Properties

Label 3360.2.ba.d.2591.14
Level $3360$
Weight $2$
Character 3360.2591
Analytic conductor $26.830$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3360.ba (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.8297350792\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 50 x^{16} - 92 x^{15} + 144 x^{14} - 244 x^{13} + 481 x^{12} - 696 x^{11} + 848 x^{10} - 2088 x^{9} + 4329 x^{8} - 6588 x^{7} + 11664 x^{6} - 22356 x^{5} + 36450 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.14
Root \(-0.504688 - 1.65689i\) of defining polynomial
Character \(\chi\) \(=\) 3360.2591
Dual form 3360.2.ba.d.2591.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.814731 + 1.52847i) q^{3} +1.00000i q^{5} +1.00000i q^{7} +(-1.67243 + 2.49058i) q^{9} +O(q^{10})\) \(q+(0.814731 + 1.52847i) q^{3} +1.00000i q^{5} +1.00000i q^{7} +(-1.67243 + 2.49058i) q^{9} -1.02863 q^{11} -4.05107 q^{13} +(-1.52847 + 0.814731i) q^{15} -3.17733i q^{17} +2.43512i q^{19} +(-1.52847 + 0.814731i) q^{21} -6.89676 q^{23} -1.00000 q^{25} +(-5.16935 - 0.527101i) q^{27} -4.16192i q^{29} -2.76217i q^{31} +(-0.838058 - 1.57223i) q^{33} -1.00000 q^{35} +0.949518 q^{37} +(-3.30053 - 6.19193i) q^{39} -5.27131i q^{41} -9.82252i q^{43} +(-2.49058 - 1.67243i) q^{45} +5.55610 q^{47} -1.00000 q^{49} +(4.85644 - 2.58867i) q^{51} +2.52469i q^{53} -1.02863i q^{55} +(-3.72201 + 1.98397i) q^{57} +13.4623 q^{59} -13.8801 q^{61} +(-2.49058 - 1.67243i) q^{63} -4.05107i q^{65} +12.3941i q^{67} +(-5.61900 - 10.5415i) q^{69} +0.483561 q^{71} -2.55005 q^{73} +(-0.814731 - 1.52847i) q^{75} -1.02863i q^{77} +4.87745i q^{79} +(-3.40597 - 8.33063i) q^{81} -8.24143 q^{83} +3.17733 q^{85} +(6.36136 - 3.39084i) q^{87} -2.15948i q^{89} -4.05107i q^{91} +(4.22189 - 2.25043i) q^{93} -2.43512 q^{95} +1.82636 q^{97} +(1.72031 - 2.56189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{3} + 8 q^{9} + O(q^{10}) \) \( 20 q + 4 q^{3} + 8 q^{9} + 8 q^{11} + 8 q^{13} + 4 q^{15} + 4 q^{21} - 8 q^{23} - 20 q^{25} - 20 q^{27} - 40 q^{33} - 20 q^{35} + 16 q^{37} - 4 q^{39} - 20 q^{49} - 4 q^{51} - 16 q^{57} + 64 q^{59} - 64 q^{61} + 8 q^{69} + 40 q^{71} + 8 q^{73} - 4 q^{75} + 8 q^{81} - 24 q^{83} + 8 q^{85} + 48 q^{87} + 72 q^{93} - 16 q^{95} + 88 q^{97} - 28 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3360\mathbb{Z}\right)^\times\).

\(n\) \(421\) \(1121\) \(1471\) \(1921\) \(2017\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.814731 + 1.52847i 0.470385 + 0.882461i
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) −1.67243 + 2.49058i −0.557476 + 0.830193i
\(10\) 0 0
\(11\) −1.02863 −0.310144 −0.155072 0.987903i \(-0.549561\pi\)
−0.155072 + 0.987903i \(0.549561\pi\)
\(12\) 0 0
\(13\) −4.05107 −1.12356 −0.561782 0.827285i \(-0.689884\pi\)
−0.561782 + 0.827285i \(0.689884\pi\)
\(14\) 0 0
\(15\) −1.52847 + 0.814731i −0.394649 + 0.210363i
\(16\) 0 0
\(17\) 3.17733i 0.770615i −0.922788 0.385308i \(-0.874095\pi\)
0.922788 0.385308i \(-0.125905\pi\)
\(18\) 0 0
\(19\) 2.43512i 0.558656i 0.960196 + 0.279328i \(0.0901116\pi\)
−0.960196 + 0.279328i \(0.909888\pi\)
\(20\) 0 0
\(21\) −1.52847 + 0.814731i −0.333539 + 0.177789i
\(22\) 0 0
\(23\) −6.89676 −1.43807 −0.719037 0.694972i \(-0.755417\pi\)
−0.719037 + 0.694972i \(0.755417\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.16935 0.527101i −0.994842 0.101441i
\(28\) 0 0
\(29\) 4.16192i 0.772849i −0.922321 0.386425i \(-0.873710\pi\)
0.922321 0.386425i \(-0.126290\pi\)
\(30\) 0 0
\(31\) 2.76217i 0.496101i −0.968747 0.248051i \(-0.920210\pi\)
0.968747 0.248051i \(-0.0797899\pi\)
\(32\) 0 0
\(33\) −0.838058 1.57223i −0.145887 0.273690i
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 0.949518 0.156100 0.0780499 0.996949i \(-0.475131\pi\)
0.0780499 + 0.996949i \(0.475131\pi\)
\(38\) 0 0
\(39\) −3.30053 6.19193i −0.528508 0.991502i
