Properties

Label 29.3.c.a.12.4
Level 29
Weight 3
Character 29.12
Analytic conductor 0.790
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 29.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.790192766645\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 91 x^{4} + 126 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 12.4
Root \(-0.486981i\) of defining polynomial
Character \(\chi\) \(=\) 29.12
Dual form 29.3.c.a.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.62492 + 2.62492i) q^{2} +(-3.11190 - 3.11190i) q^{3} +9.78036i q^{4} -4.53053i q^{5} -16.3369i q^{6} -0.745339 q^{7} +(-15.1730 + 15.1730i) q^{8} +10.3678i q^{9} +O(q^{10})\) \(q+(2.62492 + 2.62492i) q^{2} +(-3.11190 - 3.11190i) q^{3} +9.78036i q^{4} -4.53053i q^{5} -16.3369i q^{6} -0.745339 q^{7} +(-15.1730 + 15.1730i) q^{8} +10.3678i q^{9} +(11.8923 - 11.8923i) q^{10} +(0.0423096 + 0.0423096i) q^{11} +(30.4355 - 30.4355i) q^{12} +8.30191i q^{13} +(-1.95645 - 1.95645i) q^{14} +(-14.0985 + 14.0985i) q^{15} -40.5340 q^{16} +(15.2625 + 15.2625i) q^{17} +(-27.2146 + 27.2146i) q^{18} +(-25.1348 - 25.1348i) q^{19} +44.3102 q^{20} +(2.31942 + 2.31942i) q^{21} +0.222118i q^{22} +8.64367 q^{23} +94.4333 q^{24} +4.47430 q^{25} +(-21.7918 + 21.7918i) q^{26} +(4.25644 - 4.25644i) q^{27} -7.28968i q^{28} +(22.0908 - 18.7882i) q^{29} -74.0149 q^{30} +(-5.09325 - 5.09325i) q^{31} +(-45.7065 - 45.7065i) q^{32} -0.263326i q^{33} +80.1256i q^{34} +3.37678i q^{35} -101.401 q^{36} +(10.0725 - 10.0725i) q^{37} -131.953i q^{38} +(25.8347 - 25.8347i) q^{39} +(68.7415 + 68.7415i) q^{40} +(2.50571 - 2.50571i) q^{41} +12.1765i q^{42} +(-11.2668 - 11.2668i) q^{43} +(-0.413803 + 0.413803i) q^{44} +46.9716 q^{45} +(22.6889 + 22.6889i) q^{46} +(-23.0132 + 23.0132i) q^{47} +(126.138 + 126.138i) q^{48} -48.4445 q^{49} +(11.7447 + 11.7447i) q^{50} -94.9907i q^{51} -81.1956 q^{52} -42.8979 q^{53} +22.3456 q^{54} +(0.191685 - 0.191685i) q^{55} +(11.3090 - 11.3090i) q^{56} +156.434i q^{57} +(107.304 + 8.66900i) q^{58} +106.413 q^{59} +(-137.889 - 137.889i) q^{60} +(-42.3211 - 42.3211i) q^{61} -26.7387i q^{62} -7.72752i q^{63} -77.8154i q^{64} +37.6120 q^{65} +(0.691208 - 0.691208i) q^{66} +75.7926i q^{67} +(-149.273 + 149.273i) q^{68} +(-26.8982 - 26.8982i) q^{69} +(-8.86376 + 8.86376i) q^{70} +71.2051i q^{71} +(-157.310 - 157.310i) q^{72} +(-73.7928 + 73.7928i) q^{73} +52.8790 q^{74} +(-13.9236 - 13.9236i) q^{75} +(245.827 - 245.827i) q^{76} +(-0.0315350 - 0.0315350i) q^{77} +135.628 q^{78} +(-78.7399 - 78.7399i) q^{79} +183.641i q^{80} +66.8190 q^{81} +13.1546 q^{82} +15.1749 q^{83} +(-22.6847 + 22.6847i) q^{84} +(69.1473 - 69.1473i) q^{85} -59.1487i q^{86} +(-127.211 - 10.2773i) q^{87} -1.28392 q^{88} +(-22.8417 - 22.8417i) q^{89} +(123.296 + 123.296i) q^{90} -6.18773i q^{91} +84.5382i q^{92} +31.6993i q^{93} -120.816 q^{94} +(-113.874 + 113.874i) q^{95} +284.468i q^{96} +(42.8298 - 42.8298i) q^{97} +(-127.163 - 127.163i) q^{98} +(-0.438657 + 0.438657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{3} - 4q^{7} - 42q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{3} - 4q^{7} - 42q^{8} + 6q^{10} - 6q^{11} + 54q^{12} - 40q^{14} - 10q^{15} - 32q^{16} + 12q^{17} + 20q^{18} - 16q^{19} + 108q^{20} - 36q^{21} + 168q^{24} + 104q^{25} - 54q^{26} - 98q^{27} + 128q^{29} - 220q^{30} - 10q^{31} - 106q^{32} - 252q^{36} - 84q^{37} - 90q^{39} + 226q^{40} + 20q^{41} - 190q^{43} + 42q^{44} + 292q^{45} + 12q^{46} + 58q^{47} + 354q^{48} - 72q^{49} - 60q^{50} - 144q^{52} + 252q^{53} + 400q^{54} - 74q^{55} - 192q^{56} + 326q^{58} - 40q^{59} - 258q^{60} - 208q^{61} + 36q^{65} - 414q^{66} - 296q^{68} + 120q^{69} + 44q^{70} - 636q^{72} - 188q^{73} - 64q^{74} - 12q^{75} + 592q^{76} + 180q^{77} + 600q^{78} - 382q^{79} - 124q^{81} + 228q^{82} + 280q^{83} - 124q^{84} + 32q^{85} + 34q^{87} + 20q^{88} - 64q^{89} + 128q^{90} - 460q^{94} - 380q^{95} - 44q^{97} - 66q^{98} + 552q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.62492 + 2.62492i 1.31246 + 1.31246i 0.919599 + 0.392859i \(0.128514\pi\)
0.392859 + 0.919599i \(0.371486\pi\)
\(3\) −3.11190 3.11190i −1.03730 1.03730i −0.999277 0.0380218i \(-0.987894\pi\)
−0.0380218 0.999277i \(-0.512106\pi\)
\(4\) 9.78036i 2.44509i
\(5\) 4.53053i 0.906106i −0.891484 0.453053i \(-0.850335\pi\)
0.891484 0.453053i \(-0.149665\pi\)
\(6\) 16.3369i 2.72282i
\(7\) −0.745339 −0.106477 −0.0532385 0.998582i \(-0.516954\pi\)
−0.0532385 + 0.998582i \(0.516954\pi\)
\(8\) −15.1730 + 15.1730i −1.89662 + 1.89662i
\(9\) 10.3678i 1.15198i
\(10\) 11.8923 11.8923i 1.18923 1.18923i
\(11\) 0.0423096 + 0.0423096i 0.00384632 + 0.00384632i 0.709027 0.705181i \(-0.249134\pi\)
−0.705181 + 0.709027i \(0.749134\pi\)
\(12\) 30.4355 30.4355i 2.53629 2.53629i
\(13\) 8.30191i 0.638608i 0.947652 + 0.319304i \(0.103449\pi\)
−0.947652 + 0.319304i \(0.896551\pi\)
\(14\) −1.95645 1.95645i −0.139747 0.139747i
\(15\) −14.0985 + 14.0985i −0.939903 + 0.939903i
\(16\) −40.5340 −2.53338
\(17\) 15.2625 + 15.2625i 0.897795 + 0.897795i 0.995241 0.0974461i \(-0.0310673\pi\)
−0.0974461 + 0.995241i \(0.531067\pi\)
\(18\) −27.2146 + 27.2146i −1.51192 + 1.51192i
\(19\) −25.1348 25.1348i −1.32288 1.32288i −0.911431 0.411453i \(-0.865021\pi\)
−0.411453 0.911431i \(-0.634979\pi\)
\(20\) 44.3102 2.21551
\(21\) 2.31942 + 2.31942i 0.110448 + 0.110448i
\(22\) 0.222118i 0.0100963i
\(23\) 8.64367 0.375812 0.187906 0.982187i \(-0.439830\pi\)
