Properties

Label 1323.2.g.g.361.4
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{5} \)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.4
Root \(-1.29589 + 0.748185i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.g.667.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +2.59179 q^{5} +0.942820 q^{8} +O(q^{10})\) \(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +2.59179 q^{5} +0.942820 q^{8} +(0.309879 - 0.536725i) q^{10} -4.18194 q^{11} +(-1.84155 + 3.18966i) q^{13} +(-1.83009 + 3.16982i) q^{16} +(0.855536 - 1.48183i) q^{17} +(3.57780 + 6.19694i) q^{19} +(2.51769 + 4.36077i) q^{20} +(-0.500000 + 0.866025i) q^{22} +5.12476 q^{23} +1.71737 q^{25} +(0.440358 + 0.762722i) q^{26} +(-1.06238 - 1.84010i) q^{29} +(3.26793 + 5.66021i) q^{31} +(1.38044 + 2.39099i) q^{32} +(-0.204579 - 0.354341i) q^{34} +(-0.830095 - 1.43777i) q^{37} +1.71107 q^{38} +2.44359 q^{40} +(-5.10948 + 8.84988i) q^{41} +(0.830095 + 1.43777i) q^{43} +(-4.06238 - 7.03625i) q^{44} +(0.612725 - 1.06127i) q^{46} +(4.66912 - 8.08715i) q^{47} +(0.205332 - 0.355645i) q^{50} -7.15561 q^{52} +(5.32326 - 9.22015i) q^{53} -10.8387 q^{55} -0.508080 q^{58} +(3.03215 + 5.25183i) q^{59} +(3.99298 - 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(-4.77292 + 8.26693i) q^{65} +(-4.13160 - 7.15614i) q^{67} +3.32431 q^{68} -6.23912 q^{71} +(-3.57780 + 6.19694i) q^{73} -0.396990 q^{74} +(-6.95103 + 12.0395i) q^{76} +(4.91423 - 8.51170i) q^{79} +(-4.74322 + 8.21550i) q^{80} +(1.22180 + 2.11621i) q^{82} +(3.44733 + 5.97094i) q^{83} +(2.21737 - 3.84060i) q^{85} +0.396990 q^{86} -3.94282 q^{88} +(-2.51769 - 4.36077i) q^{89} +(4.97825 + 8.62258i) q^{92} +(-1.11650 - 1.93383i) q^{94} +(9.27292 + 16.0612i) q^{95} +(-1.53167 - 2.65294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} + O(q^{10}) \) \( 12q + 2q^{2} - 6q^{4} - 24q^{8} - 16q^{11} - 6q^{16} - 6q^{22} - 8q^{23} + 24q^{25} + 22q^{29} + 16q^{32} + 6q^{37} - 6q^{43} - 14q^{44} - 12q^{46} + 56q^{50} + 28q^{53} + 36q^{58} - 48q^{64} - 6q^{65} - 76q^{71} - 72q^{74} + 6q^{79} + 30q^{85} + 72q^{86} - 12q^{88} + 62q^{92} + 60q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.119562 0.207087i 0.0845428 0.146433i −0.820653 0.571426i \(-0.806390\pi\)
0.905196 + 0.424994i \(0.139724\pi\)
\(3\) 0 0
\(4\) 0.971410 + 1.68253i 0.485705 + 0.841266i
\(5\) 2.59179 1.15908 0.579542 0.814943i \(-0.303232\pi\)
0.579542 + 0.814943i \(0.303232\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.942820 0.333337
\(9\) 0 0
\(10\) 0.309879 0.536725i 0.0979922 0.169727i
\(11\) −4.18194 −1.26090 −0.630452 0.776228i \(-0.717130\pi\)
−0.630452 + 0.776228i \(0.717130\pi\)
\(12\) 0 0
\(13\) −1.84155 + 3.18966i −0.510755 + 0.884653i 0.489168 + 0.872190i \(0.337301\pi\)
−0.999922 + 0.0124633i \(0.996033\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.83009 + 3.16982i −0.457524 + 0.792454i
\(17\) 0.855536 1.48183i 0.207498 0.359397i −0.743428 0.668816i \(-0.766801\pi\)
0.950926 + 0.309419i \(0.100135\pi\)
\(18\) 0 0
\(19\) 3.57780 + 6.19694i 0.820805 + 1.42168i 0.905084 + 0.425233i \(0.139808\pi\)
−0.0842790 + 0.996442i \(0.526859\pi\)
\(20\) 2.51769 + 4.36077i 0.562973 + 0.975097i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 5.12476 1.06859 0.534294 0.845299i \(-0.320578\pi\)
0.534294 + 0.845299i \(0.320578\pi\)
\(24\) 0 0
\(25\) 1.71737 0.343474
\(26\) 0.440358 + 0.762722i 0.0863613 + 0.149582i
\(27\) 0 0
\(28\) 0 0
\(29\) −1.06238 1.84010i −0.197279 0.341698i 0.750366 0.661023i \(-0.229877\pi\)
−0.947645 + 0.319325i \(0.896544\pi\)
\(30\) 0 0
\(31\) 3.26793 + 5.66021i 0.586937 + 1.01660i 0.994631 + 0.103486i \(0.0329997\pi\)
−0.407694 + 0.913119i \(0.633667\pi\)
\(32\) 1.38044 + 2.39099i 0.244029 + 0.422671i
\(33\) 0 0
\(34\) −0.204579 0.354341i −0.0350850 0.0607689i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.830095 1.43777i −0.136467 0.236367i 0.789690 0.613506i \(-0.210241\pi\)
−0.926157 + 0.377139i \(0.876908\pi\)
\(38\) 1.71107 0.277573
\(39\) 0 0
\(40\) 2.44359 0.386366
\(41\) −5.10948 + 8.84988i −0.797967 + 1.38212i 0.122972 + 0.992410i \(0.460758\pi\)
−0.920938 + 0.389708i \(0.872576\pi\)
\(42\) 0 0
\(43\) 0.830095 + 1.43777i 0.126588 + 0.219257i 0.922353 0.386349i \(-0.126264\pi\)
−0.795764 + 0.605606i \(0.792931\pi\)
\(44\) −4.06238 7.03625i −0.612427 1.06075i
\(45\) 0 0
\(46\) 0.612725 1.06127i 0.0903414 0.156476i
\(47\) 4.66912 8.08715i 0.681061 1.17963i −0.293596 0.955930i \(-0.594852\pi\)
