Properties

Label 624.2.cn.f.305.1
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.1
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.68186 - 0.413931i) q^{3} +(-1.44076 - 1.44076i) q^{5} +(-0.918532 + 3.42801i) q^{7} +(2.65732 + 1.39235i) q^{9} +O(q^{10})\) \(q+(-1.68186 - 0.413931i) q^{3} +(-1.44076 - 1.44076i) q^{5} +(-0.918532 + 3.42801i) q^{7} +(2.65732 + 1.39235i) q^{9} +(0.0392149 + 0.146352i) q^{11} +(1.92366 - 3.04952i) q^{13} +(1.82679 + 3.01954i) q^{15} +(1.60706 + 2.78351i) q^{17} +(-1.90607 - 0.510729i) q^{19} +(2.96380 - 5.38523i) q^{21} +(4.19640 - 7.26837i) q^{23} -0.848416i q^{25} +(-3.89291 - 3.44169i) q^{27} +(0.0238088 + 0.0137460i) q^{29} +(5.54595 - 5.54595i) q^{31} +(-0.00537445 - 0.262376i) q^{33} +(6.26232 - 3.61555i) q^{35} +(3.84429 - 1.03007i) q^{37} +(-4.49761 + 4.33261i) q^{39} +(-2.53382 + 0.678935i) q^{41} +(5.90548 - 3.40953i) q^{43} +(-1.82252 - 5.83461i) q^{45} +(-4.77303 + 4.77303i) q^{47} +(-4.84536 - 2.79747i) q^{49} +(-1.55068 - 5.34670i) q^{51} -13.3755i q^{53} +(0.154359 - 0.267357i) q^{55} +(2.99434 + 1.64796i) q^{57} +(8.09489 + 2.16902i) q^{59} +(6.61697 + 11.4609i) q^{61} +(-7.21382 + 7.83040i) q^{63} +(-7.16515 + 1.62210i) q^{65} +(-1.18370 - 4.41762i) q^{67} +(-10.0664 + 10.4874i) q^{69} +(1.29021 - 4.81512i) q^{71} +(6.22036 + 6.22036i) q^{73} +(-0.351186 + 1.42692i) q^{75} -0.537715 q^{77} +13.3852 q^{79} +(5.12272 + 7.39984i) q^{81} +(1.94085 + 1.94085i) q^{83} +(1.69499 - 6.32577i) q^{85} +(-0.0343533 - 0.0329742i) q^{87} +(2.87300 + 10.7222i) q^{89} +(8.68683 + 9.39538i) q^{91} +(-11.6232 + 7.03189i) q^{93} +(2.01035 + 3.48203i) q^{95} +(-17.7357 - 4.75227i) q^{97} +(-0.0995664 + 0.443505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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
\(3\) −1.68186 0.413931i −0.971024 0.238983i
\(4\) 0 0
\(5\) −1.44076 1.44076i −0.644328 0.644328i 0.307289 0.951616i \(-0.400578\pi\)
−0.951616 + 0.307289i \(0.900578\pi\)
\(6\) 0 0
\(7\) −0.918532 + 3.42801i −0.347172 + 1.29567i 0.542881 + 0.839809i \(0.317333\pi\)
−0.890054 + 0.455856i \(0.849333\pi\)
\(8\) 0 0
\(9\) 2.65732 + 1.39235i 0.885774 + 0.464117i
\(10\) 0 0
\(11\) 0.0392149 + 0.146352i 0.0118237 + 0.0441267i 0.971586 0.236688i \(-0.0760620\pi\)
−0.959762 + 0.280815i \(0.909395\pi\)
\(12\) 0 0
\(13\) 1.92366 3.04952i 0.533526 0.845784i
\(14\) 0 0
\(15\) 1.82679 + 3.01954i 0.471674 + 0.779641i
\(16\) 0 0
\(17\) 1.60706 + 2.78351i 0.389770 + 0.675101i 0.992418 0.122905i \(-0.0392212\pi\)
−0.602648 + 0.798007i \(0.705888\pi\)
\(18\) 0 0
\(19\) −1.90607 0.510729i −0.437282 0.117169i 0.0334605 0.999440i \(-0.489347\pi\)
−0.470742 + 0.882271i \(0.656014\pi\)
\(20\) 0 0
\(21\) 2.96380 5.38523i 0.646755 1.17515i
\(22\) 0 0
\(23\) 4.19640 7.26837i 0.875009 1.51556i 0.0182561 0.999833i \(-0.494189\pi\)
0.856753 0.515727i \(-0.172478\pi\)
\(24\) 0 0
\(25\) 0.848416i 0.169683i
\(26\) 0 0
\(27\) −3.89291 3.44169i −0.749192 0.662353i
\(28\) 0 0
\(29\) 0.0238088 + 0.0137460i 0.00442119 + 0.00255258i 0.502209 0.864746i \(-0.332521\pi\)
−0.497788 + 0.867299i \(0.665854\pi\)
\(30\) 0 0
\(31\) 5.54595 5.54595i 0.996083 0.996083i −0.00390967 0.999992i \(-0.501244\pi\)
0.999992 + 0.00390967i \(0.00124449\pi\)
\(32\) 0 0
\(33\) −0.00537445 0.262376i −0.000935571 0.0456738i
\(34\) 0 0
\(35\) 6.26232 3.61555i 1.05853 0.611140i
\(36\) 0 0
\(37\) 3.84429 1.03007i 0.631997 0.169343i 0.0714212 0.997446i \(-0.477247\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(38\) 0 0
\(39\) −4.49761 + 4.33261i −0.720194 + 0.693772i
\(40\) 0 0
\(41\) −2.53382 + 0.678935i −0.395716 + 0.106032i −0.451189 0.892428i \(-0.649000\pi\)
0.0554728 + 0.998460i \(0.482333\pi\)
\(42\) 0 0
\(43\) 5.90548 3.40953i 0.900577 0.519948i 0.0231896 0.999731i \(-0.492618\pi\)
0.877387 + 0.479783i \(0.159285\pi\)
\(44\) 0 0
\(45\) −1.82252 5.83461i −0.271686 0.869772i
\(46\) 0 0
\(47\) −4.77303 + 4.77303i −0.696218 + 0.696218i −0.963593 0.267374i \(-0.913844\pi\)
0.267374 + 0.963593i \(0.413844\pi\)
\(48\) 0 0
\(49\) −4.84536 2.79747i −0.692194 0.399638i
\(50\) 0 0
\(51\) −1.55068 5.34670i −0.217138 0.748688i
\(52\) 0 0
\(53\) 13.3755i 1.83726i −0.395119 0.918630i \(-0.629297\pi\)
0.395119 0.918630i \(-0.370703\pi\)
\(54\) 0 0
\(55\) 0.154359 0.267357i 0.0208137 0.0360504i
\(56\) 0 0
\(57\) 2.99434 + 1.64796i 0.396610 + 0.218277i
\(58\) 0 0
