Properties

Label 29.3.c.a.17.1
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 17.1
Root \(-2.35663i\) of defining polynomial
Character \(\chi\) \(=\) 29.17
Dual form 29.3.c.a.12.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45515 + 1.45515i) q^{2} +(3.81178 - 3.81178i) q^{3} -0.234947i q^{4} +3.14526i q^{5} +11.0935i q^{6} +0.342313 q^{7} +(-5.47873 - 5.47873i) q^{8} -20.0593i q^{9} +O(q^{10})\) \(q+(-1.45515 + 1.45515i) q^{2} +(3.81178 - 3.81178i) q^{3} -0.234947i q^{4} +3.14526i q^{5} +11.0935i q^{6} +0.342313 q^{7} +(-5.47873 - 5.47873i) q^{8} -20.0593i q^{9} +(-4.57683 - 4.57683i) q^{10} +(-14.0269 + 14.0269i) q^{11} +(-0.895568 - 0.895568i) q^{12} -11.5162i q^{13} +(-0.498119 + 0.498119i) q^{14} +(11.9890 + 11.9890i) q^{15} +16.8846 q^{16} +(-6.37430 + 6.37430i) q^{17} +(29.1894 + 29.1894i) q^{18} +(-6.11703 + 6.11703i) q^{19} +0.738970 q^{20} +(1.30482 - 1.30482i) q^{21} -40.8226i q^{22} +15.8623 q^{23} -41.7674 q^{24} +15.1074 q^{25} +(16.7578 + 16.7578i) q^{26} +(-42.1557 - 42.1557i) q^{27} -0.0804257i q^{28} +(25.6758 - 13.4817i) q^{29} -34.8918 q^{30} +(6.18103 - 6.18103i) q^{31} +(-2.65475 + 2.65475i) q^{32} +106.935i q^{33} -18.5512i q^{34} +1.07666i q^{35} -4.71289 q^{36} +(24.2121 + 24.2121i) q^{37} -17.8024i q^{38} +(-43.8972 - 43.8972i) q^{39} +(17.2320 - 17.2320i) q^{40} +(-34.9536 - 34.9536i) q^{41} +3.79744i q^{42} +(-15.9908 + 15.9908i) q^{43} +(3.29559 + 3.29559i) q^{44} +63.0917 q^{45} +(-23.0820 + 23.0820i) q^{46} +(7.57643 + 7.57643i) q^{47} +(64.3603 - 64.3603i) q^{48} -48.8828 q^{49} +(-21.9835 + 21.9835i) q^{50} +48.5949i q^{51} -2.70570 q^{52} +62.1991 q^{53} +122.686 q^{54} +(-44.1182 - 44.1182i) q^{55} +(-1.87544 - 1.87544i) q^{56} +46.6336i q^{57} +(-17.7443 + 56.9801i) q^{58} -21.4867 q^{59} +(2.81679 - 2.81679i) q^{60} +(13.1414 - 13.1414i) q^{61} +17.9887i q^{62} -6.86658i q^{63} +59.8122i q^{64} +36.2214 q^{65} +(-155.607 - 155.607i) q^{66} +17.8272i q^{67} +(1.49763 + 1.49763i) q^{68} +(60.4635 - 60.4635i) q^{69} +(-1.56671 - 1.56671i) q^{70} -53.0072i q^{71} +(-109.900 + 109.900i) q^{72} +(5.93089 + 5.93089i) q^{73} -70.4647 q^{74} +(57.5859 - 57.5859i) q^{75} +(1.43718 + 1.43718i) q^{76} +(-4.80160 + 4.80160i) q^{77} +127.754 q^{78} +(-81.6782 + 81.6782i) q^{79} +53.1064i q^{80} -140.843 q^{81} +101.726 q^{82} -77.1462 q^{83} +(-0.306565 - 0.306565i) q^{84} +(-20.0488 - 20.0488i) q^{85} -46.5381i q^{86} +(46.4812 - 149.259i) q^{87} +153.699 q^{88} +(27.4315 - 27.4315i) q^{89} +(-91.8082 + 91.8082i) q^{90} -3.94215i q^{91} -3.72680i q^{92} -47.1215i q^{93} -22.0498 q^{94} +(-19.2396 - 19.2396i) q^{95} +20.2387i q^{96} +(48.7308 + 48.7308i) q^{97} +(71.1320 - 71.1320i) q^{98} +(281.370 + 281.370i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45515 + 1.45515i −0.727577 + 0.727577i −0.970137 0.242559i \(-0.922013\pi\)
0.242559 + 0.970137i \(0.422013\pi\)
\(3\) 3.81178 3.81178i 1.27059 1.27059i 0.324816 0.945777i \(-0.394698\pi\)
0.945777 0.324816i \(-0.105302\pi\)
\(4\) 0.234947i 0.0587369i
\(5\) 3.14526i 0.629051i 0.949249 + 0.314526i \(0.101845\pi\)
−0.949249 + 0.314526i \(0.898155\pi\)
\(6\) 11.0935i 1.84891i
\(7\) 0.342313 0.0489019 0.0244510 0.999701i \(-0.492216\pi\)
0.0244510 + 0.999701i \(0.492216\pi\)
\(8\) −5.47873 5.47873i −0.684842 0.684842i
\(9\) 20.0593i 2.22881i
\(10\) −4.57683 4.57683i −0.457683 0.457683i
\(11\) −14.0269 + 14.0269i −1.27517 + 1.27517i −0.331837 + 0.943337i \(0.607668\pi\)
−0.943337 + 0.331837i \(0.892332\pi\)
\(12\) −0.895568 0.895568i −0.0746306 0.0746306i
\(13\) 11.5162i 0.885861i −0.896556 0.442931i \(-0.853939\pi\)
0.896556 0.442931i \(-0.146061\pi\)
\(14\) −0.498119 + 0.498119i −0.0355799 + 0.0355799i
\(15\) 11.9890 + 11.9890i 0.799268 + 0.799268i
\(16\) 16.8846 1.05529
\(17\) −6.37430 + 6.37430i −0.374959 + 0.374959i −0.869280 0.494321i \(-0.835417\pi\)
0.494321 + 0.869280i \(0.335417\pi\)
\(18\) 29.1894 + 29.1894i 1.62163 + 1.62163i
\(19\) −6.11703 + 6.11703i −0.321949 + 0.321949i −0.849514 0.527565i \(-0.823105\pi\)
0.527565 + 0.849514i \(0.323105\pi\)
\(20\) 0.738970 0.0369485
\(21\) 1.30482 1.30482i 0.0621345 0.0621345i
\(22\) 40.8226i 1.85557i
\(23\) 15.8623 0.689664 0.344832 0.938664i \(-0.387936\pi\)
0.344832 + 0.938664i \(0.387936\pi\)
\(24\) −41.7674 −1.74031
\(25\) 15.1074 0.604295
\(26\) 16.7578 + 16.7578i 0.644532 + 0.644532i
\(27\) −42.1557 42.1557i −1.56132 1.56132i
\(28\) 0.0804257i 0.00287235i
\(29\) 25.6758 13.4817i 0.885371 0.464885i
\(30\) −34.8918 −1.16306
\(31\) 6.18103 6.18103i 0.199388 0.199388i −0.600350 0.799738i \(-0.704972\pi\)
0.799738 + 0.600350i \(0.204972\pi\)
\(32\) −2.65475 + 2.65475i −0.0829610 + 0.0829610i
\(33\) 106.935i 3.24045i
\(34\) 18.5512i 0.545623i
\(35\) 1.07666i 0.0307618i
\(36\) −4.71289 −0.130914
\(37\) 24.2121 + 24.2121i 0.654381 + 0.654381i 0.954045 0.299664i \(-0.0968745\pi\)
−0.299664 + 0.954045i \(0.596874\pi\)
\(38\) 17.8024i 0.468485i
\(39\) −43.8972 43.8972i −1.12557 1.12557i
\(40\) 17.2320 17.2320i 0.430800 0.430800i
\(41\) −34.9536 34.9536i −0.852526 0.852526i 0.137917 0.990444i \(-0.455959\pi\)
−0.990444 + 0.137917i \(0.955959\pi\)
\(42\) 3.79744i 0.0904152i
\(43\) −15.9908 + 15.9908i −0.371878 + 0.371878i −0.868161 0.496283i \(-0.834698\pi\)
0.496283 + 0.868161i \(0.334698\pi\)
