Properties

Label 690.3.k.a.277.9
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.9
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.95981 + 0.632643i) q^{5} -2.44949 q^{6} +(3.11187 + 3.11187i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.95981 + 0.632643i) q^{5} -2.44949 q^{6} +(3.11187 + 3.11187i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(4.32717 + 5.59246i) q^{10} -11.9521 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.79511 + 6.79511i) q^{13} +6.22373i q^{14} +(-6.84933 + 5.29968i) q^{15} -4.00000 q^{16} +(-3.44295 - 3.44295i) q^{17} +(3.00000 - 3.00000i) q^{18} +27.8436i q^{19} +(-1.26529 + 9.91963i) q^{20} -7.62248 q^{21} +(-11.9521 - 11.9521i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(24.1995 + 6.27559i) q^{25} -13.5902 q^{26} +(3.67423 + 3.67423i) q^{27} +(-6.22373 + 6.22373i) q^{28} +26.4720i q^{29} +(-12.1490 - 1.54965i) q^{30} -16.0271 q^{31} +(-4.00000 - 4.00000i) q^{32} +(14.6383 - 14.6383i) q^{33} -6.88590i q^{34} +(13.4656 + 17.4030i) q^{35} +6.00000 q^{36} +(13.6416 + 13.6416i) q^{37} +(-27.8436 + 27.8436i) q^{38} -16.6446i q^{39} +(-11.1849 + 8.65434i) q^{40} +32.3332 q^{41} +(-7.62248 - 7.62248i) q^{42} +(-22.4332 + 22.4332i) q^{43} -23.9043i q^{44} +(1.89793 - 14.8794i) q^{45} +6.78233 q^{46} +(-35.7929 - 35.7929i) q^{47} +(4.89898 - 4.89898i) q^{48} -29.6326i q^{49} +(17.9239 + 30.4751i) q^{50} +8.43348 q^{51} +(-13.5902 - 13.5902i) q^{52} +(-41.6197 + 41.6197i) q^{53} +7.34847i q^{54} +(-59.2803 - 7.56143i) q^{55} -12.4475 q^{56} +(-34.1013 - 34.1013i) q^{57} +(-26.4720 + 26.4720i) q^{58} +59.3699i q^{59} +(-10.5994 - 13.6987i) q^{60} +9.79153 q^{61} +(-16.0271 - 16.0271i) q^{62} +(9.33560 - 9.33560i) q^{63} -8.00000i q^{64} +(-38.0014 + 29.4036i) q^{65} +29.2766 q^{66} +(-35.1732 - 35.1732i) q^{67} +(6.88590 - 6.88590i) q^{68} +8.30662i q^{69} +(-3.93740 + 30.8686i) q^{70} +28.4741 q^{71} +(6.00000 + 6.00000i) q^{72} +(-2.27141 + 2.27141i) q^{73} +27.2833i q^{74} +(-37.3242 + 21.9523i) q^{75} -55.6872 q^{76} +(-37.1934 - 37.1934i) q^{77} +(16.6446 - 16.6446i) q^{78} +21.6053i q^{79} +(-19.8393 - 2.53057i) q^{80} -9.00000 q^{81} +(32.3332 + 32.3332i) q^{82} +(-48.0807 + 48.0807i) q^{83} -15.2450i q^{84} +(-14.8982 - 19.2546i) q^{85} -44.8664 q^{86} +(-32.4215 - 32.4215i) q^{87} +(23.9043 - 23.9043i) q^{88} -113.080i q^{89} +(16.7774 - 12.9815i) q^{90} -42.2909 q^{91} +(6.78233 + 6.78233i) q^{92} +(19.6291 - 19.6291i) q^{93} -71.5858i q^{94} +(-17.6151 + 138.099i) q^{95} +9.79796 q^{96} +(43.1625 + 43.1625i) q^{97} +(29.6326 - 29.6326i) q^{98} +35.8564i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 4.95981 + 0.632643i 0.991963 + 0.126529i
\(6\) −2.44949 −0.408248
\(7\) 3.11187 + 3.11187i 0.444552 + 0.444552i 0.893539 0.448986i \(-0.148215\pi\)
−0.448986 + 0.893539i \(0.648215\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 4.32717 + 5.59246i 0.432717 + 0.559246i
\(11\) −11.9521 −1.08656 −0.543278 0.839553i \(-0.682817\pi\)
−0.543278 + 0.839553i \(0.682817\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −6.79511 + 6.79511i −0.522701 + 0.522701i −0.918386 0.395685i \(-0.870507\pi\)
0.395685 + 0.918386i \(0.370507\pi\)
\(14\) 6.22373i 0.444552i
\(15\) −6.84933 + 5.29968i −0.456622 + 0.353312i
\(16\) −4.00000 −0.250000
\(17\) −3.44295 3.44295i −0.202527 0.202527i 0.598555 0.801082i \(-0.295742\pi\)
−0.801082 + 0.598555i \(0.795742\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 27.8436i 1.46545i 0.680524 + 0.732726i \(0.261752\pi\)
−0.680524 + 0.732726i \(0.738248\pi\)
\(20\) −1.26529 + 9.91963i −0.0632643 + 0.495981i
\(21\) −7.62248 −0.362975
\(22\) −11.9521 11.9521i −0.543278 0.543278i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 24.1995 + 6.27559i 0.967981 + 0.251023i
\(26\) −13.5902 −0.522701
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −6.22373 + 6.22373i −0.222276 + 0.222276i
\(29\) 26.4720i 0.912829i 0.889767 + 0.456415i \(0.150867\pi\)
−0.889767 + 0.456415i \(0.849133\pi\)
\(30\) −12.1490 1.54965i −0.404967 0.0516551i
\(31\) −16.0271 −0.517003 −0.258501 0.966011i \(-0.583229\pi\)
−0.258501 + 0.966011i \(0.583229\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 14.6383 14.6383i 0.443585 0.443585i
\(34\) 6.88590i 0.202527i
\(35\) 13.4656 + 17.4030i 0.384731 + 0.497228i
\(36\) 6.00000 0.166667
\(37\) 13.6416 + 13.6416i 0.368693 + 0.368693i 0.867000 0.498307i \(-0.166045\pi\)
−0.498307 + 0.867000i \(0.666045\pi\)
\(38\) −27.8436 + 27.8436i −0.732726 + 0.732726i
\(39\) 16.6446i 0.426783i
\(40\) −11.1849 + 8.65434i −0.279623 + 0.216359i
\(41\) 32.3332 0.788615 0.394307 0.918979i \(-0.370985\pi\)
0.394307 + 0.918979i \(0.370985\pi\)
\(42\) −7.62248 7.62248i −0.181488 0.181488i
\(43\) −22.4332 + 22.4332i −0.521702 + 0.521702i −0.918085 0.396383i \(-0.870265\pi\)
0.396383 + 0.918085i \(0.370265\pi\)
\(44\) 23.9043i 0.543278i
\(45\) 1.89793 14.8794i 0.0421762 0.330654i
\(46\) 6.78233 0.147442
\(47\) −35.7929 35.7929i −0.761551 0.761551i 0.215052 0.976603i \(-0.431008\pi\)
−0.976603 + 0.215052i \(0.931008\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 29.6326i 0.604746i
\(50\) 17.9239 + 30.4751i 0.358479 + 0.609502i
\(51\) 8.43348 0.165362
\(52\) −13.5902 13.5902i −0.261350 0.261350i
\(53\) −41.6197 + 41.6197i −0.785277 + 0.785277i −0.980716 0.195439i \(-0.937387\pi\)
