Properties

Label 672.2.q.l.193.2
Level $672$
Weight $2$
Character 672.193
Analytic conductor $5.366$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.2
Root \(0.500000 + 1.51496i\) of defining polynomial
Character \(\chi\) \(=\) 672.193
Dual form 672.2.q.l.289.2

$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −0.227452 0.393958i −0.101720 0.176184i 0.810674 0.585498i \(-0.199101\pi\)
−0.912393 + 0.409315i \(0.865768\pi\)
\(6\) 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 −0.0148132 + 0.999890i \(0.504715\pi\)
−0.858524 + 0.512774i \(0.828618\pi\)
\(12\) 0 0
\(13\) −5.88325 −1.63172 −0.815861 0.578249i \(-0.803736\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(14\) 0 0
\(15\) −0.454904 −0.117456
\(16\) 0 0
\(17\) −1.45490 + 2.51997i −0.352866 + 0.611182i −0.986750 0.162246i \(-0.948126\pi\)
0.633884 + 0.773428i \(0.281460\pi\)
\(18\) 0 0
\(19\) 2.94163 + 5.09505i 0.674856 + 1.16888i 0.976511 + 0.215467i \(0.0691274\pi\)
−0.301656 + 0.953417i \(0.597539\pi\)
\(20\) 0 0
\(21\) 0.227452 + 2.63596i 0.0496341 + 0.575213i
\(22\) 0 0
\(23\) −1.45490 2.51997i −0.303368 0.525450i 0.673528 0.739161i \(-0.264778\pi\)
−0.976897 + 0.213712i \(0.931445\pi\)
\(24\) 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 \(-0.393237\pi\)
0.329154 + 0.944276i \(0.393237\pi\)
\(30\) 0 0
\(31\) −2.16908 + 3.75696i −0.389578 + 0.674769i −0.992393 0.123112i \(-0.960713\pi\)
0.602815 + 0.797881i \(0.294046\pi\)
\(32\) 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 −0.986899 0.161338i \(-0.948419\pi\)
0.353727 0.935349i \(-0.384914\pi\)
\(38\) 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 \(-0.807681\pi\)
−0.822963 + 0.568095i \(0.807681\pi\)
\(44\) 0 0
\(45\) −0.227452 + 0.393958i −0.0339065 + 0.0587279i
\(46\) 0 0
\(47\) 2.45490 + 4.25202i 0.358085 + 0.620221i 0.987641 0.156734i \(-0.0500966\pi\)
−0.629556 + 0.776955i \(0.716763\pi\)
\(48\) 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 −0.0767730 + 0.997049i \(0.524462\pi\)
−0.825083 + 0.565012i \(0.808872\pi\)
\(54\) 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 \(-0.870571\pi\)
0.801747 + 0.597664i \(0.203904\pi\)
\(60\) 0 0
\(61\) −2.33816 4.04981i −0.299370 0.518525i 0.676622 0.736331i \(-0.263443\pi\)
−0.975992 + 0.217806i \(0.930110\pi\)
\(62\) 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 \(-0.673409\pi\)
0.999776 + 0.0211789i \(0.00674196\pi\)
\(68\) 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 −0.977197 0.212333i \(-0.931894\pi\)
0.672484 + 0.740111i \(0.265227\pi\)
\(74\) 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 0.778177 0.628045i \(-0.216144\pi\)
−0.932991 + 0.359899i \(0.882811\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −9.97345 −1.09473 −0.547364 0.836895i \(-0.684369\pi\)
−0.547364 + 0.836895i \(0.684369\pi\)
\(84\) 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 0.966300 0.257418i \(-0.0828718\pi\)
−0.706081 + 0.708131i \(0.749538\pi\)
\(90\) 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 0.0686134 + 0.997643i \(0.478142\pi\)
−0.898291 + 0.439401i \(0.855191\pi\)
\(102\) 0 0
\(103\) −0.396531 0.686812i −0.0390714 0.0676736i 0.845828 0.533455i \(-0.179107\pi\)
−0.884900 + 0.465781i \(0.845773\pi\)
\(104\) 0 0
\(105\) 0.986723 0.689160i 0.0962943 0.0672552i
\(106\) 0 0
\(107\) 5.98672 + 10.3693i 0.578758 + 1.00244i 0.995622 + 0.0934699i \(0.0297959\pi\)
−0.416864 + 0.908969i \(0.636871\pi\)
\(108\) 0 0
\(109\) 2.30634 3.99470i 0.220907 0.382623i −0.734176 0.678959i \(-0.762432\pi\)
0.955084 + 0.296336i \(0.0957649\pi\)
\(110\) 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 \(-0.248107\pi\)
−0.964370 + 0.264558i \(0.914774\pi\)
\(132\) 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 −0.792443 0.609945i \(-0.791191\pi\)
0.924450 + 0.381303i \(0.124525\pi\)
\(138\) 0 0
\(139\) 5.70287 0.483711 0.241856 0.970312i \(-0.422244\pi\)
0.241856 + 0.970312i \(0.422244\pi\)
