Properties

Label 1960.2.q.p.361.1
Level $1960$
Weight $2$
Character 1960.361
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: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.p.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20711 + 2.09077i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(-1.20711 + 2.09077i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.41421 - 2.44949i) q^{9} +(0.500000 - 0.866025i) q^{11} -0.414214 q^{13} -2.41421 q^{15} +(-1.20711 + 2.09077i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-3.12132 - 5.40629i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.414214 q^{27} +1.00000 q^{29} +(-5.12132 + 8.87039i) q^{31} +(1.20711 + 2.09077i) q^{33} +(-5.94975 - 10.3053i) q^{37} +(0.500000 - 0.866025i) q^{39} +4.58579 q^{41} -11.6569 q^{43} +(1.41421 - 2.44949i) q^{45} +(-3.79289 - 6.56948i) q^{47} +(-2.91421 - 5.04757i) q^{51} +(-3.29289 + 5.70346i) q^{53} +1.00000 q^{55} +4.82843 q^{57} +(-0.878680 + 1.52192i) q^{59} +(3.41421 + 5.91359i) q^{61} +(-0.207107 - 0.358719i) q^{65} +(0.707107 - 1.22474i) q^{67} +15.0711 q^{69} -2.48528 q^{71} +(5.41421 - 9.37769i) q^{73} +(-1.20711 - 2.09077i) q^{75} +(1.67157 + 2.89525i) q^{79} +(4.74264 - 8.21449i) q^{81} -11.3137 q^{83} -2.41421 q^{85} +(-1.20711 + 2.09077i) q^{87} +(-4.82843 - 8.36308i) q^{89} +(-12.3640 - 21.4150i) q^{93} +(1.00000 - 1.73205i) q^{95} +14.0711 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{5} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{5} + 2q^{11} + 4q^{13} - 4q^{15} - 2q^{17} - 4q^{19} - 4q^{23} - 2q^{25} + 4q^{27} + 4q^{29} - 12q^{31} + 2q^{33} - 4q^{37} + 2q^{39} + 24q^{41} - 24q^{43} - 18q^{47} - 6q^{51} - 16q^{53} + 4q^{55} + 8q^{57} - 12q^{59} + 8q^{61} + 2q^{65} + 32q^{69} + 24q^{71} + 16q^{73} - 2q^{75} + 18q^{79} + 2q^{81} - 4q^{85} - 2q^{87} - 8q^{89} - 24q^{93} + 4q^{95} + 28q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −1.20711 + 2.09077i −0.696923 + 1.20711i 0.272605 + 0.962126i \(0.412115\pi\)
−0.969528 + 0.244981i \(0.921218\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.41421 2.44949i −0.471405 0.816497i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) −0.414214 −0.114882 −0.0574411 0.998349i \(-0.518294\pi\)
−0.0574411 + 0.998349i \(0.518294\pi\)
\(14\) 0 0
\(15\) −2.41421 −0.623347
\(16\) 0 0
\(17\) −1.20711 + 2.09077i −0.292766 + 0.507086i −0.974463 0.224549i \(-0.927909\pi\)
0.681696 + 0.731635i \(0.261242\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.12132 5.40629i −0.650840 1.12729i −0.982919 0.184037i \(-0.941083\pi\)
0.332079 0.943252i \(-0.392250\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −0.414214 −0.0797154
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) −5.12132 + 8.87039i −0.919816 + 1.59317i −0.120124 + 0.992759i \(0.538329\pi\)
−0.799693 + 0.600410i \(0.795004\pi\)
\(32\) 0 0
\(33\) 1.20711 + 2.09077i 0.210130 + 0.363956i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.94975 10.3053i −0.978132 1.69418i −0.669185 0.743096i \(-0.733357\pi\)
−0.308948 0.951079i \(-0.599977\pi\)
\(38\) 0 0
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) 4.58579 0.716180 0.358090 0.933687i \(-0.383428\pi\)
0.358090 + 0.933687i \(0.383428\pi\)
\(42\) 0 0
\(43\) −11.6569 −1.77765 −0.888827 0.458243i \(-0.848479\pi\)
−0.888827 + 0.458243i \(0.848479\pi\)
\(44\) 0 0
\(45\) 1.41421 2.44949i 0.210819 0.365148i
\(46\) 0 0
\(47\) −3.79289 6.56948i −0.553250 0.958258i −0.998037 0.0626213i \(-0.980054\pi\)
0.444787 0.895636i \(-0.353279\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.91421 5.04757i −0.408072 0.706801i
\(52\) 0 0
\(53\) −3.29289 + 5.70346i −0.452314 + 0.783430i −0.998529 0.0542143i \(-0.982735\pi\)
0.546216 + 0.837645i \(0.316068\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 4.82843 0.639541
\(58\) 0 0
\(59\) −0.878680 + 1.52192i −0.114394 + 0.198137i −0.917537 0.397649i \(-0.869826\pi\)
