Properties

Label 690.3.k.a.277.15
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 277.15
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.64969 - 4.24018i) q^{5} +2.44949 q^{6} +(-5.13413 - 5.13413i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.64969 - 4.24018i) q^{5} +2.44949 q^{6} +(-5.13413 - 5.13413i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(6.88987 - 1.59048i) q^{10} -18.8487 q^{11} +(2.44949 + 2.44949i) q^{12} +(-4.85169 + 4.85169i) q^{13} -10.2683i q^{14} +(-1.94794 - 8.43834i) q^{15} -4.00000 q^{16} +(-8.28144 - 8.28144i) q^{17} +(3.00000 - 3.00000i) q^{18} -2.00840i q^{19} +(8.48036 + 5.29939i) q^{20} -12.5760 q^{21} +(-18.8487 - 18.8487i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-10.9582 - 22.4704i) q^{25} -9.70339 q^{26} +(-3.67423 - 3.67423i) q^{27} +(10.2683 - 10.2683i) q^{28} +15.3053i q^{29} +(6.49040 - 10.3863i) q^{30} -18.0217 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-23.0848 + 23.0848i) q^{33} -16.5629i q^{34} +(-35.3735 + 8.16576i) q^{35} +6.00000 q^{36} +(7.99013 + 7.99013i) q^{37} +(2.00840 - 2.00840i) q^{38} +11.8842i q^{39} +(3.18097 + 13.7797i) q^{40} -8.60556 q^{41} +(-12.5760 - 12.5760i) q^{42} +(-18.9595 + 18.9595i) q^{43} -37.6973i q^{44} +(-12.7205 - 7.94908i) q^{45} -6.78233 q^{46} +(21.2643 + 21.2643i) q^{47} +(-4.89898 + 4.89898i) q^{48} +3.71868i q^{49} +(11.5121 - 33.4286i) q^{50} -20.2853 q^{51} +(-9.70339 - 9.70339i) q^{52} +(30.6997 - 30.6997i) q^{53} -7.34847i q^{54} +(-49.9432 + 79.9217i) q^{55} +20.5365 q^{56} +(-2.45978 - 2.45978i) q^{57} +(-15.3053 + 15.3053i) q^{58} -37.0580i q^{59} +(16.8767 - 3.89587i) q^{60} +65.9013 q^{61} +(-18.0217 - 18.0217i) q^{62} +(-15.4024 + 15.4024i) q^{63} -8.00000i q^{64} +(7.71654 + 33.4276i) q^{65} -46.1696 q^{66} +(-70.4656 - 70.4656i) q^{67} +(16.5629 - 16.5629i) q^{68} +8.30662i q^{69} +(-43.5393 - 27.2078i) q^{70} -8.38441 q^{71} +(6.00000 + 6.00000i) q^{72} +(78.9935 - 78.9935i) q^{73} +15.9803i q^{74} +(-40.9415 - 14.0994i) q^{75} +4.01680 q^{76} +(96.7715 + 96.7715i) q^{77} +(-11.8842 + 11.8842i) q^{78} -103.875i q^{79} +(-10.5988 + 16.9607i) q^{80} -9.00000 q^{81} +(-8.60556 - 8.60556i) q^{82} +(37.7965 - 37.7965i) q^{83} -25.1520i q^{84} +(-57.0581 + 13.1715i) q^{85} -37.9191 q^{86} +(18.7451 + 18.7451i) q^{87} +(37.6973 - 37.6973i) q^{88} -140.211i q^{89} +(-4.77145 - 20.6696i) q^{90} +49.8185 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-22.0720 + 22.0720i) q^{93} +42.5286i q^{94} +(-8.51597 - 5.32164i) q^{95} -9.79796 q^{96} +(105.406 + 105.406i) q^{97} +(-3.71868 + 3.71868i) q^{98} +56.5460i 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
\(5\) 2.64969 4.24018i 0.529939 0.848036i
\(6\) 2.44949 0.408248
\(7\) −5.13413 5.13413i −0.733448 0.733448i 0.237853 0.971301i \(-0.423556\pi\)
−0.971301 + 0.237853i \(0.923556\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.88987 1.59048i 0.688987 0.159048i
\(11\) −18.8487 −1.71351 −0.856757 0.515720i \(-0.827524\pi\)
−0.856757 + 0.515720i \(0.827524\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −4.85169 + 4.85169i −0.373207 + 0.373207i −0.868644 0.495437i \(-0.835008\pi\)
0.495437 + 0.868644i \(0.335008\pi\)
\(14\) 10.2683i 0.733448i
\(15\) −1.94794 8.43834i −0.129862 0.562556i
\(16\) −4.00000 −0.250000
\(17\) −8.28144 8.28144i −0.487144 0.487144i 0.420260 0.907404i \(-0.361939\pi\)
−0.907404 + 0.420260i \(0.861939\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 2.00840i 0.105705i −0.998602 0.0528526i \(-0.983169\pi\)
0.998602 0.0528526i \(-0.0168313\pi\)
\(20\) 8.48036 + 5.29939i 0.424018 + 0.264969i
\(21\) −12.5760 −0.598858
\(22\) −18.8487 18.8487i −0.856757 0.856757i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −10.9582 22.4704i −0.438329 0.898814i
\(26\) −9.70339 −0.373207
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 10.2683 10.2683i 0.366724 0.366724i
\(29\) 15.3053i 0.527770i 0.964554 + 0.263885i \(0.0850040\pi\)
−0.964554 + 0.263885i \(0.914996\pi\)
\(30\) 6.49040 10.3863i 0.216347 0.346209i
\(31\) −18.0217 −0.581345 −0.290673 0.956823i \(-0.593879\pi\)
−0.290673 + 0.956823i \(0.593879\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −23.0848 + 23.0848i −0.699539 + 0.699539i
\(34\) 16.5629i 0.487144i
\(35\) −35.3735 + 8.16576i −1.01067 + 0.233307i
\(36\) 6.00000 0.166667
\(37\) 7.99013 + 7.99013i 0.215950 + 0.215950i 0.806789 0.590840i \(-0.201203\pi\)
−0.590840 + 0.806789i \(0.701203\pi\)
\(38\) 2.00840 2.00840i 0.0528526 0.0528526i
\(39\) 11.8842i 0.304722i
\(40\) 3.18097 + 13.7797i 0.0795242 + 0.344494i
\(41\) −8.60556 −0.209892 −0.104946 0.994478i \(-0.533467\pi\)
−0.104946 + 0.994478i \(0.533467\pi\)
\(42\) −12.5760 12.5760i −0.299429 0.299429i
\(43\) −18.9595 + 18.9595i −0.440920 + 0.440920i −0.892321 0.451401i \(-0.850924\pi\)
0.451401 + 0.892321i \(0.350924\pi\)
\(44\) 37.6973i 0.856757i
\(45\) −12.7205 7.94908i −0.282679 0.176646i
\(46\) −6.78233 −0.147442
\(47\) 21.2643 + 21.2643i 0.452431 + 0.452431i 0.896161 0.443729i \(-0.146345\pi\)
−0.443729 + 0.896161i \(0.646345\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 3.71868i 0.0758913i
\(50\) 11.5121 33.4286i 0.230243 0.668572i
\(51\) −20.2853 −0.397751
\(52\) −9.70339 9.70339i −0.186604 0.186604i
\(53\) 30.6997 30.6997i 0.579240 0.579240i −0.355454 0.934694i \(-0.615674\pi\)
