Properties

Label 1344.2.q.y.961.2
Level $1344$
Weight $2$
Character 1344.961
Analytic conductor $10.732$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 672)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.2
Root \(0.500000 + 1.51496i\) of defining polynomial
Character \(\chi\) \(=\) 1344.961
Dual form 1344.2.q.y.193.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.227452 - 0.393958i) q^{5} +(-2.16908 - 1.51496i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.227452 - 0.393958i) q^{5} +(-2.16908 - 1.51496i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.89653 + 5.01694i) q^{11} +5.88325 q^{13} -0.454904 q^{15} +(-1.45490 - 2.51997i) q^{17} +(-2.94163 + 5.09505i) q^{19} +(-0.227452 + 2.63596i) q^{21} +(-1.45490 + 2.51997i) q^{23} +(2.39653 + 4.15091i) q^{25} +1.00000 q^{27} -3.54510 q^{29} +(-2.16908 - 3.75696i) q^{31} +(2.89653 - 5.01694i) q^{33} +(-1.09019 + 0.509947i) q^{35} +(3.85144 - 6.67088i) q^{37} +(-2.94163 - 5.09505i) q^{39} +9.58612 q^{41} +10.7931 q^{43} +(0.227452 + 0.393958i) q^{45} +(2.45490 - 4.25202i) q^{47} +(2.40981 + 6.57212i) q^{49} +(-1.45490 + 2.51997i) q^{51} +(6.56561 + 11.3720i) q^{53} +2.63529 q^{55} +5.88325 q^{57} +(0.896531 + 1.55284i) q^{59} +(2.33816 - 4.04981i) q^{61} +(2.39653 - 1.12100i) q^{63} +(1.33816 - 2.31776i) q^{65} +(-3.94163 - 6.82710i) q^{67} +2.90981 q^{69} +0.909808 q^{71} +(-2.60347 - 4.50934i) q^{73} +(2.39653 - 4.15091i) q^{75} +(1.31764 - 15.2703i) q^{77} +(-1.37602 + 2.38333i) q^{79} +(-0.500000 - 0.866025i) q^{81} +9.97345 q^{83} -1.32368 q^{85} +(1.77255 + 3.07014i) q^{87} +(2.45490 - 4.25202i) q^{89} +(-12.7612 - 8.91288i) q^{91} +(-2.16908 + 3.75696i) q^{93} +(1.33816 + 2.31776i) q^{95} -5.79306 q^{97} -5.79306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{3} + 3q^{7} - 3q^{9} + 6q^{13} - 6q^{17} - 3q^{19} - 6q^{23} - 3q^{25} + 6q^{27} - 24q^{29} + 3q^{31} - 12q^{35} + 3q^{37} - 3q^{39} - 12q^{41} + 30q^{43} + 12q^{47} + 9q^{49} - 6q^{51} + 6q^{53} + 24q^{55} + 6q^{57} - 12q^{59} - 18q^{61} - 3q^{63} - 24q^{65} - 9q^{67} + 12q^{69} - 33q^{73} - 3q^{75} + 12q^{77} - 27q^{79} - 3q^{81} + 36q^{83} - 72q^{85} + 12q^{87} + 12q^{89} - 51q^{91} + 3q^{93} - 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) 0.227452 0.393958i 0.101720 0.176184i −0.810674 0.585498i \(-0.800899\pi\)
0.912393 + 0.409315i \(0.134232\pi\)
\(6\) 0 0
\(7\) −2.16908 1.51496i −0.819835 0.572600i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.89653 + 5.01694i 0.873337 + 1.51266i 0.858524 + 0.512774i \(0.171382\pi\)
0.0148132 + 0.999890i \(0.495285\pi\)
\(12\) 0 0
\(13\) 5.88325 1.63172 0.815861 0.578249i \(-0.196264\pi\)
0.815861 + 0.578249i \(0.196264\pi\)
\(14\) 0 0
\(15\) −0.454904 −0.117456
\(16\) 0 0
\(17\) −1.45490 2.51997i −0.352866 0.611182i 0.633884 0.773428i \(-0.281460\pi\)
−0.986750 + 0.162246i \(0.948126\pi\)
\(18\) 0 0
\(19\) −2.94163 + 5.09505i −0.674856 + 1.16888i 0.301656 + 0.953417i \(0.402461\pi\)
−0.976511 + 0.215467i \(0.930873\pi\)
\(20\) 0 0
\(21\) −0.227452 + 2.63596i −0.0496341 + 0.575213i
\(22\) 0 0
\(23\) −1.45490 + 2.51997i −0.303368 + 0.525450i −0.976897 0.213712i \(-0.931445\pi\)
0.673528 + 0.739161i \(0.264778\pi\)
\(24\) 0 0
\(25\) 2.39653 + 4.15091i 0.479306 + 0.830183i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −3.54510 −0.658308 −0.329154 0.944276i \(-0.606763\pi\)
−0.329154 + 0.944276i \(0.606763\pi\)
\(30\) 0 0
\(31\) −2.16908 3.75696i −0.389578 0.674769i 0.602815 0.797881i \(-0.294046\pi\)
−0.992393 + 0.123112i \(0.960713\pi\)
\(32\) 0 0
\(33\) 2.89653 5.01694i 0.504221 0.873337i
\(34\) 0 0
\(35\) −1.09019 + 0.509947i −0.184276 + 0.0861968i
\(36\) 0 0
\(37\) 3.85144 6.67088i 0.633172 1.09669i −0.353727 0.935349i \(-0.615086\pi\)
0.986899 0.161338i \(-0.0515808\pi\)
\(38\) 0 0
\(39\) −2.94163 5.09505i −0.471037 0.815861i
\(40\) 0 0
\(41\) 9.58612 1.49710 0.748551 0.663078i \(-0.230750\pi\)
0.748551 + 0.663078i \(0.230750\pi\)
\(42\) 0 0
\(43\) 10.7931 1.64593 0.822963 0.568095i \(-0.192319\pi\)
0.822963 + 0.568095i \(0.192319\pi\)
\(44\) 0 0
\(45\) 0.227452 + 0.393958i 0.0339065 + 0.0587279i
\(46\) 0 0
\(47\) 2.45490 4.25202i 0.358085 0.620221i −0.629556 0.776955i \(-0.716763\pi\)
