Properties

Label 1386.2.k.v.793.1
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.21870000.1
Defining polynomial: \(x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.1
Root \(0.500000 - 0.679547i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.v.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.40280 + 2.42972i) q^{5} +(-1.40280 - 2.24325i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.40280 + 2.42972i) q^{5} +(-1.40280 - 2.24325i) q^{7} -1.00000 q^{8} +(1.40280 + 2.42972i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-2.64411 + 0.0932392i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.98261 + 6.89809i) q^{17} +(3.24131 - 5.61411i) q^{19} +2.80560 q^{20} -1.00000 q^{22} +(-2.64411 + 4.57973i) q^{23} +(-1.43570 - 2.48671i) q^{25} +(-1.24131 + 2.33648i) q^{28} -5.12859 q^{29} +(4.48261 + 7.76411i) q^{31} +(0.500000 + 0.866025i) q^{32} +7.96523 q^{34} +(7.41832 - 0.261592i) q^{35} +(-5.24131 + 9.07821i) q^{37} +(-3.24131 - 5.61411i) q^{38} +(1.40280 - 2.42972i) q^{40} +5.09382 q^{41} +11.4478 q^{43} +(-0.500000 + 0.866025i) q^{44} +(2.64411 + 4.57973i) q^{46} +(0.161495 - 0.279717i) q^{47} +(-3.06430 + 6.29365i) q^{49} -2.87141 q^{50} +(4.00000 + 6.92820i) q^{53} +2.80560 q^{55} +(1.40280 + 2.24325i) q^{56} +(-2.56430 + 4.44149i) q^{58} +(-0.435704 - 0.754661i) q^{59} +(-1.07981 + 1.87029i) q^{61} +8.96523 q^{62} +1.00000 q^{64} +(3.54691 + 6.14343i) q^{67} +(3.98261 - 6.89809i) q^{68} +(3.48261 - 6.55525i) q^{70} +7.44784 q^{71} +(-6.28822 - 10.8915i) q^{73} +(5.24131 + 9.07821i) q^{74} -6.48261 q^{76} +(-1.24131 + 2.33648i) q^{77} +(-3.40280 + 5.89382i) q^{79} +(-1.40280 - 2.42972i) q^{80} +(2.54691 - 4.41138i) q^{82} -15.0938 q^{83} -22.3473 q^{85} +(5.72392 - 9.91412i) q^{86} +(0.500000 + 0.866025i) q^{88} +(0.805603 - 1.39535i) q^{89} +5.28822 q^{92} +(-0.161495 - 0.279717i) q^{94} +(9.09382 + 15.7510i) q^{95} +7.00000 q^{97} +(3.91832 + 5.80059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} - 3q^{11} + 3q^{14} - 3q^{16} + 3q^{17} + 9q^{19} - 6q^{22} + 3q^{23} - 15q^{25} + 3q^{28} - 18q^{29} + 6q^{31} + 3q^{32} + 6q^{34} + 30q^{35} - 21q^{37} - 9q^{38} - 24q^{41} + 6q^{43} - 3q^{44} - 3q^{46} + 3q^{47} - 12q^{49} - 30q^{50} + 24q^{53} - 9q^{58} - 9q^{59} + 6q^{61} + 12q^{62} + 6q^{64} - 6q^{67} + 3q^{68} - 18q^{71} + 21q^{74} - 18q^{76} + 3q^{77} - 12q^{79} - 12q^{82} - 36q^{83} + 3q^{86} + 3q^{88} - 12q^{89} - 6q^{92} - 3q^{94} + 42q^{97} + 9q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.40280 + 2.42972i −0.627352 + 1.08661i 0.360729 + 0.932671i \(0.382528\pi\)
−0.988081 + 0.153935i \(0.950805\pi\)
\(6\) 0 0
\(7\) −1.40280 2.24325i −0.530209 0.847867i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.40280 + 2.42972i 0.443605 + 0.768346i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.64411 + 0.0932392i −0.706668 + 0.0249192i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.98261 + 6.89809i 0.965926 + 1.67303i 0.707108 + 0.707106i \(0.250000\pi\)
0.258818 + 0.965926i \(0.416667\pi\)
\(18\) 0 0
\(19\) 3.24131 5.61411i 0.743607 1.28796i −0.207236 0.978291i \(-0.566447\pi\)
0.950843 0.309674i \(-0.100220\pi\)
\(20\) 2.80560 0.627352
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −2.64411 + 4.57973i −0.551335 + 0.954940i 0.446844 + 0.894612i \(0.352548\pi\)
−0.998179 + 0.0603277i \(0.980785\pi\)
\(24\) 0 0
\(25\) −1.43570 2.48671i −0.287141 0.497342i
\(26\) 0 0
\(27\) 0 0
\(28\) −1.24131 + 2.33648i −0.234585 + 0.441554i
\(29\) −5.12859 −0.952356 −0.476178 0.879349i \(-0.657978\pi\)
−0.476178 + 0.879349i \(0.657978\pi\)
\(30\) 0 0
\(31\) 4.48261 + 7.76411i 0.805101 + 1.39448i 0.916223 + 0.400669i \(0.131222\pi\)
−0.111122 + 0.993807i \(0.535444\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 7.96523 1.36602
\(35\) 7.41832 0.261592i 1.25392 0.0442171i
\(36\) 0 0
\(37\) −5.24131 + 9.07821i −0.861665 + 1.49245i 0.00865499 + 0.999963i \(0.497245\pi\)
−0.870320 + 0.492486i \(0.836088\pi\)
\(38\) −3.24131 5.61411i −0.525809 0.910728i
\(39\) 0 0
\(40\) 1.40280 2.42972i 0.221802 0.384173i
\(41\) 5.09382 0.795521 0.397760 0.917489i \(-0.369788\pi\)
0.397760 + 0.917489i \(0.369788\pi\)
\(42\) 0 0
\(43\) 11.4478 1.74578 0.872890 0.487918i \(-0.162243\pi\)
0.872890 + 0.487918i \(0.162243\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 2.64411 + 4.57973i 0.389852 + 0.675244i
\(47\) 0.161495 0.279717i 0.0235565 0.0408010i −0.854007 0.520262i \(-0.825834\pi\)
0.877563 + 0.479461i \(0.159168\pi\)
\(48\) 0 0
