Properties

Label 1014.2.e.k.991.3
Level $1014$
Weight $2$
Character 1014.991
Analytic conductor $8.097$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.3
Root \(-0.623490 - 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 1014.991
Dual form 1014.2.e.k.529.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.692021 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.178448 - 0.309081i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.692021 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.178448 - 0.309081i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.346011 - 0.599308i) q^{10} +(1.46950 + 2.54525i) q^{11} +1.00000 q^{12} -0.356896 q^{14} +(-0.346011 - 0.599308i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.35690 + 5.81431i) q^{17} +1.00000 q^{18} +(-3.60388 + 6.24210i) q^{19} +(-0.346011 + 0.599308i) q^{20} -0.356896 q^{21} +(1.46950 - 2.54525i) q^{22} +(-1.19806 - 2.07510i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.52111 q^{25} +1.00000 q^{27} +(0.178448 + 0.309081i) q^{28} +(-3.91454 - 6.78019i) q^{29} +(-0.346011 + 0.599308i) q^{30} +2.76271 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.46950 - 2.54525i) q^{33} +6.71379 q^{34} +(0.123490 - 0.213891i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.04892 + 8.74498i) q^{37} +7.20775 q^{38} +0.692021 q^{40} +(2.44504 + 4.23494i) q^{41} +(0.178448 + 0.309081i) q^{42} +(-3.29590 + 5.70866i) q^{43} -2.93900 q^{44} +(-0.346011 + 0.599308i) q^{45} +(-1.19806 + 2.07510i) q^{46} -4.98792 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.43631 + 5.95187i) q^{49} +(2.26055 + 3.91539i) q^{50} +6.71379 q^{51} -8.88769 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.01693 + 1.76137i) q^{55} +(0.178448 - 0.309081i) q^{56} +7.20775 q^{57} +(-3.91454 + 6.78019i) q^{58} +(0.821552 - 1.42297i) q^{59} +0.692021 q^{60} +(3.24698 - 5.62393i) q^{61} +(-1.38135 - 2.39258i) q^{62} +(0.178448 + 0.309081i) q^{63} +1.00000 q^{64} -2.93900 q^{66} +(6.76271 + 11.7134i) q^{67} +(-3.35690 - 5.81431i) q^{68} +(-1.19806 + 2.07510i) q^{69} -0.246980 q^{70} +(3.40581 - 5.89904i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.18598 q^{73} +(5.04892 - 8.74498i) q^{74} +(2.26055 + 3.91539i) q^{75} +(-3.60388 - 6.24210i) q^{76} +1.04892 q^{77} +15.0465 q^{79} +(-0.346011 - 0.599308i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.44504 - 4.23494i) q^{82} +14.8267 q^{83} +(0.178448 - 0.309081i) q^{84} +(-2.32304 + 4.02363i) q^{85} +6.59179 q^{86} +(-3.91454 + 6.78019i) q^{87} +(1.46950 + 2.54525i) q^{88} +(0.198062 + 0.343054i) q^{89} +0.692021 q^{90} +2.39612 q^{92} +(-1.38135 - 2.39258i) q^{93} +(2.49396 + 4.31966i) q^{94} +(-2.49396 + 4.31966i) q^{95} +1.00000 q^{96} +(-0.208947 + 0.361908i) q^{97} +(3.43631 - 5.95187i) q^{98} -2.93900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} - q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 12 q^{17} + 6 q^{18} - 4 q^{19} + 3 q^{20} + 6 q^{21} - q^{22} - 16 q^{23} - 3 q^{24} + 4 q^{25} + 6 q^{27} - 3 q^{28} - 13 q^{29} + 3 q^{30} - 18 q^{31} - 3 q^{32} - q^{33} + 24 q^{34} - 4 q^{35} - 3 q^{36} + 12 q^{37} + 8 q^{38} - 6 q^{40} + 14 q^{41} - 3 q^{42} + 8 q^{43} + 2 q^{44} + 3 q^{45} - 16 q^{46} + 8 q^{47} - 3 q^{48} + 4 q^{49} - 2 q^{50} + 24 q^{51} + 30 q^{53} - 3 q^{54} + 22 q^{55} - 3 q^{56} + 8 q^{57} - 13 q^{58} + 9 q^{59} - 6 q^{60} + 10 q^{61} + 9 q^{62} - 3 q^{63} + 6 q^{64} + 2 q^{66} + 6 q^{67} - 12 q^{68} - 16 q^{69} + 8 q^{70} - 6 q^{71} - 3 q^{72} + 10 q^{73} + 12 q^{74} - 2 q^{75} - 4 q^{76} - 12 q^{77} - 10 q^{79} + 3 q^{80} - 3 q^{81} + 14 q^{82} - 14 q^{83} - 3 q^{84} + 26 q^{85} - 16 q^{86} - 13 q^{87} - q^{88} + 10 q^{89} - 6 q^{90} + 32 q^{92} + 9 q^{93} - 4 q^{94} + 4 q^{95} + 6 q^{96} - 7 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.692021 0.309481 0.154741 0.987955i \(-0.450546\pi\)
0.154741 + 0.987955i \(0.450546\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.178448 0.309081i 0.0674470 0.116822i −0.830330 0.557272i \(-0.811848\pi\)
0.897777 + 0.440451i \(0.145181\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.346011 0.599308i −0.109418 0.189518i
\(11\) 1.46950 + 2.54525i 0.443071 + 0.767422i 0.997916 0.0645324i \(-0.0205556\pi\)
−0.554845 + 0.831954i \(0.687222\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) −0.356896 −0.0953844
\(15\) −0.346011 0.599308i −0.0893396 0.154741i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.35690 + 5.81431i −0.814167 + 1.41018i 0.0957578 + 0.995405i \(0.469473\pi\)
−0.909925 + 0.414774i \(0.863861\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.60388 + 6.24210i −0.826786 + 1.43203i 0.0737611 + 0.997276i \(0.476500\pi\)
−0.900547 + 0.434759i \(0.856834\pi\)
\(20\) −0.346011 + 0.599308i −0.0773704 + 0.134009i
\(21\) −0.356896 −0.0778811
\(22\) 1.46950 2.54525i 0.313299 0.542649i
\(23\) −1.19806 2.07510i −0.249813 0.432689i 0.713661 0.700492i \(-0.247036\pi\)
−0.963474 + 0.267802i \(0.913703\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −4.52111 −0.904221
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.178448 + 0.309081i 0.0337235 + 0.0584108i
\(29\) −3.91454 6.78019i −0.726912 1.25905i −0.958182 0.286159i \(-0.907621\pi\)
0.231270 0.972890i \(-0.425712\pi\)
\(30\) −0.346011 + 0.599308i −0.0631726 + 0.109418i
\(31\) 2.76271 0.496197 0.248099 0.968735i \(-0.420194\pi\)
0.248099 + 0.968735i \(0.420194\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 1.46950 2.54525i 0.255807 0.443071i