0.934694 + 0.355454i \(0.115674\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −49.9432 + 79.9217i −0.908058 + 1.45312i
\(56\) 20.5365 0.366724
\(57\) −2.45978 2.45978i −0.0431539 0.0431539i
\(58\) −15.3053 + 15.3053i −0.263885 + 0.263885i
\(59\) 37.0580i 0.628102i −0.949406 0.314051i \(-0.898314\pi\)
0.949406 0.314051i \(-0.101686\pi\)
\(60\) 16.8767 3.89587i 0.281278 0.0649312i
\(61\) 65.9013 1.08035 0.540175 0.841553i \(-0.318358\pi\)
0.540175 + 0.841553i \(0.318358\pi\)
\(62\) −18.0217 18.0217i −0.290673 0.290673i
\(63\) −15.4024 + 15.4024i −0.244483 + 0.244483i
\(64\) 8.00000i 0.125000i
\(65\) 7.71654 + 33.4276i 0.118716 + 0.514270i
\(66\) −46.1696 −0.699539
\(67\) −70.4656 70.4656i −1.05173 1.05173i −0.998587 0.0531382i \(-0.983078\pi\)
−0.0531382 0.998587i \(-0.516922\pi\)
\(68\) 16.5629 16.5629i 0.243572 0.243572i
\(69\) 8.30662i 0.120386i
\(70\) −43.5393 27.2078i −0.621990 0.388683i
\(71\) −8.38441 −0.118090 −0.0590452 0.998255i \(-0.518806\pi\)
−0.0590452 + 0.998255i \(0.518806\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 78.9935 78.9935i 1.08210 1.08210i 0.0857895 0.996313i \(-0.472659\pi\)
0.996313 0.0857895i \(-0.0273412\pi\)
\(74\) 15.9803i 0.215950i
\(75\) −40.9415 14.0994i −0.545887 0.187992i
\(76\) 4.01680 0.0528526
\(77\) 96.7715 + 96.7715i 1.25677 + 1.25677i
\(78\) −11.8842 + 11.8842i −0.152361 + 0.152361i
\(79\) 103.875i 1.31488i −0.753508 0.657439i \(-0.771640\pi\)
0.753508 0.657439i \(-0.228360\pi\)
\(80\) −10.5988 + 16.9607i −0.132485 + 0.212009i
\(81\) −9.00000 −0.111111
\(82\) −8.60556 8.60556i −0.104946 0.104946i
\(83\) 37.7965 37.7965i 0.455380 0.455380i −0.441756 0.897135i \(-0.645644\pi\)
0.897135 + 0.441756i \(0.145644\pi\)
\(84\) 25.1520i 0.299429i
\(85\) −57.0581 + 13.1715i −0.671272 + 0.154959i
\(86\) −37.9191 −0.440920
\(87\) 18.7451 + 18.7451i 0.215461 + 0.215461i
\(88\) 37.6973 37.6973i 0.428379 0.428379i
\(89\) 140.211i 1.57541i −0.616055 0.787703i \(-0.711270\pi\)
0.616055 0.787703i \(-0.288730\pi\)
\(90\) −4.77145 20.6696i −0.0530161 0.229662i
\(91\) 49.8185 0.547456
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −22.0720 + 22.0720i −0.237333 + 0.237333i
\(94\) 42.5286i 0.452431i
\(95\) −8.51597 5.32164i −0.0896418 0.0560173i
\(96\) −9.79796 −0.102062
\(97\) 105.406 + 105.406i 1.08666 + 1.08666i 0.995870 + 0.0907920i \(0.0289398\pi\)
0.0907920 + 0.995870i \(0.471060\pi\)
\(98\) −3.71868 + 3.71868i −0.0379457 + 0.0379457i
\(99\) 56.5460i 0.571171i
\(100\) 44.9407 21.9165i 0.449407 0.219165i
\(101\) −166.271 −1.64624 −0.823122 0.567865i \(-0.807770\pi\)
−0.823122 + 0.567865i \(0.807770\pi\)
\(102\) −20.2853 20.2853i −0.198876 0.198876i
\(103\) −10.8622 + 10.8622i −0.105458 + 0.105458i −0.757867 0.652409i \(-0.773759\pi\)
0.652409 + 0.757867i \(0.273759\pi\)
\(104\) 19.4068i 0.186604i
\(105\) −33.3226 + 53.3245i −0.317358 + 0.507853i
\(106\) 61.3995 0.579240
\(107\) 18.6728 + 18.6728i 0.174512 + 0.174512i 0.788959 0.614446i \(-0.210621\pi\)
−0.614446 + 0.788959i \(0.710621\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 102.811i 0.943220i −0.881807 0.471610i \(-0.843673\pi\)
0.881807 0.471610i \(-0.156327\pi\)
\(110\) −129.865 + 29.9785i −1.18059 + 0.272532i
\(111\) 19.5718 0.176322
\(112\) 20.5365 + 20.5365i 0.183362 + 0.183362i
\(113\) 18.3180 18.3180i 0.162106 0.162106i −0.621393 0.783499i \(-0.713433\pi\)
0.783499 + 0.621393i \(0.213433\pi\)
\(114\) 4.91955i 0.0431539i
\(115\) 5.39359 + 23.3647i 0.0469008 + 0.203171i
\(116\) −30.6107 −0.263885
\(117\) 14.5551 + 14.5551i 0.124402 + 0.124402i
\(118\) 37.0580 37.0580i 0.314051 0.314051i
\(119\) 85.0361i 0.714589i
\(120\) 20.7725 + 12.9808i 0.173105 + 0.108173i
\(121\) 234.272 1.93613
\(122\) 65.9013 + 65.9013i 0.540175 + 0.540175i
\(123\) −10.5396 + 10.5396i −0.0856880 + 0.0856880i
\(124\) 36.0434i 0.290673i
\(125\) −124.314 13.0747i −0.994515 0.104598i
\(126\) −30.8048 −0.244483
\(127\) −71.1197 71.1197i −0.559998 0.559998i 0.369309 0.929307i \(-0.379594\pi\)
−0.929307 + 0.369309i \(0.879594\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 46.4412i 0.360009i
\(130\) −25.7110 + 41.1441i −0.197777 + 0.316493i
\(131\) −135.743 −1.03621 −0.518103 0.855318i \(-0.673362\pi\)
−0.518103 + 0.855318i \(0.673362\pi\)
\(132\) −46.1696 46.1696i −0.349770 0.349770i
\(133\) −10.3114 + 10.3114i −0.0775292 + 0.0775292i
\(134\) 140.931i 1.05173i
\(135\) −25.3150 + 5.84381i −0.187519 + 0.0432875i
\(136\) 33.1258 0.243572
\(137\) −60.5881 60.5881i −0.442249 0.442249i 0.450518 0.892767i \(-0.351239\pi\)
−0.892767 + 0.450518i \(0.851239\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 227.197i 1.63451i 0.576276 + 0.817255i \(0.304506\pi\)
−0.576276 + 0.817255i \(0.695494\pi\)
\(140\) −16.3315 70.7471i −0.116654 0.505336i
\(141\) 52.0866 0.369409
\(142\) −8.38441 8.38441i −0.0590452 0.0590452i
\(143\) 91.4479 91.4479i 0.639496 0.639496i
\(144\) 12.0000i 0.0833333i
\(145\) 64.8973 + 40.5545i 0.447568 + 0.279686i
\(146\) 157.987 1.08210
\(147\) 4.55443 + 4.55443i 0.0309825 + 0.0309825i
\(148\) −15.9803 + 15.9803i −0.107975 + 0.107975i
\(149\) 140.232i 0.941152i −0.882359 0.470576i \(-0.844046\pi\)
0.882359 0.470576i \(-0.155954\pi\)
\(150\) −26.8421 55.0409i −0.178947 0.366939i
\(151\) 214.851 1.42285 0.711427 0.702760i \(-0.248049\pi\)
0.711427 + 0.702760i \(0.248049\pi\)
\(152\) 4.01680 + 4.01680i 0.0264263 + 0.0264263i
\(153\) −24.8443 + 24.8443i −0.162381 + 0.162381i