\(49\) −3.06430 + 6.29365i −0.437757 + 0.899094i
\(50\) −2.87141 −0.406078
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 + 6.92820i 0.549442 + 0.951662i 0.998313 + 0.0580651i \(0.0184931\pi\)
−0.448871 + 0.893597i \(0.648174\pi\)
\(54\) 0 0
\(55\) 2.80560 0.378307
\(56\) 1.40280 + 2.24325i 0.187457 + 0.299766i
\(57\) 0 0
\(58\) −2.56430 + 4.44149i −0.336709 + 0.583196i
\(59\) −0.435704 0.754661i −0.0567238 0.0982485i 0.836269 0.548319i \(-0.184732\pi\)
−0.892993 + 0.450071i \(0.851399\pi\)
\(60\) 0 0
\(61\) −1.07981 + 1.87029i −0.138256 + 0.239466i −0.926836 0.375465i \(-0.877483\pi\)
0.788581 + 0.614931i \(0.210816\pi\)
\(62\) 8.96523 1.13858
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.54691 + 6.14343i 0.433324 + 0.750539i 0.997157 0.0753496i \(-0.0240073\pi\)
−0.563833 + 0.825889i \(0.690674\pi\)
\(68\) 3.98261 6.89809i 0.482963 0.836516i
\(69\) 0 0
\(70\) 3.48261 6.55525i 0.416252 0.783502i
\(71\) 7.44784 0.883896 0.441948 0.897041i \(-0.354288\pi\)
0.441948 + 0.897041i \(0.354288\pi\)
\(72\) 0 0
\(73\) −6.28822 10.8915i −0.735980 1.27475i −0.954292 0.298876i \(-0.903388\pi\)
0.218312 0.975879i \(-0.429945\pi\)
\(74\) 5.24131 + 9.07821i 0.609289 + 1.05532i
\(75\) 0 0
\(76\) −6.48261 −0.743607
\(77\) −1.24131 + 2.33648i −0.141460 + 0.266267i
\(78\) 0 0
\(79\) −3.40280 + 5.89382i −0.382845 + 0.663107i −0.991468 0.130353i \(-0.958389\pi\)
0.608623 + 0.793460i \(0.291722\pi\)
\(80\) −1.40280 2.42972i −0.156838 0.271651i
\(81\) 0 0
\(82\) 2.54691 4.41138i 0.281259 0.487155i
\(83\) −15.0938 −1.65676 −0.828381 0.560165i \(-0.810738\pi\)
−0.828381 + 0.560165i \(0.810738\pi\)
\(84\) 0 0
\(85\) −22.3473 −2.42390
\(86\) 5.72392 9.91412i 0.617226 1.06907i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 0.805603 1.39535i 0.0853937 0.147906i −0.820165 0.572127i \(-0.806119\pi\)
0.905559 + 0.424221i \(0.139452\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.28822 0.551335
\(93\) 0 0
\(94\) −0.161495 0.279717i −0.0166569 0.0288507i
\(95\) 9.09382 + 15.7510i 0.933006 + 1.61601i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 3.91832 + 5.80059i 0.395810 + 0.585948i
\(99\) 0 0
\(100\) −1.43570 + 2.48671i −0.143570 + 0.248671i
\(101\) 5.36990 + 9.30094i 0.534325 + 0.925478i 0.999196 + 0.0400994i \(0.0127675\pi\)
−0.464871 + 0.885379i \(0.653899\pi\)
\(102\) 0 0
\(103\) −1.48261 + 2.56796i −0.146086 + 0.253029i −0.929778 0.368122i \(-0.880001\pi\)
0.783691 + 0.621150i \(0.213334\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) 2.41832 4.18865i 0.233787 0.404932i −0.725132 0.688610i \(-0.758221\pi\)
0.958920 + 0.283678i \(0.0915547\pi\)
\(108\) 0 0
\(109\) 5.07981 + 8.79849i 0.486558 + 0.842743i 0.999881 0.0154529i \(-0.00491901\pi\)
−0.513323 + 0.858196i \(0.671586\pi\)
\(110\) 1.40280 2.42972i 0.133752 0.231665i
\(111\) 0 0
\(112\) 2.64411 0.0932392i 0.249845 0.00881027i
\(113\) −10.9652 −1.03152 −0.515761 0.856733i \(-0.672491\pi\)
−0.515761 + 0.856733i \(0.672491\pi\)
\(114\) 0 0
\(115\) −7.41832 12.8489i −0.691762 1.19817i
\(116\) 2.56430 + 4.44149i 0.238089 + 0.412382i
\(117\) 0 0
\(118\) −0.871407 −0.0802195
\(119\) 9.88729 18.6106i 0.906366 1.70603i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 1.07981 + 1.87029i 0.0977615 + 0.169328i
\(123\) 0 0
\(124\) 4.48261 7.76411i 0.402551 0.697238i
\(125\) −5.97199 −0.534151
\(126\) 0 0
\(127\) −9.28822 −0.824196 −0.412098 0.911140i \(-0.635204\pi\)
−0.412098 + 0.911140i \(0.635204\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.48261 11.2282i 0.566389 0.981014i −0.430530 0.902576i \(-0.641674\pi\)
0.996919 0.0784377i \(-0.0249932\pi\)
\(132\) 0 0
\(133\) −17.1407 + 0.604433i −1.48629 + 0.0524110i
\(134\) 7.09382 0.612813
\(135\) 0 0
\(136\) −3.98261 6.89809i −0.341506 0.591506i
\(137\) 2.80560 + 4.85945i 0.239699 + 0.415171i 0.960628 0.277838i \(-0.0896180\pi\)
−0.720929 + 0.693009i \(0.756285\pi\)
\(138\) 0 0
\(139\) 13.1286 1.11355 0.556776 0.830662i \(-0.312038\pi\)
0.556776 + 0.830662i \(0.312038\pi\)
\(140\) −3.93570 6.29365i −0.332628 0.531911i
\(141\) 0 0
\(142\) 3.72392 6.45002i 0.312504 0.541273i
\(143\) 0 0
\(144\) 0 0
\(145\) 7.19440 12.4611i 0.597462 1.03483i
\(146\) −12.5764 −1.04083
\(147\) 0 0
\(148\) 10.4826 0.861665
\(149\) 8.36990 14.4971i 0.685689 1.18765i −0.287531 0.957771i \(-0.592834\pi\)
0.973220 0.229877i \(-0.0738323\pi\)
\(150\) 0 0
\(151\) −5.44971 9.43918i −0.443491 0.768149i 0.554455 0.832214i \(-0.312927\pi\)
−0.997946 + 0.0640648i \(0.979594\pi\)
\(152\) −3.24131 + 5.61411i −0.262905 + 0.455364i