\(40\) 0 0
\(41\) 5.27131i 0.823240i −0.911356 0.411620i \(-0.864963\pi\)
0.911356 0.411620i \(-0.135037\pi\)
\(42\) 0 0
\(43\) 9.82252i 1.49792i −0.662615 0.748960i \(-0.730553\pi\)
0.662615 0.748960i \(-0.269447\pi\)
\(44\) 0 0
\(45\) −2.49058 1.67243i −0.371274 0.249311i
\(46\) 0 0
\(47\) 5.55610 0.810441 0.405220 0.914219i \(-0.367195\pi\)
0.405220 + 0.914219i \(0.367195\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 4.85644 2.58867i 0.680038 0.362486i
\(52\) 0 0
\(53\) 2.52469i 0.346793i 0.984852 + 0.173397i \(0.0554742\pi\)
−0.984852 + 0.173397i \(0.944526\pi\)
\(54\) 0 0
\(55\) 1.02863i 0.138701i
\(56\) 0 0
\(57\) −3.72201 + 1.98397i −0.492992 + 0.262783i
\(58\) 0 0
\(59\) 13.4623 1.75264 0.876318 0.481732i \(-0.159992\pi\)
0.876318 + 0.481732i \(0.159992\pi\)
\(60\) 0 0
\(61\) −13.8801 −1.77717 −0.888585 0.458711i \(-0.848311\pi\)
−0.888585 + 0.458711i \(0.848311\pi\)
\(62\) 0 0
\(63\) −2.49058 1.67243i −0.313783 0.210706i
\(64\) 0 0
\(65\) 4.05107i 0.502473i
\(66\) 0 0
\(67\) 12.3941i 1.51418i 0.653308 + 0.757092i \(0.273381\pi\)
−0.653308 + 0.757092i \(0.726619\pi\)
\(68\) 0 0
\(69\) −5.61900 10.5415i −0.676448 1.26904i
\(70\) 0 0
\(71\) 0.483561 0.0573881 0.0286941 0.999588i \(-0.490865\pi\)
0.0286941 + 0.999588i \(0.490865\pi\)
\(72\) 0 0
\(73\) −2.55005 −0.298460 −0.149230 0.988802i \(-0.547680\pi\)
−0.149230 + 0.988802i \(0.547680\pi\)
\(74\) 0 0
\(75\) −0.814731 1.52847i −0.0940770 0.176492i
\(76\) 0 0
\(77\) 1.02863i 0.117224i
\(78\) 0 0
\(79\) 4.87745i 0.548756i 0.961622 + 0.274378i \(0.0884720\pi\)
−0.961622 + 0.274378i \(0.911528\pi\)
\(80\) 0 0
\(81\) −3.40597 8.33063i −0.378441 0.925625i
\(82\) 0 0
\(83\) −8.24143 −0.904614 −0.452307 0.891862i \(-0.649399\pi\)
−0.452307 + 0.891862i \(0.649399\pi\)
\(84\) 0 0
\(85\) 3.17733 0.344630
\(86\) 0 0
\(87\) 6.36136 3.39084i 0.682010 0.363537i
\(88\) 0 0
\(89\) 2.15948i 0.228905i −0.993429 0.114452i \(-0.963489\pi\)
0.993429 0.114452i \(-0.0365113\pi\)
\(90\) 0 0
\(91\) 4.05107i 0.424667i
\(92\) 0 0
\(93\) 4.22189 2.25043i 0.437790 0.233359i
\(94\) 0 0
\(95\) −2.43512 −0.249838
\(96\) 0 0
\(97\) 1.82636 0.185438 0.0927191 0.995692i \(-0.470444\pi\)
0.0927191 + 0.995692i \(0.470444\pi\)
\(98\) 0 0
\(99\) 1.72031 2.56189i 0.172898 0.257480i
\(100\) 0 0
\(101\) 10.7091i 1.06560i 0.846242 + 0.532798i \(0.178860\pi\)
−0.846242 + 0.532798i \(0.821140\pi\)
\(102\) 0 0
\(103\) 9.39285i 0.925505i −0.886488 0.462753i \(-0.846862\pi\)
0.886488 0.462753i \(-0.153138\pi\)
\(104\) 0 0
\(105\) −0.814731 1.52847i −0.0795096 0.149163i
\(106\) 0 0
\(107\) 2.05603 0.198764 0.0993819 0.995049i \(-0.468313\pi\)
0.0993819 + 0.995049i \(0.468313\pi\)
\(108\) 0 0
\(109\) −13.9058 −1.33194 −0.665968 0.745980i \(-0.731981\pi\)
−0.665968 + 0.745980i \(0.731981\pi\)
\(110\) 0 0
\(111\) 0.773601 + 1.45131i 0.0734270 + 0.137752i
\(112\) 0 0
\(113\) 5.76305i 0.542142i −0.962559 0.271071i \(-0.912622\pi\)
0.962559 0.271071i \(-0.0873779\pi\)
\(114\) 0 0
\(115\) 6.89676i 0.643126i
\(116\) 0 0
\(117\) 6.77512 10.0895i 0.626360 0.932775i
\(118\) 0 0
\(119\) 3.17733 0.291265
\(120\) 0 0
\(121\) −9.94192 −0.903811
\(122\) 0 0
\(123\) 8.05702 4.29470i 0.726477 0.387240i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 7.39012i 0.655767i −0.944718 0.327883i \(-0.893665\pi\)
0.944718 0.327883i \(-0.106335\pi\)
\(128\) 0 0
\(129\) 15.0134 8.00271i 1.32186 0.704599i
\(130\) 0 0
\(131\) 14.6620 1.28102 0.640511 0.767949i \(-0.278723\pi\)
0.640511 + 0.767949i \(0.278723\pi\)
\(132\) 0 0
\(133\) −2.43512 −0.211152
\(134\) 0 0
\(135\) 0.527101 5.16935i 0.0453656 0.444907i
\(136\) 0 0
\(137\) 5.50071i 0.469957i −0.972001 0.234979i \(-0.924498\pi\)
0.972001 0.234979i \(-0.0755020\pi\)
\(138\) 0 0
\(139\) 20.4943i 1.73831i 0.494544 + 0.869153i \(0.335335\pi\)
−0.494544 + 0.869153i \(0.664665\pi\)
\(140\) 0 0
