Properties

Label 690.3.g.a.461.9
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
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.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.9
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(2.16025 + 2.08166i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(2.94392 - 3.05506i) q^{6} +12.7530 q^{7} +2.82843i q^{8} +(0.333364 + 8.99382i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(2.16025 + 2.08166i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(2.94392 - 3.05506i) q^{6} +12.7530 q^{7} +2.82843i q^{8} +(0.333364 + 8.99382i) q^{9} +3.16228 q^{10} +10.4206i q^{11} +(-4.32050 - 4.16332i) q^{12} -10.0884 q^{13} -18.0355i q^{14} +(-4.65474 + 4.83047i) q^{15} +4.00000 q^{16} -0.278181i q^{17} +(12.7192 - 0.471449i) q^{18} +14.4422 q^{19} -4.47214i q^{20} +(27.5497 + 26.5474i) q^{21} +14.7369 q^{22} +4.79583i q^{23} +(-5.88783 + 6.11011i) q^{24} -5.00000 q^{25} +14.2672i q^{26} +(-18.0020 + 20.1229i) q^{27} -25.5060 q^{28} -1.71142i q^{29} +(6.83131 + 6.58279i) q^{30} -36.9908 q^{31} -5.65685i q^{32} +(-21.6921 + 22.5111i) q^{33} -0.393408 q^{34} +28.5166i q^{35} +(-0.666729 - 17.9876i) q^{36} +17.1960 q^{37} -20.4243i q^{38} +(-21.7936 - 21.0007i) q^{39} -6.32456 q^{40} -36.4515i q^{41} +(37.5437 - 38.9611i) q^{42} -41.5531 q^{43} -20.8412i q^{44} +(-20.1108 + 0.745426i) q^{45} +6.78233 q^{46} +73.4371i q^{47} +(8.64100 + 8.32665i) q^{48} +113.639 q^{49} +7.07107i q^{50} +(0.579080 - 0.600942i) q^{51} +20.1769 q^{52} -20.7239i q^{53} +(28.4580 + 25.4586i) q^{54} -23.3011 q^{55} +36.0709i q^{56} +(31.1987 + 30.0637i) q^{57} -2.42032 q^{58} +74.5843i q^{59} +(9.30948 - 9.66093i) q^{60} +77.3260 q^{61} +52.3129i q^{62} +(4.25139 + 114.698i) q^{63} -8.00000 q^{64} -22.5584i q^{65} +(31.8355 + 30.6773i) q^{66} +103.539 q^{67} +0.556363i q^{68} +(-9.98330 + 10.3602i) q^{69} +40.3285 q^{70} -56.8221i q^{71} +(-25.4384 + 0.942897i) q^{72} -39.9241 q^{73} -24.3188i q^{74} +(-10.8013 - 10.4083i) q^{75} -28.8843 q^{76} +132.894i q^{77} +(-29.6995 + 30.8207i) q^{78} +81.4578 q^{79} +8.94427i q^{80} +(-80.7777 + 5.99644i) q^{81} -51.5502 q^{82} +37.1864i q^{83} +(-55.0993 - 53.0949i) q^{84} +0.622033 q^{85} +58.7650i q^{86} +(3.56261 - 3.69711i) q^{87} -29.4739 q^{88} -129.429i q^{89} +(1.05419 + 28.4410i) q^{90} -128.658 q^{91} -9.59166i q^{92} +(-79.9094 - 77.0024i) q^{93} +103.856 q^{94} +32.2937i q^{95} +(11.7757 - 12.2202i) q^{96} +39.8372 q^{97} -160.710i q^{98} +(-93.7209 + 3.47385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 2.16025 + 2.08166i 0.720084 + 0.693887i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) 2.94392 3.05506i 0.490653 0.509176i
\(7\) 12.7530 1.82186 0.910928 0.412565i \(-0.135367\pi\)
0.910928 + 0.412565i \(0.135367\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 0.333364 + 8.99382i 0.0370405 + 0.999314i
\(10\) 3.16228 0.316228
\(11\) 10.4206i 0.947326i 0.880706 + 0.473663i \(0.157069\pi\)
−0.880706 + 0.473663i \(0.842931\pi\)
\(12\) −4.32050 4.16332i −0.360042 0.346944i
\(13\) −10.0884 −0.776034 −0.388017 0.921652i \(-0.626840\pi\)
−0.388017 + 0.921652i \(0.626840\pi\)
\(14\) 18.0355i 1.28825i
\(15\) −4.65474 + 4.83047i −0.310316 + 0.322031i
\(16\) 4.00000 0.250000
\(17\) 0.278181i 0.0163636i −0.999967 0.00818181i \(-0.997396\pi\)
0.999967 0.00818181i \(-0.00260438\pi\)
\(18\) 12.7192 0.471449i 0.706622 0.0261916i
\(19\) 14.4422 0.760114 0.380057 0.924963i \(-0.375904\pi\)
0.380057 + 0.924963i \(0.375904\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 27.5497 + 26.5474i 1.31189 + 1.26416i
\(22\) 14.7369 0.669861
\(23\) 4.79583i 0.208514i
\(24\) −5.88783 + 6.11011i −0.245326 + 0.254588i
\(25\) −5.00000 −0.200000
\(26\) 14.2672i 0.548739i
\(27\) −18.0020 + 20.1229i −0.666739 + 0.745291i
\(28\) −25.5060 −0.910928
\(29\) 1.71142i 0.0590146i −0.999565 0.0295073i \(-0.990606\pi\)
0.999565 0.0295073i \(-0.00939383\pi\)
\(30\) 6.83131 + 6.58279i 0.227710 + 0.219426i
\(31\) −36.9908 −1.19325 −0.596626 0.802520i \(-0.703492\pi\)
−0.596626 + 0.802520i \(0.703492\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −21.6921 + 22.5111i −0.657338 + 0.682154i
\(34\) −0.393408 −0.0115708
\(35\) 28.5166i 0.814759i
\(36\) −0.666729 17.9876i −0.0185202 0.499657i
\(37\) 17.1960 0.464756 0.232378 0.972626i \(-0.425349\pi\)
0.232378 + 0.972626i \(0.425349\pi\)
\(38\) 20.4243i 0.537482i
\(39\) −21.7936 21.0007i −0.558809 0.538480i
\(40\) −6.32456 −0.158114
\(41\) 36.4515i 0.889062i −0.895764 0.444531i \(-0.853370\pi\)
0.895764 0.444531i \(-0.146630\pi\)
\(42\) 37.5437 38.9611i 0.893898 0.927645i
\(43\) −41.5531 −0.966352 −0.483176 0.875523i \(-0.660517\pi\)
−0.483176 + 0.875523i \(0.660517\pi\)
\(44\) 20.8412i 0.473663i
\(45\) −20.1108 + 0.745426i −0.446907 + 0.0165650i
\(46\) 6.78233 0.147442
\(47\) 73.4371i 1.56249i 0.624224 + 0.781246i \(0.285415\pi\)
