Properties

Label 29.3.c.a.17.4
Level 29
Weight 3
Character 29.17
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 17.4
Root \(0.486981i\) of defining polynomial
Character \(\chi\) \(=\) 29.17
Dual form 29.3.c.a.12.4

$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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 0.392859 0.919599i \(-0.371486\pi\)
0.919599 0.392859i \(-0.128514\pi\)
\(3\) −3.11190 + 3.11190i −1.03730 + 1.03730i −0.0380218 + 0.999277i \(0.512106\pi\)
−0.999277 + 0.0380218i \(0.987894\pi\)
\(4\) 9.78036i 2.44509i
\(5\) 4.53053i 0.906106i 0.891484 + 0.453053i \(0.149665\pi\)
−0.891484 + 0.453053i \(0.850335\pi\)
\(6\) 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 −0.705181 0.709027i \(-0.749134\pi\)
0.709027 + 0.705181i \(0.249134\pi\)
\(12\) 30.4355 + 30.4355i 2.53629 + 2.53629i
\(13\) 8.30191i 0.638608i −0.947652 0.319304i \(-0.896551\pi\)
0.947652 0.319304i \(-0.103449\pi\)
\(14\) −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 −0.0974461 0.995241i \(-0.531067\pi\)
0.995241 + 0.0974461i \(0.0310673\pi\)
\(18\) −27.2146 27.2146i −1.51192 1.51192i
\(19\) −25.1348 + 25.1348i −1.32288 + 1.32288i −0.411453 + 0.911431i \(0.634979\pi\)
−0.911431 + 0.411453i \(0.865021\pi\)
\(20\) 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 −0.784468 0.620169i \(-0.787064\pi\)
0.620169 + 0.784468i \(0.287064\pi\)
\(32\) −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 0.829997 0.557767i \(-0.188342\pi\)
−0.557767 + 0.829997i \(0.688342\pi\)
\(38\) 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 0.737004 0.675889i \(-0.236240\pi\)
−0.675889 + 0.737004i \(0.736240\pi\)
\(42\) 12.1765i 0.289918i
\(43\) −11.2668 + 11.2668i −0.262018 + 0.262018i −0.825874 0.563855i \(-0.809318\pi\)
0.563855 + 0.825874i \(0.309318\pi\)
\(44\) −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 0.418550 0.908194i \(-0.362538\pi\)
−0.908194 + 0.418550i \(0.862538\pi\)
\(48\) 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 −0.963063 0.269275i \(-0.913216\pi\)
0.269275 + 0.963063i \(0.413216\pi\)
\(62\) 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 \(-0.808638\pi\)
0.824668 0.565616i \(-0.191362\pi\)
\(68\) −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 \(-0.832802\pi\)
0.865190 0.501445i \(-0.167198\pi\)
\(72\) −157.310 + 157.310i −2.18486 + 2.18486i
\(73\) −73.7928 73.7928i −1.01086 1.01086i −0.999940 0.0109201i \(-0.996524\pi\)
−0.0109201 0.999940i \(-0.503476\pi\)
\(74\) 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 −0.999995 0.00328762i \(-0.998954\pi\)
0.00328762 + 0.999995i \(0.498954\pi\)
\(80\) 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 −0.823689 0.567041i \(-0.808088\pi\)
0.567041 + 0.823689i \(0.308088\pi\)
\(90\) 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 0.892531 0.450987i \(-0.148928\pi\)
−0.450987 + 0.892531i \(0.648928\pi\)
\(98\) −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 −0.503334 0.864092i \(-0.667894\pi\)
0.864092 + 0.503334i \(0.167894\pi\)
\(102\) 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 \(-0.939598\pi\)
0.982050 0.188622i \(-0.0604020\pi\)
\(110\) 1.00631 0.00914829
\(111\) −62.6893 −0.564768
\(112\) 30.2116 0.269746
\(113\) 104.104 + 104.104i 0.921275 + 0.921275i 0.997120 0.0758450i \(-0.0241654\pi\)
−0.0758450 + 0.997120i \(0.524165\pi\)
\(114\) −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 −0.673808 0.738906i \(-0.735343\pi\)
0.738906 + 0.673808i \(0.235343\pi\)