0.187906 + 0.982187i \(0.439830\pi\)
\(24\) 94.4333 3.93472
\(25\) 4.47430 0.178972
\(26\) −21.7918 + 21.7918i −0.838146 + 0.838146i
\(27\) 4.25644 4.25644i 0.157646 0.157646i
\(28\) 7.28968i 0.260346i
\(29\) 22.0908 18.7882i 0.761752 0.647869i
\(30\) −74.0149 −2.46716
\(31\) −5.09325 5.09325i −0.164298 0.164298i 0.620169 0.784468i \(-0.287064\pi\)
−0.784468 + 0.620169i \(0.787064\pi\)
\(32\) −45.7065 45.7065i −1.42833 1.42833i
\(33\) 0.263326i 0.00797957i
\(34\) 80.1256i 2.35664i
\(35\) 3.37678i 0.0964794i
\(36\) −101.401 −2.81669
\(37\) 10.0725 10.0725i 0.272230 0.272230i −0.557767 0.829997i \(-0.688342\pi\)
0.829997 + 0.557767i \(0.188342\pi\)
\(38\) 131.953i 3.47246i
\(39\) 25.8347 25.8347i 0.662427 0.662427i
\(40\) 68.7415 + 68.7415i 1.71854 + 1.71854i
\(41\) 2.50571 2.50571i 0.0611149 0.0611149i −0.675889 0.737004i \(-0.736240\pi\)
0.737004 + 0.675889i \(0.236240\pi\)
\(42\) 12.1765i 0.289918i
\(43\) −11.2668 11.2668i −0.262018 0.262018i 0.563855 0.825874i \(-0.309318\pi\)
−0.825874 + 0.563855i \(0.809318\pi\)
\(44\) −0.413803 + 0.413803i −0.00940461 + 0.00940461i
\(45\) 46.9716 1.04381
\(46\) 22.6889 + 22.6889i 0.493237 + 0.493237i
\(47\) −23.0132 + 23.0132i −0.489643 + 0.489643i −0.908194 0.418550i \(-0.862538\pi\)
0.418550 + 0.908194i \(0.362538\pi\)
\(48\) 126.138 + 126.138i 2.62787 + 2.62787i
\(49\) −48.4445 −0.988663
\(50\) 11.7447 + 11.7447i 0.234893 + 0.234893i
\(51\) 94.9907i 1.86256i
\(52\) −81.1956 −1.56145
\(53\) −42.8979 −0.809394 −0.404697 0.914451i \(-0.632623\pi\)
−0.404697 + 0.914451i \(0.632623\pi\)
\(54\) 22.3456 0.413807
\(55\) 0.191685 0.191685i 0.00348518 0.00348518i
\(56\) 11.3090 11.3090i 0.201946 0.201946i
\(57\) 156.434i 2.74445i
\(58\) 107.304 + 8.66900i 1.85007 + 0.149466i
\(59\) 106.413 1.80361 0.901806 0.432140i \(-0.142241\pi\)
0.901806 + 0.432140i \(0.142241\pi\)
\(60\) −137.889 137.889i −2.29815 2.29815i
\(61\) −42.3211 42.3211i −0.693788 0.693788i 0.269275 0.963063i \(-0.413216\pi\)
−0.963063 + 0.269275i \(0.913216\pi\)
\(62\) 26.7387i 0.431269i
\(63\) 7.72752i 0.122659i
\(64\) 77.8154i 1.21587i
\(65\) 37.6120 0.578647
\(66\) 0.691208 0.691208i 0.0104729 0.0104729i
\(67\) 75.7926i 1.13123i 0.824668 + 0.565616i \(0.191362\pi\)
−0.824668 + 0.565616i \(0.808638\pi\)
\(68\) −149.273 + 149.273i −2.19519 + 2.19519i
\(69\) −26.8982 26.8982i −0.389829 0.389829i
\(70\) −8.86376 + 8.86376i −0.126625 + 0.126625i
\(71\) 71.2051i 1.00289i 0.865190 + 0.501445i \(0.167198\pi\)
−0.865190 + 0.501445i \(0.832802\pi\)
\(72\) −157.310 157.310i −2.18486 2.18486i
\(73\) −73.7928 + 73.7928i −1.01086 + 1.01086i −0.0109201 + 0.999940i \(0.503476\pi\)
−0.999940 + 0.0109201i \(0.996524\pi\)
\(74\) 52.8790 0.714581
\(75\) −13.9236 13.9236i −0.185647 0.185647i
\(76\) 245.827 245.827i 3.23457 3.23457i
\(77\) −0.0315350 0.0315350i −0.000409545 0.000409545i
\(78\) 135.628 1.73882
\(79\) −78.7399 78.7399i −0.996707 0.996707i 0.00328762 0.999995i \(-0.498954\pi\)
−0.999995 + 0.00328762i \(0.998954\pi\)
\(80\) 183.641i 2.29551i
\(81\) 66.8190 0.824925
\(82\) 13.1546 0.160421
\(83\) 15.1749 0.182830 0.0914152 0.995813i \(-0.470861\pi\)
0.0914152 + 0.995813i \(0.470861\pi\)
\(84\) −22.6847 + 22.6847i −0.270056 + 0.270056i
\(85\) 69.1473 69.1473i 0.813497 0.813497i
\(86\) 59.1487i 0.687775i
\(87\) −127.211 10.2773i −1.46220 0.118130i
\(88\) −1.28392 −0.0145900
\(89\) −22.8417 22.8417i −0.256648 0.256648i 0.567041 0.823689i \(-0.308088\pi\)
−0.823689 + 0.567041i \(0.808088\pi\)
\(90\) 123.296 + 123.296i 1.36996 + 1.36996i
\(91\) 6.18773i 0.0679971i
\(92\) 84.5382i 0.918893i
\(93\) 31.6993i 0.340853i
\(94\) −120.816 −1.28527
\(95\) −113.874 + 113.874i −1.19867 + 1.19867i
\(96\) 284.468i 2.96321i
\(97\) 42.8298 42.8298i 0.441544 0.441544i −0.450987 0.892531i \(-0.648928\pi\)
0.892531 + 0.450987i \(0.148928\pi\)
\(98\) −127.163 127.163i −1.29758 1.29758i
\(99\) −0.438657 + 0.438657i −0.00443088 + 0.00443088i
\(100\) 43.7603i 0.437603i
\(101\) 36.4365 + 36.4365i 0.360757 + 0.360757i 0.864092 0.503334i \(-0.167894\pi\)
−0.503334 + 0.864092i \(0.667894\pi\)
\(102\) 249.343 249.343i 2.44453 2.44453i
\(103\) 111.751 1.08496 0.542479 0.840070i \(-0.317486\pi\)
0.542479 + 0.840070i \(0.317486\pi\)
\(104\) −125.964 125.964i −1.21120 1.21120i
\(105\) 10.5082 10.5082i 0.100078 0.100078i
\(106\) −112.603 112.603i −1.06230 1.06230i
\(107\) 88.9678 0.831475 0.415737 0.909485i \(-0.363524\pi\)
0.415737 + 0.909485i \(0.363524\pi\)
\(108\) 41.6295 + 41.6295i 0.385459 + 0.385459i
\(109\) 41.1196i 0.377244i 0.982050 + 0.188622i \(0.0604020\pi\)
−0.982050 + 0.188622i \(0.939598\pi\)
\(110\) 1.00631 0.00914829
\(111\) −62.6893 −0.564768
\(112\) 30.2116 0.269746
\(113\) 104.104 104.104i 0.921275 0.921275i −0.0758450 0.997120i \(-0.524165\pi\)
0.997120 + 0.0758450i \(0.0241654\pi\)
\(114\) −410.625 + 410.625i −3.60198 + 3.60198i
\(115\) 39.1604i 0.340525i
\(116\) 183.755 + 216.056i 1.58410 + 1.86255i
\(117\) −86.0725 −0.735662
\(118\) 279.326 + 279.326i 2.36717 + 2.36717i
\(119\) −11.3757 11.3757i −0.0955945 0.0955945i
\(120\) 427.833i 3.56527i
\(121\) 120.996i 0.999970i
\(122\) 222.179i 1.82114i
\(123\) −15.5950 −0.126789
\(124\) 49.8138 49.8138i 0.401724 0.401724i
\(125\) 133.534i 1.06827i
\(126\) 20.2841 20.2841i 0.160985 0.160985i
\(127\) 8.26743 + 8.26743i 0.0650978 + 0.0650978i 0.738906 0.673808i \(-0.235343\pi\)
−0.673808 + 0.738906i \(0.735343\pi\)
\(128\) 21.4328 21.4328i 0.167443 0.167443i