\(59\) 8.09489 + 2.16902i 1.05386 + 0.282382i 0.743848 0.668349i \(-0.232999\pi\)
0.310017 + 0.950731i \(0.399665\pi\)
\(60\) 0 0
\(61\) 6.61697 + 11.4609i 0.847216 + 1.46742i 0.883683 + 0.468086i \(0.155056\pi\)
−0.0364673 + 0.999335i \(0.511610\pi\)
\(62\) 0 0
\(63\) −7.21382 + 7.83040i −0.908856 + 0.986538i
\(64\) 0 0
\(65\) −7.16515 + 1.62210i −0.888728 + 0.201196i
\(66\) 0 0
\(67\) −1.18370 4.41762i −0.144612 0.539698i −0.999772 0.0213353i \(-0.993208\pi\)
0.855161 0.518363i \(-0.173458\pi\)
\(68\) 0 0
\(69\) −10.0664 + 10.4874i −1.21185 + 1.26253i
\(70\) 0 0
\(71\) 1.29021 4.81512i 0.153119 0.571449i −0.846140 0.532961i \(-0.821079\pi\)
0.999259 0.0384882i \(-0.0122542\pi\)
\(72\) 0 0
\(73\) 6.22036 + 6.22036i 0.728038 + 0.728038i 0.970229 0.242191i \(-0.0778660\pi\)
−0.242191 + 0.970229i \(0.577866\pi\)
\(74\) 0 0
\(75\) −0.351186 + 1.42692i −0.0405514 + 0.164766i
\(76\) 0 0
\(77\) −0.537715 −0.0612784
\(78\) 0 0
\(79\) 13.3852 1.50596 0.752979 0.658045i \(-0.228616\pi\)
0.752979 + 0.658045i \(0.228616\pi\)
\(80\) 0 0
\(81\) 5.12272 + 7.39984i 0.569192 + 0.822205i
\(82\) 0 0
\(83\) 1.94085 + 1.94085i 0.213036 + 0.213036i 0.805556 0.592520i \(-0.201867\pi\)
−0.592520 + 0.805556i \(0.701867\pi\)
\(84\) 0 0
\(85\) 1.69499 6.32577i 0.183847 0.686126i
\(86\) 0 0
\(87\) −0.0343533 0.0329742i −0.00368306 0.00353520i
\(88\) 0 0
\(89\) 2.87300 + 10.7222i 0.304537 + 1.13655i 0.933343 + 0.358987i \(0.116878\pi\)
−0.628805 + 0.777563i \(0.716456\pi\)
\(90\) 0 0
\(91\) 8.68683 + 9.39538i 0.910627 + 0.984904i
\(92\) 0 0
\(93\) −11.6232 + 7.03189i −1.20527 + 0.729173i
\(94\) 0 0
\(95\) 2.01035 + 3.48203i 0.206257 + 0.357248i
\(96\) 0 0
\(97\) −17.7357 4.75227i −1.80079 0.482520i −0.806687 0.590978i \(-0.798742\pi\)
−0.994101 + 0.108458i \(0.965409\pi\)
\(98\) 0 0
\(99\) −0.0995664 + 0.443505i −0.0100068 + 0.0445739i
\(100\) 0 0
\(101\) 0.226814 0.392853i 0.0225688 0.0390903i −0.854520 0.519418i \(-0.826149\pi\)
0.877089 + 0.480327i \(0.159482\pi\)
\(102\) 0 0
\(103\) 10.0525i 0.990499i −0.868751 0.495250i \(-0.835077\pi\)
0.868751 0.495250i \(-0.164923\pi\)
\(104\) 0 0
\(105\) −12.0290 + 3.48870i −1.17391 + 0.340462i
\(106\) 0 0
\(107\) −11.4165 6.59132i −1.10368 0.637207i −0.166492 0.986043i \(-0.553244\pi\)
−0.937184 + 0.348836i \(0.886577\pi\)
\(108\) 0 0
\(109\) 4.43289 4.43289i 0.424594 0.424594i −0.462188 0.886782i \(-0.652936\pi\)
0.886782 + 0.462188i \(0.152936\pi\)
\(110\) 0 0
\(111\) −6.89194 + 0.141173i −0.654154 + 0.0133995i
\(112\) 0 0
\(113\) −5.33256 + 3.07875i −0.501645 + 0.289625i −0.729393 0.684095i \(-0.760197\pi\)
0.227748 + 0.973720i \(0.426864\pi\)
\(114\) 0 0
\(115\) −16.5180 + 4.42598i −1.54031 + 0.412725i
\(116\) 0 0
\(117\) 9.35777 5.42515i 0.865126 0.501555i
\(118\) 0 0
\(119\) −11.0180 + 2.95228i −1.01002 + 0.270635i
\(120\) 0 0
\(121\) 9.50640 5.48852i 0.864218 0.498957i
\(122\) 0 0
\(123\) 4.54257 0.0930490i 0.409590 0.00838994i
\(124\) 0 0
\(125\) −8.42617 + 8.42617i −0.753659 + 0.753659i
\(126\) 0 0
\(127\) −8.15516 4.70839i −0.723654 0.417802i 0.0924423 0.995718i \(-0.470533\pi\)
−0.816096 + 0.577916i \(0.803866\pi\)
\(128\) 0 0
\(129\) −11.3435 + 3.28990i −0.998740 + 0.289659i
\(130\) 0 0
\(131\) 14.8806i 1.30012i 0.759881 + 0.650062i \(0.225257\pi\)
−0.759881 + 0.650062i \(0.774743\pi\)
\(132\) 0 0
\(133\) 3.50157 6.06489i 0.303624 0.525893i
\(134\) 0 0
\(135\) 0.650108 + 10.5674i 0.0559524 + 0.909498i
\(136\) 0 0
\(137\) 8.69061 + 2.32864i 0.742489 + 0.198949i 0.610184 0.792260i \(-0.291095\pi\)
0.132305 + 0.991209i \(0.457762\pi\)
\(138\) 0 0
\(139\) 0.0458925 + 0.0794881i 0.00389255 + 0.00674210i 0.867965 0.496625i \(-0.165428\pi\)
−0.864073 + 0.503367i \(0.832094\pi\)
\(140\) 0 0
\(141\) 10.0033 6.05188i 0.842429 0.509660i
\(142\) 0 0
\(143\) 0.521738 + 0.161944i 0.0436299 + 0.0135424i
\(144\) 0 0
\(145\) −0.0144981 0.0541076i −0.00120400 0.00449339i
\(146\) 0 0
\(147\) 6.99127 + 6.71060i 0.576630 + 0.553481i
\(148\) 0 0
\(149\) 3.50013 13.0627i 0.286742 1.07014i −0.660815 0.750549i \(-0.729789\pi\)
0.947557 0.319587i \(-0.103544\pi\)
\(150\) 0 0
\(151\) −8.24642 8.24642i −0.671084 0.671084i 0.286882 0.957966i \(-0.407381\pi\)
−0.957966 + 0.286882i \(0.907381\pi\)
\(152\) 0 0
\(153\) 0.394859 + 9.63429i 0.0319224 + 0.778886i
\(154\) 0 0
\(155\) −15.9808 −1.28361
\(156\) 0 0
\(157\) −5.99636 −0.478562 −0.239281 0.970950i \(-0.576912\pi\)
