Properties

Label 20.3.b.a.11.2
Level 20
Weight 3
Character 20.11
Analytic conductor 0.545
Analytic rank 0
Dimension 4
CM No
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 20.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.544960528721\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.2
Root \(-0.309017 + 0.951057i\)
Character \(\chi\) = 20.11
Dual form 20.3.b.a.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61803 + 1.17557i) q^{2} +3.80423i q^{3} +(1.23607 - 3.80423i) q^{4} +2.23607 q^{5} +(-4.47214 - 6.15537i) q^{6} -8.50651i q^{7} +(2.47214 + 7.60845i) q^{8} -5.47214 q^{9} +O(q^{10})\) \(q+(-1.61803 + 1.17557i) q^{2} +3.80423i q^{3} +(1.23607 - 3.80423i) q^{4} +2.23607 q^{5} +(-4.47214 - 6.15537i) q^{6} -8.50651i q^{7} +(2.47214 + 7.60845i) q^{8} -5.47214 q^{9} +(-3.61803 + 2.62866i) q^{10} +1.79611i q^{11} +(14.4721 + 4.70228i) q^{12} +0.472136 q^{13} +(10.0000 + 13.7638i) q^{14} +8.50651i q^{15} +(-12.9443 - 9.40456i) q^{16} -23.8885 q^{17} +(8.85410 - 6.43288i) q^{18} -9.40456i q^{19} +(2.76393 - 8.50651i) q^{20} +32.3607 q^{21} +(-2.11146 - 2.90617i) q^{22} -16.1150i q^{23} +(-28.9443 + 9.40456i) q^{24} +5.00000 q^{25} +(-0.763932 + 0.555029i) q^{26} +13.4208i q^{27} +(-32.3607 - 10.5146i) q^{28} +6.94427 q^{29} +(-10.0000 - 13.7638i) q^{30} +47.4468i q^{31} +32.0000 q^{32} -6.83282 q^{33} +(38.6525 - 28.0827i) q^{34} -19.0211i q^{35} +(-6.76393 + 20.8172i) q^{36} +26.3607 q^{37} +(11.0557 + 15.2169i) q^{38} +1.79611i q^{39} +(5.52786 + 17.0130i) q^{40} -41.4164 q^{41} +(-52.3607 + 38.0423i) q^{42} -2.00811i q^{43} +(6.83282 + 2.22012i) q^{44} -12.2361 q^{45} +(18.9443 + 26.0746i) q^{46} -35.3481i q^{47} +(35.7771 - 49.2429i) q^{48} -23.3607 q^{49} +(-8.09017 + 5.87785i) q^{50} -90.8774i q^{51} +(0.583592 - 1.79611i) q^{52} -21.6393 q^{53} +(-15.7771 - 21.7153i) q^{54} +4.01623i q^{55} +(64.7214 - 21.0292i) q^{56} +35.7771 q^{57} +(-11.2361 + 8.16348i) q^{58} +73.8644i q^{59} +(32.3607 + 10.5146i) q^{60} -26.1378 q^{61} +(-55.7771 - 76.7706i) q^{62} +46.5488i q^{63} +(-51.7771 + 37.6183i) q^{64} +1.05573 q^{65} +(11.0557 - 8.03246i) q^{66} +88.8693i q^{67} +(-29.5279 + 90.8774i) q^{68} +61.3050 q^{69} +(22.3607 + 30.7768i) q^{70} -39.4144i q^{71} +(-13.5279 - 41.6345i) q^{72} +137.554 q^{73} +(-42.6525 + 30.9888i) q^{74} +19.0211i q^{75} +(-35.7771 - 11.6247i) q^{76} +15.2786 q^{77} +(-2.11146 - 2.90617i) q^{78} -113.703i q^{79} +(-28.9443 - 21.0292i) q^{80} -100.305 q^{81} +(67.0132 - 48.6879i) q^{82} +21.2412i q^{83} +(40.0000 - 123.107i) q^{84} -53.4164 q^{85} +(2.36068 + 3.24920i) q^{86} +26.4176i q^{87} +(-13.6656 + 4.44023i) q^{88} +67.4427 q^{89} +(19.7984 - 14.3844i) q^{90} -4.01623i q^{91} +(-61.3050 - 19.9192i) q^{92} -180.498 q^{93} +(41.5542 + 57.1944i) q^{94} -21.0292i q^{95} +121.735i q^{96} -39.1672 q^{97} +(37.7984 - 27.4621i) q^{98} -9.82857i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 4q^{4} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 4q^{4} - 8q^{8} - 4q^{9} - 10q^{10} + 40q^{12} - 16q^{13} + 40q^{14} - 16q^{16} - 24q^{17} + 22q^{18} + 20q^{20} + 40q^{21} - 80q^{22} - 80q^{24} + 20q^{25} - 12q^{26} - 40q^{28} - 8q^{29} - 40q^{30} + 128q^{32} + 80q^{33} + 92q^{34} - 36q^{36} + 16q^{37} + 80q^{38} + 40q^{40} - 112q^{41} - 120q^{42} - 80q^{44} - 40q^{45} + 40q^{46} - 4q^{49} - 10q^{50} + 56q^{52} - 176q^{53} + 80q^{54} + 80q^{56} - 36q^{58} + 40q^{60} + 128q^{61} - 80q^{62} - 64q^{64} + 40q^{65} + 80q^{66} - 136q^{68} + 120q^{69} - 72q^{72} + 264q^{73} - 108q^{74} + 240q^{77} - 80q^{78} - 80q^{80} - 276q^{81} + 116q^{82} + 160q^{84} - 160q^{85} - 80q^{86} + 160q^{88} - 88q^{89} + 30q^{90} - 120q^{92} - 400q^{93} - 120q^{94} - 264q^{97} + 102q^{98} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61803 + 1.17557i −0.809017 + 0.587785i
\(3\) 3.80423i 1.26808i 0.773302 + 0.634038i \(0.218604\pi\)
−0.773302 + 0.634038i \(0.781396\pi\)
\(4\) 1.23607 3.80423i 0.309017 0.951057i
\(5\) 2.23607 0.447214
\(6\) −4.47214 6.15537i −0.745356 1.02589i
\(7\) 8.50651i 1.21522i −0.794237 0.607608i \(-0.792129\pi\)
0.794237 0.607608i \(-0.207871\pi\)
\(8\) 2.47214 + 7.60845i 0.309017 + 0.951057i
\(9\) −5.47214 −0.608015
\(10\) −3.61803 + 2.62866i −0.361803 + 0.262866i
\(11\) 1.79611i 0.163283i 0.996662 + 0.0816415i \(0.0260162\pi\)
−0.996662 + 0.0816415i \(0.973984\pi\)
\(12\) 14.4721 + 4.70228i 1.20601 + 0.391857i
\(13\) 0.472136 0.0363182 0.0181591 0.999835i \(-0.494219\pi\)
0.0181591 + 0.999835i \(0.494219\pi\)
\(14\) 10.0000 + 13.7638i 0.714286 + 0.983130i
\(15\) 8.50651i 0.567101i
\(16\) −12.9443 9.40456i −0.809017 0.587785i
\(17\) −23.8885 −1.40521 −0.702604 0.711581i \(-0.747980\pi\)
−0.702604 + 0.711581i \(0.747980\pi\)
\(18\) 8.85410 6.43288i 0.491895 0.357382i
\(19\) 9.40456i 0.494977i −0.968891 0.247489i \(-0.920395\pi\)
0.968891 0.247489i \(-0.0796053\pi\)
\(20\) 2.76393 8.50651i 0.138197 0.425325i
\(21\) 32.3607 1.54098
\(22\) −2.11146 2.90617i −0.0959753 0.132099i
\(23\) 16.1150i 0.700650i −0.936628 0.350325i \(-0.886071\pi\)
0.936628 0.350325i \(-0.113929\pi\)
\(24\) −28.9443 + 9.40456i −1.20601 + 0.391857i
\(25\) 5.00000 0.200000
\(26\) −0.763932 + 0.555029i −0.0293820 + 0.0213473i
\(27\) 13.4208i 0.497066i
\(28\) −32.3607 10.5146i −1.15574 0.375522i
\(29\) 6.94427 0.239458 0.119729 0.992807i \(-0.461797\pi\)
0.119729 + 0.992807i \(0.461797\pi\)
