Properties

Label 784.2.bp.c.495.8
Level $784$
Weight $2$
Character 784.495
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.bp (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 495.8
Character \(\chi\) \(=\) 784.495
Dual form 784.2.bp.c.255.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30128 + 0.887199i) q^{3} +(-3.55166 - 0.266160i) q^{5} +(2.60649 + 0.454131i) q^{7} +(-0.189810 - 0.483628i) q^{9} +O(q^{10})\) \(q+(1.30128 + 0.887199i) q^{3} +(-3.55166 - 0.266160i) q^{5} +(2.60649 + 0.454131i) q^{7} +(-0.189810 - 0.483628i) q^{9} +(3.28740 + 1.29021i) q^{11} +(1.33630 - 1.06566i) q^{13} +(-4.38557 - 3.49738i) q^{15} +(4.60104 + 4.95874i) q^{17} +(1.26170 - 2.18533i) q^{19} +(2.98887 + 2.90342i) q^{21} +(-4.90853 + 5.29013i) q^{23} +(7.59929 + 1.14541i) q^{25} +(1.23345 - 5.40412i) q^{27} +(0.815942 + 3.57488i) q^{29} +(2.53827 + 4.39641i) q^{31} +(3.13316 + 4.59550i) q^{33} +(-9.13648 - 2.30666i) q^{35} +(-2.30934 - 0.712338i) q^{37} +(2.68436 - 0.201165i) q^{39} +(3.85892 + 8.01313i) q^{41} +(-0.185940 + 0.386109i) q^{43} +(0.545418 + 1.76820i) q^{45} +(12.8599 - 1.93832i) q^{47} +(6.58753 + 2.36737i) q^{49} +(1.58786 + 10.5348i) q^{51} +(-3.74376 + 1.15480i) q^{53} +(-11.3323 - 5.45735i) q^{55} +(3.58065 - 1.72435i) q^{57} +(-0.392828 - 5.24192i) q^{59} +(3.85033 - 12.4825i) q^{61} +(-0.275107 - 1.34677i) q^{63} +(-5.02972 + 3.42921i) q^{65} +(-8.82791 + 5.09679i) q^{67} +(-11.0808 + 2.52912i) q^{69} +(-11.4127 - 2.60487i) q^{71} +(0.665073 - 4.41247i) q^{73} +(8.87261 + 8.23258i) q^{75} +(7.98262 + 4.85581i) q^{77} +(-5.38475 - 3.10889i) q^{79} +(5.25704 - 4.87782i) q^{81} +(5.83732 - 7.31977i) q^{83} +(-15.0215 - 18.8364i) q^{85} +(-2.10986 + 5.37583i) q^{87} +(-7.37597 + 2.89485i) q^{89} +(3.96700 - 2.17078i) q^{91} +(-0.597487 + 7.97291i) q^{93} +(-5.06277 + 7.42573i) q^{95} +5.29761i q^{97} -1.83477i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 6q^{5} + 12q^{9} + O(q^{10}) \) \( 120q + 6q^{5} + 12q^{9} - 32q^{17} - 14q^{21} - 8q^{25} - 28q^{29} + 42q^{33} + 28q^{37} + 56q^{41} + 186q^{45} + 84q^{49} + 128q^{53} - 70q^{57} + 8q^{61} + 4q^{65} - 56q^{69} + 60q^{73} + 84q^{77} + 34q^{81} + 12q^{85} + 22q^{89} - 112q^{93} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{29}{42}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.30128 + 0.887199i 0.751296 + 0.512225i 0.877381 0.479795i \(-0.159289\pi\)
−0.126085 + 0.992019i \(0.540241\pi\)
\(4\) 0 0
\(5\) −3.55166 0.266160i −1.58835 0.119030i −0.748981 0.662592i \(-0.769456\pi\)
−0.839369 + 0.543561i \(0.817076\pi\)
\(6\) 0 0
\(7\) 2.60649 + 0.454131i 0.985159 + 0.171645i
\(8\) 0 0
\(9\) −0.189810 0.483628i −0.0632701 0.161209i
\(10\) 0 0
\(11\) 3.28740 + 1.29021i 0.991187 + 0.389012i 0.804853 0.593474i \(-0.202244\pi\)
0.186334 + 0.982486i \(0.440339\pi\)
\(12\) 0 0
\(13\) 1.33630 1.06566i 0.370623 0.295562i −0.420411 0.907334i \(-0.638114\pi\)
0.791035 + 0.611771i \(0.209543\pi\)
\(14\) 0 0
\(15\) −4.38557 3.49738i −1.13235 0.903019i
\(16\) 0 0
\(17\) 4.60104 + 4.95874i 1.11592 + 1.20267i 0.977196 + 0.212339i \(0.0681081\pi\)
0.138719 + 0.990332i \(0.455701\pi\)
\(18\) 0 0
\(19\) 1.26170 2.18533i 0.289454 0.501349i −0.684226 0.729270i \(-0.739860\pi\)
0.973679 + 0.227922i \(0.0731930\pi\)
\(20\) 0 0
\(21\) 2.98887 + 2.90342i 0.652224 + 0.633579i
\(22\) 0 0
\(23\) −4.90853 + 5.29013i −1.02350 + 1.10307i −0.0288676 + 0.999583i \(0.509190\pi\)
−0.994631 + 0.103486i \(0.967000\pi\)
\(24\) 0 0
\(25\) 7.59929 + 1.14541i 1.51986 + 0.229082i
\(26\) 0 0
\(27\) 1.23345 5.40412i 0.237378 1.04002i
\(28\) 0 0
\(29\) 0.815942 + 3.57488i 0.151517 + 0.663838i 0.992445 + 0.122691i \(0.0391525\pi\)
−0.840928 + 0.541147i \(0.817990\pi\)
\(30\) 0 0
\(31\) 2.53827 + 4.39641i 0.455886 + 0.789618i 0.998739 0.0502101i \(-0.0159891\pi\)
−0.542853 + 0.839828i \(0.682656\pi\)
\(32\) 0 0
\(33\) 3.13316 + 4.59550i 0.545413 + 0.799974i
\(34\) 0 0
\(35\) −9.13648 2.30666i −1.54435 0.389897i
\(36\) 0 0
\(37\) −2.30934 0.712338i −0.379654 0.117108i 0.0990538 0.995082i \(-0.468418\pi\)
−0.478708 + 0.877974i \(0.658895\pi\)
\(38\) 0 0
\(39\) 2.68436 0.201165i 0.429842 0.0322122i
\(40\) 0 0
\(41\) 3.85892 + 8.01313i 0.602662 + 1.25144i 0.949574 + 0.313543i \(0.101516\pi\)
−0.346912 + 0.937898i \(0.612770\pi\)
\(42\) 0 0
\(43\) −0.185940 + 0.386109i −0.0283556 + 0.0588811i −0.914666 0.404212i \(-0.867546\pi\)
0.886310 + 0.463093i \(0.153260\pi\)
\(44\) 0 0
\(45\) 0.545418 + 1.76820i 0.0813062 + 0.263588i
