Properties

Label 768.2.o.b.95.13
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 95.13
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68370 + 0.406387i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(2.66970 + 1.36847i) q^{9} +O(q^{10})\) \(q+(1.68370 + 0.406387i) q^{3} +(-2.81491 + 1.16597i) q^{5} +(-0.543879 - 0.543879i) q^{7} +(2.66970 + 1.36847i) q^{9} +(-3.96678 + 1.64309i) q^{11} +(-1.13904 + 2.74988i) q^{13} +(-5.21329 + 0.819208i) q^{15} -5.73443 q^{17} +(-0.0793211 - 0.0328559i) q^{19} +(-0.694704 - 1.13675i) q^{21} +(1.46457 + 1.46457i) q^{23} +(3.02867 - 3.02867i) q^{25} +(3.93885 + 3.38902i) q^{27} +(0.520422 - 1.25641i) q^{29} +5.64072i q^{31} +(-7.34659 + 1.15443i) q^{33} +(2.16511 + 0.896820i) q^{35} +(-4.19628 - 10.1307i) q^{37} +(-3.03532 + 4.16709i) q^{39} +(-4.93573 + 4.93573i) q^{41} +(3.50661 + 8.46571i) q^{43} +(-9.11055 - 0.739312i) q^{45} +8.98904i q^{47} -6.40839i q^{49} +(-9.65507 - 2.33040i) q^{51} +(1.04873 + 2.53186i) q^{53} +(9.25030 - 9.25030i) q^{55} +(-0.120201 - 0.0875545i) q^{57} +(-0.498592 - 1.20371i) q^{59} +(3.69353 + 1.52991i) q^{61} +(-0.707713 - 2.19627i) q^{63} -9.06875i q^{65} +(3.35550 - 8.10090i) q^{67} +(1.87072 + 3.06109i) q^{69} +(4.08070 - 4.08070i) q^{71} +(1.59075 + 1.59075i) q^{73} +(6.33018 - 3.86856i) q^{75} +(3.05109 + 1.26380i) q^{77} +0.637492 q^{79} +(5.25459 + 7.30679i) q^{81} +(-1.94530 + 4.69638i) q^{83} +(16.1419 - 6.68618i) q^{85} +(1.38682 - 1.90393i) q^{87} +(-0.902588 - 0.902588i) q^{89} +(2.11510 - 0.876104i) q^{91} +(-2.29231 + 9.49729i) q^{93} +0.261590 q^{95} -13.3054 q^{97} +(-12.8386 - 1.04184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) 1.68370 + 0.406387i 0.972085 + 0.234627i
\(4\) 0 0
\(5\) −2.81491 + 1.16597i −1.25886 + 0.521438i −0.909561 0.415571i \(-0.863582\pi\)
−0.349303 + 0.937010i \(0.613582\pi\)
\(6\) 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
\(9\) 2.66970 + 1.36847i 0.889900 + 0.456156i
\(10\) 0 0
\(11\) −3.96678 + 1.64309i −1.19603 + 0.495411i −0.889713 0.456520i \(-0.849096\pi\)
−0.306314 + 0.951930i \(0.599096\pi\)
\(12\) 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 \(-0.744774\pi\)
−0.695402 + 0.718621i \(0.744774\pi\)
\(18\) 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
\(21\) −0.694704 1.13675i −0.151597 0.248060i
\(22\) 0 0
\(23\) 1.46457 + 1.46457i 0.305385 + 0.305385i 0.843116 0.537731i \(-0.180719\pi\)
−0.537731 + 0.843116i \(0.680719\pi\)
\(24\) 0 0
\(25\) 3.02867 3.02867i 0.605733 0.605733i
\(26\) 0 0
\(27\) 3.93885 + 3.38902i 0.758032 + 0.652217i
\(28\) 0 0
\(29\) 0.520422 1.25641i 0.0966400 0.233310i −0.868165 0.496275i \(-0.834701\pi\)
0.964805 + 0.262966i \(0.0847006\pi\)
\(30\) 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
\(39\) −3.03532 + 4.16709i −0.486040 + 0.667269i
\(40\) 0 0
\(41\) −4.93573 + 4.93573i −0.770831 + 0.770831i −0.978252 0.207421i \(-0.933493\pi\)
0.207421 + 0.978252i \(0.433493\pi\)
\(42\) 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
\(45\) −9.11055 0.739312i −1.35812 0.110210i
\(46\) 0 0
\(47\) 8.98904i 1.31119i 0.755115 + 0.655593i \(0.227581\pi\)
