Properties

Label 128.4.g.a.49.7
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.7
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.65706 - 0.686375i) q^{3} +(-4.13953 + 9.99370i) q^{5} +(-24.2273 - 24.2273i) q^{7} +(-16.8172 + 16.8172i) q^{9} +O(q^{10})\) \(q+(1.65706 - 0.686375i) q^{3} +(-4.13953 + 9.99370i) q^{5} +(-24.2273 - 24.2273i) q^{7} +(-16.8172 + 16.8172i) q^{9} +(-3.73492 - 1.54705i) q^{11} +(-23.2063 - 56.0248i) q^{13} +19.4014i q^{15} +26.9981i q^{17} +(-22.7209 - 54.8531i) q^{19} +(-56.7750 - 23.5170i) q^{21} +(-76.0566 + 76.0566i) q^{23} +(5.64994 + 5.64994i) q^{25} +(-34.8562 + 84.1503i) q^{27} +(-108.152 + 44.7980i) q^{29} -176.000 q^{31} -7.25082 q^{33} +(342.410 - 141.831i) q^{35} +(129.191 - 311.894i) q^{37} +(-76.9081 - 76.9081i) q^{39} +(70.4988 - 70.4988i) q^{41} +(103.155 + 42.7281i) q^{43} +(-98.4506 - 237.681i) q^{45} +249.437i q^{47} +830.925i q^{49} +(18.5308 + 44.7374i) q^{51} +(597.516 + 247.499i) q^{53} +(30.9216 - 30.9216i) q^{55} +(-75.2996 - 75.2996i) q^{57} +(75.6443 - 182.622i) q^{59} +(-309.654 + 128.263i) q^{61} +814.869 q^{63} +655.959 q^{65} +(297.717 - 123.318i) q^{67} +(-73.8267 + 178.233i) q^{69} +(-675.279 - 675.279i) q^{71} +(350.175 - 350.175i) q^{73} +(13.2403 + 5.48429i) q^{75} +(53.0061 + 127.968i) q^{77} +564.246i q^{79} -478.776i q^{81} +(-105.327 - 254.281i) q^{83} +(-269.811 - 111.760i) q^{85} +(-148.465 + 148.465i) q^{87} +(-448.959 - 448.959i) q^{89} +(-795.106 + 1919.56i) q^{91} +(-291.641 + 120.802i) q^{93} +642.239 q^{95} -1765.41 q^{97} +(88.8278 - 36.7937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.65706 0.686375i 0.318900 0.132093i −0.217491 0.976062i \(-0.569787\pi\)
0.536391 + 0.843969i \(0.319787\pi\)
\(4\) 0 0
\(5\) −4.13953 + 9.99370i −0.370251 + 0.893864i 0.623457 + 0.781858i \(0.285728\pi\)
−0.993708 + 0.112006i \(0.964272\pi\)
\(6\) 0 0
\(7\) −24.2273 24.2273i −1.30815 1.30815i −0.922748 0.385403i \(-0.874062\pi\)
−0.385403 0.922748i \(-0.625938\pi\)
\(8\) 0 0
\(9\) −16.8172 + 16.8172i −0.622858 + 0.622858i
\(10\) 0 0
\(11\) −3.73492 1.54705i −0.102375 0.0424049i 0.330908 0.943663i \(-0.392645\pi\)
−0.433283 + 0.901258i \(0.642645\pi\)
\(12\) 0 0
\(13\) −23.2063 56.0248i −0.495097 1.19527i −0.952095 0.305802i \(-0.901076\pi\)
0.456999 0.889467i \(-0.348924\pi\)
\(14\) 0 0
\(15\) 19.4014i 0.333961i
\(16\) 0 0
\(17\) 26.9981i 0.385177i 0.981280 + 0.192589i \(0.0616883\pi\)
−0.981280 + 0.192589i \(0.938312\pi\)
\(18\) 0 0
\(19\) −22.7209 54.8531i −0.274344 0.662324i 0.725316 0.688416i \(-0.241694\pi\)
−0.999660 + 0.0260920i \(0.991694\pi\)
\(20\) 0 0
\(21\) −56.7750 23.5170i −0.589968 0.244373i
\(22\) 0 0
\(23\) −76.0566 + 76.0566i −0.689517 + 0.689517i −0.962125 0.272608i \(-0.912114\pi\)
0.272608 + 0.962125i \(0.412114\pi\)
\(24\) 0 0
\(25\) 5.64994 + 5.64994i 0.0451996 + 0.0451996i
\(26\) 0 0
\(27\) −34.8562 + 84.1503i −0.248447 + 0.599805i
\(28\) 0 0
\(29\) −108.152 + 44.7980i −0.692527 + 0.286854i −0.701053 0.713109i \(-0.747286\pi\)
0.00852531 + 0.999964i \(0.497286\pi\)
\(30\) 0 0
\(31\) −176.000 −1.01969 −0.509846 0.860266i \(-0.670298\pi\)
−0.509846 + 0.860266i \(0.670298\pi\)
\(32\) 0 0
\(33\) −7.25082 −0.0382487
\(34\) 0 0
\(35\) 342.410 141.831i 1.65365 0.684966i
\(36\) 0 0
\(37\) 129.191 311.894i 0.574021 1.38581i −0.324083 0.946029i \(-0.605056\pi\)
0.898105 0.439782i \(-0.144944\pi\)
\(38\) 0 0
\(39\) −76.9081 76.9081i −0.315773 0.315773i
\(40\) 0 0
\(41\) 70.4988 70.4988i 0.268538 0.268538i −0.559973 0.828511i \(-0.689188\pi\)
0.828511 + 0.559973i \(0.189188\pi\)
\(42\) 0 0
\(43\) 103.155 + 42.7281i 0.365836 + 0.151534i 0.558026 0.829824i \(-0.311559\pi\)
−0.192190 + 0.981358i \(0.561559\pi\)
\(44\) 0 0
\(45\) −98.4506 237.681i −0.326137 0.787364i
\(46\) 0 0
\(47\) 249.437i 0.774131i 0.922052 + 0.387066i \(0.126511\pi\)
−0.922052 + 0.387066i \(0.873489\pi\)
\(48\) 0 0
\(49\) 830.925i 2.42252i
\(50\) 0 0
\(51\) 18.5308 + 44.7374i 0.0508792 + 0.122833i
\(52\) 0 0
\(53\) 597.516 + 247.499i 1.54859 + 0.641446i 0.983060 0.183282i \(-0.0586723\pi\)
0.565528 + 0.824729i \(0.308672\pi\)
\(54\) 0 0
\(55\) 30.9216 30.9216i 0.0758085 0.0758085i