\(154\) 193.543i 1.25677i
\(155\) −47.7520 + 76.4153i −0.308078 + 0.493002i
\(156\) −23.7683 −0.152361
\(157\) 119.482 + 119.482i 0.761034 + 0.761034i 0.976509 0.215475i \(-0.0691301\pi\)
−0.215475 + 0.976509i \(0.569130\pi\)
\(158\) 103.875 103.875i 0.657439 0.657439i
\(159\) 75.1987i 0.472948i
\(160\) −27.5595 + 6.36194i −0.172247 + 0.0397621i
\(161\) 34.8214 0.216282
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 22.6345 22.6345i 0.138862 0.138862i −0.634259 0.773121i \(-0.718695\pi\)
0.773121 + 0.634259i \(0.218695\pi\)
\(164\) 17.2111i 0.104946i
\(165\) 36.7160 + 159.051i 0.222521 + 0.963948i
\(166\) 75.5930 0.455380
\(167\) −51.9716 51.9716i −0.311207 0.311207i 0.534170 0.845377i \(-0.320624\pi\)
−0.845377 + 0.534170i \(0.820624\pi\)
\(168\) 25.1520 25.1520i 0.149714 0.149714i
\(169\) 121.922i 0.721433i
\(170\) −70.2296 43.8866i −0.413115 0.258156i
\(171\) −6.02519 −0.0352351
\(172\) −37.9191 37.9191i −0.220460 0.220460i
\(173\) −182.504 + 182.504i −1.05494 + 1.05494i −0.0565364 + 0.998401i \(0.518006\pi\)
−0.998401 + 0.0565364i \(0.981994\pi\)
\(174\) 37.4903i 0.215461i
\(175\) −59.1048 + 171.627i −0.337742 + 0.980725i
\(176\) 75.3946 0.428379
\(177\) −45.3866 45.3866i −0.256422 0.256422i
\(178\) 140.211 140.211i 0.787703 0.787703i
\(179\) 23.8205i 0.133076i −0.997784 0.0665378i \(-0.978805\pi\)
0.997784 0.0665378i \(-0.0211953\pi\)
\(180\) 15.8982 25.4411i 0.0883232 0.141339i
\(181\) 210.981 1.16564 0.582820 0.812601i \(-0.301949\pi\)
0.582820 + 0.812601i \(0.301949\pi\)
\(182\) 49.8185 + 49.8185i 0.273728 + 0.273728i
\(183\) 80.7123 80.7123i 0.441051 0.441051i
\(184\) 13.5647i 0.0737210i
\(185\) 55.0510 12.7082i 0.297573 0.0686929i
\(186\) −44.1440 −0.237333
\(187\) 156.094 + 156.094i 0.834728 + 0.834728i
\(188\) −42.5286 + 42.5286i −0.226216 + 0.226216i
\(189\) 37.7280i 0.199619i
\(190\) −3.19432 13.8376i −0.0168122 0.0728295i
\(191\) 107.185 0.561180 0.280590 0.959828i \(-0.409470\pi\)
0.280590 + 0.959828i \(0.409470\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −204.925 + 204.925i −1.06179 + 1.06179i −0.0638266 + 0.997961i \(0.520330\pi\)
−0.997961 + 0.0638266i \(0.979670\pi\)
\(194\) 210.812i 1.08666i
\(195\) 50.3910 + 31.4894i 0.258415 + 0.161484i
\(196\) −7.43735 −0.0379457
\(197\) −184.161 184.161i −0.934829 0.934829i 0.0631740 0.998003i \(-0.479878\pi\)
−0.998003 + 0.0631740i \(0.979878\pi\)
\(198\) −56.5460 + 56.5460i −0.285586 + 0.285586i
\(199\) 104.404i 0.524644i −0.964980 0.262322i \(-0.915512\pi\)
0.964980 0.262322i \(-0.0844882\pi\)
\(200\) 66.8572 + 23.0243i 0.334286 + 0.115121i
\(201\) −172.605 −0.858730
\(202\) −166.271 166.271i −0.823122 0.823122i
\(203\) 78.5796 78.5796i 0.387092 0.387092i
\(204\) 40.5706i 0.198876i
\(205\) −22.8021 + 36.4891i −0.111230 + 0.177996i
\(206\) −21.7244 −0.105458
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 19.4068 19.4068i 0.0933018 0.0933018i
\(209\) 37.8556i 0.181127i
\(210\) −86.6471 + 20.0019i −0.412605 + 0.0952473i
\(211\) 129.297 0.612783 0.306391 0.951906i \(-0.400878\pi\)
0.306391 + 0.951906i \(0.400878\pi\)
\(212\) 61.3995 + 61.3995i 0.289620 + 0.289620i
\(213\) −10.2688 + 10.2688i −0.0482102 + 0.0482102i
\(214\) 37.3457i 0.174512i
\(215\) 30.1548 + 130.629i 0.140255 + 0.607576i
\(216\) 14.6969 0.0680414
\(217\) 92.5259 + 92.5259i 0.426387 + 0.426387i
\(218\) 102.811 102.811i 0.471610 0.471610i
\(219\) 193.494i 0.883533i
\(220\) −159.843 99.8864i −0.726561 0.454029i
\(221\) 80.3580 0.363611
\(222\) 19.5718 + 19.5718i 0.0881610 + 0.0881610i
\(223\) −18.4366 + 18.4366i −0.0826755 + 0.0826755i −0.747235 0.664560i \(-0.768619\pi\)
0.664560 + 0.747235i \(0.268619\pi\)
\(224\) 41.0731i 0.183362i
\(225\) −67.4111 + 32.8747i −0.299605 + 0.146110i
\(226\) 36.6359 0.162106
\(227\) −118.408 118.408i −0.521621 0.521621i 0.396439 0.918061i \(-0.370246\pi\)
−0.918061 + 0.396439i \(0.870246\pi\)
\(228\) 4.91955 4.91955i 0.0215770 0.0215770i
\(229\) 39.8738i 0.174122i 0.996203 + 0.0870608i \(0.0277474\pi\)
−0.996203 + 0.0870608i \(0.972253\pi\)
\(230\) −17.9711 + 28.7583i −0.0781352 + 0.125036i
\(231\) 237.041 1.02615
\(232\) −30.6107 30.6107i −0.131943 0.131943i
\(233\) 103.054 103.054i 0.442294 0.442294i −0.450489 0.892782i \(-0.648750\pi\)
0.892782 + 0.450489i \(0.148750\pi\)
\(234\) 29.1102i 0.124402i
\(235\) 146.508 33.8205i 0.623439 0.143917i
\(236\) 74.1160 0.314051
\(237\) −127.221 127.221i −0.536797 0.536797i
\(238\) −85.0361 + 85.0361i −0.357294 + 0.357294i
\(239\) 395.064i 1.65299i 0.562947 + 0.826493i \(0.309668\pi\)
−0.562947 + 0.826493i \(0.690332\pi\)
\(240\) 7.79175 + 33.7534i 0.0324656 + 0.140639i
\(241\) 267.186 1.10865 0.554327 0.832299i \(-0.312976\pi\)
0.554327 + 0.832299i \(0.312976\pi\)
\(242\) 234.272 + 234.272i 0.968066 + 0.968066i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 131.803i 0.540175i
\(245\) 15.7679 + 9.85336i 0.0643586 + 0.0402178i
\(246\) −21.0792 −0.0856880
\(247\) 9.74413 + 9.74413i 0.0394499 + 0.0394499i
\(248\) 36.0434 36.0434i 0.145336 0.145336i
\(249\) 92.5822i 0.371816i
\(250\) −111.240 137.389i −0.444958 0.549556i
\(251\) −335.484 −1.33659 −0.668294 0.743897i \(-0.732975\pi\)
−0.668294 + 0.743897i \(0.732975\pi\)
\(252\) −30.8048 30.8048i −0.122241 0.122241i
\(253\) 63.9189 63.9189i 0.252644 0.252644i
\(254\) 142.239i 0.559998i
\(255\) −53.7499 + 86.0133i −0.210784 + 0.337307i
