Properties

Label 210.3.c.a.29.3
Level $210$
Weight $3$
Character 210.29
Analytic conductor $5.722$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.3
Character \(\chi\) \(=\) 210.29
Dual form 210.3.c.a.29.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.01468 - 2.22285i) q^{3} +2.00000 q^{4} +(3.91845 + 3.10576i) q^{5} +(2.84919 + 3.14358i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-0.882103 + 8.95667i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.01468 - 2.22285i) q^{3} +2.00000 q^{4} +(3.91845 + 3.10576i) q^{5} +(2.84919 + 3.14358i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(-0.882103 + 8.95667i) q^{9} +(-5.54153 - 4.39221i) q^{10} +6.10339i q^{11} +(-4.02937 - 4.44570i) q^{12} +6.09265i q^{13} +3.74166i q^{14} +(-0.990810 - 14.9672i) q^{15} +4.00000 q^{16} -7.30179 q^{17} +(1.24748 - 12.6666i) q^{18} +31.7506 q^{19} +(7.83690 + 6.21152i) q^{20} +(-5.88110 + 5.33035i) q^{21} -8.63149i q^{22} +33.8856 q^{23} +(5.69838 + 6.28716i) q^{24} +(5.70852 + 24.3395i) q^{25} -8.61631i q^{26} +(21.6865 - 16.0841i) q^{27} -5.29150i q^{28} -41.0122i q^{29} +(1.40122 + 21.1669i) q^{30} +42.9120 q^{31} -5.65685 q^{32} +(13.5669 - 12.2964i) q^{33} +10.3263 q^{34} +(8.21707 - 10.3672i) q^{35} +(-1.76421 + 17.9133i) q^{36} +18.1246i q^{37} -44.9022 q^{38} +(13.5430 - 12.2748i) q^{39} +(-11.0831 - 8.78441i) q^{40} +36.4331i q^{41} +(8.31713 - 7.53825i) q^{42} +17.7024i q^{43} +12.2068i q^{44} +(-31.2737 + 32.3567i) q^{45} -47.9215 q^{46} -45.3150 q^{47} +(-8.05873 - 8.89139i) q^{48} -7.00000 q^{49} +(-8.07307 - 34.4213i) q^{50} +(14.7108 + 16.2308i) q^{51} +12.1853i q^{52} +18.1388 q^{53} +(-30.6693 + 22.7463i) q^{54} +(-18.9557 + 23.9158i) q^{55} +7.48331i q^{56} +(-63.9675 - 70.5769i) q^{57} +58.0000i q^{58} +4.22725i q^{59} +(-1.98162 - 29.9345i) q^{60} +16.8936 q^{61} -60.6867 q^{62} +(23.6971 + 2.33383i) q^{63} +8.00000 q^{64} +(-18.9223 + 23.8738i) q^{65} +(-19.1865 + 17.3897i) q^{66} -17.1392i q^{67} -14.6036 q^{68} +(-68.2688 - 75.3226i) q^{69} +(-11.6207 + 14.6615i) q^{70} -113.824i q^{71} +(2.49497 - 25.3333i) q^{72} +105.073i q^{73} -25.6320i q^{74} +(42.6022 - 61.7256i) q^{75} +63.5013 q^{76} +16.1480 q^{77} +(-19.1527 + 17.3591i) q^{78} -74.8132 q^{79} +(15.6738 + 12.4230i) q^{80} +(-79.4438 - 15.8014i) q^{81} -51.5242i q^{82} +76.5950 q^{83} +(-11.7622 + 10.6607i) q^{84} +(-28.6117 - 22.6776i) q^{85} -25.0350i q^{86} +(-91.1639 + 82.6266i) q^{87} -17.2630i q^{88} +26.8568i q^{89} +(44.2277 - 45.7592i) q^{90} +16.1196 q^{91} +67.7713 q^{92} +(-86.4541 - 95.3868i) q^{93} +64.0851 q^{94} +(124.413 + 98.6099i) q^{95} +(11.3968 + 12.5743i) q^{96} -120.087i q^{97} +9.89949 q^{98} +(-54.6660 - 5.38382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.01468 2.22285i −0.671561 0.740949i
\(4\) 2.00000 0.500000
\(5\) 3.91845 + 3.10576i 0.783690 + 0.621152i
\(6\) 2.84919 + 3.14358i 0.474865 + 0.523930i
\(7\) 2.64575i 0.377964i
\(8\) −2.82843 −0.353553
\(9\) −0.882103 + 8.95667i −0.0980115 + 0.995185i
\(10\) −5.54153 4.39221i −0.554153 0.439221i
\(11\) 6.10339i 0.554853i 0.960747 + 0.277427i \(0.0894816\pi\)
−0.960747 + 0.277427i \(0.910518\pi\)
\(12\) −4.02937 4.44570i −0.335781 0.370475i
\(13\) 6.09265i 0.468666i 0.972156 + 0.234333i \(0.0752905\pi\)
−0.972156 + 0.234333i \(0.924709\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −0.990810 14.9672i −0.0660540 0.997816i
\(16\) 4.00000 0.250000
\(17\) −7.30179 −0.429517 −0.214758 0.976667i \(-0.568896\pi\)
−0.214758 + 0.976667i \(0.568896\pi\)
\(18\) 1.24748 12.6666i 0.0693046 0.703702i
\(19\) 31.7506 1.67109 0.835543 0.549424i \(-0.185153\pi\)
0.835543 + 0.549424i \(0.185153\pi\)
\(20\) 7.83690 + 6.21152i 0.391845 + 0.310576i
\(21\) −5.88110 + 5.33035i −0.280052 + 0.253826i
\(22\) 8.63149i 0.392341i
\(23\) 33.8856 1.47329 0.736644 0.676280i \(-0.236409\pi\)
0.736644 + 0.676280i \(0.236409\pi\)
\(24\) 5.69838 + 6.28716i 0.237433 + 0.261965i
\(25\) 5.70852 + 24.3395i 0.228341 + 0.973581i
\(26\) 8.61631i 0.331397i
\(27\) 21.6865 16.0841i 0.803202 0.595706i
\(28\) 5.29150i 0.188982i
\(29\) 41.0122i 1.41421i −0.707106 0.707107i \(-0.750000\pi\)
0.707106 0.707107i \(-0.250000\pi\)
\(30\) 1.40122 + 21.1669i 0.0467072 + 0.705562i
\(31\) 42.9120 1.38426 0.692129 0.721774i \(-0.256673\pi\)
0.692129 + 0.721774i \(0.256673\pi\)
\(32\) −5.65685 −0.176777
\(33\) 13.5669 12.2964i 0.411118 0.372618i
\(34\) 10.3263 0.303714
\(35\) 8.21707 10.3672i 0.234773 0.296207i
\(36\) −1.76421 + 17.9133i −0.0490057 + 0.497593i
\(37\) 18.1246i 0.489854i 0.969542 + 0.244927i \(0.0787640\pi\)
−0.969542 + 0.244927i \(0.921236\pi\)
\(38\) −44.9022 −1.18164
\(39\) 13.5430 12.2748i 0.347257 0.314738i
\(40\) −11.0831 8.78441i −0.277076 0.219610i
\(41\) 36.4331i 0.888612i 0.895875 + 0.444306i \(0.146550\pi\)
−0.895875 + 0.444306i \(0.853450\pi\)
\(42\) 8.31713 7.53825i 0.198027 0.179482i
\(43\) 17.7024i 0.411684i 0.978585 + 0.205842i \(0.0659932\pi\)
−0.978585 + 0.205842i \(0.934007\pi\)
\(44\) 12.2068i 0.277427i
\(45\) −31.2737 + 32.3567i −0.694972 + 0.719037i
\(46\) −47.9215 −1.04177
\(47\) −45.3150 −0.964149 −0.482074 0.876130i \(-0.660116\pi\)
