Properties

Label 690.3.k.b.277.6
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.6
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-3.65385 - 3.41312i) q^{5} +2.44949 q^{6} +(0.283627 + 0.283627i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-3.65385 - 3.41312i) q^{5} +2.44949 q^{6} +(0.283627 + 0.283627i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(0.240725 + 7.06697i) q^{10} +8.31907 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-17.3963 + 17.3963i) q^{13} -0.567254i q^{14} +(8.65523 - 0.294827i) q^{15} -4.00000 q^{16} +(9.44849 + 9.44849i) q^{17} +(-3.00000 + 3.00000i) q^{18} -24.8369i q^{19} +(6.82624 - 7.30769i) q^{20} -0.694742 q^{21} +(-8.31907 - 8.31907i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(1.70120 + 24.9421i) q^{25} +34.7926 q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.567254 + 0.567254i) q^{28} +7.76969i q^{29} +(-8.95006 - 8.36041i) q^{30} -21.7619 q^{31} +(4.00000 + 4.00000i) q^{32} +(-10.1887 + 10.1887i) q^{33} -18.8970i q^{34} +(-0.0682763 - 2.00438i) q^{35} +6.00000 q^{36} +(-22.4355 - 22.4355i) q^{37} +(-24.8369 + 24.8369i) q^{38} -42.6121i q^{39} +(-14.1339 + 0.481451i) q^{40} -2.70246 q^{41} +(0.694742 + 0.694742i) q^{42} +(51.2340 - 51.2340i) q^{43} +16.6381i q^{44} +(-10.2394 + 10.9615i) q^{45} +6.78233 q^{46} +(57.3373 + 57.3373i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.8391i q^{49} +(23.2409 - 26.6433i) q^{50} -23.1440 q^{51} +(-34.7926 - 34.7926i) q^{52} +(57.8310 - 57.8310i) q^{53} -7.34847i q^{54} +(-30.3966 - 28.3940i) q^{55} +1.13451 q^{56} +(30.4189 + 30.4189i) q^{57} +(7.76969 - 7.76969i) q^{58} -17.1617i q^{59} +(0.589655 + 17.3105i) q^{60} +88.9356 q^{61} +(21.7619 + 21.7619i) q^{62} +(0.850881 - 0.850881i) q^{63} -8.00000i q^{64} +(122.939 - 4.18774i) q^{65} +20.3775 q^{66} +(53.5253 + 53.5253i) q^{67} +(-18.8970 + 18.8970i) q^{68} -8.30662i q^{69} +(-1.93611 + 2.07266i) q^{70} -43.1306 q^{71} +(-6.00000 - 6.00000i) q^{72} +(18.0830 - 18.0830i) q^{73} +44.8711i q^{74} +(-32.6312 - 28.4641i) q^{75} +49.6738 q^{76} +(2.35951 + 2.35951i) q^{77} +(-42.6121 + 42.6121i) q^{78} -155.462i q^{79} +(14.6154 + 13.6525i) q^{80} -9.00000 q^{81} +(2.70246 + 2.70246i) q^{82} +(69.5987 - 69.5987i) q^{83} -1.38948i q^{84} +(-2.27449 - 66.7722i) q^{85} -102.468 q^{86} +(-9.51588 - 9.51588i) q^{87} +(16.6381 - 16.6381i) q^{88} -67.8698i q^{89} +(21.2009 - 0.722176i) q^{90} -9.86814 q^{91} +(-6.78233 - 6.78233i) q^{92} +(26.6527 - 26.6527i) q^{93} -114.675i q^{94} +(-84.7714 + 90.7503i) q^{95} -9.79796 q^{96} +(48.4229 + 48.4229i) q^{97} +(-48.8391 + 48.8391i) q^{98} -24.9572i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

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
\(5\) −3.65385 3.41312i −0.730769 0.682624i
\(6\) 2.44949 0.408248
\(7\) 0.283627 + 0.283627i 0.0405182 + 0.0405182i 0.727076 0.686557i \(-0.240879\pi\)
−0.686557 + 0.727076i \(0.740879\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 0.240725 + 7.06697i 0.0240725 + 0.706697i
\(11\) 8.31907 0.756279 0.378140 0.925749i \(-0.376564\pi\)
0.378140 + 0.925749i \(0.376564\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −17.3963 + 17.3963i −1.33818 + 1.33818i −0.440355 + 0.897824i \(0.645147\pi\)
−0.897824 + 0.440355i \(0.854853\pi\)
\(14\) 0.567254i 0.0405182i
\(15\) 8.65523 0.294827i 0.577016 0.0196552i
\(16\) −4.00000 −0.250000
\(17\) 9.44849 + 9.44849i 0.555794 + 0.555794i 0.928107 0.372313i \(-0.121435\pi\)
−0.372313 + 0.928107i \(0.621435\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 24.8369i 1.30721i −0.756838 0.653603i \(-0.773257\pi\)
0.756838 0.653603i \(-0.226743\pi\)
\(20\) 6.82624 7.30769i 0.341312 0.365385i
\(21\) −0.694742 −0.0330829
\(22\) −8.31907 8.31907i −0.378140 0.378140i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 1.70120 + 24.9421i 0.0680480 + 0.997682i
\(26\) 34.7926 1.33818
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −0.567254 + 0.567254i −0.0202591 + 0.0202591i
\(29\) 7.76969i 0.267920i 0.990987 + 0.133960i \(0.0427694\pi\)
−0.990987 + 0.133960i \(0.957231\pi\)
\(30\) −8.95006 8.36041i −0.298335 0.278680i
\(31\) −21.7619 −0.701996 −0.350998 0.936376i \(-0.614158\pi\)
−0.350998 + 0.936376i \(0.614158\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −10.1887 + 10.1887i −0.308750 + 0.308750i
\(34\) 18.8970i 0.555794i
\(35\) −0.0682763 2.00438i −0.00195075 0.0572681i
\(36\) 6.00000 0.166667
\(37\) −22.4355 22.4355i −0.606366 0.606366i 0.335629 0.941994i \(-0.391051\pi\)
−0.941994 + 0.335629i \(0.891051\pi\)
\(38\) −24.8369 + 24.8369i −0.653603 + 0.653603i
\(39\) 42.6121i 1.09262i
\(40\) −14.1339 + 0.481451i −0.353348 + 0.0120363i
\(41\) −2.70246 −0.0659137 −0.0329569 0.999457i \(-0.510492\pi\)
−0.0329569 + 0.999457i \(0.510492\pi\)
\(42\) 0.694742 + 0.694742i 0.0165415 + 0.0165415i
\(43\) 51.2340 51.2340i 1.19149 1.19149i 0.214840 0.976649i \(-0.431077\pi\)
0.976649 0.214840i \(-0.0689231\pi\)
\(44\) 16.6381i 0.378140i
\(45\) −10.2394 + 10.9615i −0.227541 + 0.243590i
\(46\) 6.78233 0.147442
\(47\) 57.3373 + 57.3373i 1.21994 + 1.21994i 0.967651 + 0.252292i \(0.0811843\pi\)
0.252292 + 0.967651i \(0.418816\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 48.8391i 0.996717i
\(50\) 23.2409 26.6433i 0.464817 0.532865i
\(51\) −23.1440 −0.453804
\(52\) −34.7926 34.7926i −0.669089 0.669089i
\(53\) 57.8310 57.8310i 1.09115 1.09115i 0.0957461 0.995406i \(-0.469476\pi\)
