Properties

Label 1008.2.r.j.673.2
Level $1008$
Weight $2$
Character 1008.673
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.2
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.j.337.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.933463 + 1.45899i) q^{3} +(-1.23025 - 2.13086i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.25729 + 2.72382i) q^{9} +O(q^{10})\) \(q+(0.933463 + 1.45899i) q^{3} +(-1.23025 - 2.13086i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.25729 + 2.72382i) q^{9} +(2.32383 - 4.02499i) q^{11} +(-3.55408 - 6.15585i) q^{13} +(1.96050 - 3.78400i) q^{15} -4.51459 q^{17} -4.32743 q^{19} +(-1.73025 + 0.0789082i) q^{21} +(2.93346 + 5.08091i) q^{23} +(-0.527042 + 0.912864i) q^{25} +(-5.14766 + 0.708209i) q^{27} +(3.48755 - 6.04061i) q^{29} +(-3.69076 - 6.39258i) q^{31} +(8.04163 - 0.366739i) q^{33} +2.46050 q^{35} -0.726654 q^{37} +(5.66372 - 10.9316i) q^{39} +(-0.136673 - 0.236725i) q^{41} +(-2.41741 + 4.18708i) q^{43} +(7.35087 - 0.671871i) q^{45} +(1.83628 - 3.18054i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-4.21420 - 6.58673i) q^{51} +5.05408 q^{53} -11.4356 q^{55} +(-4.03950 - 6.31367i) q^{57} +(4.56654 + 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(-1.73025 - 2.45076i) q^{63} +(-8.74484 + 15.1465i) q^{65} +(-0.663715 - 1.14959i) q^{67} +(-4.67471 + 9.02273i) q^{69} -13.5218 q^{71} -4.32743 q^{73} +(-1.82383 + 0.0831759i) q^{75} +(2.32383 + 4.02499i) q^{77} +(3.21780 - 5.57339i) q^{79} +(-5.83842 - 6.84929i) q^{81} +(0.742705 - 1.28640i) q^{83} +(5.55408 + 9.61996i) q^{85} +(12.0687 - 0.550392i) q^{87} +9.83482 q^{89} +7.10817 q^{91} +(5.88151 - 11.3520i) q^{93} +(5.32383 + 9.22115i) q^{95} +(0.246304 - 0.426611i) q^{97} +(8.04163 + 11.3903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{3} - q^{5} - 3q^{7} + 8q^{9} + O(q^{10}) \) \( 6q + 2q^{3} - q^{5} - 3q^{7} + 8q^{9} + 2q^{11} - 3q^{13} - q^{15} + 4q^{17} - 6q^{19} - 4q^{21} + 14q^{23} + 6q^{25} - 7q^{27} - q^{29} - 3q^{31} + 8q^{33} + 2q^{35} - 6q^{37} + 24q^{39} + 3q^{43} + 23q^{45} + 21q^{47} - 3q^{49} - 5q^{51} + 12q^{53} - 12q^{55} - 37q^{57} + 31q^{59} - 6q^{61} - 4q^{63} - 15q^{65} + 6q^{67} + 5q^{69} - 34q^{71} - 6q^{73} + q^{75} + 2q^{77} - 9q^{79} + 8q^{81} + 20q^{83} + 15q^{85} + 23q^{87} + 24q^{89} + 6q^{91} - 3q^{93} + 20q^{95} + 9q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) 0.933463 + 1.45899i 0.538935 + 0.842347i
\(4\) 0 0
\(5\) −1.23025 2.13086i −0.550186 0.952949i −0.998261 0.0589535i \(-0.981224\pi\)
0.448075 0.893996i \(-0.352110\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) −1.25729 + 2.72382i −0.419098 + 0.907941i
\(10\) 0 0
\(11\) 2.32383 4.02499i 0.700662 1.21358i −0.267573 0.963538i \(-0.586222\pi\)
0.968234 0.250044i \(-0.0804451\pi\)
\(12\) 0 0
\(13\) −3.55408 6.15585i −0.985726 1.70733i −0.638667 0.769484i \(-0.720514\pi\)
−0.347059 0.937843i \(-0.612820\pi\)
\(14\) 0 0
\(15\) 1.96050 3.78400i 0.506200 0.977025i
\(16\) 0 0
\(17\) −4.51459 −1.09495 −0.547474 0.836822i \(-0.684411\pi\)
−0.547474 + 0.836822i \(0.684411\pi\)
\(18\) 0 0
\(19\) −4.32743 −0.992781 −0.496390 0.868099i \(-0.665342\pi\)
−0.496390 + 0.868099i \(0.665342\pi\)
\(20\) 0 0
\(21\) −1.73025 + 0.0789082i −0.377572 + 0.0172192i
\(22\) 0 0
\(23\) 2.93346 + 5.08091i 0.611669 + 1.05944i 0.990959 + 0.134164i \(0.0428350\pi\)
−0.379290 + 0.925278i \(0.623832\pi\)
\(24\) 0 0
\(25\) −0.527042 + 0.912864i −0.105408 + 0.182573i
\(26\) 0 0
\(27\) −5.14766 + 0.708209i −0.990668 + 0.136295i
\(28\) 0 0
\(29\) 3.48755 6.04061i 0.647621 1.12171i −0.336068 0.941838i \(-0.609097\pi\)
0.983689 0.179875i \(-0.0575694\pi\)
\(30\) 0 0
\(31\) −3.69076 6.39258i −0.662880 1.14814i −0.979856 0.199708i \(-0.936001\pi\)
0.316976 0.948434i \(-0.397333\pi\)
\(32\) 0 0
\(33\) 8.04163 0.366739i 1.39987 0.0638411i
\(34\) 0 0
\(35\) 2.46050 0.415901
\(36\) 0 0
\(37\) −0.726654 −0.119461 −0.0597306 0.998215i \(-0.519024\pi\)
−0.0597306 + 0.998215i \(0.519024\pi\)
\(38\) 0 0
\(39\) 5.66372 10.9316i 0.906920 1.75046i
\(40\) 0 0
\(41\) −0.136673 0.236725i −0.0213448 0.0369702i 0.855156 0.518371i \(-0.173461\pi\)
−0.876500 + 0.481401i \(0.840128\pi\)
\(42\) 0 0
\(43\) −2.41741 + 4.18708i −0.368652 + 0.638524i −0.989355 0.145522i \(-0.953514\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(44\) 0 0