0.974657 0.223703i \(-0.0718146\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.205332 0.355645i 0.0290383 0.0502958i
\(51\) 0 0
\(52\) −7.15561 −0.992305
\(53\) 5.32326 9.22015i 0.731206 1.26649i −0.225162 0.974321i \(-0.572291\pi\)
0.956368 0.292164i \(-0.0943754\pi\)
\(54\) 0 0
\(55\) −10.8387 −1.46149
\(56\) 0 0
\(57\) 0 0
\(58\) −0.508080 −0.0667142
\(59\) 3.03215 + 5.25183i 0.394752 + 0.683730i 0.993069 0.117529i \(-0.0374972\pi\)
−0.598318 + 0.801259i \(0.704164\pi\)
\(60\) 0 0
\(61\) 3.99298 6.91605i 0.511249 0.885509i −0.488666 0.872471i \(-0.662516\pi\)
0.999915 0.0130384i \(-0.00415038\pi\)
\(62\) 1.56287 0.198485
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) −4.77292 + 8.26693i −0.592007 + 1.02539i
\(66\) 0 0
\(67\) −4.13160 7.15614i −0.504755 0.874262i −0.999985 0.00549964i \(-0.998249\pi\)
0.495230 0.868762i \(-0.335084\pi\)
\(68\) 3.32431 0.403131
\(69\) 0 0
\(70\) 0 0
\(71\) −6.23912 −0.740448 −0.370224 0.928943i \(-0.620719\pi\)
−0.370224 + 0.928943i \(0.620719\pi\)
\(72\) 0 0
\(73\) −3.57780 + 6.19694i −0.418750 + 0.725297i −0.995814 0.0914022i \(-0.970865\pi\)
0.577064 + 0.816699i \(0.304198\pi\)
\(74\) −0.396990 −0.0461492
\(75\) 0 0
\(76\) −6.95103 + 12.0395i −0.797338 + 1.38103i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.91423 8.51170i 0.552894 0.957641i −0.445170 0.895446i \(-0.646857\pi\)
0.998064 0.0621945i \(-0.0198099\pi\)
\(80\) −4.74322 + 8.21550i −0.530308 + 0.918521i
\(81\) 0 0
\(82\) 1.22180 + 2.11621i 0.134925 + 0.233696i
\(83\) 3.44733 + 5.97094i 0.378393 + 0.655396i 0.990829 0.135124i \(-0.0431434\pi\)
−0.612436 + 0.790521i \(0.709810\pi\)
\(84\) 0 0
\(85\) 2.21737 3.84060i 0.240508 0.416571i
\(86\) 0.396990 0.0428085
\(87\) 0 0
\(88\) −3.94282 −0.420306
\(89\) −2.51769 4.36077i −0.266875 0.462240i 0.701178 0.712986i \(-0.252658\pi\)
−0.968053 + 0.250745i \(0.919324\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.97825 + 8.62258i 0.519018 + 0.898966i
\(93\) 0 0
\(94\) −1.11650 1.93383i −0.115158 0.199459i
\(95\) 9.27292 + 16.0612i 0.951381 + 1.64784i
\(96\) 0 0
\(97\) −1.53167 2.65294i −0.155518 0.269365i 0.777730 0.628599i \(-0.216371\pi\)
−0.933247 + 0.359234i \(0.883038\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.66827 + 2.88953i 0.166827 + 0.288953i
\(101\) 11.0997 1.10446 0.552229 0.833692i \(-0.313777\pi\)
0.552229 + 0.833692i \(0.313777\pi\)
\(102\) 0 0
\(103\) 7.98597 0.786881 0.393440 0.919350i \(-0.371285\pi\)
0.393440 + 0.919350i \(0.371285\pi\)
\(104\) −1.73625 + 3.00728i −0.170254 + 0.294888i
\(105\) 0 0
\(106\) −1.27292 2.20475i −0.123636 0.214145i
\(107\) 1.97825 + 3.42642i 0.191244 + 0.331245i 0.945663 0.325149i \(-0.105414\pi\)
−0.754419 + 0.656394i \(0.772081\pi\)
\(108\) 0 0
\(109\) −3.63160 + 6.29012i −0.347844 + 0.602484i −0.985866 0.167534i \(-0.946420\pi\)
0.638022 + 0.770018i \(0.279753\pi\)
\(110\) −1.29589 + 2.24456i −0.123559 + 0.214010i
\(111\) 0 0
\(112\) 0 0
\(113\) 3.46457 6.00082i 0.325920 0.564509i −0.655778 0.754953i \(-0.727659\pi\)
0.981698 + 0.190444i \(0.0609928\pi\)
\(114\) 0 0
\(115\) 13.2823 1.23858
\(116\) 2.06402 3.57498i 0.191639 0.331929i
\(117\) 0 0
\(118\) 1.45011 0.133494
\(119\) 0 0
\(120\) 0 0
\(121\) 6.48865 0.589877
\(122\) −0.954815 1.65379i −0.0864449 0.149727i
\(123\) 0 0
\(124\) −6.34899 + 10.9968i −0.570156 + 0.987540i
\(125\) −8.50788 −0.760968
\(126\) 0 0
\(127\) 9.11109 0.808479 0.404239 0.914653i \(-0.367536\pi\)
0.404239 + 0.914653i \(0.367536\pi\)
\(128\) −3.55718 + 6.16122i −0.314413 + 0.544580i
\(129\) 0 0
\(130\) 1.14132 + 1.97682i 0.100100 + 0.173378i
\(131\) 4.30286 0.375943 0.187971 0.982175i \(-0.439809\pi\)
0.187971 + 0.982175i \(0.439809\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.97592 −0.170694
\(135\) 0 0
\(136\) 0.806617 1.39710i 0.0691668 0.119800i
\(137\) −20.5893 −1.75907 −0.879533 0.475838i \(-0.842145\pi\)
−0.879533 + 0.475838i \(0.842145\pi\)
\(138\) 0 0
\(139\) 7.88067 13.6497i 0.668429 1.15775i −0.309914 0.950765i \(-0.600300\pi\)
0.978343 0.206989i \(-0.0663665\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.745960 + 1.29204i −0.0625996 + 0.108426i
\(143\) 7.70127 13.3390i 0.644012 1.11546i
\(144\) 0 0
\(145\) −2.75347 4.76915i −0.228663 0.396056i
\(146\) 0.855536 + 1.48183i 0.0708047 + 0.122637i
\(147\) 0 0
\(148\) 1.61273 2.79332i 0.132565 0.229610i
\(149\) −6.06758 −0.497076 −0.248538 0.968622i \(-0.579950\pi\)
