Properties

Label 105.3.l.a.22.11
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.11
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.11

$q$-expansion

\(f(q)\) \(=\) \(q+(2.41688 + 2.41688i) q^{2} +(1.22474 - 1.22474i) q^{3} +7.68258i q^{4} +(4.18124 - 2.74175i) q^{5} +5.92011 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-8.90034 + 8.90034i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(2.41688 + 2.41688i) q^{2} +(1.22474 - 1.22474i) q^{3} +7.68258i q^{4} +(4.18124 - 2.74175i) q^{5} +5.92011 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-8.90034 + 8.90034i) q^{8} -3.00000i q^{9} +(16.7320 + 3.47908i) q^{10} -20.9312 q^{11} +(9.40920 + 9.40920i) q^{12} +(-9.34319 + 9.34319i) q^{13} -9.04312i q^{14} +(1.76301 - 8.47890i) q^{15} -12.2917 q^{16} +(7.08868 + 7.08868i) q^{17} +(7.25063 - 7.25063i) q^{18} -14.9507i q^{19} +(21.0637 + 32.1228i) q^{20} -4.58258 q^{21} +(-50.5882 - 50.5882i) q^{22} +(12.9691 - 12.9691i) q^{23} +21.8013i q^{24} +(9.96562 - 22.9279i) q^{25} -45.1627 q^{26} +(-3.67423 - 3.67423i) q^{27} +(14.3728 - 14.3728i) q^{28} +39.6296i q^{29} +(24.7534 - 16.2315i) q^{30} +12.8776 q^{31} +(5.89378 + 5.89378i) q^{32} +(-25.6354 + 25.6354i) q^{33} +34.2649i q^{34} +(-12.9517 - 2.69305i) q^{35} +23.0477 q^{36} +(-31.7205 - 31.7205i) q^{37} +(36.1341 - 36.1341i) q^{38} +22.8861i q^{39} +(-12.8120 + 61.6170i) q^{40} +69.4519 q^{41} +(-11.0755 - 11.0755i) q^{42} +(4.46880 - 4.46880i) q^{43} -160.806i q^{44} +(-8.22525 - 12.5437i) q^{45} +62.6895 q^{46} +(-4.41044 - 4.41044i) q^{47} +(-15.0542 + 15.0542i) q^{48} +7.00000i q^{49} +(79.4994 - 31.3281i) q^{50} +17.3636 q^{51} +(-71.7798 - 71.7798i) q^{52} +(-48.5314 + 48.5314i) q^{53} -17.7603i q^{54} +(-87.5186 + 57.3882i) q^{55} +33.3020 q^{56} +(-18.3108 - 18.3108i) q^{57} +(-95.7797 + 95.7797i) q^{58} +29.4254i q^{59} +(65.1399 + 13.5445i) q^{60} +7.09295 q^{61} +(31.1235 + 31.1235i) q^{62} +(-5.61249 + 5.61249i) q^{63} +77.6560i q^{64} +(-13.4495 + 64.6829i) q^{65} -123.915 q^{66} +(-1.39800 - 1.39800i) q^{67} +(-54.4593 + 54.4593i) q^{68} -31.7677i q^{69} +(-24.7940 - 37.8115i) q^{70} -15.9437 q^{71} +(26.7010 + 26.7010i) q^{72} +(32.4160 - 32.4160i) q^{73} -153.329i q^{74} +(-15.8754 - 40.2861i) q^{75} +114.860 q^{76} +(39.1588 + 39.1588i) q^{77} +(-55.3128 + 55.3128i) q^{78} -66.1155i q^{79} +(-51.3947 + 33.7009i) q^{80} -9.00000 q^{81} +(167.857 + 167.857i) q^{82} +(-83.6744 + 83.6744i) q^{83} -35.2060i q^{84} +(49.0749 + 10.2041i) q^{85} +21.6011 q^{86} +(48.5361 + 48.5361i) q^{87} +(186.295 - 186.295i) q^{88} +62.7487i q^{89} +(10.4372 - 50.1961i) q^{90} +34.9590 q^{91} +(99.6363 + 99.6363i) q^{92} +(15.7717 - 15.7717i) q^{93} -21.3190i q^{94} +(-40.9912 - 62.5127i) q^{95} +14.4368 q^{96} +(-85.4547 - 85.4547i) q^{97} +(-16.9181 + 16.9181i) q^{98} +62.7937i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.41688 + 2.41688i 1.20844 + 1.20844i 0.971533 + 0.236905i \(0.0761331\pi\)
0.236905 + 0.971533i \(0.423867\pi\)
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 7.68258i 1.92065i
\(5\) 4.18124 2.74175i 0.836249 0.548350i
\(6\) 5.92011 0.986686
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) −8.90034 + 8.90034i −1.11254 + 1.11254i
\(9\) 3.00000i 0.333333i
\(10\) 16.7320 + 3.47908i 1.67320 + 0.347908i
\(11\) −20.9312 −1.90284 −0.951420 0.307897i \(-0.900375\pi\)
−0.951420 + 0.307897i \(0.900375\pi\)
\(12\) 9.40920 + 9.40920i 0.784100 + 0.784100i
\(13\) −9.34319 + 9.34319i −0.718707 + 0.718707i −0.968340 0.249633i \(-0.919690\pi\)
0.249633 + 0.968340i \(0.419690\pi\)
\(14\) 9.04312i 0.645937i
\(15\) 1.76301 8.47890i 0.117534 0.565260i
\(16\) −12.2917 −0.768233
\(17\) 7.08868 + 7.08868i 0.416981 + 0.416981i 0.884162 0.467181i \(-0.154730\pi\)
−0.467181 + 0.884162i \(0.654730\pi\)
\(18\) 7.25063 7.25063i 0.402813 0.402813i
\(19\) 14.9507i 0.786881i −0.919350 0.393440i \(-0.871285\pi\)
0.919350 0.393440i \(-0.128715\pi\)
\(20\) 21.0637 + 32.1228i 1.05319 + 1.60614i
\(21\) −4.58258 −0.218218
\(22\) −50.5882 50.5882i −2.29946 2.29946i
\(23\) 12.9691 12.9691i 0.563874 0.563874i −0.366531 0.930406i \(-0.619455\pi\)
0.930406 + 0.366531i \(0.119455\pi\)
\(24\) 21.8013i 0.908388i
\(25\) 9.96562 22.9279i 0.398625 0.917114i
\(26\) −45.1627 −1.73703
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 14.3728 14.3728i 0.513314 0.513314i
\(29\) 39.6296i 1.36654i 0.730168 + 0.683268i \(0.239442\pi\)
−0.730168 + 0.683268i \(0.760558\pi\)
\(30\) 24.7534 16.2315i 0.825115 0.541049i
\(31\) 12.8776 0.415405 0.207703 0.978192i \(-0.433401\pi\)
0.207703 + 0.978192i \(0.433401\pi\)
\(32\) 5.89378 + 5.89378i 0.184181 + 0.184181i
\(33\) −25.6354 + 25.6354i −0.776831 + 0.776831i
\(34\) 34.2649i 1.00779i
\(35\) −12.9517 2.69305i −0.370050 0.0769443i
\(36\) 23.0477 0.640215
\(37\) −31.7205 31.7205i −0.857312 0.857312i 0.133709 0.991021i \(-0.457311\pi\)
−0.991021 + 0.133709i \(0.957311\pi\)
\(38\) 36.1341 36.1341i 0.950897 0.950897i
\(39\) 22.8861i 0.586822i
\(40\) −12.8120 + 61.6170i −0.320300 + 1.54043i
\(41\) 69.4519 1.69395 0.846974 0.531634i \(-0.178422\pi\)
0.846974 + 0.531634i \(0.178422\pi\)
\(42\) −11.0755 11.0755i −0.263703 0.263703i
\(43\) 4.46880 4.46880i 0.103926 0.103926i −0.653232 0.757158i \(-0.726587\pi\)
0.757158 + 0.653232i \(0.226587\pi\)
\(44\) 160.806i 3.65468i
\(45\) −8.22525 12.5437i −0.182783 0.278750i