\(44\) 3.29559 + 3.29559i 0.0748997 + 0.0748997i
\(45\) 63.0917 1.40204
\(46\) −23.0820 + 23.0820i −0.501784 + 0.501784i
\(47\) 7.57643 + 7.57643i 0.161201 + 0.161201i 0.783098 0.621898i \(-0.213638\pi\)
−0.621898 + 0.783098i \(0.713638\pi\)
\(48\) 64.3603 64.3603i 1.34084 1.34084i
\(49\) −48.8828 −0.997609
\(50\) −21.9835 + 21.9835i −0.439671 + 0.439671i
\(51\) 48.5949i 0.952840i
\(52\) −2.70570 −0.0520327
\(53\) 62.1991 1.17357 0.586784 0.809743i \(-0.300394\pi\)
0.586784 + 0.809743i \(0.300394\pi\)
\(54\) 122.686 2.27197
\(55\) −44.1182 44.1182i −0.802150 0.802150i
\(56\) −1.87544 1.87544i −0.0334901 0.0334901i
\(57\) 46.6336i 0.818133i
\(58\) −17.7443 + 56.9801i −0.305936 + 0.982415i
\(59\) −21.4867 −0.364182 −0.182091 0.983282i \(-0.558287\pi\)
−0.182091 + 0.983282i \(0.558287\pi\)
\(60\) 2.81679 2.81679i 0.0469465 0.0469465i
\(61\) 13.1414 13.1414i 0.215432 0.215432i −0.591138 0.806570i \(-0.701321\pi\)
0.806570 + 0.591138i \(0.201321\pi\)
\(62\) 17.9887i 0.290141i
\(63\) 6.86658i 0.108993i
\(64\) 59.8122i 0.934566i
\(65\) 36.2214 0.557252
\(66\) −155.607 155.607i −2.35768 2.35768i
\(67\) 17.8272i 0.266078i 0.991111 + 0.133039i \(0.0424736\pi\)
−0.991111 + 0.133039i \(0.957526\pi\)
\(68\) 1.49763 + 1.49763i 0.0220239 + 0.0220239i
\(69\) 60.4635 60.4635i 0.876282 0.876282i
\(70\) −1.56671 1.56671i −0.0223816 0.0223816i
\(71\) 53.0072i 0.746580i −0.927715 0.373290i \(-0.878230\pi\)
0.927715 0.373290i \(-0.121770\pi\)
\(72\) −109.900 + 109.900i −1.52638 + 1.52638i
\(73\) 5.93089 + 5.93089i 0.0812450 + 0.0812450i 0.746561 0.665316i \(-0.231703\pi\)
−0.665316 + 0.746561i \(0.731703\pi\)
\(74\) −70.4647 −0.952226
\(75\) 57.5859 57.5859i 0.767813 0.767813i
\(76\) 1.43718 + 1.43718i 0.0189103 + 0.0189103i
\(77\) −4.80160 + 4.80160i −0.0623584 + 0.0623584i
\(78\) 127.754 1.63788
\(79\) −81.6782 + 81.6782i −1.03390 + 1.03390i −0.0344966 + 0.999405i \(0.510983\pi\)
−0.999405 + 0.0344966i \(0.989017\pi\)
\(80\) 53.1064i 0.663829i
\(81\) −140.843 −1.73880
\(82\) 101.726 1.24056
\(83\) −77.1462 −0.929472 −0.464736 0.885449i \(-0.653851\pi\)
−0.464736 + 0.885449i \(0.653851\pi\)
\(84\) −0.306565 0.306565i −0.00364958 0.00364958i
\(85\) −20.0488 20.0488i −0.235868 0.235868i
\(86\) 46.5381i 0.541140i
\(87\) 46.4812 149.259i 0.534267 1.71563i
\(88\) 153.699 1.74658
\(89\) 27.4315 27.4315i 0.308219 0.308219i −0.535999 0.844218i \(-0.680065\pi\)
0.844218 + 0.535999i \(0.180065\pi\)
\(90\) −91.8082 + 91.8082i −1.02009 + 1.02009i
\(91\) 3.94215i 0.0433203i
\(92\) 3.72680i 0.0405087i
\(93\) 47.1215i 0.506683i
\(94\) −22.0498 −0.234572
\(95\) −19.2396 19.2396i −0.202522 0.202522i
\(96\) 20.2387i 0.210819i
\(97\) 48.7308 + 48.7308i 0.502379 + 0.502379i 0.912177 0.409797i \(-0.134401\pi\)
−0.409797 + 0.912177i \(0.634401\pi\)
\(98\) 71.1320 71.1320i 0.725837 0.725837i
\(99\) 281.370 + 281.370i 2.84213 + 2.84213i
\(100\) 3.54944i 0.0354944i
\(101\) −36.0686 + 36.0686i −0.357115 + 0.357115i −0.862748 0.505633i \(-0.831259\pi\)
0.505633 + 0.862748i \(0.331259\pi\)
\(102\) −70.7130 70.7130i −0.693265 0.693265i
\(103\) −38.7846 −0.376549 −0.188275 0.982116i \(-0.560289\pi\)
−0.188275 + 0.982116i \(0.560289\pi\)
\(104\) −63.0941 + 63.0941i −0.606674 + 0.606674i
\(105\) 4.10400 + 4.10400i 0.0390857 + 0.0390857i
\(106\) −90.5093 + 90.5093i −0.853861 + 0.853861i
\(107\) 100.580 0.940004 0.470002 0.882665i \(-0.344253\pi\)
0.470002 + 0.882665i \(0.344253\pi\)
\(108\) −9.90438 + 9.90438i −0.0917072 + 0.0917072i
\(109\) 43.4896i 0.398988i −0.979899 0.199494i \(-0.936070\pi\)
0.979899 0.199494i \(-0.0639298\pi\)
\(110\) 128.398 1.16725
\(111\) 184.582 1.66290
\(112\) 5.77982 0.0516056
\(113\) −106.279 106.279i −0.940525 0.940525i 0.0578028 0.998328i \(-0.481591\pi\)
−0.998328 + 0.0578028i \(0.981591\pi\)
\(114\) −67.8590 67.8590i −0.595254 0.595254i
\(115\) 49.8909i 0.433834i
\(116\) −3.16748 6.03245i −0.0273059 0.0520039i
\(117\) −231.007 −1.97442
\(118\) 31.2665 31.2665i 0.264970 0.264970i
\(119\) −2.18201 + 2.18201i −0.0183362 + 0.0183362i
\(120\) 131.369i 1.09474i
\(121\) 272.508i 2.25214i
\(122\) 38.2454i 0.313487i
\(123\) −266.471 −2.16643
\(124\) −1.45222 1.45222i −0.0117114 0.0117114i
\(125\) 126.148i 1.00918i
\(126\) 9.99193 + 9.99193i 0.0793010 + 0.0793010i
\(127\) −43.0879 + 43.0879i −0.339275 + 0.339275i −0.856094 0.516820i \(-0.827116\pi\)
0.516820 + 0.856094i \(0.327116\pi\)
\(128\) −97.6550 97.6550i −0.762930 0.762930i
\(129\) 121.907i 0.945012i
\(130\) −52.7077 + 52.7077i −0.405444 + 0.405444i
\(131\) 21.6703 + 21.6703i 0.165422 + 0.165422i 0.784964 0.619542i \(-0.212682\pi\)
−0.619542 + 0.784964i \(0.712682\pi\)
\(132\) 25.1241 0.190334
\(133\) −2.09394 + 2.09394i −0.0157439 + 0.0157439i
\(134\) −25.9414 25.9414i −0.193592 0.193592i
\(135\) 132.591 132.591i 0.982152 0.982152i
\(136\) 69.8462 0.513575
\(137\) 64.9871 64.9871i 0.474359 0.474359i −0.428963 0.903322i \(-0.641121\pi\)
0.903322 + 0.428963i \(0.141121\pi\)
\(138\) 175.967i 1.27513i
\(139\) −73.6837 −0.530099 −0.265049 0.964235i \(-0.585388\pi\)
−0.265049 + 0.964235i \(0.585388\pi\)
\(140\) 0.252959 0.00180685
\(141\) 57.7594 0.409641
\(142\) 77.1336 + 77.1336i 0.543195 + 0.543195i
\(143\) 161.537 + 161.537i 1.12963 + 1.12963i
\(144\) 338.693i 2.35204i
\(145\) 42.4033 + 80.7568i 0.292436 + 0.556944i
