Properties

Label 190.2.b.b.39.4
Level $190$
Weight $2$
Character 190.39
Analytic conductor $1.517$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.51715763840\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
Defining polynomial: \(x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.4
Root \(0.432320 + 0.432320i\) of defining polynomial
Character \(\chi\) \(=\) 190.39
Dual form 190.2.b.b.39.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -2.76156i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} +2.76156 q^{6} -0.761557i q^{7} -1.00000i q^{8} -4.62620 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -2.76156i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} +2.76156 q^{6} -0.761557i q^{7} -1.00000i q^{8} -4.62620 q^{9} +(0.432320 - 2.19388i) q^{10} -0.864641 q^{11} +2.76156i q^{12} -5.62620i q^{13} +0.761557 q^{14} +(-1.19388 + 6.05852i) q^{15} +1.00000 q^{16} -3.62620i q^{17} -4.62620i q^{18} -1.00000 q^{19} +(2.19388 + 0.432320i) q^{20} -2.10308 q^{21} -0.864641i q^{22} +8.01395i q^{23} -2.76156 q^{24} +(4.62620 + 1.89692i) q^{25} +5.62620 q^{26} +4.49084i q^{27} +0.761557i q^{28} +7.35548 q^{29} +(-6.05852 - 1.19388i) q^{30} +8.11704 q^{31} +1.00000i q^{32} +2.38776i q^{33} +3.62620 q^{34} +(-0.329237 + 1.67076i) q^{35} +4.62620 q^{36} +0.476886i q^{37} -1.00000i q^{38} -15.5371 q^{39} +(-0.432320 + 2.19388i) q^{40} -2.65847 q^{41} -2.10308i q^{42} -6.86464i q^{43} +0.864641 q^{44} +(10.1493 + 2.00000i) q^{45} -8.01395 q^{46} +1.25240i q^{47} -2.76156i q^{48} +6.42003 q^{49} +(-1.89692 + 4.62620i) q^{50} -10.0140 q^{51} +5.62620i q^{52} -2.37380i q^{53} -4.49084 q^{54} +(1.89692 + 0.373802i) q^{55} -0.761557 q^{56} +2.76156i q^{57} +7.35548i q^{58} -4.49084 q^{59} +(1.19388 - 6.05852i) q^{60} -10.8646 q^{61} +8.11704i q^{62} +3.52311i q^{63} -1.00000 q^{64} +(-2.43232 + 12.3432i) q^{65} -2.38776 q^{66} +1.03228i q^{67} +3.62620i q^{68} +22.1310 q^{69} +(-1.67076 - 0.329237i) q^{70} -10.1816 q^{71} +4.62620i q^{72} -16.4017i q^{73} -0.476886 q^{74} +(5.23844 - 12.7755i) q^{75} +1.00000 q^{76} +0.658473i q^{77} -15.5371i q^{78} +12.5693 q^{79} +(-2.19388 - 0.432320i) q^{80} -1.47689 q^{81} -2.65847i q^{82} +0.270718i q^{83} +2.10308 q^{84} +(-1.56768 + 7.95543i) q^{85} +6.86464 q^{86} -20.3126i q^{87} +0.864641i q^{88} -0.387755 q^{89} +(-2.00000 + 10.1493i) q^{90} -4.28467 q^{91} -8.01395i q^{92} -22.4157i q^{93} -1.25240 q^{94} +(2.19388 + 0.432320i) q^{95} +2.76156 q^{96} -8.50479i q^{97} +6.42003i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + 2q^{5} + 4q^{6} - 10q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 2q^{5} + 4q^{6} - 10q^{9} - 8q^{14} + 8q^{15} + 6q^{16} - 6q^{19} - 2q^{20} - 20q^{21} - 4q^{24} + 10q^{25} + 16q^{26} + 16q^{29} - 16q^{30} + 8q^{31} + 4q^{34} + 8q^{35} + 10q^{36} - 20q^{39} + 4q^{41} + 18q^{45} + 6q^{49} - 4q^{50} - 12q^{51} - 4q^{54} + 4q^{55} + 8q^{56} - 4q^{59} - 8q^{60} - 60q^{61} - 6q^{64} - 12q^{65} + 16q^{66} + 44q^{69} - 20q^{70} - 16q^{71} - 28q^{74} + 44q^{75} + 6q^{76} + 2q^{80} - 34q^{81} + 20q^{84} - 12q^{85} + 36q^{86} + 28q^{89} - 12q^{90} + 12q^{91} + 28q^{94} - 2q^{95} + 4q^{96} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/190\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 2.76156i 1.59439i −0.603725 0.797193i \(-0.706317\pi\)
0.603725 0.797193i \(-0.293683\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.19388 0.432320i −0.981132 0.193340i
\(6\) 2.76156 1.12740
\(7\) 0.761557i 0.287842i −0.989589 0.143921i \(-0.954029\pi\)
0.989589 0.143921i \(-0.0459710\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −4.62620 −1.54207
\(10\) 0.432320 2.19388i 0.136712 0.693765i
\(11\) −0.864641 −0.260699 −0.130350 0.991468i \(-0.541610\pi\)
−0.130350 + 0.991468i \(0.541610\pi\)
\(12\) 2.76156i 0.797193i
\(13\) 5.62620i 1.56043i −0.625514 0.780213i \(-0.715111\pi\)
0.625514 0.780213i \(-0.284889\pi\)
\(14\) 0.761557 0.203535
\(15\) −1.19388 + 6.05852i −0.308258 + 1.56430i
\(16\) 1.00000 0.250000
\(17\) 3.62620i 0.879482i −0.898125 0.439741i \(-0.855070\pi\)
0.898125 0.439741i \(-0.144930\pi\)
\(18\) 4.62620i 1.09041i
\(19\) −1.00000 −0.229416
\(20\) 2.19388 + 0.432320i 0.490566 + 0.0966698i
\(21\) −2.10308 −0.458930
\(22\) 0.864641i 0.184342i
\(23\) 8.01395i 1.67102i 0.549472 + 0.835512i \(0.314829\pi\)
−0.549472 + 0.835512i \(0.685171\pi\)
\(24\) −2.76156 −0.563700
\(25\) 4.62620 + 1.89692i 0.925240 + 0.379383i
\(26\) 5.62620 1.10339
\(27\) 4.49084i 0.864262i
\(28\) 0.761557i 0.143921i
\(29\) 7.35548 1.36588 0.682939 0.730475i \(-0.260701\pi\)
0.682939 + 0.730475i \(0.260701\pi\)
\(30\) −6.05852 1.19388i −1.10613 0.217971i
\(31\) 8.11704 1.45786 0.728931 0.684587i \(-0.240017\pi\)