−0.248538 + 0.968622i \(0.579950\pi\)
\(150\) 0 0
\(151\) 4.48865 0.365281 0.182641 0.983180i \(-0.441536\pi\)
0.182641 + 0.983180i \(0.441536\pi\)
\(152\) 3.37323 + 5.84260i 0.273605 + 0.473897i
\(153\) 0 0
\(154\) 0 0
\(155\) 8.46978 + 14.6701i 0.680309 + 1.17833i
\(156\) 0 0
\(157\) −0.514457 0.891066i −0.0410582 0.0711148i 0.844766 0.535136i \(-0.179740\pi\)
−0.885824 + 0.464021i \(0.846406\pi\)
\(158\) −1.17511 2.03534i −0.0934865 0.161923i
\(159\) 0 0
\(160\) 3.57780 + 6.19694i 0.282850 + 0.489911i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.41423 5.91362i −0.267423 0.463190i 0.700772 0.713385i \(-0.252839\pi\)
−0.968196 + 0.250194i \(0.919505\pi\)
\(164\) −19.8536 −1.55031
\(165\) 0 0
\(166\) 1.64867 0.127962
\(167\) 8.99716 15.5835i 0.696221 1.20589i −0.273546 0.961859i \(-0.588197\pi\)
0.969767 0.244032i \(-0.0784701\pi\)
\(168\) 0 0
\(169\) −0.282630 0.489530i −0.0217408 0.0376561i
\(170\) −0.530225 0.918376i −0.0406664 0.0704362i
\(171\) 0 0
\(172\) −1.61273 + 2.79332i −0.122969 + 0.212989i
\(173\) −0.415178 + 0.719110i −0.0315654 + 0.0546729i −0.881377 0.472414i \(-0.843383\pi\)
0.849811 + 0.527087i \(0.176716\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 7.65335 13.2560i 0.576893 0.999208i
\(177\) 0 0
\(178\) −1.20408 −0.0902493
\(179\) 3.78947 6.56355i 0.283238 0.490583i −0.688942 0.724816i \(-0.741925\pi\)
0.972180 + 0.234233i \(0.0752580\pi\)
\(180\) 0 0
\(181\) 0.409157 0.0304124 0.0152062 0.999884i \(-0.495160\pi\)
0.0152062 + 0.999884i \(0.495160\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.83173 0.356200
\(185\) −2.15143 3.72639i −0.158176 0.273969i
\(186\) 0 0
\(187\) −3.57780 + 6.19694i −0.261635 + 0.453165i
\(188\) 18.1425 1.32318
\(189\) 0 0
\(190\) 4.43474 0.321730
\(191\) 8.01204 13.8773i 0.579731 1.00412i −0.415779 0.909466i \(-0.636491\pi\)
0.995510 0.0946575i \(-0.0301756\pi\)
\(192\) 0 0
\(193\) 6.18715 + 10.7164i 0.445360 + 0.771387i 0.998077 0.0619822i \(-0.0197422\pi\)
−0.552717 + 0.833369i \(0.686409\pi\)
\(194\) −0.732518 −0.0525917
\(195\) 0 0
\(196\) 0 0
\(197\) −23.1021 −1.64595 −0.822977 0.568075i \(-0.807688\pi\)
−0.822977 + 0.568075i \(0.807688\pi\)
\(198\) 0 0
\(199\) 3.37323 5.84260i 0.239122 0.414171i −0.721341 0.692580i \(-0.756474\pi\)
0.960463 + 0.278409i \(0.0898072\pi\)
\(200\) 1.61917 0.114493
\(201\) 0 0
\(202\) 1.32710 2.29860i 0.0933741 0.161729i
\(203\) 0 0
\(204\) 0 0
\(205\) −13.2427 + 22.9370i −0.924910 + 1.60199i
\(206\) 0.954815 1.65379i 0.0665251 0.115225i
\(207\) 0 0
\(208\) −6.74043 11.6748i −0.467365 0.809500i
\(209\) −14.9622 25.9153i −1.03496 1.79260i
\(210\) 0 0
\(211\) −8.44282 + 14.6234i −0.581228 + 1.00672i 0.414106 + 0.910228i \(0.364094\pi\)
−0.995334 + 0.0964875i \(0.969239\pi\)
\(212\) 20.6843 1.42060
\(213\) 0 0
\(214\) 0.946090 0.0646734
\(215\) 2.15143 + 3.72639i 0.146726 + 0.254138i
\(216\) 0 0
\(217\) 0 0
\(218\) 0.868400 + 1.50411i 0.0588155 + 0.101871i
\(219\) 0 0
\(220\) −10.5288 18.2365i −0.709854 1.22950i
\(221\) 3.15103 + 5.45774i 0.211961 + 0.367128i
\(222\) 0 0
\(223\) 2.25071 + 3.89834i 0.150719 + 0.261052i 0.931492 0.363762i \(-0.118508\pi\)
−0.780773 + 0.624815i \(0.785175\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.828460 1.43494i −0.0551084 0.0954505i
\(227\) 6.06429 0.402501 0.201251 0.979540i \(-0.435499\pi\)
0.201251 + 0.979540i \(0.435499\pi\)
\(228\) 0 0
\(229\) −11.0493 −0.730159 −0.365080 0.930976i \(-0.618958\pi\)
−0.365080 + 0.930976i \(0.618958\pi\)
\(230\) 1.58805 2.75059i 0.104713 0.181369i
\(231\) 0 0
\(232\) −1.00163 1.73488i −0.0657605 0.113901i
\(233\) −4.06922 7.04809i −0.266583 0.461736i 0.701394 0.712774i \(-0.252561\pi\)
−0.967977 + 0.251038i \(0.919228\pi\)
\(234\) 0 0
\(235\) 12.1014 20.9602i 0.789407 1.36729i
\(236\) −5.89092 + 10.2034i −0.383466 + 0.664183i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.5813 18.3273i 0.684445 1.18549i −0.289166 0.957279i \(-0.593378\pi\)
0.973611 0.228214i \(-0.0732886\pi\)
\(240\) 0 0
\(241\) 13.6915 0.881945 0.440972 0.897521i \(-0.354634\pi\)
0.440972 + 0.897521i \(0.354634\pi\)
\(242\) 0.775794 1.34371i 0.0498699 0.0863772i
\(243\) 0 0
\(244\) 15.5153 0.993265
\(245\) 0 0
\(246\) 0 0
\(247\) −26.3549 −1.67692
\(248\) 3.08107 + 5.33656i 0.195648 + 0.338872i
\(249\) 0 0
\(250\) −1.01722 + 1.76187i −0.0643344 + 0.111430i
\(251\) −15.2040 −0.959667 −0.479833 0.877360i \(-0.659303\pi\)
−0.479833 + 0.877360i \(0.659303\pi\)
