Properties

Label 690.3.k.a.277.7
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 277.7
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.90121 - 0.988992i) q^{5} -2.44949 q^{6} +(2.14995 + 2.14995i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.90121 - 0.988992i) q^{5} -2.44949 q^{6} +(2.14995 + 2.14995i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.91222 - 5.89021i) q^{10} -12.9969 q^{11} +(-2.44949 - 2.44949i) q^{12} +(10.2470 - 10.2470i) q^{13} +4.29989i q^{14} +(7.21400 - 4.79147i) q^{15} -4.00000 q^{16} +(-2.98774 - 2.98774i) q^{17} +(3.00000 - 3.00000i) q^{18} -26.4014i q^{19} +(1.97798 - 9.80243i) q^{20} -5.26627 q^{21} +(-12.9969 - 12.9969i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(23.0438 + 9.69452i) q^{25} +20.4940 q^{26} +(3.67423 + 3.67423i) q^{27} +(-4.29989 + 4.29989i) q^{28} +45.6115i q^{29} +(12.0055 + 2.42253i) q^{30} +37.4631 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.9179 - 15.9179i) q^{33} -5.97547i q^{34} +(-8.41107 - 12.6636i) q^{35} +6.00000 q^{36} +(-44.9599 - 44.9599i) q^{37} +(26.4014 - 26.4014i) q^{38} +25.0999i q^{39} +(11.7804 - 7.82444i) q^{40} +39.3742 q^{41} +(-5.26627 - 5.26627i) q^{42} +(29.7399 - 29.7399i) q^{43} -25.9939i q^{44} +(-2.96698 + 14.7036i) q^{45} +6.78233 q^{46} +(-10.2691 - 10.2691i) q^{47} +(4.89898 - 4.89898i) q^{48} -39.7555i q^{49} +(13.3493 + 32.7383i) q^{50} +7.31843 q^{51} +(20.4940 + 20.4940i) q^{52} +(34.6215 - 34.6215i) q^{53} +7.34847i q^{54} +(63.7007 + 12.8539i) q^{55} -8.59979 q^{56} +(32.3350 + 32.3350i) q^{57} +(-45.6115 + 45.6115i) q^{58} -22.8736i q^{59} +(9.58295 + 14.4280i) q^{60} -70.3445 q^{61} +(37.4631 + 37.4631i) q^{62} +(6.44984 - 6.44984i) q^{63} -8.00000i q^{64} +(-60.3568 + 40.0884i) q^{65} +31.8358 q^{66} +(19.6879 + 19.6879i) q^{67} +(5.97547 - 5.97547i) q^{68} +8.30662i q^{69} +(4.25256 - 21.0747i) q^{70} +131.287 q^{71} +(6.00000 + 6.00000i) q^{72} +(49.0534 - 49.0534i) q^{73} -89.9197i q^{74} +(-40.0961 + 16.3494i) q^{75} +52.8028 q^{76} +(-27.9427 - 27.9427i) q^{77} +(-25.0999 + 25.0999i) q^{78} -59.2011i q^{79} +(19.6049 + 3.95597i) q^{80} -9.00000 q^{81} +(39.3742 + 39.3742i) q^{82} +(-31.0483 + 31.0483i) q^{83} -10.5325i q^{84} +(11.6887 + 17.5984i) q^{85} +59.4799 q^{86} +(-55.8625 - 55.8625i) q^{87} +(25.9939 - 25.9939i) q^{88} -169.901i q^{89} +(-17.6706 + 11.7367i) q^{90} +44.0609 q^{91} +(6.78233 + 6.78233i) q^{92} +(-45.8827 + 45.8827i) q^{93} -20.5382i q^{94} +(-26.1108 + 129.399i) q^{95} +9.79796 q^{96} +(8.17591 + 8.17591i) q^{97} +(39.7555 - 39.7555i) q^{98} +38.9908i 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
\(5\) −4.90121 0.988992i −0.980243 0.197798i
\(6\) −2.44949 −0.408248
\(7\) 2.14995 + 2.14995i 0.307135 + 0.307135i 0.843797 0.536662i \(-0.180315\pi\)
−0.536662 + 0.843797i \(0.680315\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −3.91222 5.89021i −0.391222 0.589021i
\(11\) −12.9969 −1.18154 −0.590770 0.806840i \(-0.701176\pi\)
−0.590770 + 0.806840i \(0.701176\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 10.2470 10.2470i 0.788229 0.788229i −0.192975 0.981204i \(-0.561814\pi\)
0.981204 + 0.192975i \(0.0618136\pi\)
\(14\) 4.29989i 0.307135i
\(15\) 7.21400 4.79147i 0.480933 0.319432i
\(16\) −4.00000 −0.250000
\(17\) −2.98774 2.98774i −0.175749 0.175749i 0.613751 0.789500i \(-0.289660\pi\)
−0.789500 + 0.613751i \(0.789660\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 26.4014i 1.38955i −0.719228 0.694774i \(-0.755504\pi\)
0.719228 0.694774i \(-0.244496\pi\)
\(20\) 1.97798 9.80243i 0.0988992 0.490121i
\(21\) −5.26627 −0.250775
\(22\) −12.9969 12.9969i −0.590770 0.590770i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 23.0438 + 9.69452i 0.921752 + 0.387781i
\(26\) 20.4940 0.788229
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −4.29989 + 4.29989i −0.153568 + 0.153568i
\(29\) 45.6115i 1.57281i 0.617711 + 0.786406i \(0.288060\pi\)
−0.617711 + 0.786406i \(0.711940\pi\)
\(30\) 12.0055 + 2.42253i 0.400182 + 0.0807509i
\(31\) 37.4631 1.20849 0.604243 0.796800i \(-0.293476\pi\)
0.604243 + 0.796800i \(0.293476\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 15.9179 15.9179i 0.482361 0.482361i
\(34\) 5.97547i 0.175749i
\(35\) −8.41107 12.6636i −0.240316 0.361818i
\(36\) 6.00000 0.166667
\(37\) −44.9599 44.9599i −1.21513 1.21513i −0.969317 0.245815i \(-0.920945\pi\)
−0.245815 0.969317i \(-0.579055\pi\)
\(38\) 26.4014 26.4014i 0.694774 0.694774i
\(39\) 25.0999i 0.643586i
\(40\) 11.7804 7.82444i 0.294510 0.195611i
\(41\) 39.3742 0.960347 0.480173 0.877174i \(-0.340574\pi\)
0.480173 + 0.877174i \(0.340574\pi\)
\(42\) −5.26627 5.26627i −0.125387 0.125387i
\(43\) 29.7399 29.7399i 0.691627 0.691627i −0.270963 0.962590i \(-0.587342\pi\)
0.962590 + 0.270963i \(0.0873421\pi\)
\(44\) 25.9939i 0.590770i
\(45\) −2.96698 + 14.7036i −0.0659328 + 0.326748i
\(46\) 6.78233 0.147442
\(47\) −10.2691 10.2691i −0.218491 0.218491i 0.589371 0.807862i \(-0.299376\pi\)
−0.807862 + 0.589371i \(0.799376\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 39.7555i 0.811336i
\(50\) 13.3493 + 32.7383i 0.266985 + 0.654766i
\(51\) 7.31843 0.143499
\(52\) 20.4940 + 20.4940i 0.394114 + 0.394114i
\(53\) 34.6215 34.6215i 0.653235 0.653235i −0.300535 0.953771i \(-0.597165\pi\)
0.953771 + 0.300535i \(0.0971654\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 63.7007 + 12.8539i 1.15820 + 0.233707i
