Properties

Label 1456.2.s.h.1121.2
Level $1456$
Weight $2$
Character 1456.1121
Analytic conductor $11.626$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1121.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1456.1121
Dual form 1456.2.s.h.113.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 - 0.330792i) q^{3} +0.381966 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.330792i) q^{3} +0.381966 q^{5} +(0.500000 - 0.866025i) q^{7} +(1.42705 - 2.47172i) q^{9} +(-2.42705 - 4.20378i) q^{11} +(-2.50000 - 2.59808i) q^{13} +(-0.0729490 - 0.126351i) q^{15} +(-3.73607 + 6.47106i) q^{17} +(2.42705 - 4.20378i) q^{19} -0.381966 q^{21} +(2.23607 + 3.87298i) q^{23} -4.85410 q^{25} -2.23607 q^{27} +(2.04508 + 3.54219i) q^{29} -8.70820 q^{31} +(-0.927051 + 1.60570i) q^{33} +(0.190983 - 0.330792i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(-0.381966 + 1.32317i) q^{39} +(-2.61803 - 4.53457i) q^{41} +(-3.78115 + 6.54915i) q^{43} +(0.545085 - 0.944115i) q^{45} -2.23607 q^{47} +(-0.500000 - 0.866025i) q^{49} +2.85410 q^{51} +8.23607 q^{53} +(-0.927051 - 1.60570i) q^{55} -1.85410 q^{57} +(1.11803 - 1.93649i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-1.42705 - 2.47172i) q^{63} +(-0.954915 - 0.992377i) q^{65} +(0.354102 + 0.613323i) q^{67} +(0.854102 - 1.47935i) q^{69} +(4.09017 - 7.08438i) q^{71} -2.00000 q^{73} +(0.927051 + 1.60570i) q^{75} -4.85410 q^{77} -4.00000 q^{79} +(-3.85410 - 6.67550i) q^{81} +6.70820 q^{83} +(-1.42705 + 2.47172i) q^{85} +(0.781153 - 1.35300i) q^{87} +(-8.04508 - 13.9345i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(1.66312 + 2.88061i) q^{93} +(0.927051 - 1.60570i) q^{95} +(-6.07295 + 10.5187i) q^{97} -13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} + O(q^{10}) \) \( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} - 3 q^{11} - 10 q^{13} - 7 q^{15} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 6 q^{25} - 3 q^{29} - 8 q^{31} + 3 q^{33} + 3 q^{35} - 8 q^{37} - 6 q^{39} - 6 q^{41} + 5 q^{43} - 9 q^{45} - 2 q^{49} - 2 q^{51} + 24 q^{53} + 3 q^{55} + 6 q^{57} + 12 q^{61} + q^{63} - 15 q^{65} - 12 q^{67} - 10 q^{69} - 6 q^{71} - 8 q^{73} - 3 q^{75} - 6 q^{77} - 16 q^{79} - 2 q^{81} + q^{85} - 17 q^{87} - 21 q^{89} - 14 q^{91} - 9 q^{93} - 3 q^{95} - 31 q^{97} - 42 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −0.190983 0.330792i −0.110264 0.190983i 0.805613 0.592443i \(-0.201836\pi\)
−0.915877 + 0.401460i \(0.868503\pi\)
\(4\) 0 0
\(5\) 0.381966 0.170820 0.0854102 0.996346i \(-0.472780\pi\)
0.0854102 + 0.996346i \(0.472780\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) 1.42705 2.47172i 0.475684 0.823908i
\(10\) 0 0
\(11\) −2.42705 4.20378i −0.731783 1.26749i −0.956120 0.292974i \(-0.905355\pi\)
0.224337 0.974512i \(-0.427978\pi\)
\(12\) 0 0
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) 0 0
\(15\) −0.0729490 0.126351i −0.0188354 0.0326238i
\(16\) 0 0
\(17\) −3.73607 + 6.47106i −0.906130 + 1.56946i −0.0867359 + 0.996231i \(0.527644\pi\)
−0.819394 + 0.573231i \(0.805690\pi\)
\(18\) 0 0
\(19\) 2.42705 4.20378i 0.556804 0.964412i −0.440957 0.897528i \(-0.645361\pi\)
0.997761 0.0668841i \(-0.0213058\pi\)
\(20\) 0 0
\(21\) −0.381966 −0.0833518
\(22\) 0 0
\(23\) 2.23607 + 3.87298i 0.466252 + 0.807573i 0.999257 0.0385394i \(-0.0122705\pi\)
−0.533005 + 0.846112i \(0.678937\pi\)
\(24\) 0 0
\(25\) −4.85410 −0.970820
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) 2.04508 + 3.54219i 0.379763 + 0.657768i 0.991028 0.133658i \(-0.0426723\pi\)
−0.611265 + 0.791426i \(0.709339\pi\)
\(30\) 0 0
\(31\) −8.70820 −1.56404 −0.782020 0.623254i \(-0.785810\pi\)
−0.782020 + 0.623254i \(0.785810\pi\)
\(32\) 0 0
\(33\) −0.927051 + 1.60570i −0.161379 + 0.279516i
\(34\) 0 0
\(35\) 0.190983 0.330792i 0.0322820 0.0559141i
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 0 0
\(39\) −0.381966 + 1.32317i −0.0611635 + 0.211877i
\(40\) 0 0
\(41\) −2.61803 4.53457i −0.408868 0.708181i 0.585895 0.810387i \(-0.300743\pi\)
−0.994763 + 0.102206i \(0.967410\pi\)
\(42\) 0 0
\(43\) −3.78115 + 6.54915i −0.576620 + 0.998736i 0.419243 + 0.907874i \(0.362296\pi\)
