Properties

Label 1520.2.q.j.961.3
Level $1520$
Weight $2$
Character 1520.961
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3518667.1
Defining polynomial: \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.3
Root \(1.14257 - 1.97899i\) of defining polynomial
Character \(\chi\) \(=\) 1520.961
Dual form 1520.2.q.j.881.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.14257 - 1.97899i) q^{3} +(0.500000 - 0.866025i) q^{5} +1.28514 q^{7} +(-1.11094 - 1.92420i) q^{9} +O(q^{10})\) \(q+(1.14257 - 1.97899i) q^{3} +(0.500000 - 0.866025i) q^{5} +1.28514 q^{7} +(-1.11094 - 1.92420i) q^{9} -0.285142 q^{11} +(2.50000 + 4.33013i) q^{13} +(-1.14257 - 1.97899i) q^{15} +(3.11796 - 5.40046i) q^{17} +(-2.92771 - 3.22932i) q^{19} +(1.46837 - 2.54329i) q^{21} +(-2.61796 - 4.53443i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.77812 q^{27} +(-0.642571 - 1.11297i) q^{29} +1.22188 q^{31} +(-0.325796 + 0.564295i) q^{33} +(0.642571 - 1.11297i) q^{35} +10.8695 q^{37} +11.4257 q^{39} +(0.420695 - 0.728665i) q^{41} +(-2.47539 + 4.28749i) q^{43} -2.22188 q^{45} +(2.86445 + 4.96137i) q^{47} -5.34841 q^{49} +(-7.12498 - 12.3408i) q^{51} +(-6.18122 - 10.7062i) q^{53} +(-0.142571 + 0.246941i) q^{55} +(-9.73591 + 2.10419i) q^{57} +(2.86445 - 4.96137i) q^{59} +(-2.22889 - 3.86056i) q^{61} +(-1.42771 - 2.47287i) q^{63} +5.00000 q^{65} +(-0.492981 - 0.853869i) q^{67} -11.9648 q^{69} +(-1.46135 + 2.53113i) q^{71} +(0.382043 - 0.661718i) q^{73} -2.28514 q^{75} -0.366449 q^{77} +(-7.72889 + 13.3868i) q^{79} +(5.36445 - 9.29150i) q^{81} -1.66563 q^{83} +(-3.11796 - 5.40046i) q^{85} -2.93673 q^{87} +(8.01404 + 13.8807i) q^{89} +(3.21286 + 5.56483i) q^{91} +(1.39608 - 2.41808i) q^{93} +(-4.26053 + 0.920816i) q^{95} +(-5.87147 + 10.1697i) q^{97} +(0.316776 + 0.548672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9} + 10 q^{11} + 15 q^{13} - q^{15} - q^{17} + 12 q^{21} + 4 q^{23} - 3 q^{25} + 16 q^{27} + 2 q^{29} + 2 q^{31} - 11 q^{33} - 2 q^{35} - 4 q^{37} + 10 q^{39} + 2 q^{41} - q^{43} - 8 q^{45} + 6 q^{47} - 14 q^{49} - 6 q^{51} - 11 q^{53} + 5 q^{55} - 19 q^{57} + 6 q^{59} + 9 q^{61} + 9 q^{63} + 30 q^{65} - 20 q^{67} - 10 q^{69} - 29 q^{71} + 22 q^{73} - 2 q^{75} - 32 q^{77} - 24 q^{79} + 21 q^{81} + 6 q^{83} + q^{85} - 24 q^{87} + 14 q^{89} - 10 q^{91} - 6 q^{93} - 7 q^{97} - 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.14257 1.97899i 0.659664 1.14257i −0.321039 0.947066i \(-0.604032\pi\)
0.980703 0.195505i \(-0.0626347\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.28514 0.485738 0.242869 0.970059i \(-0.421911\pi\)
0.242869 + 0.970059i \(0.421911\pi\)
\(8\) 0 0
\(9\) −1.11094 1.92420i −0.370313 0.641400i
\(10\) 0 0
\(11\) −0.285142 −0.0859737 −0.0429868 0.999076i \(-0.513687\pi\)
−0.0429868 + 0.999076i \(0.513687\pi\)
\(12\) 0 0
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −1.14257 1.97899i −0.295011 0.510973i
\(16\) 0 0
\(17\) 3.11796 5.40046i 0.756216 1.30980i −0.188552 0.982063i \(-0.560379\pi\)
0.944768 0.327741i \(-0.106287\pi\)
\(18\) 0 0
\(19\) −2.92771 3.22932i −0.671664 0.740856i
\(20\) 0 0
\(21\) 1.46837 2.54329i 0.320424 0.554990i
\(22\) 0 0
\(23\) −2.61796 4.53443i −0.545882 0.945495i −0.998551 0.0538163i \(-0.982861\pi\)
0.452669 0.891679i \(-0.350472\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 1.77812 0.342200
\(28\) 0 0
\(29\) −0.642571 1.11297i −0.119322 0.206673i 0.800177 0.599764i \(-0.204739\pi\)
−0.919499 + 0.393091i \(0.871406\pi\)
\(30\) 0 0
\(31\) 1.22188 0.219455 0.109728 0.993962i \(-0.465002\pi\)
0.109728 + 0.993962i \(0.465002\pi\)
\(32\) 0 0
\(33\) −0.325796 + 0.564295i −0.0567137 + 0.0982311i
\(34\) 0 0
\(35\) 0.642571 1.11297i 0.108614 0.188126i
\(36\) 0 0
\(37\) 10.8695 1.78693 0.893464 0.449134i \(-0.148267\pi\)
0.893464 + 0.449134i \(0.148267\pi\)
\(38\) 0 0
\(39\) 11.4257 1.82958
\(40\) 0 0
\(41\) 0.420695 0.728665i 0.0657015 0.113798i −0.831303 0.555819i \(-0.812405\pi\)
0.897005 + 0.442020i \(0.145738\pi\)
\(42\) 0 0
\(43\) −2.47539 + 4.28749i −0.377493 + 0.653837i −0.990697 0.136088i \(-0.956547\pi\)
0.613204 + 0.789925i \(0.289880\pi\)
\(44\) 0 0
\(45\) −2.22188 −0.331218
\(46\) 0 0