\(252\) 0 0
\(253\) −21.4315 −1.34738
\(254\) 1.08934 1.88679i 0.0683511 0.118388i
\(255\) 0 0
\(256\) −5.80959 10.0625i −0.363099 0.628906i
\(257\) −25.6215 −1.59822 −0.799112 0.601182i \(-0.794697\pi\)
−0.799112 + 0.601182i \(0.794697\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −18.5458 −1.15016
\(261\) 0 0
\(262\) 0.514457 0.891066i 0.0317833 0.0550502i
\(263\) −7.10069 −0.437847 −0.218924 0.975742i \(-0.570255\pi\)
−0.218924 + 0.975742i \(0.570255\pi\)
\(264\) 0 0
\(265\) 13.7968 23.8967i 0.847528 1.46796i
\(266\) 0 0
\(267\) 0 0
\(268\) 8.02696 13.9031i 0.490324 0.849267i
\(269\) −8.21572 + 14.2301i −0.500922 + 0.867622i 0.499078 + 0.866557i \(0.333672\pi\)
−0.999999 + 0.00106448i \(0.999661\pi\)
\(270\) 0 0
\(271\) −6.34899 10.9968i −0.385674 0.668007i 0.606189 0.795321i \(-0.292698\pi\)
−0.991862 + 0.127314i \(0.959364\pi\)
\(272\) 3.13143 + 5.42379i 0.189871 + 0.328865i
\(273\) 0 0
\(274\) −2.46169 + 4.26378i −0.148716 + 0.257584i
\(275\) −7.18194 −0.433087
\(276\) 0 0
\(277\) −0.828460 −0.0497773 −0.0248887 0.999690i \(-0.507923\pi\)
−0.0248887 + 0.999690i \(0.507923\pi\)
\(278\) −1.88445 3.26396i −0.113022 0.195760i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.60985 + 4.52039i 0.155690 + 0.269664i 0.933310 0.359071i \(-0.116906\pi\)
−0.777620 + 0.628735i \(0.783573\pi\)
\(282\) 0 0
\(283\) 3.67708 + 6.36890i 0.218580 + 0.378592i 0.954374 0.298614i \(-0.0965242\pi\)
−0.735794 + 0.677205i \(0.763191\pi\)
\(284\) −6.06075 10.4975i −0.359639 0.622913i
\(285\) 0 0
\(286\) −1.84155 3.18966i −0.108893 0.188609i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.03611 + 12.1869i 0.413889 + 0.716877i
\(290\) −1.31684 −0.0773273
\(291\) 0 0
\(292\) −13.9021 −0.813557
\(293\) 3.91286 6.77728i 0.228592 0.395933i −0.728799 0.684728i \(-0.759921\pi\)
0.957391 + 0.288795i \(0.0932545\pi\)
\(294\) 0 0
\(295\) 7.85868 + 13.6116i 0.457550 + 0.792500i
\(296\) −0.782630 1.35556i −0.0454895 0.0787900i
\(297\) 0 0
\(298\) −0.725450 + 1.25652i −0.0420242 + 0.0727881i
\(299\) −9.43752 + 16.3463i −0.545786 + 0.945329i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.536670 0.929540i 0.0308819 0.0534890i
\(303\) 0 0
\(304\) −26.1909 −1.50215
\(305\) 10.3490 17.9249i 0.592580 1.02638i
\(306\) 0 0
\(307\) 22.6709 1.29390 0.646948 0.762534i \(-0.276045\pi\)
0.646948 + 0.762534i \(0.276045\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.05064 0.230061
\(311\) −16.1588 27.9879i −0.916281 1.58705i −0.805015 0.593255i \(-0.797843\pi\)
−0.111266 0.993791i \(-0.535491\pi\)
\(312\) 0 0
\(313\) 12.1598 21.0614i 0.687312 1.19046i −0.285392 0.958411i \(-0.592124\pi\)
0.972704 0.232048i \(-0.0745428\pi\)
\(314\) −0.246037 −0.0138847
\(315\) 0 0
\(316\) 19.0949 1.07417
\(317\) 2.56922 4.45002i 0.144302 0.249938i −0.784811 0.619736i \(-0.787240\pi\)
0.929112 + 0.369798i \(0.120573\pi\)
\(318\) 0 0
\(319\) 4.44282 + 7.69519i 0.248750 + 0.430848i
\(320\) −17.2618 −0.964964
\(321\) 0 0
\(322\) 0 0
\(323\) 12.2438 0.681262
\(324\) 0 0
\(325\) −3.16263 + 5.47783i −0.175431 + 0.303855i
\(326\) −1.63284 −0.0904349
\(327\) 0 0
\(328\) −4.81732 + 8.34384i −0.265992 + 0.460712i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.84897 10.1307i 0.321488 0.556834i −0.659307 0.751874i \(-0.729150\pi\)
0.980795 + 0.195040i \(0.0624835\pi\)
\(332\) −6.69753 + 11.6005i −0.367575 + 0.636658i
\(333\) 0 0
\(334\) −2.15143 3.72639i −0.117721 0.203899i
\(335\) −10.7082 18.5472i −0.585053 1.01334i
\(336\) 0 0
\(337\) 16.8473 29.1804i 0.917733 1.58956i 0.114883 0.993379i \(-0.463351\pi\)
0.802850 0.596181i \(-0.203316\pi\)
\(338\) −0.135167 −0.00735211
\(339\) 0 0
\(340\) 8.61590 0.467263
\(341\) −13.6663 23.6707i −0.740071 1.28184i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.782630 + 1.35556i 0.0421966 + 0.0730866i
\(345\) 0 0
\(346\) 0.0992788 + 0.171956i 0.00533726 + 0.00924441i
\(347\) 13.6557 + 23.6523i 0.733075 + 1.26972i 0.955563 + 0.294788i \(0.0952490\pi\)
−0.222488 + 0.974936i \(0.571418\pi\)
\(348\) 0 0
\(349\) −11.4585 19.8467i −0.613358 1.06237i −0.990670 0.136281i \(-0.956485\pi\)
0.377312 0.926086i \(-0.376848\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.77292 9.99898i −0.307697 0.532948i
\(353\) −10.2693 −0.546581 −0.273290 0.961932i \(-0.588112\pi\)
−0.273290 + 0.961932i \(0.588112\pi\)
\(354\) 0 0
\(355\) −16.1705 −0.858241
\(356\) 4.89142 8.47218i 0.259245 0.449025i
\(357\) 0 0
