Properties

Label 490.4.c.b.99.1
Level $490$
Weight $4$
Character 490.99
Analytic conductor $28.911$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.9109359028\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 490.99
Dual form 490.4.c.b.99.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{2} -2.00000i q^{3} -4.00000 q^{4} +(5.00000 - 10.0000i) q^{5} -4.00000 q^{6} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} -2.00000i q^{3} -4.00000 q^{4} +(5.00000 - 10.0000i) q^{5} -4.00000 q^{6} +8.00000i q^{8} +23.0000 q^{9} +(-20.0000 - 10.0000i) q^{10} -28.0000 q^{11} +8.00000i q^{12} -12.0000i q^{13} +(-20.0000 - 10.0000i) q^{15} +16.0000 q^{16} -64.0000i q^{17} -46.0000i q^{18} -60.0000 q^{19} +(-20.0000 + 40.0000i) q^{20} +56.0000i q^{22} -58.0000i q^{23} +16.0000 q^{24} +(-75.0000 - 100.000i) q^{25} -24.0000 q^{26} -100.000i q^{27} -90.0000 q^{29} +(-20.0000 + 40.0000i) q^{30} +128.000 q^{31} -32.0000i q^{32} +56.0000i q^{33} -128.000 q^{34} -92.0000 q^{36} -236.000i q^{37} +120.000i q^{38} -24.0000 q^{39} +(80.0000 + 40.0000i) q^{40} -242.000 q^{41} +362.000i q^{43} +112.000 q^{44} +(115.000 - 230.000i) q^{45} -116.000 q^{46} +226.000i q^{47} -32.0000i q^{48} +(-200.000 + 150.000i) q^{50} -128.000 q^{51} +48.0000i q^{52} -108.000i q^{53} -200.000 q^{54} +(-140.000 + 280.000i) q^{55} +120.000i q^{57} +180.000i q^{58} -20.0000 q^{59} +(80.0000 + 40.0000i) q^{60} -542.000 q^{61} -256.000i q^{62} -64.0000 q^{64} +(-120.000 - 60.0000i) q^{65} +112.000 q^{66} +434.000i q^{67} +256.000i q^{68} -116.000 q^{69} -1128.00 q^{71} +184.000i q^{72} -632.000i q^{73} -472.000 q^{74} +(-200.000 + 150.000i) q^{75} +240.000 q^{76} +48.0000i q^{78} +720.000 q^{79} +(80.0000 - 160.000i) q^{80} +421.000 q^{81} +484.000i q^{82} +478.000i q^{83} +(-640.000 - 320.000i) q^{85} +724.000 q^{86} +180.000i q^{87} -224.000i q^{88} -490.000 q^{89} +(-460.000 - 230.000i) q^{90} +232.000i q^{92} -256.000i q^{93} +452.000 q^{94} +(-300.000 + 600.000i) q^{95} -64.0000 q^{96} +1456.00i q^{97} -644.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{4} + 10 q^{5} - 8 q^{6} + 46 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{4} + 10 q^{5} - 8 q^{6} + 46 q^{9} - 40 q^{10} - 56 q^{11} - 40 q^{15} + 32 q^{16} - 120 q^{19} - 40 q^{20} + 32 q^{24} - 150 q^{25} - 48 q^{26} - 180 q^{29} - 40 q^{30} + 256 q^{31} - 256 q^{34} - 184 q^{36} - 48 q^{39} + 160 q^{40} - 484 q^{41} + 224 q^{44} + 230 q^{45} - 232 q^{46} - 400 q^{50} - 256 q^{51} - 400 q^{54} - 280 q^{55} - 40 q^{59} + 160 q^{60} - 1084 q^{61} - 128 q^{64} - 240 q^{65} + 224 q^{66} - 232 q^{69} - 2256 q^{71} - 944 q^{74} - 400 q^{75} + 480 q^{76} + 1440 q^{79} + 160 q^{80} + 842 q^{81} - 1280 q^{85} + 1448 q^{86} - 980 q^{89} - 920 q^{90} + 904 q^{94} - 600 q^{95} - 128 q^{96} - 1288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 2.00000i 0.384900i −0.981307 0.192450i \(-0.938357\pi\)
0.981307 0.192450i \(-0.0616434\pi\)
\(4\) −4.00000 −0.500000
\(5\) 5.00000 10.0000i 0.447214 0.894427i
\(6\) −4.00000 −0.272166
\(7\) 0 0
\(8\) 8.00000i 0.353553i
\(9\) 23.0000 0.851852
\(10\) −20.0000 10.0000i −0.632456 0.316228i
\(11\) −28.0000 −0.767483 −0.383742 0.923440i \(-0.625365\pi\)
−0.383742 + 0.923440i \(0.625365\pi\)
\(12\) 8.00000i 0.192450i
\(13\) 12.0000i 0.256015i −0.991773 0.128008i \(-0.959142\pi\)
0.991773 0.128008i \(-0.0408582\pi\)
\(14\) 0 0
\(15\) −20.0000 10.0000i −0.344265 0.172133i
\(16\) 16.0000 0.250000
\(17\) 64.0000i 0.913075i −0.889704 0.456538i \(-0.849089\pi\)
0.889704 0.456538i \(-0.150911\pi\)
\(18\) 46.0000i 0.602350i
\(19\) −60.0000 −0.724471 −0.362235 0.932087i \(-0.617986\pi\)
−0.362235 + 0.932087i \(0.617986\pi\)
\(20\) −20.0000 + 40.0000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 56.0000i 0.542693i
\(23\) 58.0000i 0.525819i −0.964821 0.262909i \(-0.915318\pi\)
0.964821 0.262909i \(-0.0846821\pi\)
\(24\) 16.0000 0.136083
\(25\) −75.0000 100.000i −0.600000 0.800000i
\(26\) −24.0000 −0.181030
\(27\) 100.000i 0.712778i
\(28\) 0 0
\(29\) −90.0000 −0.576296 −0.288148 0.957586i \(-0.593039\pi\)
−0.288148 + 0.957586i \(0.593039\pi\)
\(30\) −20.0000 + 40.0000i −0.121716 + 0.243432i
\(31\) 128.000 0.741596 0.370798 0.928714i \(-0.379084\pi\)
0.370798 + 0.928714i \(0.379084\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 56.0000i 0.295405i
\(34\) −128.000 −0.645642
\(35\) 0 0
\(36\) −92.0000 −0.425926