0.803143 + 0.595786i \(0.203159\pi\)
\(60\) 0 0
\(61\) 3.41421 + 5.91359i 0.437145 + 0.757158i 0.997468 0.0711166i \(-0.0226562\pi\)
−0.560323 + 0.828274i \(0.689323\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.207107 0.358719i −0.0256884 0.0444937i
\(66\) 0 0
\(67\) 0.707107 1.22474i 0.0863868 0.149626i −0.819594 0.572944i \(-0.805801\pi\)
0.905981 + 0.423318i \(0.139135\pi\)
\(68\) 0 0
\(69\) 15.0711 1.81434
\(70\) 0 0
\(71\) −2.48528 −0.294949 −0.147474 0.989066i \(-0.547114\pi\)
−0.147474 + 0.989066i \(0.547114\pi\)
\(72\) 0 0
\(73\) 5.41421 9.37769i 0.633686 1.09758i −0.353106 0.935583i \(-0.614875\pi\)
0.986792 0.161993i \(-0.0517921\pi\)
\(74\) 0 0
\(75\) −1.20711 2.09077i −0.139385 0.241421i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.67157 + 2.89525i 0.188067 + 0.325741i 0.944606 0.328208i \(-0.106445\pi\)
−0.756539 + 0.653949i \(0.773111\pi\)
\(80\) 0 0
\(81\) 4.74264 8.21449i 0.526960 0.912722i
\(82\) 0 0
\(83\) −11.3137 −1.24184 −0.620920 0.783874i \(-0.713241\pi\)
−0.620920 + 0.783874i \(0.713241\pi\)
\(84\) 0 0
\(85\) −2.41421 −0.261858
\(86\) 0 0
\(87\) −1.20711 + 2.09077i −0.129415 + 0.224154i
\(88\) 0 0
\(89\) −4.82843 8.36308i −0.511812 0.886485i −0.999906 0.0136937i \(-0.995641\pi\)
0.488094 0.872791i \(-0.337692\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −12.3640 21.4150i −1.28208 2.22063i
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) 14.0711 1.42870 0.714350 0.699788i \(-0.246722\pi\)
0.714350 + 0.699788i \(0.246722\pi\)
\(98\) 0 0
\(99\) −2.82843 −0.284268
\(100\) 0 0
\(101\) −5.24264 + 9.08052i −0.521662 + 0.903546i 0.478020 + 0.878349i \(0.341355\pi\)
−0.999683 + 0.0251967i \(0.991979\pi\)
\(102\) 0 0
\(103\) −3.37868 5.85204i −0.332911 0.576619i 0.650170 0.759789i \(-0.274698\pi\)
−0.983081 + 0.183170i \(0.941364\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.24264 + 12.5446i 0.700173 + 1.21273i 0.968406 + 0.249380i \(0.0802269\pi\)
−0.268233 + 0.963354i \(0.586440\pi\)
\(108\) 0 0
\(109\) 9.15685 15.8601i 0.877068 1.51913i 0.0225237 0.999746i \(-0.492830\pi\)
0.854544 0.519379i \(-0.173837\pi\)
\(110\) 0 0
\(111\) 28.7279 2.72673
\(112\) 0 0
\(113\) −9.07107 −0.853334 −0.426667 0.904409i \(-0.640312\pi\)
−0.426667 + 0.904409i \(0.640312\pi\)
\(114\) 0 0
\(115\) 3.12132 5.40629i 0.291065 0.504139i
\(116\) 0 0
\(117\) 0.585786 + 1.01461i 0.0541560 + 0.0938009i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) −5.53553 + 9.58783i −0.499122 + 0.864505i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 3.75736 0.333412 0.166706 0.986007i \(-0.446687\pi\)
0.166706 + 0.986007i \(0.446687\pi\)
\(128\) 0 0
\(129\) 14.0711 24.3718i 1.23889 2.14582i
\(130\) 0 0
\(131\) −10.1213 17.5306i −0.884304 1.53166i −0.846509 0.532374i \(-0.821300\pi\)
−0.0377944 0.999286i \(-0.512033\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.207107 0.358719i −0.0178249 0.0308737i
\(136\) 0 0
\(137\) 9.65685 16.7262i 0.825041 1.42901i −0.0768474 0.997043i \(-0.524485\pi\)
0.901888 0.431970i \(-0.142181\pi\)
\(138\) 0 0
\(139\) 1.41421 0.119952 0.0599760 0.998200i \(-0.480898\pi\)
0.0599760 + 0.998200i \(0.480898\pi\)
\(140\) 0 0
\(141\) 18.3137 1.54229
\(142\) 0 0
\(143\) −0.207107 + 0.358719i −0.0173191 + 0.0299976i
\(144\) 0 0
\(145\) 0.500000 + 0.866025i 0.0415227 + 0.0719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.58579 + 7.94282i 0.375682 + 0.650701i 0.990429 0.138024i \(-0.0440751\pi\)
−0.614747 + 0.788725i \(0.710742\pi\)
\(150\) 0 0
\(151\) 3.32843 5.76500i 0.270864 0.469149i −0.698220 0.715884i \(-0.746024\pi\)
0.969083 + 0.246734i \(0.0793574\pi\)
\(152\) 0 0
\(153\) 6.82843 0.552046
\(154\) 0 0
\(155\) −10.2426 −0.822709
\(156\) 0 0
\(157\) −5.24264 + 9.08052i −0.418408 + 0.724704i −0.995780 0.0917773i \(-0.970745\pi\)
0.577371 + 0.816482i \(0.304079\pi\)
\(158\) 0 0