−0.239281 + 0.970950i \(0.576912\pi\)
\(158\) 0 0
\(159\) −5.53651 + 22.4957i −0.439074 + 1.78402i
\(160\) 0 0
\(161\) 21.0615 + 21.0615i 1.65988 + 1.65988i
\(162\) 0 0
\(163\) −3.72133 + 13.8882i −0.291477 + 1.08781i 0.652499 + 0.757790i \(0.273721\pi\)
−0.943975 + 0.330016i \(0.892946\pi\)
\(164\) 0 0
\(165\) −0.370278 + 0.385764i −0.0288261 + 0.0300317i
\(166\) 0 0
\(167\) 1.36831 + 5.10660i 0.105883 + 0.395161i 0.998444 0.0557663i \(-0.0177602\pi\)
−0.892561 + 0.450927i \(0.851094\pi\)
\(168\) 0 0
\(169\) −5.59910 11.7324i −0.430700 0.902495i
\(170\) 0 0
\(171\) −4.35392 4.01108i −0.332953 0.306735i
\(172\) 0 0
\(173\) −3.05984 5.29979i −0.232635 0.402936i 0.725948 0.687750i \(-0.241401\pi\)
−0.958583 + 0.284814i \(0.908068\pi\)
\(174\) 0 0
\(175\) 2.90838 + 0.779297i 0.219853 + 0.0589093i
\(176\) 0 0
\(177\) −12.7167 6.99872i −0.955843 0.526056i
\(178\) 0 0
\(179\) −10.1144 + 17.5187i −0.755986 + 1.30941i 0.188897 + 0.981997i \(0.439509\pi\)
−0.944883 + 0.327409i \(0.893825\pi\)
\(180\) 0 0
\(181\) 4.39016i 0.326318i 0.986600 + 0.163159i \(0.0521683\pi\)
−0.986600 + 0.163159i \(0.947832\pi\)
\(182\) 0 0
\(183\) −6.38480 22.0147i −0.471978 1.62737i
\(184\) 0 0
\(185\) −7.02279 4.05461i −0.516326 0.298101i
\(186\) 0 0
\(187\) −0.344352 + 0.344352i −0.0251815 + 0.0251815i
\(188\) 0 0
\(189\) 15.3739 10.1836i 1.11829 0.740751i
\(190\) 0 0
\(191\) 12.3027 7.10298i 0.890194 0.513954i 0.0161878 0.999869i \(-0.494847\pi\)
0.874006 + 0.485915i \(0.161514\pi\)
\(192\) 0 0
\(193\) 14.1074 3.78006i 1.01547 0.272095i 0.287558 0.957763i \(-0.407157\pi\)
0.727914 + 0.685668i \(0.240490\pi\)
\(194\) 0 0
\(195\) 12.7222 + 0.237733i 0.911058 + 0.0170244i
\(196\) 0 0
\(197\) 0.668505 0.179125i 0.0476290 0.0127622i −0.234926 0.972013i \(-0.575485\pi\)
0.282555 + 0.959251i \(0.408818\pi\)
\(198\) 0 0
\(199\) 13.8158 7.97656i 0.979377 0.565443i 0.0772948 0.997008i \(-0.475372\pi\)
0.902082 + 0.431565i \(0.142038\pi\)
\(200\) 0 0
\(201\) 0.162227 + 7.91980i 0.0114426 + 0.558620i
\(202\) 0 0
\(203\) −0.0689907 + 0.0689907i −0.00484220 + 0.00484220i
\(204\) 0 0
\(205\) 4.62881 + 2.67245i 0.323290 + 0.186652i
\(206\) 0 0
\(207\) 21.2713 13.4716i 1.47846 0.936338i
\(208\) 0 0
\(209\) 0.298985i 0.0206812i
\(210\) 0 0
\(211\) −3.28525 + 5.69022i −0.226166 + 0.391731i −0.956669 0.291179i \(-0.905952\pi\)
0.730503 + 0.682910i \(0.239286\pi\)
\(212\) 0 0
\(213\) −4.16308 + 7.56431i −0.285249 + 0.518298i
\(214\) 0 0
\(215\) −13.4207 3.59607i −0.915284 0.245250i
\(216\) 0 0
\(217\) 13.9174 + 24.1057i 0.944777 + 1.63640i
\(218\) 0 0
\(219\) −7.88699 13.0366i −0.532953 0.880931i
\(220\) 0 0
\(221\) 11.5798 + 0.453757i 0.778942 + 0.0305230i
\(222\) 0 0
\(223\) −1.79575 6.70184i −0.120252 0.448788i 0.879374 0.476132i \(-0.157962\pi\)
−0.999626 + 0.0273441i \(0.991295\pi\)
\(224\) 0 0
\(225\) 1.18129 2.25452i 0.0787528 0.150301i
\(226\) 0 0
\(227\) 3.00698 11.2222i 0.199580 0.744843i −0.791453 0.611230i \(-0.790675\pi\)
0.991033 0.133614i \(-0.0426581\pi\)
\(228\) 0 0
\(229\) −18.7056 18.7056i −1.23610 1.23610i −0.961580 0.274523i \(-0.911480\pi\)
−0.274523 0.961580i \(-0.588520\pi\)
\(230\) 0 0
\(231\) 0.904363 + 0.222577i 0.0595027 + 0.0146445i
\(232\) 0 0
\(233\) −4.96187 −0.325063 −0.162531 0.986703i \(-0.551966\pi\)
−0.162531 + 0.986703i \(0.551966\pi\)
\(234\) 0 0
\(235\) 13.7536 0.897186
\(236\) 0 0
\(237\) −22.5121 5.54057i −1.46232 0.359899i
\(238\) 0 0
\(239\) 19.8475 + 19.8475i 1.28382 + 1.28382i 0.938473 + 0.345352i \(0.112240\pi\)
0.345352 + 0.938473i \(0.387760\pi\)
\(240\) 0 0
\(241\) 1.59927 5.96857i 0.103018 0.384469i −0.895095 0.445876i \(-0.852892\pi\)
0.998113 + 0.0614071i \(0.0195588\pi\)
\(242\) 0 0
\(243\) −5.55269 14.5660i −0.356206 0.934408i
\(244\) 0 0
\(245\) 2.95052 + 11.0115i 0.188502 + 0.703498i
\(246\) 0 0
\(247\) −5.22409 + 4.83012i −0.332401 + 0.307333i
\(248\) 0 0
\(249\) −2.46086 4.06761i −0.155951 0.257774i
\(250\) 0 0
\(251\) 2.16622 + 3.75201i 0.136731 + 0.236825i 0.926257 0.376892i \(-0.123007\pi\)
−0.789526 + 0.613717i \(0.789674\pi\)
\(252\) 0 0
\(253\) 1.22830 + 0.329122i 0.0772226 + 0.0206917i
\(254\) 0 0
\(255\) −5.46917 + 9.93747i −0.342492 + 0.622309i
\(256\) 0 0
\(257\) 10.6302 18.4120i 0.663093 1.14851i −0.316706 0.948524i \(-0.602577\pi\)
0.979799 0.199986i \(-0.0640898\pi\)
\(258\) 0 0
\(259\) 14.1244i 0.877648i
