Properties

Label 690.3.k.a.277.16
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.16
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-3.81857 + 3.22778i) q^{5} +2.44949 q^{6} +(3.99090 + 3.99090i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-3.81857 + 3.22778i) q^{5} +2.44949 q^{6} +(3.99090 + 3.99090i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-7.04634 - 0.590789i) q^{10} -16.7051 q^{11} +(2.44949 + 2.44949i) q^{12} +(-7.41164 + 7.41164i) q^{13} +7.98180i q^{14} +(-0.723566 + 8.62997i) q^{15} -4.00000 q^{16} +(-17.8517 - 17.8517i) q^{17} +(3.00000 - 3.00000i) q^{18} -18.0208i q^{19} +(-6.45555 - 7.63713i) q^{20} +9.77567 q^{21} +(-16.7051 - 16.7051i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(4.16290 - 24.6510i) q^{25} -14.8233 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-7.98180 + 7.98180i) q^{28} +17.7682i q^{29} +(-9.35354 + 7.90641i) q^{30} +2.15176 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-20.4595 + 20.4595i) q^{33} -35.7035i q^{34} +(-28.1212 - 2.35778i) q^{35} +6.00000 q^{36} +(34.1454 + 34.1454i) q^{37} +(18.0208 - 18.0208i) q^{38} +18.1547i q^{39} +(1.18158 - 14.0927i) q^{40} -55.9915 q^{41} +(9.77567 + 9.77567i) q^{42} +(-25.9837 + 25.9837i) q^{43} -33.4103i q^{44} +(9.68333 + 11.4557i) q^{45} +6.78233 q^{46} +(-1.36218 - 1.36218i) q^{47} +(-4.89898 + 4.89898i) q^{48} -17.1454i q^{49} +(28.8139 - 20.4881i) q^{50} -43.7276 q^{51} +(-14.8233 - 14.8233i) q^{52} +(-17.0984 + 17.0984i) q^{53} -7.34847i q^{54} +(63.7897 - 53.9205i) q^{55} -15.9636 q^{56} +(-22.0709 - 22.0709i) q^{57} +(-17.7682 + 17.7682i) q^{58} -72.1392i q^{59} +(-17.2599 - 1.44713i) q^{60} -67.4506 q^{61} +(2.15176 + 2.15176i) q^{62} +(11.9727 - 11.9727i) q^{63} -8.00000i q^{64} +(4.37872 - 52.2250i) q^{65} -40.9191 q^{66} +(29.6984 + 29.6984i) q^{67} +(35.7035 - 35.7035i) q^{68} -8.30662i q^{69} +(-25.7635 - 30.4790i) q^{70} +21.4377 q^{71} +(6.00000 + 6.00000i) q^{72} +(-73.0874 + 73.0874i) q^{73} +68.2909i q^{74} +(-25.0927 - 35.2896i) q^{75} +36.0417 q^{76} +(-66.6685 - 66.6685i) q^{77} +(-18.1547 + 18.1547i) q^{78} +86.1320i q^{79} +(15.2743 - 12.9111i) q^{80} -9.00000 q^{81} +(-55.9915 - 55.9915i) q^{82} +(-105.066 + 105.066i) q^{83} +19.5513i q^{84} +(125.789 + 10.5466i) q^{85} -51.9673 q^{86} +(21.7615 + 21.7615i) q^{87} +(33.4103 - 33.4103i) q^{88} +86.6781i q^{89} +(-1.77237 + 21.1390i) q^{90} -59.1582 q^{91} +(6.78233 + 6.78233i) q^{92} +(2.63536 - 2.63536i) q^{93} -2.72436i q^{94} +(58.1672 + 68.8137i) q^{95} -9.79796 q^{96} +(-42.2382 - 42.2382i) q^{97} +(17.1454 - 17.1454i) q^{98} +50.1154i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −3.81857 + 3.22778i −0.763713 + 0.645555i
\(6\) 2.44949 0.408248
\(7\) 3.99090 + 3.99090i 0.570128 + 0.570128i 0.932164 0.362036i \(-0.117918\pi\)
−0.362036 + 0.932164i \(0.617918\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −7.04634 0.590789i −0.704634 0.0590789i
\(11\) −16.7051 −1.51865 −0.759325 0.650712i \(-0.774471\pi\)
−0.759325 + 0.650712i \(0.774471\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −7.41164 + 7.41164i −0.570126 + 0.570126i −0.932164 0.362037i \(-0.882081\pi\)
0.362037 + 0.932164i \(0.382081\pi\)
\(14\) 7.98180i 0.570128i
\(15\) −0.723566 + 8.62997i −0.0482377 + 0.575332i
\(16\) −4.00000 −0.250000
\(17\) −17.8517 17.8517i −1.05010 1.05010i −0.998677 0.0514253i \(-0.983624\pi\)
−0.0514253 0.998677i \(-0.516376\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 18.0208i 0.948465i −0.880400 0.474232i \(-0.842726\pi\)
0.880400 0.474232i \(-0.157274\pi\)
\(20\) −6.45555 7.63713i −0.322778 0.381857i
\(21\) 9.77567 0.465508
\(22\) −16.7051 16.7051i −0.759325 0.759325i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 4.16290 24.6510i 0.166516 0.986039i
\(26\) −14.8233 −0.570126
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −7.98180 + 7.98180i −0.285064 + 0.285064i
\(29\) 17.7682i 0.612695i 0.951920 + 0.306347i \(0.0991069\pi\)
−0.951920 + 0.306347i \(0.900893\pi\)
\(30\) −9.35354 + 7.90641i −0.311785 + 0.263547i
\(31\) 2.15176 0.0694117 0.0347059 0.999398i \(-0.488951\pi\)
0.0347059 + 0.999398i \(0.488951\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −20.4595 + 20.4595i −0.619986 + 0.619986i
\(34\) 35.7035i 1.05010i
\(35\) −28.1212 2.35778i −0.803464 0.0673652i
\(36\) 6.00000 0.166667
\(37\) 34.1454 + 34.1454i 0.922850 + 0.922850i 0.997230 0.0743802i \(-0.0236978\pi\)
−0.0743802 + 0.997230i \(0.523698\pi\)
\(38\) 18.0208 18.0208i 0.474232 0.474232i
\(39\) 18.1547i 0.465506i
\(40\) 1.18158 14.0927i 0.0295395 0.352317i
\(41\) −55.9915 −1.36565 −0.682823 0.730584i \(-0.739248\pi\)
−0.682823 + 0.730584i \(0.739248\pi\)
\(42\) 9.77567 + 9.77567i 0.232754 + 0.232754i
\(43\) −25.9837 + 25.9837i −0.604271 + 0.604271i −0.941443 0.337172i \(-0.890530\pi\)
0.337172 + 0.941443i \(0.390530\pi\)
\(44\) 33.4103i 0.759325i
\(45\) 9.68333 + 11.4557i 0.215185 + 0.254571i
\(46\) 6.78233 0.147442
\(47\) −1.36218 1.36218i −0.0289826 0.0289826i 0.692467 0.721450i \(-0.256524\pi\)
−0.721450 + 0.692467i \(0.756524\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 17.1454i 0.349907i
\(50\) 28.8139 20.4881i 0.576277 0.409761i
\(51\) −43.7276 −0.857405
\(52\) −14.8233 14.8233i −0.285063 0.285063i
\(53\) −17.0984 + 17.0984i −0.322612 + 0.322612i −0.849768 0.527156i \(-0.823258\pi\)
