Properties

Label 1050.3.e.e.701.8
Level $1050$
Weight $3$
Character 1050.701
Analytic conductor $28.610$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 701.8
Character \(\chi\) \(=\) 1050.701
Dual form 1050.3.e.e.701.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(2.22285 - 2.01468i) q^{3} -2.00000 q^{4} +(2.84919 + 3.14358i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(0.882103 - 8.95667i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(2.22285 - 2.01468i) q^{3} -2.00000 q^{4} +(2.84919 + 3.14358i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(0.882103 - 8.95667i) q^{9} +6.10339i q^{11} +(-4.44570 + 4.02937i) q^{12} -6.09265 q^{13} -3.74166i q^{14} +4.00000 q^{16} +7.30179i q^{17} +(12.6666 + 1.24748i) q^{18} -31.7506 q^{19} +(-5.88110 + 5.33035i) q^{21} -8.63149 q^{22} +33.8856i q^{23} +(-5.69838 - 6.28716i) q^{24} -8.61631i q^{26} +(-16.0841 - 21.6865i) q^{27} +5.29150 q^{28} +41.0122i q^{29} +42.9120 q^{31} +5.65685i q^{32} +(12.2964 + 13.5669i) q^{33} -10.3263 q^{34} +(-1.76421 + 17.9133i) q^{36} +18.1246 q^{37} -44.9022i q^{38} +(-13.5430 + 12.2748i) q^{39} +36.4331i q^{41} +(-7.53825 - 8.31713i) q^{42} -17.7024 q^{43} -12.2068i q^{44} -47.9215 q^{46} +45.3150i q^{47} +(8.89139 - 8.05873i) q^{48} +7.00000 q^{49} +(14.7108 + 16.2308i) q^{51} +12.1853 q^{52} +18.1388i q^{53} +(30.6693 - 22.7463i) q^{54} +7.48331i q^{56} +(-70.5769 + 63.9675i) q^{57} -58.0000 q^{58} -4.22725i q^{59} +16.8936 q^{61} +60.6867i q^{62} +(-2.33383 + 23.6971i) q^{63} -8.00000 q^{64} +(-19.1865 + 17.3897i) q^{66} -17.1392 q^{67} -14.6036i q^{68} +(68.2688 + 75.3226i) q^{69} -113.824i q^{71} +(-25.3333 - 2.49497i) q^{72} -105.073 q^{73} +25.6320i q^{74} +63.5013 q^{76} -16.1480i q^{77} +(-17.3591 - 19.1527i) q^{78} +74.8132 q^{79} +(-79.4438 - 15.8014i) q^{81} -51.5242 q^{82} +76.5950i q^{83} +(11.7622 - 10.6607i) q^{84} -25.0350i q^{86} +(82.6266 + 91.1639i) q^{87} +17.2630 q^{88} -26.8568i q^{89} +16.1196 q^{91} -67.7713i q^{92} +(95.3868 - 86.4541i) q^{93} -64.0851 q^{94} +(11.3968 + 12.5743i) q^{96} -120.087 q^{97} +9.89949i q^{98} +(54.6660 + 5.38382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 48 q^{4} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 48 q^{4} - 44 q^{9} + 96 q^{16} + 80 q^{19} - 28 q^{21} + 224 q^{31} - 128 q^{34} + 88 q^{36} + 92 q^{39} - 144 q^{46} + 168 q^{49} - 284 q^{51} + 144 q^{54} - 192 q^{64} + 224 q^{66} + 152 q^{69} - 160 q^{76} + 72 q^{79} - 212 q^{81} + 56 q^{84} + 168 q^{91} + 128 q^{94} + 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 2.22285 2.01468i 0.740949 0.671561i
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) 2.84919 + 3.14358i 0.474865 + 0.523930i
\(7\) −2.64575 −0.377964
\(8\) 2.82843i 0.353553i
\(9\) 0.882103 8.95667i 0.0980115 0.995185i
\(10\) 0 0
\(11\) 6.10339i 0.554853i 0.960747 + 0.277427i \(0.0894816\pi\)
−0.960747 + 0.277427i \(0.910518\pi\)
\(12\) −4.44570 + 4.02937i −0.370475 + 0.335781i
\(13\) −6.09265 −0.468666 −0.234333 0.972156i \(-0.575291\pi\)
−0.234333 + 0.972156i \(0.575291\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 7.30179i 0.429517i 0.976667 + 0.214758i \(0.0688964\pi\)
−0.976667 + 0.214758i \(0.931104\pi\)
\(18\) 12.6666 + 1.24748i 0.703702 + 0.0693046i
\(19\) −31.7506 −1.67109 −0.835543 0.549424i \(-0.814847\pi\)
−0.835543 + 0.549424i \(0.814847\pi\)
\(20\) 0 0
\(21\) −5.88110 + 5.33035i −0.280052 + 0.253826i
\(22\) −8.63149 −0.392341
\(23\) 33.8856i 1.47329i 0.676280 + 0.736644i \(0.263591\pi\)
−0.676280 + 0.736644i \(0.736409\pi\)
\(24\) −5.69838 6.28716i −0.237433 0.261965i
\(25\) 0 0
\(26\) 8.61631i 0.331397i
\(27\) −16.0841 21.6865i −0.595706 0.803202i
\(28\) 5.29150 0.188982
\(29\) 41.0122i 1.41421i 0.707106 + 0.707107i \(0.250000\pi\)
−0.707106 + 0.707107i \(0.750000\pi\)
\(30\) 0 0
\(31\) 42.9120 1.38426 0.692129 0.721774i \(-0.256673\pi\)
0.692129 + 0.721774i \(0.256673\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 12.2964 + 13.5669i 0.372618 + 0.411118i
\(34\) −10.3263 −0.303714
\(35\) 0 0
\(36\) −1.76421 + 17.9133i −0.0490057 + 0.497593i
\(37\) 18.1246 0.489854 0.244927 0.969542i \(-0.421236\pi\)
0.244927 + 0.969542i \(0.421236\pi\)
\(38\) 44.9022i 1.18164i
\(39\) −13.5430 + 12.2748i −0.347257 + 0.314738i
\(40\) 0 0
\(41\) 36.4331i 0.888612i 0.895875 + 0.444306i \(0.146550\pi\)
−0.895875 + 0.444306i \(0.853450\pi\)
\(42\) −7.53825 8.31713i −0.179482 0.198027i
\(43\) −17.7024 −0.411684 −0.205842 0.978585i \(-0.565993\pi\)
