Properties

Label 1152.2.i.i.769.6
Level $1152$
Weight $2$
Character 1152.769
Analytic conductor $9.199$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 769.6
Root \(-1.15879 + 1.28733i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.i.385.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.69425 - 0.359877i) q^{3} +(-1.74260 + 3.01828i) q^{5} +(-1.34988 - 2.33807i) q^{7} +(2.74098 - 1.21944i) q^{9} +O(q^{10})\) \(q+(1.69425 - 0.359877i) q^{3} +(-1.74260 + 3.01828i) q^{5} +(-1.34988 - 2.33807i) q^{7} +(2.74098 - 1.21944i) q^{9} +(-2.84274 - 4.92377i) q^{11} +(1.76055 - 3.04937i) q^{13} +(-1.86620 + 5.74085i) q^{15} +7.65970 q^{17} -2.02060 q^{19} +(-3.12846 - 3.47548i) q^{21} +(-0.0370909 + 0.0642434i) q^{23} +(-3.57334 - 6.18921i) q^{25} +(4.20506 - 3.05246i) q^{27} +(2.46032 + 4.26140i) q^{29} +(3.72257 - 6.44769i) q^{31} +(-6.58827 - 7.31907i) q^{33} +9.40925 q^{35} -5.00631 q^{37} +(1.88542 - 5.79997i) q^{39} +(0.482053 - 0.834941i) q^{41} +(-0.255495 - 0.442530i) q^{43} +(-1.09582 + 10.3980i) q^{45} +(-2.83509 - 4.91053i) q^{47} +(-0.144369 + 0.250055i) q^{49} +(12.9775 - 2.75655i) q^{51} +10.4058 q^{53} +19.8151 q^{55} +(-3.42340 + 0.727166i) q^{57} +(-4.47636 + 7.75329i) q^{59} +(-1.46032 - 2.52935i) q^{61} +(-6.55114 - 4.76248i) q^{63} +(6.13589 + 10.6277i) q^{65} +(1.56829 - 2.71635i) q^{67} +(-0.0397217 + 0.122193i) q^{69} +8.19647 q^{71} +5.21796 q^{73} +(-8.28150 - 9.20012i) q^{75} +(-7.67474 + 13.2930i) q^{77} +(-0.716260 - 1.24060i) q^{79} +(6.02592 - 6.68493i) q^{81} +(1.74052 + 3.01467i) q^{83} +(-13.3478 + 23.1191i) q^{85} +(5.70198 + 6.33447i) q^{87} -12.4058 q^{89} -9.50616 q^{91} +(3.98660 - 12.2637i) q^{93} +(3.52110 - 6.09873i) q^{95} +(-3.50265 - 6.06677i) q^{97} +(-13.7962 - 10.0294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{3} - 2q^{5} - 6q^{7} - 2q^{9} + O(q^{10}) \) \( 12q - 4q^{3} - 2q^{5} - 6q^{7} - 2q^{9} - 4q^{11} + 10q^{13} - 4q^{15} + 4q^{17} - 4q^{19} + 2q^{21} - 8q^{23} - 14q^{25} + 14q^{27} - 2q^{29} - 8q^{31} - 10q^{33} - 8q^{35} - 22q^{39} - 2q^{41} + 2q^{43} + 10q^{45} + 14q^{47} - 18q^{49} + 38q^{51} + 24q^{53} + 16q^{55} - 38q^{57} - 6q^{59} + 14q^{61} + 16q^{63} - 8q^{65} - 4q^{67} - 50q^{69} + 28q^{71} + 60q^{73} - 50q^{75} + 2q^{77} - 16q^{79} + 22q^{81} - 24q^{83} + 16q^{85} + 36q^{87} - 48q^{89} + 52q^{91} + 42q^{93} + 20q^{95} - 14q^{97} - 68q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.69425 0.359877i 0.978177 0.207775i
\(4\) 0 0
\(5\) −1.74260 + 3.01828i −0.779317 + 1.34982i 0.153019 + 0.988223i \(0.451100\pi\)
−0.932336 + 0.361593i \(0.882233\pi\)
\(6\) 0 0
\(7\) −1.34988 2.33807i −0.510208 0.883706i −0.999930 0.0118274i \(-0.996235\pi\)
0.489722 0.871879i \(-0.337098\pi\)
\(8\) 0 0
\(9\) 2.74098 1.21944i 0.913659 0.406481i
\(10\) 0 0
\(11\) −2.84274 4.92377i −0.857119 1.48457i −0.874665 0.484727i \(-0.838919\pi\)
0.0175468 0.999846i \(-0.494414\pi\)
\(12\) 0 0
\(13\) 1.76055 3.04937i 0.488289 0.845742i −0.511620 0.859212i \(-0.670954\pi\)
0.999909 + 0.0134701i \(0.00428779\pi\)
\(14\) 0 0
\(15\) −1.86620 + 5.74085i −0.481851 + 1.48228i
\(16\) 0 0
\(17\) 7.65970 1.85775 0.928875 0.370392i \(-0.120777\pi\)
0.928875 + 0.370392i \(0.120777\pi\)
\(18\) 0 0
\(19\) −2.02060 −0.463557 −0.231778 0.972769i \(-0.574454\pi\)
−0.231778 + 0.972769i \(0.574454\pi\)
\(20\) 0 0
\(21\) −3.12846 3.47548i −0.682685 0.758412i
\(22\) 0 0
\(23\) −0.0370909 + 0.0642434i −0.00773399 + 0.0133957i −0.869866 0.493287i \(-0.835795\pi\)
0.862133 + 0.506683i \(0.169128\pi\)
\(24\) 0 0
\(25\) −3.57334 6.18921i −0.714669 1.23784i
\(26\) 0 0
\(27\) 4.20506 3.05246i 0.809263 0.587446i
\(28\) 0 0
\(29\) 2.46032 + 4.26140i 0.456870 + 0.791321i 0.998794 0.0491062i \(-0.0156373\pi\)
−0.541924 + 0.840428i \(0.682304\pi\)
\(30\) 0 0
\(31\) 3.72257 6.44769i 0.668594 1.15804i −0.309704 0.950833i \(-0.600230\pi\)
0.978297 0.207205i \(-0.0664368\pi\)
\(32\) 0 0
\(33\) −6.58827 7.31907i −1.14687 1.27409i
\(34\) 0 0
\(35\) 9.40925 1.59045
\(36\) 0 0
\(37\) −5.00631 −0.823033 −0.411516 0.911402i \(-0.635001\pi\)
−0.411516 + 0.911402i \(0.635001\pi\)
\(38\) 0 0
\(39\) 1.88542 5.79997i 0.301909 0.928739i
\(40\) 0 0
\(41\) 0.482053 0.834941i 0.0752841 0.130396i −0.825926 0.563779i \(-0.809347\pi\)
0.901210 + 0.433383i \(0.142680\pi\)
\(42\) 0 0