0.987641 + 0.156734i \(0.0500966\pi\)
\(48\) 0 0
\(49\) 2.40981 + 6.57212i 0.344258 + 0.938875i
\(50\) 0 0
\(51\) −1.45490 + 2.51997i −0.203727 + 0.352866i
\(52\) 0 0
\(53\) 6.56561 + 11.3720i 0.901856 + 1.56206i 0.825083 + 0.565012i \(0.191128\pi\)
0.0767730 + 0.997049i \(0.475538\pi\)
\(54\) 0 0
\(55\) 2.63529 0.355342
\(56\) 0 0
\(57\) 5.88325 0.779256
\(58\) 0 0
\(59\) 0.896531 + 1.55284i 0.116718 + 0.202162i 0.918465 0.395501i \(-0.129429\pi\)
−0.801747 + 0.597664i \(0.796096\pi\)
\(60\) 0 0
\(61\) 2.33816 4.04981i 0.299370 0.518525i −0.676622 0.736331i \(-0.736557\pi\)
0.975992 + 0.217806i \(0.0698900\pi\)
\(62\) 0 0
\(63\) 2.39653 1.12100i 0.301935 0.141233i
\(64\) 0 0
\(65\) 1.33816 2.31776i 0.165978 0.287482i
\(66\) 0 0
\(67\) −3.94163 6.82710i −0.481546 0.834063i 0.518229 0.855242i \(-0.326591\pi\)
−0.999776 + 0.0211789i \(0.993258\pi\)
\(68\) 0 0
\(69\) 2.90981 0.350300
\(70\) 0 0
\(71\) 0.909808 0.107974 0.0539872 0.998542i \(-0.482807\pi\)
0.0539872 + 0.998542i \(0.482807\pi\)
\(72\) 0 0
\(73\) −2.60347 4.50934i −0.304713 0.527778i 0.672484 0.740111i \(-0.265227\pi\)
−0.977197 + 0.212333i \(0.931894\pi\)
\(74\) 0 0
\(75\) 2.39653 4.15091i 0.276728 0.479306i
\(76\) 0 0
\(77\) 1.31764 15.2703i 0.150159 1.74021i
\(78\) 0 0
\(79\) −1.37602 + 2.38333i −0.154814 + 0.268146i −0.932991 0.359899i \(-0.882811\pi\)
0.778177 + 0.628045i \(0.216144\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 9.97345 1.09473 0.547364 0.836895i \(-0.315631\pi\)
0.547364 + 0.836895i \(0.315631\pi\)
\(84\) 0 0
\(85\) −1.32368 −0.143574
\(86\) 0 0
\(87\) 1.77255 + 3.07014i 0.190037 + 0.329154i
\(88\) 0 0
\(89\) 2.45490 4.25202i 0.260219 0.450713i −0.706081 0.708131i \(-0.749538\pi\)
0.966300 + 0.257418i \(0.0828718\pi\)
\(90\) 0 0
\(91\) −12.7612 8.91288i −1.33774 0.934324i
\(92\) 0 0
\(93\) −2.16908 + 3.75696i −0.224923 + 0.389578i
\(94\) 0 0
\(95\) 1.33816 + 2.31776i 0.137292 + 0.237797i
\(96\) 0 0
\(97\) −5.79306 −0.588196 −0.294098 0.955775i \(-0.595019\pi\)
−0.294098 + 0.955775i \(0.595019\pi\)
\(98\) 0 0
\(99\) −5.79306 −0.582225
\(100\) 0 0
\(101\) 8.33816 + 14.4421i 0.829678 + 1.43704i 0.898291 + 0.439401i \(0.144809\pi\)
−0.0686134 + 0.997643i \(0.521858\pi\)
\(102\) 0 0
\(103\) −0.396531 + 0.686812i −0.0390714 + 0.0676736i −0.884900 0.465781i \(-0.845773\pi\)
0.845828 + 0.533455i \(0.179107\pi\)
\(104\) 0 0
\(105\) 0.986723 + 0.689160i 0.0962943 + 0.0672552i
\(106\) 0 0
\(107\) −5.98672 + 10.3693i −0.578758 + 1.00244i 0.416864 + 0.908969i \(0.363129\pi\)
−0.995622 + 0.0934699i \(0.970204\pi\)
\(108\) 0 0
\(109\) −2.30634 3.99470i −0.220907 0.382623i 0.734176 0.678959i \(-0.237568\pi\)
−0.955084 + 0.296336i \(0.904235\pi\)
\(110\) 0 0
\(111\) −7.70287 −0.731124
\(112\) 0 0
\(113\) 8.00000 0.752577 0.376288 0.926503i \(-0.377200\pi\)
0.376288 + 0.926503i \(0.377200\pi\)
\(114\) 0 0
\(115\) 0.661842 + 1.14634i 0.0617171 + 0.106897i
\(116\) 0 0
\(117\) −2.94163 + 5.09505i −0.271954 + 0.471037i
\(118\) 0 0
\(119\) −0.661842 + 7.67013i −0.0606709 + 0.703119i
\(120\) 0 0
\(121\) −11.2798 + 19.5372i −1.02544 + 1.77611i
\(122\) 0 0
\(123\) −4.79306 8.30183i −0.432176 0.748551i
\(124\) 0 0
\(125\) 4.45490 0.398459
\(126\) 0 0
\(127\) 1.24797 0.110739 0.0553696 0.998466i \(-0.482366\pi\)
0.0553696 + 0.998466i \(0.482366\pi\)
\(128\) 0 0
\(129\) −5.39653 9.34707i −0.475138 0.822963i
\(130\) 0 0
\(131\) 2.89653 5.01694i 0.253071 0.438332i −0.711299 0.702890i \(-0.751893\pi\)
0.964370 + 0.264558i \(0.0852260\pi\)
\(132\) 0 0
\(133\) 14.0994 6.59512i 1.22257 0.571870i
\(134\) 0 0
\(135\) 0.227452 0.393958i 0.0195760 0.0339065i
\(136\) 0 0
\(137\) 1.54510 + 2.67618i 0.132006 + 0.228642i 0.924450 0.381303i \(-0.124525\pi\)
−0.792443 + 0.609945i \(0.791191\pi\)
\(138\) 0 0
\(139\) −5.70287 −0.483711 −0.241856 0.970312i \(-0.577756\pi\)
−0.241856 + 0.970312i \(0.577756\pi\)
\(140\) 0 0
\(141\) −4.90981 −0.413480
\(142\) 0 0
\(143\) 17.0410 + 29.5159i 1.42504 + 2.46825i
\(144\) 0 0
\(145\) −0.806339 + 1.39662i −0.0669628 + 0.115983i
\(146\) 0 0
\(147\) 4.48672 5.37302i 0.370059 0.443159i
\(148\) 0 0
\(149\) 1.54510 2.67618i 0.126579 0.219242i −0.795770 0.605599i \(-0.792934\pi\)