\(56\) −8.59979 −0.153568
\(57\) 32.3350 + 32.3350i 0.567281 + 0.567281i
\(58\) −45.6115 + 45.6115i −0.786406 + 0.786406i
\(59\) 22.8736i 0.387688i −0.981032 0.193844i \(-0.937904\pi\)
0.981032 0.193844i \(-0.0620955\pi\)
\(60\) 9.58295 + 14.4280i 0.159716 + 0.240467i
\(61\) −70.3445 −1.15319 −0.576595 0.817030i \(-0.695619\pi\)
−0.576595 + 0.817030i \(0.695619\pi\)
\(62\) 37.4631 + 37.4631i 0.604243 + 0.604243i
\(63\) 6.44984 6.44984i 0.102378 0.102378i
\(64\) 8.00000i 0.125000i
\(65\) −60.3568 + 40.0884i −0.928566 + 0.616745i
\(66\) 31.8358 0.482361
\(67\) 19.6879 + 19.6879i 0.293849 + 0.293849i 0.838599 0.544750i \(-0.183375\pi\)
−0.544750 + 0.838599i \(0.683375\pi\)
\(68\) 5.97547 5.97547i 0.0878746 0.0878746i
\(69\) 8.30662i 0.120386i
\(70\) 4.25256 21.0747i 0.0607509 0.301067i
\(71\) 131.287 1.84911 0.924557 0.381044i \(-0.124436\pi\)
0.924557 + 0.381044i \(0.124436\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 49.0534 49.0534i 0.671964 0.671964i −0.286205 0.958169i \(-0.592394\pi\)
0.958169 + 0.286205i \(0.0923937\pi\)
\(74\) 89.9197i 1.21513i
\(75\) −40.0961 + 16.3494i −0.534614 + 0.217993i
\(76\) 52.8028 0.694774
\(77\) −27.9427 27.9427i −0.362892 0.362892i
\(78\) −25.0999 + 25.0999i −0.321793 + 0.321793i
\(79\) 59.2011i 0.749381i −0.927150 0.374691i \(-0.877749\pi\)
0.927150 0.374691i \(-0.122251\pi\)
\(80\) 19.6049 + 3.95597i 0.245061 + 0.0494496i
\(81\) −9.00000 −0.111111
\(82\) 39.3742 + 39.3742i 0.480173 + 0.480173i
\(83\) −31.0483 + 31.0483i −0.374076 + 0.374076i −0.868960 0.494883i \(-0.835211\pi\)
0.494883 + 0.868960i \(0.335211\pi\)
\(84\) 10.5325i 0.125387i
\(85\) 11.6887 + 17.5984i 0.137514 + 0.207040i
\(86\) 59.4799 0.691627
\(87\) −55.8625 55.8625i −0.642097 0.642097i
\(88\) 25.9939 25.9939i 0.295385 0.295385i
\(89\) 169.901i 1.90900i −0.298219 0.954498i \(-0.596392\pi\)
0.298219 0.954498i \(-0.403608\pi\)
\(90\) −17.6706 + 11.7367i −0.196340 + 0.130407i
\(91\) 44.0609 0.484186
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −45.8827 + 45.8827i −0.493362 + 0.493362i
\(94\) 20.5382i 0.218491i
\(95\) −26.1108 + 129.399i −0.274850 + 1.36209i
\(96\) 9.79796 0.102062
\(97\) 8.17591 + 8.17591i 0.0842878 + 0.0842878i 0.747994 0.663706i \(-0.231017\pi\)
−0.663706 + 0.747994i \(0.731017\pi\)
\(98\) 39.7555 39.7555i 0.405668 0.405668i
\(99\) 38.9908i 0.393846i
\(100\) −19.3890 + 46.0876i −0.193890 + 0.460876i
\(101\) −155.093 −1.53558 −0.767788 0.640704i \(-0.778643\pi\)
−0.767788 + 0.640704i \(0.778643\pi\)
\(102\) 7.31843 + 7.31843i 0.0717493 + 0.0717493i
\(103\) −46.5485 + 46.5485i −0.451927 + 0.451927i −0.895994 0.444067i \(-0.853535\pi\)
0.444067 + 0.895994i \(0.353535\pi\)
\(104\) 40.9879i 0.394114i
\(105\) 25.8111 + 5.20830i 0.245820 + 0.0496029i
\(106\) 69.2429 0.653235
\(107\) 13.6792 + 13.6792i 0.127843 + 0.127843i 0.768133 0.640290i \(-0.221186\pi\)
−0.640290 + 0.768133i \(0.721186\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 105.153i 0.964702i 0.875978 + 0.482351i \(0.160217\pi\)
−0.875978 + 0.482351i \(0.839783\pi\)
\(110\) 50.8469 + 76.5546i 0.462244 + 0.695951i
\(111\) 110.129 0.992151
\(112\) −8.59979 8.59979i −0.0767838 0.0767838i
\(113\) −140.459 + 140.459i −1.24300 + 1.24300i −0.284254 + 0.958749i \(0.591746\pi\)
−0.958749 + 0.284254i \(0.908254\pi\)
\(114\) 64.6700i 0.567281i
\(115\) −19.9747 + 13.2670i −0.173693 + 0.115365i
\(116\) −91.2230 −0.786406
\(117\) −30.7409 30.7409i −0.262743 0.262743i
\(118\) 22.8736 22.8736i 0.193844 0.193844i
\(119\) 12.8469i 0.107958i
\(120\) −4.84505 + 24.0109i −0.0403754 + 0.200091i
\(121\) 47.9202 0.396035
\(122\) −70.3445 70.3445i −0.576595 0.576595i
\(123\) −48.2234 + 48.2234i −0.392060 + 0.392060i
\(124\) 74.9261i 0.604243i
\(125\) −103.355 70.3051i −0.826838 0.562441i
\(126\) 12.8997 0.102378
\(127\) −110.338 110.338i −0.868803 0.868803i 0.123537 0.992340i \(-0.460576\pi\)
−0.992340 + 0.123537i \(0.960576\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 72.8477i 0.564711i
\(130\) −100.445 20.2684i −0.772656 0.155910i
\(131\) 62.3911 0.476268 0.238134 0.971232i \(-0.423464\pi\)
0.238134 + 0.971232i \(0.423464\pi\)
\(132\) 31.8358 + 31.8358i 0.241181 + 0.241181i
\(133\) 56.7616 56.7616i 0.426779 0.426779i
\(134\) 39.3757i 0.293849i
\(135\) −14.3744 21.6420i −0.106477 0.160311i
\(136\) 11.9509 0.0878746
\(137\) −3.75731 3.75731i −0.0274256 0.0274256i 0.693261 0.720687i \(-0.256173\pi\)
−0.720687 + 0.693261i \(0.756173\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 244.157i 1.75652i −0.478179 0.878262i \(-0.658703\pi\)
0.478179 0.878262i \(-0.341297\pi\)
\(140\) 25.3273 16.8221i 0.180909 0.120158i
\(141\) 25.1540 0.178397
\(142\) 131.287 + 131.287i 0.924557 + 0.924557i
\(143\) −133.179 + 133.179i −0.931323 + 0.931323i
\(144\) 12.0000i 0.0833333i
\(145\) 45.1094 223.552i 0.311100 1.54174i
\(146\) 98.1067 0.671964
\(147\) 48.6903 + 48.6903i 0.331226 + 0.331226i
\(148\) 89.9197 89.9197i 0.607566 0.607566i
\(149\) 209.038i 1.40294i −0.712699 0.701470i \(-0.752527\pi\)
0.712699 0.701470i \(-0.247473\pi\)
\(150\) −56.4455 23.7466i −0.376303 0.158311i
\(151\) −97.4480 −0.645351 −0.322675 0.946510i \(-0.604582\pi\)
−0.322675 + 0.946510i \(0.604582\pi\)
\(152\) 52.8028 + 52.8028i 0.347387 + 0.347387i
\(153\) −8.96321 + 8.96321i −0.0585830 + 0.0585830i
\(154\) 55.8854i 0.362892i
