Properties

Label 768.2.o.b.95.2
Level 768
Weight 2
Character 768.95
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 95.2
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.47792 - 0.903198i) q^{3} +(2.81491 - 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(1.36847 + 2.66970i) q^{9} +O(q^{10})\) \(q+(-1.47792 - 0.903198i) q^{3} +(2.81491 - 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(1.36847 + 2.66970i) q^{9} +(3.96678 - 1.64309i) q^{11} +(-1.13904 + 2.74988i) q^{13} +(-5.21329 - 0.819208i) q^{15} +5.73443 q^{17} +(-0.0793211 - 0.0328559i) q^{19} +(0.312577 + 1.29504i) q^{21} +(-1.46457 - 1.46457i) q^{23} +(3.02867 - 3.02867i) q^{25} +(0.388788 - 5.18159i) q^{27} +(-0.520422 + 1.25641i) q^{29} +5.64072i q^{31} +(-7.34659 - 1.15443i) q^{33} +(-2.16511 - 0.896820i) q^{35} +(-4.19628 - 10.1307i) q^{37} +(4.16709 - 3.03532i) q^{39} +(4.93573 - 4.93573i) q^{41} +(3.50661 + 8.46571i) q^{43} +(6.96490 + 5.91936i) q^{45} -8.98904i q^{47} -6.40839i q^{49} +(-8.47500 - 5.17932i) q^{51} +(-1.04873 - 2.53186i) q^{53} +(9.25030 - 9.25030i) q^{55} +(0.0875545 + 0.120201i) q^{57} +(0.498592 + 1.20371i) q^{59} +(3.69353 + 1.52991i) q^{61} +(0.707713 - 2.19627i) q^{63} +9.06875i q^{65} +(3.35550 - 8.10090i) q^{67} +(0.841717 + 3.48732i) q^{69} +(-4.08070 + 4.08070i) q^{71} +(1.59075 + 1.59075i) q^{73} +(-7.21160 + 1.74063i) q^{75} +(-3.05109 - 1.26380i) q^{77} +0.637492 q^{79} +(-5.25459 + 7.30679i) q^{81} +(1.94530 - 4.69638i) q^{83} +(16.1419 - 6.68618i) q^{85} +(1.90393 - 1.38682i) q^{87} +(0.902588 + 0.902588i) q^{89} +(2.11510 - 0.876104i) q^{91} +(5.09469 - 8.33651i) q^{93} -0.261590 q^{95} -13.3054 q^{97} +(9.81497 + 8.34158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) −1.47792 0.903198i −0.853275 0.521461i
\(4\) 0 0
\(5\) 2.81491 1.16597i 1.25886 0.521438i 0.349303 0.937010i \(-0.386418\pi\)
0.909561 + 0.415571i \(0.136418\pi\)
\(6\) 0 0
\(7\) −0.543879 0.543879i −0.205567 0.205567i 0.596813 0.802380i \(-0.296433\pi\)
−0.802380 + 0.596813i \(0.796433\pi\)
\(8\) 0 0
\(9\) 1.36847 + 2.66970i 0.456156 + 0.889900i
\(10\) 0 0
\(11\) 3.96678 1.64309i 1.19603 0.495411i 0.306314 0.951930i \(-0.400904\pi\)
0.889713 + 0.456520i \(0.150904\pi\)
\(12\) 0 0
\(13\) −1.13904 + 2.74988i −0.315912 + 0.762680i 0.683550 + 0.729903i \(0.260435\pi\)
−0.999463 + 0.0327767i \(0.989565\pi\)
\(14\) 0 0
\(15\) −5.21329 0.819208i −1.34607 0.211519i
\(16\) 0 0
\(17\) 5.73443 1.39080 0.695402 0.718621i \(-0.255226\pi\)
0.695402 + 0.718621i \(0.255226\pi\)
\(18\) 0 0
\(19\) −0.0793211 0.0328559i −0.0181975 0.00753765i 0.373566 0.927604i \(-0.378135\pi\)
−0.391764 + 0.920066i \(0.628135\pi\)
\(20\) 0 0
\(21\) 0.312577 + 1.29504i 0.0682098 + 0.282600i
\(22\) 0 0
\(23\) −1.46457 1.46457i −0.305385 0.305385i 0.537731 0.843116i \(-0.319281\pi\)
−0.843116 + 0.537731i \(0.819281\pi\)
\(24\) 0 0
\(25\) 3.02867 3.02867i 0.605733 0.605733i
\(26\) 0 0
\(27\) 0.388788 5.18159i 0.0748222 0.997197i
\(28\) 0 0
\(29\) −0.520422 + 1.25641i −0.0966400 + 0.233310i −0.964805 0.262966i \(-0.915299\pi\)
0.868165 + 0.496275i \(0.165299\pi\)
\(30\) 0 0
\(31\) 5.64072i 1.01310i 0.862210 + 0.506552i \(0.169080\pi\)
−0.862210 + 0.506552i \(0.830920\pi\)
\(32\) 0 0
\(33\) −7.34659 1.15443i −1.27888 0.200961i
\(34\) 0 0
\(35\) −2.16511 0.896820i −0.365971 0.151590i
\(36\) 0 0
\(37\) −4.19628 10.1307i −0.689864 1.66548i −0.745055 0.667003i \(-0.767577\pi\)
0.0551907 0.998476i \(-0.482423\pi\)
\(38\) 0 0
\(39\) 4.16709 3.03532i 0.667269 0.486040i
\(40\) 0 0
\(41\) 4.93573 4.93573i 0.770831 0.770831i −0.207421 0.978252i \(-0.566507\pi\)
0.978252 + 0.207421i \(0.0665069\pi\)
\(42\) 0 0
\(43\) 3.50661 + 8.46571i 0.534753 + 1.29101i 0.928344 + 0.371722i \(0.121233\pi\)
−0.393591 + 0.919286i \(0.628767\pi\)
\(44\) 0 0
\(45\) 6.96490 + 5.91936i 1.03827 + 0.882406i
\(46\) 0 0
\(47\) 8.98904i 1.31119i −0.755115 0.655593i \(-0.772419\pi\)
0.755115 0.655593i \(-0.227581\pi\)
\(48\) 0 0
\(49\) 6.40839i 0.915485i
\(50\) 0 0
\(51\) −8.47500 5.17932i −1.18674 0.725250i
\(52\) 0 0
\(53\) −1.04873 2.53186i −0.144054 0.347777i 0.835341 0.549733i \(-0.185270\pi\)
−0.979395 + 0.201955i \(0.935270\pi\)
\(54\) 0 0
\(55\) 9.25030 9.25030i 1.24731 1.24731i
\(56\) 0 0