\(56\) 0 0
\(57\) −75.2996 75.2996i −0.174977 0.174977i
\(58\) 0 0
\(59\) 75.6443 182.622i 0.166916 0.402971i −0.818183 0.574958i \(-0.805019\pi\)
0.985099 + 0.171986i \(0.0550185\pi\)
\(60\) 0 0
\(61\) −309.654 + 128.263i −0.649953 + 0.269219i −0.683204 0.730228i \(-0.739414\pi\)
0.0332511 + 0.999447i \(0.489414\pi\)
\(62\) 0 0
\(63\) 814.869 1.62958
\(64\) 0 0
\(65\) 655.959 1.25172
\(66\) 0 0
\(67\) 297.717 123.318i 0.542864 0.224862i −0.0943627 0.995538i \(-0.530081\pi\)
0.637227 + 0.770676i \(0.280081\pi\)
\(68\) 0 0
\(69\) −73.8267 + 178.233i −0.128807 + 0.310968i
\(70\) 0 0
\(71\) −675.279 675.279i −1.12874 1.12874i −0.990382 0.138363i \(-0.955816\pi\)
−0.138363 0.990382i \(-0.544184\pi\)
\(72\) 0 0
\(73\) 350.175 350.175i 0.561437 0.561437i −0.368279 0.929715i \(-0.620053\pi\)
0.929715 + 0.368279i \(0.120053\pi\)
\(74\) 0 0
\(75\) 13.2403 + 5.48429i 0.0203847 + 0.00844362i
\(76\) 0 0
\(77\) 53.0061 + 127.968i 0.0784494 + 0.189393i
\(78\) 0 0
\(79\) 564.246i 0.803578i 0.915732 + 0.401789i \(0.131611\pi\)
−0.915732 + 0.401789i \(0.868389\pi\)
\(80\) 0 0
\(81\) 478.776i 0.656758i
\(82\) 0 0
\(83\) −105.327 254.281i −0.139290 0.336276i 0.838806 0.544431i \(-0.183254\pi\)
−0.978096 + 0.208155i \(0.933254\pi\)
\(84\) 0 0
\(85\) −269.811 111.760i −0.344296 0.142612i
\(86\) 0 0
\(87\) −148.465 + 148.465i −0.182956 + 0.182956i
\(88\) 0 0
\(89\) −448.959 448.959i −0.534715 0.534715i 0.387257 0.921972i \(-0.373423\pi\)
−0.921972 + 0.387257i \(0.873423\pi\)
\(90\) 0 0
\(91\) −795.106 + 1919.56i −0.915932 + 2.21125i
\(92\) 0 0
\(93\) −291.641 + 120.802i −0.325180 + 0.134694i
\(94\) 0 0
\(95\) 642.239 0.693604
\(96\) 0 0
\(97\) −1765.41 −1.84794 −0.923972 0.382459i \(-0.875077\pi\)
−0.923972 + 0.382459i \(0.875077\pi\)
\(98\) 0 0
\(99\) 88.8278 36.7937i 0.0901770 0.0373526i
\(100\) 0 0
\(101\) 298.207 719.936i 0.293790 0.709271i −0.706210 0.708003i \(-0.749596\pi\)
0.999999 0.00126791i \(-0.000403589\pi\)
\(102\) 0 0
\(103\) 228.925 + 228.925i 0.218997 + 0.218997i 0.808076 0.589079i \(-0.200509\pi\)
−0.589079 + 0.808076i \(0.700509\pi\)
\(104\) 0 0
\(105\) 470.043 470.043i 0.436872 0.436872i
\(106\) 0 0
\(107\) −1637.14 678.126i −1.47914 0.612681i −0.510221 0.860044i \(-0.670436\pi\)
−0.968923 + 0.247362i \(0.920436\pi\)
\(108\) 0 0
\(109\) 154.640 + 373.333i 0.135888 + 0.328063i 0.977145 0.212572i \(-0.0681841\pi\)
−0.841257 + 0.540635i \(0.818184\pi\)
\(110\) 0 0
\(111\) 605.498i 0.517760i
\(112\) 0 0
\(113\) 681.111i 0.567023i 0.958969 + 0.283511i \(0.0914993\pi\)
−0.958969 + 0.283511i \(0.908501\pi\)
\(114\) 0 0
\(115\) −445.249 1074.93i −0.361041 0.871629i
\(116\) 0 0
\(117\) 1332.44 + 551.916i 1.05286 + 0.436108i
\(118\) 0 0
\(119\) 654.092 654.092i 0.503870 0.503870i
\(120\) 0 0
\(121\) −929.603 929.603i −0.698424 0.698424i
\(122\) 0 0
\(123\) 68.4318 165.209i 0.0501649 0.121109i
\(124\) 0 0
\(125\) −1329.06 + 550.517i −0.951001 + 0.393918i
\(126\) 0 0
\(127\) −574.582 −0.401464 −0.200732 0.979646i \(-0.564332\pi\)
−0.200732 + 0.979646i \(0.564332\pi\)
\(128\) 0 0
\(129\) 200.261 0.136682
\(130\) 0 0
\(131\) −749.541 + 310.470i −0.499906 + 0.207068i −0.618365 0.785891i \(-0.712205\pi\)
0.118459 + 0.992959i \(0.462205\pi\)
\(132\) 0 0
\(133\) −778.476 + 1879.41i −0.507537 + 1.22530i
\(134\) 0 0
\(135\) −696.685 696.685i −0.444156 0.444156i
\(136\) 0 0
\(137\) −274.564 + 274.564i −0.171223 + 0.171223i −0.787517 0.616293i \(-0.788634\pi\)
0.616293 + 0.787517i \(0.288634\pi\)
\(138\) 0 0
\(139\) 239.497 + 99.2027i 0.146143 + 0.0605343i 0.454556 0.890718i \(-0.349798\pi\)
−0.308413 + 0.951252i \(0.599798\pi\)
\(140\) 0 0
\(141\) 171.208 + 413.331i 0.102257 + 0.246871i
\(142\) 0 0
\(143\) 245.150i 0.143360i
\(144\) 0 0
\(145\) 1266.28i 0.725233i
\(146\) 0 0
\(147\) 570.326 + 1376.89i 0.319998 + 0.772543i
\(148\) 0 0
\(149\) 176.116 + 72.9498i 0.0968323 + 0.0401092i 0.430574 0.902555i \(-0.358311\pi\)
−0.333741 + 0.942665i \(0.608311\pi\)
\(150\) 0 0
\(151\) 339.506 339.506i 0.182971 0.182971i −0.609678 0.792649i \(-0.708701\pi\)
0.792649 + 0.609678i \(0.208701\pi\)
\(152\) 0 0
\(153\) −454.032 454.032i −0.239911 0.239911i