0.995406 0.0957461i \(-0.0305237\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −30.3966 28.3940i −0.552666 0.516255i
\(56\) 1.13451 0.0202591
\(57\) 30.4189 + 30.4189i 0.533664 + 0.533664i
\(58\) 7.76969 7.76969i 0.133960 0.133960i
\(59\) 17.1617i 0.290877i −0.989367 0.145439i \(-0.953541\pi\)
0.989367 0.145439i \(-0.0464593\pi\)
\(60\) 0.589655 + 17.3105i 0.00982758 + 0.288508i
\(61\) 88.9356 1.45796 0.728980 0.684535i \(-0.239995\pi\)
0.728980 + 0.684535i \(0.239995\pi\)
\(62\) 21.7619 + 21.7619i 0.350998 + 0.350998i
\(63\) 0.850881 0.850881i 0.0135061 0.0135061i
\(64\) 8.00000i 0.125000i
\(65\) 122.939 4.18774i 1.89137 0.0644267i
\(66\) 20.3775 0.308750
\(67\) 53.5253 + 53.5253i 0.798885 + 0.798885i 0.982920 0.184034i \(-0.0589158\pi\)
−0.184034 + 0.982920i \(0.558916\pi\)
\(68\) −18.8970 + 18.8970i −0.277897 + 0.277897i
\(69\) 8.30662i 0.120386i
\(70\) −1.93611 + 2.07266i −0.0276587 + 0.0296094i
\(71\) −43.1306 −0.607474 −0.303737 0.952756i \(-0.598234\pi\)
−0.303737 + 0.952756i \(0.598234\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 18.0830 18.0830i 0.247712 0.247712i −0.572319 0.820031i \(-0.693956\pi\)
0.820031 + 0.572319i \(0.193956\pi\)
\(74\) 44.8711i 0.606366i
\(75\) −32.6312 28.4641i −0.435082 0.379522i
\(76\) 49.6738 0.653603
\(77\) 2.35951 + 2.35951i 0.0306430 + 0.0306430i
\(78\) −42.6121 + 42.6121i −0.546309 + 0.546309i
\(79\) 155.462i 1.96787i −0.178518 0.983937i \(-0.557130\pi\)
0.178518 0.983937i \(-0.442870\pi\)
\(80\) 14.6154 + 13.6525i 0.182692 + 0.170656i
\(81\) −9.00000 −0.111111
\(82\) 2.70246 + 2.70246i 0.0329569 + 0.0329569i
\(83\) 69.5987 69.5987i 0.838538 0.838538i −0.150128 0.988667i \(-0.547969\pi\)
0.988667 + 0.150128i \(0.0479686\pi\)
\(84\) 1.38948i 0.0165415i
\(85\) −2.27449 66.7722i −0.0267587 0.785556i
\(86\) −102.468 −1.19149
\(87\) −9.51588 9.51588i −0.109378 0.109378i
\(88\) 16.6381 16.6381i 0.189070 0.189070i
\(89\) 67.8698i 0.762582i −0.924455 0.381291i \(-0.875480\pi\)
0.924455 0.381291i \(-0.124520\pi\)
\(90\) 21.2009 0.722176i 0.235566 0.00802418i
\(91\) −9.86814 −0.108441
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 26.6527 26.6527i 0.286589 0.286589i
\(94\) 114.675i 1.21994i
\(95\) −84.7714 + 90.7503i −0.892330 + 0.955266i
\(96\) −9.79796 −0.102062
\(97\) 48.4229 + 48.4229i 0.499206 + 0.499206i 0.911191 0.411985i \(-0.135164\pi\)
−0.411985 + 0.911191i \(0.635164\pi\)
\(98\) −48.8391 + 48.8391i −0.498358 + 0.498358i
\(99\) 24.9572i 0.252093i
\(100\) −49.8841 + 3.40240i −0.498841 + 0.0340240i
\(101\) 84.7530 0.839138 0.419569 0.907723i \(-0.362181\pi\)
0.419569 + 0.907723i \(0.362181\pi\)
\(102\) 23.1440 + 23.1440i 0.226902 + 0.226902i
\(103\) −86.9504 + 86.9504i −0.844179 + 0.844179i −0.989399 0.145220i \(-0.953611\pi\)
0.145220 + 0.989399i \(0.453611\pi\)
\(104\) 69.5853i 0.669089i
\(105\) 2.53848 + 2.37124i 0.0241760 + 0.0225832i
\(106\) −115.662 −1.09115
\(107\) −15.5948 15.5948i −0.145746 0.145746i 0.630469 0.776214i \(-0.282863\pi\)
−0.776214 + 0.630469i \(0.782863\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 13.7730i 0.126358i 0.998002 + 0.0631789i \(0.0201239\pi\)
−0.998002 + 0.0631789i \(0.979876\pi\)
\(110\) 2.00261 + 58.7906i 0.0182056 + 0.534460i
\(111\) 54.9556 0.495096
\(112\) −1.13451 1.13451i −0.0101295 0.0101295i
\(113\) 105.051 105.051i 0.929654 0.929654i −0.0680291 0.997683i \(-0.521671\pi\)
0.997683 + 0.0680291i \(0.0216711\pi\)
\(114\) 60.8378i 0.533664i
\(115\) 23.9653 0.816340i 0.208394 0.00709861i
\(116\) −15.5394 −0.133960
\(117\) 52.1890 + 52.1890i 0.446060 + 0.446060i
\(118\) −17.1617 + 17.1617i −0.145439 + 0.145439i
\(119\) 5.35970i 0.0450395i
\(120\) 16.7208 17.9001i 0.139340 0.149168i
\(121\) −51.7930 −0.428041
\(122\) −88.9356 88.9356i −0.728980 0.728980i
\(123\) 3.30983 3.30983i 0.0269092 0.0269092i
\(124\) 43.5238i 0.350998i
\(125\) 78.9143 96.9408i 0.631315 0.775527i
\(126\) −1.70176 −0.0135061
\(127\) −22.3524 22.3524i −0.176003 0.176003i 0.613608 0.789611i \(-0.289718\pi\)
−0.789611 + 0.613608i \(0.789718\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 125.497i 0.972847i
\(130\) −127.127 118.752i −0.977900 0.913473i
\(131\) 158.682 1.21131 0.605656 0.795727i \(-0.292911\pi\)
0.605656 + 0.795727i \(0.292911\pi\)
\(132\) −20.3775 20.3775i −0.154375 0.154375i
\(133\) 7.04442 7.04442i 0.0529656 0.0529656i
\(134\) 107.051i 0.798885i
\(135\) −0.884482 25.9657i −0.00655172 0.192339i
\(136\) 37.7940 0.277897
\(137\) 9.76414 + 9.76414i 0.0712711 + 0.0712711i 0.741844 0.670573i \(-0.233952\pi\)
−0.670573 + 0.741844i \(0.733952\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 83.2727i 0.599084i 0.954083 + 0.299542i \(0.0968339\pi\)
−0.954083 + 0.299542i \(0.903166\pi\)
\(140\) 4.00877 0.136553i 0.0286341 0.000975375i
\(141\) −140.447 −0.996079
\(142\) 43.1306 + 43.1306i 0.303737 + 0.303737i
\(143\) −144.721 + 144.721i −1.01204 + 1.01204i
\(144\) 12.0000i 0.0833333i
\(145\) 26.5189 28.3892i 0.182889 0.195788i
\(146\) −36.1659 −0.247712
\(147\) 59.8155 + 59.8155i 0.406908 + 0.406908i
\(148\) 44.8711 44.8711i 0.303183 0.303183i
\(149\) 274.269i 1.84073i −0.391056 0.920367i \(-0.627890\pi\)
0.391056 0.920367i \(-0.372110\pi\)
\(150\) 4.16707 + 61.0953i 0.0277805 + 0.407302i
\(151\) −8.76603 −0.0580532 −0.0290266 0.999579i \(-0.509241\pi\)
−0.0290266 + 0.999579i \(0.509241\pi\)
\(152\) −49.6738 49.6738i −0.326801 0.326801i