\(57\) 0.0875545 + 0.120201i 0.0115969 + 0.0159210i
\(58\) 0 0
\(59\) 0.498592 + 1.20371i 0.0649111 + 0.156709i 0.953006 0.302950i \(-0.0979715\pi\)
−0.888095 + 0.459659i \(0.847972\pi\)
\(60\) 0 0
\(61\) 3.69353 + 1.52991i 0.472908 + 0.195885i 0.606392 0.795166i \(-0.292616\pi\)
−0.133484 + 0.991051i \(0.542616\pi\)
\(62\) 0 0
\(63\) 0.707713 2.19627i 0.0891634 0.276704i
\(64\) 0 0
\(65\) 9.06875i 1.12484i
\(66\) 0 0
\(67\) 3.35550 8.10090i 0.409940 0.989682i −0.575213 0.818004i \(-0.695081\pi\)
0.985153 0.171679i \(-0.0549191\pi\)
\(68\) 0 0
\(69\) 0.841717 + 3.48732i 0.101331 + 0.419824i
\(70\) 0 0
\(71\) −4.08070 + 4.08070i −0.484290 + 0.484290i −0.906499 0.422209i \(-0.861255\pi\)
0.422209 + 0.906499i \(0.361255\pi\)
\(72\) 0 0
\(73\) 1.59075 + 1.59075i 0.186183 + 0.186183i 0.794044 0.607861i \(-0.207972\pi\)
−0.607861 + 0.794044i \(0.707972\pi\)
\(74\) 0 0
\(75\) −7.21160 + 1.74063i −0.832724 + 0.200990i
\(76\) 0 0
\(77\) −3.05109 1.26380i −0.347704 0.144024i
\(78\) 0 0
\(79\) 0.637492 0.0717235 0.0358618 0.999357i \(-0.488582\pi\)
0.0358618 + 0.999357i \(0.488582\pi\)
\(80\) 0 0
\(81\) −5.25459 + 7.30679i −0.583844 + 0.811866i
\(82\) 0 0
\(83\) 1.94530 4.69638i 0.213525 0.515495i −0.780435 0.625237i \(-0.785002\pi\)
0.993960 + 0.109742i \(0.0350025\pi\)
\(84\) 0 0
\(85\) 16.1419 6.68618i 1.75083 0.725218i
\(86\) 0 0
\(87\) 1.90393 1.38682i 0.204122 0.148683i
\(88\) 0 0
\(89\) 0.902588 + 0.902588i 0.0956742 + 0.0956742i 0.753324 0.657650i \(-0.228449\pi\)
−0.657650 + 0.753324i \(0.728449\pi\)
\(90\) 0 0
\(91\) 2.11510 0.876104i 0.221723 0.0918406i
\(92\) 0 0
\(93\) 5.09469 8.33651i 0.528295 0.864456i
\(94\) 0 0
\(95\) −0.261590 −0.0268386
\(96\) 0 0
\(97\) −13.3054 −1.35095 −0.675477 0.737381i \(-0.736062\pi\)
−0.675477 + 0.737381i \(0.736062\pi\)
\(98\) 0 0
\(99\) 9.81497 + 8.34158i 0.986441 + 0.838360i
\(100\) 0 0
\(101\) −5.49437 + 2.27584i −0.546710 + 0.226455i −0.638904 0.769286i \(-0.720612\pi\)
0.0921939 + 0.995741i \(0.470612\pi\)
\(102\) 0 0
\(103\) 7.86860 + 7.86860i 0.775316 + 0.775316i 0.979030 0.203714i \(-0.0653014\pi\)
−0.203714 + 0.979030i \(0.565301\pi\)
\(104\) 0 0
\(105\) 2.38985 + 3.28095i 0.233226 + 0.320188i
\(106\) 0 0
\(107\) 0.901495 0.373412i 0.0871508 0.0360991i −0.338682 0.940901i \(-0.609981\pi\)
0.425833 + 0.904802i \(0.359981\pi\)
\(108\) 0 0
\(109\) −0.457650 + 1.10486i −0.0438349 + 0.105827i −0.944280 0.329142i \(-0.893241\pi\)
0.900446 + 0.434969i \(0.143241\pi\)
\(110\) 0 0
\(111\) −2.94829 + 18.7624i −0.279840 + 1.78085i
\(112\) 0 0
\(113\) −8.48446 −0.798151 −0.399076 0.916918i \(-0.630669\pi\)
−0.399076 + 0.916918i \(0.630669\pi\)
\(114\) 0 0
\(115\) −5.83029 2.41499i −0.543678 0.225199i
\(116\) 0 0
\(117\) −8.90010 + 0.722234i −0.822814 + 0.0667706i
\(118\) 0 0
\(119\) −3.11883 3.11883i −0.285903 0.285903i
\(120\) 0 0
\(121\) 5.25738 5.25738i 0.477944 0.477944i
\(122\) 0 0
\(123\) −11.7525 + 2.83665i −1.05969 + 0.255772i
\(124\) 0 0
\(125\) −0.835790 + 2.01777i −0.0747553 + 0.180475i
\(126\) 0 0
\(127\) 7.01144i 0.622165i 0.950383 + 0.311083i \(0.100692\pi\)
−0.950383 + 0.311083i \(0.899308\pi\)
\(128\) 0 0
\(129\) 2.46373 15.6788i 0.216920 1.38044i
\(130\) 0 0
\(131\) −4.09398 1.69578i −0.357693 0.148161i 0.196598 0.980484i \(-0.437011\pi\)
−0.554291 + 0.832323i \(0.687011\pi\)
\(132\) 0 0
\(133\) 0.0252714 + 0.0610107i 0.00219131 + 0.00529029i
\(134\) 0 0
\(135\) −4.94718 15.0390i −0.425786 1.29435i
\(136\) 0 0
\(137\) −6.04464 + 6.04464i −0.516428 + 0.516428i −0.916489 0.400061i \(-0.868989\pi\)
0.400061 + 0.916489i \(0.368989\pi\)
\(138\) 0 0
\(139\) 3.82265 + 9.22869i 0.324233 + 0.782767i 0.998999 + 0.0447354i \(0.0142445\pi\)
−0.674766 + 0.738032i \(0.735756\pi\)
\(140\) 0 0
\(141\) −8.11888 + 13.2850i −0.683733 + 1.11880i
\(142\) 0 0
\(143\) 12.7797i 1.06869i
\(144\) 0 0
\(145\) 4.14347i 0.344097i
\(146\) 0 0
\(147\) −5.78805 + 9.47106i −0.477390 + 0.781160i
\(148\) 0 0
\(149\) 4.03660 + 9.74522i 0.330691 + 0.798359i 0.998538 + 0.0540601i \(0.0172163\pi\)
−0.667846 + 0.744299i \(0.732784\pi\)
\(150\) 0 0
\(151\) −7.98901 + 7.98901i −0.650136 + 0.650136i −0.953026 0.302889i \(-0.902049\pi\)
0.302889 + 0.953026i \(0.402049\pi\)
\(152\) 0 0
