Properties

Label 768.2.n.b.289.6
Level $768$
Weight $2$
Character 768.289
Analytic conductor $6.133$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 289.6
Character \(\chi\) \(=\) 768.289
Dual form 768.2.n.b.481.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.382683 - 0.923880i) q^{3} +(-0.825824 + 0.342068i) q^{5} +(-1.17750 + 1.17750i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(0.382683 - 0.923880i) q^{3} +(-0.825824 + 0.342068i) q^{5} +(-1.17750 + 1.17750i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-1.46490 - 3.53657i) q^{11} +(-3.01061 - 1.24703i) q^{13} +0.893866i q^{15} +4.58215i q^{17} +(-3.29978 - 1.36681i) q^{19} +(0.637258 + 1.53848i) q^{21} +(-5.41196 - 5.41196i) q^{23} +(-2.97056 + 2.97056i) q^{25} +(-0.923880 + 0.382683i) q^{27} +(2.46490 - 5.95078i) q^{29} +5.25495 q^{31} -3.82796 q^{33} +(0.569623 - 1.37519i) q^{35} +(-7.33917 + 3.03998i) q^{37} +(-2.30422 + 2.30422i) q^{39} +(-1.35921 - 1.35921i) q^{41} +(-2.95781 - 7.14079i) q^{43} +(0.825824 + 0.342068i) q^{45} -8.16360i q^{47} +4.22699i q^{49} +(4.23336 + 1.75351i) q^{51} +(3.13863 + 7.57731i) q^{53} +(2.41949 + 2.41949i) q^{55} +(-2.52554 + 2.52554i) q^{57} +(0.221996 - 0.0919539i) q^{59} +(-2.66861 + 6.44260i) q^{61} +1.66523 q^{63} +2.91280 q^{65} +(-5.52539 + 13.3395i) q^{67} +(-7.07107 + 2.92893i) q^{69} +(-1.51271 + 1.51271i) q^{71} +(-9.62682 - 9.62682i) q^{73} +(1.60765 + 3.88122i) q^{75} +(5.88923 + 2.43940i) q^{77} -5.34497i q^{79} +1.00000i q^{81} +(5.64233 + 2.33713i) q^{83} +(-1.56741 - 3.78405i) q^{85} +(-4.55453 - 4.55453i) q^{87} +(5.09017 - 5.09017i) q^{89} +(5.01337 - 2.07660i) q^{91} +(2.01098 - 4.85494i) q^{93} +3.19258 q^{95} +19.0146 q^{97} +(-1.46490 + 3.53657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} - 48q^{35} - 16q^{43} + 16q^{51} + 32q^{53} - 32q^{55} + 64q^{59} + 32q^{61} - 16q^{63} + 16q^{67} + 32q^{69} - 64q^{71} + 32q^{75} + 32q^{77} - 48q^{91} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\)

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
\(3\) 0.382683 0.923880i 0.220942 0.533402i
\(4\) 0 0
\(5\) −0.825824 + 0.342068i −0.369320 + 0.152977i −0.559621 0.828748i \(-0.689053\pi\)
0.190302 + 0.981726i \(0.439053\pi\)
\(6\) 0 0
\(7\) −1.17750 + 1.17750i −0.445053 + 0.445053i −0.893706 0.448653i \(-0.851904\pi\)
0.448653 + 0.893706i \(0.351904\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) −1.46490 3.53657i −0.441683 1.06632i −0.975358 0.220627i \(-0.929189\pi\)
0.533675 0.845690i \(-0.320811\pi\)
\(12\) 0 0
\(13\) −3.01061 1.24703i −0.834992 0.345865i −0.0761151 0.997099i \(-0.524252\pi\)
−0.758877 + 0.651234i \(0.774252\pi\)
\(14\) 0 0
\(15\) 0.893866i 0.230795i
\(16\) 0 0
\(17\) 4.58215i 1.11134i 0.831404 + 0.555668i \(0.187537\pi\)
−0.831404 + 0.555668i \(0.812463\pi\)
\(18\) 0 0
\(19\) −3.29978 1.36681i −0.757021 0.313568i −0.0294181 0.999567i \(-0.509365\pi\)
−0.727602 + 0.685999i \(0.759365\pi\)
\(20\) 0 0
\(21\) 0.637258 + 1.53848i 0.139061 + 0.335723i
\(22\) 0 0
\(23\) −5.41196 5.41196i −1.12847 1.12847i −0.990426 0.138046i \(-0.955918\pi\)
−0.138046 0.990426i \(-0.544082\pi\)
\(24\) 0 0
\(25\) −2.97056 + 2.97056i −0.594112 + 0.594112i
\(26\) 0 0
\(27\) −0.923880 + 0.382683i −0.177801 + 0.0736475i
\(28\) 0 0
\(29\) 2.46490 5.95078i 0.457720 1.10503i −0.511599 0.859224i \(-0.670947\pi\)
0.969318 0.245808i \(-0.0790534\pi\)
\(30\) 0 0
\(31\) 5.25495 0.943816 0.471908 0.881648i \(-0.343565\pi\)
0.471908 + 0.881648i \(0.343565\pi\)
\(32\) 0 0
\(33\) −3.82796 −0.666362
\(34\) 0 0
\(35\) 0.569623 1.37519i 0.0962838 0.232450i
\(36\) 0 0
\(37\) −7.33917 + 3.03998i −1.20655 + 0.499770i −0.893111 0.449837i \(-0.851482\pi\)
−0.313442 + 0.949607i \(0.601482\pi\)
\(38\) 0 0
\(39\) −2.30422 + 2.30422i −0.368970 + 0.368970i
\(40\) 0 0
\(41\) −1.35921 1.35921i −0.212273 0.212273i 0.592959 0.805232i \(-0.297959\pi\)
−0.805232 + 0.592959i \(0.797959\pi\)
\(42\) 0 0
\(43\) −2.95781 7.14079i −0.451062 1.08896i −0.971919 0.235317i \(-0.924387\pi\)
0.520856 0.853644i \(-0.325613\pi\)
\(44\) 0 0
\(45\) 0.825824 + 0.342068i 0.123107 + 0.0509924i
\(46\) 0 0
\(47\) 8.16360i 1.19078i −0.803436 0.595391i \(-0.796997\pi\)
0.803436 0.595391i \(-0.203003\pi\)
\(48\) 0 0
\(49\) 4.22699i 0.603856i