\(153\) 28.3455 28.3455i 0.185265 0.185265i
\(154\) 4.71903i 0.0306430i
\(155\) 79.5146 + 74.2759i 0.512997 + 0.479200i
\(156\) 85.2242 0.546309
\(157\) −220.444 220.444i −1.40410 1.40410i −0.786468 0.617631i \(-0.788093\pi\)
−0.617631 0.786468i \(-0.711907\pi\)
\(158\) −155.462 + 155.462i −0.983937 + 0.983937i
\(159\) 141.657i 0.890922i
\(160\) −0.962902 28.2679i −0.00601814 0.176674i
\(161\) −1.92365 −0.0119482
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −61.8205 + 61.8205i −0.379267 + 0.379267i −0.870838 0.491571i \(-0.836423\pi\)
0.491571 + 0.870838i \(0.336423\pi\)
\(164\) 5.40493i 0.0329569i
\(165\) 72.0035 2.45269i 0.436385 0.0148648i
\(166\) −139.197 −0.838538
\(167\) −4.05814 4.05814i −0.0243003 0.0243003i 0.694852 0.719153i \(-0.255470\pi\)
−0.719153 + 0.694852i \(0.755470\pi\)
\(168\) −1.38948 + 1.38948i −0.00827073 + 0.00827073i
\(169\) 436.264i 2.58145i
\(170\) −64.4977 + 69.0467i −0.379398 + 0.406157i
\(171\) −74.5107 −0.435735
\(172\) 102.468 + 102.468i 0.595745 + 0.595745i
\(173\) −164.608 + 164.608i −0.951490 + 0.951490i −0.998877 0.0473870i \(-0.984911\pi\)
0.0473870 + 0.998877i \(0.484911\pi\)
\(174\) 19.0318i 0.109378i
\(175\) −6.59173 + 7.55675i −0.0376671 + 0.0431814i
\(176\) −33.2763 −0.189070
\(177\) 21.0188 + 21.0188i 0.118750 + 0.118750i
\(178\) −67.8698 + 67.8698i −0.381291 + 0.381291i
\(179\) 285.884i 1.59712i 0.601917 + 0.798559i \(0.294404\pi\)
−0.601917 + 0.798559i \(0.705596\pi\)
\(180\) −21.9231 20.4787i −0.121795 0.113771i
\(181\) 207.433 1.14604 0.573020 0.819542i \(-0.305772\pi\)
0.573020 + 0.819542i \(0.305772\pi\)
\(182\) 9.86814 + 9.86814i 0.0542205 + 0.0542205i
\(183\) −108.923 + 108.923i −0.595210 + 0.595210i
\(184\) 13.5647i 0.0737210i
\(185\) 5.40080 + 158.551i 0.0291935 + 0.857034i
\(186\) −53.3055 −0.286589
\(187\) 78.6027 + 78.6027i 0.420335 + 0.420335i
\(188\) −114.675 + 114.675i −0.609972 + 0.609972i
\(189\) 2.08422i 0.0110276i
\(190\) 175.522 5.97888i 0.923798 0.0314678i
\(191\) 17.3738 0.0909622 0.0454811 0.998965i \(-0.485518\pi\)
0.0454811 + 0.998965i \(0.485518\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −141.340 + 141.340i −0.732330 + 0.732330i −0.971081 0.238751i \(-0.923262\pi\)
0.238751 + 0.971081i \(0.423262\pi\)
\(194\) 96.8459i 0.499206i
\(195\) −145.440 + 155.698i −0.745848 + 0.798452i
\(196\) 97.6782 0.498358
\(197\) 213.280 + 213.280i 1.08264 + 1.08264i 0.996262 + 0.0863791i \(0.0275296\pi\)
0.0863791 + 0.996262i \(0.472470\pi\)
\(198\) −24.9572 + 24.9572i −0.126047 + 0.126047i
\(199\) 84.3085i 0.423661i −0.977306 0.211830i \(-0.932058\pi\)
0.977306 0.211830i \(-0.0679424\pi\)
\(200\) 53.2865 + 46.4817i 0.266433 + 0.232409i
\(201\) −131.110 −0.652287
\(202\) −84.7530 84.7530i −0.419569 0.419569i
\(203\) −2.20369 + 2.20369i −0.0108556 + 0.0108556i
\(204\) 46.2880i 0.226902i
\(205\) 9.87439 + 9.22384i 0.0481677 + 0.0449943i
\(206\) 173.901 0.844179
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 69.5853 69.5853i 0.334545 0.334545i
\(209\) 206.620i 0.988613i
\(210\) −0.167242 4.90972i −0.000796390 0.0233796i
\(211\) 301.566 1.42922 0.714612 0.699521i \(-0.246603\pi\)
0.714612 + 0.699521i \(0.246603\pi\)
\(212\) 115.662 + 115.662i 0.545576 + 0.545576i
\(213\) 52.8240 52.8240i 0.248000 0.248000i
\(214\) 31.1895i 0.145746i
\(215\) −362.069 + 12.3333i −1.68404 + 0.0573644i
\(216\) 14.6969 0.0680414
\(217\) −6.17226 6.17226i −0.0284436 0.0284436i
\(218\) 13.7730 13.7730i 0.0631789 0.0631789i
\(219\) 44.2940i 0.202256i
\(220\) 56.7880 60.7933i 0.258127 0.276333i
\(221\) −328.738 −1.48750
\(222\) −54.9556 54.9556i −0.247548 0.247548i
\(223\) 41.8331 41.8331i 0.187592 0.187592i −0.607062 0.794654i \(-0.707652\pi\)
0.794654 + 0.607062i \(0.207652\pi\)
\(224\) 2.26902i 0.0101295i
\(225\) 74.8262 5.10360i 0.332561 0.0226827i
\(226\) −210.102 −0.929654
\(227\) 135.297 + 135.297i 0.596024 + 0.596024i 0.939252 0.343228i \(-0.111520\pi\)
−0.343228 + 0.939252i \(0.611520\pi\)
\(228\) −60.8378 + 60.8378i −0.266832 + 0.266832i
\(229\) 337.019i 1.47170i 0.677145 + 0.735850i \(0.263217\pi\)
−0.677145 + 0.735850i \(0.736783\pi\)
\(230\) −24.7816 23.1489i −0.107746 0.100647i
\(231\) −5.77961 −0.0250199
\(232\) 15.5394 + 15.5394i 0.0669801 + 0.0669801i
\(233\) −104.797 + 104.797i −0.449772 + 0.449772i −0.895279 0.445506i \(-0.853024\pi\)
0.445506 + 0.895279i \(0.353024\pi\)
\(234\) 104.378i 0.446060i
\(235\) −13.8026 405.201i −0.0587343 1.72426i
\(236\) 34.3235 0.145439
\(237\) 190.401 + 190.401i 0.803381 + 0.803381i
\(238\) 5.35970 5.35970i 0.0225197 0.0225197i
\(239\) 223.047i 0.933250i −0.884455 0.466625i \(-0.845470\pi\)
0.884455 0.466625i \(-0.154530\pi\)
\(240\) −34.6209 + 1.17931i −0.144254 + 0.00491379i
\(241\) −167.112 −0.693412 −0.346706 0.937974i \(-0.612700\pi\)
−0.346706 + 0.937974i \(0.612700\pi\)
\(242\) 51.7930 + 51.7930i 0.214021 + 0.214021i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 177.871i 0.728980i
\(245\) −166.694 + 178.451i −0.680383 + 0.728370i
\(246\) −6.61966 −0.0269092
\(247\) 432.071 + 432.071i 1.74927 + 1.74927i
\(248\) −43.5238 + 43.5238i −0.175499 + 0.175499i
\(249\) 170.481i 0.684664i
\(250\) −175.855 + 18.0265i −0.703421 + 0.0721060i
\(251\) 441.419 1.75864 0.879321 0.476230i \(-0.157997\pi\)
0.879321 + 0.476230i \(0.157997\pi\)
\(252\) 1.70176 + 1.70176i 0.00675303 + 0.00675303i
\(253\) −28.2114 + 28.2114i −0.111507 + 0.111507i
\(254\) 44.7049i 0.176003i