\(153\) 7.84738 + 15.3092i 0.634423 + 1.23768i
\(154\) 0 0
\(155\) 6.57692 + 15.8781i 0.528271 + 1.27536i
\(156\) 0 0
\(157\) −2.65449 1.09953i −0.211852 0.0877518i 0.274234 0.961663i \(-0.411576\pi\)
−0.486086 + 0.873911i \(0.661576\pi\)
\(158\) 0 0
\(159\) −0.736834 + 4.68908i −0.0584347 + 0.371868i
\(160\) 0 0
\(161\) 1.59310i 0.125554i
\(162\) 0 0
\(163\) −3.51824 + 8.49377i −0.275570 + 0.665284i −0.999703 0.0243763i \(-0.992240\pi\)
0.724133 + 0.689660i \(0.242240\pi\)
\(164\) 0 0
\(165\) −22.0260 + 5.31631i −1.71472 + 0.413874i
\(166\) 0 0
\(167\) −6.70414 + 6.70414i −0.518782 + 0.518782i −0.917203 0.398421i \(-0.869558\pi\)
0.398421 + 0.917203i \(0.369558\pi\)
\(168\) 0 0
\(169\) 2.92794 + 2.92794i 0.225226 + 0.225226i
\(170\) 0 0
\(171\) −0.0208330 0.256726i −0.00159314 0.0196323i
\(172\) 0 0
\(173\) −18.7129 7.75114i −1.42272 0.589308i −0.467174 0.884165i \(-0.654728\pi\)
−0.955541 + 0.294857i \(0.904728\pi\)
\(174\) 0 0
\(175\) −3.29446 −0.249037
\(176\) 0 0
\(177\) 0.350309 2.22930i 0.0263308 0.167565i
\(178\) 0 0
\(179\) −7.00110 + 16.9021i −0.523286 + 1.26333i 0.412564 + 0.910928i \(0.364633\pi\)
−0.935851 + 0.352397i \(0.885367\pi\)
\(180\) 0 0
\(181\) −14.4907 + 6.00226i −1.07709 + 0.446144i −0.849487 0.527610i \(-0.823088\pi\)
−0.227601 + 0.973754i \(0.573088\pi\)
\(182\) 0 0
\(183\) −4.07691 5.59706i −0.301374 0.413747i
\(184\) 0 0
\(185\) −23.6243 23.6243i −1.73689 1.73689i
\(186\) 0 0
\(187\) 22.7472 9.42220i 1.66344 0.689019i
\(188\) 0 0
\(189\) −3.02961 + 2.60670i −0.220372 + 0.189610i
\(190\) 0 0
\(191\) 15.7313 1.13828 0.569139 0.822241i \(-0.307277\pi\)
0.569139 + 0.822241i \(0.307277\pi\)
\(192\) 0 0
\(193\) 12.2248 0.879962 0.439981 0.898007i \(-0.354985\pi\)
0.439981 + 0.898007i \(0.354985\pi\)
\(194\) 0 0
\(195\) 8.19087 13.4028i 0.586560 0.959797i
\(196\) 0 0
\(197\) 21.5949 8.94488i 1.53857 0.637297i 0.557365 0.830267i \(-0.311812\pi\)
0.981205 + 0.192971i \(0.0618122\pi\)
\(198\) 0 0
\(199\) −1.57778 1.57778i −0.111846 0.111846i 0.648969 0.760815i \(-0.275201\pi\)
−0.760815 + 0.648969i \(0.775201\pi\)
\(200\) 0 0
\(201\) −12.2759 + 8.94176i −0.865873 + 0.630703i
\(202\) 0 0
\(203\) 0.966382 0.400288i 0.0678267 0.0280947i
\(204\) 0 0
\(205\) 8.13869 19.6485i 0.568431 1.37231i
\(206\) 0 0
\(207\) 1.90575 5.91420i 0.132459 0.411065i
\(208\) 0 0
\(209\) −0.368634 −0.0254990
\(210\) 0 0
\(211\) 25.3543 + 10.5021i 1.74546 + 0.722994i 0.998296 + 0.0583569i \(0.0185861\pi\)
0.747166 + 0.664637i \(0.231414\pi\)
\(212\) 0 0
\(213\) 9.71660 2.34525i 0.665771 0.160694i
\(214\) 0 0
\(215\) 19.7415 + 19.7415i 1.34636 + 1.34636i
\(216\) 0 0
\(217\) 3.06787 3.06787i 0.208261 0.208261i
\(218\) 0 0
\(219\) −0.914229 3.78774i −0.0617779 0.255952i
\(220\) 0 0
\(221\) −6.53174 + 15.7690i −0.439372 + 1.06074i
\(222\) 0 0
\(223\) 23.6266i 1.58216i −0.611716 0.791078i \(-0.709520\pi\)
0.611716 0.791078i \(-0.290480\pi\)
\(224\) 0 0
\(225\) 12.2303 + 3.94100i 0.815351 + 0.262733i
\(226\) 0 0
\(227\) −16.7455 6.93620i −1.11144 0.460372i −0.250004 0.968245i \(-0.580432\pi\)
−0.861432 + 0.507873i \(0.830432\pi\)
\(228\) 0 0
\(229\) 5.05650 + 12.2075i 0.334143 + 0.806693i 0.998254 + 0.0590592i \(0.0188101\pi\)
−0.664111 + 0.747634i \(0.731190\pi\)
\(230\) 0 0
\(231\) 3.36779 + 4.62353i 0.221584 + 0.304206i
\(232\) 0 0
\(233\) 7.93372 7.93372i 0.519756 0.519756i −0.397742 0.917497i \(-0.630206\pi\)
0.917497 + 0.397742i \(0.130206\pi\)
\(234\) 0 0
\(235\) −10.4810 25.3033i −0.683703 1.65060i
\(236\) 0 0
\(237\) −0.942160 0.575782i −0.0611999 0.0374010i
\(238\) 0 0
\(239\) 16.7260i 1.08191i −0.841051 0.540956i \(-0.818063\pi\)
0.841051 0.540956i \(-0.181937\pi\)
\(240\) 0 0
\(241\) 9.00218i 0.579881i −0.957045 0.289941i \(-0.906364\pi\)
0.957045 0.289941i \(-0.0936356\pi\)
\(242\) 0 0
\(243\) 14.3653 6.05289i 0.921536 0.388293i
\(244\) 0 0
\(245\) −7.47200 18.0390i −0.477369 1.15247i
\(246\) 0 0
\(247\) 0.180700 0.180700i 0.0114976 0.0114976i
\(248\) 0 0
\(249\) −7.11675 + 5.18386i −0.451006 + 0.328514i
\(250\) 0 0
\(251\) 0.601450 + 1.45203i 0.0379632 + 0.0916513i 0.941724 0.336387i \(-0.109205\pi\)
−0.903761 + 0.428038i \(0.859205\pi\)
\(252\) 0 0
\(253\) −8.21607 3.40321i −0.516540 0.213958i
\(254\) 0 0
\(255\) −29.8953 4.69769i −1.87211 0.294181i
