Properties

Label 105.3.l.a.22.9
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.9
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.9

$q$-expansion

\(f(q)\) \(=\) \(q+(2.08980 + 2.08980i) q^{2} +(-1.22474 + 1.22474i) q^{3} +4.73454i q^{4} +(0.137153 + 4.99812i) q^{5} -5.11895 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-1.53505 + 1.53505i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(2.08980 + 2.08980i) q^{2} +(-1.22474 + 1.22474i) q^{3} +4.73454i q^{4} +(0.137153 + 4.99812i) q^{5} -5.11895 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-1.53505 + 1.53505i) q^{8} -3.00000i q^{9} +(-10.1585 + 10.7317i) q^{10} +2.70159 q^{11} +(-5.79861 - 5.79861i) q^{12} +(-2.37916 + 2.37916i) q^{13} -7.81932i q^{14} +(-6.28940 - 5.95344i) q^{15} +12.5223 q^{16} +(16.3715 + 16.3715i) q^{17} +(6.26941 - 6.26941i) q^{18} -9.18722i q^{19} +(-23.6638 + 0.649359i) q^{20} +4.58258 q^{21} +(5.64579 + 5.64579i) q^{22} +(21.4530 - 21.4530i) q^{23} -3.76010i q^{24} +(-24.9624 + 1.37102i) q^{25} -9.94394 q^{26} +(3.67423 + 3.67423i) q^{27} +(8.85752 - 8.85752i) q^{28} -52.3515i q^{29} +(-0.702081 - 25.5851i) q^{30} -5.01849 q^{31} +(32.3093 + 32.3093i) q^{32} +(-3.30876 + 3.30876i) q^{33} +68.4262i q^{34} +(9.09403 - 9.60721i) q^{35} +14.2036 q^{36} +(23.2257 + 23.2257i) q^{37} +(19.1995 - 19.1995i) q^{38} -5.82772i q^{39} +(-7.88291 - 7.46184i) q^{40} -60.5336 q^{41} +(9.57668 + 9.57668i) q^{42} +(-8.78639 + 8.78639i) q^{43} +12.7908i q^{44} +(14.9944 - 0.411460i) q^{45} +89.6651 q^{46} +(2.24235 + 2.24235i) q^{47} +(-15.3366 + 15.3366i) q^{48} +7.00000i q^{49} +(-55.0316 - 49.3013i) q^{50} -40.1017 q^{51} +(-11.2642 - 11.2642i) q^{52} +(-25.6733 + 25.6733i) q^{53} +15.3568i q^{54} +(0.370533 + 13.5029i) q^{55} +5.74364 q^{56} +(11.2520 + 11.2520i) q^{57} +(109.404 - 109.404i) q^{58} -100.980i q^{59} +(28.1868 - 29.7774i) q^{60} -82.1567 q^{61} +(-10.4877 - 10.4877i) q^{62} +(-5.61249 + 5.61249i) q^{63} +84.9509i q^{64} +(-12.2176 - 11.5650i) q^{65} -13.8293 q^{66} +(-65.1606 - 65.1606i) q^{67} +(-77.5114 + 77.5114i) q^{68} +52.5489i q^{69} +(39.0819 - 1.07245i) q^{70} -22.8905 q^{71} +(4.60516 + 4.60516i) q^{72} +(-5.38609 + 5.38609i) q^{73} +97.0741i q^{74} +(28.8934 - 32.2517i) q^{75} +43.4973 q^{76} +(-5.05422 - 5.05422i) q^{77} +(12.1788 - 12.1788i) q^{78} +117.836i q^{79} +(1.71747 + 62.5878i) q^{80} -9.00000 q^{81} +(-126.503 - 126.503i) q^{82} +(85.5086 - 85.5086i) q^{83} +21.6964i q^{84} +(-79.5811 + 84.0719i) q^{85} -36.7236 q^{86} +(64.1173 + 64.1173i) q^{87} +(-4.14709 + 4.14709i) q^{88} +119.010i q^{89} +(32.1951 + 30.4754i) q^{90} +8.90199 q^{91} +(101.570 + 101.570i) q^{92} +(6.14637 - 6.14637i) q^{93} +9.37213i q^{94} +(45.9188 - 1.26006i) q^{95} -79.1412 q^{96} +(-55.1059 - 55.1059i) q^{97} +(-14.6286 + 14.6286i) q^{98} -8.10478i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.08980 + 2.08980i 1.04490 + 1.04490i 0.998943 + 0.0459576i \(0.0146339\pi\)
0.0459576 + 0.998943i \(0.485366\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 4.73454i 1.18364i
\(5\) 0.137153 + 4.99812i 0.0274307 + 0.999624i
\(6\) −5.11895 −0.853158
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) −1.53505 + 1.53505i −0.191882 + 0.191882i
\(9\) 3.00000i 0.333333i
\(10\) −10.1585 + 10.7317i −1.01585 + 1.07317i
\(11\) 2.70159 0.245599 0.122800 0.992431i \(-0.460813\pi\)
0.122800 + 0.992431i \(0.460813\pi\)
\(12\) −5.79861 5.79861i −0.483217 0.483217i
\(13\) −2.37916 + 2.37916i −0.183012 + 0.183012i −0.792667 0.609655i \(-0.791308\pi\)
0.609655 + 0.792667i \(0.291308\pi\)
\(14\) 7.81932i 0.558523i
\(15\) −6.28940 5.95344i −0.419293 0.396896i
\(16\) 12.5223 0.782642
\(17\) 16.3715 + 16.3715i 0.963027 + 0.963027i 0.999340 0.0363138i \(-0.0115616\pi\)
−0.0363138 + 0.999340i \(0.511562\pi\)
\(18\) 6.26941 6.26941i 0.348300 0.348300i
\(19\) 9.18722i 0.483538i −0.970334 0.241769i \(-0.922272\pi\)
0.970334 0.241769i \(-0.0777276\pi\)
\(20\) −23.6638 + 0.649359i −1.18319 + 0.0324679i
\(21\) 4.58258 0.218218
\(22\) 5.64579 + 5.64579i 0.256627 + 0.256627i
\(23\) 21.4530 21.4530i 0.932740 0.932740i −0.0651365 0.997876i \(-0.520748\pi\)
0.997876 + 0.0651365i \(0.0207483\pi\)
\(24\) 3.76010i 0.156671i
\(25\) −24.9624 + 1.37102i −0.998495 + 0.0548407i
\(26\) −9.94394 −0.382459
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 8.85752 8.85752i 0.316340 0.316340i
\(29\) 52.3515i 1.80523i −0.430453 0.902613i \(-0.641646\pi\)
0.430453 0.902613i \(-0.358354\pi\)
\(30\) −0.702081 25.5851i −0.0234027 0.852837i
\(31\) −5.01849 −0.161887 −0.0809434 0.996719i \(-0.525793\pi\)
−0.0809434 + 0.996719i \(0.525793\pi\)
\(32\) 32.3093 + 32.3093i 1.00966 + 1.00966i
\(33\) −3.30876 + 3.30876i −0.100265 + 0.100265i
\(34\) 68.4262i 2.01253i
\(35\) 9.09403 9.60721i 0.259830 0.274492i
\(36\) 14.2036 0.394545
\(37\) 23.2257 + 23.2257i 0.627721 + 0.627721i 0.947494 0.319773i \(-0.103607\pi\)
−0.319773 + 0.947494i \(0.603607\pi\)
\(38\) 19.1995 19.1995i 0.505249 0.505249i
\(39\) 5.82772i 0.149429i
\(40\) −7.88291 7.46184i −0.197073 0.186546i
\(41\) −60.5336 −1.47643 −0.738215 0.674566i \(-0.764331\pi\)
−0.738215 + 0.674566i \(0.764331\pi\)
\(42\) 9.57668 + 9.57668i 0.228016 + 0.228016i
\(43\) −8.78639 + 8.78639i −0.204335 + 0.204335i −0.801854 0.597520i \(-0.796153\pi\)
0.597520 + 0.801854i \(0.296153\pi\)
\(44\) 12.7908i 0.290700i
\(45\) 14.9944 0.411460i 0.333208 0.00914356i