\(140\) 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 \(-0.207066\pi\)
−0.922349 + 0.386357i \(0.873733\pi\)
\(150\) 0 0
\(151\) −0.862740 + 1.49431i −0.0702088 + 0.121605i −0.898993 0.437964i \(-0.855700\pi\)
0.828784 + 0.559569i \(0.189033\pi\)
\(152\) 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 \(-0.761778\pi\)
0.955691 + 0.294373i \(0.0951109\pi\)
\(158\) 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 \(-0.279417\pi\)
−0.985689 + 0.168574i \(0.946084\pi\)
\(164\) 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 0.986739 + 0.162315i \(0.0518961\pi\)
−0.352801 + 0.935699i \(0.614771\pi\)
\(174\) 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 \(-0.759143\pi\)
0.958094 + 0.286453i \(0.0924762\pi\)
\(180\) 0 0
\(181\) −3.20694 −0.238370 −0.119185 0.992872i \(-0.538028\pi\)
−0.119185 + 0.992872i \(0.538028\pi\)
\(182\) 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 −0.936183 0.351514i \(-0.885667\pi\)
0.163672 0.986515i \(-0.447666\pi\)
\(192\) 0 0
\(193\) −8.20287 + 14.2078i −0.590456 + 1.02270i 0.403716 + 0.914885i \(0.367719\pi\)
−0.994171 + 0.107814i \(0.965615\pi\)
\(194\) 0 0
\(195\) 2.67632 0.191655
\(196\) 0 0
\(197\) 24.6763 1.75811 0.879057 0.476716i \(-0.158173\pi\)
0.879057 + 0.476716i \(0.158173\pi\)
\(198\) 0 0
\(199\) −6.90981 + 11.9681i −0.489823 + 0.848399i −0.999931 0.0117114i \(-0.996272\pi\)
0.510108 + 0.860110i \(0.329605\pi\)
\(200\) 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 \(-0.369423\pi\)
0.398811 + 0.917033i \(0.369423\pi\)
\(212\) 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 0.405679 + 0.914016i \(0.367035\pi\)
−0.994400 + 0.105679i \(0.966298\pi\)
\(228\) 0 0
\(229\) 12.0994 + 20.9568i 0.799551 + 1.38486i 0.919909 + 0.392132i \(0.128262\pi\)
−0.120358 + 0.992731i \(0.538404\pi\)
\(230\) 0 0
\(231\) −13.8833 6.49402i −0.913451 0.427275i
\(232\) 0 0
\(233\) −11.3382 19.6383i −0.742787 1.28655i −0.951221 0.308509i \(-0.900170\pi\)
0.208434 0.978036i \(-0.433163\pi\)
\(234\) 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 0.268200 + 0.963363i \(0.413571\pi\)
−0.968397 + 0.249413i \(0.919762\pi\)
\(242\) 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 \(-0.581521\pi\)
−0.253316 + 0.967384i \(0.581521\pi\)
\(252\) 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 0.994044 0.108976i \(-0.0347573\pi\)
−0.591398 + 0.806379i \(0.701424\pi\)
\(258\) 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 −0.970060 0.242867i \(-0.921912\pi\)
0.695359 + 0.718663i \(0.255246\pi\)
\(264\) 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 \(-0.774376\pi\)
0.943295 + 0.331957i \(0.107709\pi\)
\(270\) 0 0
\(271\) −6.68236 11.5742i −0.405924 0.703081i 0.588504 0.808494i \(-0.299717\pi\)
−0.994429 + 0.105413i \(0.966384\pi\)
\(272\) 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 \(-0.879328\pi\)
0.785003 + 0.619491i \(0.212661\pi\)
\(278\) 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 \(-0.961735\pi\)
0.600248 + 0.799814i \(0.295069\pi\)
\(284\) 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 \(-0.429265\pi\)
0.220395 + 0.975411i \(0.429265\pi\)
\(294\) 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 \(-0.729206\pi\)
−0.659439 + 0.751758i \(0.729206\pi\)
\(308\) 0 0
\(309\) −0.793062 −0.0451157
\(310\) 0 0
\(311\) −3.70287 + 6.41356i −0.209971 + 0.363680i −0.951705 0.307014i \(-0.900670\pi\)
0.741734 + 0.670694i \(0.234003\pi\)
\(312\) 0 0
\(313\) −7.29306 12.6320i −0.412228 0.714000i 0.582905 0.812540i \(-0.301916\pi\)
−0.995133 + 0.0985402i \(0.968583\pi\)
\(314\) 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 \(-0.178869\pi\)
−0.884552 + 0.466442i \(0.845536\pi\)
\(318\) 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 \(-0.0691534\pi\)
−0.674916 + 0.737895i \(0.735820\pi\)
\(332\) 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 \(-0.831338\pi\)
0.869142 + 0.494563i \(0.164672\pi\)
\(348\) 0 0