\(46\) 62.6895 1.36281
\(47\) −4.41044 4.41044i −0.0938392 0.0938392i 0.658629 0.752468i \(-0.271137\pi\)
−0.752468 + 0.658629i \(0.771137\pi\)
\(48\) −15.0542 + 15.0542i −0.313630 + 0.313630i
\(49\) 7.00000i 0.142857i
\(50\) 79.4994 31.3281i 1.58999 0.626562i
\(51\) 17.3636 0.340464
\(52\) −71.7798 71.7798i −1.38038 1.38038i
\(53\) −48.5314 + 48.5314i −0.915687 + 0.915687i −0.996712 0.0810246i \(-0.974181\pi\)
0.0810246 + 0.996712i \(0.474181\pi\)
\(54\) 17.7603i 0.328895i
\(55\) −87.5186 + 57.3882i −1.59125 + 1.04342i
\(56\) 33.3020 0.594679
\(57\) −18.3108 18.3108i −0.321243 0.321243i
\(58\) −95.7797 + 95.7797i −1.65137 + 1.65137i
\(59\) 29.4254i 0.498736i 0.968409 + 0.249368i \(0.0802229\pi\)
−0.968409 + 0.249368i \(0.919777\pi\)
\(60\) 65.1399 + 13.5445i 1.08566 + 0.225742i
\(61\) 7.09295 0.116278 0.0581389 0.998309i \(-0.481483\pi\)
0.0581389 + 0.998309i \(0.481483\pi\)
\(62\) 31.1235 + 31.1235i 0.501992 + 0.501992i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 77.6560i 1.21338i
\(65\) −13.4495 + 64.6829i −0.206915 + 0.995121i
\(66\) −123.915 −1.87750
\(67\) −1.39800 1.39800i −0.0208657 0.0208657i 0.696597 0.717463i \(-0.254697\pi\)
−0.717463 + 0.696597i \(0.754697\pi\)
\(68\) −54.4593 + 54.4593i −0.800873 + 0.800873i
\(69\) 31.7677i 0.460402i
\(70\) −24.7940 37.8115i −0.354200 0.540164i
\(71\) −15.9437 −0.224559 −0.112279 0.993677i \(-0.535815\pi\)
−0.112279 + 0.993677i \(0.535815\pi\)
\(72\) 26.7010 + 26.7010i 0.370848 + 0.370848i
\(73\) 32.4160 32.4160i 0.444055 0.444055i −0.449317 0.893372i \(-0.648333\pi\)
0.893372 + 0.449317i \(0.148333\pi\)
\(74\) 153.329i 2.07202i
\(75\) −15.8754 40.2861i −0.211672 0.537148i
\(76\) 114.860 1.51132
\(77\) 39.1588 + 39.1588i 0.508555 + 0.508555i
\(78\) −55.3128 + 55.3128i −0.709138 + 0.709138i
\(79\) 66.1155i 0.836905i −0.908239 0.418453i \(-0.862573\pi\)
0.908239 0.418453i \(-0.137427\pi\)
\(80\) −51.3947 + 33.7009i −0.642434 + 0.421261i
\(81\) −9.00000 −0.111111
\(82\) 167.857 + 167.857i 2.04703 + 2.04703i
\(83\) −83.6744 + 83.6744i −1.00812 + 1.00812i −0.00815803 + 0.999967i \(0.502597\pi\)
−0.999967 + 0.00815803i \(0.997403\pi\)
\(84\) 35.2060i 0.419119i
\(85\) 49.0749 + 10.2041i 0.577352 + 0.120048i
\(86\) 21.6011 0.251175
\(87\) 48.5361 + 48.5361i 0.557886 + 0.557886i
\(88\) 186.295 186.295i 2.11699 2.11699i
\(89\) 62.7487i 0.705042i 0.935804 + 0.352521i \(0.114675\pi\)
−0.935804 + 0.352521i \(0.885325\pi\)
\(90\) 10.4372 50.1961i 0.115969 0.557734i
\(91\) 34.9590 0.384165
\(92\) 99.6363 + 99.6363i 1.08300 + 1.08300i
\(93\) 15.7717 15.7717i 0.169589 0.169589i
\(94\) 21.3190i 0.226798i
\(95\) −40.9912 62.5127i −0.431486 0.658028i
\(96\) 14.4368 0.150383
\(97\) −85.4547 85.4547i −0.880976 0.880976i 0.112658 0.993634i \(-0.464064\pi\)
−0.993634 + 0.112658i \(0.964064\pi\)
\(98\) −16.9181 + 16.9181i −0.172634 + 0.172634i
\(99\) 62.7937i 0.634280i
\(100\) 176.145 + 76.5617i 1.76145 + 0.765617i
\(101\) 145.641 1.44199 0.720997 0.692938i \(-0.243684\pi\)
0.720997 + 0.692938i \(0.243684\pi\)
\(102\) 41.9658 + 41.9658i 0.411429 + 0.411429i
\(103\) 62.2547 62.2547i 0.604414 0.604414i −0.337067 0.941481i \(-0.609435\pi\)
0.941481 + 0.337067i \(0.109435\pi\)
\(104\) 166.315i 1.59918i
\(105\) −19.1609 + 12.5643i −0.182484 + 0.119660i
\(106\) −234.589 −2.21310
\(107\) −4.15809 4.15809i −0.0388607 0.0388607i 0.687409 0.726270i \(-0.258748\pi\)
−0.726270 + 0.687409i \(0.758748\pi\)
\(108\) 28.2276 28.2276i 0.261367 0.261367i
\(109\) 78.6347i 0.721419i 0.932678 + 0.360710i \(0.117465\pi\)
−0.932678 + 0.360710i \(0.882535\pi\)
\(110\) −350.222 72.8215i −3.18383 0.662013i
\(111\) −77.6991 −0.699992
\(112\) 22.9957 + 22.9957i 0.205319 + 0.205319i
\(113\) −107.343 + 107.343i −0.949938 + 0.949938i −0.998805 0.0488672i \(-0.984439\pi\)
0.0488672 + 0.998805i \(0.484439\pi\)
\(114\) 88.5100i 0.776404i
\(115\) 18.6690 89.7851i 0.162339 0.780740i
\(116\) −304.457 −2.62463
\(117\) 28.0296 + 28.0296i 0.239569 + 0.239569i
\(118\) −71.1176 + 71.1176i −0.602692 + 0.602692i
\(119\) 26.5234i 0.222886i
\(120\) 59.7737 + 91.1566i 0.498114 + 0.759638i
\(121\) 317.117 2.62080
\(122\) 17.1428 + 17.1428i 0.140515 + 0.140515i
\(123\) 85.0608 85.0608i 0.691552 0.691552i
\(124\) 98.9329i 0.797846i
\(125\) −21.1937 123.190i −0.169550 0.985522i
\(126\) −27.1294 −0.215312
\(127\) −116.651 116.651i −0.918514 0.918514i 0.0784074 0.996921i \(-0.475017\pi\)
−0.996921 + 0.0784074i \(0.975017\pi\)
\(128\) −164.110 + 164.110i −1.28211 + 1.28211i
\(129\) 10.9463i 0.0848548i
\(130\) −188.836 + 123.825i −1.45259 + 0.952498i
\(131\) 139.820 1.06733 0.533664 0.845697i \(-0.320815\pi\)
0.533664 + 0.845697i \(0.320815\pi\)
\(132\) −196.946 196.946i −1.49202 1.49202i
\(133\) −27.9703 + 27.9703i −0.210303 + 0.210303i
\(134\) 6.75760i 0.0504298i
\(135\) −25.4367 5.28904i −0.188420 0.0391781i
\(136\) −126.183 −0.927819
\(137\) −161.119 161.119i −1.17605 1.17605i −0.980741 0.195313i \(-0.937428\pi\)
−0.195313 0.980741i \(-0.562572\pi\)
\(138\) 76.7786 76.7786i 0.556367 0.556367i
\(139\) 201.129i 1.44697i −0.690340 0.723485i \(-0.742539\pi\)
0.690340 0.723485i \(-0.257461\pi\)
\(140\) 20.6896 99.5028i 0.147783 0.710734i
\(141\) −10.8033 −0.0766194
\(142\) −38.5339 38.5339i −0.271365 0.271365i
\(143\) 195.565 195.565i 1.36758 1.36758i
\(144\) 36.8752i 0.256078i
\(145\) 108.654 + 165.701i 0.749340 + 1.14276i
