Properties

Label 768.2.o.b.287.2
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 287.2
Character \(\chi\) \(=\) 768.287
Dual form 768.2.o.b.479.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45336 + 0.942196i) q^{3} +(-0.348970 + 0.842489i) q^{5} +(-0.471834 + 0.471834i) q^{7} +(1.22453 - 2.73871i) q^{9} +O(q^{10})\) \(q+(-1.45336 + 0.942196i) q^{3} +(-0.348970 + 0.842489i) q^{5} +(-0.471834 + 0.471834i) q^{7} +(1.22453 - 2.73871i) q^{9} +(1.24185 - 2.99808i) q^{11} +(2.51698 - 1.04257i) q^{13} +(-0.286608 - 1.55324i) q^{15} +6.24340 q^{17} +(0.683586 + 1.65032i) q^{19} +(0.241187 - 1.13031i) q^{21} +(-5.69180 + 5.69180i) q^{23} +(2.94753 + 2.94753i) q^{25} +(0.800702 + 5.13409i) q^{27} +(-5.28905 + 2.19080i) q^{29} +5.07456i q^{31} +(1.01993 + 5.52737i) q^{33} +(-0.232859 - 0.562171i) q^{35} +(6.21892 + 2.57596i) q^{37} +(-2.67579 + 3.88672i) q^{39} +(-6.43169 - 6.43169i) q^{41} +(6.04703 + 2.50476i) q^{43} +(1.88000 + 1.98738i) q^{45} -8.94964i q^{47} +6.55474i q^{49} +(-9.07393 + 5.88250i) q^{51} +(4.63157 + 1.91846i) q^{53} +(2.09248 + 2.09248i) q^{55} +(-2.54843 - 1.75445i) q^{57} +(2.67262 + 1.10704i) q^{59} +(2.36352 + 5.70603i) q^{61} +(0.714438 + 1.86999i) q^{63} +2.48436i q^{65} +(3.39948 - 1.40811i) q^{67} +(2.90947 - 13.6350i) q^{69} +(7.71934 + 7.71934i) q^{71} +(0.0492824 - 0.0492824i) q^{73} +(-7.06098 - 1.50668i) q^{75} +(0.828653 + 2.00054i) q^{77} +10.1259 q^{79} +(-6.00103 - 6.70728i) q^{81} +(-3.65135 + 1.51244i) q^{83} +(-2.17876 + 5.25999i) q^{85} +(5.62276 - 8.16735i) q^{87} +(-4.09411 + 4.09411i) q^{89} +(-0.695680 + 1.67952i) q^{91} +(-4.78123 - 7.37518i) q^{93} -1.62893 q^{95} +4.72643 q^{97} +(-6.69018 - 7.07231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) −1.45336 + 0.942196i −0.839100 + 0.543977i
\(4\) 0 0
\(5\) −0.348970 + 0.842489i −0.156064 + 0.376772i −0.982501 0.186257i \(-0.940364\pi\)
0.826437 + 0.563030i \(0.190364\pi\)
\(6\) 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
\(9\) 1.22453 2.73871i 0.408178 0.912902i
\(10\) 0 0
\(11\) 1.24185 2.99808i 0.374431 0.903956i −0.618557 0.785740i \(-0.712282\pi\)
0.992988 0.118216i \(-0.0377176\pi\)
\(12\) 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 \(-0.226604\pi\)
0.757123 + 0.653272i \(0.226604\pi\)
\(18\) 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
\(21\) 0.241187 1.13031i 0.0526313 0.246653i
\(22\) 0 0
\(23\) −5.69180 + 5.69180i −1.18682 + 1.18682i −0.208881 + 0.977941i \(0.566982\pi\)
−0.977941 + 0.208881i \(0.933018\pi\)
\(24\) 0 0
\(25\) 2.94753 + 2.94753i 0.589505 + 0.589505i
\(26\) 0 0
\(27\) 0.800702 + 5.13409i 0.154095 + 0.988056i
\(28\) 0 0
\(29\) −5.28905 + 2.19080i −0.982152 + 0.406821i −0.815222 0.579148i \(-0.803385\pi\)
−0.166930 + 0.985969i \(0.553385\pi\)
\(30\) 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
\(39\) −2.67579 + 3.88672i −0.428469 + 0.622374i
\(40\) 0 0
\(41\) −6.43169 6.43169i −1.00446 1.00446i −0.999990 0.00447060i \(-0.998577\pi\)
−0.00447060 0.999990i \(1.49858\pi\)
\(42\) 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
\(45\) 1.88000 + 1.98738i 0.280254 + 0.296262i
\(46\) 0 0