0.527156 + 0.849768i \(0.323258\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 63.7897 53.9205i 1.15981 0.980372i
\(56\) −15.9636 −0.285064
\(57\) −22.0709 22.0709i −0.387209 0.387209i
\(58\) −17.7682 + 17.7682i −0.306347 + 0.306347i
\(59\) 72.1392i 1.22270i −0.791361 0.611349i \(-0.790627\pi\)
0.791361 0.611349i \(-0.209373\pi\)
\(60\) −17.2599 1.44713i −0.287666 0.0241189i
\(61\) −67.4506 −1.10575 −0.552874 0.833265i \(-0.686469\pi\)
−0.552874 + 0.833265i \(0.686469\pi\)
\(62\) 2.15176 + 2.15176i 0.0347059 + 0.0347059i
\(63\) 11.9727 11.9727i 0.190043 0.190043i
\(64\) 8.00000i 0.125000i
\(65\) 4.37872 52.2250i 0.0673649 0.803461i
\(66\) −40.9191 −0.619986
\(67\) 29.6984 + 29.6984i 0.443259 + 0.443259i 0.893106 0.449846i \(-0.148521\pi\)
−0.449846 + 0.893106i \(0.648521\pi\)
\(68\) 35.7035 35.7035i 0.525051 0.525051i
\(69\) 8.30662i 0.120386i
\(70\) −25.7635 30.4790i −0.368050 0.435415i
\(71\) 21.4377 0.301939 0.150969 0.988538i \(-0.451760\pi\)
0.150969 + 0.988538i \(0.451760\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −73.0874 + 73.0874i −1.00120 + 1.00120i −0.00119781 + 0.999999i \(0.500381\pi\)
−0.999999 + 0.00119781i \(0.999619\pi\)
\(74\) 68.2909i 0.922850i
\(75\) −25.0927 35.2896i −0.334569 0.470529i
\(76\) 36.0417 0.474232
\(77\) −66.6685 66.6685i −0.865825 0.865825i
\(78\) −18.1547 + 18.1547i −0.232753 + 0.232753i
\(79\) 86.1320i 1.09028i 0.838346 + 0.545139i \(0.183523\pi\)
−0.838346 + 0.545139i \(0.816477\pi\)
\(80\) 15.2743 12.9111i 0.190928 0.161389i
\(81\) −9.00000 −0.111111
\(82\) −55.9915 55.9915i −0.682823 0.682823i
\(83\) −105.066 + 105.066i −1.26585 + 1.26585i −0.317640 + 0.948211i \(0.602890\pi\)
−0.948211 + 0.317640i \(0.897110\pi\)
\(84\) 19.5513i 0.232754i
\(85\) 125.789 + 10.5466i 1.47988 + 0.124078i
\(86\) −51.9673 −0.604271
\(87\) 21.7615 + 21.7615i 0.250132 + 0.250132i
\(88\) 33.4103 33.4103i 0.379662 0.379662i
\(89\) 86.6781i 0.973911i 0.873427 + 0.486955i \(0.161893\pi\)
−0.873427 + 0.486955i \(0.838107\pi\)
\(90\) −1.77237 + 21.1390i −0.0196930 + 0.234878i
\(91\) −59.1582 −0.650090
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 2.63536 2.63536i 0.0283372 0.0283372i
\(94\) 2.72436i 0.0289826i
\(95\) 58.1672 + 68.8137i 0.612287 + 0.724355i
\(96\) −9.79796 −0.102062
\(97\) −42.2382 42.2382i −0.435445 0.435445i 0.455031 0.890476i \(-0.349628\pi\)
−0.890476 + 0.455031i \(0.849628\pi\)
\(98\) 17.1454 17.1454i 0.174954 0.174954i
\(99\) 50.1154i 0.506216i
\(100\) 49.3019 + 8.32581i 0.493019 + 0.0832581i
\(101\) 61.6323 0.610221 0.305111 0.952317i \(-0.401307\pi\)
0.305111 + 0.952317i \(0.401307\pi\)
\(102\) −43.7276 43.7276i −0.428702 0.428702i
\(103\) 10.6060 10.6060i 0.102971 0.102971i −0.653744 0.756715i \(-0.726803\pi\)
0.756715 + 0.653744i \(0.226803\pi\)
\(104\) 29.6466i 0.285063i
\(105\) −37.3290 + 31.5537i −0.355515 + 0.300511i
\(106\) −34.1969 −0.322612
\(107\) 11.9686 + 11.9686i 0.111856 + 0.111856i 0.760819 0.648964i \(-0.224797\pi\)
−0.648964 + 0.760819i \(0.724797\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 36.7920i 0.337541i 0.985655 + 0.168771i \(0.0539797\pi\)
−0.985655 + 0.168771i \(0.946020\pi\)
\(110\) 117.710 + 9.86922i 1.07009 + 0.0897202i
\(111\) 83.6389 0.753504
\(112\) −15.9636 15.9636i −0.142532 0.142532i
\(113\) 45.2853 45.2853i 0.400755 0.400755i −0.477744 0.878499i \(-0.658545\pi\)
0.878499 + 0.477744i \(0.158545\pi\)
\(114\) 44.1418i 0.387209i
\(115\) −2.00346 + 23.8953i −0.0174214 + 0.207785i
\(116\) −35.5363 −0.306347
\(117\) 22.2349 + 22.2349i 0.190042 + 0.190042i
\(118\) 72.1392 72.1392i 0.611349 0.611349i
\(119\) 142.489i 1.19739i
\(120\) −15.8128 18.7071i −0.131773 0.155892i
\(121\) 158.062 1.30630
\(122\) −67.4506 67.4506i −0.552874 0.552874i
\(123\) −68.5753 + 68.5753i −0.557523 + 0.557523i
\(124\) 4.30353i 0.0347059i
\(125\) 63.6715 + 107.568i 0.509372 + 0.860546i
\(126\) 23.9454 0.190043
\(127\) 107.150 + 107.150i 0.843701 + 0.843701i 0.989338 0.145637i \(-0.0465231\pi\)
−0.145637 + 0.989338i \(0.546523\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 63.6467i 0.493385i
\(130\) 56.6037 47.8462i 0.435413 0.368048i
\(131\) 160.837 1.22776 0.613881 0.789399i \(-0.289608\pi\)
0.613881 + 0.789399i \(0.289608\pi\)
\(132\) −40.9191 40.9191i −0.309993 0.309993i
\(133\) 71.9193 71.9193i 0.540747 0.540747i
\(134\) 59.3968i 0.443259i
\(135\) 25.8899 + 2.17070i 0.191777 + 0.0160792i
\(136\) 71.4069 0.525051
\(137\) −185.661 185.661i −1.35519 1.35519i −0.879748 0.475441i \(-0.842288\pi\)
−0.475441 0.879748i \(-0.657712\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 130.439i 0.938412i 0.883089 + 0.469206i \(0.155460\pi\)
−0.883089 + 0.469206i \(0.844540\pi\)
\(140\) 4.71556 56.2425i 0.0336826 0.401732i
\(141\) −3.33665 −0.0236642
\(142\) 21.4377 + 21.4377i 0.150969 + 0.150969i
\(143\) 123.812 123.812i 0.865822 0.865822i
\(144\) 12.0000i 0.0833333i
\(145\) −57.3517 67.8489i −0.395529 0.467923i
\(146\) −146.175 −1.00120
\(147\) −20.9988 20.9988i −0.142849 0.142849i
\(148\) −68.2909 + 68.2909i −0.461425 + 0.461425i
\(149\) 5.80879i 0.0389852i 0.999810 + 0.0194926i \(0.00620507\pi\)
−0.999810 + 0.0194926i \(0.993795\pi\)
\(150\) 10.1970 60.3823i 0.0679800 0.402549i
\(151\) −118.863 −0.787173 −0.393587 0.919288i \(-0.628766\pi\)
−0.393587 + 0.919288i \(0.628766\pi\)
\(152\) 36.0417 + 36.0417i 0.237116 + 0.237116i
\(153\) −53.5552 + 53.5552i −0.350034 + 0.350034i