−0.755115 + 0.655593i \(0.772419\pi\)
\(48\) 0 0
\(49\) 6.40839i 0.915485i
\(50\) 0 0
\(51\) −9.65507 2.33040i −1.35198 0.326321i
\(52\) 0 0
\(53\) 1.04873 + 2.53186i 0.144054 + 0.347777i 0.979395 0.201955i \(-0.0647296\pi\)
−0.835341 + 0.549733i \(0.814730\pi\)
\(54\) 0 0
\(55\) 9.25030 9.25030i 1.24731 1.24731i
\(56\) 0 0
\(57\) −0.120201 0.0875545i −0.0159210 0.0115969i
\(58\) 0 0
\(59\) −0.498592 1.20371i −0.0649111 0.156709i 0.888095 0.459659i \(-0.152028\pi\)
−0.953006 + 0.302950i \(0.902028\pi\)
\(60\) 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
\(69\) 1.87072 + 3.06109i 0.225209 + 0.368512i
\(70\) 0 0
\(71\) 4.08070 4.08070i 0.484290 0.484290i −0.422209 0.906499i \(-0.638745\pi\)
0.906499 + 0.422209i \(0.138745\pi\)
\(72\) 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
\(75\) 6.33018 3.86856i 0.730946 0.446703i
\(76\) 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 −0.993960 0.109742i \(-0.964998\pi\)
0.780435 + 0.625237i \(0.214998\pi\)
\(84\) 0 0
\(85\) 16.1419 6.68618i 1.75083 0.725218i
\(86\) 0 0
\(87\) 1.38682 1.90393i 0.148683 0.204122i
\(88\) 0 0
\(89\) −0.902588 0.902588i −0.0956742 0.0956742i 0.657650 0.753324i \(-0.271551\pi\)
−0.753324 + 0.657650i \(0.771551\pi\)
\(90\) 0 0
\(91\) 2.11510 0.876104i 0.221723 0.0918406i
\(92\) 0 0
\(93\) −2.29231 + 9.49729i −0.237702 + 0.984823i
\(94\) 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
\(99\) −12.8386 1.04184i −1.29033 0.104709i
\(100\) 0 0
\(101\) 5.49437 2.27584i 0.546710 0.226455i −0.0921939 0.995741i \(-0.529388\pi\)
0.638904 + 0.769286i \(0.279388\pi\)
\(102\) 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
\(105\) 3.28095 + 2.38985i 0.320188 + 0.233226i
\(106\) 0 0
\(107\) −0.901495 + 0.373412i −0.0871508 + 0.0360991i −0.425833 0.904802i \(-0.640019\pi\)
0.338682 + 0.940901i \(0.390019\pi\)
\(108\) 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 \(-0.369331\pi\)
0.399076 + 0.916918i \(0.369331\pi\)
\(114\) 0 0
\(115\) −5.83029 2.41499i −0.543678 0.225199i
\(116\) 0 0
\(117\) −6.80402 + 5.78262i −0.629032 + 0.534604i
\(118\) 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
\(123\) −10.3161 + 6.30448i −0.930172 + 0.568456i
\(124\) 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 0.554291 0.832323i \(-0.312989\pi\)
−0.196598 + 0.980484i \(0.562989\pi\)
\(132\) 0 0
\(133\) 0.0252714 + 0.0610107i 0.00219131 + 0.00529029i
\(134\) 0 0
\(135\) −15.0390 4.94718i −1.29435 0.425786i
\(136\) 0 0
\(137\) 6.04464 6.04464i 0.516428 0.516428i −0.400061 0.916489i \(-0.631011\pi\)
0.916489 + 0.400061i \(0.131011\pi\)
\(138\) 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
\(141\) −3.65302 + 15.1348i −0.307640 + 1.27458i
\(142\) 0 0
\(143\) 12.7797i 1.06869i
\(144\) 0 0
\(145\) 4.14347i 0.344097i
\(146\) 0 0
\(147\) 2.60429 10.7898i 0.214798 0.889929i
\(148\) 0 0
\(149\) −4.03660 9.74522i −0.330691 0.798359i −0.998538 0.0540601i \(-0.982784\pi\)
0.667846 0.744299i \(1.73278\pi\)
\(150\) 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
\(153\) −15.3092 7.84738i −1.23768 0.634423i
\(154\) 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