\(256\) 0 0
\(257\) 8.28941i 0.517079i 0.966001 + 0.258539i \(0.0832412\pi\)
−0.966001 + 0.258539i \(0.916759\pi\)
\(258\) 0 0
\(259\) −3.22761 + 7.79215i −0.200554 + 0.484181i
\(260\) 0 0
\(261\) −4.06642 + 0.329986i −0.251705 + 0.0204256i
\(262\) 0 0
\(263\) −8.76126 + 8.76126i −0.540243 + 0.540243i −0.923600 0.383357i \(-0.874768\pi\)
0.383357 + 0.923600i \(0.374768\pi\)
\(264\) 0 0
\(265\) −5.90415 5.90415i −0.362689 0.362689i
\(266\) 0 0
\(267\) −0.518733 2.14916i −0.0317460 0.131527i
\(268\) 0 0
\(269\) 15.1023 + 6.25558i 0.920804 + 0.381409i 0.792182 0.610284i \(-0.208945\pi\)
0.128621 + 0.991694i \(0.458945\pi\)
\(270\) 0 0
\(271\) 17.5035 1.06326 0.531631 0.846976i \(-0.321579\pi\)
0.531631 + 0.846976i \(0.321579\pi\)
\(272\) 0 0
\(273\) −3.91724 0.615548i −0.237082 0.0372547i
\(274\) 0 0
\(275\) 7.03766 16.9904i 0.424387 1.02456i
\(276\) 0 0
\(277\) −21.3684 + 8.85109i −1.28390 + 0.531811i −0.917163 0.398512i \(-0.869527\pi\)
−0.366742 + 0.930323i \(0.619527\pi\)
\(278\) 0 0
\(279\) −15.0590 + 7.71915i −0.901561 + 0.462133i
\(280\) 0 0
\(281\) 5.93438 + 5.93438i 0.354015 + 0.354015i 0.861601 0.507586i \(-0.169462\pi\)
−0.507586 + 0.861601i \(0.669462\pi\)
\(282\) 0 0
\(283\) −23.7525 + 9.83861i −1.41194 + 0.584845i −0.952822 0.303530i \(-0.901835\pi\)
−0.459119 + 0.888375i \(0.651835\pi\)
\(284\) 0 0
\(285\) 0.386608 + 0.236268i 0.0229007 + 0.0139953i
\(286\) 0 0
\(287\) −5.36888 −0.316915
\(288\) 0 0
\(289\) 15.8837 0.934334
\(290\) 0 0
\(291\) 19.6642 + 12.0174i 1.15274 + 0.704471i
\(292\) 0 0
\(293\) 4.20032 1.73983i 0.245386 0.101642i −0.256601 0.966517i \(-0.582603\pi\)
0.501987 + 0.864875i \(0.332603\pi\)
\(294\) 0 0
\(295\) 2.80698 + 2.80698i 0.163429 + 0.163429i
\(296\) 0 0
\(297\) −6.97159 21.1930i −0.404533 1.22974i
\(298\) 0 0
\(299\) 5.69562 2.35920i 0.329386 0.136436i
\(300\) 0 0
\(301\) 2.69715 6.51149i 0.155461 0.375316i
\(302\) 0 0
\(303\) 10.1758 + 1.59900i 0.584582 + 0.0918602i
\(304\) 0 0
\(305\) 12.1808 0.697469
\(306\) 0 0
\(307\) −12.3645 5.12154i −0.705678 0.292302i 0.000836540 1.00000i \(-0.499734\pi\)
−0.706515 + 0.707698i \(0.749734\pi\)
\(308\) 0 0
\(309\) −4.52222 18.7360i −0.257260 1.06586i
\(310\) 0 0
\(311\) 10.7303 + 10.7303i 0.608462 + 0.608462i 0.942544 0.334082i \(-0.108426\pi\)
−0.334082 + 0.942544i \(0.608426\pi\)
\(312\) 0 0
\(313\) −17.8971 + 17.8971i −1.01160 + 1.01160i −0.0116708 + 0.999932i \(0.503715\pi\)
−0.999932 + 0.0116708i \(0.996285\pi\)
\(314\) 0 0
\(315\) −0.568650 7.00747i −0.0320398 0.394826i
\(316\) 0 0
\(317\) 2.59675 6.26910i 0.145848 0.352108i −0.834026 0.551725i \(-0.813970\pi\)
0.979874 + 0.199617i \(0.0639698\pi\)
\(318\) 0 0
\(319\) 5.83900i 0.326921i
\(320\) 0 0
\(321\) −1.66960 0.262358i −0.0931879 0.0146434i
\(322\) 0 0
\(323\) −0.454861 0.188410i −0.0253091 0.0104834i
\(324\) 0 0
\(325\) 4.87871 + 11.7782i 0.270622 + 0.653340i
\(326\) 0 0
\(327\) 1.67428 1.21955i 0.0925878 0.0674411i
\(328\) 0 0
\(329\) −4.88895 + 4.88895i −0.269536 + 0.269536i
\(330\) 0 0
\(331\) −4.00950 9.67979i −0.220382 0.532050i 0.774560 0.632501i \(-0.217971\pi\)
−0.994942 + 0.100451i \(0.967971\pi\)
\(332\) 0 0
\(333\) 21.3035 25.0664i 1.16742 1.37363i
\(334\) 0 0
\(335\) 26.7157i 1.45963i
\(336\) 0 0
\(337\) 4.80498i 0.261744i 0.991399 + 0.130872i \(0.0417777\pi\)
−0.991399 + 0.130872i \(0.958222\pi\)
\(338\) 0 0
\(339\) 12.5393 + 7.66315i 0.681042 + 0.416205i
\(340\) 0 0
\(341\) 9.26823 + 22.3755i 0.501903 + 1.21170i
\(342\) 0 0
\(343\) −7.29254 + 7.29254i −0.393760 + 0.393760i
\(344\) 0 0
\(345\) 6.43547 + 8.83505i 0.346474 + 0.475663i
\(346\) 0 0
\(347\) −5.87587 14.1856i −0.315433 0.761523i −0.999485 0.0320898i \(-0.989784\pi\)
0.684052 0.729434i \(1.73978\pi\)
\(348\) 0 0
\(349\) 6.41003 + 2.65512i 0.343121 + 0.142125i 0.547588 0.836748i \(-0.315546\pi\)
−0.204467 + 0.978873i \(0.565546\pi\)
\(350\) 0 0
\(351\) 13.8059 + 6.97115i 0.736905 + 0.372092i
\(352\) 0 0
\(353\) 10.7742i 0.573453i 0.958012 + 0.286726i \(0.0925671\pi\)
−0.958012 + 0.286726i \(0.907433\pi\)
\(354\) 0 0
\(355\) −6.72880 + 16.2448i −0.357128 + 0.862182i
\(356\) 0 0
\(357\) 1.79245 + 7.42630i 0.0948665 + 0.393041i
\(358\) 0 0
\(359\) 7.99933 7.99933i 0.422189 0.422189i −0.463768 0.885957i \(-0.653503\pi\)