−0.995864 + 0.0908618i \(0.971038\pi\)
\(44\) 0 0
\(45\) 0.545085 0.944115i 0.0812565 0.140740i
\(46\) 0 0
\(47\) −2.23607 −0.326164 −0.163082 0.986613i \(-0.552144\pi\)
−0.163082 + 0.986613i \(0.552144\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 2.85410 0.399654
\(52\) 0 0
\(53\) 8.23607 1.13131 0.565655 0.824642i \(-0.308623\pi\)
0.565655 + 0.824642i \(0.308623\pi\)
\(54\) 0 0
\(55\) −0.927051 1.60570i −0.125004 0.216512i
\(56\) 0 0
\(57\) −1.85410 −0.245582
\(58\) 0 0
\(59\) 1.11803 1.93649i 0.145556 0.252110i −0.784024 0.620730i \(-0.786836\pi\)
0.929580 + 0.368620i \(0.120170\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 0 0
\(63\) −1.42705 2.47172i −0.179792 0.311408i
\(64\) 0 0
\(65\) −0.954915 0.992377i −0.118443 0.123089i
\(66\) 0 0
\(67\) 0.354102 + 0.613323i 0.0432604 + 0.0749293i 0.886845 0.462067i \(-0.152892\pi\)
−0.843584 + 0.536997i \(0.819559\pi\)
\(68\) 0 0
\(69\) 0.854102 1.47935i 0.102822 0.178093i
\(70\) 0 0
\(71\) 4.09017 7.08438i 0.485414 0.840761i −0.514446 0.857523i \(-0.672002\pi\)
0.999860 + 0.0167615i \(0.00533560\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0.927051 + 1.60570i 0.107047 + 0.185410i
\(76\) 0 0
\(77\) −4.85410 −0.553176
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −3.85410 6.67550i −0.428234 0.741722i
\(82\) 0 0
\(83\) 6.70820 0.736321 0.368161 0.929762i \(-0.379988\pi\)
0.368161 + 0.929762i \(0.379988\pi\)
\(84\) 0 0
\(85\) −1.42705 + 2.47172i −0.154785 + 0.268096i
\(86\) 0 0
\(87\) 0.781153 1.35300i 0.0837484 0.145056i
\(88\) 0 0
\(89\) −8.04508 13.9345i −0.852777 1.47705i −0.878692 0.477389i \(-0.841583\pi\)
0.0259145 0.999664i \(-0.491750\pi\)
\(90\) 0 0
\(91\) −3.50000 + 0.866025i −0.366900 + 0.0907841i
\(92\) 0 0
\(93\) 1.66312 + 2.88061i 0.172457 + 0.298705i
\(94\) 0 0
\(95\) 0.927051 1.60570i 0.0951134 0.164741i
\(96\) 0 0
\(97\) −6.07295 + 10.5187i −0.616615 + 1.06801i 0.373484 + 0.927636i \(0.378163\pi\)
−0.990099 + 0.140371i \(0.955170\pi\)
\(98\) 0 0
\(99\) −13.8541 −1.39239
\(100\) 0 0
\(101\) −4.28115 7.41517i −0.425991 0.737837i 0.570522 0.821283i \(-0.306741\pi\)
−0.996512 + 0.0834451i \(0.973408\pi\)
\(102\) 0 0
\(103\) −4.70820 −0.463913 −0.231957 0.972726i \(-0.574513\pi\)
−0.231957 + 0.972726i \(0.574513\pi\)
\(104\) 0 0
\(105\) −0.145898 −0.0142382
\(106\) 0 0
\(107\) −2.80902 4.86536i −0.271558 0.470352i 0.697703 0.716387i \(-0.254206\pi\)
−0.969261 + 0.246035i \(0.920872\pi\)
\(108\) 0 0
\(109\) 10.7082 1.02566 0.512830 0.858490i \(-0.328597\pi\)
0.512830 + 0.858490i \(0.328597\pi\)
\(110\) 0 0
\(111\) −0.763932 + 1.32317i −0.0725092 + 0.125590i
\(112\) 0 0
\(113\) 3.73607 6.47106i 0.351460 0.608746i −0.635046 0.772475i \(-0.719019\pi\)
0.986505 + 0.163728i \(0.0523521\pi\)
\(114\) 0 0
\(115\) 0.854102 + 1.47935i 0.0796454 + 0.137950i
\(116\) 0 0
\(117\) −9.98936 + 2.47172i −0.923516 + 0.228511i
\(118\) 0 0
\(119\) 3.73607 + 6.47106i 0.342485 + 0.593201i
\(120\) 0 0
\(121\) −6.28115 + 10.8793i −0.571014 + 0.989025i
\(122\) 0 0
\(123\) −1.00000 + 1.73205i −0.0901670 + 0.156174i
\(124\) 0 0
\(125\) −3.76393 −0.336656
\(126\) 0 0
\(127\) −7.07295 12.2507i −0.627623 1.08707i −0.988027 0.154278i \(-0.950695\pi\)
0.360405 0.932796i \(-0.382639\pi\)
\(128\) 0 0
\(129\) 2.88854 0.254322
\(130\) 0 0
\(131\) −0.326238 −0.0285035 −0.0142518 0.999898i \(-0.504537\pi\)
−0.0142518 + 0.999898i \(0.504537\pi\)
\(132\) 0 0
\(133\) −2.42705 4.20378i −0.210452 0.364514i
\(134\) 0 0
\(135\) −0.854102 −0.0735094
\(136\) 0 0
\(137\) 0.190983 0.330792i 0.0163168 0.0282615i −0.857752 0.514064i \(-0.828139\pi\)
0.874069 + 0.485803i \(0.161473\pi\)
\(138\) 0 0
\(139\) −7.78115 + 13.4774i −0.659989 + 1.14313i 0.320629 + 0.947205i \(0.396106\pi\)
−0.980618 + 0.195929i \(0.937228\pi\)
\(140\) 0 0
\(141\) 0.427051 + 0.739674i 0.0359642 + 0.0622918i
\(142\) 0 0
\(143\) −4.85410 + 16.8151i −0.405920 + 1.40615i
\(144\) 0 0
\(145\) 0.781153 + 1.35300i 0.0648712 + 0.112360i
\(146\) 0 0
\(147\) −0.190983 + 0.330792i −0.0157520 + 0.0272833i
\(148\) 0 0
\(149\) 2.42705 4.20378i 0.198832 0.344387i −0.749318 0.662210i \(-0.769619\pi\)