−0.205842 + 0.978585i \(0.565993\pi\)
\(44\) 12.2068i 0.277427i
\(45\) 0 0
\(46\) −47.9215 −1.04177
\(47\) 45.3150i 0.964149i 0.876130 + 0.482074i \(0.160116\pi\)
−0.876130 + 0.482074i \(0.839884\pi\)
\(48\) 8.89139 8.05873i 0.185237 0.167890i
\(49\) 7.00000 0.142857
\(50\) 0 0
\(51\) 14.7108 + 16.2308i 0.288447 + 0.318250i
\(52\) 12.1853 0.234333
\(53\) 18.1388i 0.342242i 0.985250 + 0.171121i \(0.0547390\pi\)
−0.985250 + 0.171121i \(0.945261\pi\)
\(54\) 30.6693 22.7463i 0.567950 0.421228i
\(55\) 0 0
\(56\) 7.48331i 0.133631i
\(57\) −70.5769 + 63.9675i −1.23819 + 1.12224i
\(58\) −58.0000 −1.00000
\(59\) 4.22725i 0.0716482i −0.999358 0.0358241i \(-0.988594\pi\)
0.999358 0.0358241i \(-0.0114056\pi\)
\(60\) 0 0
\(61\) 16.8936 0.276944 0.138472 0.990366i \(-0.455781\pi\)
0.138472 + 0.990366i \(0.455781\pi\)
\(62\) 60.6867i 0.978818i
\(63\) −2.33383 + 23.6971i −0.0370449 + 0.376145i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −19.1865 + 17.3897i −0.290704 + 0.263481i
\(67\) −17.1392 −0.255810 −0.127905 0.991786i \(-0.540825\pi\)
−0.127905 + 0.991786i \(0.540825\pi\)
\(68\) 14.6036i 0.214758i
\(69\) 68.2688 + 75.3226i 0.989404 + 1.09163i
\(70\) 0 0
\(71\) 113.824i 1.60316i −0.597890 0.801578i \(-0.703994\pi\)
0.597890 0.801578i \(-0.296006\pi\)
\(72\) −25.3333 2.49497i −0.351851 0.0346523i
\(73\) −105.073 −1.43935 −0.719675 0.694311i \(-0.755709\pi\)
−0.719675 + 0.694311i \(0.755709\pi\)
\(74\) 25.6320i 0.346379i
\(75\) 0 0
\(76\) 63.5013 0.835543
\(77\) 16.1480i 0.209715i
\(78\) −17.3591 19.1527i −0.222553 0.245548i
\(79\) 74.8132 0.947003 0.473501 0.880793i \(-0.342990\pi\)
0.473501 + 0.880793i \(0.342990\pi\)
\(80\) 0 0
\(81\) −79.4438 15.8014i −0.980787 0.195079i
\(82\) −51.5242 −0.628344
\(83\) 76.5950i 0.922831i 0.887184 + 0.461416i \(0.152658\pi\)
−0.887184 + 0.461416i \(0.847342\pi\)
\(84\) 11.7622 10.6607i 0.140026 0.126913i
\(85\) 0 0
\(86\) 25.0350i 0.291104i
\(87\) 82.6266 + 91.1639i 0.949732 + 1.04786i
\(88\) 17.2630 0.196170
\(89\) 26.8568i 0.301762i −0.988552 0.150881i \(-0.951789\pi\)
0.988552 0.150881i \(-0.0482110\pi\)
\(90\) 0 0
\(91\) 16.1196 0.177139
\(92\) 67.7713i 0.736644i
\(93\) 95.3868 86.4541i 1.02566 0.929614i
\(94\) −64.0851 −0.681756
\(95\) 0 0
\(96\) 11.3968 + 12.5743i 0.118716 + 0.130983i
\(97\) −120.087 −1.23801 −0.619005 0.785387i \(-0.712464\pi\)
−0.619005 + 0.785387i \(0.712464\pi\)
\(98\) 9.89949i 0.101015i
\(99\) 54.6660 + 5.38382i 0.552182 + 0.0543820i
\(100\) 0 0
\(101\) 162.983i 1.61369i 0.590764 + 0.806844i \(0.298826\pi\)
−0.590764 + 0.806844i \(0.701174\pi\)
\(102\) −22.9538 + 20.8042i −0.225037 + 0.203963i
\(103\) −186.379 −1.80951 −0.904753 0.425937i \(-0.859944\pi\)
−0.904753 + 0.425937i \(0.859944\pi\)
\(104\) 17.2326i 0.165698i
\(105\) 0 0
\(106\) −25.6522 −0.242002
\(107\) 164.926i 1.54136i 0.637221 + 0.770681i \(0.280084\pi\)
−0.637221 + 0.770681i \(0.719916\pi\)
\(108\) 32.1681 + 43.3729i 0.297853 + 0.401601i
\(109\) 96.6905 0.887069 0.443535 0.896257i \(-0.353724\pi\)
0.443535 + 0.896257i \(0.353724\pi\)
\(110\) 0 0
\(111\) 40.2882 36.5153i 0.362957 0.328967i
\(112\) −10.5830 −0.0944911
\(113\) 112.284i 0.993660i 0.867848 + 0.496830i \(0.165503\pi\)
−0.867848 + 0.496830i \(0.834497\pi\)
\(114\) −90.4637 99.8107i −0.793541 0.875533i
\(115\) 0 0
\(116\) 82.0245i 0.707107i
\(117\) −5.37435 + 54.5699i −0.0459346 + 0.466409i
\(118\) 5.97823 0.0506629
\(119\) 19.3187i 0.162342i
\(120\) 0 0
\(121\) 83.7487 0.692138
\(122\) 23.8911i 0.195829i
\(123\) 73.4012 + 80.9852i 0.596757 + 0.658417i
\(124\) −85.8240 −0.692129
\(125\) 0 0
\(126\) −33.5128 3.30053i −0.265974 0.0261947i
\(127\) −197.632 −1.55616 −0.778078 0.628167i \(-0.783805\pi\)
−0.778078 + 0.628167i \(0.783805\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −39.3497 + 35.6647i −0.305037 + 0.276471i
\(130\) 0 0
\(131\) 38.0418i 0.290396i −0.989403 0.145198i \(-0.953618\pi\)
0.989403 0.145198i \(-0.0463819\pi\)
\(132\) −24.5928 27.1338i −0.186309 0.205559i
\(133\) 84.0043 0.631611
\(134\) 24.2385i 0.180885i
\(135\) 0 0
\(136\) 20.6526 0.151857
\(137\) 43.7923i 0.319652i 0.987145 + 0.159826i \(0.0510933\pi\)
−0.987145 + 0.159826i \(0.948907\pi\)
\(138\) −106.522 + 96.5467i −0.771901 + 0.699614i
\(139\) 175.928 1.26567 0.632836 0.774286i \(-0.281891\pi\)
0.632836 + 0.774286i \(0.281891\pi\)
\(140\) 0 0
\(141\) 91.2953 + 100.728i 0.647485 + 0.714385i
\(142\) 160.972 1.13360
\(143\) 37.1858i 0.260041i
\(144\) 3.52841 35.8267i 0.0245029 0.248796i