\(146\) −17.2607 −0.118224
\(147\) −186.331 + 186.331i −1.26755 + 1.26755i
\(148\) 5.68857 5.68857i 0.0384363 0.0384363i
\(149\) 94.7514i 0.635915i 0.948105 + 0.317958i \(0.102997\pi\)
−0.948105 + 0.317958i \(0.897003\pi\)
\(150\) 167.593i 1.11729i
\(151\) 174.343i 1.15459i 0.816537 + 0.577293i \(0.195891\pi\)
−0.816537 + 0.577293i \(0.804109\pi\)
\(152\) 67.0272 0.440968
\(153\) 127.864 + 127.864i 0.835713 + 0.835713i
\(154\) 13.9741i 0.0907412i
\(155\) 19.4409 + 19.4409i 0.125425 + 0.125425i
\(156\) −10.3135 + 10.3135i −0.0661124 + 0.0661124i
\(157\) −204.862 204.862i −1.30486 1.30486i −0.925078 0.379777i \(-0.876001\pi\)
−0.379777 0.925078i \(-0.623999\pi\)
\(158\) 237.709i 1.50449i
\(159\) 237.089 237.089i 1.49113 1.49113i
\(160\) −8.34988 8.34988i −0.0521867 0.0521867i
\(161\) 5.42987 0.0337259
\(162\) 204.948 204.948i 1.26511 1.26511i
\(163\) −128.935 128.935i −0.791012 0.791012i 0.190647 0.981659i \(-0.438942\pi\)
−0.981659 + 0.190647i \(0.938942\pi\)
\(164\) −8.21225 + 8.21225i −0.0500747 + 0.0500747i
\(165\) −336.338 −2.03841
\(166\) 112.260 112.260i 0.676263 0.676263i
\(167\) 266.891i 1.59815i −0.601230 0.799076i \(-0.705322\pi\)
0.601230 0.799076i \(-0.294678\pi\)
\(168\) −14.2976 −0.0851045
\(169\) 36.3773 0.215250
\(170\) 58.3482 0.343225
\(171\) 122.704 + 122.704i 0.717565 + 0.717565i
\(172\) 3.75699 + 3.75699i 0.0218430 + 0.0218430i
\(173\) 264.180i 1.52705i 0.645779 + 0.763525i \(0.276533\pi\)
−0.645779 + 0.763525i \(0.723467\pi\)
\(174\) 149.558 + 284.833i 0.859530 + 1.63697i
\(175\) 5.17145 0.0295512
\(176\) −236.839 + 236.839i −1.34567 + 1.34567i
\(177\) −81.9027 + 81.9027i −0.462727 + 0.462727i
\(178\) 79.8341i 0.448506i
\(179\) 79.9849i 0.446843i 0.974722 + 0.223421i \(0.0717226\pi\)
−0.974722 + 0.223421i \(0.928277\pi\)
\(180\) 14.8232i 0.0823513i
\(181\) 116.758 0.645074 0.322537 0.946557i \(-0.395464\pi\)
0.322537 + 0.946557i \(0.395464\pi\)
\(182\) 5.73643 + 5.73643i 0.0315189 + 0.0315189i
\(183\) 100.184i 0.547454i
\(184\) −86.9051 86.9051i −0.472310 0.472310i
\(185\) −76.1533 + 76.1533i −0.411639 + 0.411639i
\(186\) 68.5690 + 68.5690i 0.368651 + 0.368651i
\(187\) 178.823i 0.956275i
\(188\) 1.78006 1.78006i 0.00946842 0.00946842i
\(189\) −14.4305 14.4305i −0.0763517 0.0763517i
\(190\) 55.9933 0.294701
\(191\) −60.0672 + 60.0672i −0.314488 + 0.314488i −0.846645 0.532157i \(-0.821381\pi\)
0.532157 + 0.846645i \(0.321381\pi\)
\(192\) 227.991 + 227.991i 1.18745 + 1.18745i
\(193\) 155.411 155.411i 0.805241 0.805241i −0.178669 0.983909i \(-0.557179\pi\)
0.983909 + 0.178669i \(0.0571790\pi\)
\(194\) −141.822 −0.731039
\(195\) 138.068 138.068i 0.708040 0.708040i
\(196\) 11.4849i 0.0585964i
\(197\) 127.935 0.649415 0.324708 0.945814i \(-0.394734\pi\)
0.324708 + 0.945814i \(0.394734\pi\)
\(198\) −818.875 −4.13573
\(199\) −365.503 −1.83670 −0.918349 0.395772i \(-0.870477\pi\)
−0.918349 + 0.395772i \(0.870477\pi\)
\(200\) −82.7692 82.7692i −0.413846 0.413846i
\(201\) 67.9535 + 67.9535i 0.338077 + 0.338077i
\(202\) 104.971i 0.519657i
\(203\) 8.78916 4.61496i 0.0432963 0.0227338i
\(204\) 11.4172 0.0559668
\(205\) 109.938 109.938i 0.536283 0.536283i
\(206\) 56.4375 56.4375i 0.273969 0.273969i
\(207\) 318.186i 1.53713i
\(208\) 194.446i 0.934837i
\(209\) 171.606i 0.821082i
\(210\) −11.9439 −0.0568758
\(211\) 235.633 + 235.633i 1.11674 + 1.11674i 0.992216 + 0.124527i \(0.0397415\pi\)
0.124527 + 0.992216i \(0.460259\pi\)
\(212\) 14.6135i 0.0689317i
\(213\) −202.052 202.052i −0.948600 0.948600i
\(214\) −146.360 + 146.360i −0.683925 + 0.683925i
\(215\) −50.2950 50.2950i −0.233930 0.233930i
\(216\) 461.920i 2.13852i
\(217\) 2.11585 2.11585i 0.00975047 0.00975047i
\(218\) 63.2841 + 63.2841i 0.290294 + 0.290294i
\(219\) 45.2145 0.206459
\(220\) −10.3655 + 10.3655i −0.0471157 + 0.0471157i
\(221\) 73.4077 + 73.4077i 0.332161 + 0.332161i
\(222\) −268.596 + 268.596i −1.20989 + 1.20989i
\(223\) 404.109 1.81215 0.906074 0.423119i \(-0.139065\pi\)
0.906074 + 0.423119i \(0.139065\pi\)
\(224\) −0.908758 + 0.908758i −0.00405695 + 0.00405695i
\(225\) 303.044i 1.34686i
\(226\) 309.306 1.36861
\(227\) 12.2558 0.0539905 0.0269952 0.999636i \(-0.491406\pi\)
0.0269952 + 0.999636i \(0.491406\pi\)
\(228\) 10.9564 0.0480545
\(229\) 207.308 + 207.308i 0.905275 + 0.905275i 0.995886 0.0906117i \(-0.0288822\pi\)
−0.0906117 + 0.995886i \(0.528882\pi\)
\(230\) −72.5989 72.5989i −0.315648 0.315648i
\(231\) 36.6053i 0.158464i
\(232\) −214.533 66.8082i −0.924711 0.287966i
\(233\) 240.593 1.03259 0.516293 0.856412i \(-0.327311\pi\)
0.516293 + 0.856412i \(0.327311\pi\)
\(234\) 336.151 336.151i 1.43654 1.43654i
\(235\) −23.8298 + 23.8298i −0.101403 + 0.101403i
\(236\) 5.04825i 0.0213909i
\(237\) 622.679i 2.62734i
\(238\) 6.35032i 0.0266820i
\(239\) −265.870 −1.11243 −0.556213 0.831040i \(-0.687746\pi\)
−0.556213 + 0.831040i \(0.687746\pi\)
\(240\) 202.430 + 202.430i 0.843457 + 0.843457i
\(241\) 423.682i 1.75802i −0.476806 0.879008i \(-0.658206\pi\)
0.476806 0.879008i \(-0.341794\pi\)
\(242\) 396.542 + 396.542i 1.63860 + 1.63860i
\(243\) −157.460 + 157.460i −0.647982 + 0.647982i
\(244\) −3.08753 3.08753i −0.0126538 0.0126538i
\(245\) 153.749i 0.627547i
\(246\) 387.756 387.756i 1.57624 1.57624i
\(247\) 70.4449 + 70.4449i 0.285202 + 0.285202i
\(248\) −67.7285 −0.273099