0.195439 + 0.980716i \(0.437387\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −59.2803 7.56143i −1.07782 0.137481i
\(56\) −12.4475 −0.222276
\(57\) −34.1013 34.1013i −0.598268 0.598268i
\(58\) −26.4720 + 26.4720i −0.456415 + 0.456415i
\(59\) 59.3699i 1.00627i 0.864208 + 0.503135i \(0.167820\pi\)
−0.864208 + 0.503135i \(0.832180\pi\)
\(60\) −10.5994 13.6987i −0.176656 0.228311i
\(61\) 9.79153 0.160517 0.0802584 0.996774i \(-0.474425\pi\)
0.0802584 + 0.996774i \(0.474425\pi\)
\(62\) −16.0271 16.0271i −0.258501 0.258501i
\(63\) 9.33560 9.33560i 0.148184 0.148184i
\(64\) 8.00000i 0.125000i
\(65\) −38.0014 + 29.4036i −0.584636 + 0.452363i
\(66\) 29.2766 0.443585
\(67\) −35.1732 35.1732i −0.524972 0.524972i 0.394097 0.919069i \(-0.371058\pi\)
−0.919069 + 0.394097i \(0.871058\pi\)
\(68\) 6.88590 6.88590i 0.101263 0.101263i
\(69\) 8.30662i 0.120386i
\(70\) −3.93740 + 30.8686i −0.0562486 + 0.440979i
\(71\) 28.4741 0.401044 0.200522 0.979689i \(-0.435736\pi\)
0.200522 + 0.979689i \(0.435736\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −2.27141 + 2.27141i −0.0311152 + 0.0311152i −0.722493 0.691378i \(-0.757004\pi\)
0.691378 + 0.722493i \(0.257004\pi\)
\(74\) 27.2833i 0.368693i
\(75\) −37.3242 + 21.9523i −0.497656 + 0.292697i
\(76\) −55.6872 −0.732726
\(77\) −37.1934 37.1934i −0.483031 0.483031i
\(78\) 16.6446 16.6446i 0.213392 0.213392i
\(79\) 21.6053i 0.273485i 0.990607 + 0.136742i \(0.0436632\pi\)
−0.990607 + 0.136742i \(0.956337\pi\)
\(80\) −19.8393 2.53057i −0.247991 0.0316322i
\(81\) −9.00000 −0.111111
\(82\) 32.3332 + 32.3332i 0.394307 + 0.394307i
\(83\) −48.0807 + 48.0807i −0.579286 + 0.579286i −0.934706 0.355421i \(-0.884338\pi\)
0.355421 + 0.934706i \(0.384338\pi\)
\(84\) 15.2450i 0.181488i
\(85\) −14.8982 19.2546i −0.175273 0.226524i
\(86\) −44.8664 −0.521702
\(87\) −32.4215 32.4215i −0.372661 0.372661i
\(88\) 23.9043 23.9043i 0.271639 0.271639i
\(89\) 113.080i 1.27057i −0.772279 0.635283i \(-0.780883\pi\)
0.772279 0.635283i \(-0.219117\pi\)
\(90\) 16.7774 12.9815i 0.186415 0.144239i
\(91\) −42.2909 −0.464736
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 19.6291 19.6291i 0.211065 0.211065i
\(94\) 71.5858i 0.761551i
\(95\) −17.6151 + 138.099i −0.185422 + 1.45367i
\(96\) 9.79796 0.102062
\(97\) 43.1625 + 43.1625i 0.444974 + 0.444974i 0.893680 0.448705i \(-0.148115\pi\)
−0.448705 + 0.893680i \(0.648115\pi\)
\(98\) 29.6326 29.6326i 0.302373 0.302373i
\(99\) 35.8564i 0.362186i
\(100\) −12.5512 + 48.3991i −0.125512 + 0.483991i
\(101\) 53.6055 0.530747 0.265374 0.964146i \(-0.414505\pi\)
0.265374 + 0.964146i \(0.414505\pi\)
\(102\) 8.43348 + 8.43348i 0.0826811 + 0.0826811i
\(103\) −8.64457 + 8.64457i −0.0839279 + 0.0839279i −0.747824 0.663897i \(-0.768902\pi\)
0.663897 + 0.747824i \(0.268902\pi\)
\(104\) 27.1804i 0.261350i
\(105\) −37.8061 4.82231i −0.360058 0.0459268i
\(106\) −83.2394 −0.785277
\(107\) 39.5516 + 39.5516i 0.369641 + 0.369641i 0.867346 0.497705i \(-0.165824\pi\)
−0.497705 + 0.867346i \(0.665824\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 6.74005i 0.0618353i −0.999522 0.0309176i \(-0.990157\pi\)
0.999522 0.0309176i \(-0.00984296\pi\)
\(110\) −51.7189 66.8418i −0.470172 0.607652i
\(111\) −33.4151 −0.301037
\(112\) −12.4475 12.4475i −0.111138 0.111138i
\(113\) 116.074 116.074i 1.02720 1.02720i 0.0275812 0.999620i \(-0.491220\pi\)
0.999620 0.0275812i \(-0.00878050\pi\)
\(114\) 68.2026i 0.598268i
\(115\) 18.9649 14.6742i 0.164913 0.127601i
\(116\) −52.9441 −0.456415
\(117\) 20.3853 + 20.3853i 0.174234 + 0.174234i
\(118\) −59.3699 + 59.3699i −0.503135 + 0.503135i
\(119\) 21.4280i 0.180067i
\(120\) 3.09931 24.2980i 0.0258275 0.202484i
\(121\) 21.8533 0.180606
\(122\) 9.79153 + 9.79153i 0.0802584 + 0.0802584i
\(123\) −39.5999 + 39.5999i −0.321951 + 0.321951i
\(124\) 32.0542i 0.258501i
\(125\) 116.055 + 46.4354i 0.928440 + 0.371483i
\(126\) 18.6712 0.148184
\(127\) 2.15703 + 2.15703i 0.0169845 + 0.0169845i 0.715548 0.698564i \(-0.246177\pi\)
−0.698564 + 0.715548i \(0.746177\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 54.9499i 0.425968i
\(130\) −67.4050 8.59776i −0.518500 0.0661366i
\(131\) 260.534 1.98881 0.994404 0.105640i \(-0.0336892\pi\)
0.994404 + 0.105640i \(0.0336892\pi\)
\(132\) 29.2766 + 29.2766i 0.221792 + 0.221792i
\(133\) −86.6455 + 86.6455i −0.651470 + 0.651470i
\(134\) 70.3463i 0.524972i
\(135\) 15.8990 + 20.5480i 0.117771 + 0.152207i
\(136\) 13.7718 0.101263
\(137\) −0.350640 0.350640i −0.00255941 0.00255941i 0.705826 0.708385i \(-0.250576\pi\)
−0.708385 + 0.705826i \(0.750576\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 115.396i 0.830185i 0.909779 + 0.415092i \(0.136251\pi\)
−0.909779 + 0.415092i \(0.863749\pi\)
\(140\) −34.8060 + 26.9312i −0.248614 + 0.192365i
\(141\) 87.6743 0.621803
\(142\) 28.4741 + 28.4741i 0.200522 + 0.200522i
\(143\) 81.2160 81.2160i 0.567944 0.567944i
\(144\) 12.0000i 0.0833333i
\(145\) −16.7474 + 131.296i −0.115499 + 0.905493i
\(146\) −4.54282 −0.0311152
\(147\) 36.2923 + 36.2923i 0.246887 + 0.246887i
\(148\) −27.2833 + 27.2833i −0.184346 + 0.184346i
\(149\) 276.290i 1.85429i −0.374699 0.927146i \(-0.622254\pi\)
0.374699 0.927146i \(-0.377746\pi\)
\(150\) −59.2765 15.3720i −0.395177 0.102480i
\(151\) 37.7638 0.250091 0.125046 0.992151i \(-0.460092\pi\)
0.125046 + 0.992151i \(0.460092\pi\)
\(152\) −55.6872 55.6872i −0.366363 0.366363i
\(153\) −10.3289 + 10.3289i −0.0675089 + 0.0675089i