\(145\) 0 0
\(146\) 148.595i 1.01777i
\(147\) 15.5599 14.1028i 0.105850 0.0959373i
\(148\) −36.2492 −0.244927
\(149\) 150.593i 1.01069i −0.862917 0.505345i \(-0.831365\pi\)
0.862917 0.505345i \(-0.168635\pi\)
\(150\) 0 0
\(151\) −5.63028 −0.0372866 −0.0186433 0.999826i \(-0.505935\pi\)
−0.0186433 + 0.999826i \(0.505935\pi\)
\(152\) 89.8044i 0.590818i
\(153\) 65.3997 + 6.44093i 0.427449 + 0.0420976i
\(154\) 22.8368 0.148291
\(155\) 0 0
\(156\) 27.0861 24.5495i 0.173629 0.157369i
\(157\) −119.059 −0.758341 −0.379170 0.925327i \(-0.623791\pi\)
−0.379170 + 0.925327i \(0.623791\pi\)
\(158\) 105.802i 0.669632i
\(159\) 36.5440 + 40.3199i 0.229837 + 0.253584i
\(160\) 0 0
\(161\) 89.6530i 0.556851i
\(162\) 22.3466 112.350i 0.137942 0.693521i
\(163\) 74.5829 0.457564 0.228782 0.973478i \(-0.426526\pi\)
0.228782 + 0.973478i \(0.426526\pi\)
\(164\) 72.8662i 0.444306i
\(165\) 0 0
\(166\) −108.322 −0.652540
\(167\) 114.419i 0.685144i −0.939492 0.342572i \(-0.888702\pi\)
0.939492 0.342572i \(-0.111298\pi\)
\(168\) 15.0765 + 16.6343i 0.0897411 + 0.0990135i
\(169\) −131.880 −0.780353
\(170\) 0 0
\(171\) −28.0074 + 284.380i −0.163786 + 1.66304i
\(172\) 35.4048 0.205842
\(173\) 173.820i 1.00474i −0.864653 0.502370i \(-0.832462\pi\)
0.864653 0.502370i \(-0.167538\pi\)
\(174\) −128.925 + 116.852i −0.740950 + 0.671562i
\(175\) 0 0
\(176\) 24.4136i 0.138713i
\(177\) −8.51656 9.39652i −0.0481162 0.0530877i
\(178\) 37.9812 0.213378
\(179\) 134.192i 0.749677i 0.927090 + 0.374838i \(0.122302\pi\)
−0.927090 + 0.374838i \(0.877698\pi\)
\(180\) 0 0
\(181\) −199.113 −1.10007 −0.550036 0.835141i \(-0.685386\pi\)
−0.550036 + 0.835141i \(0.685386\pi\)
\(182\) 22.7966i 0.125256i
\(183\) 37.5518 34.0352i 0.205201 0.185985i
\(184\) 95.8431 0.520886
\(185\) 0 0
\(186\) 122.265 + 134.897i 0.657336 + 0.725255i
\(187\) −44.5656 −0.238319
\(188\) 90.6300i 0.482074i
\(189\) 42.5544 + 57.3770i 0.225156 + 0.303582i
\(190\) 0 0
\(191\) 224.206i 1.17385i −0.809640 0.586927i \(-0.800338\pi\)
0.809640 0.586927i \(-0.199662\pi\)
\(192\) −17.7828 + 16.1175i −0.0926187 + 0.0839451i
\(193\) 340.124 1.76230 0.881149 0.472838i \(-0.156770\pi\)
0.881149 + 0.472838i \(0.156770\pi\)
\(194\) 169.829i 0.875405i
\(195\) 0 0
\(196\) −14.0000 −0.0714286
\(197\) 115.404i 0.585805i −0.956142 0.292903i \(-0.905379\pi\)
0.956142 0.292903i \(-0.0946212\pi\)
\(198\) −7.61387 + 77.3094i −0.0384539 + 0.390452i
\(199\) −186.569 −0.937534 −0.468767 0.883322i \(-0.655302\pi\)
−0.468767 + 0.883322i \(0.655302\pi\)
\(200\) 0 0
\(201\) −38.0979 + 34.5301i −0.189542 + 0.171792i
\(202\) −230.492 −1.14105
\(203\) 108.508i 0.534523i
\(204\) −29.4216 32.4615i −0.144223 0.159125i
\(205\) 0 0
\(206\) 263.580i 1.27951i
\(207\) 303.502 + 29.8906i 1.46620 + 0.144399i
\(208\) −24.3706 −0.117166
\(209\) 193.787i 0.927208i
\(210\) 0 0
\(211\) −348.892 −1.65352 −0.826759 0.562556i \(-0.809818\pi\)
−0.826759 + 0.562556i \(0.809818\pi\)
\(212\) 36.2777i 0.171121i
\(213\) −229.320 253.014i −1.07662 1.18786i
\(214\) −233.240 −1.08991
\(215\) 0 0
\(216\) −61.3386 + 45.4926i −0.283975 + 0.210614i
\(217\) −113.534 −0.523200
\(218\) 136.741i 0.627253i
\(219\) −233.560 + 211.688i −1.06649 + 0.966611i
\(220\) 0 0
\(221\) 44.4872i 0.201300i
\(222\) 51.6404 + 56.9761i 0.232615 + 0.256649i
\(223\) −442.370 −1.98372 −0.991860 0.127331i \(-0.959359\pi\)
−0.991860 + 0.127331i \(0.959359\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −158.793 −0.702624
\(227\) 105.606i 0.465225i −0.972569 0.232613i \(-0.925273\pi\)
0.972569 0.232613i \(-0.0747274\pi\)
\(228\) 141.154 127.935i 0.619095 0.561118i
\(229\) 300.234 1.31107 0.655534 0.755166i \(-0.272444\pi\)
0.655534 + 0.755166i \(0.272444\pi\)
\(230\) 0 0
\(231\) −32.5332 35.8946i −0.140836 0.155388i
\(232\) 116.000 0.500000
\(233\) 224.338i 0.962823i −0.876495 0.481411i \(-0.840124\pi\)
0.876495 0.481411i \(-0.159876\pi\)
\(234\) −77.1734 7.60048i −0.329801 0.0324807i
\(235\) 0 0
\(236\) 8.45449i 0.0358241i
\(237\) 166.298 150.725i 0.701681 0.635970i
\(238\) 27.3208 0.114793
\(239\) 298.399i 1.24853i 0.781212 + 0.624266i \(0.214602\pi\)
−0.781212 + 0.624266i \(0.785398\pi\)
\(240\) 0 0
\(241\) 37.2693 0.154645 0.0773223 0.997006i \(-0.475363\pi\)
0.0773223 + 0.997006i \(0.475363\pi\)
\(242\) 118.438i 0.489415i
\(243\) −208.426 + 124.930i −0.857721 + 0.514115i
\(244\) −33.7872 −0.138472
\(245\) 0 0
\(246\) −114.530 + 103.805i −0.465571 + 0.421971i
\(247\) 193.446 0.783181
