Properties

Label 1008.2.r.e.337.2
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.e.673.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.41421i) q^{3} +(0.724745 - 1.25529i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.41421i) q^{3} +(0.724745 - 1.25529i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{13} +(1.05051 + 2.28024i) q^{15} +2.00000 q^{17} -2.55051 q^{19} +(1.72474 + 0.158919i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(1.44949 + 2.51059i) q^{25} +(5.00000 + 1.41421i) q^{27} +(3.44949 + 5.97469i) q^{29} +(3.00000 - 5.19615i) q^{31} +(-3.44949 - 0.317837i) q^{33} -1.44949 q^{35} +11.7980 q^{37} +(-3.55051 - 7.70674i) q^{39} +(-4.89898 + 8.48528i) q^{41} +(3.44949 + 5.97469i) q^{43} +(-4.27526 - 0.794593i) q^{45} +(4.89898 + 8.48528i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.00000 + 2.82843i) q^{51} -10.8990 q^{53} +2.89898 q^{55} +(2.55051 - 3.60697i) q^{57} +(-1.00000 + 1.73205i) q^{59} +(-3.27526 - 5.67291i) q^{61} +(-1.94949 + 2.28024i) q^{63} +(3.55051 + 6.14966i) q^{65} +(-6.44949 + 11.1708i) q^{67} +(-0.724745 - 1.57313i) q^{69} -0.101021 q^{71} -6.89898 q^{73} +(-5.00000 - 0.460702i) q^{75} +(1.00000 - 1.73205i) q^{77} +(-0.949490 - 1.64456i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +(-11.8990 - 1.09638i) q^{87} -16.8990 q^{89} +4.89898 q^{91} +(4.34847 + 9.43879i) q^{93} +(-1.84847 + 3.20164i) q^{95} +(-1.44949 - 2.51059i) q^{97} +(3.89898 - 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 2q^{5} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 2q^{5} - 2q^{7} - 4q^{9} + 4q^{11} + 14q^{15} + 8q^{17} - 20q^{19} + 2q^{21} - 2q^{23} - 4q^{25} + 20q^{27} + 4q^{29} + 12q^{31} - 4q^{33} + 4q^{35} + 8q^{37} - 24q^{39} + 4q^{43} - 22q^{45} - 2q^{49} - 8q^{51} - 24q^{53} - 8q^{55} + 20q^{57} - 4q^{59} - 18q^{61} + 2q^{63} + 24q^{65} - 16q^{67} + 2q^{69} - 20q^{71} - 8q^{73} - 20q^{75} + 4q^{77} + 6q^{79} - 28q^{81} + 4q^{83} - 4q^{85} - 28q^{87} - 48q^{89} - 12q^{93} + 22q^{95} + 4q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −1.00000 + 1.41421i −0.577350 + 0.816497i
\(4\) 0 0
\(5\) 0.724745 1.25529i 0.324116 0.561385i −0.657217 0.753701i \(-0.728267\pi\)
0.981333 + 0.192316i \(0.0615999\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) −2.44949 + 4.24264i −0.679366 + 1.17670i 0.295806 + 0.955248i \(0.404412\pi\)
−0.975172 + 0.221449i \(0.928921\pi\)
\(14\) 0 0
\(15\) 1.05051 + 2.28024i 0.271241 + 0.588755i
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −2.55051 −0.585127 −0.292564 0.956246i \(-0.594508\pi\)
−0.292564 + 0.956246i \(0.594508\pi\)
\(20\) 0 0
\(21\) 1.72474 + 0.158919i 0.376370 + 0.0346789i
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) 1.44949 + 2.51059i 0.289898 + 0.502118i
\(26\) 0 0
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) 3.44949 + 5.97469i 0.640554 + 1.10947i 0.985309 + 0.170780i \(0.0546286\pi\)
−0.344755 + 0.938693i \(0.612038\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) 0 0
\(33\) −3.44949 0.317837i −0.600479 0.0553284i
\(34\) 0 0
\(35\) −1.44949 −0.245008
\(36\) 0 0
\(37\) 11.7980 1.93957 0.969786 0.243956i \(-0.0784453\pi\)
0.969786 + 0.243956i \(0.0784453\pi\)
\(38\) 0 0
\(39\) −3.55051 7.70674i −0.568537 1.23407i
\(40\) 0 0
\(41\) −4.89898 + 8.48528i −0.765092 + 1.32518i 0.175106 + 0.984550i \(0.443973\pi\)
−0.940198 + 0.340629i \(0.889360\pi\)
\(42\) 0 0
\(43\) 3.44949 + 5.97469i 0.526042 + 0.911132i 0.999540 + 0.0303367i \(0.00965797\pi\)
−0.473497 + 0.880795i \(0.657009\pi\)
\(44\) 0 0
\(45\) −4.27526 0.794593i −0.637317 0.118451i
\(46\) 0 0
\(47\) 4.89898 + 8.48528i 0.714590 + 1.23771i 0.963118 + 0.269081i \(0.0867199\pi\)
−0.248528 + 0.968625i \(0.579947\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −2.00000 + 2.82843i −0.280056 + 0.396059i
\(52\) 0 0
\(53\) −10.8990 −1.49709 −0.748545 0.663084i \(-0.769247\pi\)
−0.748545 + 0.663084i \(0.769247\pi\)
\(54\) 0 0
\(55\) 2.89898 0.390898
\(56\) 0 0
\(57\) 2.55051 3.60697i 0.337823 0.477754i
\(58\) 0 0