\(260\) 0 0
\(261\) 0.0441285 + 0.0696779i 0.00273148 + 0.00431295i
\(262\) 0 0
\(263\) −15.0017 8.66123i −0.925044 0.534074i −0.0398032 0.999208i \(-0.512673\pi\)
−0.885241 + 0.465133i \(0.846006\pi\)
\(264\) 0 0
\(265\) −19.2708 + 19.2708i −1.18380 + 1.18380i
\(266\) 0 0
\(267\) −0.393748 19.2225i −0.0240970 1.17640i
\(268\) 0 0
\(269\) 27.3500 15.7905i 1.66756 0.962766i 0.698612 0.715500i \(-0.253801\pi\)
0.968948 0.247266i \(-0.0795321\pi\)
\(270\) 0 0
\(271\) 8.18818 2.19402i 0.497397 0.133277i −0.00139487 0.999999i \(-0.500444\pi\)
0.498792 + 0.866722i \(0.333777\pi\)
\(272\) 0 0
\(273\) −10.7210 19.3975i −0.648865 1.17399i
\(274\) 0 0
\(275\) 0.124167 0.0332705i 0.00748757 0.00200629i
\(276\) 0 0
\(277\) −16.6692 + 9.62397i −1.00156 + 0.578248i −0.908708 0.417432i \(-0.862930\pi\)
−0.0928470 + 0.995680i \(0.529597\pi\)
\(278\) 0 0
\(279\) 22.4593 7.01548i 1.34460 0.420006i
\(280\) 0 0
\(281\) −16.6481 + 16.6481i −0.993141 + 0.993141i −0.999977 0.00683587i \(-0.997824\pi\)
0.00683587 + 0.999977i \(0.497824\pi\)
\(282\) 0 0
\(283\) −8.15184 4.70646i −0.484576 0.279770i 0.237745 0.971328i \(-0.423592\pi\)
−0.722322 + 0.691557i \(0.756925\pi\)
\(284\) 0 0
\(285\) −1.93981 6.68843i −0.114905 0.396189i
\(286\) 0 0
\(287\) 9.30958i 0.549527i
\(288\) 0 0
\(289\) 3.33470 5.77587i 0.196159 0.339757i
\(290\) 0 0
\(291\) 27.8619 + 15.3340i 1.63329 + 0.898896i
\(292\) 0 0
\(293\) −25.3285 6.78675i −1.47971 0.396486i −0.573460 0.819234i \(-0.694399\pi\)
−0.906248 + 0.422747i \(0.861066\pi\)
\(294\) 0 0
\(295\) −8.53776 14.7878i −0.497088 0.860981i
\(296\) 0 0
\(297\) 0.351037 0.704701i 0.0203693 0.0408909i
\(298\) 0 0
\(299\) −14.0926 26.7788i −0.814996 1.54866i
\(300\) 0 0
\(301\) 6.26352 + 23.3758i 0.361023 + 1.34736i
\(302\) 0 0
\(303\) −0.544084 + 0.566840i −0.0312568 + 0.0325641i
\(304\) 0 0
\(305\) 6.97898 26.0459i 0.399615 1.49138i
\(306\) 0 0
\(307\) 15.7215 + 15.7215i 0.897271 + 0.897271i 0.995194 0.0979227i \(-0.0312198\pi\)
−0.0979227 + 0.995194i \(0.531220\pi\)
\(308\) 0 0
\(309\) −4.16103 + 16.9069i −0.236713 + 0.961798i
\(310\) 0 0
\(311\) −4.34210 −0.246218 −0.123109 0.992393i \(-0.539286\pi\)
−0.123109 + 0.992393i \(0.539286\pi\)
\(312\) 0 0
\(313\) 18.6341 1.05326 0.526630 0.850095i \(-0.323455\pi\)
0.526630 + 0.850095i \(0.323455\pi\)
\(314\) 0 0
\(315\) 21.6751 0.888349i 1.22126 0.0500528i
\(316\) 0 0
\(317\) 9.07889 + 9.07889i 0.509921 + 0.509921i 0.914502 0.404581i \(-0.132583\pi\)
−0.404581 + 0.914502i \(0.632583\pi\)
\(318\) 0 0
\(319\) −0.00107810 + 0.00402352i −6.03619e−5 + 0.000225274i
\(320\) 0 0
\(321\) 16.4726 + 15.8113i 0.919413 + 0.882503i
\(322\) 0 0
\(323\) −1.64155 6.12634i −0.0913382 0.340879i
\(324\) 0 0
\(325\) −2.58726 1.63206i −0.143515 0.0905304i
\(326\) 0 0
\(327\) −9.29042 + 5.62060i −0.513761 + 0.310820i
\(328\) 0 0
\(329\) −11.9778 20.7462i −0.660358 1.14377i
\(330\) 0 0
\(331\) −11.3587 3.04354i −0.624328 0.167288i −0.0672335 0.997737i \(-0.521417\pi\)
−0.557095 + 0.830449i \(0.688084\pi\)
\(332\) 0 0
\(333\) 11.6497 + 2.61535i 0.638401 + 0.143321i
\(334\) 0 0
\(335\) −4.65931 + 8.07016i −0.254565 + 0.440920i
\(336\) 0 0
\(337\) 19.7236i 1.07441i 0.843451 + 0.537206i \(0.180520\pi\)
−0.843451 + 0.537206i \(0.819480\pi\)
\(338\) 0 0
\(339\) 10.2430 2.97073i 0.556324 0.161348i
\(340\) 0 0
\(341\) 1.02914 + 0.594177i 0.0557313 + 0.0321765i
\(342\) 0 0
\(343\) −3.52597 + 3.52597i −0.190384 + 0.190384i
\(344\) 0 0
\(345\) 29.6130 0.606586i 1.59431 0.0326575i
\(346\) 0 0
\(347\) 30.5245 17.6233i 1.63864 0.946071i 0.657342 0.753593i \(-0.271681\pi\)
0.981301 0.192478i \(-0.0616525\pi\)
\(348\) 0 0
\(349\) −22.9572 + 6.15136i −1.22887 + 0.329275i −0.814139 0.580670i \(-0.802791\pi\)
−0.414730 + 0.909944i \(0.636124\pi\)
\(350\) 0 0
\(351\) −17.9841 + 5.25088i −0.959921 + 0.280271i
\(352\) 0 0
\(353\) 7.81588 2.09426i 0.415997 0.111466i −0.0447484 0.998998i \(-0.514249\pi\)
0.460746 + 0.887532i \(0.347582\pi\)
\(354\) 0 0
\(355\) −8.79631 + 5.07855i −0.466860 + 0.269542i
\(356\) 0 0
\(357\) 19.7529 0.404613i 1.04543 0.0214144i
\(358\) 0 0
\(359\) 9.77619 9.77619i 0.515968 0.515968i −0.400381 0.916349i \(-0.631122\pi\)
0.916349 + 0.400381i \(0.131122\pi\)
\(360\) 0 0
\(361\) −13.0822 7.55303i −0.688539 0.397528i
\(362\) 0 0
\(363\) −18.2603 + 5.29595i −0.958418 + 0.277965i
\(364\) 0 0
\(365\) 17.9241i 0.938190i
\(366\) 0 0