\(47\) 8.94964i 1.30544i −0.757600 0.652720i \(-0.773628\pi\)
0.757600 0.652720i \(-0.226372\pi\)
\(48\) 0 0
\(49\) 6.55474i 0.936392i
\(50\) 0 0
\(51\) −9.07393 + 5.88250i −1.27060 + 0.823715i
\(52\) 0 0
\(53\) 4.63157 + 1.91846i 0.636195 + 0.263520i 0.677382 0.735631i \(-0.263114\pi\)
−0.0411879 + 0.999151i \(0.513114\pi\)
\(54\) 0 0
\(55\) 2.09248 + 2.09248i 0.282150 + 0.282150i
\(56\) 0 0
\(57\) −2.54843 1.75445i −0.337547 0.232382i
\(58\) 0 0
\(59\) 2.67262 + 1.10704i 0.347945 + 0.144124i 0.549810 0.835290i \(-0.314700\pi\)
−0.201865 + 0.979413i \(0.564700\pi\)
\(60\) 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
\(69\) 2.90947 13.6350i 0.350259 1.64147i
\(70\) 0 0
\(71\) 7.71934 + 7.71934i 0.916117 + 0.916117i 0.996744 0.0806272i \(-0.0256923\pi\)
−0.0806272 + 0.996744i \(0.525692\pi\)
\(72\) 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
\(75\) −7.06098 1.50668i −0.815331 0.173977i
\(76\) 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 −0.573966 0.818879i \(-0.694596\pi\)
0.173179 + 0.984890i \(0.444596\pi\)
\(84\) 0 0
\(85\) −2.17876 + 5.25999i −0.236320 + 0.570526i
\(86\) 0 0
\(87\) 5.62276 8.16735i 0.602823 0.875632i
\(88\) 0 0
\(89\) −4.09411 + 4.09411i −0.433974 + 0.433974i −0.889978 0.456004i \(-0.849280\pi\)
0.456004 + 0.889978i \(0.349280\pi\)
\(90\) 0 0
\(91\) −0.695680 + 1.67952i −0.0729270 + 0.176061i
\(92\) 0 0
\(93\) −4.78123 7.37518i −0.495790 0.764771i
\(94\) 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
\(99\) −6.69018 7.07231i −0.672389 0.710794i
\(100\) 0 0
\(101\) 2.70950 6.54131i 0.269605 0.650885i −0.729859 0.683597i \(-0.760415\pi\)
0.999465 + 0.0327124i \(0.0104145\pi\)
\(102\) 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
\(105\) 0.868104 + 0.597641i 0.0847183 + 0.0583238i
\(106\) 0 0
\(107\) −0.453771 + 1.09550i −0.0438677 + 0.105906i −0.944295 0.329101i \(-0.893254\pi\)
0.900427 + 0.435007i \(0.143254\pi\)
\(108\) 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 \(-0.395934\pi\)
0.321141 + 0.947031i \(0.395934\pi\)
\(114\) 0 0
\(115\) −2.80901 6.78155i −0.261941 0.632382i
\(116\) 0 0
\(117\) 0.226845 8.16994i 0.0209718 0.755311i
\(118\) 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
\(123\) 15.4075 + 3.28768i 1.38925 + 0.296440i
\(124\) 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 0.911121 0.412139i \(-0.135218\pi\)
−0.935686 + 0.352833i \(0.885218\pi\)
\(132\) 0 0
\(133\) −1.10122 0.456140i −0.0954878 0.0395523i
\(134\) 0 0
\(135\) −4.60483 1.11706i −0.396321 0.0961414i
\(136\) 0 0
\(137\) 0.914012 + 0.914012i 0.0780893 + 0.0780893i 0.745073 0.666983i \(-0.232415\pi\)
−0.666983 + 0.745073i \(0.732415\pi\)
\(138\) 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
\(141\) 8.43231 + 13.0071i 0.710129 + 1.09539i
\(142\) 0 0
\(143\) 8.84084i 0.739308i
\(144\) 0 0
\(145\) 5.22049i 0.433538i
\(146\) 0 0
\(147\) −6.17585 9.52643i −0.509376 0.785727i
\(148\) 0 0
\(149\) 8.36760 + 3.46597i 0.685501 + 0.283944i 0.698124 0.715977i \(-0.254018\pi\)
−0.0126235 + 0.999920i \(0.504018\pi\)
\(150\) 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
\(153\) 7.64526 17.0988i 0.618083 1.38236i