\(37\) 236.000i 1.04860i −0.851534 0.524299i \(-0.824327\pi\)
0.851534 0.524299i \(-0.175673\pi\)
\(38\) 120.000i 0.512278i
\(39\) −24.0000 −0.0985404
\(40\) 80.0000 + 40.0000i 0.316228 + 0.158114i
\(41\) −242.000 −0.921806 −0.460903 0.887450i \(-0.652474\pi\)
−0.460903 + 0.887450i \(0.652474\pi\)
\(42\) 0 0
\(43\) 362.000i 1.28383i 0.766778 + 0.641913i \(0.221859\pi\)
−0.766778 + 0.641913i \(0.778141\pi\)
\(44\) 112.000 0.383742
\(45\) 115.000 230.000i 0.380960 0.761919i
\(46\) −116.000 −0.371810
\(47\) 226.000i 0.701393i 0.936489 + 0.350697i \(0.114055\pi\)
−0.936489 + 0.350697i \(0.885945\pi\)
\(48\) 32.0000i 0.0962250i
\(49\) 0 0
\(50\) −200.000 + 150.000i −0.565685 + 0.424264i
\(51\) −128.000 −0.351443
\(52\) 48.0000i 0.128008i
\(53\) 108.000i 0.279905i −0.990158 0.139952i \(-0.955305\pi\)
0.990158 0.139952i \(-0.0446949\pi\)
\(54\) −200.000 −0.504010
\(55\) −140.000 + 280.000i −0.343229 + 0.686458i
\(56\) 0 0
\(57\) 120.000i 0.278849i
\(58\) 180.000i 0.407503i
\(59\) −20.0000 −0.0441318 −0.0220659 0.999757i \(-0.507024\pi\)
−0.0220659 + 0.999757i \(0.507024\pi\)
\(60\) 80.0000 + 40.0000i 0.172133 + 0.0860663i
\(61\) −542.000 −1.13764 −0.568820 0.822462i \(-0.692600\pi\)
−0.568820 + 0.822462i \(0.692600\pi\)
\(62\) 256.000i 0.524388i
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) −120.000 60.0000i −0.228987 0.114494i
\(66\) 112.000 0.208883
\(67\) 434.000i 0.791366i 0.918387 + 0.395683i \(0.129492\pi\)
−0.918387 + 0.395683i \(0.870508\pi\)
\(68\) 256.000i 0.456538i
\(69\) −116.000 −0.202388
\(70\) 0 0
\(71\) −1128.00 −1.88548 −0.942739 0.333531i \(-0.891760\pi\)
−0.942739 + 0.333531i \(0.891760\pi\)
\(72\) 184.000i 0.301175i
\(73\) 632.000i 1.01329i −0.862155 0.506644i \(-0.830886\pi\)
0.862155 0.506644i \(-0.169114\pi\)
\(74\) −472.000 −0.741471
\(75\) −200.000 + 150.000i −0.307920 + 0.230940i
\(76\) 240.000 0.362235
\(77\) 0 0
\(78\) 48.0000i 0.0696786i
\(79\) 720.000 1.02540 0.512698 0.858569i \(-0.328646\pi\)
0.512698 + 0.858569i \(0.328646\pi\)
\(80\) 80.0000 160.000i 0.111803 0.223607i
\(81\) 421.000 0.577503
\(82\) 484.000i 0.651815i
\(83\) 478.000i 0.632136i 0.948736 + 0.316068i \(0.102363\pi\)
−0.948736 + 0.316068i \(0.897637\pi\)
\(84\) 0 0
\(85\) −640.000 320.000i −0.816679 0.408340i
\(86\) 724.000 0.907801
\(87\) 180.000i 0.221816i
\(88\) 224.000i 0.271346i
\(89\) −490.000 −0.583594 −0.291797 0.956480i \(-0.594253\pi\)
−0.291797 + 0.956480i \(0.594253\pi\)
\(90\) −460.000 230.000i −0.538758 0.269379i
\(91\) 0 0
\(92\) 232.000i 0.262909i
\(93\) 256.000i 0.285440i
\(94\) 452.000 0.495960
\(95\) −300.000 + 600.000i −0.323993 + 0.647986i
\(96\) −64.0000 −0.0680414
\(97\) 1456.00i 1.52407i 0.647538 + 0.762033i \(0.275799\pi\)
−0.647538 + 0.762033i \(0.724201\pi\)
\(98\) 0 0
\(99\) −644.000 −0.653782
\(100\) 300.000 + 400.000i 0.300000 + 0.400000i
\(101\) 578.000 0.569437 0.284719 0.958611i \(-0.408100\pi\)
0.284719 + 0.958611i \(0.408100\pi\)
\(102\) 256.000i 0.248508i
\(103\) 1462.00i 1.39859i −0.714831 0.699297i \(-0.753497\pi\)
0.714831 0.699297i \(-0.246503\pi\)
\(104\) 96.0000 0.0905151
\(105\) 0 0
\(106\) −216.000 −0.197922
\(107\) 966.000i 0.872773i −0.899759 0.436387i \(-0.856258\pi\)
0.899759 0.436387i \(-0.143742\pi\)
\(108\) 400.000i 0.356389i
\(109\) −370.000 −0.325134 −0.162567 0.986698i \(-0.551977\pi\)
−0.162567 + 0.986698i \(0.551977\pi\)
\(110\) 560.000 + 280.000i 0.485399 + 0.242700i
\(111\) −472.000 −0.403606
\(112\) 0 0
\(113\) 528.000i 0.439558i −0.975550 0.219779i \(-0.929466\pi\)
0.975550 0.219779i \(-0.0705336\pi\)
\(114\) 240.000 0.197176
\(115\) −580.000 290.000i −0.470307 0.235153i
\(116\) 360.000 0.288148
\(117\) 276.000i 0.218087i
\(118\) 40.0000i 0.0312059i
\(119\) 0 0
\(120\) 80.0000 160.000i 0.0608581 0.121716i
\(121\) −547.000 −0.410969
\(122\) 1084.00i 0.804432i
\(123\) 484.000i 0.354803i
\(124\) −512.000 −0.370798
\(125\) −1375.00 + 250.000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 1534.00i 1.07181i 0.844277 + 0.535907i \(0.180030\pi\)
−0.844277 + 0.535907i \(0.819970\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 724.000 0.494145
\(130\) −120.000 + 240.000i −0.0809592 + 0.161918i
\(131\) −12.0000 −0.00800340 −0.00400170 0.999992i \(-0.501274\pi\)
−0.00400170 + 0.999992i \(0.501274\pi\)
\(132\) 224.000i 0.147702i
\(133\) 0 0
\(134\) 868.000 0.559580
\(135\) −1000.00 500.000i −0.637528 0.318764i
