Properties

Label 784.2.bb.b.111.9
Level $784$
Weight $2$
Character 784.111
Analytic conductor $6.260$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.bb (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 111.9
Character \(\chi\) \(=\) 784.111
Dual form 784.2.bb.b.671.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0556550 - 0.0697892i) q^{3} +(-3.27604 + 2.61256i) q^{5} +(1.51276 - 2.17061i) q^{7} +(0.665790 - 2.91702i) q^{9} +O(q^{10})\) \(q+(-0.0556550 - 0.0697892i) q^{3} +(-3.27604 + 2.61256i) q^{5} +(1.51276 - 2.17061i) q^{7} +(0.665790 - 2.91702i) q^{9} +(-1.29768 + 0.296186i) q^{11} +(1.55477 - 0.354867i) q^{13} +(0.364657 + 0.0832305i) q^{15} +(-0.356067 + 0.739382i) q^{17} +5.85496 q^{19} +(-0.235678 + 0.0152307i) q^{21} +(1.52265 + 3.16182i) q^{23} +(2.79440 - 12.2431i) q^{25} +(-0.481902 + 0.232072i) q^{27} +(0.642325 + 0.309328i) q^{29} +9.57067 q^{31} +(0.0928928 + 0.0740795i) q^{33} +(0.714960 + 11.0632i) q^{35} +(-4.49018 - 2.16236i) q^{37} +(-0.111297 - 0.0887562i) q^{39} +(8.02209 - 6.39740i) q^{41} +(4.98247 + 3.97338i) q^{43} +(5.43972 + 11.2957i) q^{45} +(2.26804 + 9.93692i) q^{47} +(-2.42309 - 6.56724i) q^{49} +(0.0714178 - 0.0163006i) q^{51} +(5.11790 - 2.46465i) q^{53} +(3.47744 - 4.36057i) q^{55} +(-0.325858 - 0.408613i) q^{57} +(2.50280 - 3.13841i) q^{59} +(-4.17258 + 8.66445i) q^{61} +(-5.32452 - 5.85793i) q^{63} +(-4.16639 + 5.22449i) q^{65} -12.7266i q^{67} +(0.135918 - 0.282236i) q^{69} +(-3.72479 - 7.73461i) q^{71} +(4.61647 + 1.05368i) q^{73} +(-1.00996 + 0.486369i) q^{75} +(-1.32017 + 3.26481i) q^{77} +3.67446i q^{79} +(-8.04417 - 3.87387i) q^{81} +(2.48373 - 10.8819i) q^{83} +(-0.765185 - 3.35249i) q^{85} +(-0.0141609 - 0.0620430i) q^{87} +(-13.2955 - 3.03460i) q^{89} +(1.58173 - 3.91163i) q^{91} +(-0.532656 - 0.667929i) q^{93} +(-19.1811 + 15.2964i) q^{95} +9.96407i q^{97} +3.98254i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 24 q^{9} + O(q^{10}) \) \( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{11}{14}\right)\)

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
\(3\) −0.0556550 0.0697892i −0.0321324 0.0402928i 0.765506 0.643429i \(-0.222489\pi\)
−0.797638 + 0.603136i \(0.793917\pi\)
\(4\) 0 0
\(5\) −3.27604 + 2.61256i −1.46509 + 1.16837i −0.514678 + 0.857384i \(0.672088\pi\)
−0.950414 + 0.310988i \(0.899340\pi\)
\(6\) 0 0
\(7\) 1.51276 2.17061i 0.571771 0.820413i
\(8\) 0 0
\(9\) 0.665790 2.91702i 0.221930 0.972338i
\(10\) 0 0
\(11\) −1.29768 + 0.296186i −0.391264 + 0.0893035i −0.413627 0.910446i \(-0.635738\pi\)
0.0223629 + 0.999750i \(0.492881\pi\)
\(12\) 0 0
\(13\) 1.55477 0.354867i 0.431216 0.0984223i −0.00140297 0.999999i \(-0.500447\pi\)
0.432619 + 0.901577i \(0.357589\pi\)
\(14\) 0 0
\(15\) 0.364657 + 0.0832305i 0.0941539 + 0.0214900i
\(16\) 0 0
\(17\) −0.356067 + 0.739382i −0.0863590 + 0.179326i −0.939676 0.342067i \(-0.888873\pi\)
0.853317 + 0.521393i \(0.174587\pi\)
\(18\) 0 0
\(19\) 5.85496 1.34322 0.671609 0.740905i \(-0.265603\pi\)
0.671609 + 0.740905i \(0.265603\pi\)
\(20\) 0 0
\(21\) −0.235678 + 0.0152307i −0.0514292 + 0.00332361i
\(22\) 0 0
\(23\) 1.52265 + 3.16182i 0.317495 + 0.659285i 0.997247 0.0741573i \(-0.0236267\pi\)
−0.679752 + 0.733442i \(0.737912\pi\)
\(24\) 0 0
\(25\) 2.79440 12.2431i 0.558880 2.44861i
\(26\) 0 0
\(27\) −0.481902 + 0.232072i −0.0927421 + 0.0446623i
\(28\) 0 0
\(29\) 0.642325 + 0.309328i 0.119277 + 0.0574407i 0.492571 0.870273i \(-0.336057\pi\)
−0.373294 + 0.927713i \(0.621772\pi\)
\(30\) 0 0
\(31\) 9.57067 1.71894 0.859472 0.511184i \(-0.170793\pi\)
0.859472 + 0.511184i \(0.170793\pi\)
\(32\) 0 0
\(33\) 0.0928928 + 0.0740795i 0.0161706 + 0.0128956i
\(34\) 0 0
\(35\) 0.714960 + 11.0632i 0.120850 + 1.87002i
\(36\) 0 0
\(37\) −4.49018 2.16236i −0.738181 0.355489i 0.0267149 0.999643i \(-0.491495\pi\)
−0.764896 + 0.644154i \(0.777210\pi\)
\(38\) 0 0
\(39\) −0.111297 0.0887562i −0.0178217 0.0142124i
\(40\) 0 0
\(41\) 8.02209 6.39740i 1.25284 0.999107i 0.253344 0.967376i \(-0.418470\pi\)
0.999496 0.0317305i \(-0.0101018\pi\)
\(42\) 0 0
\(43\) 4.98247 + 3.97338i 0.759819 + 0.605935i 0.924841 0.380354i \(-0.124198\pi\)
−0.165022 + 0.986290i \(0.552769\pi\)
\(44\) 0 0
\(45\) 5.43972 + 11.2957i 0.810905 + 1.68386i
\(46\) 0 0
\(47\) 2.26804 + 9.93692i 0.330827 + 1.44945i 0.817532 + 0.575882i \(0.195341\pi\)
−0.486705 + 0.873566i \(0.661801\pi\)
\(48\) 0 0
\(49\) −2.42309 6.56724i −0.346155 0.938177i