\(153\) 0 0
\(154\) 1.40280 + 2.24325i 0.113041 + 0.180766i
\(155\) −25.1529 −2.02033
\(156\) 0 0
\(157\) −0.887286 1.53682i −0.0708132 0.122652i 0.828445 0.560071i \(-0.189226\pi\)
−0.899258 + 0.437419i \(0.855893\pi\)
\(158\) 3.40280 + 5.89382i 0.270712 + 0.468888i
\(159\) 0 0
\(160\) −2.80560 −0.221802
\(161\) 13.9826 0.493069i 1.10198 0.0388593i
\(162\) 0 0
\(163\) 2.02952 3.51524i 0.158964 0.275335i −0.775531 0.631309i \(-0.782518\pi\)
0.934496 + 0.355975i \(0.115851\pi\)
\(164\) −2.54691 4.41138i −0.198880 0.344471i
\(165\) 0 0
\(166\) −7.54691 + 13.0716i −0.585754 + 1.01456i
\(167\) −13.8684 −1.07317 −0.536584 0.843847i \(-0.680286\pi\)
−0.536584 + 0.843847i \(0.680286\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −11.1736 + 19.3533i −0.856978 + 1.48433i
\(171\) 0 0
\(172\) −5.72392 9.91412i −0.436445 0.755945i
\(173\) 8.48261 14.6923i 0.644921 1.11704i −0.339399 0.940643i \(-0.610224\pi\)
0.984320 0.176394i \(-0.0564431\pi\)
\(174\) 0 0
\(175\) −3.56430 + 6.70900i −0.269435 + 0.507153i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −0.805603 1.39535i −0.0603825 0.104586i
\(179\) −6.33513 10.9728i −0.473509 0.820142i 0.526031 0.850466i \(-0.323680\pi\)
−0.999540 + 0.0303231i \(0.990346\pi\)
\(180\) 0 0
\(181\) −2.57643 −0.191505 −0.0957523 0.995405i \(-0.530526\pi\)
−0.0957523 + 0.995405i \(0.530526\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.64411 4.57973i 0.194926 0.337622i
\(185\) −14.7050 25.4698i −1.08113 1.87258i
\(186\) 0 0
\(187\) 3.98261 6.89809i 0.291238 0.504438i
\(188\) −0.322990 −0.0235565
\(189\) 0 0
\(190\) 18.1876 1.31947
\(191\) −1.19440 + 2.06876i −0.0864235 + 0.149690i −0.905997 0.423284i \(-0.860877\pi\)
0.819573 + 0.572974i \(0.194210\pi\)
\(192\) 0 0
\(193\) 7.28822 + 12.6236i 0.524617 + 0.908664i 0.999589 + 0.0286628i \(0.00912489\pi\)
−0.474972 + 0.880001i \(0.657542\pi\)
\(194\) 3.50000 6.06218i 0.251285 0.435239i
\(195\) 0 0
\(196\) 6.98261 0.493069i 0.498758 0.0352192i
\(197\) 12.4826 0.889349 0.444675 0.895692i \(-0.353319\pi\)
0.444675 + 0.895692i \(0.353319\pi\)
\(198\) 0 0
\(199\) 7.09382 + 12.2869i 0.502867 + 0.870992i 0.999995 + 0.00331424i \(0.00105496\pi\)
−0.497127 + 0.867678i \(0.665612\pi\)
\(200\) 1.43570 + 2.48671i 0.101520 + 0.175837i
\(201\) 0 0
\(202\) 10.7398 0.755650
\(203\) 7.19440 + 11.5047i 0.504948 + 0.807471i
\(204\) 0 0
\(205\) −7.14562 + 12.3766i −0.499071 + 0.864417i
\(206\) 1.48261 + 2.56796i 0.103299 + 0.178918i
\(207\) 0 0
\(208\) 0 0
\(209\) −6.48261 −0.448412
\(210\) 0 0
\(211\) −20.8336 −1.43425 −0.717123 0.696947i \(-0.754541\pi\)
−0.717123 + 0.696947i \(0.754541\pi\)
\(212\) 4.00000 6.92820i 0.274721 0.475831i
\(213\) 0 0
\(214\) −2.41832 4.18865i −0.165313 0.286330i
\(215\) −16.0590 + 27.8151i −1.09522 + 1.89697i
\(216\) 0 0
\(217\) 11.1286 20.9471i 0.755458 1.42198i
\(218\) 10.1596 0.688096
\(219\) 0 0
\(220\) −1.40280 2.42972i −0.0945769 0.163812i
\(221\) 0 0
\(222\) 0 0
\(223\) 12.5764 0.842180 0.421090 0.907019i \(-0.361648\pi\)
0.421090 + 0.907019i \(0.361648\pi\)
\(224\) 1.24131 2.33648i 0.0829383 0.156113i
\(225\) 0 0
\(226\) −5.48261 + 9.49616i −0.364698 + 0.631675i
\(227\) 10.0295 + 17.3716i 0.665683 + 1.15300i 0.979100 + 0.203381i \(0.0651929\pi\)
−0.313417 + 0.949616i \(0.601474\pi\)
\(228\) 0 0
\(229\) 11.2882 19.5518i 0.745946 1.29202i −0.203805 0.979011i \(-0.565331\pi\)
0.949751 0.313005i \(-0.101336\pi\)
\(230\) −14.8366 −0.978299
\(231\) 0 0
\(232\) 5.12859 0.336709
\(233\) −0.371407 + 0.643296i −0.0243317 + 0.0421437i −0.877935 0.478780i \(-0.841079\pi\)
0.853603 + 0.520924i \(0.174412\pi\)
\(234\) 0 0
\(235\) 0.453091 + 0.784776i 0.0295564 + 0.0511931i
\(236\) −0.435704 + 0.754661i −0.0283619 + 0.0491242i
\(237\) 0 0
\(238\) −11.1736 17.8680i −0.724279 1.15821i
\(239\) −4.31925 −0.279389 −0.139694 0.990195i \(-0.544612\pi\)
−0.139694 + 0.990195i \(0.544612\pi\)
\(240\) 0 0
\(241\) 9.09382 + 15.7510i 0.585784 + 1.01461i 0.994777 + 0.102071i \(0.0325468\pi\)
−0.408993 + 0.912538i \(0.634120\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 2.15962 0.138256
\(245\) −10.9932 16.2741i −0.702332 1.03972i
\(246\) 0 0
\(247\) 0 0
\(248\) −4.48261 7.76411i −0.284646 0.493022i
\(249\) 0 0
\(250\) −2.98599 + 5.17189i −0.188851 + 0.327099i
\(251\) −28.6703 −1.80965 −0.904825 0.425784i \(-0.859999\pi\)
−0.904825 + 0.425784i \(0.859999\pi\)
\(252\) 0 0
\(253\) 5.28822 0.332467
\(254\) −4.64411 + 8.04383i −0.291397 + 0.504715i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.80560 + 11.7876i −0.424522 + 0.735293i −0.996376 0.0850621i \(-0.972891\pi\)