0.728931 + 0.684587i \(0.240017\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.38776i 0.415655i
\(34\) 3.62620 0.621888
\(35\) −0.329237 + 1.67076i −0.0556512 + 0.282411i
\(36\) 4.62620 0.771033
\(37\) 0.476886i 0.0783995i 0.999231 + 0.0391998i \(0.0124809\pi\)
−0.999231 + 0.0391998i \(0.987519\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −15.5371 −2.48792
\(40\) −0.432320 + 2.19388i −0.0683559 + 0.346883i
\(41\) −2.65847 −0.415184 −0.207592 0.978216i \(-0.566563\pi\)
−0.207592 + 0.978216i \(0.566563\pi\)
\(42\) 2.10308i 0.324513i
\(43\) 6.86464i 1.04685i −0.852072 0.523424i \(-0.824654\pi\)
0.852072 0.523424i \(-0.175346\pi\)
\(44\) 0.864641 0.130350
\(45\) 10.1493 + 2.00000i 1.51297 + 0.298142i
\(46\) −8.01395 −1.18159
\(47\) 1.25240i 0.182681i 0.995820 + 0.0913404i \(0.0291151\pi\)
−0.995820 + 0.0913404i \(0.970885\pi\)
\(48\) 2.76156i 0.398596i
\(49\) 6.42003 0.917147
\(50\) −1.89692 + 4.62620i −0.268264 + 0.654243i
\(51\) −10.0140 −1.40223
\(52\) 5.62620i 0.780213i
\(53\) 2.37380i 0.326067i −0.986621 0.163033i \(-0.947872\pi\)
0.986621 0.163033i \(-0.0521278\pi\)
\(54\) −4.49084 −0.611126
\(55\) 1.89692 + 0.373802i 0.255780 + 0.0504034i
\(56\) −0.761557 −0.101767
\(57\) 2.76156i 0.365777i
\(58\) 7.35548i 0.965822i
\(59\) −4.49084 −0.584657 −0.292329 0.956318i \(-0.594430\pi\)
−0.292329 + 0.956318i \(0.594430\pi\)
\(60\) 1.19388 6.05852i 0.154129 0.782151i
\(61\) −10.8646 −1.39107 −0.695537 0.718490i \(-0.744834\pi\)
−0.695537 + 0.718490i \(0.744834\pi\)
\(62\) 8.11704i 1.03086i
\(63\) 3.52311i 0.443871i
\(64\) −1.00000 −0.125000
\(65\) −2.43232 + 12.3432i −0.301692 + 1.53098i
\(66\) −2.38776 −0.293912
\(67\) 1.03228i 0.126113i 0.998010 + 0.0630563i \(0.0200848\pi\)
−0.998010 + 0.0630563i \(0.979915\pi\)
\(68\) 3.62620i 0.439741i
\(69\) 22.1310 2.66426
\(70\) −1.67076 0.329237i −0.199694 0.0393513i
\(71\) −10.1816 −1.20833 −0.604166 0.796858i \(-0.706494\pi\)
−0.604166 + 0.796858i \(0.706494\pi\)
\(72\) 4.62620i 0.545203i
\(73\) 16.4017i 1.91967i −0.280557 0.959837i \(-0.590519\pi\)
0.280557 0.959837i \(-0.409481\pi\)
\(74\) −0.476886 −0.0554368
\(75\) 5.23844 12.7755i 0.604883 1.47519i
\(76\) 1.00000 0.114708
\(77\) 0.658473i 0.0750400i
\(78\) 15.5371i 1.75923i
\(79\) 12.5693 1.41416 0.707081 0.707133i \(-0.250012\pi\)
0.707081 + 0.707133i \(0.250012\pi\)
\(80\) −2.19388 0.432320i −0.245283 0.0483349i
\(81\) −1.47689 −0.164098
\(82\) 2.65847i 0.293579i
\(83\) 0.270718i 0.0297152i 0.999890 + 0.0148576i \(0.00472949\pi\)
−0.999890 + 0.0148576i \(0.995271\pi\)
\(84\) 2.10308 0.229465
\(85\) −1.56768 + 7.95543i −0.170039 + 0.862888i
\(86\) 6.86464 0.740233
\(87\) 20.3126i 2.17774i
\(88\) 0.864641i 0.0921710i
\(89\) −0.387755 −0.0411020 −0.0205510 0.999789i \(-0.506542\pi\)
−0.0205510 + 0.999789i \(0.506542\pi\)
\(90\) −2.00000 + 10.1493i −0.210819 + 1.06983i
\(91\) −4.28467 −0.449156
\(92\) 8.01395i 0.835512i
\(93\) 22.4157i 2.32440i
\(94\) −1.25240 −0.129175
\(95\) 2.19388 + 0.432320i 0.225087 + 0.0443551i
\(96\) 2.76156 0.281850
\(97\) 8.50479i 0.863531i −0.901986 0.431765i \(-0.857891\pi\)
0.901986 0.431765i \(-0.142109\pi\)
\(98\) 6.42003i 0.648521i
\(99\) 4.00000 0.402015
\(100\) −4.62620 1.89692i −0.462620 0.189692i
\(101\) 16.4157 1.63342 0.816710 0.577049i \(-0.195796\pi\)
0.816710 + 0.577049i \(0.195796\pi\)
\(102\) 10.0140i 0.991529i
\(103\) 9.64015i 0.949872i 0.880020 + 0.474936i \(0.157529\pi\)
−0.880020 + 0.474936i \(0.842471\pi\)
\(104\) −5.62620 −0.551694
\(105\) 4.61391 + 0.909206i 0.450271 + 0.0887294i
\(106\) 2.37380 0.230564
\(107\) 4.28467i 0.414215i 0.978318 + 0.207107i \(0.0664050\pi\)
−0.978318 + 0.207107i \(0.933595\pi\)
\(108\) 4.49084i 0.432131i
\(109\) 13.4200 1.28541 0.642703 0.766116i \(-0.277813\pi\)
0.642703 + 0.766116i \(0.277813\pi\)
\(110\) −0.373802 + 1.89692i −0.0356406 + 0.180864i
\(111\) 1.31695 0.124999
\(112\) 0.761557i 0.0719604i
\(113\) 10.3232i 0.971125i 0.874202 + 0.485563i \(0.161385\pi\)
−0.874202 + 0.485563i \(0.838615\pi\)
\(114\) −2.76156 −0.258644
\(115\) 3.46460 17.5816i 0.323075 1.63950i
\(116\) −7.35548 −0.682939
\(117\) 26.0279i 2.40628i
\(118\) 4.49084i 0.413415i
\(119\) −2.76156 −0.253152
\(120\) 6.05852 + 1.19388i 0.553065 + 0.108986i
\(121\) −10.2524 −0.932036
\(122\) 10.8646i 0.983638i
\(123\) 7.34153i 0.661963i
\(124\) −8.11704 −0.728931
\(125\) −9.32924 6.16160i −0.834432 0.551110i
\(126\) −3.52311 −0.313864
\(127\) 16.9817i 1.50688i 0.657517 + 0.753440i \(0.271607\pi\)
−0.657517 + 0.753440i \(0.728393\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −18.9571 −1.66908
\(130\) −12.3432 2.43232i −1.08257 0.213329i
\(131\) 0.541436 0.0473055 0.0236528 0.999720i \(-0.492470\pi\)
0.0236528 + 0.999720i \(0.492470\pi\)