\(129\) 70.1221i 0.543582i
\(130\) 98.7284 + 98.7284i 0.759449 + 0.759449i
\(131\) −0.361622 + 0.361622i −0.00276047 + 0.00276047i −0.708486 0.705725i \(-0.750621\pi\)
0.705725 + 0.708486i \(0.250621\pi\)
\(132\) 2.57542 0.0195108
\(133\) 18.7339 + 18.7339i 0.140857 + 0.140857i
\(134\) −198.949 + 198.949i −1.48470 + 1.48470i
\(135\) −19.2839 19.2839i −0.142844 0.142844i
\(136\) −463.155 −3.40555
\(137\) −69.5740 69.5740i −0.507840 0.507840i 0.406023 0.913863i \(-0.366915\pi\)
−0.913863 + 0.406023i \(0.866915\pi\)
\(138\) 141.211i 1.02327i
\(139\) 111.380 0.801297 0.400649 0.916232i \(-0.368785\pi\)
0.400649 + 0.916232i \(0.368785\pi\)
\(140\) −33.0261 −0.235901
\(141\) 143.230 1.01581
\(142\) −186.907 + 186.907i −1.31625 + 1.31625i
\(143\) −0.351250 + 0.351250i −0.00245629 + 0.00245629i
\(144\) 420.248i 2.91839i
\(145\) −85.1205 100.083i −0.587038 0.690228i
\(146\) −387.400 −2.65342
\(147\) 150.754 + 150.754i 1.02554 + 1.02554i
\(148\) 98.5129 + 98.5129i 0.665628 + 0.665628i
\(149\) 44.5177i 0.298776i 0.988779 + 0.149388i \(0.0477304\pi\)
−0.988779 + 0.149388i \(0.952270\pi\)
\(150\) 73.0963i 0.487309i
\(151\) 70.6402i 0.467816i 0.972259 + 0.233908i \(0.0751514\pi\)
−0.972259 + 0.233908i \(0.924849\pi\)
\(152\) 762.738 5.01802
\(153\) −158.239 + 158.239i −1.03424 + 1.03424i
\(154\) 0.165553i 0.00107502i
\(155\) −23.0751 + 23.0751i −0.148872 + 0.148872i
\(156\) 252.672 + 252.672i 1.61969 + 1.61969i
\(157\) −127.354 + 127.354i −0.811173 + 0.811173i −0.984810 0.173636i \(-0.944448\pi\)
0.173636 + 0.984810i \(0.444448\pi\)
\(158\) 413.371i 2.61627i
\(159\) 133.494 + 133.494i 0.839583 + 0.839583i
\(160\) −207.075 + 207.075i −1.29422 + 1.29422i
\(161\) −6.44246 −0.0400153
\(162\) 175.394 + 175.394i 1.08268 + 1.08268i
\(163\) 83.4261 83.4261i 0.511817 0.511817i −0.403266 0.915083i \(-0.632125\pi\)
0.915083 + 0.403266i \(0.132125\pi\)
\(164\) 24.5067 + 24.5067i 0.149431 + 0.149431i
\(165\) −1.19301 −0.00723034
\(166\) 39.8329 + 39.8329i 0.239957 + 0.239957i
\(167\) 221.605i 1.32697i 0.748188 + 0.663487i \(0.230924\pi\)
−0.748188 + 0.663487i \(0.769076\pi\)
\(168\) −70.3848 −0.418957
\(169\) 100.078 0.592180
\(170\) 363.011 2.13536
\(171\) 260.592 260.592i 1.52393 1.52393i
\(172\) 110.193 110.193i 0.640658 0.640658i
\(173\) 6.62034i 0.0382679i 0.999817 + 0.0191339i \(0.00609089\pi\)
−0.999817 + 0.0191339i \(0.993909\pi\)
\(174\) −306.942 360.896i −1.76403 2.07411i
\(175\) −3.33487 −0.0190564
\(176\) −1.71498 1.71498i −0.00974418 0.00974418i
\(177\) −331.147 331.147i −1.87089 1.87089i
\(178\) 119.915i 0.673679i
\(179\) 36.9603i 0.206482i −0.994656 0.103241i \(-0.967079\pi\)
0.994656 0.103241i \(-0.0329213\pi\)
\(180\) 459.399i 2.55222i
\(181\) −192.039 −1.06099 −0.530494 0.847689i \(-0.677994\pi\)
−0.530494 + 0.847689i \(0.677994\pi\)
\(182\) 16.2423 16.2423i 0.0892433 0.0892433i
\(183\) 263.398i 1.43933i
\(184\) −131.150 + 131.150i −0.712771 + 0.712771i
\(185\) −45.6339 45.6339i −0.246669 0.246669i
\(186\) −83.2081 + 83.2081i −0.447355 + 0.447355i
\(187\) 1.29150i 0.00690642i
\(188\) −225.078 225.078i −1.19722 1.19722i
\(189\) −3.17249 + 3.17249i −0.0167857 + 0.0167857i
\(190\) −597.819 −3.14642
\(191\) −215.351 215.351i −1.12749 1.12749i −0.990584 0.136906i \(-0.956284\pi\)
−0.136906 0.990584i \(-0.543716\pi\)
\(192\) −242.153 + 242.153i −1.26122 + 1.26122i
\(193\) 130.679 + 130.679i 0.677095 + 0.677095i 0.959342 0.282247i \(-0.0910797\pi\)
−0.282247 + 0.959342i \(0.591080\pi\)
\(194\) 224.849 1.15902
\(195\) −117.045 117.045i −0.600229 0.600229i
\(196\) 473.804i 2.41737i
\(197\) −254.953 −1.29418 −0.647090 0.762414i \(-0.724014\pi\)
−0.647090 + 0.762414i \(0.724014\pi\)
\(198\) −2.30287 −0.0116307
\(199\) 168.018 0.844311 0.422155 0.906524i \(-0.361274\pi\)
0.422155 + 0.906524i \(0.361274\pi\)
\(200\) −67.8884 + 67.8884i −0.339442 + 0.339442i
\(201\) 235.859 235.859i 1.17343 1.17343i
\(202\) 191.285i 0.946957i
\(203\) −16.4651 + 14.0036i −0.0811090 + 0.0689832i
\(204\) 929.043 4.55413
\(205\) −11.3522 11.3522i −0.0553766 0.0553766i
\(206\) 293.336 + 293.336i 1.42396 + 1.42396i
\(207\) 89.6158i 0.432926i
\(208\) 336.510i 1.61783i
\(209\) 2.12688i 0.0101765i
\(210\) 55.1662 0.262696
\(211\) −111.890 + 111.890i −0.530285 + 0.530285i −0.920657 0.390372i \(-0.872346\pi\)
0.390372 + 0.920657i \(0.372346\pi\)
\(212\) 419.557i 1.97904i
\(213\) 221.583 221.583i 1.04030 1.04030i
\(214\) 233.533 + 233.533i 1.09128 + 1.09128i
\(215\) −51.0445 + 51.0445i −0.237416 + 0.237416i
\(216\) 129.166i 0.597989i
\(217\) 3.79620 + 3.79620i 0.0174940 + 0.0174940i
\(218\) −107.935 + 107.935i −0.495116 + 0.495116i
\(219\) 459.271 2.09713
\(220\) 1.87475 + 1.87475i 0.00852157 + 0.00852157i
\(221\) −126.708 + 126.708i −0.573339 + 0.573339i
\(222\) −164.554 164.554i −0.741234 0.741234i
\(223\) −57.0256 −0.255720 −0.127860 0.991792i \(-0.540811\pi\)
−0.127860 + 0.991792i \(0.540811\pi\)
\(224\) 34.0668 + 34.0668i 0.152084 + 0.152084i
\(225\) 46.3886i 0.206172i
\(226\) 546.528 2.41827
\(227\) −173.750 −0.765418 −0.382709 0.923869i \(-0.625009\pi\)
−0.382709 + 0.923869i \(0.625009\pi\)
\(228\) −1529.98 −6.71043
\(229\) −144.696 + 144.696i −0.631859 + 0.631859i −0.948534 0.316675i \(-0.897433\pi\)
0.316675 + 0.948534i \(0.397433\pi\)
\(230\) 102.793 102.793i 0.446925 0.446925i
\(231\) 0.196267i 0.000849641i
\(232\) −50.1100 + 620.255i −0.215991 + 2.67351i
\(233\) 102.871 0.441507 0.220754 0.975330i \(-0.429148\pi\)