\(45\) 7.35087 0.671871i 1.09580 0.100157i
\(46\) 0 0
\(47\) 1.83628 3.18054i 0.267850 0.463929i −0.700457 0.713695i \(-0.747020\pi\)
0.968306 + 0.249766i \(0.0803536\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −4.21420 6.58673i −0.590106 0.922327i
\(52\) 0 0
\(53\) 5.05408 0.694232 0.347116 0.937822i \(-0.387161\pi\)
0.347116 + 0.937822i \(0.387161\pi\)
\(54\) 0 0
\(55\) −11.4356 −1.54198
\(56\) 0 0
\(57\) −4.03950 6.31367i −0.535044 0.836266i
\(58\) 0 0
\(59\) 4.56654 + 7.90947i 0.594513 + 1.02973i 0.993615 + 0.112820i \(0.0359883\pi\)
−0.399103 + 0.916906i \(0.630678\pi\)
\(60\) 0 0
\(61\) 6.90856 11.9660i 0.884550 1.53209i 0.0383215 0.999265i \(-0.487799\pi\)
0.846228 0.532820i \(-0.178868\pi\)
\(62\) 0 0
\(63\) −1.73025 2.45076i −0.217991 0.308767i
\(64\) 0 0
\(65\) −8.74484 + 15.1465i −1.08466 + 1.87869i
\(66\) 0 0
\(67\) −0.663715 1.14959i −0.0810857 0.140445i 0.822631 0.568576i \(-0.192505\pi\)
−0.903717 + 0.428131i \(0.859172\pi\)
\(68\) 0 0
\(69\) −4.67471 + 9.02273i −0.562768 + 1.08621i
\(70\) 0 0
\(71\) −13.5218 −1.60474 −0.802370 0.596826i \(-0.796428\pi\)
−0.802370 + 0.596826i \(0.796428\pi\)
\(72\) 0 0
\(73\) −4.32743 −0.506487 −0.253244 0.967403i \(-0.581497\pi\)
−0.253244 + 0.967403i \(0.581497\pi\)
\(74\) 0 0
\(75\) −1.82383 + 0.0831759i −0.210598 + 0.00960433i
\(76\) 0 0
\(77\) 2.32383 + 4.02499i 0.264825 + 0.458691i
\(78\) 0 0
\(79\) 3.21780 5.57339i 0.362031 0.627056i −0.626264 0.779611i \(-0.715417\pi\)
0.988295 + 0.152555i \(0.0487502\pi\)
\(80\) 0 0
\(81\) −5.83842 6.84929i −0.648713 0.761033i
\(82\) 0 0
\(83\) 0.742705 1.28640i 0.0815225 0.141201i −0.822382 0.568936i \(-0.807355\pi\)
0.903904 + 0.427735i \(0.140688\pi\)
\(84\) 0 0
\(85\) 5.55408 + 9.61996i 0.602425 + 1.04343i
\(86\) 0 0
\(87\) 12.0687 0.550392i 1.29390 0.0590083i
\(88\) 0 0
\(89\) 9.83482 1.04249 0.521245 0.853407i \(-0.325468\pi\)
0.521245 + 0.853407i \(0.325468\pi\)
\(90\) 0 0
\(91\) 7.10817 0.745139
\(92\) 0 0
\(93\) 5.88151 11.3520i 0.609885 1.17715i
\(94\) 0 0
\(95\) 5.32383 + 9.22115i 0.546214 + 0.946070i
\(96\) 0 0
\(97\) 0.246304 0.426611i 0.0250084 0.0433158i −0.853250 0.521502i \(-0.825372\pi\)
0.878259 + 0.478186i \(0.158705\pi\)
\(98\) 0 0
\(99\) 8.04163 + 11.3903i 0.808214 + 1.14477i
\(100\) 0 0
\(101\) −1.70321 + 2.95005i −0.169476 + 0.293541i −0.938236 0.345997i \(-0.887541\pi\)
0.768760 + 0.639537i \(0.220874\pi\)
\(102\) 0 0
\(103\) 2.58113 + 4.47064i 0.254326 + 0.440505i 0.964712 0.263307i \(-0.0848131\pi\)
−0.710386 + 0.703812i \(0.751480\pi\)
\(104\) 0 0
\(105\) 2.29679 + 3.58985i 0.224144 + 0.350333i
\(106\) 0 0
\(107\) 5.76303 0.557133 0.278567 0.960417i \(-0.410141\pi\)
0.278567 + 0.960417i \(0.410141\pi\)
\(108\) 0 0
\(109\) −8.98229 −0.860347 −0.430174 0.902746i \(-0.641548\pi\)
−0.430174 + 0.902746i \(0.641548\pi\)
\(110\) 0 0
\(111\) −0.678304 1.06018i −0.0643818 0.100628i
\(112\) 0 0
\(113\) 0.679767 + 1.17739i 0.0639471 + 0.110760i 0.896226 0.443597i \(-0.146298\pi\)
−0.832279 + 0.554356i \(0.812964\pi\)
\(114\) 0 0
\(115\) 7.21780 12.5016i 0.673063 1.16578i
\(116\) 0 0
\(117\) 21.2360 1.94097i 1.96327 0.179443i
\(118\) 0 0
\(119\) 2.25729 3.90975i 0.206926 0.358406i
\(120\) 0 0
\(121\) −5.30039 9.18054i −0.481853 0.834595i
\(122\) 0 0
\(123\) 0.217799 0.420378i 0.0196383 0.0379042i
\(124\) 0 0
\(125\) −9.70895 −0.868394
\(126\) 0 0
\(127\) 0.820039 0.0727667 0.0363833 0.999338i \(-0.488416\pi\)
0.0363833 + 0.999338i \(0.488416\pi\)
\(128\) 0 0
\(129\) −8.36546 + 0.381507i −0.736538 + 0.0335898i
\(130\) 0 0
\(131\) 3.89397 + 6.74455i 0.340218 + 0.589274i 0.984473 0.175536i \(-0.0561660\pi\)
−0.644255 + 0.764810i \(0.722833\pi\)
\(132\) 0 0
\(133\) 2.16372 3.74766i 0.187618 0.324964i
\(134\) 0 0
\(135\) 7.84202 + 10.0977i 0.674934 + 0.869069i
\(136\) 0 0
\(137\) 1.49640 2.59184i 0.127846 0.221436i −0.794996 0.606615i \(-0.792527\pi\)
0.922842 + 0.385179i \(0.125860\pi\)
\(138\) 0 0
\(139\) 3.16372 + 5.47972i 0.268343 + 0.464783i 0.968434 0.249270i \(-0.0801907\pi\)
−0.700091 + 0.714053i \(0.746857\pi\)
\(140\) 0 0
\(141\) 6.35447 0.289796i 0.535143 0.0244052i
\(142\) 0 0
\(143\) −33.0364 −2.76264
\(144\) 0 0
\(145\) −17.1623 −1.42525
\(146\) 0 0
\(147\) 0.796790 1.53790i 0.0657181 0.126844i
\(148\) 0 0