\(136\) 512.000 0.322821
\(137\) 1224.00i 0.763309i 0.924305 + 0.381655i \(0.124646\pi\)
−0.924305 + 0.381655i \(0.875354\pi\)
\(138\) 232.000i 0.143110i
\(139\) 3100.00 1.89164 0.945822 0.324685i \(-0.105258\pi\)
0.945822 + 0.324685i \(0.105258\pi\)
\(140\) 0 0
\(141\) 452.000 0.269966
\(142\) 2256.00i 1.33323i
\(143\) 336.000i 0.196488i
\(144\) 368.000 0.212963
\(145\) −450.000 + 900.000i −0.257727 + 0.515455i
\(146\) −1264.00 −0.716503
\(147\) 0 0
\(148\) 944.000i 0.524299i
\(149\) −250.000 −0.137455 −0.0687275 0.997635i \(-0.521894\pi\)
−0.0687275 + 0.997635i \(0.521894\pi\)
\(150\) 300.000 + 400.000i 0.163299 + 0.217732i
\(151\) 2152.00 1.15978 0.579892 0.814694i \(-0.303095\pi\)
0.579892 + 0.814694i \(0.303095\pi\)
\(152\) 480.000i 0.256139i
\(153\) 1472.00i 0.777805i
\(154\) 0 0
\(155\) 640.000 1280.00i 0.331652 0.663304i
\(156\) 96.0000 0.0492702
\(157\) 524.000i 0.266368i −0.991091 0.133184i \(-0.957480\pi\)
0.991091 0.133184i \(-0.0425201\pi\)
\(158\) 1440.00i 0.725065i
\(159\) −216.000 −0.107735
\(160\) −320.000 160.000i −0.158114 0.0790569i
\(161\) 0 0
\(162\) 842.000i 0.408357i
\(163\) 3518.00i 1.69050i −0.534373 0.845249i \(-0.679452\pi\)
0.534373 0.845249i \(-0.320548\pi\)
\(164\) 968.000 0.460903
\(165\) 560.000 + 280.000i 0.264218 + 0.132109i
\(166\) 956.000 0.446988
\(167\) 534.000i 0.247438i −0.992317 0.123719i \(-0.960518\pi\)
0.992317 0.123719i \(-0.0394822\pi\)
\(168\) 0 0
\(169\) 2053.00 0.934456
\(170\) −640.000 + 1280.00i −0.288740 + 0.577480i
\(171\) −1380.00 −0.617142
\(172\) 1448.00i 0.641913i
\(173\) 4252.00i 1.86863i −0.356444 0.934317i \(-0.616011\pi\)
0.356444 0.934317i \(-0.383989\pi\)
\(174\) 360.000 0.156848
\(175\) 0 0
\(176\) −448.000 −0.191871
\(177\) 40.0000i 0.0169864i
\(178\) 980.000i 0.412664i
\(179\) −2500.00 −1.04390 −0.521952 0.852975i \(-0.674796\pi\)
−0.521952 + 0.852975i \(0.674796\pi\)
\(180\) −460.000 + 920.000i −0.190480 + 0.380960i
\(181\) 2578.00 1.05868 0.529340 0.848410i \(-0.322439\pi\)
0.529340 + 0.848410i \(0.322439\pi\)
\(182\) 0 0
\(183\) 1084.00i 0.437878i
\(184\) 464.000 0.185905
\(185\) −2360.00 1180.00i −0.937895 0.468948i
\(186\) −512.000 −0.201837
\(187\) 1792.00i 0.700770i
\(188\) 904.000i 0.350697i
\(189\) 0 0
\(190\) 1200.00 + 600.000i 0.458196 + 0.229098i
\(191\) −768.000 −0.290945 −0.145473 0.989362i \(-0.546470\pi\)
−0.145473 + 0.989362i \(0.546470\pi\)
\(192\) 128.000i 0.0481125i
\(193\) 2608.00i 0.972684i −0.873769 0.486342i \(-0.838331\pi\)
0.873769 0.486342i \(-0.161669\pi\)
\(194\) 2912.00 1.07768
\(195\) −120.000 + 240.000i −0.0440686 + 0.0881372i
\(196\) 0 0
\(197\) 5116.00i 1.85025i −0.379659 0.925127i \(-0.623959\pi\)
0.379659 0.925127i \(-0.376041\pi\)
\(198\) 1288.00i 0.462294i
\(199\) −3480.00 −1.23965 −0.619826 0.784739i \(-0.712797\pi\)
−0.619826 + 0.784739i \(0.712797\pi\)
\(200\) 800.000 600.000i 0.282843 0.212132i
\(201\) 868.000 0.304597
\(202\) 1156.00i 0.402653i
\(203\) 0 0
\(204\) 512.000 0.175721
\(205\) −1210.00 + 2420.00i −0.412244 + 0.824488i
\(206\) −2924.00 −0.988955
\(207\) 1334.00i 0.447920i
\(208\) 192.000i 0.0640039i
\(209\) 1680.00 0.556019
\(210\) 0 0
\(211\) 3132.00 1.02188 0.510938 0.859618i \(-0.329298\pi\)
0.510938 + 0.859618i \(0.329298\pi\)
\(212\) 432.000i 0.139952i
\(213\) 2256.00i 0.725721i
\(214\) −1932.00 −0.617144
\(215\) 3620.00 + 1810.00i 1.14829 + 0.574144i
\(216\) 800.000 0.252005
\(217\) 0 0
\(218\) 740.000i 0.229904i
\(219\) −1264.00 −0.390015
\(220\) 560.000 1120.00i 0.171615 0.343229i
\(221\) −768.000 −0.233761
\(222\) 944.000i 0.285392i
\(223\) 62.0000i 0.0186181i −0.999957 0.00930903i \(-0.997037\pi\)
0.999957 0.00930903i \(-0.00296320\pi\)
\(224\) 0 0
\(225\) −1725.00 2300.00i −0.511111 0.681481i
\(226\) −1056.00 −0.310814
\(227\) 5314.00i 1.55376i −0.629651 0.776878i \(-0.716802\pi\)
0.629651 0.776878i \(-0.283198\pi\)
\(228\) 480.000i 0.139424i
\(229\) −190.000 −0.0548277 −0.0274139 0.999624i \(-0.508727\pi\)
−0.0274139 + 0.999624i \(0.508727\pi\)
\(230\) −580.000 + 1160.00i −0.166279 + 0.332557i
\(231\) 0 0
\(232\) 720.000i 0.203751i
\(233\) 2408.00i 0.677053i −0.940957 0.338526i \(-0.890072\pi\)
0.940957 0.338526i \(-0.109928\pi\)
\(234\) −552.000 −0.154211
\(235\) 2260.00 + 1130.00i 0.627345 + 0.313673i
\(236\) 80.0000 0.0220659
\(237\) 1440.00i 0.394675i
\(238\) 0 0
\(239\) 5680.00 1.53727 0.768637 0.639685i \(-0.220935\pi\)