\(349\) 7.35263 0.393577 0.196789 0.980446i \(-0.436949\pi\)
0.196789 + 0.980446i \(0.436949\pi\)
\(350\) 0 0
\(351\) 5.88325 0.314025
\(352\) 0 0
\(353\) −9.58612 + 16.6037i −0.510218 + 0.883723i 0.489712 + 0.871884i \(0.337102\pi\)
−0.999930 + 0.0118391i \(0.996231\pi\)
\(354\) 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 0.998089 + 0.0617857i \(0.0196795\pi\)
−0.445537 + 0.895264i \(0.646987\pi\)
\(360\) 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 0.329550 + 0.944138i \(0.393103\pi\)
−0.982423 + 0.186670i \(0.940230\pi\)
\(368\) 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 0.999533 + 0.0305483i \(0.00972533\pi\)
−0.473311 + 0.880895i \(0.656941\pi\)
\(374\) 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 \(-0.679325\pi\)
−0.534034 + 0.845463i \(0.679325\pi\)
\(380\) 0 0
\(381\) 0.623983 1.08077i 0.0319676 0.0553696i
\(382\) 0 0
\(383\) −12.5861 21.7998i −0.643121 1.11392i −0.984732 0.174077i \(-0.944306\pi\)
0.341611 0.939841i \(-0.389027\pi\)
\(384\) 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 0.369899 + 0.929072i \(0.379392\pi\)
−0.989549 + 0.144194i \(0.953941\pi\)
\(390\) 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 \(-0.0958470\pi\)
−0.734352 + 0.678769i \(0.762514\pi\)
\(398\) 0 0
\(399\) −12.7612 + 8.91288i −0.638861 + 0.446202i
\(400\) 0 0
\(401\) −16.5596 28.6820i −0.826945 1.43231i −0.900423 0.435015i \(-0.856743\pi\)
0.0734778 0.997297i \(-0.476590\pi\)
\(402\) 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 −0.767281 0.641311i \(-0.778391\pi\)
0.939032 + 0.343830i \(0.111724\pi\)
\(410\) 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 \(-0.753062\pi\)
−0.713876 + 0.700272i \(0.753062\pi\)
\(420\) 0 0
\(421\) 33.2359 1.61982 0.809909 0.586556i \(-0.199516\pi\)
0.809909 + 0.586556i \(0.199516\pi\)
\(422\) 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 −0.930802 0.365523i \(-0.880890\pi\)
0.781953 + 0.623337i \(0.214224\pi\)
\(432\) 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 0.980801 + 0.195012i \(0.0624747\pi\)
−0.321515 + 0.946905i \(0.604192\pi\)
\(440\) 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 \(-0.00884512\pi\)
−0.523869 + 0.851799i \(0.675512\pi\)
\(444\) 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 0.641379 + 0.767224i \(0.278363\pi\)
0.343746 + 0.939063i \(0.388304\pi\)
\(458\) 0 0
\(459\) 1.45490 2.51997i 0.0679091 0.117622i
\(460\) 0 0
\(461\) 20.9098 0.973867 0.486933 0.873439i \(-0.338115\pi\)
0.486933 + 0.873439i \(0.338115\pi\)
\(462\) 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 \(-0.252647\pi\)
−0.968045 + 0.250778i \(0.919314\pi\)
\(468\) 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 −0.770161 0.637850i \(-0.779824\pi\)
0.937475 + 0.348054i \(0.113157\pi\)
\(480\) 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 −0.403943 0.914784i \(-0.632361\pi\)
0.994198 0.107567i \(-0.0343059\pi\)
\(488\) 0 0
\(489\) −8.85670 −0.400514
\(490\) 0 0
\(491\) 7.37919 0.333018 0.166509 0.986040i \(-0.446751\pi\)
0.166509 + 0.986040i \(0.446751\pi\)
\(492\) 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 \(-0.169162\pi\)
−0.869918 + 0.493196i \(0.835829\pi\)
\(500\) 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 \(-0.288849\pi\)
−0.990250 + 0.139298i \(0.955515\pi\)
\(510\) 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 −0.937073 0.349134i \(-0.886476\pi\)
0.770896 + 0.636962i \(0.219809\pi\)
\(522\) 0 0
\(523\) −21.2572 36.8185i −0.929511 1.60996i −0.784140 0.620584i \(-0.786896\pi\)
−0.145371 0.989377i \(-0.546438\pi\)
\(524\) 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 \(-0.264428\pi\)
−0.976661 + 0.214785i \(0.931095\pi\)
\(542\) 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 \(-0.469358\pi\)
0.0961161 + 0.995370i \(0.469358\pi\)
\(548\) 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 0.301483 + 0.953472i \(0.402518\pi\)
−0.976472 + 0.215644i \(0.930815\pi\)