\(47\) 2.86445 + 4.96137i 0.417823 + 0.723690i 0.995720 0.0924193i \(-0.0294600\pi\)
−0.577898 + 0.816109i \(0.696127\pi\)
\(48\) 0 0
\(49\) −5.34841 −0.764058
\(50\) 0 0
\(51\) −7.12498 12.3408i −0.997696 1.72806i
\(52\) 0 0
\(53\) −6.18122 10.7062i −0.849056 1.47061i −0.882051 0.471153i \(-0.843838\pi\)
0.0329952 0.999456i \(-0.489495\pi\)
\(54\) 0 0
\(55\) −0.142571 + 0.246941i −0.0192243 + 0.0332975i
\(56\) 0 0
\(57\) −9.73591 + 2.10419i −1.28955 + 0.278707i
\(58\) 0 0
\(59\) 2.86445 4.96137i 0.372919 0.645915i −0.617094 0.786889i \(-0.711690\pi\)
0.990013 + 0.140974i \(0.0450235\pi\)
\(60\) 0 0
\(61\) −2.22889 3.86056i −0.285381 0.494294i 0.687321 0.726354i \(-0.258787\pi\)
−0.972701 + 0.232060i \(0.925453\pi\)
\(62\) 0 0
\(63\) −1.42771 2.47287i −0.179875 0.311553i
\(64\) 0 0
\(65\) 5.00000 0.620174
\(66\) 0 0
\(67\) −0.492981 0.853869i −0.0602273 0.104317i 0.834340 0.551251i \(-0.185849\pi\)
−0.894567 + 0.446934i \(0.852516\pi\)
\(68\) 0 0
\(69\) −11.9648 −1.44039
\(70\) 0 0
\(71\) −1.46135 + 2.53113i −0.173430 + 0.300390i −0.939617 0.342228i \(-0.888818\pi\)
0.766187 + 0.642618i \(0.222152\pi\)
\(72\) 0 0
\(73\) 0.382043 0.661718i 0.0447148 0.0774483i −0.842802 0.538224i \(-0.819095\pi\)
0.887517 + 0.460776i \(0.152429\pi\)
\(74\) 0 0
\(75\) −2.28514 −0.263866
\(76\) 0 0
\(77\) −0.366449 −0.0417607
\(78\) 0 0
\(79\) −7.72889 + 13.3868i −0.869569 + 1.50614i −0.00713043 + 0.999975i \(0.502270\pi\)
−0.862438 + 0.506162i \(0.831064\pi\)
\(80\) 0 0
\(81\) 5.36445 9.29150i 0.596050 1.03239i
\(82\) 0 0
\(83\) −1.66563 −0.182826 −0.0914132 0.995813i \(-0.529138\pi\)
−0.0914132 + 0.995813i \(0.529138\pi\)
\(84\) 0 0
\(85\) −3.11796 5.40046i −0.338190 0.585762i
\(86\) 0 0
\(87\) −2.93673 −0.314851
\(88\) 0 0
\(89\) 8.01404 + 13.8807i 0.849486 + 1.47135i 0.881667 + 0.471871i \(0.156421\pi\)
−0.0321812 + 0.999482i \(0.510245\pi\)
\(90\) 0 0
\(91\) 3.21286 + 5.56483i 0.336799 + 0.583353i
\(92\) 0 0
\(93\) 1.39608 2.41808i 0.144767 0.250743i
\(94\) 0 0
\(95\) −4.26053 + 0.920816i −0.437121 + 0.0944737i
\(96\) 0 0
\(97\) −5.87147 + 10.1697i −0.596157 + 1.03257i 0.397225 + 0.917721i \(0.369973\pi\)
−0.993382 + 0.114853i \(0.963360\pi\)
\(98\) 0 0
\(99\) 0.316776 + 0.548672i 0.0318371 + 0.0551436i
\(100\) 0 0
\(101\) 3.95935 + 6.85779i 0.393970 + 0.682376i 0.992969 0.118374i \(-0.0377681\pi\)
−0.598999 + 0.800750i \(0.704435\pi\)
\(102\) 0 0
\(103\) 12.8202 1.26322 0.631608 0.775288i \(-0.282395\pi\)
0.631608 + 0.775288i \(0.282395\pi\)
\(104\) 0 0
\(105\) −1.46837 2.54329i −0.143298 0.248199i
\(106\) 0 0
\(107\) −13.8062 −1.33470 −0.667348 0.744746i \(-0.732571\pi\)
−0.667348 + 0.744746i \(0.732571\pi\)
\(108\) 0 0
\(109\) 4.60192 7.97076i 0.440784 0.763460i −0.556964 0.830537i \(-0.688034\pi\)
0.997748 + 0.0670767i \(0.0213672\pi\)
\(110\) 0 0
\(111\) 12.4191 21.5106i 1.17877 2.04169i
\(112\) 0 0
\(113\) −17.3273 −1.63001 −0.815005 0.579453i \(-0.803266\pi\)
−0.815005 + 0.579453i \(0.803266\pi\)
\(114\) 0 0
\(115\) −5.23591 −0.488251
\(116\) 0 0
\(117\) 5.55469 9.62101i 0.513531 0.889462i
\(118\) 0 0
\(119\) 4.00702 6.94036i 0.367323 0.636222i
\(120\) 0 0
\(121\) −10.9187 −0.992609
\(122\) 0 0
\(123\) −0.961348 1.66510i −0.0866818 0.150137i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.66563 + 8.08111i 0.414008 + 0.717082i 0.995324 0.0965956i \(-0.0307954\pi\)
−0.581316 + 0.813678i \(0.697462\pi\)
\(128\) 0 0
\(129\) 5.65661 + 9.79753i 0.498037 + 0.862625i
\(130\) 0 0
\(131\) 6.21286 10.7610i 0.542820 0.940191i −0.455921 0.890020i \(-0.650690\pi\)
0.998741 0.0501711i \(-0.0159767\pi\)
\(132\) 0 0
\(133\) −3.76253 4.15013i −0.326253 0.359862i
\(134\) 0 0
\(135\) 0.889062 1.53990i 0.0765183 0.132534i
\(136\) 0 0
\(137\) 9.26755 + 16.0519i 0.791780 + 1.37140i 0.924864 + 0.380298i \(0.124179\pi\)
−0.133084 + 0.991105i \(0.542488\pi\)
\(138\) 0 0
\(139\) −3.00702 5.20831i −0.255052 0.441763i 0.709858 0.704345i \(-0.248759\pi\)
−0.964910 + 0.262582i \(0.915426\pi\)
\(140\) 0 0
\(141\) 13.0913 1.10249
\(142\) 0 0
\(143\) −0.712856 1.23470i −0.0596120 0.103251i
\(144\) 0 0
\(145\) −1.28514 −0.106725
\(146\) 0 0
\(147\) −6.11094 + 10.5845i −0.504022 + 0.872991i