\(154\) 74.3868i 0.483031i
\(155\) −79.4913 10.1394i −0.512847 0.0654156i
\(156\) 33.2891 0.213392
\(157\) 122.971 + 122.971i 0.783253 + 0.783253i 0.980378 0.197126i \(-0.0631607\pi\)
−0.197126 + 0.980378i \(0.563161\pi\)
\(158\) −21.6053 + 21.6053i −0.136742 + 0.136742i
\(159\) 101.947i 0.641176i
\(160\) −17.3087 22.3698i −0.108179 0.139811i
\(161\) 21.1057 0.131091
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −21.6235 + 21.6235i −0.132659 + 0.132659i −0.770319 0.637659i \(-0.779903\pi\)
0.637659 + 0.770319i \(0.279903\pi\)
\(164\) 64.6664i 0.394307i
\(165\) 81.8641 63.3425i 0.496146 0.383894i
\(166\) −96.1615 −0.579286
\(167\) 79.3633 + 79.3633i 0.475229 + 0.475229i 0.903602 0.428373i \(-0.140913\pi\)
−0.428373 + 0.903602i \(0.640913\pi\)
\(168\) 15.2450 15.2450i 0.0907439 0.0907439i
\(169\) 76.6530i 0.453568i
\(170\) 4.35632 34.1528i 0.0256254 0.200899i
\(171\) 83.5308 0.488484
\(172\) −44.8664 44.8664i −0.260851 0.260851i
\(173\) 167.187 167.187i 0.966399 0.966399i −0.0330549 0.999454i \(-0.510524\pi\)
0.999454 + 0.0330549i \(0.0105236\pi\)
\(174\) 64.8430i 0.372661i
\(175\) 55.7769 + 94.8345i 0.318725 + 0.541911i
\(176\) 47.8085 0.271639
\(177\) −72.7130 72.7130i −0.410808 0.410808i
\(178\) 113.080 113.080i 0.635283 0.635283i
\(179\) 88.2952i 0.493269i −0.969109 0.246635i \(-0.920675\pi\)
0.969109 0.246635i \(-0.0793247\pi\)
\(180\) 29.7589 + 3.79586i 0.165327 + 0.0210881i
\(181\) 275.272 1.52084 0.760420 0.649432i \(-0.224993\pi\)
0.760420 + 0.649432i \(0.224993\pi\)
\(182\) −42.2909 42.2909i −0.232368 0.232368i
\(183\) −11.9921 + 11.9921i −0.0655307 + 0.0655307i
\(184\) 13.5647i 0.0737210i
\(185\) 59.0297 + 76.2903i 0.319080 + 0.412380i
\(186\) 39.2582 0.211065
\(187\) 41.1506 + 41.1506i 0.220057 + 0.220057i
\(188\) 71.5858 71.5858i 0.380775 0.380775i
\(189\) 22.8675i 0.120992i
\(190\) −155.714 + 120.484i −0.819548 + 0.634126i
\(191\) 284.801 1.49111 0.745553 0.666447i \(-0.232186\pi\)
0.745553 + 0.666447i \(0.232186\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −71.5610 + 71.5610i −0.370782 + 0.370782i −0.867762 0.496980i \(-0.834442\pi\)
0.496980 + 0.867762i \(0.334442\pi\)
\(194\) 86.3250i 0.444974i
\(195\) 10.5301 82.5539i 0.0540003 0.423353i
\(196\) 59.2652 0.302373
\(197\) 214.648 + 214.648i 1.08958 + 1.08958i 0.995571 + 0.0940112i \(0.0299690\pi\)
0.0940112 + 0.995571i \(0.470031\pi\)
\(198\) −35.8564 + 35.8564i −0.181093 + 0.181093i
\(199\) 89.3086i 0.448787i 0.974499 + 0.224394i \(0.0720401\pi\)
−0.974499 + 0.224394i \(0.927960\pi\)
\(200\) −60.9502 + 35.8479i −0.304751 + 0.179239i
\(201\) 86.1563 0.428638
\(202\) 53.6055 + 53.6055i 0.265374 + 0.265374i
\(203\) −82.3775 + 82.3775i −0.405800 + 0.405800i
\(204\) 16.8670i 0.0826811i
\(205\) 160.367 + 20.4554i 0.782277 + 0.0997823i
\(206\) −17.2891 −0.0839279
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 27.1804 27.1804i 0.130675 0.130675i
\(209\) 332.790i 1.59230i
\(210\) −32.9838 42.6284i −0.157066 0.202992i
\(211\) −320.246 −1.51775 −0.758876 0.651235i \(-0.774251\pi\)
−0.758876 + 0.651235i \(0.774251\pi\)
\(212\) −83.2394 83.2394i −0.392639 0.392639i
\(213\) −34.8735 + 34.8735i −0.163725 + 0.163725i
\(214\) 79.1032i 0.369641i
\(215\) −125.457 + 97.0723i −0.583520 + 0.451499i
\(216\) −14.6969 −0.0680414
\(217\) −49.8741 49.8741i −0.229835 0.229835i
\(218\) 6.74005 6.74005i 0.0309176 0.0309176i
\(219\) 5.56379i 0.0254055i
\(220\) 15.1229 118.561i 0.0687403 0.538912i
\(221\) 46.7905 0.211722
\(222\) −33.4151 33.4151i −0.150518 0.150518i
\(223\) −58.8321 + 58.8321i −0.263821 + 0.263821i −0.826604 0.562783i \(-0.809731\pi\)
0.562783 + 0.826604i \(0.309731\pi\)
\(224\) 24.8949i 0.111138i
\(225\) 18.8268 72.5986i 0.0836745 0.322660i
\(226\) 232.147 1.02720
\(227\) −80.2967 80.2967i −0.353730 0.353730i 0.507766 0.861495i \(-0.330472\pi\)
−0.861495 + 0.507766i \(0.830472\pi\)
\(228\) 68.2026 68.2026i 0.299134 0.299134i
\(229\) 93.0094i 0.406154i −0.979163 0.203077i \(-0.934906\pi\)
0.979163 0.203077i \(-0.0650942\pi\)
\(230\) 33.6391 + 4.29079i 0.146257 + 0.0186556i
\(231\) 91.1049 0.394393
\(232\) −52.9441 52.9441i −0.228207 0.228207i
\(233\) −182.811 + 182.811i −0.784598 + 0.784598i −0.980603 0.196005i \(-0.937203\pi\)
0.196005 + 0.980603i \(0.437203\pi\)
\(234\) 40.7707i 0.174234i
\(235\) −154.882 200.170i −0.659072 0.851788i
\(236\) −118.740 −0.503135
\(237\) −26.4610 26.4610i −0.111650 0.111650i
\(238\) 21.4280 21.4280i 0.0900337 0.0900337i
\(239\) 180.221i 0.754061i 0.926201 + 0.377030i \(0.123055\pi\)
−0.926201 + 0.377030i \(0.876945\pi\)
\(240\) 27.3973 21.1987i 0.114156 0.0883280i
\(241\) −79.4799 −0.329792 −0.164896 0.986311i \(-0.552729\pi\)
−0.164896 + 0.986311i \(0.552729\pi\)
\(242\) 21.8533 + 21.8533i 0.0903029 + 0.0903029i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 19.5831i 0.0802584i
\(245\) 18.7468 146.972i 0.0765177 0.599886i
\(246\) −79.1998 −0.321951
\(247\) −189.200 189.200i −0.765993 0.765993i
\(248\) 32.0542 32.0542i 0.129251 0.129251i
\(249\) 117.773i 0.472985i
\(250\) 69.6196 + 162.490i 0.278478 + 0.649961i
\(251\) 348.706 1.38927 0.694633 0.719364i \(-0.255567\pi\)
0.694633 + 0.719364i \(0.255567\pi\)
\(252\) 18.6712 + 18.6712i 0.0740921 + 0.0740921i
\(253\) −40.5316 + 40.5316i −0.160204 + 0.160204i
\(254\) 4.31405i 0.0169845i
\(255\) 41.8285 + 5.33538i 0.164033 + 0.0209231i
\(256\) 16.0000 0.0625000