\(43\) −0.255495 0.442530i −0.0389626 0.0674852i 0.845887 0.533363i \(-0.179072\pi\)
−0.884849 + 0.465878i \(0.845739\pi\)
\(44\) 0 0
\(45\) −1.09582 + 10.3980i −0.163355 + 1.55005i
\(46\) 0 0
\(47\) −2.83509 4.91053i −0.413541 0.716274i 0.581733 0.813380i \(-0.302375\pi\)
−0.995274 + 0.0971059i \(0.969041\pi\)
\(48\) 0 0
\(49\) −0.144369 + 0.250055i −0.0206242 + 0.0357221i
\(50\) 0 0
\(51\) 12.9775 2.75655i 1.81721 0.385994i
\(52\) 0 0
\(53\) 10.4058 1.42935 0.714676 0.699455i \(-0.246574\pi\)
0.714676 + 0.699455i \(0.246574\pi\)
\(54\) 0 0
\(55\) 19.8151 2.67187
\(56\) 0 0
\(57\) −3.42340 + 0.727166i −0.453441 + 0.0963155i
\(58\) 0 0
\(59\) −4.47636 + 7.75329i −0.582773 + 1.00939i 0.412376 + 0.911014i \(0.364699\pi\)
−0.995149 + 0.0983788i \(0.968634\pi\)
\(60\) 0 0
\(61\) −1.46032 2.52935i −0.186975 0.323849i 0.757266 0.653107i \(-0.226535\pi\)
−0.944240 + 0.329258i \(0.893202\pi\)
\(62\) 0 0
\(63\) −6.55114 4.76248i −0.825366 0.600016i
\(64\) 0 0
\(65\) 6.13589 + 10.6277i 0.761064 + 1.31820i
\(66\) 0 0
\(67\) 1.56829 2.71635i 0.191597 0.331855i −0.754183 0.656665i \(-0.771967\pi\)
0.945780 + 0.324809i \(0.105300\pi\)
\(68\) 0 0
\(69\) −0.0397217 + 0.122193i −0.00478193 + 0.0147103i
\(70\) 0 0
\(71\) 8.19647 0.972742 0.486371 0.873752i \(-0.338320\pi\)
0.486371 + 0.873752i \(0.338320\pi\)
\(72\) 0 0
\(73\) 5.21796 0.610716 0.305358 0.952238i \(-0.401224\pi\)
0.305358 + 0.952238i \(0.401224\pi\)
\(74\) 0 0
\(75\) −8.28150 9.20012i −0.956265 1.06234i
\(76\) 0 0
\(77\) −7.67474 + 13.2930i −0.874617 + 1.51488i
\(78\) 0 0
\(79\) −0.716260 1.24060i −0.0805855 0.139578i 0.822916 0.568163i \(-0.192346\pi\)
−0.903502 + 0.428585i \(0.859012\pi\)
\(80\) 0 0
\(81\) 6.02592 6.68493i 0.669546 0.742770i
\(82\) 0 0
\(83\) 1.74052 + 3.01467i 0.191047 + 0.330903i 0.945597 0.325339i \(-0.105478\pi\)
−0.754551 + 0.656242i \(0.772145\pi\)
\(84\) 0 0
\(85\) −13.3478 + 23.1191i −1.44778 + 2.50762i
\(86\) 0 0
\(87\) 5.70198 + 6.33447i 0.611316 + 0.679126i
\(88\) 0 0
\(89\) −12.4058 −1.31502 −0.657509 0.753447i \(-0.728390\pi\)
−0.657509 + 0.753447i \(0.728390\pi\)
\(90\) 0 0
\(91\) −9.50616 −0.996516
\(92\) 0 0
\(93\) 3.98660 12.2637i 0.413392 1.27168i
\(94\) 0 0
\(95\) 3.52110 6.09873i 0.361258 0.625717i
\(96\) 0 0
\(97\) −3.50265 6.06677i −0.355640 0.615987i 0.631587 0.775305i \(-0.282404\pi\)
−0.987227 + 0.159318i \(0.949071\pi\)
\(98\) 0 0
\(99\) −13.7962 10.0294i −1.38657 1.00799i
\(100\) 0 0
\(101\) −4.44237 7.69441i −0.442032 0.765623i 0.555808 0.831311i \(-0.312409\pi\)
−0.997840 + 0.0656882i \(0.979076\pi\)
\(102\) 0 0
\(103\) −2.65012 + 4.59014i −0.261124 + 0.452280i −0.966541 0.256513i \(-0.917426\pi\)
0.705417 + 0.708792i \(0.250760\pi\)
\(104\) 0 0
\(105\) 15.9416 3.38617i 1.55574 0.330456i
\(106\) 0 0
\(107\) 7.53993 0.728912 0.364456 0.931221i \(-0.381255\pi\)
0.364456 + 0.931221i \(0.381255\pi\)
\(108\) 0 0
\(109\) −13.8840 −1.32984 −0.664922 0.746913i \(-0.731535\pi\)
−0.664922 + 0.746913i \(0.731535\pi\)
\(110\) 0 0
\(111\) −8.48195 + 1.80166i −0.805072 + 0.171006i
\(112\) 0 0
\(113\) 1.36549 2.36510i 0.128454 0.222489i −0.794624 0.607102i \(-0.792332\pi\)
0.923078 + 0.384613i \(0.125665\pi\)
\(114\) 0 0
\(115\) −0.129270 0.223902i −0.0120545 0.0208789i
\(116\) 0 0
\(117\) 1.10710 10.5051i 0.102352 0.971200i
\(118\) 0 0
\(119\) −10.3397 17.9089i −0.947839 1.64171i
\(120\) 0 0
\(121\) −10.6624 + 18.4677i −0.969305 + 1.67889i
\(122\) 0 0
\(123\) 0.516244 1.58808i 0.0465481 0.143192i
\(124\) 0 0
\(125\) 7.48166 0.669180
\(126\) 0 0
\(127\) −5.89964 −0.523509 −0.261754 0.965135i \(-0.584301\pi\)
−0.261754 + 0.965135i \(0.584301\pi\)
\(128\) 0 0
\(129\) −0.592129 0.657810i −0.0521340 0.0579170i
\(130\) 0 0
\(131\) −0.566027 + 0.980388i −0.0494540 + 0.0856569i −0.889693 0.456560i \(-0.849081\pi\)
0.840239 + 0.542217i \(0.182415\pi\)
\(132\) 0 0
\(133\) 2.72757 + 4.72429i 0.236510 + 0.409648i
\(134\) 0 0
\(135\) 1.88542 + 18.0113i 0.162271 + 1.55016i
\(136\) 0 0
\(137\) 3.18182 + 5.51107i 0.271841 + 0.470843i 0.969333 0.245750i \(-0.0790341\pi\)
−0.697492 + 0.716592i \(0.745701\pi\)
\(138\) 0 0
\(139\) −11.2001 + 19.3992i −0.949983 + 1.64542i −0.204531 + 0.978860i \(0.565567\pi\)
−0.745453 + 0.666559i \(0.767767\pi\)
\(140\) 0 0
\(141\) −6.57054 7.29938i −0.553340 0.614719i
\(142\) 0 0