\(154\) 0 0
\(155\) 728.555 1758.89i 0.377542 0.911466i
\(156\) 0 0
\(157\) 1222.00 506.170i 0.621188 0.257304i −0.0498158 0.998758i \(-0.515863\pi\)
0.671004 + 0.741454i \(0.265863\pi\)
\(158\) 0 0
\(159\) 1160.00 0.578576
\(160\) 0 0
\(161\) 3685.29 1.80399
\(162\) 0 0
\(163\) −1346.92 + 557.911i −0.647231 + 0.268092i −0.682054 0.731302i \(-0.738913\pi\)
0.0348231 + 0.999393i \(0.488913\pi\)
\(164\) 0 0
\(165\) 30.0150 72.4626i 0.0141616 0.0341891i
\(166\) 0 0
\(167\) 2521.77 + 2521.77i 1.16851 + 1.16851i 0.982560 + 0.185946i \(0.0595351\pi\)
0.185946 + 0.982560i \(0.440465\pi\)
\(168\) 0 0
\(169\) −1046.74 + 1046.74i −0.476440 + 0.476440i
\(170\) 0 0
\(171\) 1304.57 + 540.372i 0.583411 + 0.241657i
\(172\) 0 0
\(173\) −541.973 1308.44i −0.238182 0.575022i 0.758913 0.651192i \(-0.225731\pi\)
−0.997095 + 0.0761701i \(0.975731\pi\)
\(174\) 0 0
\(175\) 273.766i 0.118256i
\(176\) 0 0
\(177\) 354.534i 0.150556i
\(178\) 0 0
\(179\) 54.1456 + 130.719i 0.0226091 + 0.0545833i 0.934781 0.355225i \(-0.115596\pi\)
−0.912172 + 0.409808i \(0.865596\pi\)
\(180\) 0 0
\(181\) −1585.39 656.689i −0.651055 0.269676i 0.0326139 0.999468i \(-0.489617\pi\)
−0.683669 + 0.729792i \(0.739617\pi\)
\(182\) 0 0
\(183\) −425.077 + 425.077i −0.171708 + 0.171708i
\(184\) 0 0
\(185\) 2582.18 + 2582.18i 1.02619 + 1.02619i
\(186\) 0 0
\(187\) 41.7676 100.836i 0.0163334 0.0394323i
\(188\) 0 0
\(189\) 2883.21 1194.26i 1.10964 0.459629i
\(190\) 0 0
\(191\) −2679.22 −1.01498 −0.507490 0.861658i \(-0.669427\pi\)
−0.507490 + 0.861658i \(0.669427\pi\)
\(192\) 0 0
\(193\) −3139.34 −1.17085 −0.585426 0.810726i \(-0.699073\pi\)
−0.585426 + 0.810726i \(0.699073\pi\)
\(194\) 0 0
\(195\) 1086.96 450.233i 0.399173 0.165343i
\(196\) 0 0
\(197\) 1321.44 3190.23i 0.477911 1.15378i −0.482675 0.875799i \(-0.660335\pi\)
0.960587 0.277981i \(-0.0896652\pi\)
\(198\) 0 0
\(199\) 106.853 + 106.853i 0.0380632 + 0.0380632i 0.725882 0.687819i \(-0.241432\pi\)
−0.687819 + 0.725882i \(0.741432\pi\)
\(200\) 0 0
\(201\) 408.691 408.691i 0.143417 0.143417i
\(202\) 0 0
\(203\) 3705.56 + 1534.89i 1.28118 + 0.530682i
\(204\) 0 0
\(205\) 412.712 + 996.375i 0.140610 + 0.339463i
\(206\) 0 0
\(207\) 2558.11i 0.858943i
\(208\) 0 0
\(209\) 240.022i 0.0794387i
\(210\) 0 0
\(211\) 1037.64 + 2505.10i 0.338552 + 0.817336i 0.997855 + 0.0654593i \(0.0208512\pi\)
−0.659304 + 0.751877i \(0.729149\pi\)
\(212\) 0 0
\(213\) −1582.47 655.480i −0.509056 0.210858i
\(214\) 0 0
\(215\) −854.024 + 854.024i −0.270902 + 0.270902i
\(216\) 0 0
\(217\) 4264.00 + 4264.00i 1.33391 + 1.33391i
\(218\) 0 0
\(219\) 339.908 820.611i 0.104881 0.253204i
\(220\) 0 0
\(221\) 1512.57 626.526i 0.460390 0.190700i
\(222\) 0 0
\(223\) −3307.18 −0.993119 −0.496559 0.868003i \(-0.665404\pi\)
−0.496559 + 0.868003i \(0.665404\pi\)
\(224\) 0 0
\(225\) −190.032 −0.0563058
\(226\) 0 0
\(227\) 5187.26 2148.63i 1.51670 0.628237i 0.539771 0.841812i \(-0.318511\pi\)
0.976927 + 0.213575i \(0.0685108\pi\)
\(228\) 0 0
\(229\) −1736.52 + 4192.34i −0.501103 + 1.20977i 0.447780 + 0.894144i \(0.352215\pi\)
−0.948883 + 0.315627i \(0.897785\pi\)
\(230\) 0 0
\(231\) 175.668 + 175.668i 0.0500351 + 0.0500351i
\(232\) 0 0
\(233\) −817.096 + 817.096i −0.229741 + 0.229741i −0.812585 0.582843i \(-0.801940\pi\)
0.582843 + 0.812585i \(0.301940\pi\)
\(234\) 0 0
\(235\) −2492.80 1032.55i −0.691968 0.286623i
\(236\) 0 0
\(237\) 387.284 + 934.987i 0.106147 + 0.256261i
\(238\) 0 0
\(239\) 2423.25i 0.655844i 0.944705 + 0.327922i \(0.106348\pi\)
−0.944705 + 0.327922i \(0.893652\pi\)
\(240\) 0 0
\(241\) 3879.72i 1.03699i −0.855080 0.518496i \(-0.826492\pi\)
0.855080 0.518496i \(-0.173508\pi\)
\(242\) 0 0
\(243\) −1269.74 3065.42i −0.335200 0.809246i
\(244\) 0 0
\(245\) −8304.01 3439.63i −2.16540 0.896940i
\(246\) 0 0
\(247\) −2545.87 + 2545.87i −0.655829 + 0.655829i
\(248\) 0 0
\(249\) −349.064 349.064i −0.0888394 0.0888394i
\(250\) 0 0
\(251\) 2070.97 4999.76i 0.520791 1.25730i −0.416622 0.909080i \(-0.636786\pi\)
0.937413 0.348220i \(-0.113214\pi\)
\(252\) 0 0
\(253\) 401.729 166.402i 0.0998280 0.0413501i
\(254\) 0 0
\(255\) −523.801 −0.128634
\(256\) 0 0
