Properties

Label 3330.2.d.p.1999.7
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 51 x^{6} - 124 x^{5} + 154 x^{4} - 46 x^{3} + x^{2} + 4 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 370)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.7
Root \(-1.95884 + 1.95884i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.p.1999.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-1.74265 - 1.40113i) q^{5} +3.20984i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-1.74265 - 1.40113i) q^{5} +3.20984i q^{7} -1.00000i q^{8} +(1.40113 - 1.74265i) q^{10} -3.82327 q^{11} +0.147332i q^{13} -3.20984 q^{14} +1.00000 q^{16} +0.978989i q^{17} -2.67594 q^{19} +(1.74265 + 1.40113i) q^{20} -3.82327i q^{22} +2.33616i q^{23} +(1.07367 + 4.88336i) q^{25} -0.147332 q^{26} -3.20984i q^{28} +6.30425 q^{29} -3.62372 q^{31} +1.00000i q^{32} -0.978989 q^{34} +(4.49740 - 5.59362i) q^{35} -1.00000i q^{37} -2.67594i q^{38} +(-1.40113 + 1.74265i) q^{40} -11.8265 q^{41} -4.53390i q^{43} +3.82327 q^{44} -2.33616 q^{46} +6.23085i q^{47} -3.30305 q^{49} +(-4.88336 + 1.07367i) q^{50} -0.147332i q^{52} -11.2978i q^{53} +(6.66263 + 5.35690i) q^{55} +3.20984 q^{56} +6.30425i q^{58} +6.92858 q^{59} +10.4885 q^{61} -3.62372i q^{62} -1.00000 q^{64} +(0.206432 - 0.256749i) q^{65} -2.80936i q^{67} -0.978989i q^{68} +(5.59362 + 4.49740i) q^{70} +12.3189 q^{71} -13.9966i q^{73} +1.00000 q^{74} +2.67594 q^{76} -12.2721i q^{77} -15.6057 q^{79} +(-1.74265 - 1.40113i) q^{80} -11.8265i q^{82} -13.5371i q^{83} +(1.37169 - 1.70604i) q^{85} +4.53390 q^{86} +3.82327i q^{88} -6.46929 q^{89} -0.472913 q^{91} -2.33616i q^{92} -6.23085 q^{94} +(4.66323 + 3.74934i) q^{95} +3.07063i q^{97} -3.30305i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{4} - 6 q^{5} + O(q^{10}) \) \( 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.74265 1.40113i −0.779337 0.626605i
\(6\) 0 0
\(7\) 3.20984i 1.21320i 0.795006 + 0.606602i \(0.207468\pi\)
−0.795006 + 0.606602i \(0.792532\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.40113 1.74265i 0.443076 0.551075i
\(11\) −3.82327 −1.15276 −0.576380 0.817182i \(-0.695535\pi\)
−0.576380 + 0.817182i \(0.695535\pi\)
\(12\) 0 0
\(13\) 0.147332i 0.0408626i 0.999791 + 0.0204313i \(0.00650394\pi\)
−0.999791 + 0.0204313i \(0.993496\pi\)
\(14\) −3.20984 −0.857865
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.978989i 0.237440i 0.992928 + 0.118720i \(0.0378790\pi\)
−0.992928 + 0.118720i \(0.962121\pi\)
\(18\) 0 0
\(19\) −2.67594 −0.613903 −0.306951 0.951725i \(-0.599309\pi\)
−0.306951 + 0.951725i \(0.599309\pi\)
\(20\) 1.74265 + 1.40113i 0.389669 + 0.313302i
\(21\) 0 0
\(22\) 3.82327i 0.815124i
\(23\) 2.33616i 0.487122i 0.969886 + 0.243561i \(0.0783157\pi\)
−0.969886 + 0.243561i \(0.921684\pi\)
\(24\) 0 0
\(25\) 1.07367 + 4.88336i 0.214733 + 0.976673i
\(26\) −0.147332 −0.0288942
\(27\) 0 0
\(28\) 3.20984i 0.606602i
\(29\) 6.30425 1.17067 0.585335 0.810792i \(-0.300963\pi\)
0.585335 + 0.810792i \(0.300963\pi\)
\(30\) 0 0
\(31\) −3.62372 −0.650839 −0.325420 0.945570i \(-0.605506\pi\)
−0.325420 + 0.945570i \(0.605506\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −0.978989 −0.167895
\(35\) 4.49740 5.59362i 0.760199 0.945495i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 2.67594i 0.434095i
\(39\) 0 0
\(40\) −1.40113 + 1.74265i −0.221538 + 0.275537i
\(41\) −11.8265 −1.84698 −0.923491 0.383620i \(-0.874677\pi\)
−0.923491 + 0.383620i \(0.874677\pi\)
\(42\) 0 0
\(43\) 4.53390i 0.691413i −0.938343 0.345706i \(-0.887639\pi\)
0.938343 0.345706i \(-0.112361\pi\)
\(44\) 3.82327 0.576380
\(45\) 0 0
\(46\) −2.33616 −0.344448
\(47\) 6.23085i 0.908863i 0.890782 + 0.454431i \(0.150157\pi\)
−0.890782 + 0.454431i \(0.849843\pi\)
\(48\) 0 0
\(49\) −3.30305 −0.471864
\(50\) −4.88336 + 1.07367i −0.690612 + 0.151839i
\(51\) 0 0
\(52\) 0.147332i 0.0204313i
\(53\) 11.2978i 1.55188i −0.630807 0.775939i \(-0.717276\pi\)