\(248\) 121.373i 0.489409i
\(249\) 154.315 + 170.259i 0.619738 + 0.683771i
\(250\) 0 0
\(251\) 247.604i 0.986471i −0.869896 0.493235i \(-0.835814\pi\)
0.869896 0.493235i \(-0.164186\pi\)
\(252\) 4.66765 47.3942i 0.0185224 0.188072i
\(253\) −206.817 −0.817459
\(254\) 279.494i 1.10037i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 75.6252i 0.294262i −0.989117 0.147131i \(-0.952996\pi\)
0.989117 0.147131i \(-0.0470038\pi\)
\(258\) −50.4375 55.6489i −0.195494 0.215694i
\(259\) −47.9532 −0.185147
\(260\) 0 0
\(261\) 367.333 + 36.1770i 1.40741 + 0.138609i
\(262\) 53.7993 0.205341
\(263\) 56.5685i 0.215089i 0.994200 + 0.107545i \(0.0342989\pi\)
−0.994200 + 0.107545i \(0.965701\pi\)
\(264\) 38.3730 34.7795i 0.145352 0.131740i
\(265\) 0 0
\(266\) 118.800i 0.446617i
\(267\) −54.1079 59.6985i −0.202651 0.223590i
\(268\) 34.2785 0.127905
\(269\) 253.707i 0.943149i 0.881826 + 0.471574i \(0.156314\pi\)
−0.881826 + 0.471574i \(0.843686\pi\)
\(270\) 0 0
\(271\) 256.392 0.946096 0.473048 0.881037i \(-0.343154\pi\)
0.473048 + 0.881037i \(0.343154\pi\)
\(272\) 29.2071i 0.107379i
\(273\) 35.8315 32.4760i 0.131251 0.118960i
\(274\) −61.9317 −0.226028
\(275\) 0 0
\(276\) −136.538 150.645i −0.494702 0.545816i
\(277\) 185.677 0.670312 0.335156 0.942163i \(-0.391211\pi\)
0.335156 + 0.942163i \(0.391211\pi\)
\(278\) 248.800i 0.894966i
\(279\) 37.8528 384.349i 0.135673 1.37759i
\(280\) 0 0
\(281\) 260.250i 0.926157i −0.886317 0.463078i \(-0.846745\pi\)
0.886317 0.463078i \(-0.153255\pi\)
\(282\) −142.451 + 129.111i −0.505147 + 0.457841i
\(283\) 445.523 1.57429 0.787143 0.616770i \(-0.211559\pi\)
0.787143 + 0.616770i \(0.211559\pi\)
\(284\) 227.648i 0.801578i
\(285\) 0 0
\(286\) 52.5887 0.183877
\(287\) 96.3929i 0.335864i
\(288\) 50.6666 + 4.98993i 0.175926 + 0.0173261i
\(289\) 235.684 0.815515
\(290\) 0 0
\(291\) −266.935 + 241.937i −0.917302 + 0.831399i
\(292\) 210.145 0.719675
\(293\) 173.565i 0.592371i 0.955130 + 0.296186i \(0.0957147\pi\)
−0.955130 + 0.296186i \(0.904285\pi\)
\(294\) 19.9443 + 22.0051i 0.0678379 + 0.0748472i
\(295\) 0 0
\(296\) 51.2641i 0.173189i
\(297\) 132.361 98.1673i 0.445660 0.330530i
\(298\) 212.971 0.714666
\(299\) 206.453i 0.690480i
\(300\) 0 0
\(301\) 46.8361 0.155602
\(302\) 7.96241i 0.0263656i
\(303\) 328.358 + 362.285i 1.08369 + 1.19566i
\(304\) −127.003 −0.417772
\(305\) 0 0
\(306\) −9.10885 + 92.4891i −0.0297675 + 0.302252i
\(307\) 243.521 0.793227 0.396613 0.917986i \(-0.370185\pi\)
0.396613 + 0.917986i \(0.370185\pi\)
\(308\) 32.2961i 0.104857i
\(309\) −414.292 + 375.495i −1.34075 + 1.21519i
\(310\) 0 0
\(311\) 257.759i 0.828809i −0.910093 0.414404i \(-0.863990\pi\)
0.910093 0.414404i \(-0.136010\pi\)
\(312\) 34.7183 + 38.3055i 0.111277 + 0.122774i
\(313\) −156.412 −0.499718 −0.249859 0.968282i \(-0.580384\pi\)
−0.249859 + 0.968282i \(0.580384\pi\)
\(314\) 168.376i 0.536228i
\(315\) 0 0
\(316\) −149.626 −0.473501
\(317\) 269.689i 0.850754i −0.905016 0.425377i \(-0.860142\pi\)
0.905016 0.425377i \(-0.139858\pi\)
\(318\) −57.0209 + 51.6811i −0.179311 + 0.162519i
\(319\) −250.314 −0.784682
\(320\) 0 0
\(321\) 332.273 + 366.605i 1.03512 + 1.14207i
\(322\) 126.788 0.393753
\(323\) 231.836i 0.717760i
\(324\) 158.888 + 31.6028i 0.490394 + 0.0975396i
\(325\) 0 0
\(326\) 105.476i 0.323547i
\(327\) 214.928 194.801i 0.657273 0.595721i
\(328\) 103.048 0.314172
\(329\) 119.892i 0.364414i
\(330\) 0 0
\(331\) 100.748 0.304374 0.152187 0.988352i \(-0.451368\pi\)
0.152187 + 0.988352i \(0.451368\pi\)
\(332\) 153.190i 0.461416i
\(333\) 15.9878 162.336i 0.0480113 0.487495i
\(334\) 161.813 0.484470
\(335\) 0 0
\(336\) −23.5244 + 21.3214i −0.0700131 + 0.0634566i
\(337\) 172.052 0.510541 0.255270 0.966870i \(-0.417835\pi\)
0.255270 + 0.966870i \(0.417835\pi\)
\(338\) 186.506i 0.551793i
\(339\) 226.216 + 249.589i 0.667303 + 0.736252i
\(340\) 0 0
\(341\) 261.909i 0.768060i
\(342\) −402.174 39.6084i −1.17595 0.115814i
\(343\) −18.5203 −0.0539949
\(344\) 50.0699i 0.145552i
\(345\) 0 0
\(346\) 245.818 0.710458
\(347\) 376.866i 1.08607i 0.839711 + 0.543034i \(0.182725\pi\)
−0.839711 + 0.543034i \(0.817275\pi\)
\(348\) −165.253 182.328i −0.474866 0.523931i
\(349\) 334.570 0.958652 0.479326 0.877637i \(-0.340881\pi\)
0.479326 + 0.877637i \(0.340881\pi\)
\(350\) 0 0
\(351\) 97.9946 + 132.128i 0.279187 + 0.376433i
\(352\) −34.5260 −0.0980852
\(353\) 291.223i 0.824995i 0.910959 + 0.412497i \(0.135343\pi\)
−0.910959 + 0.412497i \(0.864657\pi\)