0.571854 + 0.820356i \(0.306224\pi\)
\(258\) 0 0
\(259\) 27.7172 0.977390i 1.72226 0.0607321i
\(260\) 0 0
\(261\) 0 0
\(262\) −6.48261 11.2282i −0.400497 0.693681i
\(263\) −1.80560 3.12740i −0.111338 0.192843i 0.804972 0.593313i \(-0.202180\pi\)
−0.916310 + 0.400470i \(0.868847\pi\)
\(264\) 0 0
\(265\) −22.4448 −1.37877
\(266\) −8.04691 + 15.1465i −0.493388 + 0.928693i
\(267\) 0 0
\(268\) 3.54691 6.14343i 0.216662 0.375270i
\(269\) −4.69102 8.12508i −0.286016 0.495395i 0.686839 0.726810i \(-0.258998\pi\)
−0.972855 + 0.231415i \(0.925665\pi\)
\(270\) 0 0
\(271\) −2.80560 + 4.85945i −0.170428 + 0.295190i −0.938570 0.345090i \(-0.887848\pi\)
0.768141 + 0.640280i \(0.221182\pi\)
\(272\) −7.96523 −0.482963
\(273\) 0 0
\(274\) 5.61121 0.338985
\(275\) −1.43570 + 2.48671i −0.0865762 + 0.149954i
\(276\) 0 0
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) 6.56430 11.3697i 0.393700 0.681909i
\(279\) 0 0
\(280\) −7.41832 + 0.261592i −0.443329 + 0.0156331i
\(281\) −24.1529 −1.44084 −0.720420 0.693539i \(-0.756051\pi\)
−0.720420 + 0.693539i \(0.756051\pi\)
\(282\) 0 0
\(283\) −3.77083 6.53127i −0.224152 0.388244i 0.731912 0.681399i \(-0.238628\pi\)
−0.956065 + 0.293155i \(0.905295\pi\)
\(284\) −3.72392 6.45002i −0.220974 0.382738i
\(285\) 0 0
\(286\) 0 0
\(287\) −7.14562 11.4267i −0.421792 0.674496i
\(288\) 0 0
\(289\) −23.2224 + 40.2224i −1.36602 + 2.36602i
\(290\) −7.19440 12.4611i −0.422470 0.731739i
\(291\) 0 0
\(292\) −6.28822 + 10.8915i −0.367990 + 0.637377i
\(293\) −7.90618 −0.461884 −0.230942 0.972968i \(-0.574181\pi\)
−0.230942 + 0.972968i \(0.574181\pi\)
\(294\) 0 0
\(295\) 2.44482 0.142343
\(296\) 5.24131 9.07821i 0.304645 0.527660i
\(297\) 0 0
\(298\) −8.36990 14.4971i −0.484855 0.839794i
\(299\) 0 0
\(300\) 0 0
\(301\) −16.0590 25.6803i −0.925628 1.48019i
\(302\) −10.8994 −0.627191
\(303\) 0 0
\(304\) 3.24131 + 5.61411i 0.185902 + 0.321991i
\(305\) −3.02952 5.24729i −0.173470 0.300459i
\(306\) 0 0
\(307\) 12.8957 0.735995 0.367998 0.929827i \(-0.380043\pi\)
0.367998 + 0.929827i \(0.380043\pi\)
\(308\) 2.64411 0.0932392i 0.150662 0.00531279i
\(309\) 0 0
\(310\) −12.5764 + 21.7830i −0.714293 + 1.23719i
\(311\) 5.44971 + 9.43918i 0.309025 + 0.535247i 0.978149 0.207904i \(-0.0666641\pi\)
−0.669125 + 0.743150i \(0.733331\pi\)
\(312\) 0 0
\(313\) 4.56430 7.90559i 0.257989 0.446851i −0.707714 0.706499i \(-0.750273\pi\)
0.965703 + 0.259649i \(0.0836067\pi\)
\(314\) −1.77457 −0.100145
\(315\) 0 0
\(316\) 6.80560 0.382845
\(317\) −4.75682 + 8.23906i −0.267170 + 0.462752i −0.968130 0.250449i \(-0.919422\pi\)
0.700960 + 0.713201i \(0.252755\pi\)
\(318\) 0 0
\(319\) 2.56430 + 4.44149i 0.143573 + 0.248676i
\(320\) −1.40280 + 2.42972i −0.0784190 + 0.135826i
\(321\) 0 0
\(322\) 6.56430 12.3558i 0.365814 0.688564i
\(323\) 51.6355 2.87307
\(324\) 0 0
\(325\) 0 0
\(326\) −2.02952 3.51524i −0.112405 0.194691i
\(327\) 0 0
\(328\) −5.09382 −0.281259
\(329\) −0.854020 + 0.0301153i −0.0470837 + 0.00166031i
\(330\) 0 0
\(331\) −0.546909 + 0.947275i −0.0300609 + 0.0520669i −0.880664 0.473741i \(-0.842903\pi\)
0.850604 + 0.525807i \(0.176237\pi\)
\(332\) 7.54691 + 13.0716i 0.414190 + 0.717399i
\(333\) 0 0
\(334\) −6.93420 + 12.0104i −0.379422 + 0.657179i
\(335\) −19.9024 −1.08739
\(336\) 0 0
\(337\) −25.7988 −1.40535 −0.702676 0.711510i \(-0.748012\pi\)
−0.702676 + 0.711510i \(0.748012\pi\)
\(338\) −6.50000 + 11.2583i −0.353553 + 0.612372i
\(339\) 0 0
\(340\) 11.1736 + 19.3533i 0.605975 + 1.04958i
\(341\) 4.48261 7.76411i 0.242747 0.420450i
\(342\) 0 0
\(343\) 18.4168 1.95478i 0.994414 0.105548i
\(344\) −11.4478 −0.617226
\(345\) 0 0
\(346\) −8.48261 14.6923i −0.456028 0.789864i
\(347\) 10.3835 + 17.9848i 0.557418 + 0.965476i 0.997711 + 0.0676219i \(0.0215411\pi\)
−0.440293 + 0.897854i \(0.645126\pi\)
\(348\) 0 0
\(349\) −9.51364 −0.509254 −0.254627 0.967039i \(-0.581953\pi\)
−0.254627 + 0.967039i \(0.581953\pi\)
\(350\) 4.02801 + 6.44127i 0.215306 + 0.344300i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −6.28822 10.8915i −0.334688 0.579697i 0.648737 0.761013i \(-0.275298\pi\)
−0.983425 + 0.181316i \(0.941964\pi\)
\(354\) 0 0
\(355\) −10.4478 + 18.0962i −0.554514 + 0.960446i
\(356\) −1.61121 −0.0853937
\(357\) 0 0
\(358\) −12.6703 −0.669644
\(359\) −0.0347742 + 0.0602306i −0.00183531 + 0.00317885i −0.866942 0.498410i \(-0.833918\pi\)
0.865106 + 0.501589i \(0.167251\pi\)
\(360\) 0 0
\(361\) −11.5121 19.9396i −0.605902 1.04945i