−0.624224 + 0.781246i \(0.714585\pi\)
\(48\) 8.64100 + 8.32665i 0.180021 + 0.173472i
\(49\) 113.639 2.31916
\(50\) 7.07107i 0.141421i
\(51\) 0.579080 0.600942i 0.0113545 0.0117832i
\(52\) 20.1769 0.388017
\(53\) 20.7239i 0.391017i −0.980702 0.195509i \(-0.937364\pi\)
0.980702 0.195509i \(-0.0626358\pi\)
\(54\) 28.4580 + 25.4586i 0.527001 + 0.471456i
\(55\) −23.3011 −0.423657
\(56\) 36.0709i 0.644123i
\(57\) 31.1987 + 30.0637i 0.547346 + 0.527434i
\(58\) −2.42032 −0.0417297
\(59\) 74.5843i 1.26414i 0.774911 + 0.632070i \(0.217794\pi\)
−0.774911 + 0.632070i \(0.782206\pi\)
\(60\) 9.30948 9.66093i 0.155158 0.161016i
\(61\) 77.3260 1.26764 0.633820 0.773481i \(-0.281486\pi\)
0.633820 + 0.773481i \(0.281486\pi\)
\(62\) 52.3129i 0.843756i
\(63\) 4.25139 + 114.698i 0.0674825 + 1.82061i
\(64\) −8.00000 −0.125000
\(65\) 22.5584i 0.347053i
\(66\) 31.8355 + 30.6773i 0.482356 + 0.464808i
\(67\) 103.539 1.54536 0.772679 0.634796i \(-0.218916\pi\)
0.772679 + 0.634796i \(0.218916\pi\)
\(68\) 0.556363i 0.00818181i
\(69\) −9.98330 + 10.3602i −0.144686 + 0.150148i
\(70\) 40.3285 0.576122
\(71\) 56.8221i 0.800311i −0.916447 0.400156i \(-0.868956\pi\)
0.916447 0.400156i \(-0.131044\pi\)
\(72\) −25.4384 + 0.942897i −0.353311 + 0.0130958i
\(73\) −39.9241 −0.546905 −0.273453 0.961886i \(-0.588166\pi\)
−0.273453 + 0.961886i \(0.588166\pi\)
\(74\) 24.3188i 0.328632i
\(75\) −10.8013 10.4083i −0.144017 0.138777i
\(76\) −28.8843 −0.380057
\(77\) 132.894i 1.72589i
\(78\) −29.6995 + 30.8207i −0.380763 + 0.395138i
\(79\) 81.4578 1.03111 0.515556 0.856856i \(-0.327586\pi\)
0.515556 + 0.856856i \(0.327586\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −80.7777 + 5.99644i −0.997256 + 0.0740302i
\(82\) −51.5502 −0.628662
\(83\) 37.1864i 0.448029i 0.974586 + 0.224014i \(0.0719162\pi\)
−0.974586 + 0.224014i \(0.928084\pi\)
\(84\) −55.0993 53.0949i −0.655944 0.632082i
\(85\) 0.622033 0.00731803
\(86\) 58.7650i 0.683314i
\(87\) 3.56261 3.69711i 0.0409495 0.0424955i
\(88\) −29.4739 −0.334930
\(89\) 129.429i 1.45426i −0.686498 0.727132i \(-0.740853\pi\)
0.686498 0.727132i \(-0.259147\pi\)
\(90\) 1.05419 + 28.4410i 0.0117132 + 0.316011i
\(91\) −128.658 −1.41382
\(92\) 9.59166i 0.104257i
\(93\) −79.9094 77.0024i −0.859241 0.827982i
\(94\) 103.856 1.10485
\(95\) 32.2937i 0.339933i
\(96\) 11.7757 12.2202i 0.122663 0.127294i
\(97\) 39.8372 0.410693 0.205346 0.978689i \(-0.434168\pi\)
0.205346 + 0.978689i \(0.434168\pi\)
\(98\) 160.710i 1.63989i
\(99\) −93.7209 + 3.47385i −0.946676 + 0.0350894i
\(100\) 10.0000 0.100000
\(101\) 104.192i 1.03161i 0.856707 + 0.515804i \(0.172507\pi\)
−0.856707 + 0.515804i \(0.827493\pi\)
\(102\) −0.849860 0.818942i −0.00833196 0.00802885i
\(103\) 26.0419 0.252834 0.126417 0.991977i \(-0.459652\pi\)
0.126417 + 0.991977i \(0.459652\pi\)
\(104\) 28.5344i 0.274369i
\(105\) −59.3618 + 61.6029i −0.565351 + 0.586694i
\(106\) −29.3080 −0.276491
\(107\) 28.1668i 0.263241i −0.991300 0.131621i \(-0.957982\pi\)
0.991300 0.131621i \(-0.0420181\pi\)
\(108\) 36.0039 40.2457i 0.333370 0.372646i
\(109\) 138.704 1.27251 0.636257 0.771477i \(-0.280482\pi\)
0.636257 + 0.771477i \(0.280482\pi\)
\(110\) 32.9528i 0.299571i
\(111\) 37.1476 + 35.7962i 0.334663 + 0.322488i
\(112\) 51.0120 0.455464
\(113\) 59.4090i 0.525743i −0.964831 0.262871i \(-0.915330\pi\)
0.964831 0.262871i \(-0.0846695\pi\)
\(114\) 42.5165 44.1216i 0.372952 0.387032i
\(115\) −10.7238 −0.0932505
\(116\) 3.42285i 0.0295073i
\(117\) −3.36313 90.7336i −0.0287447 0.775501i
\(118\) 105.478 0.893882
\(119\) 3.54765i 0.0298122i
\(120\) −13.6626 13.1656i −0.113855 0.109713i
\(121\) 12.4114 0.102573
\(122\) 109.355i 0.896356i
\(123\) 75.8798 78.7444i 0.616909 0.640199i
\(124\) 73.9816 0.596626
\(125\) 11.1803i 0.0894427i
\(126\) 162.208 6.01238i 1.28736 0.0477173i
\(127\) −127.559 −1.00440 −0.502201 0.864751i \(-0.667476\pi\)
−0.502201 + 0.864751i \(0.667476\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −89.7652 86.4996i −0.695854 0.670539i
\(130\) −31.9024 −0.245403
\(131\) 24.8275i 0.189523i −0.995500 0.0947616i \(-0.969791\pi\)
0.995500 0.0947616i \(-0.0302089\pi\)
\(132\) 43.3843 45.0222i 0.328669 0.341077i
\(133\) 184.181 1.38482
\(134\) 146.426i 1.09273i
\(135\) −44.9961 40.2536i −0.333304 0.298175i
\(136\) 0.786816 0.00578541
\(137\) 48.0916i 0.351033i 0.984476 + 0.175517i \(0.0561596\pi\)
−0.984476 + 0.175517i \(0.943840\pi\)
\(138\) 14.6515 + 14.1185i 0.106171 + 0.102308i
\(139\) −243.193 −1.74959 −0.874795 0.484494i \(-0.839004\pi\)
−0.874795 + 0.484494i \(0.839004\pi\)
\(140\) 57.0331i 0.407379i
\(141\) −152.871 + 158.642i −1.08419 + 1.12512i
\(142\) −80.3586 −0.565906
\(143\) 105.127i 0.735157i
\(144\) 1.33346 + 35.9753i 0.00926012 + 0.249828i
\(145\) 3.82686 0.0263921
\(146\) 56.4612i 0.386720i
\(147\) 245.488 + 236.558i 1.66999 + 1.60924i
\(148\) −34.3920 −0.232378
\(149\) 168.605i 1.13158i −0.824551 0.565788i \(-0.808572\pi\)