\(143\) −20.0192 −1.67409
\(144\) 0 0
\(145\) −17.1495 −1.42418
\(146\) 0 0
\(147\) −0.154609 + 0.475611i −0.0127519 + 0.0392277i
\(148\) 0 0
\(149\) −0.939215 + 1.62677i −0.0769435 + 0.133270i −0.901930 0.431883i \(-0.857849\pi\)
0.824986 + 0.565153i \(0.191183\pi\)
\(150\) 0 0
\(151\) 0.183779 + 0.318315i 0.0149557 + 0.0259041i 0.873406 0.486992i \(-0.161906\pi\)
−0.858451 + 0.512896i \(0.828573\pi\)
\(152\) 0 0
\(153\) 20.9951 9.34057i 1.69735 0.755141i
\(154\) 0 0
\(155\) 12.9739 + 22.4715i 1.04209 + 1.80496i
\(156\) 0 0
\(157\) 7.15363 12.3905i 0.570922 0.988866i −0.425550 0.904935i \(-0.639919\pi\)
0.996472 0.0839309i \(-0.0267475\pi\)
\(158\) 0 0
\(159\) 17.6301 3.74482i 1.39816 0.296984i
\(160\) 0 0
\(161\) 0.200274 0.0157838
\(162\) 0 0
\(163\) 3.02958 0.237295 0.118648 0.992936i \(-0.462144\pi\)
0.118648 + 0.992936i \(0.462144\pi\)
\(164\) 0 0
\(165\) 33.5718 7.13099i 2.61356 0.555147i
\(166\) 0 0
\(167\) −0.629519 + 1.09036i −0.0487137 + 0.0843745i −0.889354 0.457219i \(-0.848846\pi\)
0.840640 + 0.541594i \(0.182179\pi\)
\(168\) 0 0
\(169\) 0.300915 + 0.521200i 0.0231473 + 0.0400923i
\(170\) 0 0
\(171\) −5.53841 + 2.46400i −0.423533 + 0.188427i
\(172\) 0 0
\(173\) 7.14845 + 12.3815i 0.543487 + 0.941347i 0.998700 + 0.0509644i \(0.0162295\pi\)
−0.455214 + 0.890382i \(0.650437\pi\)
\(174\) 0 0
\(175\) −9.64719 + 16.7094i −0.729259 + 1.26311i
\(176\) 0 0
\(177\) −4.79386 + 14.7470i −0.360329 + 1.10845i
\(178\) 0 0
\(179\) 12.7991 0.956647 0.478324 0.878184i \(-0.341245\pi\)
0.478324 + 0.878184i \(0.341245\pi\)
\(180\) 0 0
\(181\) −10.4986 −0.780355 −0.390177 0.920740i \(-0.627586\pi\)
−0.390177 + 0.920740i \(0.627586\pi\)
\(182\) 0 0
\(183\) −3.38440 3.75981i −0.250182 0.277933i
\(184\) 0 0
\(185\) 8.72403 15.1105i 0.641403 1.11094i
\(186\) 0 0
\(187\) −21.7746 37.7146i −1.59231 2.75797i
\(188\) 0 0
\(189\) −12.8132 5.71124i −0.932022 0.415431i
\(190\) 0 0
\(191\) −4.09526 7.09320i −0.296323 0.513246i 0.678969 0.734167i \(-0.262427\pi\)
−0.975292 + 0.220921i \(0.929094\pi\)
\(192\) 0 0
\(193\) −1.46146 + 2.53132i −0.105198 + 0.182208i −0.913819 0.406122i \(-0.866881\pi\)
0.808621 + 0.588330i \(0.200214\pi\)
\(194\) 0 0
\(195\) 14.2204 + 15.7978i 1.01834 + 1.13130i
\(196\) 0 0
\(197\) −4.44174 −0.316461 −0.158230 0.987402i \(-0.550579\pi\)
−0.158230 + 0.987402i \(0.550579\pi\)
\(198\) 0 0
\(199\) 14.6898 1.04133 0.520665 0.853761i \(-0.325684\pi\)
0.520665 + 0.853761i \(0.325684\pi\)
\(200\) 0 0
\(201\) 1.67952 5.16658i 0.118464 0.364422i
\(202\) 0 0
\(203\) 6.64228 11.5048i 0.466197 0.807477i
\(204\) 0 0
\(205\) 1.68006 + 2.90994i 0.117340 + 0.203239i
\(206\) 0 0
\(207\) −0.0233242 + 0.221320i −0.00162115 + 0.0153828i
\(208\) 0 0
\(209\) 5.74404 + 9.94896i 0.397323 + 0.688184i
\(210\) 0 0
\(211\) −2.04700 + 3.54551i −0.140921 + 0.244083i −0.927844 0.372969i \(-0.878340\pi\)
0.786923 + 0.617052i \(0.211673\pi\)
\(212\) 0 0
\(213\) 13.8869 2.94972i 0.951514 0.202111i
\(214\) 0 0
\(215\) 1.78091 0.121457
\(216\) 0 0
\(217\) −20.1002 −1.36449
\(218\) 0 0
\(219\) 8.84054 1.87782i 0.597388 0.126892i
\(220\) 0 0
\(221\) 13.4853 23.3572i 0.907120 1.57118i
\(222\) 0 0
\(223\) 6.24612 + 10.8186i 0.418271 + 0.724467i 0.995766 0.0919276i \(-0.0293028\pi\)
−0.577494 + 0.816395i \(0.695970\pi\)
\(224\) 0 0
\(225\) −17.3419 12.6070i −1.15612 0.840467i
\(226\) 0 0
\(227\) 4.52721 + 7.84136i 0.300482 + 0.520449i 0.976245 0.216669i \(-0.0695193\pi\)
−0.675764 + 0.737118i \(0.736186\pi\)
\(228\) 0 0
\(229\) 13.1073 22.7024i 0.866152 1.50022i 0.000252919 1.00000i \(-0.499919\pi\)
0.865899 0.500219i \(-0.166747\pi\)
\(230\) 0 0
\(231\) −8.21908 + 25.2837i −0.540776 + 1.66355i
\(232\) 0 0
\(233\) 1.41840 0.0929224 0.0464612 0.998920i \(-0.485206\pi\)
0.0464612 + 0.998920i \(0.485206\pi\)
\(234\) 0 0
\(235\) 19.7618 1.28912
\(236\) 0 0
\(237\) −1.65999 1.84412i −0.107828 0.119788i
\(238\) 0 0
\(239\) −8.18200 + 14.1716i −0.529250 + 0.916688i 0.470168 + 0.882577i \(0.344193\pi\)
−0.999418 + 0.0341107i \(0.989140\pi\)
\(240\) 0 0
\(241\) −5.17500 8.96336i −0.333351 0.577381i 0.649816 0.760092i \(-0.274846\pi\)
−0.983167 + 0.182711i \(0.941513\pi\)
\(242\) 0 0
\(243\) 7.80366 13.4945i 0.500605 0.865676i
\(244\) 0 0
\(245\) −0.503157 0.871493i −0.0321455 0.0556776i
\(246\) 0 0