\(128\) 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 0.705725 0.708486i \(-0.250621\pi\)
−0.708486 + 0.705725i \(0.750621\pi\)
\(132\) 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 −0.913863 0.406023i \(-0.866915\pi\)
0.406023 + 0.913863i \(0.366915\pi\)
\(138\) 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 \(-0.952270\pi\)
0.988779 0.149388i \(-0.0477304\pi\)
\(150\) 73.0963i 0.487309i
\(151\) 70.6402i 0.467816i −0.972259 0.233908i \(-0.924849\pi\)
0.972259 0.233908i \(-0.0751514\pi\)
\(152\) 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 0.173636 0.984810i \(-0.444448\pi\)
−0.984810 + 0.173636i \(0.944448\pi\)
\(158\) 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 0.915083 0.403266i \(-0.132125\pi\)
−0.403266 + 0.915083i \(0.632125\pi\)
\(164\) 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 \(-0.769076\pi\)
0.748188 0.663487i \(-0.230924\pi\)
\(168\) −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 \(-0.993909\pi\)
0.999817 0.0191339i \(-0.00609089\pi\)
\(174\) −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 \(0.0329213\pi\)
−0.994656 + 0.103241i \(0.967079\pi\)
\(180\) 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 −0.136906 + 0.990584i \(0.543716\pi\)
−0.990584 + 0.136906i \(0.956284\pi\)
\(192\) −242.153 242.153i −1.26122 1.26122i
\(193\) 130.679 130.679i 0.677095 0.677095i −0.282247 0.959342i \(-0.591080\pi\)
0.959342 + 0.282247i \(0.0910797\pi\)
\(194\) 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 0.390372 0.920657i \(-0.372346\pi\)
−0.920657 + 0.390372i \(0.872346\pi\)
\(212\) 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 0.316675 0.948534i \(-0.397433\pi\)
−0.948534 + 0.316675i \(0.897433\pi\)
\(230\) 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 \(0.224974\pi\)
−0.760460 + 0.649385i \(0.775026\pi\)
\(242\) 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 −0.691328 0.722541i \(-0.742974\pi\)
0.722541 + 0.691328i \(0.242974\pi\)
\(252\) 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 −0.351653 0.936130i \(-0.614380\pi\)
0.936130 + 0.351653i \(0.114380\pi\)
\(264\) 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 0.999918 + 0.0127932i \(0.00407231\pi\)
0.0127932 + 0.999918i \(0.495928\pi\)
\(270\) 101.237i 0.374953i
\(271\) −304.778 304.778i −1.12464 1.12464i −0.991034 0.133607i \(-0.957344\pi\)
−0.133607 0.991034i \(-0.542656\pi\)
\(272\) −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 \(0.154140\pi\)
−0.885027 + 0.465540i \(0.845860\pi\)
\(284\) −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 −0.836366 0.548171i \(-0.815324\pi\)
0.548171 + 0.836366i \(0.315324\pi\)
\(294\) 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 −0.318858 0.947803i \(-0.603299\pi\)
0.947803 + 0.318858i \(0.103299\pi\)
\(308\) 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 −0.893666 0.448734i \(-0.851875\pi\)
0.448734 + 0.893666i \(0.351875\pi\)
\(312\) 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 0.964819 0.262916i \(-0.0846843\pi\)
−0.262916 + 0.964819i \(0.584684\pi\)
\(318\) 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 0.970026 0.243002i \(-0.0781322\pi\)
−0.243002 + 0.970026i \(0.578132\pi\)
\(332\) 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 0.119336 0.992854i \(-0.461923\pi\)
−0.992854 + 0.119336i \(0.961923\pi\)
\(338\) 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 \(0.171225\pi\)
−0.858776 + 0.512351i \(0.828775\pi\)
\(348\) 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 \(0.0140919\pi\)
−0.999020 + 0.0442564i \(0.985908\pi\)