\(46\) 0 0
\(47\) 12.8599 1.93832i 1.87581 0.282733i 0.890693 0.454606i \(-0.150220\pi\)
0.985119 + 0.171873i \(0.0549819\pi\)
\(48\) 0 0
\(49\) 6.58753 + 2.36737i 0.941076 + 0.338196i
\(50\) 0 0
\(51\) 1.58786 + 10.5348i 0.222345 + 1.47516i
\(52\) 0 0
\(53\) −3.74376 + 1.15480i −0.514245 + 0.158624i −0.541007 0.841018i \(-0.681957\pi\)
0.0267618 + 0.999642i \(0.491480\pi\)
\(54\) 0 0
\(55\) −11.3323 5.45735i −1.52805 0.735869i
\(56\) 0 0
\(57\) 3.58065 1.72435i 0.474268 0.228396i
\(58\) 0 0
\(59\) −0.392828 5.24192i −0.0511418 0.682440i −0.962579 0.271001i \(-0.912645\pi\)
0.911437 0.411439i \(-0.134974\pi\)
\(60\) 0 0
\(61\) 3.85033 12.4825i 0.492984 1.59822i −0.277479 0.960732i \(-0.589499\pi\)
0.770463 0.637484i \(-0.220025\pi\)
\(62\) 0 0
\(63\) −0.275107 1.34677i −0.0346602 0.169677i
\(64\) 0 0
\(65\) −5.02972 + 3.42921i −0.623861 + 0.425341i
\(66\) 0 0
\(67\) −8.82791 + 5.09679i −1.07850 + 0.622672i −0.930491 0.366314i \(-0.880620\pi\)
−0.148009 + 0.988986i \(0.547286\pi\)
\(68\) 0 0
\(69\) −11.0808 + 2.52912i −1.33397 + 0.304470i
\(70\) 0 0
\(71\) −11.4127 2.60487i −1.35444 0.309142i −0.517146 0.855897i \(-0.673006\pi\)
−0.837292 + 0.546755i \(0.815863\pi\)
\(72\) 0 0
\(73\) 0.665073 4.41247i 0.0778409 0.516440i −0.915600 0.402091i \(-0.868284\pi\)
0.993441 0.114349i \(-0.0364784\pi\)
\(74\) 0 0
\(75\) 8.87261 + 8.23258i 1.02452 + 0.950616i
\(76\) 0 0
\(77\) 7.98262 + 4.85581i 0.909704 + 0.553371i
\(78\) 0 0
\(79\) −5.38475 3.10889i −0.605832 0.349777i 0.165500 0.986210i \(-0.447076\pi\)
−0.771332 + 0.636432i \(0.780409\pi\)
\(80\) 0 0
\(81\) 5.25704 4.87782i 0.584116 0.541980i
\(82\) 0 0
\(83\) 5.83732 7.31977i 0.640729 0.803449i −0.350365 0.936613i \(-0.613942\pi\)
0.991094 + 0.133164i \(0.0425138\pi\)
\(84\) 0 0
\(85\) −15.0215 18.8364i −1.62931 2.04309i
\(86\) 0 0
\(87\) −2.10986 + 5.37583i −0.226200 + 0.576349i
\(88\) 0 0
\(89\) −7.37597 + 2.89485i −0.781851 + 0.306854i −0.722489 0.691383i \(-0.757002\pi\)
−0.0593621 + 0.998237i \(0.518907\pi\)
\(90\) 0 0
\(91\) 3.96700 2.17078i 0.415855 0.227560i
\(92\) 0 0
\(93\) −0.597487 + 7.97291i −0.0619565 + 0.826753i
\(94\) 0 0
\(95\) −5.06277 + 7.42573i −0.519430 + 0.761863i
\(96\) 0 0
\(97\) 5.29761i 0.537891i 0.963155 + 0.268945i \(0.0866751\pi\)
−0.963155 + 0.268945i \(0.913325\pi\)
\(98\) 0 0
\(99\) 1.83477i 0.184402i
\(100\) 0 0
\(101\) −6.88842 + 10.1035i −0.685423 + 1.00533i 0.313031 + 0.949743i \(0.398656\pi\)
−0.998454 + 0.0555881i \(0.982297\pi\)
\(102\) 0 0
\(103\) 0.889060 11.8637i 0.0876017 1.16896i −0.764157 0.645030i \(-0.776845\pi\)
0.851759 0.523934i \(-0.175536\pi\)
\(104\) 0 0
\(105\) −9.84266 11.1075i −0.960546 1.08398i
\(106\) 0 0
\(107\) 2.47400 0.970972i 0.239170 0.0938674i −0.242729 0.970094i \(-0.578042\pi\)
0.481899 + 0.876227i \(0.339947\pi\)
\(108\) 0 0
\(109\) 2.43709 6.20959i 0.233431 0.594771i −0.765378 0.643582i \(-0.777448\pi\)
0.998808 + 0.0488103i \(0.0155430\pi\)
\(110\) 0 0
\(111\) −2.37312 2.97580i −0.225247 0.282451i
\(112\) 0 0
\(113\) 8.36228 10.4860i 0.786657 0.986437i −0.213298 0.976987i \(-0.568421\pi\)
0.999955 0.00944959i \(-0.00300794\pi\)
\(114\) 0 0
\(115\) 18.8414 17.4823i 1.75697 1.63023i
\(116\) 0 0
\(117\) −0.769029 0.443999i −0.0710968 0.0410478i
\(118\) 0 0
\(119\) 9.74062 + 15.0144i 0.892921 + 1.37636i
\(120\) 0 0
\(121\) 1.07876 + 1.00094i 0.0980691 + 0.0909948i
\(122\) 0 0
\(123\) −2.08770 + 13.8510i −0.188241 + 1.24890i
\(124\) 0 0
\(125\) −9.32361 2.12805i −0.833929 0.190339i
\(126\) 0 0
\(127\) 11.3211 2.58396i 1.00458 0.229289i 0.311576 0.950221i \(-0.399143\pi\)
0.693006 + 0.720932i \(0.256286\pi\)
\(128\) 0 0
\(129\) −0.584516 + 0.337471i −0.0514638 + 0.0297126i
\(130\) 0 0
\(131\) 3.08172 2.10108i 0.269251 0.183572i −0.421167 0.906983i \(-0.638379\pi\)
0.690417 + 0.723411i \(0.257427\pi\)
\(132\) 0 0
\(133\) 4.28103 5.12305i 0.371212 0.444225i
\(134\) 0 0
\(135\) −5.81917 + 18.8653i −0.500834 + 1.62366i
\(136\) 0 0
\(137\) 0.624269 + 8.33029i 0.0533349 + 0.711704i 0.958217 + 0.286042i \(0.0923397\pi\)
−0.904882 + 0.425662i \(0.860041\pi\)
\(138\) 0 0
\(139\) −14.6728 + 7.06605i −1.24453 + 0.599334i −0.936040 0.351893i \(-0.885538\pi\)
−0.308490 + 0.951228i \(0.599824\pi\)
\(140\) 0 0
\(141\) 18.4541 + 8.88701i 1.55411 + 0.748421i
\(142\) 0 0
\(143\) 5.76788 1.77916i 0.482334 0.148780i
\(144\) 0 0
\(145\) −1.94646 12.9139i −0.161645 1.07244i
\(146\) 0 0
\(147\) 6.47191 + 8.92507i 0.533794 + 0.736127i
\(148\) 0 0