\(148\) 0 0
\(149\) 3.39608 5.88218i 0.278218 0.481887i −0.692724 0.721203i \(-0.743590\pi\)
0.970942 + 0.239315i \(0.0769230\pi\)
\(150\) 0 0
\(151\) 15.8875 1.29291 0.646453 0.762953i \(-0.276251\pi\)
0.646453 + 0.762953i \(0.276251\pi\)
\(152\) 0 0
\(153\) −13.8554 −1.12014
\(154\) 0 0
\(155\) 0.610938 1.05818i 0.0490717 0.0849947i
\(156\) 0 0
\(157\) −3.75351 + 6.50127i −0.299563 + 0.518858i −0.976036 0.217609i \(-0.930174\pi\)
0.676473 + 0.736467i \(0.263507\pi\)
\(158\) 0 0
\(159\) −28.2500 −2.24037
\(160\) 0 0
\(161\) −3.36445 5.82739i −0.265156 0.459263i
\(162\) 0 0
\(163\) −21.8202 −1.70909 −0.854546 0.519375i \(-0.826165\pi\)
−0.854546 + 0.519375i \(0.826165\pi\)
\(164\) 0 0
\(165\) 0.325796 + 0.564295i 0.0253632 + 0.0439303i
\(166\) 0 0
\(167\) 5.64257 + 9.77322i 0.436635 + 0.756274i 0.997428 0.0716821i \(-0.0228367\pi\)
−0.560792 + 0.827957i \(0.689503\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) −2.96135 + 9.22108i −0.226460 + 0.705154i
\(172\) 0 0
\(173\) 2.92771 5.07095i 0.222590 0.385537i −0.733004 0.680225i \(-0.761882\pi\)
0.955594 + 0.294688i \(0.0952156\pi\)
\(174\) 0 0
\(175\) −0.642571 1.11297i −0.0485738 0.0841323i
\(176\) 0 0
\(177\) −6.54567 11.3374i −0.492003 0.852174i
\(178\) 0 0
\(179\) 18.7922 1.40459 0.702296 0.711885i \(-0.252158\pi\)
0.702296 + 0.711885i \(0.252158\pi\)
\(180\) 0 0
\(181\) −6.67265 11.5574i −0.495974 0.859052i 0.504015 0.863695i \(-0.331856\pi\)
−0.999989 + 0.00464265i \(0.998522\pi\)
\(182\) 0 0
\(183\) −10.1867 −0.753021
\(184\) 0 0
\(185\) 5.43473 9.41323i 0.399569 0.692075i
\(186\) 0 0
\(187\) −0.889062 + 1.53990i −0.0650146 + 0.112609i
\(188\) 0 0
\(189\) 2.28514 0.166220
\(190\) 0 0
\(191\) 0.668743 0.0483885 0.0241943 0.999707i \(-0.492298\pi\)
0.0241943 + 0.999707i \(0.492298\pi\)
\(192\) 0 0
\(193\) 1.88204 3.25979i 0.135472 0.234645i −0.790305 0.612713i \(-0.790078\pi\)
0.925778 + 0.378068i \(0.123411\pi\)
\(194\) 0 0
\(195\) 5.71286 9.89496i 0.409106 0.708593i
\(196\) 0 0
\(197\) 14.6164 1.04138 0.520688 0.853747i \(-0.325676\pi\)
0.520688 + 0.853747i \(0.325676\pi\)
\(198\) 0 0
\(199\) 5.76053 + 9.97753i 0.408353 + 0.707288i 0.994705 0.102768i \(-0.0327699\pi\)
−0.586352 + 0.810056i \(0.699437\pi\)
\(200\) 0 0
\(201\) −2.25307 −0.158919
\(202\) 0 0
\(203\) −0.825796 1.43032i −0.0579595 0.100389i
\(204\) 0 0
\(205\) −0.420695 0.728665i −0.0293826 0.0508922i
\(206\) 0 0
\(207\) −5.81678 + 10.0750i −0.404294 + 0.700257i
\(208\) 0 0
\(209\) 0.834816 + 0.920816i 0.0577454 + 0.0636941i
\(210\) 0 0
\(211\) −8.57028 + 14.8442i −0.590003 + 1.02191i 0.404229 + 0.914658i \(0.367540\pi\)
−0.994231 + 0.107257i \(0.965793\pi\)
\(212\) 0 0
\(213\) 3.33939 + 5.78399i 0.228811 + 0.396313i
\(214\) 0 0
\(215\) 2.47539 + 4.28749i 0.168820 + 0.292405i
\(216\) 0 0
\(217\) 1.57028 0.106598
\(218\) 0 0
\(219\) −0.873023 1.51212i −0.0589934 0.102180i
\(220\) 0 0
\(221\) 31.1796 2.09736
\(222\) 0 0
\(223\) 0.762085 1.31997i 0.0510330 0.0883918i −0.839380 0.543544i \(-0.817082\pi\)
0.890413 + 0.455153i \(0.150415\pi\)
\(224\) 0 0
\(225\) −1.11094 + 1.92420i −0.0740625 + 0.128280i
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 18.4397 1.21853 0.609266 0.792966i \(-0.291464\pi\)
0.609266 + 0.792966i \(0.291464\pi\)
\(230\) 0 0
\(231\) −0.418694 + 0.725199i −0.0275480 + 0.0477146i
\(232\) 0 0
\(233\) −6.35587 + 11.0087i −0.416387 + 0.721203i −0.995573 0.0939920i \(-0.970037\pi\)
0.579186 + 0.815195i \(0.303371\pi\)
\(234\) 0 0
\(235\) 5.72889 0.373712
\(236\) 0 0
\(237\) 17.6616 + 30.5908i 1.14725 + 1.98709i
\(238\) 0 0
\(239\) 10.8343 0.700811 0.350405 0.936598i \(-0.386044\pi\)
0.350405 + 0.936598i \(0.386044\pi\)
\(240\) 0 0
\(241\) 4.93673 + 8.55067i 0.318003 + 0.550797i 0.980071 0.198646i \(-0.0636545\pi\)
−0.662068 + 0.749444i \(0.730321\pi\)
\(242\) 0 0
\(243\) −9.59134 16.6127i −0.615285 1.06570i
\(244\) 0 0
\(245\) −2.67420 + 4.63186i −0.170849 + 0.295919i
\(246\) 0 0
\(247\) 6.66407 20.7507i 0.424025 1.32033i
\(248\) 0 0
\(249\) −1.90310 + 3.29626i −0.120604 + 0.208892i
\(250\) 0 0
\(251\) 8.88550 + 15.3901i 0.560848 + 0.971417i 0.997423 + 0.0717492i \(0.0228581\pi\)