0.630807 0.775939i \(-0.282724\pi\)
\(54\) 0 0
\(55\) 6.66263 + 5.35690i 0.898389 + 0.722325i
\(56\) 3.20984 0.428932
\(57\) 0 0
\(58\) 6.30425i 0.827788i
\(59\) 6.92858 0.902025 0.451012 0.892518i \(-0.351063\pi\)
0.451012 + 0.892518i \(0.351063\pi\)
\(60\) 0 0
\(61\) 10.4885 1.34291 0.671457 0.741044i \(-0.265669\pi\)
0.671457 + 0.741044i \(0.265669\pi\)
\(62\) 3.62372i 0.460213i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.206432 0.256749i 0.0256047 0.0318458i
\(66\) 0 0
\(67\) 2.80936i 0.343218i −0.985165 0.171609i \(-0.945103\pi\)
0.985165 0.171609i \(-0.0548966\pi\)
\(68\) 0.978989i 0.118720i
\(69\) 0 0
\(70\) 5.59362 + 4.49740i 0.668566 + 0.537542i
\(71\) 12.3189 1.46198 0.730990 0.682388i \(-0.239059\pi\)
0.730990 + 0.682388i \(0.239059\pi\)
\(72\) 0 0
\(73\) 13.9966i 1.63818i −0.573665 0.819090i \(-0.694479\pi\)
0.573665 0.819090i \(-0.305521\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 2.67594 0.306951
\(77\) 12.2721i 1.39853i
\(78\) 0 0
\(79\) −15.6057 −1.75578 −0.877890 0.478861i \(-0.841050\pi\)
−0.877890 + 0.478861i \(0.841050\pi\)
\(80\) −1.74265 1.40113i −0.194834 0.156651i
\(81\) 0 0
\(82\) 11.8265i 1.30601i
\(83\) 13.5371i 1.48589i −0.669354 0.742944i \(-0.733429\pi\)
0.669354 0.742944i \(-0.266571\pi\)
\(84\) 0 0
\(85\) 1.37169 1.70604i 0.148781 0.185046i
\(86\) 4.53390 0.488903
\(87\) 0 0
\(88\) 3.82327i 0.407562i
\(89\) −6.46929 −0.685743 −0.342872 0.939382i \(-0.611400\pi\)
−0.342872 + 0.939382i \(0.611400\pi\)
\(90\) 0 0
\(91\) −0.472913 −0.0495747
\(92\) 2.33616i 0.243561i
\(93\) 0 0
\(94\) −6.23085 −0.642663
\(95\) 4.66323 + 3.74934i 0.478437 + 0.384674i
\(96\) 0 0
\(97\) 3.07063i 0.311775i 0.987775 + 0.155887i \(0.0498237\pi\)
−0.987775 + 0.155887i \(0.950176\pi\)
\(98\) 3.30305i 0.333658i
\(99\) 0 0
\(100\) −1.07367 4.88336i −0.107367 0.488336i
\(101\) 6.57513 0.654250 0.327125 0.944981i \(-0.393920\pi\)
0.327125 + 0.944981i \(0.393920\pi\)
\(102\) 0 0
\(103\) 2.52180i 0.248480i −0.992252 0.124240i \(-0.960351\pi\)
0.992252 0.124240i \(-0.0396493\pi\)
\(104\) 0.147332 0.0144471
\(105\) 0 0
\(106\) 11.2978 1.09734
\(107\) 5.70291i 0.551321i 0.961255 + 0.275661i \(0.0888966\pi\)
−0.961255 + 0.275661i \(0.911103\pi\)
\(108\) 0 0
\(109\) −11.9318 −1.14286 −0.571428 0.820652i \(-0.693610\pi\)
−0.571428 + 0.820652i \(0.693610\pi\)
\(110\) −5.35690 + 6.66263i −0.510761 + 0.635257i
\(111\) 0 0
\(112\) 3.20984i 0.303301i
\(113\) 2.18044i 0.205119i 0.994727 + 0.102559i \(0.0327031\pi\)
−0.994727 + 0.102559i \(0.967297\pi\)
\(114\) 0 0
\(115\) 3.27326 4.07111i 0.305233 0.379633i
\(116\) −6.30425 −0.585335
\(117\) 0 0
\(118\) 6.92858i 0.637828i
\(119\) −3.14239 −0.288063
\(120\) 0 0
\(121\) 3.61741 0.328856
\(122\) 10.4885i 0.949583i
\(123\) 0 0
\(124\) 3.62372 0.325420
\(125\) 4.97120 10.0143i 0.444638 0.895710i
\(126\) 0 0
\(127\) 5.39390i 0.478631i 0.970942 + 0.239316i \(0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0.256749 + 0.206432i 0.0225184 + 0.0181053i
\(131\) 8.97060 0.783765 0.391883 0.920015i \(-0.371824\pi\)
0.391883 + 0.920015i \(0.371824\pi\)
\(132\) 0 0
\(133\) 8.58933i 0.744789i
\(134\) 2.80936 0.242692
\(135\) 0 0
\(136\) 0.978989 0.0839476
\(137\) 2.70352i 0.230978i −0.993309 0.115489i \(-0.963157\pi\)
0.993309 0.115489i \(-0.0368434\pi\)
\(138\) 0 0
\(139\) −4.30358 −0.365025 −0.182512 0.983204i \(-0.558423\pi\)
−0.182512 + 0.983204i \(0.558423\pi\)
\(140\) −4.49740 + 5.59362i −0.380100 + 0.472748i
\(141\) 0 0
\(142\) 12.3189i 1.03378i
\(143\) 0.563292i 0.0471048i
\(144\) 0 0
\(145\) −10.9861 8.83308i −0.912346 0.733547i
\(146\) 13.9966 1.15837
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) 21.6949 1.77732 0.888659 0.458568i \(-0.151638\pi\)
0.888659 + 0.458568i \(0.151638\pi\)
\(150\) 0 0
\(151\) 2.06744 0.168246 0.0841230 0.996455i \(-0.473191\pi\)
0.0841230 + 0.996455i \(0.473191\pi\)
\(152\) 2.67594i 0.217047i
\(153\) 0 0
\(154\) 12.2721 0.988912