\(46\) 89.6651 1.94924
\(47\) 2.24235 + 2.24235i 0.0477096 + 0.0477096i 0.730559 0.682850i \(-0.239260\pi\)
−0.682850 + 0.730559i \(0.739260\pi\)
\(48\) −15.3366 + 15.3366i −0.319512 + 0.319512i
\(49\) 7.00000i 0.142857i
\(50\) −55.0316 49.3013i −1.10063 0.986025i
\(51\) −40.1017 −0.786308
\(52\) −11.2642 11.2642i −0.216620 0.216620i
\(53\) −25.6733 + 25.6733i −0.484401 + 0.484401i −0.906534 0.422133i \(-0.861282\pi\)
0.422133 + 0.906534i \(0.361282\pi\)
\(54\) 15.3568i 0.284386i
\(55\) 0.370533 + 13.5029i 0.00673696 + 0.245507i
\(56\) 5.74364 0.102565
\(57\) 11.2520 + 11.2520i 0.197404 + 0.197404i
\(58\) 109.404 109.404i 1.88628 1.88628i
\(59\) 100.980i 1.71152i −0.517374 0.855759i \(-0.673091\pi\)
0.517374 0.855759i \(-0.326909\pi\)
\(60\) 28.1868 29.7774i 0.469781 0.496291i
\(61\) −82.1567 −1.34683 −0.673415 0.739264i \(-0.735173\pi\)
−0.673415 + 0.739264i \(0.735173\pi\)
\(62\) −10.4877 10.4877i −0.169156 0.169156i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 84.9509i 1.32736i
\(65\) −12.2176 11.5650i −0.187963 0.177923i
\(66\) −13.8293 −0.209535
\(67\) −65.1606 65.1606i −0.972546 0.972546i 0.0270874 0.999633i \(-0.491377\pi\)
−0.999633 + 0.0270874i \(0.991377\pi\)
\(68\) −77.5114 + 77.5114i −1.13987 + 1.13987i
\(69\) 52.5489i 0.761579i
\(70\) 39.0819 1.07245i 0.558313 0.0153207i
\(71\) −22.8905 −0.322402 −0.161201 0.986922i \(-0.551537\pi\)
−0.161201 + 0.986922i \(0.551537\pi\)
\(72\) 4.60516 + 4.60516i 0.0639605 + 0.0639605i
\(73\) −5.38609 + 5.38609i −0.0737820 + 0.0737820i −0.743035 0.669253i \(-0.766614\pi\)
0.669253 + 0.743035i \(0.266614\pi\)
\(74\) 97.0741i 1.31181i
\(75\) 28.8934 32.2517i 0.385245 0.430023i
\(76\) 43.4973 0.572333
\(77\) −5.05422 5.05422i −0.0656392 0.0656392i
\(78\) 12.1788 12.1788i 0.156138 0.156138i
\(79\) 117.836i 1.49159i 0.666175 + 0.745795i \(0.267930\pi\)
−0.666175 + 0.745795i \(0.732070\pi\)
\(80\) 1.71747 + 62.5878i 0.0214684 + 0.782347i
\(81\) −9.00000 −0.111111
\(82\) −126.503 126.503i −1.54272 1.54272i
\(83\) 85.5086 85.5086i 1.03022 1.03022i 0.0306951 0.999529i \(-0.490228\pi\)
0.999529 0.0306951i \(-0.00977210\pi\)
\(84\) 21.6964i 0.258291i
\(85\) −79.5811 + 84.0719i −0.936248 + 0.989081i
\(86\) −36.7236 −0.427019
\(87\) 64.1173 + 64.1173i 0.736980 + 0.736980i
\(88\) −4.14709 + 4.14709i −0.0471260 + 0.0471260i
\(89\) 119.010i 1.33719i 0.743629 + 0.668593i \(0.233103\pi\)
−0.743629 + 0.668593i \(0.766897\pi\)
\(90\) 32.1951 + 30.4754i 0.357723 + 0.338615i
\(91\) 8.90199 0.0978241
\(92\) 101.570 + 101.570i 1.10402 + 1.10402i
\(93\) 6.14637 6.14637i 0.0660900 0.0660900i
\(94\) 9.37213i 0.0997035i
\(95\) 45.9188 1.26006i 0.483356 0.0132638i
\(96\) −79.1412 −0.824388
\(97\) −55.1059 55.1059i −0.568102 0.568102i 0.363494 0.931596i \(-0.381584\pi\)
−0.931596 + 0.363494i \(0.881584\pi\)
\(98\) −14.6286 + 14.6286i −0.149272 + 0.149272i
\(99\) 8.10478i 0.0818664i
\(100\) −6.49114 118.185i −0.0649114 1.18185i
\(101\) 128.322 1.27052 0.635259 0.772299i \(-0.280893\pi\)
0.635259 + 0.772299i \(0.280893\pi\)
\(102\) −83.8046 83.8046i −0.821614 0.821614i
\(103\) 10.5985 10.5985i 0.102898 0.102898i −0.653783 0.756682i \(-0.726819\pi\)
0.756682 + 0.653783i \(0.226819\pi\)
\(104\) 7.30426i 0.0702333i
\(105\) 0.628516 + 22.9043i 0.00598586 + 0.218136i
\(106\) −107.304 −1.01230
\(107\) 138.356 + 138.356i 1.29305 + 1.29305i 0.932894 + 0.360151i \(0.117275\pi\)
0.360151 + 0.932894i \(0.382725\pi\)
\(108\) −17.3958 + 17.3958i −0.161072 + 0.161072i
\(109\) 161.387i 1.48061i −0.672271 0.740305i \(-0.734681\pi\)
0.672271 0.740305i \(-0.265319\pi\)
\(110\) −27.4440 + 28.9927i −0.249491 + 0.263570i
\(111\) −56.8911 −0.512532
\(112\) −23.4270 23.4270i −0.209170 0.209170i
\(113\) −34.2178 + 34.2178i −0.302812 + 0.302812i −0.842113 0.539301i \(-0.818689\pi\)
0.539301 + 0.842113i \(0.318689\pi\)
\(114\) 47.0289i 0.412534i
\(115\) 110.167 + 104.282i 0.957975 + 0.906803i
\(116\) 247.861 2.13673
\(117\) 7.13747 + 7.13747i 0.0610040 + 0.0610040i
\(118\) 211.027 211.027i 1.78837 1.78837i
\(119\) 61.2564i 0.514759i
\(120\) 18.7934 0.515710i 0.156612 0.00429758i
\(121\) −113.701 −0.939681
\(122\) −171.691 171.691i −1.40730 1.40730i
\(123\) 74.1383 74.1383i 0.602750 0.602750i
\(124\) 23.7603i 0.191615i
\(125\) −10.2762 124.577i −0.0822095 0.996615i
\(126\) −23.4580 −0.186174
\(127\) −13.3778 13.3778i −0.105337 0.105337i 0.652474 0.757811i \(-0.273731\pi\)
−0.757811 + 0.652474i \(0.773731\pi\)
\(128\) −48.2934 + 48.2934i −0.377292 + 0.377292i
\(129\) 21.5222i 0.166838i
\(130\) −1.36384 49.7010i −0.0104911 0.382315i
\(131\) 27.9162 0.213101 0.106550 0.994307i \(-0.466019\pi\)
0.106550 + 0.994307i \(0.466019\pi\)
\(132\) −15.6655 15.6655i −0.118678 0.118678i
\(133\) −17.1877 + 17.1877i −0.129231 + 0.129231i
\(134\) 272.345i 2.03243i
\(135\) −17.8603 + 18.8682i −0.132299 + 0.139764i
\(136\) −50.2621 −0.369574
\(137\) 69.2726 + 69.2726i 0.505639 + 0.505639i 0.913185 0.407546i \(-0.133615\pi\)
−0.407546 + 0.913185i \(0.633615\pi\)
\(138\) −109.817 + 109.817i −0.795775 + 0.795775i
\(139\) 233.891i 1.68267i −0.540513 0.841335i \(-0.681770\pi\)
0.540513 0.841335i \(-0.318230\pi\)
\(140\) 45.4858 + 43.0561i 0.324898 + 0.307544i
\(141\) −5.49261 −0.0389547
\(142\) −47.8367 47.8367i −0.336878 0.336878i
\(143\) −6.42751 + 6.42751i −0.0449477 + 0.0449477i
\(144\) 37.5668i 0.260881i
\(145\) 261.659 7.18019i 1.80455 0.0495186i
\(146\) −22.5117 −0.154190