0.824551 0.565788i \(-0.191428\pi\)
\(150\) −14.7196 + 15.2753i −0.0981305 + 0.101835i
\(151\) −64.6419 −0.428092 −0.214046 0.976824i \(-0.568664\pi\)
−0.214046 + 0.976824i \(0.568664\pi\)
\(152\) 40.8486i 0.268741i
\(153\) 2.50191 0.0927358i 0.0163524 0.000606116i
\(154\) 187.940 1.22039
\(155\) 82.7139i 0.533638i
\(156\) 43.5871 + 42.0014i 0.279404 + 0.269240i
\(157\) 101.508 0.646547 0.323274 0.946306i \(-0.395217\pi\)
0.323274 + 0.946306i \(0.395217\pi\)
\(158\) 115.199i 0.729106i
\(159\) 43.1402 44.7689i 0.271322 0.281565i
\(160\) 12.6491 0.0790569
\(161\) 61.1612i 0.379883i
\(162\) 8.48025 + 114.237i 0.0523472 + 0.705166i
\(163\) 138.601 0.850310 0.425155 0.905120i \(-0.360220\pi\)
0.425155 + 0.905120i \(0.360220\pi\)
\(164\) 72.9031i 0.444531i
\(165\) −50.3363 48.5051i −0.305069 0.293970i
\(166\) 52.5895 0.316804
\(167\) 293.071i 1.75492i −0.479651 0.877459i \(-0.659237\pi\)
0.479651 0.877459i \(-0.340763\pi\)
\(168\) −75.0875 + 77.9222i −0.446949 + 0.463823i
\(169\) −67.2234 −0.397772
\(170\) 0.879687i 0.00517463i
\(171\) 4.81451 + 129.890i 0.0281550 + 0.759593i
\(172\) 83.1063 0.483176
\(173\) 139.905i 0.808698i −0.914605 0.404349i \(-0.867498\pi\)
0.914605 0.404349i \(-0.132502\pi\)
\(174\) −5.22850 5.03829i −0.0300488 0.0289557i
\(175\) −63.7650 −0.364371
\(176\) 41.6823i 0.236832i
\(177\) −155.259 + 161.121i −0.877171 + 0.910286i
\(178\) −183.041 −1.02832
\(179\) 77.8984i 0.435187i −0.976040 0.217593i \(-0.930179\pi\)
0.976040 0.217593i \(-0.0698206\pi\)
\(180\) 40.2216 1.49085i 0.223453 0.00828251i
\(181\) −39.3128 −0.217198 −0.108599 0.994086i \(-0.534636\pi\)
−0.108599 + 0.994086i \(0.534636\pi\)
\(182\) 181.950i 0.999723i
\(183\) 167.044 + 160.967i 0.912806 + 0.879599i
\(184\) −13.5647 −0.0737210
\(185\) 38.4514i 0.207845i
\(186\) −108.898 + 113.009i −0.585472 + 0.607575i
\(187\) 2.89881 0.0155017
\(188\) 146.874i 0.781246i
\(189\) −229.579 + 256.627i −1.21470 + 1.35781i
\(190\) 45.6702 0.240369
\(191\) 112.583i 0.589440i 0.955584 + 0.294720i \(0.0952263\pi\)
−0.955584 + 0.294720i \(0.904774\pi\)
\(192\) −17.2820 16.6533i −0.0900104 0.0867359i
\(193\) −325.616 −1.68713 −0.843564 0.537029i \(-0.819547\pi\)
−0.843564 + 0.537029i \(0.819547\pi\)
\(194\) 56.3383i 0.290404i
\(195\) 46.9590 48.7319i 0.240816 0.249907i
\(196\) −227.278 −1.15958
\(197\) 232.078i 1.17806i −0.808111 0.589031i \(-0.799510\pi\)
0.808111 0.589031i \(-0.200490\pi\)
\(198\) 4.91277 + 132.541i 0.0248120 + 0.669401i
\(199\) 144.995 0.728620 0.364310 0.931278i \(-0.381305\pi\)
0.364310 + 0.931278i \(0.381305\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) 223.670 + 215.533i 1.11279 + 1.07230i
\(202\) 147.350 0.729457
\(203\) 21.8258i 0.107516i
\(204\) −1.15816 + 1.20188i −0.00567725 + 0.00589158i
\(205\) 81.5081 0.397600
\(206\) 36.8288i 0.178780i
\(207\) −43.1329 + 1.59876i −0.208371 + 0.00772348i
\(208\) −40.3537 −0.194008
\(209\) 150.496i 0.720076i
\(210\) 87.1197 + 83.9503i 0.414856 + 0.399763i
\(211\) 152.832 0.724321 0.362160 0.932116i \(-0.382039\pi\)
0.362160 + 0.932116i \(0.382039\pi\)
\(212\) 41.4478i 0.195509i
\(213\) 118.284 122.750i 0.555326 0.576291i
\(214\) −39.8339 −0.186140
\(215\) 92.9156i 0.432166i
\(216\) −56.9161 50.9172i −0.263500 0.235728i
\(217\) −471.743 −2.17393
\(218\) 196.157i 0.899803i
\(219\) −86.2460 83.1084i −0.393817 0.379491i
\(220\) 46.6023 0.211829
\(221\) 2.80642i 0.0126987i
\(222\) 50.6235 52.5347i 0.228034 0.236643i
\(223\) 275.685 1.23625 0.618127 0.786078i \(-0.287892\pi\)
0.618127 + 0.786078i \(0.287892\pi\)
\(224\) 72.1418i 0.322062i
\(225\) −1.66682 44.9691i −0.00740810 0.199863i
\(226\) −84.0169 −0.371756
\(227\) 372.107i 1.63924i −0.572909 0.819619i \(-0.694185\pi\)
0.572909 0.819619i \(-0.305815\pi\)
\(228\) −62.3974 60.1274i −0.273673 0.263717i
\(229\) −193.596 −0.845397 −0.422699 0.906270i \(-0.638917\pi\)
−0.422699 + 0.906270i \(0.638917\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −276.640 + 287.084i −1.19757 + 1.24279i
\(232\) 4.84064 0.0208648
\(233\) 339.560i 1.45734i −0.684866 0.728669i \(-0.740139\pi\)
0.684866 0.728669i \(-0.259861\pi\)
\(234\) −128.317 + 4.75618i −0.548362 + 0.0203255i
\(235\) −164.210 −0.698767
\(236\) 149.169i 0.632070i
\(237\) 175.969 + 169.568i 0.742486 + 0.715475i
\(238\) −5.01713 −0.0210804
\(239\) 190.187i 0.795764i 0.917437 + 0.397882i \(0.130255\pi\)
−0.917437 + 0.397882i \(0.869745\pi\)
\(240\) −18.6190 + 19.3219i −0.0775790 + 0.0805078i
\(241\) −4.45865 −0.0185006 −0.00925031 0.999957i \(-0.502945\pi\)
−0.00925031 + 0.999957i \(0.502945\pi\)
\(242\) 17.5523i 0.0725302i
\(243\) −186.983 155.198i −0.769476 0.638676i
\(244\) −154.652 −0.633820
\(245\) 254.104i 1.03716i
\(246\) −111.361 107.310i −0.452689 0.436220i
\(247\) −145.699 −0.589874
\(248\) 104.626i 0.421878i
\(249\) −77.4095 + 80.3319i −0.310881 + 0.322618i
\(250\) −15.8114 −0.0632456