0.768637 + 0.639685i \(0.220935\pi\)
\(240\) −320.000 160.000i −0.0860663 0.0430331i
\(241\) 278.000 0.0743052 0.0371526 0.999310i \(-0.488171\pi\)
0.0371526 + 0.999310i \(0.488171\pi\)
\(242\) 1094.00i 0.290599i
\(243\) 3542.00i 0.935059i
\(244\) 2168.00 0.568820
\(245\) 0 0
\(246\) 968.000 0.250884
\(247\) 720.000i 0.185476i
\(248\) 1024.00i 0.262194i
\(249\) 956.000 0.243309
\(250\) 500.000 + 2750.00i 0.126491 + 0.695701i
\(251\) −3252.00 −0.817787 −0.408893 0.912582i \(-0.634085\pi\)
−0.408893 + 0.912582i \(0.634085\pi\)
\(252\) 0 0
\(253\) 1624.00i 0.403557i
\(254\) 3068.00 0.757888
\(255\) −640.000 + 1280.00i −0.157170 + 0.314340i
\(256\) 256.000 0.0625000
\(257\) 1536.00i 0.372813i 0.982473 + 0.186407i \(0.0596842\pi\)
−0.982473 + 0.186407i \(0.940316\pi\)
\(258\) 1448.00i 0.349413i
\(259\) 0 0
\(260\) 480.000 + 240.000i 0.114494 + 0.0572468i
\(261\) −2070.00 −0.490919
\(262\) 24.0000i 0.00565926i
\(263\) 4858.00i 1.13900i −0.821991 0.569500i \(-0.807137\pi\)
0.821991 0.569500i \(-0.192863\pi\)
\(264\) −448.000 −0.104441
\(265\) −1080.00 540.000i −0.250354 0.125177i
\(266\) 0 0
\(267\) 980.000i 0.224626i
\(268\) 1736.00i 0.395683i
\(269\) 2610.00 0.591578 0.295789 0.955253i \(-0.404417\pi\)
0.295789 + 0.955253i \(0.404417\pi\)
\(270\) −1000.00 + 2000.00i −0.225400 + 0.450800i
\(271\) 5168.00 1.15843 0.579213 0.815176i \(-0.303360\pi\)
0.579213 + 0.815176i \(0.303360\pi\)
\(272\) 1024.00i 0.228269i
\(273\) 0 0
\(274\) 2448.00 0.539741
\(275\) 2100.00 + 2800.00i 0.460490 + 0.613987i
\(276\) 464.000 0.101194
\(277\) 1924.00i 0.417336i 0.977987 + 0.208668i \(0.0669127\pi\)
−0.977987 + 0.208668i \(0.933087\pi\)
\(278\) 6200.00i 1.33759i
\(279\) 2944.00 0.631730
\(280\) 0 0
\(281\) 3042.00 0.645803 0.322901 0.946433i \(-0.395342\pi\)
0.322901 + 0.946433i \(0.395342\pi\)
\(282\) 904.000i 0.190895i
\(283\) 1718.00i 0.360864i 0.983587 + 0.180432i \(0.0577496\pi\)
−0.983587 + 0.180432i \(0.942250\pi\)
\(284\) 4512.00 0.942739
\(285\) 1200.00 + 600.000i 0.249410 + 0.124705i
\(286\) 672.000 0.138938
\(287\) 0 0
\(288\) 736.000i 0.150588i
\(289\) 817.000 0.166294
\(290\) 1800.00 + 900.000i 0.364482 + 0.182241i
\(291\) 2912.00 0.586613
\(292\) 2528.00i 0.506644i
\(293\) 2292.00i 0.456997i −0.973544 0.228498i \(-0.926618\pi\)
0.973544 0.228498i \(-0.0733816\pi\)
\(294\) 0 0
\(295\) −100.000 + 200.000i −0.0197364 + 0.0394727i
\(296\) 1888.00 0.370736
\(297\) 2800.00i 0.547045i
\(298\) 500.000i 0.0971954i
\(299\) −696.000 −0.134618
\(300\) 800.000 600.000i 0.153960 0.115470i
\(301\) 0 0
\(302\) 4304.00i 0.820091i
\(303\) 1156.00i 0.219176i
\(304\) −960.000 −0.181118
\(305\) −2710.00 + 5420.00i −0.508768 + 1.01754i
\(306\) −2944.00 −0.549991
\(307\) 5406.00i 1.00501i 0.864576 + 0.502503i \(0.167587\pi\)
−0.864576 + 0.502503i \(0.832413\pi\)
\(308\) 0 0
\(309\) −2924.00 −0.538319
\(310\) −2560.00 1280.00i −0.469027 0.234513i
\(311\) 5688.00 1.03710 0.518548 0.855048i \(-0.326473\pi\)
0.518548 + 0.855048i \(0.326473\pi\)
\(312\) 192.000i 0.0348393i
\(313\) 7352.00i 1.32767i −0.747881 0.663833i \(-0.768928\pi\)
0.747881 0.663833i \(-0.231072\pi\)
\(314\) −1048.00 −0.188351
\(315\) 0 0
\(316\) −2880.00 −0.512698
\(317\) 3484.00i 0.617290i 0.951177 + 0.308645i \(0.0998755\pi\)
−0.951177 + 0.308645i \(0.900124\pi\)
\(318\) 432.000i 0.0761804i
\(319\) 2520.00 0.442298
\(320\) −320.000 + 640.000i −0.0559017 + 0.111803i
\(321\) −1932.00 −0.335931
\(322\) 0 0
\(323\) 3840.00i 0.661496i
\(324\) −1684.00 −0.288752
\(325\) −1200.00 + 900.000i −0.204812 + 0.153609i
\(326\) −7036.00 −1.19536
\(327\) 740.000i 0.125144i
\(328\) 1936.00i 0.325908i
\(329\) 0 0
\(330\) 560.000 1120.00i 0.0934151 0.186830i
\(331\) −7868.00 −1.30654 −0.653269 0.757125i \(-0.726603\pi\)
−0.653269 + 0.757125i \(0.726603\pi\)
\(332\) 1912.00i 0.316068i
\(333\) 5428.00i 0.893251i
\(334\) −1068.00 −0.174965
\(335\) 4340.00 + 2170.00i 0.707819 + 0.353910i
\(336\) 0 0
\(337\) 656.000i 0.106037i −0.998594 0.0530187i \(-0.983116\pi\)
0.998594 0.0530187i \(-0.0168843\pi\)
\(338\) 4106.00i 0.660760i
\(339\) −1056.00 −0.169186
\(340\) 2560.00 + 1280.00i 0.408340 + 0.204170i
\(341\) −3584.00 −0.569163
\(342\) 2760.00i 0.436385i
\(343\) 0 0
\(344\) −2896.00 −0.453901
\(345\) −580.000 + 1160.00i −0.0905106 + 0.181021i
\(346\) −8504.00 −1.32132
\(347\) 5754.00i 0.890176i 0.895487 + 0.445088i \(0.146828\pi\)