0.948150 + 0.317823i \(0.102952\pi\)
\(150\) 0 0
\(151\) 14.7082 1.19694 0.598468 0.801146i \(-0.295776\pi\)
0.598468 + 0.801146i \(0.295776\pi\)
\(152\) 0 0
\(153\) 10.6631 + 18.4691i 0.862062 + 1.49314i
\(154\) 0 0
\(155\) −3.32624 −0.267170
\(156\) 0 0
\(157\) 8.14590 0.650113 0.325057 0.945695i \(-0.394617\pi\)
0.325057 + 0.945695i \(0.394617\pi\)
\(158\) 0 0
\(159\) −1.57295 2.72443i −0.124743 0.216061i
\(160\) 0 0
\(161\) 4.47214 0.352454
\(162\) 0 0
\(163\) 4.85410 8.40755i 0.380203 0.658530i −0.610888 0.791717i \(-0.709188\pi\)
0.991091 + 0.133186i \(0.0425209\pi\)
\(164\) 0 0
\(165\) −0.354102 + 0.613323i −0.0275668 + 0.0477471i
\(166\) 0 0
\(167\) 4.88197 + 8.45581i 0.377778 + 0.654330i 0.990739 0.135783i \(-0.0433550\pi\)
−0.612961 + 0.790113i \(0.710022\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) −6.92705 11.9980i −0.529725 0.917510i
\(172\) 0 0
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 0 0
\(175\) −2.42705 + 4.20378i −0.183468 + 0.317776i
\(176\) 0 0
\(177\) −0.854102 −0.0641982
\(178\) 0 0
\(179\) −4.50000 7.79423i −0.336346 0.582568i 0.647397 0.762153i \(-0.275858\pi\)
−0.983742 + 0.179585i \(0.942524\pi\)
\(180\) 0 0
\(181\) −3.70820 −0.275629 −0.137814 0.990458i \(-0.544008\pi\)
−0.137814 + 0.990458i \(0.544008\pi\)
\(182\) 0 0
\(183\) −2.29180 −0.169414
\(184\) 0 0
\(185\) −0.763932 1.32317i −0.0561654 0.0972813i
\(186\) 0 0
\(187\) 36.2705 2.65236
\(188\) 0 0
\(189\) −1.11803 + 1.93649i −0.0813250 + 0.140859i
\(190\) 0 0
\(191\) 11.8090 20.4538i 0.854470 1.47999i −0.0226649 0.999743i \(-0.507215\pi\)
0.877135 0.480243i \(-0.159452\pi\)
\(192\) 0 0
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) 0 0
\(195\) −0.145898 + 0.505406i −0.0104480 + 0.0361928i
\(196\) 0 0
\(197\) −3.89919 6.75359i −0.277806 0.481173i 0.693034 0.720905i \(-0.256274\pi\)
−0.970839 + 0.239732i \(0.922940\pi\)
\(198\) 0 0
\(199\) 1.20820 2.09267i 0.0856473 0.148345i −0.820020 0.572336i \(-0.806038\pi\)
0.905667 + 0.423990i \(0.139371\pi\)
\(200\) 0 0
\(201\) 0.135255 0.234268i 0.00954015 0.0165240i
\(202\) 0 0
\(203\) 4.09017 0.287074
\(204\) 0 0
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 0 0
\(207\) 12.7639 0.887155
\(208\) 0 0
\(209\) −23.5623 −1.62984
\(210\) 0 0
\(211\) −4.35410 7.54153i −0.299749 0.519180i 0.676330 0.736599i \(-0.263570\pi\)
−0.976078 + 0.217419i \(0.930236\pi\)
\(212\) 0 0
\(213\) −3.12461 −0.214095
\(214\) 0 0
\(215\) −1.44427 + 2.50155i −0.0984985 + 0.170604i
\(216\) 0 0
\(217\) −4.35410 + 7.54153i −0.295576 + 0.511952i
\(218\) 0 0
\(219\) 0.381966 + 0.661585i 0.0258109 + 0.0447057i
\(220\) 0 0
\(221\) 26.1525 6.47106i 1.75921 0.435291i
\(222\) 0 0
\(223\) −6.63525 11.4926i −0.444330 0.769601i 0.553676 0.832732i \(-0.313225\pi\)
−0.998005 + 0.0631310i \(0.979891\pi\)
\(224\) 0 0
\(225\) −6.92705 + 11.9980i −0.461803 + 0.799867i
\(226\) 0 0
\(227\) −3.73607 + 6.47106i −0.247972 + 0.429499i −0.962963 0.269634i \(-0.913097\pi\)
0.714991 + 0.699133i \(0.246431\pi\)
\(228\) 0 0
\(229\) 27.1246 1.79244 0.896222 0.443605i \(-0.146301\pi\)
0.896222 + 0.443605i \(0.146301\pi\)
\(230\) 0 0
\(231\) 0.927051 + 1.60570i 0.0609955 + 0.105647i
\(232\) 0 0
\(233\) 0.381966 0.0250234 0.0125117 0.999922i \(-0.496017\pi\)
0.0125117 + 0.999922i \(0.496017\pi\)
\(234\) 0 0
\(235\) −0.854102 −0.0557155
\(236\) 0 0
\(237\) 0.763932 + 1.32317i 0.0496227 + 0.0859491i
\(238\) 0 0
\(239\) 11.2918 0.730406 0.365203 0.930928i \(-0.381000\pi\)
0.365203 + 0.930928i \(0.381000\pi\)
\(240\) 0 0
\(241\) −2.21885 + 3.84316i −0.142929 + 0.247559i −0.928598 0.371087i \(-0.878985\pi\)
0.785670 + 0.618646i \(0.212319\pi\)
\(242\) 0 0
\(243\) −4.82624 + 8.35929i −0.309603 + 0.536249i
\(244\) 0 0
\(245\) −0.190983 0.330792i −0.0122015 0.0211335i
\(246\) 0 0
\(247\) −16.9894 + 4.20378i −1.08101 + 0.267480i
\(248\) 0 0
\(249\) −1.28115 2.21902i −0.0811898 0.140625i
\(250\) 0 0
\(251\) 2.61803 4.53457i 0.165249 0.286219i −0.771495 0.636236i \(-0.780491\pi\)
0.936744 + 0.350016i \(0.113824\pi\)
\(252\) 0 0
\(253\) 10.8541 18.7999i 0.682392 1.18194i
\(254\) 0 0
\(255\) 1.09017 0.0682691