−0.482074 + 0.876130i \(0.660116\pi\)
\(48\) −8.05873 8.89139i −0.167890 0.185237i
\(49\) −7.00000 −0.142857
\(50\) −8.07307 34.4213i −0.161461 0.688426i
\(51\) 14.7108 + 16.2308i 0.288447 + 0.318250i
\(52\) 12.1853i 0.234333i
\(53\) 18.1388 0.342242 0.171121 0.985250i \(-0.445261\pi\)
0.171121 + 0.985250i \(0.445261\pi\)
\(54\) −30.6693 + 22.7463i −0.567950 + 0.421228i
\(55\) −18.9557 + 23.9158i −0.344648 + 0.434833i
\(56\) 7.48331i 0.133631i
\(57\) −63.9675 70.5769i −1.12224 1.23819i
\(58\) 58.0000i 1.00000i
\(59\) 4.22725i 0.0716482i 0.999358 + 0.0358241i \(0.0114056\pi\)
−0.999358 + 0.0358241i \(0.988594\pi\)
\(60\) −1.98162 29.9345i −0.0330270 0.498908i
\(61\) 16.8936 0.276944 0.138472 0.990366i \(-0.455781\pi\)
0.138472 + 0.990366i \(0.455781\pi\)
\(62\) −60.6867 −0.978818
\(63\) 23.6971 + 2.33383i 0.376145 + 0.0370449i
\(64\) 8.00000 0.125000
\(65\) −18.9223 + 23.8738i −0.291112 + 0.367289i
\(66\) −19.1865 + 17.3897i −0.290704 + 0.263481i
\(67\) 17.1392i 0.255810i −0.991786 0.127905i \(-0.959175\pi\)
0.991786 0.127905i \(-0.0408252\pi\)
\(68\) −14.6036 −0.214758
\(69\) −68.2688 75.3226i −0.989404 1.09163i
\(70\) −11.6207 + 14.6615i −0.166010 + 0.209450i
\(71\) 113.824i 1.60316i −0.597890 0.801578i \(-0.703994\pi\)
0.597890 0.801578i \(-0.296006\pi\)
\(72\) 2.49497 25.3333i 0.0346523 0.351851i
\(73\) 105.073i 1.43935i 0.694311 + 0.719675i \(0.255709\pi\)
−0.694311 + 0.719675i \(0.744291\pi\)
\(74\) 25.6320i 0.346379i
\(75\) 42.6022 61.7256i 0.568029 0.823008i
\(76\) 63.5013 0.835543
\(77\) 16.1480 0.209715
\(78\) −19.1527 + 17.3591i −0.245548 + 0.222553i
\(79\) −74.8132 −0.947003 −0.473501 0.880793i \(-0.657010\pi\)
−0.473501 + 0.880793i \(0.657010\pi\)
\(80\) 15.6738 + 12.4230i 0.195923 + 0.155288i
\(81\) −79.4438 15.8014i −0.980787 0.195079i
\(82\) 51.5242i 0.628344i
\(83\) 76.5950 0.922831 0.461416 0.887184i \(-0.347342\pi\)
0.461416 + 0.887184i \(0.347342\pi\)
\(84\) −11.7622 + 10.6607i −0.140026 + 0.126913i
\(85\) −28.6117 22.6776i −0.336608 0.266795i
\(86\) 25.0350i 0.291104i
\(87\) −91.1639 + 82.6266i −1.04786 + 0.949732i
\(88\) 17.2630i 0.196170i
\(89\) 26.8568i 0.301762i 0.988552 + 0.150881i \(0.0482110\pi\)
−0.988552 + 0.150881i \(0.951789\pi\)
\(90\) 44.2277 45.7592i 0.491419 0.508436i
\(91\) 16.1196 0.177139
\(92\) 67.7713 0.736644
\(93\) −86.4541 95.3868i −0.929614 1.02566i
\(94\) 64.0851 0.681756
\(95\) 124.413 + 98.6099i 1.30961 + 1.03800i
\(96\) 11.3968 + 12.5743i 0.118716 + 0.130983i
\(97\) 120.087i 1.23801i −0.785387 0.619005i \(-0.787536\pi\)
0.785387 0.619005i \(-0.212464\pi\)
\(98\) 9.89949 0.101015
\(99\) −54.6660 5.38382i −0.552182 0.0543820i
\(100\) 11.4170 + 48.6791i 0.114170 + 0.486791i
\(101\) 162.983i 1.61369i 0.590764 + 0.806844i \(0.298826\pi\)
−0.590764 + 0.806844i \(0.701174\pi\)
\(102\) −20.8042 22.9538i −0.203963 0.225037i
\(103\) 186.379i 1.80951i 0.425937 + 0.904753i \(0.359944\pi\)
−0.425937 + 0.904753i \(0.640056\pi\)
\(104\) 17.2326i 0.165698i
\(105\) −39.5996 + 2.62144i −0.377139 + 0.0249661i
\(106\) −25.6522 −0.242002
\(107\) −164.926 −1.54136 −0.770681 0.637221i \(-0.780084\pi\)
−0.770681 + 0.637221i \(0.780084\pi\)
\(108\) 43.3729 32.1681i 0.401601 0.297853i
\(109\) −96.6905 −0.887069 −0.443535 0.896257i \(-0.646276\pi\)
−0.443535 + 0.896257i \(0.646276\pi\)
\(110\) 26.8073 33.8221i 0.243703 0.307474i
\(111\) 40.2882 36.5153i 0.362957 0.328967i
\(112\) 10.5830i 0.0944911i
\(113\) 112.284 0.993660 0.496830 0.867848i \(-0.334497\pi\)
0.496830 + 0.867848i \(0.334497\pi\)
\(114\) 90.4637 + 99.8107i 0.793541 + 0.875533i
\(115\) 132.779 + 105.241i 1.15460 + 0.915136i
\(116\) 82.0245i 0.707107i
\(117\) −54.5699 5.37435i −0.466409 0.0459346i
\(118\) 5.97823i 0.0506629i
\(119\) 19.3187i 0.162342i
\(120\) 2.80243 + 42.3337i 0.0233536 + 0.352781i
\(121\) 83.7487 0.692138
\(122\) −23.8911 −0.195829
\(123\) 80.9852 73.4012i 0.658417 0.596757i
\(124\) 85.8240 0.692129
\(125\) −53.2241 + 113.103i −0.425793 + 0.904821i
\(126\) −33.5128 3.30053i −0.265974 0.0261947i
\(127\) 197.632i 1.55616i −0.628167 0.778078i \(-0.716195\pi\)
0.628167 0.778078i \(-0.283805\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 39.3497 35.6647i 0.305037 0.276471i
\(130\) 26.7602 33.7626i 0.205848 0.259712i
\(131\) 38.0418i 0.290396i −0.989403 0.145198i \(-0.953618\pi\)
0.989403 0.145198i \(-0.0463819\pi\)
\(132\) 27.1338 24.5928i 0.205559 0.186309i
\(133\) 84.0043i 0.631611i
\(134\) 24.2385i 0.180885i
\(135\) 134.931 + 4.32830i 0.999486 + 0.0320615i
\(136\) 20.6526 0.151857
\(137\) −43.7923 −0.319652 −0.159826 0.987145i \(-0.551093\pi\)
−0.159826 + 0.987145i \(0.551093\pi\)
\(138\) 96.5467 + 106.522i 0.699614 + 0.771901i
\(139\) −175.928 −1.26567 −0.632836 0.774286i \(-0.718109\pi\)
−0.632836 + 0.774286i \(0.718109\pi\)
\(140\) 16.4341 20.7345i 0.117387 0.148104i
\(141\) 91.2953 + 100.728i 0.647485 + 0.714385i
\(142\) 160.972i 1.13360i
\(143\) −37.1858 −0.260041
\(144\) −3.52841 + 35.8267i −0.0245029 + 0.248796i
\(145\) 127.374 160.704i 0.878442 1.10831i
\(146\) 148.595i 1.01777i
\(147\) 14.1028 + 15.5599i 0.0959373 + 0.105850i
\(148\) 36.2492i 0.244927i