\(249\) −294.064 + 294.064i −1.18098 + 1.18098i
\(250\) −183.565 183.565i −0.734259 0.734259i
\(251\) −211.437 + 211.437i −0.842379 + 0.842379i −0.989168 0.146789i \(-0.953106\pi\)
0.146789 + 0.989168i \(0.453106\pi\)
\(252\) −1.61328 −0.00640192
\(253\) −222.499 + 222.499i −0.879441 + 0.879441i
\(254\) 125.399i 0.493697i
\(255\) −152.843 −0.599385
\(256\) 44.9573 0.175615
\(257\) 158.690 0.617471 0.308735 0.951148i \(-0.400094\pi\)
0.308735 + 0.951148i \(0.400094\pi\)
\(258\) −177.393 177.393i −0.687569 0.687569i
\(259\) 8.28813 + 8.28813i 0.0320005 + 0.0320005i
\(260\) 8.51012i 0.0327312i
\(261\) −270.433 515.038i −1.03614 1.97333i
\(262\) −63.0671 −0.240714
\(263\) 40.2518 40.2518i 0.153049 0.153049i −0.626429 0.779478i \(-0.715484\pi\)
0.779478 + 0.626429i \(0.215484\pi\)
\(264\) 585.868 585.868i 2.21920 2.21920i
\(265\) 195.632i 0.738234i
\(266\) 6.09402i 0.0229098i
\(267\) 209.126i 0.783242i
\(268\) 4.18846 0.0156286
\(269\) −141.040 141.040i −0.524311 0.524311i 0.394559 0.918870i \(-0.370897\pi\)
−0.918870 + 0.394559i \(0.870897\pi\)
\(270\) 385.879i 1.42918i
\(271\) 24.3687 + 24.3687i 0.0899215 + 0.0899215i 0.750637 0.660715i \(-0.229747\pi\)
−0.660715 + 0.750637i \(0.729747\pi\)
\(272\) −107.627 + 107.627i −0.395689 + 0.395689i
\(273\) −15.0266 15.0266i −0.0550425 0.0550425i
\(274\) 189.133i 0.690265i
\(275\) −211.910 + 211.910i −0.770581 + 0.770581i
\(276\) −14.2057 14.2057i −0.0514701 0.0514701i
\(277\) 57.9976 0.209378 0.104689 0.994505i \(-0.466615\pi\)
0.104689 + 0.994505i \(0.466615\pi\)
\(278\) 107.221 107.221i 0.385688 0.385688i
\(279\) −123.987 123.987i −0.444399 0.444399i
\(280\) 5.89875 5.89875i 0.0210670 0.0210670i
\(281\) −352.000 −1.25267 −0.626334 0.779554i \(-0.715446\pi\)
−0.626334 + 0.779554i \(0.715446\pi\)
\(282\) −84.0488 + 84.0488i −0.298045 + 0.298045i
\(283\) 446.547i 1.57790i 0.614455 + 0.788952i \(0.289376\pi\)
−0.614455 + 0.788952i \(0.710624\pi\)
\(284\) −12.4539 −0.0438518
\(285\) −146.674 −0.514647
\(286\) −470.121 −1.64378
\(287\) −11.9651 11.9651i −0.0416902 0.0416902i
\(288\) 53.2526 + 53.2526i 0.184905 + 0.184905i
\(289\) 207.737i 0.718812i
\(290\) −179.217 55.8103i −0.617990 0.192449i
\(291\) 371.502 1.27664
\(292\) 1.39345 1.39345i 0.00477208 0.00477208i
\(293\) 14.9522 14.9522i 0.0510313 0.0510313i −0.681131 0.732162i \(-0.738511\pi\)
0.732162 + 0.681131i \(0.238511\pi\)
\(294\) 542.279i 1.84449i
\(295\) 67.5813i 0.229089i
\(296\) 265.303i 0.896295i
\(297\) 1182.63 3.98192
\(298\) −137.878 137.878i −0.462677 0.462677i
\(299\) 182.673i 0.610946i
\(300\) −13.5297 13.5297i −0.0450989 0.0450989i
\(301\) −5.47385 + 5.47385i −0.0181856 + 0.0181856i
\(302\) −253.695 253.695i −0.840051 0.840051i
\(303\) 274.971i 0.907496i
\(304\) −103.284 + 103.284i −0.339749 + 0.339749i
\(305\) 41.3330 + 41.3330i 0.135518 + 0.135518i
\(306\) −372.124 −1.21609
\(307\) 10.2622 10.2622i 0.0334274 0.0334274i −0.690196 0.723623i \(-0.742475\pi\)
0.723623 + 0.690196i \(0.242475\pi\)
\(308\) 1.12812 + 1.12812i 0.00366274 + 0.00366274i
\(309\) −147.838 + 147.838i −0.478441 + 0.478441i
\(310\) −56.5791 −0.182513
\(311\) 325.442 325.442i 1.04644 1.04644i 0.0475694 0.998868i \(-0.484852\pi\)
0.998868 0.0475694i \(-0.0151475\pi\)
\(312\) 481.002i 1.54167i
\(313\) −279.640 −0.893417 −0.446709 0.894680i \(-0.647404\pi\)
−0.446709 + 0.894680i \(0.647404\pi\)
\(314\) 596.212 1.89877
\(315\) 21.5971 0.0685624
\(316\) 19.1901 + 19.1901i 0.0607281 + 0.0607281i
\(317\) 195.785 + 195.785i 0.617619 + 0.617619i 0.944920 0.327301i \(-0.106139\pi\)
−0.327301 + 0.944920i \(0.606139\pi\)
\(318\) 690.003i 2.16982i
\(319\) −171.045 + 549.258i −0.536193 + 1.72181i
\(320\) −188.125 −0.587890
\(321\) 383.390 383.390i 1.19436 1.19436i
\(322\) −7.90130 + 7.90130i −0.0245382 + 0.0245382i
\(323\) 77.9836i 0.241435i
\(324\) 33.0906i 0.102132i
\(325\) 173.979i 0.535321i
\(326\) 375.241 1.15104
\(327\) −165.773 165.773i −0.506951 0.506951i
\(328\) 383.003i 1.16769i
\(329\) 2.59351 + 2.59351i 0.00788302 + 0.00788302i
\(330\) 489.423 489.423i 1.48310 1.48310i
\(331\) 177.780 + 177.780i 0.537100 + 0.537100i 0.922676 0.385576i \(-0.125997\pi\)
−0.385576 + 0.922676i \(0.625997\pi\)
\(332\) 18.1253i 0.0545943i
\(333\) 485.679 485.679i 1.45849 1.45849i
\(334\) 388.368 + 388.368i 1.16278 + 1.16278i
\(335\) −56.0712 −0.167377
\(336\) 22.0314 22.0314i 0.0655697 0.0655697i
\(337\) −312.630 312.630i −0.927686 0.927686i 0.0698697 0.997556i \(-0.477742\pi\)
−0.997556 + 0.0698697i \(0.977742\pi\)
\(338\) −52.9346 + 52.9346i −0.156611 + 0.156611i
\(339\) −810.227 −2.39005
\(340\) −4.71041 + 4.71041i −0.0138542 + 0.0138542i
\(341\) 173.402i 0.508509i
\(342\) −357.105 −1.04417
\(343\) −33.5066 −0.0976869
\(344\) 175.218 0.509355
\(345\) 190.173 + 190.173i 0.551226 + 0.551226i
\(346\) −384.422 384.422i −1.11105 1.11105i
\(347\) 307.039i 0.884840i −0.896808 0.442420i \(-0.854120\pi\)
0.896808 0.442420i \(-0.145880\pi\)
\(348\) −35.0681 10.9206i −0.100770 0.0313811i
\(349\) 463.827 1.32902 0.664509 0.747280i \(-0.268641\pi\)
0.664509 + 0.747280i \(0.268641\pi\)
\(350\) −7.52526 + 7.52526i −0.0215008 + 0.0215008i
\(351\) −485.473 + 485.473i −1.38311 + 1.38311i
\(352\) 74.4760i 0.211579i
\(353\) 322.072i 0.912385i 0.889881 + 0.456192i \(0.150787\pi\)