0.885957 + 0.463768i \(0.153503\pi\)
\(360\) 0 0
\(361\) −13.4298 13.4298i −0.706832 0.706832i
\(362\) 0 0
\(363\) −12.5184 + 3.02151i −0.657046 + 0.158588i
\(364\) 0 0
\(365\) 6.33256 + 2.62303i 0.331461 + 0.137296i
\(366\) 0 0
\(367\) −4.78544 −0.249798 −0.124899 0.992169i \(-0.539861\pi\)
−0.124899 + 0.992169i \(0.539861\pi\)
\(368\) 0 0
\(369\) 19.9313 + 6.42253i 1.03758 + 0.334343i
\(370\) 0 0
\(371\) −0.806641 + 1.94740i −0.0418787 + 0.101104i
\(372\) 0 0
\(373\) 24.5505 10.1691i 1.27118 0.526538i 0.357855 0.933777i \(-0.383508\pi\)
0.913322 + 0.407239i \(0.133508\pi\)
\(374\) 0 0
\(375\) 3.05768 2.22722i 0.157898 0.115013i
\(376\) 0 0
\(377\) −2.86220 2.86220i −0.147411 0.147411i
\(378\) 0 0
\(379\) −26.9921 + 11.1805i −1.38649 + 0.574304i −0.946209 0.323556i \(-0.895122\pi\)
−0.440282 + 0.897859i \(0.645122\pi\)
\(380\) 0 0
\(381\) 6.33272 10.3623i 0.324435 0.530878i
\(382\) 0 0
\(383\) 16.7272 0.854721 0.427360 0.904081i \(-0.359444\pi\)
0.427360 + 0.904081i \(0.359444\pi\)
\(384\) 0 0
\(385\) −10.0621 −0.512811
\(386\) 0 0
\(387\) −17.8022 + 20.9466i −0.904937 + 1.06478i
\(388\) 0 0
\(389\) 30.3193 12.5587i 1.53725 0.636749i 0.556294 0.830985i \(-0.312223\pi\)
0.980955 + 0.194236i \(0.0622228\pi\)
\(390\) 0 0
\(391\) −8.39850 8.39850i −0.424730 0.424730i
\(392\) 0 0
\(393\) 4.51893 + 6.20390i 0.227950 + 0.312945i
\(394\) 0 0
\(395\) 1.79448 0.743298i 0.0902901 0.0373994i
\(396\) 0 0
\(397\) −8.13703 + 19.6445i −0.408386 + 0.985931i 0.577177 + 0.816619i \(0.304154\pi\)
−0.985563 + 0.169312i \(0.945846\pi\)
\(398\) 0 0
\(399\) 0.0177556 0.112994i 0.000888894 0.00565676i
\(400\) 0 0
\(401\) −0.509396 −0.0254380 −0.0127190 0.999919i \(-0.504049\pi\)
−0.0127190 + 0.999919i \(0.504049\pi\)
\(402\) 0 0
\(403\) −15.5113 6.42500i −0.772674 0.320052i
\(404\) 0 0
\(405\) −6.27166 + 26.6946i −0.311641 + 1.32647i
\(406\) 0 0
\(407\) −33.2914 33.2914i −1.65019 1.65019i
\(408\) 0 0
\(409\) −6.54063 + 6.54063i −0.323413 + 0.323413i −0.850075 0.526662i \(-0.823443\pi\)
0.526662 + 0.850075i \(0.323443\pi\)
\(410\) 0 0
\(411\) 14.3930 3.47396i 0.709952 0.171358i
\(412\) 0 0
\(413\) 0.383497 0.925844i 0.0188707 0.0455578i
\(414\) 0 0
\(415\) 15.4880i 0.760278i
\(416\) 0 0
\(417\) 2.68578 17.0918i 0.131523 0.836990i
\(418\) 0 0
\(419\) −20.7965 8.61418i −1.01597 0.420830i −0.188343 0.982103i \(-0.560312\pi\)
−0.827631 + 0.561273i \(0.810312\pi\)
\(420\) 0 0
\(421\) 8.30131 + 20.0411i 0.404581 + 0.976745i 0.986539 + 0.163526i \(0.0522868\pi\)
−0.581958 + 0.813219i \(0.697713\pi\)
\(422\) 0 0
\(423\) 23.9980 12.3012i 1.16682 0.598105i
\(424\) 0 0
\(425\) 17.3677 17.3677i 0.842456 0.842456i
\(426\) 0 0
\(427\) −1.17675 2.84092i −0.0569468 0.137482i
\(428\) 0 0
\(429\) 11.5426 18.8873i 0.557282 0.911889i
\(430\) 0 0
\(431\) 1.97237i 0.0950057i 0.998871 + 0.0475028i \(0.0151263\pi\)
−0.998871 + 0.0475028i \(0.984874\pi\)
\(432\) 0 0
\(433\) 29.4876i 1.41709i 0.705668 + 0.708543i \(0.250647\pi\)
−0.705668 + 0.708543i \(0.749353\pi\)
\(434\) 0 0
\(435\) 3.74238 6.12370i 0.179433 0.293609i
\(436\) 0 0
\(437\) 0.0680518 + 0.164292i 0.00325536 + 0.00785913i
\(438\) 0 0
\(439\) −17.1823 + 17.1823i −0.820067 + 0.820067i −0.986117 0.166050i \(-0.946899\pi\)
0.166050 + 0.986117i \(0.446899\pi\)
\(440\) 0 0
\(441\) 17.1085 8.76968i 0.814690 0.417604i
\(442\) 0 0
\(443\) 4.22858 + 10.2087i 0.200906 + 0.485029i 0.991935 0.126749i \(-0.0404543\pi\)
−0.791029 + 0.611779i \(0.790454\pi\)
\(444\) 0 0
\(445\) 3.59309 + 1.48831i 0.170329 + 0.0705526i
\(446\) 0 0
\(447\) 2.83610 18.0485i 0.134143 0.853663i
\(448\) 0 0
\(449\) 27.4116i 1.29363i −0.762645 0.646817i \(-0.776100\pi\)
0.762645 0.646817i \(-0.223900\pi\)
\(450\) 0 0
\(451\) 11.4691 27.6888i 0.540057 1.30381i
\(452\) 0 0
\(453\) 19.0227 4.59143i 0.893766 0.215724i
\(454\) 0 0
\(455\) 4.93230 4.93230i 0.231230 0.231230i
\(456\) 0 0
\(457\) 5.05963 + 5.05963i 0.236680 + 0.236680i 0.815474 0.578794i \(-0.196477\pi\)
−0.578794 + 0.815474i \(0.696477\pi\)
\(458\) 0 0
\(459\) 2.22947 29.7134i 0.104063 1.38690i
\(460\) 0 0
\(461\) −28.5768 11.8369i −1.33095 0.551298i −0.400025 0.916504i \(-0.630999\pi\)
−0.930927 + 0.365206i \(0.880999\pi\)
\(462\) 0 0