\(257\) −170.411 170.411i −0.663077 0.663077i 0.293027 0.956104i \(-0.405337\pi\)
−0.956104 + 0.293027i \(0.905337\pi\)
\(258\) 54.9499 54.9499i 0.212984 0.212984i
\(259\) 84.9019i 0.327807i
\(260\) −58.8072 76.0027i −0.226182 0.292318i
\(261\) 79.4161 0.304276
\(262\) 260.534 + 260.534i 0.994404 + 0.994404i
\(263\) −92.8602 + 92.8602i −0.353081 + 0.353081i −0.861254 0.508174i \(-0.830321\pi\)
0.508174 + 0.861254i \(0.330321\pi\)
\(264\) 58.5532i 0.221792i
\(265\) −232.756 + 180.096i −0.878326 + 0.679606i
\(266\) −173.291 −0.651470
\(267\) 138.495 + 138.495i 0.518707 + 0.518707i
\(268\) 70.3463 70.3463i 0.262486 0.262486i
\(269\) 71.4621i 0.265658i −0.991139 0.132829i \(-0.957594\pi\)
0.991139 0.132829i \(-0.0424062\pi\)
\(270\) −4.64896 + 36.4470i −0.0172184 + 0.134989i
\(271\) 115.820 0.427380 0.213690 0.976902i \(-0.431452\pi\)
0.213690 + 0.976902i \(0.431452\pi\)
\(272\) 13.7718 + 13.7718i 0.0506316 + 0.0506316i
\(273\) 51.7956 51.7956i 0.189728 0.189728i
\(274\) 0.701280i 0.00255941i
\(275\) −289.236 75.0066i −1.05177 0.272751i
\(276\) −16.6132 −0.0601929
\(277\) 252.887 + 252.887i 0.912949 + 0.912949i 0.996503 0.0835544i \(-0.0266273\pi\)
−0.0835544 + 0.996503i \(0.526627\pi\)
\(278\) −115.396 + 115.396i −0.415092 + 0.415092i
\(279\) 48.0812i 0.172334i
\(280\) −61.7371 7.87480i −0.220490 0.0281243i
\(281\) 505.455 1.79877 0.899386 0.437156i \(-0.144014\pi\)
0.899386 + 0.437156i \(0.144014\pi\)
\(282\) 87.6743 + 87.6743i 0.310902 + 0.310902i
\(283\) −291.311 + 291.311i −1.02937 + 1.02937i −0.0298108 + 0.999556i \(0.509490\pi\)
−0.999556 + 0.0298108i \(0.990510\pi\)
\(284\) 56.9482i 0.200522i
\(285\) −147.562 190.710i −0.517762 0.669158i
\(286\) 162.432 0.567944
\(287\) 100.617 + 100.617i 0.350580 + 0.350580i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 265.292i 0.917966i
\(290\) −148.044 + 114.549i −0.510496 + 0.394997i
\(291\) −105.726 −0.363320
\(292\) −4.54282 4.54282i −0.0155576 0.0155576i
\(293\) −155.811 + 155.811i −0.531778 + 0.531778i −0.921101 0.389323i \(-0.872709\pi\)
0.389323 + 0.921101i \(0.372709\pi\)
\(294\) 72.5847i 0.246887i
\(295\) −37.5600 + 294.464i −0.127322 + 0.998182i
\(296\) −54.5666 −0.184346
\(297\) −43.9149 43.9149i −0.147862 0.147862i
\(298\) 276.290 276.290i 0.927146 0.927146i
\(299\) 46.0867i 0.154136i
\(300\) −43.9045 74.6485i −0.146348 0.248828i
\(301\) −139.618 −0.463848
\(302\) 37.7638 + 37.7638i 0.125046 + 0.125046i
\(303\) −65.6530 + 65.6530i −0.216677 + 0.216677i
\(304\) 111.374i 0.366363i
\(305\) 48.5642 + 6.19454i 0.159227 + 0.0203100i
\(306\) −20.6577 −0.0675089
\(307\) −1.45006 1.45006i −0.00472331 0.00472331i 0.704741 0.709464i \(-0.251063\pi\)
−0.709464 + 0.704741i \(0.751063\pi\)
\(308\) 74.3868 74.3868i 0.241516 0.241516i
\(309\) 21.1748i 0.0685268i
\(310\) −69.3519 89.6308i −0.223716 0.289131i
\(311\) 421.289 1.35463 0.677314 0.735694i \(-0.263144\pi\)
0.677314 + 0.735694i \(0.263144\pi\)
\(312\) 33.2891 + 33.2891i 0.106696 + 0.106696i
\(313\) −97.7145 + 97.7145i −0.312187 + 0.312187i −0.845756 0.533569i \(-0.820850\pi\)
0.533569 + 0.845756i \(0.320850\pi\)
\(314\) 245.941i 0.783253i
\(315\) 52.2089 40.3967i 0.165743 0.128244i
\(316\) −43.2106 −0.136742
\(317\) −314.471 314.471i −0.992023 0.992023i 0.00794582 0.999968i \(-0.497471\pi\)
−0.999968 + 0.00794582i \(0.997471\pi\)
\(318\) 101.947 101.947i 0.320588 0.320588i
\(319\) 316.397i 0.991841i
\(320\) 5.06115 39.6785i 0.0158161 0.123995i
\(321\) −96.8812 −0.301811
\(322\) 21.1057 + 21.1057i 0.0655457 + 0.0655457i
\(323\) 95.8641 95.8641i 0.296793 0.296793i
\(324\) 18.0000i 0.0555556i
\(325\) −207.082 + 121.795i −0.637175 + 0.374754i
\(326\) −43.2470 −0.132659
\(327\) 8.25484 + 8.25484i 0.0252442 + 0.0252442i
\(328\) −64.6664 + 64.6664i −0.197154 + 0.197154i
\(329\) 222.765i 0.677098i
\(330\) 145.207 + 18.5216i 0.440020 + 0.0561262i
\(331\) −49.4958 −0.149534 −0.0747670 0.997201i \(-0.523821\pi\)
−0.0747670 + 0.997201i \(0.523821\pi\)
\(332\) −96.1615 96.1615i −0.289643 0.289643i
\(333\) 40.9249 40.9249i 0.122898 0.122898i
\(334\) 158.727i 0.475229i
\(335\) −152.200 196.704i −0.454329 0.587177i
\(336\) 30.4899 0.0907439
\(337\) 278.322 + 278.322i 0.825883 + 0.825883i 0.986944 0.161062i \(-0.0514918\pi\)
−0.161062 + 0.986944i \(0.551492\pi\)
\(338\) −76.6530 + 76.6530i −0.226784 + 0.226784i
\(339\) 284.321i 0.838706i
\(340\) 38.5091 29.7965i 0.113262 0.0876367i
\(341\) 191.558 0.561753
\(342\) 83.5308 + 83.5308i 0.244242 + 0.244242i
\(343\) 244.694 244.694i 0.713394 0.713394i
\(344\) 89.7328i 0.260851i
\(345\) −5.25513 + 41.1993i −0.0152323 + 0.119418i
\(346\) 334.374 0.966399
\(347\) −169.044 169.044i −0.487158 0.487158i 0.420250 0.907408i \(-0.361942\pi\)
−0.907408 + 0.420250i \(0.861942\pi\)
\(348\) 64.8430 64.8430i 0.186330 0.186330i
\(349\) 407.984i 1.16901i −0.811390 0.584505i \(-0.801289\pi\)
0.811390 0.584505i \(-0.198711\pi\)
\(350\) −39.0576 + 150.611i −0.111593 + 0.430318i
\(351\) −49.9337 −0.142261
\(352\) 47.8085 + 47.8085i 0.135820 + 0.135820i
\(353\) 356.837 356.837i 1.01087 1.01087i 0.0109302 0.999940i \(-0.496521\pi\)
0.999940 0.0109302i \(-0.00347925\pi\)
\(354\) 145.426i 0.410808i
\(355\) 141.226 + 18.0139i 0.397821 + 0.0507435i
\(356\) 226.161 0.635283
\(357\) 26.2438 + 26.2438i 0.0735122 + 0.0735122i
\(358\) 88.2952 88.2952i 0.246635 0.246635i
\(359\) 321.635i 0.895919i −0.894054 0.447960i \(-0.852151\pi\)