\(354\) 13.2887 12.0442i 0.0375387 0.0340233i
\(355\) 0 0
\(356\) 53.7136i 0.150881i
\(357\) −38.9211 42.9426i −0.109023 0.120287i
\(358\) −189.776 −0.530102
\(359\) 204.579i 0.569858i 0.958549 + 0.284929i \(0.0919701\pi\)
−0.958549 + 0.284929i \(0.908030\pi\)
\(360\) 0 0
\(361\) 647.104 1.79253
\(362\) 281.589i 0.777869i
\(363\) 186.161 168.727i 0.512839 0.464813i
\(364\) −32.2393 −0.0885695
\(365\) 0 0
\(366\) 48.1331 + 53.1063i 0.131511 + 0.145099i
\(367\) −242.592 −0.661015 −0.330507 0.943803i \(-0.607220\pi\)
−0.330507 + 0.943803i \(0.607220\pi\)
\(368\) 135.543i 0.368322i
\(369\) 326.319 + 32.1378i 0.884334 + 0.0870942i
\(370\) 0 0
\(371\) 47.9909i 0.129355i
\(372\) −190.774 + 172.908i −0.512832 + 0.464807i
\(373\) 101.784 0.272880 0.136440 0.990648i \(-0.456434\pi\)
0.136440 + 0.990648i \(0.456434\pi\)
\(374\) 63.0253i 0.168517i
\(375\) 0 0
\(376\) 128.170 0.340878
\(377\) 249.873i 0.662794i
\(378\) −81.1433 + 60.1811i −0.214665 + 0.159209i
\(379\) −247.028 −0.651789 −0.325894 0.945406i \(-0.605665\pi\)
−0.325894 + 0.945406i \(0.605665\pi\)
\(380\) 0 0
\(381\) −439.306 + 398.166i −1.15303 + 1.04505i
\(382\) 317.075 0.830040
\(383\) 18.9699i 0.0495297i 0.999693 + 0.0247649i \(0.00788371\pi\)
−0.999693 + 0.0247649i \(0.992116\pi\)
\(384\) −22.7935 25.1487i −0.0593582 0.0654913i
\(385\) 0 0
\(386\) 481.008i 1.24613i
\(387\) −15.6153 + 158.554i −0.0403497 + 0.409702i
\(388\) 240.174 0.619005
\(389\) 623.289i 1.60229i −0.598473 0.801143i \(-0.704226\pi\)
0.598473 0.801143i \(-0.295774\pi\)
\(390\) 0 0
\(391\) −247.426 −0.632802
\(392\) 19.7990i 0.0505076i
\(393\) −76.6422 84.5612i −0.195018 0.215168i
\(394\) 163.205 0.414227
\(395\) 0 0
\(396\) −109.332 10.7676i −0.276091 0.0271910i
\(397\) −368.913 −0.929253 −0.464626 0.885507i \(-0.653811\pi\)
−0.464626 + 0.885507i \(0.653811\pi\)
\(398\) 263.849i 0.662937i
\(399\) 186.729 169.242i 0.467992 0.424166i
\(400\) 0 0
\(401\) 291.137i 0.726027i 0.931784 + 0.363014i \(0.118252\pi\)
−0.931784 + 0.363014i \(0.881748\pi\)
\(402\) −48.8330 53.8786i −0.121475 0.134026i
\(403\) −261.448 −0.648754
\(404\) 325.965i 0.806844i
\(405\) 0 0
\(406\) 153.454 0.377965
\(407\) 110.621i 0.271797i
\(408\) 45.9075 41.6084i 0.112518 0.101981i
\(409\) 131.054 0.320425 0.160212 0.987083i \(-0.448782\pi\)
0.160212 + 0.987083i \(0.448782\pi\)
\(410\) 0 0
\(411\) 88.2277 + 97.3437i 0.214666 + 0.236846i
\(412\) 372.758 0.904753
\(413\) 11.1842i 0.0270805i
\(414\) −42.2718 + 429.217i −0.102106 + 1.03676i
\(415\) 0 0
\(416\) 34.4652i 0.0828492i
\(417\) 391.062 354.440i 0.937799 0.849976i
\(418\) 274.056 0.655635
\(419\) 639.030i 1.52513i −0.646911 0.762566i \(-0.723939\pi\)
0.646911 0.762566i \(-0.276061\pi\)
\(420\) 0 0
\(421\) 496.330 1.17893 0.589466 0.807793i \(-0.299338\pi\)
0.589466 + 0.807793i \(0.299338\pi\)
\(422\) 493.408i 1.16921i
\(423\) 405.871 + 39.9725i 0.959506 + 0.0944976i
\(424\) 51.3044 0.121001
\(425\) 0 0
\(426\) 357.815 324.307i 0.839942 0.761284i
\(427\) −44.6962 −0.104675
\(428\) 329.851i 0.770681i
\(429\) −74.9177 82.6584i −0.174633 0.192677i
\(430\) 0 0
\(431\) 242.169i 0.561877i −0.959726 0.280939i \(-0.909354\pi\)
0.959726 0.280939i \(-0.0906457\pi\)
\(432\) −64.3363 86.7459i −0.148927 0.200801i
\(433\) 123.653 0.285574 0.142787 0.989753i \(-0.454394\pi\)
0.142787 + 0.989753i \(0.454394\pi\)
\(434\) 160.562i 0.369959i
\(435\) 0 0
\(436\) −193.381 −0.443535
\(437\) 1075.89i 2.46199i
\(438\) −299.372 330.304i −0.683497 0.754119i
\(439\) −419.828 −0.956328 −0.478164 0.878271i \(-0.658698\pi\)
−0.478164 + 0.878271i \(0.658698\pi\)
\(440\) 0 0
\(441\) 6.17472 62.6967i 0.0140016 0.142169i
\(442\) 62.9145 0.142340
\(443\) 95.9458i 0.216582i −0.994119 0.108291i \(-0.965462\pi\)
0.994119 0.108291i \(-0.0345378\pi\)
\(444\) −80.5764 + 73.0306i −0.181478 + 0.164483i
\(445\) 0 0
\(446\) 625.605i 1.40270i
\(447\) −303.397 334.745i −0.678741 0.748871i
\(448\) 21.1660 0.0472456
\(449\) 780.855i 1.73910i 0.493847 + 0.869549i \(0.335590\pi\)
−0.493847 + 0.869549i \(0.664410\pi\)
\(450\) 0 0
\(451\) −222.365 −0.493050
\(452\) 224.567i 0.496830i
\(453\) −12.5152 + 11.3432i −0.0276275 + 0.0250402i
\(454\) 149.350 0.328964
\(455\) 0 0
\(456\) 180.927 + 199.621i 0.396771 + 0.437766i
\(457\) 615.383 1.34657 0.673286 0.739383i \(-0.264882\pi\)
0.673286 + 0.739383i \(0.264882\pi\)
\(458\) 424.596i 0.927064i
\(459\) 158.350 117.442i 0.344989 0.255866i
\(460\) 0 0
\(461\) 463.592i 1.00562i −0.864396 0.502811i \(-0.832299\pi\)
