Properties

Label 690.3.k.b.553.10
Level $690$
Weight $3$
Character 690.553
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 553.10
Character \(\chi\) \(=\) 690.553
Dual form 690.3.k.b.277.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.46596 + 2.24837i) q^{5} +2.44949 q^{6} +(-8.35401 + 8.35401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.46596 + 2.24837i) q^{5} +2.44949 q^{6} +(-8.35401 + 8.35401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(2.21759 - 6.71434i) q^{10} +17.4360 q^{11} +(-2.44949 + 2.44949i) q^{12} +(11.0505 + 11.0505i) q^{13} -16.7080i q^{14} +(8.22335 + 2.71598i) q^{15} -4.00000 q^{16} +(-14.9996 + 14.9996i) q^{17} +(-3.00000 - 3.00000i) q^{18} -2.87824i q^{19} +(4.49675 + 8.93192i) q^{20} +20.4631 q^{21} +(-17.4360 + 17.4360i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(14.8896 - 20.0823i) q^{25} -22.1011 q^{26} +(3.67423 - 3.67423i) q^{27} +(16.7080 + 16.7080i) q^{28} +3.12728i q^{29} +(-10.9393 + 5.50737i) q^{30} +18.1414 q^{31} +(4.00000 - 4.00000i) q^{32} +(-21.3546 - 21.3546i) q^{33} -29.9992i q^{34} +(18.5258 - 56.0917i) q^{35} +6.00000 q^{36} +(-11.8822 + 11.8822i) q^{37} +(2.87824 + 2.87824i) q^{38} -27.0682i q^{39} +(-13.4287 - 4.43518i) q^{40} -72.2362 q^{41} +(-20.4631 + 20.4631i) q^{42} +(-43.7755 - 43.7755i) q^{43} -34.8720i q^{44} +(-6.74512 - 13.3979i) q^{45} -6.78233 q^{46} +(-61.4968 + 61.4968i) q^{47} +(4.89898 + 4.89898i) q^{48} -90.5791i q^{49} +(5.19267 + 34.9719i) q^{50} +36.7414 q^{51} +(22.1011 - 22.1011i) q^{52} +(43.0455 + 43.0455i) q^{53} +7.34847i q^{54} +(-77.8685 + 39.2026i) q^{55} -33.4161 q^{56} +(-3.52511 + 3.52511i) q^{57} +(-3.12728 - 3.12728i) q^{58} +60.4399i q^{59} +(5.43196 - 16.4467i) q^{60} +1.37448 q^{61} +(-18.1414 + 18.1414i) q^{62} +(-25.0620 - 25.0620i) q^{63} +8.00000i q^{64} +(-74.1970 - 24.5055i) q^{65} +42.7093 q^{66} +(60.8442 - 60.8442i) q^{67} +(29.9992 + 29.9992i) q^{68} -8.30662i q^{69} +(37.5659 + 74.6174i) q^{70} -89.3191 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-19.0044 - 19.0044i) q^{73} -23.7643i q^{74} +(-42.8317 + 6.35969i) q^{75} -5.75648 q^{76} +(-145.661 + 145.661i) q^{77} +(27.0682 + 27.0682i) q^{78} +44.8163i q^{79} +(17.8638 - 8.99349i) q^{80} -9.00000 q^{81} +(72.2362 - 72.2362i) q^{82} +(-1.63595 - 1.63595i) q^{83} -40.9261i q^{84} +(33.2630 - 100.712i) q^{85} +87.5510 q^{86} +(3.83012 - 3.83012i) q^{87} +(34.8720 + 34.8720i) q^{88} -16.6308i q^{89} +(20.1430 + 6.65277i) q^{90} -184.633 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.2186 - 22.2186i) q^{93} -122.994i q^{94} +(6.47135 + 12.8541i) q^{95} -9.79796 q^{96} +(53.3660 - 53.3660i) q^{97} +(90.5791 + 90.5791i) q^{98} +52.3080i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.500000 + 0.500000i
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.46596 + 2.24837i −0.893192 + 0.449675i
\(6\) 2.44949 0.408248
\(7\) −8.35401 + 8.35401i −1.19343 + 1.19343i −0.217333 + 0.976098i \(0.569736\pi\)
−0.976098 + 0.217333i \(0.930264\pi\)
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 2.21759 6.71434i 0.221759 0.671434i
\(11\) 17.4360 1.58509 0.792545 0.609813i \(-0.208756\pi\)
0.792545 + 0.609813i \(0.208756\pi\)
\(12\) −2.44949 + 2.44949i −0.204124 + 0.204124i
\(13\) 11.0505 + 11.0505i 0.850041 + 0.850041i 0.990138 0.140097i \(-0.0447413\pi\)
−0.140097 + 0.990138i \(0.544741\pi\)
\(14\) 16.7080i 1.19343i
\(15\) 8.22335 + 2.71598i 0.548223 + 0.181065i
\(16\) −4.00000 −0.250000
\(17\) −14.9996 + 14.9996i −0.882330 + 0.882330i −0.993771 0.111441i \(-0.964453\pi\)
0.111441 + 0.993771i \(0.464453\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 2.87824i 0.151486i −0.997127 0.0757431i \(-0.975867\pi\)
0.997127 0.0757431i \(-0.0241329\pi\)
\(20\) 4.49675 + 8.93192i 0.224837 + 0.446596i
\(21\) 20.4631 0.974432
\(22\) −17.4360 + 17.4360i −0.792545 + 0.792545i
\(23\) 3.39116 + 3.39116i 0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 14.8896 20.0823i 0.595585 0.803292i
\(26\) −22.1011 −0.850041
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 16.7080 + 16.7080i 0.596715 + 0.596715i
\(29\) 3.12728i 0.107837i 0.998545 + 0.0539187i \(0.0171712\pi\)
−0.998545 + 0.0539187i \(0.982829\pi\)
\(30\) −10.9393 + 5.50737i −0.364644 + 0.183579i
\(31\) 18.1414 0.585207 0.292604 0.956234i \(-0.405478\pi\)
0.292604 + 0.956234i \(0.405478\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −21.3546 21.3546i −0.647110 0.647110i
\(34\) 29.9992i 0.882330i
\(35\) 18.5258 56.0917i 0.529308 1.60262i
\(36\) 6.00000 0.166667
\(37\) −11.8822 + 11.8822i −0.321139 + 0.321139i −0.849204 0.528065i \(-0.822918\pi\)
0.528065 + 0.849204i \(0.322918\pi\)
\(38\) 2.87824 + 2.87824i 0.0757431 + 0.0757431i
\(39\) 27.0682i 0.694056i
\(40\) −13.4287 4.43518i −0.335717 0.110879i
\(41\) −72.2362 −1.76186 −0.880929 0.473248i \(-0.843081\pi\)
−0.880929 + 0.473248i \(0.843081\pi\)
\(42\) −20.4631 + 20.4631i −0.487216 + 0.487216i
\(43\) −43.7755 43.7755i −1.01803 1.01803i −0.999834 0.0181999i \(-0.994206\pi\)
−0.0181999 0.999834i \(-0.505794\pi\)
\(44\) 34.8720i 0.792545i
\(45\) −6.74512 13.3979i −0.149892 0.297731i
\(46\) −6.78233 −0.147442
\(47\) −61.4968 + 61.4968i −1.30844 + 1.30844i −0.385902 + 0.922540i \(0.626110\pi\)
−0.922540 + 0.385902i \(0.873890\pi\)
\(48\) 4.89898 + 4.89898i 0.102062 + 0.102062i
\(49\) 90.5791i 1.84855i
\(50\) 5.19267 + 34.9719i 0.103853 + 0.699439i