\(256\) 0 0
\(257\) 12.8713 + 22.2938i 0.802891 + 1.39065i 0.917706 + 0.397261i \(0.130039\pi\)
−0.114815 + 0.993387i \(0.536627\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) 11.6738 0.722588
\(262\) 0 0
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 0 0
\(265\) 3.14590 0.193251
\(266\) 0 0
\(267\) −3.07295 + 5.32250i −0.188061 + 0.325732i
\(268\) 0 0
\(269\) −6.87132 + 11.9015i −0.418952 + 0.725646i −0.995834 0.0911812i \(-0.970936\pi\)
0.576882 + 0.816827i \(0.304269\pi\)
\(270\) 0 0
\(271\) 9.20820 + 15.9491i 0.559359 + 0.968837i 0.997550 + 0.0699558i \(0.0222858\pi\)
−0.438192 + 0.898882i \(0.644381\pi\)
\(272\) 0 0
\(273\) 0.954915 + 0.992377i 0.0577941 + 0.0600614i
\(274\) 0 0
\(275\) 11.7812 + 20.4056i 0.710430 + 1.23050i
\(276\) 0 0
\(277\) 2.50000 4.33013i 0.150210 0.260172i −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) 0 0
\(279\) −12.4271 + 21.5243i −0.743988 + 1.28863i
\(280\) 0 0
\(281\) −2.18034 −0.130068 −0.0650341 0.997883i \(-0.520716\pi\)
−0.0650341 + 0.997883i \(0.520716\pi\)
\(282\) 0 0
\(283\) −6.70820 11.6190i −0.398761 0.690675i 0.594812 0.803865i \(-0.297226\pi\)
−0.993573 + 0.113190i \(0.963893\pi\)
\(284\) 0 0
\(285\) −0.708204 −0.0419504
\(286\) 0 0
\(287\) −5.23607 −0.309075
\(288\) 0 0
\(289\) −19.4164 33.6302i −1.14214 1.97825i
\(290\) 0 0
\(291\) 4.63932 0.271962
\(292\) 0 0
\(293\) 5.61803 9.73072i 0.328209 0.568475i −0.653947 0.756540i \(-0.726888\pi\)
0.982157 + 0.188065i \(0.0602216\pi\)
\(294\) 0 0
\(295\) 0.427051 0.739674i 0.0248639 0.0430655i
\(296\) 0 0
\(297\) 5.42705 + 9.39993i 0.314909 + 0.545439i
\(298\) 0 0
\(299\) 4.47214 15.4919i 0.258630 0.895922i
\(300\) 0 0
\(301\) 3.78115 + 6.54915i 0.217942 + 0.377487i
\(302\) 0 0
\(303\) −1.63525 + 2.83234i −0.0939429 + 0.162714i
\(304\) 0 0
\(305\) 1.14590 1.98475i 0.0656139 0.113647i
\(306\) 0 0
\(307\) −1.85410 −0.105819 −0.0529096 0.998599i \(-0.516850\pi\)
−0.0529096 + 0.998599i \(0.516850\pi\)
\(308\) 0 0
\(309\) 0.899187 + 1.55744i 0.0511530 + 0.0885995i
\(310\) 0 0
\(311\) 12.3262 0.698957 0.349478 0.936944i \(-0.386359\pi\)
0.349478 + 0.936944i \(0.386359\pi\)
\(312\) 0 0
\(313\) −15.1246 −0.854894 −0.427447 0.904041i \(-0.640587\pi\)
−0.427447 + 0.904041i \(0.640587\pi\)
\(314\) 0 0
\(315\) −0.545085 0.944115i −0.0307121 0.0531948i
\(316\) 0 0
\(317\) 21.7639 1.22238 0.611192 0.791482i \(-0.290690\pi\)
0.611192 + 0.791482i \(0.290690\pi\)
\(318\) 0 0
\(319\) 9.92705 17.1942i 0.555808 0.962688i
\(320\) 0 0
\(321\) −1.07295 + 1.85840i −0.0598862 + 0.103726i
\(322\) 0 0
\(323\) 18.1353 + 31.4112i 1.00907 + 1.74776i
\(324\) 0 0
\(325\) 12.1353 + 12.6113i 0.673143 + 0.699551i
\(326\) 0 0
\(327\) −2.04508 3.54219i −0.113093 0.195884i
\(328\) 0 0
\(329\) −1.11803 + 1.93649i −0.0616392 + 0.106762i
\(330\) 0 0
\(331\) −8.42705 + 14.5961i −0.463193 + 0.802273i −0.999118 0.0419923i \(-0.986630\pi\)
0.535925 + 0.844265i \(0.319963\pi\)
\(332\) 0 0
\(333\) −11.4164 −0.625615
\(334\) 0 0
\(335\) 0.135255 + 0.234268i 0.00738977 + 0.0127994i
\(336\) 0 0
\(337\) 8.56231 0.466419 0.233209 0.972427i \(-0.425077\pi\)
0.233209 + 0.972427i \(0.425077\pi\)
\(338\) 0 0
\(339\) −2.85410 −0.155014
\(340\) 0 0
\(341\) 21.1353 + 36.6073i 1.14454 + 1.98240i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.326238 0.565061i 0.0175641 0.0304218i
\(346\) 0 0
\(347\) 17.6180 30.5153i 0.945786 1.63815i 0.191615 0.981470i \(-0.438627\pi\)
0.754171 0.656679i \(-0.228039\pi\)
\(348\) 0 0
\(349\) −3.64590 6.31488i −0.195160 0.338028i 0.751793 0.659400i \(-0.229189\pi\)
−0.946953 + 0.321372i \(0.895856\pi\)
\(350\) 0 0
\(351\) 5.59017 + 5.80948i 0.298381 + 0.310087i
\(352\) 0 0
\(353\) −14.4271 24.9884i −0.767874 1.33000i −0.938713 0.344699i \(-0.887981\pi\)
0.170839 0.985299i \(-0.445352\pi\)
\(354\) 0 0
\(355\) 1.56231 2.70599i 0.0829186 0.143619i
\(356\) 0 0
\(357\) 1.42705 2.47172i 0.0755275 0.130818i
\(358\) 0 0
\(359\) 10.9098 0.575799 0.287899 0.957661i \(-0.407043\pi\)
0.287899 + 0.957661i \(0.407043\pi\)
\(360\) 0 0
\(361\) −2.28115 3.95107i −0.120061 0.207951i
\(362\) 0 0
\(363\) 4.79837 0.251849
\(364\) 0 0