\(50\) 0 0
\(51\) 0.0714178 0.0163006i 0.0100005 0.00228255i
\(52\) 0 0
\(53\) 5.11790 2.46465i 0.702998 0.338546i −0.0480027 0.998847i \(-0.515286\pi\)
0.751001 + 0.660301i \(0.229571\pi\)
\(54\) 0 0
\(55\) 3.47744 4.36057i 0.468898 0.587980i
\(56\) 0 0
\(57\) −0.325858 0.408613i −0.0431609 0.0541221i
\(58\) 0 0
\(59\) 2.50280 3.13841i 0.325836 0.408586i −0.591751 0.806121i \(-0.701563\pi\)
0.917587 + 0.397535i \(0.130134\pi\)
\(60\) 0 0
\(61\) −4.17258 + 8.66445i −0.534244 + 1.10937i 0.442857 + 0.896592i \(0.353965\pi\)
−0.977101 + 0.212776i \(0.931749\pi\)
\(62\) 0 0
\(63\) −5.32452 5.85793i −0.670826 0.738029i
\(64\) 0 0
\(65\) −4.16639 + 5.22449i −0.516778 + 0.648019i
\(66\) 0 0
\(67\) 12.7266i 1.55480i −0.629004 0.777402i \(-0.716537\pi\)
0.629004 0.777402i \(-0.283463\pi\)
\(68\) 0 0
\(69\) 0.135918 0.282236i 0.0163626 0.0339772i
\(70\) 0 0
\(71\) −3.72479 7.73461i −0.442052 0.917930i −0.996330 0.0855983i \(-0.972720\pi\)
0.554278 0.832332i \(-0.312994\pi\)
\(72\) 0 0
\(73\) 4.61647 + 1.05368i 0.540317 + 0.123324i 0.483966 0.875087i \(-0.339196\pi\)
0.0563519 + 0.998411i \(0.482053\pi\)
\(74\) 0 0
\(75\) −1.00996 + 0.486369i −0.116620 + 0.0561611i
\(76\) 0 0
\(77\) −1.32017 + 3.26481i −0.150448 + 0.372059i
\(78\) 0 0
\(79\) 3.67446i 0.413409i 0.978403 + 0.206704i \(0.0662738\pi\)
−0.978403 + 0.206704i \(0.933726\pi\)
\(80\) 0 0
\(81\) −8.04417 3.87387i −0.893796 0.430430i
\(82\) 0 0
\(83\) 2.48373 10.8819i 0.272625 1.19445i −0.634277 0.773106i \(-0.718702\pi\)
0.906902 0.421342i \(-0.138441\pi\)
\(84\) 0 0
\(85\) −0.765185 3.35249i −0.0829959 0.363629i
\(86\) 0 0
\(87\) −0.0141609 0.0620430i −0.00151821 0.00665171i
\(88\) 0 0
\(89\) −13.2955 3.03460i −1.40932 0.321667i −0.550878 0.834586i \(-0.685707\pi\)
−0.858437 + 0.512918i \(0.828564\pi\)
\(90\) 0 0
\(91\) 1.58173 3.91163i 0.165810 0.410051i
\(92\) 0 0
\(93\) −0.532656 0.667929i −0.0552338 0.0692610i
\(94\) 0 0
\(95\) −19.1811 + 15.2964i −1.96794 + 1.56938i
\(96\) 0 0
\(97\) 9.96407i 1.01170i 0.862622 + 0.505849i \(0.168821\pi\)
−0.862622 + 0.505849i \(0.831179\pi\)
\(98\) 0 0
\(99\) 3.98254i 0.400260i
\(100\) 0 0
\(101\) 5.24723 4.18453i 0.522119 0.416376i −0.326646 0.945147i \(-0.605918\pi\)
0.848765 + 0.528771i \(0.177347\pi\)
\(102\) 0 0
\(103\) −1.01325 1.27057i −0.0998382 0.125193i 0.729402 0.684085i \(-0.239798\pi\)
−0.829241 + 0.558892i \(0.811227\pi\)
\(104\) 0 0
\(105\) 0.732300 0.665619i 0.0714652 0.0649578i
\(106\) 0 0
\(107\) −3.82923 0.873996i −0.370185 0.0844923i 0.0333813 0.999443i \(-0.489372\pi\)
−0.403566 + 0.914950i \(0.632230\pi\)
\(108\) 0 0
\(109\) −1.54200 6.75594i −0.147697 0.647102i −0.993522 0.113641i \(-0.963749\pi\)
0.845825 0.533460i \(-0.179109\pi\)
\(110\) 0 0
\(111\) 0.0989919 + 0.433712i 0.00939590 + 0.0411661i
\(112\) 0 0
\(113\) 1.50661 6.60089i 0.141730 0.620960i −0.853303 0.521415i \(-0.825404\pi\)
0.995033 0.0995444i \(-0.0317385\pi\)
\(114\) 0 0
\(115\) −13.2487 6.38024i −1.23545 0.594961i
\(116\) 0 0
\(117\) 4.77156i 0.441131i
\(118\) 0 0
\(119\) 1.06626 + 1.89139i 0.0977441 + 0.173384i
\(120\) 0 0
\(121\) −8.31442 + 4.00401i −0.755856 + 0.364001i
\(122\) 0 0
\(123\) −0.892939 0.203808i −0.0805136 0.0183767i
\(124\) 0 0
\(125\) 13.7408 + 28.5331i 1.22902 + 2.55208i
\(126\) 0 0
\(127\) 5.60457 11.6380i 0.497325 1.03271i −0.489663 0.871912i \(-0.662880\pi\)
0.986988 0.160794i \(-0.0514055\pi\)
\(128\) 0 0
\(129\) 0.568861i 0.0500854i
\(130\) 0 0
\(131\) −2.89463 + 3.62975i −0.252905 + 0.317133i −0.892035 0.451965i \(-0.850723\pi\)
0.639130 + 0.769099i \(0.279294\pi\)
\(132\) 0 0
\(133\) 8.85717 12.7088i 0.768014 1.10199i
\(134\) 0 0
\(135\) 0.972432 2.01928i 0.0836936 0.173792i
\(136\) 0 0
\(137\) −2.72069 + 3.41164i −0.232444 + 0.291476i −0.884350 0.466824i \(-0.845398\pi\)
0.651906 + 0.758300i \(0.273970\pi\)
\(138\) 0 0
\(139\) 13.0776 + 16.3988i 1.10923 + 1.39093i 0.911810 + 0.410612i \(0.134685\pi\)
0.197420 + 0.980319i \(0.436744\pi\)
\(140\) 0 0
\(141\) 0.567262 0.711324i 0.0477721 0.0599043i
\(142\) 0 0
\(143\) −1.91248 + 0.921004i −0.159930 + 0.0770182i
\(144\) 0 0
\(145\) −2.91242 + 0.664742i −0.241864 + 0.0552038i
\(146\) 0 0
\(147\) −0.323465 + 0.534605i −0.0266790 + 0.0440935i
\(148\) 0 0
\(149\) 2.77038 + 12.1378i 0.226958 + 0.994369i 0.952104 + 0.305774i \(0.0989152\pi\)
−0.725146 + 0.688595i \(0.758228\pi\)
\(150\) 0 0