\(255\) 84.5646 + 78.9933i 0.331626 + 0.309777i
\(256\) 16.0000 0.0625000
\(257\) 177.198 + 177.198i 0.689485 + 0.689485i 0.962118 0.272633i \(-0.0878946\pi\)
−0.272633 + 0.962118i \(0.587895\pi\)
\(258\) 125.497 125.497i 0.486424 0.486424i
\(259\) 12.7266i 0.0491376i
\(260\) 8.37548 + 245.879i 0.0322134 + 0.945687i
\(261\) 23.3091 0.0893067
\(262\) −158.682 158.682i −0.605656 0.605656i
\(263\) −229.746 + 229.746i −0.873558 + 0.873558i −0.992858 0.119300i \(-0.961935\pi\)
0.119300 + 0.992858i \(0.461935\pi\)
\(264\) 40.7550i 0.154375i
\(265\) −408.690 + 13.9214i −1.54223 + 0.0525336i
\(266\) −14.0888 −0.0529656
\(267\) 83.1232 + 83.1232i 0.311323 + 0.311323i
\(268\) −107.051 + 107.051i −0.399443 + 0.399443i
\(269\) 216.650i 0.805389i 0.915334 + 0.402695i \(0.131926\pi\)
−0.915334 + 0.402695i \(0.868074\pi\)
\(270\) −25.0812 + 26.8502i −0.0928934 + 0.0994451i
\(271\) −149.342 −0.551076 −0.275538 0.961290i \(-0.588856\pi\)
−0.275538 + 0.961290i \(0.588856\pi\)
\(272\) −37.7940 37.7940i −0.138948 0.138948i
\(273\) 12.0860 12.0860i 0.0442709 0.0442709i
\(274\) 19.5283i 0.0712711i
\(275\) 14.1524 + 207.495i 0.0514633 + 0.754526i
\(276\) 16.6132 0.0601929
\(277\) −73.9775 73.9775i −0.267067 0.267067i 0.560850 0.827917i \(-0.310474\pi\)
−0.827917 + 0.560850i \(0.810474\pi\)
\(278\) 83.2727 83.2727i 0.299542 0.299542i
\(279\) 65.2856i 0.233999i
\(280\) −4.14532 3.87222i −0.0148047 0.0138293i
\(281\) 220.186 0.783580 0.391790 0.920055i \(-0.371856\pi\)
0.391790 + 0.920055i \(0.371856\pi\)
\(282\) 140.447 + 140.447i 0.498040 + 0.498040i
\(283\) −160.030 + 160.030i −0.565475 + 0.565475i −0.930858 0.365382i \(-0.880938\pi\)
0.365382 + 0.930858i \(0.380938\pi\)
\(284\) 86.2613i 0.303737i
\(285\) −7.32260 214.969i −0.0256933 0.754278i
\(286\) 289.443 1.01204
\(287\) −0.766492 0.766492i −0.00267070 0.00267070i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 110.452i 0.382186i
\(290\) −54.9081 + 1.87036i −0.189338 + 0.00644952i
\(291\) −118.611 −0.407600
\(292\) 36.1659 + 36.1659i 0.123856 + 0.123856i
\(293\) 272.405 272.405i 0.929710 0.929710i −0.0679767 0.997687i \(-0.521654\pi\)
0.997687 + 0.0679767i \(0.0216543\pi\)
\(294\) 119.631i 0.406908i
\(295\) −58.5751 + 62.7064i −0.198560 + 0.212564i
\(296\) −89.7421 −0.303183
\(297\) 30.5662 + 30.5662i 0.102917 + 0.102917i
\(298\) −274.269 + 274.269i −0.920367 + 0.920367i
\(299\) 117.988i 0.394607i
\(300\) 56.9282 65.2624i 0.189761 0.217541i
\(301\) 29.0627 0.0965539
\(302\) 8.76603 + 8.76603i 0.0290266 + 0.0290266i
\(303\) −103.801 + 103.801i −0.342577 + 0.342577i
\(304\) 99.3476i 0.326801i
\(305\) −324.957 303.548i −1.06543 0.995239i
\(306\) −56.6910 −0.185265
\(307\) 183.385 + 183.385i 0.597346 + 0.597346i 0.939606 0.342259i \(-0.111192\pi\)
−0.342259 + 0.939606i \(0.611192\pi\)
\(308\) −4.71903 + 4.71903i −0.0153215 + 0.0153215i
\(309\) 212.984i 0.689269i
\(310\) −5.23864 153.791i −0.0168988 0.496098i
\(311\) 17.2354 0.0554193 0.0277096 0.999616i \(-0.491179\pi\)
0.0277096 + 0.999616i \(0.491179\pi\)
\(312\) −85.2242 85.2242i −0.273155 0.273155i
\(313\) 9.90854 9.90854i 0.0316567 0.0316567i −0.691101 0.722758i \(-0.742874\pi\)
0.722758 + 0.691101i \(0.242874\pi\)
\(314\) 440.887i 1.40410i
\(315\) −6.01315 + 0.204829i −0.0190894 + 0.000650250i
\(316\) 310.924 0.983937
\(317\) 23.5479 + 23.5479i 0.0742837 + 0.0742837i 0.743272 0.668989i \(-0.233273\pi\)
−0.668989 + 0.743272i \(0.733273\pi\)
\(318\) 141.657 141.657i 0.445461 0.445461i
\(319\) 64.6366i 0.202623i
\(320\) −27.3050 + 29.2308i −0.0853280 + 0.0913462i
\(321\) 38.1992 0.119001
\(322\) 1.92365 + 1.92365i 0.00597408 + 0.00597408i
\(323\) 234.671 234.671i 0.726537 0.726537i
\(324\) 18.0000i 0.0555556i
\(325\) −463.495 404.305i −1.42614 1.24402i
\(326\) 123.641 0.379267
\(327\) −16.8684 16.8684i −0.0515854 0.0515854i
\(328\) −5.40493 + 5.40493i −0.0164784 + 0.0164784i
\(329\) 32.5248i 0.0988597i
\(330\) −74.4562 69.5508i −0.225625 0.210760i
\(331\) −376.962 −1.13886 −0.569429 0.822041i \(-0.692836\pi\)
−0.569429 + 0.822041i \(0.692836\pi\)
\(332\) 139.197 + 139.197i 0.419269 + 0.419269i
\(333\) −67.3066 + 67.3066i −0.202122 + 0.202122i
\(334\) 8.11629i 0.0243003i
\(335\) −12.8849 378.262i −0.0384624 1.12914i
\(336\) 2.77897 0.00827073
\(337\) −375.137 375.137i −1.11317 1.11317i −0.992720 0.120446i \(-0.961568\pi\)
−0.120446 0.992720i \(-0.538432\pi\)
\(338\) −436.264 + 436.264i −1.29072 + 1.29072i
\(339\) 257.321i 0.759060i
\(340\) 133.544 4.54899i 0.392778 0.0133794i
\(341\) −181.039 −0.530905
\(342\) 74.5107 + 74.5107i 0.217868 + 0.217868i
\(343\) 27.7498 27.7498i 0.0809033 0.0809033i
\(344\) 204.936i 0.595745i
\(345\) −28.3515 + 30.3511i −0.0821783 + 0.0879743i
\(346\) 329.215 0.951490
\(347\) −404.186 404.186i −1.16480 1.16480i −0.983411 0.181389i \(-0.941941\pi\)
−0.181389 0.983411i \(-0.558059\pi\)
\(348\) 19.0318 19.0318i 0.0546890 0.0546890i
\(349\) 99.8402i 0.286075i −0.989717 0.143038i \(-0.954313\pi\)
0.989717 0.143038i \(-0.0456870\pi\)
\(350\) 14.1485 0.965012i 0.0404242 0.00275718i
\(351\) −127.836 −0.364206
\(352\) 33.2763 + 33.2763i 0.0945349 + 0.0945349i
\(353\) 435.069 435.069i 1.23249 1.23249i 0.269486 0.963004i \(-0.413146\pi\)
0.963004 0.269486i \(-0.0868538\pi\)
\(354\) 42.0375i 0.118750i
\(355\) 157.593 + 147.210i 0.443923 + 0.414676i
\(356\) 135.740 0.381291
\(357\) −6.56426 6.56426i −0.0183873 0.0183873i
\(358\) 285.884 285.884i 0.798559 0.798559i