\(367\) −6.84234 + 11.8513i −0.357167 + 0.618632i −0.987486 0.157704i \(-0.949591\pi\)
0.630319 + 0.776336i \(0.282924\pi\)
\(368\) 0 0
\(369\) −7.67850 1.72382i −0.399727 0.0897382i
\(370\) 0 0
\(371\) 45.8512 + 12.2858i 2.38047 + 0.637846i
\(372\) 0 0
\(373\) −1.97549 3.42164i −0.102287 0.177166i 0.810340 0.585960i \(-0.199283\pi\)
−0.912626 + 0.408794i \(0.865949\pi\)
\(374\) 0 0
\(375\) 17.6595 10.6838i 0.911933 0.551709i
\(376\) 0 0
\(377\) 0.0877188 0.0461628i 0.00451775 0.00237751i
\(378\) 0 0
\(379\) 4.23059 + 15.7888i 0.217311 + 0.811014i 0.985340 + 0.170600i \(0.0545706\pi\)
−0.768030 + 0.640414i \(0.778763\pi\)
\(380\) 0 0
\(381\) 11.7669 + 11.2945i 0.602837 + 0.578636i
\(382\) 0 0
\(383\) −5.85081 + 21.8355i −0.298963 + 1.11574i 0.639057 + 0.769160i \(0.279325\pi\)
−0.938019 + 0.346584i \(0.887342\pi\)
\(384\) 0 0
\(385\) 0.774719 + 0.774719i 0.0394834 + 0.0394834i
\(386\) 0 0
\(387\) 20.4400 0.837728i 1.03902 0.0425841i
\(388\) 0 0
\(389\) 1.80850 0.0916947 0.0458474 0.998948i \(-0.485401\pi\)
0.0458474 + 0.998948i \(0.485401\pi\)
\(390\) 0 0
\(391\) 26.9755 1.36421
\(392\) 0 0
\(393\) 6.15954 25.0271i 0.310708 1.26245i
\(394\) 0 0
\(395\) −19.2849 19.2849i −0.970331 0.970331i
\(396\) 0 0
\(397\) −1.04738 + 3.90888i −0.0525665 + 0.196181i −0.987216 0.159391i \(-0.949047\pi\)
0.934649 + 0.355572i \(0.115714\pi\)
\(398\) 0 0
\(399\) −8.39960 + 8.75091i −0.420506 + 0.438093i
\(400\) 0 0
\(401\) 0.540214 + 2.01611i 0.0269770 + 0.100680i 0.978102 0.208128i \(-0.0667369\pi\)
−0.951125 + 0.308807i \(0.900070\pi\)
\(402\) 0 0
\(403\) −6.24398 27.5810i −0.311035 1.37391i
\(404\) 0 0
\(405\) 3.28078 18.0420i 0.163023 0.896516i
\(406\) 0 0
\(407\) 0.301506 + 0.522224i 0.0149451 + 0.0258857i
\(408\) 0 0
\(409\) −8.15394 2.18484i −0.403186 0.108033i 0.0515263 0.998672i \(-0.483591\pi\)
−0.454713 + 0.890638i \(0.650258\pi\)
\(410\) 0 0
\(411\) −13.6525 7.51377i −0.673429 0.370627i
\(412\) 0 0
\(413\) −14.8708 + 25.7570i −0.731746 + 1.26742i
\(414\) 0 0
\(415\) 5.59259i 0.274529i
\(416\) 0 0
\(417\) −0.0442823 0.152684i −0.00216851 0.00747699i
\(418\) 0 0
\(419\) 0.585414 + 0.337989i 0.0285993 + 0.0165118i 0.514232 0.857651i \(-0.328077\pi\)
−0.485632 + 0.874163i \(0.661411\pi\)
\(420\) 0 0
\(421\) 6.17588 6.17588i 0.300994 0.300994i −0.540409 0.841403i \(-0.681730\pi\)
0.841403 + 0.540409i \(0.181730\pi\)
\(422\) 0 0
\(423\) −19.3292 + 6.03776i −0.939819 + 0.293566i
\(424\) 0 0
\(425\) 2.36158 1.36346i 0.114553 0.0661374i
\(426\) 0 0
\(427\) −45.3660 + 12.1558i −2.19542 + 0.588260i
\(428\) 0 0
\(429\) −0.810458 0.488331i −0.0391293 0.0235769i
\(430\) 0 0
\(431\) 9.78631 2.62223i 0.471390 0.126309i −0.0153006 0.999883i \(-0.504871\pi\)
0.486691 + 0.873574i \(0.338204\pi\)
\(432\) 0 0
\(433\) −11.0298 + 6.36809i −0.530061 + 0.306031i −0.741041 0.671460i \(-0.765668\pi\)
0.210980 + 0.977490i \(0.432334\pi\)
\(434\) 0 0
\(435\) 0.00198698 + 0.0970028i 9.52685e−5 + 0.00465093i
\(436\) 0 0
\(437\) −11.7108 + 11.7108i −0.560203 + 0.560203i
\(438\) 0 0
\(439\) −3.07428 1.77494i −0.146727 0.0847131i 0.424839 0.905269i \(-0.360331\pi\)
−0.571566 + 0.820556i \(0.693664\pi\)
\(440\) 0 0
\(441\) −8.98063 14.1802i −0.427649 0.675248i
\(442\) 0 0
\(443\) 13.7327i 0.652461i −0.945290 0.326231i \(-0.894221\pi\)
0.945290 0.326231i \(-0.105779\pi\)
\(444\) 0 0
\(445\) 11.3088 19.5874i 0.536088 0.928532i
\(446\) 0 0
\(447\) −11.2938 + 20.5208i −0.534178 + 0.970601i
\(448\) 0 0
\(449\) −12.7370 3.41288i −0.601098 0.161064i −0.0545774 0.998510i \(-0.517381\pi\)
−0.546520 + 0.837446i \(0.684048\pi\)
\(450\) 0 0
\(451\) −0.198727 0.344205i −0.00935769 0.0162080i
\(452\) 0 0
\(453\) 10.4559 + 17.2828i 0.491261 + 0.812016i
\(454\) 0 0
\(455\) 1.02086 26.0521i 0.0478586 1.22134i
\(456\) 0 0
\(457\) −4.80678 17.9391i −0.224852 0.839157i −0.982464 0.186453i \(-0.940301\pi\)
0.757612 0.652705i \(-0.226366\pi\)
\(458\) 0 0
\(459\) 3.32383 16.3670i 0.155143 0.763946i
\(460\) 0 0
\(461\) −1.15902 + 4.32554i −0.0539812 + 0.201460i −0.987650 0.156678i \(-0.949922\pi\)
0.933669 + 0.358138i \(0.116588\pi\)
\(462\) 0 0
\(463\) −8.53278 8.53278i −0.396552 0.396552i 0.480463 0.877015i \(-0.340469\pi\)
−0.877015 + 0.480463i \(0.840469\pi\)
\(464\) 0 0
\(465\) 26.8775 + 6.61494i 1.24641 + 0.306761i
\(466\) 0 0
\(467\) −9.69885 −0.448809 −0.224405 0.974496i \(-0.572044\pi\)