\(155\) 6.31488 + 5.07731i 0.507223 + 0.407819i
\(156\) 0 0
\(157\) 18.5439i 1.47996i −0.672627 0.739982i \(-0.734834\pi\)
0.672627 0.739982i \(-0.265166\pi\)
\(158\) 15.6057i 1.24152i
\(159\) 0 0
\(160\) 1.40113 1.74265i 0.110769 0.137769i
\(161\) −7.49868 −0.590979
\(162\) 0 0
\(163\) 21.6240i 1.69372i −0.531817 0.846860i \(-0.678490\pi\)
0.531817 0.846860i \(-0.321510\pi\)
\(164\) 11.8265 0.923491
\(165\) 0 0
\(166\) 13.5371 1.05068
\(167\) 11.7729i 0.911012i −0.890233 0.455506i \(-0.849458\pi\)
0.890233 0.455506i \(-0.150542\pi\)
\(168\) 0 0
\(169\) 12.9783 0.998330
\(170\) 1.70604 + 1.37169i 0.130847 + 0.105204i
\(171\) 0 0
\(172\) 4.53390i 0.345706i
\(173\) 14.0158i 1.06560i −0.846240 0.532801i \(-0.821139\pi\)
0.846240 0.532801i \(-0.178861\pi\)
\(174\) 0 0
\(175\) −15.6748 + 3.44629i −1.18490 + 0.260515i
\(176\) −3.82327 −0.288190
\(177\) 0 0
\(178\) 6.46929i 0.484894i
\(179\) −12.4160 −0.928019 −0.464009 0.885830i \(-0.653590\pi\)
−0.464009 + 0.885830i \(0.653590\pi\)
\(180\) 0 0
\(181\) 8.19748 0.609314 0.304657 0.952462i \(-0.401458\pi\)
0.304657 + 0.952462i \(0.401458\pi\)
\(182\) 0.472913i 0.0350546i
\(183\) 0 0
\(184\) 2.33616 0.172224
\(185\) −1.40113 + 1.74265i −0.103013 + 0.128122i
\(186\) 0 0
\(187\) 3.74294i 0.273711i
\(188\) 6.23085i 0.454431i
\(189\) 0 0
\(190\) −3.74934 + 4.66323i −0.272006 + 0.338306i
\(191\) −8.00137 −0.578959 −0.289479 0.957184i \(-0.593482\pi\)
−0.289479 + 0.957184i \(0.593482\pi\)
\(192\) 0 0
\(193\) 14.0420i 1.01077i −0.862895 0.505383i \(-0.831351\pi\)
0.862895 0.505383i \(-0.168649\pi\)
\(194\) −3.07063 −0.220458
\(195\) 0 0
\(196\) 3.30305 0.235932
\(197\) 3.36608i 0.239823i 0.992785 + 0.119912i \(0.0382612\pi\)
−0.992785 + 0.119912i \(0.961739\pi\)
\(198\) 0 0
\(199\) 14.8890 1.05545 0.527725 0.849415i \(-0.323045\pi\)
0.527725 + 0.849415i \(0.323045\pi\)
\(200\) 4.88336 1.07367i 0.345306 0.0759197i
\(201\) 0 0
\(202\) 6.57513i 0.462624i
\(203\) 20.2356i 1.42026i
\(204\) 0 0
\(205\) 20.6094 + 16.5704i 1.43942 + 1.15733i
\(206\) 2.52180 0.175702
\(207\) 0 0
\(208\) 0.147332i 0.0102157i
\(209\) 10.2308 0.707683
\(210\) 0 0
\(211\) −9.80544 −0.675035 −0.337517 0.941319i \(-0.609587\pi\)
−0.337517 + 0.941319i \(0.609587\pi\)
\(212\) 11.2978i 0.775939i
\(213\) 0 0
\(214\) −5.70291 −0.389843
\(215\) −6.35258 + 7.90100i −0.433242 + 0.538844i
\(216\) 0 0
\(217\) 11.6316i 0.789601i
\(218\) 11.9318i 0.808121i
\(219\) 0 0
\(220\) −6.66263 5.35690i −0.449194 0.361162i
\(221\) −0.144237 −0.00970241
\(222\) 0 0
\(223\) 15.4447i 1.03425i −0.855910 0.517125i \(-0.827002\pi\)
0.855910 0.517125i \(-0.172998\pi\)
\(224\) −3.20984 −0.214466
\(225\) 0 0
\(226\) −2.18044 −0.145041
\(227\) 6.46090i 0.428825i 0.976743 + 0.214413i \(0.0687837\pi\)
−0.976743 + 0.214413i \(0.931216\pi\)
\(228\) 0 0
\(229\) −7.97458 −0.526975 −0.263488 0.964663i \(-0.584873\pi\)
−0.263488 + 0.964663i \(0.584873\pi\)
\(230\) 4.07111 + 3.27326i 0.268441 + 0.215832i
\(231\) 0 0
\(232\) 6.30425i 0.413894i
\(233\) 25.2907i 1.65685i −0.560103 0.828423i \(-0.689238\pi\)
0.560103 0.828423i \(-0.310762\pi\)
\(234\) 0 0
\(235\) 8.73023 10.8582i 0.569497 0.708310i
\(236\) −6.92858 −0.451012
\(237\) 0 0
\(238\) 3.14239i 0.203691i
\(239\) 5.11481 0.330850 0.165425 0.986222i \(-0.447100\pi\)
0.165425 + 0.986222i \(0.447100\pi\)
\(240\) 0 0
\(241\) 16.4415 1.05909 0.529544 0.848282i \(-0.322363\pi\)
0.529544 + 0.848282i \(0.322363\pi\)
\(242\) 3.61741i 0.232536i
\(243\) 0 0
\(244\) −10.4885 −0.671457
\(245\) 5.75606 + 4.62800i 0.367741 + 0.295672i
\(246\) 0 0
\(247\) 0.394252i 0.0250857i
\(248\) 3.62372i 0.230107i
\(249\) 0 0
\(250\) 10.0143 + 4.97120i 0.633363 + 0.314407i
\(251\) −6.35586 −0.401178 −0.200589 0.979675i \(-0.564286\pi\)
−0.200589 + 0.979675i \(0.564286\pi\)
\(252\) 0 0
\(253\) 8.93177i 0.561535i
\(254\) −5.39390 −0.338444
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 5.45772i 0.340443i −0.985406 0.170222i \(-0.945552\pi\)
