Properties

Label 456.2.q.f.49.1
Level $456$
Weight $2$
Character 456.49
Analytic conductor $3.641$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 456.49
Dual form 456.2.q.f.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.53209 + 2.65366i) q^{5} -2.06418 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.53209 + 2.65366i) q^{5} -2.06418 q^{7} +(-0.500000 - 0.866025i) q^{9} -6.45336 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.53209 + 2.65366i) q^{15} +(-0.694593 + 1.20307i) q^{17} +(-3.75877 - 2.20718i) q^{19} +(-1.03209 + 1.78763i) q^{21} +(-1.53209 - 2.65366i) q^{23} +(-2.19459 - 3.80115i) q^{25} -1.00000 q^{27} +(1.75877 + 3.04628i) q^{29} +9.45336 q^{31} +(-3.22668 + 5.58878i) q^{33} +(3.16250 - 5.47762i) q^{35} -2.38919 q^{37} -1.00000 q^{39} +(-5.06418 + 8.77141i) q^{41} +(-3.03209 + 5.25173i) q^{43} +3.06418 q^{45} +(3.00000 + 5.19615i) q^{47} -2.73917 q^{49} +(0.694593 + 1.20307i) q^{51} +(5.29086 + 9.16404i) q^{53} +(9.88713 - 17.1250i) q^{55} +(-3.79086 + 2.15160i) q^{57} +(5.59627 - 9.69302i) q^{59} +(-2.56418 - 4.44129i) q^{61} +(1.03209 + 1.78763i) q^{63} +3.06418 q^{65} +(-1.72668 - 2.99070i) q^{67} -3.06418 q^{69} +(-3.36959 + 5.83629i) q^{71} +(4.56418 - 7.90539i) q^{73} -4.38919 q^{75} +13.3209 q^{77} +(0.790859 - 1.36981i) q^{79} +(-0.500000 + 0.866025i) q^{81} -17.6459 q^{83} +(-2.12836 - 3.68642i) q^{85} +3.51754 q^{87} +(-5.22668 - 9.05288i) q^{89} +(1.03209 + 1.78763i) q^{91} +(4.72668 - 8.18685i) q^{93} +(11.6159 - 6.59289i) q^{95} +(-3.36959 + 5.83629i) q^{97} +(3.22668 + 5.58878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} - 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} - 6 q^{27} - 12 q^{29} + 30 q^{31} - 6 q^{33} + 24 q^{35} - 6 q^{37} - 6 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{47} + 12 q^{49} + 9 q^{57} + 6 q^{59} + 3 q^{61} - 3 q^{63} + 3 q^{67} - 6 q^{71} + 9 q^{73} - 18 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 24 q^{83} + 24 q^{85} - 24 q^{87} - 18 q^{89} - 3 q^{91} + 15 q^{93} + 48 q^{95} - 6 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −1.53209 + 2.65366i −0.685171 + 1.18675i 0.288212 + 0.957567i \(0.406939\pi\)
−0.973383 + 0.229184i \(0.926394\pi\)
\(6\) 0 0
\(7\) −2.06418 −0.780186 −0.390093 0.920775i \(-0.627557\pi\)
−0.390093 + 0.920775i \(0.627557\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −6.45336 −1.94576 −0.972881 0.231306i \(-0.925700\pi\)
−0.972881 + 0.231306i \(0.925700\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 1.53209 + 2.65366i 0.395584 + 0.685171i
\(16\) 0 0
\(17\) −0.694593 + 1.20307i −0.168463 + 0.291787i −0.937880 0.346960i \(-0.887214\pi\)
0.769416 + 0.638748i \(0.220547\pi\)
\(18\) 0 0
\(19\) −3.75877 2.20718i −0.862321 0.506362i
\(20\) 0 0
\(21\) −1.03209 + 1.78763i −0.225220 + 0.390093i
\(22\) 0 0
\(23\) −1.53209 2.65366i −0.319463 0.553325i 0.660913 0.750462i \(-0.270169\pi\)
−0.980376 + 0.197137i \(0.936836\pi\)
\(24\) 0 0
\(25\) −2.19459 3.80115i −0.438919 0.760229i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.75877 + 3.04628i 0.326595 + 0.565680i 0.981834 0.189742i \(-0.0607652\pi\)
−0.655238 + 0.755422i \(0.727432\pi\)
\(30\) 0 0
\(31\) 9.45336 1.69787 0.848937 0.528494i \(-0.177243\pi\)
0.848937 + 0.528494i \(0.177243\pi\)
\(32\) 0 0
\(33\) −3.22668 + 5.58878i −0.561693 + 0.972881i
\(34\) 0 0
\(35\) 3.16250 5.47762i 0.534561 0.925886i
\(36\) 0 0
\(37\) −2.38919 −0.392780 −0.196390 0.980526i \(-0.562922\pi\)
−0.196390 + 0.980526i \(0.562922\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −5.06418 + 8.77141i −0.790892 + 1.36986i 0.134524 + 0.990910i \(0.457050\pi\)
−0.925415 + 0.378954i \(0.876284\pi\)
\(42\) 0 0
\(43\) −3.03209 + 5.25173i −0.462389 + 0.800882i −0.999079 0.0428977i \(-0.986341\pi\)
0.536690 + 0.843779i \(0.319674\pi\)
\(44\) 0 0
\(45\) 3.06418 0.456781
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) −2.73917 −0.391310
\(50\) 0 0
\(51\) 0.694593 + 1.20307i 0.0972624 + 0.168463i
\(52\) 0 0
\(53\) 5.29086 + 9.16404i 0.726755 + 1.25878i 0.958247 + 0.285941i \(0.0923060\pi\)
−0.231492 + 0.972837i \(0.574361\pi\)