\(50\) 0 0
\(51\) 4.23336 + 1.75351i 0.592789 + 0.245541i
\(52\) 0 0
\(53\) 3.13863 + 7.57731i 0.431123 + 1.04082i 0.978926 + 0.204216i \(0.0654646\pi\)
−0.547802 + 0.836608i \(0.684535\pi\)
\(54\) 0 0
\(55\) 2.41949 + 2.41949i 0.326244 + 0.326244i
\(56\) 0 0
\(57\) −2.52554 + 2.52554i −0.334516 + 0.334516i
\(58\) 0 0
\(59\) 0.221996 0.0919539i 0.0289014 0.0119714i −0.368186 0.929752i \(-0.620021\pi\)
0.397087 + 0.917781i \(0.370021\pi\)
\(60\) 0 0
\(61\) −2.66861 + 6.44260i −0.341681 + 0.824891i 0.655865 + 0.754878i \(0.272304\pi\)
−0.997546 + 0.0700128i \(0.977696\pi\)
\(62\) 0 0
\(63\) 1.66523 0.209800
\(64\) 0 0
\(65\) 2.91280 0.361289
\(66\) 0 0
\(67\) −5.52539 + 13.3395i −0.675033 + 1.62968i 0.0979063 + 0.995196i \(0.468785\pi\)
−0.772940 + 0.634479i \(0.781215\pi\)
\(68\) 0 0
\(69\) −7.07107 + 2.92893i −0.851257 + 0.352602i
\(70\) 0 0
\(71\) −1.51271 + 1.51271i −0.179526 + 0.179526i −0.791149 0.611623i \(-0.790517\pi\)
0.611623 + 0.791149i \(0.290517\pi\)
\(72\) 0 0
\(73\) −9.62682 9.62682i −1.12673 1.12673i −0.990705 0.136029i \(-0.956566\pi\)
−0.136029 0.990705i \(-0.543434\pi\)
\(74\) 0 0
\(75\) 1.60765 + 3.88122i 0.185636 + 0.448165i
\(76\) 0 0
\(77\) 5.88923 + 2.43940i 0.671140 + 0.277995i
\(78\) 0 0
\(79\) 5.34497i 0.601356i −0.953726 0.300678i \(-0.902787\pi\)
0.953726 0.300678i \(-0.0972129\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 5.64233 + 2.33713i 0.619327 + 0.256533i 0.670210 0.742171i \(-0.266204\pi\)
−0.0508839 + 0.998705i \(0.516204\pi\)
\(84\) 0 0
\(85\) −1.56741 3.78405i −0.170009 0.410438i
\(86\) 0 0
\(87\) −4.55453 4.55453i −0.488297 0.488297i
\(88\) 0 0
\(89\) 5.09017 5.09017i 0.539557 0.539557i −0.383842 0.923399i \(-0.625399\pi\)
0.923399 + 0.383842i \(0.125399\pi\)
\(90\) 0 0
\(91\) 5.01337 2.07660i 0.525544 0.217687i
\(92\) 0 0
\(93\) 2.01098 4.85494i 0.208529 0.503434i
\(94\) 0 0
\(95\) 3.19258 0.327551
\(96\) 0 0
\(97\) 19.0146 1.93064 0.965319 0.261072i \(-0.0840761\pi\)
0.965319 + 0.261072i \(0.0840761\pi\)
\(98\) 0 0
\(99\) −1.46490 + 3.53657i −0.147228 + 0.355439i
\(100\) 0 0
\(101\) 3.55331 1.47183i 0.353567 0.146452i −0.198828 0.980034i \(-0.563714\pi\)
0.552396 + 0.833582i \(0.313714\pi\)
\(102\) 0 0
\(103\) −3.30552 + 3.30552i −0.325703 + 0.325703i −0.850950 0.525247i \(-0.823973\pi\)
0.525247 + 0.850950i \(0.323973\pi\)
\(104\) 0 0
\(105\) −1.05253 1.05253i −0.102716 0.102716i
\(106\) 0 0
\(107\) −4.98987 12.0466i −0.482389 1.16459i −0.958471 0.285190i \(-0.907943\pi\)
0.476082 0.879401i \(-0.342057\pi\)
\(108\) 0 0
\(109\) 4.16532 + 1.72533i 0.398966 + 0.165257i 0.573139 0.819458i \(-0.305725\pi\)
−0.174174 + 0.984715i \(0.555725\pi\)
\(110\) 0 0
\(111\) 7.94386i 0.753998i
\(112\) 0 0
\(113\) 15.7676i 1.48329i −0.670792 0.741645i \(-0.734046\pi\)
0.670792 0.741645i \(-0.265954\pi\)
\(114\) 0 0
\(115\) 6.32059 + 2.61807i 0.589398 + 0.244137i
\(116\) 0 0
\(117\) 1.24703 + 3.01061i 0.115288 + 0.278331i
\(118\) 0 0
\(119\) −5.39548 5.39548i −0.494603 0.494603i
\(120\) 0 0
\(121\) −2.58325 + 2.58325i −0.234841 + 0.234841i
\(122\) 0 0
\(123\) −1.77589 + 0.735600i −0.160127 + 0.0663268i
\(124\) 0 0
\(125\) 3.14736 7.59841i 0.281509 0.679623i
\(126\) 0 0
\(127\) −5.62550 −0.499182 −0.249591 0.968351i \(-0.580296\pi\)
−0.249591 + 0.968351i \(0.580296\pi\)
\(128\) 0 0
\(129\) −7.72914 −0.680513
\(130\) 0 0
\(131\) 2.77061 6.68884i 0.242069 0.584407i −0.755419 0.655242i \(-0.772567\pi\)
0.997488 + 0.0708355i \(0.0225665\pi\)
\(132\) 0 0
\(133\) 5.49490 2.27606i 0.476468 0.197360i
\(134\) 0 0
\(135\) 0.632058 0.632058i 0.0543989 0.0543989i
\(136\) 0 0
\(137\) 3.13785 + 3.13785i 0.268085 + 0.268085i 0.828328 0.560243i \(-0.189292\pi\)
−0.560243 + 0.828328i \(0.689292\pi\)
\(138\) 0 0
\(139\) 3.60636 + 8.70653i 0.305888 + 0.738478i 0.999830 + 0.0184473i \(0.00587229\pi\)
−0.693942 + 0.720031i \(0.744128\pi\)
\(140\) 0 0
\(141\) −7.54218 3.12407i −0.635166 0.263094i
\(142\) 0 0
\(143\) 12.4740i 1.04313i
\(144\) 0 0
\(145\) 5.75746i 0.478131i
\(146\) 0 0
\(147\) 3.90523 + 1.61760i 0.322098 + 0.133417i
\(148\) 0 0
\(149\) 1.00661 + 2.43018i 0.0824648 + 0.199088i 0.959734 0.280912i \(-0.0906368\pi\)
−0.877269 + 0.479999i \(0.840637\pi\)
\(150\) 0 0