\(463\) 8.48410 0.394290 0.197145 0.980374i \(-0.436833\pi\)
0.197145 + 0.980374i \(0.436833\pi\)
\(464\) 0 0
\(465\) 4.62093 29.4067i 0.214290 1.36371i
\(466\) 0 0
\(467\) 6.00576 14.4992i 0.277913 0.670942i −0.721864 0.692035i \(-0.756714\pi\)
0.999778 + 0.0210925i \(0.00671443\pi\)
\(468\) 0 0
\(469\) −6.23089 + 2.58092i −0.287716 + 0.119176i
\(470\) 0 0
\(471\) 2.93003 + 4.02254i 0.135008 + 0.185349i
\(472\) 0 0
\(473\) 27.8199 + 27.8199i 1.27916 + 1.27916i
\(474\) 0 0
\(475\) −0.339747 + 0.140728i −0.0155886 + 0.00645703i
\(476\) 0 0
\(477\) 5.32414 6.26455i 0.243776 0.286834i
\(478\) 0 0
\(479\) −28.2696 −1.29167 −0.645835 0.763477i \(-0.723491\pi\)
−0.645835 + 0.763477i \(0.723491\pi\)
\(480\) 0 0
\(481\) 32.6380 1.48816
\(482\) 0 0
\(483\) 1.43889 2.35447i 0.0654716 0.107132i
\(484\) 0 0
\(485\) −37.4533 + 15.5137i −1.70067 + 0.704440i
\(486\) 0 0
\(487\) −22.4971 22.4971i −1.01944 1.01944i −0.999807 0.0196335i \(-0.993750\pi\)
−0.0196335 0.999807i \(-0.506250\pi\)
\(488\) 0 0
\(489\) 12.8712 9.37542i 0.582056 0.423971i
\(490\) 0 0
\(491\) 0.871501 0.360988i 0.0393303 0.0162911i −0.362932 0.931816i \(-0.618224\pi\)
0.402262 + 0.915525i \(0.368224\pi\)
\(492\) 0 0
\(493\) −2.98432 + 7.20480i −0.134407 + 0.324488i
\(494\) 0 0
\(495\) 37.3542 + 12.0368i 1.67895 + 0.541013i
\(496\) 0 0
\(497\) 4.43881 0.199108
\(498\) 0 0
\(499\) 29.0833 + 12.0467i 1.30195 + 0.539284i 0.922524 0.385939i \(-0.126122\pi\)
0.379423 + 0.925223i \(0.376122\pi\)
\(500\) 0 0
\(501\) 15.9633 3.85299i 0.713188 0.172139i
\(502\) 0 0
\(503\) −15.9266 15.9266i −0.710132 0.710132i 0.256431 0.966563i \(-0.417454\pi\)
−0.966563 + 0.256431i \(0.917454\pi\)
\(504\) 0 0
\(505\) −12.8126 + 12.8126i −0.570152 + 0.570152i
\(506\) 0 0
\(507\) −1.68274 6.97176i −0.0747331 0.309627i
\(508\) 0 0
\(509\) 0.374204 0.903408i 0.0165863 0.0400428i −0.915369 0.402615i \(-0.868101\pi\)
0.931956 + 0.362572i \(0.118101\pi\)
\(510\) 0 0
\(511\) 1.73035i 0.0765460i
\(512\) 0 0
\(513\) −0.201085 + 0.398235i −0.00887810 + 0.0175825i
\(514\) 0 0
\(515\) 31.3239 + 12.9748i 1.38030 + 0.571738i
\(516\) 0 0
\(517\) −14.7698 35.6575i −0.649576 1.56821i
\(518\) 0 0
\(519\) 20.6553 + 28.3570i 0.906666 + 1.24473i
\(520\) 0 0
\(521\) −31.7757 + 31.7757i −1.39212 + 1.39212i −0.571558 + 0.820562i \(0.693661\pi\)
−0.820562 + 0.571558i \(0.806339\pi\)
\(522\) 0 0
\(523\) 2.56429 + 6.19074i 0.112128 + 0.270702i 0.969975 0.243203i \(-0.0781982\pi\)
−0.857847 + 0.513905i \(0.828198\pi\)
\(524\) 0 0
\(525\) 4.86893 + 2.97554i 0.212497 + 0.129863i
\(526\) 0 0
\(527\) 32.3463i 1.40903i
\(528\) 0 0
\(529\) 18.7100i 0.813480i
\(530\) 0 0
\(531\) −2.53123 + 2.97832i −0.109846 + 0.129248i
\(532\) 0 0
\(533\) 7.95069 + 19.1947i 0.344382 + 0.831413i
\(534\) 0 0
\(535\) 2.10224 2.10224i 0.0908876 0.0908876i
\(536\) 0 0
\(537\) 25.6130 18.6566i 1.10528 0.805090i
\(538\) 0 0
\(539\) −10.5296 25.4206i −0.453541 1.09494i
\(540\) 0 0
\(541\) −25.9983 10.7689i −1.11776 0.462989i −0.254154 0.967164i \(-0.581797\pi\)
−0.863602 + 0.504174i \(0.831797\pi\)
\(542\) 0 0
\(543\) 26.8373 + 4.21717i 1.15170 + 0.180976i
\(544\) 0 0
\(545\) 3.64369i 0.156079i
\(546\) 0 0
\(547\) 8.74735 21.1180i 0.374010 0.902939i −0.619053 0.785349i \(-0.712483\pi\)
0.993062 0.117590i \(-0.0375167\pi\)
\(548\) 0 0
\(549\) 0.970075 + 11.9542i 0.0414018 + 0.510195i
\(550\) 0 0
\(551\) 0.0825609 0.0825609i 0.00351721 0.00351721i
\(552\) 0 0
\(553\) −0.346719 0.346719i −0.0147440 0.0147440i
\(554\) 0 0
\(555\) 13.5773 + 56.2520i 0.576323 + 2.38777i
\(556\) 0 0
\(557\) 21.4222 + 8.87338i 0.907689 + 0.375977i 0.787171 0.616734i \(-0.211545\pi\)
0.120517 + 0.992711i \(0.461545\pi\)
\(558\) 0 0
\(559\) −27.2739 −1.15356
\(560\) 0 0
\(561\) −42.1285 6.62001i −1.77867 0.279497i
\(562\) 0 0
\(563\) 3.72042 8.98190i 0.156797 0.378542i −0.825886 0.563838i \(-0.809324\pi\)
0.982683 + 0.185296i \(0.0593243\pi\)
\(564\) 0 0
\(565\) −23.8830 + 9.89265i −1.00476 + 0.416187i
\(566\) 0 0
\(567\) 6.83187 1.11615i 0.286912 0.0468739i
\(568\) 0 0
\(569\) −8.43864 8.43864i −0.353766 0.353766i 0.507743 0.861509i \(-0.330480\pi\)
−0.861509 + 0.507743i \(0.830480\pi\)
\(570\) 0 0
\(571\) 17.9095 7.41834i 0.749488 0.310448i 0.0249551 0.999689i \(-0.492056\pi\)