\(30\) −10.0000 13.7638i −0.333333 0.458794i
\(31\) 47.4468i 1.53054i 0.643708 + 0.765271i \(0.277395\pi\)
−0.643708 + 0.765271i \(0.722605\pi\)
\(32\) 32.0000 1.00000
\(33\) −6.83282 −0.207055
\(34\) 38.6525 28.0827i 1.13684 0.825961i
\(35\) 19.0211i 0.543461i
\(36\) −6.76393 + 20.8172i −0.187887 + 0.578257i
\(37\) 26.3607 0.712451 0.356225 0.934400i \(-0.384064\pi\)
0.356225 + 0.934400i \(0.384064\pi\)
\(38\) 11.0557 + 15.2169i 0.290940 + 0.400445i
\(39\) 1.79611i 0.0460542i
\(40\) 5.52786 + 17.0130i 0.138197 + 0.425325i
\(41\) −41.4164 −1.01016 −0.505078 0.863074i \(-0.668536\pi\)
−0.505078 + 0.863074i \(0.668536\pi\)
\(42\) −52.3607 + 38.0423i −1.24668 + 0.905768i
\(43\) 2.00811i 0.0467003i −0.999727 0.0233502i \(-0.992567\pi\)
0.999727 0.0233502i \(-0.00743326\pi\)
\(44\) 6.83282 + 2.22012i 0.155291 + 0.0504572i
\(45\) −12.2361 −0.271913
\(46\) 18.9443 + 26.0746i 0.411832 + 0.566838i
\(47\) 35.3481i 0.752087i −0.926602 0.376044i \(-0.877284\pi\)
0.926602 0.376044i \(-0.122716\pi\)
\(48\) 35.7771 49.2429i 0.745356 1.02589i
\(49\) −23.3607 −0.476749
\(50\) −8.09017 + 5.87785i −0.161803 + 0.117557i
\(51\) 90.8774i 1.78191i
\(52\) 0.583592 1.79611i 0.0112229 0.0345406i
\(53\) −21.6393 −0.408289 −0.204145 0.978941i \(-0.565441\pi\)
−0.204145 + 0.978941i \(0.565441\pi\)
\(54\) −15.7771 21.7153i −0.292168 0.402135i
\(55\) 4.01623i 0.0730223i
\(56\) 64.7214 21.0292i 1.15574 0.375522i
\(57\) 35.7771 0.627668
\(58\) −11.2361 + 8.16348i −0.193725 + 0.140750i
\(59\) 73.8644i 1.25194i 0.779848 + 0.625970i \(0.215297\pi\)
−0.779848 + 0.625970i \(0.784703\pi\)
\(60\) 32.3607 + 10.5146i 0.539345 + 0.175244i
\(61\) −26.1378 −0.428488 −0.214244 0.976780i \(-0.568729\pi\)
−0.214244 + 0.976780i \(0.568729\pi\)
\(62\) −55.7771 76.7706i −0.899630 1.23824i
\(63\) 46.5488i 0.738869i
\(64\) −51.7771 + 37.6183i −0.809017 + 0.587785i
\(65\) 1.05573 0.0162420
\(66\) 11.0557 8.03246i 0.167511 0.121704i
\(67\) 88.8693i 1.32641i 0.748439 + 0.663204i \(0.230804\pi\)
−0.748439 + 0.663204i \(0.769196\pi\)
\(68\) −29.5279 + 90.8774i −0.434233 + 1.33643i
\(69\) 61.3050 0.888478
\(70\) 22.3607 + 30.7768i 0.319438 + 0.439669i
\(71\) 39.4144i 0.555132i −0.960707 0.277566i \(-0.910472\pi\)
0.960707 0.277566i \(-0.0895277\pi\)
\(72\) −13.5279 41.6345i −0.187887 0.578257i
\(73\) 137.554 1.88430 0.942152 0.335186i \(-0.108799\pi\)
0.942152 + 0.335186i \(0.108799\pi\)
\(74\) −42.6525 + 30.9888i −0.576385 + 0.418768i
\(75\) 19.0211i 0.253615i
\(76\) −35.7771 11.6247i −0.470751 0.152956i
\(77\) 15.2786 0.198424
\(78\) −2.11146 2.90617i −0.0270700 0.0372586i
\(79\) 113.703i 1.43928i −0.694350 0.719638i \(-0.744308\pi\)
0.694350 0.719638i \(-0.255692\pi\)
\(80\) −28.9443 21.0292i −0.361803 0.262866i
\(81\) −100.305 −1.23833
\(82\) 67.0132 48.6879i 0.817234 0.593755i
\(83\) 21.2412i 0.255919i 0.991779 + 0.127959i \(0.0408427\pi\)
−0.991779 + 0.127959i \(0.959157\pi\)
\(84\) 40.0000 123.107i 0.476190 1.46556i
\(85\) −53.4164 −0.628428
\(86\) 2.36068 + 3.24920i 0.0274498 + 0.0377814i
\(87\) 26.4176i 0.303650i
\(88\) −13.6656 + 4.44023i −0.155291 + 0.0504572i
\(89\) 67.4427 0.757783 0.378892 0.925441i \(-0.376305\pi\)
0.378892 + 0.925441i \(0.376305\pi\)
\(90\) 19.7984 14.3844i 0.219982 0.159826i
\(91\) 4.01623i 0.0441344i
\(92\) −61.3050 19.9192i −0.666358 0.216513i
\(93\) −180.498 −1.94084
\(94\) 41.5542 + 57.1944i 0.442066 + 0.608451i
\(95\) 21.0292i 0.221360i
\(96\) 121.735i 1.26808i
\(97\) −39.1672 −0.403785 −0.201893 0.979408i \(-0.564709\pi\)
−0.201893 + 0.979408i \(0.564709\pi\)
\(98\) 37.7984 27.4621i 0.385698 0.280226i
\(99\) 9.82857i 0.0992785i
\(100\) 6.18034 19.0211i 0.0618034 0.190211i
\(101\) 99.8885 0.988995 0.494498 0.869179i \(-0.335352\pi\)
0.494498 + 0.869179i \(0.335352\pi\)
\(102\) 106.833 + 147.043i 1.04738 + 1.44160i
\(103\) 35.7721i 0.347302i −0.984807 0.173651i \(-0.944444\pi\)
0.984807 0.173651i \(-0.0555565\pi\)
\(104\) 1.16718 + 3.59222i 0.0112229 + 0.0345406i
\(105\) 72.3607 0.689149
\(106\) 35.0132 25.4385i 0.330313 0.239986i
\(107\) 121.099i 1.13177i −0.824485 0.565884i \(-0.808535\pi\)
0.824485 0.565884i \(-0.191465\pi\)
\(108\) 51.0557 + 16.5890i 0.472738 + 0.153602i
\(109\) −197.469 −1.81164 −0.905821 0.423660i \(-0.860745\pi\)
−0.905821 + 0.423660i \(0.860745\pi\)
\(110\) −4.72136 6.49839i −0.0429215 0.0590763i
\(111\) 100.282i 0.903441i
\(112\) −80.0000 + 110.111i −0.714286 + 0.983130i
\(113\) 81.2786 0.719280 0.359640 0.933091i \(-0.382900\pi\)
0.359640 + 0.933091i \(0.382900\pi\)
\(114\) −57.8885 + 42.0585i −0.507794 + 0.368934i
\(115\) 36.0341i 0.313340i
\(116\) 8.58359 26.4176i 0.0739965 0.227738i
\(117\) −2.58359 −0.0220820
\(118\) −86.8328 119.515i −0.735871 1.01284i
\(119\) 203.208i 1.70763i
\(120\) −64.7214 + 21.0292i −0.539345 + 0.175244i
\(121\) 117.774 0.973339
\(122\) 42.2918 30.7268i 0.346654 0.251859i
\(123\) 157.557i 1.28095i
\(124\) 180.498 + 58.6475i 1.45563 + 0.472964i
\(125\) 11.1803 0.0894427
\(126\) −54.7214 75.3175i −0.434297 0.597758i
\(127\) 1.84616i 0.0145367i −0.999974 0.00726834i \(-0.997686\pi\)
0.999974 0.00726834i \(-0.00231361\pi\)
\(128\) 39.5542 121.735i 0.309017 0.951057i
\(129\) 7.63932 0.0592195
\(130\) −1.70820 + 1.24108i −0.0131400 + 0.00954679i
\(131\) 225.609i 1.72221i 0.508428 + 0.861105i \(0.330227\pi\)
−0.508428 + 0.861105i \(0.669773\pi\)