\(362\) −1.28822 + 2.23126i −0.0677071 + 0.117272i
\(363\) 0 0
\(364\) 0 0
\(365\) 35.2845 1.84687
\(366\) 0 0
\(367\) 15.7708 + 27.3159i 0.823231 + 1.42588i 0.903264 + 0.429085i \(0.141164\pi\)
−0.0800336 + 0.996792i \(0.525503\pi\)
\(368\) −2.64411 4.57973i −0.137834 0.238735i
\(369\) 0 0
\(370\) −29.4100 −1.52896
\(371\) 9.93045 18.6919i 0.515563 0.970434i
\(372\) 0 0
\(373\) −7.65624 + 13.2610i −0.396425 + 0.686629i −0.993282 0.115719i \(-0.963083\pi\)
0.596857 + 0.802348i \(0.296416\pi\)
\(374\) −3.98261 6.89809i −0.205936 0.356692i
\(375\) 0 0
\(376\) −0.161495 + 0.279717i −0.00832847 + 0.0144253i
\(377\) 0 0
\(378\) 0 0
\(379\) 16.0590 0.824898 0.412449 0.910981i \(-0.364674\pi\)
0.412449 + 0.910981i \(0.364674\pi\)
\(380\) 9.09382 15.7510i 0.466503 0.808007i
\(381\) 0 0
\(382\) 1.19440 + 2.06876i 0.0611107 + 0.105847i
\(383\) −0.369899 + 0.640684i −0.0189010 + 0.0327374i −0.875321 0.483542i \(-0.839350\pi\)
0.856420 + 0.516279i \(0.172683\pi\)
\(384\) 0 0
\(385\) −3.93570 6.29365i −0.200582 0.320754i
\(386\) 14.5764 0.741921
\(387\) 0 0
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) 1.79160 + 3.10313i 0.0908375 + 0.157335i 0.907864 0.419265i \(-0.137712\pi\)
−0.817026 + 0.576600i \(0.804379\pi\)
\(390\) 0 0
\(391\) −42.1218 −2.13019
\(392\) 3.06430 6.29365i 0.154770 0.317878i
\(393\) 0 0
\(394\) 6.24131 10.8103i 0.314432 0.544613i
\(395\) −9.54691 16.5357i −0.480357 0.832003i
\(396\) 0 0
\(397\) 12.5643 21.7620i 0.630584 1.09220i −0.356849 0.934162i \(-0.616149\pi\)
0.987433 0.158041i \(-0.0505179\pi\)
\(398\) 14.1876 0.711162
\(399\) 0 0
\(400\) 2.87141 0.143570
\(401\) −1.93420 + 3.35013i −0.0965891 + 0.167297i −0.910271 0.414014i \(-0.864127\pi\)
0.813682 + 0.581311i \(0.197460\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 5.36990 9.30094i 0.267162 0.462739i
\(405\) 0 0
\(406\) 13.5606 0.478186i 0.672999 0.0237320i
\(407\) 10.4826 0.519604
\(408\) 0 0
\(409\) −2.32299 4.02354i −0.114864 0.198951i 0.802861 0.596166i \(-0.203310\pi\)
−0.917726 + 0.397215i \(0.869977\pi\)
\(410\) 7.14562 + 12.3766i 0.352897 + 0.611235i
\(411\) 0 0
\(412\) 2.96523 0.146086
\(413\) −1.08168 + 2.03603i −0.0532262 + 0.100186i
\(414\) 0 0
\(415\) 21.1736 36.6738i 1.03937 1.80025i
\(416\) 0 0
\(417\) 0 0
\(418\) −3.24131 + 5.61411i −0.158537 + 0.274595i
\(419\) 19.5174 0.953487 0.476743 0.879043i \(-0.341817\pi\)
0.476743 + 0.879043i \(0.341817\pi\)
\(420\) 0 0
\(421\) 15.5174 0.756271 0.378136 0.925750i \(-0.376565\pi\)
0.378136 + 0.925750i \(0.376565\pi\)
\(422\) −10.4168 + 18.0424i −0.507082 + 0.878292i
\(423\) 0 0
\(424\) −4.00000 6.92820i −0.194257 0.336463i
\(425\) 11.4357 19.8072i 0.554713 0.960791i
\(426\) 0 0
\(427\) 5.71028 0.201361i 0.276340 0.00974456i
\(428\) −4.83663 −0.233787
\(429\) 0 0
\(430\) 16.0590 + 27.8151i 0.774436 + 1.34136i
\(431\) −7.19440 12.4611i −0.346542 0.600228i 0.639091 0.769131i \(-0.279311\pi\)
−0.985633 + 0.168903i \(0.945977\pi\)
\(432\) 0 0
\(433\) 2.03477 0.0977850 0.0488925 0.998804i \(-0.484431\pi\)
0.0488925 + 0.998804i \(0.484431\pi\)
\(434\) −12.5764 20.1112i −0.603688 0.965368i
\(435\) 0 0
\(436\) 5.07981 8.79849i 0.243279 0.421371i
\(437\) 17.1407 + 29.6886i 0.819952 + 1.42020i
\(438\) 0 0
\(439\) −1.61308 + 2.79393i −0.0769880 + 0.133347i −0.901949 0.431842i \(-0.857864\pi\)
0.824961 + 0.565190i \(0.191197\pi\)
\(440\) −2.80560 −0.133752
\(441\) 0 0
\(442\) 0 0
\(443\) −11.0469 + 19.1338i −0.524854 + 0.909075i 0.474727 + 0.880133i \(0.342547\pi\)
−0.999581 + 0.0289413i \(0.990786\pi\)
\(444\) 0 0
\(445\) 2.26020 + 3.91478i 0.107144 + 0.185579i
\(446\) 6.28822 10.8915i 0.297756 0.515728i
\(447\) 0 0
\(448\) −1.40280 2.24325i −0.0662761 0.105983i
\(449\) −22.2497 −1.05003 −0.525014 0.851094i \(-0.675940\pi\)
−0.525014 + 0.851094i \(0.675940\pi\)
\(450\) 0 0
\(451\) −2.54691 4.41138i −0.119929 0.207724i
\(452\) 5.48261 + 9.49616i 0.257880 + 0.446662i
\(453\) 0 0
\(454\) 20.0590 0.941418
\(455\) 0 0
\(456\) 0 0
\(457\) 9.31925 16.1414i 0.435936 0.755063i −0.561436 0.827520i \(-0.689751\pi\)
0.997372 + 0.0724572i \(0.0230841\pi\)
\(458\) −11.2882 19.5518i −0.527464 0.913594i
\(459\) 0 0
\(460\) −7.41832 + 12.8489i −0.345881 + 0.599083i
\(461\) 20.9895 0.977578 0.488789 0.872402i \(-0.337439\pi\)
0.488789 + 0.872402i \(0.337439\pi\)
\(462\) 0 0
\(463\) −5.35402 −0.248822 −0.124411 0.992231i \(-0.539704\pi\)
−0.124411 + 0.992231i \(0.539704\pi\)
\(464\) 2.56430 4.44149i 0.119044 0.206191i
\(465\) 0 0
\(466\) 0.371407 + 0.643296i 0.0172051 + 0.0298001i