\(151\) 14.3784 + 14.3784i 1.17010 + 1.17010i 0.982186 + 0.187914i \(0.0601726\pi\)
0.187914 + 0.982186i \(0.439827\pi\)
\(152\) 0 0
\(153\) 3.24007 3.24007i 0.261944 0.261944i
\(154\) 0 0
\(155\) −4.33966 + 1.79755i −0.348570 + 0.144382i
\(156\) 0 0
\(157\) 2.10034 5.07067i 0.167625 0.404684i −0.817637 0.575734i \(-0.804716\pi\)
0.985262 + 0.171051i \(0.0547162\pi\)
\(158\) 0 0
\(159\) 8.20163 0.650431
\(160\) 0 0
\(161\) 12.7452 1.00446
\(162\) 0 0
\(163\) −4.14645 + 10.0104i −0.324775 + 0.784076i 0.674189 + 0.738559i \(0.264493\pi\)
−0.998964 + 0.0455168i \(0.985507\pi\)
\(164\) 0 0
\(165\) 3.16122 1.30942i 0.246101 0.101938i
\(166\) 0 0
\(167\) 5.38194 5.38194i 0.416467 0.416467i −0.467517 0.883984i \(-0.654851\pi\)
0.883984 + 0.467517i \(0.154851\pi\)
\(168\) 0 0
\(169\) −1.68373 1.68373i −0.129518 0.129518i
\(170\) 0 0
\(171\) 1.36681 + 3.29978i 0.104523 + 0.252340i
\(172\) 0 0
\(173\) 9.62485 + 3.98675i 0.731764 + 0.303107i 0.717277 0.696788i \(-0.245388\pi\)
0.0144874 + 0.999895i \(0.495388\pi\)
\(174\) 0 0
\(175\) 6.99566i 0.528822i
\(176\) 0 0
\(177\) 0.240287i 0.0180611i
\(178\) 0 0
\(179\) −12.7809 5.29402i −0.955288 0.395693i −0.150072 0.988675i \(-0.547951\pi\)
−0.805216 + 0.592982i \(0.797951\pi\)
\(180\) 0 0
\(181\) −8.21217 19.8259i −0.610406 1.47365i −0.862556 0.505962i \(-0.831138\pi\)
0.252150 0.967688i \(-0.418862\pi\)
\(182\) 0 0
\(183\) 4.93096 + 4.93096i 0.364507 + 0.364507i
\(184\) 0 0
\(185\) 5.02098 5.02098i 0.369150 0.369150i
\(186\) 0 0
\(187\) 16.2051 6.71238i 1.18504 0.490858i
\(188\) 0 0
\(189\) 0.637258 1.53848i 0.0463537 0.111908i
\(190\) 0 0
\(191\) 10.3772 0.750866 0.375433 0.926850i \(-0.377494\pi\)
0.375433 + 0.926850i \(0.377494\pi\)
\(192\) 0 0
\(193\) −8.76090 −0.630623 −0.315312 0.948988i \(-0.602109\pi\)
−0.315312 + 0.948988i \(0.602109\pi\)
\(194\) 0 0
\(195\) 1.11468 2.69108i 0.0798240 0.192712i
\(196\) 0 0
\(197\) 4.35045 1.80201i 0.309956 0.128388i −0.222283 0.974982i \(-0.571351\pi\)
0.532239 + 0.846594i \(0.321351\pi\)
\(198\) 0 0
\(199\) −3.47990 + 3.47990i −0.246684 + 0.246684i −0.819608 0.572925i \(-0.805809\pi\)
0.572925 + 0.819608i \(0.305809\pi\)
\(200\) 0 0
\(201\) 10.2096 + 10.2096i 0.720129 + 0.720129i
\(202\) 0 0
\(203\) 4.10463 + 9.90945i 0.288088 + 0.695507i
\(204\) 0 0
\(205\) 1.58741 + 0.657527i 0.110870 + 0.0459237i
\(206\) 0 0
\(207\) 7.65367i 0.531967i
\(208\) 0 0
\(209\) 13.6721i 0.945722i
\(210\) 0 0
\(211\) −4.76129 1.97219i −0.327781 0.135771i 0.212724 0.977112i \(-0.431767\pi\)
−0.540505 + 0.841341i \(0.681767\pi\)
\(212\) 0 0
\(213\) 0.818674 + 1.97645i 0.0560946 + 0.135424i
\(214\) 0 0
\(215\) 4.88527 + 4.88527i 0.333173 + 0.333173i
\(216\) 0 0
\(217\) −6.18769 + 6.18769i −0.420048 + 0.420048i
\(218\) 0 0
\(219\) −12.5780 + 5.21000i −0.849946 + 0.352059i
\(220\) 0 0
\(221\) 5.71410 13.7951i 0.384372 0.927956i
\(222\) 0 0
\(223\) −12.6045 −0.844059 −0.422029 0.906582i \(-0.638682\pi\)
−0.422029 + 0.906582i \(0.638682\pi\)
\(224\) 0 0
\(225\) 4.20100 0.280067
\(226\) 0 0
\(227\) 1.84453 4.45310i 0.122426 0.295563i −0.850771 0.525537i \(-0.823864\pi\)
0.973197 + 0.229975i \(0.0738644\pi\)
\(228\) 0 0
\(229\) 19.3957 8.03395i 1.28170 0.530898i 0.365200 0.930929i \(-0.381001\pi\)
0.916502 + 0.400031i \(0.131001\pi\)
\(230\) 0 0
\(231\) 4.50742 4.50742i 0.296566 0.296566i
\(232\) 0 0
\(233\) 13.4162 + 13.4162i 0.878921 + 0.878921i 0.993423 0.114502i \(-0.0365271\pi\)
−0.114502 + 0.993423i \(0.536527\pi\)
\(234\) 0 0
\(235\) 2.79250 + 6.74169i 0.182163 + 0.439780i
\(236\) 0 0
\(237\) −4.93811 2.04543i −0.320765 0.132865i
\(238\) 0 0
\(239\) 4.57889i 0.296184i 0.988974 + 0.148092i \(0.0473131\pi\)
−0.988974 + 0.148092i \(0.952687\pi\)
\(240\) 0 0
\(241\) 14.5911i 0.939895i −0.882694 0.469948i \(-0.844273\pi\)
0.882694 0.469948i \(-0.155727\pi\)
\(242\) 0 0
\(243\) 0.923880 + 0.382683i 0.0592669 + 0.0245492i
\(244\) 0 0
\(245\) −1.44592 3.49075i −0.0923763 0.223016i
\(246\) 0 0
\(247\) 8.22987 + 8.22987i 0.523654 + 0.523654i
\(248\) 0 0
\(249\) 4.31845 4.31845i 0.273671 0.273671i
\(250\) 0 0
\(251\) −1.91315 + 0.792453i −0.120757 + 0.0500192i −0.442244 0.896895i \(-0.645817\pi\)
0.321487 + 0.946914i \(0.395817\pi\)
\(252\) 0 0
\(253\) −11.2118 + 27.0678i −0.704882 + 1.70174i
\(254\) 0 0