\(51\) 36.7414 0.720420
\(52\) 22.1011 22.1011i 0.425021 0.425021i
\(53\) 43.0455 + 43.0455i 0.812180 + 0.812180i 0.984960 0.172781i \(-0.0552752\pi\)
−0.172781 + 0.984960i \(0.555275\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −77.8685 + 39.2026i −1.41579 + 0.712775i
\(56\) −33.4161 −0.596715
\(57\) −3.52511 + 3.52511i −0.0618440 + 0.0618440i
\(58\) −3.12728 3.12728i −0.0539187 0.0539187i
\(59\) 60.4399i 1.02440i 0.858865 + 0.512202i \(0.171170\pi\)
−0.858865 + 0.512202i \(0.828830\pi\)
\(60\) 5.43196 16.4467i 0.0905327 0.274112i
\(61\) 1.37448 0.0225324 0.0112662 0.999937i \(-0.496414\pi\)
0.0112662 + 0.999937i \(0.496414\pi\)
\(62\) −18.1414 + 18.1414i −0.292604 + 0.292604i
\(63\) −25.0620 25.0620i −0.397810 0.397810i
\(64\) 8.00000i 0.125000i
\(65\) −74.1970 24.5055i −1.14149 0.377008i
\(66\) 42.7093 0.647110
\(67\) 60.8442 60.8442i 0.908123 0.908123i −0.0879977 0.996121i \(-0.528047\pi\)
0.996121 + 0.0879977i \(0.0280468\pi\)
\(68\) 29.9992 + 29.9992i 0.441165 + 0.441165i
\(69\) 8.30662i 0.120386i
\(70\) 37.5659 + 74.6174i 0.536656 + 1.06596i
\(71\) −89.3191 −1.25802 −0.629008 0.777399i \(-0.716539\pi\)
−0.629008 + 0.777399i \(0.716539\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) −19.0044 19.0044i −0.260334 0.260334i 0.564856 0.825190i \(-0.308932\pi\)
−0.825190 + 0.564856i \(0.808932\pi\)
\(74\) 23.7643i 0.321139i
\(75\) −42.8317 + 6.35969i −0.571089 + 0.0847959i
\(76\) −5.75648 −0.0757431
\(77\) −145.661 + 145.661i −1.89170 + 1.89170i
\(78\) 27.0682 + 27.0682i 0.347028 + 0.347028i
\(79\) 44.8163i 0.567294i 0.958929 + 0.283647i \(0.0915445\pi\)
−0.958929 + 0.283647i \(0.908456\pi\)
\(80\) 17.8638 8.99349i 0.223298 0.112419i
\(81\) −9.00000 −0.111111
\(82\) 72.2362 72.2362i 0.880929 0.880929i
\(83\) −1.63595 1.63595i −0.0197103 0.0197103i 0.697183 0.716893i \(-0.254437\pi\)
−0.716893 + 0.697183i \(0.754437\pi\)
\(84\) 40.9261i 0.487216i
\(85\) 33.2630 100.712i 0.391329 1.18485i
\(86\) 87.5510 1.01803
\(87\) 3.83012 3.83012i 0.0440244 0.0440244i
\(88\) 34.8720 + 34.8720i 0.396273 + 0.396273i
\(89\) 16.6308i 0.186863i −0.995626 0.0934313i \(-0.970216\pi\)
0.995626 0.0934313i \(-0.0297835\pi\)
\(90\) 20.1430 + 6.65277i 0.223811 + 0.0739196i
\(91\) −184.633 −2.02893
\(92\) 6.78233 6.78233i 0.0737210 0.0737210i
\(93\) −22.2186 22.2186i −0.238910 0.238910i
\(94\) 122.994i 1.30844i
\(95\) 6.47135 + 12.8541i 0.0681195 + 0.135306i
\(96\) −9.79796 −0.102062
\(97\) 53.3660 53.3660i 0.550164 0.550164i −0.376324 0.926488i \(-0.622812\pi\)
0.926488 + 0.376324i \(0.122812\pi\)
\(98\) 90.5791 + 90.5791i 0.924276 + 0.924276i
\(99\) 52.3080i 0.528363i
\(100\) −40.1646 29.7793i −0.401646 0.297793i
\(101\) −35.9808 −0.356246 −0.178123 0.984008i \(-0.557002\pi\)
−0.178123 + 0.984008i \(0.557002\pi\)
\(102\) −36.7414 + 36.7414i −0.360210 + 0.360210i
\(103\) −76.7772 76.7772i −0.745409 0.745409i 0.228204 0.973613i \(-0.426715\pi\)
−0.973613 + 0.228204i \(0.926715\pi\)
\(104\) 44.2021i 0.425021i
\(105\) −91.3873 + 46.0086i −0.870355 + 0.438177i
\(106\) −86.0910 −0.812180
\(107\) 111.941 111.941i 1.04618 1.04618i 0.0472976 0.998881i \(-0.484939\pi\)
0.998881 0.0472976i \(-0.0150609\pi\)
\(108\) −7.34847 7.34847i −0.0680414 0.0680414i
\(109\) 207.304i 1.90187i −0.309386 0.950936i \(-0.600124\pi\)
0.309386 0.950936i \(-0.399876\pi\)
\(110\) 38.6659 117.071i 0.351508 1.06428i
\(111\) 29.1052 0.262209
\(112\) 33.4161 33.4161i 0.298358 0.298358i
\(113\) −121.606 121.606i −1.07616 1.07616i −0.996850 0.0793109i \(-0.974728\pi\)
−0.0793109 0.996850i \(-0.525272\pi\)
\(114\) 7.05021i 0.0618440i
\(115\) −22.7694 7.52021i −0.197995 0.0653931i
\(116\) 6.25456 0.0539187
\(117\) −33.1516 + 33.1516i −0.283347 + 0.283347i
\(118\) −60.4399 60.4399i −0.512202 0.512202i
\(119\) 250.614i 2.10600i
\(120\) 11.0147 + 21.8787i 0.0917895 + 0.182322i
\(121\) 183.014 1.51251
\(122\) −1.37448 + 1.37448i −0.0112662 + 0.0112662i
\(123\) 88.4709 + 88.4709i 0.719276 + 0.719276i
\(124\) 36.2829i 0.292604i
\(125\) −21.3440 + 123.164i −0.170752 + 0.985314i
\(126\) 50.1241 0.397810
\(127\) −79.3364 + 79.3364i −0.624696 + 0.624696i −0.946729 0.322033i \(-0.895634\pi\)
0.322033 + 0.946729i \(0.395634\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 107.228i 0.831222i
\(130\) 98.7025 49.6915i 0.759250 0.382242i
\(131\) 77.0233 0.587964 0.293982 0.955811i \(-0.405019\pi\)
0.293982 + 0.955811i \(0.405019\pi\)
\(132\) −42.7093 + 42.7093i −0.323555 + 0.323555i
\(133\) 24.0448 + 24.0448i 0.180788 + 0.180788i
\(134\) 121.688i 0.908123i
\(135\) −8.14794 + 24.6700i −0.0603551 + 0.182741i
\(136\) −59.9985 −0.441165
\(137\) 22.4557 22.4557i 0.163910 0.163910i −0.620386 0.784296i \(-0.713024\pi\)
0.784296 + 0.620386i \(0.213024\pi\)
\(138\) 8.30662 + 8.30662i 0.0601929 + 0.0601929i
\(139\) 24.4482i 0.175887i 0.996125 + 0.0879433i \(0.0280294\pi\)
−0.996125 + 0.0879433i \(0.971971\pi\)
\(140\) −112.183 37.0515i −0.801309 0.264654i
\(141\) 150.636 1.06834
\(142\) 89.3191 89.3191i 0.629008 0.629008i
\(143\) 192.677 + 192.677i 1.34739 + 1.34739i
\(144\) 12.0000i 0.0833333i
\(145\) −7.03130 13.9663i −0.0484917 0.0963195i
\(146\) 38.0087 0.260334
\(147\) −110.936 + 110.936i −0.754669 + 0.754669i
\(148\) 23.7643 + 23.7643i 0.160570 + 0.160570i
\(149\) 188.531i 1.26531i −0.774435 0.632654i \(-0.781966\pi\)
0.774435 0.632654i \(-0.218034\pi\)
\(150\) 36.4720 49.1914i 0.243147 0.327943i