−0.224405 + 0.974496i \(0.572044\pi\)
\(468\) 0 0
\(469\) 16.2309 0.749474
\(470\) 0 0
\(471\) 10.0851 + 2.48208i 0.464695 + 0.114368i
\(472\) 0 0
\(473\) 0.730573 + 0.730573i 0.0335918 + 0.0335918i
\(474\) 0 0
\(475\) −0.433311 + 1.61714i −0.0198817 + 0.0741994i
\(476\) 0 0
\(477\) 18.6233 35.5429i 0.852703 1.62740i
\(478\) 0 0
\(479\) 6.64461 + 24.7980i 0.303600 + 1.13305i 0.934144 + 0.356897i \(0.116165\pi\)
−0.630544 + 0.776154i \(0.717168\pi\)
\(480\) 0 0
\(481\) 4.25386 13.7047i 0.193959 0.624882i
\(482\) 0 0
\(483\) −26.7046 44.1406i −1.21510 2.00847i
\(484\) 0 0
\(485\) 18.7060 + 32.3998i 0.849397 + 1.47120i
\(486\) 0 0
\(487\) 15.4146 + 4.13033i 0.698501 + 0.187163i 0.590559 0.806994i \(-0.298907\pi\)
0.107942 + 0.994157i \(0.465574\pi\)
\(488\) 0 0
\(489\) 12.0075 21.8176i 0.542998 0.986627i
\(490\) 0 0
\(491\) −6.38912 + 11.0663i −0.288337 + 0.499414i −0.973413 0.229057i \(-0.926436\pi\)
0.685076 + 0.728472i \(0.259769\pi\)
\(492\) 0 0
\(493\) 0.0883630i 0.00397967i
\(494\) 0 0
\(495\) 0.782436 0.495533i 0.0351679 0.0222726i
\(496\) 0 0
\(497\) 15.3212 + 8.84568i 0.687248 + 0.396783i
\(498\) 0 0
\(499\) −26.5255 + 26.5255i −1.18744 + 1.18744i −0.209671 + 0.977772i \(0.567239\pi\)
−0.977772 + 0.209671i \(0.932761\pi\)
\(500\) 0 0
\(501\) −0.187529 9.15498i −0.00837816 0.409015i
\(502\) 0 0
\(503\) 3.29946 1.90495i 0.147116 0.0849374i −0.424635 0.905365i \(-0.639598\pi\)
0.571751 + 0.820427i \(0.306264\pi\)
\(504\) 0 0
\(505\) −0.892792 + 0.239223i −0.0397287 + 0.0106453i
\(506\) 0 0
\(507\) 4.56050 + 22.0500i 0.202539 + 0.979274i
\(508\) 0 0
\(509\) −37.5368 + 10.0580i −1.66379 + 0.445811i −0.963426 0.267975i \(-0.913646\pi\)
−0.700364 + 0.713786i \(0.746979\pi\)
\(510\) 0 0
\(511\) −27.0370 + 15.6098i −1.19605 + 0.690539i
\(512\) 0 0
\(513\) 5.66239 + 8.54831i 0.250000 + 0.377417i
\(514\) 0 0
\(515\) −14.4832 + 14.4832i −0.638206 + 0.638206i
\(516\) 0 0
\(517\) −0.885716 0.511368i −0.0389537 0.0224900i
\(518\) 0 0
\(519\) 2.95248 + 10.1801i 0.129599 + 0.446856i
\(520\) 0 0
\(521\) 41.6988i 1.82686i −0.406996 0.913430i \(-0.633424\pi\)
0.406996 0.913430i \(-0.366576\pi\)
\(522\) 0 0
\(523\) 13.1004 22.6906i 0.572842 0.992192i −0.423430 0.905929i \(-0.639174\pi\)
0.996272 0.0862632i \(-0.0274926\pi\)
\(524\) 0 0
\(525\) −4.56892 2.51454i −0.199404 0.109743i
\(526\) 0 0
\(527\) 24.3499 + 6.52455i 1.06070 + 0.284214i
\(528\) 0 0
\(529\) −23.7195 41.0833i −1.03128 1.78623i
\(530\) 0 0
\(531\) 18.4907 + 17.0347i 0.802428 + 0.739243i
\(532\) 0 0
\(533\) −2.80377 + 9.03297i −0.121445 + 0.391261i
\(534\) 0 0
\(535\) 6.95194 + 25.9450i 0.300558 + 1.12170i
\(536\) 0 0
\(537\) 24.2625 25.2773i 1.04701 1.09080i
\(538\) 0 0
\(539\) 0.219405 0.818830i 0.00945043 0.0352695i
\(540\) 0 0
\(541\) 14.9894 + 14.9894i 0.644447 + 0.644447i 0.951645 0.307199i \(-0.0993916\pi\)
−0.307199 + 0.951645i \(0.599392\pi\)
\(542\) 0 0
\(543\) 1.81722 7.38364i 0.0779845 0.316862i
\(544\) 0 0
\(545\) −12.7735 −0.547155
\(546\) 0 0
\(547\) −23.7046 −1.01354 −0.506768 0.862082i \(-0.669160\pi\)
−0.506768 + 0.862082i \(0.669160\pi\)
\(548\) 0 0
\(549\) 1.62580 + 39.6685i 0.0693876 + 1.69301i
\(550\) 0 0
\(551\) −0.0383608 0.0383608i −0.00163422 0.00163422i
\(552\) 0 0
\(553\) −12.2948 + 45.8847i −0.522827 + 1.95122i
\(554\) 0 0
\(555\) 10.1330 + 9.72624i 0.430123 + 0.412856i
\(556\) 0 0
\(557\) 10.2264 + 38.1653i 0.433304 + 1.61711i 0.745091 + 0.666962i \(0.232406\pi\)
−0.311787 + 0.950152i \(0.600928\pi\)
\(558\) 0 0
\(559\) 0.962687 24.5676i 0.0407173 1.03910i
\(560\) 0 0
\(561\) 0.721690 0.436614i 0.0304698 0.0184339i
\(562\) 0 0
\(563\) 8.48383 + 14.6944i 0.357551 + 0.619296i 0.987551 0.157299i \(-0.0502785\pi\)
−0.630000 + 0.776595i \(0.716945\pi\)
\(564\) 0 0
\(565\) 12.1187 + 3.24719i 0.509837 + 0.136610i
\(566\) 0 0
\(567\) −30.0721 + 10.7637i −1.26291 + 0.452035i
\(568\) 0 0
\(569\) 15.2347 26.3873i 0.638674 1.10622i −0.347051 0.937846i \(-0.612817\pi\)
0.985724 0.168369i \(-0.0538499\pi\)
\(570\) 0 0
\(571\) 5.03996i 0.210916i 0.994424 + 0.105458i \(0.0336309\pi\)
−0.994424 + 0.105458i \(0.966369\pi\)
\(572\) 0 0
\(573\) −23.6316 + 6.85376i −0.987225 + 0.286320i
\(574\) 0 0
\(575\) −6.16660 3.56029i −0.257165 0.148474i
\(576\) 0 0
\(577\) 15.8862 15.8862i 0.661350 0.661350i −0.294348 0.955698i \(-0.595102\pi\)
0.955698 + 0.294348i \(0.0951024\pi\)
\(578\) 0 0