0.894054 0.447960i \(-0.147849\pi\)
\(360\) 25.9630 + 33.5547i 0.0721195 + 0.0932076i
\(361\) −414.265 −1.14755
\(362\) 275.272 + 275.272i 0.760420 + 0.760420i
\(363\) −26.7647 + 26.7647i −0.0737320 + 0.0737320i
\(364\) 84.5819i 0.232368i
\(365\) −12.7028 + 9.82878i −0.0348021 + 0.0269282i
\(366\) −23.9842 −0.0655307
\(367\) 201.984 + 201.984i 0.550364 + 0.550364i 0.926546 0.376182i \(-0.122763\pi\)
−0.376182 + 0.926546i \(0.622763\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 96.9996i 0.262872i
\(370\) −17.2606 + 135.320i −0.0466502 + 0.365730i
\(371\) −259.030 −0.698194
\(372\) 39.2582 + 39.2582i 0.105533 + 0.105533i
\(373\) 304.698 304.698i 0.816884 0.816884i −0.168771 0.985655i \(-0.553980\pi\)
0.985655 + 0.168771i \(0.0539800\pi\)
\(374\) 82.3012i 0.220057i
\(375\) −199.009 + 85.2662i −0.530691 + 0.227377i
\(376\) 143.172 0.380775
\(377\) −179.880 179.880i −0.477136 0.477136i
\(378\) −22.8675 + 22.8675i −0.0604959 + 0.0604959i
\(379\) 665.410i 1.75570i 0.478937 + 0.877849i \(0.341022\pi\)
−0.478937 + 0.877849i \(0.658978\pi\)
\(380\) −276.198 35.2301i −0.726837 0.0927108i
\(381\) −5.28361 −0.0138678
\(382\) 284.801 + 284.801i 0.745553 + 0.745553i
\(383\) −160.655 + 160.655i −0.419466 + 0.419466i −0.885020 0.465554i \(-0.845855\pi\)
0.465554 + 0.885020i \(0.345855\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −160.942 208.003i −0.418032 0.540267i
\(386\) −143.122 −0.370782
\(387\) 67.2996 + 67.2996i 0.173901 + 0.173901i
\(388\) −86.3250 + 86.3250i −0.222487 + 0.222487i
\(389\) 303.465i 0.780117i −0.920790 0.390058i \(-0.872455\pi\)
0.920790 0.390058i \(-0.127545\pi\)
\(390\) 93.0840 72.0238i 0.238677 0.184677i
\(391\) −23.3512 −0.0597218
\(392\) 59.2652 + 59.2652i 0.151187 + 0.151187i
\(393\) −319.088 + 319.088i −0.811928 + 0.811928i
\(394\) 429.295i 1.08958i
\(395\) −13.6684 + 107.158i −0.0346036 + 0.271287i
\(396\) −71.7128 −0.181093
\(397\) 69.7386 + 69.7386i 0.175664 + 0.175664i 0.789463 0.613799i \(-0.210359\pi\)
−0.613799 + 0.789463i \(0.710359\pi\)
\(398\) −89.3086 + 89.3086i −0.224394 + 0.224394i
\(399\) 212.237i 0.531923i
\(400\) −96.7981 25.1023i −0.241995 0.0627559i
\(401\) 92.9627 0.231827 0.115914 0.993259i \(-0.463020\pi\)
0.115914 + 0.993259i \(0.463020\pi\)
\(402\) 86.1563 + 86.1563i 0.214319 + 0.214319i
\(403\) 108.906 108.906i 0.270238 0.270238i
\(404\) 107.211i 0.265374i
\(405\) −44.6383 5.69379i −0.110218 0.0140587i
\(406\) −164.755 −0.405800
\(407\) −163.047 163.047i −0.400606 0.400606i
\(408\) −16.8670 + 16.8670i −0.0413406 + 0.0413406i
\(409\) 302.309i 0.739141i −0.929203 0.369571i \(-0.879505\pi\)
0.929203 0.369571i \(-0.120495\pi\)
\(410\) 139.911 + 180.822i 0.341247 + 0.441029i
\(411\) 0.858889 0.00208975
\(412\) −17.2891 17.2891i −0.0419639 0.0419639i
\(413\) −184.751 + 184.751i −0.447340 + 0.447340i
\(414\) 20.3470i 0.0491473i
\(415\) −268.889 + 208.054i −0.647926 + 0.501334i
\(416\) 54.3609 0.130675
\(417\) −141.330 141.330i −0.338921 0.338921i
\(418\) 332.790 332.790i 0.796148 0.796148i
\(419\) 654.635i 1.56237i −0.624297 0.781187i \(-0.714615\pi\)
0.624297 0.781187i \(-0.285385\pi\)
\(420\) 9.64462 75.6122i 0.0229634 0.180029i
\(421\) 77.9606 0.185180 0.0925898 0.995704i \(-0.470485\pi\)
0.0925898 + 0.995704i \(0.470485\pi\)
\(422\) −320.246 320.246i −0.758876 0.758876i
\(423\) −107.379 + 107.379i −0.253850 + 0.253850i
\(424\) 166.479i 0.392639i
\(425\) −61.7113 104.924i −0.145203 0.246881i
\(426\) −69.7470 −0.163725
\(427\) 30.4699 + 30.4699i 0.0713581 + 0.0713581i
\(428\) −79.1032 + 79.1032i −0.184821 + 0.184821i
\(429\) 198.938i 0.463724i
\(430\) −222.529 28.3844i −0.517510 0.0660103i
\(431\) 486.621 1.12905 0.564526 0.825415i \(-0.309059\pi\)
0.564526 + 0.825415i \(0.309059\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −305.280 + 305.280i −0.705034 + 0.705034i −0.965487 0.260453i \(-0.916128\pi\)
0.260453 + 0.965487i \(0.416128\pi\)
\(434\) 99.7482i 0.229835i
\(435\) −140.293 181.316i −0.322514 0.416818i
\(436\) 13.4801 0.0309176
\(437\) 94.4222 + 94.4222i 0.216069 + 0.216069i
\(438\) 5.56379 5.56379i 0.0127027 0.0127027i
\(439\) 12.3810i 0.0282028i 0.999901 + 0.0141014i \(0.00448877\pi\)
−0.999901 + 0.0141014i \(0.995511\pi\)
\(440\) 133.684 103.438i 0.303826 0.235086i
\(441\) −88.8977 −0.201582
\(442\) 46.7905 + 46.7905i 0.105861 + 0.105861i
\(443\) −35.7800 + 35.7800i −0.0807676 + 0.0807676i −0.746336 0.665569i \(-0.768189\pi\)
0.665569 + 0.746336i \(0.268189\pi\)
\(444\) 66.8301i 0.150518i
\(445\) 71.5396 560.858i 0.160763 1.26036i
\(446\) −117.664 −0.263821
\(447\) 338.384 + 338.384i 0.757012 + 0.757012i
\(448\) 24.8949 24.8949i 0.0555690 0.0555690i
\(449\) 586.729i 1.30675i 0.757036 + 0.653373i \(0.226647\pi\)
−0.757036 + 0.653373i \(0.773353\pi\)
\(450\) 91.4253 53.7718i 0.203167 0.119493i
\(451\) −386.450 −0.856875
\(452\) 232.147 + 232.147i 0.513600 + 0.513600i
\(453\) −46.2510 + 46.2510i −0.102099 + 0.102099i
\(454\) 160.593i 0.353730i
\(455\) −209.755 26.7551i −0.461001 0.0588024i
\(456\) 136.405 0.299134
\(457\) −202.555 202.555i −0.443227 0.443227i 0.449868 0.893095i \(-0.351471\pi\)
−0.893095 + 0.449868i \(0.851471\pi\)
\(458\) 93.0094 93.0094i 0.203077 0.203077i
\(459\) 25.3004i 0.0551208i
\(460\) 29.3483 + 37.9299i 0.0638007 + 0.0824563i
\(461\) −527.587 −1.14444 −0.572220 0.820100i \(-0.693918\pi\)
−0.572220 + 0.820100i \(0.693918\pi\)
\(462\) 91.1049 + 91.1049i 0.197197 + 0.197197i