\(359\) 258.473i 0.719980i −0.932956 0.359990i \(-0.882780\pi\)
0.932956 0.359990i \(-0.117220\pi\)
\(360\) 1.44435 + 42.4018i 0.00401209 + 0.117783i
\(361\) −255.872 −0.708787
\(362\) −207.433 207.433i −0.573020 0.573020i
\(363\) 63.4332 63.4332i 0.174747 0.174747i
\(364\) 19.7363i 0.0542205i
\(365\) −127.792 + 4.35303i −0.350114 + 0.0119261i
\(366\) 217.847 0.595210
\(367\) 94.6541 + 94.6541i 0.257913 + 0.257913i 0.824205 0.566292i \(-0.191622\pi\)
−0.566292 + 0.824205i \(0.691622\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 8.10739i 0.0219712i
\(370\) 153.150 163.952i 0.413920 0.443114i
\(371\) 32.8049 0.0884229
\(372\) 53.3055 + 53.3055i 0.143294 + 0.143294i
\(373\) 393.151 393.151i 1.05402 1.05402i 0.0555700 0.998455i \(-0.482302\pi\)
0.998455 0.0555700i \(-0.0176976\pi\)
\(374\) 157.205i 0.420335i
\(375\) 22.0779 + 215.378i 0.0588743 + 0.574341i
\(376\) 229.349 0.609972
\(377\) −135.164 135.164i −0.358525 0.358525i
\(378\) 2.08422 2.08422i 0.00551382 0.00551382i
\(379\) 173.870i 0.458761i −0.973337 0.229380i \(-0.926330\pi\)
0.973337 0.229380i \(-0.0736700\pi\)
\(380\) −181.501 169.543i −0.477633 0.446165i
\(381\) 54.7521 0.143706
\(382\) −17.3738 17.3738i −0.0454811 0.0454811i
\(383\) 314.104 314.104i 0.820115 0.820115i −0.166009 0.986124i \(-0.553088\pi\)
0.986124 + 0.166009i \(0.0530881\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −0.567995 16.6746i −0.00147531 0.0433107i
\(386\) 282.679 0.732330
\(387\) −153.702 153.702i −0.397163 0.397163i
\(388\) −96.8459 + 96.8459i −0.249603 + 0.249603i
\(389\) 33.5984i 0.0863712i 0.999067 + 0.0431856i \(0.0137507\pi\)
−0.999067 + 0.0431856i \(0.986249\pi\)
\(390\) 301.139 10.2578i 0.772150 0.0263021i
\(391\) −64.0828 −0.163895
\(392\) −97.6782 97.6782i −0.249179 0.249179i
\(393\) −194.345 + 194.345i −0.494516 + 0.494516i
\(394\) 426.561i 1.08264i
\(395\) −530.611 + 568.034i −1.34332 + 1.43806i
\(396\) 49.9144 0.126047
\(397\) 286.486 + 286.486i 0.721628 + 0.721628i 0.968937 0.247309i \(-0.0795462\pi\)
−0.247309 + 0.968937i \(0.579546\pi\)
\(398\) −84.3085 + 84.3085i −0.211830 + 0.211830i
\(399\) 17.2552i 0.0432462i
\(400\) −6.80480 99.7682i −0.0170120 0.249421i
\(401\) 335.115 0.835699 0.417849 0.908516i \(-0.362784\pi\)
0.417849 + 0.908516i \(0.362784\pi\)
\(402\) 131.110 + 131.110i 0.326144 + 0.326144i
\(403\) 378.577 378.577i 0.939396 0.939396i
\(404\) 169.506i 0.419569i
\(405\) 32.8846 + 30.7181i 0.0811966 + 0.0758472i
\(406\) 4.40739 0.0108556
\(407\) −186.643 186.643i −0.458582 0.458582i
\(408\) −46.2880 + 46.2880i −0.113451 + 0.113451i
\(409\) 259.446i 0.634342i −0.948368 0.317171i \(-0.897267\pi\)
0.948368 0.317171i \(-0.102733\pi\)
\(410\) −0.650552 19.0982i −0.00158671 0.0465810i
\(411\) −23.9172 −0.0581926
\(412\) −173.901 173.901i −0.422090 0.422090i
\(413\) 4.86754 4.86754i 0.0117858 0.0117858i
\(414\) 20.3470i 0.0491473i
\(415\) −491.852 + 16.7542i −1.18519 + 0.0403715i
\(416\) −139.171 −0.334545
\(417\) −101.988 101.988i −0.244575 0.244575i
\(418\) −206.620 + 206.620i −0.494306 + 0.494306i
\(419\) 71.0303i 0.169523i 0.996401 + 0.0847617i \(0.0270129\pi\)
−0.996401 + 0.0847617i \(0.972987\pi\)
\(420\) −4.74248 + 5.07696i −0.0112916 + 0.0120880i
\(421\) −356.971 −0.847912 −0.423956 0.905683i \(-0.639359\pi\)
−0.423956 + 0.905683i \(0.639359\pi\)
\(422\) −301.566 301.566i −0.714612 0.714612i
\(423\) 172.012 172.012i 0.406648 0.406648i
\(424\) 231.324i 0.545576i
\(425\) −219.591 + 251.739i −0.516685 + 0.592326i
\(426\) −105.648 −0.248000
\(427\) 25.2245 + 25.2245i 0.0590738 + 0.0590738i
\(428\) 31.1895 31.1895i 0.0728728 0.0728728i
\(429\) 354.493i 0.826325i
\(430\) 374.403 + 349.736i 0.870704 + 0.813340i
\(431\) 34.4291 0.0798818 0.0399409 0.999202i \(-0.487283\pi\)
0.0399409 + 0.999202i \(0.487283\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −121.062 + 121.062i −0.279590 + 0.279590i −0.832945 0.553356i \(-0.813347\pi\)
0.553356 + 0.832945i \(0.313347\pi\)
\(434\) 12.3445i 0.0284436i
\(435\) 2.29072 + 67.2485i 0.00526601 + 0.154594i
\(436\) −27.5460 −0.0631789
\(437\) 84.2261 + 84.2261i 0.192737 + 0.192737i
\(438\) 44.2940 44.2940i 0.101128 0.101128i
\(439\) 808.849i 1.84248i 0.388993 + 0.921241i \(0.372823\pi\)
−0.388993 + 0.921241i \(0.627177\pi\)
\(440\) −117.581 + 4.00523i −0.267230 + 0.00910279i
\(441\) −146.517 −0.332239
\(442\) 328.738 + 328.738i 0.743751 + 0.743751i
\(443\) 131.518 131.518i 0.296881 0.296881i −0.542910 0.839791i \(-0.682678\pi\)
0.839791 + 0.542910i \(0.182678\pi\)
\(444\) 109.911i 0.247548i
\(445\) −231.648 + 247.986i −0.520557 + 0.557272i
\(446\) −83.6662 −0.187592
\(447\) 335.910 + 335.910i 0.751477 + 0.751477i
\(448\) 2.26902 2.26902i 0.00506477 0.00506477i
\(449\) 653.049i 1.45445i −0.686398 0.727226i \(-0.740809\pi\)
0.686398 0.727226i \(-0.259191\pi\)
\(450\) −79.9298 69.7226i −0.177622 0.154939i
\(451\) −22.4820 −0.0498492
\(452\) 210.102 + 210.102i 0.464827 + 0.464827i
\(453\) 10.7362 10.7362i 0.0237001 0.0237001i
\(454\) 270.595i 0.596024i
\(455\) 36.0567 + 33.6812i 0.0792454 + 0.0740245i
\(456\) 121.676 0.266832
\(457\) −60.9591 60.9591i −0.133390 0.133390i 0.637259 0.770649i \(-0.280068\pi\)
−0.770649 + 0.637259i \(0.780068\pi\)
\(458\) 337.019 337.019i 0.735850 0.735850i
\(459\) 69.4320i 0.151268i
\(460\) 1.63268 + 47.9305i 0.00354930 + 0.104197i
\(461\) 156.041 0.338484 0.169242 0.985575i \(-0.445868\pi\)