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) −109.963 + 109.963i −0.742993 + 0.742993i
\(149\) 127.594i 0.856336i 0.903699 + 0.428168i \(0.140841\pi\)
−0.903699 + 0.428168i \(0.859159\pi\)
\(150\) 127.781 7.01817i 0.851874 0.0467878i
\(151\) 49.1914 0.325771 0.162886 0.986645i \(-0.447920\pi\)
0.162886 + 0.986645i \(0.447920\pi\)
\(152\) 14.1029 + 14.1029i 0.0927821 + 0.0927821i
\(153\) 49.1144 49.1144i 0.321009 0.321009i
\(154\) 21.1246i 0.137173i
\(155\) −0.688303 25.0830i −0.00444067 0.161826i
\(156\) 27.5916 0.176869
\(157\) 130.828 + 130.828i 0.833301 + 0.833301i 0.987967 0.154666i \(-0.0494302\pi\)
−0.154666 + 0.987967i \(0.549430\pi\)
\(158\) −246.253 + 246.253i −1.55856 + 1.55856i
\(159\) 62.8864i 0.395512i
\(160\) −157.054 + 165.917i −0.981589 + 1.03698i
\(161\) −80.2698 −0.498570
\(162\) −18.8082 18.8082i −0.116100 0.116100i
\(163\) −35.5824 + 35.5824i −0.218297 + 0.218297i −0.807780 0.589483i \(-0.799331\pi\)
0.589483 + 0.807780i \(0.299331\pi\)
\(164\) 286.599i 1.74756i
\(165\) −16.9914 16.0838i −0.102978 0.0974774i
\(166\) 357.392 2.15296
\(167\) 27.7479 + 27.7479i 0.166155 + 0.166155i 0.785287 0.619132i \(-0.212515\pi\)
−0.619132 + 0.785287i \(0.712515\pi\)
\(168\) −7.03449 + 7.03449i −0.0418720 + 0.0418720i
\(169\) 157.679i 0.933013i
\(170\) −342.002 + 9.38488i −2.01178 + 0.0552052i
\(171\) −27.5617 −0.161179
\(172\) −41.5995 41.5995i −0.241858 0.241858i
\(173\) −190.785 + 190.785i −1.10280 + 1.10280i −0.108732 + 0.994071i \(0.534679\pi\)
−0.994071 + 0.108732i \(0.965321\pi\)
\(174\) 267.985i 1.54014i
\(175\) 49.2653 + 44.1354i 0.281516 + 0.252202i
\(176\) 33.8301 0.192216
\(177\) 123.674 + 123.674i 0.698724 + 0.698724i
\(178\) −248.706 + 248.706i −1.39723 + 1.39723i
\(179\) 180.379i 1.00770i −0.863791 0.503851i \(-0.831916\pi\)
0.863791 0.503851i \(-0.168084\pi\)
\(180\) 1.94808 + 70.9914i 0.0108226 + 0.394397i
\(181\) −20.8061 −0.114951 −0.0574754 0.998347i \(-0.518305\pi\)
−0.0574754 + 0.998347i \(0.518305\pi\)
\(182\) 18.6034 + 18.6034i 0.102217 + 0.102217i
\(183\) 100.621 100.621i 0.549841 0.549841i
\(184\) 65.8630i 0.357951i
\(185\) −112.899 + 119.270i −0.610266 + 0.644704i
\(186\) 25.6894 0.138115
\(187\) 44.2290 + 44.2290i 0.236519 + 0.236519i
\(188\) −10.6165 + 10.6165i −0.0564708 + 0.0564708i
\(189\) 13.7477i 0.0727393i
\(190\) 98.5946 + 93.3280i 0.518919 + 0.491200i
\(191\) 221.603 1.16022 0.580112 0.814536i \(-0.303009\pi\)
0.580112 + 0.814536i \(0.303009\pi\)
\(192\) −104.043 104.043i −0.541891 0.541891i
\(193\) −188.688 + 188.688i −0.977659 + 0.977659i −0.999756 0.0220973i \(-0.992966\pi\)
0.0220973 + 0.999756i \(0.492966\pi\)
\(194\) 230.321i 1.18722i
\(195\) 29.1276 0.799292i 0.149373 0.00409893i
\(196\) −33.1418 −0.169091
\(197\) 85.7353 + 85.7353i 0.435205 + 0.435205i 0.890394 0.455190i \(-0.150429\pi\)
−0.455190 + 0.890394i \(0.650429\pi\)
\(198\) 16.9374 16.9374i 0.0855423 0.0855423i
\(199\) 106.621i 0.535783i −0.963449 0.267892i \(-0.913673\pi\)
0.963449 0.267892i \(-0.0863269\pi\)
\(200\) 36.2140 40.4231i 0.181070 0.202116i
\(201\) 159.610 0.794080
\(202\) 268.168 + 268.168i 1.32756 + 1.32756i
\(203\) −97.9408 + 97.9408i −0.482467 + 0.482467i
\(204\) 189.863i 0.930703i
\(205\) −8.30239 302.554i −0.0404995 1.47587i
\(206\) 44.2976 0.215037
\(207\) −64.3590 64.3590i −0.310913 0.310913i
\(208\) −29.7924 + 29.7924i −0.143233 + 0.143233i
\(209\) 24.8201i 0.118757i
\(210\) −46.5519 + 49.1788i −0.221676 + 0.234185i
\(211\) −210.119 −0.995827 −0.497913 0.867227i \(-0.665900\pi\)
−0.497913 + 0.867227i \(0.665900\pi\)
\(212\) −121.551 121.551i −0.573355 0.573355i
\(213\) 28.0351 28.0351i 0.131620 0.131620i
\(214\) 578.273i 2.70221i
\(215\) −45.1205 42.7103i −0.209863 0.198653i
\(216\) −11.2803 −0.0522235
\(217\) 9.38874 + 9.38874i 0.0432661 + 0.0432661i
\(218\) 337.266 337.266i 1.54709 1.54709i
\(219\) 13.1932i 0.0602428i
\(220\) −63.9300 + 1.75430i −0.290591 + 0.00797410i
\(221\) −77.9005 −0.352491
\(222\) −118.891 118.891i −0.535545 0.535545i
\(223\) −138.303 + 138.303i −0.620191 + 0.620191i −0.945580 0.325389i \(-0.894505\pi\)
0.325389 + 0.945580i \(0.394505\pi\)
\(224\) 120.890i 0.539688i
\(225\) 4.11305 + 74.8871i 0.0182802 + 0.332832i
\(226\) −143.017 −0.632818
\(227\) −286.401 286.401i −1.26168 1.26168i −0.950280 0.311397i \(-0.899203\pi\)
−0.311397 0.950280i \(-0.600797\pi\)
\(228\) −53.2731 + 53.2731i −0.233654 + 0.233654i
\(229\) 210.860i 0.920787i −0.887715 0.460394i \(-0.847708\pi\)
0.887715 0.460394i \(-0.152292\pi\)
\(230\) 12.2979 + 448.157i 0.0534690 + 1.94851i
\(231\) 12.3803 0.0535942
\(232\) 80.3624 + 80.3624i 0.346389 + 0.346389i
\(233\) 217.881 217.881i 0.935112 0.935112i −0.0629077 0.998019i \(-0.520037\pi\)
0.998019 + 0.0629077i \(0.0200374\pi\)
\(234\) 29.8318i 0.127486i
\(235\) −10.9000 + 11.5151i −0.0463829 + 0.0490003i
\(236\) 478.092 2.02581
\(237\) −144.319 144.319i −0.608939 0.608939i
\(238\) 128.014 128.014i 0.537873 0.537873i
\(239\) 103.424i 0.432737i 0.976312 + 0.216369i \(0.0694213\pi\)
−0.976312 + 0.216369i \(0.930579\pi\)
\(240\) −78.7575 74.5506i −0.328156 0.310627i
\(241\) −13.3346 −0.0553304 −0.0276652 0.999617i \(-0.508807\pi\)
−0.0276652 + 0.999617i \(0.508807\pi\)
\(242\) −237.613 237.613i −0.981874 0.981874i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 388.974i 1.59416i
\(245\) −34.9868 + 0.960074i −0.142803 + 0.00391867i
\(246\) 309.869 1.25963