\(155\) −183.614 37.0507i −1.18461 0.239037i
\(156\) −50.1997 −0.321793
\(157\) 142.961 + 142.961i 0.910581 + 0.910581i 0.996318 0.0857369i \(-0.0273245\pi\)
−0.0857369 + 0.996318i \(0.527324\pi\)
\(158\) 59.2011 59.2011i 0.374691 0.374691i
\(159\) 84.8049i 0.533364i
\(160\) 15.6489 + 23.5608i 0.0978055 + 0.147255i
\(161\) 14.5817 0.0905693
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −102.695 + 102.695i −0.630032 + 0.630032i −0.948076 0.318044i \(-0.896974\pi\)
0.318044 + 0.948076i \(0.396974\pi\)
\(164\) 78.7484i 0.480173i
\(165\) −93.7599 + 62.2744i −0.568242 + 0.377421i
\(166\) −62.0967 −0.374076
\(167\) −169.393 169.393i −1.01433 1.01433i −0.999896 0.0144364i \(-0.995405\pi\)
−0.0144364 0.999896i \(-0.504595\pi\)
\(168\) 10.5325 10.5325i 0.0626937 0.0626937i
\(169\) 41.0011i 0.242610i
\(170\) −5.90969 + 29.2871i −0.0347629 + 0.172277i
\(171\) −79.2042 −0.463183
\(172\) 59.4799 + 59.4799i 0.345813 + 0.345813i
\(173\) 91.2722 91.2722i 0.527585 0.527585i −0.392267 0.919852i \(-0.628309\pi\)
0.919852 + 0.392267i \(0.128309\pi\)
\(174\) 111.725i 0.642097i
\(175\) 28.7002 + 70.3857i 0.164001 + 0.402204i
\(176\) 51.9877 0.295385
\(177\) 28.0143 + 28.0143i 0.158273 + 0.158273i
\(178\) 169.901 169.901i 0.954498 0.954498i
\(179\) 134.161i 0.749503i −0.927125 0.374752i \(-0.877728\pi\)
0.927125 0.374752i \(-0.122272\pi\)
\(180\) −29.4073 5.93395i −0.163374 0.0329664i
\(181\) −102.342 −0.565424 −0.282712 0.959205i \(-0.591234\pi\)
−0.282712 + 0.959205i \(0.591234\pi\)
\(182\) 44.0609 + 44.0609i 0.242093 + 0.242093i
\(183\) 86.1541 86.1541i 0.470787 0.470787i
\(184\) 13.5647i 0.0737210i
\(185\) 175.893 + 264.823i 0.950773 + 1.43148i
\(186\) −91.7654 −0.493362
\(187\) 38.8314 + 38.8314i 0.207654 + 0.207654i
\(188\) 20.5382 20.5382i 0.109246 0.109246i
\(189\) 15.7988i 0.0835917i
\(190\) −155.510 + 103.288i −0.818472 + 0.543622i
\(191\) 139.686 0.731342 0.365671 0.930744i \(-0.380840\pi\)
0.365671 + 0.930744i \(0.380840\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −103.467 + 103.467i −0.536099 + 0.536099i −0.922381 0.386282i \(-0.873759\pi\)
0.386282 + 0.922381i \(0.373759\pi\)
\(194\) 16.3518i 0.0842878i
\(195\) 24.8236 123.020i 0.127300 0.630871i
\(196\) 79.5109 0.405668
\(197\) −233.769 233.769i −1.18664 1.18664i −0.977990 0.208653i \(-0.933092\pi\)
−0.208653 0.977990i \(-0.566908\pi\)
\(198\) −38.9908 + 38.9908i −0.196923 + 0.196923i
\(199\) 164.360i 0.825929i −0.910747 0.412965i \(-0.864493\pi\)
0.910747 0.412965i \(-0.135507\pi\)
\(200\) −65.4766 + 26.6985i −0.327383 + 0.133493i
\(201\) −48.2252 −0.239926
\(202\) −155.093 155.093i −0.767788 0.767788i
\(203\) −98.0624 + 98.0624i −0.483066 + 0.483066i
\(204\) 14.6369i 0.0717493i
\(205\) −192.981 38.9408i −0.941373 0.189955i
\(206\) −93.0969 −0.451927
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −40.9879 + 40.9879i −0.197057 + 0.197057i
\(209\) 343.137i 1.64181i
\(210\) 20.6028 + 31.0194i 0.0981087 + 0.147712i
\(211\) 75.9698 0.360047 0.180023 0.983662i \(-0.442383\pi\)
0.180023 + 0.983662i \(0.442383\pi\)
\(212\) 69.2429 + 69.2429i 0.326618 + 0.326618i
\(213\) −160.793 + 160.793i −0.754897 + 0.754897i
\(214\) 27.3584i 0.127843i
\(215\) −175.174 + 116.349i −0.814765 + 0.541159i
\(216\) −14.6969 −0.0680414
\(217\) 80.5436 + 80.5436i 0.371169 + 0.371169i
\(218\) −105.153 + 105.153i −0.482351 + 0.482351i
\(219\) 120.156i 0.548656i
\(220\) −25.7077 + 127.401i −0.116853 + 0.579098i
\(221\) −61.2305 −0.277061
\(222\) 110.129 + 110.129i 0.496075 + 0.496075i
\(223\) 235.175 235.175i 1.05460 1.05460i 0.0561774 0.998421i \(-0.482109\pi\)
0.998421 0.0561774i \(-0.0178912\pi\)
\(224\) 17.1996i 0.0767838i
\(225\) 29.0836 69.1314i 0.129260 0.307251i
\(226\) −280.919 −1.24300
\(227\) 22.8432 + 22.8432i 0.100631 + 0.100631i 0.755630 0.654999i \(-0.227331\pi\)
−0.654999 + 0.755630i \(0.727331\pi\)
\(228\) −64.6700 + 64.6700i −0.283640 + 0.283640i
\(229\) 93.3450i 0.407620i −0.979010 0.203810i \(-0.934667\pi\)
0.979010 0.203810i \(-0.0653325\pi\)
\(230\) −33.2416 6.70767i −0.144529 0.0291638i
\(231\) 68.4454 0.296300
\(232\) −91.2230 91.2230i −0.393203 0.393203i
\(233\) −154.261 + 154.261i −0.662063 + 0.662063i −0.955866 0.293803i \(-0.905079\pi\)
0.293803 + 0.955866i \(0.405079\pi\)
\(234\) 61.4819i 0.262743i
\(235\) 40.1749 + 60.4870i 0.170957 + 0.257391i
\(236\) 45.7471 0.193844
\(237\) 72.5063 + 72.5063i 0.305934 + 0.305934i
\(238\) 12.8469 12.8469i 0.0539788 0.0539788i
\(239\) 9.07323i 0.0379633i −0.999820 0.0189816i \(-0.993958\pi\)
0.999820 0.0189816i \(-0.00604241\pi\)
\(240\) −28.8560 + 19.1659i −0.120233 + 0.0798579i
\(241\) 253.551 1.05208 0.526039 0.850460i \(-0.323677\pi\)
0.526039 + 0.850460i \(0.323677\pi\)
\(242\) 47.9202 + 47.9202i 0.198017 + 0.198017i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 140.689i 0.576595i
\(245\) −39.3178 + 194.850i −0.160481 + 0.795306i
\(246\) −96.4468 −0.392060
\(247\) −270.535 270.535i −1.09528 1.09528i
\(248\) −74.9261 + 74.9261i −0.302121 + 0.302121i
\(249\) 76.0526i 0.305432i
\(250\) −33.0497 173.660i −0.132199 0.694639i
\(251\) 139.932 0.557498 0.278749 0.960364i \(-0.410080\pi\)
0.278749 + 0.960364i \(0.410080\pi\)
\(252\) 12.8997 + 12.8997i 0.0511892 + 0.0511892i
\(253\) −44.0747 + 44.0747i −0.174208 + 0.174208i
\(254\) 220.676i 0.868803i
\(255\) −35.8692 7.23787i −0.140663 0.0283838i
\(256\) 16.0000 0.0625000
