \(-0.116402\pi\)
−0.776622 + 0.629967i \(0.783068\pi\)
\(648\) 0 0
\(649\) −3.12311 + 5.40938i −0.122593 + 0.212337i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.2462 33.3354i 0.753162 1.30452i −0.193120 0.981175i \(-0.561861\pi\)
0.946283 0.323341i \(-0.104806\pi\)
\(654\) 0 0
\(655\) −7.56155 13.0970i −0.295454 0.511742i
\(656\) 0 0
\(657\) −2.38447 −0.0930271
\(658\) 0 0
\(659\) −0.192236 −0.00748845 −0.00374422 0.999993i \(-0.501192\pi\)
−0.00374422 + 0.999993i \(0.501192\pi\)
\(660\) 0 0
\(661\) −8.80776 15.2555i −0.342582 0.593370i 0.642329 0.766429i \(-0.277968\pi\)
−0.984911 + 0.173059i \(0.944635\pi\)
\(662\) 0 0
\(663\) −39.4654 + 68.3561i −1.53271 + 2.65473i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.684658 + 1.18586i −0.0265101 + 0.0459168i
\(668\) 0 0
\(669\) 19.2732 + 33.3822i 0.745145 + 1.29063i
\(670\) 0 0
\(671\) 10.7386 0.414560
\(672\) 0 0
\(673\) 41.6155 1.60416 0.802080 0.597216i \(-0.203727\pi\)
0.802080 + 0.597216i \(0.203727\pi\)
\(674\) 0 0
\(675\) 2.78078 + 4.81645i 0.107032 + 0.185385i
\(676\) 0 0
\(677\) −0.657671 + 1.13912i −0.0252763 + 0.0437799i −0.878387 0.477950i \(-0.841380\pi\)
0.853111 + 0.521730i \(0.174713\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −8.83475 + 15.3022i −0.338548 + 0.586383i
\(682\) 0 0
\(683\) −22.4924 38.9580i −0.860649 1.49069i −0.871304 0.490744i \(-0.836725\pi\)
0.0106552 0.999943i \(-0.496608\pi\)
\(684\) 0 0
\(685\) 7.36932 0.281567
\(686\) 0 0
\(687\) 17.7538 0.677349
\(688\) 0 0
\(689\) −43.8617 75.9708i −1.67100 2.89426i
\(690\) 0 0
\(691\) 8.24621 14.2829i 0.313701 0.543345i −0.665460 0.746434i \(-0.731764\pi\)
0.979160 + 0.203088i \(0.0650978\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.6847 18.5064i 0.405292 0.701987i
\(696\) 0 0
\(697\) 4.24621 + 7.35465i 0.160837 + 0.278577i
\(698\) 0 0
\(699\) −16.9848 −0.642426
\(700\) 0 0
\(701\) −9.31534 −0.351836 −0.175918 0.984405i \(-0.556289\pi\)
−0.175918 + 0.984405i \(0.556289\pi\)
\(702\) 0 0
\(703\) 29.3693 + 50.8691i 1.10768 + 1.91857i
\(704\) 0 0
\(705\) −1.90388 + 3.29762i −0.0717043 + 0.124196i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2.02699 3.51085i 0.0761251 0.131853i −0.825450 0.564475i \(-0.809078\pi\)
0.901575 + 0.432623i \(0.142412\pi\)
\(710\) 0 0
\(711\) 0.192236 + 0.332962i 0.00720941 + 0.0124871i
\(712\) 0 0
\(713\) −19.5076 −0.730565
\(714\) 0 0
\(715\) 10.4384 0.390376
\(716\) 0 0
\(717\) 14.0961 + 24.4152i 0.526429 + 0.911802i
\(718\) 0 0
\(719\) −11.8078 + 20.4516i −0.440355 + 0.762718i −0.997716 0.0675529i \(-0.978481\pi\)
0.557360 + 0.830271i \(0.311814\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.56155 2.70469i 0.0580748 0.100588i
\(724\) 0 0
\(725\) −0.219224 0.379706i −0.00814176 0.0141019i
\(726\) 0 0
\(727\) −48.9848 −1.81675 −0.908374 0.418159i \(-0.862675\pi\)
−0.908374 + 0.418159i \(0.862675\pi\)
\(728\) 0 0
\(729\) 29.9848 1.11055
\(730\) 0 0
\(731\) −26.9309 46.6456i −0.996074 1.72525i
\(732\) 0 0
\(733\) 8.21922 14.2361i 0.303584 0.525823i −0.673361 0.739314i \(-0.735150\pi\)
0.976945 + 0.213491i \(0.0684834\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.75379 + 3.03765i −0.0646016 + 0.111893i
\(738\) 0 0
\(739\) 3.21922 + 5.57586i 0.118421 + 0.205111i 0.919142 0.393926i \(-0.128883\pi\)
−0.800721 + 0.599037i \(0.795550\pi\)
\(740\) 0 0
\(741\) −74.3542 −2.73147
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) −0.123106 0.213225i −0.00451024 0.00781197i
\(746\) 0 0
\(747\) −3.36932 + 5.83583i −0.123277 + 0.213522i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 15.6577 27.1199i 0.571357 0.989619i −0.425070 0.905160i \(-0.639751\pi\)
0.996427 0.0844583i \(-0.0269160\pi\)
\(752\) 0 0
\(753\) 10.4384 + 18.0799i 0.380398 + 0.658869i
\(754\) 0 0
\(755\) 19.8078 0.720878
\(756\) 0 0
\(757\) 15.3693 0.558607 0.279304 0.960203i \(-0.409896\pi\)
0.279304 + 0.960203i \(0.409896\pi\)
\(758\) 0 0
\(759\) −3.80776 6.59524i −0.138213 0.239392i
\(760\) 0 0
\(761\) 13.0000 22.5167i 0.471250 0.816228i −0.528209 0.849114i \(-0.677136\pi\)
0.999459 + 0.0328858i \(0.0104698\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.12311 3.67733i 0.0767610 0.132954i
\(766\) 0 0
\(767\) 13.3693 + 23.1563i 0.482738 + 0.836127i
\(768\) 0 0
\(769\) −42.9848 −1.55007 −0.775037 0.631916i \(-0.782269\pi\)
−0.775037 + 0.631916i \(0.782269\pi\)
\(770\) 0 0
\(771\) 28.8769 1.03998
\(772\) 0 0
\(773\) −14.9039 25.8143i −0.536055 0.928475i −0.999111 0.0421462i \(-0.986580\pi\)
0.463056 0.886329i \(-0.346753\pi\)
\(774\) 0 0
\(775\) 3.12311 5.40938i 0.112185 0.194311i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.00000 + 6.92820i −0.143315 + 0.248229i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −2.43845 −0.0871430
\(784\) 0 0
\(785\) 4.24621 0.151554
\(786\) 0 0
\(787\) 16.5885 + 28.7322i 0.591318 + 1.02419i 0.994055 + 0.108877i \(0.0347254\pi\)
−0.402738 + 0.915315i \(0.631941\pi\)
\(788\) 0 0
\(789\) −7.31534 + 12.6705i −0.260433 + 0.451083i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 22.9848 39.8109i 0.816216 1.41373i
\(794\) 0 0
\(795\) −10.2462 17.7470i −0.363396 0.629420i
\(796\) 0 0
\(797\) −17.8078 −0.630783 −0.315392 0.948962i \(-0.602136\pi\)
−0.315392 + 0.948962i \(0.602136\pi\)
\(798\) 0 0
\(799\) 18.4384 0.652305
\(800\) 0 0