\(358\) −0.906150 1.56950i −0.0478915 0.0829505i
\(359\) 5.05034 + 8.74745i 0.266547 + 0.461673i 0.967968 0.251075i \(-0.0807839\pi\)
−0.701421 + 0.712747i \(0.747451\pi\)
\(360\) 0 0
\(361\) −16.1014 + 27.8884i −0.847441 + 1.46781i
\(362\) 0.0489195 0.0847311i 0.00257115 0.00445337i
\(363\) 0 0
\(364\) 0 0
\(365\) −9.27292 + 16.0612i −0.485367 + 0.840680i
\(366\) 0 0
\(367\) −7.77537 −0.405871 −0.202935 0.979192i \(-0.565048\pi\)
−0.202935 + 0.979192i \(0.565048\pi\)
\(368\) −9.37880 + 16.2446i −0.488904 + 0.846806i
\(369\) 0 0
\(370\) −1.02891 −0.0534907
\(371\) 0 0
\(372\) 0 0
\(373\) 24.1111 1.24842 0.624212 0.781255i \(-0.285420\pi\)
0.624212 + 0.781255i \(0.285420\pi\)
\(374\) 0.855536 + 1.48183i 0.0442387 + 0.0766237i
\(375\) 0 0
\(376\) 4.40214 7.62473i 0.227023 0.393215i
\(377\) 7.82573 0.403045
\(378\) 0 0
\(379\) −13.3581 −0.686161 −0.343081 0.939306i \(-0.611470\pi\)
−0.343081 + 0.939306i \(0.611470\pi\)
\(380\) −18.0156 + 31.2039i −0.924181 + 1.60073i
\(381\) 0 0
\(382\) −1.91586 3.31838i −0.0980242 0.169783i
\(383\) 9.24040 0.472162 0.236081 0.971733i \(-0.424137\pi\)
0.236081 + 0.971733i \(0.424137\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.95898 0.150608
\(387\) 0 0
\(388\) 2.97577 5.15418i 0.151072 0.261664i
\(389\) −10.4484 −0.529756 −0.264878 0.964282i \(-0.585332\pi\)
−0.264878 + 0.964282i \(0.585332\pi\)
\(390\) 0 0
\(391\) 4.38442 7.59404i 0.221730 0.384047i
\(392\) 0 0
\(393\) 0 0
\(394\) −2.76212 + 4.78413i −0.139154 + 0.241021i
\(395\) 12.7366 22.0605i 0.640850 1.10999i
\(396\) 0 0
\(397\) 0.204579 + 0.354341i 0.0102675 + 0.0177838i 0.871114 0.491082i \(-0.163398\pi\)
−0.860846 + 0.508866i \(0.830065\pi\)
\(398\) −0.806617 1.39710i −0.0404321 0.0700304i
\(399\) 0 0
\(400\) −3.14295 + 5.44375i −0.157147 + 0.272187i
\(401\) −15.2528 −0.761688 −0.380844 0.924639i \(-0.624367\pi\)
−0.380844 + 0.924639i \(0.624367\pi\)
\(402\) 0 0
\(403\) −24.0722 −1.19912
\(404\) 10.7823 + 18.6756i 0.536441 + 0.929143i
\(405\) 0 0
\(406\) 0 0
\(407\) 3.47141 + 6.01266i 0.172071 + 0.298036i
\(408\) 0 0
\(409\) 3.06335 + 5.30587i 0.151473 + 0.262359i 0.931769 0.363051i \(-0.118265\pi\)
−0.780296 + 0.625410i \(0.784932\pi\)
\(410\) 3.16664 + 5.48477i 0.156389 + 0.270874i
\(411\) 0 0
\(412\) 7.75765 + 13.4366i 0.382192 + 0.661976i
\(413\) 0 0
\(414\) 0 0
\(415\) 8.93474 + 15.4754i 0.438589 + 0.759659i
\(416\) −10.1686 −0.498557
\(417\) 0 0
\(418\) −7.15561 −0.349992
\(419\) 0.781437 1.35349i 0.0381757 0.0661223i −0.846306 0.532697i \(-0.821179\pi\)
0.884482 + 0.466574i \(0.154512\pi\)
\(420\) 0 0
\(421\) −11.6316 20.1465i −0.566889 0.981881i −0.996871 0.0790438i \(-0.974813\pi\)
0.429982 0.902838i \(-0.358520\pi\)
\(422\) 2.01887 + 3.49679i 0.0982773 + 0.170221i
\(423\) 0 0
\(424\) 5.01887 8.69295i 0.243738 0.422167i
\(425\) 1.46927 2.54485i 0.0712702 0.123444i
\(426\) 0 0
\(427\) 0 0
\(428\) −3.84338 + 6.65692i −0.185777 + 0.321775i
\(429\) 0 0
\(430\) 1.02891 0.0496187
\(431\) 0.502879 0.871011i 0.0242228 0.0419551i −0.853660 0.520831i \(-0.825622\pi\)
0.877883 + 0.478876i \(0.158956\pi\)
\(432\) 0 0
\(433\) 13.1071 0.629889 0.314945 0.949110i \(-0.398014\pi\)
0.314945 + 0.949110i \(0.398014\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −14.1111 −0.675799
\(437\) 18.3354 + 31.7579i 0.877101 + 1.51918i
\(438\) 0 0
\(439\) −9.30704 + 16.1203i −0.444201 + 0.769378i −0.997996 0.0632744i \(-0.979846\pi\)
0.553795 + 0.832653i \(0.313179\pi\)
\(440\) −10.2190 −0.487170
\(441\) 0 0
\(442\) 1.50697 0.0716792
\(443\) −0.559503 + 0.969088i −0.0265828 + 0.0460427i −0.879011 0.476802i \(-0.841796\pi\)
0.852428 + 0.522845i \(0.175129\pi\)
\(444\) 0 0
\(445\) −6.52532 11.3022i −0.309330 0.535775i
\(446\) 1.07639 0.0509687
\(447\) 0 0
\(448\) 0 0
\(449\) 39.4419 1.86138 0.930689 0.365813i \(-0.119209\pi\)
0.930689 + 0.365813i \(0.119209\pi\)
\(450\) 0 0
\(451\) 21.3676 37.0097i 1.00616 1.74272i
\(452\) 13.4621 0.633203
\(453\) 0 0
\(454\) 0.725057 1.25584i 0.0340286 0.0589393i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.1202 29.6531i 0.800852 1.38712i −0.118205 0.992989i \(-0.537714\pi\)
0.919056 0.394126i \(-0.128953\pi\)
\(458\) −1.32107 + 2.28817i −0.0617297 + 0.106919i
\(459\) 0 0
\(460\) 12.9026 + 22.3479i 0.601585 + 1.04198i
\(461\) 10.1938 + 17.6561i 0.474772 + 0.822328i 0.999583 0.0288903i \(-0.00919735\pi\)
−0.524811 + 0.851219i \(0.675864\pi\)
\(462\) 0 0