\(256\) 16.0000 0.0625000
\(257\) 63.0112 + 63.0112i 0.245180 + 0.245180i 0.818989 0.573809i \(-0.194535\pi\)
−0.573809 + 0.818989i \(0.694535\pi\)
\(258\) −46.4412 + 46.4412i −0.180005 + 0.180005i
\(259\) 82.0448i 0.316775i
\(260\) −66.8551 + 15.4331i −0.257135 + 0.0593580i
\(261\) 45.9160 0.175923
\(262\) −135.743 135.743i −0.518103 0.518103i
\(263\) −142.414 + 142.414i −0.541497 + 0.541497i −0.923968 0.382471i \(-0.875073\pi\)
0.382471 + 0.923968i \(0.375073\pi\)
\(264\) 92.3392i 0.349770i
\(265\) −48.8274 211.517i −0.184255 0.798179i
\(266\) −20.6228 −0.0775292
\(267\) −171.723 171.723i −0.643157 0.643157i
\(268\) 140.931 140.931i 0.525863 0.525863i
\(269\) 207.123i 0.769973i −0.922922 0.384987i \(-0.874206\pi\)
0.922922 0.384987i \(-0.125794\pi\)
\(270\) −31.1588 19.4712i −0.115403 0.0721156i
\(271\) −380.296 −1.40331 −0.701654 0.712518i \(-0.747555\pi\)
−0.701654 + 0.712518i \(0.747555\pi\)
\(272\) 33.1258 + 33.1258i 0.121786 + 0.121786i
\(273\) 61.0149 61.0149i 0.223498 0.223498i
\(274\) 121.176i 0.442249i
\(275\) 206.548 + 423.536i 0.751084 + 1.54013i
\(276\) −16.6132 −0.0601929
\(277\) 202.941 + 202.941i 0.732639 + 0.732639i 0.971142 0.238502i \(-0.0766565\pi\)
−0.238502 + 0.971142i \(0.576657\pi\)
\(278\) −227.197 + 227.197i −0.817255 + 0.817255i
\(279\) 54.0651i 0.193782i
\(280\) 54.4156 87.0786i 0.194341 0.310995i
\(281\) −215.868 −0.768215 −0.384108 0.923288i \(-0.625491\pi\)
−0.384108 + 0.923288i \(0.625491\pi\)
\(282\) 52.0866 + 52.0866i 0.184704 + 0.184704i
\(283\) −281.977 + 281.977i −0.996383 + 0.996383i −0.999993 0.00361003i \(-0.998851\pi\)
0.00361003 + 0.999993i \(0.498851\pi\)
\(284\) 16.7688i 0.0590452i
\(285\) −16.9475 + 3.91223i −0.0594651 + 0.0137271i
\(286\) 182.896 0.639496
\(287\) 44.1821 + 44.1821i 0.153945 + 0.153945i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 151.835i 0.525382i
\(290\) 24.3429 + 105.452i 0.0839410 + 0.363627i
\(291\) 258.191 0.887256
\(292\) 157.987 + 157.987i 0.541051 + 0.541051i
\(293\) −268.608 + 268.608i −0.916752 + 0.916752i −0.996792 0.0800393i \(-0.974495\pi\)
0.0800393 + 0.996792i \(0.474495\pi\)
\(294\) 9.10886i 0.0309825i
\(295\) −157.133 98.1924i −0.532653 0.332856i
\(296\) −31.9605 −0.107975
\(297\) 69.2544 + 69.2544i 0.233180 + 0.233180i
\(298\) 140.232 140.232i 0.470576 0.470576i
\(299\) 32.9058i 0.110053i
\(300\) 28.1988 81.8830i 0.0939961 0.272943i
\(301\) 194.682 0.646783
\(302\) 214.851 + 214.851i 0.711427 + 0.711427i
\(303\) −203.639 + 203.639i −0.672076 + 0.672076i
\(304\) 8.03359i 0.0264263i
\(305\) 174.618 279.433i 0.572519 0.916175i
\(306\) −49.6886 −0.162381
\(307\) 242.905 + 242.905i 0.791222 + 0.791222i 0.981693 0.190471i \(-0.0610014\pi\)
−0.190471 + 0.981693i \(0.561001\pi\)
\(308\) −193.543 + 193.543i −0.628387 + 0.628387i
\(309\) 26.6069i 0.0861064i
\(310\) −124.167 + 28.6632i −0.400540 + 0.0924621i
\(311\) −207.359 −0.666749 −0.333374 0.942795i \(-0.608187\pi\)
−0.333374 + 0.942795i \(0.608187\pi\)
\(312\) −23.7683 23.7683i −0.0761806 0.0761806i
\(313\) −281.476 + 281.476i −0.899286 + 0.899286i −0.995373 0.0960873i \(-0.969367\pi\)
0.0960873 + 0.995373i \(0.469367\pi\)
\(314\) 238.965i 0.761034i
\(315\) 24.4973 + 106.121i 0.0777691 + 0.336891i
\(316\) 207.751 0.657439
\(317\) 244.685 + 244.685i 0.771877 + 0.771877i 0.978435 0.206557i \(-0.0662260\pi\)
−0.206557 + 0.978435i \(0.566226\pi\)
\(318\) 75.1987 75.1987i 0.236474 0.236474i
\(319\) 288.485i 0.904342i
\(320\) −33.9214 21.1976i −0.106004 0.0662424i
\(321\) 45.7389 0.142489
\(322\) 34.8214 + 34.8214i 0.108141 + 0.108141i
\(323\) −16.6324 + 16.6324i −0.0514936 + 0.0514936i
\(324\) 18.0000i 0.0555556i
\(325\) 162.185 + 55.8533i 0.499032 + 0.171856i
\(326\) 45.2690 0.138862
\(327\) −125.917 125.917i −0.385068 0.385068i
\(328\) 17.2111 17.2111i 0.0524729 0.0524729i
\(329\) 218.347i 0.663670i
\(330\) −122.335 + 195.767i −0.370713 + 0.593234i
\(331\) 638.751 1.92976 0.964881 0.262688i \(-0.0846089\pi\)
0.964881 + 0.262688i \(0.0846089\pi\)
\(332\) 75.5930 + 75.5930i 0.227690 + 0.227690i
\(333\) 23.9704 23.9704i 0.0719832 0.0719832i
\(334\) 103.943i 0.311207i
\(335\) −485.499 + 112.074i −1.44925 + 0.334550i
\(336\) 50.3040 0.149714
\(337\) 245.749 + 245.749i 0.729225 + 0.729225i 0.970465 0.241240i \(-0.0775542\pi\)
−0.241240 + 0.970465i \(0.577554\pi\)
\(338\) −121.922 + 121.922i −0.360716 + 0.360716i
\(339\) 44.8696i 0.132359i
\(340\) −26.3430 114.116i −0.0774794 0.335636i
\(341\) 339.685 0.996144
\(342\) −6.02519 6.02519i −0.0176175 0.0176175i
\(343\) −232.480 + 232.480i −0.677785 + 0.677785i
\(344\) 75.8382i 0.220460i
\(345\) 35.2216 + 22.0100i 0.102092 + 0.0637972i
\(346\) −365.008 −1.05494
\(347\) 151.497 + 151.497i 0.436591 + 0.436591i 0.890863 0.454272i \(-0.150100\pi\)
−0.454272 + 0.890863i \(0.650100\pi\)
\(348\) −37.4903 + 37.4903i −0.107731 + 0.107731i
\(349\) 247.408i 0.708904i −0.935074 0.354452i \(-0.884667\pi\)
0.935074 0.354452i \(-0.115333\pi\)
\(350\) −230.732 + 112.522i −0.659233 + 0.321492i
\(351\) 35.6525 0.101574
\(352\) 75.3946 + 75.3946i 0.214189 + 0.214189i
\(353\) −304.079 + 304.079i −0.861415 + 0.861415i −0.991503 0.130088i \(-0.958474\pi\)
0.130088 + 0.991503i \(0.458474\pi\)
\(354\) 90.7732i 0.256422i
\(355\) −22.2161 + 35.5514i −0.0625807 + 0.100145i
\(356\) 280.422 0.787703
\(357\) 104.147 + 104.147i 0.291730 + 0.291730i
\(358\) 23.8205 23.8205i 0.0665378 0.0665378i