−0.436575 + 0.899668i \(0.643809\pi\)
\(252\) 0 0
\(253\) 0.746491 + 1.29296i 0.0469315 + 0.0812877i
\(254\) 0 0
\(255\) −14.2500 −0.892367
\(256\) 0 0
\(257\) −4.07930 7.06556i −0.254460 0.440738i 0.710289 0.703911i \(-0.248564\pi\)
−0.964749 + 0.263173i \(0.915231\pi\)
\(258\) 0 0
\(259\) 13.9688 0.867980
\(260\) 0 0
\(261\) −1.42771 + 2.47287i −0.0883733 + 0.153067i
\(262\) 0 0
\(263\) 3.15861 5.47087i 0.194768 0.337348i −0.752056 0.659099i \(-0.770938\pi\)
0.946825 + 0.321750i \(0.104271\pi\)
\(264\) 0 0
\(265\) −12.3624 −0.759419
\(266\) 0 0
\(267\) 36.6264 2.24150
\(268\) 0 0
\(269\) −4.11951 + 7.13521i −0.251171 + 0.435041i −0.963849 0.266451i \(-0.914149\pi\)
0.712677 + 0.701492i \(0.247482\pi\)
\(270\) 0 0
\(271\) −2.11094 + 3.65625i −0.128230 + 0.222101i −0.922991 0.384821i \(-0.874263\pi\)
0.794761 + 0.606923i \(0.207596\pi\)
\(272\) 0 0
\(273\) 14.6837 0.888696
\(274\) 0 0
\(275\) 0.142571 + 0.246941i 0.00859737 + 0.0148911i
\(276\) 0 0
\(277\) −9.83739 −0.591071 −0.295536 0.955332i \(-0.595498\pi\)
−0.295536 + 0.955332i \(0.595498\pi\)
\(278\) 0 0
\(279\) −1.35743 2.35114i −0.0812671 0.140759i
\(280\) 0 0
\(281\) −2.69024 4.65964i −0.160486 0.277971i 0.774557 0.632504i \(-0.217973\pi\)
−0.935043 + 0.354534i \(0.884640\pi\)
\(282\) 0 0
\(283\) −2.48240 + 4.29965i −0.147564 + 0.255588i −0.930326 0.366732i \(-0.880476\pi\)
0.782763 + 0.622320i \(0.213810\pi\)
\(284\) 0 0
\(285\) −3.04567 + 9.48365i −0.180410 + 0.561763i
\(286\) 0 0
\(287\) 0.540653 0.936439i 0.0319137 0.0552762i
\(288\) 0 0
\(289\) −10.9433 18.9544i −0.643724 1.11496i
\(290\) 0 0
\(291\) 13.4171 + 23.2392i 0.786526 + 1.36230i
\(292\) 0 0
\(293\) −3.80620 −0.222360 −0.111180 0.993800i \(-0.535463\pi\)
−0.111180 + 0.993800i \(0.535463\pi\)
\(294\) 0 0
\(295\) −2.86445 4.96137i −0.166775 0.288862i
\(296\) 0 0
\(297\) −0.507019 −0.0294202
\(298\) 0 0
\(299\) 13.0898 22.6722i 0.757002 1.31117i
\(300\) 0 0
\(301\) −3.18122 + 5.51004i −0.183363 + 0.317593i
\(302\) 0 0
\(303\) 18.0953 1.03955
\(304\) 0 0
\(305\) −4.45779 −0.255252
\(306\) 0 0
\(307\) 0.287144 0.497348i 0.0163882 0.0283851i −0.857715 0.514125i \(-0.828117\pi\)
0.874103 + 0.485740i \(0.161450\pi\)
\(308\) 0 0
\(309\) 14.6480 25.3711i 0.833297 1.44331i
\(310\) 0 0
\(311\) 8.61640 0.488591 0.244296 0.969701i \(-0.421443\pi\)
0.244296 + 0.969701i \(0.421443\pi\)
\(312\) 0 0
\(313\) 17.0617 + 29.5517i 0.964385 + 1.67036i 0.711259 + 0.702930i \(0.248125\pi\)
0.253126 + 0.967433i \(0.418541\pi\)
\(314\) 0 0
\(315\) −2.85543 −0.160885
\(316\) 0 0
\(317\) 5.53865 + 9.59323i 0.311082 + 0.538809i 0.978597 0.205787i \(-0.0659754\pi\)
−0.667515 + 0.744596i \(0.732642\pi\)
\(318\) 0 0
\(319\) 0.183224 + 0.317354i 0.0102586 + 0.0177684i
\(320\) 0 0
\(321\) −15.7746 + 27.3223i −0.880450 + 1.52498i
\(322\) 0 0
\(323\) −26.5683 + 5.74213i −1.47830 + 0.319500i
\(324\) 0 0
\(325\) 2.50000 4.33013i 0.138675 0.240192i
\(326\) 0 0
\(327\) −10.5160 18.2143i −0.581538 1.00725i
\(328\) 0 0
\(329\) 3.68122 + 6.37607i 0.202952 + 0.351524i
\(330\) 0 0
\(331\) −6.41168 −0.352418 −0.176209 0.984353i \(-0.556383\pi\)
−0.176209 + 0.984353i \(0.556383\pi\)
\(332\) 0 0
\(333\) −12.0753 20.9150i −0.661722 1.14614i
\(334\) 0 0
\(335\) −0.985963 −0.0538689
\(336\) 0 0
\(337\) 12.6336 21.8820i 0.688193 1.19199i −0.284228 0.958757i \(-0.591737\pi\)
0.972422 0.233229i \(-0.0749293\pi\)
\(338\) 0 0
\(339\) −19.7976 + 34.2905i −1.07526 + 1.86240i
\(340\) 0 0
\(341\) −0.348409 −0.0188674
\(342\) 0 0
\(343\) −15.8695 −0.856871
\(344\) 0 0
\(345\) −5.98240 + 10.3618i −0.322082 + 0.557862i
\(346\) 0 0
\(347\) 6.20428 10.7461i 0.333063 0.576882i −0.650048 0.759893i \(-0.725251\pi\)
0.983111 + 0.183011i \(0.0585844\pi\)
\(348\) 0 0
\(349\) 6.20384 0.332084 0.166042 0.986119i \(-0.446901\pi\)
0.166042 + 0.986119i \(0.446901\pi\)
\(350\) 0 0
\(351\) 4.44531 + 7.69950i 0.237273 + 0.410969i
\(352\) 0 0
\(353\) −23.3484 −1.24271 −0.621355 0.783529i \(-0.713418\pi\)
−0.621355 + 0.783529i \(0.713418\pi\)
\(354\) 0 0
\(355\) 1.46135 + 2.53113i 0.0775603 + 0.134338i
\(356\) 0 0
\(357\) −9.15661 15.8597i −0.484619 0.839385i
\(358\) 0 0