\(149\) 2.19076 + 3.79450i 0.179474 + 0.310858i 0.941700 0.336452i \(-0.109227\pi\)
−0.762227 + 0.647310i \(0.775894\pi\)
\(150\) 0 0
\(151\) 3.30039 5.71644i 0.268582 0.465197i −0.699914 0.714227i \(-0.746778\pi\)
0.968496 + 0.249030i \(0.0801117\pi\)
\(152\) 0 0
\(153\) 5.67617 12.2969i 0.458891 0.994149i
\(154\) 0 0
\(155\) −9.08113 + 15.7290i −0.729414 + 1.26338i
\(156\) 0 0
\(157\) 2.89037 + 5.00627i 0.230677 + 0.399544i 0.958007 0.286743i \(-0.0925727\pi\)
−0.727331 + 0.686287i \(0.759239\pi\)
\(158\) 0 0
\(159\) 4.71780 + 7.37385i 0.374146 + 0.584784i
\(160\) 0 0
\(161\) −5.86693 −0.462379
\(162\) 0 0
\(163\) −7.32743 −0.573929 −0.286964 0.957941i \(-0.592646\pi\)
−0.286964 + 0.957941i \(0.592646\pi\)
\(164\) 0 0
\(165\) −10.6747 16.6844i −0.831025 1.29888i
\(166\) 0 0
\(167\) −6.01459 10.4176i −0.465423 0.806136i 0.533798 0.845612i \(-0.320764\pi\)
−0.999221 + 0.0394762i \(0.987431\pi\)
\(168\) 0 0
\(169\) −18.7630 + 32.4985i −1.44331 + 2.49989i
\(170\) 0 0
\(171\) 5.44085 11.7872i 0.416073 0.901386i
\(172\) 0 0
\(173\) −2.44951 + 4.24268i −0.186233 + 0.322565i −0.943991 0.329970i \(-0.892961\pi\)
0.757758 + 0.652535i \(0.226295\pi\)
\(174\) 0 0
\(175\) −0.527042 0.912864i −0.0398406 0.0690060i
\(176\) 0 0
\(177\) −7.27714 + 14.0457i −0.546983 + 1.05574i
\(178\) 0 0
\(179\) 1.78074 0.133099 0.0665493 0.997783i \(-0.478801\pi\)
0.0665493 + 0.997783i \(0.478801\pi\)
\(180\) 0 0
\(181\) −16.9430 −1.25936 −0.629681 0.776854i \(-0.716815\pi\)
−0.629681 + 0.776854i \(0.716815\pi\)
\(182\) 0 0
\(183\) 23.9071 1.09028i 1.76726 0.0805961i
\(184\) 0 0
\(185\) 0.893968 + 1.54840i 0.0657258 + 0.113840i
\(186\) 0 0
\(187\) −10.4911 + 18.1712i −0.767189 + 1.32881i
\(188\) 0 0
\(189\) 1.96050 4.81211i 0.142606 0.350030i
\(190\) 0 0
\(191\) −2.74484 + 4.75420i −0.198610 + 0.344002i −0.948078 0.318038i \(-0.896976\pi\)
0.749468 + 0.662040i \(0.230309\pi\)
\(192\) 0 0
\(193\) 2.75370 + 4.76954i 0.198215 + 0.343319i 0.947950 0.318420i \(-0.103152\pi\)
−0.749734 + 0.661739i \(0.769819\pi\)
\(194\) 0 0
\(195\) −30.2616 + 1.38008i −2.16708 + 0.0988296i
\(196\) 0 0
\(197\) 11.6300 0.828600 0.414300 0.910140i \(-0.364026\pi\)
0.414300 + 0.910140i \(0.364026\pi\)
\(198\) 0 0
\(199\) 4.14747 0.294006 0.147003 0.989136i \(-0.453037\pi\)
0.147003 + 0.989136i \(0.453037\pi\)
\(200\) 0 0
\(201\) 1.05768 2.04145i 0.0746032 0.143993i
\(202\) 0 0
\(203\) 3.48755 + 6.04061i 0.244778 + 0.423968i
\(204\) 0 0
\(205\) −0.336285 + 0.582462i −0.0234871 + 0.0406809i
\(206\) 0 0
\(207\) −17.5277 + 1.60204i −1.21826 + 0.111349i
\(208\) 0 0
\(209\) −10.0562 + 17.4179i −0.695603 + 1.20482i
\(210\) 0 0
\(211\) −13.6082 23.5700i −0.936825 1.62263i −0.771347 0.636415i \(-0.780417\pi\)
−0.165478 0.986213i \(-0.552917\pi\)
\(212\) 0 0
\(213\) −12.6221 19.7281i −0.864851 1.35175i
\(214\) 0 0
\(215\) 11.8961 0.811308
\(216\) 0 0
\(217\) 7.38151 0.501090
\(218\) 0 0
\(219\) −4.03950 6.31367i −0.272964 0.426638i
\(220\) 0 0
\(221\) 16.0452 + 27.7912i 1.07932 + 1.86944i
\(222\) 0 0
\(223\) −1.60817 + 2.78543i −0.107691 + 0.186526i −0.914834 0.403829i \(-0.867679\pi\)
0.807144 + 0.590355i \(0.201012\pi\)
\(224\) 0 0
\(225\) −1.82383 2.58331i −0.121589 0.172221i
\(226\) 0 0
\(227\) 7.97296 13.8096i 0.529184 0.916573i −0.470237 0.882540i \(-0.655832\pi\)
0.999421 0.0340330i \(-0.0108351\pi\)
\(228\) 0 0
\(229\) 0.608168 + 1.05338i 0.0401889 + 0.0696092i 0.885420 0.464791i \(-0.153871\pi\)
−0.845231 + 0.534401i \(0.820537\pi\)
\(230\) 0 0
\(231\) −3.70321 + 7.14763i −0.243653 + 0.470279i
\(232\) 0 0
\(233\) 19.9722 1.30842 0.654210 0.756313i \(-0.273001\pi\)
0.654210 + 0.756313i \(0.273001\pi\)
\(234\) 0 0
\(235\) −9.03638 −0.589468
\(236\) 0 0
\(237\) 11.1352 0.507822i 0.723310 0.0329866i
\(238\) 0 0
\(239\) 3.00739 + 5.20896i 0.194532 + 0.336939i 0.946747 0.321978i \(-0.104348\pi\)
−0.752215 + 0.658918i \(0.771015\pi\)
\(240\) 0 0
\(241\) 9.30778 16.1215i 0.599567 1.03848i −0.393318 0.919402i \(-0.628673\pi\)
0.992885 0.119078i \(-0.0379938\pi\)
\(242\) 0 0
\(243\) 4.54309 14.9118i 0.291440 0.956589i
\(244\) 0 0
\(245\) −1.23025 + 2.13086i −0.0785979 + 0.136136i
\(246\) 0 0
\(247\) 15.3801 + 26.6390i 0.978609 + 1.69500i
\(248\) 0 0
\(249\) 2.57014 0.117211i 0.162876 0.00742796i
\(250\) 0 0
\(251\) −6.99707 −0.441651 −0.220826 0.975313i \(-0.570875\pi\)