0.169242 + 0.985575i \(0.445868\pi\)
\(462\) 5.77961 + 5.77961i 0.0125100 + 0.0125100i
\(463\) −510.074 + 510.074i −1.10167 + 1.10167i −0.107464 + 0.994209i \(0.534273\pi\)
−0.994209 + 0.107464i \(0.965727\pi\)
\(464\) 31.0787i 0.0669801i
\(465\) −188.354 + 6.41599i −0.405063 + 0.0137978i
\(466\) 209.594 0.449772
\(467\) −91.8344 91.8344i −0.196647 0.196647i 0.601914 0.798561i \(-0.294405\pi\)
−0.798561 + 0.601914i \(0.794405\pi\)
\(468\) −104.378 + 104.378i −0.223030 + 0.223030i
\(469\) 30.3625i 0.0647387i
\(470\) −391.399 + 419.004i −0.832763 + 0.891497i
\(471\) 539.974 1.14644
\(472\) −34.3235 34.3235i −0.0727193 0.0727193i
\(473\) 426.220 426.220i 0.901099 0.901099i
\(474\) 380.803i 0.803381i
\(475\) 619.483 42.2525i 1.30418 0.0889527i
\(476\) −10.7194 −0.0225197
\(477\) −173.493 173.493i −0.363717 0.363717i
\(478\) −223.047 + 223.047i −0.466625 + 0.466625i
\(479\) 283.471i 0.591797i −0.955219 0.295899i \(-0.904381\pi\)
0.955219 0.295899i \(-0.0956191\pi\)
\(480\) 35.8002 + 33.4416i 0.0745838 + 0.0696701i
\(481\) 780.592 1.62285
\(482\) 167.112 + 167.112i 0.346706 + 0.346706i
\(483\) 2.35598 2.35598i 0.00487781 0.00487781i
\(484\) 103.586i 0.214021i
\(485\) −11.6566 342.203i −0.0240343 0.705574i
\(486\) −22.0454 −0.0453609
\(487\) 564.917 + 564.917i 1.15999 + 1.15999i 0.984476 + 0.175518i \(0.0561600\pi\)
0.175518 + 0.984476i \(0.443840\pi\)
\(488\) 177.871 177.871i 0.364490 0.364490i
\(489\) 151.429i 0.309670i
\(490\) 345.144 11.7568i 0.704377 0.0239935i
\(491\) −91.4234 −0.186198 −0.0930992 0.995657i \(-0.529677\pi\)
−0.0930992 + 0.995657i \(0.529677\pi\)
\(492\) 6.61966 + 6.61966i 0.0134546 + 0.0134546i
\(493\) −73.4118 + 73.4118i −0.148908 + 0.148908i
\(494\) 864.142i 1.74927i
\(495\) −85.1820 + 91.1899i −0.172085 + 0.184222i
\(496\) 87.0475 0.175499
\(497\) −12.2330 12.2330i −0.0246137 0.0246137i
\(498\) 170.481 170.481i 0.342332 0.342332i
\(499\) 793.096i 1.58937i −0.607021 0.794685i \(-0.707636\pi\)
0.607021 0.794685i \(-0.292364\pi\)
\(500\) 193.882 + 157.829i 0.387763 + 0.315657i
\(501\) 9.94038 0.0198411
\(502\) −441.419 441.419i −0.879321 0.879321i
\(503\) −538.128 + 538.128i −1.06984 + 1.06984i −0.0724666 + 0.997371i \(0.523087\pi\)
−0.997371 + 0.0724666i \(0.976913\pi\)
\(504\) 3.40352i 0.00675303i
\(505\) −309.674 289.272i −0.613217 0.572816i
\(506\) 56.4227 0.111507
\(507\) 534.312 + 534.312i 1.05387 + 1.05387i
\(508\) 44.7049 44.7049i 0.0880017 0.0880017i
\(509\) 265.214i 0.521049i 0.965467 + 0.260524i \(0.0838954\pi\)
−0.965467 + 0.260524i \(0.916105\pi\)
\(510\) −5.57135 163.558i −0.0109242 0.320702i
\(511\) 10.2576 0.0200736
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 91.2566 91.2566i 0.177888 0.177888i
\(514\) 354.395i 0.689485i
\(515\) 614.476 20.9312i 1.19316 0.0406431i
\(516\) −250.995 −0.486424
\(517\) 476.993 + 476.993i 0.922618 + 0.922618i
\(518\) −12.7266 + 12.7266i −0.0245688 + 0.0245688i
\(519\) 403.205i 0.776888i
\(520\) 237.503 254.254i 0.456737 0.488950i
\(521\) −345.104 −0.662387 −0.331194 0.943563i \(-0.607451\pi\)
−0.331194 + 0.943563i \(0.607451\pi\)
\(522\) −23.3091 23.3091i −0.0446534 0.0446534i
\(523\) −356.976 + 356.976i −0.682554 + 0.682554i −0.960575 0.278021i \(-0.910322\pi\)
0.278021 + 0.960575i \(0.410322\pi\)
\(524\) 317.364i 0.605656i
\(525\) −1.18189 17.3283i −0.00225123 0.0330062i
\(526\) 459.491 0.873558
\(527\) −205.617 205.617i −0.390165 0.390165i
\(528\) 40.7550 40.7550i 0.0771875 0.0771875i
\(529\) 23.0000i 0.0434783i
\(530\) 422.612 + 394.769i 0.797380 + 0.744847i
\(531\) −51.4852 −0.0969590
\(532\) 14.0888 + 14.0888i 0.0264828 + 0.0264828i
\(533\) 47.0129 47.0129i 0.0882044 0.0882044i
\(534\) 166.246i 0.311323i
\(535\) 3.75406 + 110.208i 0.00701693 + 0.205996i
\(536\) 214.101 0.399443
\(537\) −350.135 350.135i −0.652021 0.652021i
\(538\) 216.650 216.650i 0.402695 0.402695i
\(539\) 406.296i 0.753796i
\(540\) 51.9314 1.76896i 0.0961693 0.00327586i
\(541\) 35.6543 0.0659044 0.0329522 0.999457i \(-0.489509\pi\)
0.0329522 + 0.999457i \(0.489509\pi\)
\(542\) 149.342 + 149.342i 0.275538 + 0.275538i
\(543\) −254.053 + 254.053i −0.467869 + 0.467869i
\(544\) 75.5880i 0.138948i
\(545\) 47.0089 50.3244i 0.0862549 0.0923384i
\(546\) −24.1719 −0.0442709
\(547\) 445.794 + 445.794i 0.814981 + 0.814981i 0.985376 0.170395i \(-0.0545044\pi\)
−0.170395 + 0.985376i \(0.554504\pi\)
\(548\) −19.5283 + 19.5283i −0.0356356 + 0.0356356i
\(549\) 266.807i 0.485987i
\(550\) 193.342 221.647i 0.351532 0.402995i
\(551\) 192.975 0.350227
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 44.0932 44.0932i 0.0797346 0.0797346i
\(554\) 147.955i 0.267067i
\(555\) −200.799 187.570i −0.361801 0.337964i
\(556\) −166.545 −0.299542
\(557\) −601.246 601.246i −1.07944 1.07944i −0.996560 0.0828770i \(-0.973589\pi\)
−0.0828770 0.996560i \(-0.526411\pi\)
\(558\) 65.2856 65.2856i 0.116999 0.116999i
\(559\) 1782.57i 3.18885i
\(560\) 0.273105 + 8.01754i 0.000487688 + 0.0143170i
\(561\) −192.537 −0.343202
\(562\) −220.186 220.186i −0.391790 0.391790i
\(563\) 179.406 179.406i 0.318660 0.318660i −0.529592 0.848252i \(-0.677655\pi\)
0.848252 + 0.529592i \(0.177655\pi\)
\(564\) 280.894i 0.498040i
\(565\) −742.392 + 25.2884i −1.31397 + 0.0447583i
\(566\) 320.059 0.565475
\(567\) −2.55264 2.55264i −0.00450202 0.00450202i
\(568\) −86.2613 + 86.2613i −0.151868 + 0.151868i
\(569\) 132.003i 0.231991i 0.993250 + 0.115995i \(0.0370058\pi\)