\(257\) −27.8299 27.8299i −0.108287 0.108287i 0.650887 0.759175i \(-0.274397\pi\)
−0.759175 + 0.650887i \(0.774397\pi\)
\(258\) −72.8477 + 72.8477i −0.282355 + 0.282355i
\(259\) 193.323i 0.746420i
\(260\) −80.1769 120.714i −0.308373 0.464283i
\(261\) 136.835 0.524270
\(262\) 62.3911 + 62.3911i 0.238134 + 0.238134i
\(263\) −224.271 + 224.271i −0.852741 + 0.852741i −0.990470 0.137729i \(-0.956020\pi\)
0.137729 + 0.990470i \(0.456020\pi\)
\(264\) 63.6717i 0.241181i
\(265\) −203.928 + 135.447i −0.769538 + 0.511120i
\(266\) 113.523 0.426779
\(267\) 208.085 + 208.085i 0.779344 + 0.779344i
\(268\) −39.3757 + 39.3757i −0.146924 + 0.146924i
\(269\) 458.186i 1.70329i 0.524117 + 0.851646i \(0.324395\pi\)
−0.524117 + 0.851646i \(0.675605\pi\)
\(270\) 7.26758 36.0164i 0.0269170 0.133394i
\(271\) 334.255 1.23341 0.616706 0.787193i \(-0.288467\pi\)
0.616706 + 0.787193i \(0.288467\pi\)
\(272\) 11.9509 + 11.9509i 0.0439373 + 0.0439373i
\(273\) −53.9634 + 53.9634i −0.197668 + 0.197668i
\(274\) 7.51462i 0.0274256i
\(275\) −299.499 125.999i −1.08909 0.458178i
\(276\) −16.6132 −0.0601929
\(277\) −200.494 200.494i −0.723807 0.723807i 0.245572 0.969378i \(-0.421024\pi\)
−0.969378 + 0.245572i \(0.921024\pi\)
\(278\) 244.157 244.157i 0.878262 0.878262i
\(279\) 112.389i 0.402829i
\(280\) 42.1494 + 8.50513i 0.150534 + 0.0303754i
\(281\) 44.8143 0.159482 0.0797408 0.996816i \(-0.474591\pi\)
0.0797408 + 0.996816i \(0.474591\pi\)
\(282\) 25.1540 + 25.1540i 0.0891986 + 0.0891986i
\(283\) 76.0560 76.0560i 0.268749 0.268749i −0.559847 0.828596i \(-0.689140\pi\)
0.828596 + 0.559847i \(0.189140\pi\)
\(284\) 262.574i 0.924557i
\(285\) −126.502 190.460i −0.443865 0.668280i
\(286\) −266.358 −0.931323
\(287\) 84.6525 + 84.6525i 0.294956 + 0.294956i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 271.147i 0.938224i
\(290\) 268.661 178.442i 0.926418 0.615318i
\(291\) −20.0268 −0.0688207
\(292\) 98.1067 + 98.1067i 0.335982 + 0.335982i
\(293\) −144.599 + 144.599i −0.493512 + 0.493512i −0.909411 0.415899i \(-0.863467\pi\)
0.415899 + 0.909411i \(0.363467\pi\)
\(294\) 97.3806i 0.331226i
\(295\) −22.6218 + 112.108i −0.0766840 + 0.380028i
\(296\) 179.839 0.607566
\(297\) −47.7538 47.7538i −0.160787 0.160787i
\(298\) 209.038 209.038i 0.701470 0.701470i
\(299\) 69.4984i 0.232436i
\(300\) −32.6989 80.1922i −0.108996 0.267307i
\(301\) 127.879 0.424846
\(302\) −97.4480 97.4480i −0.322675 0.322675i
\(303\) 189.950 189.950i 0.626896 0.626896i
\(304\) 105.606i 0.347387i
\(305\) 344.774 + 69.5702i 1.13041 + 0.228099i
\(306\) −17.9264 −0.0585830
\(307\) 168.960 + 168.960i 0.550360 + 0.550360i 0.926545 0.376185i \(-0.122764\pi\)
−0.376185 + 0.926545i \(0.622764\pi\)
\(308\) 55.8854 55.8854i 0.181446 0.181446i
\(309\) 114.020i 0.368997i
\(310\) −146.564 220.665i −0.472786 0.711823i
\(311\) 527.554 1.69631 0.848157 0.529745i \(-0.177712\pi\)
0.848157 + 0.529745i \(0.177712\pi\)
\(312\) −50.1997 50.1997i −0.160897 0.160897i
\(313\) −385.731 + 385.731i −1.23237 + 1.23237i −0.269316 + 0.963052i \(0.586798\pi\)
−0.963052 + 0.269316i \(0.913202\pi\)
\(314\) 285.922i 0.910581i
\(315\) −37.9909 + 25.2332i −0.120606 + 0.0801054i
\(316\) 118.402 0.374691
\(317\) 211.055 + 211.055i 0.665788 + 0.665788i 0.956738 0.290950i \(-0.0939714\pi\)
−0.290950 + 0.956738i \(0.593971\pi\)
\(318\) −84.8049 + 84.8049i −0.266682 + 0.266682i
\(319\) 592.810i 1.85834i
\(320\) −7.91194 + 39.2097i −0.0247248 + 0.122530i
\(321\) −33.5070 −0.104383
\(322\) 14.5817 + 14.5817i 0.0452846 + 0.0452846i
\(323\) −78.8804 + 78.8804i −0.244212 + 0.244212i
\(324\) 18.0000i 0.0555556i
\(325\) 335.469 136.790i 1.03221 0.420891i
\(326\) −205.390 −0.630032
\(327\) −128.785 128.785i −0.393838 0.393838i
\(328\) −78.7484 + 78.7484i −0.240087 + 0.240087i
\(329\) 44.1560i 0.134213i
\(330\) −156.034 31.4854i −0.472831 0.0954103i
\(331\) 136.580 0.412627 0.206313 0.978486i \(-0.433853\pi\)
0.206313 + 0.978486i \(0.433853\pi\)
\(332\) −62.0967 62.0967i −0.187038 0.187038i
\(333\) −134.880 + 134.880i −0.405044 + 0.405044i
\(334\) 338.787i 1.01433i
\(335\) −77.0232 115.966i −0.229920 0.346166i
\(336\) 21.0651 0.0626937
\(337\) −77.6053 77.6053i −0.230283 0.230283i 0.582528 0.812811i \(-0.302064\pi\)
−0.812811 + 0.582528i \(0.802064\pi\)
\(338\) 41.0011 41.0011i 0.121305 0.121305i
\(339\) 344.054i 1.01491i
\(340\) −35.1968 + 23.3774i −0.103520 + 0.0687569i
\(341\) −486.905 −1.42787
\(342\) −79.2042 79.2042i −0.231591 0.231591i
\(343\) 190.820 190.820i 0.556325 0.556325i
\(344\) 118.960i 0.345813i
\(345\) 8.21519 40.7125i 0.0238121 0.118007i
\(346\) 182.544 0.527585
\(347\) −334.981 334.981i −0.965362 0.965362i 0.0340576 0.999420i \(-0.489157\pi\)
−0.999420 + 0.0340576i \(0.989157\pi\)
\(348\) 111.725 111.725i 0.321049 0.321049i
\(349\) 462.956i 1.32652i 0.748389 + 0.663261i \(0.230828\pi\)
−0.748389 + 0.663261i \(0.769172\pi\)
\(350\) −41.6854 + 99.0859i −0.119101 + 0.283102i
\(351\) 75.2996 0.214529
\(352\) 51.9877 + 51.9877i 0.147692 + 0.147692i
\(353\) −419.637 + 419.637i −1.18877 + 1.18877i −0.211367 + 0.977407i \(0.567792\pi\)
−0.977407 + 0.211367i \(0.932208\pi\)
\(354\) 56.0286i 0.158273i
\(355\) −643.466 129.842i −1.81258 0.365752i
\(356\) 339.801 0.954498
\(357\) 15.7342 + 15.7342i 0.0440735 + 0.0440735i
\(358\) 134.161 134.161i 0.374752 0.374752i
\(359\) 253.226i 0.705366i 0.935743 + 0.352683i \(0.114731\pi\)