\(159\) −7.94975 13.7694i −0.630456 1.09198i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.46447 2.53653i −0.114706 0.198676i 0.802956 0.596038i \(-0.203259\pi\)
−0.917662 + 0.397362i \(0.869926\pi\)
\(164\) 0 0
\(165\) −1.20711 + 2.09077i −0.0939731 + 0.162766i
\(166\) 0 0
\(167\) 7.58579 0.587006 0.293503 0.955958i \(-0.405179\pi\)
0.293503 + 0.955958i \(0.405179\pi\)
\(168\) 0 0
\(169\) −12.8284 −0.986802
\(170\) 0 0
\(171\) −2.82843 + 4.89898i −0.216295 + 0.374634i
\(172\) 0 0
\(173\) 6.86396 + 11.8887i 0.521857 + 0.903883i 0.999677 + 0.0254253i \(0.00809399\pi\)
−0.477819 + 0.878458i \(0.658573\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.12132 3.67423i −0.159448 0.276172i
\(178\) 0 0
\(179\) −2.07107 + 3.58719i −0.154799 + 0.268120i −0.932986 0.359913i \(-0.882806\pi\)
0.778187 + 0.628033i \(0.216140\pi\)
\(180\) 0 0
\(181\) −25.5563 −1.89959 −0.949794 0.312875i \(-0.898708\pi\)
−0.949794 + 0.312875i \(0.898708\pi\)
\(182\) 0 0
\(183\) −16.4853 −1.21863
\(184\) 0 0
\(185\) 5.94975 10.3053i 0.437434 0.757658i
\(186\) 0 0
\(187\) 1.20711 + 2.09077i 0.0882724 + 0.152892i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.91421 11.9758i −0.500295 0.866536i −1.00000 0.000340595i \(-0.999892\pi\)
0.499705 0.866196i \(-0.333442\pi\)
\(192\) 0 0
\(193\) −0.343146 + 0.594346i −0.0247002 + 0.0427820i −0.878111 0.478456i \(-0.841196\pi\)
0.853411 + 0.521238i \(0.174530\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) −12.2426 −0.872252 −0.436126 0.899886i \(-0.643650\pi\)
−0.436126 + 0.899886i \(0.643650\pi\)
\(198\) 0 0
\(199\) 6.19239 10.7255i 0.438967 0.760313i −0.558643 0.829408i \(-0.688678\pi\)
0.997610 + 0.0690953i \(0.0220113\pi\)
\(200\) 0 0
\(201\) 1.70711 + 2.95680i 0.120410 + 0.208556i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.29289 + 3.97141i 0.160143 + 0.277375i
\(206\) 0 0
\(207\) −8.82843 + 15.2913i −0.613618 + 1.06282i
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 17.1421 1.18011 0.590057 0.807362i \(-0.299105\pi\)
0.590057 + 0.807362i \(0.299105\pi\)
\(212\) 0 0
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) −5.82843 10.0951i −0.397495 0.688482i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 13.0711 + 22.6398i 0.883261 + 1.52985i
\(220\) 0 0
\(221\) 0.500000 0.866025i 0.0336336 0.0582552i
\(222\) 0 0
\(223\) −17.3848 −1.16417 −0.582085 0.813128i \(-0.697763\pi\)
−0.582085 + 0.813128i \(0.697763\pi\)
\(224\) 0 0
\(225\) 2.82843 0.188562
\(226\) 0 0
\(227\) −0.792893 + 1.37333i −0.0526262 + 0.0911512i −0.891138 0.453732i \(-0.850093\pi\)
0.838512 + 0.544883i \(0.183426\pi\)
\(228\) 0 0
\(229\) 2.05025 + 3.55114i 0.135485 + 0.234666i 0.925782 0.378057i \(-0.123408\pi\)
−0.790298 + 0.612723i \(0.790074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.75736 3.04384i −0.115128 0.199408i 0.802703 0.596379i \(-0.203395\pi\)
−0.917831 + 0.396971i \(0.870061\pi\)
\(234\) 0 0
\(235\) 3.79289 6.56948i 0.247421 0.428546i
\(236\) 0 0
\(237\) −8.07107 −0.524272
\(238\) 0 0
\(239\) −4.65685 −0.301227 −0.150613 0.988593i \(-0.548125\pi\)
−0.150613 + 0.988593i \(0.548125\pi\)
\(240\) 0 0
\(241\) −5.19239 + 8.99348i −0.334471 + 0.579321i −0.983383 0.181543i \(-0.941891\pi\)
0.648912 + 0.760863i \(0.275224\pi\)
\(242\) 0 0
\(243\) 10.8284 + 18.7554i 0.694644 + 1.20316i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.414214 + 0.717439i 0.0263558 + 0.0456495i
\(248\) 0 0
\(249\) 13.6569 23.6544i 0.865468 1.49903i
\(250\) 0 0
\(251\) 7.55635 0.476953 0.238476 0.971148i \(-0.423352\pi\)
0.238476 + 0.971148i \(0.423352\pi\)
\(252\) 0 0
\(253\) −6.24264 −0.392471
\(254\) 0 0
\(255\) 2.91421 5.04757i 0.182495 0.316091i
\(256\) 0 0
\(257\) −5.24264 9.08052i −0.327027 0.566427i 0.654894 0.755721i \(-0.272713\pi\)
−0.981920 + 0.189294i \(0.939380\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.41421 2.44949i −0.0875376 0.151620i