0.864396 0.502811i \(-0.167701\pi\)
\(462\) 50.7627 46.0089i 0.109876 0.0995863i
\(463\) 249.784 0.539491 0.269746 0.962932i \(-0.413060\pi\)
0.269746 + 0.962932i \(0.413060\pi\)
\(464\) 164.049i 0.353554i
\(465\) 0 0
\(466\) 317.261 0.680819
\(467\) 629.113i 1.34714i 0.739124 + 0.673569i \(0.235240\pi\)
−0.739124 + 0.673569i \(0.764760\pi\)
\(468\) 10.7487 109.140i 0.0229673 0.233205i
\(469\) 45.3462 0.0966869
\(470\) 0 0
\(471\) −264.651 + 239.867i −0.561892 + 0.509272i
\(472\) −11.9565 −0.0253315
\(473\) 108.045i 0.228424i
\(474\) 213.157 + 235.181i 0.449699 + 0.496163i
\(475\) 0 0
\(476\) 38.6374i 0.0811711i
\(477\) 162.464 + 16.0003i 0.340595 + 0.0335437i
\(478\) −422.000 −0.882845
\(479\) 554.807i 1.15826i 0.815235 + 0.579131i \(0.196608\pi\)
−0.815235 + 0.579131i \(0.803392\pi\)
\(480\) 0 0
\(481\) −110.427 −0.229578
\(482\) 52.7068i 0.109350i
\(483\) −180.622 199.285i −0.373959 0.412598i
\(484\) −167.497 −0.346069
\(485\) 0 0
\(486\) −176.678 294.759i −0.363534 0.606501i
\(487\) 244.109 0.501251 0.250626 0.968084i \(-0.419364\pi\)
0.250626 + 0.968084i \(0.419364\pi\)
\(488\) 47.7823i 0.0979145i
\(489\) 165.786 150.261i 0.339032 0.307282i
\(490\) 0 0
\(491\) 170.600i 0.347454i 0.984794 + 0.173727i \(0.0555810\pi\)
−0.984794 + 0.173727i \(0.944419\pi\)
\(492\) −146.802 161.970i −0.298379 0.329208i
\(493\) −299.463 −0.607429
\(494\) 273.573i 0.553793i
\(495\) 0 0
\(496\) 171.648 0.346065
\(497\) 301.150i 0.605936i
\(498\) −240.783 + 218.234i −0.483499 + 0.438221i
\(499\) 965.312 1.93449 0.967247 0.253837i \(-0.0816927\pi\)
0.967247 + 0.253837i \(0.0816927\pi\)
\(500\) 0 0
\(501\) −230.518 254.336i −0.460116 0.507657i
\(502\) 350.165 0.697540
\(503\) 86.1692i 0.171311i 0.996325 + 0.0856553i \(0.0272984\pi\)
−0.996325 + 0.0856553i \(0.972702\pi\)
\(504\) 67.0256 + 6.60106i 0.132987 + 0.0130973i
\(505\) 0 0
\(506\) 292.484i 0.578031i
\(507\) −293.148 + 265.696i −0.578202 + 0.524054i
\(508\) 395.264 0.778078
\(509\) 115.697i 0.227303i 0.993521 + 0.113651i \(0.0362547\pi\)
−0.993521 + 0.113651i \(0.963745\pi\)
\(510\) 0 0
\(511\) 277.996 0.544023
\(512\) 22.6274i 0.0441942i
\(513\) 510.680 + 688.559i 0.995477 + 1.34222i
\(514\) 106.950 0.208074
\(515\) 0 0
\(516\) 78.6995 71.3294i 0.152518 0.138235i
\(517\) −276.575 −0.534961
\(518\) 67.8160i 0.130919i
\(519\) −350.192 386.375i −0.674744 0.744461i
\(520\) 0 0
\(521\) 527.925i 1.01329i 0.862154 + 0.506646i \(0.169115\pi\)
−0.862154 + 0.506646i \(0.830885\pi\)
\(522\) −51.1620 + 519.487i −0.0980116 + 0.995186i
\(523\) 637.700 1.21931 0.609656 0.792666i \(-0.291307\pi\)
0.609656 + 0.792666i \(0.291307\pi\)
\(524\) 76.0837i 0.145198i
\(525\) 0 0
\(526\) −79.9999 −0.152091
\(527\) 313.334i 0.594562i
\(528\) 49.1856 + 54.2676i 0.0931545 + 0.102780i
\(529\) −619.237 −1.17058
\(530\) 0 0
\(531\) −37.8620 3.72887i −0.0713033 0.00702235i
\(532\) −168.009 −0.315806
\(533\) 221.974i 0.416462i
\(534\) 84.4265 76.5202i 0.158102 0.143296i
\(535\) 0 0
\(536\) 48.4771i 0.0904423i
\(537\) 270.355 + 298.289i 0.503454 + 0.555472i
\(538\) −358.796 −0.666907
\(539\) 42.7237i 0.0792648i
\(540\) 0 0
\(541\) −749.392 −1.38520 −0.692599 0.721323i \(-0.743534\pi\)
−0.692599 + 0.721323i \(0.743534\pi\)
\(542\) 362.593i 0.668991i
\(543\) −442.598 + 401.150i −0.815098 + 0.738766i
\(544\) −41.3051 −0.0759286
\(545\) 0 0
\(546\) 45.9280 + 50.6734i 0.0841172 + 0.0928084i
\(547\) 129.416 0.236592 0.118296 0.992978i \(-0.462257\pi\)
0.118296 + 0.992978i \(0.462257\pi\)
\(548\) 87.5847i 0.159826i
\(549\) 14.9019 151.310i 0.0271437 0.275610i
\(550\) 0 0
\(551\) 1302.16i 2.36328i
\(552\) 213.045 193.093i 0.385950 0.349807i
\(553\) −197.937 −0.357933
\(554\) 262.586i 0.473982i
\(555\) 0 0
\(556\) −351.857 −0.632836
\(557\) 926.902i 1.66410i 0.554703 + 0.832049i \(0.312832\pi\)
−0.554703 + 0.832049i \(0.687168\pi\)
\(558\) 543.551 + 53.5320i 0.974106 + 0.0959354i
\(559\) 107.855 0.192942
\(560\) 0 0
\(561\) −99.0626 + 89.7856i −0.176582 + 0.160046i
\(562\) 368.049 0.654892
\(563\) 690.211i 1.22595i −0.790101 0.612976i \(-0.789972\pi\)
0.790101 0.612976i \(-0.210028\pi\)
\(564\) −182.591 201.457i −0.323742 0.357193i
\(565\) 0 0
\(566\) 630.065i 1.11319i
\(567\) 210.189 + 41.8066i 0.370703 + 0.0737330i
\(568\) −321.943 −0.566801
\(569\) 155.630i 0.273515i −0.990605 0.136757i \(-0.956332\pi\)
0.990605 0.136757i \(-0.0436680\pi\)
\(570\) 0 0
\(571\) −961.721 −1.68427 −0.842137 0.539263i \(-0.818703\pi\)
−0.842137 + 0.539263i \(0.818703\pi\)