\(463\) −358.778 + 358.778i −0.774898 + 0.774898i −0.978958 0.204060i \(-0.934586\pi\)
0.204060 + 0.978958i \(0.434586\pi\)
\(464\) 105.888i 0.228207i
\(465\) 109.775 84.9384i 0.236075 0.182663i
\(466\) −365.623 −0.784598
\(467\) −485.338 485.338i −1.03927 1.03927i −0.999197 0.0400718i \(-0.987241\pi\)
−0.0400718 0.999197i \(-0.512759\pi\)
\(468\) −40.7707 + 40.7707i −0.0871168 + 0.0871168i
\(469\) 218.908i 0.466755i
\(470\) 45.2882 355.052i 0.0963579 0.755430i
\(471\) −301.215 −0.639523
\(472\) −118.740 118.740i −0.251567 0.251567i
\(473\) 268.124 268.124i 0.566859 0.566859i
\(474\) 52.9219i 0.111650i
\(475\) −174.735 + 673.802i −0.367863 + 1.41853i
\(476\) 42.8560 0.0900337
\(477\) 124.859 + 124.859i 0.261759 + 0.261759i
\(478\) −180.221 + 180.221i −0.377030 + 0.377030i
\(479\) 319.112i 0.666204i −0.942891 0.333102i \(-0.891905\pi\)
0.942891 0.333102i \(-0.108095\pi\)
\(480\) 48.5961 + 6.19861i 0.101242 + 0.0129138i
\(481\) −185.393 −0.385432
\(482\) −79.4799 79.4799i −0.164896 0.164896i
\(483\) −25.8491 + 25.8491i −0.0535178 + 0.0535178i
\(484\) 43.7066i 0.0903029i
\(485\) 186.772 + 241.385i 0.385096 + 0.497700i
\(486\) 22.0454 0.0453609
\(487\) −394.168 394.168i −0.809380 0.809380i 0.175160 0.984540i \(-0.443956\pi\)
−0.984540 + 0.175160i \(0.943956\pi\)
\(488\) −19.5831 + 19.5831i −0.0401292 + 0.0401292i
\(489\) 52.9665i 0.108316i
\(490\) 165.719 128.225i 0.338202 0.261684i
\(491\) 403.304 0.821393 0.410696 0.911772i \(-0.365286\pi\)
0.410696 + 0.911772i \(0.365286\pi\)
\(492\) −79.1998 79.1998i −0.160975 0.160975i
\(493\) 91.1420 91.1420i 0.184872 0.184872i
\(494\) 378.400i 0.765993i
\(495\) −22.6843 + 177.841i −0.0458268 + 0.359275i
\(496\) 64.1083 0.129251
\(497\) 88.6076 + 88.6076i 0.178285 + 0.178285i
\(498\) 117.773 117.773i 0.236492 0.236492i
\(499\) 970.563i 1.94502i −0.232868 0.972508i \(-0.574811\pi\)
0.232868 0.972508i \(-0.425189\pi\)
\(500\) −92.8708 + 232.110i −0.185742 + 0.464220i
\(501\) −194.400 −0.388023
\(502\) 348.706 + 348.706i 0.694633 + 0.694633i
\(503\) −526.039 + 526.039i −1.04580 + 1.04580i −0.0469034 + 0.998899i \(0.514935\pi\)
−0.998899 + 0.0469034i \(0.985065\pi\)
\(504\) 37.3424i 0.0740921i
\(505\) 265.873 + 33.9131i 0.526481 + 0.0671547i
\(506\) −81.0633 −0.160204
\(507\) −93.8803 93.8803i −0.185168 0.185168i
\(508\) −4.31405 + 4.31405i −0.00849223 + 0.00849223i
\(509\) 928.920i 1.82499i 0.409088 + 0.912495i \(0.365847\pi\)
−0.409088 + 0.912495i \(0.634153\pi\)
\(510\) 36.4931 + 47.1639i 0.0715551 + 0.0924782i
\(511\) −14.1366 −0.0276647
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −102.304 + 102.304i −0.199423 + 0.199423i
\(514\) 340.822i 0.663077i
\(515\) −48.3444 + 37.4065i −0.0938726 + 0.0726341i
\(516\) 109.900 0.212984
\(517\) 427.801 + 427.801i 0.827468 + 0.827468i
\(518\) −84.9019 + 84.9019i −0.163903 + 0.163903i
\(519\) 409.523i 0.789061i
\(520\) 17.1955 134.810i 0.0330683 0.259250i
\(521\) −299.847 −0.575522 −0.287761 0.957702i \(-0.592911\pi\)
−0.287761 + 0.957702i \(0.592911\pi\)
\(522\) 79.4161 + 79.4161i 0.152138 + 0.152138i
\(523\) −421.509 + 421.509i −0.805944 + 0.805944i −0.984017 0.178073i \(-0.943014\pi\)
0.178073 + 0.984017i \(0.443014\pi\)
\(524\) 521.068i 0.994404i
\(525\) −184.460 47.8356i −0.351353 0.0911153i
\(526\) −185.720 −0.353081
\(527\) 55.1805 + 55.1805i 0.104707 + 0.104707i
\(528\) −58.5532 + 58.5532i −0.110896 + 0.110896i
\(529\) 23.0000i 0.0434783i
\(530\) −412.852 52.6608i −0.778966 0.0993601i
\(531\) 178.110 0.335423
\(532\) −173.291 173.291i −0.325735 0.325735i
\(533\) −219.708 + 219.708i −0.412210 + 0.412210i
\(534\) 276.989i 0.518707i
\(535\) 171.147 + 221.191i 0.319900 + 0.413440i
\(536\) 140.693 0.262486
\(537\) 108.139 + 108.139i 0.201376 + 0.201376i
\(538\) 71.4621 71.4621i 0.132829 0.132829i
\(539\) 354.172i 0.657091i
\(540\) −41.0960 + 31.7981i −0.0761037 + 0.0588853i
\(541\) −437.815 −0.809270 −0.404635 0.914478i \(-0.632601\pi\)
−0.404635 + 0.914478i \(0.632601\pi\)
\(542\) 115.820 + 115.820i 0.213690 + 0.213690i
\(543\) −337.138 + 337.138i −0.620880 + 0.620880i
\(544\) 27.5436i 0.0506316i
\(545\) 4.26404 33.4294i 0.00782394 0.0613383i
\(546\) 103.591 0.189728
\(547\) 194.907 + 194.907i 0.356321 + 0.356321i 0.862455 0.506134i \(-0.168926\pi\)
−0.506134 + 0.862455i \(0.668926\pi\)
\(548\) 0.701280 0.701280i 0.00127971 0.00127971i
\(549\) 29.3746i 0.0535056i
\(550\) −214.229 364.242i −0.389508 0.662259i
\(551\) −737.077 −1.33771
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −67.2328 + 67.2328i −0.121578 + 0.121578i
\(554\) 505.774i 0.912949i
\(555\) −165.733 21.1398i −0.298617 0.0380897i
\(556\) −230.791 −0.415092
\(557\) 496.792 + 496.792i 0.891907 + 0.891907i 0.994703 0.102795i \(-0.0327786\pi\)
−0.102795 + 0.994703i \(0.532779\pi\)
\(558\) −48.0812 + 48.0812i −0.0861671 + 0.0861671i
\(559\) 304.872i 0.545389i
\(560\) −53.8623 69.6119i −0.0961827 0.124307i
\(561\) −100.798 −0.179676
\(562\) 505.455 + 505.455i 0.899386 + 0.899386i
\(563\) −165.676 + 165.676i −0.294273 + 0.294273i −0.838766 0.544493i \(-0.816722\pi\)
0.544493 + 0.838766i \(0.316722\pi\)
\(564\) 175.349i 0.310902i
\(565\) 649.137 502.271i 1.14892 0.888975i
\(566\) −582.621 −1.02937
\(567\) −28.0068 28.0068i −0.0493947 0.0493947i
\(568\) −56.9482 + 56.9482i −0.100261 + 0.100261i
\(569\) 1045.26i 1.83702i 0.395397 + 0.918510i \(0.370607\pi\)