\(154\) 133.337i 0.865825i
\(155\) −8.21665 + 6.94541i −0.0530107 + 0.0448091i
\(156\) −36.3095 −0.232753
\(157\) 16.2859 + 16.2859i 0.103732 + 0.103732i 0.757068 0.653336i \(-0.226631\pi\)
−0.653336 + 0.757068i \(0.726631\pi\)
\(158\) −86.1320 + 86.1320i −0.545139 + 0.545139i
\(159\) 41.8824i 0.263412i
\(160\) 28.1854 + 2.36316i 0.176159 + 0.0147697i
\(161\) 27.0676 0.168122
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 126.235 126.235i 0.774448 0.774448i −0.204432 0.978881i \(-0.565535\pi\)
0.978881 + 0.204432i \(0.0655349\pi\)
\(164\) 111.983i 0.682823i
\(165\) 12.0873 144.165i 0.0732562 0.873727i
\(166\) −210.131 −1.26585
\(167\) 72.1438 + 72.1438i 0.431999 + 0.431999i 0.889308 0.457309i \(-0.151187\pi\)
−0.457309 + 0.889308i \(0.651187\pi\)
\(168\) −19.5513 + 19.5513i −0.116377 + 0.116377i
\(169\) 59.1352i 0.349912i
\(170\) 115.243 + 136.336i 0.677899 + 0.801977i
\(171\) −54.0625 −0.316155
\(172\) −51.9673 51.9673i −0.302136 0.302136i
\(173\) −109.972 + 109.972i −0.635679 + 0.635679i −0.949487 0.313808i \(-0.898395\pi\)
0.313808 + 0.949487i \(0.398395\pi\)
\(174\) 43.5229i 0.250132i
\(175\) 114.993 81.7658i 0.657104 0.467233i
\(176\) 66.8206 0.379662
\(177\) −88.3521 88.3521i −0.499165 0.499165i
\(178\) −86.6781 + 86.6781i −0.486955 + 0.486955i
\(179\) 4.73899i 0.0264748i −0.999912 0.0132374i \(-0.995786\pi\)
0.999912 0.0132374i \(-0.00421372\pi\)
\(180\) −22.9114 + 19.3667i −0.127286 + 0.107593i
\(181\) 39.1292 0.216183 0.108092 0.994141i \(-0.465526\pi\)
0.108092 + 0.994141i \(0.465526\pi\)
\(182\) −59.1582 59.1582i −0.325045 0.325045i
\(183\) −82.6098 + 82.6098i −0.451420 + 0.451420i
\(184\) 13.5647i 0.0737210i
\(185\) −240.601 20.1728i −1.30054 0.109042i
\(186\) 5.27072 0.0283372
\(187\) 298.216 + 298.216i 1.59474 + 1.59474i
\(188\) 2.72436 2.72436i 0.0144913 0.0144913i
\(189\) 29.3270i 0.155169i
\(190\) −10.6465 + 126.981i −0.0560343 + 0.668321i
\(191\) −230.340 −1.20597 −0.602984 0.797753i \(-0.706022\pi\)
−0.602984 + 0.797753i \(0.706022\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 187.139 187.139i 0.969631 0.969631i −0.0299208 0.999552i \(-0.509526\pi\)
0.999552 + 0.0299208i \(0.00952551\pi\)
\(194\) 84.4763i 0.435445i
\(195\) −58.5994 69.3251i −0.300510 0.355513i
\(196\) 34.2909 0.174954
\(197\) 87.8443 + 87.8443i 0.445910 + 0.445910i 0.893992 0.448082i \(-0.147893\pi\)
−0.448082 + 0.893992i \(0.647893\pi\)
\(198\) −50.1154 + 50.1154i −0.253108 + 0.253108i
\(199\) 211.873i 1.06469i −0.846528 0.532344i \(-0.821311\pi\)
0.846528 0.532344i \(-0.178689\pi\)
\(200\) 40.9761 + 57.6277i 0.204881 + 0.288139i
\(201\) 72.7459 0.361920
\(202\) 61.6323 + 61.6323i 0.305111 + 0.305111i
\(203\) −70.9109 + 70.9109i −0.349315 + 0.349315i
\(204\) 87.4553i 0.428702i
\(205\) 213.807 180.728i 1.04296 0.881601i
\(206\) 21.2120 0.102971
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 29.6466 29.6466i 0.142532 0.142532i
\(209\) 301.041i 1.44039i
\(210\) −68.8827 5.77536i −0.328013 0.0275017i
\(211\) 103.501 0.490527 0.245264 0.969456i \(-0.421125\pi\)
0.245264 + 0.969456i \(0.421125\pi\)
\(212\) −34.1969 34.1969i −0.161306 0.161306i
\(213\) 26.2557 26.2557i 0.123266 0.123266i
\(214\) 23.9371i 0.111856i
\(215\) 15.3509 183.090i 0.0713994 0.851580i
\(216\) 14.6969 0.0680414
\(217\) 8.58747 + 8.58747i 0.0395736 + 0.0395736i
\(218\) −36.7920 + 36.7920i −0.168771 + 0.168771i
\(219\) 179.027i 0.817474i
\(220\) 107.841 + 127.579i 0.490186 + 0.579906i
\(221\) 264.621 1.19738
\(222\) 83.6389 + 83.6389i 0.376752 + 0.376752i
\(223\) 158.145 158.145i 0.709170 0.709170i −0.257191 0.966361i \(-0.582797\pi\)
0.966361 + 0.257191i \(0.0827969\pi\)
\(224\) 31.9272i 0.142532i
\(225\) −73.9529 12.4887i −0.328680 0.0555054i
\(226\) 90.5707 0.400755
\(227\) 45.6136 + 45.6136i 0.200941 + 0.200941i 0.800403 0.599462i \(-0.204619\pi\)
−0.599462 + 0.800403i \(0.704619\pi\)
\(228\) 44.1418 44.1418i 0.193605 0.193605i
\(229\) 178.009i 0.777334i 0.921378 + 0.388667i \(0.127064\pi\)
−0.921378 + 0.388667i \(0.872936\pi\)
\(230\) −25.8988 + 21.8919i −0.112603 + 0.0951820i
\(231\) −163.304 −0.706943
\(232\) −35.5363 35.5363i −0.153174 0.153174i
\(233\) 194.951 194.951i 0.836702 0.836702i −0.151722 0.988423i \(-0.548482\pi\)
0.988423 + 0.151722i \(0.0484817\pi\)
\(234\) 44.4698i 0.190042i
\(235\) 9.59839 + 0.804762i 0.0408442 + 0.00342452i
\(236\) 144.278 0.611349
\(237\) 105.490 + 105.490i 0.445104 + 0.445104i
\(238\) 142.489 142.489i 0.598693 0.598693i
\(239\) 82.5568i 0.345426i 0.984972 + 0.172713i \(0.0552533\pi\)
−0.984972 + 0.172713i \(0.944747\pi\)
\(240\) 2.89426 34.5199i 0.0120594 0.143833i
\(241\) 108.909 0.451904 0.225952 0.974138i \(-0.427451\pi\)
0.225952 + 0.974138i \(0.427451\pi\)
\(242\) 158.062 + 158.062i 0.653148 + 0.653148i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 134.901i 0.552874i
\(245\) 55.3417 + 65.4710i 0.225884 + 0.267229i
\(246\) −137.151 −0.557523
\(247\) 133.564 + 133.564i 0.540744 + 0.540744i
\(248\) −4.30353 + 4.30353i −0.0173529 + 0.0173529i
\(249\) 257.357i 1.03356i
\(250\) −43.8968 + 171.240i −0.175587 + 0.684959i
\(251\) −421.149 −1.67788 −0.838941 0.544222i \(-0.816825\pi\)
−0.838941 + 0.544222i \(0.816825\pi\)
\(252\) 23.9454 + 23.9454i 0.0950214 + 0.0950214i
\(253\) −56.6499 + 56.6499i −0.223913 + 0.223913i
\(254\) 214.300i 0.843701i
\(255\) 166.977 141.143i 0.654812 0.553502i