\(132\) 2.38776i 0.207827i
\(133\) 0.761557i 0.0660354i
\(134\) −1.03228 −0.0891750
\(135\) 1.94148 9.85235i 0.167096 0.847955i
\(136\) −3.62620 −0.310944
\(137\) 2.87859i 0.245935i 0.992411 + 0.122967i \(0.0392411\pi\)
−0.992411 + 0.122967i \(0.960759\pi\)
\(138\) 22.1310i 1.88392i
\(139\) −3.58767 −0.304302 −0.152151 0.988357i \(-0.548620\pi\)
−0.152151 + 0.988357i \(0.548620\pi\)
\(140\) 0.329237 1.67076i 0.0278256 0.141205i
\(141\) 3.45856 0.291264
\(142\) 10.1816i 0.854420i
\(143\) 4.86464i 0.406802i
\(144\) −4.62620 −0.385517
\(145\) −16.1370 3.17992i −1.34011 0.264078i
\(146\) 16.4017 1.35742
\(147\) 17.7293i 1.46229i
\(148\) 0.476886i 0.0391998i
\(149\) 16.8401 1.37959 0.689796 0.724004i \(-0.257700\pi\)
0.689796 + 0.724004i \(0.257700\pi\)
\(150\) 12.7755 + 5.23844i 1.04312 + 0.427717i
\(151\) −16.9817 −1.38195 −0.690975 0.722879i \(-0.742818\pi\)
−0.690975 + 0.722879i \(0.742818\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 16.7755i 1.35622i
\(154\) −0.658473 −0.0530613
\(155\) −17.8078 3.50916i −1.43036 0.281863i
\(156\) 15.5371 1.24396
\(157\) 14.8401i 1.18437i 0.805804 + 0.592183i \(0.201734\pi\)
−0.805804 + 0.592183i \(0.798266\pi\)
\(158\) 12.5693i 0.999963i
\(159\) −6.55539 −0.519876
\(160\) 0.432320 2.19388i 0.0341779 0.173441i
\(161\) 6.10308 0.480990
\(162\) 1.47689i 0.116035i
\(163\) 13.3694i 1.04717i −0.851972 0.523587i \(-0.824593\pi\)
0.851972 0.523587i \(-0.175407\pi\)
\(164\) 2.65847 0.207592
\(165\) 1.03228 5.23844i 0.0803625 0.407812i
\(166\) −0.270718 −0.0210118
\(167\) 9.84632i 0.761931i 0.924589 + 0.380966i \(0.124408\pi\)
−0.924589 + 0.380966i \(0.875592\pi\)
\(168\) 2.10308i 0.162256i
\(169\) −18.6541 −1.43493
\(170\) −7.95543 1.56768i −0.610154 0.120236i
\(171\) 4.62620 0.353774
\(172\) 6.86464i 0.523424i
\(173\) 2.98168i 0.226693i −0.993556 0.113346i \(-0.963843\pi\)
0.993556 0.113346i \(-0.0361570\pi\)
\(174\) 20.3126 1.53989
\(175\) 1.44461 3.52311i 0.109202 0.266322i
\(176\) −0.864641 −0.0651748
\(177\) 12.4017i 0.932169i
\(178\) 0.387755i 0.0290635i
\(179\) −11.7938 −0.881512 −0.440756 0.897627i \(-0.645290\pi\)
−0.440756 + 0.897627i \(0.645290\pi\)
\(180\) −10.1493 2.00000i −0.756485 0.149071i
\(181\) 14.5693 1.08293 0.541465 0.840723i \(-0.317870\pi\)
0.541465 + 0.840723i \(0.317870\pi\)
\(182\) 4.28467i 0.317601i
\(183\) 30.0033i 2.21791i
\(184\) 8.01395 0.590796
\(185\) 0.206167 1.04623i 0.0151577 0.0769203i
\(186\) 22.4157 1.64360
\(187\) 3.13536i 0.229280i
\(188\) 1.25240i 0.0913404i
\(189\) 3.42003 0.248771
\(190\) −0.432320 + 2.19388i −0.0313638 + 0.159161i
\(191\) 13.2384 0.957900 0.478950 0.877842i \(-0.341017\pi\)
0.478950 + 0.877842i \(0.341017\pi\)
\(192\) 2.76156i 0.199298i
\(193\) 2.54144i 0.182937i −0.995808 0.0914683i \(-0.970844\pi\)
0.995808 0.0914683i \(-0.0291560\pi\)
\(194\) 8.50479 0.610609
\(195\) 34.0864 + 6.71699i 2.44098 + 0.481014i
\(196\) −6.42003 −0.458574
\(197\) 19.9109i 1.41859i −0.704911 0.709295i \(-0.749013\pi\)
0.704911 0.709295i \(-0.250987\pi\)
\(198\) 4.00000i 0.284268i
\(199\) 20.3126 1.43992 0.719960 0.694015i \(-0.244160\pi\)
0.719960 + 0.694015i \(0.244160\pi\)
\(200\) 1.89692 4.62620i 0.134132 0.327122i
\(201\) 2.85069 0.201072
\(202\) 16.4157i 1.15500i
\(203\) 5.60162i 0.393157i
\(204\) 10.0140 0.701117
\(205\) 5.83237 + 1.14931i 0.407350 + 0.0802715i
\(206\) −9.64015 −0.671661
\(207\) 37.0741i 2.57683i
\(208\) 5.62620i 0.390107i
\(209\) 0.864641 0.0598085
\(210\) −0.909206 + 4.61391i −0.0627412 + 0.318390i
\(211\) 18.0419 1.24205 0.621026 0.783790i \(-0.286716\pi\)
0.621026 + 0.783790i \(0.286716\pi\)
\(212\) 2.37380i 0.163033i
\(213\) 28.1170i 1.92655i
\(214\) −4.28467 −0.292894
\(215\) −2.96772 + 15.0602i −0.202397 + 1.02710i
\(216\) 4.49084 0.305563
\(217\) 6.18159i 0.419634i
\(218\) 13.4200i 0.908919i
\(219\) −45.2943 −3.06070
\(220\) −1.89692 0.373802i −0.127890 0.0252017i
\(221\) −20.4017 −1.37237
\(222\) 1.31695i 0.0883877i
\(223\) 13.5231i 0.905575i 0.891619 + 0.452787i \(0.149570\pi\)
−0.891619 + 0.452787i \(0.850430\pi\)
\(224\) 0.761557 0.0508837
\(225\) −21.4017 8.77551i −1.42678 0.585034i
\(226\) −10.3232 −0.686689
\(227\) 13.6016i 0.902771i 0.892329 + 0.451386i \(0.149070\pi\)
−0.892329 + 0.451386i \(0.850930\pi\)
\(228\) 2.76156i 0.182889i
\(229\) −13.5877 −0.897898 −0.448949 0.893557i \(-0.648202\pi\)
−0.448949 + 0.893557i \(0.648202\pi\)
\(230\) 17.5816 + 3.46460i 1.15930 + 0.228449i
\(231\) 1.81841 0.119643
\(232\) 7.35548i 0.482911i
\(233\) 25.5510i 1.67390i −0.547277 0.836952i \(-0.684336\pi\)
0.547277 0.836952i \(-0.315664\pi\)
\(234\) −26.0279 −1.70150
\(235\) 0.541436 2.74760i 0.0353194 0.179234i
\(236\) 4.49084 0.292329
\(237\) 34.7110i 2.25472i
\(238\) 2.76156i 0.179005i