\(151\) 176.089 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(152\) 5.75648 5.75648i 0.0378715 0.0378715i
\(153\) −44.9989 44.9989i −0.294110 0.294110i
\(154\) 291.321i 1.89170i
\(155\) −81.0189 + 40.7887i −0.522703 + 0.263153i
\(156\) −54.1363 −0.347028
\(157\) −32.4124 + 32.4124i −0.206449 + 0.206449i −0.802756 0.596308i \(-0.796634\pi\)
0.596308 + 0.802756i \(0.296634\pi\)
\(158\) −44.8163 44.8163i −0.283647 0.283647i
\(159\) 105.440i 0.663142i
\(160\) −8.87035 + 26.8573i −0.0554397 + 0.167858i
\(161\) −56.6597 −0.351923
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) 85.5836 + 85.5836i 0.525053 + 0.525053i 0.919093 0.394041i \(-0.128923\pi\)
−0.394041 + 0.919093i \(0.628923\pi\)
\(164\) 144.472i 0.880929i
\(165\) 143.382 + 47.3558i 0.868983 + 0.287005i
\(166\) 3.27191 0.0197103
\(167\) 68.9683 68.9683i 0.412984 0.412984i −0.469793 0.882777i \(-0.655671\pi\)
0.882777 + 0.469793i \(0.155671\pi\)
\(168\) 40.9261 + 40.9261i 0.243608 + 0.243608i
\(169\) 75.2287i 0.445140i
\(170\) 67.4495 + 133.975i 0.396762 + 0.788091i
\(171\) 8.63471 0.0504954
\(172\) −87.5510 + 87.5510i −0.509017 + 0.509017i
\(173\) 27.9513 + 27.9513i 0.161568 + 0.161568i 0.783261 0.621693i \(-0.213555\pi\)
−0.621693 + 0.783261i \(0.713555\pi\)
\(174\) 7.66025i 0.0440244i
\(175\) 43.3796 + 292.156i 0.247884 + 1.66946i
\(176\) −69.7440 −0.396273
\(177\) 74.0234 74.0234i 0.418211 0.418211i
\(178\) 16.6308 + 16.6308i 0.0934313 + 0.0934313i
\(179\) 129.232i 0.721969i 0.932572 + 0.360984i \(0.117559\pi\)
−0.932572 + 0.360984i \(0.882441\pi\)
\(180\) −26.7958 + 13.4902i −0.148865 + 0.0749458i
\(181\) 43.8532 0.242283 0.121141 0.992635i \(-0.461345\pi\)
0.121141 + 0.992635i \(0.461345\pi\)
\(182\) 184.633 184.633i 1.01447 1.01447i
\(183\) −1.68339 1.68339i −0.00919883 0.00919883i
\(184\) 13.5647i 0.0737210i
\(185\) 26.3497 79.7808i 0.142431 0.431248i
\(186\) 44.4373 0.238910
\(187\) −261.533 + 261.533i −1.39857 + 1.39857i
\(188\) 122.994 + 122.994i 0.654221 + 0.654221i
\(189\) 61.3892i 0.324811i
\(190\) −19.3255 6.38275i −0.101713 0.0335934i
\(191\) −371.805 −1.94662 −0.973311 0.229490i \(-0.926294\pi\)
−0.973311 + 0.229490i \(0.926294\pi\)
\(192\) 9.79796 9.79796i 0.0510310 0.0510310i
\(193\) −135.050 135.050i −0.699740 0.699740i 0.264614 0.964354i \(-0.414755\pi\)
−0.964354 + 0.264614i \(0.914755\pi\)
\(194\) 106.732i 0.550164i
\(195\) 60.8594 + 120.885i 0.312099 + 0.619925i
\(196\) −181.158 −0.924276
\(197\) −129.928 + 129.928i −0.659534 + 0.659534i −0.955270 0.295735i \(-0.904435\pi\)
0.295735 + 0.955270i \(0.404435\pi\)
\(198\) −52.3080 52.3080i −0.264182 0.264182i
\(199\) 191.204i 0.960823i 0.877043 + 0.480411i \(0.159513\pi\)
−0.877043 + 0.480411i \(0.840487\pi\)
\(200\) 69.9439 10.3853i 0.349719 0.0519267i
\(201\) −149.037 −0.741479
\(202\) 35.9808 35.9808i 0.178123 0.178123i
\(203\) −26.1254 26.1254i −0.128696 0.128696i
\(204\) 73.4828i 0.360210i
\(205\) 322.604 162.414i 1.57368 0.792263i
\(206\) 153.554 0.745409
\(207\) −10.1735 + 10.1735i −0.0491473 + 0.0491473i
\(208\) −44.2021 44.2021i −0.212510 0.212510i
\(209\) 50.1849i 0.240119i
\(210\) 45.3787 137.396i 0.216089 0.654266i
\(211\) −17.0920 −0.0810047 −0.0405024 0.999179i \(-0.512896\pi\)
−0.0405024 + 0.999179i \(0.512896\pi\)
\(212\) 86.0910 86.0910i 0.406090 0.406090i
\(213\) 109.393 + 109.393i 0.513582 + 0.513582i
\(214\) 223.882i 1.04618i
\(215\) 293.923 + 97.0760i 1.36708 + 0.451516i
\(216\) 14.6969 0.0680414
\(217\) −151.554 + 151.554i −0.698405 + 0.698405i
\(218\) 207.304 + 207.304i 0.950936 + 0.950936i
\(219\) 46.5510i 0.212562i
\(220\) 78.4052 + 155.737i 0.356387 + 0.707895i
\(221\) −331.508 −1.50003
\(222\) −29.1052 + 29.1052i −0.131105 + 0.131105i
\(223\) −54.8788 54.8788i −0.246093 0.246093i 0.573272 0.819365i \(-0.305674\pi\)
−0.819365 + 0.573272i \(0.805674\pi\)
\(224\) 66.8321i 0.298358i
\(225\) 60.2469 + 44.6689i 0.267764 + 0.198528i
\(226\) 243.212 1.07616
\(227\) −82.2540 + 82.2540i −0.362352 + 0.362352i −0.864678 0.502326i \(-0.832478\pi\)
0.502326 + 0.864678i \(0.332478\pi\)
\(228\) 7.05021 + 7.05021i 0.0309220 + 0.0309220i
\(229\) 429.556i 1.87579i −0.346916 0.937896i \(-0.612771\pi\)
0.346916 0.937896i \(-0.387229\pi\)
\(230\) 30.2896 15.2492i 0.131694 0.0663009i
\(231\) 356.794 1.54456
\(232\) −6.25456 + 6.25456i −0.0269593 + 0.0269593i
\(233\) −35.0961 35.0961i −0.150627 0.150627i 0.627771 0.778398i \(-0.283967\pi\)
−0.778398 + 0.627771i \(0.783967\pi\)
\(234\) 66.3032i 0.283347i
\(235\) 136.375 412.910i 0.580317 1.75706i
\(236\) 120.880 0.512202
\(237\) 54.8885 54.8885i 0.231597 0.231597i
\(238\) 250.614 + 250.614i 1.05300 + 1.05300i
\(239\) 108.716i 0.454880i 0.973792 + 0.227440i \(0.0730355\pi\)
−0.973792 + 0.227440i \(0.926965\pi\)
\(240\) −32.8934 10.8639i −0.137056 0.0452663i
\(241\) −294.692 −1.22279 −0.611394 0.791327i \(-0.709391\pi\)
−0.611394 + 0.791327i \(0.709391\pi\)
\(242\) −183.014 + 183.014i −0.756256 + 0.756256i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 2.74896i 0.0112662i
\(245\) 203.656 + 404.523i 0.831248 + 1.65111i
\(246\) −176.942 −0.719276
\(247\) 31.8061 31.8061i 0.128770 0.128770i
\(248\) 36.2829 + 36.2829i 0.146302 + 0.146302i
\(249\) 4.00725i 0.0160934i
\(250\) −101.820 144.508i −0.407281 0.578033i
\(251\) 451.400 1.79841 0.899203 0.437532i \(-0.144147\pi\)
0.899203 + 0.437532i \(0.144147\pi\)
\(252\) −50.1241 + 50.1241i −0.198905 + 0.198905i