\(365\) −0.763932 −0.0399860
\(366\) 0 0
\(367\) 12.7082 + 22.0113i 0.663363 + 1.14898i 0.979726 + 0.200340i \(0.0642047\pi\)
−0.316364 + 0.948638i \(0.602462\pi\)
\(368\) 0 0
\(369\) −14.9443 −0.777968
\(370\) 0 0
\(371\) 4.11803 7.13264i 0.213798 0.370308i
\(372\) 0 0
\(373\) 0.218847 0.379054i 0.0113315 0.0196267i −0.860304 0.509781i \(-0.829726\pi\)
0.871636 + 0.490155i \(0.163060\pi\)
\(374\) 0 0
\(375\) 0.718847 + 1.24508i 0.0371211 + 0.0642956i
\(376\) 0 0
\(377\) 4.09017 14.1688i 0.210654 0.729728i
\(378\) 0 0
\(379\) −6.42705 11.1320i −0.330135 0.571811i 0.652403 0.757872i \(-0.273761\pi\)
−0.982538 + 0.186061i \(0.940428\pi\)
\(380\) 0 0
\(381\) −2.70163 + 4.67935i −0.138408 + 0.239731i
\(382\) 0 0
\(383\) 12.4894 21.6322i 0.638176 1.10535i −0.347656 0.937622i \(-0.613022\pi\)
0.985833 0.167732i \(-0.0536443\pi\)
\(384\) 0 0
\(385\) −1.85410 −0.0944938
\(386\) 0 0
\(387\) 10.7918 + 18.6919i 0.548578 + 0.950165i
\(388\) 0 0
\(389\) 23.8885 1.21120 0.605599 0.795770i \(-0.292934\pi\)
0.605599 + 0.795770i \(0.292934\pi\)
\(390\) 0 0
\(391\) −33.4164 −1.68994
\(392\) 0 0
\(393\) 0.0623059 + 0.107917i 0.00314292 + 0.00544369i
\(394\) 0 0
\(395\) −1.52786 −0.0768752
\(396\) 0 0
\(397\) 12.7082 22.0113i 0.637806 1.10471i −0.348107 0.937455i \(-0.613175\pi\)
0.985913 0.167258i \(-0.0534914\pi\)
\(398\) 0 0
\(399\) −0.927051 + 1.60570i −0.0464106 + 0.0803855i
\(400\) 0 0
\(401\) 10.2254 + 17.7110i 0.510633 + 0.884443i 0.999924 + 0.0123222i \(0.00392237\pi\)
−0.489291 + 0.872121i \(0.662744\pi\)
\(402\) 0 0
\(403\) 21.7705 + 22.6246i 1.08447 + 1.12701i
\(404\) 0 0
\(405\) −1.47214 2.54981i −0.0731510 0.126701i
\(406\) 0 0
\(407\) −9.70820 + 16.8151i −0.481218 + 0.833494i
\(408\) 0 0
\(409\) −17.2812 + 29.9318i −0.854498 + 1.48003i 0.0226119 + 0.999744i \(0.492802\pi\)
−0.877110 + 0.480290i \(0.840532\pi\)
\(410\) 0 0
\(411\) −0.145898 −0.00719662
\(412\) 0 0
\(413\) −1.11803 1.93649i −0.0550149 0.0952885i
\(414\) 0 0
\(415\) 2.56231 0.125779
\(416\) 0 0
\(417\) 5.94427 0.291092
\(418\) 0 0
\(419\) 2.97214 + 5.14789i 0.145198 + 0.251491i 0.929447 0.368956i \(-0.120285\pi\)
−0.784249 + 0.620447i \(0.786951\pi\)
\(420\) 0 0
\(421\) −25.4164 −1.23872 −0.619360 0.785107i \(-0.712608\pi\)
−0.619360 + 0.785107i \(0.712608\pi\)
\(422\) 0 0
\(423\) −3.19098 + 5.52694i −0.155151 + 0.268729i
\(424\) 0 0
\(425\) 18.1353 31.4112i 0.879689 1.52367i
\(426\) 0 0
\(427\) −3.00000 5.19615i −0.145180 0.251459i
\(428\) 0 0
\(429\) 6.48936 1.60570i 0.313309 0.0775239i
\(430\) 0 0
\(431\) −8.39919 14.5478i −0.404575 0.700744i 0.589697 0.807624i \(-0.299247\pi\)
−0.994272 + 0.106881i \(0.965914\pi\)
\(432\) 0 0
\(433\) −0.500000 + 0.866025i −0.0240285 + 0.0416185i −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 0 0
\(435\) 0.298374 0.516799i 0.0143059 0.0247786i
\(436\) 0 0
\(437\) 21.7082 1.03844
\(438\) 0 0
\(439\) 4.07295 + 7.05455i 0.194391 + 0.336696i 0.946701 0.322114i \(-0.104394\pi\)
−0.752310 + 0.658810i \(0.771060\pi\)
\(440\) 0 0
\(441\) −2.85410 −0.135910
\(442\) 0 0
\(443\) 0.763932 0.0362955 0.0181478 0.999835i \(-0.494223\pi\)
0.0181478 + 0.999835i \(0.494223\pi\)
\(444\) 0 0
\(445\) −3.07295 5.32250i −0.145672 0.252311i
\(446\) 0 0
\(447\) −1.85410 −0.0876960
\(448\) 0 0
\(449\) −14.2361 + 24.6576i −0.671842 + 1.16366i 0.305540 + 0.952179i \(0.401163\pi\)
−0.977381 + 0.211484i \(0.932170\pi\)
\(450\) 0 0
\(451\) −12.7082 + 22.0113i −0.598406 + 1.03647i
\(452\) 0 0
\(453\) −2.80902 4.86536i −0.131979 0.228595i
\(454\) 0 0
\(455\) −1.33688 + 0.330792i −0.0626739 + 0.0155078i
\(456\) 0 0
\(457\) 5.70820 + 9.88690i 0.267019 + 0.462490i 0.968090 0.250601i \(-0.0806282\pi\)
−0.701072 + 0.713091i \(0.747295\pi\)
\(458\) 0 0
\(459\) 8.35410 14.4697i 0.389936 0.675389i
\(460\) 0 0
\(461\) −19.6074 + 33.9610i −0.913207 + 1.58172i −0.103702 + 0.994608i \(0.533069\pi\)
−0.809505 + 0.587113i \(0.800264\pi\)
\(462\) 0 0
\(463\) 6.70820 0.311757 0.155878 0.987776i \(-0.450179\pi\)
0.155878 + 0.987776i \(0.450179\pi\)
\(464\) 0 0
\(465\) 0.635255 + 1.10029i 0.0294592 + 0.0510249i
\(466\) 0 0
