Properties

Label 24.3.b.a.19.3
Level 24
Weight 3
Character 24.19
Analytic conductor 0.654
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 24.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.653952634465\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.4752.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.3
Root \(-0.866025 + 1.99551i\)
Character \(\chi\) = 24.19
Dual form 24.3.b.a.19.4

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(1.36603 - 1.46081i) q^{2}\) \(-1.73205 q^{3}\) \(+(-0.267949 - 3.99102i) q^{4}\) \(+7.98203i q^{5}\) \(+(-2.36603 + 2.53020i) q^{6}\) \(-2.13878i q^{7}\) \(+(-6.19615 - 5.06040i) q^{8}\) \(+3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+(1.36603 - 1.46081i) q^{2}\) \(-1.73205 q^{3}\) \(+(-0.267949 - 3.99102i) q^{4}\) \(+7.98203i q^{5}\) \(+(-2.36603 + 2.53020i) q^{6}\) \(-2.13878i q^{7}\) \(+(-6.19615 - 5.06040i) q^{8}\) \(+3.00000 q^{9}\) \(+(11.6603 + 10.9037i) q^{10}\) \(-8.00000 q^{11}\) \(+(0.464102 + 6.91264i) q^{12}\) \(-11.6865i q^{13}\) \(+(-3.12436 - 2.92163i) q^{14}\) \(-13.8253i q^{15}\) \(+(-15.8564 + 2.13878i) q^{16}\) \(+11.8564 q^{17}\) \(+(4.09808 - 4.38244i) q^{18}\) \(+14.9282 q^{19}\) \(+(31.8564 - 2.13878i) q^{20}\) \(+3.70447i q^{21}\) \(+(-10.9282 + 11.6865i) q^{22}\) \(+4.27756i q^{23}\) \(+(10.7321 + 8.76488i) q^{24}\) \(-38.7128 q^{25}\) \(+(-17.0718 - 15.9641i) q^{26}\) \(-5.19615 q^{27}\) \(+(-8.53590 + 0.573084i) q^{28}\) \(-0.573084i q^{29}\) \(+(-20.1962 - 18.8857i) q^{30}\) \(+57.4399i q^{31}\) \(+(-18.5359 + 26.0849i) q^{32}\) \(+13.8564 q^{33}\) \(+(16.1962 - 17.3200i) q^{34}\) \(+17.0718 q^{35}\) \(+(-0.803848 - 11.9730i) q^{36}\) \(-27.6506i q^{37}\) \(+(20.3923 - 21.8073i) q^{38}\) \(+20.2416i q^{39}\) \(+(40.3923 - 49.4579i) q^{40}\) \(-31.5692 q^{41}\) \(+(5.41154 + 5.06040i) q^{42}\) \(+28.7846 q^{43}\) \(+(2.14359 + 31.9281i) q^{44}\) \(+23.9461i q^{45}\) \(+(6.24871 + 5.84325i) q^{46}\) \(-59.5787i q^{47}\) \(+(27.4641 - 3.70447i) q^{48}\) \(+44.4256 q^{49}\) \(+(-52.8827 + 56.5522i) q^{50}\) \(-20.5359 q^{51}\) \(+(-46.6410 + 3.13139i) q^{52}\) \(-31.3550i q^{53}\) \(+(-7.09808 + 7.59061i) q^{54}\) \(-63.8562i q^{55}\) \(+(-10.8231 + 13.2522i) q^{56}\) \(-25.8564 q^{57}\) \(+(-0.837169 - 0.782847i) q^{58}\) \(-52.7846 q^{59}\) \(+(-55.1769 + 3.70447i) q^{60}\) \(+59.5787i q^{61}\) \(+(83.9090 + 78.4644i) q^{62}\) \(-6.41634i q^{63}\) \(+(12.7846 + 62.7101i) q^{64}\) \(+93.2820 q^{65}\) \(+(18.9282 - 20.2416i) q^{66}\) \(-84.7846 q^{67}\) \(+(-3.17691 - 47.3191i) q^{68}\) \(-7.40895i q^{69}\) \(+(23.3205 - 24.9387i) q^{70}\) \(+42.4685i q^{71}\) \(+(-18.5885 - 15.1812i) q^{72}\) \(-5.42563 q^{73}\) \(+(-40.3923 - 37.7714i) q^{74}\) \(+67.0526 q^{75}\) \(+(-4.00000 - 59.5787i) q^{76}\) \(+17.1102i q^{77}\) \(+(29.5692 + 27.6506i) q^{78}\) \(-44.6072i q^{79}\) \(+(-17.0718 - 126.566i) q^{80}\) \(+9.00000 q^{81}\) \(+(-43.1244 + 46.1167i) q^{82}\) \(+67.7128 q^{83}\) \(+(14.7846 - 0.992611i) q^{84}\) \(+94.6382i q^{85}\) \(+(39.3205 - 42.0489i) q^{86}\) \(+0.992611i q^{87}\) \(+(49.5692 + 40.4832i) q^{88}\) \(-133.138 q^{89}\) \(+(34.9808 + 32.7110i) q^{90}\) \(-24.9948 q^{91}\) \(+(17.0718 - 1.14617i) q^{92}\) \(-99.4888i q^{93}\) \(+(-87.0333 - 81.3860i) q^{94}\) \(+119.157i q^{95}\) \(+(32.1051 - 45.1803i) q^{96}\) \(+97.1384 q^{97}\) \(+(60.6865 - 64.8975i) q^{98}\) \(-24.0000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 36q^{14} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 32q^{19} \) \(\mathstrut +\mathstrut 72q^{20} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut -\mathstrut 44q^{25} \) \(\mathstrut -\mathstrut 96q^{26} \) \(\mathstrut -\mathstrut 48q^{28} \) \(\mathstrut -\mathstrut 60q^{30} \) \(\mathstrut -\mathstrut 88q^{32} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut -\mathstrut 24q^{36} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 120q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 84q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 64q^{44} \) \(\mathstrut -\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 96q^{48} \) \(\mathstrut -\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 118q^{50} \) \(\mathstrut -\mathstrut 96q^{51} \) \(\mathstrut -\mathstrut 48q^{52} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 168q^{56} \) \(\mathstrut -\mathstrut 48q^{57} \) \(\mathstrut +\mathstrut 156q^{58} \) \(\mathstrut -\mathstrut 128q^{59} \) \(\mathstrut -\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 204q^{62} \) \(\mathstrut -\mathstrut 32q^{64} \) \(\mathstrut +\mathstrut 96q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut -\mathstrut 256q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 200q^{73} \) \(\mathstrut -\mathstrut 120q^{74} \) \(\mathstrut +\mathstrut 192q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 48q^{78} \) \(\mathstrut -\mathstrut 96q^{80} \) \(\mathstrut +\mathstrut 36q^{81} \) \(\mathstrut -\mathstrut 124q^{82} \) \(\mathstrut +\mathstrut 160q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut +\mathstrut 88q^{86} \) \(\mathstrut +\mathstrut 32q^{88} \) \(\mathstrut -\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 288q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 168q^{94} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut +\mathstrut 56q^{97} \) \(\mathstrut +\mathstrut 170q^{98} \) \(\mathstrut -\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 1.46081i 0.683013 0.730406i
\(3\) −1.73205 −0.577350
\(4\) −0.267949 3.99102i −0.0669873 0.997754i