\(132\) −8.44582 + 25.9936i −0.0639835 + 0.196921i
\(133\) −80.0000 −0.601504
\(134\) −104.472 143.794i −0.779643 1.07309i
\(135\) 30.0098i 0.222295i
\(136\) −59.0557 181.755i −0.434233 1.33643i
\(137\) −52.8328 −0.385641 −0.192820 0.981234i \(-0.561764\pi\)
−0.192820 + 0.981234i \(0.561764\pi\)
\(138\) −99.1935 + 72.0683i −0.718793 + 0.522234i
\(139\) 125.852i 0.905407i −0.891661 0.452703i \(-0.850460\pi\)
0.891661 0.452703i \(-0.149540\pi\)
\(140\) −72.3607 23.5114i −0.516862 0.167939i
\(141\) 134.472 0.953703
\(142\) 46.3344 + 63.7738i 0.326298 + 0.449111i
\(143\) 0.848009i 0.00593013i
\(144\) 70.8328 + 51.4631i 0.491895 + 0.357382i
\(145\) 15.5279 0.107089
\(146\) −222.567 + 161.705i −1.52443 + 1.10757i
\(147\) 88.8693i 0.604553i
\(148\) 32.5836 100.282i 0.220159 0.677581i
\(149\) 132.971 0.892420 0.446210 0.894928i \(-0.352773\pi\)
0.446210 + 0.894928i \(0.352773\pi\)
\(150\) −22.3607 30.7768i −0.149071 0.205179i
\(151\) 151.221i 1.00146i −0.865603 0.500732i \(-0.833064\pi\)
0.865603 0.500732i \(-0.166936\pi\)
\(152\) 71.5542 23.2494i 0.470751 0.152956i
\(153\) 130.721 0.854388
\(154\) −24.7214 + 17.9611i −0.160528 + 0.116631i
\(155\) 106.094i 0.684480i
\(156\) 6.83282 + 2.22012i 0.0438001 + 0.0142315i
\(157\) −36.7477 −0.234062 −0.117031 0.993128i \(-0.537338\pi\)
−0.117031 + 0.993128i \(0.537338\pi\)
\(158\) 133.666 + 183.975i 0.845985 + 1.16440i
\(159\) 82.3209i 0.517741i
\(160\) 71.5542 0.447214
\(161\) −137.082 −0.851441
\(162\) 162.297 117.916i 1.00183 0.727874i
\(163\) 302.854i 1.85800i 0.370079 + 0.929000i \(0.379331\pi\)
−0.370079 + 0.929000i \(0.620669\pi\)
\(164\) −51.1935 + 157.557i −0.312155 + 0.960716i
\(165\) −15.2786 −0.0925978
\(166\) −24.9706 34.3691i −0.150425 0.207043i
\(167\) 99.3839i 0.595113i 0.954704 + 0.297557i \(0.0961717\pi\)
−0.954704 + 0.297557i \(0.903828\pi\)
\(168\) 80.0000 + 246.215i 0.476190 + 1.46556i
\(169\) −168.777 −0.998681
\(170\) 86.4296 62.7948i 0.508409 0.369381i
\(171\) 51.4631i 0.300954i
\(172\) −7.63932 2.48217i −0.0444147 0.0144312i
\(173\) −181.639 −1.04994 −0.524969 0.851121i \(-0.675923\pi\)
−0.524969 + 0.851121i \(0.675923\pi\)
\(174\) −31.0557 42.7445i −0.178481 0.245658i
\(175\) 42.5325i 0.243043i
\(176\) 16.8916 23.2494i 0.0959753 0.132099i
\(177\) −280.997 −1.58755
\(178\) −109.125 + 79.2837i −0.613060 + 0.445414i
\(179\) 260.907i 1.45758i −0.684735 0.728792i \(-0.740082\pi\)
0.684735 0.728792i \(-0.259918\pi\)
\(180\) −15.1246 + 46.5488i −0.0840256 + 0.258604i
\(181\) 157.777 0.871697 0.435848 0.900020i \(-0.356448\pi\)
0.435848 + 0.900020i \(0.356448\pi\)
\(182\) 4.72136 + 6.49839i 0.0259415 + 0.0357055i
\(183\) 99.4340i 0.543355i
\(184\) 122.610 39.8384i 0.666358 0.216513i
\(185\) 58.9443 0.318618
\(186\) 292.053 212.189i 1.57018 1.14080i
\(187\) 42.9065i 0.229447i
\(188\) −134.472 43.6926i −0.715277 0.232408i
\(189\) 114.164 0.604043
\(190\) 24.7214 + 34.0260i 0.130112 + 0.179084i
\(191\) 324.095i 1.69683i −0.529328 0.848417i \(-0.677556\pi\)
0.529328 0.848417i \(-0.322444\pi\)
\(192\) −143.108 196.972i −0.745356 1.02589i
\(193\) 181.777 0.941850 0.470925 0.882173i \(-0.343920\pi\)
0.470925 + 0.882173i \(0.343920\pi\)
\(194\) 63.3738 46.0438i 0.326669 0.237339i
\(195\) 4.01623i 0.0205960i
\(196\) −28.8754 + 88.8693i −0.147323 + 0.453415i
\(197\) 140.525 0.713324 0.356662 0.934234i \(-0.383915\pi\)
0.356662 + 0.934234i \(0.383915\pi\)
\(198\) 11.5542 + 15.9030i 0.0583544 + 0.0803180i
\(199\) 168.234i 0.845397i 0.906270 + 0.422698i \(0.138917\pi\)
−0.906270 + 0.422698i \(0.861083\pi\)
\(200\) 12.3607 + 38.0423i 0.0618034 + 0.190211i
\(201\) −338.079 −1.68198
\(202\) −161.623 + 117.426i −0.800114 + 0.581317i
\(203\) 59.0715i 0.290993i
\(204\) −345.718 112.331i −1.69470 0.550641i
\(205\) −92.6099 −0.451756
\(206\) 42.0526 + 57.8805i 0.204139 + 0.280973i
\(207\) 88.1833i 0.426006i
\(208\) −6.11146 4.44023i −0.0293820 0.0213473i
\(209\) 16.8916 0.0808213
\(210\) −117.082 + 85.0651i −0.557534 + 0.405072i
\(211\) 93.9455i 0.445240i 0.974905 + 0.222620i \(0.0714608\pi\)
−0.974905 + 0.222620i \(0.928539\pi\)
\(212\) −26.7477 + 82.3209i −0.126168 + 0.388306i
\(213\) 149.941 0.703949
\(214\) 142.361 + 195.943i 0.665237 + 0.915620i
\(215\) 4.49028i 0.0208850i
\(216\) −102.111 + 33.1780i −0.472738 + 0.153602i
\(217\) 403.607 1.85994
\(218\) 319.512 232.139i 1.46565 1.06486i
\(219\) 523.287i 2.38944i
\(220\) 15.2786 + 4.96433i 0.0694484 + 0.0225651i
\(221\) −11.2786 −0.0510346
\(222\) −117.889 162.260i −0.531029 0.730899i
\(223\) 214.035i 0.959797i 0.877324 + 0.479899i \(0.159327\pi\)
−0.877324 + 0.479899i \(0.840673\pi\)
\(224\) 272.208i 1.21522i
\(225\) −27.3607 −0.121603
\(226\) −131.512 + 95.5488i −0.581910 + 0.422782i
\(227\) 41.4225i 0.182478i −0.995829 0.0912389i \(-0.970917\pi\)
0.995829 0.0912389i \(-0.0290827\pi\)
\(228\) 44.2229 136.104i 0.193960 0.596948i
\(229\) 73.2786 0.319994 0.159997 0.987117i \(-0.448852\pi\)
0.159997 + 0.987117i \(0.448852\pi\)
\(230\) 42.3607 + 58.3045i 0.184177 + 0.253498i
\(231\) 58.1234i 0.251616i
\(232\) 17.1672 + 52.8352i 0.0739965 + 0.227738i
\(233\) −307.050 −1.31781 −0.658905 0.752227i \(-0.728980\pi\)
−0.658905 + 0.752227i \(0.728980\pi\)
\(234\) 4.18034 3.03719i 0.0178647 0.0129795i
\(235\) 79.0407i 0.336344i
\(236\) 280.997 + 91.3014i 1.19066 + 0.386870i
\(237\) 432.551 1.82511
\(238\) −238.885 328.798i −1.00372 1.38150i