\(262\) 0 0
\(263\) −9.48528 + 16.4290i −0.584888 + 1.01305i 0.410002 + 0.912085i \(0.365528\pi\)
−0.994889 + 0.100970i \(0.967805\pi\)
\(264\) 0 0
\(265\) −6.58579 −0.404562
\(266\) 0 0
\(267\) 23.3137 1.42678
\(268\) 0 0
\(269\) −9.29289 + 16.0958i −0.566598 + 0.981376i 0.430301 + 0.902685i \(0.358407\pi\)
−0.996899 + 0.0786907i \(0.974926\pi\)
\(270\) 0 0
\(271\) −1.17157 2.02922i −0.0711680 0.123267i 0.828245 0.560365i \(-0.189339\pi\)
−0.899413 + 0.437099i \(0.856006\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 6.53553 11.3199i 0.392682 0.680145i −0.600120 0.799910i \(-0.704881\pi\)
0.992802 + 0.119764i \(0.0382139\pi\)
\(278\) 0 0
\(279\) 28.9706 1.73442
\(280\) 0 0
\(281\) 18.3137 1.09250 0.546252 0.837621i \(-0.316054\pi\)
0.546252 + 0.837621i \(0.316054\pi\)
\(282\) 0 0
\(283\) −12.5208 + 21.6867i −0.744285 + 1.28914i 0.206243 + 0.978501i \(0.433876\pi\)
−0.950528 + 0.310639i \(0.899457\pi\)
\(284\) 0 0
\(285\) 2.41421 + 4.18154i 0.143006 + 0.247693i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 5.58579 + 9.67487i 0.328576 + 0.569110i
\(290\) 0 0
\(291\) −16.9853 + 29.4194i −0.995695 + 1.72459i
\(292\) 0 0
\(293\) −18.4142 −1.07577 −0.537885 0.843018i \(-0.680777\pi\)
−0.537885 + 0.843018i \(0.680777\pi\)
\(294\) 0 0
\(295\) −1.75736 −0.102317
\(296\) 0 0
\(297\) −0.207107 + 0.358719i −0.0120176 + 0.0208150i
\(298\) 0 0
\(299\) 1.29289 + 2.23936i 0.0747699 + 0.129505i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −12.6569 21.9223i −0.727117 1.25940i
\(304\) 0 0
\(305\) −3.41421 + 5.91359i −0.195497 + 0.338611i
\(306\) 0 0
\(307\) −11.9289 −0.680820 −0.340410 0.940277i \(-0.610566\pi\)
−0.340410 + 0.940277i \(0.610566\pi\)
\(308\) 0 0
\(309\) 16.3137 0.928054
\(310\) 0 0
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) 11.8640 + 20.5490i 0.670591 + 1.16150i 0.977737 + 0.209835i \(0.0672926\pi\)
−0.307146 + 0.951662i \(0.599374\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.17157 10.6895i −0.346630 0.600381i 0.639018 0.769191i \(-0.279341\pi\)
−0.985649 + 0.168811i \(0.946007\pi\)
\(318\) 0 0
\(319\) 0.500000 0.866025i 0.0279946 0.0484881i
\(320\) 0 0
\(321\) −34.9706 −1.95187
\(322\) 0 0
\(323\) 4.82843 0.268661
\(324\) 0 0
\(325\) 0.207107 0.358719i 0.0114882 0.0198982i
\(326\) 0 0
\(327\) 22.1066 + 38.2898i 1.22250 + 2.11743i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −4.75736 8.23999i −0.261488 0.452911i 0.705149 0.709059i \(-0.250880\pi\)
−0.966638 + 0.256148i \(0.917547\pi\)
\(332\) 0 0
\(333\) −16.8284 + 29.1477i −0.922192 + 1.59728i
\(334\) 0 0
\(335\) 1.41421 0.0772667
\(336\) 0 0
\(337\) −13.0711 −0.712026 −0.356013 0.934481i \(-0.615864\pi\)
−0.356013 + 0.934481i \(0.615864\pi\)
\(338\) 0 0
\(339\) 10.9497 18.9655i 0.594709 1.03007i
\(340\) 0 0
\(341\) 5.12132 + 8.87039i 0.277335 + 0.480358i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 7.53553 + 13.0519i 0.405700 + 0.702692i
\(346\) 0 0
\(347\) −14.4350 + 25.0022i −0.774913 + 1.34219i 0.159930 + 0.987128i \(0.448873\pi\)
−0.934843 + 0.355060i \(0.884460\pi\)
\(348\) 0 0
\(349\) −6.68629 −0.357909 −0.178954 0.983857i \(-0.557271\pi\)
−0.178954 + 0.983857i \(0.557271\pi\)
\(350\) 0 0
\(351\) 0.171573 0.00915788
\(352\) 0 0
\(353\) −15.1066 + 26.1654i −0.804043 + 1.39264i 0.112892 + 0.993607i \(0.463989\pi\)
−0.916935 + 0.399037i \(0.869345\pi\)
\(354\) 0 0
\(355\) −1.24264 2.15232i −0.0659525 0.114233i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.8284 + 25.6836i 0.782614 + 1.35553i 0.930414 + 0.366511i \(0.119448\pi\)
−0.147799 + 0.989017i \(0.547219\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0 0
\(363\) −24.1421 −1.26713
\(364\) 0 0
\(365\) 10.8284 0.566786
\(366\) 0 0
\(367\) −5.62132 + 9.73641i −0.293431 + 0.508237i −0.974619 0.223872i \(-0.928130\pi\)
0.681188 + 0.732108i \(0.261464\pi\)
\(368\) 0 0