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) −3.27526 5.67291i −0.419353 0.726341i 0.576521 0.817082i \(-0.304410\pi\)
−0.995875 + 0.0907408i \(0.971077\pi\)
\(62\) 0 0
\(63\) −1.94949 + 2.28024i −0.245613 + 0.287283i
\(64\) 0 0
\(65\) 3.55051 + 6.14966i 0.440387 + 0.762772i
\(66\) 0 0
\(67\) −6.44949 + 11.1708i −0.787931 + 1.36474i 0.139302 + 0.990250i \(0.455514\pi\)
−0.927233 + 0.374486i \(0.877819\pi\)
\(68\) 0 0
\(69\) −0.724745 1.57313i −0.0872490 0.189383i
\(70\) 0 0
\(71\) −0.101021 −0.0119889 −0.00599446 0.999982i \(-0.501908\pi\)
−0.00599446 + 0.999982i \(0.501908\pi\)
\(72\) 0 0
\(73\) −6.89898 −0.807464 −0.403732 0.914877i \(-0.632287\pi\)
−0.403732 + 0.914877i \(0.632287\pi\)
\(74\) 0 0
\(75\) −5.00000 0.460702i −0.577350 0.0531973i
\(76\) 0 0
\(77\) 1.00000 1.73205i 0.113961 0.197386i
\(78\) 0 0
\(79\) −0.949490 1.64456i −0.106826 0.185028i 0.807657 0.589653i \(-0.200735\pi\)
−0.914483 + 0.404625i \(0.867402\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) 1.44949 2.51059i 0.157219 0.272312i
\(86\) 0 0
\(87\) −11.8990 1.09638i −1.27570 0.117544i
\(88\) 0 0
\(89\) −16.8990 −1.79129 −0.895644 0.444771i \(-0.853285\pi\)
−0.895644 + 0.444771i \(0.853285\pi\)
\(90\) 0 0
\(91\) 4.89898 0.513553
\(92\) 0 0
\(93\) 4.34847 + 9.43879i 0.450915 + 0.978757i
\(94\) 0 0
\(95\) −1.84847 + 3.20164i −0.189649 + 0.328482i
\(96\) 0 0
\(97\) −1.44949 2.51059i −0.147173 0.254912i 0.783008 0.622011i \(-0.213684\pi\)
−0.930182 + 0.367099i \(0.880351\pi\)
\(98\) 0 0
\(99\) 3.89898 4.56048i 0.391862 0.458345i
\(100\) 0 0
\(101\) 8.62372 + 14.9367i 0.858093 + 1.48626i 0.873746 + 0.486383i \(0.161684\pi\)
−0.0156533 + 0.999877i \(0.504983\pi\)
\(102\) 0 0
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) 0 0
\(105\) 1.44949 2.04989i 0.141456 0.200049i
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 12.6969 1.21615 0.608073 0.793881i \(-0.291943\pi\)
0.608073 + 0.793881i \(0.291943\pi\)
\(110\) 0 0
\(111\) −11.7980 + 16.6848i −1.11981 + 1.58365i
\(112\) 0 0
\(113\) 3.05051 5.28364i 0.286968 0.497043i −0.686117 0.727492i \(-0.740686\pi\)
0.973084 + 0.230449i \(0.0740194\pi\)
\(114\) 0 0
\(115\) 0.724745 + 1.25529i 0.0675828 + 0.117057i
\(116\) 0 0
\(117\) 14.4495 + 2.68556i 1.33586 + 0.248280i
\(118\) 0 0
\(119\) −1.00000 1.73205i −0.0916698 0.158777i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −7.10102 15.4135i −0.640277 1.38979i
\(124\) 0 0
\(125\) 11.4495 1.02407
\(126\) 0 0
\(127\) 3.00000 0.266207 0.133103 0.991102i \(-0.457506\pi\)
0.133103 + 0.991102i \(0.457506\pi\)
\(128\) 0 0
\(129\) −11.8990 1.09638i −1.04765 0.0965306i
\(130\) 0 0
\(131\) −4.27526 + 7.40496i −0.373531 + 0.646974i −0.990106 0.140322i \(-0.955186\pi\)
0.616575 + 0.787296i \(0.288520\pi\)
\(132\) 0 0
\(133\) 1.27526 + 2.20881i 0.110579 + 0.191528i
\(134\) 0 0
\(135\) 5.39898 5.25153i 0.464670 0.451980i
\(136\) 0 0
\(137\) −3.89898 6.75323i −0.333112 0.576967i 0.650008 0.759927i \(-0.274765\pi\)
−0.983120 + 0.182960i \(0.941432\pi\)
\(138\) 0 0
\(139\) 2.27526 3.94086i 0.192985 0.334259i −0.753253 0.657730i \(-0.771517\pi\)
0.946238 + 0.323471i \(0.104850\pi\)
\(140\) 0 0
\(141\) −16.8990 1.55708i −1.42315 0.131130i
\(142\) 0 0
\(143\) −9.79796 −0.819346
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) 0 0
\(147\) −0.724745 1.57313i −0.0597759 0.129750i
\(148\) 0 0
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i \(-0.231881\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(152\) 0 0
\(153\) −2.00000 5.65685i −0.161690 0.457330i
\(154\) 0 0
\(155\) −4.34847 7.53177i −0.349277 0.604966i
\(156\) 0 0
\(157\) 4.17423 7.22999i 0.333140 0.577016i −0.649986 0.759947i \(-0.725225\pi\)
0.983126 + 0.182931i \(0.0585584\pi\)
\(158\) 0 0
\(159\) 10.8990 15.4135i 0.864345 1.22237i
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 19.7980 1.55070 0.775348 0.631534i \(-0.217575\pi\)
0.775348 + 0.631534i \(0.217575\pi\)
\(164\) 0 0
\(165\) −2.89898 + 4.09978i −0.225685 + 0.319167i
\(166\) 0 0
\(167\) −5.34847 + 9.26382i −0.413877 + 0.716856i −0.995310 0.0967384i \(-0.969159\pi\)
0.581433 + 0.813594i \(0.302492\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) 0 0