\(251\) 32.2001i 0.128287i 0.997941 + 0.0641437i \(0.0204316\pi\)
−0.997941 + 0.0641437i \(0.979568\pi\)
\(252\) −8.50279 229.396i −0.0337412 0.910303i
\(253\) −49.9754 −0.197531
\(254\) 180.396i 0.710220i
\(255\) 1.34375 + 1.29486i 0.00526959 + 0.00507789i
\(256\) 16.0000 0.0625000
\(257\) 454.545i 1.76866i −0.466863 0.884329i \(-0.654616\pi\)
0.466863 0.884329i \(-0.345384\pi\)
\(258\) −122.329 + 126.947i −0.474143 + 0.492043i
\(259\) 219.300 0.846719
\(260\) 45.1169i 0.173526i
\(261\) 15.3923 0.570528i 0.0589741 0.00218593i
\(262\) −35.1114 −0.134013
\(263\) 328.977i 1.25086i 0.780279 + 0.625432i \(0.215077\pi\)
−0.780279 + 0.625432i \(0.784923\pi\)
\(264\) −63.6709 61.3546i −0.241178 0.232404i
\(265\) 46.3401 0.174868
\(266\) 260.471i 0.979215i
\(267\) 269.428 279.600i 1.00910 1.04719i
\(268\) −207.078 −0.772679
\(269\) 35.5555i 0.132177i −0.997814 0.0660883i \(-0.978948\pi\)
0.997814 0.0660883i \(-0.0210519\pi\)
\(270\) −56.9272 + 63.6341i −0.210841 + 0.235682i
\(271\) −253.129 −0.934054 −0.467027 0.884243i \(-0.654675\pi\)
−0.467027 + 0.884243i \(0.654675\pi\)
\(272\) 1.11273i 0.00409090i
\(273\) −277.933 267.822i −1.01807 0.981033i
\(274\) 68.0118 0.248218
\(275\) 52.1029i 0.189465i
\(276\) 19.9666 20.7204i 0.0723428 0.0750739i
\(277\) −330.147 −1.19187 −0.595933 0.803034i \(-0.703218\pi\)
−0.595933 + 0.803034i \(0.703218\pi\)
\(278\) 343.927i 1.23715i
\(279\) −12.3314 332.689i −0.0441986 1.19243i
\(280\) −80.6570 −0.288061
\(281\) 151.413i 0.538838i 0.963023 + 0.269419i \(0.0868316\pi\)
−0.963023 + 0.269419i \(0.913168\pi\)
\(282\) 224.354 + 216.193i 0.795583 + 0.766640i
\(283\) −214.644 −0.758458 −0.379229 0.925303i \(-0.623811\pi\)
−0.379229 + 0.925303i \(0.623811\pi\)
\(284\) 113.644i 0.400156i
\(285\) −67.2245 + 69.7624i −0.235876 + 0.244780i
\(286\) −148.673 −0.519834
\(287\) 464.866i 1.61974i
\(288\) 50.8768 1.88579i 0.176655 0.00654790i
\(289\) 288.923 0.999732
\(290\) 5.41200i 0.0186621i
\(291\) 86.0583 + 82.9276i 0.295733 + 0.284975i
\(292\) 79.8481 0.273453
\(293\) 220.365i 0.752099i −0.926600 0.376050i \(-0.877282\pi\)
0.926600 0.376050i \(-0.122718\pi\)
\(294\) 334.543 347.173i 1.13790 1.18086i
\(295\) −166.775 −0.565341
\(296\) 48.6376i 0.164316i
\(297\) −209.692 187.591i −0.706034 0.631619i
\(298\) −238.443 −0.800145
\(299\) 48.3824i 0.161814i
\(300\) 21.6025 + 20.8166i 0.0720084 + 0.0693887i
\(301\) −529.927 −1.76055
\(302\) 91.4174i 0.302707i
\(303\) −216.893 + 225.082i −0.715820 + 0.742844i
\(304\) 57.7687 0.190029
\(305\) 172.906i 0.566906i
\(306\) −0.131148 3.53824i −0.000428589 0.0115629i
\(307\) 559.586 1.82276 0.911378 0.411571i \(-0.135020\pi\)
0.911378 + 0.411571i \(0.135020\pi\)
\(308\) 265.787i 0.862946i
\(309\) 56.2569 + 54.2104i 0.182061 + 0.175438i
\(310\) −116.975 −0.377339
\(311\) 326.410i 1.04955i 0.851241 + 0.524775i \(0.175851\pi\)
−0.851241 + 0.524775i \(0.824149\pi\)
\(312\) 59.3990 61.6415i 0.190381 0.197569i
\(313\) −450.011 −1.43773 −0.718867 0.695148i \(-0.755339\pi\)
−0.718867 + 0.695148i \(0.755339\pi\)
\(314\) 143.554i 0.457178i
\(315\) −256.473 + 9.50641i −0.814200 + 0.0301791i
\(316\) −162.916 −0.515556
\(317\) 153.743i 0.484994i −0.970152 0.242497i \(-0.922033\pi\)
0.970152 0.242497i \(-0.0779665\pi\)
\(318\) −63.3127 61.0095i −0.199097 0.191854i
\(319\) 17.8340 0.0559061
\(320\) 17.8885i 0.0559017i
\(321\) 58.6338 60.8474i 0.182660 0.189556i
\(322\) 86.4950 0.268618
\(323\) 4.01754i 0.0124382i
\(324\) 161.555 11.9929i 0.498628 0.0370151i
\(325\) 50.4422 0.155207
\(326\) 196.011i 0.601260i
\(327\) 299.635 + 288.735i 0.916316 + 0.882982i
\(328\) 103.100 0.314331
\(329\) 936.543i 2.84663i
\(330\) −68.5966 + 71.1863i −0.207868 + 0.215716i
\(331\) 498.766 1.50685 0.753423 0.657536i \(-0.228401\pi\)
0.753423 + 0.657536i \(0.228401\pi\)
\(332\) 74.3727i 0.224014i
\(333\) 5.73253 + 154.658i 0.0172148 + 0.464437i
\(334\) −414.466 −1.24092
\(335\) 231.520i 0.691105i
\(336\) 110.199 + 106.190i 0.327972 + 0.316041i
\(337\) −238.449 −0.707564 −0.353782 0.935328i \(-0.615104\pi\)
−0.353782 + 0.935328i \(0.615104\pi\)
\(338\) 95.0683i 0.281267i
\(339\) 123.669 128.338i 0.364806 0.378579i
\(340\) −1.24407 −0.00365902
\(341\) 385.466i 1.13040i
\(342\) 183.693 6.80874i 0.537113 0.0199086i
\(343\) 824.339 2.40332
\(344\) 117.530i 0.341657i
\(345\) −23.1661 22.3233i −0.0671481 0.0647053i
\(346\) −197.855 −0.571836
\(347\) 225.681i 0.650377i −0.945649 0.325189i \(-0.894572\pi\)
0.945649 0.325189i \(-0.105428\pi\)
\(348\) −7.12522 + 7.39421i −0.0204748 + 0.0212477i
\(349\) 100.694 0.288521 0.144261 0.989540i \(-0.453920\pi\)
0.144261 + 0.989540i \(0.453920\pi\)
\(350\) 90.1773i 0.257649i
\(351\) 181.612 203.008i 0.517412 0.578371i
\(352\) 58.9477 0.167465
\(353\) 443.896i 1.25749i 0.777610 + 0.628747i \(0.216432\pi\)
−0.777610 + 0.628747i \(0.783568\pi\)
\(354\) 227.859 + 219.570i 0.643670 + 0.620253i
\(355\) 127.058 0.357910