0.985406 0.170222i \(-0.0544484\pi\)
\(258\) 0 0
\(259\) 3.20984 0.199450
\(260\) −0.206432 + 0.256749i −0.0128024 + 0.0159229i
\(261\) 0 0
\(262\) 8.97060i 0.554206i
\(263\) 14.8882i 0.918044i 0.888425 + 0.459022i \(0.151800\pi\)
−0.888425 + 0.459022i \(0.848200\pi\)
\(264\) 0 0
\(265\) −15.8298 + 19.6882i −0.972414 + 1.20944i
\(266\) 8.58933 0.526646
\(267\) 0 0
\(268\) 2.80936i 0.171609i
\(269\) 15.5573 0.948546 0.474273 0.880378i \(-0.342711\pi\)
0.474273 + 0.880378i \(0.342711\pi\)
\(270\) 0 0
\(271\) 0.462920 0.0281204 0.0140602 0.999901i \(-0.495524\pi\)
0.0140602 + 0.999901i \(0.495524\pi\)
\(272\) 0.978989i 0.0593599i
\(273\) 0 0
\(274\) 2.70352 0.163326
\(275\) −4.10492 18.6704i −0.247536 1.12587i
\(276\) 0 0
\(277\) 9.12112i 0.548035i −0.961725 0.274018i \(-0.911647\pi\)
0.961725 0.274018i \(-0.0883526\pi\)
\(278\) 4.30358i 0.258111i
\(279\) 0 0
\(280\) −5.59362 4.49740i −0.334283 0.268771i
\(281\) 24.8734 1.48382 0.741912 0.670497i \(-0.233919\pi\)
0.741912 + 0.670497i \(0.233919\pi\)
\(282\) 0 0
\(283\) 19.7259i 1.17258i 0.810100 + 0.586292i \(0.199413\pi\)
−0.810100 + 0.586292i \(0.800587\pi\)
\(284\) −12.3189 −0.730990
\(285\) 0 0
\(286\) 0.563292 0.0333081
\(287\) 37.9610i 2.24077i
\(288\) 0 0
\(289\) 16.0416 0.943622
\(290\) 8.83308 10.9861i 0.518696 0.645126i
\(291\) 0 0
\(292\) 13.9966i 0.819090i
\(293\) 2.65528i 0.155123i 0.996988 + 0.0775615i \(0.0247134\pi\)
−0.996988 + 0.0775615i \(0.975287\pi\)
\(294\) 0 0
\(295\) −12.0741 9.70785i −0.702981 0.565213i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 21.6949i 1.25675i
\(299\) −0.344191 −0.0199051
\(300\) 0 0
\(301\) 14.5531 0.838825
\(302\) 2.06744i 0.118968i
\(303\) 0 0
\(304\) −2.67594 −0.153476
\(305\) −18.2778 14.6957i −1.04658 0.841476i
\(306\) 0 0
\(307\) 25.3545i 1.44706i 0.690295 + 0.723528i \(0.257481\pi\)
−0.690295 + 0.723528i \(0.742519\pi\)
\(308\) 12.2721i 0.699267i
\(309\) 0 0
\(310\) −5.07731 + 6.31488i −0.288372 + 0.358661i
\(311\) −11.1234 −0.630748 −0.315374 0.948967i \(-0.602130\pi\)
−0.315374 + 0.948967i \(0.602130\pi\)
\(312\) 0 0
\(313\) 3.49109i 0.197328i 0.995121 + 0.0986640i \(0.0314569\pi\)
−0.995121 + 0.0986640i \(0.968543\pi\)
\(314\) 18.5439 1.04649
\(315\) 0 0
\(316\) 15.6057 0.877890
\(317\) 18.3656i 1.03152i 0.856734 + 0.515759i \(0.172490\pi\)
−0.856734 + 0.515759i \(0.827510\pi\)
\(318\) 0 0
\(319\) −24.1029 −1.34950
\(320\) 1.74265 + 1.40113i 0.0974172 + 0.0783256i
\(321\) 0 0
\(322\) 7.49868i 0.417885i
\(323\) 2.61972i 0.145765i
\(324\) 0 0
\(325\) −0.719477 + 0.158186i −0.0399094 + 0.00877457i
\(326\) 21.6240 1.19764
\(327\) 0 0
\(328\) 11.8265i 0.653007i
\(329\) −20.0000 −1.10264
\(330\) 0 0
\(331\) −21.9365 −1.20574 −0.602870 0.797839i \(-0.705976\pi\)
−0.602870 + 0.797839i \(0.705976\pi\)
\(332\) 13.5371i 0.742944i
\(333\) 0 0
\(334\) 11.7729 0.644183
\(335\) −3.93628 + 4.89574i −0.215062 + 0.267483i
\(336\) 0 0
\(337\) 8.65472i 0.471453i 0.971819 + 0.235726i \(0.0757469\pi\)
−0.971819 + 0.235726i \(0.924253\pi\)
\(338\) 12.9783i 0.705926i
\(339\) 0 0
\(340\) −1.37169 + 1.70604i −0.0743904 + 0.0925228i
\(341\) 13.8545 0.750262
\(342\) 0 0
\(343\) 11.8666i 0.640737i
\(344\) −4.53390 −0.244451
\(345\) 0 0
\(346\) 14.0158 0.753495
\(347\) 21.3265i 1.14486i −0.819952 0.572432i \(-0.806000\pi\)
0.819952 0.572432i \(-0.194000\pi\)
\(348\) 0 0
\(349\) 1.16305 0.0622569 0.0311285 0.999515i \(-0.490090\pi\)
0.0311285 + 0.999515i \(0.490090\pi\)
\(350\) −3.44629 15.6748i −0.184212 0.837853i
\(351\) 0 0
\(352\) 3.82327i 0.203781i
\(353\) 0.470079i 0.0250198i 0.999922 + 0.0125099i \(0.00398213\pi\)
−0.999922 + 0.0125099i \(0.996018\pi\)
\(354\) 0 0
\(355\) −21.4675 17.2603i −1.13938 0.916083i
\(356\) 6.46929 0.342872
\(357\) 0 0
\(358\) 12.4160i 0.656208i
\(359\) −33.3086 −1.75796 −0.878981 0.476856i \(-0.841776\pi\)
−0.878981 + 0.476856i \(0.841776\pi\)
\(360\) 0 0
\(361\) −11.8393 −0.623123
\(362\) 8.19748i 0.430850i