\(149\) −1.30993 + 0.197440i −0.107313 + 0.0161749i −0.202479 0.979287i \(-0.564900\pi\)
0.0951660 + 0.995461i \(0.469662\pi\)
\(150\) 0 0
\(151\) −6.67155 21.6286i −0.542923 1.76011i −0.643778 0.765212i \(-0.722634\pi\)
0.100855 0.994901i \(-0.467842\pi\)
\(152\) 0 0
\(153\) 1.52486 3.16641i 0.123278 0.255989i
\(154\) 0 0
\(155\) −7.84491 16.2901i −0.630118 1.30845i
\(156\) 0 0
\(157\) −0.542763 + 0.0406744i −0.0433172 + 0.00324617i −0.0963711 0.995345i \(-0.530724\pi\)
0.0530539 + 0.998592i \(0.483104\pi\)
\(158\) 0 0
\(159\) −5.89622 1.81874i −0.467601 0.144236i
\(160\) 0 0
\(161\) −15.1964 + 11.5595i −1.19765 + 0.911019i
\(162\) 0 0
\(163\) 3.28737 + 4.82169i 0.257487 + 0.377664i 0.933115 0.359579i \(-0.117080\pi\)
−0.675628 + 0.737243i \(0.736127\pi\)
\(164\) 0 0
\(165\) −9.90477 17.1556i −0.771085 1.33556i
\(166\) 0 0
\(167\) 0.555158 + 2.43231i 0.0429594 + 0.188218i 0.991855 0.127373i \(-0.0406545\pi\)
−0.948895 + 0.315591i \(0.897797\pi\)
\(168\) 0 0
\(169\) −2.24271 + 9.82596i −0.172516 + 0.755843i
\(170\) 0 0
\(171\) −1.29637 0.195396i −0.0991359 0.0149423i
\(172\) 0 0
\(173\) −5.95821 + 6.42142i −0.452994 + 0.488212i −0.917712 0.397247i \(-0.869965\pi\)
0.464717 + 0.885459i \(0.346156\pi\)
\(174\) 0 0
\(175\) 19.2873 + 6.43656i 1.45798 + 0.486558i
\(176\) 0 0
\(177\) 4.13945 7.16973i 0.311140 0.538910i
\(178\) 0 0
\(179\) −6.64626 7.16296i −0.496765 0.535385i 0.434044 0.900892i \(-0.357086\pi\)
−0.930809 + 0.365507i \(0.880896\pi\)
\(180\) 0 0
\(181\) 1.59003 + 1.26800i 0.118186 + 0.0942500i 0.680799 0.732470i \(-0.261633\pi\)
−0.562613 + 0.826720i \(0.690204\pi\)
\(182\) 0 0
\(183\) 16.0848 12.8272i 1.18902 0.948214i
\(184\) 0 0
\(185\) 8.01241 + 3.14464i 0.589084 + 0.231198i
\(186\) 0 0
\(187\) 8.72762 + 22.2376i 0.638227 + 1.62618i
\(188\) 0 0
\(189\) 5.66916 13.5256i 0.412370 0.983842i
\(190\) 0 0
\(191\) −3.06050 0.229353i −0.221450 0.0165954i −0.0364569 0.999335i \(-0.511607\pi\)
−0.184993 + 0.982740i \(0.559226\pi\)
\(192\) 0 0
\(193\) −9.46724 6.45465i −0.681467 0.464616i 0.172455 0.985017i \(-0.444830\pi\)
−0.853922 + 0.520401i \(0.825782\pi\)
\(194\) 0 0
\(195\) −9.58748 −0.686574
\(196\) 0 0
\(197\) −19.1900 −1.36723 −0.683617 0.729841i \(-0.739594\pi\)
−0.683617 + 0.729841i \(0.739594\pi\)
\(198\) 0 0
\(199\) 0.245318 + 0.167255i 0.0173901 + 0.0118564i 0.571984 0.820265i \(-0.306174\pi\)
−0.554594 + 0.832121i \(0.687126\pi\)
\(200\) 0 0
\(201\) −16.0095 1.19974i −1.12922 0.0846234i
\(202\) 0 0
\(203\) 0.503279 + 9.68841i 0.0353233 + 0.679993i
\(204\) 0 0
\(205\) −11.5728 29.4870i −0.808279 2.05946i
\(206\) 0 0
\(207\) 3.49015 + 1.36978i 0.242582 + 0.0952064i
\(208\) 0 0
\(209\) 6.96723 5.55618i 0.481933 0.384329i
\(210\) 0 0
\(211\) 0.216716 + 0.172825i 0.0149194 + 0.0118978i 0.630921 0.775847i \(-0.282677\pi\)
−0.616002 + 0.787745i \(0.711249\pi\)
\(212\) 0 0
\(213\) −12.5401 13.5150i −0.859234 0.926034i
\(214\) 0 0
\(215\) 0.763163 1.32184i 0.0520473 0.0901486i
\(216\) 0 0
\(217\) 4.61941 + 12.6119i 0.313586 + 0.856150i
\(218\) 0 0
\(219\) 4.78019 5.15182i 0.323015 0.348127i
\(220\) 0 0
\(221\) 11.4327 + 1.72321i 0.769048 + 0.115915i
\(222\) 0 0
\(223\) −5.36963 + 23.5259i −0.359577 + 1.57541i 0.394673 + 0.918822i \(0.370858\pi\)
−0.754250 + 0.656587i \(0.771999\pi\)
\(224\) 0 0
\(225\) −0.888470 3.89264i −0.0592313 0.259509i
\(226\) 0 0
\(227\) −9.87817 17.1095i −0.655637 1.13560i −0.981734 0.190260i \(-0.939067\pi\)
0.326097 0.945336i \(-0.394267\pi\)
\(228\) 0 0
\(229\) 14.8131 + 21.7268i 0.978876 + 1.43575i 0.898495 + 0.438983i \(0.144661\pi\)
0.0803806 + 0.996764i \(0.474386\pi\)
\(230\) 0 0
\(231\) 6.07957 + 13.4010i 0.400006 + 0.881719i
\(232\) 0 0
\(233\) −18.2835 5.63970i −1.19779 0.369469i −0.369212 0.929345i \(-0.620373\pi\)
−0.828576 + 0.559876i \(0.810849\pi\)
\(234\) 0 0
\(235\) −46.1899 + 3.46146i −3.01310 + 0.225801i
\(236\) 0 0
\(237\) −4.24888 8.82289i −0.275994 0.573108i
\(238\) 0 0
\(239\) 11.6427 24.1762i 0.753101 1.56383i −0.0710585 0.997472i \(-0.522638\pi\)
0.824159 0.566358i \(-0.191648\pi\)
\(240\) 0 0
\(241\) 0.273352 + 0.886186i 0.0176082 + 0.0570843i 0.963951 0.266082i \(-0.0857290\pi\)
−0.946342 + 0.323166i \(0.895253\pi\)
\(242\) 0 0
\(243\) −5.27504 + 0.795085i −0.338394 + 0.0510047i
\(244\) 0 0
\(245\) −22.7666 10.1614i −1.45450 0.649190i
\(246\) 0 0
\(247\) −0.642816 4.26481i −0.0409014 0.271363i
\(248\) 0 0
\(249\) 14.0901 4.34622i 0.892924 0.275430i
\(250\) 0 0
\(251\) −28.0939 13.5293i −1.77327 0.853961i −0.963723 0.266904i \(-0.913999\pi\)