\(149\) 150.593i 1.01069i 0.862917 + 0.505345i \(0.168635\pi\)
−0.862917 + 0.505345i \(0.831365\pi\)
\(150\) −60.2486 + 87.2932i −0.401657 + 0.581955i
\(151\) −5.63028 −0.0372866 −0.0186433 0.999826i \(-0.505935\pi\)
−0.0186433 + 0.999826i \(0.505935\pi\)
\(152\) −89.8044 −0.590818
\(153\) 6.44093 65.3997i 0.0420976 0.427449i
\(154\) −22.8368 −0.148291
\(155\) 168.149 + 133.274i 1.08483 + 0.859834i
\(156\) 27.0861 24.5495i 0.173629 0.157369i
\(157\) 119.059i 0.758341i −0.925327 0.379170i \(-0.876209\pi\)
0.925327 0.379170i \(-0.123791\pi\)
\(158\) 105.802 0.669632
\(159\) −36.5440 40.3199i −0.229837 0.253584i
\(160\) −22.1661 17.5688i −0.138538 0.109805i
\(161\) 89.6530i 0.556851i
\(162\) 112.350 + 22.3466i 0.693521 + 0.137942i
\(163\) 74.5829i 0.457564i −0.973478 0.228782i \(-0.926526\pi\)
0.973478 0.228782i \(-0.0734743\pi\)
\(164\) 72.8662i 0.444306i
\(165\) 91.3509 6.04729i 0.553642 0.0366503i
\(166\) −108.322 −0.652540
\(167\) 114.419 0.685144 0.342572 0.939492i \(-0.388702\pi\)
0.342572 + 0.939492i \(0.388702\pi\)
\(168\) 16.6343 15.0765i 0.0990135 0.0897411i
\(169\) 131.880 0.780353
\(170\) 40.4630 + 32.0710i 0.238018 + 0.188653i
\(171\) −28.0074 + 284.380i −0.163786 + 1.66304i
\(172\) 35.4048i 0.205842i
\(173\) −173.820 −1.00474 −0.502370 0.864653i \(-0.667538\pi\)
−0.502370 + 0.864653i \(0.667538\pi\)
\(174\) 128.925 116.852i 0.740950 0.671562i
\(175\) 64.3963 15.1033i 0.367979 0.0863048i
\(176\) 24.4136i 0.138713i
\(177\) 9.39652 8.51656i 0.0530877 0.0481162i
\(178\) 37.9812i 0.213378i
\(179\) 134.192i 0.749677i −0.927090 0.374838i \(-0.877698\pi\)
0.927090 0.374838i \(-0.122302\pi\)
\(180\) −62.5475 + 64.7133i −0.347486 + 0.359519i
\(181\) −199.113 −1.10007 −0.550036 0.835141i \(-0.685386\pi\)
−0.550036 + 0.835141i \(0.685386\pi\)
\(182\) −22.7966 −0.125256
\(183\) −34.0352 37.5518i −0.185985 0.205201i
\(184\) −95.8431 −0.520886
\(185\) −56.2906 + 71.0203i −0.304274 + 0.383894i
\(186\) 122.265 + 134.897i 0.657336 + 0.725255i
\(187\) 44.5656i 0.238319i
\(188\) −90.6300 −0.482074
\(189\) −42.5544 57.3770i −0.225156 0.303582i
\(190\) −175.947 139.455i −0.926037 0.733976i
\(191\) 224.206i 1.17385i −0.809640 0.586927i \(-0.800338\pi\)
0.809640 0.586927i \(-0.199662\pi\)
\(192\) −16.1175 17.7828i −0.0839451 0.0926187i
\(193\) 340.124i 1.76230i −0.472838 0.881149i \(-0.656770\pi\)
0.472838 0.881149i \(-0.343230\pi\)
\(194\) 169.829i 0.875405i
\(195\) 91.1902 6.03666i 0.467642 0.0309572i
\(196\) −14.0000 −0.0714286
\(197\) 115.404 0.585805 0.292903 0.956142i \(-0.405379\pi\)
0.292903 + 0.956142i \(0.405379\pi\)
\(198\) 77.3094 + 7.61387i 0.390452 + 0.0384539i
\(199\) 186.569 0.937534 0.468767 0.883322i \(-0.344698\pi\)
0.468767 + 0.883322i \(0.344698\pi\)
\(200\) −16.1461 68.8426i −0.0807307 0.344213i
\(201\) −38.0979 + 34.5301i −0.189542 + 0.171792i
\(202\) 230.492i 1.14105i
\(203\) −108.508 −0.534523
\(204\) 29.4216 + 32.4615i 0.144223 + 0.159125i
\(205\) −113.152 + 142.761i −0.551963 + 0.696397i
\(206\) 263.580i 1.27951i
\(207\) −29.8906 + 303.502i −0.144399 + 1.46620i
\(208\) 24.3706i 0.117166i
\(209\) 193.787i 0.927208i
\(210\) 56.0023 3.70727i 0.266678 0.0176537i
\(211\) −348.892 −1.65352 −0.826759 0.562556i \(-0.809818\pi\)
−0.826759 + 0.562556i \(0.809818\pi\)
\(212\) 36.2777 0.171121
\(213\) −253.014 + 229.320i −1.18786 + 1.07662i
\(214\) 233.240 1.08991
\(215\) −54.9794 + 69.3660i −0.255718 + 0.322633i
\(216\) −61.3386 + 45.4926i −0.283975 + 0.210614i
\(217\) 113.534i 0.523200i
\(218\) 136.741 0.627253
\(219\) 233.560 211.688i 1.06649 0.966611i
\(220\) −37.9113 + 47.8317i −0.172324 + 0.217417i
\(221\) 44.4872i 0.201300i
\(222\) −56.9761 + 51.6404i −0.256649 + 0.232615i
\(223\) 442.370i 1.98372i 0.127331 + 0.991860i \(0.459359\pi\)
−0.127331 + 0.991860i \(0.540641\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −223.037 + 29.6594i −0.991274 + 0.131819i
\(226\) −158.793 −0.702624
\(227\) 105.606 0.465225 0.232613 0.972569i \(-0.425273\pi\)
0.232613 + 0.972569i \(0.425273\pi\)
\(228\) −127.935 141.154i −0.561118 0.619095i
\(229\) −300.234 −1.31107 −0.655534 0.755166i \(-0.727556\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(230\) −187.778 148.833i −0.816427 0.647099i
\(231\) −32.5332 35.8946i −0.140836 0.155388i
\(232\) 116.000i 0.500000i
\(233\) −224.338 −0.962823 −0.481411 0.876495i \(-0.659876\pi\)
−0.481411 + 0.876495i \(0.659876\pi\)
\(234\) 77.1734 + 7.60048i 0.329801 + 0.0324807i
\(235\) −177.565 140.737i −0.755594 0.598883i
\(236\) 8.45449i 0.0358241i
\(237\) 150.725 + 166.298i 0.635970 + 0.701681i
\(238\) 27.3208i 0.114793i
\(239\) 298.399i 1.24853i −0.781212 0.624266i \(-0.785398\pi\)
0.781212 0.624266i \(-0.214602\pi\)
\(240\) −3.96324 59.8690i −0.0165135 0.249454i
\(241\) 37.2693 0.154645 0.0773223 0.997006i \(-0.475363\pi\)
0.0773223 + 0.997006i \(0.475363\pi\)
\(242\) −118.438 −0.489415
\(243\) 124.930 + 208.426i 0.514115 + 0.857721i
\(244\) 33.7872 0.138472
\(245\) −27.4292 21.7403i −0.111956 0.0887360i
\(246\) −114.530 + 103.805i −0.465571 + 0.421971i
\(247\) 193.446i 0.783181i
\(248\) −121.373 −0.489409
\(249\) −154.315 170.259i −0.619738 0.683771i
\(250\) 75.2703 159.951i 0.301081 0.639805i