0.220754 + 0.975330i \(0.429148\pi\)
\(234\) −225.933 225.933i −0.965525 0.965525i
\(235\) 104.262 + 104.262i 0.443669 + 0.443669i
\(236\) 1040.76i 4.41000i
\(237\) 490.060i 2.06777i
\(238\) 59.7207i 0.250927i
\(239\) −312.152 −1.30607 −0.653037 0.757326i \(-0.726505\pi\)
−0.653037 + 0.757326i \(0.726505\pi\)
\(240\) 571.470 571.470i 2.38113 2.38113i
\(241\) 313.004i 1.29877i −0.760460 0.649385i \(-0.775026\pi\)
0.760460 0.649385i \(-0.224974\pi\)
\(242\) 317.605 317.605i 1.31242 1.31242i
\(243\) −246.242 246.242i −1.01334 1.01334i
\(244\) 413.916 413.916i 1.69638 1.69638i
\(245\) 219.479i 0.895833i
\(246\) −40.9356 40.9356i −0.166405 0.166405i
\(247\) 208.667 208.667i 0.844805 0.844805i
\(248\) 154.559 0.623223
\(249\) −47.2228 47.2228i −0.189650 0.189650i
\(250\) 350.516 350.516i 1.40206 1.40206i
\(251\) 7.83425 + 7.83425i 0.0312121 + 0.0312121i 0.722541 0.691328i \(-0.242974\pi\)
−0.691328 + 0.722541i \(0.742974\pi\)
\(252\) 75.5779 0.299912
\(253\) 0.365710 + 0.365710i 0.00144549 + 0.00144549i
\(254\) 43.4026i 0.170876i
\(255\) −430.358 −1.68768
\(256\) −198.743 −0.776340
\(257\) 68.5603 0.266771 0.133386 0.991064i \(-0.457415\pi\)
0.133386 + 0.991064i \(0.457415\pi\)
\(258\) −184.065 + 184.065i −0.713429 + 0.713429i
\(259\) −7.50744 + 7.50744i −0.0289863 + 0.0289863i
\(260\) 367.859i 1.41484i
\(261\) 194.792 + 229.033i 0.746331 + 0.877521i
\(262\) −1.89845 −0.00724600
\(263\) 153.717 + 153.717i 0.584477 + 0.584477i 0.936130 0.351653i \(-0.114380\pi\)
−0.351653 + 0.936130i \(0.614380\pi\)
\(264\) 3.99543 + 3.99543i 0.0151342 + 0.0151342i
\(265\) 194.350i 0.733397i
\(266\) 98.3500i 0.369737i
\(267\) 142.162i 0.532441i
\(268\) −741.279 −2.76597
\(269\) 272.419 272.419i 1.01271 1.01271i 0.0127932 0.999918i \(-0.495928\pi\)
0.999918 0.0127932i \(-0.00407231\pi\)
\(270\) 101.237i 0.374953i
\(271\) −304.778 + 304.778i −1.12464 + 1.12464i −0.133607 + 0.991034i \(0.542656\pi\)
−0.991034 + 0.133607i \(0.957344\pi\)
\(272\) −618.651 618.651i −2.27445 2.27445i
\(273\) −19.2556 + 19.2556i −0.0705333 + 0.0705333i
\(274\) 365.252i 1.33304i
\(275\) 0.189306 + 0.189306i 0.000688384 + 0.000688384i
\(276\) 263.074 263.074i 0.953167 0.953167i
\(277\) −26.7259 −0.0964834 −0.0482417 0.998836i \(-0.515362\pi\)
−0.0482417 + 0.998836i \(0.515362\pi\)
\(278\) 292.364 + 292.364i 1.05167 + 1.05167i
\(279\) 52.8058 52.8058i 0.189268 0.189268i
\(280\) −51.2357 51.2357i −0.182985 0.182985i
\(281\) 468.922 1.66876 0.834380 0.551189i \(-0.185826\pi\)
0.834380 + 0.551189i \(0.185826\pi\)
\(282\) 375.966 + 375.966i 1.33321 + 1.33321i
\(283\) 263.495i 0.931079i −0.885027 0.465540i \(-0.845860\pi\)
0.885027 0.465540i \(-0.154140\pi\)
\(284\) −696.412 −2.45215
\(285\) 708.728 2.48676
\(286\) −1.84400 −0.00644756
\(287\) −1.86760 + 1.86760i −0.00650733 + 0.00650733i
\(288\) 473.876 473.876i 1.64540 1.64540i
\(289\) 176.888i 0.612071i
\(290\) 39.2752 486.144i 0.135432 1.67636i
\(291\) −266.564 −0.916026
\(292\) −721.720 721.720i −2.47164 2.47164i
\(293\) −84.4413 84.4413i −0.288196 0.288196i 0.548171 0.836366i \(-0.315324\pi\)
−0.836366 + 0.548171i \(0.815324\pi\)
\(294\) 791.434i 2.69195i
\(295\) 482.108i 1.63426i
\(296\) 305.660i 1.03263i
\(297\) 0.360176 0.00121271
\(298\) −116.855 + 116.855i −0.392131 + 0.392131i
\(299\) 71.7589i 0.239996i
\(300\) 136.177 136.177i 0.453925 0.453925i
\(301\) 8.39757 + 8.39757i 0.0278989 + 0.0278989i
\(302\) −185.424 + 185.424i −0.613988 + 0.613988i
\(303\) 226.773i 0.748426i
\(304\) 1018.81 + 1018.81i 3.35136 + 3.35136i
\(305\) −191.737 + 191.737i −0.628646 + 0.628646i
\(306\) −830.726 −2.71479
\(307\) 193.086 + 193.086i 0.628945 + 0.628945i 0.947803 0.318858i \(-0.103299\pi\)
−0.318858 + 0.947803i \(0.603299\pi\)
\(308\) 0.308423 0.308423i 0.00100137 0.00100137i
\(309\) −347.756 347.756i −1.12542 1.12542i
\(310\) −121.141 −0.390776
\(311\) −138.374 138.374i −0.444932 0.444932i 0.448734 0.893666i \(-0.351875\pi\)
−0.893666 + 0.448734i \(0.851875\pi\)
\(312\) 783.977i 2.51275i
\(313\) 316.089 1.00987 0.504934 0.863158i \(-0.331517\pi\)
0.504934 + 0.863158i \(0.331517\pi\)
\(314\) −668.588 −2.12926
\(315\) −35.0098 −0.111142
\(316\) 770.104 770.104i 2.43704 2.43704i
\(317\) 222.503 222.503i 0.701902 0.701902i −0.262916 0.964819i \(-0.584684\pi\)
0.964819 + 0.262916i \(0.0846843\pi\)
\(318\) 700.820i 2.20384i
\(319\) 1.72957 + 0.139731i 0.00542186 + 0.000438028i
\(320\) −352.545 −1.10170
\(321\) −276.859 276.859i −0.862488 0.862488i
\(322\) −16.9109 16.9109i −0.0525184 0.0525184i
\(323\) 767.240i 2.37536i
\(324\) 653.514i 2.01702i
\(325\) 37.1452i 0.114293i
\(326\) 437.973 1.34348
\(327\) 127.960 127.960i 0.391314 0.391314i
\(328\) 76.0381i 0.231823i
\(329\) 17.1527 17.1527i 0.0521358 0.0521358i
\(330\) −3.13154 3.13154i −0.00948951 0.00948951i
\(331\) 240.645 240.645i 0.727024 0.727024i −0.243002 0.970026i \(-0.578132\pi\)
0.970026 + 0.243002i \(0.0781322\pi\)
\(332\) 148.416i 0.447037i
\(333\) 104.430 + 104.430i 0.313603 + 0.313603i
\(334\) −581.693 + 581.693i −1.74160 + 1.74160i
\(335\) 343.381 1.02502
\(336\) −94.0153 94.0153i −0.279807 0.279807i
\(337\) −294.375 + 294.375i −0.873517 + 0.873517i −0.992854 0.119336i \(-0.961923\pi\)
0.119336 + 0.992854i \(0.461923\pi\)
\(338\) 262.697 + 262.697i 0.777211 + 0.777211i
\(339\) −647.922 −1.91127
\(340\) 676.285 + 676.285i 1.98907 + 1.98907i
\(341\) 0.430987i 0.00126389i
\(342\) 1368.07 4.00019