\(463\) −3.40451 + 5.89679i −0.158221 + 0.274047i −0.934227 0.356678i \(-0.883909\pi\)
0.776006 + 0.630725i \(0.217243\pi\)
\(464\) 7.77704 0.361040
\(465\) 0 0
\(466\) −1.94609 −0.0901509
\(467\) 12.3956 + 21.4698i 0.573598 + 0.993502i 0.996192 + 0.0871825i \(0.0277863\pi\)
−0.422594 + 0.906319i \(0.638880\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.89372 5.01207i −0.133477 0.231190i
\(471\) 0 0
\(472\) 2.85877 + 4.95153i 0.131586 + 0.227913i
\(473\) −3.47141 6.01266i −0.159616 0.276462i
\(474\) 0 0
\(475\) 6.14441 + 10.6424i 0.281925 + 0.488309i
\(476\) 0 0
\(477\) 0 0
\(478\) −2.53022 4.38248i −0.115730 0.200450i
\(479\) 11.0997 0.507157 0.253579 0.967315i \(-0.418392\pi\)
0.253579 + 0.967315i \(0.418392\pi\)
\(480\) 0 0
\(481\) 6.11465 0.278804
\(482\) 1.63697 2.83532i 0.0745621 0.129145i
\(483\) 0 0
\(484\) 6.30314 + 10.9174i 0.286506 + 0.496244i
\(485\) −3.96978 6.87585i −0.180258 0.312216i
\(486\) 0 0
\(487\) 5.01887 8.69295i 0.227427 0.393915i −0.729618 0.683855i \(-0.760302\pi\)
0.957045 + 0.289940i \(0.0936354\pi\)
\(488\) 3.76466 6.52059i 0.170418 0.295173i
\(489\) 0 0
\(490\) 0 0
\(491\) −6.19398 + 10.7283i −0.279530 + 0.484161i −0.971268 0.237988i \(-0.923512\pi\)
0.691738 + 0.722149i \(0.256845\pi\)
\(492\) 0 0
\(493\) −3.63562 −0.163740
\(494\) −3.15103 + 5.45774i −0.141772 + 0.245556i
\(495\) 0 0
\(496\) −23.9225 −1.07415
\(497\) 0 0
\(498\) 0 0
\(499\) 10.2222 0.457608 0.228804 0.973473i \(-0.426519\pi\)
0.228804 + 0.973473i \(0.426519\pi\)
\(500\) −8.26464 14.3148i −0.369606 0.640177i
\(501\) 0 0
\(502\) −1.81781 + 3.14854i −0.0811329 + 0.140526i
\(503\) 8.45753 0.377102 0.188551 0.982063i \(-0.439621\pi\)
0.188551 + 0.982063i \(0.439621\pi\)
\(504\) 0 0
\(505\) 28.7680 1.28016
\(506\) −2.56238 + 4.43818i −0.113912 + 0.197301i
\(507\) 0 0
\(508\) 8.85060 + 15.3297i 0.392682 + 0.680145i
\(509\) 10.5657 0.468317 0.234159 0.972198i \(-0.424767\pi\)
0.234159 + 0.972198i \(0.424767\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −17.0071 −0.751616
\(513\) 0 0
\(514\) −3.06335 + 5.30587i −0.135118 + 0.234032i
\(515\) 20.6979 0.912060
\(516\) 0 0
\(517\) −19.5260 + 33.8200i −0.858752 + 1.48740i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.50000 + 7.79423i −0.197338 + 0.341800i
\(521\) 9.87788 17.1090i 0.432758 0.749558i −0.564352 0.825534i \(-0.690874\pi\)
0.997110 + 0.0759760i \(0.0242072\pi\)
\(522\) 0 0
\(523\) 16.2641 + 28.1702i 0.711179 + 1.23180i 0.964415 + 0.264394i \(0.0851718\pi\)
−0.253236 + 0.967405i \(0.581495\pi\)
\(524\) 4.17984 + 7.23970i 0.182597 + 0.316268i
\(525\) 0 0
\(526\) −0.848970 + 1.47046i −0.0370168 + 0.0641150i
\(527\) 11.1833 0.487153
\(528\) 0 0
\(529\) 3.26320 0.141878
\(530\) −3.29913 5.71426i −0.143305 0.248211i
\(531\) 0 0
\(532\) 0 0
\(533\) −18.8187 32.5950i −0.815130 1.41185i
\(534\) 0 0
\(535\) 5.12720 + 8.88057i 0.221668 + 0.383940i
\(536\) −3.89536 6.74695i −0.168254 0.291424i
\(537\) 0 0
\(538\) 1.96457 + 3.40274i 0.0846987 + 0.146702i
\(539\) 0 0
\(540\) 0 0
\(541\) −7.61109 13.1828i −0.327226 0.566773i 0.654734 0.755859i \(-0.272781\pi\)
−0.981960 + 0.189087i \(0.939447\pi\)
\(542\) −3.03638 −0.130424
\(543\) 0 0
\(544\) 4.72406 0.202542
\(545\) −9.41234 + 16.3027i −0.403180 + 0.698329i
\(546\) 0 0
\(547\) −11.6871 20.2427i −0.499706 0.865517i 0.500294 0.865856i \(-0.333225\pi\)
−1.00000 0.000339172i \(0.999892\pi\)
\(548\) −20.0007 34.6422i −0.854387 1.47984i
\(549\) 0 0
\(550\) −0.858685 + 1.48729i −0.0366144 + 0.0634181i
\(551\) 7.60199 13.1670i 0.323856 0.560934i
\(552\) 0 0
\(553\) 0 0
\(554\) −0.0990521 + 0.171563i −0.00420832 + 0.00728902i
\(555\) 0 0
\(556\) 30.6214 1.29864
\(557\) 13.8337 23.9606i 0.586151 1.01524i −0.408580 0.912723i \(-0.633976\pi\)
0.994731 0.102521i \(-0.0326908\pi\)
\(558\) 0 0
\(559\) −6.11465 −0.258622
\(560\) 0 0
\(561\) 0 0
\(562\) 1.24815 0.0526500
\(563\) −4.27912 7.41166i −0.180343 0.312364i 0.761654 0.647984i \(-0.224388\pi\)
−0.941998 + 0.335620i \(0.891054\pi\)
\(564\) 0 0
\(565\) 8.97944 15.5529i 0.377768 0.654313i
\(566\) 1.75855 0.0739175
\(567\) 0 0
\(568\) −5.88237 −0.246819
\(569\) 6.86389 11.8886i 0.287749 0.498396i −0.685523 0.728051i \(-0.740426\pi\)
0.973272 + 0.229655i \(0.0737597\pi\)
\(570\) 0 0
\(571\) −5.35868 9.28151i −0.224254 0.388419i 0.731841 0.681475i \(-0.238661\pi\)
−0.956095 + 0.293056i \(0.905328\pi\)
\(572\) 29.9244 1.25120
\(573\) 0 0
\(574\) 0 0
\(575\) 8.80111 0.367032
\(576\) 0 0