\(54\) 0 0
\(55\) 9.88713 17.1250i 1.33318 2.30914i
\(56\) 0 0
\(57\) −3.79086 + 2.15160i −0.502112 + 0.284986i
\(58\) 0 0
\(59\) 5.59627 9.69302i 0.728572 1.26192i −0.228915 0.973446i \(-0.573518\pi\)
0.957487 0.288477i \(-0.0931489\pi\)
\(60\) 0 0
\(61\) −2.56418 4.44129i −0.328309 0.568648i 0.653867 0.756609i \(-0.273146\pi\)
−0.982177 + 0.187961i \(0.939812\pi\)
\(62\) 0 0
\(63\) 1.03209 + 1.78763i 0.130031 + 0.225220i
\(64\) 0 0
\(65\) 3.06418 0.380064
\(66\) 0 0
\(67\) −1.72668 2.99070i −0.210948 0.365372i 0.741064 0.671435i \(-0.234322\pi\)
−0.952011 + 0.306063i \(0.900988\pi\)
\(68\) 0 0
\(69\) −3.06418 −0.368884
\(70\) 0 0
\(71\) −3.36959 + 5.83629i −0.399896 + 0.692640i −0.993713 0.111960i \(-0.964287\pi\)
0.593817 + 0.804600i \(0.297620\pi\)
\(72\) 0 0
\(73\) 4.56418 7.90539i 0.534197 0.925256i −0.465005 0.885308i \(-0.653948\pi\)
0.999202 0.0399477i \(-0.0127191\pi\)
\(74\) 0 0
\(75\) −4.38919 −0.506819
\(76\) 0 0
\(77\) 13.3209 1.51806
\(78\) 0 0
\(79\) 0.790859 1.36981i 0.0889786 0.154116i −0.818101 0.575075i \(-0.804973\pi\)
0.907080 + 0.420959i \(0.138306\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −17.6459 −1.93689 −0.968444 0.249230i \(-0.919823\pi\)
−0.968444 + 0.249230i \(0.919823\pi\)
\(84\) 0 0
\(85\) −2.12836 3.68642i −0.230853 0.399848i
\(86\) 0 0
\(87\) 3.51754 0.377120
\(88\) 0 0
\(89\) −5.22668 9.05288i −0.554027 0.959603i −0.997979 0.0635523i \(-0.979757\pi\)
0.443951 0.896051i \(-0.353576\pi\)
\(90\) 0 0
\(91\) 1.03209 + 1.78763i 0.108192 + 0.187395i
\(92\) 0 0
\(93\) 4.72668 8.18685i 0.490134 0.848937i
\(94\) 0 0
\(95\) 11.6159 6.59289i 1.19176 0.676416i
\(96\) 0 0
\(97\) −3.36959 + 5.83629i −0.342130 + 0.592586i −0.984828 0.173534i \(-0.944481\pi\)
0.642698 + 0.766119i \(0.277815\pi\)
\(98\) 0 0
\(99\) 3.22668 + 5.58878i 0.324294 + 0.561693i
\(100\) 0 0
\(101\) −0.305407 0.528981i −0.0303892 0.0526356i 0.850431 0.526087i \(-0.176341\pi\)
−0.880820 + 0.473451i \(0.843008\pi\)
\(102\) 0 0
\(103\) 0.0641778 0.00632362 0.00316181 0.999995i \(-0.498994\pi\)
0.00316181 + 0.999995i \(0.498994\pi\)
\(104\) 0 0
\(105\) −3.16250 5.47762i −0.308629 0.534561i
\(106\) 0 0
\(107\) 0.610815 0.0590497 0.0295248 0.999564i \(-0.490601\pi\)
0.0295248 + 0.999564i \(0.490601\pi\)
\(108\) 0 0
\(109\) −2.30541 + 3.99308i −0.220818 + 0.382468i −0.955057 0.296424i \(-0.904206\pi\)
0.734239 + 0.678891i \(0.237539\pi\)
\(110\) 0 0
\(111\) −1.19459 + 2.06910i −0.113386 + 0.196390i
\(112\) 0 0
\(113\) 17.4884 1.64517 0.822587 0.568639i \(-0.192530\pi\)
0.822587 + 0.568639i \(0.192530\pi\)
\(114\) 0 0
\(115\) 9.38919 0.875546
\(116\) 0 0
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) 1.43376 2.48335i 0.131433 0.227648i
\(120\) 0 0
\(121\) 30.6459 2.78599
\(122\) 0 0
\(123\) 5.06418 + 8.77141i 0.456622 + 0.790892i
\(124\) 0 0
\(125\) −1.87164 −0.167405
\(126\) 0 0
\(127\) −7.06418 12.2355i −0.626844 1.08573i −0.988181 0.153291i \(-0.951013\pi\)
0.361337 0.932435i \(-0.382321\pi\)
\(128\) 0 0
\(129\) 3.03209 + 5.25173i 0.266961 + 0.462389i
\(130\) 0 0
\(131\) −2.75877 + 4.77833i −0.241035 + 0.417485i −0.961009 0.276516i \(-0.910820\pi\)
0.719974 + 0.694001i \(0.244153\pi\)
\(132\) 0 0
\(133\) 7.75877 + 4.55601i 0.672771 + 0.395056i
\(134\) 0 0
\(135\) 1.53209 2.65366i 0.131861 0.228390i
\(136\) 0 0
\(137\) −8.88713 15.3930i −0.759278 1.31511i −0.943219 0.332171i \(-0.892219\pi\)
0.183941 0.982937i \(-0.441115\pi\)
\(138\) 0 0
\(139\) 5.48545 + 9.50108i 0.465270 + 0.805871i 0.999214 0.0396488i \(-0.0126239\pi\)
−0.533944 + 0.845520i \(0.679291\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 3.22668 + 5.58878i 0.269829 + 0.467357i
\(144\) 0 0
\(145\) −10.7784 −0.895095
\(146\) 0 0
\(147\) −1.36959 + 2.37219i −0.112961 + 0.195655i
\(148\) 0 0
\(149\) −6.53209 + 11.3139i −0.535130 + 0.926872i 0.464027 + 0.885821i \(0.346404\pi\)
−0.999157 + 0.0410508i \(0.986929\pi\)
\(150\) 0 0
\(151\) 4.90673 0.399304 0.199652 0.979867i \(-0.436019\pi\)
0.199652 + 0.979867i \(0.436019\pi\)
\(152\) 0 0
\(153\) 1.38919 0.112309
\(154\) 0 0
\(155\) −14.4834 + 25.0860i −1.16333 + 2.01495i