\(141\) 4.52673 + 8.49232i 0.381219 + 0.715183i
\(142\) 0 0
\(143\) 4.16706 0.348467
\(144\) 0 0
\(145\) 4.16192 0.345629
\(146\) 0 0
\(147\) −0.814731 1.52847i −0.0671979 0.126066i
\(148\) 0 0
\(149\) 10.3708i 0.849606i 0.905286 + 0.424803i \(0.139657\pi\)
−0.905286 + 0.424803i \(0.860343\pi\)
\(150\) 0 0
\(151\) 2.68583i 0.218570i −0.994010 0.109285i \(-0.965144\pi\)
0.994010 0.109285i \(-0.0348561\pi\)
\(152\) 0 0
\(153\) 7.91339 + 5.31385i 0.639759 + 0.429599i
\(154\) 0 0
\(155\) 2.76217 0.221863
\(156\) 0 0
\(157\) −24.8805 −1.98568 −0.992842 0.119438i \(-0.961891\pi\)
−0.992842 + 0.119438i \(0.961891\pi\)
\(158\) 0 0
\(159\) −3.85891 + 2.05694i −0.306031 + 0.163126i
\(160\) 0 0
\(161\) 6.89676i 0.543541i
\(162\) 0 0
\(163\) 5.77321i 0.452193i −0.974105 0.226097i \(-0.927404\pi\)
0.974105 0.226097i \(-0.0725965\pi\)
\(164\) 0 0
\(165\) 1.57223 0.838058i 0.122398 0.0652427i
\(166\) 0 0
\(167\) −13.7838 −1.06663 −0.533313 0.845918i \(-0.679053\pi\)
−0.533313 + 0.845918i \(0.679053\pi\)
\(168\) 0 0
\(169\) 3.41115 0.262396
\(170\) 0 0
\(171\) −6.06487 4.07257i −0.463792 0.311437i
\(172\) 0 0
\(173\) 2.64419i 0.201034i 0.994935 + 0.100517i \(0.0320497\pi\)
−0.994935 + 0.100517i \(0.967950\pi\)
\(174\) 0 0
\(175\) 1.00000i 0.0755929i
\(176\) 0 0
\(177\) 10.9681 + 20.5766i 0.824414 + 1.54663i
\(178\) 0 0
\(179\) 23.8234 1.78064 0.890322 0.455332i \(-0.150479\pi\)
0.890322 + 0.455332i \(0.150479\pi\)
\(180\) 0 0
\(181\) −16.5767 −1.23214 −0.616068 0.787693i \(-0.711276\pi\)
−0.616068 + 0.787693i \(0.711276\pi\)
\(182\) 0 0
\(183\) −11.3086 21.2154i −0.835954 1.56828i
\(184\) 0 0
\(185\) 0.949518i 0.0698100i
\(186\) 0 0
\(187\) 3.26830i 0.239002i
\(188\) 0 0
\(189\) 0.527101 5.16935i 0.0383410 0.376015i
\(190\) 0 0
\(191\) −5.87494 −0.425096 −0.212548 0.977151i \(-0.568176\pi\)
−0.212548 + 0.977151i \(0.568176\pi\)
\(192\) 0 0
\(193\) −1.37509 −0.0989815 −0.0494907 0.998775i \(-0.515760\pi\)
−0.0494907 + 0.998775i \(0.515760\pi\)
\(194\) 0 0
\(195\) 6.19193 3.30053i 0.443413 0.236356i
\(196\) 0 0
\(197\) 5.53554i 0.394391i −0.980364 0.197195i \(-0.936817\pi\)
0.980364 0.197195i \(-0.0631834\pi\)
\(198\) 0 0
\(199\) 14.6010i 1.03504i −0.855671 0.517520i \(-0.826855\pi\)
0.855671 0.517520i \(-0.173145\pi\)
\(200\) 0 0
\(201\) −18.9440 + 10.0979i −1.33621 + 0.712249i
\(202\) 0 0
\(203\) 4.16192 0.292110
\(204\) 0 0
\(205\) 5.27131 0.368164
\(206\) 0 0
\(207\) 11.5343 17.1769i 0.801691 1.19388i
\(208\) 0 0
\(209\) 2.50485i 0.173264i
\(210\) 0 0
\(211\) 20.9843i 1.44462i 0.691569 + 0.722311i \(0.256920\pi\)
−0.691569 + 0.722311i \(0.743080\pi\)
\(212\) 0 0
\(213\) 0.393972 + 0.739107i 0.0269945 + 0.0506428i
\(214\) 0 0
\(215\) 9.82252 0.669890
\(216\) 0 0
\(217\) 2.76217 0.187509
\(218\) 0 0
\(219\) −2.07760 3.89766i −0.140391 0.263380i
\(220\) 0 0
\(221\) 12.8716i 0.865835i
\(222\) 0 0
\(223\) 4.11921i 0.275843i 0.990443 + 0.137921i \(0.0440421\pi\)
−0.990443 + 0.137921i \(0.955958\pi\)
\(224\) 0 0
\(225\) 1.67243 2.49058i 0.111495 0.166039i
\(226\) 0 0
\(227\) 4.32987 0.287384 0.143692 0.989622i \(-0.454103\pi\)
0.143692 + 0.989622i \(0.454103\pi\)
\(228\) 0 0
\(229\) 9.56658 0.632177 0.316089 0.948730i \(-0.397630\pi\)
0.316089 + 0.948730i \(0.397630\pi\)
\(230\) 0 0
\(231\) 1.57223 0.838058i 0.103445 0.0551402i
\(232\) 0 0
\(233\) 14.9942i 0.982303i 0.871074 + 0.491152i \(0.163424\pi\)
−0.871074 + 0.491152i \(0.836576\pi\)
\(234\) 0 0
\(235\) 5.55610i 0.362440i
\(236\) 0 0
\(237\) −7.45503 + 3.97381i −0.484256 + 0.258127i
\(238\) 0 0
\(239\) −5.20979 −0.336993 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(240\) 0 0
\(241\) −22.6920 −1.46172 −0.730861 0.682526i \(-0.760881\pi\)
−0.730861 + 0.682526i \(0.760881\pi\)
\(242\) 0 0
\(243\) 9.95815 11.9931i 0.638816 0.769360i
\(244\) 0 0
\(245\) 1.00000i 0.0638877i
\(246\) 0 0
