Properties

Label 690.3.b.a.599.16
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.16
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.15

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-1.42652 + 2.63914i) q^{3} +2.00000 q^{4} +(-3.84011 + 3.20212i) q^{5} +(2.01740 - 3.73230i) q^{6} -12.7200i q^{7} -2.82843 q^{8} +(-4.93010 - 7.52955i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-1.42652 + 2.63914i) q^{3} +2.00000 q^{4} +(-3.84011 + 3.20212i) q^{5} +(2.01740 - 3.73230i) q^{6} -12.7200i q^{7} -2.82843 q^{8} +(-4.93010 - 7.52955i) q^{9} +(5.43073 - 4.52848i) q^{10} +2.23541i q^{11} +(-2.85303 + 5.27828i) q^{12} +0.635761i q^{13} +17.9888i q^{14} +(-2.97286 - 14.7025i) q^{15} +4.00000 q^{16} -9.66062 q^{17} +(6.97221 + 10.6484i) q^{18} +3.49572 q^{19} +(-7.68021 + 6.40424i) q^{20} +(33.5698 + 18.1453i) q^{21} -3.16135i q^{22} +4.79583 q^{23} +(4.03480 - 7.46461i) q^{24} +(4.49285 - 24.5930i) q^{25} -0.899101i q^{26} +(26.9044 - 2.27017i) q^{27} -25.4400i q^{28} +36.8343i q^{29} +(4.20426 + 20.7924i) q^{30} +38.8991 q^{31} -5.65685 q^{32} +(-5.89957 - 3.18886i) q^{33} +13.6622 q^{34} +(40.7310 + 48.8462i) q^{35} +(-9.86020 - 15.0591i) q^{36} +2.05039i q^{37} -4.94369 q^{38} +(-1.67786 - 0.906924i) q^{39} +(10.8615 - 9.05696i) q^{40} -20.9083i q^{41} +(-47.4749 - 25.6613i) q^{42} +44.3973i q^{43} +4.47083i q^{44} +(43.0426 + 13.1275i) q^{45} -6.78233 q^{46} -12.6819 q^{47} +(-5.70607 + 10.5566i) q^{48} -112.798 q^{49} +(-6.35385 + 34.7797i) q^{50} +(13.7810 - 25.4957i) q^{51} +1.27152i q^{52} -32.1430 q^{53} +(-38.0486 + 3.21051i) q^{54} +(-7.15807 - 8.58423i) q^{55} +35.9776i q^{56} +(-4.98670 + 9.22568i) q^{57} -52.0916i q^{58} +34.6353i q^{59} +(-5.94572 - 29.4049i) q^{60} +15.4050 q^{61} -55.0116 q^{62} +(-95.7759 + 62.7108i) q^{63} +8.00000 q^{64} +(-2.03578 - 2.44139i) q^{65} +(8.34325 + 4.50972i) q^{66} +103.378i q^{67} -19.3212 q^{68} +(-6.84134 + 12.6569i) q^{69} +(-57.6023 - 69.0789i) q^{70} -103.333i q^{71} +(13.9444 + 21.2968i) q^{72} +66.4287i q^{73} -2.89969i q^{74} +(58.4951 + 46.9395i) q^{75} +6.99144 q^{76} +28.4345 q^{77} +(2.37285 + 1.28258i) q^{78} -62.2728 q^{79} +(-15.3604 + 12.8085i) q^{80} +(-32.3883 + 74.2428i) q^{81} +29.5687i q^{82} -21.9860 q^{83} +(67.1397 + 36.2906i) q^{84} +(37.0978 - 30.9345i) q^{85} -62.7873i q^{86} +(-97.2109 - 52.5448i) q^{87} -6.32271i q^{88} +12.4162i q^{89} +(-60.8715 - 18.5651i) q^{90} +8.08687 q^{91} +9.59166 q^{92} +(-55.4902 + 102.660i) q^{93} +17.9349 q^{94} +(-13.4239 + 11.1937i) q^{95} +(8.06960 - 14.9292i) q^{96} +110.069i q^{97} +159.521 q^{98} +(16.8317 - 11.0208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −1.42652 + 2.63914i −0.475506 + 0.879713i
\(4\) 2.00000 0.500000
\(5\) −3.84011 + 3.20212i −0.768021 + 0.640424i
\(6\) 2.01740 3.73230i 0.336233 0.622051i
\(7\) 12.7200i 1.81714i −0.417730 0.908571i \(-0.637174\pi\)
0.417730 0.908571i \(-0.362826\pi\)
\(8\) −2.82843 −0.353553
\(9\) −4.93010 7.52955i −0.547789 0.836617i
\(10\) 5.43073 4.52848i 0.543073 0.452848i
\(11\) 2.23541i 0.203219i 0.994824 + 0.101610i \(0.0323993\pi\)
−0.994824 + 0.101610i \(0.967601\pi\)
\(12\) −2.85303 + 5.27828i −0.237753 + 0.439856i
\(13\) 0.635761i 0.0489047i 0.999701 + 0.0244523i \(0.00778420\pi\)
−0.999701 + 0.0244523i \(0.992216\pi\)
\(14\) 17.9888i 1.28491i
\(15\) −2.97286 14.7025i −0.198191 0.980164i
\(16\) 4.00000 0.250000
\(17\) −9.66062 −0.568272 −0.284136 0.958784i \(-0.591707\pi\)
−0.284136 + 0.958784i \(0.591707\pi\)
\(18\) 6.97221 + 10.6484i 0.387345 + 0.591577i
\(19\) 3.49572 0.183985 0.0919926 0.995760i \(-0.470676\pi\)
0.0919926 + 0.995760i \(0.470676\pi\)
\(20\) −7.68021 + 6.40424i −0.384011 + 0.320212i
\(21\) 33.5698 + 18.1453i 1.59856 + 0.864062i
\(22\) 3.16135i 0.143698i
\(23\) 4.79583 0.208514
\(24\) 4.03480 7.46461i 0.168117 0.311025i
\(25\) 4.49285 24.5930i 0.179714 0.983719i
\(26\) 0.899101i 0.0345808i
\(27\) 26.9044 2.27017i 0.996459 0.0840805i
\(28\) 25.4400i 0.908571i
\(29\) 36.8343i 1.27015i 0.772451 + 0.635075i \(0.219031\pi\)
−0.772451 + 0.635075i \(0.780969\pi\)
\(30\) 4.20426 + 20.7924i 0.140142 + 0.693080i
\(31\) 38.8991 1.25481 0.627405 0.778693i \(-0.284117\pi\)
0.627405 + 0.778693i \(0.284117\pi\)
\(32\) −5.65685 −0.176777
\(33\) −5.89957 3.18886i −0.178775 0.0966320i
\(34\) 13.6622 0.401829
\(35\) 40.7310 + 48.8462i 1.16374 + 1.39560i
\(36\) −9.86020 15.0591i −0.273894 0.418308i
\(37\) 2.05039i 0.0554160i 0.999616 + 0.0277080i \(0.00882086\pi\)
−0.999616 + 0.0277080i \(0.991179\pi\)
\(38\) −4.94369 −0.130097
\(39\) −1.67786 0.906924i −0.0430221 0.0232544i
\(40\) 10.8615 9.05696i 0.271537 0.226424i
\(41\) 20.9083i 0.509957i −0.966947 0.254979i \(-0.917932\pi\)
0.966947 0.254979i \(-0.0820685\pi\)
\(42\) −47.4749 25.6613i −1.13035 0.610984i
\(43\) 44.3973i 1.03250i 0.856439 + 0.516248i \(0.172672\pi\)
−0.856439 + 0.516248i \(0.827328\pi\)
\(44\) 4.47083i 0.101610i
\(45\) 43.0426 + 13.1275i 0.956503 + 0.291723i
\(46\) −6.78233 −0.147442
\(47\) −12.6819 −0.269828 −0.134914 0.990857i \(-0.543076\pi\)
−0.134914 + 0.990857i \(0.543076\pi\)
\(48\) −5.70607 + 10.5566i −0.118876 + 0.219928i