\(156\) 0 0
\(157\) −5.86959 + 10.1664i −0.468444 + 0.811369i −0.999350 0.0360623i \(-0.988519\pi\)
0.530906 + 0.847431i \(0.321852\pi\)
\(158\) 0 0
\(159\) 10.5817 0.839185
\(160\) 0 0
\(161\) 3.16250 + 5.47762i 0.249240 + 0.431697i
\(162\) 0 0
\(163\) −13.4534 −1.05375 −0.526874 0.849943i \(-0.676636\pi\)
−0.526874 + 0.849943i \(0.676636\pi\)
\(164\) 0 0
\(165\) −9.88713 17.1250i −0.769712 1.33318i
\(166\) 0 0
\(167\) −6.98545 12.0992i −0.540551 0.936261i −0.998872 0.0474747i \(-0.984883\pi\)
0.458322 0.888786i \(-0.348451\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) −0.0320889 + 4.35878i −0.00245390 + 0.333324i
\(172\) 0 0
\(173\) −1.75877 + 3.04628i −0.133717 + 0.231604i −0.925107 0.379708i \(-0.876025\pi\)
0.791390 + 0.611312i \(0.209358\pi\)
\(174\) 0 0
\(175\) 4.53003 + 7.84624i 0.342438 + 0.593120i
\(176\) 0 0
\(177\) −5.59627 9.69302i −0.420641 0.728572i
\(178\) 0 0
\(179\) 11.0642 0.826975 0.413488 0.910510i \(-0.364310\pi\)
0.413488 + 0.910510i \(0.364310\pi\)
\(180\) 0 0
\(181\) −10.7588 18.6347i −0.799693 1.38511i −0.919816 0.392350i \(-0.871662\pi\)
0.120123 0.992759i \(-0.461671\pi\)
\(182\) 0 0
\(183\) −5.12836 −0.379099
\(184\) 0 0
\(185\) 3.66044 6.34008i 0.269121 0.466132i
\(186\) 0 0
\(187\) 4.48246 7.76385i 0.327790 0.567749i
\(188\) 0 0
\(189\) 2.06418 0.150147
\(190\) 0 0
\(191\) −15.2317 −1.10213 −0.551065 0.834462i \(-0.685778\pi\)
−0.551065 + 0.834462i \(0.685778\pi\)
\(192\) 0 0
\(193\) −3.13041 + 5.42204i −0.225332 + 0.390287i −0.956419 0.291998i \(-0.905680\pi\)
0.731087 + 0.682284i \(0.239013\pi\)
\(194\) 0 0
\(195\) 1.53209 2.65366i 0.109715 0.190032i
\(196\) 0 0
\(197\) −6.71007 −0.478073 −0.239036 0.971011i \(-0.576832\pi\)
−0.239036 + 0.971011i \(0.576832\pi\)
\(198\) 0 0
\(199\) 12.4659 + 21.5915i 0.883681 + 1.53058i 0.847218 + 0.531245i \(0.178276\pi\)
0.0364626 + 0.999335i \(0.488391\pi\)
\(200\) 0 0
\(201\) −3.45336 −0.243581
\(202\) 0 0
\(203\) −3.63041 6.28806i −0.254805 0.441336i
\(204\) 0 0
\(205\) −15.5175 26.8772i −1.08379 1.87718i
\(206\) 0 0
\(207\) −1.53209 + 2.65366i −0.106488 + 0.184442i
\(208\) 0 0
\(209\) 24.2567 + 14.2437i 1.67787 + 0.985260i
\(210\) 0 0
\(211\) −4.48545 + 7.76903i −0.308791 + 0.534842i −0.978098 0.208144i \(-0.933258\pi\)
0.669307 + 0.742986i \(0.266591\pi\)
\(212\) 0 0
\(213\) 3.36959 + 5.83629i 0.230880 + 0.399896i
\(214\) 0 0
\(215\) −9.29086 16.0922i −0.633631 1.09748i
\(216\) 0 0
\(217\) −19.5134 −1.32466
\(218\) 0 0
\(219\) −4.56418 7.90539i −0.308419 0.534197i
\(220\) 0 0
\(221\) 1.38919 0.0934467
\(222\) 0 0
\(223\) −12.5692 + 21.7705i −0.841698 + 1.45786i 0.0467604 + 0.998906i \(0.485110\pi\)
−0.888458 + 0.458957i \(0.848223\pi\)
\(224\) 0 0
\(225\) −2.19459 + 3.80115i −0.146306 + 0.253410i
\(226\) 0 0
\(227\) −22.8384 −1.51584 −0.757920 0.652348i \(-0.773784\pi\)
−0.757920 + 0.652348i \(0.773784\pi\)
\(228\) 0 0
\(229\) −6.03508 −0.398809 −0.199405 0.979917i \(-0.563901\pi\)
−0.199405 + 0.979917i \(0.563901\pi\)
\(230\) 0 0
\(231\) 6.66044 11.5362i 0.438225 0.759028i
\(232\) 0 0
\(233\) −2.30541 + 3.99308i −0.151032 + 0.261596i −0.931607 0.363467i \(-0.881593\pi\)
0.780575 + 0.625062i \(0.214926\pi\)
\(234\) 0 0
\(235\) −18.3851 −1.19931
\(236\) 0 0
\(237\) −0.790859 1.36981i −0.0513718 0.0889786i
\(238\) 0 0
\(239\) 9.36009 0.605454 0.302727 0.953077i \(-0.402103\pi\)
0.302727 + 0.953077i \(0.402103\pi\)
\(240\) 0 0
\(241\) 10.0817 + 17.4620i 0.649421 + 1.12483i 0.983261 + 0.182200i \(0.0583218\pi\)
−0.333841 + 0.942629i \(0.608345\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 4.19665 7.26881i 0.268114 0.464388i
\(246\) 0 0
\(247\) −0.0320889 + 4.35878i −0.00204177 + 0.277343i
\(248\) 0 0
\(249\) −8.82295 + 15.2818i −0.559132 + 0.968444i
\(250\) 0 0
\(251\) −6.06418 10.5035i −0.382768 0.662973i 0.608689 0.793409i \(-0.291696\pi\)
−0.991457 + 0.130436i \(0.958362\pi\)
\(252\) 0 0
\(253\) 9.88713 + 17.1250i 0.621598 + 1.07664i
\(254\) 0 0
\(255\) −4.25671 −0.266566
\(256\) 0 0
\(257\) −15.4192 26.7069i −0.961824 1.66593i −0.717916 0.696130i \(-0.754904\pi\)