\(572\) 74.3716i 0.130020i
\(573\) −451.704 498.376i −0.788315 0.869766i
\(574\) 136.320 0.237492
\(575\) 0 0
\(576\) −7.05683 + 71.6533i −0.0122514 + 0.124398i
\(577\) −670.111 −1.16137 −0.580685 0.814128i \(-0.697215\pi\)
−0.580685 + 0.814128i \(0.697215\pi\)
\(578\) 333.307i 0.576656i
\(579\) 756.043 685.241i 1.30577 1.18349i
\(580\) 0 0
\(581\) 202.651i 0.348797i
\(582\) −342.151 377.503i −0.587888 0.648631i
\(583\) −110.708 −0.189894
\(584\) 297.190i 0.508887i
\(585\) 0 0
\(586\) −245.458 −0.418870
\(587\) 671.384i 1.14376i 0.820339 + 0.571878i \(0.193785\pi\)
−0.820339 + 0.571878i \(0.806215\pi\)
\(588\) −31.1199 + 28.2056i −0.0529249 + 0.0479686i
\(589\) −1362.48 −2.31322
\(590\) 0 0
\(591\) −232.502 256.525i −0.393404 0.434052i
\(592\) 72.4984 0.122463
\(593\) 173.594i 0.292738i −0.989230 0.146369i \(-0.953241\pi\)
0.989230 0.146369i \(-0.0467587\pi\)
\(594\) 138.830 + 187.187i 0.233720 + 0.315129i
\(595\) 0 0
\(596\) 301.186i 0.505345i
\(597\) −414.715 + 375.878i −0.694665 + 0.629612i
\(598\) 291.969 0.488243
\(599\) 561.565i 0.937504i −0.883330 0.468752i \(-0.844704\pi\)
0.883330 0.468752i \(-0.155296\pi\)
\(600\) 0 0
\(601\) 382.578 0.636568 0.318284 0.947995i \(-0.396893\pi\)
0.318284 + 0.947995i \(0.396893\pi\)
\(602\) 66.2363i 0.110027i
\(603\) −15.1186 + 153.510i −0.0250723 + 0.254578i
\(604\) 11.2606 0.0186433
\(605\) 0 0
\(606\) −512.349 + 464.369i −0.845460 + 0.766285i
\(607\) −489.748 −0.806833 −0.403417 0.915016i \(-0.632177\pi\)
−0.403417 + 0.915016i \(0.632177\pi\)
\(608\) 179.609i 0.295409i
\(609\) −218.610 241.197i −0.358965 0.396054i
\(610\) 0 0
\(611\) 276.088i 0.451863i
\(612\) −130.799 12.8819i −0.213724 0.0210488i
\(613\) −103.287 −0.168494 −0.0842472 0.996445i \(-0.526849\pi\)
−0.0842472 + 0.996445i \(0.526849\pi\)
\(614\) 344.390i 0.560896i
\(615\) 0 0
\(616\) −45.6736 −0.0741454
\(617\) 103.427i 0.167629i 0.996481 + 0.0838144i \(0.0267103\pi\)
−0.996481 + 0.0838144i \(0.973290\pi\)
\(618\) −531.030 585.898i −0.859271 0.948054i
\(619\) −1040.92 −1.68162 −0.840809 0.541332i \(-0.817920\pi\)
−0.840809 + 0.541332i \(0.817920\pi\)
\(620\) 0 0
\(621\) 734.860 545.019i 1.18335 0.877647i
\(622\) 364.527 0.586056
\(623\) 71.0564i 0.114055i
\(624\) −54.1722 + 49.0991i −0.0868144 + 0.0786844i
\(625\) 0 0
\(626\) 221.199i 0.353354i
\(627\) −390.418 430.758i −0.622677 0.687014i
\(628\) 238.119 0.379170
\(629\) 132.342i 0.210400i
\(630\) 0 0
\(631\) −1243.34 −1.97043 −0.985216 0.171315i \(-0.945198\pi\)
−0.985216 + 0.171315i \(0.945198\pi\)
\(632\) 211.604i 0.334816i
\(633\) −775.534 + 702.907i −1.22517 + 1.11044i
\(634\) 381.398 0.601574
\(635\) 0 0
\(636\) −73.0881 80.6398i −0.114918 0.126792i
\(637\) −42.6486 −0.0669522
\(638\) 353.997i 0.554854i
\(639\) −1019.48 100.405i −1.59544 0.157128i
\(640\) 0 0
\(641\) 168.859i 0.263431i 0.991288 + 0.131715i \(0.0420485\pi\)
−0.991288 + 0.131715i \(0.957951\pi\)
\(642\) −518.457 + 469.905i −0.807566 + 0.731939i
\(643\) 290.872 0.452366 0.226183 0.974085i \(-0.427375\pi\)
0.226183 + 0.974085i \(0.427375\pi\)
\(644\) 179.306i 0.278425i
\(645\) 0 0
\(646\) 327.866 0.507533
\(647\) 725.855i 1.12188i −0.827857 0.560939i \(-0.810440\pi\)
0.827857 0.560939i \(-0.189560\pi\)
\(648\) −44.6931 + 224.701i −0.0689709 + 0.346761i
\(649\) 25.8005 0.0397543
\(650\) 0 0
\(651\) −252.370 + 228.736i −0.387665 + 0.351361i
\(652\) −149.166 −0.228782
\(653\) 977.062i 1.49627i 0.663548 + 0.748133i \(0.269050\pi\)
−0.663548 + 0.748133i \(0.730950\pi\)
\(654\) 275.490 + 303.955i 0.421238 + 0.464762i
\(655\) 0 0
\(656\) 145.732i 0.222153i
\(657\) −92.6848 + 941.100i −0.141073 + 1.43242i
\(658\) 169.553 0.257680
\(659\) 157.771i 0.239409i 0.992810 + 0.119705i \(0.0381948\pi\)
−0.992810 + 0.119705i \(0.961805\pi\)
\(660\) 0 0
\(661\) 1072.89 1.62314 0.811568 0.584258i \(-0.198614\pi\)
0.811568 + 0.584258i \(0.198614\pi\)
\(662\) 142.479i 0.215225i
\(663\) −89.6277 98.8884i −0.135185 0.149153i
\(664\) 216.643 0.326270
\(665\) 0 0
\(666\) 229.578 + 22.6101i 0.344711 + 0.0339491i
\(667\) −1389.73 −2.08355
\(668\) 228.838i 0.342572i
\(669\) −983.320 + 891.235i −1.46984 + 1.33219i
\(670\) 0 0
\(671\) 103.108i 0.153663i
\(672\) −30.1530 33.2685i −0.0448706 0.0495068i
\(673\) 293.836 0.436606 0.218303 0.975881i \(-0.429948\pi\)
0.218303 + 0.975881i \(0.429948\pi\)
\(674\) 243.319i 0.361007i
\(675\) 0 0
\(676\) 263.759 0.390176
\(677\) 569.262i 0.840859i −0.907325 0.420429i \(-0.861879\pi\)
0.907325 0.420429i \(-0.138121\pi\)