\(255\) −4.09583 −0.256491
\(256\) 0 0
\(257\) −21.4012 −1.33497 −0.667485 0.744624i \(-0.732629\pi\)
−0.667485 + 0.744624i \(0.732629\pi\)
\(258\) 0 0
\(259\) 5.06229 12.2214i 0.314555 0.759403i
\(260\) 0 0
\(261\) −5.95078 + 2.46490i −0.368344 + 0.152573i
\(262\) 0 0
\(263\) −4.14877 + 4.14877i −0.255824 + 0.255824i −0.823353 0.567529i \(-0.807899\pi\)
0.567529 + 0.823353i \(0.307899\pi\)
\(264\) 0 0
\(265\) −5.18391 5.18391i −0.318445 0.318445i
\(266\) 0 0
\(267\) −2.75478 6.65062i −0.168590 0.407011i
\(268\) 0 0
\(269\) −28.0039 11.5996i −1.70743 0.707241i −1.00000 0.000457143i \(-0.999854\pi\)
−0.707430 0.706783i \(-0.750146\pi\)
\(270\) 0 0
\(271\) 10.3370i 0.627930i 0.949435 + 0.313965i \(0.101657\pi\)
−0.949435 + 0.313965i \(0.898343\pi\)
\(272\) 0 0
\(273\) 5.42643i 0.328422i
\(274\) 0 0
\(275\) 14.8572 + 6.15404i 0.895920 + 0.371102i
\(276\) 0 0
\(277\) 6.39508 + 15.4391i 0.384243 + 0.927645i 0.991135 + 0.132860i \(0.0424162\pi\)
−0.606892 + 0.794785i \(0.707584\pi\)
\(278\) 0 0
\(279\) −3.71581 3.71581i −0.222460 0.222460i
\(280\) 0 0
\(281\) 7.85631 7.85631i 0.468668 0.468668i −0.432815 0.901483i \(-0.642480\pi\)
0.901483 + 0.432815i \(0.142480\pi\)
\(282\) 0 0
\(283\) 6.76840 2.80356i 0.402340 0.166655i −0.172331 0.985039i \(-0.555130\pi\)
0.574671 + 0.818385i \(0.305130\pi\)
\(284\) 0 0
\(285\) 1.22175 2.94956i 0.0723700 0.174717i
\(286\) 0 0
\(287\) 3.20094 0.188945
\(288\) 0 0
\(289\) −3.99613 −0.235067
\(290\) 0 0
\(291\) 7.27657 17.5672i 0.426560 1.02981i
\(292\) 0 0
\(293\) −12.3397 + 5.11128i −0.720895 + 0.298604i −0.712804 0.701363i \(-0.752575\pi\)
−0.00809031 + 0.999967i \(0.502575\pi\)
\(294\) 0 0
\(295\) −0.151875 + 0.151875i −0.00884253 + 0.00884253i
\(296\) 0 0
\(297\) 2.70678 + 2.70678i 0.157063 + 0.157063i
\(298\) 0 0
\(299\) 9.54439 + 23.0422i 0.551966 + 1.33256i
\(300\) 0 0
\(301\) 11.8911 + 4.92545i 0.685392 + 0.283898i
\(302\) 0 0
\(303\) 3.84607i 0.220951i
\(304\) 0 0
\(305\) 6.23330i 0.356918i
\(306\) 0 0
\(307\) −7.47343 3.09560i −0.426531 0.176675i 0.159082 0.987265i \(-0.449146\pi\)
−0.585614 + 0.810590i \(0.699146\pi\)
\(308\) 0 0
\(309\) 1.78894 + 4.31887i 0.101769 + 0.245692i
\(310\) 0 0
\(311\) −12.5179 12.5179i −0.709823 0.709823i 0.256675 0.966498i \(-0.417373\pi\)
−0.966498 + 0.256675i \(0.917373\pi\)
\(312\) 0 0
\(313\) 2.11020 2.11020i 0.119276 0.119276i −0.644950 0.764225i \(-0.723122\pi\)
0.764225 + 0.644950i \(0.223122\pi\)
\(314\) 0 0
\(315\) −1.37519 + 0.569623i −0.0774832 + 0.0320946i
\(316\) 0 0
\(317\) −13.3122 + 32.1384i −0.747686 + 1.80507i −0.176408 + 0.984317i \(0.556448\pi\)
−0.571278 + 0.820756i \(0.693552\pi\)
\(318\) 0 0
\(319\) −24.6562 −1.38048
\(320\) 0 0
\(321\) −13.0392 −0.727776
\(322\) 0 0
\(323\) 6.26294 15.1201i 0.348479 0.841304i
\(324\) 0 0
\(325\) 12.6476 5.23880i 0.701561 0.290596i
\(326\) 0 0
\(327\) 3.18800 3.18800i 0.176297 0.176297i
\(328\) 0 0
\(329\) 9.61262 + 9.61262i 0.529961 + 0.529961i
\(330\) 0 0
\(331\) −1.26744 3.05988i −0.0696650 0.168186i 0.885212 0.465188i \(-0.154013\pi\)
−0.954877 + 0.297002i \(0.904013\pi\)
\(332\) 0 0
\(333\) 7.33917 + 3.03998i 0.402184 + 0.166590i
\(334\) 0 0
\(335\) 12.9061i 0.705136i
\(336\) 0 0
\(337\) 10.1534i 0.553088i 0.961001 + 0.276544i \(0.0891892\pi\)
−0.961001 + 0.276544i \(0.910811\pi\)
\(338\) 0 0
\(339\) −14.5674 6.03400i −0.791190 0.327722i
\(340\) 0 0
\(341\) −7.69795 18.5845i −0.416868 1.00641i
\(342\) 0 0
\(343\) −13.2198 13.2198i −0.713801 0.713801i
\(344\) 0 0
\(345\) 4.83757 4.83757i 0.260446 0.260446i
\(346\) 0 0
\(347\) −25.9794 + 10.7610i −1.39465 + 0.577681i −0.948356 0.317208i \(-0.897255\pi\)
−0.446289 + 0.894889i \(0.647255\pi\)
\(348\) 0 0
\(349\) −5.71239 + 13.7909i −0.305777 + 0.738212i 0.694055 + 0.719922i \(0.255822\pi\)
−0.999833 + 0.0182903i \(0.994178\pi\)
\(350\) 0 0
\(351\) 3.25866 0.173934
\(352\) 0 0
\(353\) −18.8434 −1.00293 −0.501467 0.865177i \(-0.667206\pi\)
−0.501467 + 0.865177i \(0.667206\pi\)
\(354\) 0 0
\(355\) 0.731784 1.76668i 0.0388391 0.0937658i
\(356\) 0 0
\(357\) −7.04954 + 2.92001i −0.373101 + 0.154543i
\(358\) 0 0
\(359\) 18.8776 18.8776i 0.996324 0.996324i −0.00366976 0.999993i \(-0.501168\pi\)
0.999993 + 0.00366976i \(0.00116812\pi\)
\(360\) 0 0