\(363\) 0 0
\(364\) 0.472913 0.0247874
\(365\) −19.6111 + 24.3912i −1.02649 + 1.27669i
\(366\) 0 0
\(367\) 11.1884i 0.584029i 0.956414 + 0.292014i \(0.0943255\pi\)
−0.956414 + 0.292014i \(0.905674\pi\)
\(368\) 2.33616i 0.121781i
\(369\) 0 0
\(370\) −1.74265 1.40113i −0.0905961 0.0728413i
\(371\) 36.2642 1.88275
\(372\) 0 0
\(373\) 23.1634i 1.19936i 0.800242 + 0.599678i \(0.204705\pi\)
−0.800242 + 0.599678i \(0.795295\pi\)
\(374\) 3.74294 0.193543
\(375\) 0 0
\(376\) 6.23085 0.321331
\(377\) 0.928820i 0.0478366i
\(378\) 0 0
\(379\) 26.7721 1.37519 0.687595 0.726095i \(-0.258667\pi\)
0.687595 + 0.726095i \(0.258667\pi\)
\(380\) −4.66323 3.74934i −0.239219 0.192337i
\(381\) 0 0
\(382\) 8.00137i 0.409386i
\(383\) 22.3189i 1.14044i −0.821492 0.570220i \(-0.806858\pi\)
0.821492 0.570220i \(-0.193142\pi\)
\(384\) 0 0
\(385\) −17.1948 + 21.3860i −0.876327 + 1.08993i
\(386\) 14.0420 0.714720
\(387\) 0 0
\(388\) 3.07063i 0.155887i
\(389\) −24.3011 −1.23211 −0.616057 0.787701i \(-0.711271\pi\)
−0.616057 + 0.787701i \(0.711271\pi\)
\(390\) 0 0
\(391\) −2.28707 −0.115662
\(392\) 3.30305i 0.166829i
\(393\) 0 0
\(394\) −3.36608 −0.169581
\(395\) 27.1953 + 21.8657i 1.36835 + 1.10018i
\(396\) 0 0
\(397\) 28.1888i 1.41476i −0.706835 0.707378i \(-0.749878\pi\)
0.706835 0.707378i \(-0.250122\pi\)
\(398\) 14.8890i 0.746316i
\(399\) 0 0
\(400\) 1.07367 + 4.88336i 0.0536833 + 0.244168i
\(401\) 15.9528 0.796644 0.398322 0.917246i \(-0.369593\pi\)
0.398322 + 0.917246i \(0.369593\pi\)
\(402\) 0 0
\(403\) 0.533891i 0.0265950i
\(404\) −6.57513 −0.327125
\(405\) 0 0
\(406\) −20.2356 −1.00428
\(407\) 3.82327i 0.189513i
\(408\) 0 0
\(409\) −31.6014 −1.56259 −0.781294 0.624164i \(-0.785440\pi\)
−0.781294 + 0.624164i \(0.785440\pi\)
\(410\) −16.5704 + 20.6094i −0.818354 + 1.01783i
\(411\) 0 0
\(412\) 2.52180i 0.124240i
\(413\) 22.2396i 1.09434i
\(414\) 0 0
\(415\) −18.9672 + 23.5904i −0.931064 + 1.15801i
\(416\) −0.147332 −0.00722356
\(417\) 0 0
\(418\) 10.2308i 0.500407i
\(419\) −18.4266 −0.900197 −0.450098 0.892979i \(-0.648611\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(420\) 0 0
\(421\) −19.1570 −0.933655 −0.466828 0.884348i \(-0.654603\pi\)
−0.466828 + 0.884348i \(0.654603\pi\)
\(422\) 9.80544i 0.477322i
\(423\) 0 0
\(424\) −11.2978 −0.548672
\(425\) −4.78076 + 1.05111i −0.231901 + 0.0509862i
\(426\) 0 0
\(427\) 33.6663i 1.62923i
\(428\) 5.70291i 0.275661i
\(429\) 0 0
\(430\) −7.90100 6.35258i −0.381020 0.306349i
\(431\) 10.3947 0.500694 0.250347 0.968156i \(-0.419455\pi\)
0.250347 + 0.968156i \(0.419455\pi\)
\(432\) 0 0
\(433\) 3.36622i 0.161770i 0.996723 + 0.0808852i \(0.0257747\pi\)
−0.996723 + 0.0808852i \(0.974225\pi\)
\(434\) 11.6316 0.558332
\(435\) 0 0
\(436\) 11.9318 0.571428
\(437\) 6.25142i 0.299046i
\(438\) 0 0
\(439\) 32.5045 1.55135 0.775677 0.631130i \(-0.217409\pi\)
0.775677 + 0.631130i \(0.217409\pi\)
\(440\) 5.35690 6.66263i 0.255380 0.317628i
\(441\) 0 0
\(442\) 0.144237i 0.00686064i
\(443\) 23.5479i 1.11879i 0.828900 + 0.559397i \(0.188967\pi\)
−0.828900 + 0.559397i \(0.811033\pi\)
\(444\) 0 0
\(445\) 11.2737 + 9.06432i 0.534425 + 0.429690i
\(446\) 15.4447 0.731325
\(447\) 0 0
\(448\) 3.20984i 0.151651i
\(449\) 12.5629 0.592878 0.296439 0.955052i \(-0.404201\pi\)
0.296439 + 0.955052i \(0.404201\pi\)
\(450\) 0 0
\(451\) 45.2158 2.12913
\(452\) 2.18044i 0.102559i
\(453\) 0 0
\(454\) −6.46090 −0.303225
\(455\) 0.824122 + 0.662612i 0.0386354 + 0.0310637i
\(456\) 0 0
\(457\) 6.53390i 0.305643i −0.988254 0.152821i \(-0.951164\pi\)
0.988254 0.152821i \(-0.0488359\pi\)
\(458\) 7.97458i 0.372628i
\(459\) 0 0
\(460\) −3.27326 + 4.07111i −0.152617 + 0.189816i
\(461\) −24.7616 −1.15326 −0.576631 0.817005i \(-0.695633\pi\)
−0.576631 + 0.817005i \(0.695633\pi\)
\(462\) 0 0
\(463\) 25.9239i 1.20479i 0.798200 + 0.602393i \(0.205786\pi\)
−0.798200 + 0.602393i \(0.794214\pi\)
\(464\) 6.30425 0.292667
\(465\) 0 0
\(466\) 25.2907 1.17157