−0.935743 + 0.352683i \(0.885269\pi\)
\(360\) −23.4733 35.3412i −0.0652037 0.0981701i
\(361\) −336.034 −0.930843
\(362\) −102.342 102.342i −0.282712 0.282712i
\(363\) −58.6900 + 58.6900i −0.161681 + 0.161681i
\(364\) 88.1218i 0.242093i
\(365\) −288.934 + 191.908i −0.791601 + 0.525774i
\(366\) 172.308 0.470787
\(367\) 133.234 + 133.234i 0.363035 + 0.363035i 0.864929 0.501894i \(-0.167363\pi\)
−0.501894 + 0.864929i \(0.667363\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 118.123i 0.320116i
\(370\) −88.9299 + 440.716i −0.240351 + 1.19112i
\(371\) 148.869 0.401263
\(372\) −91.7654 91.7654i −0.246681 0.246681i
\(373\) −158.070 + 158.070i −0.423780 + 0.423780i −0.886503 0.462723i \(-0.846872\pi\)
0.462723 + 0.886503i \(0.346872\pi\)
\(374\) 77.6628i 0.207654i
\(375\) 212.689 40.4774i 0.567170 0.107940i
\(376\) 41.0763 0.109246
\(377\) 467.380 + 467.380i 1.23974 + 1.23974i
\(378\) −15.7988 + 15.7988i −0.0417958 + 0.0417958i
\(379\) 485.673i 1.28146i −0.767766 0.640730i \(-0.778632\pi\)
0.767766 0.640730i \(-0.221368\pi\)
\(380\) −258.798 52.2216i −0.681047 0.137425i
\(381\) 270.272 0.709375
\(382\) 139.686 + 139.686i 0.365671 + 0.365671i
\(383\) 447.060 447.060i 1.16726 1.16726i 0.184410 0.982849i \(-0.440963\pi\)
0.982849 0.184410i \(-0.0590375\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 109.318 + 164.588i 0.283943 + 0.427502i
\(386\) −206.934 −0.536099
\(387\) −89.2198 89.2198i −0.230542 0.230542i
\(388\) −16.3518 + 16.3518i −0.0421439 + 0.0421439i
\(389\) 252.009i 0.647837i −0.946085 0.323919i \(-0.895000\pi\)
0.946085 0.323919i \(-0.105000\pi\)
\(390\) 147.843 98.1962i 0.379086 0.251785i
\(391\) −20.2638 −0.0518256
\(392\) 79.5109 + 79.5109i 0.202834 + 0.202834i
\(393\) −76.4132 + 76.4132i −0.194436 + 0.194436i
\(394\) 467.537i 1.18664i
\(395\) −58.5494 + 290.157i −0.148226 + 0.734575i
\(396\) −77.9816 −0.196923
\(397\) 527.251 + 527.251i 1.32809 + 1.32809i 0.907038 + 0.421050i \(0.138338\pi\)
0.421050 + 0.907038i \(0.361662\pi\)
\(398\) 164.360 164.360i 0.412965 0.412965i
\(399\) 139.037i 0.348464i
\(400\) −92.1752 38.7781i −0.230438 0.0969452i
\(401\) 337.961 0.842796 0.421398 0.906876i \(-0.361540\pi\)
0.421398 + 0.906876i \(0.361540\pi\)
\(402\) −48.2252 48.2252i −0.119963 0.119963i
\(403\) 383.883 383.883i 0.952563 0.952563i
\(404\) 310.186i 0.767788i
\(405\) 44.1109 + 8.90093i 0.108916 + 0.0219776i
\(406\) −196.125 −0.483066
\(407\) 584.340 + 584.340i 1.43573 + 1.43573i
\(408\) −14.6369 + 14.6369i −0.0358746 + 0.0358746i
\(409\) 669.062i 1.63585i 0.575327 + 0.817924i \(0.304875\pi\)
−0.575327 + 0.817924i \(0.695125\pi\)
\(410\) −154.041 231.922i −0.375709 0.565664i
\(411\) 9.20349 0.0223929
\(412\) −93.0969 93.0969i −0.225963 0.225963i
\(413\) 49.1770 49.1770i 0.119073 0.119073i
\(414\) 20.3470i 0.0491473i
\(415\) 182.881 121.468i 0.440677 0.292694i
\(416\) −81.9758 −0.197057
\(417\) 299.030 + 299.030i 0.717098 + 0.717098i
\(418\) −343.137 + 343.137i −0.820903 + 0.820903i
\(419\) 141.319i 0.337278i −0.985678 0.168639i \(-0.946063\pi\)
0.985678 0.168639i \(-0.0539372\pi\)
\(420\) −10.4166 + 51.6223i −0.0248014 + 0.122910i
\(421\) 336.422 0.799103 0.399551 0.916711i \(-0.369166\pi\)
0.399551 + 0.916711i \(0.369166\pi\)
\(422\) 75.9698 + 75.9698i 0.180023 + 0.180023i
\(423\) −30.8072 + 30.8072i −0.0728303 + 0.0728303i
\(424\) 138.486i 0.326618i
\(425\) −39.8841 97.8134i −0.0938449 0.230149i
\(426\) −321.586 −0.754897
\(427\) −151.237 151.237i −0.354185 0.354185i
\(428\) −27.3584 + 27.3584i −0.0639214 + 0.0639214i
\(429\) 326.221i 0.760422i
\(430\) −291.524 58.8252i −0.677962 0.136803i
\(431\) 568.586 1.31922 0.659612 0.751606i \(-0.270720\pi\)
0.659612 + 0.751606i \(0.270720\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 222.386 222.386i 0.513593 0.513593i −0.402032 0.915626i \(-0.631696\pi\)
0.915626 + 0.402032i \(0.131696\pi\)
\(434\) 161.087i 0.371169i
\(435\) 218.546 + 329.041i 0.502405 + 0.756417i
\(436\) −210.305 −0.482351
\(437\) −89.5315 89.5315i −0.204878 0.204878i
\(438\) −120.156 + 120.156i −0.274328 + 0.274328i
\(439\) 215.602i 0.491121i 0.969381 + 0.245561i \(0.0789720\pi\)
−0.969381 + 0.245561i \(0.921028\pi\)
\(440\) −153.109 + 101.694i −0.347975 + 0.231122i
\(441\) −119.266 −0.270445
\(442\) −61.2305 61.2305i −0.138531 0.138531i
\(443\) 282.186 282.186i 0.636988 0.636988i −0.312823 0.949811i \(-0.601275\pi\)
0.949811 + 0.312823i \(0.101275\pi\)
\(444\) 220.257i 0.496075i
\(445\) −168.030 + 832.719i −0.377596 + 1.87128i
\(446\) 470.351 1.05460
\(447\) 256.018 + 256.018i 0.572748 + 0.572748i
\(448\) 17.1996 17.1996i 0.0383919 0.0383919i
\(449\) 761.526i 1.69605i −0.529958 0.848024i \(-0.677792\pi\)
0.529958 0.848024i \(-0.322208\pi\)
\(450\) 98.2149 40.0478i 0.218255 0.0889951i
\(451\) −511.744 −1.13469
\(452\) −280.919 280.919i −0.621502 0.621502i
\(453\) 119.349 119.349i 0.263463 0.263463i
\(454\) 45.6864i 0.100631i
\(455\) −215.952 43.5759i −0.474620 0.0957712i
\(456\) −129.340 −0.283640
\(457\) 271.064 + 271.064i 0.593138 + 0.593138i 0.938478 0.345340i \(-0.112236\pi\)
−0.345340 + 0.938478i \(0.612236\pi\)
\(458\) 93.3450 93.3450i 0.203810 0.203810i
\(459\) 21.9553i 0.0478329i
\(460\) −26.5340 39.9493i −0.0576826 0.0868463i
\(461\) 29.2935 0.0635435 0.0317717 0.999495i \(-0.489885\pi\)
0.0317717 + 0.999495i \(0.489885\pi\)
\(462\) 68.4454 + 68.4454i 0.148150 + 0.148150i