\(359\) 257.894i 0.718369i −0.933267 0.359184i \(-0.883055\pi\)
0.933267 0.359184i \(-0.116945\pi\)
\(360\) 41.3392 9.54290i 0.114831 0.0265081i
\(361\) 356.966 0.988826
\(362\) 210.981 + 210.981i 0.582820 + 0.582820i
\(363\) 286.923 286.923i 0.790422 0.790422i
\(364\) 99.6370i 0.273728i
\(365\) −125.638 544.255i −0.344213 1.49111i
\(366\) 161.425 0.441051
\(367\) −293.848 293.848i −0.800675 0.800675i 0.182526 0.983201i \(-0.441573\pi\)
−0.983201 + 0.182526i \(0.941573\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 25.8167i 0.0699639i
\(370\) 67.7592 + 42.3428i 0.183133 + 0.114440i
\(371\) −315.233 −0.849685
\(372\) −44.1440 44.1440i −0.118667 0.118667i
\(373\) 414.362 414.362i 1.11089 1.11089i 0.117861 0.993030i \(-0.462396\pi\)
0.993030 0.117861i \(-0.0376037\pi\)
\(374\) 312.188i 0.834728i
\(375\) −168.267 + 136.240i −0.448711 + 0.363307i
\(376\) −85.0571 −0.226216
\(377\) −74.2568 74.2568i −0.196968 0.196968i
\(378\) −37.7280 + 37.7280i −0.0998096 + 0.0998096i
\(379\) 308.141i 0.813036i −0.913643 0.406518i \(-0.866743\pi\)
0.913643 0.406518i \(-0.133257\pi\)
\(380\) 10.6433 17.0319i 0.0280086 0.0448209i
\(381\) −174.207 −0.457236
\(382\) 107.185 + 107.185i 0.280590 + 0.280590i
\(383\) 206.195 206.195i 0.538368 0.538368i −0.384682 0.923049i \(-0.625689\pi\)
0.923049 + 0.384682i \(0.125689\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 666.744 153.914i 1.73180 0.399776i
\(386\) −409.850 −1.06179
\(387\) 56.8786 + 56.8786i 0.146973 + 0.146973i
\(388\) −210.812 + 210.812i −0.543331 + 0.543331i
\(389\) 474.840i 1.22067i −0.792144 0.610334i \(-0.791035\pi\)
0.792144 0.610334i \(-0.208965\pi\)
\(390\) 18.9016 + 81.8804i 0.0484656 + 0.209950i
\(391\) 56.1675 0.143651
\(392\) −7.43735 7.43735i −0.0189728 0.0189728i
\(393\) −166.251 + 166.251i −0.423029 + 0.423029i
\(394\) 368.322i 0.934829i
\(395\) −440.450 275.238i −1.11506 0.696805i
\(396\) −113.092 −0.285586
\(397\) −240.297 240.297i −0.605281 0.605281i 0.336428 0.941709i \(-0.390781\pi\)
−0.941709 + 0.336428i \(0.890781\pi\)
\(398\) 104.404 104.404i 0.262322 0.262322i
\(399\) 25.2576i 0.0633023i
\(400\) 43.8329 + 89.8814i 0.109582 + 0.224704i
\(401\) 201.562 0.502648 0.251324 0.967903i \(-0.419134\pi\)
0.251324 + 0.967903i \(0.419134\pi\)
\(402\) −172.605 172.605i −0.429365 0.429365i
\(403\) 87.4358 87.4358i 0.216962 0.216962i
\(404\) 332.541i 0.823122i
\(405\) −23.8473 + 38.1616i −0.0588821 + 0.0942262i
\(406\) 157.159 0.387092
\(407\) −150.603 150.603i −0.370033 0.370033i
\(408\) 40.5706 40.5706i 0.0994378 0.0994378i
\(409\) 675.609i 1.65186i −0.563775 0.825928i \(-0.690651\pi\)
0.563775 0.825928i \(-0.309349\pi\)
\(410\) −59.2912 + 13.6870i −0.144613 + 0.0333830i
\(411\) −148.410 −0.361095
\(412\) −21.7244 21.7244i −0.0527292 0.0527292i
\(413\) −190.261 + 190.261i −0.460680 + 0.460680i
\(414\) 20.3470i 0.0491473i
\(415\) −60.1148 260.413i −0.144855 0.627502i
\(416\) 38.8135 0.0933018
\(417\) 278.258 + 278.258i 0.667286 + 0.667286i
\(418\) −37.8556 + 37.8556i −0.0905637 + 0.0905637i
\(419\) 384.622i 0.917952i −0.888449 0.458976i \(-0.848216\pi\)
0.888449 0.458976i \(-0.151784\pi\)
\(420\) −106.649 66.6452i −0.253926 0.158679i
\(421\) −454.018 −1.07843 −0.539214 0.842169i \(-0.681279\pi\)
−0.539214 + 0.842169i \(0.681279\pi\)
\(422\) 129.297 + 129.297i 0.306391 + 0.306391i
\(423\) 63.7928 63.7928i 0.150810 0.150810i
\(424\) 122.799i 0.289620i
\(425\) −95.3370 + 276.837i −0.224322 + 0.651381i
\(426\) −20.5375 −0.0482102
\(427\) −338.346 338.346i −0.792380 0.792380i
\(428\) −37.3457 + 37.3457i −0.0872562 + 0.0872562i
\(429\) 224.001i 0.522146i
\(430\) −100.474 + 160.784i −0.233660 + 0.373916i
\(431\) −241.139 −0.559487 −0.279743 0.960075i \(-0.590249\pi\)
−0.279743 + 0.960075i \(0.590249\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −278.432 + 278.432i −0.643031 + 0.643031i −0.951299 0.308269i \(-0.900250\pi\)
0.308269 + 0.951299i \(0.400250\pi\)
\(434\) 185.052i 0.426387i
\(435\) 129.152 29.8138i 0.296900 0.0685375i
\(436\) 205.622 0.471610
\(437\) 6.81081 + 6.81081i 0.0155854 + 0.0155854i
\(438\) 193.494 193.494i 0.441767 0.441767i
\(439\) 439.356i 1.00081i −0.865791 0.500406i \(-0.833184\pi\)
0.865791 0.500406i \(-0.166816\pi\)
\(440\) −59.9570 259.730i −0.136266 0.590295i
\(441\) 11.1560 0.0252971
\(442\) 80.3580 + 80.3580i 0.181805 + 0.181805i
\(443\) −261.606 + 261.606i −0.590532 + 0.590532i −0.937775 0.347243i \(-0.887118\pi\)
0.347243 + 0.937775i \(0.387118\pi\)
\(444\) 39.1435i 0.0881610i
\(445\) −594.520 371.517i −1.33600 0.834869i
\(446\) −36.8733 −0.0826755
\(447\) −171.748 171.748i −0.384224 0.384224i
\(448\) −41.0731 + 41.0731i −0.0916810 + 0.0916810i
\(449\) 876.612i 1.95237i −0.216948 0.976183i \(-0.569610\pi\)
0.216948 0.976183i \(-0.430390\pi\)
\(450\) −100.286 34.5364i −0.222857 0.0767475i
\(451\) 162.203 0.359653
\(452\) 36.6359 + 36.6359i 0.0810529 + 0.0810529i
\(453\) 263.138 263.138i 0.580878 0.580878i
\(454\) 236.816i 0.521621i
\(455\) 132.004 211.239i 0.290118 0.464262i
\(456\) 9.83910 0.0215770
\(457\) 18.0348 + 18.0348i 0.0394635 + 0.0394635i 0.726563 0.687100i \(-0.241116\pi\)
−0.687100 + 0.726563i \(0.741116\pi\)
\(458\) −39.8738 + 39.8738i −0.0870608 + 0.0870608i
\(459\) 60.8559i 0.132584i
\(460\) −46.7294 + 10.7872i −0.101586 + 0.0234504i
\(461\) 746.316 1.61891 0.809453 0.587185i \(-0.199764\pi\)
0.809453 + 0.587185i \(0.199764\pi\)