−0.243909 0.969798i \(-0.578430\pi\)
\(258\) 0 0
\(259\) 4.93170 0.306441
\(260\) 0 0
\(261\) 1.75877 3.04628i 0.108865 0.188560i
\(262\) 0 0
\(263\) 5.24123 9.07808i 0.323188 0.559778i −0.657956 0.753056i \(-0.728579\pi\)
0.981144 + 0.193278i \(0.0619120\pi\)
\(264\) 0 0
\(265\) −32.4243 −1.99181
\(266\) 0 0
\(267\) −10.4534 −0.639735
\(268\) 0 0
\(269\) 0.901674 1.56175i 0.0549760 0.0952213i −0.837228 0.546854i \(-0.815825\pi\)
0.892204 + 0.451633i \(0.149158\pi\)
\(270\) 0 0
\(271\) −14.1284 + 24.4710i −0.858236 + 1.48651i 0.0153732 + 0.999882i \(0.495106\pi\)
−0.873610 + 0.486627i \(0.838227\pi\)
\(272\) 0 0
\(273\) 2.06418 0.124930
\(274\) 0 0
\(275\) 14.1625 + 24.5302i 0.854031 + 1.47923i
\(276\) 0 0
\(277\) 6.48246 0.389493 0.194747 0.980854i \(-0.437612\pi\)
0.194747 + 0.980854i \(0.437612\pi\)
\(278\) 0 0
\(279\) −4.72668 8.18685i −0.282979 0.490134i
\(280\) 0 0
\(281\) −2.92127 5.05980i −0.174269 0.301842i 0.765639 0.643270i \(-0.222423\pi\)
−0.939908 + 0.341428i \(0.889089\pi\)
\(282\) 0 0
\(283\) −8.12836 + 14.0787i −0.483181 + 0.836893i −0.999813 0.0193137i \(-0.993852\pi\)
0.516633 + 0.856207i \(0.327185\pi\)
\(284\) 0 0
\(285\) 0.0983261 13.3561i 0.00582433 0.791146i
\(286\) 0 0
\(287\) 10.4534 18.1058i 0.617043 1.06875i
\(288\) 0 0
\(289\) 7.53508 + 13.0511i 0.443240 + 0.767714i
\(290\) 0 0
\(291\) 3.36959 + 5.83629i 0.197529 + 0.342130i
\(292\) 0 0
\(293\) 26.2567 1.53393 0.766967 0.641687i \(-0.221765\pi\)
0.766967 + 0.641687i \(0.221765\pi\)
\(294\) 0 0
\(295\) 17.1480 + 29.7011i 0.998393 + 1.72927i
\(296\) 0 0
\(297\) 6.45336 0.374462
\(298\) 0 0
\(299\) −1.53209 + 2.65366i −0.0886030 + 0.153465i
\(300\) 0 0
\(301\) 6.25877 10.8405i 0.360750 0.624837i
\(302\) 0 0
\(303\) −0.610815 −0.0350904
\(304\) 0 0
\(305\) 15.7142 0.899792
\(306\) 0 0
\(307\) −7.14796 + 12.3806i −0.407955 + 0.706599i −0.994661 0.103201i \(-0.967091\pi\)
0.586705 + 0.809801i \(0.300425\pi\)
\(308\) 0 0
\(309\) 0.0320889 0.0555796i 0.00182547 0.00316181i
\(310\) 0 0
\(311\) 22.2276 1.26041 0.630206 0.776428i \(-0.282970\pi\)
0.630206 + 0.776428i \(0.282970\pi\)
\(312\) 0 0
\(313\) −1.56624 2.71280i −0.0885290 0.153337i 0.818361 0.574705i \(-0.194883\pi\)
−0.906890 + 0.421368i \(0.861550\pi\)
\(314\) 0 0
\(315\) −6.32501 −0.356374
\(316\) 0 0
\(317\) 3.04963 + 5.28211i 0.171284 + 0.296673i 0.938869 0.344274i \(-0.111875\pi\)
−0.767585 + 0.640947i \(0.778542\pi\)
\(318\) 0 0
\(319\) −11.3500 19.6588i −0.635477 1.10068i
\(320\) 0 0
\(321\) 0.305407 0.528981i 0.0170462 0.0295248i
\(322\) 0 0
\(323\) 5.26621 2.98897i 0.293020 0.166311i
\(324\) 0 0
\(325\) −2.19459 + 3.80115i −0.121734 + 0.210850i
\(326\) 0 0
\(327\) 2.30541 + 3.99308i 0.127489 + 0.220818i
\(328\) 0 0
\(329\) −6.19253 10.7258i −0.341405 0.591332i
\(330\) 0 0
\(331\) −1.93582 −0.106402 −0.0532012 0.998584i \(-0.516942\pi\)
−0.0532012 + 0.998584i \(0.516942\pi\)
\(332\) 0 0
\(333\) 1.19459 + 2.06910i 0.0654633 + 0.113386i
\(334\) 0 0
\(335\) 10.5817 0.578141
\(336\) 0 0
\(337\) 3.58378 6.20729i 0.195221 0.338132i −0.751752 0.659446i \(-0.770791\pi\)
0.946973 + 0.321313i \(0.104124\pi\)
\(338\) 0 0
\(339\) 8.74422 15.1454i 0.474921 0.822587i
\(340\) 0 0
\(341\) −61.0060 −3.30366
\(342\) 0 0
\(343\) 20.1034 1.08548
\(344\) 0 0
\(345\) 4.69459 8.13127i 0.252748 0.437773i
\(346\) 0 0
\(347\) 4.80840 8.32839i 0.258128 0.447092i −0.707612 0.706601i \(-0.750228\pi\)
0.965741 + 0.259510i \(0.0835609\pi\)
\(348\) 0 0
\(349\) 31.5134 1.68687 0.843437 0.537227i \(-0.180528\pi\)
0.843437 + 0.537227i \(0.180528\pi\)
\(350\) 0 0
\(351\) 0.500000 + 0.866025i 0.0266880 + 0.0462250i
\(352\) 0 0
\(353\) −25.8425 −1.37546 −0.687730 0.725967i \(-0.741393\pi\)
−0.687730 + 0.725967i \(0.741393\pi\)
\(354\) 0 0
\(355\) −10.3250 17.8834i −0.547995 0.949154i
\(356\) 0 0
\(357\) −1.43376 2.48335i −0.0758828 0.131433i
\(358\) 0 0
\(359\) −16.1284 + 27.9351i −0.851222 + 1.47436i 0.0288840 + 0.999583i \(0.490805\pi\)
−0.880106 + 0.474777i \(0.842529\pi\)
\(360\) 0 0
\(361\) 9.25671 + 16.5926i 0.487195 + 0.873293i
\(362\) 0 0
\(363\) 15.3229 26.5401i 0.804246 1.39300i
\(364\) 0 0