\(356\) 258.859i 0.727132i
\(357\) 7.38500 7.66380i 0.0206863 0.0214672i
\(358\) −110.165 −0.307723
\(359\) 39.2939i 0.109454i 0.998501 + 0.0547269i \(0.0174288\pi\)
−0.998501 + 0.0547269i \(0.982571\pi\)
\(360\) −2.10838 56.8819i −0.00585662 0.158005i
\(361\) −152.424 −0.422226
\(362\) 55.5968i 0.153582i
\(363\) 26.8116 + 25.8363i 0.0738613 + 0.0711743i
\(364\) 257.316 0.706911
\(365\) 89.2729i 0.244583i
\(366\) 227.641 236.235i 0.621970 0.645451i
\(367\) 9.93672 0.0270755 0.0135378 0.999908i \(-0.495691\pi\)
0.0135378 + 0.999908i \(0.495691\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 327.839 12.1516i 0.888452 0.0329313i
\(370\) 54.3784 0.146969
\(371\) 264.292i 0.712377i
\(372\) 159.819 + 154.005i 0.429620 + 0.413991i
\(373\) 680.417 1.82417 0.912087 0.409997i \(-0.134470\pi\)
0.912087 + 0.409997i \(0.134470\pi\)
\(374\) 4.09954i 0.0109613i
\(375\) 23.2737 24.1523i 0.0620632 0.0644062i
\(376\) −207.711 −0.552424
\(377\) 17.2656i 0.0457973i
\(378\) 362.925 + 324.673i 0.960119 + 0.858924i
\(379\) −602.442 −1.58956 −0.794778 0.606900i \(-0.792413\pi\)
−0.794778 + 0.606900i \(0.792413\pi\)
\(380\) 64.5874i 0.169967i
\(381\) −275.560 265.535i −0.723254 0.696942i
\(382\) 159.216 0.416797
\(383\) 92.5380i 0.241613i 0.992676 + 0.120807i \(0.0385481\pi\)
−0.992676 + 0.120807i \(0.961452\pi\)
\(384\) −23.5513 + 24.4404i −0.0613316 + 0.0636470i
\(385\) −297.159 −0.771842
\(386\) 460.490i 1.19298i
\(387\) −13.8523 373.722i −0.0357942 0.965689i
\(388\) −79.6744 −0.205346
\(389\) 512.539i 1.31758i 0.752326 + 0.658791i \(0.228932\pi\)
−0.752326 + 0.658791i \(0.771068\pi\)
\(390\) −68.9173 66.4101i −0.176711 0.170282i
\(391\) 1.33411 0.00341205
\(392\) 321.419i 0.819947i
\(393\) 51.6825 53.6337i 0.131508 0.136473i
\(394\) −328.208 −0.833015
\(395\) 182.145i 0.461127i
\(396\) 187.442 6.94771i 0.473338 0.0175447i
\(397\) 734.655 1.85052 0.925258 0.379337i \(-0.123848\pi\)
0.925258 + 0.379337i \(0.123848\pi\)
\(398\) 205.054i 0.515212i
\(399\) 397.877 + 383.402i 0.997185 + 0.960908i
\(400\) −20.0000 −0.0500000
\(401\) 264.580i 0.659799i 0.944016 + 0.329900i \(0.107015\pi\)
−0.944016 + 0.329900i \(0.892985\pi\)
\(402\) 304.810 316.318i 0.758234 0.786859i
\(403\) 373.179 0.926003
\(404\) 208.385i 0.515804i
\(405\) −13.4085 180.625i −0.0331073 0.445986i
\(406\) −30.8663 −0.0760254
\(407\) 179.192i 0.440276i
\(408\) 1.69972 + 1.63788i 0.00416598 + 0.00401442i
\(409\) −13.6447 −0.0333612 −0.0166806 0.999861i \(-0.505310\pi\)
−0.0166806 + 0.999861i \(0.505310\pi\)
\(410\) 115.270i 0.281146i
\(411\) −100.110 + 103.890i −0.243578 + 0.252773i
\(412\) −52.0837 −0.126417
\(413\) 951.173i 2.30308i
\(414\) 2.26099 + 60.9991i 0.00546132 + 0.147341i
\(415\) −83.1513 −0.200364
\(416\) 57.0688i 0.137185i
\(417\) −525.358 506.246i −1.25985 1.21402i
\(418\) 212.833 0.509171
\(419\) 664.827i 1.58670i −0.608766 0.793350i \(-0.708335\pi\)
0.608766 0.793350i \(-0.291665\pi\)
\(420\) 118.724 123.206i 0.282675 0.293347i
\(421\) −55.6544 −0.132196 −0.0660978 0.997813i \(-0.521055\pi\)
−0.0660978 + 0.997813i \(0.521055\pi\)
\(422\) 216.137i 0.512172i
\(423\) −660.480 + 24.4813i −1.56142 + 0.0578754i
\(424\) 58.6161 0.138246
\(425\) 1.39091i 0.00327272i
\(426\) −173.595 167.279i −0.407499 0.392675i
\(427\) 986.138 2.30946
\(428\) 56.3336i 0.131621i
\(429\) 218.840 227.102i 0.510116 0.529374i
\(430\) −131.403 −0.305587
\(431\) 771.728i 1.79055i −0.445513 0.895276i \(-0.646979\pi\)
0.445513 0.895276i \(-0.353021\pi\)
\(432\) −72.0078 + 80.4915i −0.166685 + 0.186323i
\(433\) 853.202 1.97044 0.985222 0.171281i \(-0.0547905\pi\)
0.985222 + 0.171281i \(0.0547905\pi\)
\(434\) 667.146i 1.53720i
\(435\) 8.26698 + 7.96623i 0.0190046 + 0.0183132i
\(436\) −277.408 −0.636257
\(437\) 69.2622i 0.158495i
\(438\) −117.533 + 121.970i −0.268340 + 0.278471i
\(439\) −593.263 −1.35140 −0.675698 0.737179i \(-0.736158\pi\)
−0.675698 + 0.737179i \(0.736158\pi\)
\(440\) 65.9056i 0.149785i
\(441\) 37.8832 + 1022.05i 0.0859028 + 2.31757i
\(442\) 3.96887 0.00897935
\(443\) 467.644i 1.05563i 0.849359 + 0.527815i \(0.176989\pi\)
−0.849359 + 0.527815i \(0.823011\pi\)
\(444\) −74.2952 71.5924i −0.167332 0.161244i
\(445\) 289.413 0.650367
\(446\) 389.877i 0.874164i
\(447\) 350.978 364.228i 0.785186 0.814829i
\(448\) −102.024 −0.227732
\(449\) 863.590i 1.92336i −0.274168 0.961682i \(-0.588403\pi\)
0.274168 0.961682i \(-0.411597\pi\)
\(450\) −63.5959 + 2.35724i −0.141324 + 0.00523832i
\(451\) 379.846 0.842231
\(452\) 118.818i 0.262871i
\(453\) −139.643 134.563i −0.308262 0.297048i
\(454\) −526.239 −1.15912
\(455\) 287.688i 0.632280i
\(456\) −85.0330 + 88.2433i −0.186476 + 0.193516i
\(457\) −352.546 −0.771435 −0.385717 0.922617i \(-0.626046\pi\)
−0.385717 + 0.922617i \(0.626046\pi\)
\(458\) 273.786i 0.597786i
\(459\) 5.59781 + 5.00781i 0.0121957 + 0.0109103i
\(460\) 21.4476 0.0466252
\(461\) 595.807i 1.29242i 0.763158 + 0.646212i \(0.223648\pi\)