\(154\) 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
\(165\) −5.01267 1.06961i −0.390236 0.0832692i
\(166\) 0 0
\(167\) 3.05737 + 3.05737i 0.236587 + 0.236587i 0.815435 0.578848i \(-0.196498\pi\)
−0.578848 + 0.815435i \(0.696498\pi\)
\(168\) 0 0
\(169\) −3.94413 + 3.94413i −0.303395 + 0.303395i
\(170\) 0 0
\(171\) 5.35683 + 0.148736i 0.409647 + 0.0113742i
\(172\) 0 0
\(173\) −7.23974 17.4783i −0.550427 1.32885i −0.917159 0.398522i \(-0.869523\pi\)
0.366732 0.930327i \(1.61952\pi\)
\(174\) 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 0.145454 0.989365i \(-0.453536\pi\)
0.802438 + 0.596736i \(0.203536\pi\)
\(180\) 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
\(183\) −8.81125 6.06605i −0.651346 0.448415i
\(184\) 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
\(189\) −2.80024 2.04464i −0.203687 0.148726i
\(190\) 0 0
\(191\) 9.70190 0.702005 0.351002 0.936375i \(-0.385841\pi\)
0.351002 + 0.936375i \(0.385841\pi\)
\(192\) 0 0
\(193\) −21.4271 −1.54235 −0.771177 0.636621i \(-0.780332\pi\)
−0.771177 + 0.636621i \(0.780332\pi\)
\(194\) 0 0
\(195\) −2.34075 3.61067i −0.167625 0.258566i
\(196\) 0 0
\(197\) −5.50419 + 13.2883i −0.392157 + 0.946751i 0.597312 + 0.802009i \(0.296235\pi\)
−0.989469 + 0.144742i \(0.953765\pi\)
\(198\) 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
\(201\) −3.61397 + 5.24947i −0.254909 + 0.370269i
\(202\) 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
\(213\) −18.4921 3.94588i −1.26706 0.270368i
\(214\) 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
\(219\) −0.0251916 + 0.118059i −0.00170229 + 0.00797769i
\(220\) 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 \(0.183128\pi\)
−0.208543 + 0.978013i \(0.566872\pi\)
\(228\) 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
\(231\) −3.08924 2.12677i −0.203257 0.139931i
\(232\) 0 0
\(233\) 0.551118 + 0.551118i 0.0361050 + 0.0361050i 0.724929 0.688824i \(-0.241873\pi\)
−0.688824 + 0.724929i \(0.741873\pi\)
\(234\) 0 0
\(235\) 7.53997 + 3.12316i 0.491854 + 0.203732i
\(236\) 0 0
\(237\) −14.7166 + 9.54056i −0.955945 + 0.619726i
\(238\) 0 0
\(239\) 1.64816i 0.106610i −0.998578 0.0533052i \(-0.983024\pi\)
0.998578 0.0533052i \(-0.0169756\pi\)
\(240\) 0 0
\(241\) 18.3719i 1.18344i 0.806145 + 0.591718i \(0.201550\pi\)
−0.806145 + 0.591718i \(0.798450\pi\)
\(242\) 0 0
\(243\) 15.0413 + 4.09398i 0.964897 + 0.262629i
\(244\) 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
\(249\) 3.88172 5.63840i 0.245994 0.357319i
\(250\) 0 0
\(251\) −26.5328 10.9903i −1.67474 0.693699i −0.675684 0.737192i \(-0.736151\pi\)
−0.999054 + 0.0434928i \(0.986151\pi\)
\(252\) 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 \(-0.855968\pi\)
0.899361 0.437206i \(-0.144032\pi\)
\(258\) 0 0
\(259\) −4.14972 + 1.71887i −0.257851 + 0.106805i
\(260\) 0 0
\(261\) −0.476679 + 17.1679i −0.0295057 + 1.06266i
\(262\) 0 0
\(263\) −17.6733 17.6733i −1.08978 1.08978i −0.995550 0.0942329i \(-0.969960\pi\)
−0.0942329 0.995550i \(1.46996\pi\)
\(264\) 0 0
\(265\) −3.23256 + 3.23256i −0.198574 + 0.198574i
\(266\) 0 0
\(267\) 2.09278 9.80768i 0.128076 0.600220i
\(268\) 0 0