−0.809545 0.587057i \(-0.800286\pi\)
\(252\) 0 0
\(253\) −22.9616 + 11.0577i −1.44359 + 0.695194i
\(254\) 0 0
\(255\) −2.83560 37.8385i −0.177572 2.36954i
\(256\) 0 0
\(257\) 8.25124 26.7499i 0.514698 1.66861i −0.208542 0.978013i \(-0.566872\pi\)
0.723240 0.690597i \(-0.242652\pi\)
\(258\) 0 0
\(259\) −5.69578 2.90544i −0.353918 0.180535i
\(260\) 0 0
\(261\) 1.57404 1.07316i 0.0974305 0.0664270i
\(262\) 0 0
\(263\) −10.0646 + 5.81082i −0.620612 + 0.358311i −0.777107 0.629368i \(-0.783314\pi\)
0.156495 + 0.987679i \(0.449980\pi\)
\(264\) 0 0
\(265\) 13.6039 3.10501i 0.835682 0.190739i
\(266\) 0 0
\(267\) −12.1665 2.77693i −0.744579 0.169945i
\(268\) 0 0
\(269\) −0.0717249 + 0.475864i −0.00437315 + 0.0290139i −0.990911 0.134519i \(-0.957051\pi\)
0.986538 + 0.163533i \(0.0522891\pi\)
\(270\) 0 0
\(271\) −0.509332 0.472591i −0.0309397 0.0287078i 0.664551 0.747243i \(-0.268623\pi\)
−0.695491 + 0.718535i \(0.744813\pi\)
\(272\) 0 0
\(273\) 7.08811 + 0.694718i 0.428992 + 0.0420463i
\(274\) 0 0
\(275\) 23.5040 + 13.5701i 1.41735 + 0.818306i
\(276\) 0 0
\(277\) −11.8139 + 10.9617i −0.709828 + 0.658624i −0.950051 0.312093i \(-0.898970\pi\)
0.240223 + 0.970718i \(0.422779\pi\)
\(278\) 0 0
\(279\) 1.64444 2.06206i 0.0984499 0.123452i
\(280\) 0 0
\(281\) 4.16927 + 5.22809i 0.248718 + 0.311882i 0.890481 0.455021i \(-0.150368\pi\)
−0.641763 + 0.766903i \(0.721797\pi\)
\(282\) 0 0
\(283\) 6.31133 16.0810i 0.375169 0.955916i −0.611216 0.791464i \(-0.709319\pi\)
0.986385 0.164452i \(-0.0525856\pi\)
\(284\) 0 0
\(285\) −13.1762 + 5.17128i −0.780490 + 0.306320i
\(286\) 0 0
\(287\) 6.41921 + 22.6386i 0.378914 + 1.33631i
\(288\) 0 0
\(289\) −2.14913 + 28.6782i −0.126420 + 1.68695i
\(290\) 0 0
\(291\) −4.70003 + 6.89368i −0.275521 + 0.404115i
\(292\) 0 0
\(293\) 8.46030i 0.494256i −0.968983 0.247128i \(-0.920513\pi\)
0.968983 0.247128i \(-0.0794868\pi\)
\(294\) 0 0
\(295\) 18.7221i 1.09004i
\(296\) 0 0
\(297\) 11.0273 16.1741i 0.639868 0.938514i
\(298\) 0 0
\(299\) −0.921762 + 12.3001i −0.0533069 + 0.711331i
\(300\) 0 0
\(301\) −0.659995 + 0.921946i −0.0380415 + 0.0531401i
\(302\) 0 0
\(303\) −17.9276 + 7.03604i −1.02991 + 0.404210i
\(304\) 0 0
\(305\) −16.9974 + 43.3087i −0.973268 + 2.47985i
\(306\) 0 0
\(307\) −2.47927 3.10891i −0.141499 0.177435i 0.706032 0.708180i \(-0.250484\pi\)
−0.847531 + 0.530745i \(0.821912\pi\)
\(308\) 0 0
\(309\) 11.6824 14.6492i 0.664587 0.833365i
\(310\) 0 0
\(311\) −4.06319 + 3.77009i −0.230402 + 0.213782i −0.786922 0.617052i \(-0.788327\pi\)
0.556520 + 0.830834i \(0.312136\pi\)
\(312\) 0 0
\(313\) 12.0395 + 6.95103i 0.680515 + 0.392895i 0.800049 0.599935i \(-0.204807\pi\)
−0.119534 + 0.992830i \(0.538140\pi\)
\(314\) 0 0
\(315\) 0.618629 + 4.85649i 0.0348558 + 0.273632i
\(316\) 0 0
\(317\) 24.1796 + 22.4353i 1.35806 + 1.26009i 0.935302 + 0.353852i \(0.115128\pi\)
0.422757 + 0.906243i \(0.361062\pi\)
\(318\) 0 0
\(319\) −1.93001 + 12.8048i −0.108060 + 0.716929i
\(320\) 0 0
\(321\) 4.08081 + 0.931419i 0.227769 + 0.0519867i
\(322\) 0 0
\(323\) 16.6416 3.79834i 0.925963 0.211345i
\(324\) 0 0
\(325\) 11.3756 6.56768i 0.631003 0.364309i
\(326\) 0 0
\(327\) 8.68048 5.91825i 0.480032 0.327280i
\(328\) 0 0
\(329\) 34.3994 + 0.787883i 1.89650 + 0.0434374i
\(330\) 0 0
\(331\) 6.80412 22.0584i 0.373988 1.21244i −0.551665 0.834066i \(-0.686007\pi\)
0.925653 0.378374i \(-0.123517\pi\)
\(332\) 0 0
\(333\) 0.0938299 + 1.25207i 0.00514185 + 0.0686132i
\(334\) 0 0
\(335\) 32.7103 15.7524i 1.78715 0.860648i
\(336\) 0 0
\(337\) 20.4737 + 9.85964i 1.11528 + 0.537089i 0.898430 0.439117i \(-0.144709\pi\)
0.216846 + 0.976206i \(0.430423\pi\)
\(338\) 0 0
\(339\) 20.1848 6.22619i 1.09629 0.338160i
\(340\) 0 0
\(341\) 2.67201 + 17.7276i 0.144697 + 0.960004i
\(342\) 0 0
\(343\) 16.0952 + 9.16212i 0.869059 + 0.494708i
\(344\) 0 0
\(345\) 40.0283 6.03330i 2.15505 0.324822i
\(346\) 0 0
\(347\) 3.30059 + 10.7003i 0.177185 + 0.574420i 0.999981 + 0.00608367i \(0.00193650\pi\)
−0.822796 + 0.568336i \(0.807587\pi\)
\(348\) 0 0
\(349\) 2.05126 4.25949i 0.109801 0.228005i −0.838826 0.544399i \(-0.816758\pi\)
0.948628 + 0.316394i \(0.102472\pi\)
\(350\) 0 0
\(351\) −4.11071 8.53598i −0.219413 0.455617i
\(352\) 0 0
\(353\) −22.9450 + 1.71949i −1.22124 + 0.0915191i −0.669701 0.742631i \(-0.733578\pi\)
−0.551537 + 0.834150i \(0.685959\pi\)
\(354\) 0 0
\(355\) 39.8407 + 12.2892i 2.11453 + 0.652245i
\(356\) 0 0
\(357\) −0.645428 + 28.1798i −0.0341597 + 1.49143i
\(358\) 0 0