\(247\) −3.55737 + 6.16154i −0.226350 + 0.392049i
\(248\) 0 0
\(249\) 4.03379 + 4.48124i 0.255631 + 0.283987i
\(250\) 0 0
\(251\) −26.9624 −1.70185 −0.850927 0.525283i \(-0.823959\pi\)
−0.850927 + 0.525283i \(0.823959\pi\)
\(252\) 0 0
\(253\) 0.421759 0.0265158
\(254\) 0 0
\(255\) −14.2946 + 43.9732i −0.895160 + 2.75371i
\(256\) 0 0
\(257\) −14.8380 + 25.7001i −0.925568 + 1.60313i −0.134922 + 0.990856i \(0.543078\pi\)
−0.790646 + 0.612274i \(0.790255\pi\)
\(258\) 0 0
\(259\) 6.75794 + 11.7051i 0.419918 + 0.727319i
\(260\) 0 0
\(261\) 11.9402 + 8.68017i 0.739080 + 0.537289i
\(262\) 0 0
\(263\) −1.46961 2.54544i −0.0906200 0.156959i 0.817152 0.576422i \(-0.195552\pi\)
−0.907772 + 0.419464i \(0.862218\pi\)
\(264\) 0 0
\(265\) −18.1333 + 31.4078i −1.11392 + 1.92936i
\(266\) 0 0
\(267\) −21.0186 + 4.46458i −1.28632 + 0.273228i
\(268\) 0 0
\(269\) 13.4251 0.818541 0.409270 0.912413i \(-0.365783\pi\)
0.409270 + 0.912413i \(0.365783\pi\)
\(270\) 0 0
\(271\) 31.3320 1.90329 0.951643 0.307207i \(-0.0993944\pi\)
0.951643 + 0.307207i \(0.0993944\pi\)
\(272\) 0 0
\(273\) −16.1058 + 3.42104i −0.974769 + 0.207051i
\(274\) 0 0
\(275\) −20.3162 + 35.1887i −1.22511 + 2.12196i
\(276\) 0 0
\(277\) 4.78089 + 8.28075i 0.287256 + 0.497542i 0.973154 0.230156i \(-0.0739236\pi\)
−0.685898 + 0.727698i \(0.740590\pi\)
\(278\) 0 0
\(279\) 2.34090 22.2124i 0.140146 1.32982i
\(280\) 0 0
\(281\) 3.39152 + 5.87429i 0.202321 + 0.350431i 0.949276 0.314444i \(-0.101818\pi\)
−0.746955 + 0.664875i \(0.768485\pi\)
\(282\) 0 0
\(283\) −9.61895 + 16.6605i −0.571787 + 0.990364i 0.424595 + 0.905383i \(0.360416\pi\)
−0.996383 + 0.0849812i \(0.972917\pi\)
\(284\) 0 0
\(285\) 3.77084 11.5999i 0.223366 0.687122i
\(286\) 0 0
\(287\) −2.60286 −0.153642
\(288\) 0 0
\(289\) 41.6710 2.45124
\(290\) 0 0
\(291\) −8.11766 9.01811i −0.475866 0.528651i
\(292\) 0 0
\(293\) 5.63884 9.76676i 0.329425 0.570580i −0.652973 0.757381i \(-0.726479\pi\)
0.982398 + 0.186801i \(0.0598119\pi\)
\(294\) 0 0
\(295\) −15.6011 27.0218i −0.908329 1.57327i
\(296\) 0 0
\(297\) −26.9835 12.0274i −1.56574 0.697900i
\(298\) 0 0
\(299\) 0.130601 + 0.226207i 0.00755285 + 0.0130819i
\(300\) 0 0
\(301\) −0.689776 + 1.19473i −0.0397580 + 0.0688629i
\(302\) 0 0
\(303\) −10.2955 11.4376i −0.591463 0.657071i
\(304\) 0 0
\(305\) 10.1790 0.582850
\(306\) 0 0
\(307\) −22.2819 −1.27169 −0.635846 0.771816i \(-0.719349\pi\)
−0.635846 + 0.771816i \(0.719349\pi\)
\(308\) 0 0
\(309\) −2.83808 + 8.73056i −0.161453 + 0.496664i
\(310\) 0 0
\(311\) −12.0604 + 20.8893i −0.683884 + 1.18452i 0.289902 + 0.957056i \(0.406377\pi\)
−0.973786 + 0.227466i \(0.926956\pi\)
\(312\) 0 0
\(313\) 14.5297 + 25.1661i 0.821265 + 1.42247i 0.904741 + 0.425962i \(0.140064\pi\)
−0.0834762 + 0.996510i \(0.526602\pi\)
\(314\) 0 0
\(315\) 25.7905 11.4741i 1.45313 0.646490i
\(316\) 0 0
\(317\) 16.2862 + 28.2085i 0.914724 + 1.58435i 0.807305 + 0.590134i \(0.200925\pi\)
0.107418 + 0.994214i \(0.465742\pi\)
\(318\) 0 0
\(319\) 13.9881 24.2281i 0.783183 1.35651i
\(320\) 0 0
\(321\) 12.7745 2.71344i 0.713005 0.151450i
\(322\) 0 0
\(323\) −15.4772 −0.861173
\(324\) 0 0
\(325\) −25.1642 −1.39586
\(326\) 0 0
\(327\) −23.5230 + 4.99652i −1.30082 + 0.276308i
\(328\) 0 0
\(329\) −7.65409 + 13.2573i −0.421984 + 0.730897i
\(330\) 0 0
\(331\) 8.05963 + 13.9597i 0.442997 + 0.767293i 0.997910 0.0646148i \(-0.0205819\pi\)
−0.554913 + 0.831908i \(0.687249\pi\)
\(332\) 0 0
\(333\) −13.7222 + 6.10492i −0.751972 + 0.334547i
\(334\) 0 0
\(335\) 5.46581 + 9.46706i 0.298629 + 0.517241i
\(336\) 0 0
\(337\) 12.6119 21.8445i 0.687015 1.18995i −0.285783 0.958294i \(-0.592254\pi\)
0.972799 0.231651i \(-0.0744128\pi\)
\(338\) 0 0
\(339\) 1.46234 4.49847i 0.0794233 0.244324i
\(340\) 0 0
\(341\) −42.3292 −2.29226
\(342\) 0 0
\(343\) −18.1188 −0.978325
\(344\) 0 0
\(345\) −0.299592 0.332824i −0.0161295 0.0179187i
\(346\) 0 0
\(347\) 2.16774 3.75464i 0.116371 0.201560i −0.801956 0.597383i \(-0.796207\pi\)
0.918327 + 0.395823i \(0.129541\pi\)
\(348\) 0 0
\(349\) −9.77744 16.9350i −0.523374 0.906511i −0.999630 0.0272042i \(-0.991340\pi\)
0.476255 0.879307i \(-0.341994\pi\)
\(350\) 0 0
\(351\) −1.90484 18.1968i −0.101673 0.971271i
\(352\) 0 0
\(353\) 9.13835 + 15.8281i 0.486385 + 0.842444i 0.999878 0.0156502i \(-0.00498183\pi\)
−0.513492 + 0.858094i \(0.671648\pi\)