\(467\) −33.6525 −1.55725 −0.778625 0.627489i \(-0.784083\pi\)
−0.778625 + 0.627489i \(0.784083\pi\)
\(468\) 0 0
\(469\) 0.708204 0.0327018
\(470\) 0 0
\(471\) −1.55573 2.69460i −0.0716842 0.124161i
\(472\) 0 0
\(473\) 36.7082 1.68785
\(474\) 0 0
\(475\) −11.7812 + 20.4056i −0.540556 + 0.936271i
\(476\) 0 0
\(477\) 11.7533 20.3573i 0.538146 0.932096i
\(478\) 0 0
\(479\) −10.9894 19.0341i −0.502117 0.869691i −0.999997 0.00244569i \(-0.999222\pi\)
0.497880 0.867246i \(-0.334112\pi\)
\(480\) 0 0
\(481\) −4.00000 + 13.8564i −0.182384 + 0.631798i
\(482\) 0 0
\(483\) −0.854102 1.47935i −0.0388630 0.0673127i
\(484\) 0 0
\(485\) −2.31966 + 4.01777i −0.105330 + 0.182438i
\(486\) 0 0
\(487\) −8.48936 + 14.7040i −0.384689 + 0.666302i −0.991726 0.128372i \(-0.959025\pi\)
0.607037 + 0.794674i \(0.292358\pi\)
\(488\) 0 0
\(489\) −3.70820 −0.167691
\(490\) 0 0
\(491\) 7.30902 + 12.6596i 0.329851 + 0.571319i 0.982482 0.186357i \(-0.0596680\pi\)
−0.652631 + 0.757676i \(0.726335\pi\)
\(492\) 0 0
\(493\) −30.5623 −1.37646
\(494\) 0 0
\(495\) −5.29180 −0.237849
\(496\) 0 0
\(497\) −4.09017 7.08438i −0.183469 0.317778i
\(498\) 0 0
\(499\) −8.14590 −0.364660 −0.182330 0.983237i \(-0.558364\pi\)
−0.182330 + 0.983237i \(0.558364\pi\)
\(500\) 0 0
\(501\) 1.86475 3.22983i 0.0833107 0.144298i
\(502\) 0 0
\(503\) 12.1910 21.1154i 0.543569 0.941489i −0.455126 0.890427i \(-0.650406\pi\)
0.998695 0.0510624i \(-0.0162607\pi\)
\(504\) 0 0
\(505\) −1.63525 2.83234i −0.0727679 0.126038i
\(506\) 0 0
\(507\) 4.39261 2.31555i 0.195083 0.102837i
\(508\) 0 0
\(509\) −15.2984 26.4976i −0.678089 1.17448i −0.975556 0.219752i \(-0.929475\pi\)
0.297467 0.954732i \(-0.403858\pi\)
\(510\) 0 0
\(511\) −1.00000 + 1.73205i −0.0442374 + 0.0766214i
\(512\) 0 0
\(513\) −5.42705 + 9.39993i −0.239610 + 0.415017i
\(514\) 0 0
\(515\) −1.79837 −0.0792458
\(516\) 0 0
\(517\) 5.42705 + 9.39993i 0.238681 + 0.413408i
\(518\) 0 0
\(519\) −3.43769 −0.150898
\(520\) 0 0
\(521\) −12.6525 −0.554315 −0.277158 0.960824i \(-0.589392\pi\)
−0.277158 + 0.960824i \(0.589392\pi\)
\(522\) 0 0
\(523\) −19.5623 33.8829i −0.855400 1.48160i −0.876274 0.481814i \(-0.839978\pi\)
0.0208736 0.999782i \(-0.493355\pi\)
\(524\) 0 0
\(525\) 1.85410 0.0809196
\(526\) 0 0
\(527\) 32.5344 56.3513i 1.41722 2.45470i
\(528\) 0 0
\(529\) 1.50000 2.59808i 0.0652174 0.112960i
\(530\) 0 0
\(531\) −3.19098 5.52694i −0.138477 0.239849i
\(532\) 0 0
\(533\) −5.23607 + 18.1383i −0.226799 + 0.785656i
\(534\) 0 0
\(535\) −1.07295 1.85840i −0.0463876 0.0803457i
\(536\) 0 0
\(537\) −1.71885 + 2.97713i −0.0741737 + 0.128473i
\(538\) 0 0
\(539\) −2.42705 + 4.20378i −0.104540 + 0.181069i
\(540\) 0 0
\(541\) 1.72949 0.0743566 0.0371783 0.999309i \(-0.488163\pi\)
0.0371783 + 0.999309i \(0.488163\pi\)
\(542\) 0 0
\(543\) 0.708204 + 1.22665i 0.0303919 + 0.0526404i
\(544\) 0 0
\(545\) 4.09017 0.175204
\(546\) 0 0
\(547\) 3.00000 0.128271 0.0641354 0.997941i \(-0.479571\pi\)
0.0641354 + 0.997941i \(0.479571\pi\)
\(548\) 0 0
\(549\) −8.56231 14.8303i −0.365430 0.632944i
\(550\) 0 0
\(551\) 19.8541 0.845813
\(552\) 0 0
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) 0 0
\(555\) −0.291796 + 0.505406i −0.0123861 + 0.0214533i
\(556\) 0 0
\(557\) −9.48936 16.4360i −0.402077 0.696418i 0.591899 0.806012i \(-0.298378\pi\)
−0.993976 + 0.109594i \(0.965045\pi\)
\(558\) 0 0
\(559\) 26.4681 6.54915i 1.11948 0.276999i
\(560\) 0 0
\(561\) −6.92705 11.9980i −0.292460 0.506556i
\(562\) 0 0
\(563\) −19.4721 + 33.7267i −0.820653 + 1.42141i 0.0845442 + 0.996420i \(0.473057\pi\)
−0.905197 + 0.424992i \(0.860277\pi\)
\(564\) 0 0
\(565\) 1.42705 2.47172i 0.0600365 0.103986i
\(566\) 0 0
\(567\) −7.70820 −0.323714
\(568\) 0 0
\(569\) 1.47214 + 2.54981i 0.0617151 + 0.106894i 0.895232 0.445600i \(-0.147010\pi\)
−0.833517 + 0.552494i \(0.813676\pi\)
\(570\) 0 0
\(571\) 35.6869 1.49345 0.746726 0.665132i \(-0.231625\pi\)
0.746726 + 0.665132i \(0.231625\pi\)
\(572\) 0 0
\(573\) −9.02129 −0.376870
\(574\) 0 0
\(575\) −10.8541 18.7999i −0.452647 0.784008i
\(576\) 0 0
\(577\) 9.83282 0.409345 0.204673 0.978830i \(-0.434387\pi\)
0.204673 + 0.978830i \(0.434387\pi\)