\(257\) −1525.85 −0.370349 −0.185175 0.982706i \(-0.559285\pi\)
−0.185175 + 0.982706i \(0.559285\pi\)
\(258\) 0 0
\(259\) −10686.3 + 4426.40i −2.56376 + 1.06194i
\(260\) 0 0
\(261\) 1065.43 2572.18i 0.252677 0.610016i
\(262\) 0 0
\(263\) −532.444 532.444i −0.124836 0.124836i 0.641928 0.766765i \(-0.278135\pi\)
−0.766765 + 0.641928i \(0.778135\pi\)
\(264\) 0 0
\(265\) −4946.87 + 4946.87i −1.14673 + 1.14673i
\(266\) 0 0
\(267\) −1052.11 435.796i −0.241153 0.0998888i
\(268\) 0 0
\(269\) −930.585 2246.63i −0.210925 0.509217i 0.782641 0.622473i \(-0.213872\pi\)
−0.993566 + 0.113256i \(0.963872\pi\)
\(270\) 0 0
\(271\) 3425.60i 0.767862i −0.923362 0.383931i \(-0.874570\pi\)
0.923362 0.383931i \(-0.125430\pi\)
\(272\) 0 0
\(273\) 3726.55i 0.826158i
\(274\) 0 0
\(275\) −12.3613 29.8428i −0.00271060 0.00654397i
\(276\) 0 0
\(277\) 4215.07 + 1745.94i 0.914293 + 0.378712i 0.789698 0.613495i \(-0.210237\pi\)
0.124594 + 0.992208i \(0.460237\pi\)
\(278\) 0 0
\(279\) 2959.81 2959.81i 0.635123 0.635123i
\(280\) 0 0
\(281\) −2404.35 2404.35i −0.510433 0.510433i 0.404226 0.914659i \(-0.367541\pi\)
−0.914659 + 0.404226i \(0.867541\pi\)
\(282\) 0 0
\(283\) 3013.10 7274.27i 0.632899 1.52795i −0.203063 0.979166i \(-0.565090\pi\)
0.835962 0.548787i \(-0.184910\pi\)
\(284\) 0 0
\(285\) 1064.23 440.817i 0.221191 0.0916201i
\(286\) 0 0
\(287\) −3415.99 −0.702577
\(288\) 0 0
\(289\) 4184.10 0.851638
\(290\) 0 0
\(291\) −2925.39 + 1211.74i −0.589310 + 0.244100i
\(292\) 0 0
\(293\) −1059.63 + 2558.17i −0.211277 + 0.510068i −0.993620 0.112780i \(-0.964025\pi\)
0.782343 + 0.622848i \(0.214025\pi\)
\(294\) 0 0
\(295\) 1511.93 + 1511.93i 0.298401 + 0.298401i
\(296\) 0 0
\(297\) 260.370 260.370i 0.0508694 0.0508694i
\(298\) 0 0
\(299\) 6026.05 + 2496.07i 1.16554 + 0.482781i
\(300\) 0 0
\(301\) −1463.97 3534.35i −0.280339 0.676799i
\(302\) 0 0
\(303\) 1397.66i 0.264994i
\(304\) 0 0
\(305\) 3625.54i 0.680648i
\(306\) 0 0
\(307\) 3277.84 + 7913.41i 0.609369 + 1.47115i 0.863688 + 0.504027i \(0.168149\pi\)
−0.254319 + 0.967120i \(0.581851\pi\)
\(308\) 0 0
\(309\) 536.470 + 222.213i 0.0987660 + 0.0409102i
\(310\) 0 0
\(311\) −5107.89 + 5107.89i −0.931324 + 0.931324i −0.997789 0.0664648i \(-0.978828\pi\)
0.0664648 + 0.997789i \(0.478828\pi\)
\(312\) 0 0
\(313\) −1761.64 1761.64i −0.318128 0.318128i 0.529920 0.848048i \(-0.322222\pi\)
−0.848048 + 0.529920i \(0.822222\pi\)
\(314\) 0 0
\(315\) −3373.17 + 8143.56i −0.603355 + 1.45663i
\(316\) 0 0
\(317\) −4091.81 + 1694.88i −0.724981 + 0.300297i −0.714488 0.699648i \(-0.753340\pi\)
−0.0104934 + 0.999945i \(0.503340\pi\)
\(318\) 0 0
\(319\) 473.243 0.0830612
\(320\) 0 0
\(321\) −3178.28 −0.552630
\(322\) 0 0
\(323\) 1480.93 613.422i 0.255112 0.105671i
\(324\) 0 0
\(325\) 185.423 447.651i 0.0316475 0.0764038i
\(326\) 0 0
\(327\) 512.493 + 512.493i 0.0866695 + 0.0866695i
\(328\) 0 0
\(329\) 6043.19 6043.19i 1.01268 1.01268i
\(330\) 0 0
\(331\) −6396.05 2649.33i −1.06211 0.439941i −0.217911 0.975969i \(-0.569924\pi\)
−0.844200 + 0.536028i \(0.819924\pi\)
\(332\) 0 0
\(333\) 3072.55 + 7417.78i 0.505629 + 1.22070i
\(334\) 0 0
\(335\) 3485.77i 0.568502i
\(336\) 0 0
\(337\) 3692.32i 0.596835i −0.954435 0.298418i \(-0.903541\pi\)
0.954435 0.298418i \(-0.0964588\pi\)
\(338\) 0 0
\(339\) 467.498 + 1128.64i 0.0748997 + 0.180824i
\(340\) 0 0
\(341\) 657.344 + 272.281i 0.104391 + 0.0432400i
\(342\) 0 0
\(343\) 11821.1 11821.1i 1.86087 1.86087i
\(344\) 0 0
\(345\) −1475.60 1475.60i −0.230272 0.230272i
\(346\) 0 0
\(347\) −3771.01 + 9104.01i −0.583395 + 1.40844i 0.306322 + 0.951928i \(0.400902\pi\)
−0.889717 + 0.456513i \(0.849098\pi\)
\(348\) 0 0
\(349\) 2347.30 972.282i 0.360023 0.149126i −0.195338 0.980736i \(-0.562580\pi\)
0.555360 + 0.831610i \(0.312580\pi\)
\(350\) 0 0
\(351\) 5523.39 0.839934
\(352\) 0 0
\(353\) 822.940 0.124081 0.0620406 0.998074i \(-0.480239\pi\)
0.0620406 + 0.998074i \(0.480239\pi\)
\(354\) 0 0
\(355\) 9543.87 3953.20i 1.42686 0.591026i
\(356\) 0 0
\(357\) 634.915 1532.82i 0.0941268 0.227242i
\(358\) 0 0
\(359\) 3701.59 + 3701.59i 0.544185 + 0.544185i 0.924753 0.380568i \(-0.124272\pi\)
−0.380568 + 0.924753i \(0.624272\pi\)