\(239\) 42.9065i 0.179525i −0.995963 0.0897625i \(-0.971389\pi\)
0.995963 0.0897625i \(-0.0286108\pi\)
\(240\) 80.0000 110.111i 0.333333 0.458794i
\(241\) −135.082 −0.560506 −0.280253 0.959926i \(-0.590418\pi\)
−0.280253 + 0.959926i \(0.590418\pi\)
\(242\) −190.562 + 138.452i −0.787448 + 0.572114i
\(243\) 260.796i 1.07323i
\(244\) −32.3081 + 99.4340i −0.132410 + 0.407516i
\(245\) −52.2361 −0.213208
\(246\) 185.220 + 254.933i 0.752926 + 1.03631i
\(247\) 4.44023i 0.0179767i
\(248\) −360.997 + 117.295i −1.45563 + 0.472964i
\(249\) −80.8065 −0.324524
\(250\) −18.0902 + 13.1433i −0.0723607 + 0.0525731i
\(251\) 221.169i 0.881152i −0.897715 0.440576i \(-0.854774\pi\)
0.897715 0.440576i \(-0.145226\pi\)
\(252\) 177.082 + 57.5374i 0.702707 + 0.228323i
\(253\) 28.9443 0.114404
\(254\) 2.17029 + 2.98715i 0.00854445 + 0.0117604i
\(255\) 203.208i 0.796894i
\(256\) 79.1084 + 243.470i 0.309017 + 0.951057i
\(257\) −257.056 −1.00022 −0.500108 0.865963i \(-0.666707\pi\)
−0.500108 + 0.865963i \(0.666707\pi\)
\(258\) −12.3607 + 8.98056i −0.0479096 + 0.0348084i
\(259\) 224.237i 0.865781i
\(260\) 1.30495 4.01623i 0.00501904 0.0154470i
\(261\) −38.0000 −0.145594
\(262\) −265.220 365.044i −1.01229 1.39330i
\(263\) 164.168i 0.624212i −0.950047 0.312106i \(-0.898966\pi\)
0.950047 0.312106i \(-0.101034\pi\)
\(264\) −16.8916 51.9872i −0.0639835 0.196921i
\(265\) −48.3870 −0.182592
\(266\) 129.443 94.0456i 0.486627 0.353555i
\(267\) 256.567i 0.960926i
\(268\) 338.079 + 109.849i 1.26149 + 0.409882i
\(269\) −35.4752 −0.131878 −0.0659391 0.997824i \(-0.521004\pi\)
−0.0659391 + 0.997824i \(0.521004\pi\)
\(270\) −35.2786 48.5569i −0.130662 0.179840i
\(271\) 298.950i 1.10314i 0.834130 + 0.551568i \(0.185970\pi\)
−0.834130 + 0.551568i \(0.814030\pi\)
\(272\) 309.220 + 224.661i 1.13684 + 0.825961i
\(273\) 15.2786 0.0559657
\(274\) 85.4853 62.1087i 0.311990 0.226674i
\(275\) 8.98056i 0.0326566i
\(276\) 75.7771 233.218i 0.274555 0.844992i
\(277\) −457.246 −1.65071 −0.825354 0.564616i \(-0.809024\pi\)
−0.825354 + 0.564616i \(0.809024\pi\)
\(278\) 147.947 + 203.632i 0.532185 + 0.732490i
\(279\) 259.635i 0.930593i
\(280\) 144.721 47.0228i 0.516862 0.167939i
\(281\) −5.63932 −0.0200688 −0.0100344 0.999950i \(-0.503194\pi\)
−0.0100344 + 0.999950i \(0.503194\pi\)
\(282\) −217.580 + 158.081i −0.771562 + 0.560573i
\(283\) 169.918i 0.600418i −0.953874 0.300209i \(-0.902944\pi\)
0.953874 0.300209i \(-0.0970563\pi\)
\(284\) −149.941 48.7188i −0.527962 0.171545i
\(285\) 80.0000 0.280702
\(286\) −0.996894 1.37211i −0.00348564 0.00479758i
\(287\) 352.309i 1.22756i
\(288\) −175.108 −0.608015
\(289\) 281.663 0.974611
\(290\) −25.1246 + 18.2541i −0.0866366 + 0.0629452i
\(291\) 149.001i 0.512030i
\(292\) 170.026 523.287i 0.582282 1.79208i
\(293\) −26.8591 −0.0916694 −0.0458347 0.998949i \(-0.514595\pi\)
−0.0458347 + 0.998949i \(0.514595\pi\)
\(294\) 104.472 + 143.794i 0.355347 + 0.489094i
\(295\) 165.166i 0.559884i
\(296\) 65.1672 + 200.564i 0.220159 + 0.677581i
\(297\) −24.1052 −0.0811624
\(298\) −215.151 + 156.316i −0.721983 + 0.524551i
\(299\) 7.60845i 0.0254463i
\(300\) 72.3607 + 23.5114i 0.241202 + 0.0783714i
\(301\) −17.0820 −0.0567510
\(302\) 177.771 + 244.681i 0.588645 + 0.810201i
\(303\) 379.999i 1.25412i
\(304\) −88.4458 + 121.735i −0.290940 + 0.400445i
\(305\) −58.4458 −0.191626
\(306\) −211.512 + 153.672i −0.691214 + 0.502197i
\(307\) 118.031i 0.384466i −0.981349 0.192233i \(-0.938427\pi\)
0.981349 0.192233i \(-0.0615730\pi\)
\(308\) 18.8854 58.1234i 0.0613164 0.188712i
\(309\) 136.085 0.440405
\(310\) −124.721 171.664i −0.402327 0.553756i
\(311\) 121.835i 0.391753i 0.980629 + 0.195877i \(0.0627552\pi\)
−0.980629 + 0.195877i \(0.937245\pi\)
\(312\) −13.6656 + 4.44023i −0.0438001 + 0.0142315i
\(313\) 219.548 0.701431 0.350716 0.936482i \(-0.385938\pi\)
0.350716 + 0.936482i \(0.385938\pi\)
\(314\) 59.4590 43.1995i 0.189360 0.137578i
\(315\) 104.086i 0.330432i
\(316\) −432.551 140.544i −1.36883 0.444761i
\(317\) 366.859 1.15728 0.578642 0.815582i \(-0.303583\pi\)
0.578642 + 0.815582i \(0.303583\pi\)
\(318\) 96.7740 + 133.198i 0.304321 + 0.418862i
\(319\) 12.4727i 0.0390993i
\(320\) −115.777 + 84.1170i −0.361803 + 0.262866i
\(321\) 460.689 1.43517
\(322\) 221.803 161.150i 0.688830 0.500465i
\(323\) 224.661i 0.695546i
\(324\) −123.984 + 381.583i −0.382666 + 1.17772i
\(325\) 2.36068 0.00726363
\(326\) −356.026 490.028i −1.09211 1.50315i
\(327\) 751.217i 2.29730i
\(328\) −102.387 315.115i −0.312155 0.960716i
\(329\) −300.689 −0.913948
\(330\) 24.7214 17.9611i 0.0749132 0.0544276i
\(331\) 162.846i 0.491981i −0.969272 0.245990i \(-0.920887\pi\)
0.969272 0.245990i \(-0.0791132\pi\)
\(332\) 80.8065 + 26.2556i 0.243393 + 0.0790832i
\(333\) −144.249 −0.433181
\(334\) −116.833 160.807i −0.349799 0.481457i
\(335\) 198.718i 0.593187i
\(336\) −418.885 304.338i −1.24668 0.905768i
\(337\) 17.1084 0.0507666 0.0253833 0.999678i \(-0.491919\pi\)
0.0253833 + 0.999678i \(0.491919\pi\)
\(338\) 273.087 198.409i 0.807950 0.587010i
\(339\) 309.202i 0.912101i
\(340\) −66.0263 + 203.208i −0.194195 + 0.597671i
\(341\) −85.2198 −0.249911
\(342\) −60.4984 83.2690i −0.176896 0.243477i
\(343\) 218.101i 0.635863i
\(344\) 15.2786 4.96433i 0.0444147 0.0144312i
\(345\) 137.082 0.397339
\(346\) 293.899 213.530i 0.849418 0.617138i
\(347\) 167.498i 0.482703i 0.970438 + 0.241351i \(0.0775906\pi\)