\(239\) 11.3309 0.732935 0.366468 0.930431i \(-0.380567\pi\)
0.366468 + 0.930431i \(0.380567\pi\)
\(240\) −1.19388 + 6.05852i −0.0770645 + 0.391076i
\(241\) −1.25240 −0.0806739 −0.0403370 0.999186i \(-0.512843\pi\)
−0.0403370 + 0.999186i \(0.512843\pi\)
\(242\) 10.2524i 0.659049i
\(243\) 17.5510i 1.12590i
\(244\) 10.8646 0.695537
\(245\) −14.0848 2.77551i −0.899842 0.177321i
\(246\) −7.34153 −0.468079
\(247\) 5.62620i 0.357986i
\(248\) 8.11704i 0.515432i
\(249\) 0.747604 0.0473775
\(250\) 6.16160 9.32924i 0.389694 0.590033i
\(251\) 10.5939 0.668682 0.334341 0.942452i \(-0.391486\pi\)
0.334341 + 0.942452i \(0.391486\pi\)
\(252\) 3.52311i 0.221935i
\(253\) 6.92919i 0.435635i
\(254\) −16.9817 −1.06553
\(255\) 21.9694 + 4.32924i 1.37578 + 0.271107i
\(256\) 1.00000 0.0625000
\(257\) 0.153681i 0.00958637i −0.999989 0.00479319i \(-0.998474\pi\)
0.999989 0.00479319i \(-0.00152572\pi\)
\(258\) 18.9571i 1.18022i
\(259\) 0.363176 0.0225666
\(260\) 2.43232 12.3432i 0.150846 0.765492i
\(261\) −34.0279 −2.10627
\(262\) 0.541436i 0.0334501i
\(263\) 0.504792i 0.0311268i −0.999879 0.0155634i \(-0.995046\pi\)
0.999879 0.0155634i \(-0.00495419\pi\)
\(264\) 2.38776 0.146956
\(265\) −1.02624 + 5.20783i −0.0630416 + 0.319915i
\(266\) −0.761557 −0.0466941
\(267\) 1.07081i 0.0655324i
\(268\) 1.03228i 0.0630563i
\(269\) 3.49521 0.213107 0.106553 0.994307i \(-0.466019\pi\)
0.106553 + 0.994307i \(0.466019\pi\)
\(270\) 9.85235 + 1.94148i 0.599595 + 0.118155i
\(271\) 5.47252 0.332432 0.166216 0.986089i \(-0.446845\pi\)
0.166216 + 0.986089i \(0.446845\pi\)
\(272\) 3.62620i 0.219871i
\(273\) 11.8324i 0.716127i
\(274\) −2.87859 −0.173902
\(275\) −4.00000 1.64015i −0.241209 0.0989049i
\(276\) −22.1310 −1.33213
\(277\) 12.9538i 0.778317i 0.921171 + 0.389158i \(0.127234\pi\)
−0.921171 + 0.389158i \(0.872766\pi\)
\(278\) 3.58767i 0.215174i
\(279\) −37.5510 −2.24812
\(280\) 1.67076 + 0.329237i 0.0998472 + 0.0196757i
\(281\) 0.153681 0.00916785 0.00458393 0.999989i \(-0.498541\pi\)
0.00458393 + 0.999989i \(0.498541\pi\)
\(282\) 3.45856i 0.205954i
\(283\) 18.2341i 1.08390i 0.840410 + 0.541952i \(0.182314\pi\)
−0.840410 + 0.541952i \(0.817686\pi\)
\(284\) 10.1816 0.604166
\(285\) 1.19388 6.05852i 0.0707192 0.358876i
\(286\) −4.86464 −0.287652
\(287\) 2.02458i 0.119507i
\(288\) 4.62620i 0.272601i
\(289\) 3.85069 0.226511
\(290\) 3.17992 16.1370i 0.186732 0.947599i
\(291\) −23.4865 −1.37680
\(292\) 16.4017i 0.959837i
\(293\) 2.03853i 0.119092i −0.998226 0.0595462i \(-0.981035\pi\)
0.998226 0.0595462i \(-0.0189654\pi\)
\(294\) 17.7293 1.03399
\(295\) 9.85235 + 1.94148i 0.573626 + 0.113037i
\(296\) 0.476886 0.0277184
\(297\) 3.88296i 0.225312i
\(298\) 16.8401i 0.975519i
\(299\) 45.0881 2.60751
\(300\) −5.23844 + 12.7755i −0.302442 + 0.737594i
\(301\) −5.22782 −0.301326
\(302\) 16.9817i 0.977186i
\(303\) 45.3328i 2.60430i
\(304\) −1.00000 −0.0573539
\(305\) 23.8357 + 4.69701i 1.36483 + 0.268950i
\(306\) −16.7755 −0.958992
\(307\) 16.5414i 0.944070i 0.881580 + 0.472035i \(0.156480\pi\)
−0.881580 + 0.472035i \(0.843520\pi\)
\(308\) 0.658473i 0.0375200i
\(309\) 26.6218 1.51446
\(310\) 3.50916 17.8078i 0.199307 1.01141i
\(311\) −21.4725 −1.21759 −0.608797 0.793326i \(-0.708348\pi\)
−0.608797 + 0.793326i \(0.708348\pi\)
\(312\) 15.5371i 0.879613i
\(313\) 1.12141i 0.0633856i 0.999498 + 0.0316928i \(0.0100898\pi\)
−0.999498 + 0.0316928i \(0.989910\pi\)
\(314\) −14.8401 −0.837473
\(315\) 1.52311 7.72928i 0.0858178 0.435496i
\(316\) −12.5693 −0.707081
\(317\) 29.8882i 1.67869i −0.543601 0.839344i \(-0.682940\pi\)
0.543601 0.839344i \(-0.317060\pi\)
\(318\) 6.55539i 0.367608i
\(319\) −6.35985 −0.356083
\(320\) 2.19388 + 0.432320i 0.122641 + 0.0241674i
\(321\) 11.8324 0.660418
\(322\) 6.10308i 0.340112i
\(323\) 3.62620i 0.201767i
\(324\) 1.47689 0.0820492
\(325\) 10.6724 26.0279i 0.592000 1.44377i
\(326\) 13.3694 0.740464
\(327\) 37.0602i 2.04943i
\(328\) 2.65847i 0.146790i
\(329\) 0.953771 0.0525831
\(330\) 5.23844 + 1.03228i 0.288367 + 0.0568249i
\(331\) 32.3126 1.77606 0.888030 0.459786i \(-0.152074\pi\)
0.888030 + 0.459786i \(0.152074\pi\)
\(332\) 0.270718i 0.0148576i
\(333\) 2.20617i 0.120897i
\(334\) −9.84632 −0.538767
\(335\) 0.446274 2.26469i 0.0243825 0.123733i
\(336\) −2.10308 −0.114733
\(337\) 26.3511i 1.43544i 0.696334 + 0.717718i \(0.254813\pi\)
−0.696334 + 0.717718i \(0.745187\pi\)
\(338\) 18.6541i 1.01465i
\(339\) 28.5081 1.54835
\(340\) 1.56768 7.95543i 0.0850194 0.431444i
\(341\) −7.01832 −0.380063
\(342\) 4.62620i 0.250156i
\(343\) 10.2201i 0.551835i
\(344\) −6.86464 −0.370117
\(345\) −48.5527 9.56768i −2.61399 0.515107i
\(346\) 2.98168 0.160296
\(347\) 2.77551i 0.148997i −0.997221 0.0744986i \(-0.976264\pi\)
0.997221 0.0744986i \(-0.0237356\pi\)