\(34\) 6.71379 1.15141
\(35\) 0.123490 0.213891i 0.0208736 0.0361541i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 5.04892 + 8.74498i 0.830037 + 1.43767i 0.898008 + 0.439979i \(0.145014\pi\)
−0.0679713 + 0.997687i \(0.521653\pi\)
\(38\) 7.20775 1.16925
\(39\) 0 0
\(40\) 0.692021 0.109418
\(41\) 2.44504 + 4.23494i 0.381851 + 0.661386i 0.991327 0.131419i \(-0.0419533\pi\)
−0.609476 + 0.792805i \(0.708620\pi\)
\(42\) 0.178448 + 0.309081i 0.0275351 + 0.0476922i
\(43\) −3.29590 + 5.70866i −0.502620 + 0.870563i 0.497376 + 0.867535i \(0.334297\pi\)
−0.999995 + 0.00302747i \(0.999036\pi\)
\(44\) −2.93900 −0.443071
\(45\) −0.346011 + 0.599308i −0.0515802 + 0.0893396i
\(46\) −1.19806 + 2.07510i −0.176645 + 0.305957i
\(47\) −4.98792 −0.727563 −0.363781 0.931484i \(-0.618514\pi\)
−0.363781 + 0.931484i \(0.618514\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 3.43631 + 5.95187i 0.490902 + 0.850267i
\(50\) 2.26055 + 3.91539i 0.319690 + 0.553720i
\(51\) 6.71379 0.940119
\(52\) 0 0
\(53\) −8.88769 −1.22082 −0.610409 0.792086i \(-0.708995\pi\)
−0.610409 + 0.792086i \(0.708995\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 1.01693 + 1.76137i 0.137122 + 0.237503i
\(56\) 0.178448 0.309081i 0.0238461 0.0413027i
\(57\) 7.20775 0.954690
\(58\) −3.91454 + 6.78019i −0.514005 + 0.890282i
\(59\) 0.821552 1.42297i 0.106957 0.185255i −0.807579 0.589759i \(-0.799223\pi\)
0.914536 + 0.404504i \(0.132556\pi\)
\(60\) 0.692021 0.0893396
\(61\) 3.24698 5.62393i 0.415733 0.720071i −0.579772 0.814779i \(-0.696858\pi\)
0.995505 + 0.0947079i \(0.0301917\pi\)
\(62\) −1.38135 2.39258i −0.175432 0.303857i
\(63\) 0.178448 + 0.309081i 0.0224823 + 0.0389405i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.93900 −0.361766
\(67\) 6.76271 + 11.7134i 0.826196 + 1.43101i 0.901001 + 0.433816i \(0.142833\pi\)
−0.0748051 + 0.997198i \(0.523833\pi\)
\(68\) −3.35690 5.81431i −0.407083 0.705089i
\(69\) −1.19806 + 2.07510i −0.144230 + 0.249813i
\(70\) −0.246980 −0.0295197
\(71\) 3.40581 5.89904i 0.404196 0.700087i −0.590032 0.807380i \(-0.700885\pi\)
0.994227 + 0.107293i \(0.0342181\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −3.18598 −0.372891 −0.186445 0.982465i \(-0.559697\pi\)
−0.186445 + 0.982465i \(0.559697\pi\)
\(74\) 5.04892 8.74498i 0.586925 1.01658i
\(75\) 2.26055 + 3.91539i 0.261026 + 0.452111i
\(76\) −3.60388 6.24210i −0.413393 0.716017i
\(77\) 1.04892 0.119535
\(78\) 0 0
\(79\) 15.0465 1.69287 0.846433 0.532495i \(-0.178745\pi\)
0.846433 + 0.532495i \(0.178745\pi\)
\(80\) −0.346011 0.599308i −0.0386852 0.0670047i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.44504 4.23494i 0.270010 0.467671i
\(83\) 14.8267 1.62744 0.813720 0.581256i \(-0.197439\pi\)
0.813720 + 0.581256i \(0.197439\pi\)
\(84\) 0.178448 0.309081i 0.0194703 0.0337235i
\(85\) −2.32304 + 4.02363i −0.251970 + 0.436424i
\(86\) 6.59179 0.710811
\(87\) −3.91454 + 6.78019i −0.419683 + 0.726912i
\(88\) 1.46950 + 2.54525i 0.156649 + 0.271325i
\(89\) 0.198062 + 0.343054i 0.0209946 + 0.0363636i 0.876332 0.481708i \(-0.159983\pi\)
−0.855337 + 0.518072i \(0.826650\pi\)
\(90\) 0.692021 0.0729455
\(91\) 0 0
\(92\) 2.39612 0.249813
\(93\) −1.38135 2.39258i −0.143240 0.248099i
\(94\) 2.49396 + 4.31966i 0.257232 + 0.445539i
\(95\) −2.49396 + 4.31966i −0.255875 + 0.443188i
\(96\) 1.00000 0.102062
\(97\) −0.208947 + 0.361908i −0.0212154 + 0.0367461i −0.876438 0.481514i \(-0.840087\pi\)
0.855223 + 0.518261i \(0.173420\pi\)
\(98\) 3.43631 5.95187i 0.347120 0.601229i
\(99\) −2.93900 −0.295381
\(100\) 2.26055 3.91539i 0.226055 0.391539i
\(101\) −5.00753 8.67330i −0.498268 0.863026i 0.501730 0.865024i \(-0.332697\pi\)
−0.999998 + 0.00199864i \(0.999364\pi\)
\(102\) −3.35690 5.81431i −0.332382 0.575703i
\(103\) −9.62565 −0.948443 −0.474222 0.880406i \(-0.657270\pi\)
−0.474222 + 0.880406i \(0.657270\pi\)
\(104\) 0 0
\(105\) −0.246980 −0.0241027
\(106\) 4.44385 + 7.69697i 0.431624 + 0.747595i
\(107\) 3.31551 + 5.74263i 0.320523 + 0.555161i 0.980596 0.196040i \(-0.0628082\pi\)
−0.660073 + 0.751201i \(0.729475\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −12.9879 −1.24402 −0.622008 0.783011i \(-0.713683\pi\)
−0.622008 + 0.783011i \(0.713683\pi\)
\(110\) 1.01693 1.76137i 0.0969601 0.167940i
\(111\) 5.04892 8.74498i 0.479222 0.830037i
\(112\) −0.356896 −0.0337235
\(113\) −0.396125 + 0.686108i −0.0372643 + 0.0645436i −0.884056 0.467381i \(-0.845198\pi\)
0.846792 + 0.531925i \(0.178531\pi\)
\(114\) −3.60388 6.24210i −0.337534 0.584626i
\(115\) −0.829085 1.43602i −0.0773126 0.133909i
\(116\) 7.82908 0.726912
\(117\) 0 0
\(118\) −1.64310 −0.151260
\(119\) 1.19806 + 2.07510i 0.109826 + 0.190225i
\(120\) −0.346011 0.599308i −0.0315863 0.0547091i
\(121\) 1.18114 2.04579i 0.107376 0.185981i
\(122\) −6.49396 −0.587935
\(123\) 2.44504 4.23494i 0.220462 0.381851i
\(124\) −1.38135 + 2.39258i −0.124049 + 0.214860i
\(125\) −6.58881 −0.589321
\(126\) 0.178448 0.309081i 0.0158974 0.0275351i
\(127\) 9.10872 + 15.7768i 0.808268 + 1.39996i 0.914062 + 0.405574i \(0.132928\pi\)
−0.105794 + 0.994388i \(0.533738\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 6.59179 0.580375
\(130\) 0 0
\(131\) 2.73556 0.239007 0.119504 0.992834i \(-0.461870\pi\)
0.119504 + 0.992834i \(0.461870\pi\)
\(132\) 1.46950 + 2.54525i 0.127904 + 0.221536i
\(133\) 1.28621 + 2.22778i 0.111528 + 0.193173i
\(134\) 6.76271 11.7134i 0.584209 1.01188i
\(135\) 0.692021 0.0595597
\(136\) −3.35690 + 5.81431i −0.287851 + 0.498573i