\(165\) 19.3339 11.8155i 1.50514 0.919838i
\(166\) 0 0
\(167\) 6.70414 6.70414i 0.518782 0.518782i −0.398421 0.917203i \(-0.630442\pi\)
0.917203 + 0.398421i \(0.130442\pi\)
\(168\) 0 0
\(169\) 2.92794 + 2.92794i 0.225226 + 0.225226i
\(170\) 0 0
\(171\) −0.166801 0.196264i −0.0127556 0.0150087i
\(172\) 0 0
\(173\) 18.7129 + 7.75114i 1.42272 + 0.589308i 0.955541 0.294857i \(-0.0952720\pi\)
0.467174 + 0.884165i \(0.345272\pi\)
\(174\) 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 \(-0.635367\pi\)
0.935851 0.352397i \(-0.114633\pi\)
\(180\) 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
\(183\) 5.59706 + 4.07691i 0.413747 + 0.301374i
\(184\) 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
\(189\) −0.299040 3.98547i −0.0217520 0.289901i
\(190\) 0 0
\(191\) −15.7313 −1.13828 −0.569139 0.822241i \(-0.692723\pi\)
−0.569139 + 0.822241i \(0.692723\pi\)
\(192\) 0 0
\(193\) 12.2248 0.879962 0.439981 0.898007i \(-0.354985\pi\)
0.439981 + 0.898007i \(0.354985\pi\)
\(194\) 0 0
\(195\) 3.68542 15.2691i 0.263918 1.09344i
\(196\) 0 0
\(197\) −21.5949 + 8.94488i −1.53857 + 0.637297i −0.981205 0.192971i \(-0.938188\pi\)
−0.557365 + 0.830267i \(0.688188\pi\)
\(198\) 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
\(201\) 8.94176 12.2759i 0.630703 0.865873i
\(202\) 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
\(213\) 8.52902 5.21233i 0.584399 0.357143i
\(214\) 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
\(219\) 2.03188 + 3.32480i 0.137302 + 0.224669i
\(220\) 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 0.861432 0.507873i \(-0.169568\pi\)
0.250004 + 0.968245i \(0.419568\pi\)
\(228\) 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
\(231\) 4.62353 + 3.36779i 0.304206 + 0.221584i
\(232\) 0 0
\(233\) −7.93372 + 7.93372i −0.519756 + 0.519756i −0.917497 0.397742i \(-0.869794\pi\)
0.397742 + 0.917497i \(0.369794\pi\)
\(234\) 0 0
\(235\) −10.4810 25.3033i −0.683703 1.65060i
\(236\) 0 0
\(237\) 1.07335 + 0.259068i 0.0697214 + 0.0168283i
\(238\) 0 0
\(239\) 16.7260i 1.08191i 0.841051 + 0.540956i \(0.181937\pi\)
−0.841051 + 0.540956i \(0.818063\pi\)
\(240\) 0 0
\(241\) 9.00218i 0.579881i −0.957045 0.289941i \(-0.906364\pi\)
0.957045 0.289941i \(-0.0936356\pi\)
\(242\) 0 0
\(243\) 5.87778 + 14.4379i 0.377060 + 0.926189i
\(244\) 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
\(249\) −5.18386 + 7.11675i −0.328514 + 0.451006i
\(250\) 0 0
\(251\) −0.601450 1.45203i −0.0379632 0.0916513i 0.903761 0.428038i \(-0.140795\pi\)
−0.941724 + 0.336387i \(0.890795\pi\)
\(252\) 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 \(-0.916759\pi\)
0.966001 0.258539i \(-0.0832412\pi\)
\(258\) 0 0
\(259\) −3.22761 + 7.79215i −0.200554 + 0.484181i
\(260\) 0 0
\(261\) 3.10873 2.64206i 0.192425 0.163539i
\(262\) 0 0
\(263\) 8.76126 8.76126i 0.540243 0.540243i −0.383357 0.923600i \(-0.625232\pi\)
0.923600 + 0.383357i \(0.125232\pi\)
\(264\) 0 0
\(265\) −5.90415 5.90415i −0.362689 0.362689i
\(266\) 0 0
\(267\) −1.15289 1.88649i −0.0705557 0.115451i
\(268\) 0 0
\(269\) −15.1023 6.25558i −0.920804 0.381409i −0.128621 0.991694i \(-0.541055\pi\)