\(269\) −6.87589 16.5999i −0.419231 1.01211i −0.982571 0.185887i \(-0.940484\pi\)
0.563340 0.826225i \(1.69048\pi\)
\(270\) 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
\(279\) 13.8977 + 6.21397i 0.832035 + 0.372021i
\(280\) 0 0
\(281\) −11.2880 + 11.2880i −0.673386 + 0.673386i −0.958495 0.285109i \(-0.907970\pi\)
0.285109 + 0.958495i \(0.407970\pi\)
\(282\) 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
\(285\) 2.36743 1.53477i 0.140234 0.0909120i
\(286\) 0 0
\(287\) 6.06938 0.358264
\(288\) 0 0
\(289\) 21.9800 1.29294
\(290\) 0 0
\(291\) −6.86923 + 4.45322i −0.402681 + 0.261053i
\(292\) 0 0
\(293\) −8.25342 + 19.9255i −0.482170 + 1.16406i 0.476406 + 0.879225i \(0.341939\pi\)
−0.958576 + 0.284836i \(0.908061\pi\)
\(294\) 0 0
\(295\) −1.86533 + 1.86533i −0.108604 + 0.108604i
\(296\) 0 0
\(297\) 16.3868 + 3.97518i 0.950857 + 0.230663i
\(298\) 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
\(309\) −2.39373 + 11.2181i −0.136175 + 0.638174i
\(310\) 0 0
\(311\) 5.22034 5.22034i 0.296018 0.296018i −0.543434 0.839452i \(-0.682876\pi\)
0.839452 + 0.543434i \(0.182876\pi\)
\(312\) 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
\(315\) −1.82477 0.0506660i −0.102814 0.00285471i
\(316\) 0 0
\(317\) 27.3117 11.3129i 1.53398 0.635393i 0.553644 0.832753i \(-0.313237\pi\)
0.980331 + 0.197360i \(0.0632367\pi\)
\(318\) 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
\(327\) 11.6455 16.9156i 0.643995 0.935436i
\(328\) 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
\(333\) 14.6701 13.8774i 0.803915 0.760479i
\(334\) 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
\(339\) −9.92291 + 6.43289i −0.538939 + 0.349386i
\(340\) 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
\(345\) 10.4721 + 7.20942i 0.563796 + 0.388142i
\(346\) 0 0
\(347\) −23.6365 9.79057i −1.26888 0.525585i −0.356253 0.934389i \(-0.615946\pi\)
−0.912622 + 0.408804i \(0.865946\pi\)
\(348\) 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 \(0.156184\pi\)
−0.882020 + 0.471213i \(0.843816\pi\)
\(354\) 0 0
\(355\) −9.19728 + 3.80964i −0.488141 + 0.202195i
\(356\) 0 0
\(357\) 1.50583 7.05696i 0.0796968 0.373494i
\(358\) 0 0
\(359\) 7.15299 + 7.15299i 0.377520 + 0.377520i 0.870207 0.492686i \(-0.163985\pi\)
−0.492686 + 0.870207i \(0.663985\pi\)
\(360\) 0 0
\(361\) 11.1788 11.1788i 0.588355 0.588355i
\(362\) 0 0
\(363\) −0.794983 0.169635i −0.0417258 0.00890352i
\(364\) 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
\(375\) 8.21166 11.9279i 0.424048 0.615952i
\(376\) 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
\(381\) 19.3010 + 29.7723i 0.988819 + 1.52528i
\(382\) 0 0
\(383\) 9.44734 0.482737 0.241368 0.970434i \(-0.422404\pi\)
0.241368 + 0.970434i \(0.422404\pi\)
\(384\) 0 0
\(385\) −1.97461 −0.100636
\(386\) 0 0
\(387\) 14.2646 13.4939i 0.725111 0.685932i
\(388\) 0 0
\(389\) 1.49354 3.60573i 0.0757256 0.182818i −0.881484 0.472215i \(-0.843455\pi\)
0.957209 + 0.289397i \(0.0934547\pi\)
\(390\) 0 0
\(391\) −35.5362 + 35.5362i −1.79714 + 1.79714i
\(392\) 0 0
\(393\) 1.04819 + 0.721620i 0.0528742 + 0.0364009i
\(394\) 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 \(-0.624259\pi\)