\(146\) 156.691 1.07323
\(147\) 8.57321 + 8.57321i 0.0583212 + 0.0583212i
\(148\) 243.696 243.696i 1.64659 1.64659i
\(149\) 23.2371i 0.155954i 0.996955 + 0.0779768i \(0.0248460\pi\)
−0.996955 + 0.0779768i \(0.975154\pi\)
\(150\) 58.9976 135.735i 0.393317 0.904903i
\(151\) −39.3517 −0.260607 −0.130304 0.991474i \(-0.541595\pi\)
−0.130304 + 0.991474i \(0.541595\pi\)
\(152\) 133.067 + 133.067i 0.875439 + 0.875439i
\(153\) 21.2660 21.2660i 0.138994 0.138994i
\(154\) 189.284i 1.22912i
\(155\) 53.8443 35.3071i 0.347382 0.227787i
\(156\) −175.824 −1.12708
\(157\) 51.1623 + 51.1623i 0.325874 + 0.325874i 0.851015 0.525141i \(-0.175987\pi\)
−0.525141 + 0.851015i \(0.675987\pi\)
\(158\) 159.793 159.793i 1.01135 1.01135i
\(159\) 118.877i 0.747656i
\(160\) 40.8026 + 8.48407i 0.255016 + 0.0530254i
\(161\) −48.5260 −0.301404
\(162\) −21.7519 21.7519i −0.134271 0.134271i
\(163\) −40.2804 + 40.2804i −0.247119 + 0.247119i −0.819787 0.572668i \(-0.805908\pi\)
0.572668 + 0.819787i \(0.305908\pi\)
\(164\) 533.570i 3.25347i
\(165\) −36.9021 + 177.474i −0.223649 + 1.07560i
\(166\) −404.461 −2.43651
\(167\) −66.9974 66.9974i −0.401182 0.401182i 0.477467 0.878649i \(-0.341555\pi\)
−0.878649 + 0.477467i \(0.841555\pi\)
\(168\) 40.7865 40.7865i 0.242777 0.242777i
\(169\) 5.59045i 0.0330796i
\(170\) 93.9458 + 143.270i 0.552622 + 0.842765i
\(171\) −44.8522 −0.262294
\(172\) 34.3319 + 34.3319i 0.199604 + 0.199604i
\(173\) 221.843 221.843i 1.28233 1.28233i 0.342991 0.939339i \(-0.388560\pi\)
0.939339 0.342991i \(-0.111440\pi\)
\(174\) 234.611i 1.34834i
\(175\) −61.5380 + 24.2501i −0.351646 + 0.138572i
\(176\) 257.281 1.46182
\(177\) 36.0387 + 36.0387i 0.203608 + 0.203608i
\(178\) −151.656 + 151.656i −0.851999 + 0.851999i
\(179\) 129.207i 0.721827i 0.932599 + 0.360914i \(0.117535\pi\)
−0.932599 + 0.360914i \(0.882465\pi\)
\(180\) 96.3683 63.1911i 0.535379 0.351062i
\(181\) 28.8400 0.159337 0.0796685 0.996821i \(-0.474614\pi\)
0.0796685 + 0.996821i \(0.474614\pi\)
\(182\) 84.4916 + 84.4916i 0.464240 + 0.464240i
\(183\) 8.68705 8.68705i 0.0474702 0.0474702i
\(184\) 230.859i 1.25467i
\(185\) −219.601 45.6616i −1.18703 0.246819i
\(186\) 76.2366 0.409874
\(187\) −148.375 148.375i −0.793448 0.793448i
\(188\) 33.8836 33.8836i 0.180232 0.180232i
\(189\) 13.7477i 0.0727393i
\(190\) 52.0148 250.156i 0.273762 1.31661i
\(191\) 29.9221 0.156660 0.0783302 0.996927i \(-0.475041\pi\)
0.0783302 + 0.996927i \(0.475041\pi\)
\(192\) 95.1088 + 95.1088i 0.495358 + 0.495358i
\(193\) −42.5417 + 42.5417i −0.220423 + 0.220423i −0.808677 0.588253i \(-0.799816\pi\)
0.588253 + 0.808677i \(0.299816\pi\)
\(194\) 413.067i 2.12921i
\(195\) 62.7478 + 95.6922i 0.321784 + 0.490729i
\(196\) −53.7781 −0.274378
\(197\) 249.093 + 249.093i 1.26443 + 1.26443i 0.948922 + 0.315509i \(0.102175\pi\)
0.315509 + 0.948922i \(0.397825\pi\)
\(198\) −151.765 + 151.765i −0.766488 + 0.766488i
\(199\) 16.7548i 0.0841949i 0.999114 + 0.0420974i \(0.0134040\pi\)
−0.999114 + 0.0420974i \(0.986596\pi\)
\(200\) 115.368 + 292.763i 0.576842 + 1.46382i
\(201\) −3.42439 −0.0170368
\(202\) 351.997 + 351.997i 1.74256 + 1.74256i
\(203\) 74.1401 74.1401i 0.365222 0.365222i
\(204\) 133.398i 0.653910i
\(205\) 290.395 190.420i 1.41656 0.928876i
\(206\) 300.924 1.46079
\(207\) −38.9073 38.9073i −0.187958 0.187958i
\(208\) 114.844 114.844i 0.552135 0.552135i
\(209\) 312.937i 1.49731i
\(210\) −76.6758 15.9432i −0.365123 0.0759198i
\(211\) 77.0276 0.365060 0.182530 0.983200i \(-0.441571\pi\)
0.182530 + 0.983200i \(0.441571\pi\)
\(212\) −372.847 372.847i −1.75871 1.75871i
\(213\) −19.5269 + 19.5269i −0.0916758 + 0.0916758i
\(214\) 20.0992i 0.0939214i
\(215\) 6.43281 30.9375i 0.0299201 0.143895i
\(216\) 65.4039 0.302796
\(217\) −24.0917 24.0917i −0.111022 0.111022i
\(218\) −190.050 + 190.050i −0.871791 + 0.871791i
\(219\) 79.4027i 0.362570i
\(220\) −440.890 672.369i −2.00404 3.05622i
\(221\) −132.462 −0.599374
\(222\) −187.789 187.789i −0.845897 0.845897i
\(223\) −44.1625 + 44.1625i −0.198038 + 0.198038i −0.799158 0.601120i \(-0.794721\pi\)
0.601120 + 0.799158i \(0.294721\pi\)
\(224\) 22.0525i 0.0984487i
\(225\) −68.7836 29.8969i −0.305705 0.132875i
\(226\) −518.869 −2.29588
\(227\) −176.500 176.500i −0.777533 0.777533i 0.201878 0.979411i \(-0.435296\pi\)
−0.979411 + 0.201878i \(0.935296\pi\)
\(228\) 140.674 140.674i 0.616993 0.616993i
\(229\) 296.743i 1.29582i 0.761716 + 0.647911i \(0.224357\pi\)
−0.761716 + 0.647911i \(0.775643\pi\)
\(230\) 262.120 171.879i 1.13965 0.747299i
\(231\) 95.9190 0.415234
\(232\) −352.717 352.717i −1.52033 1.52033i
\(233\) −88.1651 + 88.1651i −0.378391 + 0.378391i −0.870521 0.492131i \(-0.836218\pi\)
0.492131 + 0.870521i \(0.336218\pi\)
\(234\) 135.488i 0.579009i
\(235\) −30.5335 6.34881i −0.129930 0.0270162i
\(236\) −226.063 −0.957895
\(237\) −80.9746 80.9746i −0.341665 0.341665i
\(238\) 64.1038 64.1038i 0.269344 0.269344i
\(239\) 370.319i 1.54945i −0.632297 0.774726i \(-0.717888\pi\)
0.632297 0.774726i \(-0.282112\pi\)
\(240\) −21.6705 + 104.220i −0.0902938 + 0.434252i
\(241\) −202.313 −0.839471 −0.419736 0.907646i \(-0.637877\pi\)
−0.419736 + 0.907646i \(0.637877\pi\)
\(242\) 766.431 + 766.431i 3.16707 + 3.16707i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 54.4921i 0.223328i
\(245\) 19.1922 + 29.2687i 0.0783357 + 0.119464i
\(246\) 411.163 1.67139
\(247\) 139.688 + 139.688i 0.565537 + 0.565537i