\(49\) −112.798 −2.30201
\(50\) −6.35385 + 34.7797i −0.127077 + 0.695594i
\(51\) 13.7810 25.4957i 0.270217 0.499916i
\(52\) 1.27152i 0.0244523i
\(53\) −32.1430 −0.606472 −0.303236 0.952915i \(-0.598067\pi\)
−0.303236 + 0.952915i \(0.598067\pi\)
\(54\) −38.0486 + 3.21051i −0.704603 + 0.0594539i
\(55\) −7.15807 8.58423i −0.130147 0.156077i
\(56\) 35.9776i 0.642457i
\(57\) −4.98670 + 9.22568i −0.0874860 + 0.161854i
\(58\) 52.0916i 0.898131i
\(59\) 34.6353i 0.587038i 0.955953 + 0.293519i \(0.0948264\pi\)
−0.955953 + 0.293519i \(0.905174\pi\)
\(60\) −5.94572 29.4049i −0.0990953 0.490082i
\(61\) 15.4050 0.252541 0.126271 0.991996i \(-0.459699\pi\)
0.126271 + 0.991996i \(0.459699\pi\)
\(62\) −55.0116 −0.887284
\(63\) −95.7759 + 62.7108i −1.52025 + 0.995410i
\(64\) 8.00000 0.125000
\(65\) −2.03578 2.44139i −0.0313197 0.0375598i
\(66\) 8.34325 + 4.50972i 0.126413 + 0.0683292i
\(67\) 103.378i 1.54296i 0.636255 + 0.771479i \(0.280483\pi\)
−0.636255 + 0.771479i \(0.719517\pi\)
\(68\) −19.3212 −0.284136
\(69\) −6.84134 + 12.6569i −0.0991498 + 0.183433i
\(70\) −57.6023 69.0789i −0.822890 0.986841i
\(71\) 103.333i 1.45539i −0.685899 0.727697i \(-0.740591\pi\)
0.685899 0.727697i \(-0.259409\pi\)
\(72\) 13.9444 + 21.2968i 0.193673 + 0.295789i
\(73\) 66.4287i 0.909982i 0.890496 + 0.454991i \(0.150358\pi\)
−0.890496 + 0.454991i \(0.849642\pi\)
\(74\) 2.89969i 0.0391850i
\(75\) 58.4951 + 46.9395i 0.779935 + 0.625861i
\(76\) 6.99144 0.0919926
\(77\) 28.4345 0.369279
\(78\) 2.37285 + 1.28258i 0.0304212 + 0.0164434i
\(79\) −62.2728 −0.788263 −0.394131 0.919054i \(-0.628955\pi\)
−0.394131 + 0.919054i \(0.628955\pi\)
\(80\) −15.3604 + 12.8085i −0.192005 + 0.160106i
\(81\) −32.3883 + 74.2428i −0.399855 + 0.916578i
\(82\) 29.5687i 0.360594i
\(83\) −21.9860 −0.264892 −0.132446 0.991190i \(-0.542283\pi\)
−0.132446 + 0.991190i \(0.542283\pi\)
\(84\) 67.1397 + 36.2906i 0.799282 + 0.432031i
\(85\) 37.0978 30.9345i 0.436445 0.363935i
\(86\) 62.7873i 0.730085i
\(87\) −97.2109 52.5448i −1.11737 0.603963i
\(88\) 6.32271i 0.0718489i
\(89\) 12.4162i 0.139507i 0.997564 + 0.0697537i \(0.0222213\pi\)
−0.997564 + 0.0697537i \(0.977779\pi\)
\(90\) −60.8715 18.5651i −0.676350 0.206279i
\(91\) 8.08687 0.0888668
\(92\) 9.59166 0.104257
\(93\) −55.4902 + 102.660i −0.596669 + 1.10387i
\(94\) 17.9349 0.190797
\(95\) −13.4239 + 11.1937i −0.141305 + 0.117829i
\(96\) 8.06960 14.9292i 0.0840583 0.155513i
\(97\) 110.069i 1.13473i 0.823467 + 0.567364i \(0.192037\pi\)
−0.823467 + 0.567364i \(0.807963\pi\)
\(98\) 159.521 1.62776
\(99\) 16.8317 11.0208i 0.170017 0.111321i
\(100\) 8.98570 49.1859i 0.0898570 0.491859i
\(101\) 64.4166i 0.637788i 0.947790 + 0.318894i \(0.103311\pi\)
−0.947790 + 0.318894i \(0.896689\pi\)
\(102\) −19.4893 + 36.0564i −0.191072 + 0.353494i
\(103\) 144.898i 1.40677i 0.710808 + 0.703386i \(0.248329\pi\)
−0.710808 + 0.703386i \(0.751671\pi\)
\(104\) 1.79820i 0.0172904i
\(105\) −187.015 + 37.8147i −1.78110 + 0.360140i
\(106\) 45.4571 0.428841
\(107\) 166.897 1.55979 0.779893 0.625912i \(-0.215273\pi\)
0.779893 + 0.625912i \(0.215273\pi\)
\(108\) 53.8088 4.54035i 0.498229 0.0420403i
\(109\) 69.4580 0.637229 0.318615 0.947884i \(-0.396782\pi\)
0.318615 + 0.947884i \(0.396782\pi\)
\(110\) 10.1230 + 12.1399i 0.0920276 + 0.110363i
\(111\) −5.41127 2.92492i −0.0487502 0.0263506i
\(112\) 50.8800i 0.454286i
\(113\) 96.8045 0.856677 0.428339 0.903618i \(-0.359099\pi\)
0.428339 + 0.903618i \(0.359099\pi\)
\(114\) 7.05226 13.0471i 0.0618619 0.114448i
\(115\) −18.4165 + 15.3568i −0.160144 + 0.133538i
\(116\) 73.6687i 0.635075i
\(117\) 4.78699 3.13436i 0.0409145 0.0267894i
\(118\) 48.9816i 0.415099i
\(119\) 122.883i 1.03263i
\(120\) 8.40851 + 41.5848i 0.0700709 + 0.346540i
\(121\) 116.003 0.958702
\(122\) −21.7860 −0.178573
\(123\) 55.1798 + 29.8260i 0.448616 + 0.242488i
\(124\) 77.7982 0.627405
\(125\) 61.4966 + 108.826i 0.491973 + 0.870610i
\(126\) 135.448 88.6865i 1.07498 0.703861i
\(127\) 122.722i 0.966313i −0.875534 0.483156i \(-0.839490\pi\)
0.875534 0.483156i \(-0.160510\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −117.171 63.3336i −0.908300 0.490958i
\(130\) 2.87903 + 3.45265i 0.0221464 + 0.0265588i
\(131\) 217.468i 1.66006i 0.557719 + 0.830030i \(0.311677\pi\)
−0.557719 + 0.830030i \(0.688323\pi\)
\(132\) −11.7991 6.37771i −0.0893874 0.0483160i
\(133\) 44.4655i 0.334327i
\(134\) 146.199i 1.09104i
\(135\) −96.0464 + 94.8688i −0.711455 + 0.702732i
\(136\) 27.3244 0.200914
\(137\) −89.8051 −0.655512 −0.327756 0.944762i \(-0.606292\pi\)
−0.327756 + 0.944762i \(0.606292\pi\)
\(138\) 9.67511 17.8995i 0.0701095 0.129707i
\(139\) −250.096 −1.79925 −0.899626 0.436661i \(-0.856161\pi\)
−0.899626 + 0.436661i \(0.856161\pi\)
\(140\) 81.4619 + 97.6923i 0.581871 + 0.697802i
\(141\) 18.0910 33.4693i 0.128305 0.237371i
\(142\) 146.135i 1.02912i
\(143\) −1.42119 −0.00993838
\(144\) −19.7204 30.1182i −0.136947 0.209154i
\(145\) −117.948 141.448i −0.813434 0.975502i
\(146\) 93.9444i 0.643455i
\(147\) 160.909 297.690i 1.09462 2.02510i
\(148\) 4.10078i 0.0277080i
\(149\) 252.216i 1.69272i −0.532609 0.846361i \(-0.678788\pi\)