\(253\) 59.1283 + 59.1283i 0.233709 + 0.233709i
\(254\) 158.673i 0.624696i
\(255\) −164.086 + 82.6084i −0.643473 + 0.323955i
\(256\) 16.0000 0.0625000
\(257\) −185.908 + 185.908i −0.723378 + 0.723378i −0.969292 0.245914i \(-0.920912\pi\)
0.245914 + 0.969292i \(0.420912\pi\)
\(258\) −107.228 107.228i −0.415611 0.415611i
\(259\) 198.527i 0.766515i
\(260\) −49.0111 + 148.394i −0.188504 + 0.570746i
\(261\) −9.38185 −0.0359458
\(262\) −77.0233 + 77.0233i −0.293982 + 0.293982i
\(263\) 274.719 + 274.719i 1.04456 + 1.04456i 0.998960 + 0.0456006i \(0.0145202\pi\)
0.0456006 + 0.998960i \(0.485480\pi\)
\(264\) 85.4186i 0.323555i
\(265\) −289.022 95.4573i −1.09065 0.360216i
\(266\) −48.0897 −0.180788
\(267\) −20.3684 + 20.3684i −0.0762863 + 0.0762863i
\(268\) −121.688 121.688i −0.454061 0.454061i
\(269\) 427.490i 1.58918i 0.607146 + 0.794591i \(0.292314\pi\)
−0.607146 + 0.794591i \(0.707686\pi\)
\(270\) −16.5221 32.8180i −0.0611930 0.121548i
\(271\) 101.987 0.376334 0.188167 0.982137i \(-0.439745\pi\)
0.188167 + 0.982137i \(0.439745\pi\)
\(272\) 59.9985 59.9985i 0.220583 0.220583i
\(273\) 226.128 + 226.128i 0.828307 + 0.828307i
\(274\) 44.9114i 0.163910i
\(275\) 259.616 350.155i 0.944056 1.27329i
\(276\) −16.6132 −0.0601929
\(277\) −254.686 + 254.686i −0.919443 + 0.919443i −0.996989 0.0775463i \(-0.975291\pi\)
0.0775463 + 0.996989i \(0.475291\pi\)
\(278\) −24.4482 24.4482i −0.0879433 0.0879433i
\(279\) 54.4243i 0.195069i
\(280\) 149.235 75.1318i 0.532982 0.268328i
\(281\) −438.626 −1.56094 −0.780472 0.625190i \(-0.785021\pi\)
−0.780472 + 0.625190i \(0.785021\pi\)
\(282\) −150.636 + 150.636i −0.534169 + 0.534169i
\(283\) 85.3328 + 85.3328i 0.301529 + 0.301529i 0.841612 0.540083i \(-0.181607\pi\)
−0.540083 + 0.841612i \(0.681607\pi\)
\(284\) 178.638i 0.629008i
\(285\) 7.81724 23.6688i 0.0274289 0.0830482i
\(286\) −385.354 −1.34739
\(287\) 603.462 603.462i 2.10266 2.10266i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 160.977i 0.557014i
\(290\) 20.9976 + 6.93503i 0.0724056 + 0.0239139i
\(291\) −130.719 −0.449207
\(292\) −38.0087 + 38.0087i −0.130167 + 0.130167i
\(293\) −66.5716 66.5716i −0.227207 0.227207i 0.584318 0.811525i \(-0.301362\pi\)
−0.811525 + 0.584318i \(0.801362\pi\)
\(294\) 221.873i 0.754669i
\(295\) −135.891 269.922i −0.460649 0.914990i
\(296\) −47.5286 −0.160570
\(297\) 64.0639 64.0639i 0.215703 0.215703i
\(298\) 188.531 + 188.531i 0.632654 + 0.632654i
\(299\) 74.9484i 0.250663i
\(300\) 12.7194 + 85.6634i 0.0423980 + 0.285545i
\(301\) 731.402 2.42991
\(302\) −176.089 + 176.089i −0.583077 + 0.583077i
\(303\) 44.0673 + 44.0673i 0.145437 + 0.145437i
\(304\) 11.5130i 0.0378715i
\(305\) −6.13837 + 3.09034i −0.0201258 + 0.0101323i
\(306\) 89.9977 0.294110
\(307\) −292.269 + 292.269i −0.952015 + 0.952015i −0.998900 0.0468849i \(-0.985071\pi\)
0.0468849 + 0.998900i \(0.485071\pi\)
\(308\) 291.321 + 291.321i 0.945848 + 0.945848i
\(309\) 188.065i 0.608624i
\(310\) 40.2302 121.808i 0.129775 0.392928i
\(311\) −81.4097 −0.261767 −0.130884 0.991398i \(-0.541781\pi\)
−0.130884 + 0.991398i \(0.541781\pi\)
\(312\) 54.1363 54.1363i 0.173514 0.173514i
\(313\) 147.092 + 147.092i 0.469941 + 0.469941i 0.901895 0.431954i \(-0.142176\pi\)
−0.431954 + 0.901895i \(0.642176\pi\)
\(314\) 64.8248i 0.206449i
\(315\) 168.275 + 55.5773i 0.534206 + 0.176436i
\(316\) 89.6325 0.283647
\(317\) 51.5605 51.5605i 0.162651 0.162651i −0.621089 0.783740i \(-0.713309\pi\)
0.783740 + 0.621089i \(0.213309\pi\)
\(318\) 105.440 + 105.440i 0.331571 + 0.331571i
\(319\) 54.5273i 0.170932i
\(320\) −17.9870 35.7277i −0.0562093 0.111649i
\(321\) −274.199 −0.854201
\(322\) 56.6597 56.6597i 0.175962 0.175962i
\(323\) 43.1725 + 43.1725i 0.133661 + 0.133661i
\(324\) 18.0000i 0.0555556i
\(325\) 386.459 57.3818i 1.18910 0.176559i
\(326\) −171.167 −0.525053
\(327\) −253.895 + 253.895i −0.776436 + 0.776436i
\(328\) −144.472 144.472i −0.440465 0.440465i
\(329\) 1027.49i 3.12307i
\(330\) −190.738 + 96.0264i −0.577994 + 0.290989i
\(331\) −445.932 −1.34723 −0.673614 0.739084i \(-0.735259\pi\)
−0.673614 + 0.739084i \(0.735259\pi\)
\(332\) −3.27191 + 3.27191i −0.00985515 + 0.00985515i
\(333\) −35.6465 35.6465i −0.107046 0.107046i
\(334\) 137.937i 0.412984i
\(335\) −134.927 + 408.529i −0.402769 + 1.21949i
\(336\) −81.8523 −0.243608
\(337\) −178.974 + 178.974i −0.531081 + 0.531081i −0.920894 0.389813i \(-0.872540\pi\)
0.389813 + 0.920894i \(0.372540\pi\)
\(338\) −75.2287 75.2287i −0.222570 0.222570i
\(339\) 297.873i 0.878682i
\(340\) −201.425 66.5260i −0.592426 0.195665i
\(341\) 316.314 0.927607
\(342\) −8.63471 + 8.63471i −0.0252477 + 0.0252477i
\(343\) 347.352 + 347.352i 1.01269 + 1.01269i
\(344\) 175.102i 0.509017i
\(345\) 18.6764 + 37.0971i 0.0541345 + 0.107528i
\(346\) −55.9026 −0.161568
\(347\) −195.326 + 195.326i −0.562898 + 0.562898i −0.930130 0.367232i \(-0.880306\pi\)
0.367232 + 0.930130i \(0.380306\pi\)
\(348\) −7.66025 7.66025i −0.0220122 0.0220122i
\(349\) 616.027i 1.76512i −0.470200 0.882560i \(-0.655818\pi\)
0.470200 0.882560i \(-0.344182\pi\)
\(350\) −335.536 248.776i −0.958673 0.710790i
\(351\) 81.2045 0.231352
\(352\) 69.7440 69.7440i 0.198136 0.198136i
\(353\) −242.640 242.640i −0.687366 0.687366i 0.274283 0.961649i \(-0.411560\pi\)
−0.961649 + 0.274283i \(0.911560\pi\)
\(354\) 148.047i 0.418211i
\(355\) 398.896 200.823i 1.12365 0.565698i
\(356\) −33.2615 −0.0934313