\(151\) 7.09252 + 14.7278i 0.577181 + 1.19853i 0.961366 + 0.275272i \(0.0887680\pi\)
−0.384185 + 0.923256i \(0.625518\pi\)
\(152\) 0 0
\(153\) 1.91972 + 1.53093i 0.155200 + 0.123768i
\(154\) 0 0
\(155\) −31.3539 + 25.0039i −2.51841 + 2.00836i
\(156\) 0 0
\(157\) 3.19837 + 2.55061i 0.255257 + 0.203561i 0.742755 0.669563i \(-0.233519\pi\)
−0.487498 + 0.873124i \(0.662090\pi\)
\(158\) 0 0
\(159\) −0.456843 0.220004i −0.0362300 0.0174475i
\(160\) 0 0
\(161\) 9.16649 + 1.47801i 0.722421 + 0.116483i
\(162\) 0 0
\(163\) 9.55540 + 7.62018i 0.748437 + 0.596859i 0.921648 0.388026i \(-0.126843\pi\)
−0.173211 + 0.984885i \(0.555414\pi\)
\(164\) 0 0
\(165\) −0.497858 −0.0387582
\(166\) 0 0
\(167\) −3.51842 1.69438i −0.272264 0.131115i 0.292771 0.956183i \(-0.405423\pi\)
−0.565034 + 0.825067i \(0.691137\pi\)
\(168\) 0 0
\(169\) −9.42121 + 4.53701i −0.724708 + 0.349001i
\(170\) 0 0
\(171\) 3.89817 17.0790i 0.298100 1.30606i
\(172\) 0 0
\(173\) −1.16029 2.40937i −0.0882153 0.183181i 0.852194 0.523226i \(-0.175272\pi\)
−0.940409 + 0.340045i \(0.889558\pi\)
\(174\) 0 0
\(175\) −22.3477 24.5864i −1.68932 1.85856i
\(176\) 0 0
\(177\) −0.358320 −0.0269330
\(178\) 0 0
\(179\) 7.87798 16.3588i 0.588828 1.22271i −0.367392 0.930066i \(-0.619749\pi\)
0.956220 0.292648i \(-0.0945364\pi\)
\(180\) 0 0
\(181\) −18.4302 4.20658i −1.36991 0.312673i −0.526605 0.850110i \(-0.676535\pi\)
−0.843304 + 0.537437i \(0.819393\pi\)
\(182\) 0 0
\(183\) 0.836909 0.191019i 0.0618661 0.0141205i
\(184\) 0 0
\(185\) 20.3593 4.64688i 1.49685 0.341645i
\(186\) 0 0
\(187\) 0.243066 1.06494i 0.0177747 0.0778761i
\(188\) 0 0
\(189\) −0.225267 + 1.39709i −0.0163858 + 0.101623i
\(190\) 0 0
\(191\) 9.80154 7.81647i 0.709215 0.565580i −0.201063 0.979578i \(-0.564440\pi\)
0.910278 + 0.413998i \(0.135868\pi\)
\(192\) 0 0
\(193\) 9.38078 + 11.7631i 0.675243 + 0.846728i 0.994906 0.100803i \(-0.0321412\pi\)
−0.319663 + 0.947531i \(0.603570\pi\)
\(194\) 0 0
\(195\) 0.596494 0.0427158
\(196\) 0 0
\(197\) −17.4994 −1.24678 −0.623389 0.781912i \(-0.714245\pi\)
−0.623389 + 0.781912i \(0.714245\pi\)
\(198\) 0 0
\(199\) −4.17071 5.22991i −0.295654 0.370738i 0.611712 0.791081i \(-0.290481\pi\)
−0.907365 + 0.420343i \(0.861910\pi\)
\(200\) 0 0
\(201\) −0.888180 + 0.708300i −0.0626474 + 0.0499597i
\(202\) 0 0
\(203\) 1.64312 0.926298i 0.115324 0.0650134i
\(204\) 0 0
\(205\) −9.56714 + 41.9164i −0.668198 + 2.92757i
\(206\) 0 0
\(207\) 10.2368 2.33649i 0.711510 0.162397i
\(208\) 0 0
\(209\) −7.59784 + 1.73416i −0.525553 + 0.119954i
\(210\) 0 0
\(211\) −13.1756 3.00724i −0.907043 0.207027i −0.256543 0.966533i \(-0.582584\pi\)
−0.650500 + 0.759506i \(0.725441\pi\)
\(212\) 0 0
\(213\) −0.332489 + 0.690420i −0.0227818 + 0.0473068i
\(214\) 0 0
\(215\) −26.7035 −1.82116
\(216\) 0 0
\(217\) 14.4782 20.7742i 0.982842 1.41024i
\(218\) 0 0
\(219\) −0.183395 0.380823i −0.0123927 0.0257336i
\(220\) 0 0
\(221\) −0.291222 + 1.27593i −0.0195897 + 0.0858281i
\(222\) 0 0
\(223\) −18.9538 + 9.12765i −1.26924 + 0.611233i −0.942602 0.333918i \(-0.891629\pi\)
−0.326635 + 0.945150i \(0.605915\pi\)
\(224\) 0 0
\(225\) −33.8527 16.3026i −2.25685 1.08684i
\(226\) 0 0
\(227\) −16.2427 −1.07807 −0.539034 0.842284i \(-0.681211\pi\)
−0.539034 + 0.842284i \(0.681211\pi\)
\(228\) 0 0
\(229\) −6.98874 5.57333i −0.461829 0.368296i 0.364761 0.931101i \(-0.381151\pi\)
−0.826590 + 0.562805i \(0.809722\pi\)
\(230\) 0 0
\(231\) 0.301323 0.0895691i 0.0198256 0.00589321i
\(232\) 0 0
\(233\) 6.01234 + 2.89539i 0.393882 + 0.189683i 0.620332 0.784339i \(-0.286998\pi\)
−0.226450 + 0.974023i \(0.572712\pi\)
\(234\) 0 0
\(235\) −33.3910 26.6284i −2.17819 1.73705i
\(236\) 0 0
\(237\) 0.256437 0.204502i 0.0166574 0.0132838i
\(238\) 0 0
\(239\) 15.4166 + 12.2943i 0.997216 + 0.795254i 0.978850 0.204578i \(-0.0655821\pi\)
0.0183661 + 0.999831i \(0.494154\pi\)
\(240\) 0 0
\(241\) −6.69437 13.9010i −0.431223 0.895443i −0.997462 0.0712021i \(-0.977316\pi\)
0.566239 0.824241i \(-0.308398\pi\)
\(242\) 0 0
\(243\) 0.534404 + 2.34138i 0.0342821 + 0.150199i
\(244\) 0 0
\(245\) 25.0954 + 15.1841i 1.60329 + 0.970077i
\(246\) 0 0
\(247\) 9.10312 2.07773i 0.579218 0.132203i
\(248\) 0 0
\(249\) −0.897674 + 0.432297i −0.0568878 + 0.0273957i
\(250\) 0 0
\(251\) 14.5845 18.2883i 0.920563 1.15435i −0.0670988 0.997746i \(-0.521374\pi\)
0.987662 0.156603i \(-0.0500543\pi\)
\(252\) 0 0
\(253\) −2.91240 3.65203i −0.183101 0.229601i
\(254\) 0 0