−0.889881 + 0.456192i \(0.849213\pi\)
\(354\) 238.362i 0.673339i
\(355\) 166.721 0.469637
\(356\) −6.44496 6.44496i −0.0181038 0.0181038i
\(357\) 16.6347i 0.0465957i
\(358\) −116.390 116.390i −0.325113 0.325113i
\(359\) 410.933 410.933i 1.14466 1.14466i 0.157072 0.987587i \(-0.449795\pi\)
0.987587 0.157072i \(-0.0502055\pi\)
\(360\) −345.663 345.663i −0.960174 0.960174i
\(361\) 286.164i 0.792698i
\(362\) −169.902 + 169.902i −0.469341 + 0.469341i
\(363\) −1038.74 1038.74i −2.86155 2.86155i
\(364\) −0.926197 −0.00254450
\(365\) −18.6542 + 18.6542i −0.0511073 + 0.0511073i
\(366\) 145.783 + 145.783i 0.398315 + 0.398315i
\(367\) 309.094 309.094i 0.842218 0.842218i −0.146929 0.989147i \(-0.546939\pi\)
0.989147 + 0.146929i \(0.0469390\pi\)
\(368\) 267.828 0.727793
\(369\) −701.145 + 701.145i −1.90012 + 1.90012i
\(370\) 221.629i 0.598999i
\(371\) 21.2916 0.0573897
\(372\) −11.0711 −0.0297609
\(373\) 210.646 0.564734 0.282367 0.959306i \(-0.408880\pi\)
0.282367 + 0.959306i \(0.408880\pi\)
\(374\) 260.216 + 260.216i 0.695764 + 0.695764i
\(375\) 480.848 + 480.848i 1.28226 + 1.28226i
\(376\) 83.0185i 0.220794i
\(377\) −155.257 295.687i −0.411824 0.784316i
\(378\) 41.9971 0.111103
\(379\) −229.599 + 229.599i −0.605803 + 0.605803i −0.941847 0.336043i \(-0.890911\pi\)
0.336043 + 0.941847i \(0.390911\pi\)
\(380\) −4.52030 + 4.52030i −0.0118955 + 0.0118955i
\(381\) 328.483i 0.862160i
\(382\) 174.814i 0.457628i
\(383\) 248.070i 0.647701i −0.946108 0.323851i \(-0.895022\pi\)
0.946108 0.323851i \(-0.104978\pi\)
\(384\) −744.479 −1.93875
\(385\) −15.1023 15.1023i −0.0392267 0.0392267i
\(386\) 452.295i 1.17175i
\(387\) 320.764 + 320.764i 0.828847 + 0.828847i
\(388\) 11.4492 11.4492i 0.0295082 0.0295082i
\(389\) 78.1188 + 78.1188i 0.200820 + 0.200820i 0.800351 0.599532i \(-0.204646\pi\)
−0.599532 + 0.800351i \(0.704646\pi\)
\(390\) 401.820i 1.03031i
\(391\) −101.111 + 101.111i −0.258596 + 0.258596i
\(392\) 267.816 + 267.816i 0.683204 + 0.683204i
\(393\) 165.204 0.420368
\(394\) −186.165 + 186.165i −0.472500 + 0.472500i
\(395\) −256.899 256.899i −0.650377 0.650377i
\(396\) 66.1072 66.1072i 0.166937 0.166937i
\(397\) 399.382 1.00600 0.503000 0.864287i \(-0.332230\pi\)
0.503000 + 0.864287i \(0.332230\pi\)
\(398\) 531.863 531.863i 1.33634 1.33634i
\(399\) 15.9633i 0.0400083i
\(400\) 255.082 0.637704
\(401\) −585.895 −1.46109 −0.730543 0.682867i \(-0.760733\pi\)
−0.730543 + 0.682867i \(0.760733\pi\)
\(402\) −197.766 −0.491954
\(403\) −71.1820 71.1820i −0.176630 0.176630i
\(404\) 8.47423 + 8.47423i 0.0209758 + 0.0209758i
\(405\) 442.986i 1.09379i
\(406\) −6.07411 + 19.5051i −0.0149609 + 0.0480420i
\(407\) −679.242 −1.66890
\(408\) 266.238 266.238i 0.652545 0.652545i
\(409\) 243.027 243.027i 0.594198 0.594198i −0.344564 0.938763i \(-0.611973\pi\)
0.938763 + 0.344564i \(0.111973\pi\)
\(410\) 319.953i 0.780374i
\(411\) 495.433i 1.20543i
\(412\) 9.11233i 0.0221173i
\(413\) −7.35520 −0.0178092
\(414\) 463.010 + 463.010i 1.11838 + 1.11838i
\(415\) 242.645i 0.584686i
\(416\) 30.5726 + 30.5726i 0.0734919 + 0.0734919i
\(417\) −280.866 + 280.866i −0.673540 + 0.673540i
\(418\) 249.713 + 249.713i 0.597400 + 0.597400i
\(419\) 548.833i 1.30987i −0.755687 0.654933i \(-0.772697\pi\)
0.755687 0.654933i \(-0.227303\pi\)
\(420\) 0.964225 0.964225i 0.00229577 0.00229577i
\(421\) −126.907 126.907i −0.301442 0.301442i 0.540136 0.841578i \(-0.318373\pi\)
−0.841578 + 0.540136i \(0.818373\pi\)
\(422\) −685.764 −1.62503
\(423\) 151.978 151.978i 0.359286 0.359286i
\(424\) −340.772 340.772i −0.803708 0.803708i
\(425\) −96.2989 + 96.2989i −0.226586 + 0.226586i
\(426\) 588.033 1.38036
\(427\) 4.49847 4.49847i 0.0105351 0.0105351i
\(428\) 23.6311i 0.0552129i
\(429\) 1231.48 2.87059
\(430\) 146.374 0.340405
\(431\) 334.232 0.775480 0.387740 0.921769i \(-0.373256\pi\)
0.387740 + 0.921769i \(0.373256\pi\)
\(432\) −711.782 711.782i −1.64764 1.64764i
\(433\) −321.593 321.593i −0.742710 0.742710i 0.230389 0.973099i \(-0.426000\pi\)
−0.973099 + 0.230389i \(0.926000\pi\)
\(434\) 6.15778i 0.0141884i
\(435\) 469.459 + 146.195i 1.07922 + 0.336081i
\(436\) −10.2178 −0.0234353
\(437\) −97.0300 + 97.0300i −0.222037 + 0.222037i
\(438\) −65.7940 + 65.7940i −0.150215 + 0.150215i
\(439\) 493.002i 1.12301i −0.827473 0.561506i \(-0.810222\pi\)
0.827473 0.561506i \(-0.189778\pi\)
\(440\) 483.424i 1.09869i
\(441\) 980.556i 2.22348i
\(442\) −213.639 −0.483346
\(443\) 305.073 + 305.073i 0.688653 + 0.688653i 0.961934 0.273281i \(-0.0881089\pi\)
−0.273281 + 0.961934i \(0.588109\pi\)
\(444\) 43.3672i 0.0976738i
\(445\) 86.2791 + 86.2791i 0.193886 + 0.193886i
\(446\) −588.041 + 588.041i −1.31848 + 1.31848i
\(447\) 361.171 + 361.171i 0.807990 + 0.807990i
\(448\) 20.4745i 0.0457021i
\(449\) −604.469 + 604.469i −1.34626 + 1.34626i −0.456567 + 0.889689i \(0.650921\pi\)
−0.889689 + 0.456567i \(0.849079\pi\)
\(450\) 440.975 + 440.975i 0.979945 + 0.979945i
\(451\) 980.582 2.17424
\(452\) −24.9701 + 24.9701i −0.0552435 + 0.0552435i
\(453\) 664.556 + 664.556i 1.46701 + 1.46701i
\(454\) −17.8341 + 17.8341i −0.0392822 + 0.0392822i
\(455\) 12.3991 0.0272507
\(456\) 255.493 255.493i 0.560291 0.560291i
\(457\) 563.383i 1.23278i −0.787439 0.616392i \(-0.788594\pi\)
0.787439 0.616392i \(-0.211406\pi\)
\(458\) −603.330 −1.31731
\(459\) 537.426 1.17086