\(343\) 72.6291 0.211747
\(344\) 341.901 0.993897
\(345\) −121.863 + 121.863i −0.353226 + 0.353226i
\(346\) −17.3778 + 17.3778i −0.0502250 + 0.0502250i
\(347\) 355.572i 1.02470i −0.858776 0.512351i \(-0.828775\pi\)
0.858776 0.512351i \(-0.171225\pi\)
\(348\) 100.516 1244.17i 0.288838 3.57521i
\(349\) −239.336 −0.685775 −0.342888 0.939376i \(-0.611405\pi\)
−0.342888 + 0.939376i \(0.611405\pi\)
\(350\) −8.75375 8.75375i −0.0250107 0.0250107i
\(351\) 35.3366 + 35.3366i 0.100674 + 0.100674i
\(352\) 3.86764i 0.0109876i
\(353\) 31.2450i 0.0885128i −0.999020 0.0442564i \(-0.985908\pi\)
0.999020 0.0442564i \(-0.0140919\pi\)
\(354\) 1738.46i 4.91092i
\(355\) 322.597 0.908724
\(356\) 223.400 223.400i 0.627527 0.627527i
\(357\) 70.8003i 0.198320i
\(358\) 97.0177 97.0177i 0.270999 0.270999i
\(359\) 259.580 + 259.580i 0.723064 + 0.723064i 0.969228 0.246164i \(-0.0791702\pi\)
−0.246164 + 0.969228i \(0.579170\pi\)
\(360\) −712.698 + 712.698i −1.97972 + 1.97972i
\(361\) 902.516i 2.50004i
\(362\) −504.086 504.086i −1.39250 1.39250i
\(363\) −376.528 + 376.528i −1.03727 + 1.03727i
\(364\) 60.5183 0.166259
\(365\) 334.321 + 334.321i 0.915947 + 0.915947i
\(366\) −691.397 + 691.397i −1.88906 + 1.88906i
\(367\) 130.207 + 130.207i 0.354786 + 0.354786i 0.861887 0.507100i \(-0.169283\pi\)
−0.507100 + 0.861887i \(0.669283\pi\)
\(368\) −350.362 −0.952072
\(369\) 25.9787 + 25.9787i 0.0704030 + 0.0704030i
\(370\) 239.570i 0.647486i
\(371\) 31.9735 0.0861818
\(372\) −310.031 −0.833417
\(373\) −638.263 −1.71116 −0.855581 0.517669i \(-0.826800\pi\)
−0.855581 + 0.517669i \(0.826800\pi\)
\(374\) −3.39008 + 3.39008i −0.00906438 + 0.00906438i
\(375\) −415.545 + 415.545i −1.10812 + 1.10812i
\(376\) 698.358i 1.85733i
\(377\) 155.978 + 183.396i 0.413735 + 0.486461i
\(378\) −16.6550 −0.0440609
\(379\) 91.7710 + 91.7710i 0.242140 + 0.242140i 0.817735 0.575595i \(-0.195229\pi\)
−0.575595 + 0.817735i \(0.695229\pi\)
\(380\) −1113.73 1113.73i −2.93086 2.93086i
\(381\) 51.4547i 0.135052i
\(382\) 1130.55i 2.95957i
\(383\) 290.256i 0.757848i 0.925428 + 0.378924i \(0.123706\pi\)
−0.925428 + 0.378924i \(0.876294\pi\)
\(384\) −133.393 −0.347378
\(385\) −0.142870 + 0.142870i −0.000371091 + 0.000371091i
\(386\) 686.044i 1.77732i
\(387\) 116.812 116.812i 0.301839 0.301839i
\(388\) 418.891 + 418.891i 1.07962 + 1.07962i
\(389\) 404.811 404.811i 1.04065 1.04065i 0.0415071 0.999138i \(-0.486784\pi\)
0.999138 0.0415071i \(-0.0132159\pi\)
\(390\) 614.465i 1.57555i
\(391\) 131.924 + 131.924i 0.337402 + 0.337402i
\(392\) 735.046 735.046i 1.87512 1.87512i
\(393\) 2.25066 0.00572686
\(394\) −669.231 669.231i −1.69856 1.69856i
\(395\) −356.733 + 356.733i −0.903122 + 0.903122i
\(396\) −4.29022 4.29022i −0.0108339 0.0108339i
\(397\) −485.501 −1.22292 −0.611462 0.791274i \(-0.709418\pi\)
−0.611462 + 0.791274i \(0.709418\pi\)
\(398\) 441.032 + 441.032i 1.10812 + 1.10812i
\(399\) 116.596i 0.292221i
\(400\) −181.361 −0.453403
\(401\) −144.170 −0.359527 −0.179763 0.983710i \(-0.557533\pi\)
−0.179763 + 0.983710i \(0.557533\pi\)
\(402\) 1238.22 3.08015
\(403\) 42.2837 42.2837i 0.104922 0.104922i
\(404\) −356.362 + 356.362i −0.882084 + 0.882084i
\(405\) 302.725i 0.747470i
\(406\) −79.9778 6.46135i −0.196990 0.0159146i
\(407\) 0.852328 0.00209417
\(408\) 1441.29 + 1441.29i 3.53257 + 3.53257i
\(409\) 118.758 + 118.758i 0.290361 + 0.290361i 0.837223 0.546862i \(-0.184178\pi\)
−0.546862 + 0.837223i \(0.684178\pi\)
\(410\) 59.5971i 0.145359i
\(411\) 433.014i 1.05356i
\(412\) 1092.96i 2.65282i
\(413\) −79.3139 −0.192043
\(414\) −235.234 + 235.234i −0.568198 + 0.568198i
\(415\) 68.7504i 0.165664i
\(416\) 379.451 379.451i 0.912142 0.912142i
\(417\) −346.604 346.604i −0.831185 0.831185i
\(418\) 5.58289 5.58289i 0.0133562 0.0133562i
\(419\) 20.8124i 0.0496715i −0.999692 0.0248357i \(-0.992094\pi\)
0.999692 0.0248357i \(-0.00790628\pi\)
\(420\) 102.774 + 102.774i 0.244700 + 0.244700i
\(421\) 199.204 199.204i 0.473168 0.473168i −0.429770 0.902938i \(-0.641405\pi\)
0.902938 + 0.429770i \(0.141405\pi\)
\(422\) −587.404 −1.39195
\(423\) −238.597 238.597i −0.564058 0.564058i
\(424\) 650.888 650.888i 1.53511 1.53511i
\(425\) 68.2891 + 68.2891i 0.160680 + 0.160680i
\(426\) 1163.27 2.73069
\(427\) 31.5436 + 31.5436i 0.0738725 + 0.0738725i
\(428\) 870.137i 2.03303i
\(429\) 2.18611 0.00509582
\(430\) −267.975 −0.623197
\(431\) −193.044 −0.447898 −0.223949 0.974601i \(-0.571895\pi\)
−0.223949 + 0.974601i \(0.571895\pi\)
\(432\) −172.531 + 172.531i −0.399376 + 0.399376i
\(433\) 118.795 118.795i 0.274353 0.274353i −0.556497 0.830850i \(-0.687855\pi\)
0.830850 + 0.556497i \(0.187855\pi\)
\(434\) 19.9294i 0.0459203i
\(435\) −46.5616 + 576.334i −0.107038 + 1.32491i
\(436\) −402.164 −0.922395
\(437\) −217.257 217.257i −0.497155 0.497155i
\(438\) 1205.55 + 1205.55i 2.75239 + 2.75239i
\(439\) 660.370i 1.50426i −0.659015 0.752130i \(-0.729027\pi\)
0.659015 0.752130i \(-0.270973\pi\)
\(440\) 5.81685i 0.0132201i
\(441\) 502.262i 1.13892i
\(442\) −665.195 −1.50497
\(443\) 222.343 222.343i 0.501904 0.501904i −0.410125 0.912029i \(-0.634515\pi\)
0.912029 + 0.410125i \(0.134515\pi\)
\(444\) 613.124i 1.38091i
\(445\) −103.485 + 103.485i −0.232550 + 0.232550i
\(446\) −149.687 149.687i −0.335622 0.335622i
\(447\) 138.534 138.534i 0.309920 0.309920i
\(448\) 57.9988i 0.129462i
\(449\) 289.500 + 289.500i 0.644765 + 0.644765i 0.951723 0.306958i \(-0.0993111\pi\)