−0.895487 + 0.445088i \(0.853172\pi\)
\(348\) 720.000i 0.110908i
\(349\) −3110.00 −0.477004 −0.238502 0.971142i \(-0.576656\pi\)
−0.238502 + 0.971142i \(0.576656\pi\)
\(350\) 0 0
\(351\) −1200.00 −0.182482
\(352\) 896.000i 0.135673i
\(353\) 7808.00i 1.17727i 0.808397 + 0.588637i \(0.200335\pi\)
−0.808397 + 0.588637i \(0.799665\pi\)
\(354\) 80.0000 0.0120112
\(355\) −5640.00 + 11280.0i −0.843212 + 1.68642i
\(356\) 1960.00 0.291797
\(357\) 0 0
\(358\) 5000.00i 0.738151i
\(359\) 9240.00 1.35841 0.679204 0.733949i \(-0.262325\pi\)
0.679204 + 0.733949i \(0.262325\pi\)
\(360\) 1840.00 + 920.000i 0.269379 + 0.134690i
\(361\) −3259.00 −0.475142
\(362\) 5156.00i 0.748600i
\(363\) 1094.00i 0.158182i
\(364\) 0 0
\(365\) −6320.00 3160.00i −0.906312 0.453156i
\(366\) 2168.00 0.309626
\(367\) 3214.00i 0.457137i −0.973528 0.228569i \(-0.926595\pi\)
0.973528 0.228569i \(-0.0734046\pi\)
\(368\) 928.000i 0.131455i
\(369\) −5566.00 −0.785242
\(370\) −2360.00 + 4720.00i −0.331596 + 0.663192i
\(371\) 0 0
\(372\) 1024.00i 0.142720i
\(373\) 348.000i 0.0483077i −0.999708 0.0241538i \(-0.992311\pi\)
0.999708 0.0241538i \(-0.00768915\pi\)
\(374\) 3584.00 0.495519
\(375\) 500.000 + 2750.00i 0.0688530 + 0.378692i
\(376\) −1808.00 −0.247980
\(377\) 1080.00i 0.147541i
\(378\) 0 0
\(379\) −4940.00 −0.669527 −0.334764 0.942302i \(-0.608656\pi\)
−0.334764 + 0.942302i \(0.608656\pi\)
\(380\) 1200.00 2400.00i 0.161997 0.323993i
\(381\) 3068.00 0.412542
\(382\) 1536.00i 0.205729i
\(383\) 6142.00i 0.819430i −0.912214 0.409715i \(-0.865628\pi\)
0.912214 0.409715i \(-0.134372\pi\)
\(384\) 256.000 0.0340207
\(385\) 0 0
\(386\) −5216.00 −0.687791
\(387\) 8326.00i 1.09363i
\(388\) 5824.00i 0.762033i
\(389\) −3050.00 −0.397535 −0.198768 0.980047i \(-0.563694\pi\)
−0.198768 + 0.980047i \(0.563694\pi\)
\(390\) 480.000 + 240.000i 0.0623224 + 0.0311612i
\(391\) −3712.00 −0.480112
\(392\) 0 0
\(393\) 24.0000i 0.00308051i
\(394\) −10232.0 −1.30833
\(395\) 3600.00 7200.00i 0.458571 0.917143i
\(396\) 2576.00 0.326891
\(397\) 5396.00i 0.682160i 0.940034 + 0.341080i \(0.110793\pi\)
−0.940034 + 0.341080i \(0.889207\pi\)
\(398\) 6960.00i 0.876566i
\(399\) 0 0
\(400\) −1200.00 1600.00i −0.150000 0.200000i
\(401\) 14482.0 1.80348 0.901741 0.432276i \(-0.142289\pi\)
0.901741 + 0.432276i \(0.142289\pi\)
\(402\) 1736.00i 0.215383i
\(403\) 1536.00i 0.189860i
\(404\) −2312.00 −0.284719
\(405\) 2105.00 4210.00i 0.258267 0.516535i
\(406\) 0 0
\(407\) 6608.00i 0.804782i
\(408\) 1024.00i 0.124254i
\(409\) −1090.00 −0.131778 −0.0658888 0.997827i \(-0.520988\pi\)
−0.0658888 + 0.997827i \(0.520988\pi\)
\(410\) 4840.00 + 2420.00i 0.583001 + 0.291501i
\(411\) 2448.00 0.293798
\(412\) 5848.00i 0.699297i
\(413\) 0 0
\(414\) −2668.00 −0.316727
\(415\) 4780.00 + 2390.00i 0.565400 + 0.282700i
\(416\) −384.000 −0.0452576
\(417\) 6200.00i 0.728094i
\(418\) 3360.00i 0.393165i
\(419\) −7180.00 −0.837150 −0.418575 0.908182i \(-0.637470\pi\)
−0.418575 + 0.908182i \(0.637470\pi\)
\(420\) 0 0
\(421\) −8138.00 −0.942095 −0.471047 0.882108i \(-0.656124\pi\)
−0.471047 + 0.882108i \(0.656124\pi\)
\(422\) 6264.00i 0.722575i
\(423\) 5198.00i 0.597483i
\(424\) 864.000 0.0989612
\(425\) −6400.00 + 4800.00i −0.730460 + 0.547845i
\(426\) 4512.00 0.513162
\(427\) 0 0
\(428\) 3864.00i 0.436387i
\(429\) 672.000 0.0756281
\(430\) 3620.00 7240.00i 0.405981 0.811962i
\(431\) −208.000 −0.0232460 −0.0116230 0.999932i \(-0.503700\pi\)
−0.0116230 + 0.999932i \(0.503700\pi\)
\(432\) 1600.00i 0.178195i
\(433\) 12992.0i 1.44193i −0.692971 0.720965i \(-0.743699\pi\)
0.692971 0.720965i \(-0.256301\pi\)
\(434\) 0 0
\(435\) 1800.00 + 900.000i 0.198399 + 0.0991993i
\(436\) 1480.00 0.162567
\(437\) 3480.00i 0.380940i
\(438\) 2528.00i 0.275782i
\(439\) 1080.00 0.117416 0.0587080 0.998275i \(-0.481302\pi\)
0.0587080 + 0.998275i \(0.481302\pi\)
\(440\) −2240.00 1120.00i −0.242700 0.121350i
\(441\) 0 0
\(442\) 1536.00i 0.165294i
\(443\) 9078.00i 0.973609i −0.873511 0.486805i \(-0.838162\pi\)
0.873511 0.486805i \(-0.161838\pi\)
\(444\) 1888.00 0.201803
\(445\) −2450.00 + 4900.00i −0.260991 + 0.521983i
\(446\) −124.000 −0.0131650
\(447\) 500.000i 0.0529065i
\(448\) 0 0
\(449\) −14310.0 −1.50408 −0.752039 0.659119i \(-0.770929\pi\)
−0.752039 + 0.659119i \(0.770929\pi\)
\(450\) −4600.00 + 3450.00i −0.481880 + 0.361410i
\(451\) 6776.00 0.707471
\(452\) 2112.00i 0.219779i
\(453\) 4304.00i 0.446401i