−0.792182 + 0.610284i \(0.791055\pi\)
\(270\) 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
\(279\) −7.71915 + 15.0590i −0.462133 + 0.901561i
\(280\) 0 0
\(281\) −5.93438 5.93438i −0.354015 0.354015i 0.507586 0.861601i \(-0.330538\pi\)
−0.861601 + 0.507586i \(0.830538\pi\)
\(282\) 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
\(285\) 0.440440 + 0.106307i 0.0260894 + 0.00629707i
\(286\) 0 0
\(287\) 5.36888 0.316915
\(288\) 0 0
\(289\) 15.8837 0.934334
\(290\) 0 0
\(291\) −22.4023 5.40712i −1.31324 0.316971i
\(292\) 0 0
\(293\) −4.20032 + 1.73983i −0.245386 + 0.101642i −0.501987 0.864875i \(-0.667397\pi\)
0.256601 + 0.966517i \(0.417397\pi\)
\(294\) 0 0
\(295\) 2.80698 + 2.80698i 0.163429 + 0.163429i
\(296\) 0 0
\(297\) −21.1930 6.97159i −1.22974 0.404533i
\(298\) 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
\(309\) 10.0507 + 16.4461i 0.571763 + 0.935584i
\(310\) 0 0
\(311\) −10.7303 10.7303i −0.608462 0.608462i 0.334082 0.942544i \(-0.391574\pi\)
−0.942544 + 0.334082i \(0.891574\pi\)
\(312\) 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
\(315\) 4.55294 + 5.35713i 0.256529 + 0.301840i
\(316\) 0 0
\(317\) −2.59675 + 6.26910i −0.145848 + 0.352108i −0.979874 0.199617i \(-0.936030\pi\)
0.834026 + 0.551725i \(0.186030\pi\)
\(318\) 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
\(327\) −1.21955 + 1.67428i −0.0674411 + 0.0925878i
\(328\) 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
\(333\) 2.66075 32.7884i 0.145808 1.79680i
\(334\) 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
\(339\) 14.2853 + 3.44797i 0.775871 + 0.187268i
\(340\) 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
\(345\) −8.83505 6.43547i −0.475663 0.346474i
\(346\) 0 0
\(347\) 5.87587 + 14.1856i 0.315433 + 0.761523i 0.999485 + 0.0320898i \(0.0102162\pi\)
−0.684052 + 0.729434i \(0.739784\pi\)
\(348\) 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 \(-0.907433\pi\)
0.958012 0.286726i \(-0.0925671\pi\)
\(354\) 0 0
\(355\) −6.72880 + 16.2448i −0.357128 + 0.862182i
\(356\) 0 0
\(357\) 3.98373 + 6.51864i 0.210841 + 0.345003i
\(358\) 0 0
\(359\) −7.99933 + 7.99933i −0.422189 + 0.422189i −0.885957 0.463768i \(-0.846497\pi\)
0.463768 + 0.885957i \(0.346497\pi\)
\(360\) 0 0
\(361\) −13.4298 13.4298i −0.706832 0.706832i
\(362\) 0 0
\(363\) 10.9884 6.71533i 0.576741 0.352463i
\(364\) 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
\(375\) 2.22722 3.05768i 0.115013 0.157898i
\(376\) 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
\(381\) −2.84936 + 11.8052i −0.145977 + 0.604798i
\(382\) 0 0
\(383\) −16.7272 −0.854721 −0.427360 0.904081i \(-0.640556\pi\)
−0.427360 + 0.904081i \(0.640556\pi\)
\(384\) 0 0
\(385\) −10.0621 −0.512811
\(386\) 0 0
\(387\) −2.22345 + 27.3996i −0.113024 + 1.39280i
\(388\) 0 0
\(389\) −30.3193 + 12.5587i −1.53725 + 0.636749i −0.980955 0.194236i \(-0.937777\pi\)
−0.556294 + 0.830985i \(0.687777\pi\)
\(390\) 0 0
\(391\) −8.39850 8.39850i −0.424730 0.424730i
\(392\) 0 0
\(393\) 6.20390 + 4.51893i 0.312945 + 0.227950i
\(394\) 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 \(-0.495951\pi\)