\(357\) −306.938 + 306.938i −0.859771 + 0.859771i
\(358\) −129.232 129.232i −0.360984 0.360984i
\(359\) 309.086i 0.860963i 0.902599 + 0.430482i \(0.141656\pi\)
−0.902599 + 0.430482i \(0.858344\pi\)
\(360\) 13.3055 40.2860i 0.0369598 0.111906i
\(361\) 352.716 0.977052
\(362\) −43.8532 + 43.8532i −0.121141 + 0.121141i
\(363\) −224.145 224.145i −0.617480 0.617480i
\(364\) 369.265i 1.01447i
\(365\) 127.602 + 42.1439i 0.349594 + 0.115463i
\(366\) 3.36677 0.00919883
\(367\) 320.182 320.182i 0.872429 0.872429i −0.120307 0.992737i \(-0.538388\pi\)
0.992737 + 0.120307i \(0.0383880\pi\)
\(368\) −13.5647 13.5647i −0.0368605 0.0368605i
\(369\) 216.709i 0.587286i
\(370\) 53.4311 + 106.131i 0.144408 + 0.286839i
\(371\) −719.206 −1.93856
\(372\) −44.4373 + 44.4373i −0.119455 + 0.119455i
\(373\) 40.8847 + 40.8847i 0.109610 + 0.109610i 0.759785 0.650175i \(-0.225304\pi\)
−0.650175 + 0.759785i \(0.725304\pi\)
\(374\) 523.066i 1.39857i
\(375\) 176.986 124.704i 0.471962 0.332543i
\(376\) −245.987 −0.654221
\(377\) −34.5581 + 34.5581i −0.0916662 + 0.0916662i
\(378\) −61.3892 61.3892i −0.162405 0.162405i
\(379\) 235.010i 0.620079i −0.950724 0.310040i \(-0.899658\pi\)
0.950724 0.310040i \(-0.100342\pi\)
\(380\) 25.7082 12.9427i 0.0676532 0.0340598i
\(381\) 194.334 0.510062
\(382\) 371.805 371.805i 0.973311 0.973311i
\(383\) −344.365 344.365i −0.899125 0.899125i 0.0962334 0.995359i \(-0.469320\pi\)
−0.995359 + 0.0962334i \(0.969320\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 323.015 978.014i 0.839000 2.54030i
\(386\) 270.100 0.699740
\(387\) 131.326 131.326i 0.339345 0.339345i
\(388\) −106.732 106.732i −0.275082 0.275082i
\(389\) 522.732i 1.34378i −0.740649 0.671892i \(-0.765482\pi\)
0.740649 0.671892i \(-0.234518\pi\)
\(390\) −181.745 60.0261i −0.466012 0.153913i
\(391\) −101.732 −0.260185
\(392\) 181.158 181.158i 0.462138 0.462138i
\(393\) −94.3339 94.3339i −0.240035 0.240035i
\(394\) 259.857i 0.659534i
\(395\) −100.764 200.148i −0.255098 0.506703i
\(396\) 104.616 0.264182
\(397\) −130.039 + 130.039i −0.327554 + 0.327554i −0.851656 0.524101i \(-0.824401\pi\)
0.524101 + 0.851656i \(0.324401\pi\)
\(398\) −191.204 191.204i −0.480411 0.480411i
\(399\) 58.8976i 0.147613i
\(400\) −59.5585 + 80.3292i −0.148896 + 0.200823i
\(401\) 711.927 1.77538 0.887690 0.460442i \(-0.152309\pi\)
0.887690 + 0.460442i \(0.152309\pi\)
\(402\) 149.037 149.037i 0.370740 0.370740i
\(403\) 200.473 + 200.473i 0.497450 + 0.497450i
\(404\) 71.9617i 0.178123i
\(405\) 40.1937 20.2354i 0.0992436 0.0499639i
\(406\) 52.2507 0.128696
\(407\) −207.177 + 207.177i −0.509035 + 0.509035i
\(408\) 73.4828 + 73.4828i 0.180105 + 0.180105i
\(409\) 225.265i 0.550770i −0.961334 0.275385i \(-0.911195\pi\)
0.961334 0.275385i \(-0.0888054\pi\)
\(410\) −160.190 + 485.018i −0.390708 + 1.18297i
\(411\) −55.0050 −0.133832
\(412\) −153.554 + 153.554i −0.372705 + 0.372705i
\(413\) −504.916 504.916i −1.22256 1.22256i
\(414\) 20.3470i 0.0491473i
\(415\) 10.9843 + 3.62787i 0.0264683 + 0.00874187i
\(416\) 88.4043 0.212510
\(417\) 29.9428 29.9428i 0.0718054 0.0718054i
\(418\) 50.1849 + 50.1849i 0.120060 + 0.120060i
\(419\) 727.460i 1.73618i 0.496406 + 0.868090i \(0.334653\pi\)
−0.496406 + 0.868090i \(0.665347\pi\)
\(420\) 92.0173 + 182.775i 0.219089 + 0.435178i
\(421\) 188.423 0.447562 0.223781 0.974640i \(-0.428160\pi\)
0.223781 + 0.974640i \(0.428160\pi\)
\(422\) 17.0920 17.0920i 0.0405024 0.0405024i
\(423\) −184.490 184.490i −0.436147 0.436147i
\(424\) 172.182i 0.406090i
\(425\) 77.8880 + 524.566i 0.183266 + 1.23427i
\(426\) −218.786 −0.513582
\(427\) −11.4824 + 11.4824i −0.0268909 + 0.0268909i
\(428\) −223.882 223.882i −0.523089 0.523089i
\(429\) 471.960i 1.10014i
\(430\) −390.999 + 196.847i −0.909301 + 0.457784i
\(431\) 624.307 1.44851 0.724254 0.689534i \(-0.242185\pi\)
0.724254 + 0.689534i \(0.242185\pi\)
\(432\) −14.6969 + 14.6969i −0.0340207 + 0.0340207i
\(433\) 208.628 + 208.628i 0.481821 + 0.481821i 0.905713 0.423892i \(-0.139336\pi\)
−0.423892 + 0.905713i \(0.639336\pi\)
\(434\) 303.108i 0.698405i
\(435\) −8.49364 + 25.7167i −0.0195256 + 0.0591189i
\(436\) −414.608 −0.950936
\(437\) 9.76058 9.76058i 0.0223354 0.0223354i
\(438\) −46.5510 46.5510i −0.106281 0.106281i
\(439\) 555.867i 1.26621i 0.774065 + 0.633106i \(0.218220\pi\)
−0.774065 + 0.633106i \(0.781780\pi\)
\(440\) −234.142 77.3317i −0.532141 0.175754i
\(441\) 271.737 0.616184
\(442\) 331.508 331.508i 0.750017 0.750017i
\(443\) −479.179 479.179i −1.08167 1.08167i −0.996354 0.0853137i \(-0.972811\pi\)
−0.0853137 0.996354i \(-0.527189\pi\)
\(444\) 58.2104i 0.131105i
\(445\) 37.3922 + 74.2724i 0.0840273 + 0.166904i
\(446\) 109.758 0.246093
\(447\) −230.902 + 230.902i −0.516560 + 0.516560i
\(448\) −66.8321 66.8321i −0.149179 0.149179i
\(449\) 526.390i 1.17236i −0.810180 0.586181i \(-0.800631\pi\)
0.810180 0.586181i \(-0.199369\pi\)
\(450\) −104.916 + 15.5780i −0.233146 + 0.0346178i
\(451\) −1259.51 −2.79270
\(452\) −243.212 + 243.212i −0.538080 + 0.538080i
\(453\) −215.664 215.664i −0.476080 0.476080i
\(454\) 164.508i 0.362352i
\(455\) 824.562 415.123i 1.81223 0.912359i
\(456\) −14.1004 −0.0309220
\(457\) 190.661 190.661i 0.417201 0.417201i −0.467037 0.884238i \(-0.654678\pi\)
0.884238 + 0.467037i \(0.154678\pi\)
\(458\) 429.556 + 429.556i 0.937896 + 0.937896i
\(459\) 110.224i 0.240140i
\(460\) −15.0404 + 45.5388i −0.0326966 + 0.0989975i