\(579\) −25.2914 + 0.518063i −1.05107 + 0.0215299i
\(580\) 0 0
\(581\) −8.43596 + 4.87051i −0.349983 + 0.202063i
\(582\) 0 0
\(583\) 1.95752 0.524516i 0.0810723 0.0217233i
\(584\) 0 0
\(585\) −21.2986 5.66596i −0.880591 0.234259i
\(586\) 0 0
\(587\) −8.06056 + 2.15982i −0.332695 + 0.0891453i −0.421300 0.906922i \(-0.638426\pi\)
0.0886047 + 0.996067i \(0.471759\pi\)
\(588\) 0 0
\(589\) −13.4034 + 7.73848i −0.552279 + 0.318859i
\(590\) 0 0
\(591\) −1.19848 + 0.0245494i −0.0492989 + 0.00100983i
\(592\) 0 0
\(593\) −30.0266 + 30.0266i −1.23305 + 1.23305i −0.270257 + 0.962788i \(0.587109\pi\)
−0.962788 + 0.270257i \(0.912891\pi\)
\(594\) 0 0
\(595\) 20.1279 + 11.6208i 0.825163 + 0.476408i
\(596\) 0 0
\(597\) −26.5380 + 7.69669i −1.08613 + 0.315004i
\(598\) 0 0
\(599\) 17.0119i 0.695088i 0.937664 + 0.347544i \(0.112984\pi\)
−0.937664 + 0.347544i \(0.887016\pi\)
\(600\) 0 0
\(601\) −12.8220 + 22.2084i −0.523022 + 0.905901i 0.476619 + 0.879110i \(0.341862\pi\)
−0.999641 + 0.0267907i \(0.991471\pi\)
\(602\) 0 0
\(603\) 3.00541 13.3872i 0.122390 0.545168i
\(604\) 0 0
\(605\) −21.6041 5.78880i −0.878331 0.235348i
\(606\) 0 0
\(607\) 8.99964 + 15.5878i 0.365284 + 0.632691i 0.988822 0.149103i \(-0.0476385\pi\)
−0.623537 + 0.781793i \(0.714305\pi\)
\(608\) 0 0
\(609\) 0.144590 0.0874755i 0.00585910 0.00354469i
\(610\) 0 0
\(611\) 5.37377 + 23.7371i 0.217400 + 0.960301i
\(612\) 0 0
\(613\) 6.40516 + 23.9044i 0.258702 + 0.965489i 0.965993 + 0.258567i \(0.0832502\pi\)
−0.707292 + 0.706922i \(0.750083\pi\)
\(614\) 0 0
\(615\) −6.67882 6.41070i −0.269316 0.258504i
\(616\) 0 0
\(617\) −9.32585 + 34.8045i −0.375444 + 1.40118i 0.477250 + 0.878768i \(0.341634\pi\)
−0.852694 + 0.522410i \(0.825033\pi\)
\(618\) 0 0
\(619\) 8.29611 + 8.29611i 0.333449 + 0.333449i 0.853895 0.520446i \(-0.174234\pi\)
−0.520446 + 0.853895i \(0.674234\pi\)
\(620\) 0 0
\(621\) −41.3517 + 13.8525i −1.65939 + 0.555880i
\(622\) 0 0
\(623\) −39.3947 −1.57831
\(624\) 0 0
\(625\) 20.0381 0.801524
\(626\) 0 0
\(627\) −0.123759 + 0.502851i −0.00494246 + 0.0200819i
\(628\) 0 0
\(629\) 9.04524 + 9.04524i 0.360657 + 0.360657i
\(630\) 0 0
\(631\) −5.40401 + 20.1680i −0.215130 + 0.802877i 0.770990 + 0.636847i \(0.219762\pi\)
−0.986121 + 0.166030i \(0.946905\pi\)
\(632\) 0 0
\(633\) 7.88069 8.21030i 0.313229 0.326330i
\(634\) 0 0
\(635\) 4.96598 + 18.5333i 0.197069 + 0.735471i
\(636\) 0 0
\(637\) −17.8517 + 9.39464i −0.707311 + 0.372229i
\(638\) 0 0
\(639\) 10.1328 10.9989i 0.400848 0.435110i
\(640\) 0 0
\(641\) 5.39416 + 9.34296i 0.213056 + 0.369025i 0.952670 0.304008i \(-0.0983249\pi\)
−0.739613 + 0.673032i \(0.764992\pi\)
\(642\) 0 0
\(643\) 8.87352 + 2.37765i 0.349937 + 0.0937655i 0.429506 0.903064i \(-0.358688\pi\)
−0.0795687 + 0.996829i \(0.525354\pi\)
\(644\) 0 0
\(645\) 21.0832 + 11.6033i 0.830152 + 0.456881i
\(646\) 0 0
\(647\) 12.5642 21.7619i 0.493951 0.855549i −0.506024 0.862519i \(-0.668885\pi\)
0.999976 + 0.00697039i \(0.00221876\pi\)
\(648\) 0 0
\(649\) 1.26976i 0.0498424i
\(650\) 0 0
\(651\) −13.4291 46.3033i −0.526329 1.81477i
\(652\) 0 0
\(653\) 12.6456 + 7.30093i 0.494860 + 0.285708i 0.726588 0.687073i \(-0.241105\pi\)
−0.231728 + 0.972781i \(0.574438\pi\)
\(654\) 0 0
\(655\) 21.4394 21.4394i 0.837706 0.837706i
\(656\) 0 0
\(657\) 7.86858 + 25.1904i 0.306983 + 0.982771i
\(658\) 0 0
\(659\) 9.24365 5.33682i 0.360081 0.207893i −0.309035 0.951051i \(-0.600006\pi\)
0.669116 + 0.743158i \(0.266673\pi\)
\(660\) 0 0
\(661\) −39.5548 + 10.5987i −1.53850 + 0.412241i −0.925782 0.378057i \(-0.876592\pi\)
−0.612723 + 0.790298i \(0.709926\pi\)
\(662\) 0 0
\(663\) −19.2878 5.55640i −0.749077 0.215793i
\(664\) 0 0
\(665\) −13.7830 + 3.69314i −0.534481 + 0.143214i
\(666\) 0 0
\(667\) 0.199823 0.115368i 0.00773717 0.00446706i
\(668\) 0 0
\(669\) 0.246110 + 12.0149i 0.00951517 + 0.464522i
\(670\) 0 0
\(671\) −1.41784 + 1.41784i −0.0547352 + 0.0547352i
\(672\) 0 0
\(673\) 2.95408 + 1.70554i 0.113871 + 0.0657437i 0.555854 0.831280i \(-0.312391\pi\)
−0.441983 + 0.897024i \(0.645725\pi\)
\(674\) 0 0
\(675\) −2.91998 + 3.30281i −0.112390 + 0.127125i
\(676\) 0 0
\(677\) 9.33387i 0.358730i 0.983783 + 0.179365i \(0.0574043\pi\)
−0.983783 + 0.179365i \(0.942596\pi\)
\(678\) 0 0
\(679\) 32.5816 56.4330i 1.25037 2.16570i
\(680\) 0 0
\(681\) −9.70254 + 17.6295i −0.371802 + 0.675564i
\(682\) 0 0
\(683\) −20.2277 5.42001i −0.773993 0.207391i −0.149858 0.988708i \(-0.547882\pi\)