\(462\) 237.041 + 237.041i 0.513076 + 0.513076i
\(463\) −178.472 + 178.472i −0.385469 + 0.385469i −0.873068 0.487599i \(-0.837873\pi\)
0.487599 + 0.873068i \(0.337873\pi\)
\(464\) 61.2213i 0.131943i
\(465\) 35.1052 + 152.073i 0.0754950 + 0.327039i
\(466\) 206.109 0.442294
\(467\) −246.803 246.803i −0.528486 0.528486i 0.391635 0.920121i \(-0.371910\pi\)
−0.920121 + 0.391635i \(0.871910\pi\)
\(468\) −29.1102 + 29.1102i −0.0622012 + 0.0622012i
\(469\) 723.560i 1.54277i
\(470\) 180.329 + 112.688i 0.383678 + 0.239761i
\(471\) 292.671 0.621382
\(472\) 74.1160 + 74.1160i 0.157026 + 0.157026i
\(473\) 357.362 357.362i 0.755522 0.755522i
\(474\) 254.442i 0.536797i
\(475\) −45.1294 + 22.0085i −0.0950093 + 0.0463337i
\(476\) −170.072 −0.357294
\(477\) −92.0992 92.0992i −0.193080 0.193080i
\(478\) −395.064 + 395.064i −0.826493 + 0.826493i
\(479\) 171.427i 0.357886i −0.983859 0.178943i \(-0.942732\pi\)
0.983859 0.178943i \(-0.0572678\pi\)
\(480\) −25.9616 + 41.5451i −0.0540867 + 0.0865523i
\(481\) −77.5314 −0.161188
\(482\) 267.186 + 267.186i 0.554327 + 0.554327i
\(483\) 42.6473 42.6473i 0.0882967 0.0882967i
\(484\) 468.544i 0.968066i
\(485\) 726.235 167.647i 1.49739 0.345664i
\(486\) −22.0454 −0.0453609
\(487\) 68.8983 + 68.8983i 0.141475 + 0.141475i 0.774297 0.632822i \(-0.218104\pi\)
−0.632822 + 0.774297i \(0.718104\pi\)
\(488\) −131.803 + 131.803i −0.270087 + 0.270087i
\(489\) 55.4430i 0.113380i
\(490\) 5.91449 + 25.6212i 0.0120704 + 0.0522882i
\(491\) −716.560 −1.45939 −0.729695 0.683773i \(-0.760338\pi\)
−0.729695 + 0.683773i \(0.760338\pi\)
\(492\) −21.0792 21.0792i −0.0428440 0.0428440i
\(493\) 126.750 126.750i 0.257100 0.257100i
\(494\) 19.4883i 0.0394499i
\(495\) 239.765 + 149.830i 0.484374 + 0.302686i
\(496\) 72.0868 0.145336
\(497\) 43.0467 + 43.0467i 0.0866131 + 0.0866131i
\(498\) 92.5822 92.5822i 0.185908 0.185908i
\(499\) 103.164i 0.206742i 0.994643 + 0.103371i \(0.0329629\pi\)
−0.994643 + 0.103371i \(0.967037\pi\)
\(500\) 26.1495 248.629i 0.0522989 0.497257i
\(501\) −127.304 −0.254100
\(502\) −335.484 335.484i −0.668294 0.668294i
\(503\) −213.360 + 213.360i −0.424176 + 0.424176i −0.886639 0.462463i \(-0.846966\pi\)
0.462463 + 0.886639i \(0.346966\pi\)
\(504\) 61.6096i 0.122241i
\(505\) −440.566 + 705.017i −0.872409 + 1.39607i
\(506\) 127.838 0.252644
\(507\) 149.324 + 149.324i 0.294524 + 0.294524i
\(508\) 142.239 142.239i 0.279999 0.279999i
\(509\) 65.8915i 0.129453i −0.997903 0.0647264i \(-0.979383\pi\)
0.997903 0.0647264i \(-0.0206175\pi\)
\(510\) −139.763 + 32.2635i −0.274045 + 0.0632617i
\(511\) −811.127 −1.58733
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −7.37933 + 7.37933i −0.0143846 + 0.0143846i
\(514\) 126.022i 0.245180i
\(515\) 17.2762 + 74.8393i 0.0335460 + 0.145319i
\(516\) −92.8824 −0.180005
\(517\) −400.803 400.803i −0.775248 0.775248i
\(518\) 82.0448 82.0448i 0.158388 0.158388i
\(519\) 447.042i 0.861352i
\(520\) −82.2882 51.4220i −0.158247 0.0988885i
\(521\) 898.750 1.72505 0.862524 0.506016i \(-0.168882\pi\)
0.862524 + 0.506016i \(0.168882\pi\)
\(522\) 45.9160 + 45.9160i 0.0879617 + 0.0879617i
\(523\) 380.156 380.156i 0.726876 0.726876i −0.243120 0.969996i \(-0.578171\pi\)
0.969996 + 0.243120i \(0.0781709\pi\)
\(524\) 271.486i 0.518103i
\(525\) 137.811 + 282.587i 0.262497 + 0.538262i
\(526\) −284.827 −0.541497
\(527\) 149.246 + 149.246i 0.283199 + 0.283199i
\(528\) 92.3392 92.3392i 0.174885 0.174885i
\(529\) 23.0000i 0.0434783i
\(530\) 162.690 260.345i 0.306962 0.491217i
\(531\) −111.174 −0.209367
\(532\) −20.6228 20.6228i −0.0387646 0.0387646i
\(533\) 41.7516 41.7516i 0.0783331 0.0783331i
\(534\) 343.446i 0.643157i
\(535\) 128.653 29.6988i 0.240474 0.0555118i
\(536\) 281.862 0.525863
\(537\) −29.1741 29.1741i −0.0543278 0.0543278i
\(538\) 207.123 207.123i 0.384987 0.384987i
\(539\) 70.0921i 0.130041i
\(540\) −11.6876 50.6300i −0.0216437 0.0937593i
\(541\) −181.504 −0.335498 −0.167749 0.985830i \(-0.553650\pi\)
−0.167749 + 0.985830i \(0.553650\pi\)
\(542\) −380.296 380.296i −0.701654 0.701654i
\(543\) 258.398 258.398i 0.475871 0.475871i
\(544\) 66.2515i 0.121786i
\(545\) −435.937 272.418i −0.799884 0.499849i
\(546\) 122.030 0.223498
\(547\) −369.884 369.884i −0.676206 0.676206i 0.282934 0.959139i \(-0.408692\pi\)
−0.959139 + 0.282934i \(0.908692\pi\)
\(548\) 121.176 121.176i 0.221124 0.221124i
\(549\) 197.704i 0.360117i
\(550\) −216.988 + 630.084i −0.394524 + 1.14561i
\(551\) 30.7392 0.0557880
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −533.310 + 533.310i −0.964394 + 0.964394i
\(554\) 405.882i 0.732639i
\(555\) 51.8592 82.9877i 0.0934399 0.149527i
\(556\) −454.394 −0.817255
\(557\) 443.307 + 443.307i 0.795884 + 0.795884i 0.982444 0.186560i \(-0.0597338\pi\)
−0.186560 + 0.982444i \(0.559734\pi\)
\(558\) −54.0651 + 54.0651i −0.0968909 + 0.0968909i
\(559\) 183.972i 0.329109i
\(560\) 141.494 32.6630i 0.252668 0.0583268i
\(561\) 382.351 0.681552
\(562\) −215.868 215.868i −0.384108 0.384108i
\(563\) 204.223 204.223i 0.362742 0.362742i −0.502080 0.864821i \(-0.667432\pi\)
0.864821 + 0.502080i \(0.167432\pi\)
\(564\) 104.173i 0.184704i
\(565\) −29.1344 126.208i −0.0515653 0.223378i
\(566\) −563.953 −0.996383
\(567\) 46.2072 + 46.2072i 0.0814942 + 0.0814942i
\(568\) 16.7688 16.7688i 0.0295226 0.0295226i
\(569\) 54.1051i 0.0950881i 0.998869 + 0.0475440i \(0.0151394\pi\)