\(354\) 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 −0.246164 0.969228i \(-0.579170\pi\)
0.969228 + 0.246164i \(0.0791702\pi\)
\(360\) −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 −0.507100 0.861887i \(-0.669283\pi\)
0.861887 + 0.507100i \(0.169283\pi\)
\(368\) −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 −0.575595 0.817735i \(-0.695229\pi\)
0.817735 + 0.575595i \(0.195229\pi\)
\(380\) −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 \(-0.876294\pi\)
0.925428 0.378924i \(-0.123706\pi\)
\(384\) −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 0.999138 + 0.0415071i \(0.0132159\pi\)
0.0415071 + 0.999138i \(0.486784\pi\)
\(390\) 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 −0.546862 0.837223i \(-0.684178\pi\)
0.837223 + 0.546862i \(0.184178\pi\)
\(410\) 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 \(0.00790628\pi\)
−0.999692 + 0.0248357i \(0.992094\pi\)
\(420\) 102.774 102.774i 0.244700 0.244700i
\(421\) 199.204 + 199.204i 0.473168 + 0.473168i 0.902938 0.429770i \(-0.141405\pi\)
−0.429770 + 0.902938i \(0.641405\pi\)
\(422\) −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 0.830850 0.556497i \(-0.187855\pi\)
−0.556497 + 0.830850i \(0.687855\pi\)
\(434\) 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 \(0.270973\pi\)
−0.659015 + 0.752130i \(0.729027\pi\)
\(440\) 5.81685i 0.0132201i
\(441\) 502.262i 1.13892i
\(442\) −665.195 −1.50497
\(443\) 222.343 + 222.343i 0.501904 + 0.501904i 0.912029 0.410125i \(-0.134515\pi\)
−0.410125 + 0.912029i \(0.634515\pi\)
\(444\) 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 −0.306958 0.951723i \(-0.599311\pi\)
0.951723 + 0.306958i \(0.0993111\pi\)
\(450\) −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 \(-0.906784\pi\)
0.957426 0.288680i \(-0.0932165\pi\)
\(458\) −759.628 −1.65858
\(459\) 129.928 0.283067
\(460\) 383.003 0.832614
\(461\) −489.859 489.859i −1.06260 1.06260i −0.997905 0.0646957i \(-0.979392\pi\)
−0.0646957 0.997905i \(-0.520608\pi\)
\(462\) −0.515184 0.515184i −0.00111512 0.00111512i
\(463\) 606.327i 1.30956i 0.755819 + 0.654781i \(0.227239\pi\)
−0.755819 + 0.654781i \(0.772761\pi\)
\(464\) −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 −0.246171 0.969227i \(-0.579172\pi\)
0.969227 + 0.246171i \(0.0791724\pi\)
\(468\) 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 0.995510 0.0946564i \(-0.0301753\pi\)
−0.0946564 + 0.995510i \(0.530175\pi\)
\(480\) 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 0.0988377 0.995104i \(-0.468488\pi\)
−0.995104 + 0.0988377i \(0.968488\pi\)
\(492\) 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 \(-0.677296\pi\)
0.528635 0.848849i \(-0.322704\pi\)
\(500\) 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 0.700688 0.713468i \(-0.252876\pi\)
−0.713468 + 0.700688i \(0.752876\pi\)
\(504\) 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 \(-0.820414\pi\)
0.845024 0.534728i \(-0.179586\pi\)
\(522\) −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 −0.00727934 0.999974i \(-0.502317\pi\)
0.999974 + 0.00727934i \(0.00231711\pi\)
\(542\) −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 \(0.307501\pi\)
−0.568558 + 0.822643i \(0.692499\pi\)
\(558\) 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 0.0621396 0.998067i \(-0.480208\pi\)
−0.998067 + 0.0621396i \(0.980208\pi\)
\(564\) 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 0.962797 0.270224i \(-0.0870979\pi\)
−0.270224 + 0.962797i \(0.587098\pi\)