0.532609 0.846361i \(-0.321212\pi\)
\(150\) −82.7246 66.3825i −0.551497 0.442550i
\(151\) −209.187 −1.38535 −0.692673 0.721252i \(-0.743567\pi\)
−0.692673 + 0.721252i \(0.743567\pi\)
\(152\) −9.88738 −0.0650486
\(153\) 47.6278 + 72.7402i 0.311293 + 0.475426i
\(154\) −40.2124 −0.261120
\(155\) −149.377 + 124.560i −0.963721 + 0.803610i
\(156\) −3.35572 1.81385i −0.0215110 0.0116272i
\(157\) 159.472i 1.01574i 0.861433 + 0.507872i \(0.169568\pi\)
−0.861433 + 0.507872i \(0.830432\pi\)
\(158\) 88.0670 0.557386
\(159\) 45.8526 84.8299i 0.288381 0.533521i
\(160\) 21.7229 18.1139i 0.135768 0.113212i
\(161\) 61.0030i 0.378900i
\(162\) 45.8039 104.995i 0.282740 0.648119i
\(163\) 55.1297i 0.338219i 0.985597 + 0.169110i \(0.0540892\pi\)
−0.985597 + 0.169110i \(0.945911\pi\)
\(164\) 41.8165i 0.254979i
\(165\) 32.8661 6.64557i 0.199188 0.0402762i
\(166\) 31.0929 0.187307
\(167\) 303.620 1.81808 0.909042 0.416704i \(-0.136815\pi\)
0.909042 + 0.416704i \(0.136815\pi\)
\(168\) −94.9498 51.3226i −0.565177 0.305492i
\(169\) 168.596 0.997608
\(170\) −52.4643 + 43.7480i −0.308613 + 0.257341i
\(171\) −17.2342 26.3212i −0.100785 0.153925i
\(172\) 88.7947i 0.516248i
\(173\) −88.9298 −0.514045 −0.257022 0.966405i \(-0.582741\pi\)
−0.257022 + 0.966405i \(0.582741\pi\)
\(174\) 137.477 + 74.3096i 0.790097 + 0.427067i
\(175\) −312.823 57.1491i −1.78756 0.326566i
\(176\) 8.94166i 0.0508049i
\(177\) −91.4072 49.4078i −0.516425 0.279140i
\(178\) 17.5591i 0.0986467i
\(179\) 40.6656i 0.227182i 0.993528 + 0.113591i \(0.0362354\pi\)
−0.993528 + 0.113591i \(0.963765\pi\)
\(180\) 86.0853 + 26.2550i 0.478251 + 0.145861i
\(181\) 210.241 1.16155 0.580776 0.814064i \(-0.302749\pi\)
0.580776 + 0.814064i \(0.302749\pi\)
\(182\) −11.4366 −0.0628383
\(183\) −21.9755 + 40.6559i −0.120085 + 0.222164i
\(184\) −13.5647 −0.0737210
\(185\) −6.56560 7.87373i −0.0354897 0.0425607i
\(186\) 78.4750 145.183i 0.421909 0.780555i
\(187\) 21.5955i 0.115484i
\(188\) −25.3638 −0.134914
\(189\) −28.8766 342.224i −0.152786 1.81071i
\(190\) 18.9843 15.8303i 0.0999174 0.0833174i
\(191\) 318.625i 1.66820i 0.551617 + 0.834098i \(0.314011\pi\)
−0.551617 + 0.834098i \(0.685989\pi\)
\(192\) −11.4121 + 21.1131i −0.0594382 + 0.109964i
\(193\) 113.876i 0.590032i −0.955492 0.295016i \(-0.904675\pi\)
0.955492 0.295016i \(-0.0953249\pi\)
\(194\) 155.660i 0.802373i
\(195\) 9.34724 1.89003i 0.0479346 0.00969244i
\(196\) −225.597 −1.15100
\(197\) 116.479 0.591265 0.295633 0.955302i \(-0.404470\pi\)
0.295633 + 0.955302i \(0.404470\pi\)
\(198\) −23.8036 + 15.5858i −0.120220 + 0.0787161i
\(199\) 370.323 1.86092 0.930460 0.366393i \(-0.119407\pi\)
0.930460 + 0.366393i \(0.119407\pi\)
\(200\) −12.7077 + 69.5594i −0.0635385 + 0.347797i
\(201\) −272.829 147.471i −1.35736 0.733686i
\(202\) 91.0988i 0.450984i
\(203\) 468.533 2.30804
\(204\) 27.5621 50.9914i 0.135108 0.249958i
\(205\) 66.9507 + 80.2899i 0.326589 + 0.391658i
\(206\) 204.916i 0.994738i
\(207\) −23.6439 36.1105i −0.114222 0.174447i
\(208\) 2.54304i 0.0122262i
\(209\) 7.81438i 0.0373894i
\(210\) 264.479 53.4781i 1.25943 0.254658i
\(211\) −224.564 −1.06429 −0.532143 0.846654i \(-0.678613\pi\)
−0.532143 + 0.846654i \(0.678613\pi\)
\(212\) −64.2860 −0.303236
\(213\) 272.710 + 147.406i 1.28033 + 0.692048i
\(214\) −236.028 −1.10294
\(215\) −142.166 170.491i −0.661236 0.792980i
\(216\) −76.0971 + 6.42102i −0.352301 + 0.0297270i
\(217\) 494.796i 2.28017i
\(218\) −98.2285 −0.450589
\(219\) −175.314 94.7617i −0.800523 0.432702i
\(220\) −14.3161 17.1685i −0.0650733 0.0780385i
\(221\) 6.14184i 0.0277912i
\(222\) 7.65269 + 4.13646i 0.0344716 + 0.0186327i
\(223\) 197.151i 0.884087i 0.896994 + 0.442043i \(0.145746\pi\)
−0.896994 + 0.442043i \(0.854254\pi\)
\(224\) 71.9552i 0.321228i
\(225\) −207.324 + 87.4166i −0.921441 + 0.388518i
\(226\) −136.902 −0.605762
\(227\) −128.576 −0.566413 −0.283206 0.959059i \(-0.591398\pi\)
−0.283206 + 0.959059i \(0.591398\pi\)
\(228\) −9.97340 + 18.4514i −0.0437430 + 0.0809270i
\(229\) 105.653 0.461366 0.230683 0.973029i \(-0.425904\pi\)
0.230683 + 0.973029i \(0.425904\pi\)
\(230\) 26.0449 21.7178i 0.113239 0.0944254i
\(231\) −40.5623 + 75.0425i −0.175594 + 0.324859i
\(232\) 104.183i 0.449066i
\(233\) 198.584 0.852292 0.426146 0.904654i \(-0.359871\pi\)
0.426146 + 0.904654i \(0.359871\pi\)
\(234\) −6.76983 + 4.43266i −0.0289309 + 0.0189430i
\(235\) 48.6999 40.6090i 0.207233 0.172804i
\(236\) 69.2705i 0.293519i
\(237\) 88.8332 164.346i 0.374824 0.693445i
\(238\) 173.783i 0.730180i
\(239\) 91.1474i 0.381370i 0.981651 + 0.190685i \(0.0610709\pi\)
−0.981651 + 0.190685i \(0.938929\pi\)
\(240\) −11.8914 58.8098i −0.0495476 0.245041i
\(241\) 347.855 1.44338 0.721691 0.692215i \(-0.243365\pi\)
0.721691 + 0.692215i \(0.243365\pi\)
\(242\) −164.053 −0.677905
\(243\) −149.735 191.386i −0.616192 0.787596i
\(244\) 30.8100 0.126271
\(245\) 433.158 361.194i 1.76799 1.47426i
\(246\) −78.0360 42.1803i −0.317219 0.171465i
\(247\) 2.22244i 0.00899773i
\(248\) −110.023 −0.443642
\(249\) 31.3634 58.0241i 0.125957 0.233028i
\(250\) −86.9694 153.904i −0.347877 0.615615i
\(251\) 34.9738i 0.139338i −0.997570 0.0696689i \(-0.977806\pi\)