\(5\) 7.98203i 1.59641i 0.602388 + 0.798203i \(0.294216\pi\)
−0.602388 + 0.798203i \(0.705784\pi\)
\(6\) −2.36603 + 2.53020i −0.394338 + 0.421700i
\(7\) 2.13878i 0.305540i −0.988262 0.152770i \(-0.951181\pi\)
0.988262 0.152770i \(-0.0488193\pi\)
\(8\) −6.19615 5.06040i −0.774519 0.632551i
\(9\) 3.00000 0.333333
\(10\) 11.6603 + 10.9037i 1.16603 + 1.09037i
\(11\) −8.00000 −0.727273 −0.363636 0.931541i \(-0.618465\pi\)
−0.363636 + 0.931541i \(0.618465\pi\)
\(12\) 0.464102 + 6.91264i 0.0386751 + 0.576053i
\(13\) 11.6865i 0.898962i −0.893290 0.449481i \(-0.851609\pi\)
0.893290 0.449481i \(-0.148391\pi\)
\(14\) −3.12436 2.92163i −0.223168 0.208688i
\(15\) 13.8253i 0.921686i
\(16\) −15.8564 + 2.13878i −0.991025 + 0.133674i
\(17\) 11.8564 0.697436 0.348718 0.937228i \(-0.386617\pi\)
0.348718 + 0.937228i \(0.386617\pi\)
\(18\) 4.09808 4.38244i 0.227671 0.243469i
\(19\) 14.9282 0.785695 0.392847 0.919604i \(-0.371490\pi\)
0.392847 + 0.919604i \(0.371490\pi\)
\(20\) 31.8564 2.13878i 1.59282 0.106939i
\(21\) 3.70447i 0.176403i
\(22\) −10.9282 + 11.6865i −0.496737 + 0.531205i
\(23\) 4.27756i 0.185981i 0.995667 + 0.0929904i \(0.0296426\pi\)
−0.995667 + 0.0929904i \(0.970357\pi\)
\(24\) 10.7321 + 8.76488i 0.447169 + 0.365203i
\(25\) −38.7128 −1.54851
\(26\) −17.0718 15.9641i −0.656608 0.614002i
\(27\) −5.19615 −0.192450
\(28\) −8.53590 + 0.573084i −0.304854 + 0.0204673i
\(29\) 0.573084i 0.0197615i −0.999951 0.00988076i \(-0.996855\pi\)
0.999951 0.00988076i \(-0.00314519\pi\)
\(30\) −20.1962 18.8857i −0.673205 0.629523i
\(31\) 57.4399i 1.85290i 0.376417 + 0.926450i \(0.377156\pi\)
−0.376417 + 0.926450i \(0.622844\pi\)
\(32\) −18.5359 + 26.0849i −0.579247 + 0.815152i
\(33\) 13.8564 0.419891
\(34\) 16.1962 17.3200i 0.476357 0.509412i
\(35\) 17.0718 0.487766
\(36\) −0.803848 11.9730i −0.0223291 0.332585i
\(37\) 27.6506i 0.747313i −0.927567 0.373656i \(-0.878104\pi\)
0.927567 0.373656i \(-0.121896\pi\)
\(38\) 20.3923 21.8073i 0.536640 0.573877i
\(39\) 20.2416i 0.519016i
\(40\) 40.3923 49.4579i 1.00981 1.23645i
\(41\) −31.5692 −0.769981 −0.384990 0.922921i \(-0.625795\pi\)
−0.384990 + 0.922921i \(0.625795\pi\)
\(42\) 5.41154 + 5.06040i 0.128846 + 0.120486i
\(43\) 28.7846 0.669410 0.334705 0.942323i \(-0.391363\pi\)
0.334705 + 0.942323i \(0.391363\pi\)
\(44\) 2.14359 + 31.9281i 0.0487180 + 0.725639i
\(45\) 23.9461i 0.532135i
\(46\) 6.24871 + 5.84325i 0.135842 + 0.127027i
\(47\) 59.5787i 1.26763i −0.773484 0.633816i \(-0.781488\pi\)
0.773484 0.633816i \(-0.218512\pi\)
\(48\) 27.4641 3.70447i 0.572169 0.0771765i
\(49\) 44.4256 0.906645
\(50\) −52.8827 + 56.5522i −1.05765 + 1.13104i
\(51\) −20.5359 −0.402665
\(52\) −46.6410 + 3.13139i −0.896943 + 0.0602190i
\(53\) 31.3550i 0.591604i −0.955249 0.295802i \(-0.904413\pi\)
0.955249 0.295802i \(-0.0955869\pi\)
\(54\) −7.09808 + 7.59061i −0.131446 + 0.140567i
\(55\) 63.8562i 1.16102i
\(56\) −10.8231 + 13.2522i −0.193269 + 0.236646i
\(57\) −25.8564 −0.453621
\(58\) −0.837169 0.782847i −0.0144339 0.0134974i
\(59\) −52.7846 −0.894654 −0.447327 0.894370i \(-0.647624\pi\)
−0.447327 + 0.894370i \(0.647624\pi\)
\(60\) −55.1769 + 3.70447i −0.919615 + 0.0617412i
\(61\) 59.5787i 0.976700i 0.872648 + 0.488350i \(0.162401\pi\)
−0.872648 + 0.488350i \(0.837599\pi\)
\(62\) 83.9090 + 78.4644i 1.35337 + 1.26555i
\(63\) 6.41634i 0.101847i
\(64\) 12.7846 + 62.7101i 0.199760 + 0.979845i
\(65\) 93.2820 1.43511
\(66\) 18.9282 20.2416i 0.286791 0.306691i
\(67\) −84.7846 −1.26544 −0.632721 0.774380i \(-0.718062\pi\)
−0.632721 + 0.774380i \(0.718062\pi\)
\(68\) −3.17691 47.3191i −0.0467193 0.695869i
\(69\) 7.40895i 0.107376i
\(70\) 23.3205 24.9387i 0.333150 0.356267i
\(71\) 42.4685i 0.598147i 0.954230 + 0.299074i \(0.0966776\pi\)
−0.954230 + 0.299074i \(0.903322\pi\)
\(72\) −18.5885 15.1812i −0.258173 0.210850i
\(73\) −5.42563 −0.0743236 −0.0371618 0.999309i \(-0.511832\pi\)
−0.0371618 + 0.999309i \(0.511832\pi\)
\(74\) −40.3923 37.7714i −0.545842 0.510424i
\(75\) 67.0526 0.894034
\(76\) −4.00000 59.5787i −0.0526316 0.783930i
\(77\) 17.1102i 0.222211i
\(78\) 29.5692 + 27.6506i 0.379093 + 0.354494i
\(79\) 44.6072i 0.564649i −0.959319 0.282324i \(-0.908895\pi\)
0.959319 0.282324i \(-0.0911054\pi\)
\(80\) −17.0718 126.566i −0.213397 1.58208i
\(81\) 9.00000 0.111111
\(82\) −43.1244 + 46.1167i −0.525907 + 0.562399i
\(83\) 67.7128 0.815817 0.407909 0.913023i \(-0.366258\pi\)
0.407909 + 0.913023i \(0.366258\pi\)
\(84\) 14.7846 0.992611i 0.176007 0.0118168i
\(85\) 94.6382i 1.11339i
\(86\) 39.3205 42.0489i 0.457215 0.488941i
\(87\) 0.992611i 0.0114093i
\(88\) 49.5692 + 40.4832i 0.563287 + 0.460037i
\(89\) −133.138 −1.49594 −0.747969 0.663734i \(-0.768971\pi\)
−0.747969 + 0.663734i \(0.768971\pi\)
\(90\) 34.9808 + 32.7110i 0.388675 + 0.363455i
\(91\) −24.9948 −0.274669
\(92\) 17.0718 1.14617i 0.185563 0.0124583i
\(93\) 99.4888i 1.06977i
\(94\) −87.0333 81.3860i −0.925886 0.865809i
\(95\) 119.157i 1.25429i
\(96\) 32.1051 45.1803i 0.334428 0.470628i
\(97\) 97.1384 1.00143 0.500714 0.865613i \(-0.333071\pi\)
0.500714 + 0.865613i \(0.333071\pi\)
\(98\) 60.6865 64.8975i 0.619250 0.662220i
\(99\) −24.0000 −0.242424
\(100\) 10.3731 + 154.503i 0.103731 + 1.54503i
\(101\) 62.1370i 0.615218i 0.951513 + 0.307609i \(0.0995288\pi\)
−0.951513 + 0.307609i \(0.900471\pi\)
\(102\) −28.0526 + 29.9991i −0.275025 + 0.294109i
\(103\) 27.8041i 0.269943i 0.990849 + 0.134971i \(0.0430943\pi\)
−0.990849 + 0.134971i \(0.956906\pi\)
\(104\) −59.1384 + 72.4114i −0.568639 + 0.696263i
\(105\) −29.5692 −0.281612
\(106\) −45.8038 42.8318i −0.432112 0.404073i
\(107\) 37.7795 0.353079 0.176540 0.984294i \(-0.443510\pi\)