−0.220826 + 0.975313i \(0.570875\pi\)
\(252\) 0 0
\(253\) 27.2675 1.71429
\(254\) 0 0
\(255\) −8.85087 + 17.0832i −0.554263 + 1.06979i
\(256\) 0 0
\(257\) 8.88891 + 15.3960i 0.554475 + 0.960378i 0.997944 + 0.0640889i \(0.0204141\pi\)
−0.443469 + 0.896289i \(0.646253\pi\)
\(258\) 0 0
\(259\) 0.363327 0.629301i 0.0225760 0.0391028i
\(260\) 0 0
\(261\) 12.0687 + 17.0943i 0.747032 + 1.05811i
\(262\) 0 0
\(263\) −13.5993 + 23.5547i −0.838570 + 1.45245i 0.0525210 + 0.998620i \(0.483274\pi\)
−0.891091 + 0.453825i \(0.850059\pi\)
\(264\) 0 0
\(265\) −6.21780 10.7695i −0.381956 0.661568i
\(266\) 0 0
\(267\) 9.18044 + 14.3489i 0.561834 + 0.878138i
\(268\) 0 0
\(269\) 23.8961 1.45697 0.728486 0.685061i \(-0.240225\pi\)
0.728486 + 0.685061i \(0.240225\pi\)
\(270\) 0 0
\(271\) −12.2733 −0.745553 −0.372776 0.927921i \(-0.621594\pi\)
−0.372776 + 0.927921i \(0.621594\pi\)
\(272\) 0 0
\(273\) 6.63521 + 10.3707i 0.401581 + 0.627665i
\(274\) 0 0
\(275\) 2.44951 + 4.24268i 0.147711 + 0.255843i
\(276\) 0 0
\(277\) −6.39037 + 11.0684i −0.383960 + 0.665038i −0.991624 0.129156i \(-0.958773\pi\)
0.607664 + 0.794194i \(0.292107\pi\)
\(278\) 0 0
\(279\) 22.0526 2.01561i 1.32026 0.120672i
\(280\) 0 0
\(281\) 14.2573 24.6944i 0.850519 1.47314i −0.0302219 0.999543i \(-0.509621\pi\)
0.880741 0.473599i \(-0.157045\pi\)
\(282\) 0 0
\(283\) 0.363327 + 0.629301i 0.0215975 + 0.0374080i 0.876622 0.481179i \(-0.159791\pi\)
−0.855025 + 0.518587i \(0.826458\pi\)
\(284\) 0 0
\(285\) −8.48395 + 16.3750i −0.502546 + 0.969972i
\(286\) 0 0
\(287\) 0.273346 0.0161351
\(288\) 0 0
\(289\) 3.38151 0.198913
\(290\) 0 0
\(291\) 0.852336 0.0388708i 0.0499648 0.00227865i
\(292\) 0 0
\(293\) −12.7901 22.1531i −0.747204 1.29420i −0.949158 0.314800i \(-0.898062\pi\)
0.201954 0.979395i \(-0.435271\pi\)
\(294\) 0 0
\(295\) 11.2360 19.4613i 0.654184 1.13308i
\(296\) 0 0
\(297\) −9.11177 + 22.3651i −0.528718 + 1.29775i
\(298\) 0 0
\(299\) 20.8515 36.1159i 1.20588 2.08864i
\(300\) 0 0
\(301\) −2.41741 4.18708i −0.139337 0.241339i
\(302\) 0 0
\(303\) −5.89397 + 0.268795i −0.338600 + 0.0154419i
\(304\) 0 0
\(305\) −33.9971 −1.94667
\(306\) 0 0
\(307\) 6.23405 0.355796 0.177898 0.984049i \(-0.443070\pi\)
0.177898 + 0.984049i \(0.443070\pi\)
\(308\) 0 0
\(309\) −4.11323 + 7.93901i −0.233993 + 0.451635i
\(310\) 0 0
\(311\) 14.6192 + 25.3211i 0.828976 + 1.43583i 0.898842 + 0.438273i \(0.144410\pi\)
−0.0698655 + 0.997556i \(0.522257\pi\)
\(312\) 0 0
\(313\) −14.2434 + 24.6703i −0.805083 + 1.39445i 0.111151 + 0.993803i \(0.464546\pi\)
−0.916235 + 0.400642i \(0.868787\pi\)
\(314\) 0 0
\(315\) −3.09358 + 6.70198i −0.174303 + 0.377614i
\(316\) 0 0
\(317\) −0.809243 + 1.40165i −0.0454516 + 0.0787245i −0.887856 0.460121i \(-0.847806\pi\)
0.842405 + 0.538846i \(0.181139\pi\)
\(318\) 0 0
\(319\) −16.2089 28.0747i −0.907527 1.57188i
\(320\) 0 0
\(321\) 5.37957 + 8.40819i 0.300258 + 0.469300i
\(322\) 0 0
\(323\) 19.5366 1.08704
\(324\) 0 0
\(325\) 7.49261 0.415615
\(326\) 0 0
\(327\) −8.38463 13.1051i −0.463671 0.724711i
\(328\) 0 0
\(329\) 1.83628 + 3.18054i 0.101238 + 0.175349i
\(330\) 0 0
\(331\) −6.99115 + 12.1090i −0.384268 + 0.665572i −0.991667 0.128825i \(-0.958880\pi\)
0.607399 + 0.794397i \(0.292213\pi\)
\(332\) 0 0
\(333\) 0.913618 1.97928i 0.0500660 0.108464i
\(334\) 0 0
\(335\) −1.63307 + 2.82857i −0.0892244 + 0.154541i
\(336\) 0 0
\(337\) −13.8619 24.0095i −0.755104 1.30788i −0.945323 0.326137i \(-0.894253\pi\)
0.190219 0.981742i \(-0.439080\pi\)
\(338\) 0 0
\(339\) −1.08326 + 2.09082i −0.0588347 + 0.113558i
\(340\) 0 0
\(341\) −34.3068 −1.85782
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 24.9772 1.13909i 1.34473 0.0613264i
\(346\) 0 0
\(347\) 3.76449 + 6.52029i 0.202089 + 0.350028i 0.949201 0.314670i \(-0.101894\pi\)
−0.747113 + 0.664697i \(0.768560\pi\)
\(348\) 0 0
\(349\) 15.0541 26.0744i 0.805827 1.39573i −0.109905 0.993942i \(-0.535055\pi\)
0.915732 0.401791i \(-0.131612\pi\)
\(350\) 0 0
\(351\) 22.6549 + 29.1712i 1.20923 + 1.55705i
\(352\) 0 0
\(353\) 10.1819 17.6356i 0.541928 0.938647i −0.456865 0.889536i \(-0.651028\pi\)
0.998793 0.0491110i \(-0.0156388\pi\)
\(354\) 0 0
\(355\) 16.6352 + 28.8130i 0.882905 + 1.52924i
\(356\) 0 0
\(357\) 7.81138 0.356238i 0.413422 0.0188541i
\(358\) 0 0
\(359\) 16.0263 0.845833 0.422917 0.906169i \(-0.361006\pi\)