\(171\) 2.55051 + 7.21393i 0.195042 + 0.551663i
\(172\) 0 0
\(173\) 1.55051 + 2.68556i 0.117883 + 0.204180i 0.918929 0.394424i \(-0.129056\pi\)
−0.801045 + 0.598604i \(0.795723\pi\)
\(174\) 0 0
\(175\) 1.44949 2.51059i 0.109571 0.189783i
\(176\) 0 0
\(177\) −1.44949 3.14626i −0.108950 0.236488i
\(178\) 0 0
\(179\) −20.6969 −1.54696 −0.773481 0.633820i \(-0.781486\pi\)
−0.773481 + 0.633820i \(0.781486\pi\)
\(180\) 0 0
\(181\) −10.3485 −0.769196 −0.384598 0.923084i \(-0.625660\pi\)
−0.384598 + 0.923084i \(0.625660\pi\)
\(182\) 0 0
\(183\) 11.2980 + 1.04100i 0.835169 + 0.0769528i
\(184\) 0 0
\(185\) 8.55051 14.8099i 0.628646 1.08885i
\(186\) 0 0
\(187\) 2.00000 + 3.46410i 0.146254 + 0.253320i
\(188\) 0 0
\(189\) −1.27526 5.03723i −0.0927612 0.366405i
\(190\) 0 0
\(191\) 2.05051 + 3.55159i 0.148370 + 0.256984i 0.930625 0.365974i \(-0.119264\pi\)
−0.782255 + 0.622958i \(0.785931\pi\)
\(192\) 0 0
\(193\) 8.94949 15.5010i 0.644198 1.11578i −0.340288 0.940321i \(-0.610524\pi\)
0.984486 0.175463i \(-0.0561422\pi\)
\(194\) 0 0
\(195\) −12.2474 1.12848i −0.877058 0.0808124i
\(196\) 0 0
\(197\) 16.6969 1.18961 0.594804 0.803871i \(-0.297230\pi\)
0.594804 + 0.803871i \(0.297230\pi\)
\(198\) 0 0
\(199\) 2.89898 0.205503 0.102752 0.994707i \(-0.467235\pi\)
0.102752 + 0.994707i \(0.467235\pi\)
\(200\) 0 0
\(201\) −9.34847 20.2918i −0.659390 1.43127i
\(202\) 0 0
\(203\) 3.44949 5.97469i 0.242107 0.419341i
\(204\) 0 0
\(205\) 7.10102 + 12.2993i 0.495957 + 0.859022i
\(206\) 0 0
\(207\) 2.94949 + 0.548188i 0.205004 + 0.0381017i
\(208\) 0 0
\(209\) −2.55051 4.41761i −0.176422 0.305573i
\(210\) 0 0
\(211\) 6.44949 11.1708i 0.444001 0.769033i −0.553981 0.832529i \(-0.686892\pi\)
0.997982 + 0.0634968i \(0.0202253\pi\)
\(212\) 0 0
\(213\) 0.101021 0.142865i 0.00692181 0.00978892i
\(214\) 0 0
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 0 0
\(219\) 6.89898 9.75663i 0.466190 0.659292i
\(220\) 0 0
\(221\) −4.89898 + 8.48528i −0.329541 + 0.570782i
\(222\) 0 0
\(223\) −5.55051 9.61377i −0.371690 0.643785i 0.618136 0.786071i \(-0.287888\pi\)
−0.989826 + 0.142286i \(0.954555\pi\)
\(224\) 0 0
\(225\) 5.65153 6.61037i 0.376769 0.440691i
\(226\) 0 0
\(227\) −2.72474 4.71940i −0.180848 0.313237i 0.761322 0.648374i \(-0.224551\pi\)
−0.942169 + 0.335137i \(0.891217\pi\)
\(228\) 0 0
\(229\) −0.623724 + 1.08032i −0.0412169 + 0.0713897i −0.885898 0.463880i \(-0.846457\pi\)
0.844681 + 0.535270i \(0.179790\pi\)
\(230\) 0 0
\(231\) 1.44949 + 3.14626i 0.0953694 + 0.207009i
\(232\) 0 0
\(233\) −7.00000 −0.458585 −0.229293 0.973358i \(-0.573641\pi\)
−0.229293 + 0.973358i \(0.573641\pi\)
\(234\) 0 0
\(235\) 14.2020 0.926439
\(236\) 0 0
\(237\) 3.27526 + 0.301783i 0.212751 + 0.0196029i
\(238\) 0 0
\(239\) 3.39898 5.88721i 0.219862 0.380812i −0.734904 0.678171i \(-0.762773\pi\)
0.954766 + 0.297360i \(0.0961061\pi\)
\(240\) 0 0
\(241\) −0.449490 0.778539i −0.0289542 0.0501501i 0.851185 0.524865i \(-0.175884\pi\)
−0.880139 + 0.474715i \(0.842551\pi\)
\(242\) 0 0
\(243\) −1.00000 15.5563i −0.0641500 0.997940i
\(244\) 0 0
\(245\) 0.724745 + 1.25529i 0.0463023 + 0.0801979i
\(246\) 0 0
\(247\) 6.24745 10.8209i 0.397516 0.688517i
\(248\) 0 0
\(249\) −3.44949 0.317837i −0.218603 0.0201421i
\(250\) 0 0
\(251\) −17.4495 −1.10140 −0.550701 0.834703i \(-0.685640\pi\)
−0.550701 + 0.834703i \(0.685640\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) 0 0
\(255\) 2.10102 + 4.56048i 0.131571 + 0.285588i
\(256\) 0 0
\(257\) −4.10102 + 7.10318i −0.255815 + 0.443084i −0.965116 0.261821i \(-0.915677\pi\)
0.709302 + 0.704905i \(0.249010\pi\)
\(258\) 0 0
\(259\) −5.89898 10.2173i −0.366545 0.634874i
\(260\) 0 0
\(261\) 13.4495 15.7313i 0.832503 0.973744i
\(262\) 0 0
\(263\) 12.9495 + 22.4292i 0.798500 + 1.38304i 0.920593 + 0.390523i \(0.127706\pi\)
−0.122093 + 0.992519i \(0.538961\pi\)
\(264\) 0 0
\(265\) −7.89898 + 13.6814i −0.485230 + 0.840444i
\(266\) 0 0
\(267\) 16.8990 23.8988i 1.03420 1.46258i
\(268\) 0 0
\(269\) −18.3485 −1.11873 −0.559363 0.828923i \(-0.688954\pi\)