0.176540 + 0.984294i \(0.443510\pi\)
\(108\) 1.39230 + 20.7379i 0.0128917 + 0.192018i
\(109\) 141.691i 1.29992i −0.759968 0.649960i \(-0.774786\pi\)
0.759968 0.649960i \(-0.225214\pi\)
\(110\) −93.2820 87.2293i −0.848018 0.792993i
\(111\) 47.8922i 0.431461i
\(112\) 4.57437 + 33.9133i 0.0408426 + 0.302798i
\(113\) −58.2872 −0.515816 −0.257908 0.966170i \(-0.583033\pi\)
−0.257908 + 0.966170i \(0.583033\pi\)
\(114\) −35.3205 + 37.7714i −0.309829 + 0.331328i
\(115\) −34.1436 −0.296901
\(116\) −2.28719 + 0.153557i −0.0197171 + 0.00132377i
\(117\) 35.0595i 0.299654i
\(118\) −72.1051 + 77.1084i −0.611060 + 0.653461i
\(119\) 25.3582i 0.213094i
\(120\) −69.9615 + 85.6636i −0.583013 + 0.713863i
\(121\) −57.0000 −0.471074
\(122\) 87.0333 + 81.3860i 0.713388 + 0.667098i
\(123\) 54.6795 0.444549
\(124\) 229.244 15.3910i 1.84874 0.124121i
\(125\) 109.456i 0.875649i
\(126\) −9.37307 8.76488i −0.0743894 0.0695625i
\(127\) 185.152i 1.45789i −0.684571 0.728946i \(-0.740010\pi\)
0.684571 0.728946i \(-0.259990\pi\)
\(128\) 109.072 + 66.9876i 0.852123 + 0.523341i
\(129\) −49.8564 −0.386484
\(130\) 127.426 136.268i 0.980197 1.04821i
\(131\) 125.359 0.956939 0.478469 0.878104i \(-0.341192\pi\)
0.478469 + 0.878104i \(0.341192\pi\)
\(132\) −3.71281 55.3011i −0.0281274 0.418948i
\(133\) 31.9281i 0.240061i
\(134\) −115.818 + 123.854i −0.864313 + 0.924287i
\(135\) 41.4758i 0.307229i
\(136\) −73.4641 59.9982i −0.540177 0.441163i
\(137\) 99.5692 0.726783 0.363391 0.931637i \(-0.381619\pi\)
0.363391 + 0.931637i \(0.381619\pi\)
\(138\) −10.8231 10.1208i −0.0784282 0.0733392i
\(139\) 177.492 1.27692 0.638461 0.769654i \(-0.279571\pi\)
0.638461 + 0.769654i \(0.279571\pi\)
\(140\) −4.57437 68.1338i −0.0326741 0.486670i
\(141\) 103.193i 0.731867i
\(142\) 62.0385 + 58.0130i 0.436891 + 0.408542i
\(143\) 93.4920i 0.653790i
\(144\) −47.5692 + 6.41634i −0.330342 + 0.0445579i
\(145\) 4.57437 0.0315474
\(146\) −7.41154 + 7.92582i −0.0507640 + 0.0542865i
\(147\) −76.9474 −0.523452
\(148\) −110.354 + 7.40895i −0.745634 + 0.0500605i
\(149\) 87.8023i 0.589277i −0.955609 0.294639i \(-0.904801\pi\)
0.955609 0.294639i \(-0.0951993\pi\)
\(150\) 91.5955 97.9512i 0.610637 0.653008i
\(151\) 219.066i 1.45077i 0.688345 + 0.725383i \(0.258337\pi\)
−0.688345 + 0.725383i \(0.741663\pi\)
\(152\) −92.4974 75.5427i −0.608536 0.496992i
\(153\) 35.5692 0.232479
\(154\) 24.9948 + 23.3730i 0.162304 + 0.151773i
\(155\) −458.487 −2.95798
\(156\) 80.7846 5.42373i 0.517850 0.0347675i
\(157\) 253.440i 1.61427i 0.590370 + 0.807133i \(0.298982\pi\)
−0.590370 + 0.807133i \(0.701018\pi\)
\(158\) −65.1628 60.9346i −0.412423 0.385662i
\(159\) 54.3085i 0.341563i
\(160\) −208.210 147.954i −1.30131 0.924713i
\(161\) 9.14875 0.0568245
\(162\) 12.2942 13.1473i 0.0758903 0.0811563i
\(163\) −102.354 −0.627938 −0.313969 0.949433i \(-0.601659\pi\)
−0.313969 + 0.949433i \(0.601659\pi\)
\(164\) 8.45895 + 125.993i 0.0515789 + 0.768251i
\(165\) 110.602i 0.670317i
\(166\) 92.4974 98.9158i 0.557213 0.595878i
\(167\) 281.090i 1.68318i −0.540120 0.841588i \(-0.681621\pi\)
0.540120 0.841588i \(-0.318379\pi\)
\(168\) 18.7461 22.9535i 0.111584 0.136628i
\(169\) 32.4256 0.191868
\(170\) 138.249 + 129.278i 0.813228 + 0.760460i
\(171\) 44.7846 0.261898
\(172\) −7.71281 114.880i −0.0448419 0.667906i
\(173\) 242.858i 1.40381i 0.712273 + 0.701903i \(0.247666\pi\)
−0.712273 + 0.701903i \(0.752334\pi\)
\(174\) 1.45002 + 1.35593i 0.00833344 + 0.00779271i
\(175\) 82.7981i 0.473132i
\(176\) 126.851 17.1102i 0.720746 0.0972172i
\(177\) 91.4256 0.516529
\(178\) −181.870 + 194.490i −1.02174 + 1.09264i
\(179\) 318.354 1.77851 0.889257 0.457409i \(-0.151222\pi\)
0.889257 + 0.457409i \(0.151222\pi\)
\(180\) 95.5692 6.41634i 0.530940 0.0356463i
\(181\) 79.5132i 0.439299i −0.975579 0.219650i \(-0.929509\pi\)
0.975579 0.219650i \(-0.0704914\pi\)
\(182\) −34.1436 + 36.5128i −0.187602 + 0.200620i
\(183\) 103.193i 0.563898i
\(184\) 21.6462 26.5044i 0.117642 0.144046i
\(185\) 220.708 1.19301
\(186\) −145.335 135.904i −0.781369 0.730668i
\(187\) −94.8513 −0.507226
\(188\) −237.779 + 15.9641i −1.26478 + 0.0849152i
\(189\) 11.1134i 0.0588012i
\(190\) 174.067 + 162.772i 0.916140 + 0.856695i
\(191\) 352.887i 1.84758i −0.382902 0.923789i \(-0.625075\pi\)
0.382902 0.923789i \(-0.374925\pi\)
\(192\) −22.1436 108.617i −0.115331 0.565714i
\(193\) −284.277 −1.47294 −0.736469 0.676472i \(-0.763508\pi\)
−0.736469 + 0.676472i \(0.763508\pi\)
\(194\) 132.694 141.901i 0.683988 0.731449i
\(195\) −161.569 −0.828560
\(196\) −11.9038 177.303i −0.0607337 0.904609i
\(197\) 75.8087i 0.384816i −0.981315 0.192408i \(-0.938370\pi\)
0.981315 0.192408i \(-0.0616297\pi\)
\(198\) −32.7846 + 35.0595i −0.165579 + 0.177068i
\(199\) 104.186i 0.523547i 0.965129 + 0.261774i \(0.0843074\pi\)
−0.965129 + 0.261774i \(0.915693\pi\)
\(200\) 239.870 + 195.902i 1.19935 + 0.979512i
\(201\) 146.851 0.730603
\(202\) 90.7705 + 84.8807i 0.449359 + 0.420202i
\(203\) −1.22570 −0.00603793
\(204\) 5.50258 + 81.9591i 0.0269734 + 0.401760i
\(205\) 251.986i 1.22920i
\(206\) 40.6166 + 37.9811i 0.197168 + 0.184374i
\(207\) 12.8327i 0.0619936i
\(208\) 24.9948 + 185.306i 0.120168 + 0.890894i
\(209\) −119.426 −0.571414
\(210\) −40.3923 + 43.1951i −0.192344 + 0.205691i
\(211\) 136.918 0.648900 0.324450 0.945903i \(-0.394821\pi\)
0.324450 + 0.945903i \(0.394821\pi\)
\(212\) −125.138 + 8.40156i −0.590276 + 0.0396300i
\(213\) 73.5575i 0.345341i
\(214\) 51.6077 55.1887i 0.241157 0.257891i
\(215\) 229.760i 1.06865i
\(216\) 32.1962 + 26.2946i 0.149056 + 0.121734i
\(217\) 122.851 0.566135