−0.970438 + 0.241351i \(0.922409\pi\)
\(348\) 100.498 + 32.6539i 0.288789 + 0.0938331i
\(349\) −483.495 −1.38537 −0.692687 0.721239i \(-0.743573\pi\)
−0.692687 + 0.721239i \(0.743573\pi\)
\(350\) 50.0000 + 68.8191i 0.142857 + 0.196626i
\(351\) 6.33644i 0.0180525i
\(352\) 57.4756i 0.163283i
\(353\) 307.994 0.872504 0.436252 0.899825i \(-0.356306\pi\)
0.436252 + 0.899825i \(0.356306\pi\)
\(354\) 454.663 330.332i 1.28436 0.933140i
\(355\) 88.1332i 0.248263i
\(356\) 83.3638 256.567i 0.234168 0.720695i
\(357\) −773.050 −2.16540
\(358\) 306.715 + 422.157i 0.856746 + 1.17921i
\(359\) 23.2494i 0.0647615i −0.999476 0.0323807i \(-0.989691\pi\)
0.999476 0.0323807i \(-0.0103089\pi\)
\(360\) −30.2492 93.0975i −0.0840256 0.258604i
\(361\) 272.554 0.754998
\(362\) −255.289 + 185.478i −0.705217 + 0.512370i
\(363\) 448.039i 1.23427i
\(364\) −15.2786 4.96433i −0.0419743 0.0136383i
\(365\) 307.580 0.842686
\(366\) 116.892 + 160.888i 0.319376 + 0.439583i
\(367\) 517.325i 1.40960i −0.709404 0.704802i \(-0.751036\pi\)
0.709404 0.704802i \(-0.248964\pi\)
\(368\) −151.554 + 208.596i −0.411832 + 0.566838i
\(369\) 226.636 0.614190
\(370\) −95.3738 + 69.2931i −0.257767 + 0.187279i
\(371\) 184.075i 0.496159i
\(372\) −223.108 + 686.657i −0.599754 + 1.84585i
\(373\) −88.3545 −0.236875 −0.118438 0.992961i \(-0.537789\pi\)
−0.118438 + 0.992961i \(0.537789\pi\)
\(374\) 50.4396 + 69.4242i 0.134865 + 0.185626i
\(375\) 42.5325i 0.113420i
\(376\) 268.944 87.3853i 0.715277 0.232408i
\(377\) 3.27864 0.00869666
\(378\) −184.721 + 134.208i −0.488681 + 0.355047i
\(379\) 19.3332i 0.0510112i 0.999675 + 0.0255056i \(0.00811956\pi\)
−0.999675 + 0.0255056i \(0.991880\pi\)
\(380\) −80.0000 25.9936i −0.210526 0.0684041i
\(381\) 7.02321 0.0184336
\(382\) 380.997 + 524.397i 0.997374 + 1.37277i
\(383\) 431.612i 1.12692i −0.826142 0.563462i \(-0.809469\pi\)
0.826142 0.563462i \(-0.190531\pi\)
\(384\) 463.108 + 150.473i 1.20601 + 0.391857i
\(385\) 34.1641 0.0887379
\(386\) −294.122 + 213.692i −0.761973 + 0.553606i
\(387\) 10.9887i 0.0283945i
\(388\) −48.4133 + 149.001i −0.124777 + 0.384023i
\(389\) −296.354 −0.761837 −0.380918 0.924609i \(-0.624392\pi\)
−0.380918 + 0.924609i \(0.624392\pi\)
\(390\) −4.72136 6.49839i −0.0121061 0.0166625i
\(391\) 384.963i 0.984560i
\(392\) −57.7508 177.739i −0.147323 0.453415i
\(393\) −858.269 −2.18389
\(394\) −227.374 + 165.197i −0.577091 + 0.419281i
\(395\) 254.247i 0.643664i
\(396\) −37.3901 12.1488i −0.0944194 0.0306787i
\(397\) −86.1904 −0.217104 −0.108552 0.994091i \(-0.534621\pi\)
−0.108552 + 0.994091i \(0.534621\pi\)
\(398\) −197.771 272.208i −0.496912 0.683940i
\(399\) 304.338i 0.762752i
\(400\) −64.7214 47.0228i −0.161803 0.117557i
\(401\) 442.997 1.10473 0.552365 0.833602i \(-0.313725\pi\)
0.552365 + 0.833602i \(0.313725\pi\)
\(402\) 547.023 397.436i 1.36075 0.988646i
\(403\) 22.4014i 0.0555865i
\(404\) 123.469 379.999i 0.305616 0.940591i
\(405\) −224.289 −0.553799
\(406\) 69.4427 + 95.5797i 0.171041 + 0.235418i
\(407\) 47.3467i 0.116331i
\(408\) 691.437 224.661i 1.69470 0.550641i
\(409\) 63.4102 0.155037 0.0775186 0.996991i \(-0.475300\pi\)
0.0775186 + 0.996991i \(0.475300\pi\)
\(410\) 149.846 108.869i 0.365478 0.265535i
\(411\) 200.988i 0.489022i
\(412\) −136.085 44.2167i −0.330304 0.107322i
\(413\) 628.328 1.52138
\(414\) −103.666 142.684i −0.250400 0.344646i
\(415\) 47.4969i 0.114450i
\(416\) 15.1084 0.0363182
\(417\) 478.768 1.14812
\(418\) −27.3313 + 19.8573i −0.0653858 + 0.0475056i
\(419\) 435.678i 1.03980i −0.854226 0.519902i \(-0.825968\pi\)
0.854226 0.519902i \(-0.174032\pi\)
\(420\) 89.4427 275.276i 0.212959 0.655420i
\(421\) −582.912 −1.38459 −0.692294 0.721615i \(-0.743400\pi\)
−0.692294 + 0.721615i \(0.743400\pi\)
\(422\) −110.440 152.007i −0.261705 0.360206i
\(423\) 193.430i 0.457280i
\(424\) −53.4953 164.642i −0.126168 0.388306i
\(425\) −119.443 −0.281042
\(426\) −242.610 + 176.266i −0.569507 + 0.413771i
\(427\) 222.341i 0.520705i
\(428\) −460.689 149.687i −1.07638 0.349736i
\(429\) −3.22602 −0.00751986
\(430\) 5.27864 + 7.26543i 0.0122759 + 0.0168963i
\(431\) 375.882i 0.872117i 0.899918 + 0.436058i \(0.143626\pi\)
−0.899918 + 0.436058i \(0.856374\pi\)
\(432\) 126.217 173.722i 0.292168 0.402135i
\(433\) −368.164 −0.850263 −0.425132 0.905131i \(-0.639772\pi\)
−0.425132 + 0.905131i \(0.639772\pi\)
\(434\) −653.050 + 474.468i −1.50472 + 1.09324i
\(435\) 59.0715i 0.135797i
\(436\) −244.085 + 751.217i −0.559828 + 1.72297i
\(437\) −151.554 −0.346806
\(438\) −615.161 846.696i −1.40448 1.93310i
\(439\) 483.549i 1.10148i 0.834677 + 0.550739i \(0.185654\pi\)
−0.834677 + 0.550739i \(0.814346\pi\)
\(440\) −30.5573 + 9.92866i −0.0694484 + 0.0225651i
\(441\) 127.833 0.289870
\(442\) 18.2492 13.2588i 0.0412878 0.0299974i
\(443\) 279.181i 0.630205i −0.949058 0.315102i \(-0.897961\pi\)
0.949058 0.315102i \(-0.102039\pi\)
\(444\) 381.495 + 123.955i 0.859224 + 0.279179i
\(445\) 150.807 0.338891
\(446\) −251.613 346.316i −0.564155 0.776492i
\(447\) 505.850i 1.13166i
\(448\) 320.000 + 440.442i 0.714286 + 0.983130i
\(449\) 756.079 1.68392 0.841959 0.539542i \(-0.181403\pi\)
0.841959 + 0.539542i \(0.181403\pi\)
\(450\) 44.2705 32.1644i 0.0983789 0.0714765i
\(451\) 74.3885i 0.164941i
\(452\) 100.466 309.202i 0.222270 0.684076i
\(453\) 575.279 1.26993
\(454\) 48.6950 + 67.0230i 0.107258 + 0.147628i
\(455\) 8.98056i 0.0197375i