\(578\) 0 0
\(579\) 1.14590 1.98475i 0.0476219 0.0824835i
\(580\) 0 0
\(581\) 3.35410 5.80948i 0.139152 0.241018i
\(582\) 0 0
\(583\) −19.9894 34.6226i −0.827875 1.43392i
\(584\) 0 0
\(585\) −3.81559 + 0.944115i −0.157755 + 0.0390343i
\(586\) 0 0
\(587\) −15.5451 26.9249i −0.641614 1.11131i −0.985072 0.172141i \(-0.944932\pi\)
0.343458 0.939168i \(-0.388402\pi\)
\(588\) 0 0
\(589\) −21.1353 + 36.6073i −0.870863 + 1.50838i
\(590\) 0 0
\(591\) −1.48936 + 2.57964i −0.0612640 + 0.106112i
\(592\) 0 0
\(593\) 19.2016 0.788516 0.394258 0.919000i \(-0.371002\pi\)
0.394258 + 0.919000i \(0.371002\pi\)
\(594\) 0 0
\(595\) 1.42705 + 2.47172i 0.0585034 + 0.101331i
\(596\) 0 0
\(597\) −0.922986 −0.0377753
\(598\) 0 0
\(599\) 8.50658 0.347569 0.173785 0.984784i \(-0.444400\pi\)
0.173785 + 0.984784i \(0.444400\pi\)
\(600\) 0 0
\(601\) 16.6976 + 28.9210i 0.681108 + 1.17971i 0.974643 + 0.223765i \(0.0718348\pi\)
−0.293535 + 0.955948i \(0.594832\pi\)
\(602\) 0 0
\(603\) 2.02129 0.0823131
\(604\) 0 0
\(605\) −2.39919 + 4.15551i −0.0975408 + 0.168946i
\(606\) 0 0
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) 0 0
\(609\) −0.781153 1.35300i −0.0316539 0.0548262i
\(610\) 0 0
\(611\) 5.59017 + 5.80948i 0.226154 + 0.235026i
\(612\) 0 0
\(613\) −7.21885 12.5034i −0.291566 0.505008i 0.682614 0.730779i \(-0.260843\pi\)
−0.974180 + 0.225771i \(0.927510\pi\)
\(614\) 0 0
\(615\) −0.381966 + 0.661585i −0.0154024 + 0.0266777i
\(616\) 0 0
\(617\) −8.97214 + 15.5402i −0.361205 + 0.625625i −0.988159 0.153431i \(-0.950968\pi\)
0.626955 + 0.779056i \(0.284301\pi\)
\(618\) 0 0
\(619\) 17.4164 0.700025 0.350012 0.936745i \(-0.386177\pi\)
0.350012 + 0.936745i \(0.386177\pi\)
\(620\) 0 0
\(621\) −5.00000 8.66025i −0.200643 0.347524i
\(622\) 0 0
\(623\) −16.0902 −0.644639
\(624\) 0 0
\(625\) 22.8328 0.913313
\(626\) 0 0
\(627\) 4.50000 + 7.79423i 0.179713 + 0.311272i
\(628\) 0 0
\(629\) 29.8885 1.19173
\(630\) 0 0
\(631\) −19.6976 + 34.1172i −0.784148 + 1.35818i 0.145360 + 0.989379i \(0.453566\pi\)
−0.929507 + 0.368804i \(0.879767\pi\)
\(632\) 0 0
\(633\) −1.66312 + 2.88061i −0.0661030 + 0.114494i
\(634\) 0 0
\(635\) −2.70163 4.67935i −0.107211 0.185694i
\(636\) 0 0
\(637\) −1.00000 + 3.46410i −0.0396214 + 0.137253i
\(638\) 0 0
\(639\) −11.6738 20.2195i −0.461807 0.799873i
\(640\) 0 0
\(641\) 4.74671 8.22154i 0.187484 0.324731i −0.756927 0.653500i \(-0.773300\pi\)
0.944411 + 0.328768i \(0.106633\pi\)
\(642\) 0 0
\(643\) −3.50000 + 6.06218i −0.138027 + 0.239069i −0.926750 0.375680i \(-0.877409\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 0 0
\(645\) 1.10333 0.0434434
\(646\) 0 0
\(647\) 14.6180 + 25.3192i 0.574694 + 0.995400i 0.996075 + 0.0885157i \(0.0282123\pi\)
−0.421381 + 0.906884i \(0.638454\pi\)
\(648\) 0 0
\(649\) −10.8541 −0.426061
\(650\) 0 0
\(651\) 3.32624 0.130366
\(652\) 0 0
\(653\) 1.30902 + 2.26728i 0.0512258 + 0.0887257i 0.890501 0.454981i \(-0.150354\pi\)
−0.839275 + 0.543706i \(0.817021\pi\)
\(654\) 0 0
\(655\) −0.124612 −0.00486899
\(656\) 0 0
\(657\) −2.85410 + 4.94345i −0.111349 + 0.192862i
\(658\) 0 0
\(659\) 5.94427 10.2958i 0.231556 0.401067i −0.726710 0.686944i \(-0.758952\pi\)
0.958266 + 0.285877i \(0.0922850\pi\)
\(660\) 0 0
\(661\) −9.27051 16.0570i −0.360581 0.624545i 0.627476 0.778636i \(-0.284088\pi\)
−0.988057 + 0.154092i \(0.950755\pi\)
\(662\) 0 0
\(663\) −7.13525 7.41517i −0.277110 0.287982i
\(664\) 0 0
\(665\) −0.927051 1.60570i −0.0359495 0.0622664i
\(666\) 0 0
\(667\) −9.14590 + 15.8412i −0.354131 + 0.613372i
\(668\) 0 0
\(669\) −2.53444 + 4.38978i −0.0979872 + 0.169719i
\(670\) 0 0
\(671\) −29.1246 −1.12434
\(672\) 0 0
\(673\) −20.6246 35.7229i −0.795020 1.37702i −0.922826 0.385216i \(-0.874127\pi\)
0.127806 0.991799i \(-0.459207\pi\)
\(674\) 0 0
\(675\) 10.8541 0.417775
\(676\) 0 0
\(677\) 1.25735 0.0483240 0.0241620 0.999708i \(-0.492308\pi\)
0.0241620 + 0.999708i \(0.492308\pi\)
\(678\) 0 0
\(679\) 6.07295 + 10.5187i 0.233058 + 0.403669i
\(680\) 0 0
\(681\) 2.85410 0.109369
\(682\) 0 0
\(683\) −3.73607 + 6.47106i −0.142957 + 0.247608i −0.928609 0.371060i \(-0.878994\pi\)