\(365\) 13.9855 + 24.2235i 0.732032 + 1.26792i
\(366\) 0 0
\(367\) −14.6334 25.3458i −0.763858 1.32304i −0.940848 0.338828i \(-0.889970\pi\)
0.176991 0.984213i \(-0.443364\pi\)
\(368\) 0 0
\(369\) 10.1284 0.527261
\(370\) 0 0
\(371\) −10.9213 18.9162i −0.567004 0.982080i
\(372\) 0 0
\(373\) 8.03920 0.416254 0.208127 0.978102i \(-0.433263\pi\)
0.208127 + 0.978102i \(0.433263\pi\)
\(374\) 0 0
\(375\) −0.935822 + 1.62089i −0.0483257 + 0.0837025i
\(376\) 0 0
\(377\) 1.75877 3.04628i 0.0905813 0.156891i
\(378\) 0 0
\(379\) 8.19253 0.420822 0.210411 0.977613i \(-0.432520\pi\)
0.210411 + 0.977613i \(0.432520\pi\)
\(380\) 0 0
\(381\) −14.1284 −0.723818
\(382\) 0 0
\(383\) 2.74422 4.75313i 0.140223 0.242874i −0.787357 0.616497i \(-0.788551\pi\)
0.927581 + 0.373623i \(0.121885\pi\)
\(384\) 0 0
\(385\) −20.4088 + 35.3491i −1.04013 + 1.80155i
\(386\) 0 0
\(387\) 6.06418 0.308259
\(388\) 0 0
\(389\) −4.22668 7.32083i −0.214301 0.371181i 0.738755 0.673974i \(-0.235414\pi\)
−0.953056 + 0.302793i \(0.902081\pi\)
\(390\) 0 0
\(391\) 4.25671 0.215271
\(392\) 0 0
\(393\) 2.75877 + 4.77833i 0.139162 + 0.241035i
\(394\) 0 0
\(395\) 2.42333 + 4.19734i 0.121931 + 0.211191i
\(396\) 0 0
\(397\) −12.5351 + 21.7114i −0.629118 + 1.08966i 0.358611 + 0.933487i \(0.383250\pi\)
−0.987729 + 0.156177i \(0.950083\pi\)
\(398\) 0 0
\(399\) 7.82501 4.44129i 0.391740 0.222342i
\(400\) 0 0
\(401\) 12.8726 22.2960i 0.642826 1.11341i −0.341973 0.939710i \(-0.611095\pi\)
0.984799 0.173697i \(-0.0555715\pi\)
\(402\) 0 0
\(403\) −4.72668 8.18685i −0.235453 0.407816i
\(404\) 0 0
\(405\) −1.53209 2.65366i −0.0761301 0.131861i
\(406\) 0 0
\(407\) 15.4183 0.764256
\(408\) 0 0
\(409\) 3.21213 + 5.56358i 0.158830 + 0.275101i 0.934447 0.356102i \(-0.115895\pi\)
−0.775617 + 0.631204i \(0.782561\pi\)
\(410\) 0 0
\(411\) −17.7743 −0.876739
\(412\) 0 0
\(413\) −11.5517 + 20.0081i −0.568421 + 0.984535i
\(414\) 0 0
\(415\) 27.0351 46.8261i 1.32710 2.29860i
\(416\) 0 0
\(417\) 10.9709 0.537247
\(418\) 0 0
\(419\) 16.2668 0.794686 0.397343 0.917670i \(-0.369932\pi\)
0.397343 + 0.917670i \(0.369932\pi\)
\(420\) 0 0
\(421\) 14.7297 25.5125i 0.717880 1.24341i −0.243958 0.969786i \(-0.578446\pi\)
0.961838 0.273619i \(-0.0882209\pi\)
\(422\) 0 0
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 0 0
\(425\) 6.09739 0.295767
\(426\) 0 0
\(427\) 5.29292 + 9.16760i 0.256142 + 0.443651i
\(428\) 0 0
\(429\) 6.45336 0.311571
\(430\) 0 0
\(431\) 8.51754 + 14.7528i 0.410276 + 0.710618i 0.994920 0.100672i \(-0.0320992\pi\)
−0.584644 + 0.811290i \(0.698766\pi\)
\(432\) 0 0
\(433\) 6.84049 + 11.8481i 0.328733 + 0.569382i 0.982261 0.187520i \(-0.0600451\pi\)
−0.653528 + 0.756903i \(0.726712\pi\)
\(434\) 0 0
\(435\) −5.38919 + 9.33434i −0.258392 + 0.447547i
\(436\) 0 0
\(437\) −0.0983261 + 13.3561i −0.00470357 + 0.638908i
\(438\) 0 0
\(439\) −0.707081 + 1.22470i −0.0337471 + 0.0584518i −0.882406 0.470489i \(-0.844077\pi\)
0.848659 + 0.528941i \(0.177411\pi\)
\(440\) 0 0
\(441\) 1.36959 + 2.37219i 0.0652183 + 0.112961i
\(442\) 0 0
\(443\) −0.369585 0.640140i −0.0175595 0.0304140i 0.857112 0.515130i \(-0.172256\pi\)
−0.874672 + 0.484716i \(0.838923\pi\)
\(444\) 0 0
\(445\) 32.0310 1.51841
\(446\) 0 0
\(447\) 6.53209 + 11.3139i 0.308957 + 0.535130i
\(448\) 0 0
\(449\) 7.51754 0.354775 0.177387 0.984141i \(-0.443235\pi\)
0.177387 + 0.984141i \(0.443235\pi\)
\(450\) 0 0
\(451\) 32.6810 56.6051i 1.53889 2.66543i
\(452\) 0 0
\(453\) 2.45336 4.24935i 0.115269 0.199652i
\(454\) 0 0
\(455\) −6.32501 −0.296521
\(456\) 0 0
\(457\) −15.6810 −0.733525 −0.366763 0.930315i \(-0.619534\pi\)
−0.366763 + 0.930315i \(0.619534\pi\)
\(458\) 0 0
\(459\) 0.694593 1.20307i 0.0324208 0.0561545i
\(460\) 0 0
\(461\) −10.7442 + 18.6095i −0.500408 + 0.866733i 0.499592 + 0.866261i \(0.333483\pi\)
−1.00000 0.000471567i \(0.999850\pi\)
\(462\) 0 0
\(463\) −9.62092 −0.447122 −0.223561 0.974690i \(-0.571768\pi\)
−0.223561 + 0.974690i \(0.571768\pi\)
\(464\) 0 0
\(465\) 14.4834 + 25.0860i 0.671651 + 1.16333i
\(466\) 0 0
\(467\) 1.87164 0.0866094 0.0433047 0.999062i \(-0.486211\pi\)