\(247\) 21.8579 + 21.8579i 0.0884934 + 0.0884934i
\(248\) 7.70365 7.70365i 0.0310631 0.0310631i
\(249\) 209.452i 0.841174i
\(250\) 238.866 281.816i 0.955463 1.12726i
\(251\) −324.833 −1.29416 −0.647078 0.762424i \(-0.724009\pi\)
−0.647078 + 0.762424i \(0.724009\pi\)
\(252\) −26.5726 26.5726i −0.105447 0.105447i
\(253\) 57.9573 57.9573i 0.229080 0.229080i
\(254\) 55.9141i 0.220134i
\(255\) −5.50009 200.433i −0.0215690 0.786012i
\(256\) 137.956 0.538891
\(257\) 45.5488 + 45.5488i 0.177233 + 0.177233i 0.790148 0.612916i \(-0.210003\pi\)
−0.612916 + 0.790148i \(0.710003\pi\)
\(258\) 44.9771 44.9771i 0.174330 0.174330i
\(259\) 86.9025i 0.335531i
\(260\) 54.7550 57.8449i 0.210596 0.222480i
\(261\) −157.055 −0.601742
\(262\) 58.3393 + 58.3393i 0.222669 + 0.222669i
\(263\) −186.483 + 186.483i −0.709062 + 0.709062i −0.966338 0.257276i \(-0.917175\pi\)
0.257276 + 0.966338i \(0.417175\pi\)
\(264\) 10.1582i 0.0384782i
\(265\) −131.839 124.797i −0.497506 0.470931i
\(266\) −71.8379 −0.270067
\(267\) −145.756 145.756i −0.545904 0.545904i
\(268\) 308.506 308.506i 1.15114 1.15114i
\(269\) 489.403i 1.81934i 0.415330 + 0.909671i \(0.363666\pi\)
−0.415330 + 0.909671i \(0.636334\pi\)
\(270\) −76.7553 + 2.10624i −0.284279 + 0.00780090i
\(271\) 35.3651 0.130499 0.0652493 0.997869i \(-0.479216\pi\)
0.0652493 + 0.997869i \(0.479216\pi\)
\(272\) 205.008 + 205.008i 0.753705 + 0.753705i
\(273\) −10.9027 + 10.9027i −0.0399365 + 0.0399365i
\(274\) 289.532i 1.05669i
\(275\) −67.4382 + 3.70393i −0.245230 + 0.0134688i
\(276\) −248.795 −0.901432
\(277\) −88.7149 88.7149i −0.320270 0.320270i 0.528600 0.848871i \(-0.322717\pi\)
−0.848871 + 0.528600i \(0.822717\pi\)
\(278\) 488.786 488.786i 1.75822 1.75822i
\(279\) 15.0555i 0.0539623i
\(280\) 0.787760 + 28.7074i 0.00281343 + 0.102526i
\(281\) −31.7224 −0.112891 −0.0564456 0.998406i \(-0.517977\pi\)
−0.0564456 + 0.998406i \(0.517977\pi\)
\(282\) −11.4785 11.4785i −0.0407038 0.0407038i
\(283\) −111.462 + 111.462i −0.393859 + 0.393859i −0.876060 0.482202i \(-0.839837\pi\)
0.482202 + 0.876060i \(0.339837\pi\)
\(284\) 108.376i 0.381607i
\(285\) −54.6956 + 57.7821i −0.191914 + 0.202744i
\(286\) −26.8645 −0.0939317
\(287\) 113.248 + 113.248i 0.394593 + 0.394593i
\(288\) 96.9278 96.9278i 0.336555 0.336555i
\(289\) 247.049i 0.854841i
\(290\) 561.821 + 531.811i 1.93731 + 1.83383i
\(291\) 134.981 0.463854
\(292\) −25.5007 25.5007i −0.0873311 0.0873311i
\(293\) 10.3345 10.3345i 0.0352712 0.0352712i −0.689251 0.724522i \(-0.742060\pi\)
0.724522 + 0.689251i \(0.242060\pi\)
\(294\) 35.8326i 0.121880i
\(295\) 504.708 13.8497i 1.71087 0.0469481i
\(296\) −71.3053 −0.240896
\(297\) 9.92628 + 9.92628i 0.0334218 + 0.0334218i
\(298\) −266.646 + 266.646i −0.894786 + 0.894786i
\(299\) 102.080i 0.341405i
\(300\) 152.697 + 136.797i 0.508990 + 0.455990i
\(301\) 32.8756 0.109221
\(302\) 102.800 + 102.800i 0.340399 + 0.340399i
\(303\) −157.162 + 157.162i −0.518687 + 0.518687i
\(304\) 115.045i 0.378437i
\(305\) −11.2681 410.629i −0.0369445 1.34632i
\(306\) 205.279 0.670845
\(307\) 296.667 + 296.667i 0.966341 + 0.966341i 0.999452 0.0331110i \(-0.0105415\pi\)
−0.0331110 + 0.999452i \(0.510541\pi\)
\(308\) 23.9294 23.9294i 0.0776929 0.0776929i
\(309\) 25.9610i 0.0840160i
\(310\) 50.9801 53.8570i 0.164452 0.173732i
\(311\) −36.8400 −0.118457 −0.0592284 0.998244i \(-0.518864\pi\)
−0.0592284 + 0.998244i \(0.518864\pi\)
\(312\) 8.94586 + 8.94586i 0.0286726 + 0.0286726i
\(313\) −90.5345 + 90.5345i −0.289248 + 0.289248i −0.836783 0.547535i \(-0.815566\pi\)
0.547535 + 0.836783i \(0.315566\pi\)
\(314\) 546.810i 1.74143i
\(315\) −28.8216 27.2821i −0.0914973 0.0866098i
\(316\) −557.898 −1.76550
\(317\) 2.40123 + 2.40123i 0.00757485 + 0.00757485i 0.710884 0.703309i \(-0.248295\pi\)
−0.703309 + 0.710884i \(0.748295\pi\)
\(318\) 131.420 131.420i 0.413271 0.413271i
\(319\) 141.433i 0.443362i
\(320\) −424.595 + 11.6513i −1.32686 + 0.0364103i
\(321\) −338.901 −1.05577
\(322\) −167.748 167.748i −0.520957 0.520957i
\(323\) 150.408 150.408i 0.465660 0.465660i
\(324\) 42.6109i 0.131515i
\(325\) 56.1276 62.6513i 0.172700 0.192773i
\(326\) −148.720 −0.456198
\(327\) 197.657 + 197.657i 0.604457 + 0.604457i
\(328\) 92.9223 92.9223i 0.283300 0.283300i
\(329\) 8.39010i 0.0255018i
\(330\) −1.89674 69.1205i −0.00574769 0.209456i
\(331\) −288.021 −0.870154 −0.435077 0.900393i \(-0.643279\pi\)
−0.435077 + 0.900393i \(0.643279\pi\)
\(332\) 404.844 + 404.844i 1.21941 + 1.21941i
\(333\) 69.6770 69.6770i 0.209240 0.209240i
\(334\) 115.975i 0.347232i
\(335\) 316.743 334.617i 0.945502 0.998857i
\(336\) 57.3842 0.170786
\(337\) −354.146 354.146i −1.05088 1.05088i −0.998634 0.0522432i \(-0.983363\pi\)
−0.0522432 0.998634i \(-0.516637\pi\)
\(338\) −329.518 + 329.518i −0.974906 + 0.974906i
\(339\) 83.8162i 0.247245i
\(340\) −398.042 376.780i −1.17071 1.10818i
\(341\) −13.5579 −0.0397593
\(342\) −57.5984 57.5984i −0.168416 0.168416i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 26.9751i 0.0784161i
\(345\) −262.646 + 7.20727i −0.761292 + 0.0208906i
\(346\) −797.405 −2.30464
\(347\) −440.033 440.033i −1.26811 1.26811i −0.947064 0.321044i \(-0.895966\pi\)
−0.321044 0.947064i \(-0.604034\pi\)
\(348\) −303.566 + 303.566i −0.872316 + 0.872316i
\(349\) 429.577i 1.23088i −0.788184 0.615440i \(-0.788978\pi\)
0.788184 0.615440i \(-0.211022\pi\)
\(350\) 10.7204 + 195.189i 0.0306298 + 0.557683i
\(351\) −17.4832 −0.0498096