0.422917 + 0.906169i \(0.361006\pi\)
\(360\) 0 0
\(361\) −0.273346 −0.0143866
\(362\) 0 0
\(363\) 8.44659 16.3029i 0.443331 0.855680i
\(364\) 0 0
\(365\) 5.32383 + 9.22115i 0.278662 + 0.482657i
\(366\) 0 0
\(367\) −6.79893 + 11.7761i −0.354901 + 0.614707i −0.987101 0.160099i \(-0.948819\pi\)
0.632200 + 0.774805i \(0.282152\pi\)
\(368\) 0 0
\(369\) 0.816635 0.0746406i 0.0425123 0.00388563i
\(370\) 0 0
\(371\) −2.52704 + 4.37697i −0.131197 + 0.227241i
\(372\) 0 0
\(373\) 10.9641 + 18.9904i 0.567700 + 0.983285i 0.996793 + 0.0800246i \(0.0254999\pi\)
−0.429093 + 0.903260i \(0.641167\pi\)
\(374\) 0 0
\(375\) −9.06294 14.1652i −0.468008 0.731490i
\(376\) 0 0
\(377\) −49.5801 −2.55351
\(378\) 0 0
\(379\) 29.7965 1.53054 0.765271 0.643708i \(-0.222605\pi\)
0.765271 + 0.643708i \(0.222605\pi\)
\(380\) 0 0
\(381\) 0.765475 + 1.19643i 0.0392165 + 0.0612948i
\(382\) 0 0
\(383\) −0.0109905 0.0190361i −0.000561587 0.000972697i 0.865744 0.500486i \(-0.166845\pi\)
−0.866306 + 0.499514i \(0.833512\pi\)
\(384\) 0 0
\(385\) 5.71780 9.90352i 0.291406 0.504730i
\(386\) 0 0
\(387\) −8.36546 11.8490i −0.425240 0.602318i
\(388\) 0 0
\(389\) 17.6783 30.6197i 0.896326 1.55248i 0.0641702 0.997939i \(-0.479560\pi\)
0.832155 0.554543i \(-0.187107\pi\)
\(390\) 0 0
\(391\) −13.2434 22.9382i −0.669746 1.16003i
\(392\) 0 0
\(393\) −6.20535 + 11.9770i −0.313018 + 0.604162i
\(394\) 0 0
\(395\) −15.8348 −0.796736
\(396\) 0 0
\(397\) −16.9430 −0.850344 −0.425172 0.905112i \(-0.639786\pi\)
−0.425172 + 0.905112i \(0.639786\pi\)
\(398\) 0 0
\(399\) 7.48755 0.341470i 0.374846 0.0170949i
\(400\) 0 0
\(401\) 1.48181 + 2.56657i 0.0739982 + 0.128169i 0.900650 0.434545i \(-0.143091\pi\)
−0.826652 + 0.562713i \(0.809757\pi\)
\(402\) 0 0
\(403\) −26.2345 + 45.4395i −1.30683 + 2.26350i
\(404\) 0 0
\(405\) −7.41216 + 20.8672i −0.368313 + 1.03690i
\(406\) 0 0
\(407\) −1.68862 + 2.92478i −0.0837018 + 0.144976i
\(408\) 0 0
\(409\) 7.32743 + 12.6915i 0.362318 + 0.627553i 0.988342 0.152251i \(-0.0486521\pi\)
−0.626024 + 0.779804i \(0.715319\pi\)
\(410\) 0 0
\(411\) 5.17830 0.236157i 0.255427 0.0116488i
\(412\) 0 0
\(413\) −9.13307 −0.449409
\(414\) 0 0
\(415\) −3.65486 −0.179410
\(416\) 0 0
\(417\) −5.04163 + 9.73093i −0.246890 + 0.476526i
\(418\) 0 0
\(419\) −12.6352 21.8848i −0.617270 1.06914i −0.989982 0.141196i \(-0.954905\pi\)
0.372711 0.927947i \(-0.378428\pi\)
\(420\) 0 0
\(421\) 7.99854 13.8539i 0.389825 0.675196i −0.602601 0.798043i \(-0.705869\pi\)
0.992426 + 0.122846i \(0.0392022\pi\)
\(422\) 0 0
\(423\) 6.35447 + 9.00059i 0.308965 + 0.437624i
\(424\) 0 0
\(425\) 2.37938 4.12120i 0.115417 0.199908i
\(426\) 0 0
\(427\) 6.90856 + 11.9660i 0.334328 + 0.579074i
\(428\) 0 0
\(429\) −30.8382 48.1997i −1.48888 2.32710i
\(430\) 0 0
\(431\) −13.0335 −0.627799 −0.313900 0.949456i \(-0.601636\pi\)
−0.313900 + 0.949456i \(0.601636\pi\)
\(432\) 0 0
\(433\) 23.5467 1.13158 0.565791 0.824549i \(-0.308571\pi\)
0.565791 + 0.824549i \(0.308571\pi\)
\(434\) 0 0
\(435\) −16.0203 25.0395i −0.768116 1.20055i
\(436\) 0 0
\(437\) −12.6944 21.9873i −0.607253 1.05179i
\(438\) 0 0
\(439\) 3.35447 5.81012i 0.160100 0.277302i −0.774804 0.632201i \(-0.782152\pi\)
0.934904 + 0.354900i \(0.115485\pi\)
\(440\) 0 0
\(441\) 2.98755 0.273062i 0.142264 0.0130030i
\(442\) 0 0
\(443\) 17.6228 30.5235i 0.837282 1.45022i −0.0548760 0.998493i \(-0.517476\pi\)
0.892158 0.451723i \(-0.149190\pi\)
\(444\) 0 0
\(445\) −12.0993 20.9566i −0.573562 0.993439i
\(446\) 0 0
\(447\) −3.49115 + 6.73832i −0.165126 + 0.318711i
\(448\) 0 0
\(449\) −12.9387 −0.610616 −0.305308 0.952254i \(-0.598759\pi\)
−0.305308 + 0.952254i \(0.598759\pi\)
\(450\) 0 0
\(451\) −1.27042 −0.0598218
\(452\) 0 0
\(453\) 11.4210 0.520856i 0.536606 0.0244719i
\(454\) 0 0
\(455\) −8.74484 15.1465i −0.409964 0.710079i
\(456\) 0 0
\(457\) 14.5993 25.2868i 0.682927 1.18286i −0.291156 0.956675i \(-0.594040\pi\)
0.974083 0.226189i \(-0.0726267\pi\)
\(458\) 0 0
\(459\) 23.2396 3.19727i 1.08473 0.149236i
\(460\) 0 0
\(461\) 9.34348 16.1834i 0.435169 0.753735i −0.562140 0.827042i \(-0.690022\pi\)
0.997309 + 0.0733066i \(0.0233552\pi\)
\(462\) 0 0
\(463\) −19.1249 33.1253i −0.888809 1.53946i −0.841285 0.540593i \(-0.818200\pi\)
−0.0475247 0.998870i \(-0.515133\pi\)
\(464\) 0 0