\(359\) 5.54511 + 8.13319i 0.292660 + 0.429253i 0.944206 0.329356i \(-0.106832\pi\)
−0.651546 + 0.758609i \(0.725879\pi\)
\(360\) 0 0
\(361\) 6.31623 + 10.9400i 0.332433 + 0.575791i
\(362\) 0 0
\(363\) 0.515736 + 2.25958i 0.0270691 + 0.118597i
\(364\) 0 0
\(365\) −3.53653 + 15.4946i −0.185111 + 0.811023i
\(366\) 0 0
\(367\) 11.1288 + 1.67740i 0.580920 + 0.0875596i 0.432927 0.901429i \(-0.357481\pi\)
0.147993 + 0.988988i \(0.452719\pi\)
\(368\) 0 0
\(369\) 3.14291 3.38726i 0.163614 0.176333i
\(370\) 0 0
\(371\) −10.2825 + 1.30980i −0.533840 + 0.0680016i
\(372\) 0 0
\(373\) 12.7075 22.0101i 0.657972 1.13964i −0.323168 0.946342i \(-0.604748\pi\)
0.981140 0.193299i \(-0.0619188\pi\)
\(374\) 0 0
\(375\) −10.2446 11.0411i −0.529031 0.570160i
\(376\) 0 0
\(377\) 4.89996 + 3.90759i 0.252361 + 0.201251i
\(378\) 0 0
\(379\) −17.1095 + 13.6444i −0.878856 + 0.700864i −0.955119 0.296224i \(-0.904273\pi\)
0.0762629 + 0.997088i \(0.475701\pi\)
\(380\) 0 0
\(381\) 17.0244 + 6.68158i 0.872186 + 0.342308i
\(382\) 0 0
\(383\) −9.98296 25.4362i −0.510106 1.29973i −0.921538 0.388288i \(-0.873067\pi\)
0.411433 0.911440i \(-0.365029\pi\)
\(384\) 0 0
\(385\) −27.0591 19.3709i −1.37906 0.987230i
\(386\) 0 0
\(387\) 0.222027 + 0.0166386i 0.0112862 + 0.000845787i
\(388\) 0 0
\(389\) −9.47411 6.45934i −0.480357 0.327502i 0.298816 0.954311i \(-0.403408\pi\)
−0.779173 + 0.626809i \(0.784361\pi\)
\(390\) 0 0
\(391\) −48.8167 −2.46877
\(392\) 0 0
\(393\) 5.87426 0.296317
\(394\) 0 0
\(395\) 18.2973 + 12.4749i 0.920639 + 0.627681i
\(396\) 0 0
\(397\) 16.2364 + 1.21675i 0.814883 + 0.0610670i 0.475649 0.879635i \(-0.342213\pi\)
0.339234 + 0.940702i \(0.389832\pi\)
\(398\) 0 0
\(399\) 10.1160 2.86841i 0.506433 0.143600i
\(400\) 0 0
\(401\) 8.29814 + 21.1433i 0.414389 + 1.05585i 0.973891 + 0.227017i \(0.0728973\pi\)
−0.559502 + 0.828829i \(0.689007\pi\)
\(402\) 0 0
\(403\) 8.07699 + 3.16998i 0.402343 + 0.157908i
\(404\) 0 0
\(405\) −19.9695 + 15.9252i −0.992293 + 0.791327i
\(406\) 0 0
\(407\) −6.67266 5.32127i −0.330752 0.263766i
\(408\) 0 0
\(409\) −11.6711 12.5784i −0.577098 0.621964i 0.375270 0.926916i \(-0.377550\pi\)
−0.952368 + 0.304952i \(0.901360\pi\)
\(410\) 0 0
\(411\) −6.57827 + 11.3939i −0.324482 + 0.562020i
\(412\) 0 0
\(413\) 1.35662 13.8414i 0.0667548 0.681090i
\(414\) 0 0
\(415\) −22.6804 + 24.4437i −1.11334 + 1.19989i
\(416\) 0 0
\(417\) −25.3624 3.82277i −1.24200 0.187202i
\(418\) 0 0
\(419\) −1.10535 + 4.84287i −0.0540000 + 0.236590i −0.994725 0.102582i \(-0.967290\pi\)
0.940725 + 0.339172i \(0.110147\pi\)
\(420\) 0 0
\(421\) 4.52323 + 19.8176i 0.220449 + 0.965850i 0.957141 + 0.289622i \(0.0935295\pi\)
−0.736692 + 0.676228i \(0.763613\pi\)
\(422\) 0 0
\(423\) −3.37837 5.85151i −0.164262 0.284510i
\(424\) 0 0
\(425\) 29.2848 + 42.9529i 1.42052 + 2.08352i
\(426\) 0 0
\(427\) 15.7045 30.7868i 0.759994 1.48988i
\(428\) 0 0
\(429\) 9.08410 + 2.80208i 0.438585 + 0.135285i
\(430\) 0 0
\(431\) −20.4586 + 1.53316i −0.985458 + 0.0738499i −0.557699 0.830043i \(-0.688316\pi\)
−0.427759 + 0.903893i \(0.640697\pi\)
\(432\) 0 0
\(433\) −9.10273 18.9020i −0.437449 0.908373i −0.996837 0.0794673i \(-0.974678\pi\)
0.559388 0.828906i \(-0.311036\pi\)
\(434\) 0 0
\(435\) 8.92432 18.5315i 0.427888 0.888519i
\(436\) 0 0
\(437\) 5.36759 + 17.4013i 0.256767 + 0.832417i
\(438\) 0 0
\(439\) 29.4443 4.43801i 1.40530 0.211815i 0.597782 0.801659i \(-0.296049\pi\)
0.807517 + 0.589844i \(0.200811\pi\)
\(440\) 0 0
\(441\) −0.105452 3.63527i −0.00502153 0.173108i
\(442\) 0 0
\(443\) 0.983142 + 6.52272i 0.0467105 + 0.309904i 0.999970 + 0.00775087i \(0.00246720\pi\)
−0.953259 + 0.302153i \(0.902295\pi\)
\(444\) 0 0
\(445\) 26.9674 8.31834i 1.27838 0.394327i
\(446\) 0 0
\(447\) −1.87975 0.905241i −0.0889092 0.0428164i
\(448\) 0 0
\(449\) −29.4178 + 14.1668i −1.38831 + 0.668575i −0.970754 0.240077i \(-0.922827\pi\)
−0.417556 + 0.908651i \(0.637113\pi\)
\(450\) 0 0
\(451\) 2.34719 + 31.3211i 0.110525 + 1.47485i
\(452\) 0 0
\(453\) 10.5073 34.0640i 0.493678 1.60046i
\(454\) 0 0
\(455\) −14.6672 + 6.65403i −0.687610 + 0.311946i
\(456\) 0 0
\(457\) −22.4381 + 15.2980i −1.04961 + 0.715612i −0.959896 0.280356i \(-0.909548\pi\)
−0.0897138 + 0.995968i \(0.528595\pi\)
\(458\) 0 0
\(459\) 32.4728 18.7482i 1.51570 0.875089i
\(460\) 0 0
\(461\) 18.8477 4.30187i 0.877825 0.200358i 0.240217 0.970719i \(-0.422781\pi\)
0.637608 + 0.770361i \(0.279924\pi\)
\(462\) 0 0
\(463\) 2.95266 + 0.673925i 0.137222 + 0.0313199i 0.290580 0.956851i \(-0.406152\pi\)