\(456\) 88.4458 + 272.208i 0.193960 + 0.596948i
\(457\) 285.672 0.625103 0.312551 0.949901i \(-0.398816\pi\)
0.312551 + 0.949901i \(0.398816\pi\)
\(458\) −118.567 + 86.1442i −0.258881 + 0.188088i
\(459\) 320.603i 0.698482i
\(460\) −137.082 44.5407i −0.298004 0.0968275i
\(461\) −99.1146 −0.214999 −0.107500 0.994205i \(-0.534284\pi\)
−0.107500 + 0.994205i \(0.534284\pi\)
\(462\) −68.3282 94.0456i −0.147896 0.203562i
\(463\) 630.603i 1.36199i −0.732286 0.680997i \(-0.761547\pi\)
0.732286 0.680997i \(-0.238453\pi\)
\(464\) −89.8885 65.3078i −0.193725 0.140750i
\(465\) −403.607 −0.867972
\(466\) 496.817 360.958i 1.06613 0.774589i
\(467\) 496.010i 1.06212i 0.847334 + 0.531060i \(0.178206\pi\)
−0.847334 + 0.531060i \(0.821794\pi\)
\(468\) −3.19350 + 9.82857i −0.00682371 + 0.0210012i
\(469\) 755.967 1.61187
\(470\) 92.9180 + 127.891i 0.197698 + 0.272108i
\(471\) 139.796i 0.296808i
\(472\) −561.994 + 182.603i −1.19066 + 0.386870i
\(473\) 3.60680 0.00762537
\(474\) −699.882 + 508.494i −1.47655 + 1.07277i
\(475\) 47.0228i 0.0989954i
\(476\) 773.050 + 251.179i 1.62405 + 0.527687i
\(477\) 118.413 0.248246
\(478\) 50.4396 + 69.4242i 0.105522 + 0.145239i
\(479\) 579.090i 1.20896i 0.796621 + 0.604478i \(0.206618\pi\)
−0.796621 + 0.604478i \(0.793382\pi\)
\(480\) 272.208i 0.567101i
\(481\) 12.4458 0.0258749
\(482\) 218.567 158.798i 0.453459 0.329457i
\(483\) 521.491i 1.07969i
\(484\) 145.577 448.039i 0.300778 0.925700i
\(485\) −87.5805 −0.180578
\(486\) 306.584 + 421.976i 0.630830 + 0.868264i
\(487\) 626.363i 1.28617i 0.765796 + 0.643084i \(0.222345\pi\)
−0.765796 + 0.643084i \(0.777655\pi\)
\(488\) −64.6161 198.868i −0.132410 0.407516i
\(489\) −1152.13 −2.35608
\(490\) 84.5197 61.4072i 0.172489 0.125321i
\(491\) 22.3013i 0.0454201i 0.999742 + 0.0227100i \(0.00722945\pi\)
−0.999742 + 0.0227100i \(0.992771\pi\)
\(492\) −599.384 194.752i −1.21826 0.395837i
\(493\) −165.889 −0.336488
\(494\) 5.21981 + 7.18445i 0.0105664 + 0.0145434i
\(495\) 21.9773i 0.0443987i
\(496\) 446.217 614.165i 0.899630 1.23824i
\(497\) −335.279 −0.674605
\(498\) 130.748 94.9937i 0.262546 0.190750i
\(499\) 627.362i 1.25724i 0.777714 + 0.628619i \(0.216379\pi\)
−0.777714 + 0.628619i \(0.783621\pi\)
\(500\) 13.8197 42.5325i 0.0276393 0.0850651i
\(501\) −378.079 −0.754649
\(502\) 260.000 + 357.859i 0.517928 + 0.712867i
\(503\) 780.853i 1.55239i 0.630492 + 0.776196i \(0.282853\pi\)
−0.630492 + 0.776196i \(0.717147\pi\)
\(504\) −354.164 + 115.075i −0.702707 + 0.228323i
\(505\) 223.358 0.442292
\(506\) −46.8328 + 34.0260i −0.0925550 + 0.0672451i
\(507\) 642.066i 1.26640i
\(508\) −7.02321 2.28198i −0.0138252 0.00449208i
\(509\) −288.950 −0.567683 −0.283841 0.958871i \(-0.591609\pi\)
−0.283841 + 0.958871i \(0.591609\pi\)
\(510\) 238.885 + 328.798i 0.468403 + 0.644701i
\(511\) 1170.11i 2.28984i
\(512\) −414.217 300.946i −0.809017 0.587785i
\(513\) 126.217 0.246036
\(514\) 415.925 302.187i 0.809192 0.587913i
\(515\) 79.9888i 0.155318i
\(516\) 9.44272 29.0617i 0.0182998 0.0563211i
\(517\) 63.4891 0.122803
\(518\) 263.607 + 362.824i 0.508893 + 0.700432i
\(519\) 690.997i 1.33140i
\(520\) 2.60990 + 8.03246i 0.00501904 + 0.0154470i
\(521\) −602.984 −1.15736 −0.578680 0.815555i \(-0.696432\pi\)
−0.578680 + 0.815555i \(0.696432\pi\)
\(522\) 61.4853 44.6717i 0.117788 0.0855779i
\(523\) 367.962i 0.703560i 0.936083 + 0.351780i \(0.114423\pi\)
−0.936083 + 0.351780i \(0.885577\pi\)
\(524\) 858.269 + 278.869i 1.63792 + 0.532192i
\(525\) 161.803 0.308197
\(526\) 192.991 + 265.629i 0.366902 + 0.504998i
\(527\) 1133.44i 2.15073i
\(528\) 88.4458 + 64.2597i 0.167511 + 0.121704i
\(529\) 269.308 0.509089
\(530\) 78.2918 56.8823i 0.147720 0.107325i
\(531\) 404.196i 0.761198i
\(532\) −98.8854 + 304.338i −0.185875 + 0.572064i
\(533\) −19.5542 −0.0366870
\(534\) −301.613 415.135i −0.564818 0.777406i
\(535\) 270.786i 0.506142i
\(536\) −676.158 + 219.697i −1.26149 + 0.409882i
\(537\) 992.551 1.84833
\(538\) 57.4001 41.7036i 0.106692 0.0775161i
\(539\) 41.9584i 0.0778449i
\(540\) 114.164 + 37.0942i 0.211415 + 0.0686929i
\(541\) −616.885 −1.14027 −0.570134 0.821551i \(-0.693109\pi\)
−0.570134 + 0.821551i \(0.693109\pi\)
\(542\) −351.437 483.711i −0.648407 0.892455i
\(543\) 600.220i 1.10538i
\(544\) −764.433 −1.40521
\(545\) −441.554 −0.810191
\(546\) −24.7214 + 17.9611i −0.0452772 + 0.0328958i
\(547\) 97.8499i 0.178885i −0.995992 0.0894423i \(-0.971492\pi\)
0.995992 0.0894423i \(-0.0285085\pi\)
\(548\) −65.3050 + 200.988i −0.119170 + 0.366766i
\(549\) 143.029 0.260527
\(550\) −10.5573 14.5309i −0.0191951 0.0264197i
\(551\) 65.3078i 0.118526i
\(552\) 151.554 + 466.436i 0.274555 + 0.844992i
\(553\) −967.214 −1.74903
\(554\) 739.840 537.525i 1.33545 0.970262i
\(555\) 224.237i 0.404031i
\(556\) −478.768 155.561i −0.861093 0.279786i
\(557\) 896.302 1.60916 0.804580 0.593845i \(-0.202391\pi\)
0.804580 + 0.593845i \(0.202391\pi\)
\(558\) 305.220 + 420.099i 0.546989 + 0.752866i
\(559\) 0.948103i 0.00169607i
\(560\) −178.885 + 246.215i −0.319438 + 0.439669i
\(561\) 163.226 0.290955
\(562\) 9.12461 6.62942i 0.0162360 0.0117961i
\(563\) 771.186i 1.36978i 0.728647 + 0.684890i \(0.240150\pi\)
−0.728647 + 0.684890i \(0.759850\pi\)
\(564\) 166.217 511.562i 0.294710 0.907026i
\(565\) 181.745 0.321672
\(566\) 199.751 + 274.933i 0.352917 + 0.485748i
\(567\) 853.245i 1.50484i