−0.559363 + 0.828923i \(0.688954\pi\)
\(270\) 0 0
\(271\) −7.10102 −0.431356 −0.215678 0.976465i \(-0.569196\pi\)
−0.215678 + 0.976465i \(0.569196\pi\)
\(272\) 0 0
\(273\) −4.89898 + 6.92820i −0.296500 + 0.419314i
\(274\) 0 0
\(275\) −2.89898 + 5.02118i −0.174815 + 0.302789i
\(276\) 0 0
\(277\) 9.34847 + 16.1920i 0.561695 + 0.972884i 0.997349 + 0.0727700i \(0.0231839\pi\)
−0.435654 + 0.900114i \(0.643483\pi\)
\(278\) 0 0
\(279\) −17.6969 3.28913i −1.05949 0.196915i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) 0 0
\(283\) −12.7247 + 22.0399i −0.756408 + 1.31014i 0.188264 + 0.982118i \(0.439714\pi\)
−0.944672 + 0.328018i \(0.893619\pi\)
\(284\) 0 0
\(285\) −2.67934 5.81577i −0.158710 0.344497i
\(286\) 0 0
\(287\) 9.79796 0.578355
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 5.00000 + 0.460702i 0.293105 + 0.0270068i
\(292\) 0 0
\(293\) −1.37628 + 2.38378i −0.0804029 + 0.139262i −0.903423 0.428750i \(-0.858954\pi\)
0.823020 + 0.568012i \(0.192287\pi\)
\(294\) 0 0
\(295\) 1.44949 + 2.51059i 0.0843926 + 0.146172i
\(296\) 0 0
\(297\) 2.55051 + 10.0745i 0.147996 + 0.584580i
\(298\) 0 0
\(299\) −2.44949 4.24264i −0.141658 0.245358i
\(300\) 0 0
\(301\) 3.44949 5.97469i 0.198825 0.344375i
\(302\) 0 0
\(303\) −29.7474 2.74094i −1.70895 0.157463i
\(304\) 0 0
\(305\) −9.49490 −0.543676
\(306\) 0 0
\(307\) −25.2474 −1.44095 −0.720474 0.693482i \(-0.756076\pi\)
−0.720474 + 0.693482i \(0.756076\pi\)
\(308\) 0 0
\(309\) 10.1464 + 22.0239i 0.577210 + 1.25289i
\(310\) 0 0
\(311\) 15.3485 26.5843i 0.870332 1.50746i 0.00867810 0.999962i \(-0.497238\pi\)
0.861654 0.507497i \(-0.169429\pi\)
\(312\) 0 0
\(313\) 2.34847 + 4.06767i 0.132743 + 0.229918i 0.924733 0.380616i \(-0.124288\pi\)
−0.791990 + 0.610534i \(0.790955\pi\)
\(314\) 0 0
\(315\) 1.44949 + 4.09978i 0.0816695 + 0.230996i
\(316\) 0 0
\(317\) −10.3485 17.9241i −0.581228 1.00672i −0.995334 0.0964878i \(-0.969239\pi\)
0.414106 0.910229i \(-0.364094\pi\)
\(318\) 0 0
\(319\) −6.89898 + 11.9494i −0.386269 + 0.669037i
\(320\) 0 0
\(321\) −12.0000 + 16.9706i −0.669775 + 0.947204i
\(322\) 0 0
\(323\) −5.10102 −0.283828
\(324\) 0 0
\(325\) −14.2020 −0.787787
\(326\) 0 0
\(327\) −12.6969 + 17.9562i −0.702142 + 0.992979i
\(328\) 0 0
\(329\) 4.89898 8.48528i 0.270089 0.467809i
\(330\) 0 0
\(331\) 2.34847 + 4.06767i 0.129084 + 0.223579i 0.923322 0.384027i \(-0.125463\pi\)
−0.794238 + 0.607606i \(0.792130\pi\)
\(332\) 0 0
\(333\) −11.7980 33.3697i −0.646524 1.82865i
\(334\) 0 0
\(335\) 9.34847 + 16.1920i 0.510761 + 0.884665i
\(336\) 0 0
\(337\) 11.6969 20.2597i 0.637173 1.10362i −0.348877 0.937168i \(-0.613437\pi\)
0.986050 0.166447i \(-0.0532296\pi\)
\(338\) 0 0
\(339\) 4.42168 + 9.59771i 0.240153 + 0.521276i
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −2.50000 0.230351i −0.134595 0.0124017i
\(346\) 0 0
\(347\) 9.79796 16.9706i 0.525982 0.911028i −0.473560 0.880762i \(-0.657031\pi\)
0.999542 0.0302659i \(-0.00963541\pi\)
\(348\) 0 0
\(349\) −5.55051 9.61377i −0.297112 0.514613i 0.678362 0.734728i \(-0.262690\pi\)
−0.975474 + 0.220115i \(0.929357\pi\)
\(350\) 0 0
\(351\) −18.2474 + 17.7491i −0.973977 + 0.947377i
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) −0.0732141 + 0.126811i −0.00388580 + 0.00673040i
\(356\) 0 0
\(357\) 3.44949 + 0.317837i 0.182566 + 0.0168217i
\(358\) 0 0
\(359\) 8.79796 0.464339 0.232169 0.972675i \(-0.425418\pi\)
0.232169 + 0.972675i \(0.425418\pi\)
\(360\) 0 0
\(361\) −12.4949 −0.657626
\(362\) 0 0
\(363\) 5.07321 + 11.0119i 0.266275 + 0.577976i
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) 0 0
\(367\) −6.89898 11.9494i −0.360124 0.623753i 0.627857 0.778329i \(-0.283932\pi\)
−0.987981 + 0.154576i \(0.950599\pi\)
\(368\) 0 0
\(369\) 28.8990 + 5.37113i 1.50442 + 0.279610i
\(370\) 0 0
\(371\) 5.44949 + 9.43879i 0.282923 + 0.490038i
\(372\) 0 0
\(373\) 3.44949 5.97469i 0.178608 0.309358i −0.762796 0.646639i \(-0.776174\pi\)
0.941404 + 0.337281i \(0.109507\pi\)
\(374\) 0 0
\(375\) −11.4495 + 16.1920i −0.591249 + 0.836153i
\(376\) 0 0
\(377\) −33.7980 −1.74068
\(378\) 0 0
