Properties

Label 1960.2.q.p.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: \(\Q(\sqrt{2}, \sqrt{-3})\)
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 961.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.p.361.1

$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.20711 2.09077i −0.696923 1.20711i −0.969528 0.244981i \(-0.921218\pi\)
0.272605 0.962126i \(-0.412115\pi\)
\(4\) 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 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) 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 0.681696 0.731635i \(-0.261242\pi\)
−0.974463 + 0.224549i \(0.927909\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.12132 + 5.40629i −0.650840 + 1.12729i 0.332079 + 0.943252i \(0.392250\pi\)
−0.982919 + 0.184037i \(0.941083\pi\)
\(24\) 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 −0.799693 0.600410i \(-0.795004\pi\)
−0.120124 0.992759i \(-0.538329\pi\)
\(32\) 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 −0.308948 + 0.951079i \(0.599977\pi\)
−0.669185 + 0.743096i \(0.733357\pi\)
\(38\) 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 0.444787 + 0.895636i \(0.353279\pi\)
−0.998037 + 0.0626213i \(0.980054\pi\)
\(48\) 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 0.546216 0.837645i \(-0.316068\pi\)
−0.998529 + 0.0542143i \(0.982735\pi\)
\(54\) 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 0.803143 0.595786i \(-0.203159\pi\)
−0.917537 + 0.397649i \(0.869826\pi\)
\(60\) 0 0
\(61\) 3.41421 5.91359i 0.437145 0.757158i −0.560323 0.828274i \(-0.689323\pi\)
0.997468 + 0.0711166i \(0.0226562\pi\)
\(62\) 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 0.905981 0.423318i \(-0.139135\pi\)
−0.819594 + 0.572944i \(0.805801\pi\)
\(68\) 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 0.986792 + 0.161993i \(0.0517921\pi\)
−0.353106 + 0.935583i \(0.614875\pi\)
\(74\) 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 −0.756539 0.653949i \(-0.773111\pi\)
0.944606 + 0.328208i \(0.106445\pi\)
\(80\) 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 0.488094 + 0.872791i \(0.337692\pi\)
−0.999906 + 0.0136937i \(0.995641\pi\)
\(90\) 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 −0.999683 0.0251967i \(-0.991979\pi\)
0.478020 0.878349i \(-0.341355\pi\)
\(102\) 0 0
\(103\) −3.37868 + 5.85204i −0.332911 + 0.576619i −0.983081 0.183170i \(-0.941364\pi\)
0.650170 + 0.759789i \(0.274698\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.24264 12.5446i 0.700173 1.21273i −0.268233 0.963354i \(-0.586440\pi\)
0.968406 0.249380i \(-0.0802269\pi\)
\(108\) 0 0
\(109\) 9.15685 + 15.8601i 0.877068 + 1.51913i 0.854544 + 0.519379i \(0.173837\pi\)
0.0225237 + 0.999746i \(0.492830\pi\)
\(110\) 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 −0.0377944 + 0.999286i \(0.512033\pi\)
−0.846509 + 0.532374i \(0.821300\pi\)
\(132\) 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 0.901888 + 0.431970i \(0.142181\pi\)
−0.0768474 + 0.997043i \(0.524485\pi\)
\(138\) 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 −0.614747 0.788725i \(-0.710742\pi\)
0.990429 + 0.138024i \(0.0440751\pi\)
\(150\) 0 0
\(151\) 3.32843 + 5.76500i 0.270864 + 0.469149i 0.969083 0.246734i \(-0.0793574\pi\)
−0.698220 + 0.715884i \(0.746024\pi\)
\(152\) 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 0.577371 0.816482i \(-0.304079\pi\)
−0.995780 + 0.0917773i \(0.970745\pi\)
\(158\) 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 −0.917662 0.397362i \(-0.869926\pi\)
0.802956 + 0.596038i \(0.203259\pi\)
\(164\) 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 −0.477819 0.878458i \(-0.658573\pi\)
0.999677 0.0254253i \(-0.00809399\pi\)
\(174\) 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 0.778187 0.628033i \(-0.216140\pi\)
−0.932986 + 0.359913i \(0.882806\pi\)
\(180\) 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 0.499705 + 0.866196i \(0.333442\pi\)
−1.00000 0.000340595i \(0.999892\pi\)
\(192\) 0 0
\(193\) −0.343146 0.594346i −0.0247002 0.0427820i 0.853411 0.521238i \(-0.174530\pi\)
−0.878111 + 0.478456i \(0.841196\pi\)
\(194\) 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 0.997610 0.0690953i \(-0.0220113\pi\)
−0.558643 + 0.829408i \(0.688678\pi\)