0.0127190 + 0.999919i \(0.495951\pi\)
\(402\) 0 0
\(403\) −15.5113 6.42500i −0.772674 0.320052i
\(404\) 0 0
\(405\) −23.3107 14.4412i −1.15832 0.717590i
\(406\) 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
\(411\) 12.6338 7.72090i 0.623180 0.380844i
\(412\) 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 0.827631 0.561273i \(-0.189688\pi\)
0.188343 + 0.982103i \(0.439688\pi\)
\(420\) 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
\(423\) −12.3012 + 23.9980i −0.598105 + 1.16682i
\(424\) 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
\(429\) 5.19350 21.5172i 0.250745 1.03886i
\(430\) 0 0
\(431\) 1.97237i 0.0950057i −0.998871 0.0475028i \(-0.984874\pi\)
0.998871 0.0475028i \(-0.0151263\pi\)
\(432\) 0 0
\(433\) 29.4876i 1.41709i 0.705668 + 0.708543i \(0.250647\pi\)
−0.705668 + 0.708543i \(0.749353\pi\)
\(434\) 0 0
\(435\) −1.68385 + 6.97637i −0.0807346 + 0.334491i
\(436\) 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
\(441\) 8.76968 17.1085i 0.417604 0.814690i
\(442\) 0 0
\(443\) −4.22858 10.2087i −0.200906 0.485029i 0.791029 0.611779i \(-0.209546\pi\)
−0.991935 + 0.126749i \(0.959546\pi\)
\(444\) 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 \(0.223900\pi\)
−0.762645 + 0.646817i \(0.776100\pi\)
\(450\) 0 0
\(451\) 11.4691 27.6888i 0.540057 1.30381i
\(452\) 0 0
\(453\) −16.6977 + 10.2045i −0.784528 + 0.479448i
\(454\) 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
\(459\) −22.5871 19.4341i −1.05427 0.907106i
\(460\) 0 0
\(461\) 28.5768 + 11.8369i 1.33095 + 0.551298i 0.930927 0.365206i \(-0.119001\pi\)
0.400025 + 0.916504i \(0.369001\pi\)
\(462\) 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 −0.999778 0.0210925i \(-0.993286\pi\)
0.721864 + 0.692035i \(0.243286\pi\)
\(468\) 0 0
\(469\) −6.23089 + 2.58092i −0.287716 + 0.119176i
\(470\) 0 0
\(471\) −4.02254 2.93003i −0.185349 0.135008i
\(472\) 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
\(477\) −0.664971 + 8.19445i −0.0304469 + 0.375198i
\(478\) 0 0
\(479\) 28.2696 1.29167 0.645835 0.763477i \(-0.276509\pi\)
0.645835 + 0.763477i \(0.276509\pi\)
\(480\) 0 0
\(481\) 32.6380 1.48816
\(482\) 0 0
\(483\) 0.647416 2.68231i 0.0294584 0.122049i
\(484\) 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
\(489\) −9.37542 + 12.8712i −0.423971 + 0.582056i
\(490\) 0 0
\(491\) −0.871501 + 0.360988i −0.0393303 + 0.0162911i −0.402262 0.915525i \(-0.631776\pi\)
0.362932 + 0.931816i \(0.381776\pi\)
\(492\) 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
\(501\) 14.0122 8.56329i 0.626021 0.382580i
\(502\) 0 0
\(503\) 15.9266 + 15.9266i 0.710132 + 0.710132i 0.966563 0.256431i \(-0.0825465\pi\)
−0.256431 + 0.966563i \(0.582546\pi\)
\(504\) 0 0
\(505\) −12.8126 + 12.8126i −0.570152 + 0.570152i
\(506\) 0 0
\(507\) 3.73990 + 6.11966i 0.166095 + 0.271784i
\(508\) 0 0
\(509\) −0.374204 + 0.903408i −0.0165863 + 0.0400428i −0.931956 0.362572i \(-0.881899\pi\)
0.915369 + 0.402615i \(0.131899\pi\)
\(510\) 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
\(519\) 28.3570 + 20.6553i 1.24473 + 0.906666i
\(520\) 0 0