\(467\) 13.0121 22.5377i 0.602130 1.04292i −0.390368 0.920659i \(-0.627652\pi\)
0.992498 0.122261i \(-0.0390144\pi\)
\(468\) 0 0
\(469\) 8.80560 16.5746i 0.406605 0.765344i
\(470\) 0.906181 0.0417990
\(471\) 0 0
\(472\) 0.435704 + 0.754661i 0.0200549 + 0.0347361i
\(473\) −5.72392 9.91412i −0.263186 0.455852i
\(474\) 0 0
\(475\) −18.6142 −0.854079
\(476\) −21.0609 + 0.742671i −0.965326 + 0.0340403i
\(477\) 0 0
\(478\) −2.15962 + 3.74058i −0.0987789 + 0.171090i
\(479\) −1.80560 3.12740i −0.0825001 0.142894i 0.821823 0.569743i \(-0.192957\pi\)
−0.904323 + 0.426848i \(0.859624\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 18.1876 0.828424
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −9.81961 + 17.0081i −0.445886 + 0.772296i
\(486\) 0 0
\(487\) 4.03103 + 6.98195i 0.182663 + 0.316382i 0.942787 0.333397i \(-0.108195\pi\)
−0.760123 + 0.649779i \(0.774861\pi\)
\(488\) 1.07981 1.87029i 0.0488808 0.0846640i
\(489\) 0 0
\(490\) −19.5904 + 1.38336i −0.885006 + 0.0624936i
\(491\) −20.9062 −0.943483 −0.471741 0.881737i \(-0.656374\pi\)
−0.471741 + 0.881737i \(0.656374\pi\)
\(492\) 0 0
\(493\) −20.4252 35.3775i −0.919905 1.59332i
\(494\) 0 0
\(495\) 0 0
\(496\) −8.96523 −0.402551
\(497\) −10.4478 16.7073i −0.468650 0.749426i
\(498\) 0 0
\(499\) −2.48261 + 4.30001i −0.111137 + 0.192495i −0.916229 0.400655i \(-0.868783\pi\)
0.805092 + 0.593150i \(0.202116\pi\)
\(500\) 2.98599 + 5.17189i 0.133538 + 0.231294i
\(501\) 0 0
\(502\) −14.3351 + 24.8292i −0.639808 + 1.10818i
\(503\) 17.7988 0.793611 0.396806 0.917903i \(-0.370119\pi\)
0.396806 + 0.917903i \(0.370119\pi\)
\(504\) 0 0
\(505\) −30.1316 −1.34084
\(506\) 2.64411 4.57973i 0.117545 0.203594i
\(507\) 0 0
\(508\) 4.64411 + 8.04383i 0.206049 + 0.356887i
\(509\) 2.25719 3.90956i 0.100048 0.173288i −0.811656 0.584135i \(-0.801434\pi\)
0.911704 + 0.410847i \(0.134767\pi\)
\(510\) 0 0
\(511\) −15.6112 + 29.3846i −0.690599 + 1.29990i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.80560 + 11.7876i 0.300182 + 0.519931i
\(515\) −4.15962 7.20468i −0.183295 0.317476i
\(516\) 0 0
\(517\) −0.322990 −0.0142051
\(518\) 13.0121 24.4925i 0.571720 1.07614i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) 0 0
\(523\) −3.45158 + 5.97832i −0.150927 + 0.261414i −0.931569 0.363566i \(-0.881559\pi\)
0.780641 + 0.624979i \(0.214893\pi\)
\(524\) −12.9652 −0.566389
\(525\) 0 0
\(526\) −3.61121 −0.157456
\(527\) −35.7050 + 61.8429i −1.55534 + 2.69392i
\(528\) 0 0
\(529\) −2.48261 4.30001i −0.107940 0.186957i
\(530\) −11.2224 + 19.4378i −0.487470 + 0.844323i
\(531\) 0 0
\(532\) 9.09382 + 14.5421i 0.394267 + 0.630480i
\(533\) 0 0
\(534\) 0 0
\(535\) 6.78484 + 11.7517i 0.293334 + 0.508069i
\(536\) −3.54691 6.14343i −0.153203 0.265356i
\(537\) 0 0
\(538\) −9.38203 −0.404488
\(539\) 6.98261 0.493069i 0.300762 0.0212380i
\(540\) 0 0
\(541\) −1.40280 + 2.42972i −0.0603111 + 0.104462i −0.894604 0.446859i \(-0.852543\pi\)
0.834293 + 0.551321i \(0.185876\pi\)
\(542\) 2.80560 + 4.85945i 0.120511 + 0.208731i
\(543\) 0 0
\(544\) −3.98261 + 6.89809i −0.170753 + 0.295753i
\(545\) −28.5039 −1.22097
\(546\) 0 0
\(547\) 32.9274 1.40788 0.703938 0.710262i \(-0.251423\pi\)
0.703938 + 0.710262i \(0.251423\pi\)
\(548\) 2.80560 4.85945i 0.119849 0.207585i
\(549\) 0 0
\(550\) 1.43570 + 2.48671i 0.0612186 + 0.106034i
\(551\) −16.6233 + 28.7925i −0.708178 + 1.22660i
\(552\) 0 0
\(553\) 17.9947 0.634549i 0.765215 0.0269838i
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) −6.56430 11.3697i −0.278388 0.482182i
\(557\) 11.8525 + 20.5292i 0.502207 + 0.869848i 0.999997 + 0.00255037i \(0.000811808\pi\)
−0.497790 + 0.867298i \(0.665855\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −3.48261 + 6.55525i −0.147167 + 0.277010i
\(561\) 0 0
\(562\) −12.0764 + 20.9170i −0.509414 + 0.882330i
\(563\) 15.2224 + 26.3660i 0.641548 + 1.11119i 0.985087 + 0.172056i \(0.0550409\pi\)
−0.343539 + 0.939138i \(0.611626\pi\)
\(564\) 0 0
\(565\) 15.3820 26.6425i 0.647127 1.12086i
\(566\) −7.54166 −0.317000
\(567\) 0 0
\(568\) −7.44784 −0.312504
\(569\) 11.1407 19.2963i 0.467044 0.808943i −0.532248 0.846589i \(-0.678652\pi\)
0.999291 + 0.0376455i \(0.0119858\pi\)
\(570\) 0 0
\(571\) 1.43570 + 2.48671i 0.0600823 + 0.104066i 0.894502 0.447064i \(-0.147530\pi\)
−0.834420 + 0.551130i \(0.814197\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −13.4686 + 0.474943i −0.562169 + 0.0198238i
\(575\) 15.1846 0.633242
\(576\) 0 0
\(577\) 7.51214 + 13.0114i 0.312734 + 0.541672i 0.978953 0.204084i \(-0.0654217\pi\)