\(256\) 16.0000 0.0625000
\(257\) −93.7588 93.7588i −0.364820 0.364820i 0.500764 0.865584i \(-0.333053\pi\)
−0.865584 + 0.500764i \(0.833053\pi\)
\(258\) −63.6467 + 63.6467i −0.246693 + 0.246693i
\(259\) 272.542i 1.05229i
\(260\) 104.450 + 8.75743i 0.401731 + 0.0336824i
\(261\) 53.3045 0.204232
\(262\) 160.837 + 160.837i 0.613881 + 0.613881i
\(263\) −237.440 + 237.440i −0.902815 + 0.902815i −0.995679 0.0928643i \(-0.970398\pi\)
0.0928643 + 0.995679i \(0.470398\pi\)
\(264\) 81.8381i 0.309993i
\(265\) 10.1016 120.481i 0.0381191 0.454647i
\(266\) 143.839 0.540747
\(267\) 106.159 + 106.159i 0.397597 + 0.397597i
\(268\) −59.3968 + 59.3968i −0.221630 + 0.221630i
\(269\) 66.0224i 0.245436i 0.992442 + 0.122718i \(0.0391611\pi\)
−0.992442 + 0.122718i \(0.960839\pi\)
\(270\) 23.7192 + 28.0606i 0.0878490 + 0.103928i
\(271\) −301.309 −1.11184 −0.555920 0.831236i \(-0.687634\pi\)
−0.555920 + 0.831236i \(0.687634\pi\)
\(272\) 71.4069 + 71.4069i 0.262526 + 0.262526i
\(273\) −72.4537 + 72.4537i −0.265398 + 0.265398i
\(274\) 371.322i 1.35519i
\(275\) −69.5419 + 411.798i −0.252880 + 1.49745i
\(276\) 16.6132 0.0601929
\(277\) −237.920 237.920i −0.858918 0.858918i 0.132293 0.991211i \(-0.457766\pi\)
−0.991211 + 0.132293i \(0.957766\pi\)
\(278\) −130.439 + 130.439i −0.469206 + 0.469206i
\(279\) 6.45529i 0.0231372i
\(280\) 60.9581 51.5269i 0.217707 0.184025i
\(281\) −307.240 −1.09338 −0.546691 0.837334i \(-0.684113\pi\)
−0.546691 + 0.837334i \(0.684113\pi\)
\(282\) −3.33665 3.33665i −0.0118321 0.0118321i
\(283\) 74.7029 74.7029i 0.263968 0.263968i −0.562696 0.826664i \(-0.690236\pi\)
0.826664 + 0.562696i \(0.190236\pi\)
\(284\) 42.8753i 0.150969i
\(285\) 155.519 + 13.0393i 0.545682 + 0.0457518i
\(286\) 247.625 0.865822
\(287\) −223.456 223.456i −0.778594 0.778594i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 348.369i 1.20543i
\(290\) 10.4972 125.201i 0.0361974 0.431726i
\(291\) −103.462 −0.355539
\(292\) −146.175 146.175i −0.500599 0.500599i
\(293\) 10.2341 10.2341i 0.0349285 0.0349285i −0.689427 0.724355i \(-0.742138\pi\)
0.724355 + 0.689427i \(0.242138\pi\)
\(294\) 41.9976i 0.142849i
\(295\) 232.849 + 275.468i 0.789320 + 0.933791i
\(296\) −136.582 −0.461425
\(297\) 61.3786 + 61.3786i 0.206662 + 0.206662i
\(298\) −5.80879 + 5.80879i −0.0194926 + 0.0194926i
\(299\) 50.2682i 0.168121i
\(300\) 70.5793 50.1853i 0.235264 0.167284i
\(301\) −207.396 −0.689024
\(302\) −118.863 118.863i −0.393587 0.393587i
\(303\) 75.4839 75.4839i 0.249122 0.249122i
\(304\) 72.0833i 0.237116i
\(305\) 257.565 217.716i 0.844475 0.713822i
\(306\) −107.110 −0.350034
\(307\) 370.463 + 370.463i 1.20672 + 1.20672i 0.972083 + 0.234638i \(0.0753906\pi\)
0.234638 + 0.972083i \(0.424609\pi\)
\(308\) 133.337 133.337i 0.432913 0.432913i
\(309\) 25.9793i 0.0840754i
\(310\) −15.1621 1.27124i −0.0489099 0.00410077i
\(311\) −121.488 −0.390637 −0.195319 0.980740i \(-0.562574\pi\)
−0.195319 + 0.980740i \(0.562574\pi\)
\(312\) −36.3095 36.3095i −0.116377 0.116377i
\(313\) 424.047 424.047i 1.35478 1.35478i 0.474560 0.880223i \(-0.342607\pi\)
0.880223 0.474560i \(-0.157393\pi\)
\(314\) 32.5719i 0.103732i
\(315\) −7.07334 + 84.3637i −0.0224551 + 0.267821i
\(316\) −172.264 −0.545139
\(317\) 302.071 + 302.071i 0.952906 + 0.952906i 0.998940 0.0460337i \(-0.0146582\pi\)
−0.0460337 + 0.998940i \(0.514658\pi\)
\(318\) −41.8824 + 41.8824i −0.131706 + 0.131706i
\(319\) 296.820i 0.930469i
\(320\) 25.8222 + 30.5485i 0.0806944 + 0.0954642i
\(321\) 29.3168 0.0913297
\(322\) 27.0676 + 27.0676i 0.0840609 + 0.0840609i
\(323\) −321.703 + 321.703i −0.995985 + 0.995985i
\(324\) 18.0000i 0.0555556i
\(325\) 151.850 + 213.558i 0.467231 + 0.657102i
\(326\) 252.470 0.774448
\(327\) 45.0608 + 45.0608i 0.137801 + 0.137801i
\(328\) 111.983 111.983i 0.341412 0.341412i
\(329\) 10.8726i 0.0330476i
\(330\) 156.252 132.078i 0.473492 0.400235i
\(331\) −578.605 −1.74805 −0.874026 0.485879i \(-0.838499\pi\)
−0.874026 + 0.485879i \(0.838499\pi\)
\(332\) −210.131 210.131i −0.632926 0.632926i
\(333\) 102.436 102.436i 0.307617 0.307617i
\(334\) 144.288i 0.431999i
\(335\) −209.265 17.5455i −0.624672 0.0523746i
\(336\) −39.1027 −0.116377
\(337\) −141.241 141.241i −0.419113 0.419113i 0.465785 0.884898i \(-0.345772\pi\)
−0.884898 + 0.465785i \(0.845772\pi\)
\(338\) −59.1352 + 59.1352i −0.174956 + 0.174956i
\(339\) 110.926i 0.327215i
\(340\) −21.0932 + 251.579i −0.0620389 + 0.739938i
\(341\) −35.9455 −0.105412
\(342\) −54.0625 54.0625i −0.158077 0.158077i
\(343\) 263.980 263.980i 0.769620 0.769620i
\(344\) 103.935i 0.302136i
\(345\) 26.8119 + 31.7194i 0.0777157 + 0.0919403i
\(346\) −219.945 −0.635679
\(347\) −351.519 351.519i −1.01302 1.01302i −0.999914 0.0131089i \(-0.995827\pi\)
−0.0131089 0.999914i \(-0.504173\pi\)
\(348\) −43.5229 + 43.5229i −0.125066 + 0.125066i
\(349\) 579.696i 1.66102i 0.557003 + 0.830510i \(0.311951\pi\)
−0.557003 + 0.830510i \(0.688049\pi\)
\(350\) 196.759 + 33.2275i 0.562169 + 0.0949356i
\(351\) 54.4642 0.155169
\(352\) 66.8206 + 66.8206i 0.189831 + 0.189831i
\(353\) 381.406 381.406i 1.08047 1.08047i 0.0840038 0.996465i \(-0.473229\pi\)
0.996465 0.0840038i \(-0.0267708\pi\)
\(354\) 176.704i 0.499165i
\(355\) −81.8611 + 69.1960i −0.230595 + 0.194918i
\(356\) −173.356 −0.486955
\(357\) −174.513 174.513i −0.488831 0.488831i
\(358\) 4.73899 4.73899i 0.0132374 0.0132374i
\(359\) 713.563i 1.98764i 0.111002 + 0.993820i \(0.464594\pi\)