−0.993250 + 0.115995i \(0.962994\pi\)
\(570\) −207.647 + 222.292i −0.364292 + 0.389986i
\(571\) 40.8166 0.0714826 0.0357413 0.999361i \(-0.488621\pi\)
0.0357413 + 0.999361i \(0.488621\pi\)
\(572\) −289.443 289.443i −0.506019 0.506019i
\(573\) −21.2784 + 21.2784i −0.0371352 + 0.0371352i
\(574\) 1.53298i 0.00267070i
\(575\) −90.3517 78.8136i −0.157133 0.137067i
\(576\) −24.0000 −0.0416667
\(577\) −445.272 445.272i −0.771703 0.771703i 0.206701 0.978404i \(-0.433727\pi\)
−0.978404 + 0.206701i \(0.933727\pi\)
\(578\) −110.452 + 110.452i −0.191093 + 0.191093i
\(579\) 346.210i 0.597945i
\(580\) 56.7785 + 53.0378i 0.0978940 + 0.0914444i
\(581\) 39.4801 0.0679521
\(582\) 118.611 + 118.611i 0.203800 + 0.203800i
\(583\) 481.101 481.101i 0.825216 0.825216i
\(584\) 72.3318i 0.123856i
\(585\) −12.5632 368.818i −0.0214756 0.630458i
\(586\) −544.810 −0.929710
\(587\) −437.704 437.704i −0.745663 0.745663i 0.227999 0.973661i \(-0.426782\pi\)
−0.973661 + 0.227999i \(0.926782\pi\)
\(588\) −119.631 + 119.631i −0.203454 + 0.203454i
\(589\) 540.498i 0.917653i
\(590\) 121.282 4.13127i 0.205562 0.00700215i
\(591\) −522.428 −0.883973
\(592\) 89.7421 + 89.7421i 0.151591 + 0.151591i
\(593\) 605.242 605.242i 1.02064 1.02064i 0.0208625 0.999782i \(-0.493359\pi\)
0.999782 0.0208625i \(-0.00664122\pi\)
\(594\) 61.1325i 0.102917i
\(595\) 18.2933 19.5835i 0.0307450 0.0329135i
\(596\) 548.539 0.920367
\(597\) 103.256 + 103.256i 0.172959 + 0.172959i
\(598\) −117.988 + 117.988i −0.197304 + 0.197304i
\(599\) 923.521i 1.54177i 0.636974 + 0.770886i \(0.280186\pi\)
−0.636974 + 0.770886i \(0.719814\pi\)
\(600\) −122.191 + 8.33414i −0.203651 + 0.0138902i
\(601\) 858.844 1.42902 0.714512 0.699623i \(-0.246649\pi\)
0.714512 + 0.699623i \(0.246649\pi\)
\(602\) −29.0627 29.0627i −0.0482770 0.0482770i
\(603\) 160.576 160.576i 0.266295 0.266295i
\(604\) 17.5321i 0.0290266i
\(605\) 189.244 + 176.776i 0.312800 + 0.292191i
\(606\) 207.602 0.342577
\(607\) −317.963 317.963i −0.523826 0.523826i 0.394898 0.918725i \(-0.370780\pi\)
−0.918725 + 0.394898i \(0.870780\pi\)
\(608\) 99.3476 99.3476i 0.163401 0.163401i
\(609\) 5.39792i 0.00886359i
\(610\) 21.4091 + 628.505i 0.0350968 + 1.03034i
\(611\) −1994.92 −3.26500
\(612\) 56.6910 + 56.6910i 0.0926323 + 0.0926323i
\(613\) −537.516 + 537.516i −0.876861 + 0.876861i −0.993209 0.116347i \(-0.962881\pi\)
0.116347 + 0.993209i \(0.462881\pi\)
\(614\) 366.771i 0.597346i
\(615\) −23.3905 + 0.796760i −0.0380333 + 0.00129554i
\(616\) 9.43806 0.0153215
\(617\) −565.370 565.370i −0.916320 0.916320i 0.0804392 0.996760i \(-0.474368\pi\)
−0.996760 + 0.0804392i \(0.974368\pi\)
\(618\) −212.984 + 212.984i −0.344635 + 0.344635i
\(619\) 60.9967i 0.0985407i 0.998785 + 0.0492703i \(0.0156896\pi\)
−0.998785 + 0.0492703i \(0.984310\pi\)
\(620\) −148.552 + 159.029i −0.239600 + 0.256499i
\(621\) −24.9199 −0.0401286
\(622\) −17.2354 17.2354i −0.0277096 0.0277096i
\(623\) 19.2497 19.2497i 0.0308984 0.0308984i
\(624\) 170.448i 0.273155i
\(625\) −619.212 + 84.8628i −0.990739 + 0.135780i
\(626\) −19.8171 −0.0316567
\(627\) 253.057 + 253.057i 0.403599 + 0.403599i
\(628\) 440.887 440.887i 0.702049 0.702049i
\(629\) 423.964i 0.674029i
\(630\) 6.21798 + 5.80832i 0.00986981 + 0.00921956i
\(631\) 1099.71 1.74281 0.871403 0.490568i \(-0.163211\pi\)
0.871403 + 0.490568i \(0.163211\pi\)
\(632\) −310.924 310.924i −0.491968 0.491968i
\(633\) −369.342 + 369.342i −0.583479 + 0.583479i
\(634\) 47.0959i 0.0742837i
\(635\) 5.38080 + 157.964i 0.00847370 + 0.248762i
\(636\) −283.313 −0.445461
\(637\) 849.621 + 849.621i 1.33378 + 1.33378i
\(638\) 64.6366 64.6366i 0.101311 0.101311i
\(639\) 129.392i 0.202491i
\(640\) 56.5358 1.92580i 0.0883371 0.00300907i
\(641\) 524.487 0.818233 0.409116 0.912482i \(-0.365837\pi\)
0.409116 + 0.912482i \(0.365837\pi\)
\(642\) −38.1992 38.1992i −0.0595004 0.0595004i
\(643\) 409.688 409.688i 0.637151 0.637151i −0.312701 0.949852i \(-0.601234\pi\)
0.949852 + 0.312701i \(0.101234\pi\)
\(644\) 3.84730i 0.00597408i
\(645\) 428.337 458.548i 0.664089 0.710927i
\(646\) −469.343 −0.726537
\(647\) 423.917 + 423.917i 0.655204 + 0.655204i 0.954241 0.299037i \(-0.0966654\pi\)
−0.299037 + 0.954241i \(0.596665\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 142.770i 0.219984i
\(650\) 59.1892 + 867.800i 0.0910604 + 1.33508i
\(651\) 15.1189 0.0232241
\(652\) −123.641 123.641i −0.189633 0.189633i
\(653\) 579.557 579.557i 0.887530 0.887530i −0.106756 0.994285i \(-0.534046\pi\)
0.994285 + 0.106756i \(0.0340463\pi\)
\(654\) 33.7368i 0.0515854i
\(655\) −579.799 541.600i −0.885190 0.826871i
\(656\) 10.8099 0.0164784
\(657\) −54.2489 54.2489i −0.0825706 0.0825706i
\(658\) 32.5248 32.5248i 0.0494298 0.0494298i
\(659\) 417.909i 0.634156i 0.948399 + 0.317078i \(0.102702\pi\)
−0.948399 + 0.317078i \(0.897298\pi\)
\(660\) 4.90538 + 144.007i 0.00743239 + 0.218193i
\(661\) 964.858 1.45969 0.729847 0.683610i \(-0.239591\pi\)
0.729847 + 0.683610i \(0.239591\pi\)
\(662\) 376.962 + 376.962i 0.569429 + 0.569429i
\(663\) 402.620 402.620i 0.607271 0.607271i
\(664\) 278.395i 0.419269i
\(665\) −49.7827 + 1.69577i −0.0748612 + 0.00255003i
\(666\) 134.613 0.202122
\(667\) −26.3483 26.3483i −0.0395027 0.0395027i
\(668\) 8.11629 8.11629i 0.0121501 0.0121501i
\(669\) 102.470i 0.153168i
\(670\) −365.377 + 391.147i −0.545339 + 0.583801i
\(671\) 739.861 1.10263
\(672\) −2.77897 2.77897i −0.00413537 0.00413537i