\(521\) 31.7757 31.7757i 1.39212 1.39212i 0.571558 0.820562i \(-0.306339\pi\)
0.820562 0.571558i \(-0.193661\pi\)
\(522\) 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
\(525\) −5.54688 1.33882i −0.242086 0.0584310i
\(526\) 0 0
\(527\) 32.3463i 1.40903i
\(528\) 0 0
\(529\) 18.7100i 0.813480i
\(530\) 0 0
\(531\) 0.316144 3.89584i 0.0137195 0.169065i
\(532\) 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
\(537\) 18.6566 25.6130i 0.805090 1.10528i
\(538\) 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
\(549\) 7.76698 + 9.13887i 0.331487 + 0.390038i
\(550\) 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
\(555\) 30.1756 + 49.3768i 1.28088 + 2.09593i
\(556\) 0 0
\(557\) −21.4222 8.87338i −0.907689 0.375977i −0.120517 0.992711i \(-0.538455\pi\)
−0.787171 + 0.616734i \(0.788455\pi\)
\(558\) 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 −0.982683 0.185296i \(-0.940676\pi\)
0.825886 + 0.563838i \(0.190676\pi\)
\(564\) 0 0
\(565\) −23.8830 + 9.89265i −1.00476 + 0.416187i
\(566\) 0 0
\(567\) 1.11615 6.83187i 0.0468739 0.286912i
\(568\) 0 0
\(569\) 8.43864 + 8.43864i 0.353766 + 0.353766i 0.861509 0.507743i \(-0.169520\pi\)
−0.507743 + 0.861509i \(0.669520\pi\)
\(570\) 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
\(573\) −26.4868 6.39300i −1.10650 0.267071i
\(574\) 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
\(579\) 20.5829 + 4.96800i 0.855398 + 0.206463i
\(580\) 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
\(585\) 12.4103 24.2108i 0.513102 1.00099i
\(586\) 0 0
\(587\) 14.6871 6.08361i 0.606202 0.251097i −0.0584014 0.998293i \(-0.518600\pi\)
0.664604 + 0.747196i \(0.268600\pi\)
\(588\) 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 \(-0.457163\pi\)
0.134172 + 0.990958i \(0.457163\pi\)
\(594\) 0 0
\(595\) −12.4157 5.14275i −0.508994 0.210832i
\(596\) 0 0
\(597\) −2.01532 3.29770i −0.0824817 0.134966i
\(598\) 0 0
\(599\) −20.5360 20.5360i −0.839078 0.839078i 0.149659 0.988738i \(-0.452182\pi\)
−0.988738 + 0.149659i \(0.952182\pi\)
\(600\) 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
\(603\) 20.0440 17.0351i 0.816255 0.693722i
\(604\) 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
\(615\) 21.6880 29.7748i 0.874545 1.20064i
\(616\) 0 0
\(617\) −30.2757 + 30.2757i −1.21885 + 1.21885i −0.250821 + 0.968034i \(0.580701\pi\)
−0.968034 + 0.250821i \(0.919299\pi\)
\(618\) 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
\(621\) 0.805265 + 10.7322i 0.0323142 + 0.430669i
\(622\) 0 0
\(623\) 0.981797i 0.0393349i
\(624\) 0 0
\(625\) 28.0703i 1.12281i
\(626\) 0 0
\(627\) 0.620670 + 0.149808i 0.0247872 + 0.00598275i
\(628\) 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
\(633\) 38.4212 + 27.9860i 1.52710 + 1.11235i
\(634\) 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 \(-0.744019\pi\)
0.693695 0.720269i \(-0.255981\pi\)
\(642\) 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
\(645\) −25.2162 41.2616i −0.992886 1.62467i
\(646\) 0 0
\(647\) −7.01510 + 7.01510i −0.275792 + 0.275792i −0.831427 0.555635i \(-0.812475\pi\)
0.555635 + 0.831427i \(0.312475\pi\)
\(648\) 0 0
