Properties

Label 768.2.o.b.287.1
Level 768
Weight 2
Character 768.287
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 287.1
Character \(\chi\) \(=\) 768.287
Dual form 768.2.o.b.479.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69392 + 0.361451i) q^{3} +(0.348970 - 0.842489i) q^{5} +(-0.471834 + 0.471834i) q^{7} +(2.73871 - 1.22453i) q^{9} +O(q^{10})\) \(q+(-1.69392 + 0.361451i) q^{3} +(0.348970 - 0.842489i) q^{5} +(-0.471834 + 0.471834i) q^{7} +(2.73871 - 1.22453i) q^{9} +(-1.24185 + 2.99808i) q^{11} +(2.51698 - 1.04257i) q^{13} +(-0.286608 + 1.55324i) q^{15} -6.24340 q^{17} +(0.683586 + 1.65032i) q^{19} +(0.628703 - 0.969793i) q^{21} +(5.69180 - 5.69180i) q^{23} +(2.94753 + 2.94753i) q^{25} +(-4.19653 + 3.06417i) q^{27} +(5.28905 - 2.19080i) q^{29} +5.07456i q^{31} +(1.01993 - 5.52737i) q^{33} +(0.232859 + 0.562171i) q^{35} +(6.21892 + 2.57596i) q^{37} +(-3.88672 + 2.67579i) q^{39} +(6.43169 + 6.43169i) q^{41} +(6.04703 + 2.50476i) q^{43} +(-0.0759298 - 2.73466i) q^{45} +8.94964i q^{47} +6.55474i q^{49} +(10.5758 - 2.25668i) q^{51} +(-4.63157 - 1.91846i) q^{53} +(2.09248 + 2.09248i) q^{55} +(-1.75445 - 2.54843i) q^{57} +(-2.67262 - 1.10704i) q^{59} +(2.36352 + 5.70603i) q^{61} +(-0.714438 + 1.86999i) q^{63} -2.48436i q^{65} +(3.39948 - 1.40811i) q^{67} +(-7.58413 + 11.6987i) q^{69} +(-7.71934 - 7.71934i) q^{71} +(0.0492824 - 0.0492824i) q^{73} +(-6.05825 - 3.92748i) q^{75} +(-0.828653 - 2.00054i) q^{77} +10.1259 q^{79} +(6.00103 - 6.70728i) q^{81} +(3.65135 - 1.51244i) q^{83} +(-2.17876 + 5.25999i) q^{85} +(-8.16735 + 5.62276i) q^{87} +(4.09411 - 4.09411i) q^{89} +(-0.695680 + 1.67952i) q^{91} +(-1.83420 - 8.59588i) q^{93} +1.62893 q^{95} +4.72643 q^{97} +(0.270204 + 9.73155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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
\(3\) −1.69392 + 0.361451i −0.977983 + 0.208684i
\(4\) 0 0
\(5\) 0.348970 0.842489i 0.156064 0.376772i −0.826437 0.563030i \(-0.809636\pi\)
0.982501 + 0.186257i \(0.0596357\pi\)
\(6\) 0 0
\(7\) −0.471834 + 0.471834i −0.178337 + 0.178337i −0.790630 0.612294i \(-0.790247\pi\)
0.612294 + 0.790630i \(0.290247\pi\)
\(8\) 0 0
\(9\) 2.73871 1.22453i 0.912902 0.408178i
\(10\) 0 0
\(11\) −1.24185 + 2.99808i −0.374431 + 0.903956i 0.618557 + 0.785740i \(0.287718\pi\)
−0.992988 + 0.118216i \(0.962282\pi\)
\(12\) 0 0
\(13\) 2.51698 1.04257i 0.698086 0.289157i −0.00527868 0.999986i \(-0.501680\pi\)
0.703364 + 0.710830i \(0.251680\pi\)
\(14\) 0 0
\(15\) −0.286608 + 1.55324i −0.0740019 + 0.401045i
\(16\) 0 0
\(17\) −6.24340 −1.51425 −0.757123 0.653272i \(-0.773396\pi\)
−0.757123 + 0.653272i \(0.773396\pi\)
\(18\) 0 0
\(19\) 0.683586 + 1.65032i 0.156825 + 0.378610i 0.982690 0.185259i \(-0.0593123\pi\)
−0.825864 + 0.563869i \(0.809312\pi\)
\(20\) 0 0
\(21\) 0.628703 0.969793i 0.137194 0.211626i
\(22\) 0 0
\(23\) 5.69180 5.69180i 1.18682 1.18682i 0.208881 0.977941i \(-0.433018\pi\)
0.977941 0.208881i \(-0.0669821\pi\)
\(24\) 0 0
\(25\) 2.94753 + 2.94753i 0.589505 + 0.589505i
\(26\) 0 0
\(27\) −4.19653 + 3.06417i −0.807623 + 0.589699i
\(28\) 0 0
\(29\) 5.28905 2.19080i 0.982152 0.406821i 0.166930 0.985969i \(-0.446615\pi\)
0.815222 + 0.579148i \(0.196615\pi\)
\(30\) 0 0
\(31\) 5.07456i 0.911418i 0.890129 + 0.455709i \(0.150614\pi\)
−0.890129 + 0.455709i \(0.849386\pi\)
\(32\) 0 0
\(33\) 1.01993 5.52737i 0.177546 0.962191i
\(34\) 0 0
\(35\) 0.232859 + 0.562171i 0.0393604 + 0.0950243i
\(36\) 0 0
\(37\) 6.21892 + 2.57596i 1.02238 + 0.423485i 0.829958 0.557826i \(-0.188365\pi\)
0.192426 + 0.981312i \(0.438365\pi\)
\(38\) 0 0
\(39\) −3.88672 + 2.67579i −0.622374 + 0.428469i
\(40\) 0 0
\(41\) 6.43169 + 6.43169i 1.00446 + 1.00446i 0.999990 + 0.00447060i \(0.00142304\pi\)
0.00447060 + 0.999990i \(0.498577\pi\)
\(42\) 0 0
\(43\) 6.04703 + 2.50476i 0.922163 + 0.381973i 0.792700 0.609612i \(-0.208675\pi\)
0.129463 + 0.991584i \(0.458675\pi\)
\(44\) 0 0
\(45\) −0.0759298 2.73466i −0.0113189 0.407658i
\(46\) 0 0
\(47\) 8.94964i 1.30544i 0.757600 + 0.652720i \(0.226372\pi\)
−0.757600 + 0.652720i \(0.773628\pi\)
\(48\) 0 0
\(49\) 6.55474i 0.936392i
\(50\) 0 0
\(51\) 10.5758 2.25668i 1.48091 0.315999i
\(52\) 0 0
\(53\) −4.63157 1.91846i −0.636195 0.263520i 0.0411879 0.999151i \(-0.486886\pi\)