\(348\) 20.3126i 1.08887i
\(349\) −11.5510 −0.618312 −0.309156 0.951011i \(-0.600047\pi\)
−0.309156 + 0.951011i \(0.600047\pi\)
\(350\) 3.52311 + 1.44461i 0.188318 + 0.0772177i
\(351\) 25.2663 1.34862
\(352\) 0.864641i 0.0460855i
\(353\) 8.40171i 0.447178i 0.974684 + 0.223589i \(0.0717773\pi\)
−0.974684 + 0.223589i \(0.928223\pi\)
\(354\) −12.4017 −0.659143
\(355\) 22.3372 + 4.40171i 1.18553 + 0.233618i
\(356\) 0.387755 0.0205510
\(357\) 7.62620i 0.403621i
\(358\) 11.7938i 0.623323i
\(359\) −22.7895 −1.20278 −0.601391 0.798955i \(-0.705387\pi\)
−0.601391 + 0.798955i \(0.705387\pi\)
\(360\) 2.00000 10.1493i 0.105409 0.534916i
\(361\) 1.00000 0.0526316
\(362\) 14.5693i 0.765748i
\(363\) 28.3126i 1.48602i
\(364\) 4.28467 0.224578
\(365\) −7.09079 + 35.9833i −0.371149 + 1.88345i
\(366\) −30.0033 −1.56830
\(367\) 4.06455i 0.212168i 0.994357 + 0.106084i \(0.0338312\pi\)
−0.994357 + 0.106084i \(0.966169\pi\)
\(368\) 8.01395i 0.417756i
\(369\) 12.2986 0.640241
\(370\) 1.04623 + 0.206167i 0.0543908 + 0.0107181i
\(371\) −1.80779 −0.0938556
\(372\) 22.4157i 1.16220i
\(373\) 18.4017i 0.952804i 0.879227 + 0.476402i \(0.158059\pi\)
−0.879227 + 0.476402i \(0.841941\pi\)
\(374\) −3.13536 −0.162126
\(375\) −17.0156 + 25.7632i −0.878683 + 1.33041i
\(376\) 1.25240 0.0645874
\(377\) 41.3834i 2.13135i
\(378\) 3.42003i 0.175907i
\(379\) −1.23844 −0.0636145 −0.0318073 0.999494i \(-0.510126\pi\)
−0.0318073 + 0.999494i \(0.510126\pi\)
\(380\) −2.19388 0.432320i −0.112544 0.0221776i
\(381\) 46.8959 2.40255
\(382\) 13.2384i 0.677338i
\(383\) 16.8646i 0.861743i −0.902413 0.430871i \(-0.858206\pi\)
0.902413 0.430871i \(-0.141794\pi\)
\(384\) −2.76156 −0.140925
\(385\) 0.284672 1.44461i 0.0145082 0.0736242i
\(386\) 2.54144 0.129356
\(387\) 31.7572i 1.61431i
\(388\) 8.50479i 0.431765i
\(389\) −8.59392 −0.435729 −0.217865 0.975979i \(-0.569909\pi\)
−0.217865 + 0.975979i \(0.569909\pi\)
\(390\) −6.71699 + 34.0864i −0.340128 + 1.72603i
\(391\) 29.0602 1.46964
\(392\) 6.42003i 0.324261i
\(393\) 1.49521i 0.0754233i
\(394\) 19.9109 1.00310
\(395\) −27.5756 5.43398i −1.38748 0.273413i
\(396\) −4.00000 −0.201008
\(397\) 16.0558i 0.805818i 0.915240 + 0.402909i \(0.132001\pi\)
−0.915240 + 0.402909i \(0.867999\pi\)
\(398\) 20.3126i 1.01818i
\(399\) 2.10308 0.105286
\(400\) 4.62620 + 1.89692i 0.231310 + 0.0948458i
\(401\) −14.8925 −0.743698 −0.371849 0.928293i \(-0.621276\pi\)
−0.371849 + 0.928293i \(0.621276\pi\)
\(402\) 2.85069i 0.142179i
\(403\) 45.6681i 2.27489i
\(404\) −16.4157 −0.816710
\(405\) 3.24011 + 0.638488i 0.161002 + 0.0317267i
\(406\) 5.60162 0.278004
\(407\) 0.412335i 0.0204387i
\(408\) 10.0140i 0.495765i
\(409\) 18.3511 0.907404 0.453702 0.891153i \(-0.350103\pi\)
0.453702 + 0.891153i \(0.350103\pi\)
\(410\) −1.14931 + 5.83237i −0.0567605 + 0.288040i
\(411\) 7.94940 0.392115
\(412\) 9.64015i 0.474936i
\(413\) 3.42003i 0.168289i
\(414\) 37.0741 1.82209
\(415\) 0.117037 0.593923i 0.00574512 0.0291545i
\(416\) 5.62620 0.275847
\(417\) 9.90754i 0.485174i
\(418\) 0.864641i 0.0422910i
\(419\) −34.7509 −1.69769 −0.848847 0.528639i \(-0.822703\pi\)
−0.848847 + 0.528639i \(0.822703\pi\)
\(420\) −4.61391 0.909206i −0.225136 0.0443647i
\(421\) −40.1589 −1.95722 −0.978612 0.205713i \(-0.934049\pi\)
−0.978612 + 0.205713i \(0.934049\pi\)
\(422\) 18.0419i 0.878264i
\(423\) 5.79383i 0.281706i
\(424\) −2.37380 −0.115282
\(425\) 6.87859 16.7755i 0.333661 0.813732i
\(426\) −28.1170 −1.36227
\(427\) 8.27405i 0.400409i
\(428\) 4.28467i 0.207107i
\(429\) 13.4340 0.648599
\(430\) −15.0602 2.96772i −0.726266 0.143116i
\(431\) 34.9571 1.68382 0.841912 0.539615i \(-0.181430\pi\)
0.841912 + 0.539615i \(0.181430\pi\)
\(432\) 4.49084i 0.216066i
\(433\) 1.13536i 0.0545619i −0.999628 0.0272809i \(-0.991315\pi\)
0.999628 0.0272809i \(-0.00868487\pi\)
\(434\) 6.18159 0.296726
\(435\) −8.78154 + 44.5633i −0.421043 + 2.13665i
\(436\) −13.4200 −0.642703
\(437\) 8.01395i 0.383359i
\(438\) 45.2943i 2.16424i
\(439\) 6.80009 0.324551 0.162275 0.986746i \(-0.448117\pi\)
0.162275 + 0.986746i \(0.448117\pi\)
\(440\) 0.373802 1.89692i 0.0178203 0.0904319i
\(441\) −29.7003 −1.41430
\(442\) 20.4017i 0.970410i
\(443\) 38.0679i 1.80866i −0.426835 0.904330i \(-0.640371\pi\)
0.426835 0.904330i \(-0.359629\pi\)
\(444\) −1.31695 −0.0624995
\(445\) 0.850688 + 0.167635i 0.0403265 + 0.00794664i
\(446\) −13.5231 −0.640338
\(447\) 46.5048i 2.19960i
\(448\) 0.761557i 0.0359802i
\(449\) 18.5414 0.875024 0.437512 0.899212i \(-0.355860\pi\)
0.437512 + 0.899212i \(0.355860\pi\)
\(450\) 8.77551 21.4017i 0.413682 1.00889i
\(451\) 2.29862 0.108238
\(452\) 10.3232i 0.485563i
\(453\) 46.8959i 2.20336i
\(454\) −13.6016 −0.638356
\(455\) 9.40005 + 1.85235i 0.440681 + 0.0868396i