\(137\) −3.82371 + 6.62286i −0.326681 + 0.565829i −0.981851 0.189653i \(-0.939264\pi\)
0.655170 + 0.755482i \(0.272597\pi\)
\(138\) 2.39612 0.203972
\(139\) −1.69202 + 2.93067i −0.143515 + 0.248576i −0.928818 0.370536i \(-0.879174\pi\)
0.785303 + 0.619112i \(0.212507\pi\)
\(140\) 0.123490 + 0.213891i 0.0104368 + 0.0180771i
\(141\) 2.49396 + 4.31966i 0.210029 + 0.363781i
\(142\) −6.81163 −0.571619
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −2.70895 4.69203i −0.224966 0.389652i
\(146\) 1.59299 + 2.75914i 0.131837 + 0.228348i
\(147\) 3.43631 5.95187i 0.283422 0.490902i
\(148\) −10.0978 −0.830037
\(149\) 10.4085 18.0281i 0.852698 1.47692i −0.0260669 0.999660i \(-0.508298\pi\)
0.878765 0.477255i \(-0.158368\pi\)
\(150\) 2.26055 3.91539i 0.184573 0.319690i
\(151\) −0.895461 −0.0728715 −0.0364358 0.999336i \(-0.511600\pi\)
−0.0364358 + 0.999336i \(0.511600\pi\)
\(152\) −3.60388 + 6.24210i −0.292313 + 0.506301i
\(153\) −3.35690 5.81431i −0.271389 0.470059i
\(154\) −0.524459 0.908389i −0.0422621 0.0732001i
\(155\) 1.91185 0.153564
\(156\) 0 0
\(157\) 8.59179 0.685700 0.342850 0.939390i \(-0.388608\pi\)
0.342850 + 0.939390i \(0.388608\pi\)
\(158\) −7.52326 13.0307i −0.598519 1.03666i
\(159\) 4.44385 + 7.69697i 0.352420 + 0.610409i
\(160\) −0.346011 + 0.599308i −0.0273546 + 0.0473795i
\(161\) −0.855167 −0.0673966
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −0.862937 + 1.49465i −0.0675904 + 0.117070i −0.897840 0.440322i \(-0.854864\pi\)
0.830250 + 0.557392i \(0.188198\pi\)
\(164\) −4.89008 −0.381851
\(165\) 1.01693 1.76137i 0.0791676 0.137122i
\(166\) −7.41335 12.8403i −0.575387 0.996600i
\(167\) −10.5700 18.3078i −0.817933 1.41670i −0.907203 0.420694i \(-0.861787\pi\)
0.0892696 0.996007i \(-0.471547\pi\)
\(168\) −0.356896 −0.0275351
\(169\) 0 0
\(170\) 4.64609 0.356339
\(171\) −3.60388 6.24210i −0.275595 0.477345i
\(172\) −3.29590 5.70866i −0.251310 0.435281i
\(173\) −4.67725 + 8.10124i −0.355605 + 0.615926i −0.987221 0.159355i \(-0.949058\pi\)
0.631616 + 0.775281i \(0.282392\pi\)
\(174\) 7.82908 0.593521
\(175\) −0.806782 + 1.39739i −0.0609870 + 0.105633i
\(176\) 1.46950 2.54525i 0.110768 0.191855i
\(177\) −1.64310 −0.123503
\(178\) 0.198062 0.343054i 0.0148454 0.0257130i
\(179\) −1.58761 2.74983i −0.118664 0.205532i 0.800575 0.599233i \(-0.204528\pi\)
−0.919238 + 0.393701i \(0.871194\pi\)
\(180\) −0.346011 0.599308i −0.0257901 0.0446698i
\(181\) −19.7995 −1.47169 −0.735844 0.677151i \(-0.763214\pi\)
−0.735844 + 0.677151i \(0.763214\pi\)
\(182\) 0 0
\(183\) −6.49396 −0.480047
\(184\) −1.19806 2.07510i −0.0883223 0.152979i
\(185\) 3.49396 + 6.05171i 0.256881 + 0.444931i
\(186\) −1.38135 + 2.39258i −0.101286 + 0.175432i
\(187\) −19.7318 −1.44294
\(188\) 2.49396 4.31966i 0.181891 0.315044i
\(189\) 0.178448 0.309081i 0.0129802 0.0224823i
\(190\) 4.98792 0.361862
\(191\) −7.63102 + 13.2173i −0.552161 + 0.956372i 0.445957 + 0.895054i \(0.352863\pi\)
−0.998118 + 0.0613172i \(0.980470\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −2.38404 4.12928i −0.171607 0.297232i 0.767375 0.641199i \(-0.221563\pi\)
−0.938982 + 0.343967i \(0.888229\pi\)
\(194\) 0.417895 0.0300031
\(195\) 0 0
\(196\) −6.87263 −0.490902
\(197\) −6.11745 10.5957i −0.435850 0.754915i 0.561514 0.827467i \(-0.310219\pi\)
−0.997365 + 0.0725523i \(0.976886\pi\)
\(198\) 1.46950 + 2.54525i 0.104433 + 0.180883i
\(199\) 5.92423 10.2611i 0.419958 0.727388i −0.575977 0.817466i \(-0.695378\pi\)
0.995935 + 0.0900779i \(0.0287116\pi\)
\(200\) −4.52111 −0.319690
\(201\) 6.76271 11.7134i 0.477005 0.826196i
\(202\) −5.00753 + 8.67330i −0.352329 + 0.610251i
\(203\) −2.79417 −0.196112
\(204\) −3.35690 + 5.81431i −0.235030 + 0.407083i
\(205\) 1.69202 + 2.93067i 0.118176 + 0.204687i
\(206\) 4.81282 + 8.33605i 0.335325 + 0.580800i
\(207\) 2.39612 0.166542
\(208\) 0 0
\(209\) −21.1836 −1.46530
\(210\) 0.123490 + 0.213891i 0.00852161 + 0.0147599i
\(211\) 8.63102 + 14.9494i 0.594184 + 1.02916i 0.993661 + 0.112414i \(0.0358583\pi\)
−0.399477 + 0.916743i \(0.630808\pi\)
\(212\) 4.44385 7.69697i 0.305205 0.528630i
\(213\) −6.81163 −0.466725
\(214\) 3.31551 5.74263i 0.226644 0.392558i
\(215\) −2.28083 + 3.95052i −0.155551 + 0.269423i
\(216\) 1.00000 0.0680414
\(217\) 0.493000 0.853901i 0.0334670 0.0579665i
\(218\) 6.49396 + 11.2479i 0.439826 + 0.761802i
\(219\) 1.59299 + 2.75914i 0.107644 + 0.186445i
\(220\) −2.03385 −0.137122
\(221\) 0 0
\(222\) −10.0978 −0.677722
\(223\) −3.38404 5.86133i −0.226612 0.392504i 0.730190 0.683245i \(-0.239432\pi\)
−0.956802 + 0.290741i \(0.906098\pi\)
\(224\) 0.178448 + 0.309081i 0.0119231 + 0.0206513i
\(225\) 2.26055 3.91539i 0.150704 0.261026i
\(226\) 0.792249 0.0526996
\(227\) −11.8400 + 20.5074i −0.785846 + 1.36113i 0.142646 + 0.989774i \(0.454439\pi\)
−0.928492 + 0.371352i \(0.878894\pi\)
\(228\) −3.60388 + 6.24210i −0.238672 + 0.413393i
\(229\) −8.29829 −0.548366 −0.274183 0.961677i \(-0.588407\pi\)
−0.274183 + 0.961677i \(0.588407\pi\)
\(230\) −0.829085 + 1.43602i −0.0546682 + 0.0946882i
\(231\) −0.524459 0.908389i −0.0345068 0.0597676i
\(232\) −3.91454 6.78019i −0.257002 0.445141i
\(233\) −23.9651 −1.57000 −0.785002 0.619493i \(-0.787338\pi\)
−0.785002 + 0.619493i \(0.787338\pi\)
\(234\) 0 0
\(235\) −3.45175 −0.225167
\(236\) 0.821552 + 1.42297i 0.0534785 + 0.0926275i
\(237\) −7.52326 13.0307i −0.488688 0.846433i
\(238\) 1.19806 2.07510i 0.0776588 0.134509i
\(239\) 12.6160 0.816058 0.408029 0.912969i \(-0.366216\pi\)