\(461\) −138.301 −0.300003 −0.150001 0.988686i \(-0.547928\pi\)
−0.150001 + 0.988686i \(0.547928\pi\)
\(462\) −356.794 + 356.794i −0.772281 + 0.772281i
\(463\) 377.857 + 377.857i 0.816106 + 0.816106i 0.985541 0.169435i \(-0.0541943\pi\)
−0.169435 + 0.985541i \(0.554194\pi\)
\(464\) 12.5091i 0.0269593i
\(465\) 149.183 + 49.2718i 0.320824 + 0.105961i
\(466\) 70.1921 0.150627
\(467\) −121.247 + 121.247i −0.259629 + 0.259629i −0.824903 0.565274i \(-0.808770\pi\)
0.565274 + 0.824903i \(0.308770\pi\)
\(468\) 66.3032 + 66.3032i 0.141674 + 0.141674i
\(469\) 1016.59i 2.16756i
\(470\) 276.535 + 549.284i 0.588373 + 1.16869i
\(471\) 79.3939 0.168565
\(472\) −120.880 + 120.880i −0.256101 + 0.256101i
\(473\) −763.269 763.269i −1.61368 1.61368i
\(474\) 109.777i 0.231597i
\(475\) −57.8016 42.8559i −0.121688 0.0902230i
\(476\) −501.228 −1.05300
\(477\) −129.137 + 129.137i −0.270727 + 0.270727i
\(478\) −108.716 108.716i −0.227440 0.227440i
\(479\) 687.235i 1.43473i 0.696698 + 0.717364i \(0.254652\pi\)
−0.696698 + 0.717364i \(0.745348\pi\)
\(480\) 43.7573 22.0295i 0.0911611 0.0458947i
\(481\) −262.608 −0.545963
\(482\) 294.692 294.692i 0.611394 0.611394i
\(483\) 69.3937 + 69.3937i 0.143672 + 0.143672i
\(484\) 366.028i 0.756256i
\(485\) −118.344 + 358.317i −0.244008 + 0.738798i
\(486\) −22.0454 −0.0453609
\(487\) 437.113 437.113i 0.897563 0.897563i −0.0976574 0.995220i \(-0.531135\pi\)
0.995220 + 0.0976574i \(0.0311349\pi\)
\(488\) 2.74896 + 2.74896i 0.00563311 + 0.00563311i
\(489\) 209.636i 0.428704i
\(490\) −608.178 200.867i −1.24118 0.409933i
\(491\) −129.408 −0.263559 −0.131780 0.991279i \(-0.542069\pi\)
−0.131780 + 0.991279i \(0.542069\pi\)
\(492\) 176.942 176.942i 0.359638 0.359638i
\(493\) −46.9080 46.9080i −0.0951482 0.0951482i
\(494\) 63.6121i 0.128770i
\(495\) −117.608 233.605i −0.237592 0.471930i
\(496\) −72.5657 −0.146302
\(497\) 746.173 746.173i 1.50135 1.50135i
\(498\) −4.00725 4.00725i −0.00804670 0.00804670i
\(499\) 958.920i 1.92168i 0.277098 + 0.960842i \(0.410627\pi\)
−0.277098 + 0.960842i \(0.589373\pi\)
\(500\) 246.329 + 42.6880i 0.492657 + 0.0853761i
\(501\) −168.937 −0.337200
\(502\) −451.400 + 451.400i −0.899203 + 0.899203i
\(503\) −135.406 135.406i −0.269197 0.269197i 0.559580 0.828777i \(-0.310963\pi\)
−0.828777 + 0.559580i \(0.810963\pi\)
\(504\) 100.248i 0.198905i
\(505\) 160.689 80.8984i 0.318196 0.160195i
\(506\) −118.257 −0.233709
\(507\) 92.1359 92.1359i 0.181728 0.181728i
\(508\) 158.673 + 158.673i 0.312348 + 0.312348i
\(509\) 642.984i 1.26323i −0.775282 0.631615i \(-0.782392\pi\)
0.775282 0.631615i \(-0.217608\pi\)
\(510\) 81.4773 246.694i 0.159759 0.483714i
\(511\) 317.526 0.621381
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) −10.5753 10.5753i −0.0206147 0.0206147i
\(514\) 371.816i 0.723378i
\(515\) 515.508 + 170.260i 1.00099 + 0.330602i
\(516\) 214.455 0.415611
\(517\) −1072.26 + 1072.26i −2.07400 + 2.07400i
\(518\) 198.527 + 198.527i 0.383258 + 0.383258i
\(519\) 68.4664i 0.131920i
\(520\) −99.3829 197.405i −0.191121 0.379625i
\(521\) 343.522 0.659351 0.329676 0.944094i \(-0.393061\pi\)
0.329676 + 0.944094i \(0.393061\pi\)
\(522\) 9.38185 9.38185i 0.0179729 0.0179729i
\(523\) −44.8371 44.8371i −0.0857306 0.0857306i 0.662941 0.748672i \(-0.269308\pi\)
−0.748672 + 0.662941i \(0.769308\pi\)
\(524\) 154.047i 0.293982i
\(525\) 304.688 410.946i 0.580357 0.782753i
\(526\) −549.439 −1.04456
\(527\) −272.115 + 272.115i −0.516346 + 0.516346i
\(528\) 85.4186 + 85.4186i 0.161778 + 0.161778i
\(529\) 23.0000i 0.0434783i
\(530\) 384.479 193.565i 0.725433 0.365217i
\(531\) −181.320 −0.341468
\(532\) 48.0897 48.0897i 0.0903941 0.0903941i
\(533\) −798.249 798.249i −1.49765 1.49765i
\(534\) 40.7369i 0.0762863i
\(535\) −248.239 + 751.610i −0.463999 + 1.40488i
\(536\) 243.377 0.454061
\(537\) 158.277 158.277i 0.294742 0.294742i
\(538\) −427.490 427.490i −0.794591 0.794591i
\(539\) 1579.34i 2.93012i
\(540\) 49.3401 + 16.2959i 0.0913705 + 0.0301776i
\(541\) −425.664 −0.786809 −0.393404 0.919366i \(-0.628703\pi\)
−0.393404 + 0.919366i \(0.628703\pi\)
\(542\) −101.987 + 101.987i −0.188167 + 0.188167i
\(543\) −53.7089 53.7089i −0.0989115 0.0989115i
\(544\) 119.997i 0.220583i
\(545\) 466.097 + 925.812i 0.855224 + 1.69874i
\(546\) −452.256 −0.828307
\(547\) −561.015 + 561.015i −1.02562 + 1.02562i −0.0259585 + 0.999663i \(0.508264\pi\)
−0.999663 + 0.0259585i \(0.991736\pi\)
\(548\) −44.9114 44.9114i −0.0819551 0.0819551i
\(549\) 4.12344i 0.00751082i
\(550\) 90.5393 + 609.770i 0.164617 + 1.10867i
\(551\) 9.00106 0.0163359
\(552\) 16.6132 16.6132i 0.0300965 0.0300965i
\(553\) −374.396 374.396i −0.677026 0.677026i
\(554\) 509.371i 0.919443i
\(555\) −129.983 + 65.4394i −0.234203 + 0.117909i
\(556\) 48.8964 0.0879433
\(557\) 567.369 567.369i 1.01862 1.01862i 0.0187923 0.999823i \(-0.494018\pi\)
0.999823 0.0187923i \(-0.00598211\pi\)
\(558\) −54.4243 54.4243i −0.0975346 0.0975346i
\(559\) 967.485i 1.73074i
\(560\) −74.1031 + 224.367i −0.132327 + 0.400655i
\(561\) 640.623 1.14193
\(562\) 438.626 438.626i 0.780472 0.780472i
\(563\) −156.606 156.606i −0.278164 0.278164i 0.554212 0.832376i \(-0.313020\pi\)
−0.832376 + 0.554212i \(0.813020\pi\)
\(564\) 301.271i 0.534169i
\(565\) 816.505 + 269.672i 1.44514 + 0.477296i
\(566\) −170.666 −0.301529
\(567\) 75.1861 75.1861i 0.132603 0.132603i
\(568\) −178.638 178.638i −0.314504 0.314504i
\(569\) 331.356i 0.582347i 0.956670 + 0.291174i \(0.0940458\pi\)