\(359\) −18.8609 + 32.6680i −0.995440 + 1.72415i −0.415107 + 0.909773i \(0.636256\pi\)
−0.580333 + 0.814379i \(0.697078\pi\)
\(360\) 0 0
\(361\) −1.85698 + 18.9090i −0.0977360 + 0.995212i
\(362\) 0 0
\(363\) −12.4754 + 21.6080i −0.654788 + 1.13413i
\(364\) 0 0
\(365\) −0.382043 0.661718i −0.0199971 0.0346359i
\(366\) 0 0
\(367\) 14.7038 + 25.4678i 0.767534 + 1.32941i 0.938896 + 0.344200i \(0.111850\pi\)
−0.171362 + 0.985208i \(0.554817\pi\)
\(368\) 0 0
\(369\) −1.86946 −0.0973204
\(370\) 0 0
\(371\) −7.94375 13.7590i −0.412419 0.714331i
\(372\) 0 0
\(373\) −21.5491 −1.11577 −0.557886 0.829918i \(-0.688387\pi\)
−0.557886 + 0.829918i \(0.688387\pi\)
\(374\) 0 0
\(375\) −1.14257 + 1.97899i −0.0590021 + 0.102195i
\(376\) 0 0
\(377\) 3.21286 5.56483i 0.165471 0.286603i
\(378\) 0 0
\(379\) 19.3945 0.996230 0.498115 0.867111i \(-0.334026\pi\)
0.498115 + 0.867111i \(0.334026\pi\)
\(380\) 0 0
\(381\) 21.3233 1.09242
\(382\) 0 0
\(383\) 9.44331 16.3563i 0.482531 0.835767i −0.517268 0.855823i \(-0.673051\pi\)
0.999799 + 0.0200559i \(0.00638442\pi\)
\(384\) 0 0
\(385\) −0.183224 + 0.317354i −0.00933798 + 0.0161739i
\(386\) 0 0
\(387\) 11.0000 0.559161
\(388\) 0 0
\(389\) 4.54021 + 7.86387i 0.230198 + 0.398714i 0.957866 0.287215i \(-0.0927294\pi\)
−0.727668 + 0.685929i \(0.759396\pi\)
\(390\) 0 0
\(391\) −32.6507 −1.65122
\(392\) 0 0
\(393\) −14.1973 24.5904i −0.716157 1.24042i
\(394\) 0 0
\(395\) 7.72889 + 13.3868i 0.388883 + 0.673565i
\(396\) 0 0
\(397\) −8.49800 + 14.7190i −0.426502 + 0.738724i −0.996559 0.0828814i \(-0.973588\pi\)
0.570057 + 0.821605i \(0.306921\pi\)
\(398\) 0 0
\(399\) −12.5120 + 2.70419i −0.626385 + 0.135379i
\(400\) 0 0
\(401\) −0.795720 + 1.37823i −0.0397363 + 0.0688254i −0.885210 0.465192i \(-0.845985\pi\)
0.845473 + 0.534018i \(0.179318\pi\)
\(402\) 0 0
\(403\) 3.05469 + 5.29088i 0.152165 + 0.263557i
\(404\) 0 0
\(405\) −5.36445 9.29150i −0.266562 0.461698i
\(406\) 0 0
\(407\) −3.09935 −0.153629
\(408\) 0 0
\(409\) 0.998443 + 1.72935i 0.0493698 + 0.0855110i 0.889654 0.456635i \(-0.150945\pi\)
−0.840284 + 0.542146i \(0.817612\pi\)
\(410\) 0 0
\(411\) 42.3553 2.08923
\(412\) 0 0
\(413\) 3.68122 6.37607i 0.181141 0.313746i
\(414\) 0 0
\(415\) −0.832814 + 1.44248i −0.0408812 + 0.0708084i
\(416\) 0 0
\(417\) −13.7429 −0.672994
\(418\) 0 0
\(419\) 22.7781 1.11278 0.556392 0.830920i \(-0.312185\pi\)
0.556392 + 0.830920i \(0.312185\pi\)
\(420\) 0 0
\(421\) 6.92070 11.9870i 0.337294 0.584210i −0.646629 0.762805i \(-0.723822\pi\)
0.983923 + 0.178594i \(0.0571550\pi\)
\(422\) 0 0
\(423\) 6.36445 11.0235i 0.309450 0.535983i
\(424\) 0 0
\(425\) −6.23591 −0.302486
\(426\) 0 0
\(427\) −2.86445 4.96137i −0.138620 0.240097i
\(428\) 0 0
\(429\) −3.25796 −0.157296
\(430\) 0 0
\(431\) 1.71987 + 2.97891i 0.0828435 + 0.143489i 0.904470 0.426537i \(-0.140267\pi\)
−0.821627 + 0.570026i \(0.806933\pi\)
\(432\) 0 0
\(433\) 4.60036 + 7.96806i 0.221079 + 0.382920i 0.955136 0.296168i \(-0.0957087\pi\)
−0.734057 + 0.679088i \(0.762375\pi\)
\(434\) 0 0
\(435\) −1.46837 + 2.54329i −0.0704028 + 0.121941i
\(436\) 0 0
\(437\) −6.97850 + 21.7297i −0.333827 + 1.03947i
\(438\) 0 0
\(439\) −18.7550 + 32.4846i −0.895126 + 1.55040i −0.0614769 + 0.998109i \(0.519581\pi\)
−0.833649 + 0.552295i \(0.813752\pi\)
\(440\) 0 0
\(441\) 5.94175 + 10.2914i 0.282941 + 0.490067i
\(442\) 0 0
\(443\) 7.33939 + 12.7122i 0.348705 + 0.603975i 0.986020 0.166629i \(-0.0532882\pi\)
−0.637315 + 0.770604i \(0.719955\pi\)
\(444\) 0 0
\(445\) 16.0281 0.759804
\(446\) 0 0
\(447\) −7.76053 13.4416i −0.367060 0.635767i
\(448\) 0 0
\(449\) −7.39052 −0.348780 −0.174390 0.984677i \(-0.555795\pi\)
−0.174390 + 0.984677i \(0.555795\pi\)
\(450\) 0 0
\(451\) −0.119958 + 0.207773i −0.00564860 + 0.00978367i
\(452\) 0 0
\(453\) 18.1526 31.4412i 0.852884 1.47724i
\(454\) 0 0
\(455\) 6.42571 0.301242
\(456\) 0 0
\(457\) 2.30007 0.107593 0.0537963 0.998552i \(-0.482868\pi\)
0.0537963 + 0.998552i \(0.482868\pi\)
\(458\) 0 0
\(459\) 5.54411 9.60269i 0.258777 0.448215i
\(460\) 0 0
\(461\) −9.87848 + 17.1100i −0.460087 + 0.796894i −0.998965 0.0454900i \(-0.985515\pi\)
0.538878 + 0.842384i \(0.318848\pi\)
\(462\) 0 0