\(255\) −0.191381 + 0.239985i −0.0119848 + 0.0150284i
\(256\) 0 0
\(257\) 3.92857 8.15776i 0.245058 0.508867i −0.741768 0.670657i \(-0.766012\pi\)
0.986825 + 0.161790i \(0.0517266\pi\)
\(258\) 0 0
\(259\) −11.4862 + 6.47529i −0.713719 + 0.402355i
\(260\) 0 0
\(261\) 1.32997 1.66773i 0.0823229 0.103230i
\(262\) 0 0
\(263\) 20.8986i 1.28866i 0.764747 + 0.644330i \(0.222864\pi\)
−0.764747 + 0.644330i \(0.777136\pi\)
\(264\) 0 0
\(265\) −10.3274 + 21.4451i −0.634409 + 1.31736i
\(266\) 0 0
\(267\) 0.528177 + 1.09677i 0.0323239 + 0.0671212i
\(268\) 0 0
\(269\) 6.32829 + 1.44439i 0.385842 + 0.0880660i 0.411042 0.911616i \(-0.365165\pi\)
−0.0251996 + 0.999682i \(0.508022\pi\)
\(270\) 0 0
\(271\) 9.23226 4.44602i 0.560820 0.270077i −0.131924 0.991260i \(-0.542116\pi\)
0.692745 + 0.721183i \(0.256401\pi\)
\(272\) 0 0
\(273\) −0.361021 + 0.107315i −0.0218500 + 0.00649497i
\(274\) 0 0
\(275\) 16.7152i 1.00796i
\(276\) 0 0
\(277\) −6.15247 2.96287i −0.369666 0.178022i 0.239822 0.970817i \(-0.422911\pi\)
−0.609488 + 0.792795i \(0.708625\pi\)
\(278\) 0 0
\(279\) 6.37205 27.9178i 0.381485 1.67139i
\(280\) 0 0
\(281\) −4.15102 18.1868i −0.247629 1.08493i −0.933885 0.357574i \(-0.883604\pi\)
0.686256 0.727360i \(-0.259253\pi\)
\(282\) 0 0
\(283\) 3.53217 + 15.4754i 0.209966 + 0.919920i 0.964588 + 0.263761i \(0.0849629\pi\)
−0.754622 + 0.656159i \(0.772180\pi\)
\(284\) 0 0
\(285\) 2.13505 + 0.487311i 0.126469 + 0.0288658i
\(286\) 0 0
\(287\) −1.75073 27.0906i −0.103342 1.59911i
\(288\) 0 0
\(289\) 10.1794 + 12.7646i 0.598790 + 0.750859i
\(290\) 0 0
\(291\) 0.695385 0.554551i 0.0407642 0.0325083i
\(292\) 0 0
\(293\) 13.3055i 0.777318i 0.921382 + 0.388659i \(0.127062\pi\)
−0.921382 + 0.388659i \(0.872938\pi\)
\(294\) 0 0
\(295\) 16.8203i 0.979313i
\(296\) 0 0
\(297\) 0.556617 0.443887i 0.0322982 0.0257569i
\(298\) 0 0
\(299\) 3.48940 + 4.37557i 0.201797 + 0.253046i
\(300\) 0 0
\(301\) 16.1620 4.80419i 0.931560 0.276909i
\(302\) 0 0
\(303\) −0.584069 0.133310i −0.0335539 0.00765846i
\(304\) 0 0
\(305\) −8.96682 39.2862i −0.513439 2.24952i
\(306\) 0 0
\(307\) 2.39121 + 10.4766i 0.136473 + 0.597929i 0.996194 + 0.0871641i \(0.0277804\pi\)
−0.859721 + 0.510764i \(0.829362\pi\)
\(308\) 0 0
\(309\) −0.0322799 + 0.141427i −0.00183634 + 0.00804552i
\(310\) 0 0
\(311\) 21.2094 + 10.2139i 1.20267 + 0.579177i 0.924437 0.381336i \(-0.124536\pi\)
0.278236 + 0.960513i \(0.410250\pi\)
\(312\) 0 0
\(313\) 24.8263i 1.40326i 0.712540 + 0.701632i \(0.247545\pi\)
−0.712540 + 0.701632i \(0.752455\pi\)
\(314\) 0 0
\(315\) 32.7475 + 5.28021i 1.84511 + 0.297506i
\(316\) 0 0
\(317\) 15.3238 7.37957i 0.860673 0.414478i 0.0491447 0.998792i \(-0.484350\pi\)
0.811528 + 0.584314i \(0.198636\pi\)
\(318\) 0 0
\(319\) −0.925149 0.211159i −0.0517984 0.0118226i
\(320\) 0 0
\(321\) 0.152120 + 0.315881i 0.00849052 + 0.0176307i
\(322\) 0 0
\(323\) −2.08476 + 4.32905i −0.115999 + 0.240875i
\(324\) 0 0
\(325\) 20.0268i 1.11089i
\(326\) 0 0
\(327\) −0.385672 + 0.483617i −0.0213277 + 0.0267441i
\(328\) 0 0
\(329\) 25.0002 + 10.1092i 1.37830 + 0.557338i
\(330\) 0 0
\(331\) 10.9830 22.8065i 0.603681 1.25356i −0.345379 0.938463i \(-0.612250\pi\)
0.949061 0.315094i \(-0.102036\pi\)
\(332\) 0 0
\(333\) −9.29714 + 11.6583i −0.509480 + 0.638868i
\(334\) 0 0
\(335\) 33.2490 + 41.6930i 1.81659 + 2.27793i
\(336\) 0 0
\(337\) 17.2179 21.5906i 0.937920 1.17611i −0.0462580 0.998930i \(-0.514730\pi\)
0.984178 0.177185i \(-0.0566989\pi\)
\(338\) 0 0
\(339\) −0.544521 + 0.262228i −0.0295743 + 0.0142422i
\(340\) 0 0
\(341\) −12.4196 + 2.83470i −0.672561 + 0.153508i
\(342\) 0 0
\(343\) −17.9205 4.67511i −0.967615 0.252432i
\(344\) 0 0
\(345\) 0.292085 + 1.27971i 0.0157253 + 0.0688973i
\(346\) 0 0
\(347\) 13.2493 + 27.5124i 0.711258 + 1.47694i 0.871774 + 0.489909i \(0.162970\pi\)
−0.160516 + 0.987033i \(0.551316\pi\)
\(348\) 0 0
\(349\) −3.66464 2.92245i −0.196164 0.156435i 0.520482 0.853872i \(-0.325752\pi\)
−0.716646 + 0.697437i \(0.754324\pi\)
\(350\) 0 0
\(351\) −0.666894 + 0.531830i −0.0355962 + 0.0283870i
\(352\) 0 0
\(353\) 12.0153 + 9.58184i 0.639507 + 0.509990i 0.888715 0.458460i \(-0.151599\pi\)
−0.249208 + 0.968450i \(0.580170\pi\)
\(354\) 0 0
\(355\) 32.4097 + 15.6077i 1.72013 + 0.828371i
\(356\) 0 0
\(357\) 0.0726559 0.179679i 0.00384536 0.00950963i
\(358\) 0 0
\(359\) −8.10713 6.46522i −0.427878 0.341221i 0.385754 0.922602i \(-0.373941\pi\)