0.922349 + 0.386357i \(0.126267\pi\)
\(150\) 0 0
\(151\) −0.862740 1.49431i −0.0702088 0.121605i 0.828784 0.559569i \(-0.189033\pi\)
−0.898993 + 0.437964i \(0.855700\pi\)
\(152\) 0 0
\(153\) 2.90981 0.235244
\(154\) 0 0
\(155\) −1.97345 −0.158511
\(156\) 0 0
\(157\) −2.79306 4.83773i −0.222911 0.386093i 0.732780 0.680466i \(-0.238222\pi\)
−0.955691 + 0.294373i \(0.904889\pi\)
\(158\) 0 0
\(159\) 6.56561 11.3720i 0.520687 0.901856i
\(160\) 0 0
\(161\) 6.97345 3.26189i 0.549585 0.257073i
\(162\) 0 0
\(163\) 4.42835 7.67013i 0.346855 0.600771i −0.638834 0.769345i \(-0.720583\pi\)
0.985689 + 0.168574i \(0.0539162\pi\)
\(164\) 0 0
\(165\) −1.31764 2.28223i −0.102578 0.177671i
\(166\) 0 0
\(167\) 17.4057 1.34690 0.673448 0.739234i \(-0.264812\pi\)
0.673448 + 0.739234i \(0.264812\pi\)
\(168\) 0 0
\(169\) 21.6127 1.66251
\(170\) 0 0
\(171\) −2.94163 5.09505i −0.224952 0.389628i
\(172\) 0 0
\(173\) −8.33816 + 14.4421i −0.633938 + 1.09801i 0.352801 + 0.935699i \(0.385229\pi\)
−0.986739 + 0.162315i \(0.948104\pi\)
\(174\) 0 0
\(175\) 1.09019 12.6343i 0.0824108 0.955064i
\(176\) 0 0
\(177\) 0.896531 1.55284i 0.0673874 0.116718i
\(178\) 0 0
\(179\) −3.09019 5.35237i −0.230972 0.400055i 0.727123 0.686508i \(-0.240857\pi\)
−0.958094 + 0.286453i \(0.907524\pi\)
\(180\) 0 0
\(181\) 3.20694 0.238370 0.119185 0.992872i \(-0.461972\pi\)
0.119185 + 0.992872i \(0.461972\pi\)
\(182\) 0 0
\(183\) −4.67632 −0.345683
\(184\) 0 0
\(185\) −1.75203 3.03461i −0.128812 0.223109i
\(186\) 0 0
\(187\) 8.42835 14.5983i 0.616342 1.06754i
\(188\) 0 0
\(189\) −2.16908 1.51496i −0.157777 0.110197i
\(190\) 0 0
\(191\) −10.6763 + 18.4919i −0.772511 + 1.33803i 0.163672 + 0.986515i \(0.447666\pi\)
−0.936183 + 0.351514i \(0.885667\pi\)
\(192\) 0 0
\(193\) −8.20287 14.2078i −0.590456 1.02270i −0.994171 0.107814i \(-0.965615\pi\)
0.403716 0.914885i \(-0.367719\pi\)
\(194\) 0 0
\(195\) −2.67632 −0.191655
\(196\) 0 0
\(197\) −24.6763 −1.75811 −0.879057 0.476716i \(-0.841827\pi\)
−0.879057 + 0.476716i \(0.841827\pi\)
\(198\) 0 0
\(199\) −6.90981 11.9681i −0.489823 0.848399i 0.510108 0.860110i \(-0.329605\pi\)
−0.999931 + 0.0117114i \(0.996272\pi\)
\(200\) 0 0
\(201\) −3.94163 + 6.82710i −0.278021 + 0.481546i
\(202\) 0 0
\(203\) 7.68959 + 5.37067i 0.539704 + 0.376947i
\(204\) 0 0
\(205\) 2.18038 3.77654i 0.152285 0.263765i
\(206\) 0 0
\(207\) −1.45490 2.51997i −0.101123 0.175150i
\(208\) 0 0
\(209\) −34.0821 −2.35751
\(210\) 0 0
\(211\) −11.5861 −0.797622 −0.398811 0.917033i \(-0.630577\pi\)
−0.398811 + 0.917033i \(0.630577\pi\)
\(212\) 0 0
\(213\) −0.454904 0.787917i −0.0311695 0.0539872i
\(214\) 0 0
\(215\) 2.45490 4.25202i 0.167423 0.289985i
\(216\) 0 0
\(217\) −0.986723 + 11.4352i −0.0669831 + 0.776272i
\(218\) 0 0
\(219\) −2.60347 + 4.50934i −0.175926 + 0.304713i
\(220\) 0 0
\(221\) −8.55957 14.8256i −0.575779 0.997279i
\(222\) 0 0
\(223\) 20.4549 1.36976 0.684881 0.728655i \(-0.259854\pi\)
0.684881 + 0.728655i \(0.259854\pi\)
\(224\) 0 0
\(225\) −4.79306 −0.319537
\(226\) 0 0
\(227\) 8.86998 + 15.3633i 0.588721 + 1.01969i 0.994400 + 0.105679i \(0.0337017\pi\)
−0.405679 + 0.914016i \(0.632965\pi\)
\(228\) 0 0
\(229\) −12.0994 + 20.9568i −0.799551 + 1.38486i 0.120358 + 0.992731i \(0.461596\pi\)
−0.919909 + 0.392132i \(0.871738\pi\)
\(230\) 0 0
\(231\) −13.8833 + 6.49402i −0.913451 + 0.427275i
\(232\) 0 0
\(233\) −11.3382 + 19.6383i −0.742787 + 1.28655i 0.208434 + 0.978036i \(0.433163\pi\)
−0.951221 + 0.308509i \(0.900170\pi\)
\(234\) 0 0
\(235\) −1.11675 1.93426i −0.0728485 0.126177i
\(236\) 0 0
\(237\) 2.75203 0.178764
\(238\) 0 0
\(239\) 2.90981 0.188220 0.0941099 0.995562i \(-0.469999\pi\)
0.0941099 + 0.995562i \(0.469999\pi\)
\(240\) 0 0
\(241\) −10.8700 18.8274i −0.700197 1.21278i −0.968397 0.249413i \(-0.919762\pi\)
0.268200 0.963363i \(-0.413571\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 3.13726 + 0.545479i 0.200432 + 0.0348494i
\(246\) 0 0
\(247\) −17.3063 + 29.9755i −1.10118 + 1.90729i
\(248\) 0 0
\(249\) −4.98672 8.63726i −0.316021 0.547364i
\(250\) 0 0
\(251\) 8.02655 0.506632 0.253316 0.967384i \(-0.418479\pi\)
0.253316 + 0.967384i \(0.418479\pi\)
\(252\) 0 0
\(253\) −16.8567 −1.05977