−0.677382 + 0.735631i \(0.736886\pi\)
\(54\) 0 0
\(55\) 2.09248 + 2.09248i 0.282150 + 0.282150i
\(56\) 0 0
\(57\) −1.75445 2.54843i −0.232382 0.337547i
\(58\) 0 0
\(59\) −2.67262 1.10704i −0.347945 0.144124i 0.201865 0.979413i \(-0.435300\pi\)
−0.549810 + 0.835290i \(0.685300\pi\)
\(60\) 0 0
\(61\) 2.36352 + 5.70603i 0.302617 + 0.730583i 0.999905 + 0.0137912i \(0.00439002\pi\)
−0.697288 + 0.716791i \(0.745610\pi\)
\(62\) 0 0
\(63\) −0.714438 + 1.86999i −0.0900108 + 0.235597i
\(64\) 0 0
\(65\) 2.48436i 0.308146i
\(66\) 0 0
\(67\) 3.39948 1.40811i 0.415312 0.172028i −0.165235 0.986254i \(-0.552838\pi\)
0.580548 + 0.814226i \(0.302838\pi\)
\(68\) 0 0
\(69\) −7.58413 + 11.6987i −0.913022 + 1.40836i
\(70\) 0 0
\(71\) −7.71934 7.71934i −0.916117 0.916117i 0.0806272 0.996744i \(-0.474308\pi\)
−0.996744 + 0.0806272i \(0.974308\pi\)
\(72\) 0 0
\(73\) 0.0492824 0.0492824i 0.00576807 0.00576807i −0.704217 0.709985i \(-0.748702\pi\)
0.709985 + 0.704217i \(0.248702\pi\)
\(74\) 0 0
\(75\) −6.05825 3.92748i −0.699546 0.453506i
\(76\) 0 0
\(77\) −0.828653 2.00054i −0.0944337 0.227983i
\(78\) 0 0
\(79\) 10.1259 1.13925 0.569625 0.821905i \(-0.307088\pi\)
0.569625 + 0.821905i \(0.307088\pi\)
\(80\) 0 0
\(81\) 6.00103 6.70728i 0.666781 0.745254i
\(82\) 0 0
\(83\) 3.65135 1.51244i 0.400787 0.166012i −0.173179 0.984890i \(-0.555404\pi\)
0.573966 + 0.818879i \(0.305404\pi\)
\(84\) 0 0
\(85\) −2.17876 + 5.25999i −0.236320 + 0.570526i
\(86\) 0 0
\(87\) −8.16735 + 5.62276i −0.875632 + 0.602823i
\(88\) 0 0
\(89\) 4.09411 4.09411i 0.433974 0.433974i −0.456004 0.889978i \(-0.650720\pi\)
0.889978 + 0.456004i \(0.150720\pi\)
\(90\) 0 0
\(91\) −0.695680 + 1.67952i −0.0729270 + 0.176061i
\(92\) 0 0
\(93\) −1.83420 8.59588i −0.190198 0.891351i
\(94\) 0 0
\(95\) 1.62893 0.167125
\(96\) 0 0
\(97\) 4.72643 0.479896 0.239948 0.970786i \(-0.422870\pi\)
0.239948 + 0.970786i \(0.422870\pi\)
\(98\) 0 0
\(99\) 0.270204 + 9.73155i 0.0271565 + 0.978058i
\(100\) 0 0
\(101\) −2.70950 + 6.54131i −0.269605 + 0.650885i −0.999465 0.0327124i \(-0.989585\pi\)
0.729859 + 0.683597i \(0.239585\pi\)
\(102\) 0 0
\(103\) 4.68286 4.68286i 0.461416 0.461416i −0.437703 0.899119i \(-0.644208\pi\)
0.899119 + 0.437703i \(0.144208\pi\)
\(104\) 0 0
\(105\) −0.597641 0.868104i −0.0583238 0.0847183i
\(106\) 0 0
\(107\) 0.453771 1.09550i 0.0438677 0.105906i −0.900427 0.435007i \(-0.856746\pi\)
0.944295 + 0.329101i \(0.106746\pi\)
\(108\) 0 0
\(109\) −10.9543 + 4.53742i −1.04923 + 0.434606i −0.839617 0.543178i \(-0.817221\pi\)
−0.209614 + 0.977784i \(0.567221\pi\)
\(110\) 0 0
\(111\) −11.4654 2.11563i −1.08825 0.200806i
\(112\) 0 0
\(113\) −6.82755 −0.642282 −0.321141 0.947031i \(-0.604066\pi\)
−0.321141 + 0.947031i \(0.604066\pi\)
\(114\) 0 0
\(115\) −2.80901 6.78155i −0.261941 0.632382i
\(116\) 0 0
\(117\) 5.61662 5.93742i 0.519257 0.548915i
\(118\) 0 0
\(119\) 2.94585 2.94585i 0.270046 0.270046i
\(120\) 0 0
\(121\) 0.331857 + 0.331857i 0.0301688 + 0.0301688i
\(122\) 0 0
\(123\) −13.2195 8.57000i −1.19196 0.772731i
\(124\) 0 0
\(125\) 7.72430 3.19951i 0.690883 0.286173i
\(126\) 0 0
\(127\) 20.4851i 1.81776i −0.417059 0.908879i \(-0.636939\pi\)
0.417059 0.908879i \(-0.363061\pi\)
\(128\) 0 0
\(129\) −11.1485 2.05715i −0.981572 0.181122i
\(130\) 0 0
\(131\) 0.281165 + 0.678793i 0.0245655 + 0.0593064i 0.935686 0.352833i \(-0.114782\pi\)
−0.911121 + 0.412139i \(0.864782\pi\)
\(132\) 0 0
\(133\) −1.10122 0.456140i −0.0954878 0.0395523i
\(134\) 0 0
\(135\) 1.11706 + 4.60483i 0.0961414 + 0.396321i
\(136\) 0 0
\(137\) −0.914012 0.914012i −0.0780893 0.0780893i 0.666983 0.745073i \(-0.267585\pi\)
−0.745073 + 0.666983i \(0.767585\pi\)
\(138\) 0 0
\(139\) −6.07269 2.51539i −0.515079 0.213353i 0.109975 0.993934i \(-0.464923\pi\)
−0.625054 + 0.780582i \(0.714923\pi\)
\(140\) 0 0
\(141\) −3.23485 15.1599i −0.272424 1.27670i
\(142\) 0 0
\(143\) 8.84084i 0.739308i
\(144\) 0 0
\(145\) 5.22049i 0.433538i
\(146\) 0 0
\(147\) −2.36922 11.1032i −0.195410 0.915776i
\(148\) 0 0
\(149\) −8.36760 3.46597i −0.685501 0.283944i 0.0126235 0.999920i \(-0.495982\pi\)
−0.698124 + 0.715977i \(0.745982\pi\)
\(150\) 0 0
\(151\) −2.49354 2.49354i −0.202921 0.202921i 0.598329 0.801250i \(-0.295832\pi\)