−0.666219 + 0.745756i \(0.732088\pi\)
\(578\) 23.2224 + 40.2224i 0.965925 + 1.67303i
\(579\) 0 0
\(580\) −14.3888 −0.597462
\(581\) 21.1736 + 33.8591i 0.878430 + 1.40471i
\(582\) 0 0
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) 6.28822 + 10.8915i 0.260208 + 0.450694i
\(585\) 0 0
\(586\) −3.95309 + 6.84695i −0.163301 + 0.282845i
\(587\) 42.5069 1.75445 0.877223 0.480082i \(-0.159393\pi\)
0.877223 + 0.480082i \(0.159393\pi\)
\(588\) 0 0
\(589\) 58.1181 2.39471
\(590\) 1.22241 2.11728i 0.0503259 0.0871670i
\(591\) 0 0
\(592\) −5.24131 9.07821i −0.215416 0.373112i
\(593\) 7.69289 13.3245i 0.315909 0.547171i −0.663721 0.747980i \(-0.731024\pi\)
0.979630 + 0.200809i \(0.0643572\pi\)
\(594\) 0 0
\(595\) 31.3488 + 50.1304i 1.28517 + 2.05515i
\(596\) −16.7398 −0.685689
\(597\) 0 0
\(598\) 0 0
\(599\) −19.8196 34.3286i −0.809807 1.40263i −0.912997 0.407966i \(-0.866238\pi\)
0.103190 0.994662i \(-0.467095\pi\)
\(600\) 0 0
\(601\) 33.3405 1.35999 0.679994 0.733218i \(-0.261983\pi\)
0.679994 + 0.733218i \(0.261983\pi\)
\(602\) −30.2693 + 1.06739i −1.23369 + 0.0435034i
\(603\) 0 0
\(604\) −5.44971 + 9.43918i −0.221746 + 0.384075i
\(605\) −1.40280 2.42972i −0.0570320 0.0987823i
\(606\) 0 0
\(607\) −7.97923 + 13.8204i −0.323867 + 0.560954i −0.981282 0.192574i \(-0.938316\pi\)
0.657415 + 0.753528i \(0.271650\pi\)
\(608\) 6.48261 0.262905
\(609\) 0 0
\(610\) −6.05904 −0.245324
\(611\) 0 0
\(612\) 0 0
\(613\) −23.3333 40.4144i −0.942421 1.63232i −0.760834 0.648947i \(-0.775210\pi\)
−0.181587 0.983375i \(-0.558123\pi\)
\(614\) 6.44784 11.1680i 0.260214 0.450703i
\(615\) 0 0
\(616\) 1.24131 2.33648i 0.0500137 0.0941396i
\(617\) 9.28447 0.373779 0.186889 0.982381i \(-0.440159\pi\)
0.186889 + 0.982381i \(0.440159\pi\)
\(618\) 0 0
\(619\) −16.9947 29.4358i −0.683077 1.18312i −0.974037 0.226388i \(-0.927308\pi\)
0.290961 0.956735i \(-0.406025\pi\)
\(620\) 12.5764 + 21.7830i 0.505082 + 0.874827i
\(621\) 0 0
\(622\) 10.8994 0.437027
\(623\) −4.26020 + 0.150227i −0.170681 + 0.00601874i
\(624\) 0 0
\(625\) 15.5560 26.9438i 0.622241 1.07775i
\(626\) −4.56430 7.90559i −0.182426 0.315971i
\(627\) 0 0
\(628\) −0.887286 + 1.53682i −0.0354066 + 0.0613260i
\(629\) −83.4964 −3.32922
\(630\) 0 0
\(631\) −14.6460 −0.583047 −0.291524 0.956564i \(-0.594162\pi\)
−0.291524 + 0.956564i \(0.594162\pi\)
\(632\) 3.40280 5.89382i 0.135356 0.234444i
\(633\) 0 0
\(634\) 4.75682 + 8.23906i 0.188918 + 0.327215i
\(635\) 13.0295 22.5678i 0.517061 0.895576i
\(636\) 0 0
\(637\) 0 0
\(638\) 5.12859 0.203043
\(639\) 0 0
\(640\) 1.40280 + 2.42972i 0.0554506 + 0.0960432i
\(641\) 10.4826 + 18.1564i 0.414038 + 0.717135i 0.995327 0.0965620i \(-0.0307846\pi\)
−0.581289 + 0.813697i \(0.697451\pi\)
\(642\) 0 0
\(643\) −23.6733 −0.933582 −0.466791 0.884368i \(-0.654590\pi\)
−0.466791 + 0.884368i \(0.654590\pi\)
\(644\) −7.41832 11.8628i −0.292323 0.467458i
\(645\) 0 0
\(646\) 25.8177 44.7176i 1.01579 1.75939i
\(647\) −6.20840 10.7533i −0.244078 0.422755i 0.717794 0.696255i \(-0.245152\pi\)
−0.961872 + 0.273500i \(0.911818\pi\)
\(648\) 0 0
\(649\) −0.435704 + 0.754661i −0.0171029 + 0.0296230i
\(650\) 0 0
\(651\) 0 0
\(652\) −4.05904 −0.158964
\(653\) −0.0487812 + 0.0844916i −0.00190896 + 0.00330641i −0.866978 0.498346i \(-0.833941\pi\)
0.865069 + 0.501652i \(0.167274\pi\)
\(654\) 0 0
\(655\) 18.1876 + 31.5019i 0.710650 + 1.23088i
\(656\) −2.54691 + 4.41138i −0.0994401 + 0.172235i
\(657\) 0 0
\(658\) −0.400929 + 0.754661i −0.0156299 + 0.0294197i
\(659\) 35.0243 1.36435 0.682176 0.731188i \(-0.261034\pi\)
0.682176 + 0.731188i \(0.261034\pi\)
\(660\) 0 0
\(661\) −14.8177 25.6651i −0.576343 0.998256i −0.995894 0.0905240i \(-0.971146\pi\)
0.419551 0.907732i \(-0.362188\pi\)
\(662\) 0.546909 + 0.947275i 0.0212562 + 0.0368169i
\(663\) 0 0
\(664\) 15.0938 0.585754
\(665\) 22.5764 42.4951i 0.875476 1.64789i
\(666\) 0 0
\(667\) 13.5606 23.4876i 0.525067 0.909442i
\(668\) 6.93420 + 12.0104i 0.268292 + 0.464696i
\(669\) 0 0
\(670\) −9.95122 + 17.2360i −0.384449 + 0.665885i
\(671\) 2.15962 0.0833713
\(672\) 0 0
\(673\) 16.8957 0.651281 0.325640 0.945494i \(-0.394420\pi\)
0.325640 + 0.945494i \(0.394420\pi\)
\(674\) −12.8994 + 22.3425i −0.496867 + 0.860599i
\(675\) 0 0
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) 6.59533 11.4234i 0.253479 0.439038i −0.711002 0.703190i \(-0.751758\pi\)
0.964481 + 0.264151i \(0.0850918\pi\)
\(678\) 0 0
\(679\) −9.81961 15.7027i −0.376842 0.602615i
\(680\) 22.3473 0.856978
\(681\) 0 0