\(369\) −6.48528 11.2328i −0.337610 0.584758i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −11.4142 19.7700i −0.591006 1.02365i −0.994097 0.108492i \(-0.965398\pi\)
0.403092 0.915160i \(-0.367936\pi\)
\(374\) 0 0
\(375\) 1.20711 2.09077i 0.0623347 0.107967i
\(376\) 0 0
\(377\) −0.414214 −0.0213331
\(378\) 0 0
\(379\) 28.6274 1.47049 0.735246 0.677801i \(-0.237067\pi\)
0.735246 + 0.677801i \(0.237067\pi\)
\(380\) 0 0
\(381\) −4.53553 + 7.85578i −0.232362 + 0.402464i
\(382\) 0 0
\(383\) −11.4142 19.7700i −0.583239 1.01020i −0.995092 0.0989496i \(-0.968452\pi\)
0.411853 0.911250i \(-0.364882\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.4853 + 28.5533i 0.837994 + 1.45145i
\(388\) 0 0
\(389\) −5.39949 + 9.35220i −0.273765 + 0.474175i −0.969823 0.243811i \(-0.921602\pi\)
0.696058 + 0.717986i \(0.254936\pi\)
\(390\) 0 0
\(391\) 15.0711 0.762177
\(392\) 0 0
\(393\) 48.8701 2.46517
\(394\) 0 0
\(395\) −1.67157 + 2.89525i −0.0841060 + 0.145676i
\(396\) 0 0
\(397\) 2.79289 + 4.83743i 0.140171 + 0.242784i 0.927561 0.373672i \(-0.121901\pi\)
−0.787390 + 0.616456i \(0.788568\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.2279 + 21.1794i 0.610633 + 1.05765i 0.991134 + 0.132867i \(0.0424184\pi\)
−0.380501 + 0.924781i \(0.624248\pi\)
\(402\) 0 0
\(403\) 2.12132 3.67423i 0.105670 0.183027i
\(404\) 0 0
\(405\) 9.48528 0.471327
\(406\) 0 0
\(407\) −11.8995 −0.589836
\(408\) 0 0
\(409\) 16.5563 28.6764i 0.818659 1.41796i −0.0880119 0.996119i \(-0.528051\pi\)
0.906671 0.421839i \(-0.138615\pi\)
\(410\) 0 0
\(411\) 23.3137 + 40.3805i 1.14998 + 1.99182i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −5.65685 9.79796i −0.277684 0.480963i
\(416\) 0 0
\(417\) −1.70711 + 2.95680i −0.0835974 + 0.144795i
\(418\) 0 0
\(419\) −28.5858 −1.39651 −0.698254 0.715851i \(-0.746039\pi\)
−0.698254 + 0.715851i \(0.746039\pi\)
\(420\) 0 0
\(421\) −26.3137 −1.28245 −0.641226 0.767352i \(-0.721574\pi\)
−0.641226 + 0.767352i \(0.721574\pi\)
\(422\) 0 0
\(423\) −10.7279 + 18.5813i −0.521609 + 0.903454i
\(424\) 0 0
\(425\) −1.20711 2.09077i −0.0585533 0.101417i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.500000 0.866025i −0.0241402 0.0418121i
\(430\) 0 0
\(431\) −11.3284 + 19.6214i −0.545671 + 0.945130i 0.452893 + 0.891565i \(0.350392\pi\)
−0.998564 + 0.0535654i \(0.982941\pi\)
\(432\) 0 0
\(433\) 6.97056 0.334984 0.167492 0.985873i \(-0.446433\pi\)
0.167492 + 0.985873i \(0.446433\pi\)
\(434\) 0 0
\(435\) −2.41421 −0.115753
\(436\) 0 0
\(437\) −6.24264 + 10.8126i −0.298626 + 0.517235i
\(438\) 0 0
\(439\) 1.87868 + 3.25397i 0.0896645 + 0.155303i 0.907369 0.420334i \(-0.138087\pi\)
−0.817705 + 0.575638i \(0.804754\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.3848 + 30.1113i 0.825976 + 1.43063i 0.901171 + 0.433463i \(0.142709\pi\)
−0.0751957 + 0.997169i \(0.523958\pi\)
\(444\) 0 0
\(445\) 4.82843 8.36308i 0.228889 0.396448i
\(446\) 0 0
\(447\) −22.1421 −1.04729
\(448\) 0 0
\(449\) −27.4853 −1.29711 −0.648555 0.761168i \(-0.724626\pi\)
−0.648555 + 0.761168i \(0.724626\pi\)
\(450\) 0 0
\(451\) 2.29289 3.97141i 0.107968 0.187006i
\(452\) 0 0
\(453\) 8.03553 + 13.9180i 0.377542 + 0.653922i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2.46447 4.26858i −0.115283 0.199676i 0.802610 0.596504i \(-0.203444\pi\)
−0.917893 + 0.396828i \(0.870111\pi\)
\(458\) 0 0
\(459\) 0.500000 0.866025i 0.0233380 0.0404226i
\(460\) 0 0
\(461\) −32.2843 −1.50363 −0.751814 0.659375i \(-0.770821\pi\)
−0.751814 + 0.659375i \(0.770821\pi\)
\(462\) 0 0
\(463\) 25.4558 1.18303 0.591517 0.806293i \(-0.298529\pi\)
0.591517 + 0.806293i \(0.298529\pi\)
\(464\) 0 0
\(465\) 12.3640 21.4150i 0.573365 0.993097i
\(466\) 0 0
\(467\) −4.20711 7.28692i −0.194682 0.337199i 0.752114 0.659033i \(-0.229034\pi\)
−0.946796 + 0.321834i \(0.895701\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −12.6569 21.9223i −0.583197 1.01013i
\(472\) 0 0