−0.395397 + 0.918510i \(0.629393\pi\)
\(570\) 43.1479 338.272i 0.0756981 0.593460i
\(571\) 76.1504 0.133363 0.0666816 0.997774i \(-0.478759\pi\)
0.0666816 + 0.997774i \(0.478759\pi\)
\(572\) 162.432 + 162.432i 0.283972 + 0.283972i
\(573\) −348.809 + 348.809i −0.608741 + 0.608741i
\(574\) 201.233i 0.350580i
\(575\) 103.346 60.7830i 0.179732 0.105710i
\(576\) −24.0000 −0.0416667
\(577\) −356.490 356.490i −0.617833 0.617833i 0.327142 0.944975i \(-0.393914\pi\)
−0.944975 + 0.327142i \(0.893914\pi\)
\(578\) 265.292 265.292i 0.458983 0.458983i
\(579\) 175.288i 0.302743i
\(580\) −262.593 33.4947i −0.452746 0.0577495i
\(581\) −299.242 −0.515046
\(582\) −105.726 105.726i −0.181660 0.181660i
\(583\) 497.444 497.444i 0.853248 0.853248i
\(584\) 9.08564i 0.0155576i
\(585\) 88.2108 + 114.004i 0.150788 + 0.194879i
\(586\) −311.622 −0.531778
\(587\) −82.5345 82.5345i −0.140604 0.140604i 0.633301 0.773905i \(-0.281699\pi\)
−0.773905 + 0.633301i \(0.781699\pi\)
\(588\) −72.5847 + 72.5847i −0.123443 + 0.123443i
\(589\) 446.251i 0.757642i
\(590\) −332.024 + 256.904i −0.562752 + 0.435430i
\(591\) −525.777 −0.889640
\(592\) −54.5666 54.5666i −0.0921732 0.0921732i
\(593\) 542.153 542.153i 0.914255 0.914255i −0.0823485 0.996604i \(-0.526242\pi\)
0.996604 + 0.0823485i \(0.0262420\pi\)
\(594\) 87.8298i 0.147862i
\(595\) 13.5563 106.279i 0.0227837 0.178620i
\(596\) 552.579 0.927146
\(597\) −109.380 109.380i −0.183217 0.183217i
\(598\) −46.0867 + 46.0867i −0.0770680 + 0.0770680i
\(599\) 846.862i 1.41379i −0.707317 0.706896i \(-0.750095\pi\)
0.707317 0.706896i \(-0.249905\pi\)
\(600\) 30.7440 118.553i 0.0512399 0.197588i
\(601\) −768.954 −1.27946 −0.639729 0.768600i \(-0.720953\pi\)
−0.639729 + 0.768600i \(0.720953\pi\)
\(602\) −139.618 139.618i −0.231924 0.231924i
\(603\) −105.519 + 105.519i −0.174991 + 0.174991i
\(604\) 75.5275i 0.125046i
\(605\) 108.388 + 13.8253i 0.179154 + 0.0228518i
\(606\) −131.306 −0.216677
\(607\) 203.884 + 203.884i 0.335889 + 0.335889i 0.854818 0.518929i \(-0.173669\pi\)
−0.518929 + 0.854818i \(0.673669\pi\)
\(608\) 111.374 111.374i 0.183181 0.183181i
\(609\) 201.783i 0.331335i
\(610\) 42.3696 + 54.7587i 0.0694584 + 0.0897684i
\(611\) 486.433 0.796126
\(612\) −20.6577 20.6577i −0.0337544 0.0337544i
\(613\) −68.5345 + 68.5345i −0.111802 + 0.111802i −0.760795 0.648993i \(-0.775191\pi\)
0.648993 + 0.760795i \(0.275191\pi\)
\(614\) 2.90011i 0.00472331i
\(615\) −221.461 + 171.356i −0.360099 + 0.278627i
\(616\) 148.774 0.241516
\(617\) −150.157 150.157i −0.243366 0.243366i 0.574875 0.818241i \(-0.305051\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(618\) 21.1748 21.1748i 0.0342634 0.0342634i
\(619\) 457.106i 0.738459i −0.929338 0.369230i \(-0.879622\pi\)
0.929338 0.369230i \(-0.120378\pi\)
\(620\) 20.2788 158.983i 0.0327078 0.256424i
\(621\) 24.9199 0.0401286
\(622\) 421.289 + 421.289i 0.677314 + 0.677314i
\(623\) 351.891 351.891i 0.564833 0.564833i
\(624\) 66.5782i 0.106696i
\(625\) 546.234 + 303.732i 0.873974 + 0.485972i
\(626\) −195.429 −0.312187
\(627\) 407.583 + 407.583i 0.650052 + 0.650052i
\(628\) −245.941 + 245.941i −0.391626 + 0.391626i
\(629\) 93.9350i 0.149340i
\(630\) 92.6057 + 11.8122i 0.146993 + 0.0187495i
\(631\) −305.258 −0.483768 −0.241884 0.970305i \(-0.577765\pi\)
−0.241884 + 0.970305i \(0.577765\pi\)
\(632\) −43.2106 43.2106i −0.0683712 0.0683712i
\(633\) 392.219 392.219i 0.619620 0.619620i
\(634\) 628.942i 0.992023i
\(635\) 9.33382 + 12.0631i 0.0146989 + 0.0189970i
\(636\) 203.894 0.320588
\(637\) 201.357 + 201.357i 0.316101 + 0.316101i
\(638\) 316.397 316.397i 0.495920 0.495920i
\(639\) 85.4223i 0.133681i
\(640\) 44.7397 34.6174i 0.0699057 0.0540896i
\(641\) 280.793 0.438055 0.219028 0.975719i \(-0.429711\pi\)
0.219028 + 0.975719i \(0.429711\pi\)
\(642\) −96.8812 96.8812i −0.150905 0.150905i
\(643\) −713.836 + 713.836i −1.11017 + 1.11017i −0.117038 + 0.993127i \(0.537340\pi\)
−0.993127 + 0.117038i \(0.962660\pi\)
\(644\) 42.2114i 0.0655457i
\(645\) 34.7637 272.541i 0.0538972 0.422545i
\(646\) 191.728 0.296793
\(647\) 397.749 + 397.749i 0.614759 + 0.614759i 0.944182 0.329424i \(-0.106854\pi\)
−0.329424 + 0.944182i \(0.606854\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 709.597i 1.09337i
\(650\) −328.877 85.2866i −0.505964 0.131210i
\(651\) 122.166 0.187659
\(652\) −43.2470 43.2470i −0.0663297 0.0663297i
\(653\) −217.770 + 217.770i −0.333491 + 0.333491i −0.853911 0.520419i \(-0.825776\pi\)
0.520419 + 0.853911i \(0.325776\pi\)
\(654\) 16.5097i 0.0252442i
\(655\) 1292.20 + 164.825i 1.97282 + 0.251641i
\(656\) −129.333 −0.197154
\(657\) 6.81423 + 6.81423i 0.0103717 + 0.0103717i
\(658\) 222.765 222.765i 0.338549 0.338549i
\(659\) 1073.09i 1.62836i 0.580610 + 0.814182i \(0.302814\pi\)
−0.580610 + 0.814182i \(0.697186\pi\)
\(660\) 126.685 + 163.728i 0.191947 + 0.248073i
\(661\) −326.114 −0.493365 −0.246683 0.969096i \(-0.579340\pi\)
−0.246683 + 0.969096i \(0.579340\pi\)
\(662\) −49.4958 49.4958i −0.0747670 0.0747670i
\(663\) −57.3064 + 57.3064i −0.0864350 + 0.0864350i
\(664\) 192.323i 0.289643i
\(665\) −484.561 + 374.930i −0.728664 + 0.563804i
\(666\) 81.8498 0.122898
\(667\) 89.7711 + 89.7711i 0.134589 + 0.134589i
\(668\) −158.727 + 158.727i −0.237615 + 0.237615i
\(669\) 144.109i 0.215409i
\(670\) 44.5041 348.905i 0.0664240 0.520753i
\(671\) −117.030 −0.174411
\(672\) 30.4899 + 30.4899i 0.0453719 + 0.0453719i