−0.763158 + 0.646212i \(0.776352\pi\)
\(462\) 405.998 + 391.228i 0.878783 + 0.846813i
\(463\) 671.390 1.45009 0.725043 0.688704i \(-0.241820\pi\)
0.725043 + 0.688704i \(0.241820\pi\)
\(464\) 6.84570i 0.0147537i
\(465\) 172.182 178.683i 0.370285 0.384264i
\(466\) −480.210 −1.03049
\(467\) 797.745i 1.70823i −0.520082 0.854116i \(-0.674099\pi\)
0.520082 0.854116i \(-0.325901\pi\)
\(468\) 6.72625 + 181.467i 0.0143723 + 0.387751i
\(469\) 1320.43 2.81542
\(470\) 232.228i 0.494103i
\(471\) 219.282 + 211.305i 0.465568 + 0.448631i
\(472\) −210.956 −0.446941
\(473\) 433.008i 0.915450i
\(474\) 239.805 248.858i 0.505917 0.525017i
\(475\) −72.2109 −0.152023
\(476\) 7.09529i 0.0149061i
\(477\) 186.387 6.90862i 0.390749 0.0144835i
\(478\) 268.966 0.562690
\(479\) 706.387i 1.47471i −0.675505 0.737356i \(-0.736074\pi\)
0.675505 0.737356i \(-0.263926\pi\)
\(480\) 27.3252 + 26.3312i 0.0569276 + 0.0548566i
\(481\) −173.481 −0.360666
\(482\) 6.30548i 0.0130819i
\(483\) −127.317 + 132.124i −0.263596 + 0.273548i
\(484\) −24.8227 −0.0512866
\(485\) 89.0787i 0.183667i
\(486\) −219.483 + 264.433i −0.451612 + 0.544102i
\(487\) 747.631 1.53518 0.767589 0.640943i \(-0.221456\pi\)
0.767589 + 0.640943i \(0.221456\pi\)
\(488\) 218.711i 0.448178i
\(489\) 299.412 + 288.520i 0.612294 + 0.590020i
\(490\) 359.358 0.733383
\(491\) 526.765i 1.07284i 0.843951 + 0.536420i \(0.180224\pi\)
−0.843951 + 0.536420i \(0.819776\pi\)
\(492\) −151.760 + 157.489i −0.308454 + 0.320099i
\(493\) −0.476087 −0.000965693
\(494\) 206.049i 0.417104i
\(495\) −7.76777 209.566i −0.0156925 0.423366i
\(496\) −147.963 −0.298313
\(497\) 724.652i 1.45805i
\(498\) 113.606 + 109.474i 0.228125 + 0.219826i
\(499\) 836.489 1.67633 0.838165 0.545417i \(-0.183629\pi\)
0.838165 + 0.545417i \(0.183629\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 610.076 633.108i 1.21772 1.26369i
\(502\) 45.5378 0.0907128
\(503\) 378.646i 0.752775i −0.926462 0.376387i \(-0.877166\pi\)
0.926462 0.376387i \(-0.122834\pi\)
\(504\) −324.415 + 12.0248i −0.643681 + 0.0238587i
\(505\) −232.981 −0.461349
\(506\) 70.6759i 0.139676i
\(507\) −145.219 139.937i −0.286429 0.276009i
\(508\) 255.118 0.502201
\(509\) 449.590i 0.883280i 0.897192 + 0.441640i \(0.145603\pi\)
−0.897192 + 0.441640i \(0.854397\pi\)
\(510\) 1.83121 1.90034i 0.00359061 0.00372616i
\(511\) −509.151 −0.996382
\(512\) 22.6274i 0.0441942i
\(513\) −259.987 + 290.618i −0.506798 + 0.566507i
\(514\) −642.824 −1.25063
\(515\) 58.2314i 0.113071i
\(516\) 179.530 + 172.999i 0.347927 + 0.335270i
\(517\) −765.258 −1.48019
\(518\) 310.137i 0.598721i
\(519\) 291.234 302.229i 0.561145 0.582330i
\(520\) 63.8049 0.122702
\(521\) 644.286i 1.23663i 0.785929 + 0.618317i \(0.212185\pi\)
−0.785929 + 0.618317i \(0.787815\pi\)
\(522\) −0.806849 21.7679i −0.00154569 0.0417010i
\(523\) 312.889 0.598257 0.299129 0.954213i \(-0.403304\pi\)
0.299129 + 0.954213i \(0.403304\pi\)
\(524\) 49.6551i 0.0947616i
\(525\) −137.748 132.737i −0.262378 0.252833i
\(526\) 465.244 0.884494
\(527\) 10.2902i 0.0195259i
\(528\) −86.7686 + 90.0443i −0.164334 + 0.170538i
\(529\) −23.0000 −0.0434783
\(530\) 65.5348i 0.123651i
\(531\) −670.798 + 24.8637i −1.26327 + 0.0468244i
\(532\) −368.362 −0.692409
\(533\) 367.739i 0.689942i
\(534\) −395.414 381.029i −0.740476 0.713538i
\(535\) 62.9829 0.117725
\(536\) 292.853i 0.546367i
\(537\) 162.158 168.280i 0.301971 0.313371i
\(538\) −50.2831 −0.0934629
\(539\) 1184.18i 2.19700i
\(540\) 89.9922 + 80.5072i 0.166652 + 0.149087i
\(541\) −25.0281 −0.0462627 −0.0231314 0.999732i \(-0.507364\pi\)
−0.0231314 + 0.999732i \(0.507364\pi\)
\(542\) 357.978i 0.660476i
\(543\) −84.9256 81.8361i −0.156401 0.150711i
\(544\) −1.57363 −0.00289271
\(545\) 310.152i 0.569086i
\(546\) −378.758 + 393.057i −0.693695 + 0.719884i
\(547\) −285.873 −0.522619 −0.261310 0.965255i \(-0.584154\pi\)
−0.261310 + 0.965255i \(0.584154\pi\)
\(548\) 96.1832i 0.175517i
\(549\) 25.7777 + 695.456i 0.0469540 + 1.26677i
\(550\) −73.6847 −0.133972
\(551\) 24.7167i 0.0448579i
\(552\) −29.3031 28.2370i −0.0530853 0.0511541i
\(553\) 1038.83 1.87854
\(554\) 466.898i 0.842776i
\(555\) −80.0428 + 83.0646i −0.144221 + 0.149666i
\(556\) 486.386 0.874795
\(557\) 768.565i 1.37983i 0.723890 + 0.689915i \(0.242352\pi\)
−0.723890 + 0.689915i \(0.757648\pi\)
\(558\) −470.493 + 17.4393i −0.843177 + 0.0312531i
\(559\) 419.206 0.749922
\(560\) 114.066i 0.203690i
\(561\) 6.26216 + 6.03435i 0.0111625 + 0.0107564i
\(562\) 214.131 0.381016
\(563\) 472.921i 0.840002i 0.907524 + 0.420001i \(0.137970\pi\)
−0.907524 + 0.420001i \(0.862030\pi\)
\(564\) 305.742 317.285i 0.542096 0.562562i
\(565\) 132.842 0.235119
\(566\) 303.552i 0.536311i
\(567\) −1030.16 + 76.4726i −1.81686 + 0.134872i
\(568\) 160.717 0.282953
\(569\) 44.6673i 0.0785013i −0.999229 0.0392507i \(-0.987503\pi\)
0.999229 0.0392507i \(-0.0124971\pi\)