\(456\) 2.76156 0.129322
\(457\) 16.3738i 0.765934i 0.923762 + 0.382967i \(0.125098\pi\)
−0.923762 + 0.382967i \(0.874902\pi\)
\(458\) 13.5877i 0.634910i
\(459\) 16.2847 0.760103
\(460\) −3.46460 + 17.5816i −0.161538 + 0.819748i
\(461\) 1.70470 0.0793959 0.0396979 0.999212i \(-0.487360\pi\)
0.0396979 + 0.999212i \(0.487360\pi\)
\(462\) 1.81841i 0.0846002i
\(463\) 10.0279i 0.466036i 0.972472 + 0.233018i \(0.0748602\pi\)
−0.972472 + 0.233018i \(0.925140\pi\)
\(464\) 7.35548 0.341470
\(465\) −9.69075 + 49.1772i −0.449398 + 2.28054i
\(466\) 25.5510 1.18363
\(467\) 32.7509i 1.51553i 0.652526 + 0.757766i \(0.273709\pi\)
−0.652526 + 0.757766i \(0.726291\pi\)
\(468\) 26.0279i 1.20314i
\(469\) 0.786137 0.0363004
\(470\) 2.74760 + 0.541436i 0.126738 + 0.0249746i
\(471\) 40.9817 1.88834
\(472\) 4.49084i 0.206708i
\(473\) 5.93545i 0.272912i
\(474\) 34.7110 1.59433
\(475\) −4.62620 1.89692i −0.212265 0.0870365i
\(476\) 2.76156 0.126576
\(477\) 10.9817i 0.502816i
\(478\) 11.3309i 0.518263i
\(479\) −27.2803 −1.24647 −0.623234 0.782035i \(-0.714182\pi\)
−0.623234 + 0.782035i \(0.714182\pi\)
\(480\) −6.05852 1.19388i −0.276532 0.0544928i
\(481\) 2.68305 0.122337
\(482\) 1.25240i 0.0570451i
\(483\) 16.8540i 0.766884i
\(484\) 10.2524 0.466018
\(485\) −3.67680 + 18.6585i −0.166955 + 0.847238i
\(486\) −17.5510 −0.796130
\(487\) 11.0741i 0.501817i −0.968011 0.250908i \(-0.919271\pi\)
0.968011 0.250908i \(-0.0807293\pi\)
\(488\) 10.8646i 0.491819i
\(489\) −36.9205 −1.66960
\(490\) 2.77551 14.0848i 0.125385 0.636285i
\(491\) 8.11704 0.366317 0.183158 0.983083i \(-0.441368\pi\)
0.183158 + 0.983083i \(0.441368\pi\)
\(492\) 7.34153i 0.330982i
\(493\) 26.6724i 1.20127i
\(494\) −5.62620 −0.253135
\(495\) −8.77551 1.72928i −0.394430 0.0777254i
\(496\) 8.11704 0.364466
\(497\) 7.75386i 0.347808i
\(498\) 0.747604i 0.0335009i
\(499\) −0.295298 −0.0132193 −0.00660967 0.999978i \(-0.502104\pi\)
−0.00660967 + 0.999978i \(0.502104\pi\)
\(500\) 9.32924 + 6.16160i 0.417216 + 0.275555i
\(501\) 27.1912 1.21481
\(502\) 10.5939i 0.472830i
\(503\) 19.6016i 0.873993i −0.899463 0.436996i \(-0.856042\pi\)
0.899463 0.436996i \(-0.143958\pi\)
\(504\) 3.52311 0.156932
\(505\) −36.0140 7.09683i −1.60260 0.315805i
\(506\) 6.92919 0.308040
\(507\) 51.5144i 2.28783i
\(508\) 16.9817i 0.753440i
\(509\) 1.79383 0.0795102 0.0397551 0.999209i \(-0.487342\pi\)
0.0397551 + 0.999209i \(0.487342\pi\)
\(510\) −4.32924 + 21.9694i −0.191702 + 0.972821i
\(511\) −12.4908 −0.552562
\(512\) 1.00000i 0.0441942i
\(513\) 4.49084i 0.198275i
\(514\) 0.153681 0.00677859
\(515\) 4.16763 21.1493i 0.183648 0.931950i
\(516\) 18.9571 0.834540
\(517\) 1.08287i 0.0476247i
\(518\) 0.363176i 0.0159570i
\(519\) −8.23407 −0.361436
\(520\) 12.3432 + 2.43232i 0.541285 + 0.106664i
\(521\) −2.61850 −0.114719 −0.0573593 0.998354i \(-0.518268\pi\)
−0.0573593 + 0.998354i \(0.518268\pi\)
\(522\) 34.0279i 1.48936i
\(523\) 14.9956i 0.655713i −0.944728 0.327857i \(-0.893674\pi\)
0.944728 0.327857i \(-0.106326\pi\)
\(524\) −0.541436 −0.0236528
\(525\) −9.72928 3.98937i −0.424621 0.174111i
\(526\) 0.504792 0.0220100
\(527\) 29.4340i 1.28216i
\(528\) 2.38776i 0.103914i
\(529\) −41.2234 −1.79232
\(530\) −5.20783 1.02624i −0.226214 0.0445772i
\(531\) 20.7755 0.901580
\(532\) 0.761557i 0.0330177i
\(533\) 14.9571i 0.647864i
\(534\) −1.07081 −0.0463384
\(535\) 1.85235 9.40005i 0.0800841 0.406399i
\(536\) 1.03228 0.0445875
\(537\) 32.5693i 1.40547i
\(538\) 3.49521i 0.150689i
\(539\) −5.55102 −0.239099
\(540\) −1.94148 + 9.85235i −0.0835481 + 0.423978i
\(541\) 3.40608 0.146439 0.0732194 0.997316i \(-0.476673\pi\)
0.0732194 + 0.997316i \(0.476673\pi\)
\(542\) 5.47252i 0.235065i
\(543\) 40.2341i 1.72661i
\(544\) 3.62620 0.155472
\(545\) −29.4419 5.80175i −1.26115 0.248520i
\(546\) −11.8324 −0.506378
\(547\) 4.74760i 0.202993i 0.994836 + 0.101496i \(0.0323630\pi\)
−0.994836 + 0.101496i \(0.967637\pi\)
\(548\) 2.87859i 0.122967i
\(549\) 50.2620 2.14513
\(550\) 1.64015 4.00000i 0.0699363 0.170561i
\(551\) −7.35548 −0.313354
\(552\) 22.1310i 0.941958i
\(553\) 9.57227i 0.407054i
\(554\) −12.9538 −0.550353
\(555\) −2.88922 0.569343i −0.122641 0.0241673i
\(556\) 3.58767 0.152151
\(557\) 43.0462i 1.82393i 0.410271 + 0.911964i \(0.365434\pi\)
−0.410271 + 0.911964i \(0.634566\pi\)
\(558\) 37.5510i 1.58966i
\(559\) −38.6218 −1.63353
\(560\) −0.329237 + 1.67076i −0.0139128 + 0.0706026i
\(561\) 8.65847 0.365561
\(562\) 0.153681i 0.00648265i
\(563\) 17.0096i 0.716869i −0.933555 0.358434i \(-0.883311\pi\)
0.933555 0.358434i \(-0.116689\pi\)
\(564\) −3.45856 −0.145632
\(565\) 4.46293 22.6478i 0.187757 0.952802i
\(566\) −18.2341 −0.766435
\(567\) 1.12473i 0.0472343i
\(568\) 10.1816i 0.427210i