\(254\) 0 0
\(255\) 0.661842 + 1.14634i 0.0414461 + 0.0717868i
\(256\) 0 0
\(257\) 6.45490 11.1802i 0.402646 0.697403i −0.591398 0.806379i \(-0.701424\pi\)
0.994044 + 0.108976i \(0.0347573\pi\)
\(258\) 0 0
\(259\) −18.4602 + 8.63491i −1.14706 + 0.536547i
\(260\) 0 0
\(261\) 1.77255 3.07014i 0.109718 0.190037i
\(262\) 0 0
\(263\) −4.45490 7.71612i −0.274701 0.475796i 0.695359 0.718663i \(-0.255246\pi\)
−0.970060 + 0.242867i \(0.921912\pi\)
\(264\) 0 0
\(265\) 5.97345 0.366946
\(266\) 0 0
\(267\) −4.90981 −0.300475
\(268\) 0 0
\(269\) −3.02051 5.23168i −0.184164 0.318981i 0.759130 0.650938i \(-0.225624\pi\)
−0.943295 + 0.331957i \(0.892291\pi\)
\(270\) 0 0
\(271\) −6.68236 + 11.5742i −0.405924 + 0.703081i −0.994429 0.105413i \(-0.966384\pi\)
0.588504 + 0.808494i \(0.299717\pi\)
\(272\) 0 0
\(273\) −1.33816 + 15.5080i −0.0809890 + 0.938587i
\(274\) 0 0
\(275\) −13.8833 + 24.0465i −0.837192 + 1.45006i
\(276\) 0 0
\(277\) 2.39653 + 4.15091i 0.143994 + 0.249404i 0.928997 0.370087i \(-0.120672\pi\)
−0.785003 + 0.619491i \(0.787339\pi\)
\(278\) 0 0
\(279\) 4.33816 0.259719
\(280\) 0 0
\(281\) 7.32368 0.436894 0.218447 0.975849i \(-0.429901\pi\)
0.218447 + 0.975849i \(0.429901\pi\)
\(282\) 0 0
\(283\) 6.60347 + 11.4375i 0.392535 + 0.679891i 0.992783 0.119923i \(-0.0382647\pi\)
−0.600248 + 0.799814i \(0.704931\pi\)
\(284\) 0 0
\(285\) 1.33816 2.31776i 0.0792656 0.137292i
\(286\) 0 0
\(287\) −20.7931 14.5226i −1.22738 0.857240i
\(288\) 0 0
\(289\) 4.26651 7.38981i 0.250971 0.434695i
\(290\) 0 0
\(291\) 2.89653 + 5.01694i 0.169798 + 0.294098i
\(292\) 0 0
\(293\) −7.54510 −0.440789 −0.220395 0.975411i \(-0.570735\pi\)
−0.220395 + 0.975411i \(0.570735\pi\)
\(294\) 0 0
\(295\) 0.815671 0.0474902
\(296\) 0 0
\(297\) 2.89653 + 5.01694i 0.168074 + 0.291112i
\(298\) 0 0
\(299\) −8.55957 + 14.8256i −0.495013 + 0.857387i
\(300\) 0 0
\(301\) −23.4110 16.3510i −1.34939 0.942458i
\(302\) 0 0
\(303\) 8.33816 14.4421i 0.479015 0.829678i
\(304\) 0 0
\(305\) −1.06364 1.84227i −0.0609037 0.105488i
\(306\) 0 0
\(307\) 23.1086 1.31888 0.659439 0.751758i \(-0.270794\pi\)
0.659439 + 0.751758i \(0.270794\pi\)
\(308\) 0 0
\(309\) 0.793062 0.0451157
\(310\) 0 0
\(311\) −3.70287 6.41356i −0.209971 0.363680i 0.741734 0.670694i \(-0.234003\pi\)
−0.951705 + 0.307014i \(0.900670\pi\)
\(312\) 0 0
\(313\) −7.29306 + 12.6320i −0.412228 + 0.714000i −0.995133 0.0985402i \(-0.968583\pi\)
0.582905 + 0.812540i \(0.301916\pi\)
\(314\) 0 0
\(315\) 0.103469 1.19911i 0.00582981 0.0675620i
\(316\) 0 0
\(317\) 0.682356 1.18188i 0.0383249 0.0663807i −0.846227 0.532823i \(-0.821131\pi\)
0.884552 + 0.466442i \(0.154464\pi\)
\(318\) 0 0
\(319\) −10.2685 17.7855i −0.574925 0.995799i
\(320\) 0 0
\(321\) 11.9734 0.668293
\(322\) 0 0
\(323\) 17.1191 0.952534
\(324\) 0 0
\(325\) 14.0994 + 24.4209i 0.782094 + 1.35463i
\(326\) 0 0
\(327\) −2.30634 + 3.99470i −0.127541 + 0.220907i
\(328\) 0 0
\(329\) −11.7665 + 5.50389i −0.648709 + 0.303439i
\(330\) 0 0
\(331\) −5.48672 + 9.50328i −0.301578 + 0.522348i −0.976493 0.215547i \(-0.930847\pi\)
0.674916 + 0.737895i \(0.264180\pi\)
\(332\) 0 0
\(333\) 3.85144 + 6.67088i 0.211057 + 0.365562i
\(334\) 0 0
\(335\) −3.58612 −0.195931
\(336\) 0 0
\(337\) −22.1722 −1.20780 −0.603900 0.797060i \(-0.706387\pi\)
−0.603900 + 0.797060i \(0.706387\pi\)
\(338\) 0 0
\(339\) −4.00000 6.92820i −0.217250 0.376288i
\(340\) 0 0
\(341\) 12.5656 21.7643i 0.680466 1.17860i
\(342\) 0 0
\(343\) 4.72942 17.9062i 0.255365 0.966845i
\(344\) 0 0
\(345\) 0.661842 1.14634i 0.0356324 0.0617171i
\(346\) 0 0
\(347\) −0.116746 0.202210i −0.00626725 0.0108552i 0.862875 0.505418i \(-0.168662\pi\)
−0.869142 + 0.494563i \(0.835328\pi\)
\(348\) 0 0
\(349\) −7.35263 −0.393577 −0.196789 0.980446i \(-0.563051\pi\)
−0.196789 + 0.980446i \(0.563051\pi\)
\(350\) 0 0
\(351\) 5.88325 0.314025
\(352\) 0 0
\(353\) −9.58612 16.6037i −0.510218 0.883723i −0.999930 0.0118391i \(-0.996231\pi\)
0.489712 0.871884i \(-0.337102\pi\)
\(354\) 0 0
\(355\) 0.206938 0.358427i 0.0109831 0.0190233i
\(356\) 0 0
\(357\) 6.97345 3.26189i 0.369074 0.172638i
\(358\) 0 0
\(359\) 10.4694 18.1335i 0.552553 0.957049i −0.445537 0.895264i \(-0.646987\pi\)