\(361\) −4.41468 4.41468i −0.232352 0.232352i
\(362\) 0 0
\(363\) 1.39805 + 3.37519i 0.0733785 + 0.177151i
\(364\) 0 0
\(365\) 11.2431 + 4.65704i 0.588490 + 0.243760i
\(366\) 0 0
\(367\) 25.6668i 1.33980i −0.742453 0.669898i \(-0.766338\pi\)
0.742453 0.669898i \(-0.233662\pi\)
\(368\) 0 0
\(369\) 1.92221i 0.100066i
\(370\) 0 0
\(371\) −12.6180 5.22655i −0.655094 0.271349i
\(372\) 0 0
\(373\) −3.11418 7.51829i −0.161246 0.389282i 0.822521 0.568735i \(-0.192567\pi\)
−0.983767 + 0.179453i \(0.942567\pi\)
\(374\) 0 0
\(375\) −5.81557 5.81557i −0.300315 0.300315i
\(376\) 0 0
\(377\) −14.8417 + 14.8417i −0.764384 + 0.764384i
\(378\) 0 0
\(379\) −5.17051 + 2.14170i −0.265591 + 0.110012i −0.511505 0.859280i \(-0.670912\pi\)
0.245914 + 0.969292i \(0.420912\pi\)
\(380\) 0 0
\(381\) −2.15278 + 5.19728i −0.110290 + 0.266265i
\(382\) 0 0
\(383\) −33.8865 −1.73152 −0.865758 0.500462i \(-0.833163\pi\)
−0.865758 + 0.500462i \(0.833163\pi\)
\(384\) 0 0
\(385\) −5.69790 −0.290392
\(386\) 0 0
\(387\) −2.95781 + 7.14079i −0.150354 + 0.362987i
\(388\) 0 0
\(389\) 3.06573 1.26987i 0.155439 0.0643847i −0.303608 0.952797i \(-0.598191\pi\)
0.459046 + 0.888412i \(0.348191\pi\)
\(390\) 0 0
\(391\) 24.7984 24.7984i 1.25411 1.25411i
\(392\) 0 0
\(393\) −5.11942 5.11942i −0.258240 0.258240i
\(394\) 0 0
\(395\) 1.82834 + 4.41400i 0.0919938 + 0.222093i
\(396\) 0 0
\(397\) −21.9201 9.07961i −1.10014 0.455693i −0.242608 0.970124i \(-0.578003\pi\)
−0.857531 + 0.514432i \(0.828003\pi\)
\(398\) 0 0
\(399\) 5.94764i 0.297754i
\(400\) 0 0
\(401\) 7.03254i 0.351188i −0.984463 0.175594i \(-0.943815\pi\)
0.984463 0.175594i \(-0.0561846\pi\)
\(402\) 0 0
\(403\) −15.8206 6.55310i −0.788079 0.326433i
\(404\) 0 0
\(405\) −0.342068 0.825824i −0.0169975 0.0410355i
\(406\) 0 0
\(407\) 21.5023 + 21.5023i 1.06583 + 1.06583i
\(408\) 0 0
\(409\) −5.52966 + 5.52966i −0.273424 + 0.273424i −0.830477 0.557053i \(-0.811932\pi\)
0.557053 + 0.830477i \(0.311932\pi\)
\(410\) 0 0
\(411\) 4.09980 1.69819i 0.202228 0.0837657i
\(412\) 0 0
\(413\) −0.153125 + 0.369676i −0.00753478 + 0.0181906i
\(414\) 0 0
\(415\) −5.45903 −0.267973
\(416\) 0 0
\(417\) 9.42388 0.461489
\(418\) 0 0
\(419\) −7.37792 + 17.8119i −0.360435 + 0.870167i 0.634801 + 0.772675i \(0.281082\pi\)
−0.995236 + 0.0974917i \(0.968918\pi\)
\(420\) 0 0
\(421\) 5.73622 2.37602i 0.279566 0.115800i −0.238495 0.971144i \(-0.576654\pi\)
0.518061 + 0.855344i \(0.326654\pi\)
\(422\) 0 0
\(423\) −5.77253 + 5.77253i −0.280670 + 0.280670i
\(424\) 0 0
\(425\) −13.6116 13.6116i −0.660257 0.660257i
\(426\) 0 0
\(427\) −4.44387 10.7284i −0.215054 0.519186i
\(428\) 0 0
\(429\) 11.5245 + 4.77360i 0.556407 + 0.230471i
\(430\) 0 0
\(431\) 16.9436i 0.816146i 0.912949 + 0.408073i \(0.133799\pi\)
−0.912949 + 0.408073i \(0.866201\pi\)
\(432\) 0 0
\(433\) 26.4587i 1.27152i −0.771886 0.635761i \(-0.780686\pi\)
0.771886 0.635761i \(-0.219314\pi\)
\(434\) 0 0
\(435\) 5.31920 + 2.20328i 0.255036 + 0.105639i
\(436\) 0 0
\(437\) 10.4611 + 25.2554i 0.500424 + 1.20813i
\(438\) 0 0
\(439\) −9.68299 9.68299i −0.462144 0.462144i 0.437214 0.899358i \(-0.355965\pi\)
−0.899358 + 0.437214i \(0.855965\pi\)
\(440\) 0 0
\(441\) 2.98894 2.98894i 0.142330 0.142330i
\(442\) 0 0
\(443\) 10.4314 4.32084i 0.495612 0.205289i −0.120855 0.992670i \(-0.538563\pi\)
0.616467 + 0.787381i \(0.288563\pi\)
\(444\) 0 0
\(445\) −2.46240 + 5.94476i −0.116729 + 0.281809i
\(446\) 0 0
\(447\) 2.63040 0.124414
\(448\) 0 0
\(449\) −23.6353 −1.11542 −0.557708 0.830037i \(-0.688319\pi\)
−0.557708 + 0.830037i \(0.688319\pi\)
\(450\) 0 0
\(451\) −2.81585 + 6.79805i −0.132593 + 0.320108i
\(452\) 0 0
\(453\) 18.7863 7.78155i 0.882658 0.365609i
\(454\) 0 0
\(455\) −3.42982 + 3.42982i −0.160792 + 0.160792i
\(456\) 0 0
\(457\) 23.4812 + 23.4812i 1.09840 + 1.09840i 0.994597 + 0.103807i \(0.0331025\pi\)
0.103807 + 0.994597i \(0.466898\pi\)
\(458\) 0 0
\(459\) −1.75351 4.23336i −0.0818470 0.197596i
\(460\) 0 0
\(461\) −25.8692 10.7154i −1.20485 0.499064i −0.312286 0.949988i \(-0.601095\pi\)
−0.892562 + 0.450924i \(0.851095\pi\)
\(462\) 0 0
\(463\) 19.5222i 0.907272i −0.891187 0.453636i \(-0.850127\pi\)
0.891187 0.453636i \(-0.149873\pi\)
\(464\) 0 0
\(465\) 4.69722i 0.217828i
\(466\) 0 0