\(569\) 19.7572 0.828264 0.414132 0.910217i \(-0.364085\pi\)
0.414132 + 0.910217i \(0.364085\pi\)
\(570\) 6.05852 + 1.19388i 0.253763 + 0.0500060i
\(571\) −11.3973 −0.476964 −0.238482 0.971147i \(-0.576650\pi\)
−0.238482 + 0.971147i \(0.576650\pi\)
\(572\) 4.86464i 0.203401i
\(573\) 36.5587i 1.52726i
\(574\) −2.02458 −0.0845043
\(575\) −15.2018 + 37.0741i −0.633959 + 1.54610i
\(576\) 4.62620 0.192758
\(577\) 18.3372i 0.763386i −0.924289 0.381693i \(-0.875341\pi\)
0.924289 0.381693i \(-0.124659\pi\)
\(578\) 3.85069i 0.160167i
\(579\) −7.01832 −0.291672
\(580\) 16.1370 + 3.17992i 0.670053 + 0.132039i
\(581\) 0.206167 0.00855327
\(582\) 23.4865i 0.973546i
\(583\) 2.05249i 0.0850053i
\(584\) −16.4017 −0.678708
\(585\) 11.2524 57.1020i 0.465229 2.36088i
\(586\) 2.03853 0.0842110
\(587\) 11.9475i 0.493127i −0.969127 0.246563i \(-0.920699\pi\)
0.969127 0.246563i \(-0.0793013\pi\)
\(588\) 17.7293i 0.731143i
\(589\) −8.11704 −0.334457
\(590\) −1.94148 + 9.85235i −0.0799295 + 0.405615i
\(591\) −54.9850 −2.26178
\(592\) 0.476886i 0.0195999i
\(593\) 24.3911i 1.00162i 0.865557 + 0.500811i \(0.166965\pi\)
−0.865557 + 0.500811i \(0.833035\pi\)
\(594\) 3.88296 0.159320
\(595\) 6.05852 + 1.19388i 0.248375 + 0.0489442i
\(596\) −16.8401 −0.689796
\(597\) 56.0943i 2.29579i
\(598\) 45.0881i 1.84379i
\(599\) 21.0708 0.860930 0.430465 0.902607i \(-0.358350\pi\)
0.430465 + 0.902607i \(0.358350\pi\)
\(600\) −12.7755 5.23844i −0.521558 0.213859i
\(601\) 32.3878 1.32112 0.660562 0.750771i \(-0.270318\pi\)
0.660562 + 0.750771i \(0.270318\pi\)
\(602\) 5.22782i 0.213070i
\(603\) 4.77551i 0.194474i
\(604\) 16.9817 0.690975
\(605\) 22.4925 + 4.43232i 0.914450 + 0.180199i
\(606\) 45.3328 1.84152
\(607\) 19.0183i 0.771930i 0.922513 + 0.385965i \(0.126131\pi\)
−0.922513 + 0.385965i \(0.873869\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −15.4692 −0.626843
\(610\) −4.69701 + 23.8357i −0.190176 + 0.965079i
\(611\) 7.04623 0.285060
\(612\) 16.7755i 0.678110i
\(613\) 23.5756i 0.952210i 0.879389 + 0.476105i \(0.157952\pi\)
−0.879389 + 0.476105i \(0.842048\pi\)
\(614\) −16.5414 −0.667558
\(615\) 3.17389 16.1064i 0.127984 0.649473i
\(616\) 0.658473 0.0265307
\(617\) 26.2707i 1.05762i −0.848740 0.528810i \(-0.822639\pi\)
0.848740 0.528810i \(-0.177361\pi\)
\(618\) 26.6218i 1.07089i
\(619\) −11.4985 −0.462165 −0.231083 0.972934i \(-0.574227\pi\)
−0.231083 + 0.972934i \(0.574227\pi\)
\(620\) 17.8078 + 3.50916i 0.715178 + 0.140931i
\(621\) −35.9894 −1.44420
\(622\) 21.4725i 0.860969i
\(623\) 0.295298i 0.0118309i
\(624\) −15.5371 −0.621980
\(625\) 17.8034 + 17.5510i 0.712137 + 0.702041i
\(626\) −1.12141 −0.0448204
\(627\) 2.38776i 0.0953578i
\(628\) 14.8401i 0.592183i
\(629\) 1.72928 0.0689510
\(630\) 7.72928 + 1.52311i 0.307942 + 0.0606823i
\(631\) −45.8130 −1.82379 −0.911893 0.410427i \(-0.865380\pi\)
−0.911893 + 0.410427i \(0.865380\pi\)
\(632\) 12.5693i 0.499982i
\(633\) 49.8236i 1.98031i
\(634\) 29.8882 1.18701
\(635\) 7.34153 37.2557i 0.291340 1.47845i
\(636\) 6.55539 0.259938
\(637\) 36.1204i 1.43114i
\(638\) 6.35985i 0.251789i
\(639\) 47.1020 1.86333
\(640\) −0.432320 + 2.19388i −0.0170890 + 0.0867206i
\(641\) 1.36943 0.0540894 0.0270447 0.999634i \(-0.491390\pi\)
0.0270447 + 0.999634i \(0.491390\pi\)
\(642\) 11.8324i 0.466986i
\(643\) 24.7389i 0.975606i 0.872954 + 0.487803i \(0.162201\pi\)
−0.872954 + 0.487803i \(0.837799\pi\)
\(644\) −6.10308 −0.240495
\(645\) 41.5896 + 8.19554i 1.63759 + 0.322699i
\(646\) −3.62620 −0.142671
\(647\) 6.82611i 0.268362i −0.990957 0.134181i \(-0.957160\pi\)
0.990957 0.134181i \(-0.0428404\pi\)
\(648\) 1.47689i 0.0580175i
\(649\) 3.88296 0.152420
\(650\) 26.0279 + 10.6724i 1.02090 + 0.418607i
\(651\) −17.0708 −0.669058
\(652\) 13.3694i 0.523587i
\(653\) 6.91713i 0.270688i −0.990799 0.135344i \(-0.956786\pi\)
0.990799 0.135344i \(-0.0432140\pi\)
\(654\) 37.0602 1.44917
\(655\) −1.18785 0.234074i −0.0464130 0.00914603i
\(656\) −2.65847 −0.103796
\(657\) 75.8776i 2.96027i
\(658\) 0.953771i 0.0371819i
\(659\) −9.44461 −0.367910 −0.183955 0.982935i \(-0.558890\pi\)
−0.183955 + 0.982935i \(0.558890\pi\)
\(660\) −1.03228 + 5.23844i −0.0401813 + 0.203906i
\(661\) −22.1955 −0.863306 −0.431653 0.902040i \(-0.642070\pi\)
−0.431653 + 0.902040i \(0.642070\pi\)
\(662\) 32.3126i 1.25586i
\(663\) 56.3405i 2.18808i
\(664\) 0.270718 0.0105059
\(665\) 0.329237 1.67076i 0.0127673 0.0647894i
\(666\) 2.20617 0.0854873
\(667\) 58.9465i 2.28242i
\(668\) 9.84632i 0.380966i
\(669\) 37.3449 1.44384
\(670\) 2.26469 + 0.446274i 0.0874925 + 0.0172411i
\(671\) 9.39401 0.362652
\(672\) 2.10308i 0.0811282i
\(673\) 12.2986i 0.474077i −0.971500 0.237039i \(-0.923823\pi\)
0.971500 0.237039i \(-0.0761768\pi\)
\(674\) −26.3511 −1.01501