−0.998869 + 0.0475440i \(0.984861\pi\)
\(570\) −20.8598 13.0353i −0.0365961 0.0228690i
\(571\) −1055.98 −1.84935 −0.924674 0.380759i \(-0.875663\pi\)
−0.924674 + 0.380759i \(0.875663\pi\)
\(572\) 182.896 + 182.896i 0.319748 + 0.319748i
\(573\) 131.275 131.275i 0.229101 0.229101i
\(574\) 88.3642i 0.153945i
\(575\) 113.362 + 39.0395i 0.197151 + 0.0678948i
\(576\) −24.0000 −0.0416667
\(577\) 128.192 + 128.192i 0.222171 + 0.222171i 0.809412 0.587241i \(-0.199786\pi\)
−0.587241 + 0.809412i \(0.699786\pi\)
\(578\) 151.835 151.835i 0.262691 0.262691i
\(579\) 501.962i 0.866946i
\(580\) −81.1089 + 129.795i −0.139843 + 0.223784i
\(581\) −388.105 −0.667995
\(582\) 258.191 + 258.191i 0.443628 + 0.443628i
\(583\) −578.649 + 578.649i −0.992537 + 0.992537i
\(584\) 315.974i 0.541051i
\(585\) 100.283 23.1496i 0.171423 0.0395720i
\(586\) −537.217 −0.916752
\(587\) −18.1091 18.1091i −0.0308503 0.0308503i 0.691513 0.722364i \(-0.256944\pi\)
−0.722364 + 0.691513i \(0.756944\pi\)
\(588\) −9.10886 + 9.10886i −0.0154913 + 0.0154913i
\(589\) 36.1948i 0.0614512i
\(590\) −58.9402 255.325i −0.0998986 0.432754i
\(591\) −451.101 −0.763284
\(592\) −31.9605 31.9605i −0.0539874 0.0539874i
\(593\) −696.941 + 696.941i −1.17528 + 1.17528i −0.194348 + 0.980933i \(0.562259\pi\)
−0.980933 + 0.194348i \(0.937741\pi\)
\(594\) 138.509i 0.233180i
\(595\) 360.568 + 225.320i 0.605997 + 0.378688i
\(596\) 280.463 0.470576
\(597\) −127.868 127.868i −0.214185 0.214185i
\(598\) 32.9058 32.9058i 0.0550264 0.0550264i
\(599\) 757.584i 1.26475i −0.774663 0.632374i \(-0.782081\pi\)
0.774663 0.632374i \(-0.217919\pi\)
\(600\) 110.082 53.6842i 0.183470 0.0894736i
\(601\) 642.457 1.06898 0.534490 0.845175i \(-0.320504\pi\)
0.534490 + 0.845175i \(0.320504\pi\)
\(602\) 194.682 + 194.682i 0.323391 + 0.323391i
\(603\) −211.397 + 211.397i −0.350575 + 0.350575i
\(604\) 429.702i 0.711427i
\(605\) 620.749 993.355i 1.02603 1.64191i
\(606\) −407.278 −0.672076
\(607\) −590.328 590.328i −0.972534 0.972534i 0.0270991 0.999633i \(-0.491373\pi\)
−0.999633 + 0.0270991i \(0.991373\pi\)
\(608\) −8.03359 + 8.03359i −0.0132131 + 0.0132131i
\(609\) 192.480i 0.316059i
\(610\) 454.052 104.815i 0.744347 0.171828i
\(611\) −206.335 −0.337701
\(612\) −49.6886 49.6886i −0.0811906 0.0811906i
\(613\) 411.975 411.975i 0.672064 0.672064i −0.286128 0.958191i \(-0.592368\pi\)
0.958191 + 0.286128i \(0.0923682\pi\)
\(614\) 485.810i 0.791222i
\(615\) 16.7631 + 72.6167i 0.0272571 + 0.118076i
\(616\) −387.086 −0.628387
\(617\) −401.638 401.638i −0.650953 0.650953i 0.302270 0.953222i \(-0.402256\pi\)
−0.953222 + 0.302270i \(0.902256\pi\)
\(618\) −26.6069 + 26.6069i −0.0430532 + 0.0430532i
\(619\) 753.916i 1.21796i 0.793186 + 0.608979i \(0.208421\pi\)
−0.793186 + 0.608979i \(0.791579\pi\)
\(620\) −152.831 95.5041i −0.246501 0.154039i
\(621\) 24.9199 0.0401286
\(622\) −207.359 207.359i −0.333374 0.333374i
\(623\) −719.863 + 719.863i −1.15548 + 1.15548i
\(624\) 47.5367i 0.0761806i
\(625\) −384.834 + 492.471i −0.615735 + 0.787953i
\(626\) −562.953 −0.899286
\(627\) 46.3635 + 46.3635i 0.0739449 + 0.0739449i
\(628\) −238.965 + 238.965i −0.380517 + 0.380517i
\(629\) 132.340i 0.210397i
\(630\) −81.6233 + 130.618i −0.129561 + 0.207330i
\(631\) 737.230 1.16835 0.584176 0.811627i \(-0.301418\pi\)
0.584176 + 0.811627i \(0.301418\pi\)
\(632\) 207.751 + 207.751i 0.328719 + 0.328719i
\(633\) 158.356 158.356i 0.250167 0.250167i
\(634\) 489.370i 0.771877i
\(635\) −490.006 + 113.115i −0.771662 + 0.178133i
\(636\) 150.397 0.236474
\(637\) −18.0419 18.0419i −0.0283232 0.0283232i
\(638\) 288.485 288.485i 0.452171 0.452171i
\(639\) 25.1532i 0.0393634i
\(640\) −12.7239 55.1190i −0.0198810 0.0861234i
\(641\) −310.531 −0.484448 −0.242224 0.970220i \(-0.577877\pi\)
−0.242224 + 0.970220i \(0.577877\pi\)
\(642\) 45.7389 + 45.7389i 0.0712444 + 0.0712444i
\(643\) 433.442 433.442i 0.674093 0.674093i −0.284564 0.958657i \(-0.591849\pi\)
0.958657 + 0.284564i \(0.0918487\pi\)
\(644\) 69.6428i 0.108141i
\(645\) 196.919 + 123.055i 0.305301 + 0.190783i
\(646\) −33.2649 −0.0514936
\(647\) −123.580 123.580i −0.191005 0.191005i 0.605125 0.796130i \(-0.293123\pi\)
−0.796130 + 0.605125i \(0.793123\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 698.494i 1.07626i
\(650\) 106.332 + 218.039i 0.163588 + 0.335444i
\(651\) 226.641 0.348143
\(652\) 45.2690 + 45.2690i 0.0694310 + 0.0694310i
\(653\) −14.9705 + 14.9705i −0.0229257 + 0.0229257i −0.718477 0.695551i \(-0.755160\pi\)
0.695551 + 0.718477i \(0.255160\pi\)
\(654\) 251.834i 0.385068i
\(655\) −359.678 + 575.575i −0.549126 + 0.878740i
\(656\) 34.4223 0.0524729
\(657\) −236.981 236.981i −0.360701 0.360701i
\(658\) 218.347 218.347i 0.331835 0.331835i
\(659\) 340.257i 0.516324i −0.966102 0.258162i \(-0.916883\pi\)
0.966102 0.258162i \(-0.0831168\pi\)
\(660\) −318.103 + 73.4320i −0.481974 + 0.111261i
\(661\) 694.682 1.05096 0.525478 0.850807i \(-0.323886\pi\)
0.525478 + 0.850807i \(0.323886\pi\)
\(662\) 638.751 + 638.751i 0.964881 + 0.964881i
\(663\) 98.4181 98.4181i 0.148444 0.148444i
\(664\) 151.186i 0.227690i
\(665\) 16.4001 + 71.0441i 0.0246618 + 0.106833i
\(666\) 47.9408 0.0719832
\(667\) −51.9029 51.9029i −0.0778155 0.0778155i
\(668\) 103.943 103.943i 0.155604 0.155604i
\(669\) 45.1604i 0.0675043i
\(670\) −597.573 373.425i −0.891901 0.557350i
\(671\) −1242.15 −1.85119
\(672\) 50.3040 + 50.3040i 0.0748572 + 0.0748572i