\(463\) −233.316 + 233.316i −0.503922 + 0.503922i −0.912654 0.408733i \(-0.865971\pi\)
0.408733 + 0.912654i \(0.365971\pi\)
\(464\) 182.446i 0.393203i
\(465\) 270.258 179.503i 0.581201 0.386028i
\(466\) −308.521 −0.662063
\(467\) −407.377 407.377i −0.872328 0.872328i 0.120398 0.992726i \(-0.461583\pi\)
−0.992726 + 0.120398i \(0.961583\pi\)
\(468\) 61.4819 61.4819i 0.131371 0.131371i
\(469\) 84.6557i 0.180503i
\(470\) −20.3121 + 100.662i −0.0432172 + 0.214174i
\(471\) −350.182 −0.743486
\(472\) 45.7471 + 45.7471i 0.0969219 + 0.0969219i
\(473\) −386.528 + 386.528i −0.817184 + 0.817184i
\(474\) 145.013i 0.305934i
\(475\) 255.949 608.388i 0.538840 1.28082i
\(476\) 25.6939 0.0539788
\(477\) −103.864 103.864i −0.217745 0.217745i
\(478\) 9.07323 9.07323i 0.0189816 0.0189816i
\(479\) 703.739i 1.46918i 0.678509 + 0.734592i \(0.262626\pi\)
−0.678509 + 0.734592i \(0.737374\pi\)
\(480\) −48.0219 9.69011i −0.100046 0.0201877i
\(481\) −921.405 −1.91560
\(482\) 253.551 + 253.551i 0.526039 + 0.526039i
\(483\) −17.8588 + 17.8588i −0.0369747 + 0.0369747i
\(484\) 95.8404i 0.198017i
\(485\) −31.9860 48.1578i −0.0659505 0.0992944i
\(486\) 22.0454 0.0453609
\(487\) 407.800 + 407.800i 0.837372 + 0.837372i 0.988512 0.151141i \(-0.0482946\pi\)
−0.151141 + 0.988512i \(0.548295\pi\)
\(488\) 140.689 140.689i 0.288297 0.288297i
\(489\) 251.551i 0.514419i
\(490\) −234.168 + 155.532i −0.477893 + 0.317413i
\(491\) −198.942 −0.405178 −0.202589 0.979264i \(-0.564936\pi\)
−0.202589 + 0.979264i \(0.564936\pi\)
\(492\) −96.4468 96.4468i −0.196030 0.196030i
\(493\) 136.275 136.275i 0.276420 0.276420i
\(494\) 541.069i 1.09528i
\(495\) 38.5616 191.102i 0.0779022 0.386065i
\(496\) −149.852 −0.302121
\(497\) 282.260 + 282.260i 0.567928 + 0.567928i
\(498\) 76.0526 76.0526i 0.152716 0.152716i
\(499\) 460.033i 0.921910i −0.887424 0.460955i \(-0.847507\pi\)
0.887424 0.460955i \(-0.152493\pi\)
\(500\) 140.610 206.709i 0.281220 0.413419i
\(501\) 414.928 0.828199
\(502\) 139.932 + 139.932i 0.278749 + 0.278749i
\(503\) −7.49816 + 7.49816i −0.0149069 + 0.0149069i −0.714521 0.699614i \(-0.753355\pi\)
0.699614 + 0.714521i \(0.253355\pi\)
\(504\) 25.7994i 0.0511892i
\(505\) 760.145 + 153.386i 1.50524 + 0.303735i
\(506\) −88.1495 −0.174208
\(507\) 50.2158 + 50.2158i 0.0990450 + 0.0990450i
\(508\) 220.676 220.676i 0.434402 0.434402i
\(509\) 485.709i 0.954241i −0.878838 0.477120i \(-0.841681\pi\)
0.878838 0.477120i \(-0.158319\pi\)
\(510\) −28.6313 43.1070i −0.0561398 0.0845236i
\(511\) 210.924 0.412768
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 97.0050 97.0050i 0.189094 0.189094i
\(514\) 55.6598i 0.108287i
\(515\) 274.180 182.108i 0.532388 0.353607i
\(516\) −145.695 −0.282355
\(517\) 133.466 + 133.466i 0.258156 + 0.258156i
\(518\) 193.323 193.323i 0.373210 0.373210i
\(519\) 223.570i 0.430771i
\(520\) 40.5367 200.890i 0.0779552 0.386328i
\(521\) −125.674 −0.241217 −0.120609 0.992700i \(-0.538485\pi\)
−0.120609 + 0.992700i \(0.538485\pi\)
\(522\) 136.835 + 136.835i 0.262135 + 0.262135i
\(523\) 378.858 378.858i 0.724393 0.724393i −0.245103 0.969497i \(-0.578822\pi\)
0.969497 + 0.245103i \(0.0788219\pi\)
\(524\) 124.782i 0.238134i
\(525\) −121.355 51.0540i −0.231152 0.0972458i
\(526\) −448.542 −0.852741
\(527\) −111.930 111.930i −0.212390 0.212390i
\(528\) −63.6717 + 63.6717i −0.120590 + 0.120590i
\(529\) 23.0000i 0.0434783i
\(530\) −339.374 68.4807i −0.640329 0.129209i
\(531\) −68.6207 −0.129229
\(532\) 113.523 + 113.523i 0.213390 + 0.213390i
\(533\) 403.467 403.467i 0.756973 0.756973i
\(534\) 416.170i 0.779344i
\(535\) −53.5160 80.5732i −0.100030 0.150604i
\(536\) −78.7514 −0.146924
\(537\) 164.313 + 164.313i 0.305983 + 0.305983i
\(538\) −458.186 + 458.186i −0.851646 + 0.851646i
\(539\) 516.699i 0.958625i
\(540\) 43.2840 28.7488i 0.0801555 0.0532386i
\(541\) 377.104 0.697050 0.348525 0.937300i \(-0.386683\pi\)
0.348525 + 0.937300i \(0.386683\pi\)
\(542\) 334.255 + 334.255i 0.616706 + 0.616706i
\(543\) 125.343 125.343i 0.230833 0.230833i
\(544\) 23.9019i 0.0439373i
\(545\) 103.995 515.375i 0.190817 0.945643i
\(546\) −107.927 −0.197668
\(547\) 444.740 + 444.740i 0.813052 + 0.813052i 0.985090 0.172038i \(-0.0550352\pi\)
−0.172038 + 0.985090i \(0.555035\pi\)
\(548\) 7.51462 7.51462i 0.0137128 0.0137128i
\(549\) 211.034i 0.384396i
\(550\) −173.499 425.498i −0.315454 0.773632i
\(551\) 1204.21 2.18550
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 127.279 127.279i 0.230161 0.230161i
\(554\) 400.989i 0.723807i
\(555\) −539.764 108.916i −0.972549 0.196246i
\(556\) 488.314 0.878262
\(557\) −583.468 583.468i −1.04752 1.04752i −0.998813 0.0487058i \(-0.984490\pi\)
−0.0487058 0.998813i \(-0.515510\pi\)
\(558\) 112.389 112.389i 0.201414 0.201414i
\(559\) 609.489i 1.09032i
\(560\) 33.6443 + 50.6545i 0.0600791 + 0.0904545i
\(561\) −95.1171 −0.169549
\(562\) 44.8143 + 44.8143i 0.0797408 + 0.0797408i
\(563\) −38.5193 + 38.5193i −0.0684179 + 0.0684179i −0.740488 0.672070i \(-0.765405\pi\)
0.672070 + 0.740488i \(0.265405\pi\)
\(564\) 50.3080i 0.0891986i
\(565\) 827.335 549.508i 1.46431 0.972581i
\(566\) 152.112 0.268749
\(567\) −19.3495 19.3495i −0.0341261 0.0341261i
\(568\) −262.574 + 262.574i −0.462278 + 0.462278i
\(569\) 72.1680i 0.126833i 0.997987 + 0.0634165i \(0.0201997\pi\)
−0.997987 + 0.0634165i \(0.979800\pi\)
\(570\) 63.9581 316.961i 0.112207 0.556073i