\(218\) −206.985 193.554i −0.949470 0.887862i
\(219\) 9.39746 0.0429108
\(220\) −254.851 + 17.1102i −1.15841 + 0.0777738i
\(221\) 138.560i 0.626968i
\(222\) 69.9615 + 65.4219i 0.315142 + 0.294693i
\(223\) 53.1624i 0.238396i 0.992870 + 0.119198i \(0.0380324\pi\)
−0.992870 + 0.119198i \(0.961968\pi\)
\(224\) 55.7898 + 39.6442i 0.249061 + 0.176983i
\(225\) −116.138 −0.516171
\(226\) −79.6218 + 85.1467i −0.352309 + 0.376755i
\(227\) −119.846 −0.527956 −0.263978 0.964529i \(-0.585035\pi\)
−0.263978 + 0.964529i \(0.585035\pi\)
\(228\) 6.92820 + 103.193i 0.0303869 + 0.452602i
\(229\) 214.103i 0.934946i −0.884007 0.467473i \(-0.845164\pi\)
0.884007 0.467473i \(-0.154836\pi\)
\(230\) −46.6410 + 49.8774i −0.202787 + 0.216858i
\(231\) 29.6358i 0.128293i
\(232\) −2.90004 + 3.55092i −0.0125002 + 0.0153057i
\(233\) −127.436 −0.546935 −0.273468 0.961881i \(-0.588171\pi\)
−0.273468 + 0.961881i \(0.588171\pi\)
\(234\) −51.2154 47.8922i −0.218869 0.204667i
\(235\) 475.559 2.02365
\(236\) 14.1436 + 210.664i 0.0599305 + 0.892645i
\(237\) 77.2620i 0.326000i
\(238\) −37.0436 34.6400i −0.155646 0.145546i
\(239\) 319.281i 1.33590i 0.744204 + 0.667952i \(0.232829\pi\)
−0.744204 + 0.667952i \(0.767171\pi\)
\(240\) 29.5692 + 219.219i 0.123205 + 0.913414i
\(241\) −247.415 −1.02662 −0.513310 0.858203i \(-0.671581\pi\)
−0.513310 + 0.858203i \(0.671581\pi\)
\(242\) −77.8634 + 83.2663i −0.321750 + 0.344076i
\(243\) −15.5885 −0.0641500
\(244\) 237.779 15.9641i 0.974506 0.0654265i
\(245\) 354.607i 1.44737i
\(246\) 74.6936 79.8765i 0.303632 0.324701i
\(247\) 174.459i 0.706310i
\(248\) 290.669 355.906i 1.17205 1.43511i
\(249\) −117.282 −0.471012
\(250\) −159.895 149.520i −0.639580 0.598079i
\(251\) −214.851 −0.855981 −0.427991 0.903783i \(-0.640778\pi\)
−0.427991 + 0.903783i \(0.640778\pi\)
\(252\) −25.6077 + 1.71925i −0.101618 + 0.00682243i
\(253\) 34.2205i 0.135259i
\(254\) −270.473 252.923i −1.06485 0.995759i
\(255\) 163.918i 0.642816i
\(256\) 246.851 67.8267i 0.964263 0.264948i
\(257\) −84.2769 −0.327926 −0.163963 0.986467i \(-0.552428\pi\)
−0.163963 + 0.986467i \(0.552428\pi\)
\(258\) −68.1051 + 72.8309i −0.263973 + 0.282290i
\(259\) −59.1384 −0.228334
\(260\) −24.9948 372.290i −0.0961340 1.43188i
\(261\) 1.71925i 0.00658717i
\(262\) 171.244 183.126i 0.653601 0.698954i
\(263\) 277.120i 1.05369i 0.849962 + 0.526844i \(0.176625\pi\)
−0.849962 + 0.526844i \(0.823375\pi\)
\(264\) −85.8564 70.1190i −0.325214 0.265602i
\(265\) 250.277 0.944441
\(266\) −46.6410 43.6146i −0.175342 0.163965i
\(267\) 230.603 0.863680
\(268\) 22.7180 + 338.377i 0.0847685 + 1.26260i
\(269\) 123.701i 0.459855i −0.973208 0.229927i \(-0.926151\pi\)
0.973208 0.229927i \(-0.0738489\pi\)
\(270\) −60.5885 56.6571i −0.224402 0.209841i
\(271\) 197.985i 0.730572i 0.930895 + 0.365286i \(0.119029\pi\)
−0.930895 + 0.365286i \(0.880971\pi\)
\(272\) −188.000 + 25.3582i −0.691176 + 0.0932288i
\(273\) 43.2923 0.158580
\(274\) 136.014 145.452i 0.496402 0.530847i
\(275\) 309.703 1.12619
\(276\) −29.5692 + 1.98522i −0.107135 + 0.00719283i
\(277\) 247.709i 0.894256i 0.894470 + 0.447128i \(0.147553\pi\)
−0.894470 + 0.447128i \(0.852447\pi\)
\(278\) 242.459 259.283i 0.872154 0.932673i
\(279\) 172.320i 0.617633i
\(280\) −105.779 86.3902i −0.377784 0.308536i
\(281\) 443.128 1.57697 0.788484 0.615055i \(-0.210866\pi\)
0.788484 + 0.615055i \(0.210866\pi\)
\(282\) 150.746 + 140.965i 0.534561 + 0.499875i
\(283\) −294.620 −1.04106 −0.520531 0.853843i \(-0.674266\pi\)
−0.520531 + 0.853843i \(0.674266\pi\)
\(284\) 169.492 11.3794i 0.596804 0.0400683i
\(285\) 206.387i 0.724164i
\(286\) 136.574 + 127.712i 0.477533 + 0.446547i
\(287\) 67.5196i 0.235260i
\(288\) −55.6077 + 78.2546i −0.193082 + 0.271717i
\(289\) −148.426 −0.513583
\(290\) 6.24871 6.68231i 0.0215473 0.0230424i
\(291\) −168.249 −0.578174
\(292\) 1.45379 + 21.6538i 0.00497874 + 0.0741567i
\(293\) 66.7217i 0.227719i 0.993497 + 0.113859i \(0.0363214\pi\)
−0.993497 + 0.113859i \(0.963679\pi\)
\(294\) −105.112 + 112.406i −0.357524 + 0.382333i
\(295\) 421.328i 1.42823i
\(296\) −139.923 + 171.327i −0.472713 + 0.578808i
\(297\) 41.5692 0.139964
\(298\) −128.263 119.940i −0.430412 0.402484i
\(299\) 49.9897 0.167190
\(300\) −17.9667 267.608i −0.0598889 0.892026i
\(301\) 61.5639i 0.204531i
\(302\) 320.014 + 299.249i 1.05965 + 0.990892i
\(303\) 107.624i 0.355196i
\(304\) −236.708 + 31.9281i −0.778644 + 0.105027i
\(305\) −475.559 −1.55921
\(306\) 48.5885 51.9600i 0.158786 0.169804i
\(307\) −524.210 −1.70753 −0.853763 0.520662i \(-0.825685\pi\)
−0.853763 + 0.520662i \(0.825685\pi\)
\(308\) 68.2872 4.58467i 0.221712 0.0148853i
\(309\) 48.1582i 0.155852i
\(310\) −626.305 + 669.764i −2.02034 + 2.16053i
\(311\) 362.057i 1.16417i −0.813128 0.582085i \(-0.802237\pi\)
0.813128 0.582085i \(-0.197763\pi\)
\(312\) 102.431 125.420i 0.328304 0.401988i
\(313\) 252.277 0.805996 0.402998 0.915201i \(-0.367968\pi\)
0.402998 + 0.915201i \(0.367968\pi\)
\(314\) 370.228 + 346.205i 1.17907 + 1.10256i
\(315\) 51.2154 0.162589
\(316\) −178.028 + 11.9525i −0.563380 + 0.0378243i
\(317\) 80.3934i 0.253607i 0.991928 + 0.126803i \(0.0404717\pi\)
−0.991928 + 0.126803i \(0.959528\pi\)
\(318\) 79.3346 + 74.1868i 0.249480 + 0.233292i
\(319\) 4.58467i 0.0143720i
\(320\) −500.554 + 102.047i −1.56423 + 0.318897i
\(321\) −65.4359 −0.203850
\(322\) 12.4974 13.3646i 0.0388119 0.0415050i
\(323\) 176.995 0.547972
\(324\) −2.41154 35.9191i −0.00744303 0.110862i
\(325\) 452.417i 1.39205i
\(326\) −139.818 + 149.520i −0.428889 + 0.458650i
\(327\) 245.417i 0.750509i
\(328\) 195.608 + 159.753i 0.596365 + 0.487052i