−0.306958 + 0.951723i \(0.599311\pi\)
\(450\) −121.766 + 121.766i −0.270592 + 0.270592i
\(451\) 0.212031 0.000470135
\(452\) 1018.17 + 1018.17i 2.25260 + 2.25260i
\(453\) 219.825 219.825i 0.485265 0.485265i
\(454\) −456.079 456.079i −1.00458 1.00458i
\(455\) −28.0337 −0.0616125
\(456\) −2373.56 2373.56i −5.20518 5.20518i
\(457\) 263.854i 0.577361i 0.957426 + 0.288680i \(0.0932165\pi\)
−0.957426 + 0.288680i \(0.906784\pi\)
\(458\) −759.628 −1.65858
\(459\) 129.928 0.283067
\(460\) 383.003 0.832614
\(461\) −489.859 + 489.859i −1.06260 + 1.06260i −0.0646957 + 0.997905i \(0.520608\pi\)
−0.997905 + 0.0646957i \(0.979392\pi\)
\(462\) −0.515184 + 0.515184i −0.00111512 + 0.00111512i
\(463\) 606.327i 1.30956i −0.755819 0.654781i \(-0.772761\pi\)
0.755819 0.654781i \(-0.227239\pi\)
\(464\) −895.428 + 761.561i −1.92980 + 1.64130i
\(465\) 143.615 0.308849
\(466\) 270.028 + 270.028i 0.579459 + 0.579459i
\(467\) 337.667 + 337.667i 0.723056 + 0.723056i 0.969227 0.246171i \(-0.0791724\pi\)
−0.246171 + 0.969227i \(0.579172\pi\)
\(468\) 841.820i 1.79876i
\(469\) 56.4912i 0.120450i
\(470\) 547.359i 1.16459i
\(471\) 792.626 1.68286
\(472\) −1614.60 + 1614.60i −3.42077 + 3.42077i
\(473\) 0.953385i 0.00201561i
\(474\) −1286.37 + 1286.37i −2.71385 + 2.71385i
\(475\) −112.461 112.461i −0.236759 0.236759i
\(476\) 111.259 111.259i 0.233737 0.233737i
\(477\) 444.757i 0.932404i
\(478\) −819.372 819.372i −1.71417 1.71417i
\(479\) 431.509 431.509i 0.900854 0.900854i −0.0946564 0.995510i \(-0.530175\pi\)
0.995510 + 0.0946564i \(0.0301753\pi\)
\(480\) 1288.79 2.68498
\(481\) 83.6211 + 83.6211i 0.173848 + 0.173848i
\(482\) 821.608 821.608i 1.70458 1.70458i
\(483\) 20.0483 + 20.0483i 0.0415078 + 0.0415078i
\(484\) 1183.39 2.44502
\(485\) −194.042 194.042i −0.400086 0.400086i
\(486\) 1292.73i 2.65993i
\(487\) −317.203 −0.651341 −0.325670 0.945483i \(-0.605590\pi\)
−0.325670 + 0.945483i \(0.605590\pi\)
\(488\) 1284.27 2.63171
\(489\) −519.227 −1.06181
\(490\) −576.114 + 576.114i −1.17574 + 1.17574i
\(491\) −440.067 + 440.067i −0.896266 + 0.896266i −0.995104 0.0988377i \(-0.968488\pi\)
0.0988377 + 0.995104i \(0.468488\pi\)
\(492\) 152.525i 0.310010i
\(493\) 623.916 + 50.4057i 1.26555 + 0.102243i
\(494\) 1095.47 2.21754
\(495\) 1.98735 + 1.98735i 0.00401485 + 0.00401485i
\(496\) 206.450 + 206.450i 0.416230 + 0.416230i
\(497\) 53.0720i 0.106785i
\(498\) 247.912i 0.497814i
\(499\) 847.151i 1.69770i 0.528635 + 0.848849i \(0.322704\pi\)
−0.528635 + 0.848849i \(0.677296\pi\)
\(500\) 1306.01 2.61203
\(501\) 689.610 689.610i 1.37647 1.37647i
\(502\) 41.1285i 0.0819292i
\(503\) −6.42815 + 6.42815i −0.0127796 + 0.0127796i −0.713468 0.700688i \(-0.752876\pi\)
0.700688 + 0.713468i \(0.252876\pi\)
\(504\) 117.249 + 117.249i 0.232638 + 0.232638i
\(505\) 165.077 165.077i 0.326884 0.326884i
\(506\) 1.91991i 0.00379430i
\(507\) −311.433 311.433i −0.614267 0.614267i
\(508\) −80.8584 + 80.8584i −0.159170 + 0.159170i
\(509\) −476.056 −0.935277 −0.467638 0.883920i \(-0.654895\pi\)
−0.467638 + 0.883920i \(0.654895\pi\)
\(510\) −1129.65 1129.65i −2.21501 2.21501i
\(511\) 55.0007 55.0007i 0.107633 0.107633i
\(512\) −607.415 607.415i −1.18636 1.18636i
\(513\) −213.970 −0.417095
\(514\) 179.965 + 179.965i 0.350126 + 0.350126i
\(515\) 506.289i 0.983086i
\(516\) −685.819 −1.32911
\(517\) −1.94736 −0.00376665
\(518\) −39.4128 −0.0760865
\(519\) 20.6018 20.6018i 0.0396952 0.0396952i
\(520\) −570.686 + 570.686i −1.09747 + 1.09747i
\(521\) 557.186i 1.06946i 0.845024 + 0.534728i \(0.179586\pi\)
−0.845024 + 0.534728i \(0.820414\pi\)
\(522\) −89.8785 + 1112.51i −0.172181 + 2.13124i
\(523\) 456.134 0.872149 0.436074 0.899911i \(-0.356368\pi\)
0.436074 + 0.899911i \(0.356368\pi\)
\(524\) −3.53679 3.53679i −0.00674960 0.00674960i
\(525\) 10.3778 + 10.3778i 0.0197672 + 0.0197672i
\(526\) 806.990i 1.53420i
\(527\) 155.472i 0.295013i
\(528\) 10.6737i 0.0202153i
\(529\) −454.287 −0.858766
\(530\) −510.153 + 510.153i −0.962552 + 0.962552i
\(531\) 1103.27i 2.07772i
\(532\) −183.225 + 183.225i −0.344407 + 0.344407i
\(533\) 20.8022 + 20.8022i 0.0390285 + 0.0390285i
\(534\) −373.163 + 373.163i −0.698806 + 0.698806i
\(535\) 403.071i 0.753404i
\(536\) −1150.00 1150.00i −2.14552 2.14552i
\(537\) −115.017 + 115.017i −0.214184 + 0.214184i
\(538\) 1430.16 2.65828
\(539\) −2.04966 2.04966i −0.00380272 0.00380272i
\(540\) 188.604 188.604i 0.349266 0.349266i
\(541\) 537.048 + 537.048i 0.992694 + 0.992694i 0.999974 0.00727934i \(-0.00231711\pi\)
−0.00727934 + 0.999974i \(0.502317\pi\)
\(542\) −1600.03 −2.95209
\(543\) 597.605 + 597.605i 1.10056 + 1.10056i
\(544\) 1395.19i 2.56469i
\(545\) 186.293 0.341823
\(546\) −101.089 −0.185144
\(547\) 353.235 0.645768 0.322884 0.946439i \(-0.395348\pi\)
0.322884 + 0.946439i \(0.395348\pi\)
\(548\) 680.459 680.459i 1.24171 1.24171i
\(549\) 438.776 438.776i 0.799229 0.799229i
\(550\) 0.993823i 0.00180695i
\(551\) −1027.49 83.0098i −1.86477 0.150653i
\(552\) 816.250 1.47871
\(553\) 58.6879 + 58.6879i 0.106126 + 0.106126i
\(554\) −70.1532 70.1532i −0.126630 0.126630i
\(555\) 284.016i 0.511740i
\(556\) 1089.34i 1.95924i
\(557\) 916.424i 1.64529i −0.568558 0.822643i \(-0.692499\pi\)
0.568558 0.822643i \(-0.307501\pi\)
\(558\) 277.221 0.496813
\(559\) 93.5358 93.5358i 0.167327 0.167327i
\(560\) 136.874i 0.244419i
\(561\) 4.01902 4.01902i 0.00716402 0.00716402i
\(562\) 1230.88 + 1230.88i 2.19018 + 2.19018i