\(673\) −263.331 + 263.331i −0.391280 + 0.391280i −0.875143 0.483864i \(-0.839233\pi\)
0.483864 + 0.875143i \(0.339233\pi\)
\(674\) 750.274i 1.11317i
\(675\) −85.3923 + 97.8936i −0.126507 + 0.145027i
\(676\) 872.528 1.29072
\(677\) 47.8727 + 47.8727i 0.0707130 + 0.0707130i 0.741579 0.670866i \(-0.234077\pi\)
−0.670866 + 0.741579i \(0.734077\pi\)
\(678\) 257.321 257.321i 0.379530 0.379530i
\(679\) 27.4681i 0.0404538i
\(680\) −138.093 128.995i −0.203079 0.189699i
\(681\) −331.409 −0.486651
\(682\) 181.039 + 181.039i 0.265453 + 0.265453i
\(683\) 491.209 491.209i 0.719193 0.719193i −0.249247 0.968440i \(-0.580183\pi\)
0.968440 + 0.249247i \(0.0801832\pi\)
\(684\) 149.021i 0.217868i
\(685\) −2.35048 69.0029i −0.00343135 0.100734i
\(686\) −55.4996 −0.0809033
\(687\) −412.763 412.763i −0.600819 0.600819i
\(688\) −204.936 + 204.936i −0.297872 + 0.297872i
\(689\) 2012.10i 2.92031i
\(690\) 58.7027 1.99962i 0.0850763 0.00289799i
\(691\) −356.833 −0.516400 −0.258200 0.966091i \(-0.583129\pi\)
−0.258200 + 0.966091i \(0.583129\pi\)
\(692\) −329.215 329.215i −0.475745 0.475745i
\(693\) 7.07854 7.07854i 0.0102143 0.0102143i
\(694\) 808.372i 1.16480i
\(695\) 284.220 304.266i 0.408950 0.437793i
\(696\) −38.0635 −0.0546890
\(697\) −25.5342 25.5342i −0.0366344 0.0366344i
\(698\) −99.8402 + 99.8402i −0.143038 + 0.143038i
\(699\) 256.699i 0.367238i
\(700\) −15.1135 13.1835i −0.0215907 0.0188335i
\(701\) 512.770 0.731483 0.365742 0.930716i \(-0.380815\pi\)
0.365742 + 0.930716i \(0.380815\pi\)
\(702\) 127.836 + 127.836i 0.182103 + 0.182103i
\(703\) −557.229 + 557.229i −0.792645 + 0.792645i
\(704\) 66.5526i 0.0945349i
\(705\) 513.173 + 479.363i 0.727904 + 0.679948i
\(706\) −870.138 −1.23249
\(707\) 24.0382 + 24.0382i 0.0340003 + 0.0340003i
\(708\) −42.0375 + 42.0375i −0.0593750 + 0.0593750i
\(709\) 557.179i 0.785865i −0.919567 0.392933i \(-0.871461\pi\)
0.919567 0.392933i \(-0.128539\pi\)
\(710\) −10.3826 304.803i −0.0146234 0.429300i
\(711\) −466.386 −0.655958
\(712\) −135.740 135.740i −0.190646 0.190646i
\(713\) 73.7981 73.7981i 0.103504 0.103504i
\(714\) 13.1285i 0.0183873i
\(715\) 1022.74 34.8381i 1.43041 0.0487246i
\(716\) −571.768 −0.798559
\(717\) 273.175 + 273.175i 0.380998 + 0.380998i
\(718\) −258.473 + 258.473i −0.359990 + 0.359990i
\(719\) 704.591i 0.979960i 0.871734 + 0.489980i \(0.162996\pi\)
−0.871734 + 0.489980i \(0.837004\pi\)
\(720\) 40.9575 43.8462i 0.0568854 0.0608975i
\(721\) −49.3230 −0.0684092
\(722\) 255.872 + 255.872i 0.354393 + 0.354393i
\(723\) 204.670 204.670i 0.283084 0.283084i
\(724\) 414.866i 0.573020i
\(725\) −193.792 + 13.2178i −0.267299 + 0.0182314i
\(726\) −126.866 −0.174747
\(727\) −103.504 103.504i −0.142372 0.142372i 0.632328 0.774700i \(-0.282099\pi\)
−0.774700 + 0.632328i \(0.782099\pi\)
\(728\) −19.7363 + 19.7363i −0.0271103 + 0.0271103i
\(729\) 27.0000i 0.0370370i
\(730\) 132.145 + 123.439i 0.181020 + 0.169094i
\(731\) 968.169 1.32444
\(732\) −217.847 217.847i −0.297605 0.297605i
\(733\) 399.591 399.591i 0.545145 0.545145i −0.379887 0.925033i \(-0.624037\pi\)
0.925033 + 0.379887i \(0.124037\pi\)
\(734\) 189.308i 0.257913i
\(735\) −14.3991 422.714i −0.0195906 0.575121i
\(736\) −27.1293 −0.0368605
\(737\) 445.281 + 445.281i 0.604181 + 0.604181i
\(738\) 8.10739 8.10739i 0.0109856 0.0109856i
\(739\) 463.718i 0.627494i 0.949507 + 0.313747i \(0.101584\pi\)
−0.949507 + 0.313747i \(0.898416\pi\)
\(740\) −317.102 + 10.8016i −0.428517 + 0.0145968i
\(741\) −1058.35 −1.42828
\(742\) −32.8049 32.8049i −0.0442115 0.0442115i
\(743\) 142.650 142.650i 0.191992 0.191992i −0.604564 0.796556i \(-0.706653\pi\)
0.796556 + 0.604564i \(0.206653\pi\)
\(744\) 106.611i 0.143294i
\(745\) −936.115 + 1002.14i −1.25653 + 1.34515i
\(746\) −786.302 −1.05402
\(747\) −208.796 208.796i −0.279513 0.279513i
\(748\) −157.205 + 157.205i −0.210168 + 0.210168i
\(749\) 8.84620i 0.0118107i
\(750\) 193.300 237.456i 0.257733 0.316607i
\(751\) −786.317 −1.04703 −0.523513 0.852017i \(-0.675379\pi\)
−0.523513 + 0.852017i \(0.675379\pi\)
\(752\) −229.349 229.349i −0.304986 0.304986i
\(753\) −540.626 + 540.626i −0.717963 + 0.717963i
\(754\) 270.328i 0.358525i
\(755\) 32.0297 + 29.9195i 0.0424235 + 0.0396285i
\(756\) −4.16845 −0.00551382
\(757\) 303.467 + 303.467i 0.400881 + 0.400881i 0.878543 0.477663i \(-0.158516\pi\)
−0.477663 + 0.878543i \(0.658516\pi\)
\(758\) −173.870 + 173.870i −0.229380 + 0.229380i
\(759\) 69.1034i 0.0910454i
\(760\) 11.9578 + 351.043i 0.0157339 + 0.461899i
\(761\) −76.0064 −0.0998770 −0.0499385 0.998752i \(-0.515903\pi\)
−0.0499385 + 0.998752i \(0.515903\pi\)
\(762\) −54.7521 54.7521i −0.0718531 0.0718531i
\(763\) −3.90640 + 3.90640i −0.00511979 + 0.00511979i
\(764\) 34.7476i 0.0454811i
\(765\) −200.317 + 6.82348i −0.261852 + 0.00891958i
\(766\) −628.208 −0.820115
\(767\) 298.551 + 298.551i 0.389245 + 0.389245i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 731.164i 0.950798i −0.879770 0.475399i \(-0.842304\pi\)
0.879770 0.475399i \(-0.157696\pi\)
\(770\) −16.1066 + 17.2426i −0.0209177 + 0.0223930i
\(771\) −434.044 −0.562962
\(772\) −282.679 282.679i −0.366165 0.366165i
\(773\) −637.671 + 637.671i −0.824931 + 0.824931i −0.986810 0.161880i \(-0.948244\pi\)
0.161880 + 0.986810i \(0.448244\pi\)
\(774\) 307.404i 0.397163i
\(775\) −37.0213 542.786i −0.0477694 0.700369i
\(776\) 193.692 0.249603
\(777\) 15.5869 + 15.5869i 0.0200604 + 0.0200604i
\(778\) 33.5984 33.5984i 0.0431856 0.0431856i