\(329\) −127.426 −0.387312
\(330\) 161.569 + 151.085i 0.489604 + 0.457835i
\(331\) 172.056 0.519808 0.259904 0.965635i \(-0.416309\pi\)
0.259904 + 0.965635i \(0.416309\pi\)
\(332\) −18.1436 270.243i −0.0546494 0.813985i
\(333\) 82.9517i 0.249104i
\(334\) −410.620 383.977i −1.22940 1.14963i
\(335\) 676.753i 2.02016i
\(336\) −7.92305 58.7396i −0.0235805 0.174820i
\(337\) 564.277 1.67441 0.837206 0.546888i \(-0.184187\pi\)
0.837206 + 0.546888i \(0.184187\pi\)
\(338\) 44.2942 47.3678i 0.131048 0.140141i
\(339\) 100.956 0.297806
\(340\) 377.703 25.3582i 1.11089 0.0745830i
\(341\) 459.519i 1.34756i
\(342\) 61.1769 65.4219i 0.178880 0.191292i
\(343\) 199.817i 0.582556i
\(344\) −178.354 145.662i −0.518470 0.423435i
\(345\) 59.1384 0.171416
\(346\) 354.771 + 331.751i 1.02535 + 0.958817i
\(347\) −286.123 −0.824562 −0.412281 0.911057i \(-0.635268\pi\)
−0.412281 + 0.911057i \(0.635268\pi\)
\(348\) 3.96152 0.265969i 0.0113837 0.000764279i
\(349\) 421.021i 1.20636i 0.797603 + 0.603182i \(0.206101\pi\)
−0.797603 + 0.603182i \(0.793899\pi\)
\(350\) 120.953 + 113.104i 0.345579 + 0.323155i
\(351\) 60.7249i 0.173005i
\(352\) 148.287 208.679i 0.421270 0.592838i
\(353\) 429.138 1.21569 0.607845 0.794056i \(-0.292034\pi\)
0.607845 + 0.794056i \(0.292034\pi\)
\(354\) 124.890 133.556i 0.352796 0.377276i
\(355\) −338.985 −0.954886
\(356\) 35.6743 + 531.358i 0.100209 + 1.49258i
\(357\) 43.9217i 0.123030i
\(358\) 434.879 465.055i 1.21475 1.29904i
\(359\) 263.673i 0.734465i 0.930129 + 0.367233i \(0.119695\pi\)
−0.930129 + 0.367233i \(0.880305\pi\)
\(360\) 121.177 148.374i 0.336603 0.412149i
\(361\) −138.149 −0.382684
\(362\) −116.154 108.617i −0.320867 0.300047i
\(363\) 98.7269 0.271975
\(364\) 6.69735 + 99.7548i 0.0183993 + 0.274052i
\(365\) 43.3075i 0.118651i
\(366\) −150.746 140.965i −0.411875 0.385149i
\(367\) 129.544i 0.352981i −0.984302 0.176491i \(-0.943525\pi\)
0.984302 0.176491i \(-0.0564745\pi\)
\(368\) −9.14875 67.8267i −0.0248607 0.184312i
\(369\) −94.7077 −0.256660
\(370\) 301.492 322.413i 0.814844 0.871385i
\(371\) −67.0615 −0.180759
\(372\) −397.061 + 26.6580i −1.06737 + 0.0716612i
\(373\) 302.478i 0.810933i −0.914110 0.405467i \(-0.867109\pi\)
0.914110 0.405467i \(-0.132891\pi\)
\(374\) −129.569 + 138.560i −0.346442 + 0.370481i
\(375\) 189.584i 0.505556i
\(376\) −301.492 + 369.159i −0.801841 + 0.981805i
\(377\) −6.69735 −0.0177649
\(378\) 16.2346 + 15.1812i 0.0429488 + 0.0401619i
\(379\) −116.210 −0.306623 −0.153312 0.988178i \(-0.548994\pi\)
−0.153312 + 0.988178i \(0.548994\pi\)
\(380\) 475.559 31.9281i 1.25147 0.0840214i
\(381\) 320.693i 0.841715i
\(382\) −515.503 482.053i −1.34948 1.26192i
\(383\) 566.151i 1.47820i 0.673595 + 0.739101i \(0.264749\pi\)
−0.673595 + 0.739101i \(0.735251\pi\)
\(384\) −188.918 116.026i −0.491974 0.302151i
\(385\) −136.574 −0.354739
\(386\) −388.329 + 415.275i −1.00603 + 1.07584i
\(387\) 86.3538 0.223137
\(388\) −26.0282 387.681i −0.0670829 0.999178i
\(389\) 350.104i 0.900011i −0.893026 0.450006i \(-0.851422\pi\)
0.893026 0.450006i \(-0.148578\pi\)
\(390\) −220.708 + 236.022i −0.565917 + 0.605186i
\(391\) 50.7165i 0.129710i
\(392\) −275.268 224.812i −0.702214 0.573499i
\(393\) −217.128 −0.552489
\(394\) −110.742 103.557i −0.281072 0.262834i
\(395\) 356.056 0.901408
\(396\) 6.43078 + 95.7844i 0.0162393 + 0.241880i
\(397\) 544.149i 1.37065i 0.728236 + 0.685326i \(0.240340\pi\)
−0.728236 + 0.685326i \(0.759660\pi\)
\(398\) 152.196 + 142.321i 0.382402 + 0.357589i
\(399\) 55.3011i 0.138599i
\(400\) 613.846 82.7981i 1.53462 0.206995i
\(401\) −296.431 −0.739229 −0.369614 0.929185i \(-0.620510\pi\)
−0.369614 + 0.929185i \(0.620510\pi\)
\(402\) 200.603 214.522i 0.499011 0.533637i
\(403\) 671.272 1.66569
\(404\) 247.990 16.6496i 0.613836 0.0412118i
\(405\) 71.8383i 0.177378i
\(406\) −1.67434 + 1.79052i −0.00412398 + 0.00441014i
\(407\) 221.205i 0.543500i
\(408\) 127.244 + 103.920i 0.311871 + 0.254706i
\(409\) −247.415 −0.604927 −0.302464 0.953161i \(-0.597809\pi\)
−0.302464 + 0.953161i \(0.597809\pi\)
\(410\) −368.105 344.220i −0.897817 0.839561i
\(411\) −172.459 −0.419608
\(412\) 110.967 7.45009i 0.269337 0.0180827i
\(413\) 112.895i 0.273353i
\(414\) 18.7461 + 17.5298i 0.0452805 + 0.0423424i
\(415\) 540.486i 1.30238i
\(416\) 304.841 + 216.620i 0.732791 + 0.520721i
\(417\) −307.426 −0.737232
\(418\) −163.138 + 174.459i −0.390283 + 0.417365i
\(419\) −92.1333 −0.219889 −0.109944 0.993938i \(-0.535067\pi\)
−0.109944 + 0.993938i \(0.535067\pi\)
\(420\) 7.92305 + 118.011i 0.0188644 + 0.280979i
\(421\) 445.540i 1.05829i −0.848531 0.529145i \(-0.822513\pi\)
0.848531 0.529145i \(-0.177487\pi\)
\(422\) 187.033 200.011i 0.443207 0.473961i
\(423\) 178.736i 0.422544i
\(424\) −158.669 + 194.281i −0.374220 + 0.458209i
\(425\) −458.995 −1.07999
\(426\) −107.454 100.481i −0.252239 0.235872i
\(427\) 127.426 0.298421
\(428\) −10.1230 150.778i −0.0236518 0.352286i
\(429\) 161.933i 0.377466i
\(430\) 335.636 + 313.857i 0.780549 + 0.729901i
\(431\) 186.677i 0.433125i −0.976269 0.216563i \(-0.930515\pi\)
0.976269 0.216563i \(-0.0694845\pi\)
\(432\) 82.3923 11.1134i 0.190723 0.0257255i
\(433\) 291.128 0.672351 0.336176 0.941799i \(-0.390866\pi\)
0.336176 + 0.941799i \(0.390866\pi\)
\(434\) 167.818 179.463i 0.386677 0.413509i
\(435\) −7.92305 −0.0182139
\(436\) −565.492 + 37.9661i −1.29700 + 0.0870782i
\(437\) 63.8562i 0.146124i
\(438\) 12.8372 13.7279i 0.0293086 0.0313423i
\(439\) 87.6899i 0.199749i 0.995000 + 0.0998746i \(0.0318442\pi\)
−0.995000 + 0.0998746i \(0.968156\pi\)
\(440\) −323.138 + 395.663i −0.734406 + 0.899234i