\(454\) −10628.0 −1.09867
\(455\) 0 0
\(456\) −960.000 −0.0985880
\(457\) 2344.00i 0.239929i 0.992778 + 0.119965i \(0.0382781\pi\)
−0.992778 + 0.119965i \(0.961722\pi\)
\(458\) 380.000i 0.0387691i
\(459\) −6400.00 −0.650820
\(460\) 2320.00 + 1160.00i 0.235153 + 0.117577i
\(461\) −11382.0 −1.14992 −0.574959 0.818182i \(-0.694982\pi\)
−0.574959 + 0.818182i \(0.694982\pi\)
\(462\) 0 0
\(463\) 16062.0i 1.61223i 0.591756 + 0.806117i \(0.298435\pi\)
−0.591756 + 0.806117i \(0.701565\pi\)
\(464\) −1440.00 −0.144074
\(465\) −2560.00 1280.00i −0.255306 0.127653i
\(466\) −4816.00 −0.478749
\(467\) 17166.0i 1.70096i 0.526008 + 0.850479i \(0.323688\pi\)
−0.526008 + 0.850479i \(0.676312\pi\)
\(468\) 1104.00i 0.109044i
\(469\) 0 0
\(470\) 2260.00 4520.00i 0.221800 0.443600i
\(471\) −1048.00 −0.102525
\(472\) 160.000i 0.0156030i
\(473\) 10136.0i 0.985315i
\(474\) −2880.00 −0.279078
\(475\) 4500.00 + 6000.00i 0.434682 + 0.579577i
\(476\) 0 0
\(477\) 2484.00i 0.238437i
\(478\) 11360.0i 1.08702i
\(479\) 7520.00 0.717323 0.358661 0.933468i \(-0.383233\pi\)
0.358661 + 0.933468i \(0.383233\pi\)
\(480\) −320.000 + 640.000i −0.0304290 + 0.0608581i
\(481\) −2832.00 −0.268458
\(482\) 556.000i 0.0525417i
\(483\) 0 0
\(484\) 2188.00 0.205485
\(485\) 14560.0 + 7280.00i 1.36317 + 0.681583i
\(486\) −7084.00 −0.661187
\(487\) 11814.0i 1.09927i 0.835406 + 0.549634i \(0.185233\pi\)
−0.835406 + 0.549634i \(0.814767\pi\)
\(488\) 4336.00i 0.402216i
\(489\) −7036.00 −0.650673
\(490\) 0 0
\(491\) 14052.0 1.29156 0.645782 0.763522i \(-0.276532\pi\)
0.645782 + 0.763522i \(0.276532\pi\)
\(492\) 1936.00i 0.177402i
\(493\) 5760.00i 0.526202i
\(494\) 1440.00 0.131151
\(495\) −3220.00 + 6440.00i −0.292380 + 0.584761i
\(496\) 2048.00 0.185399
\(497\) 0 0
\(498\) 1912.00i 0.172046i
\(499\) −7620.00 −0.683603 −0.341802 0.939772i \(-0.611037\pi\)
−0.341802 + 0.939772i \(0.611037\pi\)
\(500\) 5500.00 1000.00i 0.491935 0.0894427i
\(501\) −1068.00 −0.0952390
\(502\) 6504.00i 0.578262i
\(503\) 1818.00i 0.161154i 0.996748 + 0.0805772i \(0.0256763\pi\)
−0.996748 + 0.0805772i \(0.974324\pi\)
\(504\) 0 0
\(505\) 2890.00 5780.00i 0.254660 0.509320i
\(506\) 3248.00 0.285358
\(507\) 4106.00i 0.359672i
\(508\) 6136.00i 0.535907i
\(509\) 17850.0 1.55440 0.777198 0.629256i \(-0.216640\pi\)
0.777198 + 0.629256i \(0.216640\pi\)
\(510\) 2560.00 + 1280.00i 0.222272 + 0.111136i
\(511\) 0 0
\(512\) 512.000i 0.0441942i
\(513\) 6000.00i 0.516387i
\(514\) 3072.00 0.263619
\(515\) −14620.0 7310.00i −1.25094 0.625470i
\(516\) −2896.00 −0.247072
\(517\) 6328.00i 0.538308i
\(518\) 0 0
\(519\) −8504.00 −0.719237
\(520\) 480.000 960.000i 0.0404796 0.0809592i
\(521\) 19238.0 1.61772 0.808860 0.588001i \(-0.200085\pi\)
0.808860 + 0.588001i \(0.200085\pi\)
\(522\) 4140.00i 0.347132i
\(523\) 6278.00i 0.524891i 0.964947 + 0.262445i \(0.0845289\pi\)
−0.964947 + 0.262445i \(0.915471\pi\)
\(524\) 48.0000 0.00400170
\(525\) 0 0
\(526\) −9716.00 −0.805395
\(527\) 8192.00i 0.677133i
\(528\) 896.000i 0.0738511i
\(529\) 8803.00 0.723514
\(530\) −1080.00 + 2160.00i −0.0885136 + 0.177027i
\(531\) −460.000 −0.0375938
\(532\) 0 0
\(533\) 2904.00i 0.235997i
\(534\) 1960.00 0.158834
\(535\) −9660.00 4830.00i −0.780632 0.390316i
\(536\) −3472.00 −0.279790
\(537\) 5000.00i 0.401799i
\(538\) 5220.00i 0.418309i
\(539\) 0 0
\(540\) 4000.00 + 2000.00i 0.318764 + 0.159382i
\(541\) −9818.00 −0.780238 −0.390119 0.920764i \(-0.627566\pi\)
−0.390119 + 0.920764i \(0.627566\pi\)
\(542\) 10336.0i 0.819131i
\(543\) 5156.00i 0.407486i
\(544\) −2048.00 −0.161410
\(545\) −1850.00 + 3700.00i −0.145404 + 0.290808i
\(546\) 0 0
\(547\) 12514.0i 0.978172i 0.872236 + 0.489086i \(0.162670\pi\)
−0.872236 + 0.489086i \(0.837330\pi\)
\(548\) 4896.00i 0.381655i
\(549\) −12466.0 −0.969100
\(550\) 5600.00 4200.00i 0.434154 0.325616i
\(551\) 5400.00 0.417509
\(552\) 928.000i 0.0715549i
\(553\) 0 0
\(554\) 3848.00 0.295101
\(555\) −2360.00 + 4720.00i −0.180498 + 0.360996i
\(556\) −12400.0 −0.945822
\(557\) 10596.0i 0.806045i −0.915190 0.403022i \(-0.867960\pi\)
0.915190 0.403022i \(-0.132040\pi\)
\(558\) 5888.00i 0.446701i
\(559\) 4344.00 0.328679
\(560\) 0 0
\(561\) 3584.00 0.269727
\(562\) 6084.00i 0.456651i
\(563\) 14002.0i 1.04816i −0.851669 0.524080i \(-0.824409\pi\)
0.851669 0.524080i \(-0.175591\pi\)
\(564\) −1808.00 −0.134983
\(565\) −5280.00 2640.00i −0.393153 0.196576i
\(566\) 3436.00 0.255169