−0.111002 + 0.993820i \(0.535406\pi\)
\(360\) −42.2781 3.54474i −0.117439 0.00984649i
\(361\) 36.2497 0.100415
\(362\) 39.1292 + 39.1292i 0.108092 + 0.108092i
\(363\) 193.585 193.585i 0.533293 0.533293i
\(364\) 118.316i 0.325045i
\(365\) 43.1792 514.999i 0.118299 1.41096i
\(366\) −165.220 −0.451420
\(367\) −501.508 501.508i −1.36651 1.36651i −0.865366 0.501140i \(-0.832914\pi\)
−0.501140 0.865366i \(-0.667086\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 167.975i 0.455215i
\(370\) −220.428 260.773i −0.595751 0.704793i
\(371\) −136.476 −0.367861
\(372\) 5.27072 + 5.27072i 0.0141686 + 0.0141686i
\(373\) 432.197 432.197i 1.15871 1.15871i 0.173952 0.984754i \(-0.444346\pi\)
0.984754 0.173952i \(-0.0556538\pi\)
\(374\) 596.432i 1.59474i
\(375\) 209.725 + 53.7624i 0.559267 + 0.143366i
\(376\) 5.44872 0.0144913
\(377\) −131.691 131.691i −0.349313 0.349313i
\(378\) 29.3270 29.3270i 0.0775847 0.0775847i
\(379\) 132.672i 0.350059i 0.984563 + 0.175029i \(0.0560020\pi\)
−0.984563 + 0.175029i \(0.943998\pi\)
\(380\) −137.627 + 116.334i −0.362178 + 0.306143i
\(381\) 262.463 0.688879
\(382\) −230.340 230.340i −0.602984 0.602984i
\(383\) −387.528 + 387.528i −1.01182 + 1.01182i −0.0118921 + 0.999929i \(0.503785\pi\)
−0.999929 + 0.0118921i \(0.996215\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 469.769 + 39.3871i 1.22018 + 0.102304i
\(386\) 374.278 0.969631
\(387\) 77.9510 + 77.9510i 0.201424 + 0.201424i
\(388\) 84.4763 84.4763i 0.217722 0.217722i
\(389\) 141.741i 0.364374i 0.983264 + 0.182187i \(0.0583175\pi\)
−0.983264 + 0.182187i \(0.941682\pi\)
\(390\) 10.7256 127.925i 0.0275016 0.328012i
\(391\) −121.076 −0.309658
\(392\) 34.2909 + 34.2909i 0.0874768 + 0.0874768i
\(393\) 196.984 196.984i 0.501231 0.501231i
\(394\) 175.689i 0.445910i
\(395\) −278.015 328.901i −0.703835 0.832660i
\(396\) −100.231 −0.253108
\(397\) −57.7135 57.7135i −0.145374 0.145374i 0.630674 0.776048i \(-0.282779\pi\)
−0.776048 + 0.630674i \(0.782779\pi\)
\(398\) 211.873 211.873i 0.532344 0.532344i
\(399\) 176.166i 0.441518i
\(400\) −16.6516 + 98.6039i −0.0416290 + 0.246510i
\(401\) 409.746 1.02181 0.510906 0.859637i \(-0.329310\pi\)
0.510906 + 0.859637i \(0.329310\pi\)
\(402\) 72.7459 + 72.7459i 0.180960 + 0.180960i
\(403\) −15.9481 + 15.9481i −0.0395734 + 0.0395734i
\(404\) 123.265i 0.305111i
\(405\) 34.3671 29.0500i 0.0848570 0.0717284i
\(406\) −141.822 −0.349315
\(407\) −570.404 570.404i −1.40149 1.40149i
\(408\) 87.4553 87.4553i 0.214351 0.214351i
\(409\) 664.563i 1.62485i −0.583066 0.812424i \(-0.698147\pi\)
0.583066 0.812424i \(-0.301853\pi\)
\(410\) 394.535 + 33.0792i 0.962281 + 0.0806809i
\(411\) −454.774 −1.10651
\(412\) 21.2120 + 21.2120i 0.0514855 + 0.0514855i
\(413\) 287.900 287.900i 0.697095 0.697095i
\(414\) 20.3470i 0.0491473i
\(415\) 62.0717 740.329i 0.149570 1.78392i
\(416\) 59.2931 0.142532
\(417\) 159.755 + 159.755i 0.383105 + 0.383105i
\(418\) −301.041 + 301.041i −0.720193 + 0.720193i
\(419\) 287.529i 0.686226i −0.939294 0.343113i \(-0.888519\pi\)
0.939294 0.343113i \(-0.111481\pi\)
\(420\) −63.1074 74.6581i −0.150256 0.177757i
\(421\) −363.794 −0.864118 −0.432059 0.901845i \(-0.642213\pi\)
−0.432059 + 0.901845i \(0.642213\pi\)
\(422\) 103.501 + 103.501i 0.245264 + 0.245264i
\(423\) −4.08654 + 4.08654i −0.00966085 + 0.00966085i
\(424\) 68.3938i 0.161306i
\(425\) −514.378 + 365.748i −1.21030 + 0.860582i
\(426\) 52.5113 0.123266
\(427\) −269.189 269.189i −0.630419 0.630419i
\(428\) −23.9371 + 23.9371i −0.0559278 + 0.0559278i
\(429\) 303.277i 0.706940i
\(430\) 198.441 167.739i 0.461490 0.390091i
\(431\) −833.171 −1.93311 −0.966556 0.256456i \(-0.917445\pi\)
−0.966556 + 0.256456i \(0.917445\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −365.422 + 365.422i −0.843930 + 0.843930i −0.989367 0.145437i \(-0.953541\pi\)
0.145437 + 0.989367i \(0.453541\pi\)
\(434\) 17.1749i 0.0395736i
\(435\) −153.339 12.8564i −0.352503 0.0295550i
\(436\) −73.5840 −0.168771
\(437\) −61.1116 61.1116i −0.139843 0.139843i
\(438\) −179.027 + 179.027i −0.408737 + 0.408737i
\(439\) 134.041i 0.305332i −0.988278 0.152666i \(-0.951214\pi\)
0.988278 0.152666i \(-0.0487859\pi\)
\(440\) −19.7384 + 235.420i −0.0448601 + 0.535046i
\(441\) −51.4363 −0.116636
\(442\) 264.621 + 264.621i 0.598691 + 0.598691i
\(443\) 423.762 423.762i 0.956572 0.956572i −0.0425232 0.999095i \(-0.513540\pi\)
0.999095 + 0.0425232i \(0.0135396\pi\)
\(444\) 167.278i 0.376752i
\(445\) −279.778 330.986i −0.628714 0.743789i
\(446\) 316.290 0.709170
\(447\) 7.11428 + 7.11428i 0.0159156 + 0.0159156i
\(448\) 31.9272 31.9272i 0.0712661 0.0712661i
\(449\) 78.0600i 0.173853i 0.996215 + 0.0869265i \(0.0277045\pi\)
−0.996215 + 0.0869265i \(0.972295\pi\)
\(450\) −61.4642 86.4416i −0.136587 0.192092i
\(451\) 935.346 2.07394
\(452\) 90.5707 + 90.5707i 0.200378 + 0.200378i
\(453\) −145.577 + 145.577i −0.321362 + 0.321362i
\(454\) 91.2271i 0.200941i
\(455\) 225.900 190.950i 0.496483 0.419669i
\(456\) 88.2837 0.193605
\(457\) 142.520 + 142.520i 0.311860 + 0.311860i 0.845630 0.533770i \(-0.179225\pi\)
−0.533770 + 0.845630i \(0.679225\pi\)
\(458\) −178.009 + 178.009i −0.388667 + 0.388667i
\(459\) 131.183i 0.285802i
\(460\) −47.7906 4.00693i −0.103893 0.00871071i
\(461\) 602.901 1.30781 0.653905 0.756576i \(-0.273129\pi\)
0.653905 + 0.756576i \(0.273129\pi\)
\(462\) −163.304 163.304i −0.353472 0.353472i