\(467\) 28.8182i 1.33355i 0.745261 + 0.666773i \(0.232325\pi\)
−0.745261 + 0.666773i \(0.767675\pi\)
\(468\) 0 0
\(469\) 9.01759 0.416394
\(470\) 10.8582 + 8.73023i 0.500851 + 0.402696i
\(471\) 0 0
\(472\) 6.92858i 0.318914i
\(473\) 17.3343i 0.797033i
\(474\) 0 0
\(475\) −2.87307 13.0676i −0.131825 0.599582i
\(476\) 3.14239 0.144031
\(477\) 0 0
\(478\) 5.11481i 0.233946i
\(479\) −41.7873 −1.90931 −0.954655 0.297714i \(-0.903776\pi\)
−0.954655 + 0.297714i \(0.903776\pi\)
\(480\) 0 0
\(481\) 0.147332 0.00671778
\(482\) 16.4415i 0.748888i
\(483\) 0 0
\(484\) −3.61741 −0.164428
\(485\) 4.30235 5.35103i 0.195360 0.242978i
\(486\) 0 0
\(487\) 9.34463i 0.423446i −0.977330 0.211723i \(-0.932093\pi\)
0.977330 0.211723i \(-0.0679074\pi\)
\(488\) 10.4885i 0.474791i
\(489\) 0 0
\(490\) −4.62800 + 5.75606i −0.209072 + 0.260032i
\(491\) 10.7558 0.485404 0.242702 0.970101i \(-0.421966\pi\)
0.242702 + 0.970101i \(0.421966\pi\)
\(492\) 0 0
\(493\) 6.17179i 0.277963i
\(494\) 0.394252 0.0177383
\(495\) 0 0
\(496\) −3.62372 −0.162710
\(497\) 39.5415i 1.77368i
\(498\) 0 0
\(499\) −29.0702 −1.30136 −0.650680 0.759352i \(-0.725516\pi\)
−0.650680 + 0.759352i \(0.725516\pi\)
\(500\) −4.97120 + 10.0143i −0.222319 + 0.447855i
\(501\) 0 0
\(502\) 6.35586i 0.283676i
\(503\) 36.2683i 1.61712i −0.588412 0.808561i \(-0.700247\pi\)
0.588412 0.808561i \(-0.299753\pi\)
\(504\) 0 0
\(505\) −11.4582 9.21261i −0.509881 0.409956i
\(506\) 8.93177 0.397065
\(507\) 0 0
\(508\) 5.39390i 0.239316i
\(509\) −22.2170 −0.984751 −0.492375 0.870383i \(-0.663871\pi\)
−0.492375 + 0.870383i \(0.663871\pi\)
\(510\) 0 0
\(511\) 44.9268 1.98745
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 5.45772 0.240730
\(515\) −3.53337 + 4.39462i −0.155699 + 0.193650i
\(516\) 0 0
\(517\) 23.8222i 1.04770i
\(518\) 3.20984i 0.141032i
\(519\) 0 0
\(520\) −0.256749 0.206432i −0.0112592 0.00905263i
\(521\) −41.2732 −1.80821 −0.904107 0.427306i \(-0.859463\pi\)
−0.904107 + 0.427306i \(0.859463\pi\)
\(522\) 0 0
\(523\) 11.0354i 0.482545i 0.970457 + 0.241273i \(0.0775648\pi\)
−0.970457 + 0.241273i \(0.922435\pi\)
\(524\) −8.97060 −0.391883
\(525\) 0 0
\(526\) −14.8882 −0.649155
\(527\) 3.54758i 0.154535i
\(528\) 0 0
\(529\) 17.5424 0.762712
\(530\) −19.6882 15.8298i −0.855201 0.687601i
\(531\) 0 0
\(532\) 8.58933i 0.372395i
\(533\) 1.74242i 0.0754726i
\(534\) 0 0
\(535\) 7.99052 9.93818i 0.345460 0.429665i
\(536\) −2.80936 −0.121346
\(537\) 0 0
\(538\) 15.5573i 0.670723i
\(539\) 12.6285 0.543946
\(540\) 0 0
\(541\) −32.2338 −1.38584 −0.692920 0.721014i \(-0.743676\pi\)
−0.692920 + 0.721014i \(0.743676\pi\)
\(542\) 0.462920i 0.0198841i
\(543\) 0 0
\(544\) −0.978989 −0.0419738
\(545\) 20.7929 + 16.7180i 0.890670 + 0.716119i
\(546\) 0 0
\(547\) 15.0234i 0.642355i −0.947019 0.321177i \(-0.895921\pi\)
0.947019 0.321177i \(-0.104079\pi\)
\(548\) 2.70352i 0.115489i
\(549\) 0 0
\(550\) 18.6704 4.10492i 0.796110 0.175034i
\(551\) −16.8698 −0.718677
\(552\) 0 0
\(553\) 50.0918i 2.13012i
\(554\) 9.12112 0.387519
\(555\) 0 0
\(556\) 4.30358 0.182512
\(557\) 39.1275i 1.65788i 0.559334 + 0.828942i \(0.311057\pi\)
−0.559334 + 0.828942i \(0.688943\pi\)
\(558\) 0 0
\(559\) 0.667989 0.0282529
\(560\) 4.49740 5.59362i 0.190050 0.236374i
\(561\) 0 0
\(562\) 24.8734i 1.04922i
\(563\) 27.1970i 1.14622i 0.819479 + 0.573109i \(0.194263\pi\)
−0.819479 + 0.573109i \(0.805737\pi\)
\(564\) 0 0
\(565\) 3.05508 3.79975i 0.128528 0.159857i
\(566\) −19.7259 −0.829142
\(567\) 0 0
\(568\) 12.3189i 0.516888i
\(569\) −33.4499 −1.40229 −0.701146 0.713018i \(-0.747328\pi\)
−0.701146 + 0.713018i \(0.747328\pi\)
\(570\) 0 0
\(571\) 28.9145 1.21003 0.605017 0.796213i \(-0.293166\pi\)
0.605017 + 0.796213i \(0.293166\pi\)
\(572\) 0.563292i 0.0235524i
\(573\) 0 0
\(574\) 37.9610 1.58446
\(575\) −11.4083 + 2.50825i −0.475759 + 0.104601i
\(576\) 0 0
\(577\) 33.5613i 1.39717i −0.715525 0.698587i \(-0.753812\pi\)
0.715525 0.698587i \(-0.246188\pi\)