\(247\) 9.86485i 0.627686i
\(248\) 0 0
\(249\) −6.71454 12.5968i −0.425517 0.798287i
\(250\) 0 0
\(251\) 9.35580 0.590533 0.295267 0.955415i \(-0.404592\pi\)
0.295267 + 0.955415i \(0.404592\pi\)
\(252\) 0 0
\(253\) 7.09423 0.446010
\(254\) 0 0
\(255\) 2.58867 + 4.85644i 0.162109 + 0.304122i
\(256\) 0 0
\(257\) 13.1927i 0.822938i −0.911424 0.411469i \(-0.865016\pi\)
0.911424 0.411469i \(-0.134984\pi\)
\(258\) 0 0
\(259\) 0.949518i 0.0590002i
\(260\) 0 0
\(261\) 10.3656 + 6.96051i 0.641614 + 0.430845i
\(262\) 0 0
\(263\) −24.1870 −1.49143 −0.745716 0.666264i \(-0.767893\pi\)
−0.745716 + 0.666264i \(0.767893\pi\)
\(264\) 0 0
\(265\) −2.52469 −0.155091
\(266\) 0 0
\(267\) 3.30070 1.75940i 0.201999 0.107673i
\(268\) 0 0
\(269\) 2.26475i 0.138084i −0.997614 0.0690420i \(-0.978006\pi\)
0.997614 0.0690420i \(-0.0219942\pi\)
\(270\) 0 0
\(271\) 20.4324i 1.24118i −0.784136 0.620589i \(-0.786894\pi\)
0.784136 0.620589i \(-0.213106\pi\)
\(272\) 0 0
\(273\) 6.19193 3.30053i 0.374752 0.199757i
\(274\) 0 0
\(275\) 1.02863 0.0620289
\(276\) 0 0
\(277\) −23.4294 −1.40774 −0.703869 0.710330i \(-0.748546\pi\)
−0.703869 + 0.710330i \(0.748546\pi\)
\(278\) 0 0
\(279\) 6.87941 + 4.61954i 0.411860 + 0.276564i
\(280\) 0 0
\(281\) 9.47571i 0.565274i 0.959227 + 0.282637i \(0.0912091\pi\)
−0.959227 + 0.282637i \(0.908791\pi\)
\(282\) 0 0
\(283\) 18.9834i 1.12845i −0.825622 0.564224i \(-0.809176\pi\)
0.825622 0.564224i \(-0.190824\pi\)
\(284\) 0 0
\(285\) −1.98397 3.72201i −0.117520 0.220473i
\(286\) 0 0
\(287\) 5.27131 0.311155
\(288\) 0 0
\(289\) 6.90459 0.406152
\(290\) 0 0
\(291\) 1.48799 + 2.79153i 0.0872274 + 0.163642i
\(292\) 0 0
\(293\) 19.2408i 1.12406i −0.827117 0.562029i \(-0.810021\pi\)
0.827117 0.562029i \(-0.189979\pi\)
\(294\) 0 0
\(295\) 13.4623i 0.783803i
\(296\) 0 0
\(297\) 5.31736 + 0.542193i 0.308544 + 0.0314612i
\(298\) 0 0
\(299\) 27.9392 1.61577
\(300\) 0 0
\(301\) 9.82252 0.566161
\(302\) 0 0
\(303\) −16.3685 + 8.72505i −0.940348 + 0.501241i
\(304\) 0 0
\(305\) 13.8801i 0.794775i
\(306\) 0 0
\(307\) 5.41175i 0.308865i −0.988003 0.154432i \(-0.950645\pi\)
0.988003 0.154432i \(-0.0493549\pi\)
\(308\) 0 0
\(309\) 14.3567 7.65264i 0.816722 0.435344i
\(310\) 0 0
\(311\) −24.7401 −1.40288 −0.701441 0.712727i \(-0.747460\pi\)
−0.701441 + 0.712727i \(0.747460\pi\)
\(312\) 0 0
\(313\) −11.1213 −0.628616 −0.314308 0.949321i \(-0.601772\pi\)
−0.314308 + 0.949321i \(0.601772\pi\)
\(314\) 0 0
\(315\) 1.67243 2.49058i 0.0942306 0.140328i
\(316\) 0 0
\(317\) 13.7615i 0.772925i 0.922305 + 0.386463i \(0.126303\pi\)
−0.922305 + 0.386463i \(0.873697\pi\)
\(318\) 0 0
\(319\) 4.28109i 0.239695i
\(320\) 0 0
\(321\) 1.67511 + 3.14257i 0.0934955 + 0.175401i
\(322\) 0 0
\(323\) 7.73719 0.430509
\(324\) 0 0
\(325\) 4.05107 0.224713
\(326\) 0 0
\(327\) −11.3295 21.2546i −0.626523 1.17538i
\(328\) 0 0
\(329\) 5.55610i 0.306318i
\(330\) 0 0
\(331\) 14.8523i 0.816357i 0.912902 + 0.408179i \(0.133836\pi\)
−0.912902 + 0.408179i \(0.866164\pi\)
\(332\) 0 0
\(333\) −1.58800 + 2.36485i −0.0870219 + 0.129593i
\(334\) 0 0
\(335\) −12.3941 −0.677164
\(336\) 0 0
\(337\) −33.2100 −1.80907 −0.904533 0.426403i \(-0.859780\pi\)
−0.904533 + 0.426403i \(0.859780\pi\)
\(338\) 0 0
\(339\) 8.80864 4.69533i 0.478420 0.255016i
\(340\) 0 0
\(341\) 2.84126i 0.153863i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 10.5415 5.61900i 0.567534 0.302517i
\(346\) 0 0
\(347\) 2.21271 0.118784 0.0593922 0.998235i \(-0.481084\pi\)
0.0593922 + 0.998235i \(0.481084\pi\)
\(348\) 0 0
\(349\) −8.24785 −0.441497 −0.220749 0.975331i \(-0.570850\pi\)
−0.220749 + 0.975331i \(0.570850\pi\)
\(350\) 0 0
\(351\) 20.9414 + 2.13532i 1.11777 + 0.113975i
\(352\) 0 0
\(353\) 27.6601i 1.47220i −0.676874 0.736099i \(-0.736666\pi\)
0.676874 0.736099i \(-0.263334\pi\)
\(354\) 0 0
\(355\) 0.483561i 0.0256647i
\(356\) 0 0