0.724532 + 0.689241i \(0.242056\pi\)
\(572\) 0 0
\(573\) −23.2495 14.2085i −0.971264 0.593568i
\(574\) 0 0
\(575\) −8.87142 −0.369964
\(576\) 0 0
\(577\) −31.3503 −1.30513 −0.652565 0.757733i \(-0.726307\pi\)
−0.652565 + 0.757733i \(0.726307\pi\)
\(578\) 0 0
\(579\) −18.0672 11.0414i −0.750849 0.458866i
\(580\) 0 0
\(581\) −3.61227 + 1.49625i −0.149862 + 0.0620750i
\(582\) 0 0
\(583\) −8.32014 8.32014i −0.344585 0.344585i
\(584\) 0 0
\(585\) −24.2108 + 12.4103i −1.00099 + 0.513102i
\(586\) 0 0
\(587\) −14.6871 + 6.08361i −0.606202 + 0.251097i −0.664604 0.747196i \(-0.731400\pi\)
0.0584014 + 0.998293i \(0.481400\pi\)
\(588\) 0 0
\(589\) 0.185331 0.447428i 0.00763642 0.0184360i
\(590\) 0 0
\(591\) −39.9944 6.28465i −1.64515 0.258516i
\(592\) 0 0
\(593\) −6.53460 −0.268344 −0.134172 0.990958i \(-0.542837\pi\)
−0.134172 + 0.990958i \(0.542837\pi\)
\(594\) 0 0
\(595\) −12.4157 5.14275i −0.508994 0.210832i
\(596\) 0 0
\(597\) 0.906779 + 3.75688i 0.0371120 + 0.153759i
\(598\) 0 0
\(599\) 20.5360 + 20.5360i 0.839078 + 0.839078i 0.988738 0.149659i \(-0.0478177\pi\)
−0.149659 + 0.988738i \(0.547818\pi\)
\(600\) 0 0
\(601\) −1.20249 + 1.20249i −0.0490506 + 0.0490506i −0.731207 0.682156i \(-0.761042\pi\)
0.682156 + 0.731207i \(0.261042\pi\)
\(602\) 0 0
\(603\) 26.2189 2.12763i 1.06771 0.0866440i
\(604\) 0 0
\(605\) 8.66907 20.9290i 0.352448 0.850884i
\(606\) 0 0
\(607\) 42.2470i 1.71475i 0.514692 + 0.857375i \(0.327906\pi\)
−0.514692 + 0.857375i \(0.672094\pi\)
\(608\) 0 0
\(609\) −1.78977 0.281241i −0.0725251 0.0113965i
\(610\) 0 0
\(611\) 24.7188 + 10.2389i 1.00002 + 0.414220i
\(612\) 0 0
\(613\) 3.20549 + 7.73873i 0.129468 + 0.312564i 0.975300 0.220886i \(-0.0708950\pi\)
−0.845831 + 0.533451i \(0.820895\pi\)
\(614\) 0 0
\(615\) −29.7748 + 21.6880i −1.20064 + 0.874545i
\(616\) 0 0
\(617\) 30.2757 30.2757i 1.21885 1.21885i 0.250821 0.968034i \(-0.419299\pi\)
0.968034 0.250821i \(-0.0807005\pi\)
\(618\) 0 0
\(619\) −7.03045 16.9730i −0.282578 0.682203i 0.717317 0.696747i \(-0.245370\pi\)
−0.999894 + 0.0145446i \(0.995370\pi\)
\(620\) 0 0
\(621\) −8.15823 + 7.01941i −0.327379 + 0.281679i
\(622\) 0 0
\(623\) 0.981797i 0.0393349i
\(624\) 0 0
\(625\) 28.0703i 1.12281i
\(626\) 0 0
\(627\) 0.544810 + 0.332949i 0.0217576 + 0.0132967i
\(628\) 0 0
\(629\) −24.0633 58.0939i −0.959465 2.31635i
\(630\) 0 0
\(631\) 0.699961 0.699961i 0.0278650 0.0278650i −0.693037 0.720902i \(-0.743728\pi\)
0.720902 + 0.693037i \(0.243728\pi\)
\(632\) 0 0
\(633\) −27.9860 38.4212i −1.11235 1.52710i
\(634\) 0 0
\(635\) 8.17515 + 19.7366i 0.324421 + 0.783221i
\(636\) 0 0
\(637\) 17.6223 + 7.29941i 0.698222 + 0.289213i
\(638\) 0 0
\(639\) −16.4785 5.30993i −0.651881 0.210058i
\(640\) 0 0
\(641\) 36.4715i 1.44054i 0.693695 + 0.720269i \(0.255981\pi\)
−0.693695 + 0.720269i \(0.744019\pi\)
\(642\) 0 0
\(643\) −13.4470 + 32.4640i −0.530298 + 1.28025i 0.401027 + 0.916066i \(0.368653\pi\)
−0.931326 + 0.364187i \(0.881347\pi\)
\(644\) 0 0
\(645\) −11.3458 47.0069i −0.446741 1.85089i
\(646\) 0 0
\(647\) 7.01510 7.01510i 0.275792 0.275792i −0.555635 0.831427i \(-0.687525\pi\)
0.831427 + 0.555635i \(0.187525\pi\)
\(648\) 0 0
\(649\) 3.95560 + 3.95560i 0.155271 + 0.155271i
\(650\) 0 0
\(651\) −7.30494 + 1.76316i −0.286303 + 0.0691036i
\(652\) 0 0
\(653\) −7.33264 3.03728i −0.286948 0.118858i 0.234567 0.972100i \(-0.424633\pi\)
−0.521515 + 0.853242i \(0.674633\pi\)
\(654\) 0 0
\(655\) −13.5014 −0.527544
\(656\) 0 0
\(657\) −2.06993 + 6.42370i −0.0807556 + 0.250612i
\(658\) 0 0
\(659\) −9.46381 + 22.8477i −0.368658 + 0.890018i 0.625313 + 0.780374i \(0.284971\pi\)
−0.993971 + 0.109644i \(0.965029\pi\)
\(660\) 0 0
\(661\) 4.59417 1.90297i 0.178693 0.0740169i −0.291543 0.956558i \(-0.594169\pi\)
0.470236 + 0.882541i \(0.344169\pi\)
\(662\) 0 0
\(663\) 23.8959 17.4058i 0.928039 0.675986i
\(664\) 0 0
\(665\) 0.142273 + 0.142273i 0.00551713 + 0.00551713i
\(666\) 0 0
\(667\) 2.60230 1.07791i 0.100762 0.0417368i
\(668\) 0 0
\(669\) −21.3395 + 34.9181i −0.825033 + 1.35001i
\(670\) 0 0
\(671\) 17.1652 0.662654
\(672\) 0 0
\(673\) −14.0193 −0.540404 −0.270202 0.962804i \(-0.587090\pi\)
−0.270202 + 0.962804i \(0.587090\pi\)
\(674\) 0 0
\(675\) −14.5158 16.8708i −0.558713 0.649358i