0.0433047 + 0.999062i \(0.486211\pi\)
\(468\) 0 0
\(469\) 3.56418 + 6.17334i 0.164578 + 0.285058i
\(470\) 0 0
\(471\) 5.86959 + 10.1664i 0.270456 + 0.468444i
\(472\) 0 0
\(473\) 19.5672 33.8913i 0.899699 1.55833i
\(474\) 0 0
\(475\) −0.140844 + 19.1315i −0.00646237 + 0.877813i
\(476\) 0 0
\(477\) 5.29086 9.16404i 0.242252 0.419592i
\(478\) 0 0
\(479\) −3.36959 5.83629i −0.153960 0.266667i 0.778720 0.627372i \(-0.215869\pi\)
−0.932680 + 0.360705i \(0.882536\pi\)
\(480\) 0 0
\(481\) 1.19459 + 2.06910i 0.0544687 + 0.0943426i
\(482\) 0 0
\(483\) 6.32501 0.287798
\(484\) 0 0
\(485\) −10.3250 17.8834i −0.468834 0.812045i
\(486\) 0 0
\(487\) −2.38507 −0.108078 −0.0540388 0.998539i \(-0.517209\pi\)
−0.0540388 + 0.998539i \(0.517209\pi\)
\(488\) 0 0
\(489\) −6.72668 + 11.6510i −0.304191 + 0.526874i
\(490\) 0 0
\(491\) 5.36959 9.30039i 0.242326 0.419721i −0.719050 0.694958i \(-0.755423\pi\)
0.961376 + 0.275237i \(0.0887563\pi\)
\(492\) 0 0
\(493\) −4.88652 −0.220078
\(494\) 0 0
\(495\) −19.7743 −0.888787
\(496\) 0 0
\(497\) 6.95542 12.0471i 0.311993 0.540388i
\(498\) 0 0
\(499\) −14.2733 + 24.7221i −0.638961 + 1.10671i 0.346700 + 0.937976i \(0.387302\pi\)
−0.985661 + 0.168738i \(0.946031\pi\)
\(500\) 0 0
\(501\) −13.9709 −0.624174
\(502\) 0 0
\(503\) −1.75877 3.04628i −0.0784197 0.135827i 0.824149 0.566374i \(-0.191654\pi\)
−0.902568 + 0.430547i \(0.858321\pi\)
\(504\) 0 0
\(505\) 1.87164 0.0832871
\(506\) 0 0
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 0 0
\(509\) −3.61081 6.25411i −0.160047 0.277209i 0.774839 0.632159i \(-0.217831\pi\)
−0.934885 + 0.354950i \(0.884498\pi\)
\(510\) 0 0
\(511\) −9.42127 + 16.3181i −0.416773 + 0.721871i
\(512\) 0 0
\(513\) 3.75877 + 2.20718i 0.165954 + 0.0974494i
\(514\) 0 0
\(515\) −0.0983261 + 0.170306i −0.00433276 + 0.00750457i
\(516\) 0 0
\(517\) −19.3601 33.5327i −0.851456 1.47476i
\(518\) 0 0
\(519\) 1.75877 + 3.04628i 0.0772015 + 0.133717i
\(520\) 0 0
\(521\) 16.8075 0.736348 0.368174 0.929757i \(-0.379983\pi\)
0.368174 + 0.929757i \(0.379983\pi\)
\(522\) 0 0
\(523\) 3.88413 + 6.72752i 0.169841 + 0.294174i 0.938364 0.345649i \(-0.112341\pi\)
−0.768523 + 0.639823i \(0.779008\pi\)
\(524\) 0 0
\(525\) 9.06006 0.395413
\(526\) 0 0
\(527\) −6.56624 + 11.3731i −0.286030 + 0.495418i
\(528\) 0 0
\(529\) 6.80541 11.7873i 0.295887 0.512492i
\(530\) 0 0
\(531\) −11.1925 −0.485715
\(532\) 0 0
\(533\) 10.1284 0.438708
\(534\) 0 0
\(535\) −0.935822 + 1.62089i −0.0404591 + 0.0700773i
\(536\) 0 0
\(537\) 5.53209 9.58186i 0.238727 0.413488i
\(538\) 0 0
\(539\) 17.6769 0.761396
\(540\) 0 0
\(541\) 18.1655 + 31.4636i 0.780996 + 1.35272i 0.931362 + 0.364094i \(0.118621\pi\)
−0.150367 + 0.988630i \(0.548045\pi\)
\(542\) 0 0
\(543\) −21.5175 −0.923406
\(544\) 0 0
\(545\) −7.06418 12.2355i −0.302596 0.524112i
\(546\) 0 0
\(547\) −15.8105 27.3845i −0.676006 1.17088i −0.976174 0.216991i \(-0.930376\pi\)
0.300167 0.953887i \(-0.402958\pi\)
\(548\) 0 0
\(549\) −2.56418 + 4.44129i −0.109436 + 0.189549i
\(550\) 0 0
\(551\) 0.112874 15.3322i 0.00480859 0.653173i
\(552\) 0 0
\(553\) −1.63247 + 2.82753i −0.0694199 + 0.120239i
\(554\) 0 0
\(555\) −3.66044 6.34008i −0.155377 0.269121i
\(556\) 0 0
\(557\) −2.01960 3.49805i −0.0855732 0.148217i 0.820062 0.572275i \(-0.193939\pi\)
−0.905635 + 0.424057i \(0.860605\pi\)
\(558\) 0 0
\(559\) 6.06418 0.256487
\(560\) 0 0
\(561\) −4.48246 7.76385i −0.189250 0.327790i
\(562\) 0 0
\(563\) −8.61081 −0.362903 −0.181451 0.983400i \(-0.558079\pi\)
−0.181451 + 0.983400i \(0.558079\pi\)
\(564\) 0 0
\(565\) −26.7939 + 46.4083i −1.12723 + 1.95241i
\(566\) 0 0
\(567\) 1.03209 1.78763i 0.0433437 0.0750734i
\(568\) 0 0
\(569\) −27.6851 −1.16062 −0.580310 0.814396i \(-0.697069\pi\)
−0.580310 + 0.814396i \(0.697069\pi\)
\(570\) 0 0
\(571\) 24.1533 1.01079 0.505393 0.862889i \(-0.331348\pi\)
0.505393 + 0.862889i \(0.331348\pi\)
\(572\) 0 0
\(573\) −7.61587 + 13.1911i −0.318157 + 0.551065i
\(574\) 0 0
\(575\) −6.72462 + 11.6474i −0.280436 + 0.485730i
\(576\) 0 0
\(577\) 28.8675 1.20177 0.600885 0.799335i \(-0.294815\pi\)
0.600885 + 0.799335i \(0.294815\pi\)
\(578\) 0 0