\(673\) 557.149 557.149i 0.827859 0.827859i −0.159361 0.987220i \(-0.550943\pi\)
0.987220 + 0.159361i \(0.0509435\pi\)
\(674\) 556.645i 0.825883i
\(675\) 65.8568 + 111.973i 0.0975656 + 0.165885i
\(676\) −153.306 −0.226784
\(677\) −819.127 819.127i −1.20994 1.20994i −0.971047 0.238890i \(-0.923216\pi\)
−0.238890 0.971047i \(-0.576784\pi\)
\(678\) −284.321 + 284.321i −0.419353 + 0.419353i
\(679\) 268.632i 0.395629i
\(680\) 68.3056 + 8.71264i 0.100449 + 0.0128127i
\(681\) 196.686 0.288819
\(682\) 191.558 + 191.558i 0.280876 + 0.280876i
\(683\) 220.351 220.351i 0.322622 0.322622i −0.527150 0.849772i \(-0.676739\pi\)
0.849772 + 0.527150i \(0.176739\pi\)
\(684\) 167.062i 0.244242i
\(685\) −1.51728 1.96094i −0.00221501 0.00286268i
\(686\) 489.388 0.713394
\(687\) 113.913 + 113.913i 0.165812 + 0.165812i
\(688\) 89.7328 89.7328i 0.130426 0.130426i
\(689\) 565.621i 0.820930i
\(690\) −46.4544 + 35.9442i −0.0673253 + 0.0520930i
\(691\) −256.102 −0.370626 −0.185313 0.982680i \(-0.559330\pi\)
−0.185313 + 0.982680i \(0.559330\pi\)
\(692\) 334.374 + 334.374i 0.483199 + 0.483199i
\(693\) −111.580 + 111.580i −0.161010 + 0.161010i
\(694\) 338.088i 0.487158i
\(695\) −73.0043 + 572.341i −0.105042 + 0.823512i
\(696\) 129.686 0.186330
\(697\) −111.322 111.322i −0.159715 0.159715i
\(698\) 407.984 407.984i 0.584505 0.584505i
\(699\) 447.794i 0.640622i
\(700\) −189.669 + 111.554i −0.270956 + 0.159363i
\(701\) −58.5051 −0.0834595 −0.0417297 0.999129i \(-0.513287\pi\)
−0.0417297 + 0.999129i \(0.513287\pi\)
\(702\) −49.9337 49.9337i −0.0711306 0.0711306i
\(703\) −379.832 + 379.832i −0.540302 + 0.540302i
\(704\) 95.6170i 0.135820i
\(705\) 434.848 + 55.4665i 0.616806 + 0.0786759i
\(706\) 713.675 1.01087
\(707\) 166.813 + 166.813i 0.235945 + 0.235945i
\(708\) 145.426 145.426i 0.205404 0.205404i
\(709\) 775.572i 1.09390i −0.837167 0.546948i \(-0.815789\pi\)
0.837167 0.546948i \(-0.184211\pi\)
\(710\) 123.212 + 159.240i 0.173539 + 0.224282i
\(711\) 64.8159 0.0911615
\(712\) 226.161 + 226.161i 0.317642 + 0.317642i
\(713\) −54.3505 + 54.3505i −0.0762279 + 0.0762279i
\(714\) 52.4877i 0.0735122i
\(715\) 454.197 351.436i 0.635241 0.491518i
\(716\) 176.590 0.246635
\(717\) −220.724 220.724i −0.307844 0.307844i
\(718\) 321.635 321.635i 0.447960 0.447960i
\(719\) 434.665i 0.604541i 0.953222 + 0.302271i \(0.0977446\pi\)
−0.953222 + 0.302271i \(0.902255\pi\)
\(720\) −7.59172 + 59.5178i −0.0105441 + 0.0826636i
\(721\) −53.8015 −0.0746207
\(722\) −414.265 414.265i −0.573775 0.573775i
\(723\) 97.3426 97.3426i 0.134637 0.134637i
\(724\) 550.544i 0.760420i
\(725\) −166.128 + 640.611i −0.229141 + 0.883601i
\(726\) −53.5294 −0.0737320
\(727\) −495.930 495.930i −0.682159 0.682159i 0.278327 0.960486i \(-0.410220\pi\)
−0.960486 + 0.278327i \(0.910220\pi\)
\(728\) 84.5819 84.5819i 0.116184 0.116184i
\(729\) 27.0000i 0.0370370i
\(730\) −22.5315 2.87398i −0.0308651 0.00393696i
\(731\) 154.473 0.211317
\(732\) −23.9842 23.9842i −0.0327654 0.0327654i
\(733\) 2.73615 2.73615i 0.00373282 0.00373282i −0.705238 0.708971i \(-0.749160\pi\)
0.708971 + 0.705238i \(0.249160\pi\)
\(734\) 403.967i 0.550364i
\(735\) 157.043 + 202.963i 0.213664 + 0.276141i
\(736\) −27.1293 −0.0368605
\(737\) 420.394 + 420.394i 0.570412 + 0.570412i
\(738\) 96.9996 96.9996i 0.131436 0.131436i
\(739\) 850.579i 1.15099i −0.817807 0.575493i \(-0.804810\pi\)
0.817807 0.575493i \(-0.195190\pi\)
\(740\) −152.581 + 118.059i −0.206190 + 0.159540i
\(741\) 463.444 0.625431
\(742\) −259.030 259.030i −0.349097 0.349097i
\(743\) −946.760 + 946.760i −1.27424 + 1.27424i −0.330397 + 0.943842i \(0.607183\pi\)
−0.943842 + 0.330397i \(0.892817\pi\)
\(744\) 78.5163i 0.105533i
\(745\) 174.793 1370.35i 0.234621 1.83939i
\(746\) 609.395 0.816884
\(747\) 144.242 + 144.242i 0.193095 + 0.193095i
\(748\) −82.3012 + 82.3012i −0.110028 + 0.110028i
\(749\) 246.159i 0.328650i
\(750\) −284.275 113.743i −0.379034 0.151657i
\(751\) 1016.35 1.35333 0.676666 0.736290i \(-0.263424\pi\)
0.676666 + 0.736290i \(0.263424\pi\)
\(752\) 143.172 + 143.172i 0.190388 + 0.190388i
\(753\) −427.075 + 427.075i −0.567165 + 0.567165i
\(754\) 359.761i 0.477136i
\(755\) 187.301 + 23.8910i 0.248081 + 0.0316437i
\(756\) −45.7349 −0.0604959
\(757\) −286.507 286.507i −0.378477 0.378477i 0.492075 0.870553i \(-0.336238\pi\)
−0.870553 + 0.492075i \(0.836238\pi\)
\(758\) −665.410 + 665.410i −0.877849 + 0.877849i
\(759\) 99.2818i 0.130806i
\(760\) −240.968 311.428i −0.317063 0.409774i
\(761\) 1051.65 1.38193 0.690964 0.722889i \(-0.257186\pi\)
0.690964 + 0.722889i \(0.257186\pi\)
\(762\) −5.28361 5.28361i −0.00693388 0.00693388i
\(763\) 20.9741 20.9741i 0.0274890 0.0274890i
\(764\) 569.602i 0.745553i
\(765\) −57.7637 + 44.6947i −0.0755081 + 0.0584245i
\(766\) −321.311 −0.419466
\(767\) −403.425 403.425i −0.525978 0.525978i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 1147.01i 1.49155i −0.666195 0.745777i \(-0.732078\pi\)
0.666195 0.745777i \(-0.267922\pi\)
\(770\) 47.0603 368.945i 0.0611173 0.479149i
\(771\) 417.420 0.541400
\(772\) −143.122 143.122i −0.185391 0.185391i
\(773\) 535.350 535.350i 0.692561 0.692561i −0.270234 0.962795i \(-0.587101\pi\)
0.962795 + 0.270234i \(0.0871009\pi\)
\(774\) 134.599i 0.173901i
\(775\) −387.848 100.579i −0.500449 0.129780i
\(776\) −172.650 −0.222487
\(777\) −103.983 103.983i −0.133826 0.133826i
\(778\) 303.465 303.465i 0.390058 0.390058i
\(779\) 900.272i