−0.801250 + 0.598329i \(0.795832\pi\)
\(152\) 0 0
\(153\) −17.0988 + 7.64526i −1.38236 + 0.618083i
\(154\) 0 0
\(155\) 4.27526 + 1.77087i 0.343397 + 0.142240i
\(156\) 0 0
\(157\) −3.52366 8.50687i −0.281219 0.678922i 0.718646 0.695376i \(-0.244762\pi\)
−0.999865 + 0.0164542i \(0.994762\pi\)
\(158\) 0 0
\(159\) 8.53892 + 1.57562i 0.677180 + 0.124955i
\(160\) 0 0
\(161\) 5.37117i 0.423308i
\(162\) 0 0
\(163\) 9.76152 4.04335i 0.764581 0.316700i 0.0339057 0.999425i \(-0.489205\pi\)
0.730675 + 0.682725i \(0.239205\pi\)
\(164\) 0 0
\(165\) −4.30082 2.78816i −0.334819 0.217058i
\(166\) 0 0
\(167\) −3.05737 3.05737i −0.236587 0.236587i 0.578848 0.815435i \(-0.303502\pi\)
−0.815435 + 0.578848i \(0.803502\pi\)
\(168\) 0 0
\(169\) −3.94413 + 3.94413i −0.303395 + 0.303395i
\(170\) 0 0
\(171\) 3.89302 + 3.68268i 0.297707 + 0.281621i
\(172\) 0 0
\(173\) 7.23974 + 17.4783i 0.550427 + 1.32885i 0.917159 + 0.398522i \(0.130477\pi\)
−0.366732 + 0.930327i \(0.619523\pi\)
\(174\) 0 0
\(175\) −2.78149 −0.210261
\(176\) 0 0
\(177\) 4.92733 + 0.909205i 0.370361 + 0.0683400i
\(178\) 0 0
\(179\) −12.6819 + 5.25303i −0.947892 + 0.392630i −0.802438 0.596736i \(-0.796464\pi\)
−0.145454 + 0.989365i \(0.546464\pi\)
\(180\) 0 0
\(181\) −3.26250 + 7.87637i −0.242500 + 0.585446i −0.997530 0.0702439i \(-0.977622\pi\)
0.755030 + 0.655690i \(0.227622\pi\)
\(182\) 0 0
\(183\) −6.06605 8.81125i −0.448415 0.651346i
\(184\) 0 0
\(185\) 4.34043 4.34043i 0.319115 0.319115i
\(186\) 0 0
\(187\) 7.75334 18.7182i 0.566981 1.36881i
\(188\) 0 0
\(189\) 0.534288 3.42585i 0.0388637 0.249194i
\(190\) 0 0
\(191\) −9.70190 −0.702005 −0.351002 0.936375i \(-0.614159\pi\)
−0.351002 + 0.936375i \(0.614159\pi\)
\(192\) 0 0
\(193\) −21.4271 −1.54235 −0.771177 0.636621i \(-0.780332\pi\)
−0.771177 + 0.636621i \(0.780332\pi\)
\(194\) 0 0
\(195\) 0.897972 + 4.20829i 0.0643051 + 0.301362i
\(196\) 0 0
\(197\) 5.50419 13.2883i 0.392157 0.946751i −0.597312 0.802009i \(-0.703765\pi\)
0.989469 0.144742i \(-0.0462354\pi\)
\(198\) 0 0
\(199\) 6.75982 6.75982i 0.479191 0.479191i −0.425682 0.904873i \(-0.639966\pi\)
0.904873 + 0.425682i \(0.139966\pi\)
\(200\) 0 0
\(201\) −5.24947 + 3.61397i −0.370269 + 0.254909i
\(202\) 0 0
\(203\) −1.46186 + 3.52925i −0.102603 + 0.247705i
\(204\) 0 0
\(205\) 7.66309 3.17416i 0.535213 0.221693i
\(206\) 0 0
\(207\) 8.61836 22.5580i 0.599017 1.56789i
\(208\) 0 0
\(209\) −5.79672 −0.400967
\(210\) 0 0
\(211\) 2.53702 + 6.12491i 0.174656 + 0.421656i 0.986830 0.161758i \(-0.0517164\pi\)
−0.812175 + 0.583414i \(0.801716\pi\)
\(212\) 0 0
\(213\) 15.8661 + 10.2858i 1.08713 + 0.704768i
\(214\) 0 0
\(215\) 4.22047 4.22047i 0.287834 0.287834i
\(216\) 0 0
\(217\) −2.39435 2.39435i −0.162539 0.162539i
\(218\) 0 0
\(219\) −0.0656672 + 0.101294i −0.00443738 + 0.00684478i
\(220\) 0 0
\(221\) −15.7145 + 6.50917i −1.05707 + 0.437854i
\(222\) 0 0
\(223\) 8.81813i 0.590506i 0.955419 + 0.295253i \(0.0954039\pi\)
−0.955419 + 0.295253i \(0.904596\pi\)
\(224\) 0 0
\(225\) 11.6818 + 4.46306i 0.778784 + 0.297537i
\(226\) 0 0
\(227\) −9.49912 22.9329i −0.630479 1.52211i −0.839022 0.544097i \(-0.816872\pi\)
0.208543 0.978013i \(1.56687\pi\)
\(228\) 0 0
\(229\) −17.9702 7.44351i −1.18751 0.491881i −0.300563 0.953762i \(-0.597175\pi\)
−0.886942 + 0.461881i \(0.847175\pi\)
\(230\) 0 0
\(231\) 2.12677 + 3.08924i 0.139931 + 0.203257i
\(232\) 0 0
\(233\) −0.551118 0.551118i −0.0361050 0.0361050i 0.688824 0.724929i \(-0.258127\pi\)
−0.724929 + 0.688824i \(0.758127\pi\)
\(234\) 0 0
\(235\) 7.53997 + 3.12316i 0.491854 + 0.203732i
\(236\) 0 0
\(237\) −17.1524 + 3.66001i −1.11417 + 0.237743i
\(238\) 0 0
\(239\) 1.64816i 0.106610i 0.998578 + 0.0533052i \(0.0169756\pi\)
−0.998578 + 0.0533052i \(0.983024\pi\)
\(240\) 0 0
\(241\) 18.3719i 1.18344i 0.806145 + 0.591718i \(0.201550\pi\)
−0.806145 + 0.591718i \(0.798450\pi\)
\(242\) 0 0
\(243\) −7.74089 + 13.5307i −0.496578 + 0.867992i
\(244\) 0 0
\(245\) 5.52230 + 2.28741i 0.352807 + 0.146137i
\(246\) 0 0
\(247\) 3.44115 + 3.44115i 0.218955 + 0.218955i
\(248\) 0 0
\(249\) −5.63840 + 3.88172i −0.357319 + 0.245994i
\(250\) 0 0
\(251\) 26.5328 + 10.9903i 1.67474 + 0.693699i 0.999054 0.0434928i \(-0.0138486\pi\)
0.675684 + 0.737192i \(0.263849\pi\)
\(252\) 0 0