\(577\) −22.8177 + 39.5214i −0.949912 + 1.64530i −0.204307 + 0.978907i \(0.565494\pi\)
−0.745605 + 0.666389i \(0.767839\pi\)
\(578\) 3.36500 0.139965
\(579\) 0 0
\(580\) 5.34950 9.26560i 0.222126 0.384733i
\(581\) 0 0
\(582\) 0 0
\(583\) −22.2616 + 38.5582i −0.921980 + 1.59692i
\(584\) −3.37323 + 5.84260i −0.139585 + 0.241768i
\(585\) 0 0
\(586\) −0.935657 1.62060i −0.0386516 0.0669466i
\(587\) 5.10948 + 8.84988i 0.210891 + 0.365274i 0.951994 0.306118i \(-0.0990302\pi\)
−0.741103 + 0.671392i \(0.765697\pi\)
\(588\) 0 0
\(589\) −23.3840 + 40.5023i −0.963521 + 1.66887i
\(590\) 3.75839 0.154730
\(591\) 0 0
\(592\) 6.07661 0.249747
\(593\) −5.69804 9.86929i −0.233990 0.405283i 0.724988 0.688761i \(-0.241845\pi\)
−0.958979 + 0.283478i \(0.908512\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −5.89411 10.2089i −0.241432 0.418173i
\(597\) 0 0
\(598\) 2.25673 + 3.90877i 0.0922846 + 0.159842i
\(599\) −17.2873 29.9424i −0.706339 1.22341i −0.966206 0.257771i \(-0.917012\pi\)
0.259867 0.965644i \(-0.416321\pi\)
\(600\) 0 0
\(601\) −19.4207 33.6376i −0.792187 1.37211i −0.924610 0.380915i \(-0.875609\pi\)
0.132423 0.991193i \(-0.457724\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.36032 + 7.55230i 0.177419 + 0.307299i
\(605\) 16.8172 0.683717
\(606\) 0 0
\(607\) 41.3325 1.67763 0.838817 0.544414i \(-0.183248\pi\)
0.838817 + 0.544414i \(0.183248\pi\)
\(608\) −9.87788 + 17.1090i −0.400601 + 0.693861i
\(609\) 0 0
\(610\) −2.47468 4.28627i −0.100197 0.173546i
\(611\) 17.1969 + 29.7858i 0.695710 + 1.20501i
\(612\) 0 0
\(613\) 14.3285 24.8176i 0.578721 1.00237i −0.416905 0.908950i \(-0.636885\pi\)
0.995626 0.0934244i \(-0.0297813\pi\)
\(614\) 2.71057 4.69485i 0.109390 0.189469i
\(615\) 0 0
\(616\) 0 0
\(617\) −16.8518 + 29.1883i −0.678430 + 1.17508i 0.297024 + 0.954870i \(0.404006\pi\)
−0.975454 + 0.220205i \(0.929327\pi\)
\(618\) 0 0
\(619\) −1.43807 −0.0578010 −0.0289005 0.999582i \(-0.509201\pi\)
−0.0289005 + 0.999582i \(0.509201\pi\)
\(620\) −16.4552 + 28.5013i −0.660859 + 1.14464i
\(621\) 0 0
\(622\) −7.72789 −0.309860
\(623\) 0 0
\(624\) 0 0
\(625\) −30.6375 −1.22550
\(626\) −2.90769 5.03626i −0.116215 0.201290i
\(627\) 0 0
\(628\) 0.999498 1.73118i 0.0398843 0.0690816i
\(629\) −2.84071 −0.113266
\(630\) 0 0
\(631\) −30.7680 −1.22486 −0.612428 0.790527i \(-0.709807\pi\)
−0.612428 + 0.790527i \(0.709807\pi\)
\(632\) 4.63323 8.02500i 0.184300 0.319217i
\(633\) 0 0
\(634\) −0.614360 1.06410i −0.0243993 0.0422609i
\(635\) 23.6140 0.937094
\(636\) 0 0
\(637\) 0 0
\(638\) 2.12476 0.0841202
\(639\) 0 0
\(640\) −9.21946 + 15.9686i −0.364431 + 0.631213i
\(641\) −9.23912 −0.364923 −0.182462 0.983213i \(-0.558407\pi\)
−0.182462 + 0.983213i \(0.558407\pi\)
\(642\) 0 0
\(643\) −12.7795 + 22.1348i −0.503976 + 0.872912i 0.496013 + 0.868315i \(0.334797\pi\)
−0.999989 + 0.00459728i \(0.998537\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.46389 2.53552i 0.0575958 0.0997588i
\(647\) −14.1556 + 24.5181i −0.556512 + 0.963908i 0.441272 + 0.897374i \(0.354528\pi\)
−0.997784 + 0.0665343i \(0.978806\pi\)
\(648\) 0 0
\(649\) −12.6803 21.9629i −0.497744 0.862118i
\(650\) 0.756258 + 1.30988i 0.0296629 + 0.0513776i
\(651\) 0 0
\(652\) 6.63323 11.4891i 0.259778 0.449948i
\(653\) 8.35021 0.326769 0.163385 0.986562i \(-0.447759\pi\)
0.163385 + 0.986562i \(0.447759\pi\)
\(654\) 0 0
\(655\) 11.1521 0.435749
\(656\) −18.7017 32.3922i −0.730177 1.26470i
\(657\) 0 0
\(658\) 0 0
\(659\) −16.7862 29.0745i −0.653897 1.13258i −0.982169 0.188000i \(-0.939799\pi\)
0.328272 0.944583i \(-0.393534\pi\)
\(660\) 0 0
\(661\) −8.47668 14.6820i −0.329705 0.571065i 0.652748 0.757575i \(-0.273616\pi\)
−0.982453 + 0.186509i \(0.940283\pi\)
\(662\) −1.39862 2.42249i −0.0543591 0.0941527i
\(663\) 0 0
\(664\) 3.25021 + 5.62952i 0.126133 + 0.218468i
\(665\) 0 0
\(666\) 0 0
\(667\) −5.44445 9.43007i −0.210810 0.365134i
\(668\) 34.9597 1.35263
\(669\) 0 0
\(670\) −5.12118 −0.197848
\(671\) −16.6984 + 28.9225i −0.644636 + 1.11654i
\(672\) 0 0
\(673\) 22.2157 + 38.4788i 0.856354 + 1.48325i 0.875384 + 0.483429i \(0.160609\pi\)
−0.0190299 + 0.999819i \(0.506058\pi\)
\(674\) −4.02859 6.97772i −0.155175 0.268772i
\(675\) 0 0
\(676\) 0.549100 0.951068i 0.0211192 0.0365796i
\(677\) 7.18681 12.4479i 0.276212 0.478412i −0.694229 0.719755i \(-0.744254\pi\)
0.970440 + 0.241342i \(0.0775876\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.09058 3.62099i 0.0801701 0.138859i