\(467\) −5.42932 2.24890i −0.251239 0.104067i 0.253510 0.967333i \(-0.418415\pi\)
−0.504749 + 0.863266i \(0.668415\pi\)
\(468\) 0 0
\(469\) −9.20107 22.2133i −0.424866 1.02572i
\(470\) 0 0
\(471\) −3.88092 3.88092i −0.178824 0.178824i
\(472\) 0 0
\(473\) −20.9211 + 20.9211i −0.961951 + 0.961951i
\(474\) 0 0
\(475\) 13.8624 5.74198i 0.636049 0.263460i
\(476\) 0 0
\(477\) 3.13863 7.57731i 0.143708 0.346941i
\(478\) 0 0
\(479\) −14.2300 −0.650187 −0.325094 0.945682i \(-0.605396\pi\)
−0.325094 + 0.945682i \(0.605396\pi\)
\(480\) 0 0
\(481\) 25.8863 1.18031
\(482\) 0 0
\(483\) 4.87736 11.7750i 0.221928 0.535781i
\(484\) 0 0
\(485\) −15.7027 + 6.50427i −0.713023 + 0.295344i
\(486\) 0 0
\(487\) −17.2727 + 17.2727i −0.782700 + 0.782700i −0.980286 0.197586i \(-0.936690\pi\)
0.197586 + 0.980286i \(0.436690\pi\)
\(488\) 0 0
\(489\) 7.66164 + 7.66164i 0.346471 + 0.346471i
\(490\) 0 0
\(491\) −2.16195 5.21940i −0.0975673 0.235548i 0.867558 0.497335i \(-0.165688\pi\)
−0.965126 + 0.261787i \(0.915688\pi\)
\(492\) 0 0
\(493\) 27.2674 + 11.2945i 1.22806 + 0.508680i
\(494\) 0 0
\(495\) 3.42168i 0.153793i
\(496\) 0 0
\(497\) 3.56243i 0.159797i
\(498\) 0 0
\(499\) −14.2581 5.90591i −0.638281 0.264385i 0.0399860 0.999200i \(-0.487269\pi\)
−0.678267 + 0.734816i \(0.737269\pi\)
\(500\) 0 0
\(501\) −2.91268 7.03184i −0.130129 0.314159i
\(502\) 0 0
\(503\) 9.06568 + 9.06568i 0.404219 + 0.404219i 0.879717 0.475498i \(-0.157732\pi\)
−0.475498 + 0.879717i \(0.657732\pi\)
\(504\) 0 0
\(505\) −2.43094 + 2.43094i −0.108176 + 0.108176i
\(506\) 0 0
\(507\) −2.19990 + 0.911227i −0.0977008 + 0.0404690i
\(508\) 0 0
\(509\) −8.46300 + 20.4315i −0.375116 + 0.905610i 0.617750 + 0.786375i \(0.288044\pi\)
−0.992866 + 0.119236i \(0.961956\pi\)
\(510\) 0 0
\(511\) 22.6711 1.00291
\(512\) 0 0
\(513\) 3.57165 0.157692
\(514\) 0 0
\(515\) 1.59907 3.86049i 0.0704633 0.170114i
\(516\) 0 0
\(517\) −28.8712 + 11.9588i −1.26975 + 0.525949i
\(518\) 0 0
\(519\) 7.36654 7.36654i 0.323355 0.323355i
\(520\) 0 0
\(521\) −6.25345 6.25345i −0.273969 0.273969i 0.556727 0.830696i \(-0.312057\pi\)
−0.830696 + 0.556727i \(0.812057\pi\)
\(522\) 0 0
\(523\) 0.570636 + 1.37764i 0.0249522 + 0.0602399i 0.935865 0.352360i \(-0.114621\pi\)
−0.910912 + 0.412600i \(0.864621\pi\)
\(524\) 0 0
\(525\) −6.46315 2.67712i −0.282075 0.116839i
\(526\) 0 0
\(527\) 24.0790i 1.04890i
\(528\) 0 0
\(529\) 35.5787i 1.54690i
\(530\) 0 0
\(531\) −0.221996 0.0919539i −0.00963382 0.00399046i
\(532\) 0 0
\(533\) 2.39707 + 5.78703i 0.103829 + 0.250664i
\(534\) 0 0
\(535\) 8.24152 + 8.24152i 0.356312 + 0.356312i
\(536\) 0 0
\(537\) −9.78207 + 9.78207i −0.422127 + 0.422127i
\(538\) 0 0
\(539\) 14.9491 6.19211i 0.643902 0.266713i
\(540\) 0 0
\(541\) 12.3150 29.7310i 0.529463 1.27824i −0.402413 0.915458i \(-0.631828\pi\)
0.931876 0.362778i \(-0.118172\pi\)
\(542\) 0 0
\(543\) −21.4594 −0.920912
\(544\) 0 0
\(545\) −4.03000 −0.172626
\(546\) 0 0
\(547\) 12.9326 31.2221i 0.552959 1.33496i −0.362287 0.932067i \(-0.618004\pi\)
0.915246 0.402895i \(-0.131996\pi\)
\(548\) 0 0
\(549\) 6.44260 2.66861i 0.274964 0.113894i
\(550\) 0 0
\(551\) −16.2672 + 16.2672i −0.693006 + 0.693006i
\(552\) 0 0
\(553\) 6.29369 + 6.29369i 0.267635 + 0.267635i
\(554\) 0 0
\(555\) −2.71734 6.56023i −0.115345 0.278466i
\(556\) 0 0
\(557\) 2.78310 + 1.15280i 0.117924 + 0.0488456i 0.440865 0.897573i \(-0.354672\pi\)
−0.322941 + 0.946419i \(0.604672\pi\)
\(558\) 0 0
\(559\) 25.1866i 1.06528i
\(560\) 0 0
\(561\) 17.5403i 0.740552i
\(562\) 0 0
\(563\) 35.0055 + 14.4998i 1.47531 + 0.611092i 0.968062 0.250709i \(-0.0806638\pi\)
0.507245 + 0.861802i \(0.330664\pi\)
\(564\) 0 0
\(565\) 5.39358 + 13.0213i 0.226910 + 0.547808i
\(566\) 0 0
\(567\) −1.17750 1.17750i −0.0494503 0.0494503i
\(568\) 0 0
\(569\) 11.2443 11.2443i 0.471387 0.471387i −0.430976 0.902363i \(-0.641831\pi\)
0.902363 + 0.430976i \(0.141831\pi\)
\(570\) 0 0
\(571\) −17.4655 + 7.23445i −0.730909 + 0.302752i −0.716925 0.697150i \(-0.754451\pi\)
−0.0139834 + 0.999902i \(0.504451\pi\)
\(572\) 0 0
\(573\) 3.97117 9.58726i 0.165898 0.400514i
\(574\) 0 0
\(575\) 32.1531 1.34088
\(576\) 0 0
\(577\) −1.06924 −0.0445129 −0.0222564 0.999752i \(-0.507085\pi\)
−0.0222564 + 0.999752i \(0.507085\pi\)
\(578\) 0 0