\(463\) −28.9468 −1.34527 −0.672635 0.739974i \(-0.734838\pi\)
−0.672635 + 0.739974i \(0.734838\pi\)
\(464\) 0 0
\(465\) −1.39608 2.41808i −0.0647417 0.112136i
\(466\) 0 0
\(467\) 3.31722 0.153503 0.0767513 0.997050i \(-0.475545\pi\)
0.0767513 + 0.997050i \(0.475545\pi\)
\(468\) 0 0
\(469\) −0.633551 1.09734i −0.0292547 0.0506706i
\(470\) 0 0
\(471\) 8.57730 + 14.8563i 0.395221 + 0.684543i
\(472\) 0 0
\(473\) 0.705838 1.22255i 0.0324544 0.0562127i
\(474\) 0 0
\(475\) −1.33281 + 4.15013i −0.0611537 + 0.190421i
\(476\) 0 0
\(477\) −13.7339 + 23.7878i −0.628833 + 1.08917i
\(478\) 0 0
\(479\) −19.7535 34.2141i −0.902561 1.56328i −0.824158 0.566360i \(-0.808351\pi\)
−0.0784026 0.996922i \(-0.524982\pi\)
\(480\) 0 0
\(481\) 27.1737 + 47.0662i 1.23901 + 2.14603i
\(482\) 0 0
\(483\) −15.3765 −0.699654
\(484\) 0 0
\(485\) 5.87147 + 10.1697i 0.266610 + 0.461781i
\(486\) 0 0
\(487\) 24.7781 1.12280 0.561402 0.827543i \(-0.310262\pi\)
0.561402 + 0.827543i \(0.310262\pi\)
\(488\) 0 0
\(489\) −24.9312 + 43.1821i −1.12743 + 1.95276i
\(490\) 0 0
\(491\) −6.81176 + 11.7983i −0.307410 + 0.532450i −0.977795 0.209563i \(-0.932796\pi\)
0.670385 + 0.742014i \(0.266129\pi\)
\(492\) 0 0
\(493\) −8.01404 −0.360934
\(494\) 0 0
\(495\) 0.633551 0.0284760
\(496\) 0 0
\(497\) −1.87804 + 3.25286i −0.0842416 + 0.145911i
\(498\) 0 0
\(499\) 4.09490 7.09257i 0.183313 0.317507i −0.759694 0.650281i \(-0.774651\pi\)
0.943007 + 0.332774i \(0.107985\pi\)
\(500\) 0 0
\(501\) 25.7882 1.15213
\(502\) 0 0
\(503\) 9.14257 + 15.8354i 0.407647 + 0.706065i 0.994626 0.103537i \(-0.0330160\pi\)
−0.586978 + 0.809603i \(0.699683\pi\)
\(504\) 0 0
\(505\) 7.91869 0.352377
\(506\) 0 0
\(507\) 13.7109 + 23.7479i 0.608920 + 1.05468i
\(508\) 0 0
\(509\) −5.94220 10.2922i −0.263383 0.456193i 0.703756 0.710442i \(-0.251505\pi\)
−0.967139 + 0.254249i \(0.918172\pi\)
\(510\) 0 0
\(511\) 0.490980 0.850402i 0.0217197 0.0376196i
\(512\) 0 0
\(513\) −5.20584 5.74213i −0.229843 0.253521i
\(514\) 0 0
\(515\) 6.41012 11.1026i 0.282464 0.489241i
\(516\) 0 0
\(517\) −0.816776 1.41470i −0.0359218 0.0622183i
\(518\) 0 0
\(519\) −6.69024 11.5878i −0.293669 0.508650i
\(520\) 0 0
\(521\) 21.3725 0.936345 0.468173 0.883637i \(-0.344913\pi\)
0.468173 + 0.883637i \(0.344913\pi\)
\(522\) 0 0
\(523\) −2.88862 5.00323i −0.126310 0.218776i 0.795934 0.605383i \(-0.206980\pi\)
−0.922244 + 0.386607i \(0.873647\pi\)
\(524\) 0 0
\(525\) −2.93673 −0.128170
\(526\) 0 0
\(527\) 3.80976 6.59869i 0.165956 0.287444i
\(528\) 0 0
\(529\) −2.20739 + 3.82332i −0.0959737 + 0.166231i
\(530\) 0 0
\(531\) −12.7289 −0.552387
\(532\) 0 0
\(533\) 4.20695 0.182223
\(534\) 0 0
\(535\) −6.90310 + 11.9565i −0.298447 + 0.516925i
\(536\) 0 0
\(537\) 21.4714 37.1895i 0.926559 1.60485i
\(538\) 0 0
\(539\) 1.52506 0.0656889
\(540\) 0 0
\(541\) −1.31678 2.28072i −0.0566126 0.0980559i 0.836330 0.548226i \(-0.184697\pi\)
−0.892943 + 0.450170i \(0.851363\pi\)
\(542\) 0 0
\(543\) −30.4959 −1.30870
\(544\) 0 0
\(545\) −4.60192 7.97076i −0.197125 0.341430i
\(546\) 0 0
\(547\) −18.1812 31.4908i −0.777373 1.34645i −0.933451 0.358705i \(-0.883218\pi\)
0.156078 0.987745i \(-0.450115\pi\)
\(548\) 0 0
\(549\) −4.95233 + 8.57768i −0.211360 + 0.366087i
\(550\) 0 0
\(551\) −1.71286 + 5.33351i −0.0729701 + 0.227215i
\(552\) 0 0
\(553\) −9.93273 + 17.2040i −0.422383 + 0.731588i
\(554\) 0 0
\(555\) −12.4191 21.5106i −0.527163 0.913073i
\(556\) 0 0
\(557\) −11.9824 20.7541i −0.507711 0.879381i −0.999960 0.00892662i \(-0.997159\pi\)
0.492249 0.870454i \(-0.336175\pi\)
\(558\) 0 0
\(559\) −24.7539 −1.04698
\(560\) 0 0
\(561\) 2.03163 + 3.51889i 0.0857756 + 0.148568i
\(562\) 0 0
\(563\) 8.52017 0.359082 0.179541 0.983750i \(-0.442539\pi\)
0.179541 + 0.983750i \(0.442539\pi\)
\(564\) 0 0
\(565\) −8.66363 + 15.0058i −0.364482 + 0.631301i
\(566\) 0 0
\(567\) 6.89408 11.9409i 0.289524 0.501470i
\(568\) 0 0
\(569\) 16.3734 0.686407 0.343204 0.939261i \(-0.388488\pi\)
0.343204 + 0.939261i \(0.388488\pi\)
\(570\) 0 0
\(571\) 5.21876 0.218398 0.109199 0.994020i \(-0.465171\pi\)
0.109199 + 0.994020i \(0.465171\pi\)
\(572\) 0 0
\(573\) 0.764087 1.32344i 0.0319202 0.0552874i
\(574\) 0 0