\(676\) 0 0
\(677\) −25.4610 + 10.5463i −0.978545 + 0.405327i −0.813886 0.581024i \(-0.802652\pi\)
−0.164659 + 0.986351i \(0.552652\pi\)
\(678\) 0 0
\(679\) 7.23650 + 7.23650i 0.277712 + 0.277712i
\(680\) 0 0
\(681\) 18.4836 + 25.3756i 0.708294 + 0.972395i
\(682\) 0 0
\(683\) 7.18630 2.97666i 0.274976 0.113899i −0.240934 0.970541i \(-0.577454\pi\)
0.515910 + 0.856643i \(0.327454\pi\)
\(684\) 0 0
\(685\) −9.96720 + 24.0630i −0.380827 + 0.919398i
\(686\) 0 0
\(687\) 3.55268 22.6086i 0.135543 0.862573i
\(688\) 0 0
\(689\) 8.15685 0.310751
\(690\) 0 0
\(691\) −21.5412 8.92265i −0.819466 0.339434i −0.0667419 0.997770i \(-0.521260\pi\)
−0.752724 + 0.658336i \(0.771260\pi\)
\(692\) 0 0
\(693\) −0.801343 9.87496i −0.0304405 0.375119i
\(694\) 0 0
\(695\) 21.5208 + 21.5208i 0.816330 + 0.816330i
\(696\) 0 0
\(697\) 28.3036 28.3036i 1.07207 1.07207i
\(698\) 0 0
\(699\) −18.8911 + 4.55965i −0.714527 + 0.172462i
\(700\) 0 0
\(701\) −12.8390 + 30.9961i −0.484922 + 1.17071i 0.472322 + 0.881426i \(0.343416\pi\)
−0.957244 + 0.289280i \(0.906584\pi\)
\(702\) 0 0
\(703\) 0.941452i 0.0355075i
\(704\) 0 0
\(705\) −7.36389 + 46.8625i −0.277340 + 1.76494i
\(706\) 0 0
\(707\) 4.22606 + 1.75049i 0.158937 + 0.0658339i
\(708\) 0 0
\(709\) 0.0401422 + 0.0969118i 0.00150757 + 0.00363960i 0.924632 0.380863i \(-0.124373\pi\)
−0.923124 + 0.384502i \(0.874373\pi\)
\(710\) 0 0
\(711\) 0.872388 + 1.70191i 0.0327171 + 0.0638267i
\(712\) 0 0
\(713\) 8.26126 8.26126i 0.309387 0.309387i
\(714\) 0 0
\(715\) 14.9008 + 35.9737i 0.557258 + 1.34534i
\(716\) 0 0
\(717\) −15.1068 + 24.7195i −0.564175 + 0.923168i
\(718\) 0 0
\(719\) 7.25362i 0.270515i −0.990811 0.135257i \(-0.956814\pi\)
0.990811 0.135257i \(-0.0431861\pi\)
\(720\) 0 0
\(721\) 8.55913i 0.318759i
\(722\) 0 0
\(723\) −8.13075 + 13.3045i −0.302386 + 0.494798i
\(724\) 0 0
\(725\) 2.22906 + 5.38143i 0.0827853 + 0.199861i
\(726\) 0 0
\(727\) 33.8662 33.8662i 1.25603 1.25603i 0.303055 0.952973i \(-0.401993\pi\)
0.952973 0.303055i \(-0.0980066\pi\)
\(728\) 0 0
\(729\) −26.6977 4.02907i −0.988803 0.149225i
\(730\) 0 0
\(731\) 20.1084 + 48.5460i 0.743736 + 1.79554i
\(732\) 0 0
\(733\) 46.5930 + 19.2995i 1.72095 + 0.712842i 0.999799 + 0.0200663i \(0.00638774\pi\)
0.721153 + 0.692775i \(0.243612\pi\)
\(734\) 0 0
\(735\) −5.24981 + 33.4088i −0.193642 + 1.23230i
\(736\) 0 0
\(737\) 37.6478i 1.38678i
\(738\) 0 0
\(739\) 11.4353 27.6072i 0.420653 1.01555i −0.561502 0.827475i \(-0.689776\pi\)
0.982155 0.188072i \(-0.0602237\pi\)
\(740\) 0 0
\(741\) −0.430266 + 0.103851i −0.0158062 + 0.00381507i
\(742\) 0 0
\(743\) −31.4330 + 31.4330i −1.15317 + 1.15317i −0.167252 + 0.985914i \(0.553489\pi\)
−0.985914 + 0.167252i \(0.946511\pi\)
\(744\) 0 0
\(745\) 22.7253 + 22.7253i 0.832590 + 0.832590i
\(746\) 0 0
\(747\) 15.2000 1.23347i 0.556139 0.0451301i
\(748\) 0 0
\(749\) −0.693395 0.287214i −0.0253361 0.0104946i
\(750\) 0 0
\(751\) −9.38556 −0.342484 −0.171242 0.985229i \(-0.554778\pi\)
−0.171242 + 0.985229i \(0.554778\pi\)
\(752\) 0 0
\(753\) 0.422577 2.68920i 0.0153996 0.0980001i
\(754\) 0 0
\(755\) −13.1733 + 31.8033i −0.479427 + 1.15744i
\(756\) 0 0
\(757\) 21.2091 8.78508i 0.770857 0.319299i 0.0376373 0.999291i \(-0.488017\pi\)
0.733219 + 0.679992i \(0.238017\pi\)
\(758\) 0 0
\(759\) 9.06889 + 12.4504i 0.329180 + 0.451921i
\(760\) 0 0
\(761\) −17.8648 17.8648i −0.647599 0.647599i 0.304813 0.952412i \(-0.401406\pi\)
−0.952412 + 0.304813i \(0.901406\pi\)
\(762\) 0 0
\(763\) 0.849818 0.352006i 0.0307655 0.0127435i
\(764\) 0 0
\(765\) 39.9397 + 33.9441i 1.44402 + 1.22725i
\(766\) 0 0
\(767\) −3.87797 −0.140025
\(768\) 0 0
\(769\) −1.71307 −0.0617750 −0.0308875 0.999523i \(-0.509833\pi\)
−0.0308875 + 0.999523i \(0.509833\pi\)
\(770\) 0 0
\(771\) 7.48697 12.2510i 0.269637 0.441210i
\(772\) 0 0
\(773\) −25.0667 + 10.3830i −0.901587 + 0.373450i −0.784830 0.619711i \(-0.787250\pi\)
−0.116757 + 0.993161i \(0.537250\pi\)
\(774\) 0 0
\(775\) 17.0839 + 17.0839i 0.613671 + 0.613671i
\(776\) 0 0
\(777\) 11.8080 8.60096i 0.423609 0.308558i
\(778\) 0 0
\(779\) −0.553675 + 0.229340i −0.0198375 + 0.00821694i
\(780\) 0 0
\(781\) −9.48225 + 22.8922i −0.339302 + 0.819146i
\(782\) 0 0
\(783\) 6.30787 + 3.18509i 0.225425