\(253\) 9.99614 + 24.1328i 0.628452 + 1.51722i
\(254\) 0 0
\(255\) 1.78941 9.69750i 0.112057 0.607281i
\(256\) 0 0
\(257\) 14.0179i 0.874413i 0.899361 + 0.437206i \(0.144032\pi\)
−0.899361 + 0.437206i \(0.855968\pi\)
\(258\) 0 0
\(259\) −4.14972 + 1.71887i −0.257851 + 0.106805i
\(260\) 0 0
\(261\) 11.8025 12.4766i 0.730554 0.772281i
\(262\) 0 0
\(263\) 17.6733 + 17.6733i 1.08978 + 1.08978i 0.995550 + 0.0942329i \(0.0300398\pi\)
0.0942329 + 0.995550i \(0.469960\pi\)
\(264\) 0 0
\(265\) −3.23256 + 3.23256i −0.198574 + 0.198574i
\(266\) 0 0
\(267\) −5.45526 + 8.41489i −0.333856 + 0.514983i
\(268\) 0 0
\(269\) 6.87589 + 16.5999i 0.419231 + 1.01211i 0.982571 + 0.185887i \(0.0595160\pi\)
−0.563340 + 0.826225i \(0.690484\pi\)
\(270\) 0 0
\(271\) −0.0752921 −0.00457367 −0.00228683 0.999997i \(-0.500728\pi\)
−0.00228683 + 0.999997i \(0.500728\pi\)
\(272\) 0 0
\(273\) 0.571360 3.09642i 0.0345803 0.187404i
\(274\) 0 0
\(275\) −12.4973 + 5.17655i −0.753616 + 0.312158i
\(276\) 0 0
\(277\) 6.16828 14.8915i 0.370616 0.894746i −0.623030 0.782198i \(-0.714099\pi\)
0.993646 0.112548i \(-0.0359013\pi\)
\(278\) 0 0
\(279\) 6.21397 + 13.8977i 0.372021 + 0.832035i
\(280\) 0 0
\(281\) 11.2880 11.2880i 0.673386 0.673386i −0.285109 0.958495i \(-0.592030\pi\)
0.958495 + 0.285109i \(0.0920299\pi\)
\(282\) 0 0
\(283\) −6.30429 + 15.2199i −0.374751 + 0.904729i 0.618180 + 0.786037i \(0.287870\pi\)
−0.992931 + 0.118692i \(0.962130\pi\)
\(284\) 0 0
\(285\) −2.75927 + 0.588778i −0.163445 + 0.0348762i
\(286\) 0 0
\(287\) −6.06938 −0.358264
\(288\) 0 0
\(289\) 21.9800 1.29294
\(290\) 0 0
\(291\) −8.00618 + 1.70837i −0.469331 + 0.100147i
\(292\) 0 0
\(293\) 8.25342 19.9255i 0.482170 1.16406i −0.476406 0.879225i \(-0.658061\pi\)
0.958576 0.284836i \(-0.0919391\pi\)
\(294\) 0 0
\(295\) −1.86533 + 1.86533i −0.108604 + 0.108604i
\(296\) 0 0
\(297\) −3.97518 16.3868i −0.230663 0.950857i
\(298\) 0 0
\(299\) 8.39207 20.2603i 0.485326 1.17168i
\(300\) 0 0
\(301\) −4.03503 + 1.67136i −0.232575 + 0.0963358i
\(302\) 0 0
\(303\) 2.22530 12.0598i 0.127840 0.692817i
\(304\) 0 0
\(305\) 5.63207 0.322491
\(306\) 0 0
\(307\) −1.32663 3.20278i −0.0757149 0.182792i 0.881490 0.472202i \(-0.156541\pi\)
−0.957205 + 0.289410i \(0.906541\pi\)
\(308\) 0 0
\(309\) −6.23975 + 9.62500i −0.354967 + 0.547547i
\(310\) 0 0
\(311\) −5.22034 + 5.22034i −0.296018 + 0.296018i −0.839452 0.543434i \(-0.817124\pi\)
0.543434 + 0.839452i \(0.317124\pi\)
\(312\) 0 0
\(313\) 3.87084 + 3.87084i 0.218793 + 0.218793i 0.807989 0.589197i \(-0.200556\pi\)
−0.589197 + 0.807989i \(0.700556\pi\)
\(314\) 0 0
\(315\) 1.32613 + 1.25448i 0.0747190 + 0.0706818i
\(316\) 0 0
\(317\) −27.3117 + 11.3129i −1.53398 + 0.635393i −0.980331 0.197360i \(-0.936763\pi\)
−0.553644 + 0.832753i \(0.686763\pi\)
\(318\) 0 0
\(319\) 18.5776i 1.04015i
\(320\) 0 0
\(321\) −0.372681 + 2.01970i −0.0208010 + 0.112729i
\(322\) 0 0
\(323\) −4.26790 10.3036i −0.237472 0.573309i
\(324\) 0 0
\(325\) 10.4919 + 4.34588i 0.581985 + 0.241066i
\(326\) 0 0
\(327\) 16.9156 11.6455i 0.935436 0.643995i
\(328\) 0 0
\(329\) −4.22275 4.22275i −0.232808 0.232808i
\(330\) 0 0
\(331\) −9.20994 3.81488i −0.506224 0.209685i 0.114930 0.993374i \(-0.463336\pi\)
−0.621154 + 0.783689i \(0.713336\pi\)
\(332\) 0 0
\(333\) 20.1861 0.560483i 1.10619 0.0307143i
\(334\) 0 0
\(335\) 3.35541i 0.183326i
\(336\) 0 0
\(337\) 29.5659i 1.61056i −0.592895 0.805280i \(-0.702015\pi\)
0.592895 0.805280i \(-0.297985\pi\)
\(338\) 0 0
\(339\) 11.5653 2.46782i 0.628141 0.134034i
\(340\) 0 0
\(341\) −15.2139 6.30182i −0.823881 0.341263i
\(342\) 0 0
\(343\) −6.39559 6.39559i −0.345330 0.345330i
\(344\) 0 0
\(345\) 7.20942 + 10.4721i 0.388142 + 0.563796i
\(346\) 0 0
\(347\) 23.6365 + 9.79057i 1.26888 + 0.525585i 0.912622 0.408804i \(-0.134054\pi\)
0.356253 + 0.934389i \(0.384054\pi\)
\(348\) 0 0
\(349\) −10.2166 24.6651i −0.546883 1.32029i −0.919785 0.392423i \(-0.871637\pi\)
0.372902 0.927871i \(-0.378363\pi\)
\(350\) 0 0
\(351\) −7.36800 + 12.0876i −0.393274 + 0.645190i
\(352\) 0 0
\(353\) 17.7066i 0.942426i −0.882020 0.471213i \(-0.843816\pi\)
0.882020 0.471213i \(-0.156184\pi\)
\(354\) 0 0
\(355\) −9.19728 + 3.80964i −0.488141 + 0.202195i
\(356\) 0 0
\(357\) −3.92524 + 6.05480i −0.207746 + 0.320454i