\(460\) 11.7217 0.0254820
\(461\) −371.986 371.986i −0.806911 0.806911i 0.177254 0.984165i \(-0.443279\pi\)
−0.984165 + 0.177254i \(0.943279\pi\)
\(462\) −53.2663 53.2663i −0.115295 0.115295i
\(463\) 13.1023i 0.0282986i −0.999900 0.0141493i \(-0.995496\pi\)
0.999900 0.0141493i \(-0.00450402\pi\)
\(464\) 433.525 227.632i 0.934320 0.490587i
\(465\) 148.209 0.318729
\(466\) −350.100 + 350.100i −0.751287 + 0.751287i
\(467\) −192.103 + 192.103i −0.411356 + 0.411356i −0.882211 0.470854i \(-0.843946\pi\)
0.470854 + 0.882211i \(0.343946\pi\)
\(468\) 54.2745i 0.115971i
\(469\) 6.10250i 0.0130117i
\(470\) 69.3521i 0.147558i
\(471\) −1561.78 −3.31588
\(472\) 117.720 + 117.720i 0.249407 + 0.249407i
\(473\) 448.602i 0.948419i
\(474\) −906.093 906.093i −1.91159 1.91159i
\(475\) −92.4122 + 92.4122i −0.194552 + 0.194552i
\(476\) 0.512657 + 0.512657i 0.00107701 + 0.00107701i
\(477\) 1247.67i 2.61566i
\(478\) 386.882 386.882i 0.809376 0.809376i
\(479\) 237.779 + 237.779i 0.496407 + 0.496407i 0.910317 0.413911i \(-0.135837\pi\)
−0.413911 + 0.910317i \(0.635837\pi\)
\(480\) −63.6558 −0.132616
\(481\) 278.831 278.831i 0.579691 0.579691i
\(482\) 616.523 + 616.523i 1.27909 + 1.27909i
\(483\) 20.6975 20.6975i 0.0428519 0.0428519i
\(484\) −64.0252 −0.132283
\(485\) −153.271 + 153.271i −0.316022 + 0.316022i
\(486\) 458.256i 0.942914i
\(487\) −754.182 −1.54863 −0.774314 0.632802i \(-0.781905\pi\)
−0.774314 + 0.632802i \(0.781905\pi\)
\(488\) −143.996 −0.295074
\(489\) −982.943 −2.01011
\(490\) 223.728 + 223.728i 0.456589 + 0.456589i
\(491\) 451.910 + 451.910i 0.920388 + 0.920388i 0.997057 0.0766690i \(-0.0244285\pi\)
−0.0766690 + 0.997057i \(0.524428\pi\)
\(492\) 62.6066i 0.127249i
\(493\) −77.7288 + 249.601i −0.157665 + 0.506290i
\(494\) −205.016 −0.415013
\(495\) −884.982 + 884.982i −1.78784 + 1.78784i
\(496\) 104.364 104.364i 0.210412 0.210412i
\(497\) 18.1451i 0.0365092i
\(498\) 855.818i 1.71851i
\(499\) 292.373i 0.585918i 0.956125 + 0.292959i \(0.0946399\pi\)
−0.956125 + 0.292959i \(0.905360\pi\)
\(500\) 29.6381 0.0592763
\(501\) −1017.33 1017.33i −2.03060 2.03060i
\(502\) 615.347i 1.22579i
\(503\) 510.905 + 510.905i 1.01572 + 1.01572i 0.999875 + 0.0158408i \(0.00504249\pi\)
0.0158408 + 0.999875i \(0.494958\pi\)
\(504\) −37.6201 + 37.6201i −0.0746431 + 0.0746431i
\(505\) −113.445 113.445i −0.224644 0.224644i
\(506\) 647.540i 1.27972i
\(507\) 138.662 138.662i 0.273496 0.273496i
\(508\) 10.1234 + 10.1234i 0.0199279 + 0.0199279i
\(509\) −10.9652 −0.0215427 −0.0107714 0.999942i \(-0.503429\pi\)
−0.0107714 + 0.999942i \(0.503429\pi\)
\(510\) 222.410 222.410i 0.436099 0.436099i
\(511\) 2.03022 + 2.03022i 0.00397304 + 0.00397304i
\(512\) 325.200 325.200i 0.635157 0.635157i
\(513\) 515.736 1.00533
\(514\) −230.918 + 230.918i −0.449257 + 0.449257i
\(515\) 121.987i 0.236869i
\(516\) 28.6416 0.0555070
\(517\) −212.548 −0.411118
\(518\) −24.1210 −0.0465657
\(519\) 1006.99 + 1006.99i 1.94026 + 1.94026i
\(520\) −198.447 198.447i −0.381629 0.381629i
\(521\) 93.8560i 0.180146i 0.995935 + 0.0900729i \(0.0287100\pi\)
−0.995935 + 0.0900729i \(0.971290\pi\)
\(522\) 1142.98 + 355.938i 2.18962 + 0.681874i
\(523\) 32.4183 0.0619853 0.0309926 0.999520i \(-0.490133\pi\)
0.0309926 + 0.999520i \(0.490133\pi\)
\(524\) 5.09137 5.09137i 0.00971636 0.00971636i
\(525\) 19.7124 19.7124i 0.0375475 0.0375475i
\(526\) 117.145i 0.222709i
\(527\) 78.7995i 0.149525i
\(528\) 1805.55i 3.41961i
\(529\) −277.388 −0.524364
\(530\) −284.675 284.675i −0.537122 0.537122i
\(531\) 431.009i 0.811694i
\(532\) 0.491966 + 0.491966i 0.000924749 + 0.000924749i
\(533\) −402.532 + 402.532i −0.755220 + 0.755220i
\(534\) 304.310 + 304.310i 0.569869 + 0.569869i
\(535\) 316.351i 0.591311i
\(536\) 97.6706 97.6706i 0.182221 0.182221i
\(537\) 304.885 + 304.885i 0.567756 + 0.567756i
\(538\) 410.469 0.762953
\(539\) 685.675 685.675i 1.27212 1.27212i
\(540\) −31.1518 31.1518i −0.0576885 0.0576885i
\(541\) −249.329 + 249.329i −0.460867 + 0.460867i −0.898940 0.438072i \(-0.855661\pi\)
0.438072 + 0.898940i \(0.355661\pi\)
\(542\) −70.9205 −0.130850
\(543\) 445.058 445.058i 0.819627 0.819627i
\(544\) 33.8444i 0.0622139i
\(545\) 136.786 0.250984
\(546\) 43.7320 0.0800953
\(547\) 387.586 0.708566 0.354283 0.935138i \(-0.384725\pi\)
0.354283 + 0.935138i \(0.384725\pi\)
\(548\) −15.2686 15.2686i −0.0278623 0.0278623i
\(549\) −263.607 263.607i −0.480159 0.480159i
\(550\) 616.723i 1.12131i
\(551\) −74.5917 + 239.527i −0.135375 + 0.434714i
\(552\) −662.526 −1.20023
\(553\) −27.9596 + 27.9596i −0.0505598 + 0.0505598i
\(554\) −84.3955 + 84.3955i −0.152338 + 0.152338i
\(555\) 580.559i 1.04605i
\(556\) 17.3118i 0.0311363i
\(557\) 352.548i 0.632941i −0.948602 0.316471i \(-0.897502\pi\)
0.948602 0.316471i \(-0.102498\pi\)
\(558\) 360.841 0.646669
\(559\) 184.153 + 184.153i 0.329432 + 0.329432i
\(560\) 18.1790i 0.0324625i
\(561\) −681.636 681.636i −1.21504 1.21504i
\(562\) 512.214 512.214i 0.911413 0.911413i
\(563\) −151.066 151.066i −0.268324 0.268324i 0.560101 0.828425i \(-0.310762\pi\)
−0.828425 + 0.560101i \(0.810762\pi\)
\(564\) 13.5704i 0.0240610i
\(565\) 334.276 334.276i 0.591638 0.591638i
\(566\) −649.795 649.795i −1.14805 1.14805i
\(567\) −48.2123 −0.0850306
\(568\) −290.412 + 290.412i −0.511289 + 0.511289i