\(379\) −22.4949 −1.15549 −0.577743 0.816219i \(-0.696066\pi\)
−0.577743 + 0.816219i \(0.696066\pi\)
\(380\) 0 0
\(381\) −3.00000 + 4.24264i −0.153695 + 0.217357i
\(382\) 0 0
\(383\) −1.44949 + 2.51059i −0.0740655 + 0.128285i −0.900679 0.434484i \(-0.856931\pi\)
0.826614 + 0.562769i \(0.190264\pi\)
\(384\) 0 0
\(385\) −1.44949 2.51059i −0.0738728 0.127952i
\(386\) 0 0
\(387\) 13.4495 15.7313i 0.683676 0.799668i
\(388\) 0 0
\(389\) 12.4495 + 21.5631i 0.631214 + 1.09330i 0.987304 + 0.158843i \(0.0507764\pi\)
−0.356090 + 0.934452i \(0.615890\pi\)
\(390\) 0 0
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) −6.19694 13.4511i −0.312594 0.678517i
\(394\) 0 0
\(395\) −2.75255 −0.138496
\(396\) 0 0
\(397\) 38.6969 1.94214 0.971072 0.238788i \(-0.0767500\pi\)
0.971072 + 0.238788i \(0.0767500\pi\)
\(398\) 0 0
\(399\) −4.39898 0.405324i −0.220224 0.0202916i
\(400\) 0 0
\(401\) 9.94949 17.2330i 0.496854 0.860576i −0.503140 0.864205i \(-0.667822\pi\)
0.999993 + 0.00362911i \(0.00115518\pi\)
\(402\) 0 0
\(403\) 14.6969 + 25.4558i 0.732107 + 1.26805i
\(404\) 0 0
\(405\) 2.02781 + 12.8868i 0.100763 + 0.640352i
\(406\) 0 0
\(407\) 11.7980 + 20.4347i 0.584803 + 1.01291i
\(408\) 0 0
\(409\) 6.89898 11.9494i 0.341133 0.590859i −0.643511 0.765437i \(-0.722523\pi\)
0.984643 + 0.174578i \(0.0558562\pi\)
\(410\) 0 0
\(411\) 13.4495 + 1.23924i 0.663414 + 0.0611272i
\(412\) 0 0
\(413\) 2.00000 0.0984136
\(414\) 0 0
\(415\) 2.89898 0.142305
\(416\) 0 0
\(417\) 3.29796 + 7.15855i 0.161502 + 0.350556i
\(418\) 0 0
\(419\) 14.7247 25.5040i 0.719351 1.24595i −0.241906 0.970300i \(-0.577773\pi\)
0.961257 0.275653i \(-0.0888940\pi\)
\(420\) 0 0
\(421\) −11.4495 19.8311i −0.558014 0.966509i −0.997662 0.0683385i \(-0.978230\pi\)
0.439648 0.898170i \(-0.355103\pi\)
\(422\) 0 0
\(423\) 19.1010 22.3417i 0.928723 1.08629i
\(424\) 0 0
\(425\) 2.89898 + 5.02118i 0.140621 + 0.243563i
\(426\) 0 0
\(427\) −3.27526 + 5.67291i −0.158501 + 0.274531i
\(428\) 0 0
\(429\) 9.79796 13.8564i 0.473050 0.668994i
\(430\) 0 0
\(431\) −31.5959 −1.52192 −0.760961 0.648798i \(-0.775272\pi\)
−0.760961 + 0.648798i \(0.775272\pi\)
\(432\) 0 0
\(433\) −7.79796 −0.374746 −0.187373 0.982289i \(-0.559997\pi\)
−0.187373 + 0.982289i \(0.559997\pi\)
\(434\) 0 0
\(435\) −10.0000 + 14.1421i −0.479463 + 0.678064i
\(436\) 0 0
\(437\) 1.27526 2.20881i 0.0610037 0.105662i
\(438\) 0 0
\(439\) 1.10102 + 1.90702i 0.0525488 + 0.0910173i 0.891103 0.453801i \(-0.149932\pi\)
−0.838554 + 0.544818i \(0.816599\pi\)
\(440\) 0 0
\(441\) 2.94949 + 0.548188i 0.140452 + 0.0261042i
\(442\) 0 0
\(443\) −7.44949 12.9029i −0.353936 0.613035i 0.632999 0.774152i \(-0.281824\pi\)
−0.986935 + 0.161117i \(0.948490\pi\)
\(444\) 0 0
\(445\) −12.2474 + 21.2132i −0.580585 + 1.00560i
\(446\) 0 0
\(447\) 4.34847 + 9.43879i 0.205676 + 0.446440i
\(448\) 0 0
\(449\) 20.5959 0.971981 0.485991 0.873964i \(-0.338459\pi\)
0.485991 + 0.873964i \(0.338459\pi\)
\(450\) 0 0
\(451\) −19.5959 −0.922736
\(452\) 0 0
\(453\) 8.62372 + 0.794593i 0.405178 + 0.0373332i
\(454\) 0 0
\(455\) 3.55051 6.14966i 0.166450 0.288301i
\(456\) 0 0
\(457\) 8.74745 + 15.1510i 0.409188 + 0.708735i 0.994799 0.101857i \(-0.0324785\pi\)
−0.585611 + 0.810593i \(0.699145\pi\)
\(458\) 0 0
\(459\) 10.0000 + 2.82843i 0.466760 + 0.132020i
\(460\) 0 0
\(461\) −2.82577 4.89437i −0.131609 0.227954i 0.792688 0.609628i \(-0.208681\pi\)
−0.924297 + 0.381674i \(0.875348\pi\)
\(462\) 0 0
\(463\) 1.84847 3.20164i 0.0859057 0.148793i −0.819871 0.572548i \(-0.805955\pi\)
0.905777 + 0.423755i \(0.139288\pi\)
\(464\) 0 0
\(465\) 15.0000 + 1.38211i 0.695608 + 0.0640936i
\(466\) 0 0
\(467\) −10.0000 −0.462745 −0.231372 0.972865i \(-0.574322\pi\)
−0.231372 + 0.972865i \(0.574322\pi\)
\(468\) 0 0
\(469\) 12.8990 0.595620
\(470\) 0 0
\(471\) 6.05051 + 13.1332i 0.278793 + 0.605148i
\(472\) 0 0
\(473\) −6.89898 + 11.9494i −0.317215 + 0.549433i
\(474\) 0 0
\(475\) −3.69694 6.40329i −0.169627 0.293803i
\(476\) 0 0
\(477\) 10.8990 + 30.8270i 0.499030 + 1.41147i
\(478\) 0 0
\(479\) 4.79796 + 8.31031i 0.219224 + 0.379708i 0.954571 0.297983i \(-0.0963140\pi\)