\(354\) 0 0
\(355\) −14.2832 + 24.7392i −0.758074 + 1.31302i
\(356\) 0 0
\(357\) −23.9631 26.6212i −1.26826 1.40894i
\(358\) 0 0
\(359\) 3.41976 0.180488 0.0902440 0.995920i \(-0.471235\pi\)
0.0902440 + 0.995920i \(0.471235\pi\)
\(360\) 0 0
\(361\) −14.9172 −0.785115
\(362\) 0 0
\(363\) −11.4186 + 35.1261i −0.599321 + 1.84364i
\(364\) 0 0
\(365\) −9.09285 + 15.7493i −0.475941 + 0.824355i
\(366\) 0 0
\(367\) −5.46341 9.46291i −0.285188 0.493960i 0.687467 0.726216i \(-0.258723\pi\)
−0.972655 + 0.232256i \(0.925389\pi\)
\(368\) 0 0
\(369\) 0.303134 2.87639i 0.0157805 0.149739i
\(370\) 0 0
\(371\) −14.0467 24.3296i −0.729267 1.26313i
\(372\) 0 0
\(373\) 10.4603 18.1178i 0.541615 0.938104i −0.457197 0.889366i \(-0.651147\pi\)
0.998812 0.0487387i \(-0.0155202\pi\)
\(374\) 0 0
\(375\) 12.6758 2.69247i 0.654576 0.139039i
\(376\) 0 0
\(377\) 17.3261 0.892338
\(378\) 0 0
\(379\) 18.0219 0.925725 0.462862 0.886430i \(-0.346822\pi\)
0.462862 + 0.886430i \(0.346822\pi\)
\(380\) 0 0
\(381\) −9.99548 + 2.12314i −0.512084 + 0.108772i
\(382\) 0 0
\(383\) 12.4732 21.6042i 0.637350 1.10392i −0.348662 0.937249i \(-0.613364\pi\)
0.986012 0.166674i \(-0.0533028\pi\)
\(384\) 0 0
\(385\) −26.7481 46.3290i −1.36321 2.36115i
\(386\) 0 0
\(387\) −1.23995 0.901403i −0.0630300 0.0458209i
\(388\) 0 0
\(389\) −6.96347 12.0611i −0.353062 0.611522i 0.633722 0.773561i \(-0.281526\pi\)
−0.986784 + 0.162039i \(0.948193\pi\)
\(390\) 0 0
\(391\) −0.284105 + 0.492085i −0.0143678 + 0.0248858i
\(392\) 0 0
\(393\) −0.606174 + 1.86472i −0.0305774 + 0.0940629i
\(394\) 0 0
\(395\) 4.99263 0.251206
\(396\) 0 0
\(397\) −6.54840 −0.328655 −0.164327 0.986406i \(-0.552545\pi\)
−0.164327 + 0.986406i \(0.552545\pi\)
\(398\) 0 0
\(399\) 6.32135 + 7.02255i 0.316464 + 0.351567i
\(400\) 0 0
\(401\) −12.1738 + 21.0857i −0.607933 + 1.05297i 0.383648 + 0.923480i \(0.374668\pi\)
−0.991581 + 0.129491i \(0.958666\pi\)
\(402\) 0 0
\(403\) −13.1076 22.7030i −0.652934 1.13092i
\(404\) 0 0
\(405\) 9.67622 + 29.8371i 0.480815 + 1.48262i
\(406\) 0 0
\(407\) 14.2317 + 24.6499i 0.705437 + 1.22185i
\(408\) 0 0
\(409\) 8.08792 14.0087i 0.399922 0.692685i −0.593794 0.804617i \(-0.702371\pi\)
0.993716 + 0.111932i \(0.0357040\pi\)
\(410\) 0 0
\(411\) 7.37411 + 8.19208i 0.363738 + 0.404086i
\(412\) 0 0
\(413\) 24.1703 1.18934
\(414\) 0 0
\(415\) −12.1322 −0.595544
\(416\) 0 0
\(417\) −11.9945 + 36.8978i −0.587374 + 1.80689i
\(418\) 0 0
\(419\) 17.2436 29.8668i 0.842405 1.45909i −0.0454518 0.998967i \(-0.514473\pi\)
0.887856 0.460121i \(-0.152194\pi\)
\(420\) 0 0
\(421\) 15.6909 + 27.1774i 0.764728 + 1.32455i 0.940390 + 0.340097i \(0.110460\pi\)
−0.175662 + 0.984451i \(0.556207\pi\)
\(422\) 0 0
\(423\) −13.7590 10.0024i −0.668987 0.486333i
\(424\) 0 0
\(425\) −27.3708 47.4075i −1.32768 2.29960i
\(426\) 0 0
\(427\) −3.94252 + 6.82864i −0.190792 + 0.330461i
\(428\) 0 0
\(429\) −33.9175 + 7.20443i −1.63755 + 0.347833i
\(430\) 0 0
\(431\) 12.1491 0.585200 0.292600 0.956235i \(-0.405480\pi\)
0.292600 + 0.956235i \(0.405480\pi\)
\(432\) 0 0
\(433\) 2.40374 0.115517 0.0577583 0.998331i \(-0.481605\pi\)
0.0577583 + 0.998331i \(0.481605\pi\)
\(434\) 0 0
\(435\) −29.0555 + 6.17169i −1.39310 + 0.295910i
\(436\) 0 0
\(437\) 0.0749458 0.129810i 0.00358514 0.00620965i
\(438\) 0 0
\(439\) 18.6941 + 32.3792i 0.892222 + 1.54537i 0.837206 + 0.546888i \(0.184188\pi\)
0.0550162 + 0.998485i \(0.482479\pi\)
\(440\) 0 0
\(441\) −0.0907850 + 0.861444i −0.00432310 + 0.0410212i
\(442\) 0 0
\(443\) 4.22340 + 7.31515i 0.200660 + 0.347553i 0.948741 0.316054i \(-0.102358\pi\)
−0.748081 + 0.663607i \(0.769025\pi\)
\(444\) 0 0
\(445\) 21.6185 37.4443i 1.02481 1.77503i
\(446\) 0 0
\(447\) −1.00583 + 3.09415i −0.0475741 + 0.146348i
\(448\) 0 0
\(449\) 18.6531 0.880295 0.440147 0.897926i \(-0.354926\pi\)
0.440147 + 0.897926i \(0.354926\pi\)
\(450\) 0 0
\(451\) −5.48141 −0.258109
\(452\) 0 0
\(453\) 0.425922 + 0.473167i 0.0200116 + 0.0222313i
\(454\) 0 0
\(455\) 16.5655 28.6922i 0.776601 1.34511i
\(456\) 0 0
\(457\) −8.91748 15.4455i −0.417142 0.722511i 0.578509 0.815676i \(-0.303635\pi\)
−0.995651 + 0.0931650i \(0.970302\pi\)
\(458\) 0 0
\(459\) 32.2095 23.3809i 1.50341 1.09133i
\(460\) 0 0
\(461\) 10.0563 + 17.4181i 0.468370 + 0.811240i 0.999347 0.0361463i \(-0.0115082\pi\)