−0.380531 + 0.924768i \(0.624259\pi\)
\(402\) 0 0
\(403\) 5.29058 + 12.7726i 0.263542 + 0.636248i
\(404\) 0 0
\(405\) 7.74499 2.71516i 0.384852 0.134917i
\(406\) 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
\(411\) −2.18957 0.467214i −0.108004 0.0230460i
\(412\) 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 \(-0.939902\pi\)
0.561828 0.827254i \(1.68990\pi\)
\(420\) 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
\(423\) −24.5104 10.9591i −1.19174 0.532852i
\(424\) 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
\(429\) 8.32980 + 12.8490i 0.402166 + 0.620353i
\(430\) 0 0
\(431\) 6.75028i 0.325150i 0.986696 + 0.162575i \(0.0519799\pi\)
−0.986696 + 0.162575i \(0.948020\pi\)
\(432\) 0 0
\(433\) 12.8840i 0.619163i 0.950873 + 0.309582i \(0.100189\pi\)
−0.950873 + 0.309582i \(0.899811\pi\)
\(434\) 0 0
\(435\) 4.91872 + 7.58727i 0.235835 + 0.363782i
\(436\) 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
\(441\) 17.9515 + 8.02651i 0.854834 + 0.382215i
\(442\) 0 0
\(443\) 11.4418 + 4.73933i 0.543614 + 0.225172i 0.637554 0.770406i \(-0.279946\pi\)
−0.0939401 + 0.995578i \(0.529946\pi\)
\(444\) 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 \(-0.766211\pi\)
0.742187 0.670193i \(-0.233789\pi\)
\(450\) 0 0
\(451\) −27.2699 + 11.2956i −1.28409 + 0.531887i
\(452\) 0 0
\(453\) 5.97342 + 1.27462i 0.280656 + 0.0598868i
\(454\) 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
\(459\) 4.99910 + 32.0542i 0.233338 + 1.49616i
\(460\) 0 0
\(461\) 2.67493 + 6.45785i 0.124584 + 0.300772i 0.973850 0.227194i \(-0.0729550\pi\)
−0.849266 + 0.527965i \(0.822955\pi\)
\(462\) 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 0.284022 0.958818i \(-0.408331\pi\)
0.878821 + 0.477153i \(0.158331\pi\)
\(468\) 0 0
\(469\) −0.939596 + 2.26839i −0.0433865 + 0.104744i
\(470\) 0 0
\(471\) 13.1363 + 9.04360i 0.605289 + 0.416707i
\(472\) 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
\(477\) 10.9256 10.3353i 0.500249 0.473220i
\(478\) 0 0
\(479\) −17.4339 −0.796575 −0.398288 0.917261i \(-0.630395\pi\)
−0.398288 + 0.917261i \(0.630395\pi\)
\(480\) 0 0
\(481\) 18.3385 0.836165
\(482\) 0 0
\(483\) 5.06069 + 7.80627i 0.230270 + 0.355198i
\(484\) 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
\(489\) −10.3774 + 15.0737i −0.469283 + 0.681657i
\(490\) 0 0
\(491\) 5.45046 13.1586i 0.245976 0.593839i −0.751879 0.659301i \(-0.770852\pi\)
0.997855 + 0.0654625i \(0.0208523\pi\)
\(492\) 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
\(501\) −7.32412 1.56283i −0.327218 0.0698222i
\(502\) 0 0
\(503\) −10.2138 + 10.2138i −0.455412 + 0.455412i −0.897146 0.441734i \(-0.854364\pi\)
0.441734 + 0.897146i \(0.354364\pi\)
\(504\) 0 0
\(505\) 4.56545 + 4.56545i 0.203160 + 0.203160i
\(506\) 0 0
\(507\) 2.01612 9.44840i 0.0895389 0.419618i
\(508\) 0 0
\(509\) −36.6825 + 15.1944i −1.62592 + 0.673480i −0.994766 0.102175i \(-0.967420\pi\)
−0.631157 + 0.775655i \(0.717420\pi\)
\(510\) 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
\(519\) 26.9899 + 18.5810i 1.18473 + 0.815617i
\(520\) 0 0
\(521\) −0.526260 0.526260i −0.0230559 0.0230559i 0.695485 0.718541i \(-0.255190\pi\)