0.408029 + 0.912969i \(0.366216\pi\)
\(240\) −0.346011 + 0.599308i −0.0223349 + 0.0386852i
\(241\) −13.1969 + 22.8576i −0.850085 + 1.47239i 0.0310462 + 0.999518i \(0.490116\pi\)
−0.881131 + 0.472872i \(0.843217\pi\)
\(242\) −2.36227 −0.151853
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.24698 + 5.62393i 0.207867 + 0.360035i
\(245\) 2.37800 + 4.11882i 0.151925 + 0.263142i
\(246\) −4.89008 −0.311780
\(247\) 0 0
\(248\) 2.76271 0.175432
\(249\) −7.41335 12.8403i −0.469802 0.813720i
\(250\) 3.29440 + 5.70608i 0.208356 + 0.360884i
\(251\) 15.0172 26.0106i 0.947879 1.64177i 0.197996 0.980203i \(-0.436557\pi\)
0.749882 0.661571i \(-0.230110\pi\)
\(252\) −0.356896 −0.0224823
\(253\) 3.52111 6.09873i 0.221370 0.383424i
\(254\) 9.10872 15.7768i 0.571532 0.989922i
\(255\) 4.64609 0.290949
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.63102 9.75322i −0.351254 0.608389i 0.635216 0.772335i \(-0.280911\pi\)
−0.986469 + 0.163946i \(0.947578\pi\)
\(258\) −3.29590 5.70866i −0.205194 0.355406i
\(259\) 3.60388 0.223934
\(260\) 0 0
\(261\) 7.82908 0.484608
\(262\) −1.36778 2.36907i −0.0845018 0.146361i
\(263\) 2.77479 + 4.80608i 0.171101 + 0.296355i 0.938805 0.344449i \(-0.111934\pi\)
−0.767704 + 0.640804i \(0.778601\pi\)
\(264\) 1.46950 2.54525i 0.0904415 0.156649i
\(265\) −6.15047 −0.377821
\(266\) 1.28621 2.22778i 0.0788625 0.136594i
\(267\) 0.198062 0.343054i 0.0121212 0.0209946i
\(268\) −13.5254 −0.826196
\(269\) −8.34362 + 14.4516i −0.508719 + 0.881128i 0.491230 + 0.871030i \(0.336548\pi\)
−0.999949 + 0.0100977i \(0.996786\pi\)
\(270\) −0.346011 0.599308i −0.0210575 0.0364727i
\(271\) 3.30678 + 5.72751i 0.200873 + 0.347922i 0.948810 0.315848i \(-0.102289\pi\)
−0.747937 + 0.663770i \(0.768956\pi\)
\(272\) 6.71379 0.407083
\(273\) 0 0
\(274\) 7.64742 0.461997
\(275\) −6.64377 11.5073i −0.400634 0.693919i
\(276\) −1.19806 2.07510i −0.0721149 0.124907i
\(277\) 10.8998 18.8790i 0.654904 1.13433i −0.327014 0.945019i \(-0.606042\pi\)
0.981918 0.189307i \(-0.0606242\pi\)
\(278\) 3.38404 0.202961
\(279\) −1.38135 + 2.39258i −0.0826995 + 0.143240i
\(280\) 0.123490 0.213891i 0.00737993 0.0127824i
\(281\) 20.5918 1.22840 0.614202 0.789149i \(-0.289478\pi\)
0.614202 + 0.789149i \(0.289478\pi\)
\(282\) 2.49396 4.31966i 0.148513 0.257232i
\(283\) 6.50604 + 11.2688i 0.386744 + 0.669860i 0.992009 0.126163i \(-0.0402664\pi\)
−0.605265 + 0.796024i \(0.706933\pi\)
\(284\) 3.40581 + 5.89904i 0.202098 + 0.350044i
\(285\) 4.98792 0.295459
\(286\) 0 0
\(287\) 1.74525 0.103019
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −14.0375 24.3137i −0.825735 1.43022i
\(290\) −2.70895 + 4.69203i −0.159075 + 0.275526i
\(291\) 0.417895 0.0244974
\(292\) 1.59299 2.75914i 0.0932227 0.161466i
\(293\) 7.46950 12.9376i 0.436373 0.755820i −0.561034 0.827793i \(-0.689596\pi\)
0.997407 + 0.0719730i \(0.0229295\pi\)
\(294\) −6.87263 −0.400820
\(295\) 0.568532 0.984726i 0.0331012 0.0573329i
\(296\) 5.04892 + 8.74498i 0.293462 + 0.508292i
\(297\) 1.46950 + 2.54525i 0.0852691 + 0.147690i
\(298\) −20.8170 −1.20590
\(299\) 0 0
\(300\) −4.52111 −0.261026
\(301\) 1.17629 + 2.03740i 0.0678003 + 0.117434i
\(302\) 0.447730 + 0.775492i 0.0257640 + 0.0446245i
\(303\) −5.00753 + 8.67330i −0.287675 + 0.498268i
\(304\) 7.20775 0.413393
\(305\) 2.24698 3.89188i 0.128662 0.222849i
\(306\) −3.35690 + 5.81431i −0.191901 + 0.332382i
\(307\) 26.0301 1.48562 0.742809 0.669503i \(-0.233493\pi\)
0.742809 + 0.669503i \(0.233493\pi\)
\(308\) −0.524459 + 0.908389i −0.0298838 + 0.0517603i
\(309\) 4.81282 + 8.33605i 0.273792 + 0.474222i
\(310\) −0.955927 1.65571i −0.0542930 0.0940382i
\(311\) −4.81163 −0.272842 −0.136421 0.990651i \(-0.543560\pi\)
−0.136421 + 0.990651i \(0.543560\pi\)
\(312\) 0 0
\(313\) −26.0411 −1.47193 −0.735966 0.677018i \(-0.763272\pi\)
−0.735966 + 0.677018i \(0.763272\pi\)
\(314\) −4.29590 7.44071i −0.242431 0.419904i
\(315\) 0.123490 + 0.213891i 0.00695786 + 0.0120514i
\(316\) −7.52326 + 13.0307i −0.423217 + 0.733033i
\(317\) −11.5211 −0.647090 −0.323545 0.946213i \(-0.604875\pi\)
−0.323545 + 0.946213i \(0.604875\pi\)
\(318\) 4.44385 7.69697i 0.249198 0.431624i
\(319\) 11.5048 19.9270i 0.644148 1.11570i
\(320\) 0.692021 0.0386852
\(321\) 3.31551 5.74263i 0.185054 0.320523i
\(322\) 0.427583 + 0.740596i 0.0238283 + 0.0412718i
\(323\) −24.1957 41.9081i −1.34628 2.33183i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 1.72587 0.0955873
\(327\) 6.49396 + 11.2479i 0.359117 + 0.622008i
\(328\) 2.44504 + 4.23494i 0.135005 + 0.233835i
\(329\) −0.890084 + 1.54167i −0.0490719 + 0.0849950i
\(330\) −2.03385 −0.111960
\(331\) −1.71917 + 2.97769i −0.0944940 + 0.163668i −0.909397 0.415928i \(-0.863457\pi\)
0.814903 + 0.579597i \(0.196790\pi\)
\(332\) −7.41335 + 12.8403i −0.406860 + 0.704703i
\(333\) −10.0978 −0.553358
\(334\) −10.5700 + 18.3078i −0.578366 + 1.00176i
\(335\) 4.67994 + 8.10589i 0.255692 + 0.442872i
\(336\) 0.178448 + 0.309081i 0.00973513 + 0.0168617i
\(337\) 8.20105 0.446739 0.223370 0.974734i \(-0.428294\pi\)
0.223370 + 0.974734i \(0.428294\pi\)
\(338\) 0 0
\(339\) 0.792249 0.0430291
\(340\) −2.32304 4.02363i −0.125985 0.218212i
\(341\) 4.05980 + 7.03178i 0.219851 + 0.380792i
\(342\) −3.60388 + 6.24210i −0.194875 + 0.337534i
\(343\) 4.95108 0.267333
\(344\) −3.29590 + 5.70866i −0.177703 + 0.307790i
\(345\) −0.829085 + 1.43602i −0.0446364 + 0.0773126i
\(346\) 9.35450 0.502901
\(347\) −3.93147 + 6.80950i −0.211052 + 0.365553i −0.952044 0.305961i \(-0.901022\pi\)