\(251\) 247.604i 0.986471i −0.869896 0.493235i \(-0.835814\pi\)
0.869896 0.493235i \(-0.164186\pi\)
\(252\) 47.3942 + 4.66765i 0.188072 + 0.0185224i
\(253\) 206.817i 0.817459i
\(254\) 279.494i 1.10037i
\(255\) 7.23468 + 109.288i 0.0283713 + 0.428579i
\(256\) 16.0000 0.0625000
\(257\) 75.6252 0.294262 0.147131 0.989117i \(-0.452996\pi\)
0.147131 + 0.989117i \(0.452996\pi\)
\(258\) −55.6489 + 50.4375i −0.215694 + 0.195494i
\(259\) 47.9532 0.185147
\(260\) −37.8446 + 47.7475i −0.145556 + 0.183644i
\(261\) 367.333 + 36.1770i 1.40741 + 0.138609i
\(262\) 53.7993i 0.205341i
\(263\) 56.5685 0.215089 0.107545 0.994200i \(-0.465701\pi\)
0.107545 + 0.994200i \(0.465701\pi\)
\(264\) −38.3730 + 34.7795i −0.145352 + 0.131740i
\(265\) 71.0762 + 56.3349i 0.268212 + 0.212584i
\(266\) 118.800i 0.446617i
\(267\) 59.6985 54.1079i 0.223590 0.202651i
\(268\) 34.2785i 0.127905i
\(269\) 253.707i 0.943149i −0.881826 0.471574i \(-0.843686\pi\)
0.881826 0.471574i \(-0.156314\pi\)
\(270\) −190.821 6.12114i −0.706743 0.0226709i
\(271\) 256.392 0.946096 0.473048 0.881037i \(-0.343154\pi\)
0.473048 + 0.881037i \(0.343154\pi\)
\(272\) −29.2071 −0.107379
\(273\) −32.4760 35.8315i −0.118960 0.131251i
\(274\) 61.9317 0.226028
\(275\) −148.554 + 34.8413i −0.540195 + 0.126696i
\(276\) −136.538 150.645i −0.494702 0.545816i
\(277\) 185.677i 0.670312i 0.942163 + 0.335156i \(0.108789\pi\)
−0.942163 + 0.335156i \(0.891211\pi\)
\(278\) 248.800 0.894966
\(279\) −37.8528 + 384.349i −0.135673 + 1.37759i
\(280\) −23.2414 + 29.3230i −0.0830049 + 0.104725i
\(281\) 260.250i 0.926157i −0.886317 0.463078i \(-0.846745\pi\)
0.886317 0.463078i \(-0.153255\pi\)
\(282\) −129.111 142.451i −0.457841 0.505147i
\(283\) 445.523i 1.57429i −0.616770 0.787143i \(-0.711559\pi\)
0.616770 0.787143i \(-0.288441\pi\)
\(284\) 227.648i 0.801578i
\(285\) −31.4588 475.220i −0.110382 1.66744i
\(286\) 52.5887 0.183877
\(287\) 96.3929 0.335864
\(288\) 4.98993 50.6666i 0.0173261 0.175926i
\(289\) −235.684 −0.815515
\(290\) −180.134 + 227.270i −0.621152 + 0.783691i
\(291\) −266.935 + 241.937i −0.917302 + 0.831399i
\(292\) 210.145i 0.719675i
\(293\) 173.565 0.592371 0.296186 0.955130i \(-0.404285\pi\)
0.296186 + 0.955130i \(0.404285\pi\)
\(294\) −19.9443 22.0051i −0.0678379 0.0748472i
\(295\) −13.1288 + 16.5643i −0.0445044 + 0.0561500i
\(296\) 51.2641i 0.173189i
\(297\) 98.1673 + 132.361i 0.330530 + 0.445660i
\(298\) 212.971i 0.714666i
\(299\) 206.453i 0.690480i
\(300\) 85.2044 123.451i 0.284015 0.411504i
\(301\) 46.8361 0.155602
\(302\) 7.96241 0.0263656
\(303\) 362.285 328.358i 1.19566 1.08369i
\(304\) 127.003 0.417772
\(305\) 66.1967 + 52.4674i 0.217038 + 0.172024i
\(306\) −9.10885 + 92.4891i −0.0297675 + 0.302252i
\(307\) 243.521i 0.793227i 0.917986 + 0.396613i \(0.129815\pi\)
−0.917986 + 0.396613i \(0.870185\pi\)
\(308\) 32.2961 0.104857
\(309\) 414.292 375.495i 1.34075 1.21519i
\(310\) −237.798 188.478i −0.767090 0.607995i
\(311\) 257.759i 0.828809i −0.910093 0.414404i \(-0.863990\pi\)
0.910093 0.414404i \(-0.136010\pi\)
\(312\) −38.3055 + 34.7183i −0.122774 + 0.111277i
\(313\) 156.412i 0.499718i 0.968282 + 0.249859i \(0.0803842\pi\)
−0.968282 + 0.249859i \(0.919616\pi\)
\(314\) 168.376i 0.536228i
\(315\) 85.6077 + 82.7425i 0.271770 + 0.262675i
\(316\) −149.626 −0.473501
\(317\) 269.689 0.850754 0.425377 0.905016i \(-0.360142\pi\)
0.425377 + 0.905016i \(0.360142\pi\)
\(318\) 51.6811 + 57.0209i 0.162519 + 0.179311i
\(319\) 250.314 0.784682
\(320\) 31.3476 + 24.8461i 0.0979613 + 0.0776440i
\(321\) 332.273 + 366.605i 1.03512 + 1.14207i
\(322\) 126.788i 0.393753i
\(323\) −231.836 −0.717760
\(324\) −158.888 31.6028i −0.490394 0.0975396i
\(325\) −148.292 + 34.7801i −0.456284 + 0.107016i
\(326\) 105.476i 0.323547i
\(327\) 194.801 + 214.928i 0.595721 + 0.657273i
\(328\) 103.048i 0.314172i
\(329\) 119.892i 0.364414i
\(330\) −129.190 + 8.55217i −0.391484 + 0.0259157i
\(331\) 100.748 0.304374 0.152187 0.988352i \(-0.451368\pi\)
0.152187 + 0.988352i \(0.451368\pi\)
\(332\) 153.190 0.461416
\(333\) −162.336 15.9878i −0.487495 0.0480113i
\(334\) −161.813 −0.484470
\(335\) 53.2304 67.1593i 0.158897 0.200475i
\(336\) −23.5244 + 21.3214i −0.0700131 + 0.0634566i
\(337\) 172.052i 0.510541i 0.966870 + 0.255270i \(0.0821645\pi\)
−0.966870 + 0.255270i \(0.917835\pi\)
\(338\) −186.506 −0.551793
\(339\) −226.216 249.589i −0.667303 0.736252i
\(340\) −57.2234 45.3552i −0.168304 0.133398i
\(341\) 261.909i 0.768060i
\(342\) 39.6084 402.174i 0.115814 1.17595i
\(343\) 18.5203i 0.0539949i
\(344\) 50.0699i 0.145552i
\(345\) −33.5742 507.175i −0.0973166 1.47007i
\(346\) 245.818 0.710458
\(347\) −376.866 −1.08607 −0.543034 0.839711i \(-0.682725\pi\)
−0.543034 + 0.839711i \(0.682725\pi\)
\(348\) −182.328 + 165.253i −0.523931 + 0.474866i
\(349\) −334.570 −0.958652 −0.479326 0.877637i \(-0.659119\pi\)
−0.479326 + 0.877637i \(0.659119\pi\)
\(350\) −91.0702 + 21.3593i −0.260201 + 0.0610267i
\(351\) 97.9946 + 132.128i 0.279187 + 0.376433i
\(352\) 34.5260i 0.0980852i
\(353\) 291.223 0.824995 0.412497 0.910959i \(-0.364657\pi\)
0.412497 + 0.910959i \(0.364657\pi\)