\(463\) −170.407 + 170.407i −0.368049 + 0.368049i −0.866765 0.498716i \(-0.833805\pi\)
0.498716 + 0.866765i \(0.333805\pi\)
\(464\) 71.0726i 0.153174i
\(465\) −1.55694 + 18.5697i −0.00334827 + 0.0399348i
\(466\) 389.903 0.836702
\(467\) −466.315 466.315i −0.998533 0.998533i 0.00146594 0.999999i \(-0.499533\pi\)
−0.999999 + 0.00146594i \(0.999533\pi\)
\(468\) −44.4698 + 44.4698i −0.0950210 + 0.0950210i
\(469\) 237.046i 0.505430i
\(470\) 8.79363 + 10.4032i 0.0187099 + 0.0221344i
\(471\) 39.8922 0.0846969
\(472\) 144.278 + 144.278i 0.305675 + 0.305675i
\(473\) 434.061 434.061i 0.917676 0.917676i
\(474\) 210.979i 0.445104i
\(475\) −444.231 75.0190i −0.935223 0.157935i
\(476\) 284.978 0.598693
\(477\) 51.2953 + 51.2953i 0.107537 + 0.107537i
\(478\) −82.5568 + 82.5568i −0.172713 + 0.172713i
\(479\) 538.427i 1.12406i 0.827115 + 0.562032i \(0.189980\pi\)
−0.827115 + 0.562032i \(0.810020\pi\)
\(480\) 37.4142 31.6256i 0.0779462 0.0658867i
\(481\) −506.147 −1.05228
\(482\) 108.909 + 108.909i 0.225952 + 0.225952i
\(483\) 33.1509 33.1509i 0.0686354 0.0686354i
\(484\) 316.124i 0.653148i
\(485\) 297.625 + 24.9539i 0.613659 + 0.0514512i
\(486\) −22.0454 −0.0453609
\(487\) −174.119 174.119i −0.357533 0.357533i 0.505370 0.862903i \(-0.331356\pi\)
−0.862903 + 0.505370i \(0.831356\pi\)
\(488\) 134.901 134.901i 0.276437 0.276437i
\(489\) 309.211i 0.632334i
\(490\) −10.1293 + 120.813i −0.0206721 + 0.246557i
\(491\) 498.635 1.01555 0.507775 0.861490i \(-0.330468\pi\)
0.507775 + 0.861490i \(0.330468\pi\)
\(492\) −137.151 137.151i −0.278761 0.278761i
\(493\) 317.192 317.192i 0.643392 0.643392i
\(494\) 267.128i 0.540744i
\(495\) −161.761 191.369i −0.326791 0.386604i
\(496\) −8.60705 −0.0173529
\(497\) 85.5556 + 85.5556i 0.172144 + 0.172144i
\(498\) −257.357 + 257.357i −0.516782 + 0.516782i
\(499\) 281.223i 0.563574i −0.959477 0.281787i \(-0.909073\pi\)
0.959477 0.281787i \(-0.0909272\pi\)
\(500\) −215.137 + 127.343i −0.430273 + 0.254686i
\(501\) 176.716 0.352726
\(502\) −421.149 421.149i −0.838941 0.838941i
\(503\) 44.0788 44.0788i 0.0876318 0.0876318i −0.661932 0.749564i \(-0.730263\pi\)
0.749564 + 0.661932i \(0.230263\pi\)
\(504\) 47.8908i 0.0950214i
\(505\) −235.347 + 198.935i −0.466034 + 0.393932i
\(506\) −113.300 −0.223913
\(507\) 72.4255 + 72.4255i 0.142851 + 0.142851i
\(508\) −214.300 + 214.300i −0.421851 + 0.421851i
\(509\) 126.037i 0.247617i −0.992306 0.123808i \(-0.960489\pi\)
0.992306 0.123808i \(-0.0395108\pi\)
\(510\) 308.120 + 25.8338i 0.604157 + 0.0506546i
\(511\) −583.369 −1.14162
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −66.2128 + 66.2128i −0.129070 + 0.129070i
\(514\) 187.518i 0.364820i
\(515\) −6.26592 + 74.7336i −0.0121668 + 0.145114i
\(516\) −127.293 −0.246693
\(517\) 22.7554 + 22.7554i 0.0440143 + 0.0440143i
\(518\) −272.542 + 272.542i −0.526143 + 0.526143i
\(519\) 269.376i 0.519029i
\(520\) 95.6925 + 113.207i 0.184024 + 0.217706i
\(521\) −237.283 −0.455437 −0.227719 0.973727i \(-0.573127\pi\)
−0.227719 + 0.973727i \(0.573127\pi\)
\(522\) 53.3045 + 53.3045i 0.102116 + 0.102116i
\(523\) −700.159 + 700.159i −1.33874 + 1.33874i −0.441449 + 0.897286i \(0.645535\pi\)
−0.897286 + 0.441449i \(0.854465\pi\)
\(524\) 321.673i 0.613881i
\(525\) 40.6952 240.980i 0.0775146 0.459009i
\(526\) −474.880 −0.902815
\(527\) −38.4127 38.4127i −0.0728894 0.0728894i
\(528\) 81.8381 81.8381i 0.154996 0.154996i
\(529\) 23.0000i 0.0434783i
\(530\) 130.583 110.380i 0.246383 0.208264i
\(531\) −216.418 −0.407566
\(532\) 143.839 + 143.839i 0.270373 + 0.270373i
\(533\) 414.989 414.989i 0.778591 0.778591i
\(534\) 212.317i 0.397597i
\(535\) −84.3345 7.07089i −0.157635 0.0132166i
\(536\) −118.794 −0.221630
\(537\) −5.80405 5.80405i −0.0108083 0.0108083i
\(538\) −66.0224 + 66.0224i −0.122718 + 0.122718i
\(539\) 286.417i 0.531386i
\(540\) −4.34140 + 51.7798i −0.00803962 + 0.0958886i
\(541\) −150.854 −0.278842 −0.139421 0.990233i \(-0.544524\pi\)
−0.139421 + 0.990233i \(0.544524\pi\)
\(542\) −301.309 301.309i −0.555920 0.555920i
\(543\) 47.9233 47.9233i 0.0882565 0.0882565i
\(544\) 142.814i 0.262526i
\(545\) −118.756 140.493i −0.217902 0.257785i
\(546\) −144.907 −0.265398
\(547\) 124.017 + 124.017i 0.226722 + 0.226722i 0.811322 0.584600i \(-0.198748\pi\)
−0.584600 + 0.811322i \(0.698748\pi\)
\(548\) 371.322 371.322i 0.677594 0.677594i
\(549\) 202.352i 0.368583i
\(550\) −481.340 + 342.256i −0.875163 + 0.622284i
\(551\) 320.197 0.581120
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) −343.744 + 343.744i −0.621598 + 0.621598i
\(554\) 475.841i 0.858918i
\(555\) −319.381 + 269.968i −0.575461 + 0.486428i
\(556\) −260.878 −0.469206
\(557\) −772.395 772.395i −1.38671 1.38671i −0.832139 0.554567i \(-0.812884\pi\)
−0.554567 0.832139i \(-0.687116\pi\)
\(558\) 6.45529 6.45529i 0.0115686 0.0115686i
\(559\) 385.163i 0.689021i
\(560\) 112.485 + 9.43112i 0.200866 + 0.0168413i
\(561\) 730.477 1.30210
\(562\) −307.240 307.240i −0.546691 0.546691i
\(563\) −169.515 + 169.515i −0.301093 + 0.301093i −0.841441 0.540349i \(-0.818292\pi\)
0.540349 + 0.841441i \(0.318292\pi\)
\(564\) 6.67329i 0.0118321i
\(565\) −26.7541 + 319.096i −0.0473524 + 0.564772i
\(566\) 149.406 0.263968
\(567\) −35.9181 35.9181i −0.0633476 0.0633476i
\(568\) −42.8753 + 42.8753i −0.0754847 + 0.0754847i
\(569\) 755.411i 1.32761i 0.747905 + 0.663805i \(0.231060\pi\)