−0.813632 + 0.581380i \(0.802513\pi\)
\(360\) 0 0
\(361\) 15.2805 0.804237
\(362\) 0 0
\(363\) 0.742176 + 0.357413i 0.0389541 + 0.0187593i
\(364\) 0 0
\(365\) −17.8766 + 8.60890i −0.935703 + 0.450611i
\(366\) 0 0
\(367\) 4.15917 18.2225i 0.217107 0.951207i −0.742496 0.669850i \(-0.766358\pi\)
0.959603 0.281357i \(-0.0907845\pi\)
\(368\) 0 0
\(369\) −13.3203 27.6599i −0.693427 1.43992i
\(370\) 0 0
\(371\) 2.39239 14.8374i 0.124206 0.770320i
\(372\) 0 0
\(373\) −10.9832 −0.568687 −0.284343 0.958723i \(-0.591776\pi\)
−0.284343 + 0.958723i \(0.591776\pi\)
\(374\) 0 0
\(375\) 1.22656 2.54697i 0.0633391 0.131525i
\(376\) 0 0
\(377\) 1.10844 + 0.252994i 0.0570876 + 0.0130299i
\(378\) 0 0
\(379\) −4.37177 + 0.997828i −0.224563 + 0.0512550i −0.333322 0.942813i \(-0.608170\pi\)
0.108759 + 0.994068i \(0.465312\pi\)
\(380\) 0 0
\(381\) −1.12413 + 0.256575i −0.0575909 + 0.0131447i
\(382\) 0 0
\(383\) −4.25886 + 18.6593i −0.217618 + 0.953445i 0.741615 + 0.670826i \(0.234060\pi\)
−0.959232 + 0.282619i \(0.908797\pi\)
\(384\) 0 0
\(385\) −4.20455 14.1447i −0.214284 0.720880i
\(386\) 0 0
\(387\) 14.9077 11.8885i 0.757801 0.604326i
\(388\) 0 0
\(389\) −10.5715 13.2562i −0.535995 0.672116i 0.437924 0.899012i \(-0.355714\pi\)
−0.973919 + 0.226896i \(0.927142\pi\)
\(390\) 0 0
\(391\) −2.87996 −0.145646
\(392\) 0 0
\(393\) 0.414418 0.0209046
\(394\) 0 0
\(395\) −9.59973 12.0377i −0.483015 0.605682i
\(396\) 0 0
\(397\) −10.4752 + 8.35372i −0.525737 + 0.419261i −0.850060 0.526685i \(-0.823435\pi\)
0.324324 + 0.945946i \(0.394863\pi\)
\(398\) 0 0
\(399\) −1.37988 + 0.0891751i −0.0690806 + 0.00446434i
\(400\) 0 0
\(401\) 3.92245 17.1854i 0.195878 0.858196i −0.777481 0.628907i \(-0.783503\pi\)
0.973358 0.229289i \(-0.0736402\pi\)
\(402\) 0 0
\(403\) 14.8802 3.39631i 0.741236 0.169182i
\(404\) 0 0
\(405\) 36.4737 8.32489i 1.81240 0.413667i
\(406\) 0 0
\(407\) 6.46726 + 1.47611i 0.320570 + 0.0731681i
\(408\) 0 0
\(409\) −4.14500 + 8.60718i −0.204957 + 0.425597i −0.977956 0.208809i \(-0.933041\pi\)
0.772999 + 0.634407i \(0.218756\pi\)
\(410\) 0 0
\(411\) 0.389516 0.0192134
\(412\) 0 0
\(413\) −3.02611 10.1803i −0.148905 0.500938i
\(414\) 0 0
\(415\) 20.2929 + 42.1386i 0.996139 + 2.06850i
\(416\) 0 0
\(417\) 0.416625 1.82535i 0.0204022 0.0893880i
\(418\) 0 0
\(419\) −27.0650 + 13.0338i −1.32221 + 0.636743i −0.955884 0.293744i \(-0.905099\pi\)
−0.366326 + 0.930487i \(0.619385\pi\)
\(420\) 0 0
\(421\) −8.09208 3.89694i −0.394384 0.189925i 0.226172 0.974087i \(-0.427379\pi\)
−0.620556 + 0.784162i \(0.713093\pi\)
\(422\) 0 0
\(423\) 30.4962 1.48278
\(424\) 0 0
\(425\) 8.05731 + 6.42549i 0.390837 + 0.311682i
\(426\) 0 0
\(427\) 12.4950 + 22.1643i 0.604675 + 1.07261i
\(428\) 0 0
\(429\) 0.170716 + 0.0822123i 0.00824222 + 0.00396925i
\(430\) 0 0
\(431\) −23.9689 19.1145i −1.15454 0.920715i −0.156781 0.987633i \(-0.550112\pi\)
−0.997758 + 0.0669186i \(0.978683\pi\)
\(432\) 0 0
\(433\) 12.9560 10.3321i 0.622628 0.496529i −0.260616 0.965442i \(-0.583926\pi\)
0.883244 + 0.468913i \(0.155354\pi\)
\(434\) 0 0
\(435\) 0.208483 + 0.166259i 0.00999598 + 0.00797153i
\(436\) 0 0
\(437\) 8.91506 + 18.5123i 0.426465 + 0.885564i
\(438\) 0 0
\(439\) −3.23513 14.1740i −0.154404 0.676490i −0.991573 0.129546i \(-0.958648\pi\)
0.837169 0.546944i \(-0.184209\pi\)
\(440\) 0 0
\(441\) −20.7700 + 2.69579i −0.989048 + 0.128371i
\(442\) 0 0
\(443\) −12.2818 + 2.80324i −0.583526 + 0.133186i −0.504086 0.863654i \(-0.668170\pi\)
−0.0794401 + 0.996840i \(0.525313\pi\)
\(444\) 0 0
\(445\) 51.4846 24.7937i 2.44060 1.17533i
\(446\) 0 0
\(447\) 0.692903 0.868873i 0.0327732 0.0410963i
\(448\) 0 0
\(449\) 14.2791 + 17.9054i 0.673871 + 0.845008i 0.994774 0.102104i \(-0.0325575\pi\)
−0.320902 + 0.947112i \(0.603986\pi\)
\(450\) 0 0
\(451\) −8.51526 + 10.6778i −0.400968 + 0.502798i
\(452\) 0 0
\(453\) 0.633104 1.31465i 0.0297458 0.0617679i
\(454\) 0 0
\(455\) 5.03756 + 16.9470i 0.236164 + 0.794489i
\(456\) 0 0
\(457\) −24.6134 + 30.8643i −1.15137 + 1.44377i −0.275445 + 0.961317i \(0.588825\pi\)
−0.875922 + 0.482452i \(0.839746\pi\)
\(458\) 0 0
\(459\) 0.438943i 0.0204881i
\(460\) 0 0
\(461\) −1.98370 + 4.11919i −0.0923900 + 0.191850i −0.942043 0.335493i \(-0.891097\pi\)
0.849653 + 0.527342i \(0.176812\pi\)
\(462\) 0 0
\(463\) −8.40671 17.4567i −0.390693 0.811282i −0.999834 0.0182203i \(-0.994200\pi\)
0.609141 0.793062i \(-0.291514\pi\)
\(464\) 0 0