\(354\) −13.2887 + 12.0442i −0.0375387 + 0.0340233i
\(355\) 353.510 446.014i 0.995804 1.25638i
\(356\) 53.7136i 0.150881i
\(357\) 42.9426 38.9211i 0.120287 0.109023i
\(358\) 189.776i 0.530102i
\(359\) 204.579i 0.569858i −0.958549 0.284929i \(-0.908030\pi\)
0.958549 0.284929i \(-0.0919701\pi\)
\(360\) 88.4555 91.5185i 0.245710 0.254218i
\(361\) 647.104 1.79253
\(362\) 281.589 0.777869
\(363\) −168.727 186.161i −0.464813 0.512839i
\(364\) 32.2393 0.0885695
\(365\) −326.330 + 411.722i −0.894055 + 1.12800i
\(366\) 48.1331 + 53.1063i 0.131511 + 0.145099i
\(367\) 242.592i 0.661015i −0.943803 0.330507i \(-0.892780\pi\)
0.943803 0.330507i \(-0.107220\pi\)
\(368\) 135.543 0.368322
\(369\) −326.319 32.1378i −0.884334 0.0870942i
\(370\) 79.6069 100.438i 0.215154 0.271454i
\(371\) 47.9909i 0.129355i
\(372\) −172.908 190.774i −0.464807 0.512832i
\(373\) 101.784i 0.272880i −0.990648 0.136440i \(-0.956434\pi\)
0.990648 0.136440i \(-0.0435660\pi\)
\(374\) 63.0253i 0.168517i
\(375\) 358.640 109.557i 0.956372 0.292151i
\(376\) 128.170 0.340878
\(377\) 249.873 0.662794
\(378\) 60.1811 + 81.1433i 0.159209 + 0.214665i
\(379\) 247.028 0.651789 0.325894 0.945406i \(-0.394335\pi\)
0.325894 + 0.945406i \(0.394335\pi\)
\(380\) 248.827 + 197.220i 0.654807 + 0.518999i
\(381\) −439.306 + 398.166i −1.15303 + 1.04505i
\(382\) 317.075i 0.830040i
\(383\) 18.9699 0.0495297 0.0247649 0.999693i \(-0.492116\pi\)
0.0247649 + 0.999693i \(0.492116\pi\)
\(384\) 22.7935 + 25.1487i 0.0593582 + 0.0654913i
\(385\) 63.2753 + 50.1519i 0.164352 + 0.130265i
\(386\) 481.008i 1.24613i
\(387\) −158.554 15.6153i −0.409702 0.0403497i
\(388\) 240.174i 0.619005i
\(389\) 623.289i 1.60229i 0.598473 + 0.801143i \(0.295774\pi\)
−0.598473 + 0.801143i \(0.704226\pi\)
\(390\) −128.962 + 8.53712i −0.330673 + 0.0218901i
\(391\) −247.426 −0.632802
\(392\) 19.7990 0.0505076
\(393\) −84.5612 + 76.6422i −0.215168 + 0.195018i
\(394\) −163.205 −0.414227
\(395\) −293.152 232.352i −0.742157 0.588232i
\(396\) −109.332 10.7676i −0.276091 0.0271910i
\(397\) 368.913i 0.929253i −0.885507 0.464626i \(-0.846189\pi\)
0.885507 0.464626i \(-0.153811\pi\)
\(398\) −263.849 −0.662937
\(399\) −186.729 + 169.242i −0.467992 + 0.424166i
\(400\) 22.8341 + 97.3581i 0.0570852 + 0.243395i
\(401\) 291.137i 0.726027i 0.931784 + 0.363014i \(0.118252\pi\)
−0.931784 + 0.363014i \(0.881748\pi\)
\(402\) 53.8786 48.8330i 0.134026 0.121475i
\(403\) 261.448i 0.648754i
\(404\) 325.965i 0.806844i
\(405\) −262.221 308.650i −0.647460 0.762100i
\(406\) 153.454 0.377965
\(407\) −110.621 −0.271797
\(408\) −41.6084 45.9075i −0.101981 0.112518i
\(409\) −131.054 −0.320425 −0.160212 0.987083i \(-0.551218\pi\)
−0.160212 + 0.987083i \(0.551218\pi\)
\(410\) 160.022 201.895i 0.390297 0.492427i
\(411\) 88.2277 + 97.3437i 0.214666 + 0.236846i
\(412\) 372.758i 0.904753i
\(413\) 11.1842 0.0270805
\(414\) 42.2718 429.217i 0.102106 1.03676i
\(415\) 300.134 + 237.886i 0.723214 + 0.573218i
\(416\) 34.4652i 0.0828492i
\(417\) 354.440 + 391.062i 0.849976 + 0.937799i
\(418\) 274.056i 0.655635i
\(419\) 639.030i 1.52513i 0.646911 + 0.762566i \(0.276061\pi\)
−0.646911 + 0.762566i \(0.723939\pi\)
\(420\) −79.1992 + 5.24287i −0.188570 + 0.0124830i
\(421\) 496.330 1.17893 0.589466 0.807793i \(-0.299338\pi\)
0.589466 + 0.807793i \(0.299338\pi\)
\(422\) 493.408 1.16921
\(423\) 39.9725 405.871i 0.0944976 0.959506i
\(424\) −51.3044 −0.121001
\(425\) −41.6824 177.722i −0.0980763 0.418170i
\(426\) 357.815 324.307i 0.839942 0.761284i
\(427\) 44.6962i 0.104675i
\(428\) −329.851 −0.770681
\(429\) 74.9177 + 82.6584i 0.174633 + 0.192677i
\(430\) 77.7526 98.0983i 0.180820 0.228136i
\(431\) 242.169i 0.561877i −0.959726 0.280939i \(-0.909354\pi\)
0.959726 0.280939i \(-0.0906457\pi\)
\(432\) 86.7459 64.3363i 0.200801 0.148927i
\(433\) 123.653i 0.285574i −0.989753 0.142787i \(-0.954394\pi\)
0.989753 0.142787i \(-0.0456063\pi\)
\(434\) 160.562i 0.369959i
\(435\) −613.840 + 40.6353i −1.41113 + 0.0934145i
\(436\) −193.381 −0.443535
\(437\) 1075.89 2.46199
\(438\) −330.304 + 299.372i −0.754119 + 0.683497i
\(439\) 419.828 0.956328 0.478164 0.878271i \(-0.341302\pi\)
0.478164 + 0.878271i \(0.341302\pi\)
\(440\) 53.6147 67.6442i 0.121852 0.153737i
\(441\) 6.17472 62.6967i 0.0140016 0.142169i
\(442\) 62.9145i 0.142340i
\(443\) −95.9458 −0.216582 −0.108291 0.994119i \(-0.534538\pi\)
−0.108291 + 0.994119i \(0.534538\pi\)
\(444\) 80.5764 73.0306i 0.181478 0.164483i
\(445\) −83.4107 + 105.237i −0.187440 + 0.236488i
\(446\) 625.605i 1.40270i
\(447\) 334.745 303.397i 0.748871 0.678741i
\(448\) 21.1660i 0.0472456i
\(449\) 780.855i 1.73910i −0.493847 0.869549i \(-0.664410\pi\)
0.493847 0.869549i \(-0.335590\pi\)
\(450\) 315.421 41.9447i 0.700936 0.0932104i
\(451\) −222.365 −0.493050
\(452\) 224.567 0.496830
\(453\) 11.3432 + 12.5152i 0.0250402 + 0.0276275i
\(454\) −149.350 −0.328964
\(455\) 63.1640 + 50.0637i 0.138822 + 0.110030i
\(456\) 180.927 + 199.621i 0.396771 + 0.437766i
\(457\) 615.383i 1.34657i 0.739383 + 0.673286i \(0.235118\pi\)
−0.739383 + 0.673286i \(0.764882\pi\)
\(458\) 424.596 0.927064
\(459\) −158.350 + 117.442i −0.344989 + 0.255866i
\(460\) 265.559 + 210.481i 0.577301 + 0.457568i