\(360\) 0 0
\(361\) 2357.42 2357.42i 0.343698 0.343698i
\(362\) 0 0
\(363\) −2178.46 902.347i −0.314985 0.130471i
\(364\) 0 0
\(365\) 2049.99 + 4949.10i 0.293976 + 0.709720i
\(366\) 0 0
\(367\) 3736.68i 0.531479i −0.964045 0.265740i \(-0.914384\pi\)
0.964045 0.265740i \(-0.0856162\pi\)
\(368\) 0 0
\(369\) 2371.18i 0.334522i
\(370\) 0 0
\(371\) −8479.97 20472.5i −1.18668 2.86490i
\(372\) 0 0
\(373\) 8948.08 + 3706.42i 1.24213 + 0.514507i 0.904379 0.426729i \(-0.140334\pi\)
0.337750 + 0.941236i \(0.390334\pi\)
\(374\) 0 0
\(375\) −1824.47 + 1824.47i −0.251241 + 0.251241i
\(376\) 0 0
\(377\) 5019.60 + 5019.60i 0.685736 + 0.685736i
\(378\) 0 0
\(379\) −761.220 + 1837.75i −0.103170 + 0.249073i −0.967032 0.254654i \(-0.918038\pi\)
0.863863 + 0.503727i \(0.168038\pi\)
\(380\) 0 0
\(381\) −952.114 + 394.379i −0.128027 + 0.0530305i
\(382\) 0 0
\(383\) 12159.8 1.62229 0.811143 0.584848i \(-0.198846\pi\)
0.811143 + 0.584848i \(0.198846\pi\)
\(384\) 0 0
\(385\) −1498.29 −0.198338
\(386\) 0 0
\(387\) −2453.33 + 1016.20i −0.322248 + 0.133480i
\(388\) 0 0
\(389\) −2365.98 + 5711.99i −0.308381 + 0.744497i 0.691377 + 0.722494i \(0.257004\pi\)
−0.999758 + 0.0220031i \(0.992996\pi\)
\(390\) 0 0
\(391\) −2053.39 2053.39i −0.265586 0.265586i
\(392\) 0 0
\(393\) −1028.93 + 1028.93i −0.132068 + 0.132068i
\(394\) 0 0
\(395\) −5638.91 2335.71i −0.718289 0.297525i
\(396\) 0 0
\(397\) −533.914 1288.98i −0.0674972 0.162953i 0.886531 0.462669i \(-0.153108\pi\)
−0.954028 + 0.299716i \(0.903108\pi\)
\(398\) 0 0
\(399\) 3648.61i 0.457792i
\(400\) 0 0
\(401\) 4956.51i 0.617248i 0.951184 + 0.308624i \(0.0998685\pi\)
−0.951184 + 0.308624i \(0.900131\pi\)
\(402\) 0 0
\(403\) 4084.29 + 9860.35i 0.504846 + 1.21881i
\(404\) 0 0
\(405\) 4784.75 + 1981.91i 0.587052 + 0.243165i
\(406\) 0 0
\(407\) −965.032 + 965.032i −0.117530 + 0.117530i
\(408\) 0 0
\(409\) −3226.79 3226.79i −0.390108 0.390108i 0.484618 0.874726i \(-0.338959\pi\)
−0.874726 + 0.484618i \(0.838959\pi\)
\(410\) 0 0
\(411\) −266.514 + 643.422i −0.0319858 + 0.0772205i
\(412\) 0 0
\(413\) −6257.08 + 2591.77i −0.745499 + 0.308796i
\(414\) 0 0
\(415\) 2977.21 0.352158
\(416\) 0 0
\(417\) 464.949 0.0546011
\(418\) 0 0
\(419\) 1822.54 754.920i 0.212498 0.0880197i −0.273895 0.961760i \(-0.588312\pi\)
0.486394 + 0.873740i \(0.338312\pi\)
\(420\) 0 0
\(421\) −215.665 + 520.662i −0.0249664 + 0.0602743i −0.935871 0.352343i \(-0.885385\pi\)
0.910905 + 0.412617i \(0.135385\pi\)
\(422\) 0 0
\(423\) −4194.83 4194.83i −0.482174 0.482174i
\(424\) 0 0
\(425\) −152.538 + 152.538i −0.0174098 + 0.0174098i
\(426\) 0 0
\(427\) 10609.5 + 4394.61i 1.20242 + 0.498057i
\(428\) 0 0
\(429\) 168.264 + 406.226i 0.0189368 + 0.0457175i
\(430\) 0 0
\(431\) 2199.14i 0.245775i 0.992421 + 0.122888i \(0.0392155\pi\)
−0.992421 + 0.122888i \(0.960785\pi\)
\(432\) 0 0
\(433\) 273.133i 0.0303139i −0.999885 0.0151569i \(-0.995175\pi\)
0.999885 0.0151569i \(-0.00482479\pi\)
\(434\) 0 0
\(435\) −869.143 2098.30i −0.0957982 0.231277i
\(436\) 0 0
\(437\) 5900.01 + 2443.87i 0.645849 + 0.267519i
\(438\) 0 0
\(439\) −2910.64 + 2910.64i −0.316440 + 0.316440i −0.847398 0.530958i \(-0.821832\pi\)
0.530958 + 0.847398i \(0.321832\pi\)
\(440\) 0 0
\(441\) −13973.8 13973.8i −1.50889 1.50889i
\(442\) 0 0
\(443\) −1439.20 + 3474.54i −0.154353 + 0.372642i −0.982073 0.188499i \(-0.939638\pi\)
0.827720 + 0.561142i \(0.189638\pi\)
\(444\) 0 0
\(445\) 6345.25 2628.29i 0.675941 0.279984i
\(446\) 0 0
\(447\) 341.905 0.0361780
\(448\) 0 0
\(449\) 13543.2 1.42348 0.711738 0.702445i \(-0.247908\pi\)
0.711738 + 0.702445i \(0.247908\pi\)
\(450\) 0 0
\(451\) −372.373 + 154.242i −0.0388788 + 0.0161041i
\(452\) 0 0
\(453\) 329.552 795.609i 0.0341804 0.0825187i
\(454\) 0 0
\(455\) −15892.1 15892.1i −1.63744 1.63744i
\(456\) 0 0
\(457\) 3832.14 3832.14i 0.392253 0.392253i −0.483237 0.875490i \(-0.660539\pi\)
0.875490 + 0.483237i \(0.160539\pi\)
\(458\) 0 0
\(459\) −2271.90 941.053i −0.231031 0.0956963i
\(460\) 0 0
\(461\) −6014.95 14521.4i −0.607688 1.46709i −0.865508 0.500895i \(-0.833004\pi\)
0.257821 0.966193i \(-0.416996\pi\)
\(462\) 0 0