\(441\) 133.277 0.302215
\(442\) −202.410 189.276i −0.457942 0.428227i
\(443\) 20.7077 0.0467441 0.0233721 0.999727i \(-0.492560\pi\)
0.0233721 + 0.999727i \(0.492560\pi\)
\(444\) 191.138 12.8327i 0.430492 0.0289024i
\(445\) 1062.72i 2.38812i
\(446\) 77.6603 + 72.6211i 0.174126 + 0.162828i
\(447\) 152.078i 0.340219i
\(448\) 134.123 27.3435i 0.299382 0.0610345i
\(449\) 584.410 1.30158 0.650791 0.759257i \(-0.274437\pi\)
0.650791 + 0.759257i \(0.274437\pi\)
\(450\) −158.648 + 169.657i −0.352551 + 0.377015i
\(451\) 252.554 0.559986
\(452\) 15.6180 + 232.625i 0.0345531 + 0.514657i
\(453\) 379.433i 0.837600i
\(454\) −163.713 + 175.073i −0.360601 + 0.385623i
\(455\) 199.510i 0.438483i
\(456\) 160.210 + 130.844i 0.351338 + 0.286938i
\(457\) −269.692 −0.590136 −0.295068 0.955476i \(-0.595342\pi\)
−0.295068 + 0.955476i \(0.595342\pi\)
\(458\) −312.764 292.470i −0.682891 0.638580i
\(459\) −61.6077 −0.134222
\(460\) 9.14875 + 136.268i 0.0198886 + 0.296234i
\(461\) 44.4948i 0.0965181i −0.998835 0.0482590i \(-0.984633\pi\)
0.998835 0.0482590i \(-0.0153673\pi\)
\(462\) −43.2923 40.4832i −0.0937064 0.0876261i
\(463\) 611.065i 1.31980i −0.751355 0.659898i \(-0.770600\pi\)
0.751355 0.659898i \(-0.229400\pi\)
\(464\) 1.22570 + 9.08705i 0.00264159 + 0.0195842i
\(465\) 794.123 1.70779
\(466\) −174.081 + 186.160i −0.373564 + 0.399485i
\(467\) 146.410 0.313512 0.156756 0.987637i \(-0.449896\pi\)
0.156756 + 0.987637i \(0.449896\pi\)
\(468\) −139.923 + 9.39417i −0.298981 + 0.0200730i
\(469\) 181.336i 0.386643i
\(470\) 649.626 694.703i 1.38218 1.47809i
\(471\) 438.971i 0.931997i
\(472\) 327.061 + 267.111i 0.692927 + 0.565914i
\(473\) −230.277 −0.486843
\(474\) 112.865 + 105.542i 0.238113 + 0.222662i
\(475\) −577.913 −1.21666
\(476\) −101.205 + 6.79472i −0.212616 + 0.0142746i
\(477\) 94.0651i 0.197201i
\(478\) 466.410 + 436.146i 0.975753 + 0.912440i
\(479\) 191.876i 0.400576i −0.979737 0.200288i \(-0.935812\pi\)
0.979737 0.200288i \(-0.0641878\pi\)
\(480\) 360.631 + 256.264i 0.751314 + 0.533883i
\(481\) −323.138 −0.671805
\(482\) −337.976 + 361.428i −0.701194 + 0.749850i
\(483\) −15.8461 −0.0328077
\(484\) 15.2731 + 227.488i 0.0315560 + 0.470016i
\(485\) 775.362i 1.59868i
\(486\) −21.2942 + 22.7718i −0.0438153 + 0.0468556i
\(487\) 610.758i 1.25412i 0.778969 + 0.627062i \(0.215743\pi\)
−0.778969 + 0.627062i \(0.784257\pi\)
\(488\) 301.492 369.159i 0.617812 0.756473i
\(489\) 177.282 0.362540
\(490\) 518.014 + 484.402i 1.05717 + 0.988575i
\(491\) −142.354 −0.289926 −0.144963 0.989437i \(-0.546306\pi\)
−0.144963 + 0.989437i \(0.546306\pi\)
\(492\) −14.6513 218.227i −0.0297791 0.443550i
\(493\) 6.79472i 0.0137824i
\(494\) −254.851 238.315i −0.515893 0.482419i
\(495\) 191.569i 0.387008i
\(496\) −122.851 910.791i −0.247684 1.83627i
\(497\) 90.8306 0.182758
\(498\) −160.210 + 171.327i −0.321707 + 0.344030i
\(499\) 91.3693 0.183105 0.0915524 0.995800i \(-0.470817\pi\)
0.0915524 + 0.995800i \(0.470817\pi\)
\(500\) −436.841 + 29.3287i −0.873682 + 0.0586573i
\(501\) 486.863i 0.971782i
\(502\) −293.492 + 313.857i −0.584646 + 0.625214i
\(503\) 230.067i 0.457389i −0.973498 0.228695i \(-0.926554\pi\)
0.973498 0.228695i \(-0.0734457\pi\)
\(504\) −32.4693 + 39.7566i −0.0644231 + 0.0788821i
\(505\) −495.979 −0.982137
\(506\) −49.9897 46.7460i −0.0987939 0.0923834i
\(507\) −56.1628 −0.110775
\(508\) −738.946 + 49.6114i −1.45462 + 0.0976603i
\(509\) 527.387i 1.03612i 0.855343 + 0.518062i \(0.173346\pi\)
−0.855343 + 0.518062i \(0.826654\pi\)
\(510\) −239.454 223.916i −0.469517 0.439052i
\(511\) 11.6042i 0.0227088i
\(512\) 238.123 453.256i 0.465084 0.885267i
\(513\) −77.5692 −0.151207
\(514\) −115.124 + 123.113i −0.223977 + 0.239519i
\(515\) −221.933 −0.430939
\(516\) 13.3590 + 198.978i 0.0258895 + 0.385616i
\(517\) 476.630i 0.921914i
\(518\) −80.7846 + 86.3902i −0.155955 + 0.166776i
\(519\) 420.643i 0.810487i
\(520\) −577.990 472.045i −1.11152 0.907779i
\(521\) 191.856 0.368246 0.184123 0.982903i \(-0.441055\pi\)
0.184123 + 0.982903i \(0.441055\pi\)
\(522\) −2.51151 2.34854i −0.00481131 0.00449912i
\(523\) 105.492 0.201706 0.100853 0.994901i \(-0.467843\pi\)
0.100853 + 0.994901i \(0.467843\pi\)
\(524\) −33.5898 500.310i −0.0641027 0.954789i
\(525\) 143.411i 0.273163i
\(526\) 404.820 + 378.553i 0.769620 + 0.719682i
\(527\) 681.031i 1.29228i
\(528\) −219.713 + 29.6358i −0.416123 + 0.0561284i
\(529\) 510.703 0.965411
\(530\) 341.885 365.608i 0.645065 0.689826i
\(531\) −158.354 −0.298218
\(532\) −127.426 + 8.55511i −0.239522 + 0.0160810i
\(533\) 368.934i 0.692184i
\(534\) 315.009 336.867i 0.589904 0.630837i
\(535\) 301.557i 0.563658i
\(536\) 525.338 + 429.044i 0.980109 + 0.800456i
\(537\) −551.405 −1.02682
\(538\) −180.704 168.979i −0.335881 0.314087i
\(539\) −355.405 −0.659378
\(540\) −165.531 + 11.1134i −0.306538 + 0.0205804i
\(541\) 459.744i 0.849804i −0.905239 0.424902i \(-0.860309\pi\)
0.905239 0.424902i \(-0.139691\pi\)
\(542\) 289.219 + 270.453i 0.533615 + 0.498990i
\(543\) 137.721i 0.253630i
\(544\) −219.769 + 309.273i −0.403987 + 0.568516i
\(545\) 1130.98 2.07520
\(546\) 59.1384 63.2420i 0.108312 0.115828i
\(547\) 67.3693 0.123161 0.0615807 0.998102i \(-0.480386\pi\)
0.0615807 + 0.998102i \(0.480386\pi\)
\(548\) −26.6795 397.382i −0.0486852 0.725150i
\(549\) 178.736i 0.325567i
\(550\) 423.061 452.417i 0.769203 0.822577i
\(551\) 8.55511i 0.0155265i
\(552\) −37.4923 + 45.9070i −0.0679208 + 0.0831648i
\(553\) −95.4050 −0.172523
\(554\) 361.856 + 338.377i 0.653170 + 0.610788i
\(555\) −382.277 −0.688787
\(556\) −47.5589 708.374i −0.0855376 1.27405i
\(557\) 476.671i 0.855782i −0.903830 0.427891i \(-0.859257\pi\)