\(678\) −352.973 + 319.918i −0.520609 + 0.471855i
\(679\) 317.720 0.467924
\(680\) 0 0
\(681\) −212.763 234.746i −0.312427 0.344708i
\(682\) −370.395 −0.543101
\(683\) 21.2129i 0.0310585i 0.999879 + 0.0155292i \(0.00494331\pi\)
−0.999879 + 0.0155292i \(0.995057\pi\)
\(684\) 56.0147 568.760i 0.0818928 0.831520i
\(685\) 0 0
\(686\) 26.1916i 0.0381802i
\(687\) 667.375 604.877i 0.971434 0.880462i
\(688\) −70.8096 −0.102921
\(689\) 110.514i 0.160397i
\(690\) 0 0
\(691\) −698.350 −1.01064 −0.505318 0.862933i \(-0.668625\pi\)
−0.505318 + 0.862933i \(0.668625\pi\)
\(692\) 347.640i 0.502370i
\(693\) −144.633 14.2442i −0.208705 0.0205545i
\(694\) −532.969 −0.767966
\(695\) 0 0
\(696\) 257.851 233.703i 0.370475 0.335781i
\(697\) −266.027 −0.381674
\(698\) 473.153i 0.677869i
\(699\) −451.969 498.669i −0.646594 0.713403i
\(700\) 0 0
\(701\) 1019.57i 1.45445i 0.686399 + 0.727225i \(0.259190\pi\)
−0.686399 + 0.727225i \(0.740810\pi\)
\(702\) −186.857 + 138.585i −0.266179 + 0.197415i
\(703\) −575.468 −0.818588
\(704\) 48.8271i 0.0693567i
\(705\) 0 0
\(706\) −411.852 −0.583359
\(707\) 431.211i 0.609917i
\(708\) 17.0331 + 18.7930i 0.0240581 + 0.0265438i
\(709\) 482.736 0.680869 0.340435 0.940268i \(-0.389426\pi\)
0.340435 + 0.940268i \(0.389426\pi\)
\(710\) 0 0
\(711\) 65.9930 670.077i 0.0928171 0.942443i
\(712\) −75.9625 −0.106689
\(713\) 1454.10i 2.03941i
\(714\) 60.7299 55.0427i 0.0850559 0.0770906i
\(715\) 0 0
\(716\) 268.384i 0.374838i
\(717\) 601.180 + 663.296i 0.838466 + 0.925099i
\(718\) −289.319 −0.402951
\(719\) 1275.40i 1.77385i −0.461915 0.886924i \(-0.652838\pi\)
0.461915 0.886924i \(-0.347162\pi\)
\(720\) 0 0
\(721\) 493.113 0.683929
\(722\) 915.143i 1.26751i
\(723\) 82.8441 75.0859i 0.114584 0.103853i
\(724\) 398.226 0.550036
\(725\) 0 0
\(726\) 238.616 + 263.271i 0.328672 + 0.362632i
\(727\) −90.3245 −0.124243 −0.0621214 0.998069i \(-0.519787\pi\)
−0.0621214 + 0.998069i \(0.519787\pi\)
\(728\) 45.5932i 0.0626281i
\(729\) −211.606 + 697.613i −0.290268 + 0.956945i
\(730\) 0 0
\(731\) 129.259i 0.176825i
\(732\) −75.1037 + 68.0704i −0.102601 + 0.0929924i
\(733\) 515.475 0.703240 0.351620 0.936143i \(-0.385631\pi\)
0.351620 + 0.936143i \(0.385631\pi\)
\(734\) 343.077i 0.467408i
\(735\) 0 0
\(736\) −191.686 −0.260443
\(737\) 104.607i 0.141937i
\(738\) −45.4497 + 461.485i −0.0615849 + 0.625318i
\(739\) 91.7703 0.124182 0.0620909 0.998071i \(-0.480223\pi\)
0.0620909 + 0.998071i \(0.480223\pi\)
\(740\) 0 0
\(741\) 430.000 389.732i 0.580297 0.525954i
\(742\) 67.8694 0.0914681
\(743\) 680.829i 0.916324i 0.888869 + 0.458162i \(0.151492\pi\)
−0.888869 + 0.458162i \(0.848508\pi\)
\(744\) −244.529 269.795i −0.328668 0.362627i
\(745\) 0 0
\(746\) 143.944i 0.192955i
\(747\) 686.036 + 67.5647i 0.918388 + 0.0904481i
\(748\) 89.1313 0.119159
\(749\) 436.352i 0.582580i
\(750\) 0 0
\(751\) 275.733 0.367155 0.183577 0.983005i \(-0.441232\pi\)
0.183577 + 0.983005i \(0.441232\pi\)
\(752\) 181.260i 0.241037i
\(753\) −498.844 550.386i −0.662475 0.730925i
\(754\) 353.374 0.468666
\(755\) 0 0
\(756\) −85.1089 114.754i −0.112578 0.151791i
\(757\) −622.898 −0.822851 −0.411425 0.911443i \(-0.634969\pi\)
−0.411425 + 0.911443i \(0.634969\pi\)
\(758\) 349.350i 0.460884i
\(759\) −459.723 + 416.671i −0.605696 + 0.548974i
\(760\) 0 0
\(761\) 1122.56i 1.47511i 0.675288 + 0.737554i \(0.264019\pi\)
−0.675288 + 0.737554i \(0.735981\pi\)
\(762\) −563.091 621.272i −0.738965 0.815317i
\(763\) −255.819 −0.335281
\(764\) 448.412i 0.586927i
\(765\) 0 0
\(766\) −26.8275 −0.0350228
\(767\) 25.7551i 0.0335791i
\(768\) 35.5656 32.2349i 0.0463093 0.0419726i
\(769\) −344.788 −0.448359 −0.224179 0.974548i \(-0.571970\pi\)
−0.224179 + 0.974548i \(0.571970\pi\)
\(770\) 0 0
\(771\) −152.361 168.103i −0.197615 0.218033i
\(772\) −680.247 −0.881149
\(773\) 235.375i 0.304495i −0.988342 0.152248i \(-0.951349\pi\)
0.988342 0.152248i \(-0.0486511\pi\)
\(774\) −224.230 22.0834i −0.289703 0.0285316i
\(775\) 0 0
\(776\) 339.657i 0.437702i
\(777\) −106.593 + 96.6104i −0.137185 + 0.124338i
\(778\) 881.464 1.13299
\(779\) 1156.77i 1.48495i
\(780\) 0 0
\(781\) 694.713 0.889517
\(782\) 349.913i 0.447459i
\(783\) 889.410 659.643i 1.13590 0.842456i
\(784\) 28.0000 0.0357143
\(785\) 0 0
\(786\) 119.588 108.388i 0.152147 0.137899i
\(787\) −579.779 −0.736695 −0.368348 0.929688i \(-0.620076\pi\)
−0.368348 + 0.929688i \(0.620076\pi\)
\(788\) 230.807i 0.292903i
\(789\) 113.968 + 125.743i 0.144446 + 0.159370i
\(790\)