0.998089 0.0617857i \(-0.0196795\pi\)
\(360\) 0 0
\(361\) −7.80634 13.5210i −0.410860 0.711630i
\(362\) 0 0
\(363\) 22.5596 1.18407
\(364\) 0 0
\(365\) −2.36866 −0.123981
\(366\) 0 0
\(367\) −12.5072 21.6632i −0.652872 1.13081i −0.982423 0.186670i \(-0.940230\pi\)
0.329550 0.944138i \(-0.393103\pi\)
\(368\) 0 0
\(369\) −4.79306 + 8.30183i −0.249517 + 0.432176i
\(370\) 0 0
\(371\) 2.98672 34.6133i 0.155063 1.79703i
\(372\) 0 0
\(373\) −10.1630 + 17.6029i −0.526222 + 0.911444i 0.473311 + 0.880895i \(0.343059\pi\)
−0.999533 + 0.0305483i \(0.990275\pi\)
\(374\) 0 0
\(375\) −2.22745 3.85806i −0.115025 0.199229i
\(376\) 0 0
\(377\) −20.8567 −1.07417
\(378\) 0 0
\(379\) 20.7931 1.06807 0.534034 0.845463i \(-0.320675\pi\)
0.534034 + 0.845463i \(0.320675\pi\)
\(380\) 0 0
\(381\) −0.623983 1.08077i −0.0319676 0.0553696i
\(382\) 0 0
\(383\) −12.5861 + 21.7998i −0.643121 + 1.11392i 0.341611 + 0.939841i \(0.389027\pi\)
−0.984732 + 0.174077i \(0.944306\pi\)
\(384\) 0 0
\(385\) −5.71615 3.99235i −0.291322 0.203469i
\(386\) 0 0
\(387\) −5.39653 + 9.34707i −0.274321 + 0.475138i
\(388\) 0 0
\(389\) 12.2214 + 21.1681i 0.619650 + 1.07327i 0.989549 + 0.144194i \(0.0460589\pi\)
−0.369899 + 0.929072i \(0.620608\pi\)
\(390\) 0 0
\(391\) 8.46698 0.428194
\(392\) 0 0
\(393\) −5.79306 −0.292221
\(394\) 0 0
\(395\) 0.625956 + 1.08419i 0.0314952 + 0.0545514i
\(396\) 0 0
\(397\) −4.39653 + 7.61502i −0.220656 + 0.382187i −0.955007 0.296583i \(-0.904153\pi\)
0.734352 + 0.678769i \(0.237486\pi\)
\(398\) 0 0
\(399\) −12.7612 8.91288i −0.638861 0.446202i
\(400\) 0 0
\(401\) −16.5596 + 28.6820i −0.826945 + 1.43231i 0.0734778 + 0.997297i \(0.476590\pi\)
−0.900423 + 0.435015i \(0.856743\pi\)
\(402\) 0 0
\(403\) −12.7612 22.1031i −0.635683 1.10103i
\(404\) 0 0
\(405\) −0.454904 −0.0226044
\(406\) 0 0
\(407\) 44.6232 2.21189
\(408\) 0 0
\(409\) 3.47345 + 6.01618i 0.171751 + 0.297481i 0.939032 0.343830i \(-0.111724\pi\)
−0.767281 + 0.641311i \(0.778391\pi\)
\(410\) 0 0
\(411\) 1.54510 2.67618i 0.0762140 0.132006i
\(412\) 0 0
\(413\) 0.407836 4.72643i 0.0200683 0.232573i
\(414\) 0 0
\(415\) 2.26848 3.92912i 0.111355 0.192873i
\(416\) 0 0
\(417\) 2.85144 + 4.93883i 0.139635 + 0.241856i
\(418\) 0 0
\(419\) 29.2254 1.42775 0.713876 0.700272i \(-0.246938\pi\)
0.713876 + 0.700272i \(0.246938\pi\)
\(420\) 0 0
\(421\) −33.2359 −1.61982 −0.809909 0.586556i \(-0.800484\pi\)
−0.809909 + 0.586556i \(0.800484\pi\)
\(422\) 0 0
\(423\) 2.45490 + 4.25202i 0.119362 + 0.206740i
\(424\) 0 0
\(425\) 6.97345 12.0784i 0.338262 0.585887i
\(426\) 0 0
\(427\) −11.2069 + 5.24215i −0.542342 + 0.253685i
\(428\) 0 0
\(429\) 17.0410 29.5159i 0.822749 1.42504i
\(430\) 0 0
\(431\) −3.09019 5.35237i −0.148849 0.257815i 0.781953 0.623337i \(-0.214224\pi\)
−0.930802 + 0.365523i \(0.880890\pi\)
\(432\) 0 0
\(433\) 16.6127 0.798354 0.399177 0.916874i \(-0.369296\pi\)
0.399177 + 0.916874i \(0.369296\pi\)
\(434\) 0 0
\(435\) 1.61268 0.0773220
\(436\) 0 0
\(437\) −8.55957 14.8256i −0.409460 0.709205i
\(438\) 0 0
\(439\) 13.8136 23.9258i 0.659286 1.14192i −0.321515 0.946905i \(-0.604192\pi\)
0.980801 0.195012i \(-0.0624747\pi\)
\(440\) 0 0
\(441\) −6.89653 1.19911i −0.328406 0.0571003i
\(442\) 0 0
\(443\) −10.0133 + 17.3435i −0.475745 + 0.824015i −0.999614 0.0277842i \(-0.991155\pi\)
0.523869 + 0.851799i \(0.324488\pi\)
\(444\) 0 0
\(445\) −1.11675 1.93426i −0.0529388 0.0916927i
\(446\) 0 0
\(447\) −3.09019 −0.146161
\(448\) 0 0
\(449\) 15.0371 0.709644 0.354822 0.934934i \(-0.384541\pi\)
0.354822 + 0.934934i \(0.384541\pi\)
\(450\) 0 0
\(451\) 27.7665 + 48.0930i 1.30747 + 2.26461i
\(452\) 0 0
\(453\) −0.862740 + 1.49431i −0.0405351 + 0.0702088i
\(454\) 0 0
\(455\) −6.41388 + 3.00015i −0.300687 + 0.140649i
\(456\) 0 0
\(457\) 21.0596 36.4762i 0.985125 1.70629i 0.343746 0.939063i \(-0.388304\pi\)
0.641379 0.767224i \(-0.278363\pi\)
\(458\) 0 0
\(459\) −1.45490 2.51997i −0.0679091 0.117622i
\(460\) 0 0
\(461\) −20.9098 −0.973867 −0.486933 0.873439i \(-0.661885\pi\)
−0.486933 + 0.873439i \(0.661885\pi\)
\(462\) 0 0
\(463\) −38.1457 −1.77278 −0.886390 0.462939i \(-0.846795\pi\)
−0.886390 + 0.462939i \(0.846795\pi\)
\(464\) 0 0
\(465\) 0.986723 + 1.70905i 0.0457582 + 0.0792555i