−0.153358 + 0.988171i \(0.549009\pi\)
\(464\) 0 0
\(465\) 4.24414 28.1580i 0.196817 1.30580i
\(466\) 0 0
\(467\) −11.6095 10.7720i −0.537223 0.498470i 0.364253 0.931300i \(-0.381324\pi\)
−0.901475 + 0.432830i \(0.857515\pi\)
\(468\) 0 0
\(469\) −25.3244 + 9.27569i −1.16937 + 0.428312i
\(470\) 0 0
\(471\) −0.742374 0.428610i −0.0342068 0.0197493i
\(472\) 0 0
\(473\) −1.10942 + 1.02939i −0.0510112 + 0.0473315i
\(474\) 0 0
\(475\) 12.0911 15.1618i 0.554778 0.695670i
\(476\) 0 0
\(477\) 1.26910 + 1.59140i 0.0581079 + 0.0728650i
\(478\) 0 0
\(479\) −1.01058 + 2.57491i −0.0461746 + 0.117651i −0.952100 0.305785i \(-0.901081\pi\)
0.905926 + 0.423436i \(0.139176\pi\)
\(480\) 0 0
\(481\) −3.84509 + 1.50909i −0.175321 + 0.0688085i
\(482\) 0 0
\(483\) −30.0304 + 1.55998i −1.36643 + 0.0709814i
\(484\) 0 0
\(485\) 1.41001 18.8153i 0.0640253 0.854359i
\(486\) 0 0
\(487\) 21.6192 31.7095i 0.979658 1.43689i 0.0817802 0.996650i \(-0.473939\pi\)
0.897878 0.440244i \(-0.145108\pi\)
\(488\) 0 0
\(489\) 9.19094i 0.415629i
\(490\) 0 0
\(491\) 33.8831i 1.52912i −0.644551 0.764561i \(-0.722956\pi\)
0.644551 0.764561i \(-0.277044\pi\)
\(492\) 0 0
\(493\) −13.9727 + 20.4942i −0.629299 + 0.923011i
\(494\) 0 0
\(495\) −0.488343 + 6.51648i −0.0219494 + 0.292894i
\(496\) 0 0
\(497\) −28.5641 11.9724i −1.28127 0.537037i
\(498\) 0 0
\(499\) −30.7013 + 12.0494i −1.37438 + 0.539404i −0.933634 0.358228i \(-0.883381\pi\)
−0.440745 + 0.897632i \(0.645286\pi\)
\(500\) 0 0
\(501\) −1.43552 + 3.65765i −0.0641345 + 0.163412i
\(502\) 0 0
\(503\) 5.95459 + 7.46682i 0.265502 + 0.332929i 0.896655 0.442729i \(-0.145990\pi\)
−0.631153 + 0.775658i \(0.717418\pi\)
\(504\) 0 0
\(505\) 27.1544 34.0506i 1.20836 1.51523i
\(506\) 0 0
\(507\) −11.6360 + 10.7966i −0.516772 + 0.479495i
\(508\) 0 0
\(509\) 6.46266 + 3.73122i 0.286452 + 0.165383i 0.636341 0.771408i \(-0.280447\pi\)
−0.349889 + 0.936791i \(0.613781\pi\)
\(510\) 0 0
\(511\) 3.73734 11.1990i 0.165330 0.495415i
\(512\) 0 0
\(513\) −10.2535 9.51387i −0.452704 0.420048i
\(514\) 0 0
\(515\) −6.31528 + 41.8991i −0.278284 + 1.84630i
\(516\) 0 0
\(517\) 44.7765 + 10.2199i 1.96927 + 0.449472i
\(518\) 0 0
\(519\) −13.4504 + 3.06996i −0.590407 + 0.134756i
\(520\) 0 0
\(521\) −2.39895 + 1.38503i −0.105100 + 0.0606794i −0.551629 0.834090i \(-0.685993\pi\)
0.446529 + 0.894769i \(0.352660\pi\)
\(522\) 0 0
\(523\) 15.4215 10.5142i 0.674334 0.459753i −0.177115 0.984190i \(-0.556677\pi\)
0.851449 + 0.524437i \(0.175724\pi\)
\(524\) 0 0
\(525\) 19.3877 + 25.4874i 0.846147 + 1.11236i
\(526\) 0 0
\(527\) −10.1220 + 32.8146i −0.440920 + 1.42943i
\(528\) 0 0
\(529\) −2.17309 28.9978i −0.0944821 1.26078i
\(530\) 0 0
\(531\) −2.46058 + 1.18495i −0.106780 + 0.0514225i
\(532\) 0 0
\(533\) 13.6960 + 6.59564i 0.593239 + 0.285689i
\(534\) 0 0
\(535\) −9.04522 + 2.79008i −0.391059 + 0.120626i
\(536\) 0 0
\(537\) −2.29368 15.2176i −0.0989797 0.656688i
\(538\) 0 0
\(539\) 18.6014 + 16.2818i 0.801220 + 0.701305i
\(540\) 0 0
\(541\) 10.9373 1.64853i 0.470231 0.0708759i 0.0903474 0.995910i \(-0.471202\pi\)
0.379883 + 0.925034i \(0.375964\pi\)
\(542\) 0 0
\(543\) 0.944101 + 3.06070i 0.0405152 + 0.131347i
\(544\) 0 0
\(545\) −10.3084 + 21.4057i −0.441565 + 0.916920i
\(546\) 0 0
\(547\) −8.20100 17.0295i −0.350649 0.728131i 0.648812 0.760949i \(-0.275266\pi\)
−0.999461 + 0.0328178i \(0.989552\pi\)
\(548\) 0 0
\(549\) −6.76771 + 0.507170i −0.288839 + 0.0216455i
\(550\) 0 0
\(551\) 8.84175 + 2.72732i 0.376671 + 0.116188i
\(552\) 0 0
\(553\) −12.6234 10.5487i −0.536803 0.448574i
\(554\) 0 0
\(555\) 7.63648 + 11.2007i 0.324151 + 0.475442i
\(556\) 0 0
\(557\) −11.4347 19.8054i −0.484502 0.839183i 0.515339 0.856986i \(-0.327666\pi\)
−0.999842 + 0.0178037i \(0.994333\pi\)
\(558\) 0 0
\(559\) 0.162990 + 0.714108i 0.00689376 + 0.0302035i
\(560\) 0 0
\(561\) −8.37210 + 36.6806i −0.353470 + 1.54865i
\(562\) 0 0
\(563\) 10.8046 + 1.62853i 0.455358 + 0.0686342i 0.372717 0.927945i \(-0.378426\pi\)
0.0826413 + 0.996579i \(0.473664\pi\)
\(564\) 0 0
\(565\) −32.4909 + 35.0169i −1.36690 + 1.47317i
\(566\) 0 0
\(567\) 15.9176 10.3266i 0.668475 0.433676i
\(568\) 0 0
\(569\) −2.81437 + 4.87463i −0.117984 + 0.204355i −0.918969 0.394330i \(-0.870977\pi\)
0.800984 + 0.598685i \(0.204310\pi\)
\(570\) 0 0
\(571\) 22.2051 + 23.9314i 0.929255 + 1.00150i 0.999992 + 0.00400343i \(0.00127433\pi\)
−0.0707373 + 0.997495i \(0.522535\pi\)
\(572\) 0 0
\(573\) −3.77909 3.01372i −0.157874 0.125900i