\(465\) 3.49001 + 0.796572i 0.161845 + 0.0369401i
\(466\) 0 0
\(467\) 18.3849 8.85370i 0.850752 0.409700i 0.0428950 0.999080i \(-0.486342\pi\)
0.807856 + 0.589379i \(0.200628\pi\)
\(468\) 0 0
\(469\) −27.6245 19.2524i −1.27558 0.888992i
\(470\) 0 0
\(471\) 0.365166i 0.0168259i
\(472\) 0 0
\(473\) −7.64249 3.68043i −0.351402 0.169226i
\(474\) 0 0
\(475\) 16.3611 71.6826i 0.750699 3.28903i
\(476\) 0 0
\(477\) −3.78198 16.5699i −0.173165 0.758686i
\(478\) 0 0
\(479\) −5.74876 25.1870i −0.262668 1.15082i −0.918345 0.395781i \(-0.870474\pi\)
0.655677 0.755041i \(-0.272383\pi\)
\(480\) 0 0
\(481\) −7.74856 1.76856i −0.353304 0.0806393i
\(482\) 0 0
\(483\) −0.407012 0.721980i −0.0185197 0.0328512i
\(484\) 0 0
\(485\) −26.0317 32.6427i −1.18204 1.48223i
\(486\) 0 0
\(487\) −22.3637 + 17.8345i −1.01340 + 0.808156i −0.981525 0.191336i \(-0.938718\pi\)
−0.0318713 + 0.999492i \(0.510147\pi\)
\(488\) 0 0
\(489\) 1.09097i 0.0493351i
\(490\) 0 0
\(491\) 2.41607i 0.109036i 0.998513 + 0.0545179i \(0.0173622\pi\)
−0.998513 + 0.0545179i \(0.982638\pi\)
\(492\) 0 0
\(493\) −0.457422 + 0.364782i −0.0206013 + 0.0164290i
\(494\) 0 0
\(495\) −10.4046 13.0470i −0.467653 0.586418i
\(496\) 0 0
\(497\) −22.4236 3.61558i −1.00583 0.162181i
\(498\) 0 0
\(499\) −1.40569 0.320839i −0.0629272 0.0143627i 0.190941 0.981601i \(-0.438846\pi\)
−0.253869 + 0.967239i \(0.581703\pi\)
\(500\) 0 0
\(501\) 0.0775683 + 0.339849i 0.00346549 + 0.0151833i
\(502\) 0 0
\(503\) 3.07606 + 13.4771i 0.137155 + 0.600913i 0.996052 + 0.0887664i \(0.0282925\pi\)
−0.858898 + 0.512147i \(0.828850\pi\)
\(504\) 0 0
\(505\) −6.25784 + 27.4174i −0.278470 + 1.22006i
\(506\) 0 0
\(507\) 0.840972 + 0.404991i 0.0373489 + 0.0179863i
\(508\) 0 0
\(509\) 4.25026i 0.188389i −0.995554 0.0941947i \(-0.969972\pi\)
0.995554 0.0941947i \(-0.0300276\pi\)
\(510\) 0 0
\(511\) 9.27077 8.42659i 0.410115 0.372770i
\(512\) 0 0
\(513\) −2.82152 + 1.35877i −0.124573 + 0.0599912i
\(514\) 0 0
\(515\) 6.63888 + 1.51528i 0.292544 + 0.0667713i
\(516\) 0 0
\(517\) −5.88636 12.2231i −0.258882 0.537573i
\(518\) 0 0
\(519\) −0.103572 + 0.215069i −0.00454630 + 0.00944049i
\(520\) 0 0
\(521\) 41.1357i 1.80219i 0.433626 + 0.901093i \(0.357234\pi\)
−0.433626 + 0.901093i \(0.642766\pi\)
\(522\) 0 0
\(523\) −19.8003 + 24.8288i −0.865807 + 1.08569i 0.129752 + 0.991546i \(0.458582\pi\)
−0.995559 + 0.0941407i \(0.969990\pi\)
\(524\) 0 0
\(525\) −0.472108 + 2.92798i −0.0206045 + 0.127788i
\(526\) 0 0
\(527\) −3.40780 + 7.07638i −0.148446 + 0.308252i
\(528\) 0 0
\(529\) 6.66163 8.35342i 0.289636 0.363192i
\(530\) 0 0
\(531\) −7.48844 9.39021i −0.324971 0.407501i
\(532\) 0 0
\(533\) 10.2023 12.7933i 0.441911 0.554139i
\(534\) 0 0
\(535\) 14.8281 7.14082i 0.641074 0.308725i
\(536\) 0 0
\(537\) −1.58012 + 0.360651i −0.0681871 + 0.0155633i
\(538\) 0 0
\(539\) 5.08951 + 7.80447i 0.219221 + 0.336162i
\(540\) 0 0
\(541\) −1.37088 6.00621i −0.0589387 0.258227i 0.936871 0.349675i \(-0.113708\pi\)
−0.995810 + 0.0914473i \(0.970851\pi\)
\(542\) 0 0
\(543\) 0.732162 + 1.52035i 0.0314201 + 0.0652444i
\(544\) 0 0
\(545\) 22.7019 + 18.1042i 0.972444 + 0.775499i
\(546\) 0 0
\(547\) 23.6635 18.8710i 1.01178 0.806865i 0.0305127 0.999534i \(-0.490286\pi\)
0.981264 + 0.192670i \(0.0617146\pi\)
\(548\) 0 0
\(549\) 22.4963 + 17.9402i 0.960117 + 0.765668i
\(550\) 0 0
\(551\) 3.76079 + 1.81110i 0.160215 + 0.0771554i
\(552\) 0 0
\(553\) 7.97581 + 5.55859i 0.339166 + 0.236375i
\(554\) 0 0
\(555\) −1.45740 1.16224i −0.0618632 0.0493342i
\(556\) 0 0
\(557\) −39.6120 −1.67842 −0.839208 0.543811i \(-0.816981\pi\)
−0.839208 + 0.543811i \(0.816981\pi\)
\(558\) 0 0
\(559\) 9.15662 + 4.40960i 0.387284 + 0.186506i
\(560\) 0 0
\(561\) −0.0878491 + 0.0423059i −0.00370899 + 0.00178616i
\(562\) 0 0
\(563\) −8.68269 + 38.0414i −0.365932 + 1.60325i 0.371903 + 0.928271i \(0.378705\pi\)
−0.737835 + 0.674981i \(0.764152\pi\)
\(564\) 0 0
\(565\) 12.3095 + 25.5609i 0.517864 + 1.07536i
\(566\) 0 0
\(567\) −20.5776 + 11.6005i −0.864177 + 0.487175i
\(568\) 0 0
\(569\) 26.7518 1.12149 0.560747 0.827987i \(-0.310514\pi\)
0.560747 + 0.827987i \(0.310514\pi\)
\(570\) 0 0
\(571\) 8.88230 18.4443i 0.371713 0.771870i −0.628268 0.777997i \(-0.716236\pi\)
0.999981 + 0.00612706i \(0.00195032\pi\)
\(572\) 0 0
\(573\) −1.09101 0.249016i −0.0455776 0.0104028i
\(574\) 0 0
\(575\) 42.9653 9.80655i 1.79178 0.408961i
\(576\) 0 0