−0.624135 + 0.781317i \(0.714548\pi\)
\(684\) 0 0
\(685\) −9.16608 15.8761i −0.350218 0.606595i
\(686\) 0 0
\(687\) 23.7175 + 39.2032i 0.904878 + 1.49569i
\(688\) 0 0
\(689\) −40.7887 25.7298i −1.55392 0.980226i
\(690\) 0 0
\(691\) 0.861578 + 3.21545i 0.0327760 + 0.122322i 0.980376 0.197139i \(-0.0631650\pi\)
−0.947600 + 0.319461i \(0.896498\pi\)
\(692\) 0 0
\(693\) −1.42888 0.748688i −0.0542788 0.0284403i
\(694\) 0 0
\(695\) 0.0484033 0.180643i 0.00183604 0.00685220i
\(696\) 0 0
\(697\) −5.96184 5.96184i −0.225821 0.225821i
\(698\) 0 0
\(699\) 8.34518 + 2.05387i 0.315644 + 0.0776846i
\(700\) 0 0
\(701\) 11.9388 0.450923 0.225462 0.974252i \(-0.427611\pi\)
0.225462 + 0.974252i \(0.427611\pi\)
\(702\) 0 0
\(703\) −7.85356 −0.296203
\(704\) 0 0
\(705\) −23.1317 5.69304i −0.871189 0.214412i
\(706\) 0 0
\(707\) 1.13837 + 1.13837i 0.0428127 + 0.0428127i
\(708\) 0 0
\(709\) −1.31499 + 4.90761i −0.0493855 + 0.184309i −0.986212 0.165484i \(-0.947081\pi\)
0.936827 + 0.349793i \(0.113748\pi\)
\(710\) 0 0
\(711\) 35.5689 + 18.6369i 1.33394 + 0.698940i
\(712\) 0 0
\(713\) −17.0370 63.5831i −0.638042 2.38120i
\(714\) 0 0
\(715\) −0.518377 0.985023i −0.0193862 0.0368378i
\(716\) 0 0
\(717\) −25.1652 41.5962i −0.939812 1.55344i
\(718\) 0 0
\(719\) 1.78171 + 3.08602i 0.0664468 + 0.115089i 0.897335 0.441350i \(-0.145500\pi\)
−0.830888 + 0.556440i \(0.812167\pi\)
\(720\) 0 0
\(721\) 34.4599 + 9.23351i 1.28336 + 0.343874i
\(722\) 0 0
\(723\) −5.16033 + 9.37632i −0.191915 + 0.348709i
\(724\) 0 0
\(725\) 0.0116624 0.0201998i 0.000433129 0.000750202i
\(726\) 0 0
\(727\) 30.2149i 1.12061i −0.828287 0.560304i \(-0.810684\pi\)
0.828287 0.560304i \(-0.189316\pi\)
\(728\) 0 0
\(729\) 3.30956 + 26.7964i 0.122576 + 0.992459i
\(730\) 0 0
\(731\) 18.9809 + 10.9587i 0.702036 + 0.405321i
\(732\) 0 0
\(733\) −4.27805 + 4.27805i −0.158013 + 0.158013i −0.781686 0.623672i \(-0.785640\pi\)
0.623672 + 0.781686i \(0.285640\pi\)
\(734\) 0 0
\(735\) −0.404372 19.7411i −0.0149155 0.728162i
\(736\) 0 0
\(737\) 0.600109 0.346473i 0.0221053 0.0127625i
\(738\) 0 0
\(739\) 22.8637 6.12632i 0.841056 0.225360i 0.187525 0.982260i \(-0.439954\pi\)
0.653531 + 0.756900i \(0.273287\pi\)
\(740\) 0 0
\(741\) 10.7855 5.96118i 0.396217 0.218989i
\(742\) 0 0
\(743\) −45.0215 + 12.0635i −1.65168 + 0.442566i −0.960082 0.279717i \(-0.909759\pi\)
−0.691597 + 0.722284i \(0.743093\pi\)
\(744\) 0 0
\(745\) −23.8630 + 13.7773i −0.874274 + 0.504762i
\(746\) 0 0
\(747\) 2.45512 + 7.85979i 0.0898280 + 0.287575i
\(748\) 0 0
\(749\) 33.0815 33.0815i 1.20877 1.20877i
\(750\) 0 0
\(751\) −38.1177 22.0072i −1.39093 0.803056i −0.397514 0.917596i \(-0.630127\pi\)
−0.993419 + 0.114540i \(0.963460\pi\)
\(752\) 0 0
\(753\) −2.09022 7.20703i −0.0761718 0.262639i
\(754\) 0 0
\(755\) 23.7622i 0.864796i
\(756\) 0 0
\(757\) 15.5726 26.9726i 0.565996 0.980334i −0.430960 0.902371i \(-0.641825\pi\)
0.996956 0.0779632i \(-0.0248417\pi\)
\(758\) 0 0
\(759\) −1.92960 1.06197i −0.0700400 0.0385471i
\(760\) 0 0
\(761\) 35.3991 + 9.48515i 1.28322 + 0.343836i 0.835080 0.550129i \(-0.185422\pi\)
0.448136 + 0.893966i \(0.352088\pi\)
\(762\) 0 0
\(763\) 11.1242 + 19.2677i 0.402724 + 0.697538i
\(764\) 0 0
\(765\) 13.3118 14.4496i 0.481290 0.522427i
\(766\) 0 0
\(767\) 22.1862 20.5131i 0.801098 0.740683i
\(768\) 0 0
\(769\) −0.493875 1.84317i −0.0178096 0.0664663i 0.956449 0.291899i \(-0.0942871\pi\)
−0.974259 + 0.225433i \(0.927620\pi\)
\(770\) 0 0
\(771\) −25.4998 + 26.5663i −0.918353 + 0.956763i
\(772\) 0 0
\(773\) 7.52425 28.0809i 0.270629 1.01000i −0.688086 0.725629i \(-0.741549\pi\)
0.958714 0.284371i \(-0.0917846\pi\)
\(774\) 0 0
\(775\) −4.70528 4.70528i −0.169019 0.169019i
\(776\) 0 0
\(777\) 5.84653 23.7553i 0.209743 0.852217i
\(778\) 0 0
\(779\) 5.17639 0.185463
\(780\) 0 0
\(781\) 0.755297 0.0270266
\(782\) 0 0
\(783\) −0.0453762 0.135455i −0.00162161 0.00484076i
\(784\) 0 0
\(785\) 8.63933 + 8.63933i 0.308351 + 0.308351i
\(786\) 0 0
\(787\) 11.8946 44.3912i 0.423996 1.58237i −0.342110 0.939660i \(-0.611142\pi\)
0.766106 0.642714i \(-0.222192\pi\)
\(788\) 0 0
\(789\) 21.6456 + 20.7767i 0.770605 + 0.739669i
\(790\) 0 0
\(791\) −5.65587 21.1080i −0.201099 0.750513i
\(792\) 0 0
\(793\) 47.6790 + 1.86831i 1.69313 + 0.0663457i
\(794\) 0 0
\(795\) 40.3877 24.4341i 1.43240 0.866588i
\(796\) 0 0
\(797\)