\(682\) −4.48261 7.76411i −0.171648 0.297303i
\(683\) 4.91832 + 8.51877i 0.188194 + 0.325962i 0.944648 0.328085i \(-0.106403\pi\)
−0.756454 + 0.654047i \(0.773070\pi\)
\(684\) 0 0
\(685\) −15.7428 −0.601502
\(686\) 7.51552 16.9268i 0.286944 0.646269i
\(687\) 0 0
\(688\) −5.72392 + 9.91412i −0.218222 + 0.377972i
\(689\) 0 0
\(690\) 0 0
\(691\) 24.9947 43.2922i 0.950845 1.64691i 0.207243 0.978290i \(-0.433551\pi\)
0.743602 0.668622i \(-0.233116\pi\)
\(692\) −16.9652 −0.644921
\(693\) 0 0
\(694\) 20.7671 0.788308
\(695\) −18.4168 + 31.8988i −0.698589 + 1.20999i
\(696\) 0 0
\(697\) 20.2867 + 35.1376i 0.768414 + 1.33093i
\(698\) −4.75682 + 8.23906i −0.180048 + 0.311853i
\(699\) 0 0
\(700\) 7.59231 0.267728i 0.286962 0.0101192i
\(701\) 17.7050 0.668710 0.334355 0.942447i \(-0.391482\pi\)
0.334355 + 0.942447i \(0.391482\pi\)
\(702\) 0 0
\(703\) 33.9774 + 58.8505i 1.28148 + 2.21959i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −12.5764 −0.473320
\(707\) 13.3314 25.0934i 0.501378 0.943733i
\(708\) 0 0
\(709\) 15.9774 27.6736i 0.600042 1.03930i −0.392772 0.919636i \(-0.628484\pi\)
0.992814 0.119668i \(-0.0381830\pi\)
\(710\) 10.4478 + 18.0962i 0.392100 + 0.679138i
\(711\) 0 0
\(712\) −0.805603 + 1.39535i −0.0301912 + 0.0522928i
\(713\) −47.4100 −1.77552
\(714\) 0 0
\(715\) 0 0
\(716\) −6.33513 + 10.9728i −0.236755 + 0.410071i
\(717\) 0 0
\(718\) 0.0347742 + 0.0602306i 0.00129776 + 0.00224779i
\(719\) 10.8975 18.8751i 0.406410 0.703923i −0.588074 0.808807i \(-0.700114\pi\)
0.994484 + 0.104884i \(0.0334471\pi\)
\(720\) 0 0
\(721\) 7.84038 0.276475i 0.291991 0.0102965i
\(722\) −23.0243 −0.856875
\(723\) 0 0
\(724\) 1.28822 + 2.23126i 0.0478762 + 0.0829239i
\(725\) 7.36314 + 12.7533i 0.273460 + 0.473647i
\(726\) 0 0
\(727\) −4.84714 −0.179770 −0.0898852 0.995952i \(-0.528650\pi\)
−0.0898852 + 0.995952i \(0.528650\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 17.6422 30.5572i 0.652968 1.13097i
\(731\) 45.5923 + 78.9682i 1.68629 + 2.92074i
\(732\) 0 0
\(733\) −6.11459 + 10.5908i −0.225847 + 0.391179i −0.956573 0.291492i \(-0.905848\pi\)
0.730726 + 0.682671i \(0.239182\pi\)
\(734\) 31.5417 1.16422
\(735\) 0 0
\(736\) −5.28822 −0.194926
\(737\) 3.54691 6.14343i 0.130652 0.226296i
\(738\) 0 0
\(739\) 0.517387 + 0.896141i 0.0190324 + 0.0329651i 0.875385 0.483427i \(-0.160608\pi\)
−0.856352 + 0.516392i \(0.827275\pi\)
\(740\) −14.7050 + 25.4698i −0.540567 + 0.936290i
\(741\) 0 0
\(742\) −11.2224 17.9460i −0.411988 0.658817i
\(743\) 23.9925 0.880200 0.440100 0.897949i \(-0.354943\pi\)
0.440100 + 0.897949i \(0.354943\pi\)
\(744\) 0 0
\(745\) 23.4826 + 40.6731i 0.860336 + 1.49015i
\(746\) 7.65624 + 13.2610i 0.280315 + 0.485520i
\(747\) 0 0
\(748\) −7.96523 −0.291238
\(749\) −12.7886 + 0.450964i −0.467285 + 0.0164779i
\(750\) 0 0
\(751\) −10.2534 + 17.7595i −0.374153 + 0.648053i −0.990200 0.139657i \(-0.955400\pi\)
0.616047 + 0.787710i \(0.288733\pi\)
\(752\) 0.161495 + 0.279717i 0.00588912 + 0.0102002i
\(753\) 0 0
\(754\) 0 0
\(755\) 30.5794 1.11290
\(756\) 0 0
\(757\) −16.8019 −0.610674 −0.305337 0.952244i \(-0.598769\pi\)
−0.305337 + 0.952244i \(0.598769\pi\)
\(758\) 8.02952 13.9075i 0.291645 0.505145i
\(759\) 0 0
\(760\) −9.09382 15.7510i −0.329867 0.571347i
\(761\) −7.25495 + 12.5659i −0.262992 + 0.455515i −0.967036 0.254642i \(-0.918043\pi\)
0.704044 + 0.710157i \(0.251376\pi\)
\(762\) 0 0
\(763\) 12.6112 23.7378i 0.456556 0.859366i
\(764\) 2.38879 0.0864235
\(765\) 0 0
\(766\) 0.369899 + 0.640684i 0.0133650 + 0.0231489i
\(767\) 0 0
\(768\) 0 0
\(769\) 3.35402 0.120949 0.0604745 0.998170i \(-0.480739\pi\)
0.0604745 + 0.998170i \(0.480739\pi\)
\(770\) −7.41832 + 0.261592i −0.267338 + 0.00942712i
\(771\) 0 0
\(772\) 7.28822 12.6236i 0.262309 0.454332i
\(773\) 0.920188 + 1.59381i 0.0330969 + 0.0573255i 0.882099 0.471063i \(-0.156130\pi\)
−0.849003 + 0.528389i \(0.822796\pi\)
\(774\) 0 0
\(775\) 12.8714 22.2939i 0.462355 0.800822i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 3.58319 0.128464
\(779\) 16.5106 28.5972i 0.591555 1.02460i
\(780\) 0 0
\(781\) −3.72392 6.45002i −0.133252 0.230800i
\(782\) −21.0609 + 36.4786i −0.753137 + 1.30447i
\(783\) 0 0
\(784\) −3.91832 5.80059i −0.139940 0.207164i
\(785\) 4.97875 0.177699
\(786\) 0 0
\(787\) −5.79347 10.0346i −0.206515 0.357694i 0.744099 0.668069i \(-0.232879\pi\)
−0.950614 + 0.310375i \(0.899545\pi\)
\(788\) −6.24131 10.8103i −0.222337 0.385100i
\(789\) 0 0
\(790\) −19.0938 −0.679328
\(791\) 15.3820 + 24.5977i 0.546922 + 0.874593i
\(792\) 0 0