0.997570 0.0696689i \(-0.0221943\pi\)
\(252\) −191.552 + 125.422i −0.760126 + 0.497705i
\(253\) 10.7207i 0.0423742i
\(254\) 173.555i 0.683286i
\(255\) 28.7197 + 142.035i 0.112626 + 0.556999i
\(256\) 16.0000 0.0625000
\(257\) −386.706 −1.50469 −0.752347 0.658767i \(-0.771078\pi\)
−0.752347 + 0.658767i \(0.771078\pi\)
\(258\) 165.704 + 89.5672i 0.642265 + 0.347160i
\(259\) 26.0810 0.100699
\(260\) −4.07156 4.88278i −0.0156599 0.0187799i
\(261\) 277.346 181.597i 1.06263 0.695773i
\(262\) 307.546i 1.17384i
\(263\) 194.450 0.739353 0.369676 0.929161i \(-0.379469\pi\)
0.369676 + 0.929161i \(0.379469\pi\)
\(264\) 16.6865 + 9.01945i 0.0632064 + 0.0341646i
\(265\) 123.433 102.926i 0.465784 0.388399i
\(266\) 62.8838i 0.236405i
\(267\) −32.7680 17.7119i −0.122726 0.0663366i
\(268\) 206.756i 0.771479i
\(269\) 218.046i 0.810578i −0.914189 0.405289i \(-0.867171\pi\)
0.914189 0.405289i \(-0.132829\pi\)
\(270\) 135.830 134.165i 0.503074 0.496907i
\(271\) 71.7319 0.264693 0.132347 0.991203i \(-0.457749\pi\)
0.132347 + 0.991203i \(0.457749\pi\)
\(272\) −38.6425 −0.142068
\(273\) −11.5361 + 21.3424i −0.0422566 + 0.0781772i
\(274\) 127.004 0.463517
\(275\) 54.9755 + 10.0434i 0.199911 + 0.0365214i
\(276\) −13.6827 + 25.3137i −0.0495749 + 0.0917164i
\(277\) 349.558i 1.26194i 0.775807 + 0.630971i \(0.217343\pi\)
−0.775807 + 0.630971i \(0.782657\pi\)
\(278\) 353.689 1.27226
\(279\) −191.776 292.893i −0.687371 1.04979i
\(280\) −115.205 138.158i −0.411445 0.493421i
\(281\) 211.507i 0.752695i −0.926479 0.376348i \(-0.877180\pi\)
0.926479 0.376348i \(-0.122820\pi\)
\(282\) −25.5845 + 47.3327i −0.0907251 + 0.167847i
\(283\) 372.989i 1.31798i 0.752151 + 0.658991i \(0.229017\pi\)
−0.752151 + 0.658991i \(0.770983\pi\)
\(284\) 206.666i 0.727697i
\(285\) −10.3923 51.3956i −0.0364641 0.180336i
\(286\) 2.00986 0.00702750
\(287\) −265.953 −0.926665
\(288\) 27.8888 + 42.5936i 0.0968363 + 0.147894i
\(289\) −195.672 −0.677067
\(290\) 166.804 + 200.037i 0.575185 + 0.689784i
\(291\) −290.486 157.015i −0.998234 0.539569i
\(292\) 132.857i 0.454991i
\(293\) 396.910 1.35464 0.677321 0.735688i \(-0.263141\pi\)
0.677321 + 0.735688i \(0.263141\pi\)
\(294\) −227.559 + 420.998i −0.774011 + 1.43197i
\(295\) −110.906 133.003i −0.375953 0.450858i
\(296\) 5.79939i 0.0195925i
\(297\) 5.07478 + 60.1425i 0.0170868 + 0.202500i
\(298\) 356.687i 1.19694i
\(299\) 3.04900i 0.0101973i
\(300\) 116.990 + 93.8791i 0.389967 + 0.312930i
\(301\) 564.734 1.87619
\(302\) 295.835 0.979587
\(303\) −170.004 91.8914i −0.561070 0.303272i
\(304\) 13.9829 0.0459963
\(305\) −59.1569 + 49.3287i −0.193957 + 0.161733i
\(306\) −67.3559 102.870i −0.220117 0.336177i
\(307\) 286.658i 0.933738i −0.884326 0.466869i \(-0.845382\pi\)
0.884326 0.466869i \(-0.154618\pi\)
\(308\) 56.8689 0.184639
\(309\) −382.405 206.699i −1.23756 0.668928i
\(310\) 211.251 176.154i 0.681454 0.568238i
\(311\) 97.0383i 0.312020i 0.987755 + 0.156010i \(0.0498632\pi\)
−0.987755 + 0.156010i \(0.950137\pi\)
\(312\) 4.74571 + 2.56517i 0.0152106 + 0.00822169i
\(313\) 250.556i 0.800497i −0.916407 0.400249i \(-0.868924\pi\)
0.916407 0.400249i \(-0.131076\pi\)
\(314\) 225.527i 0.718239i
\(315\) 166.982 547.502i 0.530102 1.73810i
\(316\) −124.546 −0.394131
\(317\) −375.250 −1.18375 −0.591877 0.806029i \(-0.701613\pi\)
−0.591877 + 0.806029i \(0.701613\pi\)
\(318\) −64.8453 + 119.968i −0.203916 + 0.377256i
\(319\) −82.3400 −0.258119
\(320\) −30.7209 + 25.6170i −0.0960027 + 0.0800530i
\(321\) −238.082 + 440.465i −0.741687 + 1.37216i
\(322\) 86.2712i 0.267923i
\(323\) −33.7708 −0.104554
\(324\) −64.7765 + 148.486i −0.199928 + 0.458289i
\(325\) 15.6352 + 2.85638i 0.0481084 + 0.00878886i
\(326\) 77.9652i 0.239157i
\(327\) −99.0830 + 183.309i −0.303006 + 0.560579i
\(328\) 59.1375i 0.180297i
\(329\) 161.314i 0.490315i
\(330\) −46.4797 + 9.39825i −0.140847 + 0.0284796i
\(331\) −388.785 −1.17458 −0.587288 0.809378i \(-0.699804\pi\)
−0.587288 + 0.809378i \(0.699804\pi\)
\(332\) −43.9720 −0.132446
\(333\) 15.4385 10.1086i 0.0463620 0.0303563i
\(334\) −429.384 −1.28558
\(335\) −331.029 396.983i −0.988148 1.18503i
\(336\) 134.279 + 72.5812i 0.399641 + 0.216015i
\(337\) 12.3879i 0.0367594i 0.999831 + 0.0183797i \(0.00585077\pi\)
−0.999831 + 0.0183797i \(0.994149\pi\)
\(338\) −238.430 −0.705416
\(339\) −138.093 + 255.480i −0.407355 + 0.753630i
\(340\) 74.1957 61.8690i 0.218223 0.181968i
\(341\) 86.9556i 0.255002i
\(342\) 24.3729 + 37.2238i 0.0712657 + 0.108841i
\(343\) 811.515i 2.36593i
\(344\) 125.575i 0.365043i
\(345\) −14.2573 70.5105i −0.0413256 0.204378i
\(346\) 125.766 0.363485
\(347\) 229.016 0.659989 0.329995 0.943983i \(-0.392953\pi\)
0.329995 + 0.943983i \(0.392953\pi\)
\(348\) −194.422 105.090i −0.558683 0.301982i
\(349\) 319.299 0.914896 0.457448 0.889236i \(-0.348764\pi\)
0.457448 + 0.889236i \(0.348764\pi\)
\(350\) 442.398 + 80.8210i 1.26399 + 0.230917i
\(351\) 1.44329 + 17.1048i 0.00411193 + 0.0487315i
\(352\) 12.6454i 0.0359245i
\(353\) 570.384 1.61582 0.807909 0.589308i \(-0.200599\pi\)
0.807909 + 0.589308i \(0.200599\pi\)
\(354\) 129.269 + 69.8732i 0.365168 + 0.197382i
\(355\) 330.885 + 396.810i 0.932069 + 1.11777i