\(578\) 16.0416i 0.667242i
\(579\) 0 0
\(580\) 10.9861 + 8.83308i 0.456173 + 0.366774i
\(581\) 43.4518 1.80268
\(582\) 0 0
\(583\) 43.1948i 1.78894i
\(584\) −13.9966 −0.579184
\(585\) 0 0
\(586\) −2.65528 −0.109689
\(587\) 4.83581i 0.199595i −0.995008 0.0997976i \(-0.968180\pi\)
0.995008 0.0997976i \(-0.0318195\pi\)
\(588\) 0 0
\(589\) 9.69686 0.399552
\(590\) 9.70785 12.0741i 0.399666 0.497083i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 43.1680i 1.77270i −0.463020 0.886348i \(-0.653234\pi\)
0.463020 0.886348i \(-0.346766\pi\)
\(594\) 0 0
\(595\) 5.47610 + 4.40290i 0.224498 + 0.180501i
\(596\) −21.6949 −0.888659
\(597\) 0 0
\(598\) 0.344191i 0.0140750i
\(599\) −38.7714 −1.58416 −0.792078 0.610420i \(-0.791001\pi\)
−0.792078 + 0.610420i \(0.791001\pi\)
\(600\) 0 0
\(601\) 1.56064 0.0636597 0.0318299 0.999493i \(-0.489867\pi\)
0.0318299 + 0.999493i \(0.489867\pi\)
\(602\) 14.5531i 0.593139i
\(603\) 0 0
\(604\) −2.06744 −0.0841230
\(605\) −6.30389 5.06847i −0.256289 0.206062i
\(606\) 0 0
\(607\) 21.0494i 0.854370i −0.904164 0.427185i \(-0.859505\pi\)
0.904164 0.427185i \(-0.140495\pi\)
\(608\) 2.67594i 0.108524i
\(609\) 0 0
\(610\) 14.6957 18.2778i 0.595013 0.740045i
\(611\) −0.918005 −0.0371385
\(612\) 0 0
\(613\) 5.28786i 0.213574i −0.994282 0.106787i \(-0.965944\pi\)
0.994282 0.106787i \(-0.0340564\pi\)
\(614\) −25.3545 −1.02322
\(615\) 0 0
\(616\) −12.2721 −0.494456
\(617\) 34.8545i 1.40319i −0.712576 0.701595i \(-0.752472\pi\)
0.712576 0.701595i \(-0.247528\pi\)
\(618\) 0 0
\(619\) 7.30122 0.293461 0.146730 0.989177i \(-0.453125\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(620\) −6.31488 5.07731i −0.253612 0.203910i
\(621\) 0 0
\(622\) 11.1234i 0.446006i
\(623\) 20.7654i 0.831946i
\(624\) 0 0
\(625\) −22.6945 + 10.4862i −0.907779 + 0.419448i
\(626\) −3.49109 −0.139532
\(627\) 0 0
\(628\) 18.5439i 0.739982i
\(629\) 0.978989 0.0390348
\(630\) 0 0
\(631\) 24.2752 0.966381 0.483190 0.875515i \(-0.339478\pi\)
0.483190 + 0.875515i \(0.339478\pi\)
\(632\) 15.6057i 0.620762i
\(633\) 0 0
\(634\) −18.3656 −0.729393
\(635\) 7.55756 9.39969i 0.299913 0.373015i
\(636\) 0 0
\(637\) 0.486646i 0.0192816i
\(638\) 24.1029i 0.954241i
\(639\) 0 0
\(640\) −1.40113 + 1.74265i −0.0553845 + 0.0688843i
\(641\) 8.22087 0.324705 0.162353 0.986733i \(-0.448092\pi\)
0.162353 + 0.986733i \(0.448092\pi\)
\(642\) 0 0
\(643\) 29.7758i 1.17424i 0.809499 + 0.587121i \(0.199739\pi\)
−0.809499 + 0.587121i \(0.800261\pi\)
\(644\) 7.49868 0.295489
\(645\) 0 0
\(646\) 2.61972 0.103071
\(647\) 35.6356i 1.40098i −0.713662 0.700490i \(-0.752965\pi\)
0.713662 0.700490i \(-0.247035\pi\)
\(648\) 0 0
\(649\) −26.4899 −1.03982
\(650\) −0.158186 0.719477i −0.00620455 0.0282202i
\(651\) 0 0
\(652\) 21.6240i 0.846860i
\(653\) 37.6128i 1.47190i −0.677035 0.735951i \(-0.736736\pi\)
0.677035 0.735951i \(-0.263264\pi\)
\(654\) 0 0
\(655\) −15.6326 12.5690i −0.610818 0.491111i
\(656\) −11.8265 −0.461746
\(657\) 0 0
\(658\) 20.0000i 0.779681i
\(659\) 45.0553 1.75510 0.877552 0.479481i \(-0.159175\pi\)
0.877552 + 0.479481i \(0.159175\pi\)
\(660\) 0 0
\(661\) 7.32365 0.284857 0.142429 0.989805i \(-0.454509\pi\)
0.142429 + 0.989805i \(0.454509\pi\)
\(662\) 21.9365i 0.852587i
\(663\) 0 0
\(664\) −13.5371 −0.525341
\(665\) −12.0348 + 14.9682i −0.466688 + 0.580442i
\(666\) 0 0
\(667\) 14.7277i 0.570260i
\(668\) 11.7729i 0.455506i
\(669\) 0 0
\(670\) −4.89574 3.93628i −0.189139 0.152072i
\(671\) −40.1003 −1.54806
\(672\) 0 0
\(673\) 8.58807i 0.331046i −0.986206 0.165523i \(-0.947069\pi\)
0.986206 0.165523i \(-0.0529312\pi\)
\(674\) −8.65472 −0.333368
\(675\) 0 0
\(676\) −12.9783 −0.499165
\(677\) 9.13523i 0.351096i −0.984471 0.175548i \(-0.943830\pi\)
0.984471 0.175548i \(-0.0561697\pi\)
\(678\) 0 0
\(679\) −9.85621 −0.378247
\(680\) −1.70604 1.37169i −0.0654235 0.0526020i
\(681\) 0 0
\(682\) 13.8545i 0.530515i
\(683\) 40.7414i 1.55893i 0.626449 + 0.779463i \(0.284508\pi\)