\(352\) 87.2865 + 87.2865i 0.247973 + 0.247973i
\(353\) 240.557 240.557i 0.681463 0.681463i −0.278867 0.960330i \(-0.589959\pi\)
0.960330 + 0.278867i \(0.0899587\pi\)
\(354\) 516.909i 1.46020i
\(355\) −3.13952 114.410i −0.00884371 0.322281i
\(356\) −563.456 −1.58274
\(357\) 75.0234 + 75.0234i 0.210150 + 0.210150i
\(358\) 376.956 376.956i 1.05295 1.05295i
\(359\) 53.5007i 0.149027i −0.997220 0.0745135i \(-0.976260\pi\)
0.997220 0.0745135i \(-0.0237404\pi\)
\(360\) −22.3855 + 23.6487i −0.0621820 + 0.0656909i
\(361\) 276.595 0.766191
\(362\) −43.4806 43.4806i −0.120112 0.120112i
\(363\) 139.255 139.255i 0.383623 0.383623i
\(364\) 42.1469i 0.115788i
\(365\) −27.6590 26.1816i −0.0757781 0.0717304i
\(366\) 420.556 1.14906
\(367\) 1.26172 + 1.26172i 0.00343792 + 0.00343792i 0.708824 0.705386i \(-0.249226\pi\)
−0.705386 + 0.708824i \(0.749226\pi\)
\(368\) 268.640 268.640i 0.730001 0.730001i
\(369\) 181.601i 0.492143i
\(370\) −485.188 + 13.3140i −1.31132 + 0.0359839i
\(371\) 96.0606 0.258923
\(372\) 29.1003 + 29.1003i 0.0782266 + 0.0782266i
\(373\) −48.6449 + 48.6449i −0.130415 + 0.130415i −0.769301 0.638886i \(-0.779396\pi\)
0.638886 + 0.769301i \(0.279396\pi\)
\(374\) 184.860i 0.494277i
\(375\) 165.161 + 139.989i 0.440428 + 0.373305i
\(376\) −6.88425 −0.0183092
\(377\) 124.553 + 124.553i 0.330378 + 0.330378i
\(378\) 28.7300 28.7300i 0.0760054 0.0760054i
\(379\) 482.025i 1.27183i 0.771758 + 0.635917i \(0.219378\pi\)
−0.771758 + 0.635917i \(0.780622\pi\)
\(380\) 5.96581 + 217.405i 0.0156995 + 0.572118i
\(381\) 32.7689 0.0860076
\(382\) 463.106 + 463.106i 1.21232 + 1.21232i
\(383\) −75.2958 + 75.2958i −0.196595 + 0.196595i −0.798539 0.601944i \(-0.794393\pi\)
0.601944 + 0.798539i \(0.294393\pi\)
\(384\) 118.294i 0.308058i
\(385\) 24.5684 25.9548i 0.0638139 0.0674150i
\(386\) −788.641 −2.04311
\(387\) 26.3592 + 26.3592i 0.0681115 + 0.0681115i
\(388\) 260.901 260.901i 0.672426 0.672426i
\(389\) 270.881i 0.696353i 0.937429 + 0.348176i \(0.113199\pi\)
−0.937429 + 0.348176i \(0.886801\pi\)
\(390\) 62.5414 + 59.2007i 0.160363 + 0.151797i
\(391\) 702.434 1.79651
\(392\) −10.7454 10.7454i −0.0274117 0.0274117i
\(393\) −34.1902 + 34.1902i −0.0869979 + 0.0869979i
\(394\) 358.340i 0.909492i
\(395\) −588.957 + 16.1616i −1.49103 + 0.0409153i
\(396\) 38.3724 0.0969001
\(397\) −62.2126 62.2126i −0.156707 0.156707i 0.624399 0.781106i \(-0.285344\pi\)
−0.781106 + 0.624399i \(0.785344\pi\)
\(398\) 222.817 222.817i 0.559841 0.559841i
\(399\) 42.1012i 0.105517i
\(400\) −312.586 + 17.1683i −0.781464 + 0.0429206i
\(401\) 520.801 1.29876 0.649378 0.760466i \(-0.275029\pi\)
0.649378 + 0.760466i \(0.275029\pi\)
\(402\) 333.554 + 333.554i 0.829735 + 0.829735i
\(403\) 11.9398 11.9398i 0.0296273 0.0296273i
\(404\) 607.547i 1.50383i
\(405\) −1.23438 44.9831i −0.00304785 0.111069i
\(406\) −409.354 −1.00826
\(407\) 62.7463 + 62.7463i 0.154168 + 0.154168i
\(408\) 61.5582 61.5582i 0.150878 0.150878i
\(409\) 575.516i 1.40713i −0.710631 0.703564i \(-0.751591\pi\)
0.710631 0.703564i \(-0.248409\pi\)
\(410\) 614.928 649.629i 1.49982 1.58446i
\(411\) −169.682 −0.412853
\(412\) 50.1791 + 50.1791i 0.121794 + 0.121794i
\(413\) −188.916 + 188.916i −0.457423 + 0.457423i
\(414\) 268.995i 0.649747i
\(415\) 439.110 + 415.654i 1.05810 + 1.00158i
\(416\) −153.738 −0.369562
\(417\) 286.457 + 286.457i 0.686947 + 0.686947i
\(418\) 51.8692 51.8692i 0.124089 0.124089i
\(419\) 113.474i 0.270822i −0.990790 0.135411i \(-0.956765\pi\)
0.990790 0.135411i \(-0.0432355\pi\)
\(420\) −108.441 + 2.97574i −0.258193 + 0.00708509i
\(421\) 737.737 1.75234 0.876172 0.481999i \(-0.160089\pi\)
0.876172 + 0.481999i \(0.160089\pi\)
\(422\) −439.108 439.108i −1.04054 1.04054i
\(423\) 6.72705 6.72705i 0.0159032 0.0159032i
\(424\) 78.8196i 0.185895i
\(425\) −431.116 386.225i −1.01439 0.908764i
\(426\) 117.176 0.275060
\(427\) 153.701 + 153.701i 0.359956 + 0.359956i
\(428\) −655.052 + 655.052i −1.53049 + 1.53049i
\(429\) 15.7441i 0.0366996i
\(430\) −5.03677 183.549i −0.0117134 0.426858i
\(431\) 626.096 1.45266 0.726329 0.687347i \(-0.241225\pi\)
0.726329 + 0.687347i \(0.241225\pi\)
\(432\) 46.0097 + 46.0097i 0.106504 + 0.106504i
\(433\) 99.3139 99.3139i 0.229362 0.229362i −0.583064 0.812426i \(-0.698146\pi\)
0.812426 + 0.583064i \(0.198146\pi\)
\(434\) 39.2412i 0.0904176i
\(435\) −311.672 + 329.260i −0.716487 + 0.756919i
\(436\) 764.092 1.75250
\(437\) −197.094 197.094i −0.451015 0.451015i
\(438\) 27.5711 27.5711i 0.0629477 0.0629477i
\(439\) 249.762i 0.568933i 0.958686 + 0.284467i \(0.0918165\pi\)
−0.958686 + 0.284467i \(0.908183\pi\)
\(440\) −21.2964 20.1588i −0.0484009 0.0458155i
\(441\) 21.0000 0.0476190
\(442\) −162.797 162.797i −0.368318 0.368318i
\(443\) −213.838 + 213.838i −0.482704 + 0.482704i −0.905994 0.423290i \(-0.860875\pi\)
0.423290 + 0.905994i \(0.360875\pi\)
\(444\) 269.353i 0.606651i
\(445\) −594.824 + 16.3226i −1.33668 + 0.0366799i
\(446\) −578.050 −1.29608
\(447\) −156.270 156.270i −0.349598 0.349598i
\(448\) 158.929 158.929i 0.354751 0.354751i
\(449\) 540.540i 1.20387i 0.798544 + 0.601937i \(0.205604\pi\)
−0.798544 + 0.601937i \(0.794396\pi\)
\(450\) −147.904 + 165.095i −0.328675 + 0.366877i
\(451\) −163.537 −0.362610
\(452\) −162.006 162.006i −0.358420 0.358420i
\(453\) −60.2470 + 60.2470i −0.132995 + 0.132995i
\(454\) 1197.04i 2.63666i
\(455\) 1.22094 + 44.4932i 0.00268338 + 0.0977873i
\(456\) −34.5448 −0.0757562