−0.747905 + 0.663805i \(0.768940\pi\)
\(570\) 142.480 + 168.559i 0.249965 + 0.295717i
\(571\) 300.261 0.525851 0.262926 0.964816i \(-0.415313\pi\)
0.262926 + 0.964816i \(0.415313\pi\)
\(572\) 247.625 + 247.625i 0.432911 + 0.432911i
\(573\) −282.108 + 282.108i −0.492334 + 0.492334i
\(574\) 446.913i 0.778594i
\(575\) −69.4784 97.7126i −0.120832 0.169935i
\(576\) −24.0000 −0.0416667
\(577\) 693.168 + 693.168i 1.20133 + 1.20133i 0.973762 + 0.227569i \(0.0730778\pi\)
0.227569 + 0.973762i \(0.426922\pi\)
\(578\) −348.369 + 348.369i −0.602715 + 0.602715i
\(579\) 458.395i 0.791701i
\(580\) 135.698 114.703i 0.233962 0.197764i
\(581\) −838.613 −1.44340
\(582\) −103.462 103.462i −0.177770 0.177770i
\(583\) 285.632 285.632i 0.489935 0.489935i
\(584\) 292.350i 0.500599i
\(585\) −156.675 13.1362i −0.267820 0.0224550i
\(586\) 20.4681 0.0349285
\(587\) 233.532 + 233.532i 0.397839 + 0.397839i 0.877470 0.479631i \(-0.159229\pi\)
−0.479631 + 0.877470i \(0.659229\pi\)
\(588\) 41.9976 41.9976i 0.0714245 0.0714245i
\(589\) 38.7766i 0.0658346i
\(590\) −42.6191 + 508.318i −0.0722357 + 0.861555i
\(591\) 215.174 0.364084
\(592\) −136.582 136.582i −0.230712 0.230712i
\(593\) 582.754 582.754i 0.982722 0.982722i −0.0171309 0.999853i \(-0.505453\pi\)
0.999853 + 0.0171309i \(0.00545322\pi\)
\(594\) 122.757i 0.206662i
\(595\) 459.923 + 544.104i 0.772979 + 0.914460i
\(596\) −11.6176 −0.0194926
\(597\) −259.490 259.490i −0.434657 0.434657i
\(598\) −50.2682 + 50.2682i −0.0840605 + 0.0840605i
\(599\) 573.521i 0.957465i −0.877961 0.478732i \(-0.841096\pi\)
0.877961 0.478732i \(-0.158904\pi\)
\(600\) 120.765 + 20.3940i 0.201274 + 0.0339900i
\(601\) −847.669 −1.41043 −0.705215 0.708993i \(-0.749150\pi\)
−0.705215 + 0.708993i \(0.749150\pi\)
\(602\) −207.396 207.396i −0.344512 0.344512i
\(603\) 89.0951 89.0951i 0.147753 0.147753i
\(604\) 237.726i 0.393587i
\(605\) −603.569 + 510.188i −0.997635 + 0.843286i
\(606\) 150.968 0.249122
\(607\) −700.957 700.957i −1.15479 1.15479i −0.985580 0.169208i \(-0.945879\pi\)
−0.169208 0.985580i \(-0.554121\pi\)
\(608\) −72.0833 + 72.0833i −0.118558 + 0.118558i
\(609\) 173.696i 0.285214i
\(610\) 475.280 + 39.8491i 0.779148 + 0.0653264i
\(611\) 20.1920 0.0330474
\(612\) −107.110 107.110i −0.175017 0.175017i
\(613\) −342.192 + 342.192i −0.558225 + 0.558225i −0.928802 0.370577i \(-0.879160\pi\)
0.370577 + 0.928802i \(0.379160\pi\)
\(614\) 740.927i 1.20672i
\(615\) 40.5136 483.205i 0.0658757 0.785700i
\(616\) 266.674 0.432913
\(617\) −57.6784 57.6784i −0.0934820 0.0934820i 0.658819 0.752301i \(-0.271056\pi\)
−0.752301 + 0.658819i \(0.771056\pi\)
\(618\) 25.9793 25.9793i 0.0420377 0.0420377i
\(619\) 706.959i 1.14210i −0.820916 0.571050i \(-0.806536\pi\)
0.820916 0.571050i \(-0.193464\pi\)
\(620\) −13.8908 16.4333i −0.0224046 0.0265053i
\(621\) −24.9199 −0.0401286
\(622\) −121.488 121.488i −0.195319 0.195319i
\(623\) −345.923 + 345.923i −0.555254 + 0.555254i
\(624\) 72.6189i 0.116377i
\(625\) −590.340 205.239i −0.944545 0.328383i
\(626\) 848.094 1.35478
\(627\) 368.698 + 368.698i 0.588035 + 0.588035i
\(628\) −32.5719 + 32.5719i −0.0518660 + 0.0518660i
\(629\) 1219.11i 1.93817i
\(630\) −91.4371 + 77.2904i −0.145138 + 0.122683i
\(631\) −209.729 −0.332376 −0.166188 0.986094i \(-0.553146\pi\)
−0.166188 + 0.986094i \(0.553146\pi\)
\(632\) −172.264 172.264i −0.272569 0.272569i
\(633\) 126.763 126.763i 0.200257 0.200257i
\(634\) 604.142i 0.952906i
\(635\) −755.016 63.3031i −1.18900 0.0996899i
\(636\) −83.7649 −0.131706
\(637\) 127.076 + 127.076i 0.199491 + 0.199491i
\(638\) 296.820 296.820i 0.465234 0.465234i
\(639\) 64.3130i 0.100646i
\(640\) −4.72631 + 56.3708i −0.00738487 + 0.0880793i
\(641\) 199.911 0.311873 0.155937 0.987767i \(-0.450160\pi\)
0.155937 + 0.987767i \(0.450160\pi\)
\(642\) 29.3168 + 29.3168i 0.0456649 + 0.0456649i
\(643\) 396.479 396.479i 0.616607 0.616607i −0.328052 0.944660i \(-0.606392\pi\)
0.944660 + 0.328052i \(0.106392\pi\)
\(644\) 54.1352i 0.0840609i
\(645\) −205.437 243.039i −0.318508 0.376805i
\(646\) −643.406 −0.995985
\(647\) −326.847 326.847i −0.505173 0.505173i 0.407868 0.913041i \(-0.366272\pi\)
−0.913041 + 0.407868i \(0.866272\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1205.10i 1.85685i
\(650\) −61.7079 + 365.408i −0.0949352 + 0.562166i
\(651\) 21.0349 0.0323117
\(652\) 252.470 + 252.470i 0.387224 + 0.387224i
\(653\) 810.388 810.388i 1.24102 1.24102i 0.281446 0.959577i \(-0.409186\pi\)
0.959577 0.281446i \(-0.0908141\pi\)
\(654\) 90.1216i 0.137801i
\(655\) −614.166 + 519.145i −0.937658 + 0.792588i
\(656\) 223.966 0.341412
\(657\) 219.262 + 219.262i 0.333732 + 0.333732i
\(658\) 10.8726 10.8726i 0.0165238 0.0165238i
\(659\) 1229.80i 1.86615i 0.359676 + 0.933077i \(0.382887\pi\)
−0.359676 + 0.933077i \(0.617113\pi\)
\(660\) 288.330 + 24.1746i 0.436863 + 0.0366281i
\(661\) −267.953 −0.405376 −0.202688 0.979243i \(-0.564968\pi\)
−0.202688 + 0.979243i \(0.564968\pi\)
\(662\) −578.605 578.605i −0.874026 0.874026i
\(663\) 324.094 324.094i 0.488829 0.488829i
\(664\) 420.263i 0.632926i
\(665\) −42.4892 + 506.768i −0.0638935 + 0.762057i
\(666\) 204.873 0.307617
\(667\) 60.2547 + 60.2547i 0.0903369 + 0.0903369i
\(668\) −144.288 + 144.288i −0.216000 + 0.216000i
\(669\) 387.374i 0.579035i
\(670\) −191.720 226.811i −0.286149 0.338523i
\(671\) 1126.77 1.67924
\(672\) −39.1027 39.1027i −0.0581885 0.0581885i