\(577\) 7.84383 1.79030i 0.326543 0.0745313i −0.0561069 0.998425i \(-0.517869\pi\)
0.382650 + 0.923894i \(0.375012\pi\)
\(578\) 0 0
\(579\) 0.298851 1.30935i 0.0124198 0.0544149i
\(580\) 0 0
\(581\) −19.8631 21.8530i −0.824062 0.906616i
\(582\) 0 0
\(583\) −5.91139 + 4.71417i −0.244825 + 0.195241i
\(584\) 0 0
\(585\) 12.4660 + 15.6318i 0.515405 + 0.646297i
\(586\) 0 0
\(587\) 4.31024 0.177902 0.0889512 0.996036i \(-0.471648\pi\)
0.0889512 + 0.996036i \(0.471648\pi\)
\(588\) 0 0
\(589\) 56.0359 2.30892
\(590\) 0 0
\(591\) 0.973927 + 1.22127i 0.0400620 + 0.0502362i
\(592\) 0 0
\(593\) −23.8170 + 18.9934i −0.978047 + 0.779967i −0.975493 0.220030i \(-0.929384\pi\)
−0.00255407 + 0.999997i \(0.500813\pi\)
\(594\) 0 0
\(595\) −8.43450 3.41062i −0.345781 0.139822i
\(596\) 0 0
\(597\) −0.132870 + 0.582141i −0.00543800 + 0.0238254i
\(598\) 0 0
\(599\) −7.23546 + 1.65145i −0.295633 + 0.0674762i −0.367765 0.929919i \(-0.619877\pi\)
0.0721321 + 0.997395i \(0.477020\pi\)
\(600\) 0 0
\(601\) 6.60432 1.50739i 0.269396 0.0614879i −0.0856889 0.996322i \(-0.527309\pi\)
0.355085 + 0.934834i \(0.384452\pi\)
\(602\) 0 0
\(603\) −37.1237 8.47325i −1.51180 0.345058i
\(604\) 0 0
\(605\) 16.7777 34.8392i 0.682110 1.41642i
\(606\) 0 0
\(607\) 10.5994 0.430218 0.215109 0.976590i \(-0.430989\pi\)
0.215109 + 0.976590i \(0.430989\pi\)
\(608\) 0 0
\(609\) −0.156093 0.0631186i −0.00632522 0.00255770i
\(610\) 0 0
\(611\) 7.05256 + 14.6448i 0.285316 + 0.592465i
\(612\) 0 0
\(613\) 3.28448 14.3903i 0.132659 0.581217i −0.864278 0.503014i \(-0.832224\pi\)
0.996937 0.0782036i \(-0.0249184\pi\)
\(614\) 0 0
\(615\) 3.45777 1.66517i 0.139431 0.0671463i
\(616\) 0 0
\(617\) 36.9865 + 17.8118i 1.48902 + 0.717074i 0.988859 0.148858i \(-0.0475598\pi\)
0.500161 + 0.865932i \(0.333274\pi\)
\(618\) 0 0
\(619\) 3.53198 0.141962 0.0709811 0.997478i \(-0.477387\pi\)
0.0709811 + 0.997478i \(0.477387\pi\)
\(620\) 0 0
\(621\) −1.46754 1.17032i −0.0588903 0.0469635i
\(622\) 0 0
\(623\) −26.6998 + 24.2686i −1.06971 + 0.972301i
\(624\) 0 0
\(625\) −62.9884 30.3336i −2.51954 1.21334i
\(626\) 0 0
\(627\) 0.543883 + 0.433732i 0.0217206 + 0.0173216i
\(628\) 0 0
\(629\) 3.19761 2.55001i 0.127497 0.101676i
\(630\) 0 0
\(631\) 13.6273 + 10.8674i 0.542493 + 0.432623i 0.856010 0.516959i \(-0.172936\pi\)
−0.313518 + 0.949582i \(0.601507\pi\)
\(632\) 0 0
\(633\) 0.523414 + 1.08688i 0.0208038 + 0.0431996i
\(634\) 0 0
\(635\) 12.0442 + 52.7689i 0.477958 + 2.09407i
\(636\) 0 0
\(637\) −6.09785 9.35069i −0.241605 0.370488i
\(638\) 0 0
\(639\) −25.0419 + 5.71565i −0.990643 + 0.226108i
\(640\) 0 0
\(641\) −20.0483 + 9.65477i −0.791862 + 0.381341i −0.785674 0.618640i \(-0.787684\pi\)
−0.00618750 + 0.999981i \(0.501970\pi\)
\(642\) 0 0
\(643\) −17.7520 + 22.2603i −0.700071 + 0.877861i −0.997029 0.0770293i \(-0.975456\pi\)
0.296958 + 0.954891i \(0.404028\pi\)
\(644\) 0 0
\(645\) 1.48618 + 1.86361i 0.0585184 + 0.0733797i
\(646\) 0 0
\(647\) 19.4743 24.4200i 0.765615 0.960051i −0.234312 0.972162i \(-0.575284\pi\)
0.999927 + 0.0121108i \(0.00385507\pi\)
\(648\) 0 0
\(649\) −2.31827 + 4.81393i −0.0909999 + 0.188963i
\(650\) 0 0
\(651\) −2.25560 + 0.145768i −0.0884038 + 0.00571310i
\(652\) 0 0
\(653\) 18.7441 23.5044i 0.733514 0.919797i −0.265504 0.964110i \(-0.585538\pi\)
0.999018 + 0.0443125i \(0.0141097\pi\)
\(654\) 0 0
\(655\) 19.4536i 0.760116i
\(656\) 0 0
\(657\) 6.14720 12.7648i 0.239825 0.498002i
\(658\) 0 0
\(659\) −14.0682 29.2130i −0.548020 1.13798i −0.972578 0.232575i \(-0.925285\pi\)
0.424558 0.905401i \(-0.360429\pi\)
\(660\) 0 0
\(661\) −29.1469 6.65260i −1.13368 0.258756i −0.385799 0.922583i \(-0.626074\pi\)
−0.747886 + 0.663827i \(0.768931\pi\)
\(662\) 0 0
\(663\) 0.105254 0.0506876i 0.00408772 0.00196854i
\(664\) 0 0
\(665\) 4.18606 + 64.7745i 0.162328 + 2.51185i
\(666\) 0 0
\(667\) 2.50192i 0.0968746i
\(668\) 0 0
\(669\) 1.69188 + 0.814768i 0.0654120 + 0.0315007i
\(670\) 0 0
\(671\) 2.84837 12.4795i 0.109960 0.481766i
\(672\) 0 0
\(673\) 6.00174 + 26.2954i 0.231350 + 1.01361i 0.948521 + 0.316714i \(0.102580\pi\)
−0.717171 + 0.696897i \(0.754563\pi\)
\(674\) 0 0
\(675\) 1.49464 + 6.54846i 0.0575289 + 0.252051i
\(676\) 0 0
\(677\) −29.7326 6.78628i −1.14272 0.260818i −0.391056 0.920367i \(-0.627890\pi\)
−0.751661 + 0.659549i \(0.770747\pi\)
\(678\) 0 0
\(679\) 21.6281 + 15.0733i 0.830011 + 0.578460i
\(680\) 0 0
\(681\) 0.903989 + 1.13357i 0.0346410 + 0.0434384i
\(682\) 0 0