\(463\) 13168.4i 1.32178i 0.750481 + 0.660892i \(0.229822\pi\)
−0.750481 + 0.660892i \(0.770178\pi\)
\(464\) 0 0
\(465\) 3414.64i 0.340537i
\(466\) 0 0
\(467\) 2737.75 + 6609.51i 0.271280 + 0.654929i 0.999539 0.0303741i \(-0.00966986\pi\)
−0.728258 + 0.685303i \(0.759670\pi\)
\(468\) 0 0
\(469\) −10200.6 4225.21i −1.00430 0.415996i
\(470\) 0 0
\(471\) 1677.50 1677.50i 0.164109 0.164109i
\(472\) 0 0
\(473\) −319.172 319.172i −0.0310265 0.0310265i
\(474\) 0 0
\(475\) 181.545 438.289i 0.0175365 0.0423370i
\(476\) 0 0
\(477\) −14210.8 + 5886.29i −1.36408 + 0.565021i
\(478\) 0 0
\(479\) 2141.84 0.204307 0.102153 0.994769i \(-0.467427\pi\)
0.102153 + 0.994769i \(0.467427\pi\)
\(480\) 0 0
\(481\) −20471.8 −1.94061
\(482\) 0 0
\(483\) 6106.74 2529.49i 0.575292 0.238294i
\(484\) 0 0
\(485\) 7307.98 17643.0i 0.684203 1.65181i
\(486\) 0 0
\(487\) 3210.83 + 3210.83i 0.298761 + 0.298761i 0.840528 0.541767i \(-0.182245\pi\)
−0.541767 + 0.840528i \(0.682245\pi\)
\(488\) 0 0
\(489\) −1848.98 + 1848.98i −0.170989 + 0.170989i
\(490\) 0 0
\(491\) −10597.1 4389.47i −0.974015 0.403450i −0.161810 0.986822i \(-0.551733\pi\)
−0.812205 + 0.583372i \(0.801733\pi\)
\(492\) 0 0
\(493\) −1209.46 2919.90i −0.110490 0.266746i
\(494\) 0 0
\(495\) 1040.03i 0.0944358i
\(496\) 0 0
\(497\) 32720.4i 2.95314i
\(498\) 0 0
\(499\) −3963.81 9569.49i −0.355600 0.858495i −0.995908 0.0903763i \(-0.971193\pi\)
0.640307 0.768119i \(-0.278807\pi\)
\(500\) 0 0
\(501\) 5909.60 + 2447.83i 0.526989 + 0.218286i
\(502\) 0 0
\(503\) −13198.2 + 13198.2i −1.16994 + 1.16994i −0.187716 + 0.982223i \(0.560108\pi\)
−0.982223 + 0.187716i \(0.939892\pi\)
\(504\) 0 0
\(505\) 5960.39 + 5960.39i 0.525216 + 0.525216i
\(506\) 0 0
\(507\) −1016.05 + 2452.96i −0.0890027 + 0.214871i
\(508\) 0 0
\(509\) −14481.7 + 5998.52i −1.26108 + 0.522357i −0.910241 0.414078i \(-0.864104\pi\)
−0.350840 + 0.936435i \(0.614104\pi\)
\(510\) 0 0
\(511\) −16967.6 −1.46889
\(512\) 0 0
\(513\) 5407.87 0.465426
\(514\) 0 0
\(515\) −3235.45 + 1340.17i −0.276837 + 0.114670i
\(516\) 0 0
\(517\) 385.893 931.628i 0.0328270 0.0792514i
\(518\) 0 0
\(519\) −1796.16 1796.16i −0.151913 0.151913i
\(520\) 0 0
\(521\) 1814.60 1814.60i 0.152590 0.152590i −0.626684 0.779274i \(-0.715588\pi\)
0.779274 + 0.626684i \(0.215588\pi\)
\(522\) 0 0
\(523\) −4063.96 1683.35i −0.339779 0.140741i 0.206268 0.978496i \(-0.433868\pi\)
−0.546047 + 0.837754i \(0.683868\pi\)
\(524\) 0 0
\(525\) −187.906 453.645i −0.0156207 0.0377118i
\(526\) 0 0
\(527\) 4751.66i 0.392762i
\(528\) 0 0
\(529\) 597.782i 0.0491314i
\(530\) 0 0
\(531\) 1799.05 + 4343.30i 0.147029 + 0.354959i
\(532\) 0 0
\(533\) −5585.70 2313.67i −0.453927 0.188023i
\(534\) 0 0
\(535\) 13554.0 13554.0i 1.09531 1.09531i
\(536\) 0 0
\(537\) 179.445 + 179.445i 0.0144201 + 0.0144201i
\(538\) 0 0
\(539\) 1285.48 3103.44i 0.102727 0.248004i
\(540\) 0 0
\(541\) 5389.43 2232.38i 0.428299 0.177407i −0.158111 0.987421i \(-0.550541\pi\)
0.586411 + 0.810014i \(0.300541\pi\)
\(542\) 0 0
\(543\) −3077.81 −0.243244
\(544\) 0 0
\(545\) −4371.11 −0.343556
\(546\) 0 0
\(547\) 20016.3 8291.01i 1.56460 0.648077i 0.578716 0.815529i \(-0.303554\pi\)
0.985880 + 0.167452i \(0.0535539\pi\)
\(548\) 0 0
\(549\) 3050.48 7364.51i 0.237143 0.572513i
\(550\) 0 0
\(551\) 4914.61 + 4914.61i 0.379981 + 0.379981i
\(552\) 0 0
\(553\) 13670.2 13670.2i 1.05120 1.05120i
\(554\) 0 0
\(555\) 6051.17 + 2506.48i 0.462807 + 0.191701i
\(556\) 0 0
\(557\) 819.599 + 1978.69i 0.0623474 + 0.150520i 0.951983 0.306152i \(-0.0990414\pi\)
−0.889635 + 0.456672i \(0.849041\pi\)
\(558\) 0 0
\(559\) 6770.79i 0.512297i
\(560\) 0 0
\(561\) 195.759i 0.0147325i
\(562\) 0 0
\(563\) −4297.82 10375.9i −0.321726 0.776715i −0.999154 0.0411260i \(-0.986905\pi\)
0.677428 0.735589i \(-0.263095\pi\)
\(564\) 0 0
\(565\) −6806.82 2819.48i −0.506841 0.209940i
\(566\) 0 0
\(567\) −11599.5 + 11599.5i −0.859139 + 0.859139i
\(568\) 0 0
\(569\) 3794.16 + 3794.16i 0.279542 + 0.279542i 0.832926 0.553384i \(-0.186664\pi\)
−0.553384 + 0.832926i \(0.686664\pi\)
\(570\) 0 0
\(571\) 3323.60 8023.87i 0.243587 0.588071i −0.754047 0.656820i \(-0.771901\pi\)
0.997634 + 0.0687495i \(0.0219009\pi\)