\(473\) −5.82843 + 10.0951i −0.267991 + 0.464175i
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) 18.6274 0.852891
\(478\) 0 0
\(479\) 20.2635 35.0973i 0.925861 1.60364i 0.135690 0.990751i \(-0.456675\pi\)
0.790171 0.612887i \(-0.209992\pi\)
\(480\) 0 0
\(481\) 2.46447 + 4.26858i 0.112370 + 0.194631i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.03553 + 12.1859i 0.319467 + 0.553333i
\(486\) 0 0
\(487\) −0.636039 + 1.10165i −0.0288217 + 0.0499206i −0.880076 0.474832i \(-0.842509\pi\)
0.851255 + 0.524753i \(0.175842\pi\)
\(488\) 0 0
\(489\) 7.07107 0.319765
\(490\) 0 0
\(491\) −11.4853 −0.518323 −0.259162 0.965834i \(-0.583446\pi\)
−0.259162 + 0.965834i \(0.583446\pi\)
\(492\) 0 0
\(493\) −1.20711 + 2.09077i −0.0543654 + 0.0941636i
\(494\) 0 0
\(495\) −1.41421 2.44949i −0.0635642 0.110096i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 13.3995 + 23.2086i 0.599844 + 1.03896i 0.992844 + 0.119421i \(0.0381039\pi\)
−0.393000 + 0.919539i \(0.628563\pi\)
\(500\) 0 0
\(501\) −9.15685 + 15.8601i −0.409098 + 0.708579i
\(502\) 0 0
\(503\) −17.0416 −0.759849 −0.379924 0.925018i \(-0.624050\pi\)
−0.379924 + 0.925018i \(0.624050\pi\)
\(504\) 0 0
\(505\) −10.4853 −0.466589
\(506\) 0 0
\(507\) 15.4853 26.8213i 0.687725 1.19118i
\(508\) 0 0
\(509\) −8.12132 14.0665i −0.359971 0.623488i 0.627984 0.778226i \(-0.283880\pi\)
−0.987956 + 0.154738i \(0.950547\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0.414214 + 0.717439i 0.0182880 + 0.0316757i
\(514\) 0 0
\(515\) 3.37868 5.85204i 0.148882 0.257872i
\(516\) 0 0
\(517\) −7.58579 −0.333623
\(518\) 0 0
\(519\) −33.1421 −1.45478
\(520\) 0 0
\(521\) −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i \(-0.875291\pi\)
0.792797 + 0.609486i \(0.208624\pi\)
\(522\) 0 0
\(523\) 7.75736 + 13.4361i 0.339206 + 0.587521i 0.984284 0.176595i \(-0.0565084\pi\)
−0.645078 + 0.764117i \(0.723175\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.3640 21.4150i −0.538583 0.932852i
\(528\) 0 0
\(529\) −7.98528 + 13.8309i −0.347186 + 0.601344i
\(530\) 0 0
\(531\) 4.97056 0.215704
\(532\) 0 0
\(533\) −1.89949 −0.0822763
\(534\) 0 0
\(535\) −7.24264 + 12.5446i −0.313127 + 0.542351i
\(536\) 0 0
\(537\) −5.00000 8.66025i −0.215766 0.373718i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 6.15685 + 10.6640i 0.264704 + 0.458480i 0.967486 0.252925i \(-0.0813925\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(542\) 0 0
\(543\) 30.8492 53.4325i 1.32387 2.29301i
\(544\) 0 0
\(545\) 18.3137 0.784473
\(546\) 0 0
\(547\) 35.1127 1.50131 0.750655 0.660694i \(-0.229738\pi\)
0.750655 + 0.660694i \(0.229738\pi\)
\(548\) 0 0
\(549\) 9.65685 16.7262i 0.412144 0.713855i
\(550\) 0 0
\(551\) −1.00000 1.73205i −0.0426014 0.0737878i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 14.3640 + 24.8791i 0.609716 + 1.05606i
\(556\) 0 0
\(557\) −1.07107 + 1.85514i −0.0453826 + 0.0786050i −0.887824 0.460182i \(-0.847784\pi\)
0.842442 + 0.538787i \(0.181117\pi\)
\(558\) 0 0
\(559\) 4.82843 0.204221
\(560\) 0 0
\(561\) −5.82843 −0.246076
\(562\) 0 0
\(563\) −13.9706 + 24.1977i −0.588789 + 1.01981i 0.405602 + 0.914050i \(0.367062\pi\)
−0.994391 + 0.105763i \(0.966272\pi\)
\(564\) 0 0
\(565\) −4.53553 7.85578i −0.190811 0.330495i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17.0711 + 29.5680i 0.715656 + 1.23955i 0.962706 + 0.270550i \(0.0872057\pi\)
−0.247049 + 0.969003i \(0.579461\pi\)
\(570\) 0 0
\(571\) 11.7279 20.3134i 0.490798 0.850088i −0.509146 0.860680i \(-0.670039\pi\)
0.999944 + 0.0105929i \(0.00337187\pi\)
\(572\) 0 0
\(573\) 33.3848 1.39467
\(574\) 0 0
\(575\) 6.24264 0.260336
\(576\) 0 0
\(577\) 18.2071 31.5356i 0.757972 1.31285i −0.185912 0.982566i \(-0.559524\pi\)
0.943883 0.330279i \(-0.107143\pi\)
\(578\) 0 0
\(579\) −0.828427 1.43488i −0.0344283 0.0596315i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.29289 + 5.70346i 0.136378 + 0.236213i