\(357\) 2.58867 + 4.85644i 0.137007 + 0.257030i
\(358\) 0 0
\(359\) 22.8086 1.20379 0.601895 0.798575i \(-0.294412\pi\)
0.601895 + 0.798575i \(0.294412\pi\)
\(360\) 0 0
\(361\) 13.0702 0.687904
\(362\) 0 0
\(363\) −8.09998 15.1959i −0.425139 0.797578i
\(364\) 0 0
\(365\) 2.55005i 0.133475i
\(366\) 0 0
\(367\) 34.2006i 1.78526i 0.450791 + 0.892630i \(0.351142\pi\)
−0.450791 + 0.892630i \(0.648858\pi\)
\(368\) 0 0
\(369\) 13.1286 + 8.81588i 0.683448 + 0.458936i
\(370\) 0 0
\(371\) −2.52469 −0.131075
\(372\) 0 0
\(373\) 10.5027 0.543808 0.271904 0.962324i \(-0.412347\pi\)
0.271904 + 0.962324i \(0.412347\pi\)
\(374\) 0 0
\(375\) 1.52847 0.814731i 0.0789297 0.0420725i
\(376\) 0 0
\(377\) 16.8602i 0.868346i
\(378\) 0 0
\(379\) 22.7093i 1.16650i −0.812293 0.583250i \(-0.801781\pi\)
0.812293 0.583250i \(-0.198219\pi\)
\(380\) 0 0
\(381\) 11.2956 6.02095i 0.578689 0.308463i
\(382\) 0 0
\(383\) −8.68651 −0.443860 −0.221930 0.975063i \(-0.571236\pi\)
−0.221930 + 0.975063i \(0.571236\pi\)
\(384\) 0 0
\(385\) 1.02863 0.0524239
\(386\) 0 0
\(387\) 24.4638 + 16.4275i 1.24356 + 0.835055i
\(388\) 0 0
\(389\) 18.1956i 0.922555i −0.887256 0.461278i \(-0.847391\pi\)
0.887256 0.461278i \(-0.152609\pi\)
\(390\) 0 0
\(391\) 21.9133i 1.10820i
\(392\) 0 0
\(393\) 11.9455 + 22.4103i 0.602573 + 1.13045i
\(394\) 0 0
\(395\) −4.87745 −0.245411
\(396\) 0 0
\(397\) 13.9987 0.702577 0.351288 0.936267i \(-0.385744\pi\)
0.351288 + 0.936267i \(0.385744\pi\)
\(398\) 0 0
\(399\) −1.98397 3.72201i −0.0993227 0.186333i
\(400\) 0 0
\(401\) 27.7434i 1.38544i 0.721206 + 0.692720i \(0.243588\pi\)
−0.721206 + 0.692720i \(0.756412\pi\)
\(402\) 0 0
\(403\) 11.1898i 0.557401i
\(404\) 0 0
\(405\) 8.33063 3.40597i 0.413952 0.169244i
\(406\) 0 0
\(407\) −0.976705 −0.0484135
\(408\) 0 0
\(409\) −23.9399 −1.18375 −0.591877 0.806028i \(-0.701613\pi\)
−0.591877 + 0.806028i \(0.701613\pi\)
\(410\) 0 0
\(411\) 8.40765 4.48159i 0.414719 0.221061i
\(412\) 0 0
\(413\) 13.4623i 0.662434i
\(414\) 0 0
\(415\) 8.24143i 0.404556i
\(416\) 0 0
\(417\) −31.3249 + 16.6974i −1.53399 + 0.817673i
\(418\) 0 0
\(419\) −16.1582 −0.789378 −0.394689 0.918815i \(-0.629148\pi\)
−0.394689 + 0.918815i \(0.629148\pi\)
\(420\) 0 0
\(421\) 29.9591 1.46012 0.730060 0.683383i \(-0.239492\pi\)
0.730060 + 0.683383i \(0.239492\pi\)
\(422\) 0 0
\(423\) −9.29218 + 13.8379i −0.451801 + 0.672822i
\(424\) 0 0
\(425\) 3.17733i 0.154123i
\(426\) 0 0
\(427\) 13.8801i 0.671707i
\(428\) 0 0
\(429\) 3.39503 + 6.36922i 0.163914 + 0.307509i
\(430\) 0 0
\(431\) −1.19384 −0.0575053 −0.0287526 0.999587i \(-0.509154\pi\)
−0.0287526 + 0.999587i \(0.509154\pi\)
\(432\) 0 0
\(433\) −23.3012 −1.11979 −0.559893 0.828565i \(-0.689158\pi\)
−0.559893 + 0.828565i \(0.689158\pi\)
\(434\) 0 0
\(435\) 3.39084 + 6.36136i 0.162579 + 0.305004i
\(436\) 0 0
\(437\) 16.7945i 0.803388i
\(438\) 0 0
\(439\) 1.58614i 0.0757025i 0.999283 + 0.0378512i \(0.0120513\pi\)
−0.999283 + 0.0378512i \(0.987949\pi\)
\(440\) 0 0
\(441\) 1.67243 2.49058i 0.0796394 0.118599i
\(442\) 0 0
\(443\) −12.8564 −0.610824 −0.305412 0.952220i \(-0.598794\pi\)
−0.305412 + 0.952220i \(0.598794\pi\)
\(444\) 0 0
\(445\) 2.15948 0.102369
\(446\) 0 0
\(447\) −15.8514 + 8.44938i −0.749745 + 0.399642i
\(448\) 0 0
\(449\) 2.04478i 0.0964993i 0.998835 + 0.0482497i \(0.0153643\pi\)
−0.998835 + 0.0482497i \(0.984636\pi\)
\(450\) 0 0
\(451\) 5.42224i 0.255323i
\(452\) 0 0
\(453\) 4.10521 2.18823i 0.192879 0.102812i
\(454\) 0 0
\(455\) 4.05107 0.189917
\(456\) 0 0
\(457\) 25.8392 1.20871 0.604353 0.796717i \(-0.293432\pi\)
0.604353 + 0.796717i \(0.293432\pi\)
\(458\) 0 0
\(459\) −1.67477 + 16.4247i −0.0781717 + 0.766640i
\(460\) 0 0
\(461\) 34.7726i 1.61952i 0.586760 + 0.809761i \(0.300403\pi\)
−0.586760 + 0.809761i \(0.699597\pi\)
\(462\) 0 0
\(463\) 8.82104i 0.409949i 0.978767 + 0.204974i \(0.0657111\pi\)