\(358\) 0 0
\(359\) −7.15299 7.15299i −0.377520 0.377520i 0.492686 0.870207i \(-0.336015\pi\)
−0.870207 + 0.492686i \(0.836015\pi\)
\(360\) 0 0
\(361\) 11.1788 11.1788i 0.588355 0.588355i
\(362\) 0 0
\(363\) −0.682088 0.442188i −0.0358003 0.0232089i
\(364\) 0 0
\(365\) −0.0243218 0.0587180i −0.00127306 0.00307344i
\(366\) 0 0
\(367\) −18.0884 −0.944205 −0.472102 0.881544i \(-0.656505\pi\)
−0.472102 + 0.881544i \(0.656505\pi\)
\(368\) 0 0
\(369\) 25.4903 + 9.73868i 1.32697 + 0.506975i
\(370\) 0 0
\(371\) 3.09053 1.28014i 0.160452 0.0664615i
\(372\) 0 0
\(373\) 4.46880 10.7886i 0.231386 0.558614i −0.764955 0.644084i \(-0.777239\pi\)
0.996341 + 0.0854691i \(0.0272389\pi\)
\(374\) 0 0
\(375\) −11.9279 + 8.21166i −0.615952 + 0.424048i
\(376\) 0 0
\(377\) 11.0284 11.0284i 0.567992 0.567992i
\(378\) 0 0
\(379\) −1.31108 + 3.16523i −0.0673457 + 0.162587i −0.953969 0.299906i \(-0.903045\pi\)
0.886623 + 0.462493i \(0.153045\pi\)
\(380\) 0 0
\(381\) 7.40436 + 34.7001i 0.379337 + 1.77774i
\(382\) 0 0
\(383\) −9.44734 −0.482737 −0.241368 0.970434i \(-0.577596\pi\)
−0.241368 + 0.970434i \(0.577596\pi\)
\(384\) 0 0
\(385\) −1.97461 −0.100636
\(386\) 0 0
\(387\) 19.6282 0.544992i 0.997758 0.0277035i
\(388\) 0 0
\(389\) −1.49354 + 3.60573i −0.0757256 + 0.182818i −0.957209 0.289397i \(-0.906545\pi\)
0.881484 + 0.472215i \(0.156545\pi\)
\(390\) 0 0
\(391\) −35.5362 + 35.5362i −1.79714 + 1.79714i
\(392\) 0 0
\(393\) −0.721620 1.04819i −0.0364009 0.0528742i
\(394\) 0 0
\(395\) 3.53363 8.53094i 0.177796 0.429238i
\(396\) 0 0
\(397\) 35.3001 14.6218i 1.77166 0.733845i 0.777136 0.629333i \(-0.216672\pi\)
0.994524 0.104512i \(-0.0333281\pi\)
\(398\) 0 0
\(399\) 2.03025 + 0.374626i 0.101639 + 0.0187548i
\(400\) 0 0
\(401\) 15.2403 0.761063 0.380531 0.924768i \(-0.375741\pi\)
0.380531 + 0.924768i \(0.375741\pi\)
\(402\) 0 0
\(403\) 5.29058 + 12.7726i 0.263542 + 0.636248i
\(404\) 0 0
\(405\) −3.55663 7.39644i −0.176730 0.367532i
\(406\) 0 0
\(407\) −15.4459 + 15.4459i −0.765624 + 0.765624i
\(408\) 0 0
\(409\) −10.0840 10.0840i −0.498621 0.498621i 0.412387 0.911009i \(-0.364695\pi\)
−0.911009 + 0.412387i \(0.864695\pi\)
\(410\) 0 0
\(411\) 1.87863 + 1.21789i 0.0926660 + 0.0600741i
\(412\) 0 0
\(413\) 1.78337 0.738696i 0.0877540 0.0363489i
\(414\) 0 0
\(415\) 3.60401i 0.176914i
\(416\) 0 0
\(417\) 11.1958 + 2.06588i 0.548262 + 0.101167i
\(418\) 0 0
\(419\) 8.60540 + 20.7753i 0.420401 + 1.01494i 0.982229 + 0.187684i \(0.0600982\pi\)
−0.561828 + 0.827254i \(0.689902\pi\)
\(420\) 0 0
\(421\) 26.9768 + 11.1742i 1.31477 + 0.544596i 0.926273 0.376854i \(-0.122994\pi\)
0.388498 + 0.921450i \(0.372994\pi\)
\(422\) 0 0
\(423\) 10.9591 + 24.5104i 0.532852 + 1.19174i
\(424\) 0 0
\(425\) −18.4026 18.4026i −0.892656 0.892656i
\(426\) 0 0
\(427\) −3.80749 1.57711i −0.184257 0.0763219i
\(428\) 0 0
\(429\) −3.19553 14.9756i −0.154282 0.723031i
\(430\) 0 0
\(431\) 6.75028i 0.325150i −0.986696 0.162575i \(-0.948020\pi\)
0.986696 0.162575i \(-0.0519799\pi\)
\(432\) 0 0
\(433\) 12.8840i 0.619163i 0.950873 + 0.309582i \(0.100189\pi\)
−0.950873 + 0.309582i \(0.899811\pi\)
\(434\) 0 0
\(435\) 1.88695 + 8.84307i 0.0904723 + 0.423993i
\(436\) 0 0
\(437\) 13.2841 + 5.50247i 0.635467 + 0.263219i
\(438\) 0 0
\(439\) 12.4797 + 12.4797i 0.595625 + 0.595625i 0.939145 0.343521i \(-0.111620\pi\)
−0.343521 + 0.939145i \(0.611620\pi\)
\(440\) 0 0
\(441\) 8.02651 + 17.9515i 0.382215 + 0.854834i
\(442\) 0 0
\(443\) −11.4418 4.73933i −0.543614 0.225172i 0.0939401 0.995578i \(-0.470054\pi\)
−0.637554 + 0.770406i \(0.720054\pi\)
\(444\) 0 0
\(445\) −2.02052 4.87796i −0.0957817 0.231238i
\(446\) 0 0
\(447\) 15.4268 + 2.84660i 0.729663 + 0.134639i
\(448\) 0 0
\(449\) 28.4023i 1.34039i 0.742187 + 0.670193i \(0.233789\pi\)
−0.742187 + 0.670193i \(0.766211\pi\)
\(450\) 0 0
\(451\) −27.2699 + 11.2956i −1.28409 + 0.531887i
\(452\) 0 0
\(453\) 5.12514 + 3.32256i 0.240800 + 0.156107i
\(454\) 0 0
\(455\) 1.17220 + 1.17220i 0.0549538 + 0.0549538i
\(456\) 0 0
\(457\) 2.18179 2.18179i 0.102060 0.102060i −0.654233 0.756293i \(-0.727008\pi\)
0.756293 + 0.654233i \(0.227008\pi\)
\(458\) 0 0
\(459\) 26.2006 19.1308i 1.22294 0.892950i
\(460\) 0 0