\(681\) 0 0
\(682\) −6.53585 −0.250271
\(683\) −16.1546 + 27.9806i −0.618138 + 1.07065i 0.371687 + 0.928358i \(0.378780\pi\)
−0.989825 + 0.142289i \(0.954554\pi\)
\(684\) 0 0
\(685\) −53.3632 −2.03890
\(686\) 0 0
\(687\) 0 0
\(688\) −6.07661 −0.231669
\(689\) 19.6061 + 33.9588i 0.746934 + 1.29373i
\(690\) 0 0
\(691\) −14.4981 + 25.1114i −0.551533 + 0.955283i 0.446631 + 0.894718i \(0.352624\pi\)
−0.998164 + 0.0605650i \(0.980710\pi\)
\(692\) −1.61323 −0.0613259
\(693\) 0 0
\(694\) 6.53078 0.247905
\(695\) 20.4250 35.3772i 0.774765 1.34193i
\(696\) 0 0
\(697\) 8.74269 + 15.1428i 0.331153 + 0.573574i
\(698\) −5.47997 −0.207420
\(699\) 0 0
\(700\) 0 0
\(701\) 26.3912 0.996783 0.498392 0.866952i \(-0.333924\pi\)
0.498392 + 0.866952i \(0.333924\pi\)
\(702\) 0 0
\(703\) 5.93984 10.2881i 0.224025 0.388023i
\(704\) 27.8525 1.04973
\(705\) 0 0
\(706\) −1.22782 + 2.12664i −0.0462095 + 0.0800372i
\(707\) 0 0
\(708\) 0 0
\(709\) 3.94282 6.82916i 0.148076 0.256475i −0.782441 0.622725i \(-0.786025\pi\)
0.930516 + 0.366251i \(0.119359\pi\)
\(710\) −1.93337 + 3.34870i −0.0725581 + 0.125674i
\(711\) 0 0
\(712\) −2.37373 4.11142i −0.0889592 0.154082i
\(713\) 16.7473 + 29.0073i 0.627193 + 1.08633i
\(714\) 0 0
\(715\) 19.9601 34.5718i 0.746464 1.29291i
\(716\) 14.7245 0.550281
\(717\) 0 0
\(718\) 2.41531 0.0901385
\(719\) 16.5754 + 28.7095i 0.618159 + 1.07068i 0.989822 + 0.142314i \(0.0454544\pi\)
−0.371663 + 0.928368i \(0.621212\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.85021 + 6.66877i 0.143290 + 0.248186i
\(723\) 0 0
\(724\) 0.397460 + 0.688420i 0.0147715 + 0.0255849i
\(725\) −1.82450 3.16013i −0.0677603 0.117364i
\(726\) 0 0
\(727\) 16.5502 + 28.6658i 0.613814 + 1.06316i 0.990591 + 0.136853i \(0.0436989\pi\)
−0.376777 + 0.926304i \(0.622968\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.21737 + 3.84060i 0.0820685 + 0.142147i
\(731\) 2.84071 0.105067
\(732\) 0 0
\(733\) 44.5589 1.64582 0.822911 0.568170i \(-0.192349\pi\)
0.822911 + 0.568170i \(0.192349\pi\)
\(734\) −0.929636 + 1.61018i −0.0343135 + 0.0594327i
\(735\) 0 0
\(736\) 7.07442 + 12.2533i 0.260767 + 0.451661i
\(737\) 17.2781 + 29.9266i 0.636448 + 1.10236i
\(738\) 0 0
\(739\) −19.9045 + 34.4756i −0.732199 + 1.26821i 0.223742 + 0.974648i \(0.428173\pi\)
−0.955941 + 0.293558i \(0.905161\pi\)
\(740\) 4.17984 7.23970i 0.153654 0.266137i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.37072 9.30237i 0.197033 0.341271i −0.750532 0.660834i \(-0.770203\pi\)
0.947565 + 0.319563i \(0.103536\pi\)
\(744\) 0 0
\(745\) −15.7259 −0.576152
\(746\) 2.88276 4.99309i 0.105545 0.182810i
\(747\) 0 0
\(748\) −13.9021 −0.508310
\(749\) 0 0
\(750\) 0 0
\(751\) 19.7141 0.719378 0.359689 0.933072i \(-0.382883\pi\)
0.359689 + 0.933072i \(0.382883\pi\)
\(752\) 17.0899 + 29.6005i 0.623203 + 1.07942i
\(753\) 0 0
\(754\) 0.935657 1.62060i 0.0340746 0.0590189i
\(755\) 11.6336 0.423391
\(756\) 0 0
\(757\) 35.3549 1.28499 0.642497 0.766288i \(-0.277898\pi\)
0.642497 + 0.766288i \(0.277898\pi\)
\(758\) −1.59712 + 2.76629i −0.0580100 + 0.100476i
\(759\) 0 0
\(760\) 8.74269 + 15.1428i 0.317131 + 0.549286i
\(761\) −39.1144 −1.41790 −0.708948 0.705261i \(-0.750830\pi\)
−0.708948 + 0.705261i \(0.750830\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 31.1319 1.12631
\(765\) 0 0
\(766\) 1.10480 1.91357i 0.0399180 0.0691399i
\(767\) −22.3354 −0.806486
\(768\) 0 0
\(769\) −18.9240 + 32.7773i −0.682415 + 1.18198i 0.291826 + 0.956471i \(0.405737\pi\)
−0.974242 + 0.225507i \(0.927596\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.0205 + 20.8201i −0.432628 + 0.749333i
\(773\) −14.9133 + 25.8305i −0.536393 + 0.929059i 0.462702 + 0.886514i \(0.346880\pi\)
−0.999095 + 0.0425453i \(0.986453\pi\)
\(774\) 0 0
\(775\) 5.61224 + 9.72068i 0.201598 + 0.349177i
\(776\) −1.44409 2.50124i −0.0518399 0.0897894i
\(777\) 0 0
\(778\) −1.24923 + 2.16373i −0.0447870 + 0.0775734i
\(779\) −73.1229 −2.61990
\(780\) 0 0
\(781\) 26.0917 0.933633
\(782\) −1.04842 1.81591i −0.0374913 0.0649369i
\(783\) 0 0
\(784\) 0 0
\(785\) −1.33336 2.30946i −0.0475898 0.0824280i
\(786\) 0 0
\(787\) 8.81030 + 15.2599i 0.314053 + 0.543956i 0.979236 0.202724i \(-0.0649796\pi\)
−0.665182 + 0.746681i \(0.731646\pi\)
\(788\) −22.4416 38.8700i −0.799448 1.38468i
\(789\) 0 0
\(790\) −3.04563 5.27518i −0.108359 0.187683i
\(791\) 0 0
\(792\) 0 0
\(793\) 14.7066 + 25.4725i 0.522246 + 0.904556i
\(794\) 0.0978390 0.00347218
\(795\) 0