−0.978767 + 0.204974i \(0.934289\pi\)
\(464\) 0 0
\(465\) 2.25043 + 4.22189i 0.104361 + 0.195786i
\(466\) 0 0
\(467\) −23.8590 −1.10406 −0.552032 0.833823i \(-0.686147\pi\)
−0.552032 + 0.833823i \(0.686147\pi\)
\(468\) 0 0
\(469\) −12.3941 −0.572308
\(470\) 0 0
\(471\) −20.2709 38.0291i −0.934036 1.75229i
\(472\) 0 0
\(473\) 10.1038i 0.464571i
\(474\) 0 0
\(475\) 2.43512i 0.111731i
\(476\) 0 0
\(477\) −6.28795 4.22237i −0.287905 0.193329i
\(478\) 0 0
\(479\) 14.3238 0.654471 0.327236 0.944943i \(-0.393883\pi\)
0.327236 + 0.944943i \(0.393883\pi\)
\(480\) 0 0
\(481\) −3.84656 −0.175388
\(482\) 0 0
\(483\) 10.5415 5.61900i 0.479654 0.255673i
\(484\) 0 0
\(485\) 1.82636i 0.0829305i
\(486\) 0 0
\(487\) 10.6405i 0.482169i 0.970504 + 0.241085i \(0.0775031\pi\)
−0.970504 + 0.241085i \(0.922497\pi\)
\(488\) 0 0
\(489\) 8.82417 4.70361i 0.399043 0.212705i
\(490\) 0 0
\(491\) −19.6682 −0.887614 −0.443807 0.896122i \(-0.646372\pi\)
−0.443807 + 0.896122i \(0.646372\pi\)
\(492\) 0 0
\(493\) −13.2238 −0.595569
\(494\) 0 0
\(495\) 2.56189 + 1.72031i 0.115148 + 0.0773223i
\(496\) 0 0
\(497\) 0.483561i 0.0216907i
\(498\) 0 0
\(499\) 16.3530i 0.732060i 0.930603 + 0.366030i \(0.119283\pi\)
−0.930603 + 0.366030i \(0.880717\pi\)
\(500\) 0 0
\(501\) −11.2301 21.0682i −0.501725 0.941256i
\(502\) 0 0
\(503\) −35.6697 −1.59043 −0.795217 0.606324i \(-0.792643\pi\)
−0.795217 + 0.606324i \(0.792643\pi\)
\(504\) 0 0
\(505\) −10.7091 −0.476549
\(506\) 0 0
\(507\) 2.77917 + 5.21384i 0.123427 + 0.231555i
\(508\) 0 0
\(509\) 35.4015i 1.56915i −0.620037 0.784573i \(-0.712882\pi\)
0.620037 0.784573i \(-0.287118\pi\)
\(510\) 0 0
\(511\) 2.55005i 0.112807i
\(512\) 0 0
\(513\) 1.28356 12.5880i 0.0566704 0.555774i
\(514\) 0 0
\(515\) 9.39285 0.413898
\(516\) 0 0
\(517\) −5.71518 −0.251354
\(518\) 0 0
\(519\) −4.04156 + 2.15430i −0.177405 + 0.0945634i
\(520\) 0 0
\(521\) 38.5904i 1.69068i −0.534232 0.845338i \(-0.679399\pi\)
0.534232 0.845338i \(-0.320601\pi\)
\(522\) 0 0
\(523\) 7.35480i 0.321603i 0.986987 + 0.160801i \(0.0514079\pi\)
−0.986987 + 0.160801i \(0.948592\pi\)
\(524\) 0 0
\(525\) 1.52847 0.814731i 0.0667078 0.0355578i
\(526\) 0 0
\(527\) −8.77633 −0.382303
\(528\) 0 0
\(529\) 24.5653 1.06806
\(530\) 0 0
\(531\) −22.5147 + 33.5288i −0.977053 + 1.45503i
\(532\) 0 0
\(533\) 21.3544i 0.924963i
\(534\) 0 0
\(535\) 2.05603i 0.0888898i
\(536\) 0 0
\(537\) 19.4096 + 36.4133i 0.837588 + 1.57135i
\(538\) 0 0
\(539\) 1.02863 0.0443063
\(540\) 0 0
\(541\) −10.0900 −0.433801 −0.216901 0.976194i \(-0.569595\pi\)
−0.216901 + 0.976194i \(0.569595\pi\)
\(542\) 0 0
\(543\) −13.5056 25.3370i −0.579579 1.08731i
\(544\) 0 0
\(545\) 13.9058i 0.595660i
\(546\) 0 0
\(547\) 7.00161i 0.299367i 0.988734 + 0.149684i \(0.0478255\pi\)
−0.988734 + 0.149684i \(0.952174\pi\)
\(548\) 0 0
\(549\) 23.2135 34.5696i 0.990730 1.47539i
\(550\) 0 0
\(551\) 10.1348 0.431757
\(552\) 0 0
\(553\) −4.87745 −0.207410
\(554\) 0 0
\(555\) −1.45131 + 0.773601i −0.0616046 + 0.0328376i
\(556\) 0 0
\(557\) 23.3180i 0.988017i 0.869457 + 0.494008i \(0.164469\pi\)
−0.869457 + 0.494008i \(0.835531\pi\)
\(558\) 0 0
\(559\) 39.7917i 1.68301i
\(560\) 0 0
\(561\) −4.99549 + 2.66279i −0.210910 + 0.112423i
\(562\) 0 0
\(563\) −8.70223 −0.366755 −0.183378 0.983043i \(-0.558703\pi\)
−0.183378 + 0.983043i \(0.558703\pi\)
\(564\) 0 0
\(565\) 5.76305 0.242453
\(566\) 0 0
\(567\) 8.33063 3.40597i 0.349854 0.143037i
\(568\) 0 0
\(569\) 34.7542i 1.45697i −0.685062 0.728485i \(-0.740225\pi\)
0.685062 0.728485i \(-0.259775\pi\)
\(570\) 0 0
\(571\) 29.5985i 1.23866i 0.785131 + 0.619330i \(0.212596\pi\)
−0.785131 + 0.619330i \(0.787404\pi\)
\(572\) 0 0
\(573\) −4.78649 8.97966i −0.199959 0.375131i
\(574\) 0 0
\(575\) 6.89676 0.287615
\(576\) 0 0
\(577\) 26.2723 1.09373 0.546864 0.837221i \(-0.315821\pi\)