\(356\) 24.8323i 0.0697537i
\(357\) −324.305 175.295i −0.908419 0.491022i
\(358\) 57.5099i 0.160642i
\(359\) 589.158i 1.64111i 0.571569 + 0.820554i \(0.306335\pi\)
−0.571569 + 0.820554i \(0.693665\pi\)
\(360\) −121.743 37.1302i −0.338175 0.103140i
\(361\) −348.780 −0.966149
\(362\) −297.325 −0.821341
\(363\) −165.480 + 306.148i −0.455868 + 0.843382i
\(364\) 16.1737 0.0444334
\(365\) −212.713 255.093i −0.582774 0.698886i
\(366\) 31.0781 57.4962i 0.0849127 0.157093i
\(367\) 306.861i 0.836134i −0.908416 0.418067i \(-0.862708\pi\)
0.908416 0.418067i \(-0.137292\pi\)
\(368\) 19.1833 0.0521286
\(369\) −157.430 + 103.080i −0.426639 + 0.279349i
\(370\) 9.28516 + 11.1351i 0.0250950 + 0.0300950i
\(371\) 408.859i 1.10205i
\(372\) −110.980 + 205.320i −0.298335 + 0.551936i
\(373\) 543.484i 1.45706i 0.685013 + 0.728531i \(0.259796\pi\)
−0.685013 + 0.728531i \(0.740204\pi\)
\(374\) 30.5406i 0.0816595i
\(375\) −374.934 + 7.05548i −0.999823 + 0.0188146i
\(376\) 35.8698 0.0953985
\(377\) −23.4178 −0.0621162
\(378\) 40.8377 + 483.978i 0.108036 + 1.28036i
\(379\) −73.5844 −0.194154 −0.0970770 0.995277i \(-0.530949\pi\)
−0.0970770 + 0.995277i \(0.530949\pi\)
\(380\) −26.8479 + 22.3874i −0.0706523 + 0.0589143i
\(381\) 323.880 + 175.065i 0.850078 + 0.459487i
\(382\) 450.604i 1.17959i
\(383\) 20.0331 0.0523056 0.0261528 0.999658i \(-0.491674\pi\)
0.0261528 + 0.999658i \(0.491674\pi\)
\(384\) 16.1392 29.8584i 0.0420292 0.0777563i
\(385\) −109.191 + 91.0506i −0.283614 + 0.236495i
\(386\) 161.045i 0.417215i
\(387\) 334.292 218.883i 0.863804 0.565590i
\(388\) 220.137i 0.567364i
\(389\) 209.712i 0.539105i 0.962986 + 0.269552i \(0.0868758\pi\)
−0.962986 + 0.269552i \(0.913124\pi\)
\(390\) −13.2190 + 2.67290i −0.0338949 + 0.00685359i
\(391\) −46.3307 −0.118493
\(392\) 319.042 0.813882
\(393\) −573.928 310.222i −1.46038 0.789368i
\(394\) −164.727 −0.418088
\(395\) 239.134 199.405i 0.605403 0.504823i
\(396\) 33.6633 22.0416i 0.0850084 0.0556607i
\(397\) 157.646i 0.397094i −0.980091 0.198547i \(-0.936378\pi\)
0.980091 0.198547i \(-0.0636222\pi\)
\(398\) −523.716 −1.31587
\(399\) 117.351 + 63.4308i 0.294112 + 0.158975i
\(400\) 17.9714 98.3719i 0.0449285 0.245930i
\(401\) 322.191i 0.803469i 0.915756 + 0.401735i \(0.131593\pi\)
−0.915756 + 0.401735i \(0.868407\pi\)
\(402\) 385.839 + 208.555i 0.959798 + 0.518794i
\(403\) 24.7305i 0.0613661i
\(404\) 128.833i 0.318894i
\(405\) −113.360 388.812i −0.279901 0.960029i
\(406\) −662.605 −1.63203
\(407\) −4.58348 −0.0112616
\(408\) −38.9787 + 72.1128i −0.0955360 + 0.176747i
\(409\) 435.863 1.06568 0.532839 0.846216i \(-0.321125\pi\)
0.532839 + 0.846216i \(0.321125\pi\)
\(410\) −94.6827 113.547i −0.230933 0.276944i
\(411\) 128.109 237.008i 0.311700 0.576662i
\(412\) 289.795i 0.703386i
\(413\) 440.560 1.06673
\(414\) 33.4375 + 51.0679i 0.0807670 + 0.123352i
\(415\) 84.4286 70.4018i 0.203442 0.169643i
\(416\) 3.59641i 0.00864521i
\(417\) 356.766 660.038i 0.855555 1.58283i
\(418\) 11.0512i 0.0264383i
\(419\) 80.0264i 0.190994i −0.995430 0.0954970i \(-0.969556\pi\)
0.995430 0.0954970i \(-0.0304440\pi\)
\(420\) −374.030 + 75.6295i −0.890548 + 0.180070i
\(421\) 374.853 0.890388 0.445194 0.895434i \(-0.353135\pi\)
0.445194 + 0.895434i \(0.353135\pi\)
\(422\) 317.582 0.752564
\(423\) 62.5230 + 95.4890i 0.147809 + 0.225742i
\(424\) 90.9142 0.214420
\(425\) −43.4037 + 237.583i −0.102126 + 0.559020i
\(426\) −385.670 208.464i −0.905329 0.489352i
\(427\) 195.952i 0.458903i
\(428\) 333.794 0.779893
\(429\) 2.02735 3.75071i 0.00472576 0.00874292i
\(430\) 201.053 + 241.110i 0.467564 + 0.560721i
\(431\) 773.014i 1.79354i 0.442501 + 0.896768i \(0.354091\pi\)
−0.442501 + 0.896768i \(0.645909\pi\)
\(432\) 107.618 9.08070i 0.249115 0.0210201i
\(433\) 415.396i 0.959344i −0.877448 0.479672i \(-0.840756\pi\)
0.877448 0.479672i \(-0.159244\pi\)
\(434\) 699.748i 1.61232i
\(435\) 541.555 109.503i 1.24495 0.251732i
\(436\) 138.916 0.318615
\(437\) 16.7649 0.0383636
\(438\) 247.932 + 134.013i 0.566055 + 0.305966i
\(439\) −262.230 −0.597335 −0.298668 0.954357i \(-0.596542\pi\)
−0.298668 + 0.954357i \(0.596542\pi\)
\(440\) 20.2461 + 24.2799i 0.0460138 + 0.0551815i
\(441\) 556.107 + 849.321i 1.26101 + 1.92590i
\(442\) 8.68588i 0.0196513i
\(443\) −771.627 −1.74182 −0.870910 0.491442i \(-0.836470\pi\)
−0.870910 + 0.491442i \(0.836470\pi\)
\(444\) −10.8225 5.84984i −0.0243751 0.0131753i
\(445\) −39.7580 47.6794i −0.0893439 0.107145i
\(446\) 278.814i 0.625144i
\(447\) 665.632 + 359.790i 1.48911 + 0.804899i
\(448\) 101.760i 0.227143i
\(449\) 166.554i 0.370943i −0.982650 0.185472i \(-0.940619\pi\)
0.982650 0.185472i \(-0.0593813\pi\)
\(450\) 293.201 123.626i 0.651557 0.274724i
\(451\) 46.7386 0.103633
\(452\) 193.609 0.428339
\(453\) 298.409 552.074i 0.658740 1.21871i
\(454\) 181.833 0.400514
\(455\) −31.0545 + 25.8951i −0.0682516 + 0.0569124i
\(456\) 14.1045 26.0942i 0.0309310 0.0572241i
\(457\) 324.543i 0.710159i −0.934836 0.355079i \(-0.884454\pi\)
0.934836 0.355079i \(-0.115546\pi\)
\(458\) −149.416 −0.326235
\(459\) −259.913 + 21.9313i −0.566260 + 0.0477806i
\(460\) −36.8330 + 30.7137i −0.0800718 + 0.0667688i