\(570\) 98.6590 + 95.0698i 0.173086 + 0.166789i
\(571\) −502.895 −0.880726 −0.440363 0.897820i \(-0.645150\pi\)
−0.440363 + 0.897820i \(0.645150\pi\)
\(572\) 210.255i 0.367578i
\(573\) −234.360 + 243.207i −0.409005 + 0.424446i
\(574\) −657.420 −1.14533
\(575\) 23.9792i 0.0417029i
\(576\) −2.66692 71.9506i −0.00463006 0.124914i
\(577\) −94.3235 −0.163472 −0.0817361 0.996654i \(-0.526046\pi\)
−0.0817361 + 0.996654i \(0.526046\pi\)
\(578\) 408.598i 0.706917i
\(579\) −703.411 677.822i −1.21487 1.17068i
\(580\) −7.65372 −0.0131961
\(581\) 474.238i 0.816244i
\(582\) 117.277 121.705i 0.201507 0.209115i
\(583\) 215.955 0.370421
\(584\) 112.922i 0.193360i
\(585\) 202.887 7.52018i 0.346815 0.0128550i
\(586\) −311.643 −0.531814
\(587\) 883.355i 1.50486i −0.658670 0.752432i \(-0.728881\pi\)
0.658670 0.752432i \(-0.271119\pi\)
\(588\) −490.977 473.115i −0.834994 0.804618i
\(589\) −534.227 −0.907008
\(590\) 235.856i 0.399756i
\(591\) 483.108 501.347i 0.817442 0.848303i
\(592\) 68.7839 0.116189
\(593\) 951.840i 1.60513i −0.596567 0.802563i \(-0.703469\pi\)
0.596567 0.802563i \(-0.296531\pi\)
\(594\) −265.294 + 296.549i −0.446622 + 0.499241i
\(595\) 7.93278 0.0133324
\(596\) 337.209i 0.565788i
\(597\) 313.226 + 301.831i 0.524667 + 0.505580i
\(598\) −68.4231 −0.114420
\(599\) 118.761i 0.198265i −0.995074 0.0991326i \(-0.968393\pi\)
0.995074 0.0991326i \(-0.0316068\pi\)
\(600\) 29.4392 30.5506i 0.0490653 0.0509176i
\(601\) 40.5976 0.0675500 0.0337750 0.999429i \(-0.489247\pi\)
0.0337750 + 0.999429i \(0.489247\pi\)
\(602\) 749.430i 1.24490i
\(603\) 34.5162 + 931.212i 0.0572409 + 1.54430i
\(604\) 129.284 0.214046
\(605\) 27.7526i 0.0458721i
\(606\) 318.314 + 306.734i 0.525270 + 0.506161i
\(607\) −1154.28 −1.90162 −0.950809 0.309777i \(-0.899746\pi\)
−0.950809 + 0.309777i \(0.899746\pi\)
\(608\) 81.6973i 0.134370i
\(609\) 45.4339 47.1492i 0.0746041 0.0774206i
\(610\) 244.526 0.400863
\(611\) 740.865i 1.21255i
\(612\) −5.00383 + 0.185472i −0.00817619 + 0.000303058i
\(613\) −673.217 −1.09823 −0.549117 0.835746i \(-0.685036\pi\)
−0.549117 + 0.835746i \(0.685036\pi\)
\(614\) 791.374i 1.28888i
\(615\) 176.078 + 169.672i 0.286306 + 0.275890i
\(616\) −375.880 −0.610195
\(617\) 376.318i 0.609916i 0.952366 + 0.304958i \(0.0986424\pi\)
−0.952366 + 0.304958i \(0.901358\pi\)
\(618\) 76.6650 79.5593i 0.124053 0.128737i
\(619\) 276.885 0.447310 0.223655 0.974668i \(-0.428201\pi\)
0.223655 + 0.974668i \(0.428201\pi\)
\(620\) 165.428i 0.266819i
\(621\) −96.5059 86.3343i −0.155404 0.139025i
\(622\) 461.613 0.742144
\(623\) 1650.61i 2.64946i
\(624\) −87.1742 84.0029i −0.139702 0.134620i
\(625\) 25.0000 0.0400000
\(626\) 636.411i 1.01663i
\(627\) −313.282 + 325.109i −0.499652 + 0.518515i
\(628\) −203.016 −0.323274
\(629\) 4.78360i 0.00760509i
\(630\) 13.4441 + 362.707i 0.0213398 + 0.575726i
\(631\) −760.606 −1.20540 −0.602699 0.797969i \(-0.705908\pi\)
−0.602699 + 0.797969i \(0.705908\pi\)
\(632\) 230.397i 0.364553i
\(633\) 330.155 + 318.144i 0.521572 + 0.502597i
\(634\) −217.426 −0.342943
\(635\) 285.231i 0.449183i
\(636\) −86.2804 + 89.5377i −0.135661 + 0.140783i
\(637\) −1146.44 −1.79975
\(638\) 25.2212i 0.0395316i
\(639\) 511.048 18.9425i 0.799762 0.0296439i
\(640\) −25.2982 −0.0395285
\(641\) 292.499i 0.456316i −0.973624 0.228158i \(-0.926730\pi\)
0.973624 0.228158i \(-0.0732703\pi\)
\(642\) −86.0512 82.9207i −0.134036 0.129160i
\(643\) 487.514 0.758187 0.379094 0.925358i \(-0.376236\pi\)
0.379094 + 0.925358i \(0.376236\pi\)
\(644\) 122.322i 0.189942i
\(645\) 193.419 200.721i 0.299874 0.311195i
\(646\) −5.68166 −0.00879515
\(647\) 764.731i 1.18196i 0.806685 + 0.590982i \(0.201260\pi\)
−0.806685 + 0.590982i \(0.798740\pi\)
\(648\) −16.9605 228.474i −0.0261736 0.352583i
\(649\) −777.212 −1.19755
\(650\) 71.3360i 0.109748i
\(651\) −1019.08 982.010i −1.56541 1.50846i
\(652\) −277.201 −0.425155
\(653\) 398.531i 0.610308i −0.952303 0.305154i \(-0.901292\pi\)
0.952303 0.305154i \(-0.0987079\pi\)
\(654\) 408.333 423.749i 0.624362 0.647934i
\(655\) 55.5161 0.0847573
\(656\) 145.806i 0.222265i
\(657\) −13.3093 359.070i −0.0202576 0.546530i
\(658\) 1324.47 2.01287
\(659\) 828.825i 1.25770i 0.777526 + 0.628850i \(0.216474\pi\)
−0.777526 + 0.628850i \(0.783526\pi\)
\(660\) 100.673 + 97.0102i 0.152534 + 0.146985i
\(661\) −1248.13 −1.88825 −0.944124 0.329591i \(-0.893089\pi\)
−0.944124 + 0.329591i \(0.893089\pi\)
\(662\) 705.362i 1.06550i
\(663\) −5.84201 + 6.06256i −0.00881148 + 0.00914413i
\(664\) −105.179 −0.158402
\(665\) 411.841i 0.619310i
\(666\) 218.719 8.10702i 0.328407 0.0121727i
\(667\) 8.20770 0.0123054
\(668\) 586.143i 0.877459i
\(669\) 595.548 + 573.883i 0.890206 + 0.857821i
\(670\) 327.419 0.488685
\(671\) 805.782i 1.20087i
\(672\) 150.175 155.844i 0.223475 0.231911i
\(673\) −1228.15 −1.82489 −0.912447 0.409195i \(-0.865810\pi\)
−0.912447 + 0.409195i \(0.865810\pi\)
\(674\) 337.218i 0.500323i