0.740992 + 0.671514i \(0.234356\pi\)
\(348\) −3.91454 6.78019i −0.209841 0.363456i
\(349\) 9.36227 + 16.2159i 0.501151 + 0.868019i 0.999999 + 0.00132953i \(0.000423203\pi\)
−0.498848 + 0.866689i \(0.666243\pi\)
\(350\) 1.61356 0.0862486
\(351\) 0 0
\(352\) −2.93900 −0.156649
\(353\) 15.7724 + 27.3186i 0.839480 + 1.45402i 0.890330 + 0.455316i \(0.150474\pi\)
−0.0508500 + 0.998706i \(0.516193\pi\)
\(354\) 0.821552 + 1.42297i 0.0436650 + 0.0756300i
\(355\) 2.35690 4.08226i 0.125091 0.216664i
\(356\) −0.396125 −0.0209946
\(357\) 1.19806 2.07510i 0.0634082 0.109826i
\(358\) −1.58761 + 2.74983i −0.0839080 + 0.145333i
\(359\) 2.39612 0.126463 0.0632313 0.997999i \(-0.479859\pi\)
0.0632313 + 0.997999i \(0.479859\pi\)
\(360\) −0.346011 + 0.599308i −0.0182364 + 0.0315863i
\(361\) −16.4758 28.5370i −0.867149 1.50195i
\(362\) 9.89977 + 17.1469i 0.520320 + 0.901222i
\(363\) −2.36227 −0.123987
\(364\) 0 0
\(365\) −2.20477 −0.115403
\(366\) 3.24698 + 5.62393i 0.169722 + 0.293968i
\(367\) 0.00215593 + 0.00373419i 0.000112539 + 0.000194923i 0.866082 0.499903i \(-0.166631\pi\)
−0.865969 + 0.500097i \(0.833298\pi\)
\(368\) −1.19806 + 2.07510i −0.0624533 + 0.108172i
\(369\) −4.89008 −0.254568
\(370\) 3.49396 6.05171i 0.181642 0.314614i
\(371\) −1.58599 + 2.74702i −0.0823405 + 0.142618i
\(372\) 2.76271 0.143240
\(373\) 16.1564 27.9838i 0.836549 1.44895i −0.0562144 0.998419i \(-0.517903\pi\)
0.892763 0.450526i \(-0.148764\pi\)
\(374\) 9.86592 + 17.0883i 0.510155 + 0.883614i
\(375\) 3.29440 + 5.70608i 0.170122 + 0.294661i
\(376\) −4.98792 −0.257232
\(377\) 0 0
\(378\) −0.356896 −0.0183567
\(379\) −9.87800 17.1092i −0.507399 0.878841i −0.999963 0.00856468i \(-0.997274\pi\)
0.492564 0.870276i \(-0.336060\pi\)
\(380\) −2.49396 4.31966i −0.127937 0.221594i
\(381\) 9.10872 15.7768i 0.466654 0.808268i
\(382\) 15.2620 0.780874
\(383\) −14.4058 + 24.9516i −0.736103 + 1.27497i 0.218135 + 0.975919i \(0.430003\pi\)
−0.954238 + 0.299049i \(0.903331\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0.725873 0.0369939
\(386\) −2.38404 + 4.12928i −0.121345 + 0.210175i
\(387\) −3.29590 5.70866i −0.167540 0.290188i
\(388\) −0.208947 0.361908i −0.0106077 0.0183731i
\(389\) 34.7821 1.76352 0.881761 0.471697i \(-0.156358\pi\)
0.881761 + 0.471697i \(0.156358\pi\)
\(390\) 0 0
\(391\) 16.0871 0.813559
\(392\) 3.43631 + 5.95187i 0.173560 + 0.300615i
\(393\) −1.36778 2.36907i −0.0689954 0.119504i
\(394\) −6.11745 + 10.5957i −0.308193 + 0.533805i
\(395\) 10.4125 0.523911
\(396\) 1.46950 2.54525i 0.0738452 0.127904i
\(397\) 2.57673 4.46302i 0.129322 0.223993i −0.794092 0.607798i \(-0.792053\pi\)
0.923414 + 0.383805i \(0.125386\pi\)
\(398\) −11.8485 −0.593910
\(399\) 1.28621 2.22778i 0.0643910 0.111528i
\(400\) 2.26055 + 3.91539i 0.113028 + 0.195770i
\(401\) −6.66248 11.5398i −0.332708 0.576268i 0.650333 0.759649i \(-0.274629\pi\)
−0.983042 + 0.183381i \(0.941296\pi\)
\(402\) −13.5254 −0.674587
\(403\) 0 0
\(404\) 10.0151 0.498268
\(405\) −0.346011 0.599308i −0.0171934 0.0297799i
\(406\) 1.39708 + 2.41982i 0.0693361 + 0.120094i
\(407\) −14.8388 + 25.7015i −0.735531 + 1.27398i
\(408\) 6.71379 0.332382
\(409\) 12.0118 20.8051i 0.593947 1.02875i −0.399747 0.916626i \(-0.630902\pi\)
0.993694 0.112122i \(-0.0357647\pi\)
\(410\) 1.69202 2.93067i 0.0835630 0.144735i
\(411\) 7.64742 0.377219
\(412\) 4.81282 8.33605i 0.237111 0.410688i
\(413\) −0.293209 0.507852i −0.0144278 0.0249898i
\(414\) −1.19806 2.07510i −0.0588815 0.101986i
\(415\) 10.2604 0.503663
\(416\) 0 0
\(417\) 3.38404 0.165717
\(418\) 10.5918 + 18.3455i 0.518062 + 0.897309i
\(419\) −6.90246 11.9554i −0.337207 0.584060i 0.646699 0.762745i \(-0.276149\pi\)
−0.983906 + 0.178685i \(0.942816\pi\)
\(420\) 0.123490 0.213891i 0.00602569 0.0104368i
\(421\) 7.72587 0.376536 0.188268 0.982118i \(-0.439713\pi\)
0.188268 + 0.982118i \(0.439713\pi\)
\(422\) 8.63102 14.9494i 0.420152 0.727724i
\(423\) 2.49396 4.31966i 0.121260 0.210029i
\(424\) −8.88769 −0.431624
\(425\) 15.1769 26.2871i 0.736187 1.27511i
\(426\) 3.40581 + 5.89904i 0.165012 + 0.285809i
\(427\) −1.15883 2.00716i −0.0560799 0.0971332i
\(428\) −6.63102 −0.320523
\(429\) 0 0
\(430\) 4.56166 0.219983
\(431\) −0.320060 0.554360i −0.0154168 0.0267026i 0.858214 0.513292i \(-0.171574\pi\)
−0.873631 + 0.486589i \(0.838241\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −10.6380 + 18.4256i −0.511231 + 0.885478i 0.488685 + 0.872461i \(0.337477\pi\)
−0.999915 + 0.0130171i \(0.995856\pi\)
\(434\) −0.985999 −0.0473295
\(435\) −2.70895 + 4.69203i −0.129884 + 0.224966i
\(436\) 6.49396 11.2479i 0.311004 0.538675i
\(437\) 17.2707 0.826168
\(438\) 1.59299 2.75914i 0.0761160 0.131837i
\(439\) −6.35905 11.0142i −0.303501 0.525679i 0.673425 0.739255i \(-0.264822\pi\)
−0.976926 + 0.213576i \(0.931489\pi\)
\(440\) 1.01693 + 1.76137i 0.0484800 + 0.0839699i
\(441\) −6.87263 −0.327268
\(442\) 0 0
\(443\) 22.5972 1.07362 0.536812 0.843702i \(-0.319628\pi\)
0.536812 + 0.843702i \(0.319628\pi\)
\(444\) 5.04892 + 8.74498i 0.239611 + 0.415018i
\(445\) 0.137063 + 0.237401i 0.00649743 + 0.0112539i
\(446\) −3.38404 + 5.86133i −0.160239 + 0.277542i
\(447\) −20.8170 −0.984610
\(448\) 0.178448 0.309081i 0.00843087 0.0146027i
\(449\) −5.82371 + 10.0870i −0.274838 + 0.476033i −0.970094 0.242729i \(-0.921957\pi\)
0.695256 + 0.718762i \(0.255291\pi\)
\(450\) −4.52111 −0.213127
\(451\) −7.18598 + 12.4465i −0.338375 + 0.586082i
\(452\) −0.396125 0.686108i −0.0186321 0.0322718i
\(453\) 0.447730 + 0.775492i 0.0210362 + 0.0364358i