\(248\) −114.615 + 114.615i −0.462156 + 0.462156i
\(249\) 204.959i 0.823130i
\(250\) 246.513 348.958i 0.986051 1.39583i
\(251\) −358.910 −1.42992 −0.714960 0.699165i \(-0.753555\pi\)
−0.714960 + 0.699165i \(0.753555\pi\)
\(252\) −43.1184 43.1184i −0.171105 0.171105i
\(253\) −271.459 + 271.459i −1.07296 + 1.07296i
\(254\) 563.863i 2.21993i
\(255\) 72.6016 47.6068i 0.284712 0.186693i
\(256\) −482.642 −1.88532
\(257\) −157.946 157.946i −0.614576 0.614576i 0.329559 0.944135i \(-0.393100\pi\)
−0.944135 + 0.329559i \(0.893100\pi\)
\(258\) 26.4558 26.4558i 0.102542 0.102542i
\(259\) 118.687i 0.458252i
\(260\) −496.931 103.327i −1.91127 0.397410i
\(261\) 118.889 0.455512
\(262\) 337.927 + 337.927i 1.28980 + 1.28980i
\(263\) 9.79809 9.79809i 0.0372551 0.0372551i −0.688234 0.725489i \(-0.741614\pi\)
0.725489 + 0.688234i \(0.241614\pi\)
\(264\) 456.328i 1.72852i
\(265\) −69.8608 + 335.983i −0.263626 + 1.26786i
\(266\) −135.201 −0.508276
\(267\) 76.8512 + 76.8512i 0.287832 + 0.287832i
\(268\) 10.7403 10.7403i 0.0400756 0.0400756i
\(269\) 143.504i 0.533473i −0.963770 0.266736i \(-0.914055\pi\)
0.963770 0.266736i \(-0.0859453\pi\)
\(270\) −48.6944 74.2603i −0.180350 0.275038i
\(271\) −29.4732 −0.108757 −0.0543785 0.998520i \(-0.517318\pi\)
−0.0543785 + 0.998520i \(0.517318\pi\)
\(272\) −87.1321 87.1321i −0.320339 0.320339i
\(273\) 42.8159 42.8159i 0.156835 0.156835i
\(274\) 778.811i 2.84238i
\(275\) −208.593 + 479.908i −0.758519 + 1.74512i
\(276\) 244.058 0.884268
\(277\) 189.827 + 189.827i 0.685295 + 0.685295i 0.961188 0.275894i \(-0.0889738\pi\)
−0.275894 + 0.961188i \(0.588974\pi\)
\(278\) 486.103 486.103i 1.74857 1.74857i
\(279\) 38.6327i 0.138468i
\(280\) 139.244 91.3058i 0.497300 0.326092i
\(281\) −61.2502 −0.217972 −0.108986 0.994043i \(-0.534760\pi\)
−0.108986 + 0.994043i \(0.534760\pi\)
\(282\) −26.1103 26.1103i −0.0925898 0.0925898i
\(283\) −176.415 + 176.415i −0.623375 + 0.623375i −0.946393 0.323018i \(-0.895303\pi\)
0.323018 + 0.946393i \(0.395303\pi\)
\(284\) 122.489i 0.431298i
\(285\) −126.766 26.3584i −0.444792 0.0924855i
\(286\) 945.310 3.30528
\(287\) −129.933 129.933i −0.452727 0.452727i
\(288\) 17.6813 17.6813i 0.0613935 0.0613935i
\(289\) 188.501i 0.652254i
\(290\) −137.874 + 663.083i −0.475429 + 2.28649i
\(291\) −209.320 −0.719314
\(292\) 249.039 + 249.039i 0.852873 + 0.852873i
\(293\) −92.7415 + 92.7415i −0.316524 + 0.316524i −0.847430 0.530907i \(-0.821852\pi\)
0.530907 + 0.847430i \(0.321852\pi\)
\(294\) 41.4408i 0.140955i
\(295\) 80.6772 + 123.035i 0.273482 + 0.417068i
\(296\) 564.647 1.90759
\(297\) 76.9063 + 76.9063i 0.258944 + 0.258944i
\(298\) −56.1612 + 56.1612i −0.188460 + 0.188460i
\(299\) 242.346i 0.810521i
\(300\) 309.501 121.964i 1.03167 0.406548i
\(301\) −16.7207 −0.0555505
\(302\) −95.1081 95.1081i −0.314927 0.314927i
\(303\) 178.374 178.374i 0.588692 0.588692i
\(304\) 183.770i 0.604508i
\(305\) 29.6573 19.4471i 0.0972372 0.0637609i
\(306\) 102.795 0.335931
\(307\) −228.867 228.867i −0.745494 0.745494i 0.228135 0.973629i \(-0.426737\pi\)
−0.973629 + 0.228135i \(0.926737\pi\)
\(308\) −300.840 + 300.840i −0.976754 + 0.976754i
\(309\) 152.492i 0.493502i
\(310\) 215.468 + 44.8021i 0.695057 + 0.144523i
\(311\) 291.118 0.936070 0.468035 0.883710i \(-0.344962\pi\)
0.468035 + 0.883710i \(0.344962\pi\)
\(312\) −203.694 203.694i −0.652864 0.652864i
\(313\) 251.667 251.667i 0.804049 0.804049i −0.179677 0.983726i \(-0.557505\pi\)
0.983726 + 0.179677i \(0.0575052\pi\)
\(314\) 247.306i 0.787598i
\(315\) −8.07915 + 38.8552i −0.0256481 + 0.123350i
\(316\) 507.938 1.60740
\(317\) 30.4080 + 30.4080i 0.0959244 + 0.0959244i 0.753440 0.657516i \(-0.228393\pi\)
−0.657516 + 0.753440i \(0.728393\pi\)
\(318\) −287.312 + 287.312i −0.903496 + 0.903496i
\(319\) 829.495i 2.60030i
\(320\) 212.913 + 324.699i 0.665354 + 1.01468i
\(321\) −10.1852 −0.0317296
\(322\) −117.281 117.281i −0.364228 0.364228i
\(323\) 105.981 105.981i 0.328114 0.328114i
\(324\) 69.1432i 0.213405i
\(325\) 121.109 + 307.330i 0.372642 + 0.945631i
\(326\) −194.705 −0.597255
\(327\) 96.3075 + 96.3075i 0.294518 + 0.294518i
\(328\) −618.146 + 618.146i −1.88459 + 1.88459i
\(329\) 16.5024i 0.0501592i
\(330\) −518.120 + 339.745i −1.57006 + 1.02953i
\(331\) −600.898 −1.81540 −0.907701 0.419617i \(-0.862164\pi\)
−0.907701 + 0.419617i \(0.862164\pi\)
\(332\) −642.835 642.835i −1.93625 1.93625i
\(333\) −95.1616 + 95.1616i −0.285771 + 0.285771i
\(334\) 323.849i 0.969607i
\(335\) −9.67836 2.01242i −0.0288906 0.00600722i
\(336\) 56.3278 0.167642
\(337\) −18.3744 18.3744i −0.0545235 0.0545235i 0.679319 0.733843i \(-0.262275\pi\)
−0.733843 + 0.679319i \(0.762275\pi\)
\(338\) 13.5114 13.5114i 0.0399746 0.0399746i
\(339\) 262.936i 0.775621i
\(340\) −78.3940 + 377.022i −0.230570 + 1.10889i
\(341\) −269.543 −0.790450
\(342\) −108.402 108.402i −0.316966 0.316966i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 79.5477i 0.231243i
\(345\) −87.0991 132.829i −0.252461 0.385010i
\(346\) 1072.33 3.09923
\(347\) 274.252 + 274.252i 0.790351 + 0.790351i 0.981551 0.191200i \(-0.0612379\pi\)
−0.191200 + 0.981551i \(0.561238\pi\)
\(348\) −372.882 + 372.882i −1.07150 + 1.07150i
\(349\) 218.995i 0.627494i −0.949507 0.313747i \(-0.898416\pi\)
0.949507 0.313747i \(-0.101584\pi\)
\(350\) −207.339 90.1203i −0.592398 0.257487i
\(351\) 68.6582 0.195607