\(579\) 3.13041 + 5.42204i 0.130096 + 0.225332i
\(580\) 0 0
\(581\) 36.4243 1.51113
\(582\) 0 0
\(583\) −34.1438 59.1389i −1.41409 2.44928i
\(584\) 0 0
\(585\) −1.53209 2.65366i −0.0633441 0.109715i
\(586\) 0 0
\(587\) −5.14290 + 8.90777i −0.212270 + 0.367663i −0.952425 0.304774i \(-0.901419\pi\)
0.740154 + 0.672437i \(0.234752\pi\)
\(588\) 0 0
\(589\) −35.5330 20.8653i −1.46411 0.859739i
\(590\) 0 0
\(591\) −3.35504 + 5.81109i −0.138008 + 0.239036i
\(592\) 0 0
\(593\) 7.96585 + 13.7973i 0.327118 + 0.566586i 0.981939 0.189199i \(-0.0605891\pi\)
−0.654820 + 0.755784i \(0.727256\pi\)
\(594\) 0 0
\(595\) 4.39330 + 7.60943i 0.180108 + 0.311956i
\(596\) 0 0
\(597\) 24.9317 1.02039
\(598\) 0 0
\(599\) 9.03003 + 15.6405i 0.368957 + 0.639052i 0.989403 0.145197i \(-0.0463816\pi\)
−0.620446 + 0.784249i \(0.713048\pi\)
\(600\) 0 0
\(601\) −7.86753 −0.320923 −0.160462 0.987042i \(-0.551298\pi\)
−0.160462 + 0.987042i \(0.551298\pi\)
\(602\) 0 0
\(603\) −1.72668 + 2.99070i −0.0703159 + 0.121791i
\(604\) 0 0
\(605\) −46.9522 + 81.3237i −1.90888 + 3.30628i
\(606\) 0 0
\(607\) −17.2668 −0.700838 −0.350419 0.936593i \(-0.613961\pi\)
−0.350419 + 0.936593i \(0.613961\pi\)
\(608\) 0 0
\(609\) −7.26083 −0.294224
\(610\) 0 0
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) 0 0
\(613\) 13.7939 23.8917i 0.557128 0.964975i −0.440606 0.897701i \(-0.645236\pi\)
0.997735 0.0672742i \(-0.0214302\pi\)
\(614\) 0 0
\(615\) −31.0351 −1.25146
\(616\) 0 0
\(617\) −8.24628 14.2830i −0.331983 0.575011i 0.650918 0.759148i \(-0.274384\pi\)
−0.982901 + 0.184137i \(0.941051\pi\)
\(618\) 0 0
\(619\) 24.4884 0.984274 0.492137 0.870518i \(-0.336216\pi\)
0.492137 + 0.870518i \(0.336216\pi\)
\(620\) 0 0
\(621\) 1.53209 + 2.65366i 0.0614806 + 0.106488i
\(622\) 0 0
\(623\) 10.7888 + 18.6867i 0.432244 + 0.748669i
\(624\) 0 0
\(625\) 13.8405 23.9724i 0.553620 0.958897i
\(626\) 0 0
\(627\) 24.4638 13.8851i 0.976990 0.554516i
\(628\) 0 0
\(629\) 1.65951 2.87436i 0.0661690 0.114608i
\(630\) 0 0
\(631\) −9.83544 17.0355i −0.391543 0.678172i 0.601111 0.799166i \(-0.294725\pi\)
−0.992653 + 0.120994i \(0.961392\pi\)
\(632\) 0 0
\(633\) 4.48545 + 7.76903i 0.178281 + 0.308791i
\(634\) 0 0
\(635\) 43.2918 1.71798
\(636\) 0 0
\(637\) 1.36959 + 2.37219i 0.0542649 + 0.0939896i
\(638\) 0 0
\(639\) 6.73917 0.266597
\(640\) 0 0
\(641\) −4.06418 + 7.03936i −0.160525 + 0.278038i −0.935057 0.354497i \(-0.884652\pi\)
0.774532 + 0.632535i \(0.217986\pi\)
\(642\) 0 0
\(643\) −3.91921 + 6.78828i −0.154559 + 0.267704i −0.932898 0.360140i \(-0.882729\pi\)
0.778340 + 0.627844i \(0.216062\pi\)
\(644\) 0 0
\(645\) −18.5817 −0.731654
\(646\) 0 0
\(647\) −39.7743 −1.56369 −0.781844 0.623475i \(-0.785720\pi\)
−0.781844 + 0.623475i \(0.785720\pi\)
\(648\) 0 0
\(649\) −36.1147 + 62.5526i −1.41763 + 2.45540i
\(650\) 0 0
\(651\) −9.75671 + 16.8991i −0.382396 + 0.662329i
\(652\) 0 0
\(653\) 8.94593 0.350081 0.175041 0.984561i \(-0.443994\pi\)
0.175041 + 0.984561i \(0.443994\pi\)
\(654\) 0 0
\(655\) −8.45336 14.6417i −0.330300 0.572097i
\(656\) 0 0
\(657\) −9.12836 −0.356131
\(658\) 0 0
\(659\) 5.93676 + 10.2828i 0.231263 + 0.400560i 0.958180 0.286166i \(-0.0923808\pi\)
−0.726917 + 0.686725i \(0.759047\pi\)
\(660\) 0 0
\(661\) −21.9067 37.9436i −0.852073 1.47583i −0.879334 0.476205i \(-0.842012\pi\)
0.0272613 0.999628i \(-0.491321\pi\)
\(662\) 0 0
\(663\) 0.694593 1.20307i 0.0269757 0.0467234i
\(664\) 0 0
\(665\) −23.9772 + 13.6089i −0.929796 + 0.527730i
\(666\) 0 0
\(667\) 5.38919 9.33434i 0.208670 0.361427i
\(668\) 0 0
\(669\) 12.5692 + 21.7705i 0.485955 + 0.841698i
\(670\) 0 0
\(671\) 16.5476 + 28.6612i 0.638812 + 1.10645i
\(672\) 0 0
\(673\) −37.6810 −1.45249 −0.726247 0.687433i \(-0.758737\pi\)
−0.726247 + 0.687433i \(0.758737\pi\)
\(674\) 0 0
\(675\) 2.19459 + 3.80115i 0.0844699 + 0.146306i
\(676\) 0 0
\(677\) −35.1052 −1.34920 −0.674602 0.738182i \(-0.735685\pi\)
−0.674602 + 0.738182i \(0.735685\pi\)
\(678\) 0 0
\(679\) 6.95542 12.0471i 0.266925 0.462327i
\(680\) 0 0
\(681\) −11.4192 + 19.7787i −0.437585 + 0.757920i
\(682\) 0 0