\(461\) −2.67493 6.45785i −0.124584 0.300772i 0.849266 0.527965i \(-0.177045\pi\)
−0.973850 + 0.227194i \(0.927045\pi\)
\(462\) 0 0
\(463\) −14.4928 −0.673537 −0.336768 0.941588i \(-0.609334\pi\)
−0.336768 + 0.941588i \(0.609334\pi\)
\(464\) 0 0
\(465\) −7.88201 1.45441i −0.365520 0.0674467i
\(466\) 0 0
\(467\) −25.1292 + 10.4089i −1.16284 + 0.481665i −0.878821 0.477153i \(-0.841669\pi\)
−0.284022 + 0.958818i \(0.591669\pi\)
\(468\) 0 0
\(469\) −0.939596 + 2.26839i −0.0433865 + 0.104744i
\(470\) 0 0
\(471\) 9.04360 + 13.1363i 0.416707 + 0.605289i
\(472\) 0 0
\(473\) −15.0190 + 15.0190i −0.690573 + 0.690573i
\(474\) 0 0
\(475\) −2.84948 + 6.87926i −0.130743 + 0.315642i
\(476\) 0 0
\(477\) −15.0337 + 0.417422i −0.688347 + 0.0191125i
\(478\) 0 0
\(479\) 17.4339 0.796575 0.398288 0.917261i \(-0.369605\pi\)
0.398288 + 0.917261i \(0.369605\pi\)
\(480\) 0 0
\(481\) 18.3385 0.836165
\(482\) 0 0
\(483\) −1.94141 9.09832i −0.0883374 0.413988i
\(484\) 0 0
\(485\) 1.64938 3.98197i 0.0748947 0.180812i
\(486\) 0 0
\(487\) 17.8550 17.8550i 0.809087 0.809087i −0.175408 0.984496i \(-0.556125\pi\)
0.984496 + 0.175408i \(0.0561245\pi\)
\(488\) 0 0
\(489\) −15.0737 + 10.3774i −0.681657 + 0.469283i
\(490\) 0 0
\(491\) −5.45046 + 13.1586i −0.245976 + 0.593839i −0.997855 0.0654625i \(-0.979148\pi\)
0.751879 + 0.659301i \(0.229148\pi\)
\(492\) 0 0
\(493\) −33.0217 + 13.6780i −1.48722 + 0.616027i
\(494\) 0 0
\(495\) 8.29302 + 3.16838i 0.372743 + 0.142408i
\(496\) 0 0
\(497\) 7.28450 0.326754
\(498\) 0 0
\(499\) 0.698157 + 1.68550i 0.0312538 + 0.0754533i 0.938736 0.344638i \(-0.111998\pi\)
−0.907482 + 0.420091i \(0.861998\pi\)
\(500\) 0 0
\(501\) 6.28402 + 4.07384i 0.280750 + 0.182006i
\(502\) 0 0
\(503\) 10.2138 10.2138i 0.455412 0.455412i −0.441734 0.897146i \(-0.645636\pi\)
0.897146 + 0.441734i \(0.145636\pi\)
\(504\) 0 0
\(505\) 4.56545 + 4.56545i 0.203160 + 0.203160i
\(506\) 0 0
\(507\) 5.25542 8.10664i 0.233401 0.360028i
\(508\) 0 0
\(509\) 36.6825 15.1944i 1.62592 0.673480i 0.631157 0.775655i \(-0.282580\pi\)
0.994766 + 0.102175i \(0.0325803\pi\)
\(510\) 0 0
\(511\) 0.0465063i 0.00205732i
\(512\) 0 0
\(513\) −7.92556 4.83101i −0.349922 0.213294i
\(514\) 0 0
\(515\) −2.31108 5.57944i −0.101838 0.245859i
\(516\) 0 0
\(517\) −26.8318 11.1141i −1.18006 0.488797i
\(518\) 0 0
\(519\) −18.5810 26.9899i −0.815617 1.18473i
\(520\) 0 0
\(521\) 0.526260 + 0.526260i 0.0230559 + 0.0230559i 0.718541 0.695485i \(-0.244810\pi\)
−0.695485 + 0.718541i \(0.744810\pi\)
\(522\) 0 0
\(523\) 4.11152 + 1.70305i 0.179784 + 0.0744691i 0.470760 0.882261i \(-0.343980\pi\)
−0.290975 + 0.956731i \(0.593980\pi\)
\(524\) 0 0
\(525\) 4.71161 1.00537i 0.205632 0.0438780i
\(526\) 0 0
\(527\) 31.6825i 1.38011i
\(528\) 0 0
\(529\) 41.7931i 1.81709i
\(530\) 0 0
\(531\) −8.67512 + 0.240871i −0.376468 + 0.0104529i
\(532\) 0 0
\(533\) 22.8939 + 9.48297i 0.991646 + 0.410753i
\(534\) 0 0
\(535\) −0.764595 0.764595i −0.0330563 0.0330563i
\(536\) 0 0
\(537\) 19.5834 13.4821i 0.845087 0.581795i
\(538\) 0 0
\(539\) −19.6517 8.13999i −0.846457 0.350614i
\(540\) 0 0
\(541\) −2.79932 6.75816i −0.120352 0.290556i 0.852210 0.523201i \(-0.175262\pi\)
−0.972562 + 0.232645i \(0.925262\pi\)
\(542\) 0 0
\(543\) 2.67948 14.5212i 0.114988 0.623162i
\(544\) 0 0
\(545\) 10.8123i 0.463148i
\(546\) 0 0
\(547\) 12.5442 5.19596i 0.536349 0.222163i −0.0980322 0.995183i \(-0.531255\pi\)
0.634382 + 0.773020i \(0.281255\pi\)
\(548\) 0 0
\(549\) 13.4602 + 12.7329i 0.574468 + 0.543429i
\(550\) 0 0
\(551\) 7.23105 + 7.23105i 0.308053 + 0.308053i
\(552\) 0 0
\(553\) −4.77774 + 4.77774i −0.203170 + 0.203170i
\(554\) 0 0
\(555\) −5.78348 + 8.92118i −0.245495 + 0.378683i
\(556\) 0 0
\(557\) −4.26094 10.2868i −0.180542 0.435866i 0.807537 0.589817i \(-0.200800\pi\)
−0.988078 + 0.153951i \(0.950800\pi\)
\(558\) 0 0
\(559\) 17.8317 0.754199
\(560\) 0 0
\(561\) −6.36780 + 34.5096i −0.268849 + 1.45699i
\(562\) 0 0
\(563\) 16.5626 6.86044i 0.698029 0.289133i −0.00531196 0.999986i \(-0.501691\pi\)
0.703341 + 0.710853i \(0.251691\pi\)
\(564\) 0 0
\(565\) −2.38261 + 5.75213i −0.100237 + 0.241994i
\(566\) 0 0
\(567\) 0.333236 + 5.99622i 0.0139946 + 0.251817i
\(568\) 0 0
\(569\) −22.0173 + 22.0173i −0.923014 + 0.923014i −0.997241 0.0742272i \(-0.976351\pi\)