\(466\) 0 0
\(467\) 5.76651 9.98789i 0.266842 0.462184i −0.701202 0.712962i \(-0.747353\pi\)
0.968045 + 0.250778i \(0.0806864\pi\)
\(468\) 0 0
\(469\) −1.79306 + 20.7799i −0.0827959 + 0.959527i
\(470\) 0 0
\(471\) −2.79306 + 4.83773i −0.128698 + 0.222911i
\(472\) 0 0
\(473\) 31.2624 + 54.1481i 1.43745 + 2.48973i
\(474\) 0 0
\(475\) −28.1988 −1.29385
\(476\) 0 0
\(477\) −13.1312 −0.601237
\(478\) 0 0
\(479\) 3.66184 + 6.34250i 0.167314 + 0.289796i 0.937475 0.348054i \(-0.113157\pi\)
−0.770161 + 0.637850i \(0.779824\pi\)
\(480\) 0 0
\(481\) 22.6590 39.2465i 1.03316 1.78949i
\(482\) 0 0
\(483\) −6.31160 4.40824i −0.287188 0.200582i
\(484\) 0 0
\(485\) −1.31764 + 2.28223i −0.0598311 + 0.103631i
\(486\) 0 0
\(487\) 13.0258 + 22.5613i 0.590254 + 1.02235i 0.994198 + 0.107567i \(0.0343059\pi\)
−0.403943 + 0.914784i \(0.632361\pi\)
\(488\) 0 0
\(489\) −8.85670 −0.400514
\(490\) 0 0
\(491\) −7.37919 −0.333018 −0.166509 0.986040i \(-0.553249\pi\)
−0.166509 + 0.986040i \(0.553249\pi\)
\(492\) 0 0
\(493\) 5.15777 + 8.93353i 0.232294 + 0.402346i
\(494\) 0 0
\(495\) −1.31764 + 2.28223i −0.0592237 + 0.102578i
\(496\) 0 0
\(497\) −1.97345 1.37832i −0.0885211 0.0618261i
\(498\) 0 0
\(499\) 0.175119 0.303315i 0.00783940 0.0135782i −0.862079 0.506774i \(-0.830838\pi\)
0.869918 + 0.493196i \(0.164171\pi\)
\(500\) 0 0
\(501\) −8.70287 15.0738i −0.388816 0.673448i
\(502\) 0 0
\(503\) −14.9098 −0.664795 −0.332398 0.943139i \(-0.607858\pi\)
−0.332398 + 0.943139i \(0.607858\pi\)
\(504\) 0 0
\(505\) 7.58612 0.337578
\(506\) 0 0
\(507\) −10.8063 18.7171i −0.479926 0.831257i
\(508\) 0 0
\(509\) 8.44886 14.6339i 0.374489 0.648635i −0.615761 0.787933i \(-0.711151\pi\)
0.990250 + 0.139298i \(0.0444847\pi\)
\(510\) 0 0
\(511\) −1.18433 + 13.7253i −0.0523916 + 0.607170i
\(512\) 0 0
\(513\) −2.94163 + 5.09505i −0.129876 + 0.224952i
\(514\) 0 0
\(515\) 0.180384 + 0.312434i 0.00794865 + 0.0137675i
\(516\) 0 0
\(517\) 28.4428 1.25091
\(518\) 0 0
\(519\) 16.6763 0.732009
\(520\) 0 0
\(521\) −3.79306 6.56978i −0.166177 0.287827i 0.770896 0.636962i \(-0.219809\pi\)
−0.937073 + 0.349134i \(0.886476\pi\)
\(522\) 0 0
\(523\) 21.2572 36.8185i 0.929511 1.60996i 0.145371 0.989377i \(-0.453562\pi\)
0.784140 0.620584i \(-0.213104\pi\)
\(524\) 0 0
\(525\) −11.4867 + 5.37302i −0.501322 + 0.234498i
\(526\) 0 0
\(527\) −6.31160 + 10.9320i −0.274938 + 0.476206i
\(528\) 0 0
\(529\) 7.26651 + 12.5860i 0.315935 + 0.547216i
\(530\) 0 0
\(531\) −1.79306 −0.0778123
\(532\) 0 0
\(533\) 56.3976 2.44285
\(534\) 0 0
\(535\) 2.72338 + 4.71704i 0.117742 + 0.203935i
\(536\) 0 0
\(537\) −3.09019 + 5.35237i −0.133352 + 0.230972i
\(538\) 0 0
\(539\) −25.9919 + 31.1262i −1.11955 + 1.34070i
\(540\) 0 0
\(541\) 7.03182 12.1795i 0.302322 0.523636i −0.674340 0.738421i \(-0.735572\pi\)
0.976661 + 0.214785i \(0.0689050\pi\)
\(542\) 0 0
\(543\) −1.60347 2.77729i −0.0688114 0.119185i
\(544\) 0 0
\(545\) −2.09833 −0.0898824
\(546\) 0 0
\(547\) −4.49593 −0.192232 −0.0961161 0.995370i \(-0.530642\pi\)
−0.0961161 + 0.995370i \(0.530642\pi\)
\(548\) 0 0
\(549\) 2.33816 + 4.04981i 0.0997902 + 0.172842i
\(550\) 0 0
\(551\) 10.4283 18.0624i 0.444263 0.769485i
\(552\) 0 0
\(553\) 6.59533 3.08503i 0.280462 0.131189i
\(554\) 0 0
\(555\) −1.75203 + 3.03461i −0.0743697 + 0.128812i
\(556\) 0 0
\(557\) 15.9303 + 27.5921i 0.674989 + 1.16912i 0.976472 + 0.215644i \(0.0691852\pi\)
−0.301483 + 0.953472i \(0.597482\pi\)
\(558\) 0 0
\(559\) 63.4983 2.68569
\(560\) 0 0
\(561\) −16.8567 −0.711690
\(562\) 0 0
\(563\) −23.0688 39.9563i −0.972233 1.68396i −0.688779 0.724972i \(-0.741853\pi\)
−0.283454 0.958986i \(-0.591480\pi\)
\(564\) 0 0
\(565\) 1.81962 3.15167i 0.0765518 0.132592i
\(566\) 0 0
\(567\) −0.227452 + 2.63596i −0.00955209 + 0.110700i
\(568\) 0 0
\(569\) 8.31160 14.3961i 0.348441 0.603517i −0.637532 0.770424i \(-0.720045\pi\)
0.985973 + 0.166907i \(0.0533780\pi\)
\(570\) 0 0
\(571\) −18.2532 31.6155i −0.763874 1.32307i −0.940840 0.338852i \(-0.889962\pi\)
0.176966 0.984217i \(-0.443372\pi\)
\(572\) 0 0
\(573\) 21.3526 0.892019
\(574\) 0 0
\(575\) −13.9469 −0.581626
\(576\) 0 0
\(577\) 7.59019 + 13.1466i 0.315984 + 0.547300i 0.979646 0.200732i \(-0.0643321\pi\)