\(572\) 0 0
\(573\) −4439.61 + 1838.95i −0.323678 + 0.134072i
\(574\) 0 0
\(575\) −859.431 −0.0623318
\(576\) 0 0
\(577\) 7285.88 0.525676 0.262838 0.964840i \(-0.415342\pi\)
0.262838 + 0.964840i \(0.415342\pi\)
\(578\) 0 0
\(579\) −5202.06 + 2154.76i −0.373385 + 0.154661i
\(580\) 0 0
\(581\) −3608.76 + 8712.31i −0.257688 + 0.622113i
\(582\) 0 0
\(583\) −1848.78 1848.78i −0.131336 0.131336i
\(584\) 0 0
\(585\) −11031.4 + 11031.4i −0.779642 + 0.779642i
\(586\) 0 0
\(587\) 24501.2 + 10148.7i 1.72278 + 0.713600i 0.999740 + 0.0227951i \(0.00725653\pi\)
0.723042 + 0.690804i \(0.242743\pi\)
\(588\) 0 0
\(589\) 3998.87 + 9654.12i 0.279746 + 0.675367i
\(590\) 0 0
\(591\) 6193.40i 0.431070i
\(592\) 0 0
\(593\) 9134.01i 0.632528i −0.948671 0.316264i \(-0.897572\pi\)
0.948671 0.316264i \(-0.102428\pi\)
\(594\) 0 0
\(595\) 3829.17 + 9244.44i 0.263833 + 0.636950i
\(596\) 0 0
\(597\) 250.401 + 103.720i 0.0171662 + 0.00711049i
\(598\) 0 0
\(599\) −5461.25 + 5461.25i −0.372522 + 0.372522i −0.868395 0.495873i \(-0.834848\pi\)
0.495873 + 0.868395i \(0.334848\pi\)
\(600\) 0 0
\(601\) 14729.8 + 14729.8i 0.999738 + 0.999738i 1.00000 0.000262159i \(-8.34479e-5\pi\)
−0.000262159 1.00000i \(0.500083\pi\)
\(602\) 0 0
\(603\) −2932.89 + 7080.62i −0.198070 + 0.478184i
\(604\) 0 0
\(605\) 13138.3 5442.06i 0.882888 0.365704i
\(606\) 0 0
\(607\) −881.096 −0.0589169 −0.0294585 0.999566i \(-0.509378\pi\)
−0.0294585 + 0.999566i \(0.509378\pi\)
\(608\) 0 0
\(609\) 7193.83 0.478668
\(610\) 0 0
\(611\) 13974.7 5788.51i 0.925295 0.383270i
\(612\) 0 0
\(613\) −1693.73 + 4089.02i −0.111597 + 0.269419i −0.969804 0.243884i \(-0.921578\pi\)
0.858207 + 0.513303i \(0.171578\pi\)
\(614\) 0 0
\(615\) 1367.77 + 1367.77i 0.0896813 + 0.0896813i
\(616\) 0 0
\(617\) −21041.5 + 21041.5i −1.37293 + 1.37293i −0.516863 + 0.856068i \(0.672900\pi\)
−0.856068 + 0.516863i \(0.827100\pi\)
\(618\) 0 0
\(619\) −6142.30 2544.22i −0.398837 0.165204i 0.174244 0.984703i \(-0.444252\pi\)
−0.573081 + 0.819499i \(0.694252\pi\)
\(620\) 0 0
\(621\) −3749.14 9051.24i −0.242267 0.584885i
\(622\) 0 0
\(623\) 21754.2i 1.39898i
\(624\) 0 0
\(625\) 14562.4i 0.931992i
\(626\) 0 0
\(627\) 164.745 + 397.730i 0.0104933 + 0.0253330i
\(628\) 0 0
\(629\) 8420.55 + 3487.90i 0.533783 + 0.221100i
\(630\) 0 0
\(631\) 12002.6 12002.6i 0.757234 0.757234i −0.218584 0.975818i \(-0.570144\pi\)
0.975818 + 0.218584i \(0.0701438\pi\)
\(632\) 0 0
\(633\) 3438.87 + 3438.87i 0.215929 + 0.215929i
\(634\) 0 0
\(635\) 2378.50 5742.20i 0.148642 0.358854i
\(636\) 0 0
\(637\) 46552.4 19282.6i 2.89556 1.19938i
\(638\) 0 0
\(639\) 22712.6 1.40610
\(640\) 0 0
\(641\) 8356.78 0.514934 0.257467 0.966287i \(-0.417112\pi\)
0.257467 + 0.966287i \(0.417112\pi\)
\(642\) 0 0
\(643\) −24447.4 + 10126.4i −1.49939 + 0.621070i −0.973337 0.229379i \(-0.926330\pi\)
−0.526058 + 0.850449i \(0.676330\pi\)
\(644\) 0 0
\(645\) −828.984 + 2001.34i −0.0506065 + 0.122175i
\(646\) 0 0
\(647\) −12516.3 12516.3i −0.760533 0.760533i 0.215885 0.976419i \(-0.430736\pi\)
−0.976419 + 0.215885i \(0.930736\pi\)
\(648\) 0 0
\(649\) −565.051 + 565.051i −0.0341759 + 0.0341759i
\(650\) 0 0
\(651\) 9992.38 + 4138.98i 0.601585 + 0.249185i
\(652\) 0 0
\(653\) −1943.05 4690.95i −0.116443 0.281119i 0.854903 0.518788i \(-0.173617\pi\)
−0.971346 + 0.237669i \(0.923617\pi\)
\(654\) 0 0
\(655\) 8775.89i 0.523515i
\(656\) 0 0
\(657\) 11777.9i 0.699391i
\(658\) 0 0
\(659\) 3982.05 + 9613.52i 0.235385 + 0.568269i 0.996795 0.0800014i \(-0.0254925\pi\)
−0.761410 + 0.648271i \(0.775492\pi\)
\(660\) 0 0
\(661\) −2718.83 1126.18i −0.159985 0.0662680i 0.301254 0.953544i \(-0.402595\pi\)
−0.461239 + 0.887276i \(0.652595\pi\)
\(662\) 0 0
\(663\) 2076.38 2076.38i 0.121629 0.121629i
\(664\) 0 0
\(665\) −15559.7 15559.7i −0.907339 0.907339i
\(666\) 0 0
\(667\) 4818.48 11632.8i 0.279719 0.675301i
\(668\) 0 0
\(669\) −5480.19 + 2269.97i −0.316706 + 0.131184i
\(670\) 0 0
\(671\) 1354.96 0.0779548
\(672\) 0 0
\(673\) −4348.42 −0.249063 −0.124531 0.992216i \(-0.539743\pi\)
−0.124531 + 0.992216i \(0.539743\pi\)
\(674\) 0 0
\(675\) −672.380 + 278.509i −0.0383406 + 0.0158812i
\(676\) 0 0