\(584\) 0 0
\(585\) −0.585786 + 1.01461i −0.0242193 + 0.0419490i
\(586\) 0 0
\(587\) −13.8579 −0.571975 −0.285988 0.958233i \(-0.592322\pi\)
−0.285988 + 0.958233i \(0.592322\pi\)
\(588\) 0 0
\(589\) 20.4853 0.844081
\(590\) 0 0
\(591\) 14.7782 25.5965i 0.607893 1.05290i
\(592\) 0 0
\(593\) −4.72183 8.17844i −0.193902 0.335848i 0.752638 0.658435i \(-0.228781\pi\)
−0.946540 + 0.322586i \(0.895448\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14.9497 + 25.8937i 0.611852 + 1.05976i
\(598\) 0 0
\(599\) 18.1569 31.4486i 0.741869 1.28495i −0.209774 0.977750i \(-0.567273\pi\)
0.951643 0.307205i \(-0.0993937\pi\)
\(600\) 0 0
\(601\) −18.2843 −0.745831 −0.372915 0.927865i \(-0.621642\pi\)
−0.372915 + 0.927865i \(0.621642\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) −5.00000 + 8.66025i −0.203279 + 0.352089i
\(606\) 0 0
\(607\) −10.0355 17.3821i −0.407330 0.705516i 0.587260 0.809398i \(-0.300207\pi\)
−0.994590 + 0.103883i \(0.966873\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.57107 + 2.72117i 0.0635586 + 0.110087i
\(612\) 0 0
\(613\) −14.6569 + 25.3864i −0.591985 + 1.02535i 0.401980 + 0.915648i \(0.368322\pi\)
−0.993965 + 0.109699i \(0.965011\pi\)
\(614\) 0 0
\(615\) −11.0711 −0.446429
\(616\) 0 0
\(617\) −11.4142 −0.459519 −0.229759 0.973247i \(-0.573794\pi\)
−0.229759 + 0.973247i \(0.573794\pi\)
\(618\) 0 0
\(619\) 7.53553 13.0519i 0.302879 0.524601i −0.673908 0.738815i \(-0.735386\pi\)
0.976787 + 0.214214i \(0.0687190\pi\)
\(620\) 0 0
\(621\) 1.29289 + 2.23936i 0.0518820 + 0.0898623i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 2.41421 4.18154i 0.0964144 0.166995i
\(628\) 0 0
\(629\) 28.7279 1.14546
\(630\) 0 0
\(631\) −37.6274 −1.49792 −0.748962 0.662613i \(-0.769447\pi\)
−0.748962 + 0.662613i \(0.769447\pi\)
\(632\) 0 0
\(633\) −20.6924 + 35.8403i −0.822449 + 1.42452i
\(634\) 0 0
\(635\) 1.87868 + 3.25397i 0.0745531 + 0.129130i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3.51472 + 6.08767i 0.139040 + 0.240825i
\(640\) 0 0
\(641\) −16.1421 + 27.9590i −0.637576 + 1.10431i 0.348387 + 0.937351i \(0.386729\pi\)
−0.985963 + 0.166963i \(0.946604\pi\)
\(642\) 0 0
\(643\) −30.2132 −1.19149 −0.595746 0.803173i \(-0.703144\pi\)
−0.595746 + 0.803173i \(0.703144\pi\)
\(644\) 0 0
\(645\) 28.1421 1.10810
\(646\) 0 0
\(647\) −9.07107 + 15.7116i −0.356620 + 0.617685i −0.987394 0.158282i \(-0.949404\pi\)
0.630773 + 0.775967i \(0.282738\pi\)
\(648\) 0 0
\(649\) 0.878680 + 1.52192i 0.0344912 + 0.0597405i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.1421 + 19.2987i 0.436025 + 0.755218i 0.997379 0.0723580i \(-0.0230524\pi\)
−0.561353 + 0.827576i \(0.689719\pi\)
\(654\) 0 0
\(655\) 10.1213 17.5306i 0.395473 0.684979i
\(656\) 0 0
\(657\) −30.6274 −1.19489
\(658\) 0 0
\(659\) 17.4853 0.681130 0.340565 0.940221i \(-0.389382\pi\)
0.340565 + 0.940221i \(0.389382\pi\)
\(660\) 0 0
\(661\) 15.4142 26.6982i 0.599543 1.03844i −0.393345 0.919391i \(-0.628682\pi\)
0.992888 0.119049i \(-0.0379845\pi\)
\(662\) 0 0
\(663\) 1.20711 + 2.09077i 0.0468801 + 0.0811988i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.12132 5.40629i −0.120858 0.209332i
\(668\) 0 0
\(669\) 20.9853 36.3476i 0.811338 1.40528i
\(670\) 0 0
\(671\) 6.82843 0.263609
\(672\) 0 0
\(673\) 50.8284 1.95929 0.979646 0.200733i \(-0.0643324\pi\)
0.979646 + 0.200733i \(0.0643324\pi\)
\(674\) 0 0
\(675\) 0.207107 0.358719i 0.00797154 0.0138071i
\(676\) 0 0
\(677\) −18.0355 31.2385i −0.693162 1.20059i −0.970796 0.239905i \(-0.922884\pi\)
0.277635 0.960687i \(-0.410450\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.91421 3.31552i −0.0733528 0.127051i
\(682\) 0 0
\(683\) 6.58579 11.4069i 0.251998 0.436474i −0.712078 0.702101i \(-0.752246\pi\)
0.964076 + 0.265627i \(0.0855790\pi\)
\(684\) 0 0
\(685\) 19.3137 0.737939
\(686\) 0 0
\(687\) −9.89949 −0.377689
\(688\) 0 0