\(568\) 299.882 97.4377i 0.527962 0.171545i
\(569\) 8.74767 0.0153738 0.00768688 0.999970i \(-0.497553\pi\)
0.00768688 + 0.999970i \(0.497553\pi\)
\(570\) −129.443 + 94.0456i −0.227092 + 0.164992i
\(571\) 511.138i 0.895164i 0.894243 + 0.447582i \(0.147715\pi\)
−0.894243 + 0.447582i \(0.852285\pi\)
\(572\) 3.22602 + 1.04820i 0.00563989 + 0.00183251i
\(573\) 1232.93 2.15171
\(574\) −414.164 570.048i −0.721540 0.993115i
\(575\) 80.5748i 0.140130i
\(576\) 283.331 205.852i 0.491895 0.357382i
\(577\) −713.712 −1.23694 −0.618468 0.785810i \(-0.712246\pi\)
−0.618468 + 0.785810i \(0.712246\pi\)
\(578\) −455.740 + 331.114i −0.788477 + 0.572862i
\(579\) 691.521i 1.19434i
\(580\) 19.1935 59.0715i 0.0330922 0.101847i
\(581\) 180.689 0.310996
\(582\) 175.161 + 241.088i 0.300964 + 0.414241i
\(583\) 38.8666i 0.0666666i
\(584\) 340.053 + 1046.57i 0.582282 + 1.79208i
\(585\) −5.77709 −0.00987536
\(586\) 43.4590 31.5748i 0.0741621 0.0538819i
\(587\) 422.169i 0.719198i −0.933107 0.359599i \(-0.882914\pi\)
0.933107 0.359599i \(-0.117086\pi\)
\(588\) −338.079 109.849i −0.574964 0.186817i
\(589\) 446.217 0.757584
\(590\) −194.164 267.244i −0.329092 0.452956i
\(591\) 534.588i 0.904548i
\(592\) −341.220 247.911i −0.576385 0.418768i
\(593\) −308.663 −0.520510 −0.260255 0.965540i \(-0.583807\pi\)
−0.260255 + 0.965540i \(0.583807\pi\)
\(594\) 39.0031 28.3374i 0.0656618 0.0477061i
\(595\) 454.387i 0.763676i
\(596\) 164.361 505.850i 0.275773 0.848742i
\(597\) −640.000 −1.07203
\(598\) 8.94427 + 12.3107i 0.0149570 + 0.0205865i
\(599\) 462.196i 0.771612i −0.922580 0.385806i \(-0.873923\pi\)
0.922580 0.385806i \(-0.126077\pi\)
\(600\) −144.721 + 47.0228i −0.241202 + 0.0783714i
\(601\) 355.358 0.591277 0.295639 0.955300i \(-0.404468\pi\)
0.295639 + 0.955300i \(0.404468\pi\)
\(602\) 27.6393 20.0811i 0.0459125 0.0333574i
\(603\) 486.305i 0.806476i
\(604\) −575.279 186.919i −0.952448 0.309469i
\(605\) 263.351 0.435290
\(606\) −446.715 614.851i −0.737154 1.01461i
\(607\) 630.403i 1.03856i 0.854605 + 0.519278i \(0.173799\pi\)
−0.854605 + 0.519278i \(0.826201\pi\)
\(608\) 300.946i 0.494977i
\(609\) 224.721 0.369001
\(610\) 94.5673 68.7072i 0.155028 0.112635i
\(611\) 16.6891i 0.0273144i
\(612\) 161.580 497.294i 0.264020 0.812571i
\(613\) 812.525 1.32549 0.662745 0.748846i \(-0.269392\pi\)
0.662745 + 0.748846i \(0.269392\pi\)
\(614\) 138.754 + 190.978i 0.225984 + 0.311040i
\(615\) 352.309i 0.572860i
\(616\) 37.7709 + 116.247i 0.0613164 + 0.188712i
\(617\) −437.935 −0.709781 −0.354891 0.934908i \(-0.615482\pi\)
−0.354891 + 0.934908i \(0.615482\pi\)
\(618\) −220.190 + 159.978i −0.356295 + 0.258864i
\(619\) 770.250i 1.24435i −0.782880 0.622173i \(-0.786250\pi\)
0.782880 0.622173i \(-0.213750\pi\)
\(620\) 403.607 + 131.140i 0.650979 + 0.211516i
\(621\) 216.276 0.348270
\(622\) −143.226 197.134i −0.230267 0.316935i
\(623\) 573.702i 0.920870i
\(624\) 16.8916 23.2494i 0.0270700 0.0372586i
\(625\) 25.0000 0.0400000
\(626\) −355.236 + 258.094i −0.567470 + 0.412291i
\(627\) 64.2597i 0.102487i
\(628\) −45.4226 + 139.796i −0.0723290 + 0.222606i
\(629\) −629.718 −1.00114
\(630\) −122.361 168.415i −0.194223 0.267325i
\(631\) 875.496i 1.38747i −0.720228 0.693737i \(-0.755963\pi\)
0.720228 0.693737i \(-0.244037\pi\)
\(632\) 865.102 281.089i 1.36883 0.444761i
\(633\) −357.390 −0.564597
\(634\) −593.591 + 431.269i −0.936263 + 0.680235i
\(635\) 4.12814i 0.00650100i
\(636\) −313.167 101.754i −0.492401 0.159991i
\(637\) −11.0294 −0.0173146
\(638\) −14.6625 20.1812i −0.0229820 0.0316320i
\(639\) 215.681i 0.337529i
\(640\) 88.4458 272.208i 0.138197 0.425325i
\(641\) 842.571 1.31446 0.657232 0.753689i \(-0.271727\pi\)
0.657232 + 0.753689i \(0.271727\pi\)
\(642\) −745.410 + 541.572i −1.16108 + 0.843570i
\(643\) 1153.20i 1.79348i −0.442563 0.896738i \(-0.645931\pi\)
0.442563 0.896738i \(-0.354069\pi\)
\(644\) −169.443 + 521.491i −0.263110 + 0.809769i
\(645\) 17.0820 0.0264838
\(646\) −264.105 363.510i −0.408832 0.562708i
\(647\) 355.751i 0.549847i −0.961466 0.274924i \(-0.911347\pi\)
0.961466 0.274924i \(-0.0886526\pi\)
\(648\) −247.967 763.165i −0.382666 1.17772i
\(649\) −132.669 −0.204420
\(650\) −3.81966 + 2.77515i −0.00587640 + 0.00426945i
\(651\) 1535.41i 2.35854i
\(652\) 1152.13 + 374.348i 1.76706 + 0.574154i
\(653\) −557.915 −0.854387 −0.427194 0.904160i \(-0.640498\pi\)
−0.427194 + 0.904160i \(0.640498\pi\)
\(654\) 883.108 + 1215.49i 1.35032 + 1.85855i
\(655\) 504.478i 0.770195i
\(656\) 536.105 + 389.503i 0.817234 + 0.593755i
\(657\) −752.715 −1.14569
\(658\) 486.525 353.481i 0.739399 0.537205i
\(659\) 284.157i 0.431194i 0.976482 + 0.215597i \(0.0691697\pi\)
−0.976482 + 0.215597i \(0.930830\pi\)
\(660\) −18.8854 + 58.1234i −0.0286143 + 0.0880658i
\(661\) 716.735 1.08432 0.542160 0.840275i \(-0.317607\pi\)
0.542160 + 0.840275i \(0.317607\pi\)
\(662\) 191.437 + 263.490i 0.289179 + 0.398021i
\(663\) 42.9065i 0.0647157i
\(664\) −161.613 + 52.5112i −0.243393 + 0.0790832i
\(665\) −178.885 −0.269001
\(666\) 233.400 169.575i 0.350451 0.254617i
\(667\) 111.907i 0.167776i
\(668\) 378.079 + 122.845i 0.565986 + 0.183900i
\(669\) −814.237 −1.21710
\(670\) −233.607 321.532i −0.348667 0.479899i
\(671\) 46.9464i 0.0699648i
\(672\) 1035.54 1.54098
\(673\) −695.378 −1.03325 −0.516625 0.856212i \(-0.672812\pi\)
−0.516625 + 0.856212i \(0.672812\pi\)
\(674\) −27.6819 + 20.1121i −0.0410711 + 0.0298399i