\(675\) −8.51875 + 20.7755i −0.327887 + 0.799650i
\(676\) 18.6541 0.717466
\(677\) 35.9527i 1.38178i −0.722962 0.690888i \(-0.757220\pi\)
0.722962 0.690888i \(-0.242780\pi\)
\(678\) 28.5081i 1.09485i
\(679\) −6.47689 −0.248560
\(680\) 7.95543 + 1.56768i 0.305077 + 0.0601178i
\(681\) 37.5616 1.43937
\(682\) 7.01832i 0.268745i
\(683\) 9.00958i 0.344742i 0.985032 + 0.172371i \(0.0551428\pi\)
−0.985032 + 0.172371i \(0.944857\pi\)
\(684\) −4.62620 −0.176887
\(685\) 1.24448 6.31528i 0.0475490 0.241295i
\(686\) 10.2201 0.390206
\(687\) 37.5231i 1.43160i
\(688\) 6.86464i 0.261712i
\(689\) −13.3555 −0.508803
\(690\) 9.56768 48.5527i 0.364235 1.84837i
\(691\) −9.11078 −0.346590 −0.173295 0.984870i \(-0.555441\pi\)
−0.173295 + 0.984870i \(0.555441\pi\)
\(692\) 2.98168i 0.113346i
\(693\) 3.04623i 0.115717i
\(694\) 2.77551 0.105357
\(695\) 7.87090 + 1.55102i 0.298560 + 0.0588336i
\(696\) −20.3126 −0.769946
\(697\) 9.64015i 0.365147i
\(698\) 11.5510i 0.437213i
\(699\) −70.5606 −2.66885
\(700\) −1.44461 + 3.52311i −0.0546011 + 0.133161i
\(701\) −14.7476 −0.557009 −0.278505 0.960435i \(-0.589839\pi\)
−0.278505 + 0.960435i \(0.589839\pi\)
\(702\) 25.2663i 0.953617i
\(703\) 0.476886i 0.0179861i
\(704\) 0.864641 0.0325874
\(705\) −7.58767 1.49521i −0.285768 0.0563128i
\(706\) −8.40171 −0.316202
\(707\) 12.5015i 0.470166i
\(708\) 12.4017i 0.466085i
\(709\) 8.63389 0.324253 0.162126 0.986770i \(-0.448165\pi\)
0.162126 + 0.986770i \(0.448165\pi\)
\(710\) −4.40171 + 22.3372i −0.165193 + 0.838299i
\(711\) −58.1483 −2.18073
\(712\) 0.387755i 0.0145317i
\(713\) 65.0496i 2.43613i
\(714\) −7.62620 −0.285403
\(715\) 2.10308 10.6724i 0.0786509 0.399126i
\(716\) 11.7938 0.440756
\(717\) 31.2909i 1.16858i
\(718\) 22.7895i 0.850495i
\(719\) 38.2759 1.42745 0.713726 0.700425i \(-0.247006\pi\)
0.713726 + 0.700425i \(0.247006\pi\)
\(720\) 10.1493 + 2.00000i 0.378243 + 0.0745356i
\(721\) 7.34153 0.273413
\(722\) 1.00000i 0.0372161i
\(723\) 3.45856i 0.128625i
\(724\) −14.5693 −0.541465
\(725\) 34.0279 + 13.9527i 1.26376 + 0.518191i
\(726\) −28.3126 −1.05078
\(727\) 31.1893i 1.15675i −0.815772 0.578373i \(-0.803688\pi\)
0.815772 0.578373i \(-0.196312\pi\)
\(728\) 4.28467i 0.158800i
\(729\) 44.0375 1.63102
\(730\) −35.9833 7.09079i −1.33180 0.262442i
\(731\) −24.8925 −0.920684
\(732\) 30.0033i 1.10895i
\(733\) 13.9634i 0.515748i 0.966179 + 0.257874i \(0.0830220\pi\)
−0.966179 + 0.257874i \(0.916978\pi\)
\(734\) −4.06455 −0.150025
\(735\) −7.66473 + 38.8959i −0.282718 + 1.43470i
\(736\) −8.01395 −0.295398
\(737\) 0.892548i 0.0328774i
\(738\) 12.2986i 0.452719i
\(739\) −9.02165 −0.331867 −0.165933 0.986137i \(-0.553064\pi\)
−0.165933 + 0.986137i \(0.553064\pi\)
\(740\) −0.206167 + 1.04623i −0.00757886 + 0.0384601i
\(741\) 15.5371 0.570768
\(742\) 1.80779i 0.0663659i
\(743\) 15.0342i 0.551550i 0.961222 + 0.275775i \(0.0889345\pi\)
−0.961222 + 0.275775i \(0.911066\pi\)
\(744\) −22.4157 −0.821798
\(745\) −36.9450 7.28030i −1.35356 0.266730i
\(746\) −18.4017 −0.673734
\(747\) 1.25240i 0.0458228i
\(748\) 3.13536i 0.114640i
\(749\) 3.26302 0.119228
\(750\) −25.7632 17.0156i −0.940740 0.621322i
\(751\) 29.6681 1.08260 0.541301 0.840829i \(-0.317932\pi\)
0.541301 + 0.840829i \(0.317932\pi\)
\(752\) 1.25240i 0.0456702i
\(753\) 29.2557i 1.06614i
\(754\) 41.3834 1.50709
\(755\) 37.2557 + 7.34153i 1.35587 + 0.267186i
\(756\) −3.42003 −0.124385
\(757\) 10.5819i 0.384604i 0.981336 + 0.192302i \(0.0615953\pi\)
−0.981336 + 0.192302i \(0.938405\pi\)
\(758\) 1.23844i 0.0449823i
\(759\) −19.1354 −0.694570
\(760\) 0.432320 2.19388i 0.0156819 0.0795803i
\(761\) −0.979789 −0.0355173 −0.0177587 0.999842i \(-0.505653\pi\)
−0.0177587 + 0.999842i \(0.505653\pi\)
\(762\) 46.8959i 1.69886i
\(763\) 10.2201i 0.369993i
\(764\) −13.2384 −0.478950
\(765\) 7.25240 36.8034i 0.262211 1.33063i
\(766\) 16.8646 0.609344
\(767\) 25.2663i 0.912315i
\(768\) 2.76156i 0.0996491i
\(769\) −43.1772 −1.55701 −0.778505 0.627638i \(-0.784022\pi\)
−0.778505 + 0.627638i \(0.784022\pi\)
\(770\) 1.44461 + 0.284672i 0.0520601 + 0.0102589i
\(771\) −0.424399 −0.0152844
\(772\) 2.54144i 0.0914683i
\(773\) 37.5250i 1.34968i −0.737964 0.674840i \(-0.764213\pi\)
0.737964 0.674840i \(-0.235787\pi\)
\(774\) −31.7572 −1.14149
\(775\) 37.5510 + 15.3973i 1.34887 + 0.553089i
\(776\) −8.50479 −0.305304
\(777\) 1.00293i 0.0359799i
\(778\) 8.59392i 0.308107i
\(779\) 2.65847 0.0952497
\(780\) −34.0864 6.71699i −1.22049 0.240507i
\(781\) 8.80342 0.315011
\(782\) 29.0602i 1.03919i
\(783\) 33.0323i 1.18048i
\(784\) 6.42003 0.229287
\(785\) 6.41566 32.5573i 0.228985 1.16202i
\(786\) 1.49521 0.0533323
\(787\) 22.5833i 0.805008i 0.915418 + 0.402504i \(0.131860\pi\)
−0.915418 + 0.402504i \(0.868140\pi\)
\(788\) 19.9109i