−0.735347 + 0.677691i \(0.762981\pi\)
\(480\) 0 0
\(481\) −28.8990 + 50.0545i −1.31768 + 2.28229i
\(482\) 0 0
\(483\) −1.00000 + 1.41421i −0.0455016 + 0.0643489i
\(484\) 0 0
\(485\) −4.20204 −0.190805
\(486\) 0 0
\(487\) 36.3939 1.64916 0.824582 0.565742i \(-0.191410\pi\)
0.824582 + 0.565742i \(0.191410\pi\)
\(488\) 0 0
\(489\) −19.7980 + 27.9985i −0.895295 + 1.26614i
\(490\) 0 0
\(491\) 7.89898 13.6814i 0.356476 0.617434i −0.630893 0.775869i \(-0.717312\pi\)
0.987369 + 0.158435i \(0.0506448\pi\)
\(492\) 0 0
\(493\) 6.89898 + 11.9494i 0.310714 + 0.538173i
\(494\) 0 0
\(495\) −2.89898 8.19955i −0.130299 0.368542i
\(496\) 0 0
\(497\) 0.0505103 + 0.0874863i 0.00226569 + 0.00392430i
\(498\) 0 0
\(499\) −12.6969 + 21.9917i −0.568393 + 0.984486i 0.428332 + 0.903621i \(0.359101\pi\)
−0.996725 + 0.0808642i \(0.974232\pi\)
\(500\) 0 0
\(501\) −7.75255 16.8277i −0.346358 0.751806i
\(502\) 0 0
\(503\) 24.4949 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) 0 0
\(507\) 18.9722 + 1.74810i 0.842585 + 0.0776361i
\(508\) 0 0
\(509\) 3.55051 6.14966i 0.157374 0.272579i −0.776547 0.630059i \(-0.783031\pi\)
0.933921 + 0.357480i \(0.116364\pi\)
\(510\) 0 0
\(511\) 3.44949 + 5.97469i 0.152596 + 0.264305i
\(512\) 0 0
\(513\) −12.7526 3.60697i −0.563039 0.159251i
\(514\) 0 0
\(515\) −10.1464 17.5741i −0.447105 0.774409i
\(516\) 0 0
\(517\) −9.79796 + 16.9706i −0.430914 + 0.746364i
\(518\) 0 0
\(519\) −5.34847 0.492810i −0.234772 0.0216320i
\(520\) 0 0
\(521\) −9.30306 −0.407575 −0.203787 0.979015i \(-0.565325\pi\)
−0.203787 + 0.979015i \(0.565325\pi\)
\(522\) 0 0
\(523\) 14.3485 0.627415 0.313707 0.949520i \(-0.398429\pi\)
0.313707 + 0.949520i \(0.398429\pi\)
\(524\) 0 0
\(525\) 2.10102 + 4.56048i 0.0916961 + 0.199036i
\(526\) 0 0
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 5.89898 + 1.09638i 0.255994 + 0.0475787i
\(532\) 0 0
\(533\) −24.0000 41.5692i −1.03956 1.80056i
\(534\) 0 0
\(535\) 8.69694 15.0635i 0.376001 0.651254i
\(536\) 0 0
\(537\) 20.6969 29.2699i 0.893139 1.26309i
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −18.4949 −0.795158 −0.397579 0.917568i \(-0.630149\pi\)
−0.397579 + 0.917568i \(0.630149\pi\)
\(542\) 0 0
\(543\) 10.3485 14.6349i 0.444095 0.628046i
\(544\) 0 0
\(545\) 9.20204 15.9384i 0.394172 0.682726i
\(546\) 0 0
\(547\) −3.79796 6.57826i −0.162389 0.281266i 0.773336 0.633996i \(-0.218587\pi\)
−0.935725 + 0.352730i \(0.885253\pi\)
\(548\) 0 0
\(549\) −12.7702 + 14.9367i −0.545017 + 0.637484i
\(550\) 0 0
\(551\) −8.79796 15.2385i −0.374806 0.649182i
\(552\) 0 0
\(553\) −0.949490 + 1.64456i −0.0403764 + 0.0699340i
\(554\) 0 0
\(555\) 12.3939 + 26.9022i 0.526091 + 1.14193i
\(556\) 0 0
\(557\) −12.8990 −0.546547 −0.273274 0.961936i \(-0.588106\pi\)
−0.273274 + 0.961936i \(0.588106\pi\)
\(558\) 0 0
\(559\) −33.7980 −1.42950
\(560\) 0 0
\(561\) −6.89898 0.635674i −0.291275 0.0268382i
\(562\) 0 0
\(563\) −19.9722 + 34.5929i −0.841728 + 1.45791i 0.0467054 + 0.998909i \(0.485128\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(564\) 0 0
\(565\) −4.42168 7.65858i −0.186022 0.322199i
\(566\) 0 0
\(567\) 8.39898 + 3.23375i 0.352724 + 0.135805i
\(568\) 0 0
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 0 0
\(571\) 16.8990 29.2699i 0.707200 1.22491i −0.258691 0.965960i \(-0.583291\pi\)
0.965892 0.258947i \(-0.0833754\pi\)
\(572\) 0 0
\(573\) −7.07321 0.651729i −0.295488 0.0272263i
\(574\) 0 0
\(575\) −2.89898 −0.120896
\(576\) 0 0
\(577\) −15.5959 −0.649267 −0.324633 0.945840i \(-0.605241\pi\)
−0.324633 + 0.945840i \(0.605241\pi\)
\(578\) 0 0
\(579\) 12.9722 + 28.1575i 0.539106 + 1.17018i
\(580\) 0 0
\(581\) 1.00000 1.73205i 0.0414870 0.0718576i
\(582\) 0 0
\(583\) −10.8990 18.8776i −0.451390 0.781830i
\(584\) 0 0
\(585\) 13.8434 16.1920i 0.572353 0.669458i
\(586\) 0 0
\(587\) 8.07321 + 13.9832i 0.333217 + 0.577149i 0.983141 0.182850i \(-0.0585324\pi\)
−0.649924 + 0.760000i \(0.725199\pi\)
\(588\) 0 0
\(589\) −7.65153 + 13.2528i −0.315276 + 0.546074i
\(590\) 0 0
\(591\) −16.6969 + 23.6130i −0.686820 + 0.971311i
\(592\) 0 0