\(465\) −31.4253 + 1.43315i −1.45731 + 0.0664608i
\(466\) 0 0
\(467\) 15.2877 0.707432 0.353716 0.935353i \(-0.384918\pi\)
0.353716 + 0.935353i \(0.384918\pi\)
\(468\) 0 0
\(469\) 1.32743 0.0612950
\(470\) 0 0
\(471\) −4.60603 + 8.89018i −0.212235 + 0.409638i
\(472\) 0 0
\(473\) 11.2353 + 19.4601i 0.516600 + 0.894778i
\(474\) 0 0
\(475\) 2.28074 3.95035i 0.104647 0.181255i
\(476\) 0 0
\(477\) −6.35447 + 13.7664i −0.290951 + 0.630322i
\(478\) 0 0
\(479\) 5.51605 9.55408i 0.252035 0.436537i −0.712051 0.702128i \(-0.752234\pi\)
0.964086 + 0.265591i \(0.0855669\pi\)
\(480\) 0 0
\(481\) 2.58259 + 4.47318i 0.117756 + 0.203959i
\(482\) 0 0
\(483\) −5.47656 8.55978i −0.249192 0.389483i
\(484\) 0 0
\(485\) −1.21206 −0.0550370
\(486\) 0 0
\(487\) −16.6008 −0.752253 −0.376126 0.926568i \(-0.622744\pi\)
−0.376126 + 0.926568i \(0.622744\pi\)
\(488\) 0 0
\(489\) −6.83988 10.6906i −0.309310 0.483447i
\(490\) 0 0
\(491\) −13.3633 23.1460i −0.603079 1.04456i −0.992352 0.123440i \(-0.960607\pi\)
0.389273 0.921122i \(-0.372726\pi\)
\(492\) 0 0
\(493\) −15.7448 + 27.2709i −0.709112 + 1.22822i
\(494\) 0 0
\(495\) 14.3779 31.1485i 0.646239 1.40002i
\(496\) 0 0
\(497\) 6.76089 11.7102i 0.303268 0.525275i
\(498\) 0 0
\(499\) 0.618485 + 1.07125i 0.0276872 + 0.0479557i 0.879537 0.475830i \(-0.157852\pi\)
−0.851850 + 0.523786i \(0.824519\pi\)
\(500\) 0 0
\(501\) 9.58472 18.4996i 0.428214 0.826503i
\(502\) 0 0
\(503\) 1.07179 0.0477889 0.0238944 0.999714i \(-0.492393\pi\)
0.0238944 + 0.999714i \(0.492393\pi\)
\(504\) 0 0
\(505\) 8.38151 0.372973
\(506\) 0 0
\(507\) −64.9296 + 2.96112i −2.88362 + 0.131508i
\(508\) 0 0
\(509\) −10.0344 17.3801i −0.444768 0.770362i 0.553268 0.833004i \(-0.313381\pi\)
−0.998036 + 0.0626420i \(0.980047\pi\)
\(510\) 0 0
\(511\) 2.16372 3.74766i 0.0957171 0.165787i
\(512\) 0 0
\(513\) 22.2762 3.06472i 0.983516 0.135311i
\(514\) 0 0
\(515\) 6.35087 11.0000i 0.279853 0.484720i
\(516\) 0 0
\(517\) −8.53443 14.7821i −0.375344 0.650115i
\(518\) 0 0
\(519\) −8.47656 + 0.386574i −0.372080 + 0.0169687i
\(520\) 0 0
\(521\) −30.8860 −1.35314 −0.676570 0.736379i \(-0.736534\pi\)
−0.676570 + 0.736379i \(0.736534\pi\)
\(522\) 0 0
\(523\) 7.39922 0.323545 0.161773 0.986828i \(-0.448279\pi\)
0.161773 + 0.986828i \(0.448279\pi\)
\(524\) 0 0
\(525\) 0.839883 1.62107i 0.0366555 0.0707494i
\(526\) 0 0
\(527\) 16.6623 + 28.8599i 0.725819 + 1.25716i
\(528\) 0 0
\(529\) −5.71041 + 9.89072i −0.248279 + 0.430031i
\(530\) 0 0
\(531\) −27.2855 + 2.49390i −1.18409 + 0.108226i
\(532\) 0 0
\(533\) −0.971495 + 1.68268i −0.0420801 + 0.0728849i
\(534\) 0 0
\(535\) −7.08998 12.2802i −0.306527 0.530920i
\(536\) 0 0
\(537\) 1.66225 + 2.59808i 0.0717315 + 0.112115i
\(538\) 0 0
\(539\) −4.64766 −0.200189
\(540\) 0 0
\(541\) 22.6696 0.974644 0.487322 0.873222i \(-0.337974\pi\)
0.487322 + 0.873222i \(0.337974\pi\)
\(542\) 0 0
\(543\) −15.8157 24.7196i −0.678715 1.06082i
\(544\) 0 0
\(545\) 11.0505 + 19.1400i 0.473351 + 0.819868i
\(546\) 0 0
\(547\) −3.07373 + 5.32386i −0.131423 + 0.227632i −0.924225 0.381847i \(-0.875288\pi\)
0.792802 + 0.609479i \(0.208621\pi\)
\(548\) 0 0
\(549\) 23.9071 + 33.8624i 1.02033 + 1.44521i
\(550\) 0 0
\(551\) −15.0921 + 26.1403i −0.642946 + 1.11361i
\(552\) 0 0
\(553\) 3.21780 + 5.57339i 0.136835 + 0.237005i
\(554\) 0 0
\(555\) −1.42461 + 2.74966i −0.0604713 + 0.116717i
\(556\) 0 0
\(557\) 29.6739 1.25732 0.628662 0.777679i \(-0.283603\pi\)
0.628662 + 0.777679i \(0.283603\pi\)
\(558\) 0 0
\(559\) 34.3667 1.45356
\(560\) 0 0
\(561\) −36.3047 + 1.65568i −1.53278 + 0.0699027i
\(562\) 0 0
\(563\) −14.6555 25.3841i −0.617657 1.06981i −0.989912 0.141683i \(-0.954749\pi\)
0.372255 0.928131i \(-0.378585\pi\)
\(564\) 0 0
\(565\) 1.67257 2.89698i 0.0703655 0.121877i
\(566\) 0 0
\(567\) 8.85087 1.63157i 0.371702 0.0685196i
\(568\) 0 0
\(569\) 18.4430 31.9442i 0.773170 1.33917i −0.162647 0.986684i \(-0.552003\pi\)
0.935817 0.352486i \(-0.114664\pi\)
\(570\) 0 0
\(571\) 16.1893 + 28.0407i 0.677501 + 1.17347i 0.975731 + 0.218972i \(0.0702703\pi\)
−0.298230 + 0.954494i \(0.596396\pi\)
\(572\) 0 0
\(573\) −9.49854 + 0.433181i −0.396807 + 0.0180964i
\(574\) 0 0
\(575\) −6.18423 −0.257900
\(576\) 0 0
\(577\) 23.0187 0.958280 0.479140 0.877739i \(-0.340949\pi\)
0.479140 + 0.877739i \(0.340949\pi\)
\(578\) 0 0