\(461\) 463.592i 1.00562i −0.864396 0.502811i \(-0.832299\pi\)
0.864396 0.502811i \(-0.167701\pi\)
\(462\) 46.0089 + 50.7627i 0.0995863 + 0.109876i
\(463\) 249.784i 0.539491i −0.962932 0.269746i \(-0.913060\pi\)
0.962932 0.269746i \(-0.0869396\pi\)
\(464\) 164.049i 0.353554i
\(465\) −42.5176 642.274i −0.0914357 1.38123i
\(466\) 317.261 0.680819
\(467\) −629.113 −1.34714 −0.673569 0.739124i \(-0.735240\pi\)
−0.673569 + 0.739124i \(0.735240\pi\)
\(468\) −109.140 10.7487i −0.233205 0.0229673i
\(469\) −45.3462 −0.0966869
\(470\) 251.114 + 199.033i 0.534286 + 0.423474i
\(471\) −264.651 + 239.867i −0.561892 + 0.509272i
\(472\) 11.9565i 0.0253315i
\(473\) −108.045 −0.228424
\(474\) −213.157 235.181i −0.449699 0.496163i
\(475\) 181.249 + 772.796i 0.381578 + 1.62694i
\(476\) 38.6374i 0.0811711i
\(477\) −16.0003 + 162.464i −0.0335437 + 0.340595i
\(478\) 422.000i 0.882845i
\(479\) 554.807i 1.15826i −0.815235 0.579131i \(-0.803392\pi\)
0.815235 0.579131i \(-0.196608\pi\)
\(480\) 5.60487 + 84.6675i 0.0116768 + 0.176391i
\(481\) −110.427 −0.229578
\(482\) −52.7068 −0.109350
\(483\) −199.285 + 180.622i −0.412598 + 0.373959i
\(484\) 167.497 0.346069
\(485\) 372.961 470.555i 0.768992 0.970216i
\(486\) −176.678 294.759i −0.363534 0.606501i
\(487\) 244.109i 0.501251i 0.968084 + 0.250626i \(0.0806363\pi\)
−0.968084 + 0.250626i \(0.919364\pi\)
\(488\) −47.7823 −0.0979145
\(489\) −165.786 + 150.261i −0.339032 + 0.307282i
\(490\) 38.7907 + 30.7454i 0.0791647 + 0.0627458i
\(491\) 170.600i 0.347454i 0.984794 + 0.173727i \(0.0555810\pi\)
−0.984794 + 0.173727i \(0.944419\pi\)
\(492\) 161.970 146.802i 0.329208 0.298379i
\(493\) 299.463i 0.607429i
\(494\) 273.573i 0.553793i
\(495\) −197.485 190.876i −0.398960 0.385607i
\(496\) 171.648 0.346065
\(497\) −301.150 −0.605936
\(498\) 218.234 + 240.783i 0.438221 + 0.483499i
\(499\) −965.312 −1.93449 −0.967247 0.253837i \(-0.918307\pi\)
−0.967247 + 0.253837i \(0.918307\pi\)
\(500\) −106.448 + 226.205i −0.212897 + 0.452410i
\(501\) −230.518 254.336i −0.460116 0.507657i
\(502\) 350.165i 0.697540i
\(503\) 86.1692 0.171311 0.0856553 0.996325i \(-0.472702\pi\)
0.0856553 + 0.996325i \(0.472702\pi\)
\(504\) −67.0256 6.60106i −0.132987 0.0130973i
\(505\) −506.184 + 638.639i −1.00235 + 1.26463i
\(506\) 292.484i 0.578031i
\(507\) −265.696 293.148i −0.524054 0.578202i
\(508\) 395.264i 0.778078i
\(509\) 115.697i 0.227303i −0.993521 0.113651i \(-0.963745\pi\)
0.993521 0.113651i \(-0.0362547\pi\)
\(510\) −10.2314 154.556i −0.0200615 0.303051i
\(511\) 277.996 0.544023
\(512\) −22.6274 −0.0441942
\(513\) 688.559 510.680i 1.34222 0.995477i
\(514\) −106.950 −0.208074
\(515\) −578.848 + 730.317i −1.12398 + 1.41809i
\(516\) 78.6995 71.3294i 0.152518 0.138235i
\(517\) 276.575i 0.534961i
\(518\) −67.8160 −0.130919
\(519\) 350.192 + 386.375i 0.674744 + 0.744461i
\(520\) 53.5204 67.5252i 0.102924 0.129856i
\(521\) 527.925i 1.01329i 0.862154 + 0.506646i \(0.169115\pi\)
−0.862154 + 0.506646i \(0.830885\pi\)
\(522\) −519.487 51.1620i −0.995186 0.0980116i
\(523\) 637.700i 1.21931i −0.792666 0.609656i \(-0.791307\pi\)
0.792666 0.609656i \(-0.208693\pi\)
\(524\) 76.0837i 0.145198i
\(525\) −163.311 112.715i −0.311068 0.214695i
\(526\) −79.9999 −0.152091
\(527\) −313.334 −0.594562
\(528\) 54.2676 49.1856i 0.102780 0.0931545i
\(529\) 619.237 1.17058
\(530\) −100.517 79.6696i −0.189655 0.150320i
\(531\) −37.8620 3.72887i −0.0713033 0.00702235i
\(532\) 168.009i 0.315806i
\(533\) −221.974 −0.416462
\(534\) −84.4265 + 76.5202i −0.158102 + 0.143296i
\(535\) −646.253 512.220i −1.20795 0.957420i
\(536\) 48.4771i 0.0904423i
\(537\) −298.289 + 270.355i −0.555472 + 0.503454i
\(538\) 358.796i 0.666907i
\(539\) 42.7237i 0.0792648i
\(540\) 269.861 + 8.65660i 0.499743 + 0.0160307i
\(541\) −749.392 −1.38520 −0.692599 0.721323i \(-0.743534\pi\)
−0.692599 + 0.721323i \(0.743534\pi\)
\(542\) −362.593 −0.668991
\(543\) 401.150 + 442.598i 0.738766 + 0.815098i
\(544\) 41.3051 0.0759286
\(545\) −378.877 300.297i −0.695187 0.551005i
\(546\) 45.9280 + 50.6734i 0.0841172 + 0.0928084i
\(547\) 129.416i 0.236592i 0.992978 + 0.118296i \(0.0377432\pi\)
−0.992978 + 0.118296i \(0.962257\pi\)
\(548\) −87.5847 −0.159826
\(549\) −14.9019 + 151.310i −0.0271437 + 0.275610i
\(550\) 210.087 49.2731i 0.381975 0.0895874i
\(551\) 1302.16i 2.36328i
\(552\) 193.093 + 213.045i 0.349807 + 0.385950i
\(553\) 197.937i 0.357933i
\(554\) 262.586i 0.473982i
\(555\) 271.275 17.9580i 0.488784 0.0323568i
\(556\) −351.857 −0.632836
\(557\) −926.902 −1.66410 −0.832049 0.554703i \(-0.812832\pi\)
−0.832049 + 0.554703i \(0.812832\pi\)
\(558\) 53.5320 543.551i 0.0959354 0.974106i
\(559\) −107.855 −0.192942
\(560\) 32.8683 41.4690i 0.0586933 0.0740518i
\(561\) −99.0626 + 89.7856i −0.176582 + 0.160046i
\(562\) 368.049i 0.654892i
\(563\) −690.211 −1.22595 −0.612976 0.790101i \(-0.710028\pi\)
−0.612976 + 0.790101i \(0.710028\pi\)
\(564\) 182.591 + 201.457i 0.323742 + 0.357193i
\(565\) 439.978 + 348.726i 0.778722 + 0.617214i
\(566\) 630.065i 1.11319i
\(567\) −41.8066 + 210.189i −0.0737330 + 0.370703i
\(568\) 321.943i 0.566801i