−0.530977 + 0.847386i \(0.678175\pi\)
\(462\) 0 0
\(463\) −4.10747 + 7.11435i −0.190890 + 0.330632i −0.945546 0.325490i \(-0.894471\pi\)
0.754655 + 0.656122i \(0.227804\pi\)
\(464\) 0 0
\(465\) 30.0681 + 33.4034i 1.39438 + 1.54905i
\(466\) 0 0
\(467\) 19.3274 0.894364 0.447182 0.894443i \(-0.352428\pi\)
0.447182 + 0.894443i \(0.352428\pi\)
\(468\) 0 0
\(469\) −8.46802 −0.391017
\(470\) 0 0
\(471\) 7.66102 23.5670i 0.353001 1.08591i
\(472\) 0 0
\(473\) −1.45261 + 2.51600i −0.0667911 + 0.115686i
\(474\) 0 0
\(475\) 7.22029 + 12.5059i 0.331290 + 0.573811i
\(476\) 0 0
\(477\) 28.5222 12.6893i 1.30594 0.581005i
\(478\) 0 0
\(479\) 21.1597 + 36.6498i 0.966814 + 1.67457i 0.704661 + 0.709544i \(0.251099\pi\)
0.262152 + 0.965027i \(0.415568\pi\)
\(480\) 0 0
\(481\) −8.81387 + 15.2661i −0.401878 + 0.696073i
\(482\) 0 0
\(483\) 0.339314 0.0720738i 0.0154393 0.00327947i
\(484\) 0 0
\(485\) 24.4149 1.10863
\(486\) 0 0
\(487\) −1.36060 −0.0616547 −0.0308273 0.999525i \(-0.509814\pi\)
−0.0308273 + 0.999525i \(0.509814\pi\)
\(488\) 0 0
\(489\) 5.13287 1.09028i 0.232116 0.0493040i
\(490\) 0 0
\(491\) 15.6328 27.0768i 0.705497 1.22196i −0.261015 0.965335i \(-0.584057\pi\)
0.966512 0.256622i \(-0.0826096\pi\)
\(492\) 0 0
\(493\) 18.8453 + 32.6410i 0.848750 + 1.47008i
\(494\) 0 0
\(495\) 54.3127 24.1634i 2.44118 1.08606i
\(496\) 0 0
\(497\) −11.0643 19.1639i −0.496301 0.859618i
\(498\) 0 0
\(499\) 7.37981 12.7822i 0.330366 0.572210i −0.652218 0.758032i \(-0.726161\pi\)
0.982584 + 0.185821i \(0.0594946\pi\)
\(500\) 0 0
\(501\) −0.674169 + 2.07389i −0.0301196 + 0.0926547i
\(502\) 0 0
\(503\) −44.6336 −1.99011 −0.995056 0.0993124i \(-0.968336\pi\)
−0.995056 + 0.0993124i \(0.968336\pi\)
\(504\) 0 0
\(505\) 30.9652 1.37793
\(506\) 0 0
\(507\) 0.697393 + 0.774751i 0.0309723 + 0.0344079i
\(508\) 0 0
\(509\) −0.854549 + 1.48012i −0.0378772 + 0.0656053i −0.884343 0.466839i \(-0.845393\pi\)
0.846465 + 0.532444i \(0.178726\pi\)
\(510\) 0 0
\(511\) −7.04364 12.1999i −0.311592 0.539694i
\(512\) 0 0
\(513\) −8.49673 + 6.16779i −0.375140 + 0.272315i
\(514\) 0 0
\(515\) −9.23621 15.9976i −0.406996 0.704938i
\(516\) 0 0
\(517\) −16.1189 + 27.9187i −0.708907 + 1.22786i
\(518\) 0 0
\(519\) 16.5671 + 18.4048i 0.727214 + 0.807880i
\(520\) 0 0
\(521\) −10.6018 −0.464475 −0.232237 0.972659i \(-0.574605\pi\)
−0.232237 + 0.972659i \(0.574605\pi\)
\(522\) 0 0
\(523\) 27.1565 1.18747 0.593736 0.804660i \(-0.297652\pi\)
0.593736 + 0.804660i \(0.297652\pi\)
\(524\) 0 0
\(525\) −10.3314 + 31.7818i −0.450901 + 1.38707i
\(526\) 0 0
\(527\) 28.5138 49.3874i 1.24208 2.15135i
\(528\) 0 0
\(529\) 11.4972 + 19.9138i 0.499880 + 0.865818i
\(530\) 0 0
\(531\) −2.81491 + 26.7103i −0.122157 + 1.15913i
\(532\) 0 0
\(533\) −1.69736 2.93991i −0.0735208 0.127342i
\(534\) 0 0
\(535\) −13.1391 + 22.7576i −0.568053 + 0.983897i
\(536\) 0 0
\(537\) 21.6848 4.60609i 0.935770 0.198767i
\(538\) 0 0
\(539\) 1.64162 0.0707094
\(540\) 0 0
\(541\) 35.1225 1.51003 0.755017 0.655705i \(-0.227629\pi\)
0.755017 + 0.655705i \(0.227629\pi\)
\(542\) 0 0
\(543\) −17.7873 + 3.77820i −0.763325 + 0.162138i
\(544\) 0 0
\(545\) 24.1943 41.9057i 1.03637 1.79504i
\(546\) 0 0
\(547\) −13.0029 22.5218i −0.555966 0.962961i −0.997828 0.0658781i \(-0.979015\pi\)
0.441862 0.897083i \(-0.354318\pi\)
\(548\) 0 0
\(549\) −7.08709 5.15210i −0.302470 0.219886i
\(550\) 0 0
\(551\) −4.97131 8.61057i −0.211785 0.366822i
\(552\) 0 0
\(553\) −1.93373 + 3.34932i −0.0822307 + 0.142428i
\(554\) 0 0
\(555\) 9.34279 28.7405i 0.396580 1.21997i
\(556\) 0 0
\(557\) −28.8670 −1.22314 −0.611568 0.791192i \(-0.709461\pi\)
−0.611568 + 0.791192i \(0.709461\pi\)
\(558\) 0 0
\(559\) −1.79925 −0.0761000
\(560\) 0 0
\(561\) −50.4642 56.0619i −2.13060 2.36694i
\(562\) 0 0
\(563\) −0.876491 + 1.51813i −0.0369397 + 0.0639815i −0.883904 0.467668i \(-0.845094\pi\)
0.846964 + 0.531649i \(0.178428\pi\)
\(564\) 0 0
\(565\) 4.75901 + 8.24285i 0.200213 + 0.346779i
\(566\) 0 0
\(567\) −23.7641 5.06511i −0.997998 0.212715i
\(568\) 0 0
\(569\) −13.3974 23.2049i −0.561647 0.972801i −0.997353 0.0727120i \(-0.976835\pi\)
0.435706 0.900089i \(-0.356499\pi\)
\(570\) 0 0
\(571\) 12.6759 21.9553i 0.530471 0.918803i −0.468897 0.883253i \(-0.655348\pi\)
0.999368 0.0355497i \(-0.0113182\pi\)
\(572\) 0 0
\(573\) −9.49108 10.5439i −0.396496 0.440477i