\(563\) −526.927 + 526.927i −0.935928 + 0.935928i −0.998067 0.0621396i \(-0.980208\pi\)
0.0621396 + 0.998067i \(0.480208\pi\)
\(564\) 1400.84i 2.48375i
\(565\) −471.646 471.646i −0.834772 0.834772i
\(566\) 691.653 691.653i 1.22200 1.22200i
\(567\) −49.8028 −0.0878356
\(568\) −1080.39 1080.39i −1.90210 1.90210i
\(569\) 394.074 394.074i 0.692573 0.692573i −0.270224 0.962797i \(-0.587098\pi\)
0.962797 + 0.270224i \(0.0870979\pi\)
\(570\) 1860.35 + 1860.35i 3.26377 + 3.26377i
\(571\) −552.975 −0.968432 −0.484216 0.874949i \(-0.660895\pi\)
−0.484216 + 0.874949i \(0.660895\pi\)
\(572\) −3.43535 3.43535i −0.00600586 0.00600586i
\(573\) 1340.30i 2.33909i
\(574\) −9.80460 −0.0170812
\(575\) 38.6744 0.0672598
\(576\) 806.774 1.40065
\(577\) 167.445 167.445i 0.290200 0.290200i −0.546959 0.837159i \(-0.684215\pi\)
0.837159 + 0.546959i \(0.184215\pi\)
\(578\) −464.317 + 464.317i −0.803317 + 0.803317i
\(579\) 813.321i 1.40470i
\(580\) 978.848 832.510i 1.68767 1.43536i
\(581\) −11.3105 −0.0194672
\(582\) −699.707 699.707i −1.20225 1.20225i
\(583\) −1.81499 1.81499i −0.00311319 0.00311319i
\(584\) 2239.31i 3.83444i
\(585\) 389.954i 0.666588i
\(586\) 443.303i 0.756489i
\(587\) 38.0082 0.0647500 0.0323750 0.999476i \(-0.489693\pi\)
0.0323750 + 0.999476i \(0.489693\pi\)
\(588\) −1474.43 + 1474.43i −2.50753 + 2.50753i
\(589\) 256.036i 0.434696i
\(590\) 1265.49 1265.49i 2.14490 2.14490i
\(591\) 793.388 + 793.388i 1.34245 + 1.34245i
\(592\) −408.280 + 408.280i −0.689661 + 0.689661i
\(593\) 627.850i 1.05877i −0.848382 0.529385i \(-0.822423\pi\)
0.848382 0.529385i \(-0.177577\pi\)
\(594\) 0.945432 + 0.945432i 0.00159164 + 0.00159164i
\(595\) −51.5381 + 51.5381i −0.0866187 + 0.0866187i
\(596\) −435.399 −0.730535
\(597\) −522.854 522.854i −0.875802 0.875802i
\(598\) −188.361 + 188.361i −0.314985 + 0.314985i
\(599\) 674.702 + 674.702i 1.12638 + 1.12638i 0.990761 + 0.135619i \(0.0433024\pi\)
0.135619 + 0.990761i \(0.456698\pi\)
\(600\) 422.523 0.704205
\(601\) −500.527 500.527i −0.832823 0.832823i 0.155079 0.987902i \(-0.450437\pi\)
−0.987902 + 0.155079i \(0.950437\pi\)
\(602\) 44.0858i 0.0732322i
\(603\) −785.802 −1.30315
\(604\) −690.886 −1.14385
\(605\) −548.178 −0.906079
\(606\) 595.260 595.260i 0.982278 0.982278i
\(607\) 780.373 780.373i 1.28562 1.28562i 0.348204 0.937419i \(-0.386792\pi\)
0.937419 0.348204i \(-0.113208\pi\)
\(608\) 2297.65i 3.77903i
\(609\) 94.8155 + 7.66007i 0.155690 + 0.0125781i
\(610\) −1006.59 −1.65014
\(611\) −191.054 191.054i −0.312690 0.312690i
\(612\) −1547.63 1547.63i −2.52881 2.52881i
\(613\) 830.453i 1.35473i 0.735645 + 0.677367i \(0.236879\pi\)
−0.735645 + 0.677367i \(0.763121\pi\)
\(614\) 1013.67i 1.65093i
\(615\) 70.6537i 0.114884i
\(616\) 0.956957 0.00155350
\(617\) 69.2239 69.2239i 0.112194 0.112194i −0.648781 0.760975i \(-0.724721\pi\)
0.760975 + 0.648781i \(0.224721\pi\)
\(618\) 1825.66i 2.95414i
\(619\) −331.072 + 331.072i −0.534849 + 0.534849i −0.922012 0.387162i \(-0.873455\pi\)
0.387162 + 0.922012i \(0.373455\pi\)
\(620\) −225.683 225.683i −0.364005 0.364005i
\(621\) 36.7912 36.7912i 0.0592452 0.0592452i
\(622\) 726.439i 1.16791i
\(623\) 17.0248 + 17.0248i 0.0273271 + 0.0273271i
\(624\) −1047.18 + 1047.18i −1.67818 + 1.67818i
\(625\) −493.123 −0.788997
\(626\) 829.706 + 829.706i 1.32541 + 1.32541i
\(627\) −6.61864 + 6.61864i −0.0105561 + 0.0105561i
\(628\) −1245.57 1245.57i −1.98339 1.98339i
\(629\) 307.464 0.488814
\(630\) −91.8977 91.8977i −0.145869 0.145869i
\(631\) 681.376i 1.07984i 0.841718 + 0.539918i \(0.181545\pi\)
−0.841718 + 0.539918i \(0.818455\pi\)
\(632\) 2389.43 3.78075
\(633\) 696.381 1.10013
\(634\) 1168.10 1.84243
\(635\) 37.4558 37.4558i 0.0589855 0.0589855i
\(636\) −1305.62 + 1305.62i −2.05286 + 2.05286i
\(637\) 402.181i 0.631368i
\(638\) 4.17320 + 4.90676i 0.00654107 + 0.00769085i
\(639\) −738.240 −1.15531
\(640\) −97.1018 97.1018i −0.151722 0.151722i
\(641\) −517.626 517.626i −0.807529 0.807529i 0.176730 0.984259i \(-0.443448\pi\)
−0.984259 + 0.176730i \(0.943448\pi\)
\(642\) 1453.46i 2.26396i
\(643\) 867.657i 1.34939i −0.738097 0.674694i \(-0.764275\pi\)
0.738097 0.674694i \(-0.235725\pi\)
\(644\) 63.0096i 0.0978410i
\(645\) 317.690 0.492543
\(646\) 2013.94 2013.94i 3.11756 3.11756i
\(647\) 357.347i 0.552314i 0.961113 + 0.276157i \(0.0890609\pi\)
−0.961113 + 0.276157i \(0.910939\pi\)
\(648\) −1013.84 + 1013.84i −1.56457 + 1.56457i
\(649\) 4.50229 + 4.50229i 0.00693728 + 0.00693728i
\(650\) −97.5031 + 97.5031i −0.150005 + 0.150005i
\(651\) 23.6268i 0.0362930i
\(652\) 815.937 + 815.937i 1.25144 + 1.25144i
\(653\) −700.906 + 700.906i −1.07336 + 1.07336i −0.0762758 + 0.997087i \(0.524303\pi\)
−0.997087 + 0.0762758i \(0.975697\pi\)
\(654\) 671.767 1.02717
\(655\) 1.63834 + 1.63834i 0.00250128 + 0.00250128i
\(656\) −101.566 + 101.566i −0.154827 + 0.154827i
\(657\) −765.069 765.069i −1.16449 1.16449i
\(658\) 90.0486 0.136852
\(659\) 760.878 + 760.878i 1.15459 + 1.15459i 0.985621 + 0.168974i \(0.0540453\pi\)
0.168974 + 0.985621i \(0.445955\pi\)
\(660\) 11.6680i 0.0176788i
\(661\) −204.176 −0.308889 −0.154444 0.988001i \(-0.549359\pi\)
−0.154444 + 0.988001i \(0.549359\pi\)
\(662\) 1263.34 1.90838
\(663\) 788.604 1.18945
\(664\) −230.248 + 230.248i −0.346760 + 0.346760i
\(665\) 84.8747 84.8747i 0.127631 0.127631i
\(666\) 548.239i 0.823182i
\(667\) 190.945 162.399i 0.286275 0.243477i
\(668\) −2167.37 −3.24457
\(669\) 177.458 + 177.458i 0.265258 + 0.265258i