\(683\) 37.6168 1.43937 0.719683 0.694302i \(-0.244287\pi\)
0.719683 + 0.694302i \(0.244287\pi\)
\(684\) 0 0
\(685\) 54.4635 2.08094
\(686\) 0 0
\(687\) −3.01754 + 5.22653i −0.115126 + 0.199405i
\(688\) 0 0
\(689\) 5.29086 9.16404i 0.201566 0.349122i
\(690\) 0 0
\(691\) −2.69997 −0.102712 −0.0513558 0.998680i \(-0.516354\pi\)
−0.0513558 + 0.998680i \(0.516354\pi\)
\(692\) 0 0
\(693\) −6.66044 11.5362i −0.253009 0.438225i
\(694\) 0 0
\(695\) −33.6168 −1.27516
\(696\) 0 0
\(697\) −7.03508 12.1851i −0.266473 0.461544i
\(698\) 0 0
\(699\) 2.30541 + 3.99308i 0.0871985 + 0.151032i
\(700\) 0 0
\(701\) 10.8821 18.8483i 0.411010 0.711891i −0.583990 0.811761i \(-0.698509\pi\)
0.995000 + 0.0998700i \(0.0318427\pi\)
\(702\) 0 0
\(703\) 8.98040 + 5.27336i 0.338702 + 0.198889i
\(704\) 0 0
\(705\) −9.19253 + 15.9219i −0.346211 + 0.599655i
\(706\) 0 0
\(707\) 0.630415 + 1.09191i 0.0237092 + 0.0410655i
\(708\) 0 0
\(709\) 13.3033 + 23.0421i 0.499618 + 0.865363i 1.00000 0.000441366i \(-0.000140491\pi\)
−0.500382 + 0.865805i \(0.666807\pi\)
\(710\) 0 0
\(711\) −1.58172 −0.0593191
\(712\) 0 0
\(713\) −14.4834 25.0860i −0.542407 0.939477i
\(714\) 0 0
\(715\) −19.7743 −0.739515
\(716\) 0 0
\(717\) 4.68004 8.10608i 0.174779 0.302727i
\(718\) 0 0
\(719\) 3.81790 6.61279i 0.142383 0.246615i −0.786010 0.618214i \(-0.787857\pi\)
0.928394 + 0.371598i \(0.121190\pi\)
\(720\) 0 0
\(721\) −0.132474 −0.00493360
\(722\) 0 0
\(723\) 20.1634 0.749886
\(724\) 0 0
\(725\) 7.71957 13.3707i 0.286698 0.496575i
\(726\) 0 0
\(727\) −20.3726 + 35.2863i −0.755577 + 1.30870i 0.189510 + 0.981879i \(0.439310\pi\)
−0.945087 + 0.326819i \(0.894023\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.21213 7.29563i −0.155791 0.269839i
\(732\) 0 0
\(733\) 48.4742 1.79044 0.895218 0.445628i \(-0.147020\pi\)
0.895218 + 0.445628i \(0.147020\pi\)
\(734\) 0 0
\(735\) −4.19665 7.26881i −0.154796 0.268114i
\(736\) 0 0
\(737\) 11.1429 + 19.3001i 0.410454 + 0.710927i
\(738\) 0 0
\(739\) 5.30840 9.19442i 0.195273 0.338222i −0.751717 0.659486i \(-0.770774\pi\)
0.946990 + 0.321263i \(0.104107\pi\)
\(740\) 0 0
\(741\) 3.75877 + 2.20718i 0.138082 + 0.0810828i
\(742\) 0 0
\(743\) −23.7793 + 41.1870i −0.872378 + 1.51100i −0.0128483 + 0.999917i \(0.504090\pi\)
−0.859530 + 0.511086i \(0.829243\pi\)
\(744\) 0 0
\(745\) −20.0155 34.6678i −0.733311 1.27013i
\(746\) 0 0
\(747\) 8.82295 + 15.2818i 0.322815 + 0.559132i
\(748\) 0 0
\(749\) −1.26083 −0.0460697
\(750\) 0 0
\(751\) 7.96791 + 13.8008i 0.290753 + 0.503599i 0.973988 0.226599i \(-0.0727608\pi\)
−0.683235 + 0.730199i \(0.739427\pi\)
\(752\) 0 0
\(753\) −12.1284 −0.441982
\(754\) 0 0
\(755\) −7.51754 + 13.0208i −0.273591 + 0.473874i
\(756\) 0 0
\(757\) 9.17499 15.8916i 0.333471 0.577588i −0.649719 0.760174i \(-0.725113\pi\)
0.983190 + 0.182586i \(0.0584468\pi\)
\(758\) 0 0
\(759\) 19.7743 0.717760
\(760\) 0 0
\(761\) −36.7802 −1.33328 −0.666641 0.745379i \(-0.732269\pi\)
−0.666641 + 0.745379i \(0.732269\pi\)
\(762\) 0 0
\(763\) 4.75877 8.24243i 0.172279 0.298396i
\(764\) 0 0
\(765\) −2.12836 + 3.68642i −0.0769509 + 0.133283i
\(766\) 0 0
\(767\) −11.1925 −0.404139
\(768\) 0 0
\(769\) −21.0175 36.4034i −0.757912 1.31274i −0.943914 0.330193i \(-0.892886\pi\)
0.186002 0.982549i \(-0.440447\pi\)
\(770\) 0 0
\(771\) −30.8384 −1.11062
\(772\) 0 0
\(773\) −22.9709 39.7868i −0.826206 1.43103i −0.900994 0.433831i \(-0.857161\pi\)
0.0747881 0.997199i \(-0.476172\pi\)
\(774\) 0 0
\(775\) −20.7463 35.9336i −0.745228 1.29077i
\(776\) 0 0
\(777\) 2.46585 4.27098i 0.0884619 0.153221i
\(778\) 0 0
\(779\) 38.3952 21.7922i 1.37565 0.780786i
\(780\) 0 0
\(781\) 21.7452 37.6637i 0.778103 1.34771i
\(782\) 0 0
\(783\) −1.75877 3.04628i −0.0628533 0.108865i
\(784\) 0 0
\(785\) −17.9855 31.1517i −0.641928 1.11185i
\(786\) 0 0
\(787\) −17.3250 −0.617570 −0.308785 0.951132i \(-0.599922\pi\)
−0.308785 + 0.951132i \(0.599922\pi\)
\(788\) 0 0
\(789\) −5.24123 9.07808i −0.186593 0.323188i
\(790\) 0 0
\(791\) −36.0993 −1.28354
\(792\) 0 0
\(793\) −2.56418 + 4.44129i −0.0910566 + 0.157715i
\(794\) 0 0
\(795\) −16.2121 + 28.0802i −0.574985 + 0.995903i
\(796\)