\(569\) 155.630i 0.273515i 0.990605 + 0.136757i \(0.0436680\pi\)
−0.990605 + 0.136757i \(0.956332\pi\)
\(570\) 44.4895 + 672.062i 0.0780518 + 1.17906i
\(571\) −961.721 −1.68427 −0.842137 0.539263i \(-0.818703\pi\)
−0.842137 + 0.539263i \(0.818703\pi\)
\(572\) −74.3716 −0.130020
\(573\) −498.376 + 451.704i −0.869766 + 0.788315i
\(574\) −136.320 −0.237492
\(575\) 193.437 + 824.761i 0.336412 + 1.43437i
\(576\) −7.05683 + 71.6533i −0.0122514 + 0.124398i
\(577\) 670.111i 1.16137i −0.814128 0.580685i \(-0.802785\pi\)
0.814128 0.580685i \(-0.197215\pi\)
\(578\) 333.307 0.576656
\(579\) −756.043 + 685.241i −1.30577 + 1.18349i
\(580\) 254.748 321.409i 0.439221 0.554153i
\(581\) 202.651i 0.348797i
\(582\) 377.503 342.151i 0.648631 0.587888i
\(583\) 110.708i 0.189894i
\(584\) 297.190i 0.508887i
\(585\) −197.138 190.540i −0.336988 0.325709i
\(586\) −245.458 −0.418870
\(587\) −671.384 −1.14376 −0.571878 0.820339i \(-0.693785\pi\)
−0.571878 + 0.820339i \(0.693785\pi\)
\(588\) 28.2056 + 31.1199i 0.0479686 + 0.0529249i
\(589\) 1362.48 2.31322
\(590\) 18.5669 23.4254i 0.0314694 0.0397041i
\(591\) −232.502 256.525i −0.393404 0.434052i
\(592\) 72.4984i 0.122463i
\(593\) −173.594 −0.292738 −0.146369 0.989230i \(-0.546759\pi\)
−0.146369 + 0.989230i \(0.546759\pi\)
\(594\) −138.830 187.187i −0.233720 0.315129i
\(595\) −59.9993 + 75.6994i −0.100839 + 0.127226i
\(596\) 301.186i 0.505345i
\(597\) −375.878 414.715i −0.629612 0.694665i
\(598\) 291.969i 0.488243i
\(599\) 561.565i 0.937504i 0.883330 + 0.468752i \(0.155296\pi\)
−0.883330 + 0.468752i \(0.844704\pi\)
\(600\) −120.497 + 174.586i −0.200829 + 0.290977i
\(601\) 382.578 0.636568 0.318284 0.947995i \(-0.396893\pi\)
0.318284 + 0.947995i \(0.396893\pi\)
\(602\) −66.2363 −0.110027
\(603\) 153.510 + 15.1186i 0.254578 + 0.0250723i
\(604\) −11.2606 −0.0186433
\(605\) 328.165 + 260.103i 0.542422 + 0.429923i
\(606\) −512.349 + 464.369i −0.845460 + 0.766285i
\(607\) 489.748i 0.806833i −0.915016 0.403417i \(-0.867823\pi\)
0.915016 0.403417i \(-0.132177\pi\)
\(608\) −179.609 −0.295409
\(609\) 218.610 + 241.197i 0.358965 + 0.396054i
\(610\) −93.6162 74.2001i −0.153469 0.121639i
\(611\) 276.088i 0.451863i
\(612\) 12.8819 130.799i 0.0210488 0.213724i
\(613\) 103.287i 0.168494i 0.996445 + 0.0842472i \(0.0268486\pi\)
−0.996445 + 0.0842472i \(0.973151\pi\)
\(614\) 344.390i 0.560896i
\(615\) 545.303 36.0983i 0.886672 0.0586964i
\(616\) −45.6736 −0.0741454
\(617\) −103.427 −0.167629 −0.0838144 0.996481i \(-0.526710\pi\)
−0.0838144 + 0.996481i \(0.526710\pi\)
\(618\) −585.898 + 531.030i −0.948054 + 0.859271i
\(619\) 1040.92 1.68162 0.840809 0.541332i \(-0.182080\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(620\) 336.297 + 266.549i 0.542415 + 0.429917i
\(621\) 734.860 545.019i 1.18335 0.877647i
\(622\) 364.527i 0.586056i
\(623\) 71.0564 0.114055
\(624\) 54.1722 49.0991i 0.0868144 0.0786844i
\(625\) −559.826 + 277.886i −0.895721 + 0.444617i
\(626\) 221.199i 0.353354i
\(627\) 430.758 390.418i 0.687014 0.622677i
\(628\) 238.119i 0.379170i
\(629\) 132.342i 0.210400i
\(630\) −121.068 117.016i −0.192171 0.185739i
\(631\) −1243.34 −1.97043 −0.985216 0.171315i \(-0.945198\pi\)
−0.985216 + 0.171315i \(0.945198\pi\)
\(632\) 211.604 0.334816
\(633\) 702.907 + 775.534i 1.11044 + 1.22517i
\(634\) −381.398 −0.601574
\(635\) 613.797 774.411i 0.966609 1.21954i
\(636\) −73.0881 80.6398i −0.114918 0.126792i
\(637\) 42.6486i 0.0669522i
\(638\) −353.997 −0.554854
\(639\) 1019.48 + 100.405i 1.59544 + 0.157128i
\(640\) −44.3322 35.1377i −0.0692691 0.0549026i
\(641\) 168.859i 0.263431i 0.991288 + 0.131715i \(0.0420485\pi\)
−0.991288 + 0.131715i \(0.957951\pi\)
\(642\) −469.905 518.457i −0.731939 0.807566i
\(643\) 290.872i 0.452366i −0.974085 0.226183i \(-0.927375\pi\)
0.974085 0.226183i \(-0.0726248\pi\)
\(644\) 179.306i 0.278425i
\(645\) 264.956 17.5397i 0.410785 0.0271933i
\(646\) 327.866 0.507533
\(647\) 725.855 1.12188 0.560939 0.827857i \(-0.310440\pi\)
0.560939 + 0.827857i \(0.310440\pi\)
\(648\) 224.701 + 44.6931i 0.346761 + 0.0689709i
\(649\) −25.8005 −0.0397543
\(650\) 209.717 49.1864i 0.322642 0.0756714i
\(651\) −252.370 + 228.736i −0.387665 + 0.351361i
\(652\) 149.166i 0.228782i
\(653\) 977.062 1.49627 0.748133 0.663548i \(-0.230950\pi\)
0.748133 + 0.663548i \(0.230950\pi\)
\(654\) −275.490 303.955i −0.421238 0.464762i
\(655\) 118.149 149.065i 0.180380 0.227580i
\(656\) 145.732i 0.222153i
\(657\) −941.100 92.6848i −1.43242 0.141073i
\(658\) 169.553i 0.257680i
\(659\) 157.771i 0.239409i −0.992810 0.119705i \(-0.961805\pi\)
0.992810 0.119705i \(-0.0381948\pi\)
\(660\) 182.702 12.0946i 0.276821 0.0183251i
\(661\) 1072.89 1.62314 0.811568 0.584258i \(-0.198614\pi\)
0.811568 + 0.584258i \(0.198614\pi\)
\(662\) −142.479 −0.215225
\(663\) −98.8884 + 89.6277i −0.149153 + 0.135185i
\(664\) −216.643 −0.326270
\(665\) 260.897 329.167i 0.392327 0.494988i
\(666\) 229.578 + 22.6101i 0.344711 + 0.0339491i
\(667\) 1389.73i 2.08355i
\(668\) 228.838 0.342572
\(669\) 983.320 891.235i 1.46984 1.33219i
\(670\) −75.2791 + 94.9776i −0.112357 + 0.141758i
\(671\) 103.108i 0.153663i
\(672\) 33.2685 30.1530i 0.0495068 0.0448706i