0.903830 0.427891i \(-0.140743\pi\)
\(558\) 251.727 + 235.393i 0.451123 + 0.421851i
\(559\) 336.391i 0.601774i
\(560\) −270.697 + 36.5128i −0.483388 + 0.0652014i
\(561\) 164.287 0.292847
\(562\) 605.324 647.327i 1.07709 1.15183i
\(563\) −910.123 −1.61656 −0.808280 0.588799i \(-0.799601\pi\)
−0.808280 + 0.588799i \(0.799601\pi\)
\(564\) 411.846 27.6506i 0.730224 0.0490258i
\(565\) 465.250i 0.823452i
\(566\) −402.459 + 430.385i −0.711058 + 0.760398i
\(567\) 19.2490i 0.0339489i
\(568\) 214.908 263.141i 0.378358 0.463276i
\(569\) −124.123 −0.218142 −0.109071 0.994034i \(-0.534788\pi\)
−0.109071 + 0.994034i \(0.534788\pi\)
\(570\) −301.492 281.929i −0.528934 0.494613i
\(571\) 945.031 1.65504 0.827522 0.561433i \(-0.189750\pi\)
0.827522 + 0.561433i \(0.189750\pi\)
\(572\) 373.128 25.0511i 0.652322 0.0437957i
\(573\) 611.219i 1.06670i
\(574\) 98.6335 + 92.2335i 0.171835 + 0.160685i
\(575\) 165.596i 0.287994i
\(576\) 38.3538 + 188.130i 0.0665865 + 0.326615i
\(577\) 215.682 0.373799 0.186899 0.982379i \(-0.440156\pi\)
0.186899 + 0.982379i \(0.440156\pi\)
\(578\) −202.753 + 216.822i −0.350784 + 0.375125i
\(579\) 492.382 0.850401
\(580\) −1.22570 18.2564i −0.00211328 0.0314765i
\(581\) 144.823i 0.249265i
\(582\) −229.832 + 245.780i −0.394900 + 0.422302i
\(583\) 250.840i 0.430258i
\(584\) 33.6180 + 27.4559i 0.0575651 + 0.0470135i
\(585\) 279.846 0.478369
\(586\) 97.4679 + 91.1435i 0.166327 + 0.155535i
\(587\) 900.785 1.53456 0.767278 0.641314i \(-0.221611\pi\)
0.767278 + 0.641314i \(0.221611\pi\)
\(588\) 20.6180 + 307.098i 0.0350646 + 0.522276i
\(589\) 857.475i 1.45581i
\(590\) −615.482 575.545i −1.04319 0.975500i
\(591\) 131.305i 0.222174i
\(592\) 59.1384 + 438.439i 0.0998960 + 0.740606i
\(593\) −508.585 −0.857647 −0.428824 0.903388i \(-0.641072\pi\)
−0.428824 + 0.903388i \(0.641072\pi\)
\(594\) 56.7846 60.7249i 0.0955970 0.102230i
\(595\) 202.410 0.340185
\(596\) −350.420 + 23.5266i −0.587954 + 0.0394741i
\(597\) 180.455i 0.302270i
\(598\) 68.2872 73.0256i 0.114193 0.122116i
\(599\) 846.934i 1.41391i −0.707257 0.706957i \(-0.750067\pi\)
0.707257 0.706957i \(-0.249933\pi\)
\(600\) −415.468 339.313i −0.692446 0.565522i
\(601\) −406.000 −0.675541 −0.337770 0.941229i \(-0.609673\pi\)
−0.337770 + 0.941229i \(0.609673\pi\)
\(602\) −89.9334 84.0979i −0.149391 0.139697i
\(603\) −254.354 −0.421814
\(604\) 874.295 58.6985i 1.44751 0.0971829i
\(605\) 454.976i 0.752026i
\(606\) −157.219 147.018i −0.259438 0.242603i
\(607\) 771.156i 1.27044i −0.772332 0.635219i \(-0.780910\pi\)
0.772332 0.635219i \(-0.219090\pi\)
\(608\) −276.708 + 389.400i −0.455111 + 0.640461i
\(609\) 2.12297 0.00348600
\(610\) −649.626 + 694.703i −1.06496 + 1.13886i
\(611\) −696.267 −1.13955
\(612\) −9.53074 141.957i −0.0155731 0.231956i
\(613\) 336.699i 0.549264i −0.961549 0.274632i \(-0.911444\pi\)
0.961549 0.274632i \(-0.0885560\pi\)
\(614\) −716.084 + 765.773i −1.16626 + 1.24719i
\(615\) 436.453i 0.709680i
\(616\) 86.5847 106.018i 0.140560 0.172106i
\(617\) −908.831 −1.47298 −0.736492 0.676447i \(-0.763519\pi\)
−0.736492 + 0.676447i \(0.763519\pi\)
\(618\) −70.3501 65.7853i −0.113835 0.106449i
\(619\) −1047.77 −1.69268 −0.846340 0.532643i \(-0.821199\pi\)
−0.846340 + 0.532643i \(0.821199\pi\)
\(620\) 122.851 + 1829.83i 0.198147 + 2.95134i
\(621\) 22.2268i 0.0357920i
\(622\) −528.897 494.579i −0.850317 0.795143i
\(623\) 284.754i 0.457068i
\(624\) −43.2923 320.959i −0.0693788 0.514358i
\(625\) −94.1384 −0.150622
\(626\) 344.617 368.529i 0.550506 0.588705i
\(627\) 206.851 0.329906
\(628\) 1011.48 67.9090i 1.61064 0.108135i
\(629\) 327.836i 0.521202i
\(630\) 69.9615 74.8161i 0.111050 0.118756i
\(631\) 610.758i 0.967921i 0.875090 + 0.483961i \(0.160802\pi\)
−0.875090 + 0.483961i \(0.839198\pi\)
\(632\) −225.731 + 276.393i −0.357169 + 0.437331i
\(633\) −237.149 −0.374643
\(634\) 117.440 + 109.819i 0.185236 + 0.173217i
\(635\) 1477.89 2.32739
\(636\) 216.746 14.5519i 0.340796 0.0228804i
\(637\) 519.180i 0.815040i
\(638\) 6.69735 + 6.26278i 0.0104974 + 0.00981627i
\(639\) 127.405i 0.199382i
\(640\) −534.697 + 870.614i −0.835465 + 1.36034i
\(641\) 9.60015 0.0149768 0.00748842 0.999972i \(-0.497616\pi\)
0.00748842 + 0.999972i \(0.497616\pi\)
\(642\) −89.3872 + 95.5897i −0.139232 + 0.148894i
\(643\) 86.1999 0.134059 0.0670295 0.997751i \(-0.478648\pi\)
0.0670295 + 0.997751i \(0.478648\pi\)
\(644\) −2.45140 36.5128i −0.00380652 0.0566969i
\(645\) 397.955i 0.616985i
\(646\) 241.779 258.556i 0.374272 0.400242i
\(647\) 352.580i 0.544946i −0.962163 0.272473i \(-0.912158\pi\)
0.962163 0.272473i \(-0.0878416\pi\)
\(648\) −55.7654 45.5436i −0.0860577 0.0702834i
\(649\) 422.277 0.650658
\(650\) 660.897 + 618.014i 1.01677 + 0.950790i
\(651\) −212.785 −0.326858
\(652\) 27.4256 + 408.496i 0.0420638 + 0.626527i
\(653\) 319.322i 0.489008i −0.969648 0.244504i \(-0.921375\pi\)
0.969648 0.244504i \(-0.0786252\pi\)
\(654\) 358.508 + 335.245i 0.548177 + 0.512607i
\(655\) 1000.62i 1.52766i
\(656\) 500.574 67.5196i 0.763071 0.102926i
\(657\) −16.2769 −0.0247745
\(658\) −174.067 + 186.145i −0.264539 + 0.282895i
\(659\) 275.328 0.417797 0.208898 0.977937i \(-0.433012\pi\)
0.208898 + 0.977937i \(0.433012\pi\)
\(660\) 441.415 29.6358i 0.668811 0.0449027i
\(661\) 133.668i 0.202221i −0.994875 0.101111i \(-0.967760\pi\)
0.994875 0.101111i \(-0.0322396\pi\)
\(662\) 235.033 251.342i 0.355035 0.379671i
\(663\) 239.993i 0.361980i
\(664\) −419.559 342.654i −0.631866 0.516046i
\(665\) 254.851 0.383235
\(666\) −121.177 113.314i −0.181947 0.170141i
\(667\) 2.45140 0.00367526