\(579\) −3.35265 + 8.09401i −0.139331 + 0.336376i
\(580\) 0 0
\(581\) −9.39581 + 3.89187i −0.389804 + 0.161462i
\(582\) 0 0
\(583\) 22.2000 22.2000i 0.919429 0.919429i
\(584\) 0 0
\(585\) −2.05966 2.05966i −0.0851565 0.0851565i
\(586\) 0 0
\(587\) −5.82611 14.0655i −0.240469 0.580544i 0.756860 0.653577i \(-0.226732\pi\)
−0.997330 + 0.0730327i \(0.976732\pi\)
\(588\) 0 0
\(589\) −17.3402 7.18253i −0.714488 0.295951i
\(590\) 0 0
\(591\) 4.70889i 0.193698i
\(592\) 0 0
\(593\) 41.5874i 1.70779i 0.520447 + 0.853894i \(0.325765\pi\)
−0.520447 + 0.853894i \(0.674235\pi\)
\(594\) 0 0
\(595\) 6.30134 + 2.61010i 0.258330 + 0.107004i
\(596\) 0 0
\(597\) 1.88331 + 4.54671i 0.0770787 + 0.186084i
\(598\) 0 0
\(599\) −2.97009 2.97009i −0.121354 0.121354i 0.643821 0.765176i \(-0.277348\pi\)
−0.765176 + 0.643821i \(0.777348\pi\)
\(600\) 0 0
\(601\) 24.7211 24.7211i 1.00840 1.00840i 0.00843176 0.999964i \(-0.497316\pi\)
0.999964 0.00843176i \(-0.00268394\pi\)
\(602\) 0 0
\(603\) 13.3395 5.52539i 0.543225 0.225011i
\(604\) 0 0
\(605\) 1.24967 3.01696i 0.0508062 0.122657i
\(606\) 0 0
\(607\) 6.96020 0.282506 0.141253 0.989974i \(-0.454887\pi\)
0.141253 + 0.989974i \(0.454887\pi\)
\(608\) 0 0
\(609\) 10.7259 0.434636
\(610\) 0 0
\(611\) −10.1803 + 24.5774i −0.411850 + 0.994294i
\(612\) 0 0
\(613\) −7.35571 + 3.04684i −0.297094 + 0.123061i −0.526252 0.850329i \(-0.676403\pi\)
0.229157 + 0.973389i \(0.426403\pi\)
\(614\) 0 0
\(615\) 1.21495 1.21495i 0.0489916 0.0489916i
\(616\) 0 0
\(617\) −9.81719 9.81719i −0.395225 0.395225i 0.481320 0.876545i \(-0.340158\pi\)
−0.876545 + 0.481320i \(0.840158\pi\)
\(618\) 0 0
\(619\) −4.68397 11.3081i −0.188265 0.454511i 0.801361 0.598181i \(-0.204110\pi\)
−0.989626 + 0.143670i \(0.954110\pi\)
\(620\) 0 0
\(621\) 7.07107 + 2.92893i 0.283752 + 0.117534i
\(622\) 0 0
\(623\) 11.9873i 0.480262i
\(624\) 0 0
\(625\) 13.6535i 0.546138i
\(626\) 0 0
\(627\) 12.6314 + 5.23210i 0.504450 + 0.208950i
\(628\) 0 0
\(629\) −13.9297 33.6292i −0.555412 1.34088i
\(630\) 0 0
\(631\) 29.7384 + 29.7384i 1.18387 + 1.18387i 0.978735 + 0.205130i \(0.0657619\pi\)
0.205130 + 0.978735i \(0.434238\pi\)
\(632\) 0 0
\(633\) −3.64414 + 3.64414i −0.144841 + 0.144841i
\(634\) 0 0
\(635\) 4.64567 1.92430i 0.184358 0.0763635i
\(636\) 0 0
\(637\) 5.27121 12.7258i 0.208853 0.504215i
\(638\) 0 0
\(639\) 2.13930 0.0846293
\(640\) 0 0
\(641\) 10.7253 0.423623 0.211811 0.977311i \(-0.432064\pi\)
0.211811 + 0.977311i \(0.432064\pi\)
\(642\) 0 0
\(643\) −6.96903 + 16.8247i −0.274832 + 0.663502i −0.999677 0.0254092i \(-0.991911\pi\)
0.724846 + 0.688911i \(0.241911\pi\)
\(644\) 0 0
\(645\) 6.38291 2.64389i 0.251327 0.104103i
\(646\) 0 0
\(647\) −33.4123 + 33.4123i −1.31357 + 1.31357i −0.394808 + 0.918764i \(0.629189\pi\)
−0.918764 + 0.394808i \(0.870811\pi\)
\(648\) 0 0
\(649\) −0.650403 0.650403i −0.0255306 0.0255306i
\(650\) 0 0
\(651\) 3.34876 + 8.08461i 0.131248 + 0.316861i
\(652\) 0 0
\(653\) 10.9408 + 4.53181i 0.428145 + 0.177343i 0.586341 0.810064i \(-0.300568\pi\)
−0.158196 + 0.987408i \(0.550568\pi\)
\(654\) 0 0
\(655\) 6.47154i 0.252864i
\(656\) 0 0
\(657\) 13.6144i 0.531148i
\(658\) 0 0
\(659\) −0.739338 0.306244i −0.0288005 0.0119296i 0.368237 0.929732i \(-0.379962\pi\)
−0.397037 + 0.917803i \(0.629962\pi\)
\(660\) 0 0
\(661\) −3.14127 7.58370i −0.122181 0.294972i 0.850941 0.525262i \(-0.176033\pi\)
−0.973122 + 0.230290i \(0.926033\pi\)
\(662\) 0 0
\(663\) −10.5583 10.5583i −0.410050 0.410050i
\(664\) 0 0
\(665\) −3.75926 + 3.75926i −0.145778 + 0.145778i
\(666\) 0 0
\(667\) −45.5453 + 18.8655i −1.76352 + 0.730475i
\(668\) 0 0
\(669\) −4.82353 + 11.6450i −0.186488 + 0.450223i
\(670\) 0 0
\(671\) 26.6940 1.03051
\(672\) 0 0
\(673\) 32.0221 1.23436 0.617180 0.786822i \(-0.288275\pi\)
0.617180 + 0.786822i \(0.288275\pi\)
\(674\) 0 0
\(675\) 1.60765 3.88122i 0.0618787 0.149388i
\(676\) 0 0
\(677\) 22.8528 9.46594i 0.878304 0.363805i 0.102465 0.994737i \(-0.467327\pi\)
0.775839 + 0.630931i \(0.217327\pi\)
\(678\) 0 0
\(679\) −22.3897 + 22.3897i −0.859236 + 0.859236i
\(680\) 0 0
\(681\) −3.40825 3.40825i −0.130605 0.130605i
\(682\) 0 0
\(683\) 6.46834 + 15.6160i 0.247504 + 0.597528i 0.997991 0.0633577i \(-0.0201809\pi\)
−0.750487 + 0.660885i \(0.770181\pi\)