\(571\) −653.227 −1.14401 −0.572003 0.820252i \(-0.693833\pi\)
−0.572003 + 0.820252i \(0.693833\pi\)
\(572\) −266.358 266.358i −0.465662 0.465662i
\(573\) −171.080 + 171.080i −0.298569 + 0.298569i
\(574\) 169.305i 0.294956i
\(575\) 111.021 45.2696i 0.193080 0.0787297i
\(576\) −24.0000 −0.0416667
\(577\) 401.108 + 401.108i 0.695161 + 0.695161i 0.963363 0.268202i \(-0.0864293\pi\)
−0.268202 + 0.963363i \(0.586429\pi\)
\(578\) 271.147 271.147i 0.469112 0.469112i
\(579\) 253.442i 0.437723i
\(580\) 447.104 + 90.2189i 0.770868 + 0.155550i
\(581\) −133.505 −0.229784
\(582\) −20.0268 20.0268i −0.0344103 0.0344103i
\(583\) −449.973 + 449.973i −0.771823 + 0.771823i
\(584\) 196.213i 0.335982i
\(585\) 120.265 + 181.070i 0.205582 + 0.309522i
\(586\) −289.198 −0.493512
\(587\) −341.521 341.521i −0.581807 0.581807i 0.353593 0.935400i \(-0.384960\pi\)
−0.935400 + 0.353593i \(0.884960\pi\)
\(588\) −97.3806 + 97.3806i −0.165613 + 0.165613i
\(589\) 989.077i 1.67925i
\(590\) −134.730 + 89.4865i −0.228356 + 0.151672i
\(591\) 572.614 0.968890
\(592\) 179.839 + 179.839i 0.303783 + 0.303783i
\(593\) −4.85045 + 4.85045i −0.00817952 + 0.00817952i −0.711185 0.703005i \(-0.751841\pi\)
0.703005 + 0.711185i \(0.251841\pi\)
\(594\) 95.5075i 0.160787i
\(595\) −12.7055 + 62.9656i −0.0213538 + 0.105825i
\(596\) 418.076 0.701470
\(597\) 201.299 + 201.299i 0.337184 + 0.337184i
\(598\) 69.4984 69.4984i 0.116218 0.116218i
\(599\) 555.468i 0.927326i −0.886012 0.463663i \(-0.846535\pi\)
0.886012 0.463663i \(-0.153465\pi\)
\(600\) 47.4933 112.891i 0.0791555 0.188152i
\(601\) 705.957 1.17464 0.587319 0.809356i \(-0.300183\pi\)
0.587319 + 0.809356i \(0.300183\pi\)
\(602\) 127.879 + 127.879i 0.212423 + 0.212423i
\(603\) 59.0636 59.0636i 0.0979495 0.0979495i
\(604\) 194.896i 0.322675i
\(605\) −234.867 47.3927i −0.388210 0.0783351i
\(606\) 379.899 0.626896
\(607\) 429.607 + 429.607i 0.707755 + 0.707755i 0.966063 0.258308i \(-0.0831648\pi\)
−0.258308 + 0.966063i \(0.583165\pi\)
\(608\) −105.606 + 105.606i −0.173693 + 0.173693i
\(609\) 240.203i 0.394422i
\(610\) 275.203 + 414.344i 0.451153 + 0.679252i
\(611\) −210.454 −0.344442
\(612\) −17.9264 17.9264i −0.0292915 0.0292915i
\(613\) 396.285 396.285i 0.646468 0.646468i −0.305670 0.952138i \(-0.598880\pi\)
0.952138 + 0.305670i \(0.0988803\pi\)
\(614\) 337.921i 0.550360i
\(615\) 284.046 188.661i 0.461863 0.306765i
\(616\) 111.771 0.181446
\(617\) −800.870 800.870i −1.29801 1.29801i −0.929707 0.368299i \(-0.879940\pi\)
−0.368299 0.929707i \(-0.620060\pi\)
\(618\) 114.020 114.020i 0.184498 0.184498i
\(619\) 480.925i 0.776939i 0.921462 + 0.388469i \(0.126996\pi\)
−0.921462 + 0.388469i \(0.873004\pi\)
\(620\) 74.1013 367.229i 0.119518 0.592305i
\(621\) 24.9199 0.0401286
\(622\) 527.554 + 527.554i 0.848157 + 0.848157i
\(623\) 365.277 365.277i 0.586320 0.586320i
\(624\) 100.399i 0.160897i
\(625\) 437.032 + 446.797i 0.699252 + 0.714875i
\(626\) −771.462 −1.23237
\(627\) −420.256 420.256i −0.670264 0.670264i
\(628\) −285.922 + 285.922i −0.455290 + 0.455290i
\(629\) 268.656i 0.427117i
\(630\) −63.2241 12.7577i −0.100356 0.0202503i
\(631\) −205.865 −0.326251 −0.163126 0.986605i \(-0.552158\pi\)
−0.163126 + 0.986605i \(0.552158\pi\)
\(632\) 118.402 + 118.402i 0.187345 + 0.187345i
\(633\) −93.0437 + 93.0437i −0.146988 + 0.146988i
\(634\) 422.110i 0.665788i
\(635\) 431.667 + 649.913i 0.679790 + 1.02349i
\(636\) −169.610 −0.266682
\(637\) −407.373 407.373i −0.639518 0.639518i
\(638\) 592.810 592.810i 0.929169 0.929169i
\(639\) 393.861i 0.616371i
\(640\) −47.1216 + 31.2978i −0.0736276 + 0.0489028i
\(641\) 652.976 1.01868 0.509342 0.860564i \(-0.329889\pi\)
0.509342 + 0.860564i \(0.329889\pi\)
\(642\) −33.5070 33.5070i −0.0521916 0.0521916i
\(643\) −702.135 + 702.135i −1.09197 + 1.09197i −0.0966483 + 0.995319i \(0.530812\pi\)
−0.995319 + 0.0966483i \(0.969188\pi\)
\(644\) 29.1633i 0.0452846i
\(645\) 72.0458 357.042i 0.111699 0.553554i
\(646\) −157.761 −0.244212
\(647\) −575.223 575.223i −0.889062 0.889062i 0.105371 0.994433i \(-0.466397\pi\)
−0.994433 + 0.105371i \(0.966397\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 297.286i 0.458068i
\(650\) 472.258 + 198.679i 0.726551 + 0.305660i
\(651\) −197.291 −0.303058
\(652\) −205.390 205.390i −0.315016 0.315016i
\(653\) −260.357 + 260.357i −0.398708 + 0.398708i −0.877777 0.479069i \(-0.840974\pi\)
0.479069 + 0.877777i \(0.340974\pi\)
\(654\) 257.570i 0.393838i
\(655\) −305.792 61.7043i −0.466858 0.0942050i
\(656\) −157.497 −0.240087
\(657\) −147.160 147.160i −0.223988 0.223988i
\(658\) 44.1560 44.1560i 0.0671063 0.0671063i
\(659\) 421.514i 0.639626i −0.947481 0.319813i \(-0.896380\pi\)
0.947481 0.319813i \(-0.103620\pi\)
\(660\) −124.549 187.520i −0.188710 0.284121i
\(661\) −190.516 −0.288224 −0.144112 0.989561i \(-0.546033\pi\)
−0.144112 + 0.989561i \(0.546033\pi\)
\(662\) 136.580 + 136.580i 0.206313 + 0.206313i
\(663\) 74.9917 74.9917i 0.113110 0.113110i
\(664\) 124.193i 0.187038i
\(665\) −334.338 + 222.064i −0.502764 + 0.333931i
\(666\) −269.759 −0.405044
\(667\) 154.676 + 154.676i 0.231898 + 0.231898i
\(668\) 338.787 338.787i 0.507166 0.507166i
\(669\) 576.060i 0.861076i
\(670\) 38.9423 192.989i 0.0581228 0.288043i
\(671\) 914.263 1.36254
\(672\) 21.0651 + 21.0651i 0.0313469 + 0.0313469i
\(673\) −268.061 + 268.061i −0.398308 + 0.398308i −0.877636 0.479328i \(-0.840880\pi\)