0.785652 + 0.618669i \(0.212328\pi\)
\(684\) 0 0
\(685\) 0.0729490 0.126351i 0.00278724 0.00482764i
\(686\) 0 0
\(687\) −5.18034 8.97261i −0.197642 0.342326i
\(688\) 0 0
\(689\) −20.5902 21.3979i −0.784423 0.815196i
\(690\) 0 0
\(691\) 0.427051 + 0.739674i 0.0162458 + 0.0281385i 0.874034 0.485865i \(-0.161495\pi\)
−0.857788 + 0.514003i \(0.828162\pi\)
\(692\) 0 0
\(693\) −6.92705 + 11.9980i −0.263137 + 0.455766i
\(694\) 0 0
\(695\) −2.97214 + 5.14789i −0.112740 + 0.195271i
\(696\) 0 0
\(697\) 39.1246 1.48195
\(698\) 0 0
\(699\) −0.0729490 0.126351i −0.00275919 0.00477905i
\(700\) 0 0
\(701\) 6.76393 0.255470 0.127735 0.991808i \(-0.459229\pi\)
0.127735 + 0.991808i \(0.459229\pi\)
\(702\) 0 0
\(703\) −19.4164 −0.732304
\(704\) 0 0
\(705\) 0.163119 + 0.282530i 0.00614342 + 0.0106407i
\(706\) 0 0
\(707\) −8.56231 −0.322019
\(708\) 0 0
\(709\) −1.71885 + 2.97713i −0.0645527 + 0.111808i −0.896495 0.443053i \(-0.853895\pi\)
0.831943 + 0.554861i \(0.187229\pi\)
\(710\) 0 0
\(711\) −5.70820 + 9.88690i −0.214074 + 0.370788i
\(712\) 0 0
\(713\) −19.4721 33.7267i −0.729237 1.26308i
\(714\) 0 0
\(715\) −1.85410 + 6.42280i −0.0693395 + 0.240199i
\(716\) 0 0
\(717\) −2.15654 3.73524i −0.0805375 0.139495i
\(718\) 0 0
\(719\) −16.0623 + 27.8207i −0.599023 + 1.03754i 0.393943 + 0.919135i \(0.371111\pi\)
−0.992966 + 0.118403i \(0.962222\pi\)
\(720\) 0 0
\(721\) −2.35410 + 4.07742i −0.0876713 + 0.151851i
\(722\) 0 0
\(723\) 1.69505 0.0630395
\(724\) 0 0
\(725\) −9.92705 17.1942i −0.368681 0.638575i
\(726\) 0 0
\(727\) 17.2918 0.641317 0.320659 0.947195i \(-0.396096\pi\)
0.320659 + 0.947195i \(0.396096\pi\)
\(728\) 0 0
\(729\) −19.4377 −0.719915
\(730\) 0 0
\(731\) −28.2533 48.9361i −1.04499 1.80997i
\(732\) 0 0
\(733\) 1.27051 0.0469274 0.0234637 0.999725i \(-0.492531\pi\)
0.0234637 + 0.999725i \(0.492531\pi\)
\(734\) 0 0
\(735\) −0.0729490 + 0.126351i −0.00269077 + 0.00466054i
\(736\) 0 0
\(737\) 1.71885 2.97713i 0.0633145 0.109664i
\(738\) 0 0
\(739\) −23.5623 40.8111i −0.866753 1.50126i −0.865296 0.501262i \(-0.832869\pi\)
−0.00145790 0.999999i \(-0.500464\pi\)
\(740\) 0 0
\(741\) 4.63525 + 4.81710i 0.170280 + 0.176961i
\(742\) 0 0
\(743\) 11.8369 + 20.5021i 0.434253 + 0.752148i 0.997234 0.0743213i \(-0.0236790\pi\)
−0.562981 + 0.826470i \(0.690346\pi\)
\(744\) 0 0
\(745\) 0.927051 1.60570i 0.0339645 0.0588283i
\(746\) 0 0
\(747\) 9.57295 16.5808i 0.350256 0.606661i
\(748\) 0 0
\(749\) −5.61803 −0.205278
\(750\) 0 0
\(751\) 4.64590 + 8.04693i 0.169531 + 0.293637i 0.938255 0.345944i \(-0.112441\pi\)
−0.768724 + 0.639581i \(0.779108\pi\)
\(752\) 0 0
\(753\) −2.00000 −0.0728841
\(754\) 0 0
\(755\) 5.61803 0.204461
\(756\) 0 0
\(757\) −14.0000 24.2487i −0.508839 0.881334i −0.999948 0.0102362i \(-0.996742\pi\)
0.491109 0.871098i \(-0.336592\pi\)
\(758\) 0 0
\(759\) −8.29180 −0.300973
\(760\) 0 0
\(761\) 11.0729 19.1789i 0.401394 0.695235i −0.592500 0.805570i \(-0.701859\pi\)
0.993894 + 0.110335i \(0.0351925\pi\)
\(762\) 0 0
\(763\) 5.35410 9.27358i 0.193832 0.335726i
\(764\) 0 0
\(765\) 4.07295 + 7.05455i 0.147258 + 0.255058i
\(766\) 0 0
\(767\) −7.82624 + 1.93649i −0.282589 + 0.0699227i
\(768\) 0 0
\(769\) −4.20820 7.28882i −0.151752 0.262842i 0.780120 0.625630i \(-0.215158\pi\)
−0.931872 + 0.362788i \(0.881825\pi\)
\(770\) 0 0
\(771\) 4.91641 8.51547i 0.177060 0.306677i
\(772\) 0 0
\(773\) 9.68034 16.7668i 0.348178 0.603061i −0.637748 0.770245i \(-0.720134\pi\)
0.985926 + 0.167184i \(0.0534673\pi\)
\(774\) 0 0
\(775\) 42.2705 1.51840
\(776\) 0 0
\(777\) 0.763932 + 1.32317i 0.0274059 + 0.0474684i
\(778\) 0 0
\(779\) −25.4164 −0.910637
\(780\) 0 0
\(781\) −39.7082 −1.42087
\(782\) 0 0
\(783\) −4.57295 7.92058i −0.163424 0.283058i
\(784\) 0 0
\(785\) 3.11146 0.111053
\(786\) 0 0
\(787\) 14.7082 25.4754i 0.524291 0.908098i −0.475309 0.879819i \(-0.657664\pi\)
0.999600 0.0282796i \(-0.00900287\pi\)
\(788\) 0 0
\(789\) 1.71885 2.97713i 0.0611926 0.105989i
\(790\) 0 0
\(791\) −3.73607 6.47106i −0.132839 0.230084i
\(792\) 0 0
\(793\) −21.0000 + 5.19615i −0.745732 + 0.184521i
\(794\) 0 0
\(795\) −0.600813 1.04064i −0.0213086 0.0369077i