\(570\) 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 0.837159 0.546959i \(-0.184215\pi\)
−0.546959 + 0.837159i \(0.684215\pi\)
\(578\) −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 \(0.177577\pi\)
−0.848382 + 0.529385i \(0.822423\pi\)
\(594\) 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 0.135619 0.990761i \(-0.456698\pi\)
0.990761 0.135619i \(-0.0433024\pi\)
\(600\) 422.523 0.704205
\(601\) −500.527 + 500.527i −0.832823 + 0.832823i −0.987902 0.155079i \(-0.950437\pi\)
0.155079 + 0.987902i \(0.450437\pi\)
\(602\) 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 0.937419 + 0.348204i \(0.113208\pi\)
0.348204 + 0.937419i \(0.386792\pi\)
\(608\) 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 \(-0.763121\pi\)
0.735645 0.677367i \(-0.236879\pi\)
\(614\) 1013.67i 1.65093i
\(615\) 70.6537i 0.114884i
\(616\) 0.956957 0.00155350
\(617\) 69.2239 + 69.2239i 0.112194 + 0.112194i 0.760975 0.648781i \(-0.224721\pi\)
−0.648781 + 0.760975i \(0.724721\pi\)
\(618\) 1825.66i 2.95414i
\(619\) −331.072 331.072i −0.534849 0.534849i 0.387162 0.922012i \(-0.373455\pi\)
−0.922012 + 0.387162i \(0.873455\pi\)
\(620\) −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 \(-0.818455\pi\)
0.841718 0.539918i \(-0.181545\pi\)
\(632\) 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 −0.984259 0.176730i \(-0.943448\pi\)
0.176730 + 0.984259i \(0.443448\pi\)
\(642\) 1453.46i 2.26396i
\(643\) 867.657i 1.34939i 0.738097 + 0.674694i \(0.235725\pi\)
−0.738097 + 0.674694i \(0.764275\pi\)
\(644\) 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 \(-0.910939\pi\)
0.961113 0.276157i \(-0.0890609\pi\)
\(648\) −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 −0.997087 0.0762758i \(-0.975697\pi\)
−0.0762758 0.997087i \(-0.524303\pi\)
\(654\) 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 0.168974 0.985621i \(-0.445955\pi\)
0.985621 0.168974i \(-0.0540453\pi\)
\(660\) 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 \(0.0608426\pi\)
−0.981788 + 0.189981i \(0.939157\pi\)
\(674\) −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 −0.986456 0.164026i \(-0.947552\pi\)
−0.164026 0.986456i \(-0.552448\pi\)
\(678\) −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 \(0.0896269\pi\)
−0.960620 + 0.277865i \(0.910373\pi\)
\(702\) 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 \(0.143277\pi\)
−0.900396 + 0.435072i \(0.856723\pi\)
\(710\) 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 −0.607034 0.794676i \(-0.707641\pi\)
0.794676 + 0.607034i \(0.207641\pi\)
\(728\) 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 0.189449 0.981890i \(-0.439330\pi\)
−0.981890 + 0.189449i \(0.939330\pi\)
\(734\) 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 −0.997804 0.0662318i \(-0.978902\pi\)
0.0662318 + 0.997804i \(0.478902\pi\)
\(740\) 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 0.776212 0.630472i \(-0.217139\pi\)
−0.630472 + 0.776212i \(0.717139\pi\)
\(744\) −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 0.948588 0.316514i \(-0.102512\pi\)
−0.316514 + 0.948588i \(0.602512\pi\)
\(752\) 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 −0.605140 0.796119i \(-0.706883\pi\)
0.796119 + 0.605140i \(0.206883\pi\)
\(758\) 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 0.860726 0.509068i \(-0.170010\pi\)
−0.509068 + 0.860726i \(0.670010\pi\)
\(770\) −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 0.236191 0.971707i \(-0.424101\pi\)
0.971707 0.236191i \(-0.0758991\pi\)
\(774\) 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