0.546864 + 0.837221i \(0.315821\pi\)
\(578\) 0 0
\(579\) −1.12033 2.10179i −0.0465594 0.0873473i
\(580\) 0 0
\(581\) 8.24143i 0.341912i
\(582\) 0 0
\(583\) 2.59698i 0.107556i
\(584\) 0 0
\(585\) 10.0895 + 6.77512i 0.417150 + 0.280117i
\(586\) 0 0
\(587\) 4.95283 0.204425 0.102213 0.994763i \(-0.467408\pi\)
0.102213 + 0.994763i \(0.467408\pi\)
\(588\) 0 0
\(589\) 6.72624 0.277150
\(590\) 0 0
\(591\) 8.46090 4.50998i 0.348035 0.185516i
\(592\) 0 0
\(593\) 30.1056i 1.23629i 0.786065 + 0.618144i \(0.212115\pi\)
−0.786065 + 0.618144i \(0.787885\pi\)
\(594\) 0 0
\(595\) 3.17733i 0.130258i
\(596\) 0 0
\(597\) 22.3172 11.8959i 0.913383 0.486867i
\(598\) 0 0
\(599\) −4.31960 −0.176494 −0.0882470 0.996099i \(-0.528126\pi\)
−0.0882470 + 0.996099i \(0.528126\pi\)
\(600\) 0 0
\(601\) −30.7553 −1.25454 −0.627268 0.778803i \(-0.715827\pi\)
−0.627268 + 0.778803i \(0.715827\pi\)
\(602\) 0 0
\(603\) −30.8686 20.7283i −1.25707 0.844121i
\(604\) 0 0
\(605\) 9.94192i 0.404196i
\(606\) 0 0
\(607\) 16.2187i 0.658298i −0.944278 0.329149i \(-0.893238\pi\)
0.944278 0.329149i \(-0.106762\pi\)
\(608\) 0 0
\(609\) 3.39084 + 6.36136i 0.137404 + 0.257775i
\(610\) 0 0
\(611\) −22.5081 −0.910582
\(612\) 0 0
\(613\) 0.0300119 0.00121217 0.000606084 1.00000i \(-0.499807\pi\)
0.000606084 1.00000i \(0.499807\pi\)
\(614\) 0 0
\(615\) 4.29470 + 8.05702i 0.173179 + 0.324891i
\(616\) 0 0
\(617\) 13.9151i 0.560200i 0.959971 + 0.280100i \(0.0903676\pi\)
−0.959971 + 0.280100i \(0.909632\pi\)
\(618\) 0 0
\(619\) 19.7421i 0.793501i 0.917926 + 0.396750i \(0.129862\pi\)
−0.917926 + 0.396750i \(0.870138\pi\)
\(620\) 0 0
\(621\) 35.6517 + 3.63529i 1.43066 + 0.145879i
\(622\) 0 0
\(623\) 2.15948 0.0865178
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 3.82858 2.04078i 0.152899 0.0815007i
\(628\) 0 0
\(629\) 3.01693i 0.120293i
\(630\) 0 0
\(631\) 4.60553i 0.183343i −0.995789 0.0916716i \(-0.970779\pi\)
0.995789 0.0916716i \(-0.0292210\pi\)
\(632\) 0 0
\(633\) −32.0739 + 17.0966i −1.27482 + 0.679528i
\(634\) 0 0
\(635\) 7.39012 0.293268
\(636\) 0 0
\(637\) 4.05107 0.160509
\(638\) 0 0
\(639\) −0.808721 + 1.20435i −0.0319925 + 0.0476432i
\(640\) 0 0
\(641\) 41.2011i 1.62735i −0.581322 0.813674i \(-0.697464\pi\)
0.581322 0.813674i \(-0.302536\pi\)
\(642\) 0 0
\(643\) 11.2120i 0.442156i 0.975256 + 0.221078i \(0.0709576\pi\)
−0.975256 + 0.221078i \(0.929042\pi\)
\(644\) 0 0
\(645\) 8.00271 + 15.0134i 0.315106 + 0.591152i
\(646\) 0 0
\(647\) −6.63691 −0.260924 −0.130462 0.991453i \(-0.541646\pi\)
−0.130462 + 0.991453i \(0.541646\pi\)
\(648\) 0 0
\(649\) −13.8477 −0.543570
\(650\) 0 0
\(651\) 2.25043 + 4.22189i 0.0882012 + 0.165469i
\(652\) 0 0
\(653\) 37.8238i 1.48016i 0.672518 + 0.740081i \(0.265213\pi\)
−0.672518 + 0.740081i \(0.734787\pi\)
\(654\) 0 0
\(655\) 14.6620i 0.572890i
\(656\) 0 0
\(657\) 4.26477 6.35109i 0.166384 0.247780i
\(658\) 0 0
\(659\) 30.3589 1.18262 0.591308 0.806446i \(-0.298612\pi\)
0.591308 + 0.806446i \(0.298612\pi\)
\(660\) 0 0
\(661\) −33.8441 −1.31638 −0.658192 0.752850i \(-0.728679\pi\)
−0.658192 + 0.752850i \(0.728679\pi\)
\(662\) 0 0
\(663\) −19.6738 + 10.4869i −0.764066 + 0.407276i
\(664\) 0 0
\(665\) 2.43512i 0.0944301i
\(666\) 0 0
\(667\) 28.7038i 1.11141i
\(668\) 0 0
\(669\) −6.29608 + 3.35605i −0.243421 + 0.129752i
\(670\) 0 0
\(671\) 14.2776 0.551179
\(672\) 0 0
\(673\) 6.93411 0.267290 0.133645 0.991029i \(-0.457332\pi\)
0.133645 + 0.991029i \(0.457332\pi\)
\(674\) 0 0
\(675\) 5.16935 + 0.527101i 0.198968 + 0.0202881i
\(676\) 0 0
\(677\) 48.8801i 1.87861i −0.343079 0.939307i \(-0.611470\pi\)
0.343079 0.939307i \(-0.388530\pi\)
\(678\) 0 0
\(679\) 1.82636i 0.0700891i
\(680\) 0 0
\(681\) 3.52768 + 6.61807i 0.135181 + 0.253605i
\(682\) 0 0
\(683\) 22.4825 0.860267 0.430134 0.902765i \(-0.358466\pi\)
0.430134 + 0.902765i \(0.358466\pi\)
\(684\) 0 0