\(673\) −625.021 + 625.021i −0.928709 + 0.928709i −0.997623 0.0689133i \(-0.978047\pi\)
0.0689133 + 0.997623i \(0.478047\pi\)
\(674\) 491.498i 0.729225i
\(675\) −42.2983 + 122.824i −0.0626641 + 0.181962i
\(676\) −243.844 −0.360716
\(677\) −144.970 144.970i −0.214135 0.214135i 0.591886 0.806021i \(-0.298383\pi\)
−0.806021 + 0.591886i \(0.798383\pi\)
\(678\) 44.8696 44.8696i 0.0661794 0.0661794i
\(679\) 1082.34i 1.59402i
\(680\) 87.7732 140.459i 0.129078 0.206558i
\(681\) −290.039 −0.425902
\(682\) 339.685 + 339.685i 0.498072 + 0.498072i
\(683\) −31.1325 + 31.1325i −0.0455820 + 0.0455820i −0.729530 0.683948i \(-0.760261\pi\)
0.683948 + 0.729530i \(0.260261\pi\)
\(684\) 12.0504i 0.0176175i
\(685\) −417.444 + 96.3644i −0.609408 + 0.140678i
\(686\) −464.961 −0.677785
\(687\) 48.8353 + 48.8353i 0.0710848 + 0.0710848i
\(688\) 75.8382 75.8382i 0.110230 0.110230i
\(689\) 297.891i 0.432353i
\(690\) 13.2116 + 57.2316i 0.0191472 + 0.0829443i
\(691\) 287.872 0.416603 0.208301 0.978065i \(-0.433207\pi\)
0.208301 + 0.978065i \(0.433207\pi\)
\(692\) −365.008 365.008i −0.527468 0.527468i
\(693\) 290.315 290.315i 0.418924 0.418924i
\(694\) 302.994i 0.436591i
\(695\) 963.356 + 602.003i 1.38612 + 0.866191i
\(696\) −74.9805 −0.107731
\(697\) 71.2665 + 71.2665i 0.102247 + 0.102247i
\(698\) 247.408 247.408i 0.354452 0.354452i
\(699\) 252.431i 0.361131i
\(700\) −343.254 118.210i −0.490363 0.168871i
\(701\) 366.250 0.522468 0.261234 0.965276i \(-0.415871\pi\)
0.261234 + 0.965276i \(0.415871\pi\)
\(702\) 35.6525 + 35.6525i 0.0507871 + 0.0507871i
\(703\) 16.0474 16.0474i 0.0228270 0.0228270i
\(704\) 150.789i 0.214189i
\(705\) 138.014 220.857i 0.195764 0.313272i
\(706\) −608.159 −0.861415
\(707\) 853.656 + 853.656i 1.20743 + 1.20743i
\(708\) 90.7732 90.7732i 0.128211 0.128211i
\(709\) 113.568i 0.160180i −0.996788 0.0800902i \(-0.974479\pi\)
0.996788 0.0800902i \(-0.0255208\pi\)
\(710\) −57.7675 + 13.3353i −0.0813627 + 0.0187821i
\(711\) −311.626 −0.438293
\(712\) 280.422 + 280.422i 0.393852 + 0.393852i
\(713\) 61.1146 61.1146i 0.0857147 0.0857147i
\(714\) 208.295i 0.291730i
\(715\) −145.446 630.065i −0.203422 0.881209i
\(716\) 47.6410 0.0665378
\(717\) 483.852 + 483.852i 0.674829 + 0.674829i
\(718\) 257.894 257.894i 0.359184 0.359184i
\(719\) 597.111i 0.830475i −0.909713 0.415237i \(-0.863699\pi\)
0.909713 0.415237i \(-0.136301\pi\)
\(720\) 50.8821 + 31.7963i 0.0706696 + 0.0441616i
\(721\) 111.536 0.154696
\(722\) 356.966 + 356.966i 0.494413 + 0.494413i
\(723\) 327.234 327.234i 0.452606 0.452606i
\(724\) 421.962i 0.582820i
\(725\) 343.916 167.719i 0.474367 0.231337i
\(726\) 573.847 0.790422
\(727\) −648.585 648.585i −0.892138 0.892138i 0.102586 0.994724i \(-0.467288\pi\)
−0.994724 + 0.102586i \(0.967288\pi\)
\(728\) −99.6370 + 99.6370i −0.136864 + 0.136864i
\(729\) 27.0000i 0.0370370i
\(730\) 418.617 669.893i 0.573448 0.917662i
\(731\) 314.025 0.429582
\(732\) 161.425 + 161.425i 0.220525 + 0.220525i
\(733\) 998.046 998.046i 1.36159 1.36159i 0.489699 0.871892i \(-0.337107\pi\)
0.871892 0.489699i \(-0.162893\pi\)
\(734\) 587.695i 0.800675i
\(735\) 31.3794 7.24375i 0.0426931 0.00985544i
\(736\) 27.1293 0.0368605
\(737\) 1328.18 + 1328.18i 1.80215 + 1.80215i
\(738\) −25.8167 + 25.8167i −0.0349820 + 0.0349820i
\(739\) 1236.71i 1.67349i 0.547592 + 0.836745i \(0.315544\pi\)
−0.547592 + 0.836745i \(0.684456\pi\)
\(740\) 25.4164 + 110.102i 0.0343464 + 0.148787i
\(741\) 23.8681 0.0322107
\(742\) −315.233 315.233i −0.424843 0.424843i
\(743\) 666.268 666.268i 0.896727 0.896727i −0.0984183 0.995145i \(-0.531378\pi\)
0.995145 + 0.0984183i \(0.0313783\pi\)
\(744\) 88.2880i 0.118667i
\(745\) −594.607 371.571i −0.798131 0.498753i
\(746\) 828.725 1.11089
\(747\) −113.390 113.390i −0.151793 0.151793i
\(748\) −312.188 + 312.188i −0.417364 + 0.417364i
\(749\) 191.738i 0.255992i
\(750\) −304.507 32.0264i −0.406009 0.0427019i
\(751\) 546.487 0.727679 0.363840 0.931462i \(-0.381466\pi\)
0.363840 + 0.931462i \(0.381466\pi\)
\(752\) −85.0571 85.0571i −0.113108 0.113108i
\(753\) −410.882 + 410.882i −0.545660 + 0.545660i
\(754\) 148.514i 0.196968i
\(755\) 569.290 911.007i 0.754026 1.20663i
\(756\) −75.4561 −0.0998096
\(757\) 395.410 + 395.410i 0.522338 + 0.522338i 0.918277 0.395939i \(-0.129581\pi\)
−0.395939 + 0.918277i \(0.629581\pi\)
\(758\) 308.141 308.141i 0.406518 0.406518i
\(759\) 156.569i 0.206283i
\(760\) 27.6752 6.38865i 0.0364148 0.00840612i
\(761\) 61.4799 0.0807883 0.0403941 0.999184i \(-0.487139\pi\)
0.0403941 + 0.999184i \(0.487139\pi\)
\(762\) −174.207 174.207i −0.228618 0.228618i
\(763\) −527.845 + 527.845i −0.691802 + 0.691802i
\(764\) 214.371i 0.280590i
\(765\) 39.5145 + 171.174i 0.0516529 + 0.223757i
\(766\) 412.390 0.538368
\(767\) 179.794 + 179.794i 0.234412 + 0.234412i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 430.433i 0.559731i 0.960039 + 0.279865i \(0.0902899\pi\)
−0.960039 + 0.279865i \(0.909710\pi\)
\(770\) 820.657 + 512.830i 1.06579 + 0.666013i
\(771\) 154.345 0.200188
\(772\) −409.850 409.850i −0.530894 0.530894i
\(773\) 171.075 171.075i 0.221313 0.221313i −0.587738 0.809051i \(-0.699981\pi\)
0.809051 + 0.587738i \(0.199981\pi\)
\(774\) 113.757i 0.146973i
\(775\) 197.486 + 404.954i 0.254821 + 0.522522i
\(776\) −421.625 −0.543331
\(777\) −100.484 100.484i −0.129323 0.129323i
\(778\) 474.840 474.840i 0.610334 0.610334i
\(779\) 17.2834i