\(454\) 23.6799 1.11135
\(455\) 0 0
\(456\) 7.20775 0.337534
\(457\) 10.5945 + 18.3502i 0.495589 + 0.858385i 0.999987 0.00508594i \(-0.00161891\pi\)
−0.504398 + 0.863471i \(0.668286\pi\)
\(458\) 4.14914 + 7.18653i 0.193877 + 0.335804i
\(459\) −3.35690 + 5.81431i −0.156686 + 0.271389i
\(460\) 1.65817 0.0773126
\(461\) −12.0347 + 20.8447i −0.560511 + 0.970833i 0.436941 + 0.899490i \(0.356062\pi\)
−0.997452 + 0.0713432i \(0.977271\pi\)
\(462\) −0.524459 + 0.908389i −0.0244000 + 0.0422621i
\(463\) −18.1715 −0.844502 −0.422251 0.906479i \(-0.638760\pi\)
−0.422251 + 0.906479i \(0.638760\pi\)
\(464\) −3.91454 + 6.78019i −0.181728 + 0.314762i
\(465\) −0.955927 1.65571i −0.0443301 0.0767819i
\(466\) 11.9825 + 20.7544i 0.555081 + 0.961428i
\(467\) −2.93123 −0.135641 −0.0678206 0.997698i \(-0.521605\pi\)
−0.0678206 + 0.997698i \(0.521605\pi\)
\(468\) 0 0
\(469\) 4.82717 0.222898
\(470\) 1.72587 + 2.98930i 0.0796086 + 0.137886i
\(471\) −4.29590 7.44071i −0.197944 0.342850i
\(472\) 0.821552 1.42297i 0.0378150 0.0654975i
\(473\) −19.3733 −0.890785
\(474\) −7.52326 + 13.0307i −0.345555 + 0.598519i
\(475\) 16.2935 28.2212i 0.747597 1.29488i
\(476\) −2.39612 −0.109826
\(477\) 4.44385 7.69697i 0.203470 0.352420i
\(478\) −6.30798 10.9257i −0.288520 0.499732i
\(479\) 15.3545 + 26.5948i 0.701565 + 1.21515i 0.967917 + 0.251271i \(0.0808484\pi\)
−0.266352 + 0.963876i \(0.585818\pi\)
\(480\) 0.692021 0.0315863
\(481\) 0 0
\(482\) 26.3937 1.20220
\(483\) 0.427583 + 0.740596i 0.0194557 + 0.0336983i
\(484\) 1.18114 + 2.04579i 0.0536880 + 0.0929904i
\(485\) −0.144596 + 0.250448i −0.00656577 + 0.0113722i
\(486\) 1.00000 0.0453609
\(487\) −12.0749 + 20.9143i −0.547164 + 0.947717i 0.451303 + 0.892371i \(0.350959\pi\)
−0.998467 + 0.0553458i \(0.982374\pi\)
\(488\) 3.24698 5.62393i 0.146984 0.254584i
\(489\) 1.72587 0.0780467
\(490\) 2.37800 4.11882i 0.107427 0.186069i
\(491\) −7.29859 12.6415i −0.329381 0.570504i 0.653009 0.757351i \(-0.273507\pi\)
−0.982389 + 0.186847i \(0.940173\pi\)
\(492\) 2.44504 + 4.23494i 0.110231 + 0.190926i
\(493\) 52.5628 2.36731
\(494\) 0 0
\(495\) −2.03385 −0.0914148
\(496\) −1.38135 2.39258i −0.0620246 0.107430i
\(497\) −1.21552 2.10534i −0.0545236 0.0944376i
\(498\) −7.41335 + 12.8403i −0.332200 + 0.575387i
\(499\) 6.85517 0.306879 0.153440 0.988158i \(-0.450965\pi\)
0.153440 + 0.988158i \(0.450965\pi\)
\(500\) 3.29440 5.70608i 0.147330 0.255184i
\(501\) −10.5700 + 18.3078i −0.472234 + 0.817933i
\(502\) −30.0344 −1.34050
\(503\) 13.3666 23.1516i 0.595987 1.03228i −0.397420 0.917637i \(-0.630094\pi\)
0.993407 0.114642i \(-0.0365722\pi\)
\(504\) 0.178448 + 0.309081i 0.00794870 + 0.0137676i
\(505\) −3.46532 6.00211i −0.154205 0.267090i
\(506\) −7.04221 −0.313065
\(507\) 0 0
\(508\) −18.2174 −0.808268
\(509\) 10.3297 + 17.8916i 0.457858 + 0.793033i 0.998848 0.0479959i \(-0.0152835\pi\)
−0.540989 + 0.841029i \(0.681950\pi\)
\(510\) −2.32304 4.02363i −0.102866 0.178169i
\(511\) −0.568532 + 0.984726i −0.0251504 + 0.0435617i
\(512\) 1.00000 0.0441942
\(513\) −3.60388 + 6.24210i −0.159115 + 0.275595i
\(514\) −5.63102 + 9.75322i −0.248374 + 0.430196i
\(515\) −6.66115 −0.293525
\(516\) −3.29590 + 5.70866i −0.145094 + 0.251310i
\(517\) −7.32975 12.6955i −0.322362 0.558347i
\(518\) −1.80194 3.12105i −0.0791726 0.137131i
\(519\) 9.35450 0.410617
\(520\) 0 0
\(521\) −15.0965 −0.661390 −0.330695 0.943738i \(-0.607283\pi\)
−0.330695 + 0.943738i \(0.607283\pi\)
\(522\) −3.91454 6.78019i −0.171335 0.296761i
\(523\) −0.0174584 0.0302388i −0.000763402 0.00132225i 0.865643 0.500661i \(-0.166910\pi\)
−0.866407 + 0.499339i \(0.833576\pi\)
\(524\) −1.36778 + 2.36907i −0.0597518 + 0.103493i
\(525\) 1.61356 0.0704217
\(526\) 2.77479 4.80608i 0.120987 0.209555i
\(527\) −9.27413 + 16.0633i −0.403987 + 0.699727i
\(528\) −2.93900 −0.127904
\(529\) 8.62929 14.9464i 0.375187 0.649842i
\(530\) 3.07524 + 5.32647i 0.133580 + 0.231367i
\(531\) 0.821552 + 1.42297i 0.0356523 + 0.0617516i
\(532\) −2.57242 −0.111528
\(533\) 0 0
\(534\) −0.396125 −0.0171420
\(535\) 2.29440 + 3.97403i 0.0991958 + 0.171812i
\(536\) 6.76271 + 11.7134i 0.292105 + 0.505940i
\(537\) −1.58761 + 2.74983i −0.0685106 + 0.118664i
\(538\) 16.6872 0.719438
\(539\) −10.0993 + 17.4925i −0.435009 + 0.753457i
\(540\) −0.346011 + 0.599308i −0.0148899 + 0.0257901i
\(541\) 13.0858 0.562600 0.281300 0.959620i \(-0.409234\pi\)
0.281300 + 0.959620i \(0.409234\pi\)
\(542\) 3.30678 5.72751i 0.142038 0.246018i
\(543\) 9.89977 + 17.1469i 0.424840 + 0.735844i
\(544\) −3.35690 5.81431i −0.143926 0.249287i
\(545\) −8.98792 −0.385000
\(546\) 0 0
\(547\) −5.97584 −0.255508 −0.127754 0.991806i \(-0.540777\pi\)
−0.127754 + 0.991806i \(0.540777\pi\)
\(548\) −3.82371 6.62286i −0.163341 0.282914i
\(549\) 3.24698 + 5.62393i 0.138578 + 0.240024i
\(550\) −6.64377 + 11.5073i −0.283291 + 0.490675i
\(551\) 56.4301 2.40400
\(552\) −1.19806 + 2.07510i −0.0509929 + 0.0883223i
\(553\) 2.68502 4.65059i 0.114179 0.197763i
\(554\) −21.7995 −0.926174
\(555\) 3.49396 6.05171i 0.148310 0.256881i
\(556\) −1.69202 2.93067i −0.0717577 0.124288i
\(557\) 5.21983 + 9.04102i 0.221171 + 0.383080i 0.955164 0.296077i \(-0.0956786\pi\)
−0.733993 + 0.679158i \(0.762345\pi\)
\(558\) 2.76271 0.116955
\(559\) 0 0
\(560\) −0.246980 −0.0104368
\(561\) 9.86592 + 17.0883i 0.416539 + 0.721468i
\(562\) −10.2959 17.8330i −0.434306 0.752240i
\(563\) 2.83028 4.90219i 0.119282 0.206603i −0.800201 0.599732i \(-0.795274\pi\)