\(689\) 1.36396 2.36245i 0.0519628 0.0900022i
\(690\) 0 0
\(691\) −5.07107 8.78335i −0.192913 0.334134i 0.753302 0.657675i \(-0.228460\pi\)
−0.946214 + 0.323541i \(0.895127\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.707107 + 1.22474i 0.0268221 + 0.0464572i
\(696\) 0 0
\(697\) −5.53553 + 9.58783i −0.209673 + 0.363165i
\(698\) 0 0
\(699\) 8.48528 0.320943
\(700\) 0 0
\(701\) −37.1421 −1.40284 −0.701420 0.712749i \(-0.747450\pi\)
−0.701420 + 0.712749i \(0.747450\pi\)
\(702\) 0 0
\(703\) −11.8995 + 20.6105i −0.448798 + 0.777341i
\(704\) 0 0
\(705\) 9.15685 + 15.8601i 0.344867 + 0.597327i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 10.6716 + 18.4837i 0.400779 + 0.694170i 0.993820 0.111002i \(-0.0354061\pi\)
−0.593041 + 0.805172i \(0.702073\pi\)
\(710\) 0 0
\(711\) 4.72792 8.18900i 0.177311 0.307112i
\(712\) 0 0
\(713\) 63.9411 2.39461
\(714\) 0 0
\(715\) −0.414214 −0.0154907
\(716\) 0 0
\(717\) 5.62132 9.73641i 0.209932 0.363613i
\(718\) 0 0
\(719\) −24.8492 43.0402i −0.926720 1.60513i −0.788771 0.614688i \(-0.789282\pi\)
−0.137950 0.990439i \(-0.544051\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −12.5355 21.7122i −0.466202 0.807485i
\(724\) 0 0
\(725\) −0.500000 + 0.866025i −0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) 41.3137 1.53224 0.766120 0.642697i \(-0.222185\pi\)
0.766120 + 0.642697i \(0.222185\pi\)
\(728\) 0 0
\(729\) −23.8284 −0.882534
\(730\) 0 0
\(731\) 14.0711 24.3718i 0.520437 0.901424i
\(732\) 0 0
\(733\) 13.3492 + 23.1216i 0.493066 + 0.854015i 0.999968 0.00798883i \(-0.00254295\pi\)
−0.506903 + 0.862003i \(0.669210\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.707107 1.22474i −0.0260466 0.0451141i
\(738\) 0 0
\(739\) 2.39949 4.15605i 0.0882668 0.152883i −0.818512 0.574490i \(-0.805201\pi\)
0.906779 + 0.421607i \(0.138534\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) −5.89949 −0.216431 −0.108216 0.994127i \(-0.534514\pi\)
−0.108216 + 0.994127i \(0.534514\pi\)
\(744\) 0 0
\(745\) −4.58579 + 7.94282i −0.168010 + 0.291002i
\(746\) 0 0
\(747\) 16.0000 + 27.7128i 0.585409 + 1.01396i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −12.8137 22.1940i −0.467579 0.809870i 0.531735 0.846911i \(-0.321540\pi\)
−0.999314 + 0.0370405i \(0.988207\pi\)
\(752\) 0 0
\(753\) −9.12132 + 15.7986i −0.332399 + 0.575733i
\(754\) 0 0
\(755\) 6.65685 0.242268
\(756\) 0 0
\(757\) −36.7696 −1.33641 −0.668206 0.743976i \(-0.732938\pi\)
−0.668206 + 0.743976i \(0.732938\pi\)
\(758\) 0 0
\(759\) 7.53553 13.0519i 0.273523 0.473755i
\(760\) 0 0
\(761\) −2.22183 3.84831i −0.0805411 0.139501i 0.822941 0.568126i \(-0.192331\pi\)
−0.903482 + 0.428625i \(0.858998\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3.41421 + 5.91359i 0.123441 + 0.213806i
\(766\) 0 0
\(767\) 0.363961 0.630399i 0.0131419 0.0227624i
\(768\) 0 0
\(769\) −18.4853 −0.666596 −0.333298 0.942821i \(-0.608162\pi\)
−0.333298 + 0.942821i \(0.608162\pi\)
\(770\) 0 0
\(771\) 25.3137 0.911651
\(772\) 0 0
\(773\) 10.6924 18.5198i 0.384578 0.666109i −0.607132 0.794601i \(-0.707680\pi\)
0.991711 + 0.128491i \(0.0410135\pi\)
\(774\) 0 0
\(775\) −5.12132 8.87039i −0.183963 0.318634i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.58579 7.94282i −0.164303 0.284581i
\(780\) 0 0
\(781\) −1.24264 + 2.15232i −0.0444652 + 0.0770160i
\(782\) 0 0
\(783\) −0.414214 −0.0148028
\(784\) 0 0
\(785\) −10.4853 −0.374236
\(786\) 0 0
\(787\) 21.4203 37.1011i 0.763552 1.32251i −0.177457 0.984128i \(-0.556787\pi\)
0.941009 0.338382i \(-0.109879\pi\)
\(788\) 0 0
\(789\) −22.8995 39.6631i −0.815244 1.41204i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.41421 2.44949i −0.0502202 0.0869839i
\(794\) 0 0
\(795\) 7.94975 13.7694i 0.281948 0.488349i
\(796\) 0 0
\(797\) 35.9289 1.27267 0.636334 0.771414i \(-0.280450\pi\)
0.636334 + 0.771414i \(0.280450\pi\)
\(798\) 0 0
\(799\) 18.3137 0.647892
\(800\) 0