\(683\) −31.0604 + 24.7698i −1.18849 + 0.947790i −0.999416 0.0341722i \(-0.989121\pi\)
−0.189076 + 0.981963i \(0.560549\pi\)
\(684\) 0 0
\(685\) 18.2846i 0.698620i
\(686\) 0 0
\(687\) 0.797922i 0.0304426i
\(688\) 0 0
\(689\) 7.08255 5.64815i 0.269824 0.215177i
\(690\) 0 0
\(691\) 2.63286 + 3.30151i 0.100159 + 0.125595i 0.829385 0.558678i \(-0.188691\pi\)
−0.729226 + 0.684273i \(0.760120\pi\)
\(692\) 0 0
\(693\) 8.64454 + 6.02464i 0.328379 + 0.228857i
\(694\) 0 0
\(695\) −85.6858 19.5572i −3.25025 0.741848i
\(696\) 0 0
\(697\) 1.87372 + 8.20929i 0.0709721 + 0.310949i
\(698\) 0 0
\(699\) −0.132550 0.580740i −0.00501350 0.0219656i
\(700\) 0 0
\(701\) −0.506981 + 2.22123i −0.0191484 + 0.0838947i −0.983599 0.180368i \(-0.942271\pi\)
0.964451 + 0.264262i \(0.0851284\pi\)
\(702\) 0 0
\(703\) −26.2898 12.6605i −0.991539 0.477500i
\(704\) 0 0
\(705\) 3.81233i 0.143581i
\(706\) 0 0
\(707\) −1.14515 17.7199i −0.0430678 0.666425i
\(708\) 0 0
\(709\) 3.54940 1.70930i 0.133301 0.0641942i −0.366045 0.930597i \(-0.619288\pi\)
0.499345 + 0.866403i \(0.333574\pi\)
\(710\) 0 0
\(711\) 10.7184 + 2.44642i 0.401973 + 0.0917478i
\(712\) 0 0
\(713\) 14.5728 + 30.2607i 0.545756 + 1.13327i
\(714\) 0 0
\(715\) 3.85921 8.01373i 0.144326 0.299696i
\(716\) 0 0
\(717\) 1.76015i 0.0657341i
\(718\) 0 0
\(719\) −5.52467 + 6.92771i −0.206035 + 0.258360i −0.874103 0.485740i \(-0.838550\pi\)
0.668068 + 0.744100i \(0.267122\pi\)
\(720\) 0 0
\(721\) −4.29072 + 0.277288i −0.159795 + 0.0103267i
\(722\) 0 0
\(723\) −0.597565 + 1.24086i −0.0222237 + 0.0461479i
\(724\) 0 0
\(725\) 5.58204 6.99965i 0.207312 0.259961i
\(726\) 0 0
\(727\) −4.22044 5.29226i −0.156527 0.196279i 0.697384 0.716698i \(-0.254347\pi\)
−0.853911 + 0.520419i \(0.825776\pi\)
\(728\) 0 0
\(729\) −16.5665 + 20.7738i −0.613576 + 0.769400i
\(730\) 0 0
\(731\) −4.71194 + 2.26915i −0.174277 + 0.0839276i
\(732\) 0 0
\(733\) 28.2958 6.45833i 1.04513 0.238544i 0.334709 0.942322i \(-0.391362\pi\)
0.710420 + 0.703778i \(0.248505\pi\)
\(734\) 0 0
\(735\) −0.337001 2.59646i −0.0124305 0.0957720i
\(736\) 0 0
\(737\) 3.76945 + 16.5150i 0.138849 + 0.608339i
\(738\) 0 0
\(739\) −13.7031 28.4547i −0.504075 1.04672i −0.985412 0.170187i \(-0.945563\pi\)
0.481337 0.876536i \(-0.340152\pi\)
\(740\) 0 0
\(741\) −0.651638 0.519664i −0.0239385 0.0190903i
\(742\) 0 0
\(743\) −13.7093 + 10.9328i −0.502946 + 0.401086i −0.841831 0.539742i \(-0.818522\pi\)
0.338885 + 0.940828i \(0.389950\pi\)
\(744\) 0 0
\(745\) −40.7867 32.5263i −1.49431 1.19167i
\(746\) 0 0
\(747\) −30.0891 14.4902i −1.10090 0.530168i
\(748\) 0 0
\(749\) −7.68982 + 6.98960i −0.280980 + 0.255394i
\(750\) 0 0
\(751\) −2.55543 2.03789i −0.0932490 0.0743636i 0.575756 0.817622i \(-0.304708\pi\)
−0.669005 + 0.743258i \(0.733279\pi\)
\(752\) 0 0
\(753\) −2.08803 −0.0760919
\(754\) 0 0
\(755\) −61.7125 29.7192i −2.24595 1.08159i
\(756\) 0 0
\(757\) 5.14216 2.47633i 0.186895 0.0900039i −0.338096 0.941112i \(-0.609783\pi\)
0.524991 + 0.851108i \(0.324069\pi\)
\(758\) 0 0
\(759\) −0.0927827 + 0.406508i −0.00336780 + 0.0147553i
\(760\) 0 0
\(761\) −0.0881927 0.183134i −0.00319698 0.00663860i 0.899364 0.437200i \(-0.144030\pi\)
−0.902561 + 0.430561i \(0.858316\pi\)
\(762\) 0 0
\(763\) −16.9972 6.87307i −0.615340 0.248822i
\(764\) 0 0
\(765\) −10.2887 −0.371990
\(766\) 0 0
\(767\) 2.77756 5.76767i 0.100292 0.208258i
\(768\) 0 0
\(769\) −41.4807 9.46770i −1.49583 0.341414i −0.605176 0.796092i \(-0.706897\pi\)
−0.890656 + 0.454678i \(0.849754\pi\)
\(770\) 0 0
\(771\) −0.787968 + 0.179849i −0.0283780 + 0.00647709i
\(772\) 0 0
\(773\) −46.7547 + 10.6715i −1.68165 + 0.383826i −0.953453 0.301542i \(-0.902499\pi\)
−0.728197 + 0.685368i \(0.759641\pi\)
\(774\) 0 0
\(775\) 26.7443 117.174i 0.960683 4.20903i
\(776\) 0 0
\(777\) 1.09117 + 0.441231i 0.0391455 + 0.0158291i
\(778\) 0 0
\(779\) 46.9690 37.4565i 1.68284 1.34202i
\(780\) 0 0
\(781\) 7.12446 + 8.93379i 0.254933 + 0.319676i
\(782\) 0 0
\(783\) −0.381324 −0.0136274
\(784\) 0 0
\(785\) −17.1416 −0.611810
\(786\) 0 0
\(787\) 23.6943 + 29.7117i 0.844611 + 1.05911i 0.997486 + 0.0708631i \(0.0225754\pi\)
−0.152875 + 0.988246i \(0.548853\pi\)
\(788\) 0 0
\(789\) 1.45849 1.16311i 0.0519238 0.0414078i
\(790\) 0 0
\(791\) −12.0488 13.2559i −0.428406 0.471324i
\(792\) 0 0
\(793\) −3.41269 + 14.9520i −0.121188 + 0.530959i
\(794\) 0 0
\(795\) 2.07141 0.472786i 0.0734654 0.0167680i
\(796\) 0 0