\(200\) 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 0.838512 0.544883i \(-0.183426\pi\)
−0.891138 + 0.453732i \(0.850093\pi\)
\(228\) 0 0
\(229\) 2.05025 3.55114i 0.135485 0.234666i −0.790298 0.612723i \(-0.790074\pi\)
0.925782 + 0.378057i \(0.123408\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.75736 + 3.04384i −0.115128 + 0.199408i −0.917831 0.396971i \(-0.870061\pi\)
0.802703 + 0.596379i \(0.203395\pi\)
\(234\) 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 0.648912 0.760863i \(-0.275224\pi\)
−0.983383 + 0.181543i \(0.941891\pi\)
\(242\) 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 −0.981920 0.189294i \(-0.939380\pi\)
0.654894 + 0.755721i \(0.272713\pi\)
\(258\) 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 −0.994889 0.100970i \(-0.967805\pi\)
0.410002 0.912085i \(-0.365528\pi\)
\(264\) 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 −0.996899 0.0786907i \(-0.974926\pi\)
0.430301 0.902685i \(-0.358407\pi\)
\(270\) 0 0
\(271\) −1.17157 + 2.02922i −0.0711680 + 0.123267i −0.899413 0.437099i \(-0.856006\pi\)
0.828245 + 0.560365i \(0.189339\pi\)
\(272\) 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 0.992802 0.119764i \(-0.0382139\pi\)
−0.600120 + 0.799910i \(0.704881\pi\)
\(278\) 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 −0.950528 0.310639i \(-0.899457\pi\)
0.206243 0.978501i \(-0.433876\pi\)
\(284\) 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 0.688726 0.725022i \(-0.258170\pi\)
−0.972250 + 0.233944i \(0.924837\pi\)
\(312\) 0 0
\(313\) 11.8640 20.5490i 0.670591 1.16150i −0.307146 0.951662i \(-0.599374\pi\)
0.977737 0.209835i \(-0.0672926\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.17157 + 10.6895i −0.346630 + 0.600381i −0.985649 0.168811i \(-0.946007\pi\)
0.639018 + 0.769191i \(0.279341\pi\)
\(318\) 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 −0.966638 0.256148i \(-0.917547\pi\)
0.705149 + 0.709059i \(0.250880\pi\)
\(332\) 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 −0.934843 0.355060i \(-0.884460\pi\)
0.159930 0.987128i \(-0.448873\pi\)
\(348\) 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 −0.916935 0.399037i \(-0.869345\pi\)
0.112892 0.993607i \(-0.463989\pi\)
\(354\) 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 −0.147799 0.989017i \(-0.547219\pi\)
0.930414 0.366511i \(-0.119448\pi\)
\(360\) 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 0.681188 0.732108i \(-0.261464\pi\)
−0.974619 + 0.223872i \(0.928130\pi\)
\(368\) 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 0.403092 + 0.915160i \(0.367936\pi\)
−0.994097 + 0.108492i \(0.965398\pi\)
\(374\) 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 0.411853 + 0.911250i \(0.364882\pi\)
−0.995092 + 0.0989496i \(0.968452\pi\)
\(384\) 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 0.696058 0.717986i \(-0.254936\pi\)
−0.969823 + 0.243811i \(0.921602\pi\)
\(390\) 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 −0.787390 0.616456i \(-0.788568\pi\)
0.927561 + 0.373672i \(0.121901\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.2279 21.1794i 0.610633 1.05765i −0.380501 0.924781i \(-0.624248\pi\)
0.991134 0.132867i \(-0.0424184\pi\)
\(402\) 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 0.906671 + 0.421839i \(0.138615\pi\)
−0.0880119 + 0.996119i \(0.528051\pi\)
\(410\) 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 −0.998564 0.0535654i \(-0.982941\pi\)
0.452893 0.891565i \(-0.350392\pi\)
\(432\) 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 −0.817705 0.575638i \(-0.804754\pi\)
0.907369 + 0.420334i \(0.138087\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.3848 30.1113i 0.825976 1.43063i −0.0751957 0.997169i \(-0.523958\pi\)
0.901171 0.433463i \(-0.142709\pi\)
\(444\) 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 −0.917893 0.396828i \(-0.870111\pi\)
0.802610 + 0.596504i \(0.203444\pi\)
\(458\) 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 −0.946796 0.321834i \(-0.895701\pi\)
0.752114 + 0.659033i \(0.229034\pi\)
\(468\) 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 0.790171 + 0.612887i \(0.209992\pi\)
0.135690 + 0.990751i \(0.456675\pi\)
\(480\) 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 0.851255 0.524753i \(-0.175842\pi\)