\(352\) −123.364 123.364i −0.350466 0.350466i
\(353\) 77.0417 77.0417i 0.218248 0.218248i −0.589512 0.807760i \(-0.700680\pi\)
0.807760 + 0.589512i \(0.200680\pi\)
\(354\) 174.202i 0.492096i
\(355\) −66.6644 + 43.7136i −0.187787 + 0.123137i
\(356\) −482.072 −1.35413
\(357\) −32.4844 32.4844i −0.0909927 0.0909927i
\(358\) −312.277 + 312.277i −0.872283 + 0.872283i
\(359\) 532.713i 1.48388i 0.670466 + 0.741940i \(0.266094\pi\)
−0.670466 + 0.741940i \(0.733906\pi\)
\(360\) 184.851 + 38.4360i 0.513475 + 0.106767i
\(361\) 137.476 0.380819
\(362\) 69.7027 + 69.7027i 0.192549 + 0.192549i
\(363\) 388.387 388.387i 1.06994 1.06994i
\(364\) 268.576i 0.737845i
\(365\) 46.6627 224.416i 0.127843 0.614838i
\(366\) 41.9910 0.114730
\(367\) 367.459 + 367.459i 1.00125 + 1.00125i 0.999999 + 0.00125078i \(0.000398137\pi\)
0.00125078 + 0.999999i \(0.499602\pi\)
\(368\) −159.413 + 159.413i −0.433187 + 0.433187i
\(369\) 208.356i 0.564649i
\(370\) −420.390 641.107i −1.13619 1.73272i
\(371\) 181.588 0.489456
\(372\) 121.168 + 121.168i 0.325719 + 0.325719i
\(373\) 30.1723 30.1723i 0.0808908 0.0808908i −0.665504 0.746395i \(-0.731783\pi\)
0.746395 + 0.665504i \(0.231783\pi\)
\(374\) 717.207i 1.91767i
\(375\) −176.833 124.920i −0.471556 0.333119i
\(376\) 78.5089 0.208800
\(377\) −370.267 370.267i −0.982139 0.982139i
\(378\) −33.2266 + 33.2266i −0.0879009 + 0.0879009i
\(379\) 254.898i 0.672555i 0.941763 + 0.336277i \(0.109168\pi\)
−0.941763 + 0.336277i \(0.890832\pi\)
\(380\) 480.259 314.918i 1.26384 0.828732i
\(381\) −285.736 −0.749964
\(382\) 72.3181 + 72.3181i 0.189314 + 0.189314i
\(383\) 104.737 104.737i 0.273465 0.273465i −0.557028 0.830493i \(-0.688059\pi\)
0.830493 + 0.557028i \(0.188059\pi\)
\(384\) 401.985i 1.04684i
\(385\) 271.096 + 56.3688i 0.704145 + 0.146413i
\(386\) −205.636 −0.532736
\(387\) −13.4064 13.4064i −0.0346418 0.0346418i
\(388\) 656.512 656.512i 1.69204 1.69204i
\(389\) 667.039i 1.71475i −0.514689 0.857377i \(-0.672092\pi\)
0.514689 0.857377i \(-0.327908\pi\)
\(390\) −79.6224 + 382.930i −0.204160 + 0.981872i
\(391\) 183.868 0.470250
\(392\) −62.3024 62.3024i −0.158935 0.158935i
\(393\) 171.244 171.244i 0.435735 0.435735i
\(394\) 1204.05i 3.05598i
\(395\) −181.272 276.445i −0.458917 0.699861i
\(396\) −482.418 −1.21823
\(397\) −171.665 171.665i −0.432406 0.432406i 0.457040 0.889446i \(-0.348910\pi\)
−0.889446 + 0.457040i \(0.848910\pi\)
\(398\) −40.4942 + 40.4942i −0.101744 + 0.101744i
\(399\) 68.5129i 0.171711i
\(400\) −122.495 + 281.823i −0.306237 + 0.704558i
\(401\) 686.098 1.71097 0.855484 0.517829i \(-0.173260\pi\)
0.855484 + 0.517829i \(0.173260\pi\)
\(402\) −8.27633 8.27633i −0.0205879 0.0205879i
\(403\) −120.318 + 120.318i −0.298555 + 0.298555i
\(404\) 1118.90i 2.76956i
\(405\) −37.6312 + 24.6757i −0.0929166 + 0.0609278i
\(406\) 358.375 0.882697
\(407\) 663.950 + 663.950i 1.63133 + 1.63133i
\(408\) −154.542 + 154.542i −0.378780 + 0.378780i
\(409\) 556.252i 1.36003i −0.733198 0.680015i \(-0.761973\pi\)
0.733198 0.680015i \(-0.238027\pi\)
\(410\) 1162.07 + 241.629i 2.83432 + 0.589339i
\(411\) −394.660 −0.960244
\(412\) 478.277 + 478.277i 1.16087 + 1.16087i
\(413\) 55.0499 55.0499i 0.133293 0.133293i
\(414\) 188.068i 0.454272i
\(415\) −120.449 + 579.277i −0.290238 + 1.39585i
\(416\) −110.133 −0.264744
\(417\) −246.331 246.331i −0.590723 0.590723i
\(418\) −756.331 + 756.331i −1.80940 + 1.80940i
\(419\) 143.631i 0.342794i 0.985202 + 0.171397i \(0.0548280\pi\)
−0.985202 + 0.171397i \(0.945172\pi\)
\(420\) −96.5261 147.205i −0.229824 0.350488i
\(421\) 110.369 0.262159 0.131080 0.991372i \(-0.458156\pi\)
0.131080 + 0.991372i \(0.458156\pi\)
\(422\) 186.166 + 186.166i 0.441152 + 0.441152i
\(423\) −13.2313 + 13.2313i −0.0312797 + 0.0312797i
\(424\) 863.893i 2.03748i
\(425\) 233.171 91.8851i 0.548638 0.216200i
\(426\) −94.3884 −0.221569
\(427\) −13.2697 13.2697i −0.0310766 0.0310766i
\(428\) 31.9449 31.9449i 0.0746376 0.0746376i
\(429\) 479.033i 1.11663i
\(430\) 90.3193 59.2247i 0.210045 0.137732i
\(431\) 439.840 1.02051 0.510255 0.860023i \(-0.329551\pi\)
0.510255 + 0.860023i \(0.329551\pi\)
\(432\) 45.1627 + 45.1627i 0.104543 + 0.104543i
\(433\) −118.543 + 118.543i −0.273770 + 0.273770i −0.830616 0.556846i \(-0.812011\pi\)
0.556846 + 0.830616i \(0.312011\pi\)
\(434\) 116.453i 0.268326i
\(435\) 336.015 + 69.8675i 0.772449 + 0.160615i
\(436\) −604.118 −1.38559
\(437\) −193.898 193.898i −0.443702 0.443702i
\(438\) 191.907 191.907i 0.438143 0.438143i
\(439\) 351.519i 0.800727i 0.916356 + 0.400363i \(0.131116\pi\)
−0.916356 + 0.400363i \(0.868884\pi\)
\(440\) 268.171 1289.72i 0.609480 2.93118i
\(441\) 21.0000 0.0476190
\(442\) −320.144 320.144i −0.724307 0.724307i
\(443\) −41.1332 + 41.1332i −0.0928514 + 0.0928514i −0.752007 0.659155i \(-0.770914\pi\)
0.659155 + 0.752007i \(0.270914\pi\)
\(444\) 596.930i 1.34444i
\(445\) 172.041 + 262.368i 0.386610 + 0.589590i
\(446\) −213.470 −0.478633
\(447\) 28.4595 + 28.4595i 0.0636678 + 0.0636678i
\(448\) 145.281 145.281i 0.324288 0.324288i
\(449\) 209.909i 0.467503i 0.972296 + 0.233751i \(0.0751002\pi\)
−0.972296 + 0.233751i \(0.924900\pi\)
\(450\) −93.9844 238.498i −0.208854 0.529996i
\(451\) −1453.71 −3.22331
\(452\) −824.671 824.671i −1.82449 1.82449i
\(453\) −48.1957 + 48.1957i −0.106392 + 0.106392i
\(454\) 853.157i 1.87920i
\(455\) 146.172 95.8489i 0.321258 0.210657i
\(456\) 325.945 0.714793