−0.956670 + 0.291174i \(0.905954\pi\)
\(570\) 15.8515 + 31.4860i 0.0278097 + 0.0552386i
\(571\) −859.490 −1.50524 −0.752618 0.658457i \(-0.771209\pi\)
−0.752618 + 0.658457i \(0.771209\pi\)
\(572\) 385.354 385.354i 0.673696 0.673696i
\(573\) 455.366 + 455.366i 0.794705 + 0.794705i
\(574\) 1206.92i 2.10266i
\(575\) 118.596 17.6092i 0.206253 0.0306247i
\(576\) −24.0000 −0.0416667
\(577\) 20.7204 20.7204i 0.0359106 0.0359106i −0.688923 0.724834i \(-0.741916\pi\)
0.724834 + 0.688923i \(0.241916\pi\)
\(578\) 160.977 + 160.977i 0.278507 + 0.278507i
\(579\) 330.803i 0.571336i
\(580\) −27.9326 + 14.0626i −0.0481597 + 0.0242459i
\(581\) 27.3336 0.0470457
\(582\) 130.719 130.719i 0.224604 0.224604i
\(583\) 750.541 + 750.541i 1.28738 + 1.28738i
\(584\) 76.0175i 0.130167i
\(585\) 73.5166 222.591i 0.125669 0.380497i
\(586\) 133.143 0.227207
\(587\) −103.084 + 103.084i −0.175612 + 0.175612i −0.789440 0.613828i \(-0.789629\pi\)
0.613828 + 0.789440i \(0.289629\pi\)
\(588\) 221.873 + 221.873i 0.377334 + 0.377334i
\(589\) 52.2154i 0.0886509i
\(590\) 405.814 + 134.031i 0.687820 + 0.227171i
\(591\) 318.258 0.538508
\(592\) 47.5286 47.5286i 0.0802849 0.0802849i
\(593\) 489.343 + 489.343i 0.825199 + 0.825199i 0.986848 0.161649i \(-0.0516814\pi\)
−0.161649 + 0.986848i \(0.551681\pi\)
\(594\) 128.128i 0.215703i
\(595\) 563.474 + 1119.23i 0.947015 + 1.88106i
\(596\) −377.062 −0.632654
\(597\) 234.176 234.176i 0.392254 0.392254i
\(598\) −74.9484 74.9484i −0.125332 0.125332i
\(599\) 351.503i 0.586816i 0.955987 + 0.293408i \(0.0947894\pi\)
−0.955987 + 0.293408i \(0.905211\pi\)
\(600\) −98.3828 72.9440i −0.163971 0.121573i
\(601\) −985.264 −1.63937 −0.819687 0.572811i \(-0.805853\pi\)
−0.819687 + 0.572811i \(0.805853\pi\)
\(602\) −731.402 + 731.402i −1.21495 + 1.21495i
\(603\) 182.533 + 182.533i 0.302708 + 0.302708i
\(604\) 352.178i 0.583077i
\(605\) −817.333 + 411.483i −1.35096 + 0.680138i
\(606\) −88.1347 −0.145437
\(607\) 167.150 167.150i 0.275371 0.275371i −0.555887 0.831258i \(-0.687621\pi\)
0.831258 + 0.555887i \(0.187621\pi\)
\(608\) −11.5130 11.5130i −0.0189358 0.0189358i
\(609\) 63.9938i 0.105080i
\(610\) 3.04803 9.22871i 0.00499677 0.0151290i
\(611\) −1359.14 −2.22446
\(612\) −89.9977 + 89.9977i −0.147055 + 0.147055i
\(613\) 50.3714 + 50.3714i 0.0821719 + 0.0821719i 0.746998 0.664826i \(-0.231494\pi\)
−0.664826 + 0.746998i \(0.731494\pi\)
\(614\) 584.537i 0.952015i
\(615\) −594.023 196.192i −0.965892 0.319012i
\(616\) −582.642 −0.945848
\(617\) −318.895 + 318.895i −0.516848 + 0.516848i −0.916616 0.399768i \(-0.869091\pi\)
0.399768 + 0.916616i \(0.369091\pi\)
\(618\) −188.065 188.065i −0.304312 0.304312i
\(619\) 316.148i 0.510741i −0.966843 0.255370i \(-0.917803\pi\)
0.966843 0.255370i \(-0.0821974\pi\)
\(620\) 81.5774 + 162.038i 0.131577 + 0.261351i
\(621\) 24.9199 0.0401286
\(622\) 81.4097 81.4097i 0.130884 0.130884i
\(623\) 138.934 + 138.934i 0.223007 + 0.223007i
\(624\) 108.273i 0.173514i
\(625\) −181.598 598.036i −0.290556 0.956858i
\(626\) −294.183 −0.469941
\(627\) −61.4637 + 61.4637i −0.0980283 + 0.0980283i
\(628\) 64.8248 + 64.8248i 0.103224 + 0.103224i
\(629\) 356.456i 0.566702i
\(630\) −223.852 + 112.698i −0.355321 + 0.178885i
\(631\) 605.041 0.958861 0.479430 0.877580i \(-0.340843\pi\)
0.479430 + 0.877580i \(0.340843\pi\)
\(632\) −89.6325 + 89.6325i −0.141824 + 0.141824i
\(633\) 20.9333 + 20.9333i 0.0330700 + 0.0330700i
\(634\) 103.121i 0.162651i
\(635\) 175.935 532.691i 0.277064 0.838884i
\(636\) −210.879 −0.331571
\(637\) 1000.95 1000.95i 1.57135 1.57135i
\(638\) −54.5273 54.5273i −0.0854659 0.0854659i
\(639\) 267.957i 0.419338i
\(640\) 53.7147 + 17.7407i 0.0839292 + 0.0277199i
\(641\) −465.040 −0.725491 −0.362745 0.931888i \(-0.618161\pi\)
−0.362745 + 0.931888i \(0.618161\pi\)
\(642\) 274.199 274.199i 0.427101 0.427101i
\(643\) −348.885 348.885i −0.542590 0.542590i 0.381697 0.924287i \(-0.375340\pi\)
−0.924287 + 0.381697i \(0.875340\pi\)
\(644\) 113.319i 0.175962i
\(645\) −241.088 478.874i −0.373779 0.742441i
\(646\) −86.3449 −0.133661
\(647\) −190.931 + 190.931i −0.295102 + 0.295102i −0.839092 0.543990i \(-0.816913\pi\)
0.543990 + 0.839092i \(0.316913\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 1053.83i 1.62377i
\(650\) −329.077 + 443.840i −0.506272 + 0.682831i
\(651\) 371.229 0.570245
\(652\) 171.167 171.167i 0.262526 0.262526i
\(653\) −149.378 149.378i −0.228756 0.228756i 0.583417 0.812173i \(-0.301715\pi\)
−0.812173 + 0.583417i \(0.801715\pi\)
\(654\) 507.789i 0.776436i
\(655\) −343.983 + 173.177i −0.525165 + 0.264393i
\(656\) 288.945 0.440465
\(657\) 57.0131 57.0131i 0.0867780 0.0867780i
\(658\) 1027.49 + 1027.49i 1.56153 + 1.56153i
\(659\) 577.391i 0.876163i 0.898935 + 0.438081i \(0.144342\pi\)
−0.898935 + 0.438081i \(0.855658\pi\)
\(660\) 94.7116 286.764i 0.143502 0.434492i
\(661\) 734.430 1.11109 0.555545 0.831487i \(-0.312510\pi\)
0.555545 + 0.831487i \(0.312510\pi\)
\(662\) 445.932 445.932i 0.673614 0.673614i
\(663\) 406.012 + 406.012i 0.612386 + 0.612386i
\(664\) 6.54382i 0.00985515i
\(665\) −161.445 53.3216i −0.242775 0.0801828i
\(666\) 71.2929 0.107046
\(667\) −10.6051 + 10.6051i −0.0158997 + 0.0158997i
\(668\) −137.937 137.937i −0.206492 0.206492i
\(669\) 134.425i 0.200934i
\(670\) −273.601 543.456i −0.408360 0.811129i
\(671\) 23.9654 0.0357160
\(672\) 81.8523 81.8523i 0.121804 0.121804i