\(579\) −4.38823 + 8.46980i −0.182369 + 0.351993i
\(580\) 0 0
\(581\) 0.742705 + 1.28640i 0.0308126 + 0.0533690i
\(582\) 0 0
\(583\) 11.7448 20.3427i 0.486422 0.842507i
\(584\) 0 0
\(585\) −30.2616 42.8630i −1.25116 1.77217i
\(586\) 0 0
\(587\) 2.87052 4.97189i 0.118479 0.205212i −0.800686 0.599084i \(-0.795531\pi\)
0.919165 + 0.393872i \(0.128865\pi\)
\(588\) 0 0
\(589\) 15.9715 + 27.6634i 0.658094 + 1.13985i
\(590\) 0 0
\(591\) 10.8561 + 16.9680i 0.446562 + 0.697969i
\(592\) 0 0
\(593\) 27.7453 1.13936 0.569682 0.821865i \(-0.307066\pi\)
0.569682 + 0.821865i \(0.307066\pi\)
\(594\) 0 0
\(595\) −11.1082 −0.455391
\(596\) 0 0
\(597\) 3.87151 + 6.05111i 0.158450 + 0.247655i
\(598\) 0 0
\(599\) 2.05408 + 3.55778i 0.0839276 + 0.145367i 0.904934 0.425552i \(-0.139920\pi\)
−0.821006 + 0.570919i \(0.806587\pi\)
\(600\) 0 0
\(601\) −7.80924 + 13.5260i −0.318546 + 0.551737i −0.980185 0.198085i \(-0.936528\pi\)
0.661639 + 0.749822i \(0.269861\pi\)
\(602\) 0 0
\(603\) 3.96576 0.362471i 0.161498 0.0147610i
\(604\) 0 0
\(605\) −13.0416 + 22.5888i −0.530218 + 0.918364i
\(606\) 0 0
\(607\) −0.280738 0.486253i −0.0113948 0.0197364i 0.860272 0.509836i \(-0.170294\pi\)
−0.871667 + 0.490099i \(0.836960\pi\)
\(608\) 0 0
\(609\) −5.55768 + 10.7270i −0.225209 + 0.434679i
\(610\) 0 0
\(611\) −26.1052 −1.05611
\(612\) 0 0
\(613\) −20.2016 −0.815933 −0.407967 0.912997i \(-0.633762\pi\)
−0.407967 + 0.912997i \(0.633762\pi\)
\(614\) 0 0
\(615\) −1.16372 + 0.0530713i −0.0469255 + 0.00214004i
\(616\) 0 0
\(617\) 11.4569 + 19.8439i 0.461238 + 0.798887i 0.999023 0.0441948i \(-0.0140722\pi\)
−0.537785 + 0.843082i \(0.680739\pi\)
\(618\) 0 0
\(619\) 19.8515 34.3839i 0.797901 1.38201i −0.123080 0.992397i \(-0.539277\pi\)
0.920981 0.389608i \(-0.127390\pi\)
\(620\) 0 0
\(621\) −18.6988 24.0773i −0.750358 0.966188i
\(622\) 0 0
\(623\) −4.91741 + 8.51721i −0.197012 + 0.341235i
\(624\) 0 0
\(625\) 14.5797 + 25.2527i 0.583187 + 1.01011i
\(626\) 0 0
\(627\) −34.7996 + 1.58704i −1.38976 + 0.0633802i
\(628\) 0 0
\(629\) 3.28054 0.130804
\(630\) 0 0
\(631\) 31.0364 1.23554 0.617769 0.786359i \(-0.288037\pi\)
0.617769 + 0.786359i \(0.288037\pi\)
\(632\) 0 0
\(633\) 21.6857 41.8559i 0.861929 1.66362i
\(634\) 0 0
\(635\) −1.00885 1.74739i −0.0400352 0.0693429i
\(636\) 0 0
\(637\) −3.55408 + 6.15585i −0.140818 + 0.243904i
\(638\) 0 0
\(639\) 17.0009 36.8309i 0.672544 1.45701i
\(640\) 0 0
\(641\) 14.7932 25.6226i 0.584296 1.01203i −0.410667 0.911785i \(-0.634704\pi\)
0.994963 0.100245i \(-0.0319626\pi\)
\(642\) 0 0
\(643\) 12.8442 + 22.2467i 0.506524 + 0.877325i 0.999972 + 0.00754978i \(0.00240319\pi\)
−0.493447 + 0.869776i \(0.664263\pi\)
\(644\) 0 0
\(645\) 11.1046 + 17.3563i 0.437242 + 0.683403i
\(646\) 0 0
\(647\) −17.0177 −0.669035 −0.334518 0.942390i \(-0.608573\pi\)
−0.334518 + 0.942390i \(0.608573\pi\)
\(648\) 0 0
\(649\) 42.4475 1.66621
\(650\) 0 0
\(651\) 6.89037 + 10.7695i 0.270055 + 0.422092i
\(652\) 0 0
\(653\) −0.735508 1.27394i −0.0287827 0.0498530i 0.851275 0.524719i \(-0.175830\pi\)
−0.880058 + 0.474866i \(0.842496\pi\)
\(654\) 0 0
\(655\) 9.58113 16.5950i 0.374366 0.648420i
\(656\) 0 0
\(657\) 5.44085 11.7872i 0.212268 0.459861i
\(658\) 0 0
\(659\) −20.7003 + 35.8539i −0.806369 + 1.39667i 0.108995 + 0.994042i \(0.465237\pi\)
−0.915363 + 0.402629i \(0.868096\pi\)
\(660\) 0 0
\(661\) −19.1352 33.1432i −0.744273 1.28912i −0.950533 0.310622i \(-0.899463\pi\)
0.206260 0.978497i \(-0.433871\pi\)
\(662\) 0 0
\(663\) −25.5693 + 49.3518i −0.993031 + 1.91667i
\(664\) 0 0
\(665\) −10.6477 −0.412899
\(666\) 0 0
\(667\) 40.9224 1.58452
\(668\) 0 0
\(669\) −5.56507 + 0.253795i −0.215158 + 0.00981230i
\(670\) 0 0
\(671\) −32.1086 55.6138i −1.23954 2.14695i
\(672\) 0 0
\(673\) 15.2448 26.4048i 0.587645 1.01783i −0.406894 0.913475i \(-0.633388\pi\)
0.994540 0.104357i \(-0.0332783\pi\)
\(674\) 0 0
\(675\) 2.06654 5.07237i 0.0795411 0.195236i
\(676\) 0 0
\(677\) −22.4626 + 38.9064i −0.863309 + 1.49530i 0.00540665 + 0.999985i \(0.498279\pi\)
−0.868716 + 0.495310i \(0.835054\pi\)
\(678\) 0 0
\(679\) 0.246304 + 0.426611i 0.00945228 + 0.0163718i
\(680\) 0 0
\(681\) 27.5905 1.25826i 1.05727 0.0482168i
\(682\) 0 0
\(683\) 48.3973 1.85187 0.925935 0.377683i \(-0.123279\pi\)
0.925935 + 0.377683i \(0.123279\pi\)
\(684\) 0 0
\(685\) −7.36381 −0.281357