\(457\) −156.842 156.842i −0.343199 0.343199i 0.514370 0.857568i \(-0.328026\pi\)
−0.857568 + 0.514370i \(0.828026\pi\)
\(458\) −717.192 + 717.192i −1.56592 + 1.56592i
\(459\) 52.0909i 0.113488i
\(460\) 689.781 + 143.426i 1.49952 + 0.311795i
\(461\) 274.147 0.594680 0.297340 0.954772i \(-0.403901\pi\)
0.297340 + 0.954772i \(0.403901\pi\)
\(462\) 231.824 + 231.824i 0.501784 + 0.501784i
\(463\) 483.190 483.190i 1.04361 1.04361i 0.0446032 0.999005i \(-0.485798\pi\)
0.999005 0.0446032i \(-0.0142023\pi\)
\(464\) 487.116i 1.04982i
\(465\) 22.7033 109.188i 0.0488244 0.234812i
\(466\) −426.168 −0.914524
\(467\) 8.70901 + 8.70901i 0.0186489 + 0.0186489i 0.716370 0.697721i \(-0.245802\pi\)
−0.697721 + 0.716370i \(0.745802\pi\)
\(468\) −215.339 + 215.339i −0.460127 + 0.460127i
\(469\) 5.23085i 0.0111532i
\(470\) −58.4513 89.1399i −0.124365 0.189659i
\(471\) 125.321 0.266075
\(472\) −261.896 261.896i −0.554865 0.554865i
\(473\) −93.5374 + 93.5374i −0.197754 + 0.197754i
\(474\) 391.411i 0.825762i
\(475\) −342.788 148.993i −0.721659 0.313670i
\(476\) 203.768 0.428084
\(477\) 145.594 + 145.594i 0.305229 + 0.305229i
\(478\) 895.015 895.015i 1.87242 1.87242i
\(479\) 806.280i 1.68326i 0.540056 + 0.841629i \(0.318403\pi\)
−0.540056 + 0.841629i \(0.681597\pi\)
\(480\) 60.3636 39.5820i 0.125758 0.0824624i
\(481\) 592.742 1.23231
\(482\) −488.965 488.965i −1.01445 1.01445i
\(483\) −59.4319 + 59.4319i −0.123047 + 0.123047i
\(484\) 2436.27i 5.03362i
\(485\) −591.602 123.012i −1.21980 0.253632i
\(486\) −53.2810 −0.109632
\(487\) −153.496 153.496i −0.315186 0.315186i 0.531729 0.846915i \(-0.321543\pi\)
−0.846915 + 0.531729i \(0.821543\pi\)
\(488\) −63.1297 + 63.1297i −0.129364 + 0.129364i
\(489\) 98.6663i 0.201772i
\(490\) −24.3536 + 117.124i −0.0497012 + 0.239029i
\(491\) −180.954 −0.368543 −0.184271 0.982875i \(-0.558993\pi\)
−0.184271 + 0.982875i \(0.558993\pi\)
\(492\) 653.487 + 653.487i 1.32823 + 1.32823i
\(493\) −280.921 + 280.921i −0.569820 + 0.569820i
\(494\) 675.215i 1.36683i
\(495\) 172.165 + 262.556i 0.347807 + 0.530416i
\(496\) −158.288 −0.319128
\(497\) 29.8279 + 29.8279i 0.0600159 + 0.0600159i
\(498\) −495.362 + 495.362i −0.994702 + 0.994702i
\(499\) 13.9603i 0.0279765i 0.999902 + 0.0139883i \(0.00445275\pi\)
−0.999902 + 0.0139883i \(0.995547\pi\)
\(500\) 946.419 162.823i 1.89284 0.325645i
\(501\) −164.109 −0.327564
\(502\) −867.441 867.441i −1.72797 1.72797i
\(503\) 358.510 358.510i 0.712743 0.712743i −0.254365 0.967108i \(-0.581866\pi\)
0.967108 + 0.254365i \(0.0818664\pi\)
\(504\) 99.9061i 0.198226i
\(505\) 608.962 399.312i 1.20587 0.790717i
\(506\) −1312.17 −2.59322
\(507\) −6.84688 6.84688i −0.0135047 0.0135047i
\(508\) 896.183 896.183i 1.76414 1.76414i
\(509\) 446.506i 0.877223i −0.898677 0.438611i \(-0.855470\pi\)
0.898677 0.438611i \(-0.144530\pi\)
\(510\) 290.529 + 60.4095i 0.569664 + 0.118450i
\(511\) −121.290 −0.237357
\(512\) −510.047 510.047i −0.996186 0.996186i
\(513\) −54.9325 + 54.9325i −0.107081 + 0.107081i
\(514\) 763.472i 1.48535i
\(515\) 89.6153 430.989i 0.174010 0.836871i
\(516\) 84.0956 0.162976
\(517\) 92.3160 + 92.3160i 0.178561 + 0.178561i
\(518\) −286.853 + 286.853i −0.553770 + 0.553770i
\(519\) 543.402i 1.04702i
\(520\) −455.995 695.405i −0.876913 1.33732i
\(521\) −682.112 −1.30924 −0.654618 0.755960i \(-0.727171\pi\)
−0.654618 + 0.755960i \(0.727171\pi\)
\(522\) 287.339 + 287.339i 0.550458 + 0.550458i
\(523\) −252.224 + 252.224i −0.482263 + 0.482263i −0.905854 0.423591i \(-0.860769\pi\)
0.423591 + 0.905854i \(0.360769\pi\)
\(524\) 1074.18i 2.04996i
\(525\) −45.6682 + 105.069i −0.0869870 + 0.200131i
\(526\) 47.3615 0.0900410
\(527\) 91.2849 + 91.2849i 0.173216 + 0.173216i
\(528\) 315.104 315.104i 0.596787 0.596787i
\(529\) 192.604i 0.364091i
\(530\) −980.874 + 643.184i −1.85071 + 1.21356i
\(531\) 88.2763 0.166245
\(532\) −214.884 214.884i −0.403917 0.403917i
\(533\) −648.902 + 648.902i −1.21745 + 1.21745i
\(534\) 371.479i 0.695654i
\(535\) −28.7864 5.98555i −0.0538064 0.0111879i
\(536\) 24.8854 0.0464280
\(537\) 158.246 + 158.246i 0.294685 + 0.294685i
\(538\) 346.832 346.832i 0.644669 0.644669i
\(539\) 146.519i 0.271834i
\(540\) 40.6335 195.420i 0.0752472 0.361888i
\(541\) 225.356 0.416554 0.208277 0.978070i \(-0.433214\pi\)
0.208277 + 0.978070i \(0.433214\pi\)
\(542\) −71.2330 71.2330i −0.131426 0.131426i
\(543\) 35.3217 35.3217i 0.0650491 0.0650491i
\(544\) 83.5582i 0.153600i
\(545\) 215.597 + 328.791i 0.395590 + 0.603286i
\(546\) 206.961 0.379050
\(547\) 211.802 + 211.802i 0.387207 + 0.387207i 0.873690 0.486483i \(-0.161720\pi\)
−0.486483 + 0.873690i \(0.661720\pi\)
\(548\) 1237.81 1237.81i 2.25878 2.25878i
\(549\) 21.2788i 0.0387593i
\(550\) −1664.02 + 655.736i −3.02549 + 1.19225i
\(551\) 592.491 1.07530
\(552\) 282.743 + 282.743i 0.512216 + 0.512216i
\(553\) −123.691 + 123.691i −0.223672 + 0.223672i
\(554\) 917.575i 1.65627i
\(555\) −324.879 + 213.032i −0.585368 + 0.383841i
\(556\) 1545.19 2.77912
\(557\) −74.4003 74.4003i −0.133573 0.133573i 0.637159 0.770732i \(-0.280109\pi\)
−0.770732 + 0.637159i \(0.780109\pi\)
\(558\) 93.3704 93.3704i 0.167331 0.167331i
\(559\) 83.5057i 0.149384i
\(560\) 159.199 + 33.1022i 0.284284 + 0.0591111i
\(561\) −363.442 −0.647848
\(562\) −148.034 148.034i −0.263406 0.263406i
\(563\) −340.172 + 340.172i −0.604214 + 0.604214i −0.941428 0.337214i \(-0.890515\pi\)