\(457\) −236.212 236.212i −0.516876 0.516876i 0.399749 0.916625i \(-0.369097\pi\)
−0.916625 + 0.399749i \(0.869097\pi\)
\(458\) 440.656 440.656i 0.962131 0.962131i
\(459\) 120.305i 0.262103i
\(460\) −493.729 + 521.591i −1.07332 + 1.13389i
\(461\) 156.987 0.340536 0.170268 0.985398i \(-0.445537\pi\)
0.170268 + 0.985398i \(0.445537\pi\)
\(462\) 25.8723 + 25.8723i 0.0560006 + 0.0560006i
\(463\) −269.161 + 269.161i −0.581342 + 0.581342i −0.935272 0.353930i \(-0.884845\pi\)
0.353930 + 0.935272i \(0.384845\pi\)
\(464\) 655.560i 1.41284i
\(465\) 31.5633 + 29.8773i 0.0678781 + 0.0642523i
\(466\) 910.656 1.95420
\(467\) 114.700 + 114.700i 0.245610 + 0.245610i 0.819166 0.573556i \(-0.194436\pi\)
−0.573556 + 0.819166i \(0.694436\pi\)
\(468\) −33.7927 + 33.7927i −0.0722066 + 0.0722066i
\(469\) 243.808i 0.519848i
\(470\) −46.8430 + 1.28542i −0.0996660 + 0.00273494i
\(471\) −320.462 −0.680387
\(472\) 155.009 + 155.009i 0.328409 + 0.328409i
\(473\) −23.7372 + 23.7372i −0.0501844 + 0.0501844i
\(474\) 603.195i 1.27256i
\(475\) 12.5958 + 229.335i 0.0265176 + 0.482810i
\(476\) 290.021 0.609288
\(477\) 77.0198 + 77.0198i 0.161467 + 0.161467i
\(478\) −216.136 + 216.136i −0.452168 + 0.452168i
\(479\) 158.331i 0.330546i −0.986248 0.165273i \(-0.947149\pi\)
0.986248 0.165273i \(-0.0528505\pi\)
\(480\) −10.8545 395.557i −0.0226135 0.824077i
\(481\) −110.515 −0.229761
\(482\) −27.8667 27.8667i −0.0578148 0.0578148i
\(483\) 98.3101 98.3101i 0.203541 0.203541i
\(484\) 538.324i 1.11224i
\(485\) 267.868 282.984i 0.552305 0.583472i
\(486\) 46.0705 0.0947953
\(487\) 220.865 + 220.865i 0.453521 + 0.453521i 0.896521 0.443000i \(-0.146086\pi\)
−0.443000 + 0.896521i \(0.646086\pi\)
\(488\) 126.115 126.115i 0.258432 0.258432i
\(489\) 87.1588i 0.178239i
\(490\) −75.1219 71.1092i −0.153310 0.145121i
\(491\) 925.802 1.88554 0.942772 0.333439i \(-0.108209\pi\)
0.942772 + 0.333439i \(0.108209\pi\)
\(492\) 351.011 + 351.011i 0.713437 + 0.713437i
\(493\) 857.071 857.071i 1.73848 1.73848i
\(494\) 91.3572i 0.184934i
\(495\) 40.5086 1.11160i 0.0818356 0.00224565i
\(496\) −62.8429 −0.126699
\(497\) 42.8243 + 42.8243i 0.0861656 + 0.0861656i
\(498\) −437.714 + 437.714i −0.878944 + 0.878944i
\(499\) 114.955i 0.230370i −0.993344 0.115185i \(-0.963254\pi\)
0.993344 0.115185i \(-0.0367461\pi\)
\(500\) 589.815 48.6531i 1.17963 0.0973061i
\(501\) −67.9683 −0.135665
\(502\) −678.837 678.837i −1.35226 1.35226i
\(503\) −46.4397 + 46.4397i −0.0923254 + 0.0923254i −0.751761 0.659436i \(-0.770795\pi\)
0.659436 + 0.751761i \(0.270795\pi\)
\(504\) 17.2309i 0.0341883i
\(505\) 17.5998 + 641.370i 0.0348512 + 1.27004i
\(506\) 242.239 0.478732
\(507\) −193.117 193.117i −0.380901 0.380901i
\(508\) 63.3380 63.3380i 0.124681 0.124681i
\(509\) 185.083i 0.363621i −0.983334 0.181811i \(-0.941804\pi\)
0.983334 0.181811i \(-0.0581958\pi\)
\(510\) 407.371 430.360i 0.798767 0.843842i
\(511\) 20.1529 0.0394381
\(512\) 481.475 + 481.475i 0.940380 + 0.940380i
\(513\) 33.7560 33.7560i 0.0658012 0.0658012i
\(514\) 190.376i 0.370381i
\(515\) 54.4262 + 51.5190i 0.105682 + 0.100037i
\(516\) 101.898 0.197476
\(517\) 6.05791 + 6.05791i 0.0117174 + 0.0117174i
\(518\) 181.609 181.609i 0.350597 0.350597i
\(519\) 467.326i 0.900435i
\(520\) 36.5076 1.00180i 0.0702069 0.00192655i
\(521\) −275.217 −0.528248 −0.264124 0.964489i \(-0.585083\pi\)
−0.264124 + 0.964489i \(0.585083\pi\)
\(522\) −328.213 328.213i −0.628761 0.628761i
\(523\) −424.281 + 424.281i −0.811245 + 0.811245i −0.984821 0.173576i \(-0.944468\pi\)
0.173576 + 0.984821i \(0.444468\pi\)
\(524\) 132.170i 0.252233i
\(525\) −114.392 + 6.28279i −0.217889 + 0.0119672i
\(526\) −779.426 −1.48180
\(527\) −82.1600 82.1600i −0.155901 0.155901i
\(528\) −41.4332 + 41.4332i −0.0784719 + 0.0784719i
\(529\) 391.464i 0.740007i
\(530\) −14.7171 536.318i −0.0277681 1.01192i
\(531\) −302.939 −0.570506
\(532\) −81.3760 81.3760i −0.152962 0.152962i
\(533\) 144.019 144.019i 0.270205 0.270205i
\(534\) 609.204i 1.14083i
\(535\) −672.543 + 710.495i −1.25709 + 1.32803i
\(536\) 200.050 0.373227
\(537\) 220.918 + 220.918i 0.411392 + 0.411392i
\(538\) −1022.76 + 1022.76i −1.90103 + 1.90103i
\(539\) 18.9111i 0.0350856i
\(540\) −89.3323 84.5605i −0.165430 0.156594i
\(541\) −484.593 −0.895735 −0.447868 0.894100i \(-0.647816\pi\)
−0.447868 + 0.894100i \(0.647816\pi\)
\(542\) 73.9061 + 73.9061i 0.136358 + 0.136358i
\(543\) 25.4821 25.4821i 0.0469284 0.0469284i
\(544\) 1057.90i 1.94467i
\(545\) 806.629 22.1347i 1.48005 0.0406142i
\(546\) −45.5688 −0.0834594
\(547\) −367.275 367.275i −0.671436 0.671436i 0.286611 0.958047i \(-0.407471\pi\)
−0.958047 + 0.286611i \(0.907471\pi\)
\(548\) −327.974 + 327.974i −0.598493 + 0.598493i
\(549\) 246.470i 0.448944i
\(550\) −148.673 133.192i −0.270314 0.242167i
\(551\) −480.965 −0.872895
\(552\) −80.6654 80.6654i −0.146133 0.146133i
\(553\) 220.450 220.450i 0.398644 0.398644i
\(554\) 370.793i 0.669302i
\(555\) −7.80280 284.348i −0.0140591 0.512339i
\(556\) 1107.37 1.99167
\(557\) 532.387 + 532.387i 0.955811 + 0.955811i 0.999064 0.0432528i \(-0.0137721\pi\)
−0.0432528 + 0.999064i \(0.513772\pi\)
\(558\) −31.4630 + 31.4630i −0.0563853 + 0.0563853i
\(559\) 41.8084i 0.0747914i
\(560\) 113.878 120.304i 0.203353 0.214829i
\(561\) −108.338 −0.193117
\(562\) −66.2936 66.2936i −0.117960 0.117960i
\(563\) −724.535 + 724.535i −1.28692 + 1.28692i −0.350268 + 0.936649i \(0.613910\pi\)