\(461\) 575.072i 1.24744i −0.781646 0.623722i \(-0.785620\pi\)
0.781646 0.623722i \(-0.214380\pi\)
\(462\) 57.3637 106.126i 0.124164 0.229710i
\(463\) 768.386i 1.65958i 0.558074 + 0.829791i \(0.311540\pi\)
−0.558074 + 0.829791i \(0.688460\pi\)
\(464\) 147.337i 0.317537i
\(465\) −115.642 571.912i −0.248691 1.22992i
\(466\) −280.840 −0.602662
\(467\) 619.812 1.32722 0.663610 0.748079i \(-0.269023\pi\)
0.663610 + 0.748079i \(0.269023\pi\)
\(468\) 9.57398 6.26872i 0.0204572 0.0133947i
\(469\) 1314.97 2.80378
\(470\) −68.8720 + 57.4298i −0.146536 + 0.122191i
\(471\) −420.868 227.489i −0.893563 0.482992i
\(472\) 97.9633i 0.207549i
\(473\) −99.2465 −0.209823
\(474\) −125.629 + 232.421i −0.265040 + 0.490340i
\(475\) 15.7057 85.9701i 0.0330647 0.180990i
\(476\) 245.766i 0.516316i
\(477\) 158.468 + 242.023i 0.332219 + 0.507385i
\(478\) 128.902i 0.269669i
\(479\) 330.303i 0.689568i −0.938682 0.344784i \(-0.887952\pi\)
0.938682 0.344784i \(-0.112048\pi\)
\(480\) 16.8170 + 83.1696i 0.0350355 + 0.173270i
\(481\) −1.30356 −0.00271010
\(482\) −491.942 −1.02063
\(483\) 160.995 + 87.0218i 0.333323 + 0.180169i
\(484\) 232.006 0.479351
\(485\) −352.453 422.675i −0.726707 0.871495i
\(486\) 211.757 + 270.660i 0.435714 + 0.556914i
\(487\) 766.837i 1.57461i 0.616562 + 0.787307i \(0.288525\pi\)
−0.616562 + 0.787307i \(0.711475\pi\)
\(488\) −43.5719 −0.0892867
\(489\) −145.495 78.6435i −0.297536 0.160825i
\(490\) −612.578 + 510.805i −1.25016 + 1.04246i
\(491\) 171.008i 0.348286i −0.984720 0.174143i \(-0.944285\pi\)
0.984720 0.174143i \(-0.0557154\pi\)
\(492\) 110.360 + 59.6520i 0.224308 + 0.121244i
\(493\) 355.843i 0.721790i
\(494\) 3.14301i 0.00636236i
\(495\) −29.3454 + 96.2181i −0.0592837 + 0.194380i
\(496\) 155.596 0.313702
\(497\) −1314.39 −2.64466
\(498\) −44.3546 + 82.0585i −0.0890654 + 0.164776i
\(499\) 659.800 1.32224 0.661122 0.750278i \(-0.270081\pi\)
0.661122 + 0.750278i \(0.270081\pi\)
\(500\) 122.993 + 217.653i 0.245987 + 0.435305i
\(501\) −433.119 + 801.295i −0.864509 + 1.59939i
\(502\) 49.4604i 0.0985268i
\(503\) −398.315 −0.791879 −0.395939 0.918277i \(-0.629581\pi\)
−0.395939 + 0.918277i \(0.629581\pi\)
\(504\) 270.895 177.373i 0.537490 0.351931i
\(505\) −206.270 247.367i −0.408455 0.489835i
\(506\) 15.1613i 0.0299631i
\(507\) −240.505 + 444.948i −0.474368 + 0.877609i
\(508\) 245.443i 0.483156i
\(509\) 380.104i 0.746765i 0.927677 + 0.373383i \(0.121802\pi\)
−0.927677 + 0.373383i \(0.878198\pi\)
\(510\) −40.6157 200.868i −0.0796387 0.393858i
\(511\) 844.973 1.65357
\(512\) −22.6274 −0.0441942
\(513\) 94.0502 7.93589i 0.183334 0.0154696i
\(514\) 546.885 1.06398
\(515\) −463.979 556.422i −0.900931 1.08043i
\(516\) −234.341 126.667i −0.454150 0.245479i
\(517\) 28.3493i 0.0548343i
\(518\) −36.8841 −0.0712048
\(519\) 126.860 234.698i 0.244431 0.452212i
\(520\) 5.75806 + 6.90529i 0.0110732 + 0.0132794i
\(521\) 66.7813i 0.128179i −0.997944 0.0640895i \(-0.979586\pi\)
0.997944 0.0640895i \(-0.0204143\pi\)
\(522\) −392.226 + 256.817i −0.751392 + 0.491986i
\(523\) 496.177i 0.948713i 0.880333 + 0.474357i \(0.157319\pi\)
−0.880333 + 0.474357i \(0.842681\pi\)
\(524\) 434.936i 0.830030i
\(525\) 597.071 744.058i 1.13728 1.41725i
\(526\) −274.993 −0.522801
\(527\) −375.790 −0.713073
\(528\) −23.5983 12.7554i −0.0446937 0.0241580i
\(529\) 23.0000 0.0434783
\(530\) −174.560 + 145.559i −0.329359 + 0.274640i
\(531\) 260.788 170.755i 0.491126 0.321573i
\(532\) 88.9311i 0.167164i
\(533\) 13.2926 0.0249393
\(534\) 46.3409 + 25.0484i 0.0867807 + 0.0469071i
\(535\) −640.903 + 534.425i −1.19795 + 0.998925i
\(536\) 292.398i 0.545518i
\(537\) −107.322 58.0102i −0.199855 0.108026i
\(538\) 308.363i 0.573166i
\(539\) 252.151i 0.467813i
\(540\) −192.093 + 189.738i −0.355727 + 0.351366i
\(541\) −146.067 −0.269994 −0.134997 0.990846i \(-0.543102\pi\)
−0.134997 + 0.990846i \(0.543102\pi\)
\(542\) −101.444 −0.187167
\(543\) −299.912 + 554.854i −0.552324 + 1.02183i
\(544\) 54.6487 0.100457
\(545\) −266.726 + 222.413i −0.489406 + 0.408097i
\(546\) 16.3145 30.1827i 0.0298800 0.0552796i
\(547\) 243.641i 0.445414i −0.974885 0.222707i \(-0.928511\pi\)
0.974885 0.222707i \(-0.0714893\pi\)
\(548\) −179.610 −0.327756
\(549\) −75.9482 115.993i −0.138339 0.211280i
\(550\) −77.7471 14.2035i −0.141358 0.0258245i
\(551\) 128.762i 0.233689i
\(552\) 19.3502 35.7990i 0.0350547 0.0648533i
\(553\) 792.110i 1.43239i
\(554\) 494.349i 0.892327i
\(555\) 30.1458 6.09553i 0.0543168 0.0109829i
\(556\) −500.192 −0.899626
\(557\) −994.901 −1.78618 −0.893089 0.449880i \(-0.851467\pi\)
−0.893089 + 0.449880i \(0.851467\pi\)
\(558\) 271.213 + 414.213i 0.486044 + 0.742317i
\(559\) −28.2261 −0.0504939
\(560\) 162.924 + 195.385i 0.290935 + 0.348901i
\(561\) 56.9935 + 30.8063i 0.101593 + 0.0549133i
\(562\) 299.117i 0.532236i
\(563\) 290.294 0.515620 0.257810 0.966196i \(-0.416999\pi\)
0.257810 + 0.966196i \(0.416999\pi\)
\(564\) 36.1819 66.9386i 0.0641523 0.118685i
\(565\) −371.740 + 309.980i −0.657946 + 0.548637i
\(566\) 527.486i 0.931954i
\(567\) 944.369 + 411.979i 1.66555 + 0.726594i
\(568\) 292.270i 0.514559i
\(569\) 20.8696i 0.0366777i 0.999832 + 0.0183388i \(0.00583776\pi\)