\(593\) 14.6969 0.603531 0.301765 0.953382i \(-0.402424\pi\)
0.301765 + 0.953382i \(0.402424\pi\)
\(594\) 0 0
\(595\) −2.89898 −0.118847
\(596\) 0 0
\(597\) −2.89898 + 4.09978i −0.118647 + 0.167793i
\(598\) 0 0
\(599\) −16.8990 + 29.2699i −0.690474 + 1.19594i 0.281209 + 0.959646i \(0.409264\pi\)
−0.971683 + 0.236289i \(0.924069\pi\)
\(600\) 0 0
\(601\) −8.34847 14.4600i −0.340541 0.589835i 0.643992 0.765032i \(-0.277277\pi\)
−0.984533 + 0.175198i \(0.943944\pi\)
\(602\) 0 0
\(603\) 38.0454 + 7.07107i 1.54933 + 0.287956i
\(604\) 0 0
\(605\) −5.07321 8.78706i −0.206255 0.357245i
\(606\) 0 0
\(607\) 10.3485 17.9241i 0.420031 0.727516i −0.575911 0.817513i \(-0.695352\pi\)
0.995942 + 0.0899969i \(0.0286857\pi\)
\(608\) 0 0
\(609\) 5.00000 + 10.8530i 0.202610 + 0.439786i
\(610\) 0 0
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) −14.6969 −0.593604 −0.296802 0.954939i \(-0.595920\pi\)
−0.296802 + 0.954939i \(0.595920\pi\)
\(614\) 0 0
\(615\) −24.4949 2.25697i −0.987730 0.0910098i
\(616\) 0 0
\(617\) 7.69694 13.3315i 0.309867 0.536706i −0.668466 0.743743i \(-0.733049\pi\)
0.978333 + 0.207037i \(0.0663821\pi\)
\(618\) 0 0
\(619\) 15.0732 + 26.1076i 0.605844 + 1.04935i 0.991918 + 0.126884i \(0.0404976\pi\)
−0.386074 + 0.922468i \(0.626169\pi\)
\(620\) 0 0
\(621\) −3.72474 + 3.62302i −0.149469 + 0.145387i
\(622\) 0 0
\(623\) 8.44949 + 14.6349i 0.338522 + 0.586337i
\(624\) 0 0
\(625\) 1.05051 1.81954i 0.0420204 0.0727815i
\(626\) 0 0
\(627\) 8.79796 + 0.810647i 0.351357 + 0.0323741i
\(628\) 0 0
\(629\) 23.5959 0.940831
\(630\) 0 0
\(631\) −27.8990 −1.11064 −0.555320 0.831636i \(-0.687404\pi\)
−0.555320 + 0.831636i \(0.687404\pi\)
\(632\) 0 0
\(633\) 9.34847 + 20.2918i 0.371568 + 0.806527i
\(634\) 0 0
\(635\) 2.17423 3.76588i 0.0862819 0.149445i
\(636\) 0 0
\(637\) −2.44949 4.24264i −0.0970523 0.168100i
\(638\) 0 0
\(639\) 0.101021 + 0.285729i 0.00399631 + 0.0113033i
\(640\) 0 0
\(641\) 3.74745 + 6.49077i 0.148015 + 0.256370i 0.930494 0.366308i \(-0.119378\pi\)
−0.782479 + 0.622678i \(0.786045\pi\)
\(642\) 0 0
\(643\) −19.6969 + 34.1161i −0.776771 + 1.34541i 0.157022 + 0.987595i \(0.449811\pi\)
−0.933793 + 0.357812i \(0.883523\pi\)
\(644\) 0 0
\(645\) −10.0000 + 14.1421i −0.393750 + 0.556846i
\(646\) 0 0
\(647\) 50.6969 1.99310 0.996551 0.0829807i \(-0.0264440\pi\)
0.996551 + 0.0829807i \(0.0264440\pi\)
\(648\) 0 0
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) 6.00000 8.48528i 0.235159 0.332564i
\(652\) 0 0
\(653\) −4.89898 + 8.48528i −0.191712 + 0.332055i −0.945818 0.324698i \(-0.894737\pi\)
0.754106 + 0.656753i \(0.228071\pi\)
\(654\) 0 0
\(655\) 6.19694 + 10.7334i 0.242134 + 0.419389i
\(656\) 0 0
\(657\) 6.89898 + 19.5133i 0.269155 + 0.761285i
\(658\) 0 0
\(659\) −12.3485 21.3882i −0.481028 0.833165i 0.518735 0.854935i \(-0.326403\pi\)
−0.999763 + 0.0217701i \(0.993070\pi\)
\(660\) 0 0
\(661\) −2.27526 + 3.94086i −0.0884972 + 0.153282i −0.906876 0.421397i \(-0.861540\pi\)
0.818379 + 0.574679i \(0.194873\pi\)
\(662\) 0 0
\(663\) −7.10102 15.4135i −0.275781 0.598610i
\(664\) 0 0
\(665\) 3.69694 0.143361
\(666\) 0 0
\(667\) −6.89898 −0.267130
\(668\) 0 0
\(669\) 19.1464 + 1.76416i 0.740244 + 0.0682063i
\(670\) 0 0
\(671\) 6.55051 11.3458i 0.252880 0.438000i
\(672\) 0 0
\(673\) 4.29796 + 7.44428i 0.165674 + 0.286956i 0.936894 0.349612i \(-0.113687\pi\)
−0.771220 + 0.636568i \(0.780353\pi\)
\(674\) 0 0
\(675\) 3.69694 + 14.6028i 0.142295 + 0.562063i
\(676\) 0 0
\(677\) −7.34847 12.7279i −0.282425 0.489174i 0.689557 0.724232i \(-0.257805\pi\)
−0.971981 + 0.235058i \(0.924472\pi\)
\(678\) 0 0
\(679\) −1.44949 + 2.51059i −0.0556263 + 0.0963476i
\(680\) 0 0
\(681\) 9.39898 + 0.866025i 0.360170 + 0.0331862i
\(682\) 0 0
\(683\) −51.7980 −1.98199 −0.990997 0.133885i \(-0.957255\pi\)
−0.990997 + 0.133885i \(0.957255\pi\)
\(684\) 0 0
\(685\) −11.3031 −0.431868
\(686\) 0 0
\(687\) −0.904082 1.96240i −0.0344929 0.0748703i
\(688\) 0 0
\(689\) 26.6969 46.2405i 1.01707 1.76162i
\(690\) 0 0
\(691\) 25.5227 + 44.2066i 0.970929 + 1.68170i 0.692762 + 0.721167i \(0.256394\pi\)
0.278168 + 0.960533i \(0.410273\pi\)