\(574\) 0 0
\(575\) 0.530154 0.0221090
\(576\) 0 0
\(577\) 33.8507 1.40922 0.704612 0.709593i \(-0.251121\pi\)
0.704612 + 0.709593i \(0.251121\pi\)
\(578\) 0 0
\(579\) −1.56511 + 4.81463i −0.0650438 + 0.200089i
\(580\) 0 0
\(581\) 4.69900 8.13890i 0.194947 0.337659i
\(582\) 0 0
\(583\) −29.5811 51.2360i −1.22513 2.12198i
\(584\) 0 0
\(585\) 29.7782 + 21.6479i 1.23118 + 0.895028i
\(586\) 0 0
\(587\) 11.2279 + 19.4474i 0.463427 + 0.802679i 0.999129 0.0417284i \(-0.0132864\pi\)
−0.535702 + 0.844407i \(0.679953\pi\)
\(588\) 0 0
\(589\) −7.52182 + 13.0282i −0.309931 + 0.536817i
\(590\) 0 0
\(591\) −7.52543 + 1.59848i −0.309555 + 0.0657526i
\(592\) 0 0
\(593\) −9.35530 −0.384176 −0.192088 0.981378i \(-0.561526\pi\)
−0.192088 + 0.981378i \(0.561526\pi\)
\(594\) 0 0
\(595\) 72.0721 2.95467
\(596\) 0 0
\(597\) 24.8882 5.28651i 1.01860 0.216362i
\(598\) 0 0
\(599\) −12.2259 + 21.1759i −0.499538 + 0.865226i −1.00000 0.000533153i \(-0.999830\pi\)
0.500462 + 0.865759i \(0.333164\pi\)
\(600\) 0 0
\(601\) −6.64643 11.5120i −0.271114 0.469583i 0.698034 0.716065i \(-0.254059\pi\)
−0.969147 + 0.246482i \(0.920725\pi\)
\(602\) 0 0
\(603\) 0.986201 9.35790i 0.0401612 0.381083i
\(604\) 0 0
\(605\) −37.1605 64.3639i −1.51079 2.61677i
\(606\) 0 0
\(607\) −18.1403 + 31.4198i −0.736290 + 1.27529i 0.217864 + 0.975979i \(0.430091\pi\)
−0.954155 + 0.299313i \(0.903242\pi\)
\(608\) 0 0
\(609\) 7.11340 21.8824i 0.288250 0.886719i
\(610\) 0 0
\(611\) −19.9653 −0.807710
\(612\) 0 0
\(613\) −6.73390 −0.271980 −0.135990 0.990710i \(-0.543421\pi\)
−0.135990 + 0.990710i \(0.543421\pi\)
\(614\) 0 0
\(615\) 3.89366 + 4.32556i 0.157007 + 0.174424i
\(616\) 0 0
\(617\) 0.553446 0.958597i 0.0222809 0.0385917i −0.854670 0.519172i \(-0.826241\pi\)
0.876951 + 0.480580i \(0.159574\pi\)
\(618\) 0 0
\(619\) −7.60418 13.1708i −0.305638 0.529380i 0.671765 0.740764i \(-0.265536\pi\)
−0.977403 + 0.211384i \(0.932203\pi\)
\(620\) 0 0
\(621\) 0.0401307 + 0.383365i 0.00161039 + 0.0153839i
\(622\) 0 0
\(623\) 16.7464 + 29.0057i 0.670932 + 1.16209i
\(624\) 0 0
\(625\) 4.82915 8.36432i 0.193166 0.334573i
\(626\) 0 0
\(627\) 13.3122 + 14.7889i 0.531640 + 0.590612i
\(628\) 0 0
\(629\) −38.3469 −1.52899
\(630\) 0 0
\(631\) 29.2163 1.16308 0.581541 0.813517i \(-0.302450\pi\)
0.581541 + 0.813517i \(0.302450\pi\)
\(632\) 0 0
\(633\) −2.19219 + 6.74365i −0.0871316 + 0.268036i
\(634\) 0 0
\(635\) 10.2807 17.8068i 0.407979 0.706641i
\(636\) 0 0
\(637\) 0.508339 + 0.880468i 0.0201411 + 0.0348854i
\(638\) 0 0
\(639\) 22.4663 9.99513i 0.888755 0.395401i
\(640\) 0 0
\(641\) −13.4412 23.2809i −0.530897 0.919540i −0.999350 0.0360519i \(-0.988522\pi\)
0.468453 0.883488i \(-0.344811\pi\)
\(642\) 0 0
\(643\) 6.36207 11.0194i 0.250896 0.434564i −0.712877 0.701289i \(-0.752608\pi\)
0.963773 + 0.266725i \(0.0859416\pi\)
\(644\) 0 0
\(645\) 3.01730 0.640907i 0.118806 0.0252357i
\(646\) 0 0
\(647\) 47.3838 1.86285 0.931425 0.363933i \(-0.118566\pi\)
0.931425 + 0.363933i \(0.118566\pi\)
\(648\) 0 0
\(649\) 50.9006 1.99802
\(650\) 0 0
\(651\) −34.0547 + 7.23358i −1.33471 + 0.283506i
\(652\) 0 0
\(653\) −4.13506 + 7.16213i −0.161817 + 0.280276i −0.935521 0.353272i \(-0.885069\pi\)
0.773703 + 0.633548i \(0.218402\pi\)
\(654\) 0 0
\(655\) −1.97272 3.41686i −0.0770807 0.133508i
\(656\) 0 0
\(657\) 14.3023 6.36301i 0.557987 0.248245i
\(658\) 0 0
\(659\) −1.00770 1.74539i −0.0392544 0.0679906i 0.845731 0.533610i \(-0.179165\pi\)
−0.884985 + 0.465619i \(0.845832\pi\)
\(660\) 0 0
\(661\) −1.70432 + 2.95196i −0.0662902 + 0.114818i −0.897266 0.441491i \(-0.854450\pi\)
0.830975 + 0.556309i \(0.187783\pi\)
\(662\) 0 0
\(663\) 14.4418 44.4261i 0.560872 1.72537i
\(664\) 0 0
\(665\) −19.0123 −0.737266
\(666\) 0 0
\(667\) −0.365022 −0.0141337
\(668\) 0 0
\(669\) 14.4759 + 16.0816i 0.559669 + 0.621750i
\(670\) 0 0
\(671\) −8.30261 + 14.3805i −0.320519 + 0.555155i
\(672\) 0 0
\(673\) 7.56791 + 13.1080i 0.291722 + 0.505277i 0.974217 0.225613i \(-0.0724386\pi\)
−0.682495 + 0.730890i \(0.739105\pi\)
\(674\) 0 0
\(675\) −33.9184 15.1185i −1.30552 0.581912i
\(676\) 0 0
\(677\) −9.31110 16.1273i −0.357855 0.619822i 0.629748 0.776800i \(-0.283158\pi\)
−0.987602 + 0.156978i \(0.949825\pi\)
\(678\) 0 0
\(679\) −9.45634 + 16.3789i −0.362901 + 0.628563i
\(680\) 0 0