0.0742272 + 0.997241i \(0.476351\pi\)
\(570\) 0 0
\(571\) −13.9626 + 33.7086i −0.584315 + 1.41066i 0.304551 + 0.952496i \(0.401494\pi\)
−0.888866 + 0.458166i \(0.848506\pi\)
\(572\) 0 0
\(573\) 16.4342 3.50676i 0.686549 0.146497i
\(574\) 0 0
\(575\) 33.5535 1.39928
\(576\) 0 0
\(577\) −24.0941 −1.00305 −0.501526 0.865143i \(-0.667228\pi\)
−0.501526 + 0.865143i \(0.667228\pi\)
\(578\) 0 0
\(579\) 36.2957 7.74483i 1.50840 0.321864i
\(580\) 0 0
\(581\) −1.00921 + 2.43645i −0.0418691 + 0.101081i
\(582\) 0 0
\(583\) 11.5034 11.5034i 0.476422 0.476422i
\(584\) 0 0
\(585\) −3.04218 6.80392i −0.125779 0.281308i
\(586\) 0 0
\(587\) −6.34332 + 15.3141i −0.261817 + 0.632082i −0.999051 0.0435555i \(-0.986131\pi\)
0.737234 + 0.675637i \(0.236131\pi\)
\(588\) 0 0
\(589\) −8.37466 + 3.46890i −0.345072 + 0.142933i
\(590\) 0 0
\(591\) −4.52057 + 24.4987i −0.185952 + 1.00774i
\(592\) 0 0
\(593\) −21.6814 −0.890349 −0.445174 0.895444i \(-0.646858\pi\)
−0.445174 + 0.895444i \(0.646858\pi\)
\(594\) 0 0
\(595\) −1.45383 3.50986i −0.0596013 0.143890i
\(596\) 0 0
\(597\) −9.00722 + 13.8939i −0.368641 + 0.568640i
\(598\) 0 0
\(599\) 17.5864 17.5864i 0.718559 0.718559i −0.249751 0.968310i \(-0.580349\pi\)
0.968310 + 0.249751i \(0.0803487\pi\)
\(600\) 0 0
\(601\) 5.95620 + 5.95620i 0.242958 + 0.242958i 0.818073 0.575115i \(-0.195043\pi\)
−0.575115 + 0.818073i \(0.695043\pi\)
\(602\) 0 0
\(603\) 7.58589 8.01918i 0.308922 0.326566i
\(604\) 0 0
\(605\) 0.395394 0.163778i 0.0160751 0.00665851i
\(606\) 0 0
\(607\) 0.123708i 0.00502116i −0.999997 0.00251058i \(-0.999201\pi\)
0.999997 0.00251058i \(-0.000799143\pi\)
\(608\) 0 0
\(609\) 1.20062 6.50665i 0.0486517 0.263663i
\(610\) 0 0
\(611\) 9.33062 + 22.5261i 0.377476 + 0.911308i
\(612\) 0 0
\(613\) −22.5390 9.33597i −0.910343 0.377076i −0.122155 0.992511i \(-0.538980\pi\)
−0.788188 + 0.615435i \(0.788980\pi\)
\(614\) 0 0
\(615\) −11.8333 + 8.14659i −0.477166 + 0.328502i
\(616\) 0 0
\(617\) 10.8400 + 10.8400i 0.436403 + 0.436403i 0.890799 0.454397i \(-0.150145\pi\)
−0.454397 + 0.890799i \(0.650145\pi\)
\(618\) 0 0
\(619\) −18.8328 7.80078i −0.756952 0.313540i −0.0293776 0.999568i \(-0.509353\pi\)
−0.727575 + 0.686028i \(0.759353\pi\)
\(620\) 0 0
\(621\) −6.44519 + 41.3264i −0.258636 + 1.65837i
\(622\) 0 0
\(623\) 3.86348i 0.154787i
\(624\) 0 0
\(625\) 13.2180i 0.528720i
\(626\) 0 0
\(627\) 9.81915 2.09523i 0.392139 0.0836753i
\(628\) 0 0
\(629\) −38.8272 16.0827i −1.54814 0.641261i
\(630\) 0 0
\(631\) −17.8628 17.8628i −0.711107 0.711107i 0.255660 0.966767i \(-0.417707\pi\)
−0.966767 + 0.255660i \(0.917707\pi\)
\(632\) 0 0
\(633\) −6.51136 9.45808i −0.258803 0.375925i
\(634\) 0 0
\(635\) −17.2585 7.14869i −0.684881 0.283687i
\(636\) 0 0
\(637\) 6.83377 + 16.4982i 0.270764 + 0.653682i
\(638\) 0 0
\(639\) −30.5936 11.6884i −1.21026 0.462386i
\(640\) 0 0
\(641\) 35.0585i 1.38473i −0.721548 0.692364i \(-0.756569\pi\)
0.721548 0.692364i \(-0.243431\pi\)
\(642\) 0 0
\(643\) −25.3200 + 10.4879i −0.998524 + 0.413602i −0.821256 0.570561i \(-0.806726\pi\)
−0.177268 + 0.984163i \(0.556726\pi\)
\(644\) 0 0
\(645\) −5.62363 + 8.67461i −0.221430 + 0.341562i
\(646\) 0 0
\(647\) −12.7202 12.7202i −0.500084 0.500084i 0.411380 0.911464i \(-0.365047\pi\)
−0.911464 + 0.411380i \(0.865047\pi\)
\(648\) 0 0
\(649\) 6.63797 6.63797i 0.260563 0.260563i
\(650\) 0 0
\(651\) 4.92127 + 3.19039i 0.192880 + 0.125041i
\(652\) 0 0
\(653\) −9.79087 23.6372i −0.383146 0.924997i −0.991353 0.131218i \(-0.958111\pi\)
0.608207 0.793778i \(1.70811\pi\)
\(654\) 0 0
\(655\) 0.669993 0.0261788
\(656\) 0 0
\(657\) 0.0746221 0.195318i 0.00291128 0.00762009i
\(658\) 0 0
\(659\) 20.3402 8.42518i 0.792341 0.328198i 0.0504566 0.998726i \(-0.483932\pi\)
0.741884 + 0.670528i \(0.233932\pi\)
\(660\) 0 0
\(661\) 1.08432 2.61778i 0.0421751 0.101820i −0.901388 0.433012i \(-0.857451\pi\)
0.943563 + 0.331192i \(0.107451\pi\)
\(662\) 0 0
\(663\) 24.2664 16.7060i 0.942427 0.648808i
\(664\) 0 0
\(665\) −0.768585 + 0.768585i −0.0298045 + 0.0298045i
\(666\) 0 0
\(667\) 17.6346 42.5738i 0.682816 1.64846i
\(668\) 0 0
\(669\) −3.18732 14.9372i −0.123229 0.577505i
\(670\) 0 0
\(671\) −20.0423 −0.773724
\(672\) 0 0
\(673\) 6.03385 0.232588 0.116294 0.993215i \(-0.462899\pi\)