0.479328 + 0.877636i \(0.340880\pi\)
\(674\) 155.211i 0.230283i
\(675\) 49.0483 + 120.288i 0.0726642 + 0.178205i
\(676\) 82.0021 0.121305
\(677\) 242.456 + 242.456i 0.358133 + 0.358133i 0.863124 0.504991i \(-0.168504\pi\)
−0.504991 + 0.863124i \(0.668504\pi\)
\(678\) 344.054 344.054i 0.507454 0.507454i
\(679\) 35.1556i 0.0517755i
\(680\) −58.5741 11.8194i −0.0861384 0.0173815i
\(681\) −55.9541 −0.0821647
\(682\) −486.905 486.905i −0.713937 0.713937i
\(683\) −636.304 + 636.304i −0.931630 + 0.931630i −0.997808 0.0661774i \(-0.978920\pi\)
0.0661774 + 0.997808i \(0.478920\pi\)
\(684\) 158.408i 0.231591i
\(685\) 14.6994 + 22.1313i 0.0214590 + 0.0323085i
\(686\) 381.639 0.556325
\(687\) 114.324 + 114.324i 0.166410 + 0.166410i
\(688\) −118.960 + 118.960i −0.172907 + 0.172907i
\(689\) 709.531i 1.02980i
\(690\) 48.9277 32.4974i 0.0709097 0.0470976i
\(691\) −761.609 −1.10218 −0.551092 0.834445i \(-0.685789\pi\)
−0.551092 + 0.834445i \(0.685789\pi\)
\(692\) 182.544 + 182.544i 0.263792 + 0.263792i
\(693\) −83.8282 + 83.8282i −0.120964 + 0.120964i
\(694\) 669.961i 0.965362i
\(695\) −241.469 + 1196.67i −0.347438 + 1.72182i
\(696\) 223.450 0.321049
\(697\) −117.640 117.640i −0.168780 0.168780i
\(698\) −462.956 + 462.956i −0.663261 + 0.663261i
\(699\) 377.860i 0.540572i
\(700\) −140.771 + 57.4004i −0.201102 + 0.0820006i
\(701\) −752.904 −1.07404 −0.537022 0.843569i \(-0.680451\pi\)
−0.537022 + 0.843569i \(0.680451\pi\)
\(702\) 75.2996 + 75.2996i 0.107264 + 0.107264i
\(703\) −1187.00 + 1187.00i −1.68848 + 1.68848i
\(704\) 103.975i 0.147692i
\(705\) −123.285 24.8771i −0.174873 0.0352867i
\(706\) −839.274 −1.18877
\(707\) −333.442 333.442i −0.471630 0.471630i
\(708\) −56.0286 + 56.0286i −0.0791364 + 0.0791364i
\(709\) 492.812i 0.695080i 0.937665 + 0.347540i \(0.112983\pi\)
−0.937665 + 0.347540i \(0.887017\pi\)
\(710\) −513.624 773.308i −0.723414 1.08917i
\(711\) −177.603 −0.249794
\(712\) 339.801 + 339.801i 0.477249 + 0.477249i
\(713\) 127.043 127.043i 0.178181 0.178181i
\(714\) 31.4685i 0.0440735i
\(715\) 784.453 521.027i 1.09714 0.728709i
\(716\) 268.322 0.374752
\(717\) 11.1124 + 11.1124i 0.0154984 + 0.0154984i
\(718\) −253.226 + 253.226i −0.352683 + 0.352683i
\(719\) 66.9427i 0.0931052i −0.998916 0.0465526i \(-0.985176\pi\)
0.998916 0.0465526i \(-0.0148235\pi\)
\(720\) 11.8679 58.8146i 0.0164832 0.0816869i
\(721\) −200.153 −0.277605
\(722\) −336.034 336.034i −0.465422 0.465422i
\(723\) −310.535 + 310.535i −0.429509 + 0.429509i
\(724\) 204.684i 0.282712i
\(725\) −442.182 + 1051.06i −0.609906 + 1.44974i
\(726\) −117.380 −0.161681
\(727\) −264.488 264.488i −0.363807 0.363807i 0.501406 0.865212i \(-0.332816\pi\)
−0.865212 + 0.501406i \(0.832816\pi\)
\(728\) −88.1218 + 88.1218i −0.121046 + 0.121046i
\(729\) 27.0000i 0.0370370i
\(730\) −480.842 97.0268i −0.658688 0.132913i
\(731\) −177.710 −0.243106
\(732\) 172.308 + 172.308i 0.235394 + 0.235394i
\(733\) 0.545555 0.545555i 0.000744277 0.000744277i −0.706735 0.707479i \(-0.749832\pi\)
0.707479 + 0.706735i \(0.249832\pi\)
\(734\) 266.467i 0.363035i
\(735\) −190.487 286.796i −0.259166 0.390198i
\(736\) −27.1293 −0.0368605
\(737\) −255.882 255.882i −0.347194 0.347194i
\(738\) 118.123 118.123i 0.160058 0.160058i
\(739\) 682.594i 0.923673i −0.886965 0.461836i \(-0.847191\pi\)
0.886965 0.461836i \(-0.152809\pi\)
\(740\) −529.646 + 351.786i −0.715738 + 0.475386i
\(741\) 662.672 0.894294
\(742\) 148.869 + 148.869i 0.200632 + 0.200632i
\(743\) −390.572 + 390.572i −0.525670 + 0.525670i −0.919278 0.393609i \(-0.871227\pi\)
0.393609 + 0.919278i \(0.371227\pi\)
\(744\) 183.531i 0.246681i
\(745\) −206.737 + 1024.54i −0.277499 + 1.37522i
\(746\) −316.140 −0.423780
\(747\) 93.1450 + 93.1450i 0.124692 + 0.124692i
\(748\) −77.6628 + 77.6628i −0.103827 + 0.103827i
\(749\) 58.8190i 0.0785301i
\(750\) 253.166 + 172.212i 0.337555 + 0.229615i
\(751\) −39.5226 −0.0526266 −0.0263133 0.999654i \(-0.508377\pi\)
−0.0263133 + 0.999654i \(0.508377\pi\)
\(752\) 41.0763 + 41.0763i 0.0546228 + 0.0546228i
\(753\) −171.381 + 171.381i −0.227598 + 0.227598i
\(754\) 934.760i 1.23974i
\(755\) 477.613 + 96.3753i 0.632601 + 0.127649i
\(756\) −31.5976 −0.0417958
\(757\) 775.732 + 775.732i 1.02474 + 1.02474i 0.999686 + 0.0250588i \(0.00797731\pi\)
0.0250588 + 0.999686i \(0.492023\pi\)
\(758\) 485.673 485.673i 0.640730 0.640730i
\(759\) 107.961i 0.142241i
\(760\) −206.576 311.019i −0.271811 0.409236i
\(761\) −993.258 −1.30520 −0.652600 0.757702i \(-0.726322\pi\)
−0.652600 + 0.757702i \(0.726322\pi\)
\(762\) 270.272 + 270.272i 0.354687 + 0.354687i
\(763\) −226.072 + 226.072i −0.296294 + 0.296294i
\(764\) 279.373i 0.365671i
\(765\) 52.7951 35.0660i 0.0690132 0.0458380i
\(766\) 894.121 1.16726
\(767\) −234.385 234.385i −0.305587 0.305587i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 938.784i 1.22079i 0.792099 + 0.610393i \(0.208988\pi\)
−0.792099 + 0.610393i \(0.791012\pi\)
\(770\) −55.2703 + 273.906i −0.0717796 + 0.355723i
\(771\) 68.1690 0.0884163
\(772\) −206.934 206.934i −0.268049 0.268049i
\(773\) 709.202 709.202i 0.917467 0.917467i −0.0793776 0.996845i \(-0.525293\pi\)
0.996845 + 0.0793776i \(0.0252933\pi\)
\(774\) 178.440i 0.230542i
\(775\) 863.291 + 363.187i 1.11392 + 0.468628i
\(776\) −32.7036 −0.0421439
\(777\) 236.771 + 236.771i 0.304725 + 0.304725i
\(778\) 252.009 252.009i 0.323919 0.323919i
\(779\) 1039.53i