\(575\) −2.61796 + 4.53443i −0.109176 + 0.189099i
\(576\) 0 0
\(577\) −32.0390 −1.33380 −0.666900 0.745147i \(-0.732379\pi\)
−0.666900 + 0.745147i \(0.732379\pi\)
\(578\) 0 0
\(579\) −4.30074 7.44910i −0.178733 0.309574i
\(580\) 0 0
\(581\) −2.14057 −0.0888058
\(582\) 0 0
\(583\) 1.76253 + 3.05279i 0.0729965 + 0.126434i
\(584\) 0 0
\(585\) −5.55469 9.62101i −0.229658 0.397780i
\(586\) 0 0
\(587\) −1.67220 + 2.89634i −0.0690192 + 0.119545i −0.898470 0.439035i \(-0.855320\pi\)
0.829451 + 0.558580i \(0.188654\pi\)
\(588\) 0 0
\(589\) −3.57730 3.94583i −0.147400 0.162585i
\(590\) 0 0
\(591\) 16.7003 28.9257i 0.686958 1.18985i
\(592\) 0 0
\(593\) −21.1054 36.5556i −0.866694 1.50116i −0.865355 0.501159i \(-0.832907\pi\)
−0.00133875 0.999999i \(-0.500426\pi\)
\(594\) 0 0
\(595\) −4.00702 6.94036i −0.164272 0.284527i
\(596\) 0 0
\(597\) 26.3273 1.07750
\(598\) 0 0
\(599\) −2.60938 4.51958i −0.106616 0.184665i 0.807781 0.589483i \(-0.200668\pi\)
−0.914397 + 0.404818i \(0.867335\pi\)
\(600\) 0 0
\(601\) −10.1546 −0.414215 −0.207108 0.978318i \(-0.566405\pi\)
−0.207108 + 0.978318i \(0.566405\pi\)
\(602\) 0 0
\(603\) −1.09534 + 1.89719i −0.0446058 + 0.0772596i
\(604\) 0 0
\(605\) −5.45935 + 9.45587i −0.221954 + 0.384436i
\(606\) 0 0
\(607\) −42.8764 −1.74030 −0.870149 0.492788i \(-0.835978\pi\)
−0.870149 + 0.492788i \(0.835978\pi\)
\(608\) 0 0
\(609\) −3.77412 −0.152935
\(610\) 0 0
\(611\) −14.3222 + 24.8068i −0.579416 + 1.00358i
\(612\) 0 0
\(613\) −12.5367 + 21.7141i −0.506351 + 0.877025i 0.493622 + 0.869676i \(0.335672\pi\)
−0.999973 + 0.00734857i \(0.997661\pi\)
\(614\) 0 0
\(615\) −1.92270 −0.0775306
\(616\) 0 0
\(617\) 2.74849 + 4.76053i 0.110650 + 0.191652i 0.916033 0.401104i \(-0.131373\pi\)
−0.805382 + 0.592756i \(0.798040\pi\)
\(618\) 0 0
\(619\) −15.4899 −0.622590 −0.311295 0.950313i \(-0.600763\pi\)
−0.311295 + 0.950313i \(0.600763\pi\)
\(620\) 0 0
\(621\) −4.65505 8.06279i −0.186801 0.323548i
\(622\) 0 0
\(623\) 10.2992 + 17.8387i 0.412628 + 0.714693i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 2.77612 0.599995i 0.110868 0.0239615i
\(628\) 0 0
\(629\) 33.8905 58.7001i 1.35130 2.34053i
\(630\) 0 0
\(631\) 20.6616 + 35.7870i 0.822526 + 1.42466i 0.903795 + 0.427965i \(0.140769\pi\)
−0.0812689 + 0.996692i \(0.525897\pi\)
\(632\) 0 0
\(633\) 19.5843 + 33.9210i 0.778407 + 1.34824i
\(634\) 0 0
\(635\) 9.33126 0.370300
\(636\) 0 0
\(637\) −13.3710 23.1593i −0.529779 0.917604i
\(638\) 0 0
\(639\) 6.49387 0.256894
\(640\) 0 0
\(641\) 15.3358 26.5624i 0.605729 1.04915i −0.386207 0.922412i \(-0.626215\pi\)
0.991936 0.126741i \(-0.0404517\pi\)
\(642\) 0 0
\(643\) −4.00902 + 6.94383i −0.158100 + 0.273838i −0.934184 0.356793i \(-0.883870\pi\)
0.776083 + 0.630630i \(0.217204\pi\)
\(644\) 0 0
\(645\) 11.3132 0.445457
\(646\) 0 0
\(647\) −10.0272 −0.394209 −0.197105 0.980382i \(-0.563154\pi\)
−0.197105 + 0.980382i \(0.563154\pi\)
\(648\) 0 0
\(649\) −0.816776 + 1.41470i −0.0320612 + 0.0555317i
\(650\) 0 0
\(651\) 1.79416 3.10758i 0.0703188 0.121796i
\(652\) 0 0
\(653\) 20.4117 0.798771 0.399385 0.916783i \(-0.369224\pi\)
0.399385 + 0.916783i \(0.369224\pi\)
\(654\) 0 0
\(655\) −6.21286 10.7610i −0.242756 0.420466i
\(656\) 0 0
\(657\) −1.69771 −0.0662338
\(658\) 0 0
\(659\) −18.4874 32.0212i −0.720168 1.24737i −0.960932 0.276783i \(-0.910732\pi\)
0.240765 0.970584i \(-0.422602\pi\)
\(660\) 0 0
\(661\) −1.59646 2.76514i −0.0620950 0.107552i 0.833307 0.552811i \(-0.186445\pi\)
−0.895402 + 0.445259i \(0.853112\pi\)
\(662\) 0 0
\(663\) 35.6249 61.7041i 1.38356 2.39639i
\(664\) 0 0
\(665\) −5.47539 + 1.18338i −0.212326 + 0.0458895i
\(666\) 0 0
\(667\) −3.36445 + 5.82739i −0.130272 + 0.225638i
\(668\) 0 0
\(669\) −1.74147 3.01632i −0.0673292 0.116618i
\(670\) 0 0
\(671\) 0.635553 + 1.10081i 0.0245352 + 0.0424963i
\(672\) 0 0
\(673\) −15.0742 −0.581067 −0.290534 0.956865i \(-0.593833\pi\)
−0.290534 + 0.956865i \(0.593833\pi\)
\(674\) 0 0
\(675\) −0.889062 1.53990i −0.0342200 0.0592708i
\(676\) 0 0
\(677\) 17.9648 0.690444 0.345222 0.938521i \(-0.387804\pi\)
0.345222 + 0.938521i \(0.387804\pi\)
\(678\) 0 0
\(679\) −7.54567 + 13.0695i −0.289576 + 0.501561i
\(680\) 0 0