\(692\) 0 0
\(693\) −5.89898 1.09638i −0.224084 0.0416479i
\(694\) 0 0
\(695\) −3.29796 5.71223i −0.125099 0.216677i
\(696\) 0 0
\(697\) −9.79796 + 16.9706i −0.371124 + 0.642806i
\(698\) 0 0
\(699\) 7.00000 9.89949i 0.264764 0.374433i
\(700\) 0 0
\(701\) −7.39388 −0.279263 −0.139631 0.990204i \(-0.544592\pi\)
−0.139631 + 0.990204i \(0.544592\pi\)
\(702\) 0 0
\(703\) −30.0908 −1.13490
\(704\) 0 0
\(705\) −14.2020 + 20.0847i −0.534880 + 0.756434i
\(706\) 0 0
\(707\) 8.62372 14.9367i 0.324329 0.561754i
\(708\) 0 0
\(709\) −13.7980 23.8988i −0.518193 0.897537i −0.999777 0.0211367i \(-0.993271\pi\)
0.481583 0.876400i \(-0.340062\pi\)
\(710\) 0 0
\(711\) −3.70204 + 4.33013i −0.138837 + 0.162392i
\(712\) 0 0
\(713\) 3.00000 + 5.19615i 0.112351 + 0.194597i
\(714\) 0 0
\(715\) −7.10102 + 12.2993i −0.265563 + 0.459969i
\(716\) 0 0
\(717\) 4.92679 + 10.6941i 0.183994 + 0.399378i
\(718\) 0 0
\(719\) −9.79796 −0.365402 −0.182701 0.983169i \(-0.558484\pi\)
−0.182701 + 0.983169i \(0.558484\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 1.55051 + 0.142865i 0.0576641 + 0.00531319i
\(724\) 0 0
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) 0 0
\(727\) −4.24745 7.35680i −0.157529 0.272848i 0.776448 0.630181i \(-0.217019\pi\)
−0.933977 + 0.357333i \(0.883686\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) 6.89898 + 11.9494i 0.255168 + 0.441964i
\(732\) 0 0
\(733\) 8.72474 15.1117i 0.322256 0.558163i −0.658697 0.752408i \(-0.728892\pi\)
0.980953 + 0.194245i \(0.0622255\pi\)
\(734\) 0 0
\(735\) −2.50000 0.230351i −0.0922139 0.00849662i
\(736\) 0 0
\(737\) −25.7980 −0.950280
\(738\) 0 0
\(739\) −13.5959 −0.500134 −0.250067 0.968229i \(-0.580453\pi\)
−0.250067 + 0.968229i \(0.580453\pi\)
\(740\) 0 0
\(741\) 9.05561 + 19.6561i 0.332666 + 0.722086i
\(742\) 0 0
\(743\) 18.0000 31.1769i 0.660356 1.14377i −0.320166 0.947361i \(-0.603739\pi\)
0.980522 0.196409i \(-0.0629279\pi\)
\(744\) 0 0
\(745\) −4.34847 7.53177i −0.159316 0.275943i
\(746\) 0 0
\(747\) 3.89898 4.56048i 0.142656 0.166859i
\(748\) 0 0
\(749\) −6.00000 10.3923i −0.219235 0.379727i
\(750\) 0 0
\(751\) 0.702041 1.21597i 0.0256178 0.0443714i −0.852932 0.522022i \(-0.825178\pi\)
0.878550 + 0.477650i \(0.158511\pi\)
\(752\) 0 0
\(753\) 17.4495 24.6773i 0.635895 0.899291i
\(754\) 0 0
\(755\) −7.24745 −0.263762
\(756\) 0 0
\(757\) −35.3939 −1.28641 −0.643206 0.765693i \(-0.722396\pi\)
−0.643206 + 0.765693i \(0.722396\pi\)
\(758\) 0 0
\(759\) 2.00000 2.82843i 0.0725954 0.102665i
\(760\) 0 0
\(761\) −1.00000 + 1.73205i −0.0362500 + 0.0627868i −0.883581 0.468278i \(-0.844875\pi\)
0.847331 + 0.531065i \(0.178208\pi\)
\(762\) 0 0
\(763\) −6.34847 10.9959i −0.229830 0.398077i
\(764\) 0 0
\(765\) −8.55051 1.58919i −0.309144 0.0574571i
\(766\) 0 0
\(767\) −4.89898 8.48528i −0.176892 0.306386i
\(768\) 0 0
\(769\) 17.0454 29.5235i 0.614673 1.06465i −0.375769 0.926714i \(-0.622621\pi\)
0.990442 0.137932i \(-0.0440454\pi\)
\(770\) 0 0
\(771\) −5.94439 12.9029i −0.214082 0.464686i
\(772\) 0 0
\(773\) 33.9444 1.22089 0.610447 0.792057i \(-0.290990\pi\)
0.610447 + 0.792057i \(0.290990\pi\)
\(774\) 0 0
\(775\) 17.3939 0.624807
\(776\) 0 0
\(777\) 20.3485 + 1.87492i 0.729997 + 0.0672622i
\(778\) 0 0
\(779\) 12.4949 21.6418i 0.447676 0.775398i
\(780\) 0 0
\(781\) −0.101021 0.174973i −0.00361480 0.00626101i
\(782\) 0 0
\(783\) 8.79796 + 34.7518i 0.314413 + 1.24193i
\(784\) 0 0
\(785\) −6.05051 10.4798i −0.215952 0.374040i
\(786\) 0 0
\(787\) −5.69694 + 9.86739i −0.203074 + 0.351734i −0.949517 0.313715i \(-0.898427\pi\)
0.746443 + 0.665449i \(0.231760\pi\)
\(788\) 0 0
\(789\) −44.6691 4.11583i −1.59026 0.146527i
\(790\) 0 0
\(791\) −6.10102 −0.216927
\(792\) 0 0
\(793\) 32.0908 1.13958
\(794\) 0 0
\(795\) −11.4495 24.8523i −0.406072 0.881419i
\(796\) 0 0
\(797\) 8.97219 15.5403i 0.317811 0.550465i −0.662220 0.749310i \(-0.730385\pi\)
0.980031 + 0.198844i \(0.0637188\pi\)
\(798\) 0 0
\(799\) 9.79796 + 16.9706i 0.346627 + 0.600375i
\(800\) 0 0
\(801\) 16.8990 + 47.7975i 0.597096 + 1.68884i
\(802\) 0 0
\(803\) −6.89898 11.9494i −0.243460