−0.999832 + 0.0183388i \(0.994162\pi\)
\(570\) 14.6969 + 72.6844i 0.0257840 + 0.127516i
\(571\) 296.178 0.518700 0.259350 0.965783i \(-0.416492\pi\)
0.259350 + 0.965783i \(0.416492\pi\)
\(572\) −2.84238 −0.00496919
\(573\) −840.896 454.525i −1.46753 0.793237i
\(574\) 376.114 0.655251
\(575\) 21.5470 117.944i 0.0374730 0.205120i
\(576\) −39.4408 60.2364i −0.0684736 0.104577i
\(577\) 48.7618i 0.0845093i −0.999107 0.0422546i \(-0.986546\pi\)
0.999107 0.0422546i \(-0.0134541\pi\)
\(578\) 276.723 0.478759
\(579\) 300.535 + 162.446i 0.519058 + 0.280563i
\(580\) −235.896 282.896i −0.406717 0.487751i
\(581\) 279.662i 0.481346i
\(582\) 410.809 + 222.052i 0.705858 + 0.381533i
\(583\) 71.8530i 0.123247i
\(584\) 187.889i 0.321727i
\(585\) −8.34596 + 27.3648i −0.0142666 + 0.0467775i
\(586\) −561.316 −0.957876
\(587\) −151.973 −0.258897 −0.129448 0.991586i \(-0.541321\pi\)
−0.129448 + 0.991586i \(0.541321\pi\)
\(588\) 321.818 595.381i 0.547309 1.01255i
\(589\) 135.980 0.230866
\(590\) 156.845 + 188.095i 0.265839 + 0.318805i
\(591\) −166.160 + 307.405i −0.281150 + 0.520144i
\(592\) 8.20157i 0.0138540i
\(593\) −392.414 −0.661744 −0.330872 0.943676i \(-0.607343\pi\)
−0.330872 + 0.943676i \(0.607343\pi\)
\(594\) −7.17682 85.0543i −0.0120822 0.143189i
\(595\) −393.486 471.884i −0.661322 0.793083i
\(596\) 504.431i 0.846361i
\(597\) −528.272 + 977.334i −0.884878 + 1.63708i
\(598\) 4.31194i 0.00721060i
\(599\) 569.828i 0.951298i −0.879635 0.475649i \(-0.842213\pi\)
0.879635 0.475649i \(-0.157787\pi\)
\(600\) −165.449 132.765i −0.275749 0.221275i
\(601\) −1040.37 −1.73107 −0.865536 0.500846i \(-0.833022\pi\)
−0.865536 + 0.500846i \(0.833022\pi\)
\(602\) −798.655 −1.32667
\(603\) 778.392 509.665i 1.29086 0.845215i
\(604\) −418.374 −0.692673
\(605\) −445.464 + 371.455i −0.736304 + 0.613976i
\(606\) 240.422 + 129.954i 0.396737 + 0.214446i
\(607\) 835.820i 1.37697i −0.725252 0.688484i \(-0.758277\pi\)
0.725252 0.688484i \(-0.241723\pi\)
\(608\) −19.7748 −0.0325243
\(609\) −668.370 + 1236.52i −1.09749 + 2.03041i
\(610\) 83.6604 69.7613i 0.137148 0.114363i
\(611\) 8.06265i 0.0131958i
\(612\) 95.2556 + 145.480i 0.155646 + 0.237713i
\(613\) 254.053i 0.414442i −0.978294 0.207221i \(-0.933558\pi\)
0.978294 0.207221i \(-0.0664419\pi\)
\(614\) 405.395i 0.660253i
\(615\) −307.403 + 62.1573i −0.499842 + 0.101069i
\(616\) −80.4248 −0.130560
\(617\) −1014.01 −1.64345 −0.821727 0.569882i \(-0.806989\pi\)
−0.821727 + 0.569882i \(0.806989\pi\)
\(618\) 540.802 + 292.316i 0.875084 + 0.473004i
\(619\) 334.784 0.540846 0.270423 0.962742i \(-0.412836\pi\)
0.270423 + 0.962742i \(0.412836\pi\)
\(620\) −298.753 + 249.119i −0.481860 + 0.401805i
\(621\) 129.029 10.8874i 0.207776 0.0175320i
\(622\) 137.233i 0.220632i
\(623\) 157.934 0.253505
\(624\) −6.71144 3.62769i −0.0107555 0.00581361i
\(625\) −584.629 220.985i −0.935406 0.353576i
\(626\) 354.339i 0.566037i
\(627\) −20.6232 11.1473i −0.0328919 0.0177789i
\(628\) 318.944i 0.507872i
\(629\) 19.8081i 0.0314914i
\(630\) −236.148 + 774.285i −0.374838 + 1.22902i
\(631\) 936.585 1.48429 0.742144 0.670241i \(-0.233809\pi\)
0.742144 + 0.670241i \(0.233809\pi\)
\(632\) 176.134 0.278693
\(633\) 320.345 592.656i 0.506074 0.936266i
\(634\) 530.683 0.837040
\(635\) 392.970 + 471.265i 0.618850 + 0.742149i
\(636\) 91.7051 169.660i 0.144190 0.266761i
\(637\) 71.7127i 0.112579i
\(638\) 116.446 0.182518
\(639\) −778.051 + 509.442i −1.21761 + 0.797248i
\(640\) 43.4459 36.2279i 0.0678842 0.0566060i
\(641\) 247.737i 0.386486i −0.981151 0.193243i \(-0.938100\pi\)
0.981151 0.193243i \(-0.0619005\pi\)
\(642\) 336.698 622.911i 0.524452 0.970266i
\(643\) 721.358i 1.12186i −0.827862 0.560932i \(-0.810443\pi\)
0.827862 0.560932i \(-0.189557\pi\)
\(644\) 122.006i 0.189450i
\(645\) 652.750 131.987i 1.01202 0.204631i
\(646\) 47.7591 0.0739306
\(647\) −505.748 −0.781682 −0.390841 0.920458i \(-0.627816\pi\)
−0.390841 + 0.920458i \(0.627816\pi\)
\(648\) 91.6079 209.990i 0.141370 0.324059i
\(649\) −77.4241 −0.119298
\(650\) −22.1116 4.03953i −0.0340178 0.00621466i
\(651\) 1305.84 + 705.836i 2.00589 + 1.08423i
\(652\) 110.259i 0.169110i
\(653\) −937.577 −1.43580 −0.717900 0.696146i \(-0.754896\pi\)
−0.717900 + 0.696146i \(0.754896\pi\)
\(654\) 140.125 259.238i 0.214258 0.396389i
\(655\) −696.358 835.100i −1.06314 1.27496i
\(656\) 83.6330i 0.127489i
\(657\) 500.178 327.500i 0.761306 0.498478i
\(658\) 228.132i 0.346705i
\(659\) 194.845i 0.295668i −0.989012 0.147834i \(-0.952770\pi\)
0.989012 0.147834i \(-0.0472301\pi\)
\(660\) 65.7322 13.2911i 0.0995942 0.0201381i
\(661\) −1079.58 −1.63325 −0.816627 0.577166i \(-0.804159\pi\)
−0.816627 + 0.577166i \(0.804159\pi\)
\(662\) 549.824 0.830551
\(663\) 16.2092 + 8.76145i 0.0244482 + 0.0132149i
\(664\) 62.1858 0.0936533
\(665\) 142.384 + 170.752i 0.214111 + 0.256771i
\(666\) −21.8334 + 14.2958i −0.0327829 + 0.0214651i
\(667\) 176.651i 0.264844i
\(668\) 607.240 0.909042
\(669\) −520.310 281.240i −0.777742 0.420388i
\(670\) 468.146 + 561.419i 0.698726 + 0.837939i
\(671\) 34.4366i 0.0513213i
\(672\) −189.900 102.645i −0.282589 0.152746i
\(673\) 1017.14i 1.51135i −0.654949 0.755673i \(-0.727310\pi\)