\(681\) −4.57028 + 7.91597i −0.175134 + 0.303340i
\(682\) 0 0
\(683\) 3.78524 0.144838 0.0724191 0.997374i \(-0.476928\pi\)
0.0724191 + 0.997374i \(0.476928\pi\)
\(684\) 0 0
\(685\) 18.5351 0.708190
\(686\) 0 0
\(687\) 21.0687 36.4921i 0.803822 1.39226i
\(688\) 0 0
\(689\) 30.9061 53.5310i 1.17743 2.03937i
\(690\) 0 0
\(691\) 10.3335 0.393104 0.196552 0.980493i \(-0.437026\pi\)
0.196552 + 0.980493i \(0.437026\pi\)
\(692\) 0 0
\(693\) 0.407102 + 0.705121i 0.0154645 + 0.0267853i
\(694\) 0 0
\(695\) −6.01404 −0.228125
\(696\) 0 0
\(697\) −2.62342 4.54389i −0.0993690 0.172112i
\(698\) 0 0
\(699\) 14.5241 + 25.1564i 0.549351 + 0.951504i
\(700\) 0 0
\(701\) −17.9980 + 31.1734i −0.679775 + 1.17740i 0.295273 + 0.955413i \(0.404589\pi\)
−0.975048 + 0.221992i \(0.928744\pi\)
\(702\) 0 0
\(703\) −31.8227 35.1010i −1.20022 1.32386i
\(704\) 0 0
\(705\) 6.54567 11.3374i 0.246524 0.426992i
\(706\) 0 0
\(707\) 5.08832 + 8.81324i 0.191366 + 0.331456i
\(708\) 0 0
\(709\) −4.40266 7.62562i −0.165345 0.286386i 0.771433 0.636311i \(-0.219540\pi\)
−0.936778 + 0.349925i \(0.886207\pi\)
\(710\) 0 0
\(711\) 34.3453 1.28805
\(712\) 0 0
\(713\) −3.19882 5.54052i −0.119797 0.207494i
\(714\) 0 0
\(715\) −1.42571 −0.0533186
\(716\) 0 0
\(717\) 12.3789 21.4409i 0.462300 0.800726i
\(718\) 0 0
\(719\) 9.49600 16.4475i 0.354141 0.613390i −0.632830 0.774291i \(-0.718107\pi\)
0.986971 + 0.160901i \(0.0514400\pi\)
\(720\) 0 0
\(721\) 16.4758 0.613592
\(722\) 0 0
\(723\) 22.5623 0.839100
\(724\) 0 0
\(725\) −0.642571 + 1.11297i −0.0238645 + 0.0413345i
\(726\) 0 0
\(727\) 2.04567 3.54321i 0.0758697 0.131410i −0.825594 0.564264i \(-0.809160\pi\)
0.901464 + 0.432854i \(0.142493\pi\)
\(728\) 0 0
\(729\) −11.6485 −0.431425
\(730\) 0 0
\(731\) 15.4363 + 26.7364i 0.570932 + 0.988883i
\(732\) 0 0
\(733\) −50.4678 −1.86407 −0.932036 0.362366i \(-0.881969\pi\)
−0.932036 + 0.362366i \(0.881969\pi\)
\(734\) 0 0
\(735\) 6.11094 + 10.5845i 0.225405 + 0.390414i
\(736\) 0 0
\(737\) 0.140570 + 0.243474i 0.00517796 + 0.00896849i
\(738\) 0 0
\(739\) 17.1148 29.6438i 0.629580 1.09046i −0.358056 0.933700i \(-0.616560\pi\)
0.987636 0.156764i \(-0.0501062\pi\)
\(740\) 0 0
\(741\) −33.4512 36.8973i −1.22886 1.35545i
\(742\) 0 0
\(743\) 11.2996 19.5715i 0.414543 0.718010i −0.580837 0.814020i \(-0.697275\pi\)
0.995380 + 0.0960101i \(0.0306081\pi\)
\(744\) 0 0
\(745\) −3.39608 5.88218i −0.124423 0.215507i
\(746\) 0 0
\(747\) 1.85041 + 3.20500i 0.0677030 + 0.117265i
\(748\) 0 0
\(749\) −17.7429 −0.648313
\(750\) 0 0
\(751\) −12.7199 22.0315i −0.464155 0.803940i 0.535008 0.844847i \(-0.320309\pi\)
−0.999163 + 0.0409072i \(0.986975\pi\)
\(752\) 0 0
\(753\) 40.6093 1.47988
\(754\) 0 0
\(755\) 7.94375 13.7590i 0.289103 0.500741i
\(756\) 0 0
\(757\) −21.4015 + 37.0686i −0.777852 + 1.34728i 0.155325 + 0.987863i \(0.450357\pi\)
−0.933177 + 0.359416i \(0.882976\pi\)
\(758\) 0 0
\(759\) 3.41168 0.123836
\(760\) 0 0
\(761\) −29.8944 −1.08367 −0.541836 0.840484i \(-0.682271\pi\)
−0.541836 + 0.840484i \(0.682271\pi\)
\(762\) 0 0
\(763\) 5.91412 10.2436i 0.214106 0.370842i
\(764\) 0 0
\(765\) −6.92771 + 11.9992i −0.250472 + 0.433830i
\(766\) 0 0
\(767\) 28.6445 1.03429
\(768\) 0 0
\(769\) 8.32179 + 14.4138i 0.300092 + 0.519774i 0.976156 0.217068i \(-0.0696494\pi\)
−0.676065 + 0.736842i \(0.736316\pi\)
\(770\) 0 0
\(771\) −18.6436 −0.671432
\(772\) 0 0
\(773\) −3.05669 5.29435i −0.109942 0.190424i 0.805805 0.592181i \(-0.201733\pi\)
−0.915746 + 0.401757i \(0.868400\pi\)
\(774\) 0 0
\(775\) −0.610938 1.05818i −0.0219455 0.0380108i
\(776\) 0 0
\(777\) 15.9604 27.6442i 0.572575 0.991729i
\(778\) 0 0
\(779\) −3.58477 + 0.774765i −0.128438 + 0.0277588i
\(780\) 0 0
\(781\) 0.416692 0.721732i 0.0149104 0.0258256i
\(782\) 0 0
\(783\) −1.14257 1.97899i −0.0408322 0.0707234i
\(784\) 0 0
\(785\) 3.75351 + 6.50127i 0.133968 + 0.232040i
\(786\) 0 0
\(787\) 18.7781 0.669368 0.334684 0.942330i \(-0.391370\pi\)
0.334684 + 0.942330i \(0.391370\pi\)
\(788\) 0 0
\(789\) −7.21787 12.5017i −0.256963 0.445073i
\(790\) 0 0
\(791\) −22.2680 −0.791759
\(792\) 0 0
\(793\) 11.1445 19.3028i 0.395752 0.685462i
\(794\) 0 0
\(795\) −14.1250 +