0.919483 + 0.393129i \(0.128607\pi\)
\(564\) −4.98792 −0.210029
\(565\) −0.274127 + 0.474801i −0.0115326 + 0.0199750i
\(566\) 6.50604 11.2688i 0.273469 0.473663i
\(567\) −0.356896 −0.0149882
\(568\) 3.40581 5.89904i 0.142905 0.247518i
\(569\) −10.3284 17.8893i −0.432990 0.749961i 0.564139 0.825680i \(-0.309208\pi\)
−0.997129 + 0.0757191i \(0.975875\pi\)
\(570\) −2.49396 4.31966i −0.104460 0.180931i
\(571\) 44.3672 1.85671 0.928354 0.371697i \(-0.121224\pi\)
0.928354 + 0.371697i \(0.121224\pi\)
\(572\) 0 0
\(573\) 15.2620 0.637581
\(574\) −0.872625 1.51143i −0.0364227 0.0630859i
\(575\) 5.41657 + 9.38177i 0.225886 + 0.391247i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 29.4426 1.22571 0.612857 0.790194i \(-0.290020\pi\)
0.612857 + 0.790194i \(0.290020\pi\)
\(578\) −14.0375 + 24.3137i −0.583883 + 1.01132i
\(579\) −2.38404 + 4.12928i −0.0990774 + 0.171607i
\(580\) 5.41789 0.224966
\(581\) 2.64579 4.58265i 0.109766 0.190120i
\(582\) −0.208947 0.361908i −0.00866115 0.0150015i
\(583\) −13.0605 22.6214i −0.540909 0.936882i
\(584\) −3.18598 −0.131837
\(585\) 0 0
\(586\) −14.9390 −0.617124
\(587\) 9.78179 + 16.9426i 0.403738 + 0.699294i 0.994174 0.107790i \(-0.0343775\pi\)
−0.590436 + 0.807085i \(0.701044\pi\)
\(588\) 3.43631 + 5.95187i 0.141711 + 0.245451i
\(589\) −9.95646 + 17.2451i −0.410249 + 0.710572i
\(590\) −1.13706 −0.0468122
\(591\) −6.11745 + 10.5957i −0.251638 + 0.435850i
\(592\) 5.04892 8.74498i 0.207509 0.359417i
\(593\) −10.8793 −0.446761 −0.223380 0.974731i \(-0.571709\pi\)
−0.223380 + 0.974731i \(0.571709\pi\)
\(594\) 1.46950 2.54525i 0.0602943 0.104433i
\(595\) 0.829085 + 1.43602i 0.0339892 + 0.0588710i
\(596\) 10.4085 + 18.0281i 0.426349 + 0.738458i
\(597\) −11.8485 −0.484925
\(598\) 0 0
\(599\) 16.0543 0.655961 0.327980 0.944685i \(-0.393632\pi\)
0.327980 + 0.944685i \(0.393632\pi\)
\(600\) 2.26055 + 3.91539i 0.0922867 + 0.159845i
\(601\) −6.44773 11.1678i −0.263008 0.455544i 0.704032 0.710169i \(-0.251381\pi\)
−0.967040 + 0.254625i \(0.918048\pi\)
\(602\) 1.17629 2.03740i 0.0479421 0.0830381i
\(603\) −13.5254 −0.550798
\(604\) 0.447730 0.775492i 0.0182179 0.0315543i
\(605\) 0.817372 1.41573i 0.0332309 0.0575576i
\(606\) 10.0151 0.406834
\(607\) −22.2371 + 38.5157i −0.902574 + 1.56330i −0.0784334 + 0.996919i \(0.524992\pi\)
−0.824141 + 0.566385i \(0.808342\pi\)
\(608\) −3.60388 6.24210i −0.146156 0.253150i
\(609\) 1.39708 + 2.41982i 0.0566127 + 0.0980561i
\(610\) −4.49396 −0.181955
\(611\) 0 0
\(612\) 6.71379 0.271389
\(613\) −21.0127 36.3950i −0.848694 1.46998i −0.882374 0.470548i \(-0.844056\pi\)
0.0336804 0.999433i \(-0.489277\pi\)
\(614\) −13.0151 22.5428i −0.525245 0.909752i
\(615\) 1.69202 2.93067i 0.0682289 0.118176i
\(616\) 1.04892 0.0422621
\(617\) 8.33273 14.4327i 0.335463 0.581039i −0.648111 0.761546i \(-0.724441\pi\)
0.983574 + 0.180507i \(0.0577739\pi\)
\(618\) 4.81282 8.33605i 0.193600 0.335325i
\(619\) 39.7512 1.59774 0.798868 0.601506i \(-0.205432\pi\)
0.798868 + 0.601506i \(0.205432\pi\)
\(620\) −0.955927 + 1.65571i −0.0383910 + 0.0664951i
\(621\) −1.19806 2.07510i −0.0480766 0.0832711i
\(622\) 2.40581 + 4.16699i 0.0964643 + 0.167081i
\(623\) 0.141375 0.00566408
\(624\) 0 0
\(625\) 18.0459 0.721837
\(626\) 13.0206 + 22.5523i 0.520407 + 0.901371i
\(627\) 10.5918 + 18.3455i 0.422996 + 0.732650i
\(628\) −4.29590 + 7.44071i −0.171425 + 0.296917i
\(629\) −67.7948 −2.70315
\(630\) 0.123490 0.213891i 0.00491995 0.00852161i
\(631\) −7.28836 + 12.6238i −0.290145 + 0.502546i −0.973844 0.227218i \(-0.927037\pi\)
0.683699 + 0.729764i \(0.260370\pi\)
\(632\) 15.0465 0.598519
\(633\) 8.63102 14.9494i 0.343052 0.594184i
\(634\) 5.76055 + 9.97757i 0.228781 + 0.396260i
\(635\) 6.30343 + 10.9179i 0.250144 + 0.433262i
\(636\) −8.88769 −0.352420
\(637\) 0 0
\(638\) −23.0097 −0.910962
\(639\) 3.40581 + 5.89904i 0.134732 + 0.233362i
\(640\) −0.346011 0.599308i −0.0136773 0.0236897i
\(641\) −19.2174 + 33.2856i −0.759043 + 1.31470i 0.184296 + 0.982871i \(0.441000\pi\)
−0.943339 + 0.331831i \(0.892334\pi\)
\(642\) −6.63102 −0.261706
\(643\) 0.521106 0.902583i 0.0205504 0.0355944i −0.855567 0.517692i \(-0.826791\pi\)
0.876118 + 0.482097i \(0.160125\pi\)
\(644\) 0.427583 0.740596i 0.0168491 0.0291836i
\(645\) 4.56166 0.179615
\(646\) −24.1957 + 41.9081i −0.951966 + 1.64885i
\(647\) 14.0804 + 24.3879i 0.553557 + 0.958788i 0.998014 + 0.0629884i \(0.0200631\pi\)
−0.444458 + 0.895800i \(0.646604\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 4.82908 0.189558
\(650\) 0 0
\(651\) −0.985999 −0.0386444
\(652\) −0.862937 1.49465i −0.0337952 0.0585350i
\(653\) −5.31013 9.19742i −0.207802 0.359923i 0.743220 0.669047i \(-0.233298\pi\)
−0.951022 + 0.309124i \(0.899964\pi\)
\(654\) 6.49396 11.2479i 0.253934 0.439826i
\(655\) 1.89307 0.0739683
\(656\) 2.44504 4.23494i 0.0954628 0.165347i
\(657\) 1.59299 2.75914i 0.0621485 0.107644i
\(658\) 1.78017 0.0693982
\(659\) 20.1814 34.9553i 0.786157 1.36166i −0.142148 0.989845i \(-0.545401\pi\)
0.928305 0.371818i \(-0.121266\pi\)
\(660\) 1.01693 + 1.76137i 0.0395838 + 0.0685611i
\(661\) 15.9584 + 27.6407i 0.620709 + 1.07510i 0.989354 + 0.145529i \(0.0464885\pi\)
−0.368645 + 0.929570i \(0.620178\pi\)
\(662\) 3.43834 0.133635
\(663\) 0 0
\(664\) 14.8267 0.575387
\(665\) 0.890084 + 1.54167i 0.0345160 + 0.0597834i
\(666\) 5.04892 + 8.74498i 0.195642 + 0.338861i
\(667\) −9.37973 + 16.2462i −0.363185 + 0.629054i
\(668\) 21.1400 0.817933
\(669\) −3.38404 + 5.86133i −0.130835 + 0.226612i