−0.718541 + 0.695485i \(0.755190\pi\)
\(522\) 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
\(525\) 4.04252 2.62071i 0.176430 0.114377i
\(526\) 0 0
\(527\) 31.6825i 1.38011i
\(528\) 0 0
\(529\) 41.7931i 1.81709i
\(530\) 0 0
\(531\) 6.30456 5.96392i 0.273595 0.258812i
\(532\) 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
\(537\) −13.4821 + 19.5834i −0.581795 + 0.845087i
\(538\) 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
\(549\) 18.5214 + 0.514259i 0.790472 + 0.0219481i
\(550\) 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
\(555\) 2.21869 10.3978i 0.0941783 0.441361i
\(556\) 0 0
\(557\) 4.26094 + 10.2868i 0.180542 + 0.435866i 0.988078 0.153951i \(-0.0491998\pi\)
−0.807537 + 0.589817i \(0.799200\pi\)
\(558\) 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 −0.703341 0.710853i \(-0.748309\pi\)
0.00531196 + 0.999986i \(0.498309\pi\)
\(564\) 0 0
\(565\) −2.38261 + 5.75213i −0.100237 + 0.241994i
\(566\) 0 0
\(567\) 5.99622 + 0.333236i 0.251817 + 0.0139946i
\(568\) 0 0
\(569\) 22.0173 22.0173i 0.923014 0.923014i −0.0742272 0.997241i \(-0.523649\pi\)
0.997241 + 0.0742272i \(0.0236490\pi\)
\(570\) 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
\(573\) −14.1004 + 9.14108i −0.589052 + 0.381874i
\(574\) 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
\(579\) 31.1413 20.1885i 1.29419 0.839005i
\(580\) 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
\(585\) 6.80392 + 3.04218i 0.281308 + 0.125779i
\(586\) 0 0
\(587\) 6.34332 15.3141i 0.261817 0.632082i −0.737234 0.675637i \(-0.763869\pi\)
0.999051 + 0.0435555i \(0.0138685\pi\)
\(588\) 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 \(-0.353142\pi\)
0.445174 + 0.895444i \(0.353142\pi\)
\(594\) 0 0
\(595\) −1.45383 3.50986i −0.0596013 0.143890i
\(596\) 0 0
\(597\) −3.45541 + 16.1935i −0.141420 + 0.662758i
\(598\) 0 0
\(599\) −17.5864 + 17.5864i −0.718559 + 0.718559i −0.968310 0.249751i \(-0.919651\pi\)
0.249751 + 0.968310i \(0.419651\pi\)
\(600\) 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
\(603\) 0.306380 11.0345i 0.0124768 0.449358i
\(604\) 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
\(615\) −8.14659 + 11.8333i −0.328502 + 0.477166i
\(616\) 0 0
\(617\) −10.8400 10.8400i −0.436403 0.436403i 0.454397 0.890799i \(-0.349855\pi\)
−0.890799 + 0.454397i \(0.849855\pi\)
\(618\) 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
\(621\) −33.7796 24.6648i −1.35553 0.989763i
\(622\) 0 0
\(623\) 3.86348i 0.154787i
\(624\) 0 0
\(625\) 13.2180i 0.528720i
\(626\) 0 0
\(627\) −8.42474 + 5.46164i −0.336452 + 0.218117i
\(628\) 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
\(633\) −9.45808 6.51136i −0.375925 0.258803i
\(634\) 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 \(0.243431\pi\)
−0.721548 + 0.692364i \(0.756569\pi\)
\(642\) 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
\(645\) 2.15737 10.1104i 0.0849464 0.398096i
\(646\) 0 0
\(647\) 12.7202 + 12.7202i 0.500084 + 0.500084i 0.911464 0.411380i \(-0.134953\pi\)
−0.411380 + 0.911464i \(0.634953\pi\)
\(648\) 0 0
\(649\) 6.63797 6.63797i 0.260563 0.260563i