\(684\) 0 0
\(685\) −3.66467 1.51796i −0.140020 0.0579981i
\(686\) 0 0
\(687\) 20.9937i 0.800960i
\(688\) 0 0
\(689\) 26.7263i 1.01819i
\(690\) 0 0
\(691\) 23.6307 + 9.78817i 0.898955 + 0.372359i 0.783818 0.620990i \(-0.213269\pi\)
0.115137 + 0.993350i \(0.463269\pi\)
\(692\) 0 0
\(693\) −2.43940 5.88923i −0.0926650 0.223713i
\(694\) 0 0
\(695\) −5.95644 5.95644i −0.225941 0.225941i
\(696\) 0 0
\(697\) 6.22811 6.22811i 0.235907 0.235907i
\(698\) 0 0
\(699\) 17.5290 7.26077i 0.663009 0.274628i
\(700\) 0 0
\(701\) 9.69117 23.3965i 0.366030 0.883675i −0.628362 0.777921i \(-0.716274\pi\)
0.994392 0.105754i \(-0.0337257\pi\)
\(702\) 0 0
\(703\) 28.3727 1.07010
\(704\) 0 0
\(705\) 7.29716 0.274827
\(706\) 0 0
\(707\) −2.45094 + 5.91709i −0.0921771 + 0.222535i
\(708\) 0 0
\(709\) 11.9720 4.95898i 0.449619 0.186238i −0.146372 0.989230i \(-0.546760\pi\)
0.595991 + 0.802991i \(0.296760\pi\)
\(710\) 0 0
\(711\) −3.77946 + 3.77946i −0.141741 + 0.141741i
\(712\) 0 0
\(713\) −28.4396 28.4396i −1.06507 1.06507i
\(714\) 0 0
\(715\) −4.26695 10.3013i −0.159575 0.385248i
\(716\) 0 0
\(717\) 4.23034 + 1.75226i 0.157985 + 0.0654395i
\(718\) 0 0
\(719\) 18.7152i 0.697960i −0.937130 0.348980i \(-0.886528\pi\)
0.937130 0.348980i \(-0.113472\pi\)
\(720\) 0 0
\(721\) 7.78449i 0.289910i
\(722\) 0 0
\(723\) −13.4804 5.58377i −0.501342 0.207663i
\(724\) 0 0
\(725\) 10.3550 + 24.9993i 0.384576 + 0.928449i
\(726\) 0 0
\(727\) −37.4952 37.4952i −1.39062 1.39062i −0.823931 0.566690i \(-0.808224\pi\)
−0.566690 0.823931i \(-0.691776\pi\)
\(728\) 0 0
\(729\) 0.707107 0.707107i 0.0261891 0.0261891i
\(730\) 0 0
\(731\) 32.7202 13.5532i 1.21020 0.501282i
\(732\) 0 0
\(733\) 11.1057 26.8115i 0.410198 0.990305i −0.574887 0.818233i \(-0.694954\pi\)
0.985084 0.172072i \(-0.0550461\pi\)
\(734\) 0 0
\(735\) −3.77836 −0.139367
\(736\) 0 0
\(737\) 55.2701 2.03590
\(738\) 0 0
\(739\) 0.383327 0.925433i 0.0141009 0.0340426i −0.916672 0.399640i \(-0.869135\pi\)
0.930773 + 0.365597i \(0.119135\pi\)
\(740\) 0 0
\(741\) 10.7528 4.45397i 0.395015 0.163621i
\(742\) 0 0
\(743\) 34.4148 34.4148i 1.26256 1.26256i 0.312708 0.949849i \(-0.398764\pi\)
0.949849 0.312708i \(-0.101236\pi\)
\(744\) 0 0
\(745\) −1.66257 1.66257i −0.0609118 0.0609118i
\(746\) 0 0
\(747\) −2.33713 5.64233i −0.0855111 0.206442i
\(748\) 0 0
\(749\) 20.0605 + 8.30931i 0.732993 + 0.303616i
\(750\) 0 0
\(751\) 20.2742i 0.739816i 0.929068 + 0.369908i \(0.120611\pi\)
−0.929068 + 0.369908i \(0.879389\pi\)
\(752\) 0 0
\(753\) 2.07078i 0.0754634i
\(754\) 0 0
\(755\) −16.7924 6.95566i −0.611139 0.253142i
\(756\) 0 0
\(757\) 18.5068 + 44.6794i 0.672641 + 1.62390i 0.777106 + 0.629370i \(0.216687\pi\)
−0.104465 + 0.994529i \(0.533313\pi\)
\(758\) 0 0
\(759\) 20.7168 + 20.7168i 0.751971 + 0.751971i
\(760\) 0 0
\(761\) 13.1682 13.1682i 0.477345 0.477345i −0.426936 0.904282i \(-0.640407\pi\)
0.904282 + 0.426936i \(0.140407\pi\)
\(762\) 0 0
\(763\) −6.93624 + 2.87308i −0.251109 + 0.104013i
\(764\) 0 0
\(765\) −1.56741 + 3.78405i −0.0566697 + 0.136813i
\(766\) 0 0
\(767\) −0.783013 −0.0282730
\(768\) 0 0
\(769\) −40.4343 −1.45810 −0.729049 0.684461i \(-0.760037\pi\)
−0.729049 + 0.684461i \(0.760037\pi\)
\(770\) 0 0
\(771\) −8.18988 + 19.7721i −0.294951 + 0.712075i
\(772\) 0 0
\(773\) −2.36151 + 0.978168i −0.0849375 + 0.0351823i −0.424748 0.905312i \(-0.639637\pi\)
0.339810 + 0.940494i \(0.389637\pi\)
\(774\) 0 0
\(775\) −15.6101 + 15.6101i −0.560732 + 0.560732i
\(776\) 0 0
\(777\) −9.35389 9.35389i −0.335569 0.335569i
\(778\) 0 0
\(779\) 2.62731 + 6.34288i 0.0941330 + 0.227257i
\(780\) 0 0
\(781\) 7.56578 + 3.13385i 0.270725 + 0.112138i
\(782\) 0 0
\(783\) 6.44108i 0.230185i
\(784\) 0 0
\(785\) 4.90594i 0.175101i
\(786\) 0 0
\(787\) 27.5997 + 11.4322i 0.983825 + 0.407514i 0.815841 0.578276i \(-0.196274\pi\)
0.167984 + 0.985790i \(0.446274\pi\)
\(788\) 0 0
\(789\) 2.24530 + 5.42063i 0.0799348 + 0.192980i
\(790\) 0 0
\(791\) 18.5663 + 18.5663i 0.660142 + 0.660142i
\(792\) 0 0
\(793\) 16.0683 16.0683i 0.570602 0.570602i
\(794\) 0 0
\(795\) −6.77310 + 2.80551i −0.240217 + 0.0995012i
\(796\) 0 0
\(797\) 21.0345 50.7818i 0.745080 1.79878i 0.161238 0.986916i \(-0.448451\pi\)
0.583842 0.811867i \(-0.301549\pi\)
\(798\) 0