0.654949 0.755673i \(-0.272690\pi\)
\(674\) 17.5192i 0.0259928i
\(675\) 65.0471 671.859i 0.0963661 0.995346i
\(676\) 337.192 0.498804
\(677\) 1006.78 1.48712 0.743560 0.668669i \(-0.233136\pi\)
0.743560 + 0.668669i \(0.233136\pi\)
\(678\) 195.293 361.304i 0.288043 0.532897i
\(679\) 1400.07 2.06196
\(680\) −104.929 + 87.4959i −0.154307 + 0.128670i
\(681\) 183.415 339.329i 0.269332 0.498280i
\(682\) 122.974i 0.180314i
\(683\) 75.4398 0.110454 0.0552268 0.998474i \(-0.482412\pi\)
0.0552268 + 0.998474i \(0.482412\pi\)
\(684\) −34.4685 52.6424i −0.0503925 0.0769625i
\(685\) 344.861 287.567i 0.503447 0.419805i
\(686\) 1147.66i 1.67297i
\(687\) −150.715 + 278.832i −0.219382 + 0.405869i
\(688\) 177.589i 0.258124i
\(689\) 20.4353i 0.0296593i
\(690\) 20.1629 + 99.7169i 0.0292216 + 0.144517i
\(691\) −983.980 −1.42399 −0.711997 0.702182i \(-0.752209\pi\)
−0.711997 + 0.702182i \(0.752209\pi\)
\(692\) −177.860 −0.257022
\(693\) −140.185 214.099i −0.202287 0.308945i
\(694\) −323.878 −0.466683
\(695\) 960.396 800.838i 1.38186 1.15228i
\(696\) 274.954 + 148.619i 0.395049 + 0.213533i
\(697\) 201.987i 0.289795i
\(698\) −451.556 −0.646929
\(699\) −283.284 + 524.091i −0.405270 + 0.749772i
\(700\) −625.645 114.298i −0.893779 0.163283i
\(701\) 667.926i 0.952819i −0.879224 0.476409i \(-0.841938\pi\)
0.879224 0.476409i \(-0.158062\pi\)
\(702\) −2.04112 24.1898i −0.00290757 0.0344584i
\(703\) 7.16759i 0.0101957i
\(704\) 17.8833i 0.0254024i
\(705\) 37.7015 + 186.455i 0.0534773 + 0.264475i
\(706\) −806.644 −1.14256
\(707\) 819.379 1.15895
\(708\) −182.814 98.8156i −0.258212 0.139570i
\(709\) −322.487 −0.454848 −0.227424 0.973796i \(-0.573030\pi\)
−0.227424 + 0.973796i \(0.573030\pi\)
\(710\) −467.941 561.174i −0.659072 0.790385i
\(711\) 307.011 + 468.886i 0.431801 + 0.659474i
\(712\) 35.1182i 0.0493233i
\(713\) 186.554 0.261646
\(714\) 458.637 + 247.904i 0.642349 + 0.347205i
\(715\) 5.45752 4.55082i 0.00763289 0.00636478i
\(716\) 81.3313i 0.113591i
\(717\) −240.551 130.023i −0.335496 0.181344i
\(718\) 833.195i 1.16044i
\(719\) 787.862i 1.09577i 0.836552 + 0.547887i \(0.184568\pi\)
−0.836552 + 0.547887i \(0.815432\pi\)
\(720\) 172.171 + 52.5101i 0.239126 + 0.0729307i
\(721\) 1843.10 2.55631
\(722\) 493.249 0.683171
\(723\) −496.221 + 918.038i −0.686337 + 1.26976i
\(724\) 420.482 0.580776
\(725\) 905.866 + 165.491i 1.24947 + 0.228264i
\(726\) 234.024 432.958i 0.322347 0.596361i
\(727\) 518.452i 0.713139i 0.934269 + 0.356569i \(0.116054\pi\)
−0.934269 + 0.356569i \(0.883946\pi\)
\(728\) −22.8731 −0.0314191
\(729\) 718.693 122.155i 0.985861 0.167566i
\(730\) 300.821 + 360.756i 0.412084 + 0.494187i
\(731\) 428.906i 0.586739i
\(732\) −43.9510 + 81.3119i −0.0600424 + 0.111082i
\(733\) 541.297i 0.738468i −0.929336 0.369234i \(-0.879620\pi\)
0.929336 0.369234i \(-0.120380\pi\)
\(734\) 433.967i 0.591236i
\(735\) 335.333 + 1658.41i 0.456236 + 2.25634i
\(736\) −27.1293 −0.0368605
\(737\) −231.093 −0.313559
\(738\) 222.639 145.777i 0.301679 0.197529i
\(739\) −1010.45 −1.36732 −0.683661 0.729799i \(-0.739613\pi\)
−0.683661 + 0.729799i \(0.739613\pi\)
\(740\) −13.1312 15.7475i −0.0177449 0.0212803i
\(741\) −5.86533 3.17035i −0.00791542 0.00427847i
\(742\) 578.214i 0.779264i
\(743\) 630.503 0.848591 0.424296 0.905524i \(-0.360522\pi\)
0.424296 + 0.905524i \(0.360522\pi\)
\(744\) 156.950 290.367i 0.210954 0.390278i
\(745\) 807.625 + 968.535i 1.08406 + 1.30005i
\(746\) 768.602i 1.03030i
\(747\) 108.393 + 165.545i 0.145105 + 0.221613i
\(748\) 43.1910i 0.0577420i
\(749\) 2122.93i 2.83435i
\(750\) 530.236 9.97796i 0.706982 0.0133039i
\(751\) −1188.40 −1.58243 −0.791213 0.611540i \(-0.790550\pi\)
−0.791213 + 0.611540i \(0.790550\pi\)
\(752\) −50.7276 −0.0674569
\(753\) 92.3007 + 49.8907i 0.122577 + 0.0662560i
\(754\) 33.1178 0.0439228
\(755\) 803.301 669.842i 1.06397 0.887208i
\(756\) −57.7532 684.448i −0.0763932 0.905354i
\(757\) 319.200i 0.421665i 0.977522 + 0.210832i \(0.0676174\pi\)
−0.977522 + 0.210832i \(0.932383\pi\)
\(758\) 104.064 0.137288
\(759\) −28.2933 15.2932i −0.0372771 0.0201492i
\(760\) 37.9686 31.6606i 0.0499587 0.0416587i
\(761\) 124.010i 0.162956i −0.996675 0.0814782i \(-0.974036\pi\)
0.996675 0.0814782i \(-0.0259641\pi\)
\(762\) −458.035 247.579i −0.601096 0.324907i
\(763\) 883.506i 1.15794i
\(764\) 637.251i 0.834098i
\(765\) −415.819 126.820i −0.543554 0.165778i
\(766\) −28.3310 −0.0369857
\(767\) −22.0197 −0.0287089
\(768\) −22.8243 + 42.2262i −0.0297191 + 0.0549820i
\(769\) 1004.95 1.30683 0.653413 0.757002i \(-0.273337\pi\)
0.653413 + 0.757002i \(0.273337\pi\)
\(770\) 154.420 128.765i 0.200545 0.167227i
\(771\) 551.643 1020.57i 0.715491 1.32370i
\(772\) 227.752i 0.295016i
\(773\) −943.044 −1.21998 −0.609990 0.792409i \(-0.708826\pi\)
−0.609990 + 0.792409i \(0.708826\pi\)
\(774\) −472.760 + 309.548i −0.610802 + 0.399932i
\(775\) 174.768 956.645i 0.225507 1.23438i
\(776\) 311.321i 0.401187i
\(777\) −37.2050 + 68.8313i −0.0478828 + 0.0885860i
\(778\) 296.577i 0.381205i
\(779\) 73.0894i 0.0938246i
\(780\) 18.6945 3.78005i 0.0239673 0.00484622i
\(781\) 230.992 0.295764
\(782\) 65.5215 0.0837871