−0.936649 + 0.350268i \(0.886090\pi\)
\(564\) 26.0050i 0.0461082i
\(565\) −175.718 166.332i −0.311005 0.294392i
\(566\) −465.867 −0.823087
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) 35.1382 35.1382i 0.0618630 0.0618630i
\(569\) 63.5327i 0.111657i −0.998440 0.0558284i \(-0.982220\pi\)
0.998440 0.0558284i \(-0.0177800\pi\)
\(570\) −235.056 + 6.45018i −0.412379 + 0.0113161i
\(571\) 186.947 0.327403 0.163701 0.986510i \(-0.447657\pi\)
0.163701 + 0.986510i \(0.447657\pi\)
\(572\) −30.4314 30.4314i −0.0532017 0.0532017i
\(573\) −271.407 + 271.407i −0.473660 + 0.473660i
\(574\) 473.332i 0.824620i
\(575\) −506.106 + 564.931i −0.880184 + 0.982488i
\(576\) 254.853 0.442452
\(577\) 650.925 + 650.925i 1.12812 + 1.12812i 0.990483 + 0.137637i \(0.0439506\pi\)
0.137637 + 0.990483i \(0.456049\pi\)
\(578\) −516.283 + 516.283i −0.893224 + 0.893224i
\(579\) 462.190i 0.798255i
\(580\) 33.9949 + 1238.84i 0.0586120 + 2.13593i
\(581\) −319.944 −0.550678
\(582\) 282.084 + 282.084i 0.484681 + 0.484681i
\(583\) −69.3587 + 69.3587i −0.118969 + 0.118969i
\(584\) 16.5359i 0.0283148i
\(585\) −34.6950 + 36.6529i −0.0593077 + 0.0626545i
\(586\) 43.1939 0.0737098
\(587\) −451.044 451.044i −0.768389 0.768389i 0.209434 0.977823i \(-0.432838\pi\)
−0.977823 + 0.209434i \(0.932838\pi\)
\(588\) 40.5903 40.5903i 0.0690311 0.0690311i
\(589\) 46.1060i 0.0782785i
\(590\) 1083.68 + 1025.80i 1.83675 + 1.73864i
\(591\) −210.008 −0.355343
\(592\) 290.838 + 290.838i 0.491281 + 0.491281i
\(593\) 459.882 459.882i 0.775518 0.775518i −0.203547 0.979065i \(-0.565247\pi\)
0.979065 + 0.203547i \(0.0652471\pi\)
\(594\) 41.4879i 0.0698450i
\(595\) 306.167 8.40152i 0.514566 0.0141202i
\(596\) −604.100 −1.01359
\(597\) 130.583 + 130.583i 0.218733 + 0.218733i
\(598\) −213.327 + 213.327i −0.356735 + 0.356735i
\(599\) 415.835i 0.694216i 0.937825 + 0.347108i \(0.112836\pi\)
−0.937825 + 0.347108i \(0.887164\pi\)
\(600\) 5.15516 + 93.8609i 0.00859193 + 0.156435i
\(601\) −693.471 −1.15386 −0.576931 0.816793i \(-0.695750\pi\)
−0.576931 + 0.816793i \(0.695750\pi\)
\(602\) 68.7036 + 68.7036i 0.114126 + 0.114126i
\(603\) −195.482 + 195.482i −0.324182 + 0.324182i
\(604\) 232.899i 0.385594i
\(605\) −15.5945 568.293i −0.0257761 0.939327i
\(606\) −656.875 −1.08395
\(607\) 247.205 + 247.205i 0.407257 + 0.407257i 0.880781 0.473524i \(-0.157018\pi\)
−0.473524 + 0.880781i \(0.657018\pi\)
\(608\) 296.833 296.833i 0.488211 0.488211i
\(609\) 239.905i 0.393933i
\(610\) 834.585 881.681i 1.36817 1.44538i
\(611\) −10.6698 −0.0174629
\(612\) 232.534 + 232.534i 0.379958 + 0.379958i
\(613\) 512.566 512.566i 0.836159 0.836159i −0.152192 0.988351i \(-0.548633\pi\)
0.988351 + 0.152192i \(0.0486331\pi\)
\(614\) 1239.95i 2.01946i
\(615\) 380.720 + 360.383i 0.619057 + 0.585989i
\(616\) 15.5170 0.0251899
\(617\) −700.942 700.942i −1.13605 1.13605i −0.989152 0.146897i \(-0.953072\pi\)
−0.146897 0.989152i \(-0.546928\pi\)
\(618\) −54.2532 + 54.2532i −0.0877884 + 0.0877884i
\(619\) 354.521i 0.572732i 0.958120 + 0.286366i \(0.0924473\pi\)
−0.958120 + 0.286366i \(0.907553\pi\)
\(620\) 118.757 3.25880i 0.191543 0.00525613i
\(621\) 157.647 0.253860
\(622\) −76.9884 76.9884i −0.123776 0.123776i
\(623\) 222.646 222.646i 0.357378 0.357378i
\(624\) 72.9763i 0.116949i
\(625\) 621.241 68.4477i 0.993985 0.109516i
\(626\) −378.398 −0.604470
\(627\) 30.3983 + 30.3983i 0.0484822 + 0.0484822i
\(628\) −619.412 + 619.412i −0.986325 + 0.986325i
\(629\) 760.476i 1.20902i
\(630\) −3.21734 117.246i −0.00510689 0.186104i
\(631\) 930.684 1.47494 0.737468 0.675383i \(-0.236021\pi\)
0.737468 + 0.675383i \(0.236021\pi\)
\(632\) −180.884 180.884i −0.286209 0.286209i
\(633\) 257.343 257.343i 0.406545 0.406545i
\(634\) 10.0362i 0.0158299i
\(635\) 65.0292 68.6989i 0.102408 0.108187i
\(636\) 297.738 0.468142
\(637\) −16.6541 16.6541i −0.0261446 0.0261446i
\(638\) 295.566 295.566i 0.463270 0.463270i
\(639\) 68.6716i 0.107467i
\(640\) −248.000 234.753i −0.387500 0.366801i
\(641\) −499.986 −0.780009 −0.390005 0.920813i \(-0.627527\pi\)
−0.390005 + 0.920813i \(0.627527\pi\)
\(642\) −708.236 708.236i −1.10317 1.10317i
\(643\) −385.589 + 385.589i −0.599672 + 0.599672i −0.940225 0.340554i \(-0.889386\pi\)
0.340554 + 0.940225i \(0.389386\pi\)
\(644\) 380.041i 0.590126i
\(645\) 107.570 2.95184i 0.166776 0.00457649i
\(646\) 628.647 0.973137
\(647\) −84.6226 84.6226i −0.130792 0.130792i 0.638680 0.769472i \(-0.279481\pi\)
−0.769472 + 0.638680i \(0.779481\pi\)
\(648\) 13.8155 13.8155i 0.0213202 0.0213202i
\(649\) 272.806i 0.420348i
\(650\) 248.224 13.6333i 0.381884 0.0209743i
\(651\) −22.9976 −0.0353266
\(652\) −168.467 168.467i −0.258384 0.258384i
\(653\) −132.499 + 132.499i −0.202907 + 0.202907i −0.801244 0.598337i \(-0.795828\pi\)
0.598337 + 0.801244i \(0.295828\pi\)
\(654\) 826.130i 1.26320i
\(655\) 3.82880 + 139.528i 0.00584549 + 0.213020i
\(656\) −758.018 −1.15552
\(657\) 16.1583 + 16.1583i 0.0245940 + 0.0245940i
\(658\) 17.5337 17.5337i 0.0266469 0.0266469i
\(659\) 921.339i 1.39809i −0.715080 0.699043i \(-0.753610\pi\)
0.715080 0.699043i \(-0.246390\pi\)
\(660\) 76.1493 80.4465i 0.115378 0.121889i
\(661\) 705.918 1.06795 0.533977 0.845499i \(-0.320697\pi\)
0.533977 + 0.845499i \(0.320697\pi\)
\(662\) −601.907 601.907i −0.909224 0.909224i
\(663\) 95.4083 95.4083i 0.143904 0.143904i
\(664\) 262.520i 0.395362i
\(665\) −88.2636 83.5489i −0.132727 0.125637i