0.337214 + 0.941428i \(0.390515\pi\)
\(564\) 82.9975i 0.147159i
\(565\) −154.520 + 743.135i −0.273486 + 1.31528i
\(566\) −852.747 −1.50662
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) 141.904 141.904i 0.249831 0.249831i
\(569\) 672.360i 1.18165i 0.806799 + 0.590826i \(0.201198\pi\)
−0.806799 + 0.590826i \(0.798802\pi\)
\(570\) −242.672 370.082i −0.425741 0.649267i
\(571\) 613.562 1.07454 0.537269 0.843411i \(-0.319456\pi\)
0.537269 + 0.843411i \(0.319456\pi\)
\(572\) 1502.44 + 1502.44i 2.62664 + 2.62664i
\(573\) 36.6470 36.6470i 0.0639563 0.0639563i
\(574\) 628.062i 1.09418i
\(575\) −168.109 426.599i −0.292363 0.741911i
\(576\) 232.968 0.404458
\(577\) −81.3337 81.3337i −0.140960 0.140960i 0.633106 0.774065i \(-0.281780\pi\)
−0.774065 + 0.633106i \(0.781780\pi\)
\(578\) 455.584 455.584i 0.788208 0.788208i
\(579\) 104.205i 0.179975i
\(580\) −1273.01 + 834.746i −2.19485 + 1.43922i
\(581\) 313.081 0.538865
\(582\) −505.901 505.901i −0.869246 0.869246i
\(583\) 1015.82 1015.82i 1.74241 1.74241i
\(584\) 577.028i 0.988061i
\(585\) 194.049 + 40.3484i 0.331707 + 0.0689717i
\(586\) −448.289 −0.764999
\(587\) 819.321 + 819.321i 1.39578 + 1.39578i 0.811694 + 0.584082i \(0.198546\pi\)
0.584082 + 0.811694i \(0.301454\pi\)
\(588\) −65.8644 + 65.8644i −0.112014 + 0.112014i
\(589\) 192.529i 0.326874i
\(590\) −102.373 + 492.347i −0.173514 + 0.834486i
\(591\) 610.151 1.03240
\(592\) 389.900 + 389.900i 0.658615 + 0.658615i
\(593\) −308.110 + 308.110i −0.519578 + 0.519578i −0.917444 0.397865i \(-0.869751\pi\)
0.397865 + 0.917444i \(0.369751\pi\)
\(594\) 371.746i 0.625835i
\(595\) −72.7205 110.901i −0.122219 0.186388i
\(596\) −178.521 −0.299532
\(597\) 20.5203 + 20.5203i 0.0343724 + 0.0343724i
\(598\) −585.720 + 585.720i −0.979464 + 0.979464i
\(599\) 458.753i 0.765864i 0.923776 + 0.382932i \(0.125086\pi\)
−0.923776 + 0.382932i \(0.874914\pi\)
\(600\) 499.857 + 217.263i 0.833095 + 0.362106i
\(601\) 829.765 1.38064 0.690320 0.723504i \(-0.257470\pi\)
0.690320 + 0.723504i \(0.257470\pi\)
\(602\) −40.4119 40.4119i −0.0671294 0.0671294i
\(603\) −4.19401 + 4.19401i −0.00695524 + 0.00695524i
\(604\) 302.322i 0.500534i
\(605\) 1325.94 869.454i 2.19164 1.43711i
\(606\) 862.214 1.42279
\(607\) −249.775 249.775i −0.411490 0.411490i 0.470767 0.882258i \(-0.343977\pi\)
−0.882258 + 0.470767i \(0.843977\pi\)
\(608\) 88.1163 88.1163i 0.144928 0.144928i
\(609\) 181.605i 0.298203i
\(610\) 118.679 + 24.6769i 0.194556 + 0.0404540i
\(611\) 82.4152 0.134886
\(612\) 163.378 + 163.378i 0.266958 + 0.266958i
\(613\) 90.9769 90.9769i 0.148413 0.148413i −0.628996 0.777409i \(-0.716534\pi\)
0.777409 + 0.628996i \(0.216534\pi\)
\(614\) 1106.29i 1.80177i
\(615\) 122.445 588.876i 0.199097 0.957522i
\(616\) −697.053 −1.13158
\(617\) −445.593 445.593i −0.722193 0.722193i 0.246858 0.969052i \(-0.420602\pi\)
−0.969052 + 0.246858i \(0.920602\pi\)
\(618\) 368.555 368.555i 0.596367 0.596367i
\(619\) 943.969i 1.52499i 0.646994 + 0.762495i \(0.276026\pi\)
−0.646994 + 0.762495i \(0.723974\pi\)
\(620\) 271.249 + 413.663i 0.437499 + 0.667198i
\(621\) −95.3031 −0.153467
\(622\) 703.595 + 703.595i 1.13118 + 1.13118i
\(623\) 117.392 117.392i 0.188430 0.188430i
\(624\) 281.309i 0.450816i
\(625\) −426.373 456.980i −0.682197 0.731169i
\(626\) 1216.50 1.94329
\(627\) 383.268 + 383.268i 0.611273 + 0.611273i
\(628\) −393.058 + 393.058i −0.625889 + 0.625889i
\(629\) 449.713i 0.714965i
\(630\) −113.435 + 74.3819i −0.180055 + 0.118067i
\(631\) −1001.49 −1.58714 −0.793570 0.608478i \(-0.791780\pi\)
−0.793570 + 0.608478i \(0.791780\pi\)
\(632\) 588.451 + 588.451i 0.931093 + 0.931093i
\(633\) 94.3392 94.3392i 0.149035 0.149035i
\(634\) 146.985i 0.231837i
\(635\) −807.576 167.919i −1.27177 0.264439i
\(636\) −913.284 −1.43598
\(637\) −65.4023 65.4023i −0.102672 0.102672i
\(638\) 2004.79 2004.79i 3.14230 3.14230i
\(639\) 47.8310i 0.0748529i
\(640\) −236.235 + 1136.13i −0.369118 + 1.77521i
\(641\) −878.051 −1.36981 −0.684907 0.728630i \(-0.740157\pi\)
−0.684907 + 0.728630i \(0.740157\pi\)
\(642\) −24.6164 24.6164i −0.0383433 0.0383433i
\(643\) −551.380 + 551.380i −0.857511 + 0.857511i −0.991044 0.133533i \(-0.957368\pi\)
0.133533 + 0.991044i \(0.457368\pi\)
\(644\) 372.805i 0.578889i
\(645\) −30.0119 45.7691i −0.0465301 0.0709598i
\(646\) 512.286 0.793012
\(647\) 315.391 + 315.391i 0.487466 + 0.487466i 0.907506 0.420039i \(-0.137984\pi\)
−0.420039 + 0.907506i \(0.637984\pi\)
\(648\) 80.1031 80.1031i 0.123616 0.123616i
\(649\) 615.911i 0.949015i
\(650\) −450.074 + 1035.48i −0.692421 + 1.59305i
\(651\) −59.0124 −0.0906489
\(652\) −309.457 309.457i −0.474628 0.474628i
\(653\) −825.176 + 825.176i −1.26367 + 1.26367i −0.314368 + 0.949301i \(0.601793\pi\)
−0.949301 + 0.314368i \(0.898207\pi\)
\(654\) 465.526i 0.711814i
\(655\) 584.621 383.351i 0.892552 0.585269i
\(656\) −853.684 −1.30135
\(657\) −97.2481 97.2481i −0.148018 0.148018i
\(658\) −39.8842 + 39.8842i −0.0606143 + 0.0606143i
\(659\) 956.471i 1.45140i −0.688012 0.725699i \(-0.741517\pi\)
0.688012 0.725699i \(-0.258483\pi\)
\(660\) −1363.46 283.503i −2.06584 0.429550i
\(661\) 18.2815 0.0276573 0.0138286 0.999904i \(-0.495598\pi\)
0.0138286 + 0.999904i \(0.495598\pi\)
\(662\) −1452.30 1452.30i −2.19380 2.19380i
\(663\) −162.232 + 162.232i −0.244694 + 0.244694i
\(664\) 1489.46i 2.24316i
\(665\) −40.2631 + 193.638i −0.0605460 + 0.291185i