\(677\) −4462.91 + 10774.4i −0.253358 + 0.611661i −0.998471 0.0552774i \(-0.982396\pi\)
0.745113 + 0.666939i \(0.232396\pi\)
\(678\) 0 0
\(679\) 42771.2 + 42771.2i 2.41739 + 2.41739i
\(680\) 0 0
\(681\) 7120.81 7120.81i 0.400690 0.400690i
\(682\) 0 0
\(683\) −19860.3 8226.41i −1.11264 0.460871i −0.250794 0.968040i \(-0.580692\pi\)
−0.861846 + 0.507170i \(0.830692\pi\)
\(684\) 0 0
\(685\) −1607.35 3880.48i −0.0896548 0.216446i
\(686\) 0 0
\(687\) 8138.84i 0.451989i
\(688\) 0 0
\(689\) 39219.3i 2.16856i
\(690\) 0 0
\(691\) 764.618 + 1845.95i 0.0420947 + 0.101626i 0.943528 0.331291i \(-0.107484\pi\)
−0.901434 + 0.432917i \(0.857484\pi\)
\(692\) 0 0
\(693\) −3043.47 1260.65i −0.166828 0.0691024i
\(694\) 0 0
\(695\) −1982.81 + 1982.81i −0.108219 + 0.108219i
\(696\) 0 0
\(697\) 1903.34 + 1903.34i 0.103435 + 0.103435i
\(698\) 0 0
\(699\) −793.139 + 1914.81i −0.0429174 + 0.103612i
\(700\) 0 0
\(701\) −22956.1 + 9508.72i −1.23686 + 0.512324i −0.902732 0.430203i \(-0.858442\pi\)
−0.334128 + 0.942528i \(0.608442\pi\)
\(702\) 0 0
\(703\) −20043.6 −1.07533
\(704\) 0 0
\(705\) −4839.43 −0.258530
\(706\) 0 0
\(707\) −24666.9 + 10217.4i −1.31215 + 0.543512i
\(708\) 0 0
\(709\) −6852.40 + 16543.2i −0.362972 + 0.876292i 0.631891 + 0.775058i \(0.282279\pi\)
−0.994863 + 0.101234i \(0.967721\pi\)
\(710\) 0 0
\(711\) −9489.02 9489.02i −0.500515 0.500515i
\(712\) 0 0
\(713\) 13385.9 13385.9i 0.703096 0.703096i
\(714\) 0 0
\(715\) −2449.95 1014.80i −0.128144 0.0530790i
\(716\) 0 0
\(717\) 1663.25 + 4015.45i 0.0866324 + 0.209149i
\(718\) 0 0
\(719\) 29422.6i 1.52612i −0.646329 0.763059i \(-0.723697\pi\)
0.646329 0.763059i \(-0.276303\pi\)
\(720\) 0 0
\(721\) 11092.5i 0.572962i
\(722\) 0 0
\(723\) −2662.94 6428.92i −0.136979 0.330697i
\(724\) 0 0
\(725\) −864.158 357.946i −0.0442676 0.0183362i
\(726\) 0 0
\(727\) 11609.7 11609.7i 0.592267 0.592267i −0.345976 0.938243i \(-0.612452\pi\)
0.938243 + 0.345976i \(0.112452\pi\)
\(728\) 0 0
\(729\) 4932.69 + 4932.69i 0.250607 + 0.250607i
\(730\) 0 0
\(731\) −1153.58 + 2784.99i −0.0583675 + 0.140912i
\(732\) 0 0
\(733\) −11834.5 + 4902.00i −0.596338 + 0.247011i −0.660375 0.750936i \(-0.729603\pi\)
0.0640365 + 0.997948i \(0.479603\pi\)
\(734\) 0 0
\(735\) −16121.1 −0.809028
\(736\) 0 0
\(737\) −1302.73 −0.0651108
\(738\) 0 0
\(739\) −16285.3 + 6745.57i −0.810640 + 0.335778i −0.749209 0.662333i \(-0.769566\pi\)
−0.0614306 + 0.998111i \(0.519566\pi\)
\(740\) 0 0
\(741\) −2471.23 + 5966.07i −0.122514 + 0.295775i
\(742\) 0 0
\(743\) 20708.3 + 20708.3i 1.02249 + 1.02249i 0.999741 + 0.0227537i \(0.00724334\pi\)
0.0227537 + 0.999741i \(0.492757\pi\)
\(744\) 0 0
\(745\) −1458.08 + 1458.08i −0.0717044 + 0.0717044i
\(746\) 0 0
\(747\) 6047.57 + 2504.99i 0.296210 + 0.122694i
\(748\) 0 0
\(749\) 23234.3 + 56092.7i 1.13346 + 2.73642i
\(750\) 0 0
\(751\) 26417.1i 1.28359i −0.766878 0.641793i \(-0.778191\pi\)
0.766878 0.641793i \(-0.221809\pi\)
\(752\) 0 0
\(753\) 9706.35i 0.469746i
\(754\) 0 0
\(755\) 1987.53 + 4798.32i 0.0958061 + 0.231296i
\(756\) 0 0
\(757\) −20911.7 8661.89i −1.00402 0.415881i −0.180753 0.983528i \(-0.557854\pi\)
−0.823272 + 0.567648i \(0.807854\pi\)
\(758\) 0 0
\(759\) 551.473 551.473i 0.0263731 0.0263731i
\(760\) 0 0
\(761\) −8497.64 8497.64i −0.404782 0.404782i 0.475132 0.879914i \(-0.342400\pi\)
−0.879914 + 0.475132i \(0.842400\pi\)
\(762\) 0 0
\(763\) 5298.35 12791.4i 0.251393 0.606918i
\(764\) 0 0
\(765\) 6416.94 2657.98i 0.303275 0.125620i
\(766\) 0 0
\(767\) −11986.8 −0.564298
\(768\) 0 0
\(769\) −31834.2 −1.49281 −0.746405 0.665492i \(-0.768222\pi\)
−0.746405 + 0.665492i \(0.768222\pi\)
\(770\) 0 0
\(771\) −2528.41 + 1047.30i −0.118105 + 0.0489205i
\(772\) 0 0
\(773\) 14033.5 33879.9i 0.652976 1.57642i −0.155463 0.987842i \(-0.549687\pi\)
0.808438 0.588581i \(-0.200313\pi\)
\(774\) 0 0
\(775\) −994.388 994.388i −0.0460896 0.0460896i
\(776\) 0 0
\(777\) −14669.6 + 14669.6i −0.677308 + 0.677308i
\(778\) 0 0
\(779\) −5468.87 2265.28i −0.251531 0.104188i
\(780\) 0 0
\(781\) 1477.42 + 3566.80i 0.0676904 + 0.163419i
\(782\) 0 0
\(783\) 10662.5i 0.486650i
\(784\) 0 0
\(785\) 14307.6i 0.650525i
\(786\) 0 0