\(558\) 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 0.283454 0.958986i \(-0.408520\pi\)
0.688779 0.724972i \(-0.258147\pi\)
\(564\) 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 0.985973 0.166907i \(-0.0533780\pi\)
−0.637532 + 0.770424i \(0.720045\pi\)
\(570\) 0 0
\(571\) 18.2532 31.6155i 0.763874 1.32307i −0.176966 0.984217i \(-0.556628\pi\)
0.940840 0.338852i \(-0.110038\pi\)
\(572\) 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 −0.663662 0.748032i \(-0.730999\pi\)
0.979646 + 0.200732i \(0.0643321\pi\)
\(578\) 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 \(-0.554173\pi\)
−0.169368 + 0.985553i \(0.554173\pi\)
\(588\) 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 0.917421 0.397918i \(-0.130267\pi\)
−0.803318 + 0.595550i \(0.796934\pi\)
\(594\) 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 0.231139 + 0.972921i \(0.425755\pi\)
−0.958143 + 0.286288i \(0.907578\pi\)
\(600\) 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 0.963635 0.267223i \(-0.0861061\pi\)
−0.713239 + 0.700920i \(0.752773\pi\)
\(608\) 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 \(-0.693287\pi\)
0.996505 + 0.0835312i \(0.0266198\pi\)
\(614\) 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 \(-0.954122\pi\)
0.619203 + 0.785231i \(0.287456\pi\)
\(620\) 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 −0.100005 + 0.994987i \(0.531886\pi\)
−0.811681 + 0.584100i \(0.801447\pi\)
\(642\) 0 0
\(643\) 31.0555 1.22471 0.612355 0.790583i \(-0.290222\pi\)
0.612355 + 0.790583i \(0.290222\pi\)
\(644\) 0 0
\(645\) 4.90981 0.193324
\(646\) 0 0
\(647\) 8.51854 14.7545i 0.334898 0.580061i −0.648567 0.761158i \(-0.724631\pi\)
0.983465 + 0.181097i \(0.0579647\pi\)
\(648\) 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 \(-0.115756\pi\)
−0.775343 + 0.631541i \(0.782423\pi\)
\(654\) 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 \(-0.204362\pi\)
0.800887 + 0.598815i \(0.204362\pi\)
\(660\) 0 0
\(661\) 6.67105 11.5546i 0.259474 0.449422i −0.706627 0.707586i \(-0.749784\pi\)
0.966101 + 0.258164i \(0.0831175\pi\)
\(662\) 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 −0.988796 0.149272i \(-0.952307\pi\)
0.365124 0.930959i \(-0.381026\pi\)
\(678\) 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 −0.258666 0.965967i \(-0.583283\pi\)
0.965885 0.258973i \(-0.0833839\pi\)
\(684\) 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 \(-0.0792845\pi\)
−0.698056 + 0.716044i \(0.745951\pi\)
\(692\) 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 \(-0.922565\pi\)
−0.970556 + 0.240876i \(0.922565\pi\)
\(702\) 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 \(-0.323381\pi\)
−0.999511 + 0.0312621i \(0.990047\pi\)
\(710\) 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 0.932160 0.362047i \(-0.117922\pi\)
−0.779622 + 0.626251i \(0.784589\pi\)
\(720\) 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 \(-0.0368931\pi\)
−0.596796 + 0.802393i \(0.703560\pi\)
\(734\) 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 \(-0.841192\pi\)
0.853419 + 0.521226i \(0.174525\pi\)
\(740\) 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 0.724180 0.689611i \(-0.242218\pi\)
−0.959311 + 0.282353i \(0.908885\pi\)
\(752\) 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 \(-0.659209\pi\)
−0.479575 + 0.877501i \(0.659209\pi\)
\(758\) 0 0
\(759\) 8.42835 14.5983i 0.305930 0.529886i
\(760\) 0 0
\(761\) −15.2214 26.3643i −0.551776 0.955704i −0.998147 0.0608556i \(-0.980617\pi\)
0.446371 0.894848i \(-0.352716\pi\)
\(762\) 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 0.289877 + 0.957064i \(0.406386\pi\)
−0.973780 + 0.227491i \(0.926948\pi\)
\(774\) 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 0.434274 + 0.900781i \(0.357005\pi\)
−0.997236 + 0.0742978i \(0.976328\pi\)
\(788\) 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 1.60154 0.800768 0.598974i \(-0.204425\pi\)
0.800768 + 0.598974i \(0.204425\pi\)
\(798\)