\(666\) 291.222 0.437271
\(667\) −1123.10 1123.10i −1.68381 1.68381i
\(668\) −131.374 + 131.374i −0.196667 + 0.196667i
\(669\) 338.771i 0.506384i
\(670\) 1361.21 37.3531i 2.03166 0.0557509i
\(671\) −221.954 −0.330781
\(672\) 148.060 + 148.060i 0.220327 + 0.220327i
\(673\) 480.376 480.376i 0.713783 0.713783i −0.253542 0.967324i \(-0.581595\pi\)
0.967324 + 0.253542i \(0.0815955\pi\)
\(674\) 1480.19i 2.19613i
\(675\) −96.7551 86.6802i −0.143341 0.128415i
\(676\) −746.539 −1.10435
\(677\) 146.784 + 146.784i 0.216815 + 0.216815i 0.807155 0.590340i \(-0.201006\pi\)
−0.590340 + 0.807155i \(0.701006\pi\)
\(678\) 175.159 175.159i 0.258347 0.258347i
\(679\) 206.187i 0.303663i
\(680\) −6.89361 251.216i −0.0101377 0.369435i
\(681\) 701.536 1.03016
\(682\) −28.3334 28.3334i −0.0415445 0.0415445i
\(683\) −88.7069 + 88.7069i −0.129878 + 0.129878i −0.769058 0.639179i \(-0.779274\pi\)
0.639179 + 0.769058i \(0.279274\pi\)
\(684\) 130.492i 0.190778i
\(685\) −336.731 + 355.733i −0.491579 + 0.519319i
\(686\) 54.7353 0.0797890
\(687\) 258.250 + 258.250i 0.375910 + 0.375910i
\(688\) −110.025 + 110.025i −0.159921 + 0.159921i
\(689\) 122.161i 0.177303i
\(690\) −563.940 533.816i −0.817304 0.773646i
\(691\) −664.952 −0.962304 −0.481152 0.876637i \(-0.659781\pi\)
−0.481152 + 0.876637i \(0.659781\pi\)
\(692\) −903.280 903.280i −1.30532 1.30532i
\(693\) −15.1626 + 15.1626i −0.0218797 + 0.0218797i
\(694\) 1839.17i 2.65009i
\(695\) 1169.02 32.0790i 1.68204 0.0461568i
\(696\) −196.847 −0.282826
\(697\) −991.023 991.023i −1.42184 1.42184i
\(698\) 897.731 897.731i 1.28615 1.28615i
\(699\) 533.697i 0.763515i
\(700\) −208.961 + 233.249i −0.298516 + 0.333212i
\(701\) −137.923 −0.196751 −0.0983757 0.995149i \(-0.531365\pi\)
−0.0983757 + 0.995149i \(0.531365\pi\)
\(702\) −36.5364 36.5364i −0.0520461 0.0520461i
\(703\) 213.380 213.380i 0.303527 0.303527i
\(704\) 229.503i 0.325998i
\(705\) −0.753330 27.4527i −0.00106855 0.0389400i
\(706\) 1005.43 1.42412
\(707\) −240.069 240.069i −0.339560 0.339560i
\(708\) −585.541 + 585.541i −0.827035 + 0.827035i
\(709\) 371.525i 0.524013i 0.965066 + 0.262006i \(0.0843842\pi\)
−0.965066 + 0.262006i \(0.915616\pi\)
\(710\) 232.533 245.655i 0.327511 0.345992i
\(711\) 353.507 0.497197
\(712\) −182.686 182.686i −0.256581 0.256581i
\(713\) −107.662 + 107.662i −0.150998 + 0.150998i
\(714\) 313.568i 0.439171i
\(715\) −33.0070 31.2439i −0.0461637 0.0436978i
\(716\) 854.010 1.19275
\(717\) −126.668 126.668i −0.176664 0.176664i
\(718\) 111.806 111.806i 0.155718 0.155718i
\(719\) 85.5943i 0.119046i 0.998227 + 0.0595232i \(0.0189580\pi\)
−0.998227 + 0.0595232i \(0.981042\pi\)
\(720\) 187.763 5.15241i 0.260782 0.00715613i
\(721\) −39.6560 −0.0550014
\(722\) 578.029 + 578.029i 0.800594 + 0.800594i
\(723\) 16.3315 16.3315i 0.0225886 0.0225886i
\(724\) 98.5073i 0.136060i
\(725\) 71.7749 + 1306.82i 0.0989999 + 1.80251i
\(726\) 582.032 0.801696
\(727\) 589.673 + 589.673i 0.811104 + 0.811104i 0.984799 0.173695i \(-0.0555707\pi\)
−0.173695 + 0.984799i \(0.555571\pi\)
\(728\) −13.6650 + 13.6650i −0.0187706 + 0.0187706i
\(729\) 27.0000i 0.0370370i
\(730\) −3.08756 112.516i −0.00422953 0.154132i
\(731\) −287.692 −0.393559
\(732\) 476.394 + 476.394i 0.650812 + 0.650812i
\(733\) 1019.17 1019.17i 1.39040 1.39040i 0.565992 0.824411i \(-0.308493\pi\)
0.824411 0.565992i \(-0.191507\pi\)
\(734\) 5.27347i 0.00718457i
\(735\) 41.6741 44.0258i 0.0566994 0.0598990i
\(736\) 1386.26 1.88351
\(737\) −176.037 176.037i −0.238857 0.238857i
\(738\) −379.510 + 379.510i −0.514241 + 0.514241i
\(739\) 54.4746i 0.0737139i 0.999321 + 0.0368570i \(0.0117346\pi\)
−0.999321 + 0.0368570i \(0.988265\pi\)
\(740\) −564.690 534.526i −0.763094 0.722333i
\(741\) −53.5406 −0.0722545
\(742\) 200.748 + 200.748i 0.270549 + 0.270549i
\(743\) 247.895 247.895i 0.333641 0.333641i −0.520326 0.853968i \(-0.674190\pi\)
0.853968 + 0.520326i \(0.174190\pi\)
\(744\) 18.8700i 0.0253629i
\(745\) −637.730 + 17.5000i −0.856014 + 0.0234899i
\(746\) −203.316 −0.272542
\(747\) −256.526 256.526i −0.343408 0.343408i
\(748\) −209.404 + 209.404i −0.279952 + 0.279952i
\(749\) 517.680i 0.691162i
\(750\) 52.6033 + 637.703i 0.0701377 + 0.850270i
\(751\) −1361.29 −1.81263 −0.906316 0.422600i \(-0.861117\pi\)
−0.906316 + 0.422600i \(0.861117\pi\)
\(752\) 28.0793 + 28.0793i 0.0373395 + 0.0373395i
\(753\) 397.838 397.838i 0.528337 0.528337i
\(754\) 520.580i 0.690425i
\(755\) 6.74677 + 245.865i 0.00893612 + 0.325648i
\(756\) 65.0892 0.0860969
\(757\) 178.475 + 178.475i 0.235767 + 0.235767i 0.815095 0.579328i \(-0.196685\pi\)
−0.579328 + 0.815095i \(0.696685\pi\)
\(758\) −1007.34 + 1007.34i −1.32894 + 1.32894i
\(759\) 141.966i 0.187043i
\(760\) −68.5536 + 72.4221i −0.0902021 + 0.0952922i
\(761\) 815.185 1.07120 0.535601 0.844471i \(-0.320085\pi\)
0.535601 + 0.844471i \(0.320085\pi\)
\(762\) 68.4805 + 68.4805i 0.0898694 + 0.0898694i
\(763\) −301.927 + 301.927i −0.395710 + 0.395710i
\(764\) 1049.19i 1.37328i
\(765\) 252.216 + 238.743i 0.329694 + 0.312083i
\(766\) −314.707 −0.410844
\(767\) 240.246 + 240.246i 0.313229 + 0.313229i
\(768\) −168.961 + 168.961i −0.220001 + 0.220001i
\(769\) 327.202i 0.425490i 0.977108 + 0.212745i \(0.0682403\pi\)
−0.977108 + 0.212745i \(0.931760\pi\)
\(770\) 105.583 2.89731i 0.137121 0.00376274i
\(771\) −111.571 −0.144710
\(772\) −893.352 893.352i −1.15719 1.15719i
\(773\) 224.127 224.127i 0.289944 0.289944i −0.547114 0.837058i