\(685\) 5.50071 0.210171
\(686\) 0 0
\(687\) 7.79418 + 14.6222i 0.297367 + 0.557872i
\(688\) 0 0
\(689\) 10.2277i 0.389644i
\(690\) 0 0
\(691\) 46.8158i 1.78096i 0.455024 + 0.890479i \(0.349631\pi\)
−0.455024 + 0.890479i \(0.650369\pi\)
\(692\) 0 0
\(693\) 2.56189 + 1.72031i 0.0973181 + 0.0653493i
\(694\) 0 0
\(695\) −20.4943 −0.777394
\(696\) 0 0
\(697\) −16.7487 −0.634401
\(698\) 0 0
\(699\) −22.9182 + 12.2162i −0.866845 + 0.462061i
\(700\) 0 0
\(701\) 31.7316i 1.19848i 0.800568 + 0.599242i \(0.204531\pi\)
−0.800568 + 0.599242i \(0.795469\pi\)
\(702\) 0 0
\(703\) 2.31219i 0.0872060i
\(704\) 0 0
\(705\) −8.49232 + 4.52673i −0.319839 + 0.170486i
\(706\) 0 0
\(707\) −10.7091 −0.402758
\(708\) 0 0
\(709\) 45.2570 1.69966 0.849830 0.527057i \(-0.176704\pi\)
0.849830 + 0.527057i \(0.176704\pi\)
\(710\) 0 0
\(711\) −12.1477 8.15719i −0.455574 0.305919i
\(712\) 0 0
\(713\) 19.0500i 0.713430i
\(714\) 0 0
\(715\) 4.16706i 0.155839i
\(716\) 0 0
\(717\) −4.24457 7.96299i −0.158517 0.297383i
\(718\) 0 0
\(719\) −3.35064 −0.124958 −0.0624789 0.998046i \(-0.519901\pi\)
−0.0624789 + 0.998046i \(0.519901\pi\)
\(720\) 0 0
\(721\) 9.39285 0.349808
\(722\) 0 0
\(723\) −18.4879 34.6840i −0.687572 1.28991i
\(724\) 0 0
\(725\) 4.16192i 0.154570i
\(726\) 0 0
\(727\) 14.8966i 0.552486i 0.961088 + 0.276243i \(0.0890895\pi\)
−0.961088 + 0.276243i \(0.910911\pi\)
\(728\) 0 0
\(729\) 26.4443 + 5.44954i 0.979420 + 0.201835i
\(730\) 0 0
\(731\) −31.2094 −1.15432
\(732\) 0 0
\(733\) −7.15703 −0.264351 −0.132175 0.991226i \(-0.542196\pi\)
−0.132175 + 0.991226i \(0.542196\pi\)
\(734\) 0 0
\(735\) 1.52847 0.814731i 0.0563784 0.0300518i
\(736\) 0 0
\(737\) 12.7490i 0.469615i
\(738\) 0 0
\(739\) 54.2406i 1.99527i 0.0687121 + 0.997637i \(0.478111\pi\)
−0.0687121 + 0.997637i \(0.521889\pi\)
\(740\) 0 0
\(741\) 15.0781 8.03720i 0.553908 0.295254i
\(742\) 0 0
\(743\) −9.20435 −0.337675 −0.168837 0.985644i \(-0.554001\pi\)
−0.168837 + 0.985644i \(0.554001\pi\)
\(744\) 0 0
\(745\) −10.3708 −0.379956
\(746\) 0 0
\(747\) 13.7832 20.5259i 0.504301 0.751004i
\(748\) 0 0
\(749\) 2.05603i 0.0751256i
\(750\) 0 0
\(751\) 4.30009i 0.156912i 0.996918 + 0.0784562i \(0.0249991\pi\)
−0.996918 + 0.0784562i \(0.975001\pi\)
\(752\) 0 0
\(753\) 7.62246 + 14.3000i 0.277778 + 0.521123i
\(754\) 0 0
\(755\) 2.68583 0.0977474
\(756\) 0 0
\(757\) 16.7794 0.609857 0.304929 0.952375i \(-0.401367\pi\)
0.304929 + 0.952375i \(0.401367\pi\)
\(758\) 0 0
\(759\) 5.77988 + 10.8433i 0.209797 + 0.393587i
\(760\) 0 0
\(761\) 26.3871i 0.956531i 0.878215 + 0.478266i \(0.158734\pi\)
−0.878215 + 0.478266i \(0.841266\pi\)
\(762\) 0 0
\(763\) 13.9058i 0.503424i
\(764\) 0 0
\(765\) −5.31385 + 7.91339i −0.192123 + 0.286109i
\(766\) 0 0
\(767\) −54.5365 −1.96920
\(768\) 0 0
\(769\) −24.9362 −0.899221 −0.449611 0.893225i \(-0.648437\pi\)
−0.449611 + 0.893225i \(0.648437\pi\)
\(770\) 0 0
\(771\) 20.1646 10.7485i 0.726211 0.387098i
\(772\) 0 0
\(773\) 45.5450i 1.63814i 0.573694 + 0.819070i \(0.305510\pi\)
−0.573694 + 0.819070i \(0.694490\pi\)
\(774\) 0 0
\(775\) 2.76217i 0.0992202i
\(776\) 0 0
\(777\) −1.45131 + 0.773601i −0.0520654 + 0.0277528i
\(778\) 0 0
\(779\) 12.8363 0.459908
\(780\) 0 0
\(781\) −0.497406 −0.0177986
\(782\) 0 0
\(783\) −2.19375 + 21.5144i −0.0783983 + 0.768863i
\(784\) 0 0
\(785\) 24.8805i 0.888025i
\(786\) 0 0
\(787\) 32.5394i 1.15990i 0.814651 + 0.579952i \(0.196929\pi\)
−0.814651 + 0.579952i \(0.803071\pi\)
\(788\) 0 0
\(789\) −19.7059 36.9690i −0.701547 1.31613i
\(790\) 0 0
\(791\) 5.76305 0.204911
\(792\) 0 0
\(793\) 56.2294 1.99677
\(794\) 0 0
\(795\) −2.05694 3.85891i −0.0729523 0.136861i
\(796\) 0 0
\(797\) 40.2915i 1.42720i −0.700555 0.713599i \(-0.747064\pi\)
0.700555 0.713599i \(-0.252936\pi\)
\(798\) 0 0
\(799\) 17.6536i 0.624538i
\(800\) 0 0
\(801\) 5.37836 + 3.61158i 0.190035 + 0.127609i