\(670\) 4.67994 8.10589i 0.180802 0.313158i
\(671\) 19.0858 0.736797
\(672\) 0.178448 0.309081i 0.00688378 0.0119231i
\(673\) −1.91401 3.31516i −0.0737797 0.127790i 0.826775 0.562532i \(-0.190173\pi\)
−0.900555 + 0.434742i \(0.856839\pi\)
\(674\) −4.10052 7.10231i −0.157946 0.273571i
\(675\) −4.52111 −0.174017
\(676\) 0 0
\(677\) 1.78927 0.0687670 0.0343835 0.999409i \(-0.489053\pi\)
0.0343835 + 0.999409i \(0.489053\pi\)
\(678\) −0.396125 0.686108i −0.0152131 0.0263498i
\(679\) 0.0745725 + 0.129163i 0.00286183 + 0.00495683i
\(680\) −2.32304 + 4.02363i −0.0890847 + 0.154299i
\(681\) 23.6799 0.907417
\(682\) 4.05980 7.03178i 0.155458 0.269261i
\(683\) −0.379863 + 0.657941i −0.0145350 + 0.0251754i −0.873201 0.487359i \(-0.837960\pi\)
0.858666 + 0.512535i \(0.171293\pi\)
\(684\) 7.20775 0.275595
\(685\) −2.64609 + 4.58316i −0.101102 + 0.175114i
\(686\) −2.47554 4.28776i −0.0945166 0.163708i
\(687\) 4.14914 + 7.18653i 0.158300 + 0.274183i
\(688\) 6.59179 0.251310
\(689\) 0 0
\(690\) 1.65817 0.0631254
\(691\) −2.32975 4.03524i −0.0886278 0.153508i 0.818304 0.574786i \(-0.194915\pi\)
−0.906931 + 0.421278i \(0.861582\pi\)
\(692\) −4.67725 8.10124i −0.177802 0.307963i
\(693\) −0.524459 + 0.908389i −0.0199225 + 0.0345068i
\(694\) 7.86294 0.298473
\(695\) −1.17092 + 2.02808i −0.0444153 + 0.0769296i
\(696\) −3.91454 + 6.78019i −0.148380 + 0.257002i
\(697\) −32.8310 −1.24356
\(698\) 9.36227 16.2159i 0.354367 0.613782i
\(699\) 11.9825 + 20.7544i 0.453221 + 0.785002i
\(700\) −0.806782 1.39739i −0.0304935 0.0528163i
\(701\) −24.3284 −0.918872 −0.459436 0.888211i \(-0.651948\pi\)
−0.459436 + 0.888211i \(0.651948\pi\)
\(702\) 0 0
\(703\) −72.7827 −2.74505
\(704\) 1.46950 + 2.54525i 0.0553839 + 0.0959277i
\(705\) 1.72587 + 2.98930i 0.0650001 + 0.112584i
\(706\) 15.7724 27.3186i 0.593602 1.02815i
\(707\) −3.57434 −0.134427
\(708\) 0.821552 1.42297i 0.0308758 0.0534785i
\(709\) 14.6963 25.4548i 0.551932 0.955975i −0.446203 0.894932i \(-0.647224\pi\)
0.998135 0.0610430i \(-0.0194427\pi\)
\(710\) −4.71379 −0.176905
\(711\) −7.52326 + 13.0307i −0.282144 + 0.488688i
\(712\) 0.198062 + 0.343054i 0.00742270 + 0.0128565i
\(713\) −3.30990 5.73291i −0.123957 0.214699i
\(714\) −2.39612 −0.0896727
\(715\) 0 0
\(716\) 3.17523 0.118664
\(717\) −6.30798 10.9257i −0.235576 0.408029i
\(718\) −1.19806 2.07510i −0.0447113 0.0774422i
\(719\) 25.7439 44.5898i 0.960086 1.66292i 0.237812 0.971311i \(-0.423570\pi\)
0.722274 0.691607i \(-0.243097\pi\)
\(720\) 0.692021 0.0257901
\(721\) −1.71768 + 2.97510i −0.0639696 + 0.110799i
\(722\) −16.4758 + 28.5370i −0.613167 + 1.06204i
\(723\) 26.3937 0.981593
\(724\) 9.89977 17.1469i 0.367922 0.637260i
\(725\) 17.6981 + 30.6539i 0.657290 + 1.13846i
\(726\) 1.18114 + 2.04579i 0.0438361 + 0.0759263i
\(727\) −3.67324 −0.136233 −0.0681164 0.997677i \(-0.521699\pi\)
−0.0681164 + 0.997677i \(0.521699\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.10238 + 1.90938i 0.0408010 + 0.0706695i
\(731\) −22.1280 38.3268i −0.818432 1.41757i
\(732\) 3.24698 5.62393i 0.120012 0.207867i
\(733\) 18.3612 0.678187 0.339093 0.940753i \(-0.389880\pi\)
0.339093 + 0.940753i \(0.389880\pi\)
\(734\) 0.00215593 0.00373419i 7.95770e−5 0.000137831i
\(735\) 2.37800 4.11882i 0.0877139 0.151925i
\(736\) 2.39612 0.0883223
\(737\) −19.8756 + 34.4256i −0.732127 + 1.26808i
\(738\) 2.44504 + 4.23494i 0.0900032 + 0.155890i
\(739\) −0.841166 1.45694i −0.0309428 0.0535945i 0.850139 0.526558i \(-0.176518\pi\)
−0.881082 + 0.472963i \(0.843184\pi\)
\(740\) −6.98792 −0.256881
\(741\) 0 0
\(742\) 3.17198 0.116447
\(743\) −24.1468 41.8234i −0.885858 1.53435i −0.844727 0.535198i \(-0.820237\pi\)
−0.0411318 0.999154i \(-0.513096\pi\)
\(744\) −1.38135 2.39258i −0.0506429 0.0877161i
\(745\) 7.20291 12.4758i 0.263894 0.457078i
\(746\) −32.3129 −1.18306
\(747\) −7.41335 + 12.8403i −0.271240 + 0.469802i
\(748\) 9.86592 17.0883i 0.360734 0.624809i
\(749\) 2.36658 0.0864731
\(750\) 3.29440 5.70608i 0.120295 0.208356i
\(751\) −5.85056 10.1335i −0.213490 0.369775i 0.739314 0.673360i \(-0.235150\pi\)
−0.952804 + 0.303585i \(0.901816\pi\)
\(752\) 2.49396 + 4.31966i 0.0909453 + 0.157522i
\(753\) −30.0344 −1.09452
\(754\) 0 0
\(755\) −0.619678 −0.0225524
\(756\) 0.178448 + 0.309081i 0.00649009 + 0.0112412i
\(757\) −12.5918 21.8096i −0.457657 0.792684i 0.541180 0.840907i \(-0.317978\pi\)
−0.998837 + 0.0482223i \(0.984644\pi\)
\(758\) −9.87800 + 17.1092i −0.358785 + 0.621434i
\(759\) −7.04221 −0.255616
\(760\) −2.49396 + 4.31966i −0.0904654 + 0.156691i
\(761\) −11.2078 + 19.4124i −0.406281 + 0.703699i −0.994470 0.105025i \(-0.966508\pi\)
0.588189 + 0.808724i \(0.299841\pi\)
\(762\) −18.2174 −0.659948
\(763\) −2.31767 + 4.01432i −0.0839052 + 0.145328i
\(764\) −7.63102 13.2173i −0.276081 0.478186i
\(765\) −2.32304 4.02363i −0.0839898 0.145475i
\(766\) 28.8116 1.04101
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 0.0663757 + 0.114966i 0.00239357 + 0.00414579i 0.867220 0.497926i \(-0.165905\pi\)
−0.864826 + 0.502071i \(0.832571\pi\)
\(770\) −0.362937 0.628625i −0.0130793 0.0226541i
\(771\) −5.63102 + 9.75322i −0.202796 + 0.351254i
\(772\) 4.76809 0.171607
\(773\) 24.0347 41.6293i 0.864467 1.49730i −0.00310775 0.999995i \(-0.500989\pi\)
0.867575 0.497306i \(-0.165677\pi\)
\(774\) −3.29590 + 5.70866i −0.118469 + 0.205194i
\(775\) −12.4905 −0.448672
\(776\) −0.208947 + 0.361908i −0.00750077 + 0.0129917i
\(777\) −1.80194 3.12105i −0.0646442 0.111967i
\(778\) −17.3910 30.1222i −0.623499 1.07993i<