\(675\) 90.0098 100.614i 0.133348 0.149058i
\(676\) 134.447 0.198886
\(677\) 197.067i 0.291089i −0.989352 0.145544i \(-0.953507\pi\)
0.989352 0.145544i \(-0.0464934\pi\)
\(678\) −181.498 174.895i −0.267696 0.257957i
\(679\) 508.044 0.748223
\(680\) 1.75937i 0.00258731i
\(681\) 774.601 803.844i 1.13745 1.18039i
\(682\) −545.131 −0.799312
\(683\) 650.986i 0.953127i 0.879140 + 0.476564i \(0.158118\pi\)
−0.879140 + 0.476564i \(0.841882\pi\)
\(684\) −9.62901 259.781i −0.0140775 0.379796i
\(685\) −107.536 −0.156987
\(686\) 1165.79i 1.69940i
\(687\) −418.216 403.001i −0.608757 0.586610i
\(688\) −166.213 −0.241588
\(689\) 209.072i 0.303443i
\(690\) −31.5700 + 32.7618i −0.0457536 + 0.0474809i
\(691\) 485.418 0.702486 0.351243 0.936284i \(-0.385759\pi\)
0.351243 + 0.936284i \(0.385759\pi\)
\(692\) 279.809i 0.404349i
\(693\) −1195.22 + 44.3020i −1.72471 + 0.0639279i
\(694\) −319.161 −0.459886
\(695\) 543.796i 0.782440i
\(696\) 10.4570 + 10.0766i 0.0150244 + 0.0144778i
\(697\) −10.1401 −0.0145483
\(698\) 142.403i 0.204015i
\(699\) 706.848 733.534i 1.01123 1.04940i
\(700\) 127.530 0.182186
\(701\) 1073.24i 1.53101i −0.643431 0.765504i \(-0.722490\pi\)
0.643431 0.765504i \(-0.277510\pi\)
\(702\) −287.097 256.838i −0.408970 0.365865i
\(703\) 248.347 0.353268
\(704\) 83.3647i 0.118416i
\(705\) −354.735 341.830i −0.503171 0.484866i
\(706\) 627.763 0.889183
\(707\) 1328.77i 1.87944i
\(708\) 310.518 322.241i 0.438585 0.455143i
\(709\) −83.9792 −0.118447 −0.0592237 0.998245i \(-0.518863\pi\)
−0.0592237 + 0.998245i \(0.518863\pi\)
\(710\) 179.687i 0.253081i
\(711\) 27.1551 + 732.617i 0.0381929 + 1.03040i
\(712\) 366.082 0.514160
\(713\) 177.402i 0.248810i
\(714\) −10.8383 10.4440i −0.0151796 0.0146274i
\(715\) 235.072 0.328772
\(716\) 155.797i 0.217593i
\(717\) −395.906 + 410.853i −0.552170 + 0.573016i
\(718\) 55.5700 0.0773955
\(719\) 638.283i 0.887737i 0.896092 + 0.443868i \(0.146394\pi\)
−0.896092 + 0.443868i \(0.853606\pi\)
\(720\) −80.4432 + 2.98170i −0.111727 + 0.00414125i
\(721\) 332.112 0.460626
\(722\) 215.560i 0.298559i
\(723\) −9.63180 9.28140i −0.0133220 0.0128374i
\(724\) 78.6257 0.108599
\(725\) 8.55712i 0.0118029i
\(726\) 36.5380 37.9174i 0.0503278 0.0522278i
\(727\) 344.419 0.473754 0.236877 0.971540i \(-0.423876\pi\)
0.236877 + 0.971540i \(0.423876\pi\)
\(728\) 363.899i 0.499861i
\(729\) −80.8594 724.502i −0.110918 0.993830i
\(730\) −126.251 −0.172947
\(731\) 11.5593i 0.0158130i
\(732\) −334.087 321.933i −0.456403 0.439799i
\(733\) −511.714 −0.698109 −0.349054 0.937103i \(-0.613497\pi\)
−0.349054 + 0.937103i \(0.613497\pi\)
\(734\) 14.0526i 0.0191453i
\(735\) −528.959 + 548.929i −0.719672 + 0.746842i
\(736\) 27.1293 0.0368605
\(737\) 1078.94i 1.46396i
\(738\) −17.1850 463.634i −0.0232859 0.628230i
\(739\) 256.144 0.346608 0.173304 0.984868i \(-0.444556\pi\)
0.173304 + 0.984868i \(0.444556\pi\)
\(740\) 76.9027i 0.103923i
\(741\) −314.746 303.296i −0.424759 0.409306i
\(742\) −373.765 −0.503727
\(743\) 74.9836i 0.100920i 0.998726 + 0.0504600i \(0.0160687\pi\)
−0.998726 + 0.0504600i \(0.983931\pi\)
\(744\) 217.796 226.018i 0.292736 0.303787i
\(745\) 377.012 0.506056
\(746\) 962.255i 1.28989i
\(747\) −334.448 + 12.3966i −0.447721 + 0.0165952i
\(748\) −5.79763 −0.00775084
\(749\) 359.211i 0.479588i
\(750\) −34.1566 32.9140i −0.0455421 0.0438853i
\(751\) −920.046 −1.22509 −0.612547 0.790434i \(-0.709855\pi\)
−0.612547 + 0.790434i \(0.709855\pi\)
\(752\) 293.748i 0.390623i
\(753\) −67.0298 + 69.5603i −0.0890170 + 0.0923776i
\(754\) 24.4172 0.0323836
\(755\) 144.544i 0.191449i
\(756\) 459.158 513.254i 0.607351 0.678907i
\(757\) 1040.64 1.37469 0.687344 0.726332i \(-0.258777\pi\)
0.687344 + 0.726332i \(0.258777\pi\)
\(758\) 851.982i 1.12399i
\(759\) −107.959 104.032i −0.142239 0.137064i
\(760\) −91.3403 −0.120185
\(761\) 1047.60i 1.37662i 0.725419 + 0.688308i \(0.241646\pi\)
−0.725419 + 0.688308i \(0.758354\pi\)
\(762\) −375.523 + 389.700i −0.492813 + 0.511418i
\(763\) 1768.89 2.31834
\(764\) 225.166i 0.294720i
\(765\) 0.207364 + 5.59445i 0.000271063 + 0.00731301i
\(766\) 130.868 0.170847
\(767\) 752.439i 0.981015i
\(768\) 34.5640 + 33.3066i 0.0450052 + 0.0433680i
\(769\) 650.393 0.845764 0.422882 0.906185i \(-0.361018\pi\)
0.422882 + 0.906185i \(0.361018\pi\)
\(770\) 420.247i 0.545775i
\(771\) 946.210 981.932i 1.22725 1.27358i
\(772\) 651.231 0.843564
\(773\) 1302.06i 1.68442i 0.539149 + 0.842210i \(0.318746\pi\)
−0.539149 + 0.842210i \(0.681254\pi\)
\(774\) −528.522 + 19.5902i −0.682845 + 0.0253103i
\(775\) 184.954 0.238650
\(776\) 112.677i 0.145202i
\(777\) 473.743 + 456.509i 0.609708 + 0.587528i
\(778\) 724.840 0.931671
\(779\) 526.439i 0.675788i
\(780\) −93.9181 + 97.4637i −0.120408 + 0.124953i
\(781\) 592.120 0.758156
\(782\) 1.88672i 0.00241268i
\(783\) 34.4388 + 30.8090i 0.0439831 + 0.0393474i
\(784\) 454.555 0.579790
\(785\) 226.979i 0.289145i
\(786\) −75.8495 73.0902i