−0.880076 + 0.474832i \(0.842509\pi\)
\(488\) 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 −0.393000 0.919539i \(-0.628563\pi\)
0.992844 0.119421i \(-0.0381039\pi\)
\(500\) 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 −0.987956 0.154738i \(-0.950547\pi\)
0.627984 + 0.778226i \(0.283880\pi\)
\(510\) 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 0.792797 0.609486i \(-0.208624\pi\)
−0.924229 + 0.381839i \(0.875291\pi\)
\(522\) 0 0
\(523\) 7.75736 13.4361i 0.339206 0.587521i −0.645078 0.764117i \(-0.723175\pi\)
0.984284 + 0.176595i \(0.0565084\pi\)
\(524\) 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 −0.702782 0.711405i \(-0.748059\pi\)
0.967486 + 0.252925i \(0.0813925\pi\)
\(542\) 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 0.842442 0.538787i \(-0.181117\pi\)
−0.887824 + 0.460182i \(0.847784\pi\)
\(558\) 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 −0.994391 0.105763i \(-0.966272\pi\)
0.405602 0.914050i \(-0.367062\pi\)
\(564\) 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 −0.247049 0.969003i \(-0.579461\pi\)
0.962706 0.270550i \(-0.0872057\pi\)
\(570\) 0 0
\(571\) 11.7279 + 20.3134i 0.490798 + 0.850088i 0.999944 0.0105929i \(-0.00337187\pi\)
−0.509146 + 0.860680i \(0.670039\pi\)
\(572\) 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 0.943883 + 0.330279i \(0.107143\pi\)
−0.185912 + 0.982566i \(0.559524\pi\)
\(578\) 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 −0.946540 0.322586i \(-0.895448\pi\)
0.752638 + 0.658435i \(0.228781\pi\)
\(594\) 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 0.951643 + 0.307205i \(0.0993937\pi\)
−0.209774 + 0.977750i \(0.567273\pi\)
\(600\) 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 −0.994590 0.103883i \(-0.966873\pi\)
0.587260 + 0.809398i \(0.300207\pi\)
\(608\) 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 −0.993965 0.109699i \(-0.965011\pi\)
0.401980 0.915648i \(-0.368322\pi\)
\(614\) 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 0.976787 0.214214i \(-0.0687190\pi\)
−0.673908 + 0.738815i \(0.735386\pi\)
\(620\) 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 −0.985963 0.166963i \(-0.946604\pi\)
0.348387 0.937351i \(-0.386729\pi\)
\(642\) 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 0.630773 0.775967i \(-0.282738\pi\)
−0.987394 + 0.158282i \(0.949404\pi\)
\(648\) 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 −0.561353 0.827576i \(-0.689719\pi\)
0.997379 + 0.0723580i \(0.0230524\pi\)
\(654\) 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 0.992888 + 0.119049i \(0.0379845\pi\)
−0.393345 + 0.919391i \(0.628682\pi\)
\(662\) 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 0.277635 + 0.960687i \(0.410450\pi\)
−0.970796 + 0.239905i \(0.922884\pi\)
\(678\) 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 0.964076 0.265627i \(-0.0855790\pi\)
−0.712078 + 0.702101i \(0.752246\pi\)
\(684\) 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 −0.946214 0.323541i \(-0.895127\pi\)
0.753302 + 0.657675i \(0.228460\pi\)
\(692\) 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 −0.593041 0.805172i \(-0.702073\pi\)
0.993820 + 0.111002i \(0.0354061\pi\)
\(710\) 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 −0.137950 + 0.990439i \(0.544051\pi\)
−0.788771 + 0.614688i \(0.789282\pi\)
\(720\) 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 −0.506903 0.862003i \(-0.669210\pi\)
0.999968 + 0.00798883i \(0.00254295\pi\)
\(734\) 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 0.906779 0.421607i \(-0.138534\pi\)
−0.818512 + 0.574490i \(0.805201\pi\)
\(740\) 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 −0.999314 0.0370405i \(-0.988207\pi\)
0.531735 + 0.846911i \(0.321540\pi\)
\(752\) 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 −0.903482 0.428625i \(-0.858998\pi\)
0.822941 + 0.568126i \(0.192331\pi\)
\(762\) 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 0.991711 0.128491i \(-0.0410135\pi\)
−0.607132 + 0.794601i \(0.707680\pi\)
\(774\) 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 0.941009 + 0.338382i \(0.109879\pi\)
−0.177457 + 0.984128i \(0.556787\pi\)
\(788\) 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