\(666\) −459.988 −0.690672
\(667\) 513.960 + 513.960i 0.770555 + 0.770555i
\(668\) 514.713 514.713i 0.770528 0.770528i
\(669\) 108.176i 0.161697i
\(670\) −18.5276 28.2552i −0.0276532 0.0421719i
\(671\) −148.464 −0.221258
\(672\) −27.0087 27.0087i −0.0401915 0.0401915i
\(673\) −829.059 + 829.059i −1.23189 + 1.23189i −0.268647 + 0.963239i \(0.586576\pi\)
−0.963239 + 0.268647i \(0.913424\pi\)
\(674\) 88.8173i 0.131776i
\(675\) −120.858 + 47.6263i −0.179049 + 0.0705575i
\(676\) 42.9491 0.0635342
\(677\) −421.712 421.712i −0.622913 0.622913i 0.323362 0.946275i \(-0.395187\pi\)
−0.946275 + 0.323362i \(0.895187\pi\)
\(678\) −635.483 + 635.483i −0.937290 + 0.937290i
\(679\) 319.742i 0.470901i
\(680\) −527.603 + 345.963i −0.775887 + 0.508769i
\(681\) −432.335 −0.634853
\(682\) −651.453 651.453i −0.955209 0.955209i
\(683\) −40.2821 + 40.2821i −0.0589782 + 0.0589782i −0.735981 0.677003i \(-0.763279\pi\)
0.677003 + 0.735981i \(0.263279\pi\)
\(684\) 344.581i 0.503773i
\(685\) −1115.43 231.931i −1.62836 0.338585i
\(686\) 63.3019 0.0922768
\(687\) 363.435 + 363.435i 0.529017 + 0.529017i
\(688\) −54.9293 + 54.9293i −0.0798390 + 0.0798390i
\(689\) 906.877i 1.31622i
\(690\) 110.522 531.538i 0.160177 0.770345i
\(691\) 499.429 0.722763 0.361381 0.932418i \(-0.382305\pi\)
0.361381 + 0.932418i \(0.382305\pi\)
\(692\) 1704.33 + 1704.33i 2.46290 + 2.46290i
\(693\) 117.476 117.476i 0.169518 0.169518i
\(694\) 1325.67i 1.91018i
\(695\) −551.445 840.969i −0.793446 1.21003i
\(696\) −863.976 −1.24134
\(697\) 492.322 + 492.322i 0.706344 + 0.706344i
\(698\) 529.285 529.285i 0.758287 0.758287i
\(699\) 215.959i 0.308955i
\(700\) −186.304 472.771i −0.266148 0.675387i
\(701\) 29.9935 0.0427867 0.0213934 0.999771i \(-0.493190\pi\)
0.0213934 + 0.999771i \(0.493190\pi\)
\(702\) 165.938 + 165.938i 0.236379 + 0.236379i
\(703\) −474.245 + 474.245i −0.674602 + 0.674602i
\(704\) 1625.44i 2.30886i
\(705\) −45.1714 + 29.6200i −0.0640729 + 0.0420143i
\(706\) 372.401 0.527480
\(707\) −272.470 272.470i −0.385389 0.385389i
\(708\) −276.870 + 276.870i −0.391059 + 0.391059i
\(709\) 983.508i 1.38718i −0.720372 0.693588i \(-0.756029\pi\)
0.720372 0.693588i \(-0.243971\pi\)
\(710\) −266.770 55.4694i −0.375732 0.0781259i
\(711\) −198.347 −0.278968
\(712\) −558.485 558.485i −0.784389 0.784389i
\(713\) 167.011 167.011i 0.234236 0.234236i
\(714\) 157.022i 0.219918i
\(715\) 281.514 1353.89i 0.393726 1.89356i
\(716\) −992.644 −1.38637
\(717\) −453.546 453.546i −0.632561 0.632561i
\(718\) −1287.50 + 1287.50i −1.79318 + 1.79318i
\(719\) 59.3020i 0.0824784i 0.999149 + 0.0412392i \(0.0131306\pi\)
−0.999149 + 0.0412392i \(0.986869\pi\)
\(720\) 101.103 + 154.184i 0.140420 + 0.214145i
\(721\) −232.936 −0.323073
\(722\) 332.261 + 332.261i 0.460196 + 0.460196i
\(723\) −247.781 + 247.781i −0.342713 + 0.342713i
\(724\) 221.566i 0.306030i
\(725\) 908.621 + 394.933i 1.25327 + 0.544735i
\(726\) 1877.37 2.58590
\(727\) −25.0937 25.0937i −0.0345168 0.0345168i 0.689638 0.724155i \(-0.257770\pi\)
−0.724155 + 0.689638i \(0.757770\pi\)
\(728\) −311.147 + 311.147i −0.427400 + 0.427400i
\(729\) 27.0000i 0.0370370i
\(730\) 655.164 429.608i 0.897485 0.588504i
\(731\) 63.3557 0.0866699
\(732\) 66.7390 + 66.7390i 0.0911734 + 0.0911734i
\(733\) 611.839 611.839i 0.834706 0.834706i −0.153451 0.988156i \(-0.549039\pi\)
0.988156 + 0.153451i \(0.0490386\pi\)
\(734\) 1776.20i 2.41990i
\(735\) 59.3523 + 12.3411i 0.0807514 + 0.0167906i
\(736\) 152.874 0.207709
\(737\) 29.2619 + 29.2619i 0.0397041 + 0.0397041i
\(738\) 503.570 503.570i 0.682344 0.682344i
\(739\) 566.278i 0.766277i 0.923691 + 0.383138i \(0.125157\pi\)
−0.923691 + 0.383138i \(0.874843\pi\)
\(740\) 350.799 1687.10i 0.474052 2.27987i
\(741\) 342.163 0.461759
\(742\) 438.876 + 438.876i 0.591477 + 0.591477i
\(743\) 65.5539 65.5539i 0.0882287 0.0882287i −0.661615 0.749844i \(-0.730129\pi\)
0.749844 + 0.661615i \(0.230129\pi\)
\(744\) 280.748i 0.377349i
\(745\) 63.7103 + 97.1600i 0.0855172 + 0.130416i
\(746\) 145.845 0.195503
\(747\) 251.023 + 251.023i 0.336042 + 0.336042i
\(748\) 1139.90 1139.90i 1.52393 1.52393i
\(749\) 15.5582i 0.0207719i
\(750\) −125.469 729.300i −0.167293 0.972400i
\(751\) −99.3347 −0.132270 −0.0661350 0.997811i \(-0.521067\pi\)
−0.0661350 + 0.997811i \(0.521067\pi\)
\(752\) 54.2120 + 54.2120i 0.0720904 + 0.0720904i
\(753\) −439.573 + 439.573i −0.583763 + 0.583763i
\(754\) 1789.78i 2.37371i
\(755\) −164.539 + 107.892i −0.217932 + 0.142904i
\(756\) −105.618 −0.139706
\(757\) 605.866 + 605.866i 0.800351 + 0.800351i 0.983150 0.182799i \(-0.0585159\pi\)
−0.182799 + 0.983150i \(0.558516\pi\)
\(758\) −616.058 + 616.058i −0.812741 + 0.812741i
\(759\) 664.937i 0.876070i
\(760\) 921.220 + 191.549i 1.21213 + 0.252038i
\(761\) 126.096 0.165698 0.0828489 0.996562i \(-0.473598\pi\)
0.0828489 + 0.996562i \(0.473598\pi\)
\(762\) −690.589 690.589i −0.906285 0.906285i
\(763\) 147.112 147.112i 0.192807 0.192807i
\(764\) 229.879i 0.300889i
\(765\) 30.6124 147.225i 0.0400161 0.192451i
\(766\) 506.273 0.660931
\(767\) −274.927 274.927i −0.358445 0.358445i
\(768\) −591.114 + 591.114i −0.769679 + 0.769679i
\(769\) 115.901i 0.150716i 0.997157 + 0.0753582i \(0.0240100\pi\)
−0.997157 + 0.0753582i \(0.975990\pi\)
\(770\) 518.969 + 791.442i 0.673985 + 1.02785i
\(771\) −386.887 −0.501799
\(772\) −326.830 326.830i −0.423355 0.423355i
\(773\)