\(574\) 0 0
\(575\) −43.3607 + 34.5790i −1.80826 + 1.44204i
\(576\) 0 0
\(577\) −3.20066 1.25617i −0.133245 0.0522949i 0.297782 0.954634i \(-0.403753\pi\)
−0.431027 + 0.902339i \(0.641849\pi\)
\(578\) 0 0
\(579\) −6.59298 16.7986i −0.273995 0.698128i
\(580\) 0 0
\(581\) 18.5390 16.4280i 0.769128 0.681547i
\(582\) 0 0
\(583\) −13.7971 1.03395i −0.571419 0.0428220i
\(584\) 0 0
\(585\) 2.61316 + 1.78162i 0.108041 + 0.0736609i
\(586\) 0 0
\(587\) 4.50362 0.185884 0.0929421 0.995672i \(-0.470373\pi\)
0.0929421 + 0.995672i \(0.470373\pi\)
\(588\) 0 0
\(589\) 12.8101 0.527832
\(590\) 0 0
\(591\) −24.9717 17.0254i −1.02720 0.700331i
\(592\) 0 0
\(593\) −22.1208 1.65772i −0.908391 0.0680745i −0.387667 0.921800i \(-0.626719\pi\)
−0.520724 + 0.853725i \(0.674338\pi\)
\(594\) 0 0
\(595\) −30.5991 55.9184i −1.25444 2.29243i
\(596\) 0 0
\(597\) 0.170839 + 0.435292i 0.00699199 + 0.0178153i
\(598\) 0 0
\(599\) −4.36118 1.71164i −0.178193 0.0699355i 0.274567 0.961568i \(-0.411465\pi\)
−0.452760 + 0.891632i \(0.649561\pi\)
\(600\) 0 0
\(601\) 15.4581 12.3275i 0.630550 0.502847i −0.255273 0.966869i \(-0.582165\pi\)
0.885824 + 0.464022i \(0.153594\pi\)
\(602\) 0 0
\(603\) 4.14058 + 3.30200i 0.168617 + 0.134468i
\(604\) 0 0
\(605\) −3.56498 3.84213i −0.144937 0.156205i
\(606\) 0 0
\(607\) 16.5186 28.6111i 0.670470 1.16129i −0.307301 0.951612i \(-0.599426\pi\)
0.977771 0.209676i \(-0.0672409\pi\)
\(608\) 0 0
\(609\) −7.94064 + 13.0539i −0.321771 + 0.528969i
\(610\) 0 0
\(611\) 15.1191 16.2945i 0.611654 0.659207i
\(612\) 0 0
\(613\) 27.3112 + 4.11650i 1.10309 + 0.166264i 0.675249 0.737590i \(-0.264036\pi\)
0.427841 + 0.903854i \(0.359274\pi\)
\(614\) 0 0
\(615\) 11.1014 48.6383i 0.447650 1.96128i
\(616\) 0 0
\(617\) −4.25471 18.6411i −0.171288 0.750463i −0.985470 0.169852i \(-0.945671\pi\)
0.814181 0.580611i \(-0.197186\pi\)
\(618\) 0 0
\(619\) 17.7456 + 30.7363i 0.713256 + 1.23540i 0.963628 + 0.267246i \(0.0861136\pi\)
−0.250373 + 0.968150i \(0.580553\pi\)
\(620\) 0 0
\(621\) 22.5340 + 33.0514i 0.904260 + 1.32631i
\(622\) 0 0
\(623\) −20.5400 + 4.19574i −0.822917 + 0.168099i
\(624\) 0 0
\(625\) −4.17059 1.28646i −0.166824 0.0514583i
\(626\) 0 0
\(627\) 13.9958 1.04884i 0.558937 0.0418866i
\(628\) 0 0
\(629\) −7.09308 14.7289i −0.282819 0.587281i
\(630\) 0 0
\(631\) −9.71542 + 20.1743i −0.386765 + 0.803126i 0.613148 + 0.789968i \(0.289903\pi\)
−0.999913 + 0.0131580i \(0.995812\pi\)
\(632\) 0 0
\(633\) 0.128678 + 0.417165i 0.00511451 + 0.0165808i
\(634\) 0 0
\(635\) −40.8963 + 6.16413i −1.62292 + 0.244616i
\(636\) 0 0
\(637\) 11.3258 3.85658i 0.448743 0.152803i
\(638\) 0 0
\(639\) 0.906455 + 6.01394i 0.0358588 + 0.237908i
\(640\) 0 0
\(641\) 31.4722 9.70789i 1.24308 0.383439i 0.397654 0.917535i \(-0.369824\pi\)
0.845424 + 0.534097i \(0.179348\pi\)
\(642\) 0 0
\(643\) −17.6790 8.51375i −0.697191 0.335749i 0.0514960 0.998673i \(-0.483601\pi\)
−0.748687 + 0.662924i \(0.769315\pi\)
\(644\) 0 0
\(645\) 2.16582 1.04301i 0.0852792 0.0410683i
\(646\) 0 0
\(647\) 3.74351 + 49.9537i 0.147173 + 1.96388i 0.247386 + 0.968917i \(0.420428\pi\)
−0.100213 + 0.994966i \(0.531953\pi\)
\(648\) 0 0
\(649\) 5.47178 17.7391i 0.214786 0.696320i
\(650\) 0 0
\(651\) −5.17809 + 20.5099i −0.202945 + 0.803848i
\(652\) 0 0
\(653\) −4.72140 + 3.21899i −0.184763 + 0.125969i −0.652169 0.758073i \(-0.726141\pi\)
0.467407 + 0.884042i \(0.345188\pi\)
\(654\) 0 0
\(655\) −11.5044 + 6.64209i −0.449515 + 0.259528i
\(656\) 0 0
\(657\) −2.26023 + 0.515883i −0.0881801 + 0.0201265i
\(658\) 0 0
\(659\) −5.79992 1.32379i −0.225933 0.0515677i 0.108056 0.994145i \(-0.465538\pi\)
−0.333988 + 0.942577i \(0.608395\pi\)
\(660\) 0 0
\(661\) −1.58827 + 10.5375i −0.0617764 + 0.409859i 0.936474 + 0.350736i \(0.114069\pi\)
−0.998251 + 0.0591233i \(0.981170\pi\)
\(662\) 0 0
\(663\) 13.3484 + 12.3855i 0.518408 + 0.481012i
\(664\) 0 0
\(665\) −16.5683 + 17.0559i −0.642491 + 0.661399i
\(666\) 0 0
\(667\) −22.9166 13.2309i −0.887336 0.512304i
\(668\) 0 0
\(669\) −27.8595 + 25.8499i −1.07711 + 0.999414i
\(670\) 0 0
\(671\) 28.7625 36.0671i 1.11037 1.39235i
\(672\) 0 0
\(673\) −28.4019 35.6149i −1.09481 1.37285i −0.921678 0.387955i \(-0.873182\pi\)
−0.173135 0.984898i \(-0.555390\pi\)
\(674\) 0 0
\(675\) 15.5633 39.6546i 0.599031 1.52631i
\(676\) 0 0
\(677\) 26.9043 10.5592i 1.03402 0.405822i 0.213197 0.977009i \(-0.431612\pi\)
0.820820 + 0.571188i \(0.193517\pi\)
\(678\) 0 0
\(679\) −2.40581 + 13.8081i −0.0923265 + 0.529908i
\(680\) 0 0