\(668\) −1121.84 + 75.3179i −1.67939 + 0.112751i
\(669\) 92.0799i 0.137638i
\(670\) −988.610 924.462i −1.47554 1.37979i
\(671\) 476.630i 0.710327i
\(672\) −96.6307 68.6657i −0.143796 0.102181i
\(673\) 187.703 0.278904 0.139452 0.990229i \(-0.455466\pi\)
0.139452 + 0.990229i \(0.455466\pi\)
\(674\) 770.817 824.303i 1.14364 1.22300i
\(675\) 201.158 0.298011
\(676\) −8.68842 129.411i −0.0128527 0.191437i
\(677\) 1169.84i 1.72797i −0.503515 0.863986i \(-0.667960\pi\)
0.503515 0.863986i \(-0.332040\pi\)
\(678\) 137.909 147.478i 0.203406 0.217520i
\(679\) 207.758i 0.305976i
\(680\) 478.908 586.393i 0.704276 0.862342i
\(681\) 207.580 0.304816
\(682\) −671.272 627.715i −0.984269 0.920403i
\(683\) 89.4566 0.130976 0.0654880 0.997853i \(-0.479140\pi\)
0.0654880 + 0.997853i \(0.479140\pi\)
\(684\) −12.0000 178.736i −0.0175439 0.261310i
\(685\) 794.765i 1.16024i
\(686\) −291.895 272.955i −0.425503 0.397893i
\(687\) 370.837i 0.539791i
\(688\) −456.420 + 61.5639i −0.663402 + 0.0894824i
\(689\) −366.431 −0.531830
\(690\) 80.7846 86.3902i 0.117079 0.125203i
\(691\) 139.103 0.201306 0.100653 0.994922i \(-0.467907\pi\)
0.100653 + 0.994922i \(0.467907\pi\)
\(692\) 969.251 65.0737i 1.40065 0.0940371i
\(693\) 51.3307i 0.0740703i
\(694\) −390.851 + 417.972i −0.563186 + 0.602265i
\(695\) 1416.75i 2.03849i
\(696\) 5.02301 6.15037i 0.00721697 0.00883673i
\(697\) −374.297 −0.537012
\(698\) 615.033 + 575.126i 0.881137 + 0.823962i
\(699\) 220.726 0.315773
\(700\) 330.449 22.1857i 0.472069 0.0316938i
\(701\) 1218.34i 1.73801i 0.494804 + 0.869004i \(0.335240\pi\)
−0.494804 + 0.869004i \(0.664760\pi\)
\(702\) 88.7077 + 82.9517i 0.126364 + 0.118165i
\(703\) 412.773i 0.587160i
\(704\) −102.277 501.681i −0.145280 0.712615i
\(705\) −823.692 −1.16836
\(706\) 586.214 626.891i 0.830331 0.887948i
\(707\) 132.897 0.187974
\(708\) −24.4974 364.881i −0.0346009 0.515369i
\(709\) 1080.13i 1.52346i 0.647895 + 0.761730i \(0.275649\pi\)
−0.647895 + 0.761730i \(0.724351\pi\)
\(710\) −463.061 + 495.193i −0.652199 + 0.697455i
\(711\) 133.822i 0.188216i
\(712\) 824.946 + 673.734i 1.15863 + 0.946256i
\(713\) −245.703 −0.344604
\(714\) 64.1615 + 59.9982i 0.0898620 + 0.0840311i
\(715\) −746.256 −1.04372
\(716\) −85.3027 1270.56i −0.119138 1.77452i
\(717\) 553.011i 0.771285i
\(718\) 385.177 + 360.184i 0.536458 + 0.501649i
\(719\) 20.7736i 0.0288923i 0.999896 + 0.0144461i \(0.00459851\pi\)
−0.999896 + 0.0144461i \(0.995401\pi\)
\(720\) −51.2154 379.699i −0.0711325 0.527360i
\(721\) 59.4669 0.0824783
\(722\) −188.715 + 201.809i −0.261378 + 0.279515i
\(723\) 428.536 0.592719
\(724\) −317.338 + 21.3055i −0.438313 + 0.0294275i
\(725\) 22.1857i 0.0306010i
\(726\) 134.863 144.222i 0.185762 0.198652i
\(727\) 1031.17i 1.41838i −0.705015 0.709192i \(-0.749060\pi\)
0.705015 0.709192i \(-0.250940\pi\)
\(728\) 154.872 + 126.484i 0.212736 + 0.173742i
\(729\) 27.0000 0.0370370
\(730\) −63.2642 59.1592i −0.0866633 0.0810399i
\(731\) 341.282 0.466870
\(732\) −411.846 + 27.6506i −0.562631 + 0.0377740i
\(733\) 881.072i 1.20201i 0.799246 + 0.601004i \(0.205233\pi\)
−0.799246 + 0.601004i \(0.794767\pi\)
\(734\) −189.240 176.961i −0.257820 0.241091i
\(735\) 614.197i 0.835642i
\(736\) −111.580 79.2884i −0.151603 0.107729i
\(737\) 678.277 0.920321
\(738\) −129.373 + 138.350i −0.175302 + 0.187466i
\(739\) −671.195 −0.908247 −0.454124 0.890939i \(-0.650048\pi\)
−0.454124 + 0.890939i \(0.650048\pi\)
\(740\) −59.1384 880.848i −0.0799168 1.19033i
\(741\) 302.171i 0.407788i
\(742\) −91.6077 + 97.9643i −0.123461 + 0.132027i
\(743\) 254.197i 0.342122i 0.985260 + 0.171061i \(0.0547195\pi\)
−0.985260 + 0.171061i \(0.945281\pi\)
\(744\) −503.454 + 616.448i −0.676685 + 0.828559i
\(745\) 700.841 0.940726
\(746\) −441.864 413.193i −0.592311 0.553878i
\(747\) 203.138 0.271939
\(748\) 25.4153 + 378.553i 0.0339777 + 0.506087i
\(749\) 80.8019i 0.107880i
\(750\) 276.946 + 258.976i 0.369261 + 0.345301i
\(751\) 728.994i 0.970698i 0.874320 + 0.485349i \(0.161307\pi\)
−0.874320 + 0.485349i \(0.838693\pi\)
\(752\) 127.426 + 944.704i 0.169449 + 1.25626i
\(753\) 372.133 0.494201
\(754\) −9.14875 + 9.78357i −0.0121336 + 0.0129756i
\(755\) −1748.59 −2.31601
\(756\) 44.3538 2.97783i 0.0586691 0.00393893i
\(757\) 372.679i 0.492311i −0.969230 0.246155i \(-0.920833\pi\)
0.969230 0.246155i \(-0.0791674\pi\)
\(758\) −158.746 + 169.761i −0.209428 + 0.223960i
\(759\) 59.2716i 0.0780917i
\(760\) 602.985 738.317i 0.793401 0.971470i
\(761\) 1257.80 1.65283 0.826416 0.563060i \(-0.190376\pi\)
0.826416 + 0.563060i \(0.190376\pi\)
\(762\) 468.473 + 438.075i 0.614794 + 0.574902i
\(763\) −303.046 −0.397177
\(764\) −1408.38 + 94.5559i −1.84343 + 0.123764i
\(765\) 283.915i 0.371130i
\(766\) 827.041 + 773.377i 1.07969 + 1.00963i
\(767\) 616.868i 0.804260i
\(768\) −427.559 + 117.479i −0.556717 + 0.152968i
\(769\) 247.703 0.322110 0.161055 0.986945i \(-0.448510\pi\)
0.161055 + 0.986945i \(0.448510\pi\)
\(770\) −186.564 + 199.510i −0.242291 + 0.259103i
\(771\) 145.972 0.189328
\(772\) 76.1718 + 1134.55i 0.0986681 + 1.46963i
\(773\) 587.805i 0.760420i 0.924900 + 0.380210i \(0.124148\pi\)
−0.924900 + 0.380210i \(0.875852\pi\)
\(774\) 117.962 126.147i 0.152405 0.162980i
\(775\) 2223.66i 2.86924i
\(776\) −601.885 491.560i −0.775624 0.633453i
\(777\) 102.431 0.131829
\(778\) −511.437 478.251i −0.657374 0.614719i
\(779\) −471.272 −0.604970
\(780\) 43.2923 + 644.825i 0.0555030 + 0.826699i
\(781\) 339.748i 0.435016i
\(782\) 74.0873 + 69.2800i 0.0947407 + 0.0885933i
\(783\) 2.97783i 0.00380311i
\(784\) −704.431 + 95.0166i −0.898509 + 0.121195i
\(785\) −2022.96 −2.57702
\(786