−0.663662 + 0.748032i \(0.730999\pi\)
\(578\) 0 0
\(579\) −8.20287 + 14.2078i −0.340900 + 0.590456i
\(580\) 0 0
\(581\) −21.6332 15.1093i −0.897496 0.626841i
\(582\) 0 0
\(583\) −38.0350 + 65.8785i −1.57525 + 2.72841i
\(584\) 0 0
\(585\) 1.33816 + 2.31776i 0.0553260 + 0.0958275i
\(586\) 0 0
\(587\) 8.20694 0.338737 0.169368 0.985553i \(-0.445827\pi\)
0.169368 + 0.985553i \(0.445827\pi\)
\(588\) 0 0
\(589\) 25.5225 1.05164
\(590\) 0 0
\(591\) 12.3382 + 21.3703i 0.507524 + 0.879057i
\(592\) 0 0
\(593\) 2.77859 4.81266i 0.114103 0.197632i −0.803318 0.595550i \(-0.796934\pi\)
0.917421 + 0.397918i \(0.130267\pi\)
\(594\) 0 0
\(595\) 2.87117 + 2.00532i 0.117707 + 0.0822103i
\(596\) 0 0
\(597\) −6.90981 + 11.9681i −0.282800 + 0.489823i
\(598\) 0 0
\(599\) −17.7931 30.8185i −0.727005 1.25921i −0.958143 0.286288i \(-0.907578\pi\)
0.231139 0.972921i \(-0.425755\pi\)
\(600\) 0 0
\(601\) 1.18038 0.0481489 0.0240744 0.999710i \(-0.492336\pi\)
0.0240744 + 0.999710i \(0.492336\pi\)
\(602\) 0 0
\(603\) 7.88325 0.321031
\(604\) 0 0
\(605\) 5.13122 + 8.88753i 0.208614 + 0.361330i
\(606\) 0 0
\(607\) 6.16908 10.6852i 0.250395 0.433697i −0.713239 0.700920i \(-0.752773\pi\)
0.963635 + 0.267223i \(0.0861061\pi\)
\(608\) 0 0
\(609\) 0.806339 9.34472i 0.0326745 0.378667i
\(610\) 0 0
\(611\) 14.4428 25.0157i 0.584294 1.01203i
\(612\) 0 0
\(613\) −10.5451 18.2646i −0.425912 0.737702i 0.570593 0.821233i \(-0.306713\pi\)
−0.996505 + 0.0835312i \(0.973380\pi\)
\(614\) 0 0
\(615\) −4.36077 −0.175843
\(616\) 0 0
\(617\) 15.3526 0.618074 0.309037 0.951050i \(-0.399993\pi\)
0.309037 + 0.951050i \(0.399993\pi\)
\(618\) 0 0
\(619\) 9.21615 + 15.9628i 0.370428 + 0.641601i 0.989631 0.143630i \(-0.0458776\pi\)
−0.619203 + 0.785231i \(0.712544\pi\)
\(620\) 0 0
\(621\) −1.45490 + 2.51997i −0.0583833 + 0.101123i
\(622\) 0 0
\(623\) −11.7665 + 5.50389i −0.471415 + 0.220509i
\(624\) 0 0
\(625\) −10.9694 + 18.9995i −0.438775 + 0.759981i
\(626\) 0 0
\(627\) 17.0410 + 29.5159i 0.680553 + 1.17875i
\(628\) 0 0
\(629\) −22.4139 −0.893700
\(630\) 0 0
\(631\) 5.91375 0.235423 0.117711 0.993048i \(-0.462444\pi\)
0.117711 + 0.993048i \(0.462444\pi\)
\(632\) 0 0
\(633\) 5.79306 + 10.0339i 0.230254 + 0.398811i
\(634\) 0 0
\(635\) 0.283853 0.491647i 0.0112643 0.0195104i
\(636\) 0 0
\(637\) 14.1775 + 38.6655i 0.561734 + 1.53198i
\(638\) 0 0
\(639\) −0.454904 + 0.787917i −0.0179957 + 0.0311695i
\(640\) 0 0
\(641\) −23.0821 39.9793i −0.911686 1.57909i −0.811681 0.584100i \(-0.801447\pi\)
−0.100005 0.994987i \(-0.531886\pi\)
\(642\) 0 0
\(643\) −31.0555 −1.22471 −0.612355 0.790583i \(-0.709778\pi\)
−0.612355 + 0.790583i \(0.709778\pi\)
\(644\) 0 0
\(645\) −4.90981 −0.193324
\(646\) 0 0
\(647\) 8.51854 + 14.7545i 0.334898 + 0.580061i 0.983465 0.181097i \(-0.0579647\pi\)
−0.648567 + 0.761158i \(0.724631\pi\)
\(648\) 0 0
\(649\) −5.19366 + 8.99568i −0.203869 + 0.353111i
\(650\) 0 0
\(651\) 10.3965 4.86307i 0.407472 0.190599i
\(652\) 0 0
\(653\) −4.06968 + 7.04889i −0.159259 + 0.275844i −0.934602 0.355696i \(-0.884244\pi\)
0.775343 + 0.631541i \(0.217577\pi\)
\(654\) 0 0
\(655\) −1.31764 2.28223i −0.0514846 0.0891740i
\(656\) 0 0
\(657\) 5.20694 0.203142
\(658\) 0 0
\(659\) −41.1191 −1.60177 −0.800887 0.598815i \(-0.795638\pi\)
−0.800887 + 0.598815i \(0.795638\pi\)
\(660\) 0 0
\(661\) −6.67105 11.5546i −0.259474 0.449422i 0.706627 0.707586i \(-0.250216\pi\)
−0.966101 + 0.258164i \(0.916882\pi\)
\(662\) 0 0
\(663\) −8.55957 + 14.8256i −0.332426 + 0.575779i
\(664\) 0 0
\(665\) 0.608734 7.05465i 0.0236057 0.273568i
\(666\) 0 0
\(667\) 5.15777 8.93353i 0.199710 0.345908i
\(668\) 0 0
\(669\) −10.2275 17.7145i −0.395416 0.684881i
\(670\) 0 0
\(671\) 27.0902 1.04581
\(672\) 0 0
\(673\) 9.75837 0.376158 0.188079 0.982154i \(-0.439774\pi\)
0.188079 + 0.982154i \(0.439774\pi\)
\(674\) 0 0
\(675\) 2.39653 + 4.15091i 0.0922425 + 0.159769i
\(676\) 0 0
\(677\) 16.2275 28.1068i 0.623672 1.08023i −0.365124 0.930959i \(-0.618974\pi\)
0.988796 0.149272i \(-0.0476931\pi\)
\(678\) 0 0
\(679\) 12.5656 + 8.77624i 0.482224 + 0.336801i
\(680\) 0 0
\(681\) 8.86998 15.3633i 0.339898 0.588721i
\(682\) 0 0