\(675\) 67.1040i 0.0994133i
\(676\) −208.620 + 642.066i −0.308609 + 0.949802i
\(677\) −820.237 −1.21158 −0.605788 0.795626i \(-0.707142\pi\)
−0.605788 + 0.795626i \(0.707142\pi\)
\(678\) −363.489 500.300i −0.536120 0.737905i
\(679\) 333.176i 0.490686i
\(680\) −132.053 406.416i −0.194195 0.597671i
\(681\) 157.580 0.231396
\(682\) 137.889 100.182i 0.202183 0.146894i
\(683\) 335.508i 0.491227i 0.969368 + 0.245613i \(0.0789894\pi\)
−0.969368 + 0.245613i \(0.921011\pi\)
\(684\) 195.777 + 63.6118i 0.286224 + 0.0929998i
\(685\) −118.138 −0.172464
\(686\) 256.393 + 352.895i 0.373751 + 0.514424i
\(687\) 278.769i 0.405777i
\(688\) −18.8854 + 25.9936i −0.0274498 + 0.0377814i
\(689\) −10.2167 −0.0148283
\(690\) −221.803 + 161.150i −0.321454 + 0.233550i
\(691\) 336.568i 0.487074i 0.969892 + 0.243537i \(0.0783077\pi\)
−0.969892 + 0.243537i \(0.921692\pi\)
\(692\) −224.519 + 690.997i −0.324449 + 0.998551i
\(693\) −83.6068 −0.120645
\(694\) −196.906 271.017i −0.283726 0.390515i
\(695\) 281.413i 0.404910i
\(696\) −200.997 + 65.3078i −0.288789 + 0.0938331i
\(697\) 989.378 1.41948
\(698\) 782.312 568.383i 1.12079 0.814302i
\(699\) 1168.09i 1.67108i
\(700\) −161.803 52.5731i −0.231148 0.0751044i
\(701\) −429.364 −0.612502 −0.306251 0.951951i \(-0.599075\pi\)
−0.306251 + 0.951951i \(0.599075\pi\)
\(702\) −7.44893 10.2526i −0.0106110 0.0146048i
\(703\) 247.911i 0.352647i
\(704\) −67.5666 92.9974i −0.0959753 0.132099i
\(705\) 300.689 0.426509
\(706\) −498.344 + 362.068i −0.705870 + 0.512845i
\(707\) 849.703i 1.20184i
\(708\) −347.331 + 1068.98i −0.490581 + 1.50985i
\(709\) 1224.60 1.72722 0.863609 0.504162i \(-0.168199\pi\)
0.863609 + 0.504162i \(0.168199\pi\)
\(710\) 103.607 + 142.603i 0.145925 + 0.200849i
\(711\) 622.197i 0.875101i
\(712\) 166.728 + 513.135i 0.234168 + 0.720695i
\(713\) 764.604 1.07238
\(714\) 1250.82 908.774i 1.75185 1.27279i
\(715\) 1.89621i 0.00265204i
\(716\) −992.551 322.499i −1.38624 0.450418i
\(717\) 163.226 0.227651
\(718\) 27.3313 + 37.6183i 0.0380658 + 0.0523931i
\(719\) 496.022i 0.689877i 0.938625 + 0.344939i \(0.112100\pi\)
−0.938625 + 0.344939i \(0.887900\pi\)
\(720\) 158.387 + 115.075i 0.219982 + 0.159826i
\(721\) −304.296 −0.422047
\(722\) −441.002 + 320.407i −0.610806 + 0.443777i
\(723\) 513.883i 0.710764i
\(724\) 195.023 600.220i 0.269369 0.829033i
\(725\) 34.7214 0.0478915
\(726\) −526.701 724.942i −0.725484 0.998543i
\(727\) 152.843i 0.210238i −0.994460 0.105119i \(-0.966478\pi\)
0.994460 0.105119i \(-0.0335224\pi\)
\(728\) 30.5573 9.92866i 0.0419743 0.0136383i
\(729\) 89.3808 0.122607
\(730\) −497.676 + 361.583i −0.681748 + 0.495319i
\(731\) 47.9709i 0.0656237i
\(732\) −378.269 122.907i −0.516761 0.167906i
\(733\) −761.286 −1.03859 −0.519295 0.854595i \(-0.673805\pi\)
−0.519295 + 0.854595i \(0.673805\pi\)
\(734\) 608.152 + 837.049i 0.828544 + 1.14039i
\(735\) 198.718i 0.270364i
\(736\) 515.679i 0.700650i
\(737\) −159.619 −0.216580
\(738\) −366.705 + 266.427i −0.496890 + 0.361012i
\(739\) 183.975i 0.248951i −0.992223 0.124476i \(-0.960275\pi\)
0.992223 0.124476i \(-0.0397249\pi\)
\(740\) 72.8591 224.237i 0.0984583 0.303023i
\(741\) 16.8916 0.0227957
\(742\) −216.393 297.840i −0.291635 0.401401i
\(743\) 495.247i 0.666551i 0.942830 + 0.333275i \(0.108154\pi\)
−0.942830 + 0.333275i \(0.891846\pi\)
\(744\) −446.217 1373.31i −0.599754 1.84585i
\(745\) 297.331 0.399102
\(746\) 142.961 103.867i 0.191636 0.139232i
\(747\) 116.235i 0.155602i
\(748\) −163.226 53.0353i −0.218217 0.0709029i
\(749\) −1030.13 −1.37534
\(750\) −50.0000 68.8191i −0.0666667 0.0917588i
\(751\) 800.059i 1.06533i 0.846328 + 0.532663i \(0.178809\pi\)
−0.846328 + 0.532663i \(0.821191\pi\)
\(752\) −332.433 + 457.555i −0.442066 + 0.608451i
\(753\) 841.378 1.11737
\(754\) −5.30495 + 3.85427i −0.00703574 + 0.00511177i
\(755\) 338.140i 0.447868i
\(756\) 141.115 434.306i 0.186659 0.574479i
\(757\) −276.367 −0.365082 −0.182541 0.983198i \(-0.558432\pi\)
−0.182541 + 0.983198i \(0.558432\pi\)
\(758\) −22.7276 31.2818i −0.0299836 0.0412689i
\(759\) 110.111i 0.145073i
\(760\) 160.000 51.9872i 0.210526 0.0684041i
\(761\) 891.207 1.17110 0.585550 0.810636i \(-0.300879\pi\)
0.585550 + 0.810636i \(0.300879\pi\)
\(762\) −11.3638 + 8.25627i −0.0149131 + 0.0108350i
\(763\) 1679.77i 2.20154i
\(764\) −1232.93 400.604i −1.61379 0.524351i
\(765\) 292.302 0.382094
\(766\) 507.390 + 698.363i 0.662389 + 0.911700i
\(767\) 34.8740i 0.0454681i
\(768\) −926.217 + 300.946i −1.20601 + 0.391857i
\(769\) −835.430 −1.08639 −0.543193 0.839608i \(-0.682785\pi\)
−0.543193 + 0.839608i \(0.682785\pi\)
\(770\) −55.2786 + 40.1623i −0.0717904 + 0.0521588i
\(771\) 977.898i 1.26835i
\(772\) 224.689 691.521i 0.291048 0.895753i
\(773\) 213.522 0.276225 0.138112 0.990417i \(-0.455897\pi\)
0.138112 + 0.990417i \(0.455897\pi\)
\(774\) −12.9180 17.7800i −0.0166899 0.0229716i
\(775\) 237.234i 0.306109i
\(776\) −96.8266 298.002i −0.124777 0.384023i
\(777\) 853.050 1.09788
\(778\) 479.512 348.386i 0.616339 0.447796i
\(779\) 389.503i 0.500004i
\(780\) 15.2786 + 4.96433i 0.0195880 + 0.00636453i
\(781\) 70.7926 0.0906436
\(782\) −452.551 622.883i −0.578710 0.796526i
\(783\) 93.1976i 0.119026i
\(784\) 302.387 + 219.697i 0.385698 + 0.280226i
\(785\) −82.1703 −0.104676
\(786\) 1388.71 1008.96i 1.76681 1.28366i
\(787\) 370.182i 0.470371i −0.971951 0.235185i \(-0.924430\pi\)