\(673\) 293.836i 0.436606i −0.975881 0.218303i \(-0.929948\pi\)
0.975881 0.218303i \(-0.0700521\pi\)
\(674\) 243.319i 0.361007i
\(675\) 515.276 + 436.022i 0.763372 + 0.645959i
\(676\) 263.759 0.390176
\(677\) 569.262 0.840859 0.420429 0.907325i \(-0.361879\pi\)
0.420429 + 0.907325i \(0.361879\pi\)
\(678\) 319.918 + 352.973i 0.471855 + 0.520609i
\(679\) −317.720 −0.467924
\(680\) 80.9261 + 64.1419i 0.119009 + 0.0943263i
\(681\) −212.763 234.746i −0.312427 0.344708i
\(682\) 370.395i 0.543101i
\(683\) 21.2129 0.0310585 0.0155292 0.999879i \(-0.495057\pi\)
0.0155292 + 0.999879i \(0.495057\pi\)
\(684\) −56.0147 + 568.760i −0.0818928 + 0.831520i
\(685\) −171.598 136.008i −0.250508 0.198552i
\(686\) 26.1916i 0.0381802i
\(687\) 604.877 + 667.375i 0.880462 + 0.971434i
\(688\) 70.8096i 0.102921i
\(689\) 110.514i 0.160397i
\(690\) 47.4811 + 717.253i 0.0688132 + 1.03950i
\(691\) −698.350 −1.01064 −0.505318 0.862933i \(-0.668625\pi\)
−0.505318 + 0.862933i \(0.668625\pi\)
\(692\) −347.640 −0.502370
\(693\) −14.2442 + 144.633i −0.0205545 + 0.208705i
\(694\) 532.969 0.767966
\(695\) −689.367 546.391i −0.991895 0.786175i
\(696\) 257.851 233.703i 0.370475 0.335781i
\(697\) 266.027i 0.381674i
\(698\) 473.153 0.677869
\(699\) 451.969 + 498.669i 0.646594 + 0.713403i
\(700\) 128.793 30.2067i 0.183990 0.0431524i
\(701\) 1019.57i 1.45445i 0.686399 + 0.727225i \(0.259190\pi\)
−0.686399 + 0.727225i \(0.740810\pi\)
\(702\) −138.585 186.857i −0.197415 0.266179i
\(703\) 575.468i 0.818588i
\(704\) 48.8271i 0.0693567i
\(705\) 44.8985 + 678.240i 0.0636858 + 0.962043i
\(706\) −411.852 −0.583359
\(707\) 431.211 0.609917
\(708\) 18.7930 17.0331i 0.0265438 0.0240581i
\(709\) −482.736 −0.680869 −0.340435 0.940268i \(-0.610574\pi\)
−0.340435 + 0.940268i \(0.610574\pi\)
\(710\) −499.939 + 630.759i −0.704139 + 0.888394i
\(711\) 65.9930 670.077i 0.0928171 0.942443i
\(712\) 75.9625i 0.106689i
\(713\) 1454.10 2.03941
\(714\) −60.7299 + 55.0427i −0.0850559 + 0.0770906i
\(715\) −145.711 115.490i −0.203791 0.161525i
\(716\) 268.384i 0.374838i
\(717\) −663.296 + 601.180i −0.925099 + 0.838466i
\(718\) 289.319i 0.402951i
\(719\) 1275.40i 1.77385i 0.461915 + 0.886924i \(0.347162\pi\)
−0.461915 + 0.886924i \(0.652838\pi\)
\(720\) −125.095 + 129.427i −0.173743 + 0.179759i
\(721\) 493.113 0.683929
\(722\) −915.143 −1.26751
\(723\) −75.0859 82.8441i −0.103853 0.114584i
\(724\) −398.226 −0.550036
\(725\) 998.218 234.119i 1.37685 0.322923i
\(726\) 238.616 + 263.271i 0.328672 + 0.362632i
\(727\) 90.3245i 0.124243i −0.998069 0.0621214i \(-0.980213\pi\)
0.998069 0.0621214i \(-0.0197866\pi\)
\(728\) −45.5932 −0.0626281
\(729\) 211.606 697.613i 0.290268 0.956945i
\(730\) 461.500 582.262i 0.632192 0.797620i
\(731\) 129.259i 0.176825i
\(732\) −68.0704 75.1037i −0.0929924 0.102601i
\(733\) 515.475i 0.703240i −0.936143 0.351620i \(-0.885631\pi\)
0.936143 0.351620i \(-0.114369\pi\)
\(734\) 343.077i 0.467408i
\(735\) 6.93567 + 104.771i 0.00943628 + 0.142545i
\(736\) −191.686 −0.260443
\(737\) 104.607 0.141937
\(738\) 461.485 + 45.4497i 0.625318 + 0.0615849i
\(739\) −91.7703 −0.124182 −0.0620909 0.998071i \(-0.519777\pi\)
−0.0620909 + 0.998071i \(0.519777\pi\)
\(740\) −112.581 + 142.041i −0.152137 + 0.191947i
\(741\) 430.000 389.732i 0.580297 0.525954i
\(742\) 67.8694i 0.0914681i
\(743\) 680.829 0.916324 0.458162 0.888869i \(-0.348508\pi\)
0.458162 + 0.888869i \(0.348508\pi\)
\(744\) 244.529 + 269.795i 0.328668 + 0.362627i
\(745\) −467.705 + 590.091i −0.627792 + 0.792069i
\(746\) 143.944i 0.192955i
\(747\) −67.5647 + 686.036i −0.0904481 + 0.918388i
\(748\) 89.1313i 0.119159i
\(749\) 436.352i 0.582580i
\(750\) −507.193 + 154.937i −0.676257 + 0.206582i
\(751\) 275.733 0.367155 0.183577 0.983005i \(-0.441232\pi\)
0.183577 + 0.983005i \(0.441232\pi\)
\(752\) −181.260 −0.241037
\(753\) −550.386 + 498.844i −0.730925 + 0.662475i
\(754\) −353.374 −0.468666
\(755\) −22.0620 17.4863i −0.0292211 0.0231606i
\(756\) −85.1089 114.754i −0.112578 0.151791i
\(757\) 622.898i 0.822851i −0.911443 0.411425i \(-0.865031\pi\)
0.911443 0.411425i \(-0.134969\pi\)
\(758\) −349.350 −0.460884
\(759\) 459.723 416.671i 0.605696 0.548974i
\(760\) −351.894 278.911i −0.463019 0.366988i
\(761\) 1122.56i 1.47511i 0.675288 + 0.737554i \(0.264019\pi\)
−0.675288 + 0.737554i \(0.735981\pi\)
\(762\) 621.272 563.091i 0.815317 0.738965i
\(763\) 255.819i 0.335281i
\(764\) 448.412i 0.586927i
\(765\) 228.354 236.261i 0.298502 0.308839i
\(766\) −26.8275 −0.0350228
\(767\) −25.7551 −0.0335791
\(768\) −32.2349 35.5656i −0.0419726 0.0463093i
\(769\) 344.788 0.448359 0.224179 0.974548i \(-0.428030\pi\)
0.224179 + 0.974548i \(0.428030\pi\)
\(770\) −89.4848 70.9256i −0.116214 0.0921111i
\(771\) −152.361 168.103i −0.197615 0.218033i
\(772\) 680.247i 0.881149i
\(773\) −235.375 −0.304495 −0.152248 0.988342i \(-0.548651\pi\)
−0.152248 + 0.988342i \(0.548651\pi\)
\(774\) 224.230 + 22.0834i 0.289703 + 0.0285316i
\(775\) 244.964 + 1044.46i 0.316083 + 1.34769i
\(776\) 339.657i 0.437702i
\(777\) −96.6104 106.593i −0.124338 0.137185i
\(778\) 881.464i 1.13299i
\(779\) 1156.77i 1.48495i
\(780\) 182.380 12.0733i 0.233821 0.0154786i