\(686\) 0 0
\(687\) −0.969165 + 1.87060i −0.0369759 + 0.0713679i
\(688\) 0 0
\(689\) −17.9626 31.1122i −0.684322 1.18528i
\(690\) 0 0
\(691\) 9.19076 15.9189i 0.349633 0.605582i −0.636551 0.771234i \(-0.719640\pi\)
0.986184 + 0.165652i \(0.0529730\pi\)
\(692\) 0 0
\(693\) −13.8851 + 1.26910i −0.527452 + 0.0482092i
\(694\) 0 0
\(695\) 7.78434 13.4829i 0.295277 0.511434i
\(696\) 0 0
\(697\) 0.617023 + 1.06871i 0.0233714 + 0.0404805i
\(698\) 0 0
\(699\) 18.6433 + 29.1392i 0.705153 + 1.10214i
\(700\) 0 0
\(701\) −27.0292 −1.02088 −0.510439 0.859914i \(-0.670517\pi\)
−0.510439 + 0.859914i \(0.670517\pi\)
\(702\) 0 0
\(703\) 3.14454 0.118599
\(704\) 0 0
\(705\) −8.43512 13.1840i −0.317685 0.496537i
\(706\) 0 0
\(707\) −1.70321 2.95005i −0.0640558 0.110948i
\(708\) 0 0
\(709\) −2.49261 + 4.31732i −0.0936119 + 0.162141i −0.909028 0.416734i \(-0.863175\pi\)
0.815417 + 0.578875i \(0.196508\pi\)
\(710\) 0 0
\(711\) 11.1352 + 15.7721i 0.417603 + 0.591500i
\(712\) 0 0
\(713\) 21.6534 37.5048i 0.810926 1.40457i
\(714\) 0 0
\(715\) 40.6431 + 70.3959i 1.51997 + 2.63266i
\(716\) 0 0
\(717\) −4.79252 + 9.25012i −0.178980 + 0.345452i
\(718\) 0 0
\(719\) −15.6942 −0.585293 −0.292647 0.956221i \(-0.594536\pi\)
−0.292647 + 0.956221i \(0.594536\pi\)
\(720\) 0 0
\(721\) −5.16225 −0.192252
\(722\) 0 0
\(723\) 32.2096 1.46892i 1.19789 0.0546298i
\(724\) 0 0
\(725\) 3.67617 + 6.36731i 0.136529 + 0.236476i
\(726\) 0 0
\(727\) 10.9071 18.8916i 0.404522 0.700652i −0.589744 0.807590i \(-0.700771\pi\)
0.994266 + 0.106938i \(0.0341047\pi\)
\(728\) 0 0
\(729\) 25.9969 7.29124i 0.962847 0.270046i
\(730\) 0 0
\(731\) 10.9136 18.9029i 0.403655 0.699151i
\(732\) 0 0
\(733\) 12.0074 + 20.7974i 0.443503 + 0.768170i 0.997947 0.0640514i \(-0.0204022\pi\)
−0.554443 + 0.832221i \(0.687069\pi\)
\(734\) 0 0
\(735\) −4.25729 + 0.194154i −0.157033 + 0.00716148i
\(736\) 0 0
\(737\) −6.16945 −0.227255
\(738\) 0 0
\(739\) −18.7089 −0.688220 −0.344110 0.938929i \(-0.611819\pi\)
−0.344110 + 0.938929i \(0.611819\pi\)
\(740\) 0 0
\(741\) −24.5093 + 47.3059i −0.900373 + 1.73782i
\(742\) 0 0
\(743\) −20.1534 34.9067i −0.739356 1.28060i −0.952785 0.303644i \(-0.901797\pi\)
0.213429 0.976959i \(-0.431537\pi\)
\(744\) 0 0
\(745\) 5.39037 9.33639i 0.197488 0.342059i
\(746\) 0 0
\(747\) 2.57014 + 3.64039i 0.0940364 + 0.133195i
\(748\) 0 0
\(749\) −2.88151 + 4.99093i −0.105288 + 0.182365i
\(750\) 0 0
\(751\) −10.5629 18.2955i −0.385447 0.667614i 0.606384 0.795172i \(-0.292619\pi\)
−0.991831 + 0.127558i \(0.959286\pi\)
\(752\) 0 0
\(753\) −6.53151 10.2087i −0.238021 0.372024i
\(754\) 0 0
\(755\) −16.2412 −0.591079
\(756\) 0 0
\(757\) 8.85934 0.321998 0.160999 0.986955i \(-0.448528\pi\)
0.160999 + 0.986955i \(0.448528\pi\)
\(758\) 0 0
\(759\) 25.4532 + 39.7830i 0.923892 + 1.44403i
\(760\) 0 0
\(761\) −0.694551 1.20300i −0.0251774 0.0436086i 0.853162 0.521646i \(-0.174682\pi\)
−0.878340 + 0.478037i \(0.841348\pi\)
\(762\) 0 0
\(763\) 4.49115 7.77889i 0.162590 0.281615i
\(764\) 0 0
\(765\) −33.1862 + 3.03322i −1.19985 + 0.109666i
\(766\) 0 0
\(767\) 32.4597 56.2219i 1.17205 2.03005i
\(768\) 0 0
\(769\) 18.9626 + 32.8443i 0.683810 + 1.18439i 0.973809 + 0.227367i \(0.0730118\pi\)
−0.289999 + 0.957027i \(0.593655\pi\)
\(770\) 0 0
\(771\) −14.1652 + 27.3404i −0.510146 + 0.984642i
\(772\) 0 0
\(773\) 1.31596 0.0473318 0.0236659 0.999720i \(-0.492466\pi\)
0.0236659 + 0.999720i \(0.492466\pi\)
\(774\) 0 0
\(775\) 7.78074 0.279492
\(776\) 0 0
\(777\) 1.25729 0.0573390i 0.0451052 0.00205702i
\(778\) 0 0
\(779\) 0.591443 + 1.02441i 0.0211907 + 0.0367033i
\(780\) 0 0
\(781\) −31.4224 + 54.4251i −1.12438 + 1.94748i
\(782\) 0 0
\(783\) −13.6747 + 33.5649i −0.488694 + 1.19951i
\(784\) 0 0
\(785\) 7.11177 12.3179i 0.253830 0.439646i
\(786\) 0 0
\(787\) 6.12928 + 10.6162i 0.218485 + 0.378428i 0.954345 0.298706i \(-0.0965551\pi\)
−0.735860 + 0.677134i \(0.763222\pi\)
\(788\) 0 0
\(789\) −47.0605 + 2.14620i −1.67540 + 0.0764066i
\(790\) 0 0
\(791\) −1.35953 −0.0483395
\(792\) 0 0
\(793\) −98.2144 −3.48769
\(794\) 0 0
\(795\) 9.90856 19.1247i 0.351420 0.678282i
\(796\) 0 0
\(797\) −10.7178 18.5638i −0.379644 0.657563i 0.611366 0.791348i \(-0.290620\pi\)
−0.991010 + 0.133785i \(0.957287\pi\)
\(798\) 0 0
\(799\) −8.29007 + 14.3588i −0.293282 + 0.507979i
\(800\) 0 0