\(650\) 0 0
\(651\) 5.73581 + 1.22392i 0.224804 + 0.0479691i
\(652\) 0 0
\(653\) 9.79087 + 23.6372i 0.383146 + 0.924997i 0.991353 + 0.131218i \(0.0418889\pi\)
−0.608207 + 0.793778i \(0.708111\pi\)
\(654\) 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 −0.741884 0.670528i \(-0.766068\pi\)
−0.0504566 + 0.998726i \(0.516068\pi\)
\(660\) 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
\(663\) −16.7060 + 24.2664i −0.648808 + 0.942427i
\(664\) 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
\(669\) −8.30840 12.8160i −0.321221 0.495493i
\(670\) 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
\(675\) −12.7728 + 17.4930i −0.491624 + 0.673304i
\(676\) 0 0
\(677\) 1.92640 4.65075i 0.0740377 0.178743i −0.882528 0.470260i \(-0.844160\pi\)
0.956566 + 0.291517i \(0.0941601\pi\)
\(678\) 0 0
\(679\) −2.23009 + 2.23009i −0.0855831 + 0.0855831i
\(680\) 0 0
\(681\) −35.4130 24.3798i −1.35703 0.934237i
\(682\) 0 0
\(683\) 5.29070 12.7729i 0.202443 0.488740i −0.789754 0.613424i \(-0.789792\pi\)
0.992197 + 0.124684i \(0.0397916\pi\)
\(684\) 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
\(693\) 6.49362 + 0.180300i 0.246672 + 0.00684904i
\(694\) 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
\(699\) −1.32024 0.281714i −0.0499359 0.0106554i
\(700\) 0 0
\(701\) −21.6433 + 8.96496i −0.817457 + 0.338602i −0.751925 0.659249i \(-0.770874\pi\)
−0.0655321 + 0.997850i \(0.520874\pi\)
\(702\) 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
\(711\) 12.3995 27.7318i 0.465017 1.04002i
\(712\) 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
\(717\) 1.55289 + 2.39537i 0.0579936 + 0.0894568i
\(718\) 0 0
\(719\) 50.4878i 1.88288i −0.337182 0.941439i \(-0.609474\pi\)
0.337182 0.941439i \(-0.390526\pi\)
\(720\) 0 0
\(721\) 4.41907i 0.164575i
\(722\) 0 0
\(723\) −17.3099 26.7010i −0.643762 0.993022i
\(724\) 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
\(729\) −25.7178 + 8.22175i −0.952509 + 0.304509i
\(730\) 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
\(741\) −8.24348 1.75901i −0.302832 0.0646188i
\(742\) 0 0
\(743\) 7.22016 + 7.22016i 0.264882 + 0.264882i 0.827034 0.562152i \(-0.190026\pi\)
−0.562152 + 0.827034i \(0.690026\pi\)
\(744\) 0 0
\(745\) −5.84009 + 5.84009i −0.213964 + 0.213964i
\(746\) 0 0
\(747\) −0.329080 + 11.8520i −0.0120404 + 0.433642i
\(748\) 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
\(759\) −37.2659 25.6555i −1.35267 0.931234i
\(760\) 0 0
\(761\) 8.55374 8.55374i 0.310073 0.310073i −0.534865 0.844938i \(-0.679637\pi\)
0.844938 + 0.534865i \(0.179637\pi\)
\(762\) 0 0
\(763\) 3.02770 7.30953i 0.109610 0.264623i
\(764\) 0 0
\(765\) 11.7376 + 12.4080i 0.424374 + 0.448613i
\(766\) 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
\(771\) 13.2076 + 20.3731i 0.475660 + 0.733720i
\(772\) 0 0
\(773\) 13.4148 32.3861i 0.482496 1.16485i −0.475924 0.879486i \(-0.657886\pi\)
0.958420 0.285361i \(-0.0921136\pi\)
\(774\) 0 0
\(775\) −14.9574 + 14.9574i −0.537286 + 0.537286i
\(776\) 0 0
\(777\) 4.41155 6.40800i 0.158263 0.229886i
\(778\) 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
\(783\) −15.4827