\(569\) 431.698 + 431.698i 0.758697 + 0.758697i 0.976085 0.217389i \(-0.0697539\pi\)
−0.217389 + 0.976085i \(0.569754\pi\)
\(570\) 213.434 213.434i 0.374446 0.374446i
\(571\) 66.0488 0.115672 0.0578361 0.998326i \(-0.481580\pi\)
0.0578361 + 0.998326i \(0.481580\pi\)
\(572\) 37.9526 37.9526i 0.0663507 0.0663507i
\(573\) 457.926i 0.799172i
\(574\) 34.8221 0.0606656
\(575\) 239.637 0.416760
\(576\) 1199.79 2.08297
\(577\) −392.139 392.139i −0.679616 0.679616i 0.280297 0.959913i \(-0.409567\pi\)
−0.959913 + 0.280297i \(0.909567\pi\)
\(578\) −302.289 302.289i −0.522991 0.522991i
\(579\) 1184.79i 2.04627i
\(580\) 18.9736 9.96254i 0.0327131 0.0171768i
\(581\) −26.4082 −0.0454530
\(582\) −540.593 + 540.593i −0.928853 + 0.928853i
\(583\) −872.461 + 872.461i −1.49650 + 1.49650i
\(584\) 64.9875i 0.111280i
\(585\) 726.576i 1.24201i
\(586\) 43.5154i 0.0742584i
\(587\) 195.193 0.332527 0.166263 0.986081i \(-0.446830\pi\)
0.166263 + 0.986081i \(0.446830\pi\)
\(588\) 43.7779 + 43.7779i 0.0744522 + 0.0744522i
\(589\) 75.6192i 0.128386i
\(590\) 98.3412 + 98.3412i 0.166680 + 0.166680i
\(591\) 487.659 487.659i 0.825143 0.825143i
\(592\) 408.811 + 408.811i 0.690560 + 0.690560i
\(593\) 128.271i 0.216309i −0.994134 0.108155i \(-0.965506\pi\)
0.994134 0.108155i \(-0.0344942\pi\)
\(594\) −1720.91 + 1720.91i −2.89715 + 2.89715i
\(595\) −6.86298 6.86298i −0.0115344 0.0115344i
\(596\) 22.2616 0.0373517
\(597\) −1393.22 + 1393.22i −2.33370 + 2.33370i
\(598\) 265.817 + 265.817i 0.444511 + 0.444511i
\(599\) 717.619 717.619i 1.19803 1.19803i 0.223271 0.974756i \(-0.428326\pi\)
0.974756 0.223271i \(-0.0716736\pi\)
\(600\) −630.996 −1.05166
\(601\) −9.96872 + 9.96872i −0.0165869 + 0.0165869i −0.715352 0.698765i \(-0.753733\pi\)
0.698765 + 0.715352i \(0.253733\pi\)
\(602\) 15.9306i 0.0264628i
\(603\) 357.602 0.593038
\(604\) 40.9613 0.0678168
\(605\) 857.109 1.41671
\(606\) −400.126 400.126i −0.660273 0.660273i
\(607\) −162.407 162.407i −0.267556 0.267556i 0.560559 0.828115i \(-0.310586\pi\)
−0.828115 + 0.560559i \(0.810586\pi\)
\(608\) 32.4784i 0.0534184i
\(609\) 15.9111 51.0935i 0.0261267 0.0838974i
\(610\) −120.292 −0.197200
\(611\) 87.2517 87.2517i 0.142801 0.142801i
\(612\) 30.0414 30.0414i 0.0490872 0.0490872i
\(613\) 376.150i 0.613621i 0.951771 + 0.306811i \(0.0992619\pi\)
−0.951771 + 0.306811i \(0.900738\pi\)
\(614\) 29.8662i 0.0486420i
\(615\) 838.118i 1.36279i
\(616\) 52.6134 0.0854113
\(617\) 373.217 + 373.217i 0.604889 + 0.604889i 0.941606 0.336717i \(-0.109316\pi\)
−0.336717 + 0.941606i \(0.609316\pi\)
\(618\) 430.255i 0.696205i
\(619\) −196.763 196.763i −0.317872 0.317872i 0.530077 0.847949i \(-0.322163\pi\)
−0.847949 + 0.530077i \(0.822163\pi\)
\(620\) 4.56760 4.56760i 0.00736709 0.00736709i
\(621\) −668.685 668.685i −1.07679 1.07679i
\(622\) 947.137i 1.52273i
\(623\) 9.39017 9.39017i 0.0150725 0.0150725i
\(624\) −741.186 741.186i −1.18780 1.18780i
\(625\) −19.0833 −0.0305333
\(626\) 406.919 406.919i 0.650030 0.650030i
\(627\) −654.125 654.125i −1.04326 1.04326i
\(628\) −48.1319 + 48.1319i −0.0766431 + 0.0766431i
\(629\) −308.670 −0.490732
\(630\) −31.4272 + 31.4272i −0.0498844 + 0.0498844i
\(631\) 335.146i 0.531135i 0.964092 + 0.265567i \(0.0855592\pi\)
−0.964092 + 0.265567i \(0.914441\pi\)
\(632\) 894.986 1.41612
\(633\) 1796.36 2.83785
\(634\) −569.795 −0.898730
\(635\) −135.522 135.522i −0.213421 0.213421i
\(636\) −55.7035 55.7035i −0.0875841 0.0875841i
\(637\) 562.944i 0.883743i
\(638\) −550.357 1048.15i −0.862629 1.64287i
\(639\) −1063.29 −1.66399
\(640\) 307.150 307.150i 0.479922 0.479922i
\(641\) −343.144 + 343.144i −0.535326 + 0.535326i −0.922152 0.386827i \(-0.873571\pi\)
0.386827 + 0.922152i \(0.373571\pi\)
\(642\) 1115.78i 1.73798i
\(643\) 561.006i 0.872482i −0.899830 0.436241i \(-0.856310\pi\)
0.899830 0.436241i \(-0.143690\pi\)
\(644\) 1.27573i 0.00198095i
\(645\) −383.427 −0.594461
\(646\) 113.478 + 113.478i 0.175663 + 0.175663i
\(647\) 930.722i 1.43852i 0.694741 + 0.719260i \(0.255519\pi\)
−0.694741 + 0.719260i \(0.744481\pi\)
\(648\) 771.639 + 771.639i 1.19080 + 1.19080i
\(649\) 301.393 301.393i 0.464395 0.464395i
\(650\) 253.167 + 253.167i 0.389487 + 0.389487i
\(651\) 16.1303i 0.0247777i
\(652\) −30.2929 + 30.2929i −0.0464616 + 0.0464616i
\(653\) 168.866 + 168.866i 0.258600 + 0.258600i 0.824484 0.565885i \(-0.191465\pi\)
−0.565885 + 0.824484i \(0.691465\pi\)
\(654\) 482.450 0.737692
\(655\) −68.1585 + 68.1585i −0.104059 + 0.104059i
\(656\) −590.177 590.177i −0.899660 0.899660i
\(657\) 118.970 118.970i 0.181080 0.181080i
\(658\) −7.54793 −0.0114710
\(659\) −414.083 + 414.083i −0.628350 + 0.628350i −0.947653 0.319303i \(-0.896551\pi\)
0.319303 + 0.947653i \(0.396551\pi\)
\(660\) 79.0217i 0.119730i
\(661\) −732.973 −1.10888 −0.554442 0.832222i \(-0.687068\pi\)
−0.554442 + 0.832222i \(0.687068\pi\)
\(662\) −517.395 −0.781563
\(663\) 559.628 0.844084
\(664\) 422.663 + 422.663i 0.636541 + 0.636541i
\(665\) −6.58598 6.58598i −0.00990374 0.00990374i
\(666\) 1413.47i 2.12233i
\(667\) 407.276 213.850i 0.610608 0.320614i
\(668\) −62.7054 −0.0938704
\(669\) 1540.37 1540.37i 2.30250 2.30250i
\(670\) 81.5922 81.5922i 0.121779 0.121779i
\(671\) 368.666i 0.549427i
\(672\) 6.92797i 0.0103095i
\(673\) 503.554i 0.748223i 0.927384 + 0.374112i \(0.122052\pi\)