0.116294 + 0.993215i \(0.462899\pi\)
\(674\) 0 0
\(675\) −21.4011 3.33767i −0.823729 0.128467i
\(676\) 0 0
\(677\) −1.92640 + 4.65075i −0.0740377 + 0.178743i −0.956566 0.291517i \(-0.905840\pi\)
0.882528 + 0.470260i \(0.155840\pi\)
\(678\) 0 0
\(679\) −2.23009 + 2.23009i −0.0855831 + 0.0855831i
\(680\) 0 0
\(681\) 24.3798 + 35.4130i 0.934237 + 1.35703i
\(682\) 0 0
\(683\) −5.29070 + 12.7729i −0.202443 + 0.488740i −0.992197 0.124684i \(-0.960208\pi\)
0.789754 + 0.613424i \(0.210208\pi\)
\(684\) 0 0
\(685\) −1.08901 + 0.451082i −0.0416088 + 0.0172349i
\(686\) 0 0
\(687\) 33.1305 + 6.11333i 1.26401 + 0.233238i
\(688\) 0 0
\(689\) −13.6577 −0.520317
\(690\) 0 0
\(691\) −11.3594 27.4241i −0.432134 1.04326i −0.978598 0.205781i \(-0.934027\pi\)
0.546464 0.837482i \(-0.315973\pi\)
\(692\) 0 0
\(693\) −4.71917 4.46419i −0.179267 0.169581i
\(694\) 0 0
\(695\) −4.23838 + 4.23838i −0.160771 + 0.160771i
\(696\) 0 0
\(697\) −40.1556 40.1556i −1.52100 1.52100i
\(698\) 0 0
\(699\) 1.13275 + 0.734346i 0.0428446 + 0.0277755i
\(700\) 0 0
\(701\) 21.6433 8.96496i 0.817457 0.338602i 0.0655321 0.997850i \(-0.479126\pi\)
0.751925 + 0.659249i \(0.229126\pi\)
\(702\) 0 0
\(703\) 12.0241i 0.453498i
\(704\) 0 0
\(705\) −13.9010 2.56504i −0.523540 0.0966050i
\(706\) 0 0
\(707\) −1.80798 4.36485i −0.0679961 0.164157i
\(708\) 0 0
\(709\) −4.37997 1.81424i −0.164493 0.0681354i 0.298917 0.954279i \(-0.403375\pi\)
−0.463411 + 0.886144i \(0.653375\pi\)
\(710\) 0 0
\(711\) 27.7318 12.3995i 1.04002 0.465017i
\(712\) 0 0
\(713\) 28.8834 + 28.8834i 1.08169 + 1.08169i
\(714\) 0 0
\(715\) 7.44831 + 3.08519i 0.278551 + 0.115380i
\(716\) 0 0
\(717\) −0.595728 2.79184i −0.0222479 0.104263i
\(718\) 0 0
\(719\) 50.4878i 1.88288i 0.337182 + 0.941439i \(0.390526\pi\)
−0.337182 + 0.941439i \(0.609474\pi\)
\(720\) 0 0
\(721\) 4.41907i 0.164575i
\(722\) 0 0
\(723\) −6.64053 31.1204i −0.246964 1.15738i
\(724\) 0 0
\(725\) 22.0471 + 9.13219i 0.818807 + 0.339161i
\(726\) 0 0
\(727\) −34.3899 34.3899i −1.27545 1.27545i −0.943185 0.332267i \(-0.892186\pi\)
−0.332267 0.943185i \(-0.607814\pi\)
\(728\) 0 0
\(729\) 8.22175 25.7178i 0.304509 0.952509i
\(730\) 0 0
\(731\) −37.7540 15.6382i −1.39638 0.578401i
\(732\) 0 0
\(733\) −18.4767 44.6066i −0.682451 1.64758i −0.759461 0.650552i \(-0.774537\pi\)
0.0770104 0.997030i \(-0.475463\pi\)
\(734\) 0 0
\(735\) −10.1811 1.87864i −0.375536 0.0692948i
\(736\) 0 0
\(737\) 11.9406i 0.439837i
\(738\) 0 0
\(739\) 45.4385 18.8212i 1.67148 0.692350i 0.672617 0.739991i \(-0.265170\pi\)
0.998865 + 0.0476402i \(0.0151701\pi\)
\(740\) 0 0
\(741\) −7.07283 4.58522i −0.259827 0.168442i
\(742\) 0 0
\(743\) −7.22016 7.22016i −0.264882 0.264882i 0.562152 0.827034i \(-0.309974\pi\)
−0.827034 + 0.562152i \(0.809974\pi\)
\(744\) 0 0
\(745\) −5.84009 + 5.84009i −0.213964 + 0.213964i
\(746\) 0 0
\(747\) 8.14793 8.61332i 0.298117 0.315145i
\(748\) 0 0
\(749\) 0.302790 + 0.731000i 0.0110637 + 0.0267102i
\(750\) 0 0
\(751\) −26.3211 −0.960472 −0.480236 0.877139i \(-0.659449\pi\)
−0.480236 + 0.877139i \(0.659449\pi\)
\(752\) 0 0
\(753\) −48.9168 9.02627i −1.78263 0.328935i
\(754\) 0 0
\(755\) −2.97095 + 1.23061i −0.108124 + 0.0447864i
\(756\) 0 0
\(757\) 6.71850 16.2199i 0.244188 0.589522i −0.753503 0.657445i \(-0.771637\pi\)
0.997691 + 0.0679230i \(0.0216372\pi\)
\(758\) 0 0
\(759\) −25.6555 37.2659i −0.931234 1.35267i
\(760\) 0 0
\(761\) −8.55374 + 8.55374i −0.310073 + 0.310073i −0.844938 0.534865i \(-0.820363\pi\)
0.534865 + 0.844938i \(0.320363\pi\)
\(762\) 0 0
\(763\) 3.02770 7.30953i 0.109610 0.264623i
\(764\) 0 0
\(765\) 0.474060 + 17.0735i 0.0171397 + 0.617295i
\(766\) 0 0
\(767\) −7.88110 −0.284570
\(768\) 0 0
\(769\) −50.1936 −1.81003 −0.905014 0.425381i \(-0.860140\pi\)
−0.905014 + 0.425381i \(0.860140\pi\)
\(770\) 0 0
\(771\) −5.06678 23.7452i −0.182476 0.855161i
\(772\) 0 0
\(773\) −13.4148 + 32.3861i −0.482496 + 1.16485i 0.475924 + 0.879486i \(0.342114\pi\)
−0.958420 + 0.285361i \(0.907886\pi\)
\(774\) 0 0
\(775\) −14.9574 + 14.9574i −0.537286 + 0.537286i
\(776\) 0 0
\(777\) 6.40800 4.41155i 0.229886 0.158263i
\(778\) 0 0
\(779\) −6.21775 + 15.0110i −0.222774 + 0.537824i
\(780\) 0 0
\(781\) 32.7295 13.5570i 1.17115 0.485107i
\(782\) 0 0
\(783\) −15.48