\(681\) 10.4922 + 11.6560i 0.402060 + 0.446659i
\(682\) 0 0
\(683\) −38.4656 −1.47185 −0.735923 0.677066i \(-0.763251\pi\)
−0.735923 + 0.677066i \(0.763251\pi\)
\(684\) 0 0
\(685\) −22.1786 −0.847401
\(686\) 0 0
\(687\) 14.0369 43.1806i 0.535542 1.64744i
\(688\) 0 0
\(689\) 18.3200 31.7312i 0.697938 1.20886i
\(690\) 0 0
\(691\) −11.2999 19.5720i −0.429869 0.744555i 0.566992 0.823723i \(-0.308107\pi\)
−0.996861 + 0.0791683i \(0.974774\pi\)
\(692\) 0 0
\(693\) −4.82618 + 45.7948i −0.183331 + 1.73960i
\(694\) 0 0
\(695\) −39.0348 67.6103i −1.48068 2.56460i
\(696\) 0 0
\(697\) 3.69238 6.39540i 0.139859 0.242243i
\(698\) 0 0
\(699\) 2.40312 0.510449i 0.0908945 0.0193069i
\(700\) 0 0
\(701\) −37.8883 −1.43102 −0.715510 0.698602i \(-0.753806\pi\)
−0.715510 + 0.698602i \(0.753806\pi\)
\(702\) 0 0
\(703\) 10.1157 0.381523
\(704\) 0 0
\(705\) 33.4814 7.11181i 1.26098 0.267846i
\(706\) 0 0
\(707\) −11.9934 + 20.7731i −0.451057 + 0.781253i
\(708\) 0 0
\(709\) 7.75701 + 13.4355i 0.291321 + 0.504582i 0.974122 0.226022i \(-0.0725720\pi\)
−0.682802 + 0.730604i \(0.739239\pi\)
\(710\) 0 0
\(711\) −3.47609 2.52701i −0.130364 0.0947704i
\(712\) 0 0
\(713\) 0.276147 + 0.478301i 0.0103418 + 0.0179125i
\(714\) 0 0
\(715\) 34.8855 60.4235i 1.30464 2.25971i
\(716\) 0 0
\(717\) −8.76233 + 26.9548i −0.327235 + 1.00665i
\(718\) 0 0
\(719\) −29.8701 −1.11397 −0.556983 0.830524i \(-0.688041\pi\)
−0.556983 + 0.830524i \(0.688041\pi\)
\(720\) 0 0
\(721\) 14.3094 0.532910
\(722\) 0 0
\(723\) −11.9935 13.3238i −0.446041 0.495518i
\(724\) 0 0
\(725\) 17.5831 30.4549i 0.653021 1.13107i
\(726\) 0 0
\(727\) 2.80759 + 4.86288i 0.104128 + 0.180354i 0.913381 0.407105i \(-0.133462\pi\)
−0.809254 + 0.587459i \(0.800128\pi\)
\(728\) 0 0
\(729\) 8.36500 25.6715i 0.309815 0.950797i
\(730\) 0 0
\(731\) −1.95701 3.38965i −0.0723828 0.125371i
\(732\) 0 0
\(733\) 6.02803 10.4409i 0.222650 0.385642i −0.732962 0.680270i \(-0.761863\pi\)
0.955612 + 0.294628i \(0.0951958\pi\)
\(734\) 0 0
\(735\) −1.16610 1.29545i −0.0430124 0.0477835i
\(736\) 0 0
\(737\) −17.8329 −0.656885
\(738\) 0 0
\(739\) 43.8187 1.61190 0.805948 0.591986i \(-0.201656\pi\)
0.805948 + 0.591986i \(0.201656\pi\)
\(740\) 0 0
\(741\) −3.80968 + 11.7194i −0.139952 + 0.430523i
\(742\) 0 0
\(743\) −15.0004 + 25.9814i −0.550310 + 0.953164i 0.447942 + 0.894062i \(0.352157\pi\)
−0.998252 + 0.0591018i \(0.981176\pi\)
\(744\) 0 0
\(745\) −3.27336 5.66963i −0.119927 0.207719i
\(746\) 0 0
\(747\) 8.44694 + 6.14067i 0.309058 + 0.224676i
\(748\) 0 0
\(749\) −10.1780 17.6288i −0.371897 0.644144i
\(750\) 0 0
\(751\) −4.69583 + 8.13342i −0.171353 + 0.296793i −0.938893 0.344208i \(-0.888147\pi\)
0.767540 + 0.641001i \(0.221481\pi\)
\(752\) 0 0
\(753\) −45.6812 + 9.70316i −1.66471 + 0.353603i
\(754\) 0 0
\(755\) −1.28102 −0.0466210
\(756\) 0 0
\(757\) 21.7285 0.789737 0.394868 0.918738i \(-0.370790\pi\)
0.394868 + 0.918738i \(0.370790\pi\)
\(758\) 0 0
\(759\) 0.714567 0.151781i 0.0259371 0.00550932i
\(760\) 0 0
\(761\) −6.78398 + 11.7502i −0.245919 + 0.425944i −0.962390 0.271673i \(-0.912423\pi\)
0.716471 + 0.697617i \(0.245756\pi\)
\(762\) 0 0
\(763\) 18.7417 + 32.4617i 0.678497 + 1.17519i
\(764\) 0 0
\(765\) −8.39365 + 79.6459i −0.303473 + 2.87961i
\(766\) 0 0
\(767\) 15.7617 + 27.3001i 0.569124 + 0.985751i
\(768\) 0 0
\(769\) −21.3949 + 37.0571i −0.771520 + 1.33631i 0.165209 + 0.986259i \(0.447170\pi\)
−0.936730 + 0.350054i \(0.886163\pi\)
\(770\) 0 0
\(771\) −15.8904 + 48.8823i −0.572278 + 1.76045i
\(772\) 0 0
\(773\) 12.4288 0.447034 0.223517 0.974700i \(-0.428246\pi\)
0.223517 + 0.974700i \(0.428246\pi\)
\(774\) 0 0
\(775\) −53.2081 −1.91129
\(776\) 0 0
\(777\) 15.6620 + 17.3993i 0.561873 + 0.624198i
\(778\) 0 0
\(779\) −0.974036 + 1.68708i −0.0348984 + 0.0604459i
\(780\) 0 0
\(781\) −23.3004 40.3576i −0.833756 1.44411i
\(782\) 0 0
\(783\) 23.3535 + 10.4094i 0.834586 + 0.372001i
\(784\) 0 0
\(785\) 24.9319 + 43.1833i 0.889858 + 1.54128i
\(786\) 0 0
\(787\) −21.5079 + 37.2527i −0.766673 + 1.32792i 0.172684 + 0.984977i \(0.444756\pi\)
−0.939357 + 0.342940i \(0.888577\pi\)
\(788\) 0 0
\(789\) −3.40593 3.78374i −0.121254 0.134705i
\(790\) 0 0
\(791\) −7.37300 −0.262154
\(792\) 0 0
\(793\) −10.2839 −0.365191
\(794\) 0 0
\(795\) −19.4194 + 59.7384i −0.688736 + 2.11870i
\(796\) 0