−0.927384 + 0.374112i \(0.877948\pi\)
\(674\) 909.851 1.34993
\(675\) −636.862 636.862i −0.943499 0.943499i
\(676\) 8.54675i 0.0126431i
\(677\) 257.461 + 257.461i 0.380298 + 0.380298i 0.871209 0.490912i \(-0.163336\pi\)
−0.490912 + 0.871209i \(0.663336\pi\)
\(678\) 1179.01 1179.01i 1.73895 1.73895i
\(679\) 16.6812 + 16.6812i 0.0245673 + 0.0245673i
\(680\) 219.684i 0.323065i
\(681\) 46.7165 46.7165i 0.0685999 0.0685999i
\(682\) −252.326 252.326i −0.369980 0.369980i
\(683\) −840.114 −1.23004 −0.615018 0.788513i \(-0.710851\pi\)
−0.615018 + 0.788513i \(0.710851\pi\)
\(684\) 28.8289 28.8289i 0.0421475 0.0421475i
\(685\) 204.401 + 204.401i 0.298396 + 0.298396i
\(686\) 48.7573 48.7573i 0.0710748 0.0710748i
\(687\) 1580.42 2.30047
\(688\) −269.997 + 269.997i −0.392438 + 0.392438i
\(689\) 716.297i 1.03962i
\(690\) −553.462 −0.802119
\(691\) −347.277 −0.502571 −0.251286 0.967913i \(-0.580853\pi\)
−0.251286 + 0.967913i \(0.580853\pi\)
\(692\) 62.0683 0.0896941
\(693\) 96.3169 + 96.3169i 0.138985 + 0.138985i
\(694\) 446.790 + 446.790i 0.643789 + 0.643789i
\(695\) 231.754i 0.333459i
\(696\) −1072.41 + 563.095i −1.54082 + 0.809044i
\(697\) 445.609 0.639325
\(698\) −674.940 + 674.940i −0.966963 + 0.966963i
\(699\) 917.087 917.087i 1.31200 1.31200i
\(700\) 1.21502i 0.00173574i
\(701\) 384.210i 0.548088i 0.961717 + 0.274044i \(0.0883615\pi\)
−0.961717 + 0.274044i \(0.911639\pi\)
\(702\) 1412.88i 2.01265i
\(703\) −296.212 −0.421355
\(704\) −838.981 838.981i −1.19173 1.19173i
\(705\) 181.668i 0.257685i
\(706\) −468.664 468.664i −0.663830 0.663830i
\(707\) −12.3468 + 12.3468i −0.0174636 + 0.0174636i
\(708\) 19.2428 + 19.2428i 0.0271791 + 0.0271791i
\(709\) 689.774i 0.972883i 0.873713 + 0.486442i \(0.161705\pi\)
−0.873713 + 0.486442i \(0.838295\pi\)
\(710\) −242.605 + 242.605i −0.341697 + 0.341697i
\(711\) 1638.41 + 1638.41i 2.30437 + 2.30437i
\(712\) −300.580 −0.422162
\(713\) 98.0452 98.0452i 0.137511 0.137511i
\(714\) −24.2060 24.2060i −0.0339020 0.0339020i
\(715\) −508.074 + 508.074i −0.710593 + 0.710593i
\(716\) 18.7922 0.0262461
\(717\) −1013.44 + 1013.44i −1.41344 + 1.41344i
\(718\) 1195.94i 1.66566i
\(719\) −1313.45 −1.82677 −0.913387 0.407092i \(-0.866543\pi\)
−0.913387 + 0.407092i \(0.866543\pi\)
\(720\) 1065.28 1.47955
\(721\) −13.2765 −0.0184140
\(722\) −416.413 416.413i −0.576749 0.576749i
\(723\) −1614.98 1614.98i −2.23372 2.23372i
\(724\) 27.4321i 0.0378896i
\(725\) 387.893 203.672i 0.535025 0.280928i
\(726\) 3023.06 4.16399
\(727\) 767.639 767.639i 1.05590 1.05590i 0.0575571 0.998342i \(-0.481669\pi\)
0.998342 0.0575571i \(-0.0183311\pi\)
\(728\) −21.5980 + 21.5980i −0.0296675 + 0.0296675i
\(729\) 67.1807i 0.0921546i
\(730\) 54.2894i 0.0743690i
\(731\) 203.860i 0.278878i
\(732\) −23.5380 −0.0321557
\(733\) −640.227 640.227i −0.873434 0.873434i 0.119411 0.992845i \(-0.461899\pi\)
−0.992845 + 0.119411i \(0.961899\pi\)
\(734\) 899.559i 1.22556i
\(735\) −586.057 586.057i −0.797357 0.797357i
\(736\) −42.1104 + 42.1104i −0.0572152 + 0.0572152i
\(737\) −250.061 250.061i −0.339296 0.339296i
\(738\) 2040.55i 2.76497i
\(739\) −126.689 + 126.689i −0.171433 + 0.171433i −0.787609 0.616175i \(-0.788681\pi\)
0.616175 + 0.787609i \(0.288681\pi\)
\(740\) 17.8920 + 17.8920i 0.0241784 + 0.0241784i
\(741\) 537.041 0.724752
\(742\) −30.9825 + 30.9825i −0.0417555 + 0.0417555i
\(743\) 547.079 + 547.079i 0.736310 + 0.736310i 0.971862 0.235551i \(-0.0756896\pi\)
−0.235551 + 0.971862i \(0.575690\pi\)
\(744\) −258.166 + 258.166i −0.346997 + 0.346997i
\(745\) −298.017 −0.400023
\(746\) −306.522 + 306.522i −0.410887 + 0.410887i
\(747\) 1547.50i 2.07162i
\(748\) −42.0141 −0.0561686
\(749\) 34.4300 0.0459680
\(750\) −1399.42 −1.86589
\(751\) −819.975 819.975i −1.09184 1.09184i −0.995332 0.0965128i \(-0.969231\pi\)
−0.0965128 0.995332i \(-0.530769\pi\)
\(752\) 127.925 + 127.925i 0.170113 + 0.170113i
\(753\) 1611.90i 2.14064i
\(754\) 656.194 + 204.347i 0.870283 + 0.271017i
\(755\) −548.352 −0.726294
\(756\) −3.39040 + 3.39040i −0.00448466 + 0.00448466i
\(757\) 499.757 499.757i 0.660181 0.660181i −0.295242 0.955423i \(-0.595400\pi\)
0.955423 + 0.295242i \(0.0954003\pi\)
\(758\) 668.205i 0.881537i
\(759\) 1696.23i 2.23482i
\(760\) 210.818i 0.277392i
\(761\) 1105.01 1.45205 0.726023 0.687670i \(-0.241367\pi\)
0.726023 + 0.687670i \(0.241367\pi\)
\(762\) −477.993 477.993i −0.627288 0.627288i
\(763\) 14.8871i 0.0195113i
\(764\) 14.1126 + 14.1126i 0.0184720 + 0.0184720i
\(765\) −402.165 + 402.165i −0.525707 + 0.525707i
\(766\) 360.980 + 360.980i 0.471253 + 0.471253i
\(767\) 247.445i 0.322615i
\(768\) 171.367 171.367i 0.223135 0.223135i
\(769\) −379.661 379.661i −0.493707 0.493707i 0.415765 0.909472i \(-0.363514\pi\)
−0.909472 + 0.415765i \(0.863514\pi\)
\(770\) 43.9522 0.0570808
\(771\) 604.891 604.891i 0.784554 0.784554i
\(772\) −36.5135 36.5135i −0.0472973 0.0472973i
\(773\) −912.108 + 912.108i −1.17996 + 1.17996i −0.200204 + 0.979754i \(0.564160\pi\)
−0.979754 + 0.200204i \(0.935840\pi\)
\(774\) −933.522 −1.20610
\(775\) 93.3791 93.3791i 0.120489 0.120489i
\(776\) 533.966i 0.688100i
\(777\) 63.1850 0.0813192
\(778\) −227.350 −0.292223
\(779\) 427.624 0.548940
\(780\) −32.4387 32.4387i −0.0415881 0.0415881i
\(781\) 743.527 + 743.527i 0.952019 + 0.952019i
\(782\) 294.264i 0.376296i