\(673\) −473.159 + 473.159i −0.703060 + 0.703060i −0.965066 0.262006i \(-0.915616\pi\)
0.262006 + 0.965066i \(0.415616\pi\)
\(674\) 282.482i 0.419113i
\(675\) −105.869 + 75.2780i −0.156843 + 0.111523i
\(676\) −118.270 −0.174956
\(677\) −477.245 477.245i −0.704941 0.704941i 0.260526 0.965467i \(-0.416104\pi\)
−0.965467 + 0.260526i \(0.916104\pi\)
\(678\) 110.926 110.926i 0.163608 0.163608i
\(679\) 337.136i 0.496519i
\(680\) −272.672 + 230.486i −0.400989 + 0.338950i
\(681\) 111.730 0.164067
\(682\) −35.9455 35.9455i −0.0527060 0.0527060i
\(683\) −841.661 + 841.661i −1.23230 + 1.23230i −0.269221 + 0.963078i \(0.586766\pi\)
−0.963078 + 0.269221i \(0.913234\pi\)
\(684\) 108.125i 0.158077i
\(685\) 1308.23 + 109.686i 1.90983 + 0.160126i
\(686\) 527.960 0.769620
\(687\) 218.016 + 218.016i 0.317345 + 0.317345i
\(688\) 103.935 103.935i 0.151068 0.151068i
\(689\) 253.455i 0.367859i
\(690\) −4.90746 + 58.5313i −0.00711227 + 0.0848280i
\(691\) −621.298 −0.899129 −0.449565 0.893248i \(-0.648421\pi\)
−0.449565 + 0.893248i \(0.648421\pi\)
\(692\) −219.945 219.945i −0.317839 0.317839i
\(693\) −200.006 + 200.006i −0.288608 + 0.288608i
\(694\) 703.038i 1.01302i
\(695\) −421.029 498.091i −0.605797 0.716678i
\(696\) −87.0458 −0.125066
\(697\) 999.546 + 999.546i 1.43407 + 1.43407i
\(698\) −579.696 + 579.696i −0.830510 + 0.830510i
\(699\) 477.532i 0.683164i
\(700\) 163.532 + 229.987i 0.233617 + 0.328552i
\(701\) 1084.61 1.54724 0.773619 0.633651i \(-0.218444\pi\)
0.773619 + 0.633651i \(0.218444\pi\)
\(702\) 54.4642 + 54.4642i 0.0775843 + 0.0775843i
\(703\) 615.329 615.329i 0.875290 0.875290i
\(704\) 133.641i 0.189831i
\(705\) 12.7412 10.7700i 0.0180726 0.0152765i
\(706\) 762.811 1.08047
\(707\) 245.968 + 245.968i 0.347904 + 0.347904i
\(708\) 176.704 176.704i 0.249582 0.249582i
\(709\) 1187.52i 1.67492i 0.546500 + 0.837459i \(0.315960\pi\)
−0.546500 + 0.837459i \(0.684040\pi\)
\(710\) −151.057 12.6651i −0.212757 0.0178382i
\(711\) 258.396 0.363426
\(712\) −173.356 173.356i −0.243478 0.243478i
\(713\) 7.29699 7.29699i 0.0102342 0.0102342i
\(714\) 349.025i 0.488831i
\(715\) −73.1471 + 872.425i −0.102304 + 1.22018i
\(716\) 9.47797 0.0132374
\(717\) 101.111 + 101.111i 0.141019 + 0.141019i
\(718\) −713.563 + 713.563i −0.993820 + 0.993820i
\(719\) 311.822i 0.433689i 0.976206 + 0.216844i \(0.0695764\pi\)
−0.976206 + 0.216844i \(0.930424\pi\)
\(720\) −38.7333 45.8228i −0.0537963 0.0636428i
\(721\) 84.6550 0.117413
\(722\) 36.2497 + 36.2497i 0.0502074 + 0.0502074i
\(723\) 133.386 133.386i 0.184489 0.184489i
\(724\) 78.2584i 0.108092i
\(725\) 438.002 + 73.9671i 0.604141 + 0.102024i
\(726\) 387.171 0.533293
\(727\) 319.511 + 319.511i 0.439493 + 0.439493i 0.891841 0.452348i \(-0.149414\pi\)
−0.452348 + 0.891841i \(0.649414\pi\)
\(728\) 118.316 118.316i 0.162523 0.162523i
\(729\) 27.0000i 0.0370370i
\(730\) 558.178 471.820i 0.764628 0.646328i
\(731\) 927.707 1.26909
\(732\) −165.220 165.220i −0.225710 0.225710i
\(733\) −623.340 + 623.340i −0.850396 + 0.850396i −0.990182 0.139786i \(-0.955359\pi\)
0.139786 + 0.990182i \(0.455359\pi\)
\(734\) 1003.02i 1.36651i
\(735\) 147.965 + 12.4059i 0.201313 + 0.0168787i
\(736\) −27.1293 −0.0368605
\(737\) −496.116 496.116i −0.673156 0.673156i
\(738\) −167.975 + 167.975i −0.227608 + 0.227608i
\(739\) 744.713i 1.00773i 0.863782 + 0.503865i \(0.168089\pi\)
−0.863782 + 0.503865i \(0.831911\pi\)
\(740\) 40.3455 481.201i 0.0545210 0.650272i
\(741\) 327.163 0.441516
\(742\) −136.476 136.476i −0.183930 0.183930i
\(743\) 542.987 542.987i 0.730803 0.730803i −0.239976 0.970779i \(-0.577139\pi\)
0.970779 + 0.239976i \(0.0771394\pi\)
\(744\) 10.5414i 0.0141686i
\(745\) −18.7495 22.1812i −0.0251671 0.0297735i
\(746\) 864.395 1.15871
\(747\) 315.197 + 315.197i 0.421950 + 0.421950i
\(748\) −596.432 + 596.432i −0.797368 + 0.797368i
\(749\) 95.5306i 0.127544i
\(750\) 155.963 + 263.487i 0.207950 + 0.351317i
\(751\) −581.183 −0.773879 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(752\) 5.44872 + 5.44872i 0.00724564 + 0.00724564i
\(753\) −515.800 + 515.800i −0.684993 + 0.684993i
\(754\) 263.382i 0.349313i
\(755\) 453.887 383.664i 0.601175 0.508164i
\(756\) 58.6540 0.0775847
\(757\) 448.860 + 448.860i 0.592946 + 0.592946i 0.938426 0.345480i \(-0.112284\pi\)
−0.345480 + 0.938426i \(0.612284\pi\)
\(758\) −132.672 + 132.672i −0.175029 + 0.175029i
\(759\) 138.763i 0.182824i
\(760\) −253.962 21.2930i −0.334160 0.0280171i
\(761\) 450.906 0.592518 0.296259 0.955108i \(-0.404261\pi\)
0.296259 + 0.955108i \(0.404261\pi\)
\(762\) 262.463 + 262.463i 0.344440 + 0.344440i
\(763\) −146.833 + 146.833i −0.192442 + 0.192442i
\(764\) 460.680i 0.602984i
\(765\) 31.6398 377.368i 0.0413593 0.493292i
\(766\) −775.055 −1.01182
\(767\) 534.670 + 534.670i 0.697092 + 0.697092i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 968.892i 1.25994i −0.776620 0.629969i \(-0.783068\pi\)
0.776620 0.629969i \(-0.216932\pi\)
\(770\) 430.382 + 509.157i 0.558938 + 0.661242i
\(771\) −229.661 −0.297875
\(772\) 374.278 + 374.278i 0.484816 + 0.484816i
\(773\) 1017.80 1017.80i 1.31669 1.31669i 0.400306 0.916382i \(-0.368904\pi\)
0.916382 0.400306i \(-0.131096\pi\)
\(774\) 155.902i 0.201424i
\(775\) 8.95759 53.0431i 0.0115582 0.0684427i
\(776\) 168.953 0.217722
\(777\) 333.794 + 333.794i 0.429594 + 0.429594i
\(778\) −141.741 + 141.741i −0.182187 + 0.182187i
\(779\) 1009.01i 1.29527i