\(567\) 0 0
\(568\) 9024.00i 0.666617i
\(569\) 7330.00 0.540052 0.270026 0.962853i \(-0.412968\pi\)
0.270026 + 0.962853i \(0.412968\pi\)
\(570\) 1200.00 2400.00i 0.0881798 0.176360i
\(571\) 5812.00 0.425963 0.212981 0.977056i \(-0.431683\pi\)
0.212981 + 0.977056i \(0.431683\pi\)
\(572\) 1344.00i 0.0982438i
\(573\) 1536.00i 0.111985i
\(574\) 0 0
\(575\) −5800.00 + 4350.00i −0.420655 + 0.315491i
\(576\) −1472.00 −0.106481
\(577\) 16736.0i 1.20750i 0.797173 + 0.603751i \(0.206328\pi\)
−0.797173 + 0.603751i \(0.793672\pi\)
\(578\) 1634.00i 0.117587i
\(579\) −5216.00 −0.374386
\(580\) 1800.00 3600.00i 0.128864 0.257727i
\(581\) 0 0
\(582\) 5824.00i 0.414798i
\(583\) 3024.00i 0.214822i
\(584\) 5056.00 0.358251
\(585\) −2760.00 1380.00i −0.195063 0.0975316i
\(586\) −4584.00 −0.323146
\(587\) 7434.00i 0.522716i −0.965242 0.261358i \(-0.915830\pi\)
0.965242 0.261358i \(-0.0841702\pi\)
\(588\) 0 0
\(589\) −7680.00 −0.537265
\(590\) 400.000 + 200.000i 0.0279114 + 0.0139557i
\(591\) −10232.0 −0.712163
\(592\) 3776.00i 0.262150i
\(593\) 25872.0i 1.79163i −0.444429 0.895814i \(-0.646593\pi\)
0.444429 0.895814i \(-0.353407\pi\)
\(594\) 5600.00 0.386820
\(595\) 0 0
\(596\) 1000.00 0.0687275
\(597\) 6960.00i 0.477142i
\(598\) 1392.00i 0.0951892i
\(599\) 3720.00 0.253748 0.126874 0.991919i \(-0.459506\pi\)
0.126874 + 0.991919i \(0.459506\pi\)
\(600\) −1200.00 1600.00i −0.0816497 0.108866i
\(601\) 12958.0 0.879481 0.439740 0.898125i \(-0.355070\pi\)
0.439740 + 0.898125i \(0.355070\pi\)
\(602\) 0 0
\(603\) 9982.00i 0.674127i
\(604\) −8608.00 −0.579892
\(605\) −2735.00 + 5470.00i −0.183791 + 0.367582i
\(606\) −2312.00 −0.154981
\(607\) 7214.00i 0.482384i −0.970477 0.241192i \(-0.922462\pi\)
0.970477 0.241192i \(-0.0775384\pi\)
\(608\) 1920.00i 0.128070i
\(609\) 0 0
\(610\) 10840.0 + 5420.00i 0.719506 + 0.359753i
\(611\) 2712.00 0.179568
\(612\) 5888.00i 0.388902i
\(613\) 4828.00i 0.318109i −0.987270 0.159055i \(-0.949155\pi\)
0.987270 0.159055i \(-0.0508446\pi\)
\(614\) 10812.0 0.710646
\(615\) 4840.00 + 2420.00i 0.317346 + 0.158673i
\(616\) 0 0
\(617\) 27656.0i 1.80452i −0.431193 0.902260i \(-0.641907\pi\)
0.431193 0.902260i \(-0.358093\pi\)
\(618\) 5848.00i 0.380649i
\(619\) −21220.0 −1.37787 −0.688937 0.724821i \(-0.741922\pi\)
−0.688937 + 0.724821i \(0.741922\pi\)
\(620\) −2560.00 + 5120.00i −0.165826 + 0.331652i
\(621\) −5800.00 −0.374792
\(622\) 11376.0i 0.733338i
\(623\) 0 0
\(624\) −384.000 −0.0246351
\(625\) −4375.00 + 15000.0i −0.280000 + 0.960000i
\(626\) −14704.0 −0.938802
\(627\) 3360.00i 0.214012i
\(628\) 2096.00i 0.133184i
\(629\) −15104.0 −0.957450
\(630\) 0 0
\(631\) 17672.0 1.11491 0.557457 0.830206i \(-0.311777\pi\)
0.557457 + 0.830206i \(0.311777\pi\)
\(632\) 5760.00i 0.362532i
\(633\) 6264.00i 0.393320i
\(634\) 6968.00 0.436490
\(635\) 15340.0 + 7670.00i 0.958660 + 0.479330i
\(636\) 864.000 0.0538677
\(637\) 0 0
\(638\) 5040.00i 0.312752i
\(639\) −25944.0 −1.60615
\(640\) 1280.00 + 640.000i 0.0790569 + 0.0395285i
\(641\) 7322.00 0.451173 0.225586 0.974223i \(-0.427570\pi\)
0.225586 + 0.974223i \(0.427570\pi\)
\(642\) 3864.00i 0.237539i
\(643\) 8238.00i 0.505249i 0.967564 + 0.252624i \(0.0812937\pi\)
−0.967564 + 0.252624i \(0.918706\pi\)
\(644\) 0 0
\(645\) 3620.00 7240.00i 0.220988 0.441976i
\(646\) 7680.00 0.467749
\(647\) 6426.00i 0.390467i 0.980757 + 0.195233i \(0.0625465\pi\)
−0.980757 + 0.195233i \(0.937454\pi\)
\(648\) 3368.00i 0.204178i
\(649\) 560.000 0.0338705
\(650\) 1800.00 + 2400.00i 0.108618 + 0.144824i
\(651\) 0 0
\(652\) 14072.0i 0.845249i
\(653\) 5908.00i 0.354055i −0.984206 0.177027i \(-0.943352\pi\)
0.984206 0.177027i \(-0.0566482\pi\)
\(654\) 1480.00 0.0884902
\(655\) −60.0000 + 120.000i −0.00357923 + 0.00715845i
\(656\) −3872.00 −0.230452
\(657\) 14536.0i 0.863171i
\(658\) 0 0
\(659\) 26780.0 1.58301 0.791503 0.611166i \(-0.209299\pi\)
0.791503 + 0.611166i \(0.209299\pi\)
\(660\) −2240.00 1120.00i −0.132109 0.0660545i
\(661\) 24538.0 1.44390 0.721950 0.691945i \(-0.243246\pi\)
0.721950 + 0.691945i \(0.243246\pi\)
\(662\) 15736.0i 0.923863i
\(663\) 1536.00i 0.0899748i
\(664\) −3824.00 −0.223494
\(665\) 0 0
\(666\) −10856.0 −0.631624
\(667\) 5220.00i 0.303027i
\(668\) 2136.00i 0.123719i
\(669\) −124.000 −0.00716609
\(670\) 4340.00 8680.00i 0.250252 0.500504i
\(671\) 15176.0 0.873119
\(672\) 0 0
\(673\) 28848.0i 1.65232i −0.563439 0.826158i \(-0.690522\pi\)