\(683\) −18.4827 32.0129i −0.707219 1.22494i −0.965885 0.258973i \(-0.916616\pi\)
0.258666 0.965967i \(-0.416717\pi\)
\(684\) 0 0
\(685\) 1.40574 0.0537106
\(686\) 0 0
\(687\) 24.1988 0.923242
\(688\) 0 0
\(689\) 38.6272 + 66.9042i 1.47158 + 2.54885i
\(690\) 0 0
\(691\) −7.12596 + 12.3425i −0.271084 + 0.469531i −0.969140 0.246512i \(-0.920715\pi\)
0.698056 + 0.716044i \(0.254049\pi\)
\(692\) 0 0
\(693\) 12.5656 + 8.77624i 0.477328 + 0.333382i
\(694\) 0 0
\(695\) −1.29713 + 2.24669i −0.0492029 + 0.0852220i
\(696\) 0 0
\(697\) −13.9469 24.1567i −0.528276 0.915001i
\(698\) 0 0
\(699\) 22.6763 0.857697
\(700\) 0 0
\(701\) 51.3937 1.94111 0.970556 0.240876i \(-0.0774347\pi\)
0.970556 + 0.240876i \(0.0774347\pi\)
\(702\) 0 0
\(703\) 22.6590 + 39.2465i 0.854599 + 1.48021i
\(704\) 0 0
\(705\) −1.11675 + 1.93426i −0.0420591 + 0.0728485i
\(706\) 0 0
\(707\) 3.79306 43.9580i 0.142653 1.65321i
\(708\) 0 0
\(709\) 12.5861 21.7998i 0.472682 0.818709i −0.526829 0.849971i \(-0.676619\pi\)
0.999511 + 0.0312621i \(0.00995266\pi\)
\(710\) 0 0
\(711\) −1.37602 2.38333i −0.0516047 0.0893819i
\(712\) 0 0
\(713\) 12.6232 0.472743
\(714\) 0 0
\(715\) 15.5041 0.579819
\(716\) 0 0
\(717\) −1.45490 2.51997i −0.0543344 0.0941099i
\(718\) 0 0
\(719\) 4.09019 7.08442i 0.152538 0.264204i −0.779622 0.626251i \(-0.784589\pi\)
0.932160 + 0.362047i \(0.117922\pi\)
\(720\) 0 0
\(721\) 1.90060 0.889022i 0.0707820 0.0331089i
\(722\) 0 0
\(723\) −10.8700 + 18.8274i −0.404259 + 0.700197i
\(724\) 0 0
\(725\) −8.49593 14.7154i −0.315531 0.546516i
\(726\) 0 0
\(727\) −26.9614 −0.999942 −0.499971 0.866042i \(-0.666656\pi\)
−0.499971 + 0.866042i \(0.666656\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −15.7029 27.1982i −0.580792 1.00596i
\(732\) 0 0
\(733\) −10.7347 + 18.5930i −0.396495 + 0.686749i −0.993291 0.115644i \(-0.963107\pi\)
0.596796 + 0.802393i \(0.296440\pi\)
\(734\) 0 0
\(735\) −1.09623 2.98969i −0.0404351 0.110276i
\(736\) 0 0
\(737\) 22.8341 39.5498i 0.841105 1.45684i
\(738\) 0 0
\(739\) 0.671052 + 1.16230i 0.0246850 + 0.0427557i 0.878104 0.478470i \(-0.158808\pi\)
−0.853419 + 0.521226i \(0.825475\pi\)
\(740\) 0 0
\(741\) 34.6127 1.27153
\(742\) 0 0
\(743\) −26.9919 −0.990236 −0.495118 0.868826i \(-0.664875\pi\)
−0.495118 + 0.868826i \(0.664875\pi\)
\(744\) 0 0
\(745\) −0.702870 1.21741i −0.0257512 0.0446024i
\(746\) 0 0
\(747\) −4.98672 + 8.63726i −0.182455 + 0.316021i
\(748\) 0 0
\(749\) 28.6947 13.4222i 1.04848 0.490437i
\(750\) 0 0
\(751\) −6.44360 + 11.1606i −0.235130 + 0.407258i −0.959311 0.282353i \(-0.908885\pi\)
0.724180 + 0.689611i \(0.242218\pi\)
\(752\) 0 0
\(753\) −4.01328 6.95120i −0.146252 0.253316i
\(754\) 0 0
\(755\) −0.784928 −0.0285664
\(756\) 0 0
\(757\) 26.3897 0.959151 0.479575 0.877501i \(-0.340791\pi\)
0.479575 + 0.877501i \(0.340791\pi\)
\(758\) 0 0
\(759\) 8.42835 + 14.5983i 0.305930 + 0.529886i
\(760\) 0 0
\(761\) −15.2214 + 26.3643i −0.551776 + 0.955704i 0.446371 + 0.894848i \(0.352716\pi\)
−0.998147 + 0.0608556i \(0.980617\pi\)
\(762\) 0 0
\(763\) −1.04916 + 12.1588i −0.0379823 + 0.440179i
\(764\) 0 0
\(765\) 0.661842 1.14634i 0.0239289 0.0414461i
\(766\) 0 0
\(767\) 5.27452 + 9.13574i 0.190452 + 0.329872i
\(768\) 0 0
\(769\) 42.1191 1.51886 0.759428 0.650592i \(-0.225479\pi\)
0.759428 + 0.650592i \(0.225479\pi\)
\(770\) 0 0
\(771\) −12.9098 −0.464935
\(772\) 0 0
\(773\) 19.0145 + 32.9340i 0.683903 + 1.18455i 0.973780 + 0.227491i \(0.0730522\pi\)
−0.289877 + 0.957064i \(0.593614\pi\)
\(774\) 0 0
\(775\) 10.3965 18.0073i 0.373454 0.646842i
\(776\) 0 0
\(777\) 16.7081 + 11.6695i 0.599401 + 0.418642i
\(778\) 0 0
\(779\) −28.1988 + 48.8418i −1.01033 + 1.74994i
\(780\) 0 0
\(781\) 2.63529 + 4.56445i 0.0942980 + 0.163329i
\(782\) 0 0
\(783\) −3.54510 −0.126691
\(784\) 0 0
\(785\) −2.54115 −0.0906976
\(786\) 0 0
\(787\) 15.7931 + 27.3544i 0.562962 + 0.975079i 0.997236 + 0.0742978i \(0.0236716\pi\)
−0.434274 + 0.900781i \(0.642995\pi\)
\(788\) 0 0
\(789\) −4.45490 + 7.71612i −0.158599 + 0.274701i
\(790\) 0 0
\(791\) −17.3526 12.1197i −0.616989 0.430925i
\(792\) 0 0
\(793\) 13.7560 23.8261i 0.488489 0.846088i
\(794\) 0 0
\(795\) −2.98672 5.17316i −0.105928 0.183473i
\(796\) 0 0
\(797\) −45.2133