\(670\) 901.345 + 901.345i 1.34529 + 1.34529i
\(671\) 3.58117i 0.00533707i
\(672\) 212.025i 0.315513i
\(673\) 255.714i 0.379962i −0.981788 0.189981i \(-0.939157\pi\)
0.981788 0.189981i \(-0.0608426\pi\)
\(674\) −1545.42 −2.29291
\(675\) 19.0446 19.0446i 0.0282142 0.0282142i
\(676\) 978.802i 1.44793i
\(677\) −778.876 + 778.876i −1.15048 + 1.15048i −0.164026 + 0.986456i \(0.552448\pi\)
−0.986456 + 0.164026i \(0.947552\pi\)
\(678\) −1700.74 1700.74i −2.50847 2.50847i
\(679\) −31.9227 + 31.9227i −0.0470143 + 0.0470143i
\(680\) 2098.34i 3.08579i
\(681\) 540.692 + 540.692i 0.793967 + 0.793967i
\(682\) 1.13130 1.13130i 0.00165880 0.00165880i
\(683\) −712.500 −1.04319 −0.521596 0.853193i \(-0.674663\pi\)
−0.521596 + 0.853193i \(0.674663\pi\)
\(684\) 2548.69 + 2548.69i 3.72615 + 3.72615i
\(685\) −315.207 + 315.207i −0.460156 + 0.460156i
\(686\) 190.645 + 190.645i 0.277909 + 0.277909i
\(687\) 900.556 1.31085
\(688\) 456.688 + 456.688i 0.663790 + 0.663790i
\(689\) 356.134i 0.516886i
\(690\) −639.760 −0.927189
\(691\) 85.2702 0.123401 0.0617006 0.998095i \(-0.480348\pi\)
0.0617006 + 0.998095i \(0.480348\pi\)
\(692\) −64.7493 −0.0935684
\(693\) 0.326948 0.326948i 0.000471787 0.000471787i
\(694\) 933.346 933.346i 1.34488 1.34488i
\(695\) 504.612i 0.726060i
\(696\) 2086.11 1774.23i 2.99728 2.54919i
\(697\) 76.4869 0.109737
\(698\) −628.235 628.235i −0.900051 0.900051i
\(699\) −320.124 320.124i −0.457975 0.457975i
\(700\) 32.6162i 0.0465946i
\(701\) 389.567i 0.555731i −0.960620 0.277865i \(-0.910373\pi\)
0.960620 0.277865i \(-0.0896269\pi\)
\(702\) 185.511i 0.264261i
\(703\) −506.342 −0.720258
\(704\) 3.29233 3.29233i 0.00467661 0.00467661i
\(705\) 648.906i 0.920434i
\(706\) 82.0155 82.0155i 0.116169 0.116169i
\(707\) −27.1575 27.1575i −0.0384123 0.0384123i
\(708\) 3238.73 3238.73i 4.57448 4.57448i
\(709\) 616.933i 0.870145i −0.900396 0.435072i \(-0.856723\pi\)
0.900396 0.435072i \(-0.143277\pi\)
\(710\) 846.790 + 846.790i 1.19266 + 1.19266i
\(711\) 816.359 816.359i 1.14818 1.14818i
\(712\) 693.151 0.973527
\(713\) −44.0244 44.0244i −0.0617452 0.0617452i
\(714\) −185.845 + 185.845i −0.260287 + 0.260287i
\(715\) 1.59135 + 1.59135i 0.00222566 + 0.00222566i
\(716\) 361.485 0.504868
\(717\) 971.384 + 971.384i 1.35479 + 1.35479i
\(718\) 1362.75i 1.89798i
\(719\) 273.210 0.379986 0.189993 0.981785i \(-0.439153\pi\)
0.189993 + 0.981785i \(0.439153\pi\)
\(720\) −1903.95 −2.64437
\(721\) −83.2920 −0.115523
\(722\) −2369.03 + 2369.03i −3.28120 + 3.28120i
\(723\) −974.035 + 974.035i −1.34721 + 1.34721i
\(724\) 1878.21i 2.59421i
\(725\) 98.8409 84.0641i 0.136332 0.115950i
\(726\) −1976.71 −2.72274
\(727\) 136.415 + 136.415i 0.187641 + 0.187641i 0.794676 0.607034i \(-0.207641\pi\)
−0.607034 + 0.794676i \(0.707641\pi\)
\(728\) 93.8862 + 93.8862i 0.128965 + 0.128965i
\(729\) 931.186i 1.27735i
\(730\) 1755.13i 2.40428i
\(731\) 343.919i 0.470477i
\(732\) −2576.12 −3.51930
\(733\) −580.859 + 580.859i −0.792441 + 0.792441i −0.981890 0.189449i \(-0.939330\pi\)
0.189449 + 0.981890i \(0.439330\pi\)
\(734\) 683.563i 0.931284i
\(735\) 682.996 682.996i 0.929247 0.929247i
\(736\) −395.072 395.072i −0.536782 0.536782i
\(737\) −3.20675 + 3.20675i −0.00435109 + 0.00435109i
\(738\) 136.384i 0.184802i
\(739\) −688.432 688.432i −0.931572 0.931572i 0.0662318 0.997804i \(-0.478902\pi\)
−0.997804 + 0.0662318i \(0.978902\pi\)
\(740\) 446.316 446.316i 0.603129 0.603129i
\(741\) −1298.70 −1.75263
\(742\) 83.9276 + 83.9276i 0.113110 + 0.113110i
\(743\) 108.284 108.284i 0.145739 0.145739i −0.630472 0.776212i \(-0.717139\pi\)
0.776212 + 0.630472i \(0.217139\pi\)
\(744\) −480.973 480.973i −0.646469 0.646469i
\(745\) 201.689 0.270723
\(746\) −1675.39 1675.39i −2.24583 2.24583i
\(747\) 157.330i 0.210616i
\(748\) −12.6313 −0.0168868
\(749\) −66.3112 −0.0885329
\(750\) −2181.54 −2.90872
\(751\) 474.687 474.687i 0.632074 0.632074i −0.316514 0.948588i \(-0.602512\pi\)
0.948588 + 0.316514i \(0.102512\pi\)
\(752\) 932.819 932.819i 1.24045 1.24045i
\(753\) 48.7587i 0.0647526i
\(754\) −71.9693 + 890.827i −0.0954500 + 1.18147i
\(755\) 320.037 0.423891
\(756\) −31.0281 31.0281i −0.0410425 0.0410425i
\(757\) 144.571 + 144.571i 0.190979 + 0.190979i 0.796119 0.605140i \(-0.206883\pi\)
−0.605140 + 0.796119i \(0.706883\pi\)
\(758\) 481.782i 0.635597i
\(759\) 2.27610i 0.00299882i
\(760\) 3455.61i 4.54685i
\(761\) 279.009 0.366635 0.183318 0.983054i \(-0.441316\pi\)
0.183318 + 0.983054i \(0.441316\pi\)
\(762\) 135.064 135.064i 0.177250 0.177250i
\(763\) 30.6480i 0.0401678i
\(764\) 2106.21 2106.21i 2.75681 2.75681i
\(765\) 716.905 + 716.905i 0.937130 + 0.937130i
\(766\) −761.897 + 761.897i −0.994644 + 0.994644i
\(767\) 883.432i 1.15180i
\(768\) 618.468 + 618.468i 0.805297 + 0.805297i
\(769\) 270.425 270.425i 0.351658 0.351658i −0.509068 0.860726i \(-0.670010\pi\)
0.860726 + 0.509068i \(0.170010\pi\)
\(770\) −0.750044 −0.000974083
\(771\) −213.352 213.352i −0.276722 0.276722i
\(772\) −1278.09 + 1278.09i −1.65556 + 1.65556i
\(773\) 933.705 + 933.705i 1.20790 + 1.20790i 0.971707 + 0.236191i \(0.0758991\pi\)
0.236191 + 0.971707i \(0.424101\pi\)
\(774\) 613.242 0.792302
\(775\) −22.7887 22.7887i −0.0294048 0.0294048i
\(776\) 1299.71i 1.67488i
\(777\) 46.7248 0.0601348
\(778\) 2125.19 2.73161
\(779\) −125.961 −0.161696
\(780\) 1144.74 1144.74i 1.46762 1.46762i
\(781\) −3.01266 + 3.01266i −0.00385744 + 0.00385744i
\(782\) 692.579i 0.885651i
\(783\) 14.0573