0.563439 0.826158i \(-0.309478\pi\)
\(674\) −1312.00 −0.0749798
\(675\) −10000.0 + 7500.00i −0.570222 + 0.427667i
\(676\) −8212.00 −0.467228
\(677\) 26884.0i 1.52620i −0.646282 0.763099i \(-0.723677\pi\)
0.646282 0.763099i \(-0.276323\pi\)
\(678\) 2112.00i 0.119633i
\(679\) 0 0
\(680\) 2560.00 5120.00i 0.144370 0.288740i
\(681\) −10628.0 −0.598041
\(682\) 7168.00i 0.402459i
\(683\) 14282.0i 0.800125i 0.916488 + 0.400063i \(0.131012\pi\)
−0.916488 + 0.400063i \(0.868988\pi\)
\(684\) 5520.00 0.308571
\(685\) 12240.0 + 6120.00i 0.682725 + 0.341362i
\(686\) 0 0
\(687\) 380.000i 0.0211032i
\(688\) 5792.00i 0.320956i
\(689\) −1296.00 −0.0716599
\(690\) 2320.00 + 1160.00i 0.128001 + 0.0640006i
\(691\) 3428.00 0.188723 0.0943613 0.995538i \(-0.469919\pi\)
0.0943613 + 0.995538i \(0.469919\pi\)
\(692\) 17008.0i 0.934317i
\(693\) 0 0
\(694\) 11508.0 0.629449
\(695\) 15500.0 31000.0i 0.845969 1.69194i
\(696\) −1440.00 −0.0784239
\(697\) 15488.0i 0.841678i
\(698\) 6220.00i 0.337293i
\(699\) −4816.00 −0.260598
\(700\) 0 0
\(701\) 26942.0 1.45162 0.725810 0.687895i \(-0.241465\pi\)
0.725810 + 0.687895i \(0.241465\pi\)
\(702\) 2400.00i 0.129034i
\(703\) 14160.0i 0.759679i
\(704\) 1792.00 0.0959354
\(705\) 2260.00 4520.00i 0.120733 0.241465i
\(706\) 15616.0 0.832459
\(707\) 0 0
\(708\) 160.000i 0.00849318i
\(709\) 1950.00 0.103292 0.0516458 0.998665i \(-0.483553\pi\)
0.0516458 + 0.998665i \(0.483553\pi\)
\(710\) 22560.0 + 11280.0i 1.19248 + 0.596241i
\(711\) 16560.0 0.873486
\(712\) 3920.00i 0.206332i
\(713\) 7424.00i 0.389945i
\(714\) 0 0
\(715\) 3360.00 + 1680.00i 0.175744 + 0.0878719i
\(716\) 10000.0 0.521952
\(717\) 11360.0i 0.591697i
\(718\) 18480.0i 0.960540i
\(719\) 12080.0 0.626576 0.313288 0.949658i \(-0.398570\pi\)
0.313288 + 0.949658i \(0.398570\pi\)
\(720\) 1840.00 3680.00i 0.0952399 0.190480i
\(721\) 0 0
\(722\) 6518.00i 0.335976i
\(723\) 556.000i 0.0286001i
\(724\) −10312.0 −0.529340
\(725\) 6750.00 + 9000.00i 0.345778 + 0.461037i
\(726\) 2188.00 0.111852
\(727\) 17226.0i 0.878785i 0.898295 + 0.439393i \(0.144806\pi\)
−0.898295 + 0.439393i \(0.855194\pi\)
\(728\) 0 0
\(729\) 4283.00 0.217599
\(730\) −6320.00 + 12640.0i −0.320430 + 0.640859i
\(731\) 23168.0 1.17223
\(732\) 4336.00i 0.218939i
\(733\) 788.000i 0.0397073i 0.999803 + 0.0198536i \(0.00632003\pi\)
−0.999803 + 0.0198536i \(0.993680\pi\)
\(734\) −6428.00 −0.323245
\(735\) 0 0
\(736\) −1856.00 −0.0929525
\(737\) 12152.0i 0.607360i
\(738\) 11132.0i 0.555250i
\(739\) 2060.00 0.102542 0.0512709 0.998685i \(-0.483673\pi\)
0.0512709 + 0.998685i \(0.483673\pi\)
\(740\) 9440.00 + 4720.00i 0.468948 + 0.234474i
\(741\) 1440.00 0.0713896
\(742\) 0 0
\(743\) 3258.00i 0.160867i −0.996760 0.0804337i \(-0.974369\pi\)
0.996760 0.0804337i \(-0.0256305\pi\)
\(744\) 2048.00 0.100918
\(745\) −1250.00 + 2500.00i −0.0614718 + 0.122944i
\(746\) −696.000 −0.0341587
\(747\) 10994.0i 0.538487i
\(748\) 7168.00i 0.350385i
\(749\) 0 0
\(750\) 5500.00 1000.00i 0.267775 0.0486864i
\(751\) −4528.00 −0.220012 −0.110006 0.993931i \(-0.535087\pi\)
−0.110006 + 0.993931i \(0.535087\pi\)
\(752\) 3616.00i 0.175348i
\(753\) 6504.00i 0.314766i
\(754\) 2160.00 0.104327
\(755\) 10760.0 21520.0i 0.518671 1.03734i
\(756\) 0 0
\(757\) 18236.0i 0.875560i −0.899082 0.437780i \(-0.855765\pi\)
0.899082 0.437780i \(-0.144235\pi\)
\(758\) 9880.00i 0.473427i
\(759\) 3248.00 0.155329
\(760\) −4800.00 2400.00i −0.229098 0.114549i
\(761\) 18678.0 0.889720 0.444860 0.895600i \(-0.353253\pi\)
0.444860 + 0.895600i \(0.353253\pi\)
\(762\) 6136.00i 0.291711i
\(763\) 0 0
\(764\) 3072.00 0.145473
\(765\) −14720.0 7360.00i −0.695690 0.347845i
\(766\) −12284.0 −0.579424
\(767\) 240.000i 0.0112984i
\(768\) 512.000i 0.0240563i
\(769\) 27390.0 1.28441 0.642203 0.766534i \(-0.278020\pi\)
0.642203 + 0.766534i \(0.278020\pi\)
\(770\) 0 0
\(771\) 3072.00 0.143496
\(772\) 10432.0i 0.486342i
\(773\) 9252.00i 0.430493i −0.976560 0.215247i \(-0.930944\pi\)
0.976560 0.215247i \(-0.0690555\pi\)
\(774\) 16652.0 0.773312
\(775\) −9600.00 12800.0i −0.444958 0.593277i
\(776\) −11648.0 −0.538839
\(777\) 0 0
\(778\) 6100.00i 0.281100i
\(779\) 14520.0 0.667822
\(780\) 480.000 960.000i 0.0220343 0.0440686i
\(781\) 31584.0 1.44707
\(782\) 7424.00i 0.339491i
\(783\) 9000.00i 0.410771i
\(784\) 0 0
\(785\) −5240.00 2620.00i −0.238247 0.119123i
\(786\) 48.0000 0.00217825
\(787\)