\(673\) −310.291 310.291i −0.461057 0.461057i 0.437945 0.899002i \(-0.355706\pi\)
−0.899002 + 0.437945i \(0.855706\pi\)
\(674\) 357.949i 0.531081i
\(675\) −19.0791 128.495i −0.0282653 0.190363i
\(676\) 150.457 0.222570
\(677\) 474.216 474.216i 0.700467 0.700467i −0.264044 0.964511i \(-0.585056\pi\)
0.964511 + 0.264044i \(0.0850564\pi\)
\(678\) −297.873 297.873i −0.439341 0.439341i
\(679\) 891.640i 1.31317i
\(680\) 267.951 134.899i 0.394045 0.198381i
\(681\) 201.480 0.295860
\(682\) −316.314 + 316.314i −0.463803 + 0.463803i
\(683\) −640.291 640.291i −0.937469 0.937469i 0.0606878 0.998157i \(-0.480671\pi\)
−0.998157 + 0.0606878i \(0.980671\pi\)
\(684\) 17.2694i 0.0252477i
\(685\) −49.7975 + 150.775i −0.0726971 + 0.220110i
\(686\) −694.705 −1.01269
\(687\) −526.097 + 526.097i −0.765789 + 0.765789i
\(688\) 175.102 + 175.102i 0.254509 + 0.254509i
\(689\) 951.352i 1.38077i
\(690\) −55.7735 18.4207i −0.0808311 0.0266966i
\(691\) 270.091 0.390870 0.195435 0.980717i \(-0.437388\pi\)
0.195435 + 0.980717i \(0.437388\pi\)
\(692\) 55.9026 55.9026i 0.0807841 0.0807841i
\(693\) −436.982 436.982i −0.630565 0.630565i
\(694\) 390.651i 0.562898i
\(695\) −54.9687 109.185i −0.0790917 0.157100i
\(696\) 15.3205 0.0220122
\(697\) 1083.52 1083.52i 1.55454 1.55454i
\(698\) 616.027 + 616.027i 0.882560 + 0.882560i
\(699\) 85.9674i 0.122986i
\(700\) 584.312 86.7593i 0.834732 0.123942i
\(701\) −713.112 −1.01728 −0.508639 0.860980i \(-0.669851\pi\)
−0.508639 + 0.860980i \(0.669851\pi\)
\(702\) −81.2045 + 81.2045i −0.115676 + 0.115676i
\(703\) 34.1997 + 34.1997i 0.0486482 + 0.0486482i
\(704\) 139.488i 0.198136i
\(705\) −672.733 + 338.685i −0.954232 + 0.480405i
\(706\) 485.281 0.687366
\(707\) 300.584 300.584i 0.425155 0.425155i
\(708\) −148.047 148.047i −0.209106 0.209106i
\(709\) 1353.88i 1.90956i 0.297314 + 0.954780i \(0.403909\pi\)
−0.297314 + 0.954780i \(0.596091\pi\)
\(710\) −198.073 + 599.718i −0.278976 + 0.844674i
\(711\) −134.449 −0.189098
\(712\) 33.2615 33.2615i 0.0467156 0.0467156i
\(713\) 61.5206 + 61.5206i 0.0862841 + 0.0862841i
\(714\) 613.876i 0.859771i
\(715\) −1293.70 427.278i −1.80937 0.597592i
\(716\) 258.465 0.360984
\(717\) 133.150 133.150i 0.185704 0.185704i
\(718\) −309.086 309.086i −0.430482 0.430482i
\(719\) 652.637i 0.907701i 0.891078 + 0.453850i \(0.149950\pi\)
−0.891078 + 0.453850i \(0.850050\pi\)
\(720\) 26.9805 + 53.5915i 0.0374729 + 0.0744327i
\(721\) 1282.79 1.77919
\(722\) −352.716 + 352.716i −0.488526 + 0.488526i
\(723\) 360.922 + 360.922i 0.499201 + 0.499201i
\(724\) 87.7063i 0.121141i
\(725\) 62.8030 + 46.5641i 0.0866249 + 0.0642263i
\(726\) 448.291 0.617480
\(727\) 532.109 532.109i 0.731924 0.731924i −0.239076 0.971001i \(-0.576845\pi\)
0.971001 + 0.239076i \(0.0768446\pi\)
\(728\) −369.265 369.265i −0.507233 0.507233i
\(729\) 27.0000i 0.0370370i
\(730\) −169.746 + 85.4579i −0.232528 + 0.117066i
\(731\) 1313.23 1.79649
\(732\) −3.36677 + 3.36677i −0.00459942 + 0.00459942i
\(733\) −486.414 486.414i −0.663594 0.663594i 0.292631 0.956225i \(-0.405469\pi\)
−0.956225 + 0.292631i \(0.905469\pi\)
\(734\) 640.363i 0.872429i
\(735\) 246.011 744.863i 0.334709 1.01342i
\(736\) 27.1293 0.0368605
\(737\) 1060.88 1060.88i 1.43946 1.43946i
\(738\) 216.709 + 216.709i 0.293643 + 0.293643i
\(739\) 161.727i 0.218846i 0.993995 + 0.109423i \(0.0349003\pi\)
−0.993995 + 0.109423i \(0.965100\pi\)
\(740\) −159.562 52.6995i −0.215624 0.0712155i
\(741\) −77.9086 −0.105140
\(742\) 719.206 719.206i 0.969280 0.969280i
\(743\) −993.064 993.064i −1.33656 1.33656i −0.899368 0.437192i \(-0.855973\pi\)
−0.437192 0.899368i \(-0.644027\pi\)
\(744\) 88.8745i 0.119455i
\(745\) 423.888 + 841.971i 0.568977 + 1.13016i
\(746\) −81.7694 −0.109610
\(747\) 4.90786 4.90786i 0.00657010 0.00657010i
\(748\) 523.066 + 523.066i 0.699287 + 0.699287i
\(749\) 1870.31i 2.49708i
\(750\) −52.2820 + 301.690i −0.0697093 + 0.402253i
\(751\) 158.149 0.210585 0.105292 0.994441i \(-0.466422\pi\)
0.105292 + 0.994441i \(0.466422\pi\)
\(752\) 245.987 245.987i 0.327110 0.327110i
\(753\) −552.850 552.850i −0.734196 0.734196i
\(754\) 69.1163i 0.0916662i
\(755\) −786.408 + 395.914i −1.04160 + 0.524390i
\(756\) 122.778 0.162405
\(757\) −121.557 + 121.557i −0.160577 + 0.160577i −0.782822 0.622245i \(-0.786221\pi\)
0.622245 + 0.782822i \(0.286221\pi\)
\(758\) 235.010 + 235.010i 0.310040 + 0.310040i
\(759\) 144.834i 0.190822i
\(760\) −12.7655 + 38.6509i −0.0167967 + 0.0508565i
\(761\) −15.5981 −0.0204969 −0.0102484 0.999947i \(-0.503262\pi\)
−0.0102484 + 0.999947i \(0.503262\pi\)
\(762\) −194.334 + 194.334i −0.255031 + 0.255031i
\(763\) 1731.82 + 1731.82i 2.26975 + 2.26975i
\(764\) 743.610i 0.973311i
\(765\) 302.137 + 99.7889i 0.394951 + 0.130443i
\(766\) 688.730 0.899125
\(767\) −667.893 + 667.893i −0.870786 + 0.870786i
\(768\) −19.5959 19.5959i −0.0255155 0.0255155i
\(769\) 744.420i 0.968037i 0.875058 + 0.484018i \(0.160823\pi\)
−0.875058 + 0.484018i \(0.839177\pi\)
\(770\) 654.999 + 1301.03i 0.850647 + 1.68965i
\(771\) 455.380 0.590635
\(772\) −270.100 + 270.100i −0.349870 + 0.349870i
\(773\) 157.930 + 157.930i 0.204308 + 0.204308i 0.801843 0.597535i \(-0.203853\pi\)
−0.597535 + 0.801843i \(0.703853\pi\)
\(774\) 262.653i 0.339345i
\(775\) 270.119 364.322i 0.348541 0.470093i
\(776\) 213.464 0.275082
\(777\) −243.145 + 243.145i −0.312929 + 0.312929i
\(778\) 522.732 + 522.732i 0.671892 + 0.671892i
\(779\)