−0.626449 + 0.779463i \(0.715492\pi\)
\(684\) 0 0
\(685\) −3.78799 + 4.71130i −0.144732 + 0.180009i
\(686\) −11.8666 −0.453069
\(687\) 0 0
\(688\) 4.53390i 0.172853i
\(689\) 1.66454 0.0634139
\(690\) 0 0
\(691\) −28.7543 −1.09387 −0.546933 0.837176i \(-0.684205\pi\)
−0.546933 + 0.837176i \(0.684205\pi\)
\(692\) 14.0158i 0.532801i
\(693\) 0 0
\(694\) 21.3265 0.809541
\(695\) 7.49964 + 6.02988i 0.284477 + 0.228726i
\(696\) 0 0
\(697\) 11.5780i 0.438547i
\(698\) 1.16305i 0.0440223i
\(699\) 0 0
\(700\) 15.6748 3.44629i 0.592452 0.130258i
\(701\) 7.87020 0.297253 0.148627 0.988893i \(-0.452515\pi\)
0.148627 + 0.988893i \(0.452515\pi\)
\(702\) 0 0
\(703\) 2.67594i 0.100925i
\(704\) 3.82327 0.144095
\(705\) 0 0
\(706\) −0.470079 −0.0176917
\(707\) 21.1051i 0.793738i
\(708\) 0 0
\(709\) −33.0458 −1.24106 −0.620530 0.784182i \(-0.713083\pi\)
−0.620530 + 0.784182i \(0.713083\pi\)
\(710\) 17.2603 21.4675i 0.647769 0.805660i
\(711\) 0 0
\(712\) 6.46929i 0.242447i
\(713\) 8.46558i 0.317039i
\(714\) 0 0
\(715\) −0.789245 + 0.981621i −0.0295161 + 0.0367105i
\(716\) 12.4160 0.464009
\(717\) 0 0
\(718\) 33.3086i 1.24307i
\(719\) 4.94138 0.184282 0.0921412 0.995746i \(-0.470629\pi\)
0.0921412 + 0.995746i \(0.470629\pi\)
\(720\) 0 0
\(721\) 8.09456 0.301457
\(722\) 11.8393i 0.440615i
\(723\) 0 0
\(724\) −8.19748 −0.304657
\(725\) 6.76866 + 30.7859i 0.251382 + 1.14336i
\(726\) 0 0
\(727\) 42.5178i 1.57690i −0.615101 0.788448i \(-0.710885\pi\)
0.615101 0.788448i \(-0.289115\pi\)
\(728\) 0.472913i 0.0175273i
\(729\) 0 0
\(730\) −24.3912 19.6111i −0.902759 0.725839i
\(731\) 4.43863 0.164169
\(732\) 0 0
\(733\) 10.2114i 0.377167i 0.982057 + 0.188584i \(0.0603896\pi\)
−0.982057 + 0.188584i \(0.939610\pi\)
\(734\) −11.1884 −0.412971
\(735\) 0 0
\(736\) −2.33616 −0.0861119
\(737\) 10.7410i 0.395648i
\(738\) 0 0
\(739\) −25.5528 −0.939975 −0.469988 0.882673i \(-0.655742\pi\)
−0.469988 + 0.882673i \(0.655742\pi\)
\(740\) 1.40113 1.74265i 0.0515066 0.0640611i
\(741\) 0 0
\(742\) 36.2642i 1.33130i
\(743\) 44.2852i 1.62467i −0.583193 0.812334i \(-0.698197\pi\)
0.583193 0.812334i \(-0.301803\pi\)
\(744\) 0 0
\(745\) −37.8067 30.3974i −1.38513 1.11368i
\(746\) −23.1634 −0.848072
\(747\) 0 0
\(748\) 3.74294i 0.136855i
\(749\) −18.3054 −0.668865
\(750\) 0 0
\(751\) 41.2897 1.50668 0.753342 0.657629i \(-0.228440\pi\)
0.753342 + 0.657629i \(0.228440\pi\)
\(752\) 6.23085i 0.227216i
\(753\) 0 0
\(754\) −0.928820 −0.0338256
\(755\) −3.60283 2.89676i −0.131120 0.105424i
\(756\) 0 0
\(757\) 6.57802i 0.239082i −0.992829 0.119541i \(-0.961858\pi\)
0.992829 0.119541i \(-0.0381423\pi\)
\(758\) 26.7721i 0.972406i
\(759\) 0 0
\(760\) 3.74934 4.66323i 0.136003 0.169153i
\(761\) −20.3166 −0.736475 −0.368237 0.929732i \(-0.620039\pi\)
−0.368237 + 0.929732i \(0.620039\pi\)
\(762\) 0 0
\(763\) 38.2990i 1.38652i
\(764\) 8.00137 0.289479
\(765\) 0 0
\(766\) 22.3189 0.806413
\(767\) 1.02080i 0.0368591i
\(768\) 0 0
\(769\) −25.2435 −0.910303 −0.455151 0.890414i \(-0.650415\pi\)
−0.455151 + 0.890414i \(0.650415\pi\)
\(770\) −21.3860 17.1948i −0.770696 0.619657i
\(771\) 0 0
\(772\) 14.0420i 0.505383i
\(773\) 48.9781i 1.76162i 0.473470 + 0.880810i \(0.343001\pi\)
−0.473470 + 0.880810i \(0.656999\pi\)
\(774\) 0 0
\(775\) −3.89067 17.6959i −0.139757 0.635657i
\(776\) 3.07063 0.110229
\(777\) 0 0
\(778\) 24.3011i 0.871237i
\(779\) 31.6469 1.13387
\(780\) 0 0
\(781\) −47.0984 −1.68531
\(782\) 2.28707i 0.0817855i
\(783\) 0 0
\(784\) −3.30305 −0.117966
\(785\) −25.9824 + 32.3155i −0.927352 + 1.15339i
\(786\) 0 0
\(787\) 3.78073i 0.134768i 0.997727 + 0.0673842i \(0.0214653\pi\)
−0.997727 + 0.0673842i \(0.978535\pi\)
\(788\) 3.36608i 0.119912i
\(789\) 0 0
\(790\) −21.8657 + 27.1953i −0.777945 + 0.967566i
\(791\) −6.99886 −0.248851
\(792\) 0 0
\(793\) 1.54529i 0.0548750i
\(794\) 28.1888 1.00038
\(795\) 0 0
\(796\) −14.8890 −0.527725
\(797\) 29.5487i 1.04667i −0.852128 0.523334i