\(649\) 3.95560 + 3.95560i 0.155271 + 0.155271i
\(650\) 0 0
\(651\) 6.41212 3.91863i 0.251311 0.153583i
\(652\) 0 0
\(653\) 7.33264 + 3.03728i 0.286948 + 0.118858i 0.521515 0.853242i \(-0.325367\pi\)
−0.234567 + 0.972100i \(0.575367\pi\)
\(654\) 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 \(-0.715029\pi\)
0.993971 0.109644i \(-0.0349712\pi\)
\(660\) 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
\(663\) 17.4058 23.8959i 0.675986 0.928039i
\(664\) 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
\(669\) 9.60154 39.7802i 0.371217 1.53799i
\(670\) 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
\(675\) 22.1937 1.66525i 0.854235 0.0640954i
\(676\) 0 0
\(677\) 25.4610 10.5463i 0.978545 0.405327i 0.164659 0.986351i \(-0.447348\pi\)
0.813886 + 0.581024i \(0.197348\pi\)
\(678\) 0 0
\(679\) 7.23650 + 7.23650i 0.277712 + 0.277712i
\(680\) 0 0
\(681\) 25.3756 + 18.4836i 0.972395 + 0.708294i
\(682\) 0 0
\(683\) −7.18630 + 2.97666i −0.274976 + 0.113899i −0.515910 0.856643i \(-0.672546\pi\)
0.240934 + 0.970541i \(0.422546\pi\)
\(684\) 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
\(693\) 6.41602 + 7.54929i 0.243724 + 0.286774i
\(694\) 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
\(699\) −16.5822 + 10.1339i −0.627196 + 0.383298i
\(700\) 0 0
\(701\) 12.8390 30.9961i 0.484922 1.17071i −0.472322 0.881426i \(-0.656584\pi\)
0.957244 0.289280i \(-0.0934160\pi\)
\(702\) 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
\(711\) 1.70191 + 0.872388i 0.0638267 + 0.0327171i
\(712\) 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
\(717\) −6.79720 + 28.1615i −0.253846 + 1.05171i
\(718\) 0 0
\(719\) 7.25362i 0.270515i 0.990811 + 0.135257i \(0.0431861\pi\)
−0.990811 + 0.135257i \(0.956814\pi\)
\(720\) 0 0
\(721\) 8.55913i 0.318759i
\(722\) 0 0
\(723\) 3.65837 15.1570i 0.136056 0.563694i
\(724\) 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
\(729\) 4.02907 + 26.6977i 0.149225 + 0.988803i
\(730\) 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
\(741\) 0.377678 0.230810i 0.0138743 0.00847902i
\(742\) 0 0
\(743\) 31.4330 31.4330i 1.15317 1.15317i 0.167252 0.985914i \(-0.446511\pi\)
0.985914 0.167252i \(-0.0534894\pi\)
\(744\) 0 0
\(745\) 22.7253 + 22.7253i 0.832590 + 0.832590i
\(746\) 0 0
\(747\) −11.6202 + 9.87584i −0.425162 + 0.361338i
\(748\) 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
\(759\) −12.4504 9.06889i −0.451921 0.329180i
\(760\) 0 0
\(761\) 17.8648 + 17.8648i 0.647599 + 0.647599i 0.952412 0.304813i \(-0.0985941\pi\)
−0.304813 + 0.952412i \(0.598594\pi\)
\(762\) 0 0
\(763\) 0.849818 0.352006i 0.0307655 0.0127435i
\(764\) 0 0
\(765\) 52.2438 + 4.23953i 1.88888 + 0.153281i
\(766\) 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
\(771\) 3.36870 13.9569i 0.121321 0.502645i
\(772\) 0 0
\(773\) 25.0667 10.3830i 0.901587 0.373450i 0.116757 0.993161i \(-0.462750\pi\)
0.784830 + 0.619711i \(0.212750\pi\)
\(774\) 0 0
\(775\) 17.0839 + 17.0839i 0.613671 + 0.613671i
\(776\) 0 0
\(777\) −8.60096 + 11.8080i −0.308558 + 0.423609i
\(778\) 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