\(681\) 2.32524 31.0282i 0.0891034 1.18900i
\(682\) 0 0
\(683\) 20.1617 29.5718i 0.771466 1.13153i −0.216413 0.976302i \(-0.569436\pi\)
0.987878 0.155230i \(-0.0496120\pi\)
\(684\) 0 0
\(685\) 29.7525i 1.13678i
\(686\) 0 0
\(687\) 41.4148i 1.58008i
\(688\) 0 0
\(689\) −3.77216 + 5.53275i −0.143708 + 0.210781i
\(690\) 0 0
\(691\) −1.40657 + 18.7694i −0.0535085 + 0.714021i 0.904352 + 0.426787i \(0.140355\pi\)
−0.957861 + 0.287234i \(0.907264\pi\)
\(692\) 0 0
\(693\) 0.833227 4.78231i 0.0316517 0.181665i
\(694\) 0 0
\(695\) 53.9935 21.1909i 2.04809 0.803816i
\(696\) 0 0
\(697\) −21.9800 + 56.0041i −0.832551 + 2.12131i
\(698\) 0 0
\(699\) −18.7884 23.5599i −0.710642 0.891117i
\(700\) 0 0
\(701\) −10.3833 + 13.0203i −0.392172 + 0.491769i −0.938246 0.345969i \(-0.887550\pi\)
0.546074 + 0.837737i \(0.316122\pi\)
\(702\) 0 0
\(703\) −4.47039 + 4.14792i −0.168604 + 0.156442i
\(704\) 0 0
\(705\) −63.1772 36.4753i −2.37939 1.37374i
\(706\) 0 0
\(707\) −22.5428 + 23.2063i −0.847811 + 0.872761i
\(708\) 0 0
\(709\) 0.980841 + 0.910088i 0.0368363 + 0.0341791i 0.698376 0.715731i \(-0.253906\pi\)
−0.661540 + 0.749910i \(0.730097\pi\)
\(710\) 0 0
\(711\) −0.481466 + 3.19432i −0.0180564 + 0.119796i
\(712\) 0 0
\(713\) −35.7167 8.15211i −1.33760 0.305299i
\(714\) 0 0
\(715\) −20.9591 + 4.78377i −0.783825 + 0.178903i
\(716\) 0 0
\(717\) 36.5995 21.1307i 1.36683 0.789142i
\(718\) 0 0
\(719\) 8.07862 5.50791i 0.301282 0.205410i −0.403237 0.915095i \(-0.632115\pi\)
0.704519 + 0.709685i \(0.251163\pi\)
\(720\) 0 0
\(721\) 7.70499 30.5188i 0.286949 1.13658i
\(722\) 0 0
\(723\) −0.430515 + 1.39570i −0.0160110 + 0.0519065i
\(724\) 0 0
\(725\) 2.10589 + 28.1011i 0.0782106 + 1.04365i
\(726\) 0 0
\(727\) 26.2048 12.6196i 0.971884 0.468034i 0.120578 0.992704i \(-0.461525\pi\)
0.851306 + 0.524669i \(0.175811\pi\)
\(728\) 0 0
\(729\) −26.9535 12.9801i −0.998277 0.480745i
\(730\) 0 0
\(731\) −2.77013 + 0.854472i −0.102457 + 0.0316038i
\(732\) 0 0
\(733\) −6.46457 42.8896i −0.238774 1.58416i −0.711326 0.702862i \(-0.751905\pi\)
0.472552 0.881303i \(-0.343333\pi\)
\(734\) 0 0
\(735\) −20.6105 33.4214i −0.760230 1.23277i
\(736\) 0 0
\(737\) −35.5967 + 5.36534i −1.31122 + 0.197635i
\(738\) 0 0
\(739\) 6.75574 + 21.9016i 0.248514 + 0.805662i 0.990771 + 0.135547i \(0.0432791\pi\)
−0.742257 + 0.670115i \(0.766245\pi\)
\(740\) 0 0
\(741\) 2.94725 6.12002i 0.108270 0.224825i
\(742\) 0 0
\(743\) −4.34466 9.02179i −0.159390 0.330977i 0.805945 0.591990i \(-0.201658\pi\)
−0.965335 + 0.261013i \(0.915943\pi\)
\(744\) 0 0
\(745\) 4.70496 0.352588i 0.172376 0.0129178i
\(746\) 0 0
\(747\) −4.64803 1.43373i −0.170063 0.0524574i
\(748\) 0 0
\(749\) 6.88938 1.40731i 0.251733 0.0514218i
\(750\) 0 0
\(751\) −10.7004 15.6947i −0.390464 0.572706i 0.579798 0.814760i \(-0.303131\pi\)
−0.970263 + 0.242054i \(0.922179\pi\)
\(752\) 0 0
\(753\) −24.5549 42.5303i −0.894829 1.54989i
\(754\) 0 0
\(755\) 17.9384 + 78.5932i 0.652845 + 2.86030i
\(756\) 0 0
\(757\) 2.84508 12.4651i 0.103406 0.453052i −0.896543 0.442957i \(-0.853929\pi\)
0.999949 0.0100949i \(-0.00321336\pi\)
\(758\) 0 0
\(759\) −39.6900 5.98230i −1.44066 0.217144i
\(760\) 0 0
\(761\) −11.5297 + 12.4260i −0.417950 + 0.450443i −0.906571 0.422053i \(-0.861310\pi\)
0.488621 + 0.872496i \(0.337500\pi\)
\(762\) 0 0
\(763\) 9.17220 15.0785i 0.332056 0.545877i
\(764\) 0 0
\(765\) −6.25857 + 10.8402i −0.226279 + 0.391927i
\(766\) 0 0
\(767\) −6.11107 6.58616i −0.220658 0.237813i
\(768\) 0 0
\(769\) −33.2688 26.5310i −1.19970 0.956732i −0.199970 0.979802i \(-0.564085\pi\)
−0.999734 + 0.0230699i \(0.992656\pi\)
\(770\) 0 0
\(771\) 34.4696 27.4886i 1.24139 0.989979i
\(772\) 0 0
\(773\) −21.4078 8.40196i −0.769987 0.302198i −0.0523626 0.998628i \(-0.516675\pi\)
−0.717624 + 0.696431i \(0.754770\pi\)
\(774\) 0 0
\(775\) 14.2533 + 36.3169i 0.511995 + 1.30454i
\(776\) 0 0
\(777\) −4.83410 8.83409i −0.173423 0.316921i
\(778\) 0 0
\(779\) 22.3801 + 1.67716i 0.801851 + 0.0600904i
\(780\) 0 0
\(781\) −34.1572 23.2880i −1.22224 0.833310i
\(782\) 0 0
\(783\) 20.3255 0.726373
\(784\) 0 0
\(785\) 1.93853 0.0691892
\(786\) 0 0
\(787\) 6.56143 + 4.47351i 0.233890 + 0.159463i 0.674594 0.738189i \(-0.264319\pi\)
−0.440704 + 0.897652i \(0.645271\pi\)
\(788\) 0 0
\(789\) −18.2523 1.36782i −0.649799 0.0486957i
\(790\) 0 0
\(791\) 26.5582 23.5339i 0.944299 0.836771i
\(792\) 0 0
\(793\) −8.15692 20.7835i −0.289661 0.738044i
\(794\) 0 0
\(795\) 20.4573 + 8.02890i 0.725545 + 0.284756i
\(796\) 0