Properties

Label 320.6.l.a.81.17
Level 320
Weight 6
Character 320.81
Analytic conductor 51.323
Analytic rank 0
Dimension 80
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 81.17
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.17

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.86003 - 3.86003i) q^{3} +(-17.6777 + 17.6777i) q^{5} +20.3706i q^{7} -213.200i q^{9} +O(q^{10})\) \(q+(-3.86003 - 3.86003i) q^{3} +(-17.6777 + 17.6777i) q^{5} +20.3706i q^{7} -213.200i q^{9} +(268.702 - 268.702i) q^{11} +(621.797 + 621.797i) q^{13} +136.473 q^{15} -2094.53 q^{17} +(370.318 + 370.318i) q^{19} +(78.6312 - 78.6312i) q^{21} +3608.29i q^{23} -625.000i q^{25} +(-1760.95 + 1760.95i) q^{27} +(-5957.69 - 5957.69i) q^{29} +10314.0 q^{31} -2074.39 q^{33} +(-360.105 - 360.105i) q^{35} +(2830.29 - 2830.29i) q^{37} -4800.32i q^{39} -2923.54i q^{41} +(7107.96 - 7107.96i) q^{43} +(3768.88 + 3768.88i) q^{45} +470.452 q^{47} +16392.0 q^{49} +(8084.96 + 8084.96i) q^{51} +(-5934.20 + 5934.20i) q^{53} +9500.04i q^{55} -2858.88i q^{57} +(8405.61 - 8405.61i) q^{59} +(-27548.1 - 27548.1i) q^{61} +4343.02 q^{63} -21983.9 q^{65} +(-49797.3 - 49797.3i) q^{67} +(13928.1 - 13928.1i) q^{69} -70220.5i q^{71} -54478.8i q^{73} +(-2412.52 + 2412.52i) q^{75} +(5473.61 + 5473.61i) q^{77} +69249.4 q^{79} -38213.0 q^{81} +(21656.9 + 21656.9i) q^{83} +(37026.4 - 37026.4i) q^{85} +45993.8i q^{87} +3328.58i q^{89} +(-12666.4 + 12666.4i) q^{91} +(-39812.5 - 39812.5i) q^{93} -13092.7 q^{95} +128648. q^{97} +(-57287.2 - 57287.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −3.86003 3.86003i −0.247621 0.247621i 0.572372 0.819994i \(-0.306023\pi\)
−0.819994 + 0.572372i \(0.806023\pi\)
\(4\) 0 0
\(5\) −17.6777 + 17.6777i −0.316228 + 0.316228i
\(6\) 0 0
\(7\) 20.3706i 0.157130i 0.996909 + 0.0785649i \(0.0250338\pi\)
−0.996909 + 0.0785649i \(0.974966\pi\)
\(8\) 0 0
\(9\) 213.200i 0.877367i
\(10\) 0 0
\(11\) 268.702 268.702i 0.669558 0.669558i −0.288055 0.957614i \(-0.593009\pi\)
0.957614 + 0.288055i \(0.0930087\pi\)
\(12\) 0 0
\(13\) 621.797 + 621.797i 1.02045 + 1.02045i 0.999787 + 0.0206604i \(0.00657687\pi\)
0.0206604 + 0.999787i \(0.493423\pi\)
\(14\) 0 0
\(15\) 136.473 0.156609
\(16\) 0 0
\(17\) −2094.53 −1.75778 −0.878890 0.477025i \(-0.841715\pi\)
−0.878890 + 0.477025i \(0.841715\pi\)
\(18\) 0 0
\(19\) 370.318 + 370.318i 0.235337 + 0.235337i 0.814916 0.579579i \(-0.196783\pi\)
−0.579579 + 0.814916i \(0.696783\pi\)
\(20\) 0 0
\(21\) 78.6312 78.6312i 0.0389087 0.0389087i
\(22\) 0 0
\(23\) 3608.29i 1.42227i 0.703055 + 0.711135i \(0.251819\pi\)
−0.703055 + 0.711135i \(0.748181\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −1760.95 + 1760.95i −0.464876 + 0.464876i
\(28\) 0 0
\(29\) −5957.69 5957.69i −1.31548 1.31548i −0.917316 0.398160i \(-0.869649\pi\)
−0.398160 0.917316i \(-0.630351\pi\)
\(30\) 0 0
\(31\) 10314.0 1.92763 0.963816 0.266569i \(-0.0858902\pi\)
0.963816 + 0.266569i \(0.0858902\pi\)
\(32\) 0 0
\(33\) −2074.39 −0.331594
\(34\) 0 0
\(35\) −360.105 360.105i −0.0496888 0.0496888i
\(36\) 0 0
\(37\) 2830.29 2830.29i 0.339881 0.339881i −0.516441 0.856322i \(-0.672744\pi\)
0.856322 + 0.516441i \(0.172744\pi\)
\(38\) 0 0
\(39\) 4800.32i 0.505369i
\(40\) 0 0
\(41\) 2923.54i 0.271612i −0.990735 0.135806i \(-0.956638\pi\)
0.990735 0.135806i \(-0.0433624\pi\)
\(42\) 0 0
\(43\) 7107.96 7107.96i 0.586238 0.586238i −0.350372 0.936610i \(-0.613945\pi\)
0.936610 + 0.350372i \(0.113945\pi\)
\(44\) 0 0
\(45\) 3768.88 + 3768.88i 0.277448 + 0.277448i
\(46\) 0 0
\(47\) 470.452 0.0310650 0.0155325 0.999879i \(-0.495056\pi\)
0.0155325 + 0.999879i \(0.495056\pi\)
\(48\) 0 0
\(49\) 16392.0 0.975310
\(50\) 0 0
\(51\) 8084.96 + 8084.96i 0.435264 + 0.435264i
\(52\) 0 0
\(53\) −5934.20 + 5934.20i −0.290183 + 0.290183i −0.837153 0.546969i \(-0.815781\pi\)
0.546969 + 0.837153i \(0.315781\pi\)
\(54\) 0 0
\(55\) 9500.04i 0.423466i
\(56\) 0 0
\(57\) 2858.88i 0.116549i
\(58\) 0 0
\(59\) 8405.61 8405.61i 0.314369 0.314369i −0.532231 0.846599i \(-0.678646\pi\)
0.846599 + 0.532231i \(0.178646\pi\)
\(60\) 0 0
\(61\) −27548.1 27548.1i −0.947911 0.947911i 0.0507975 0.998709i \(-0.483824\pi\)
−0.998709 + 0.0507975i \(0.983824\pi\)
\(62\) 0 0
\(63\) 4343.02 0.137861
\(64\) 0 0
\(65\) −21983.9 −0.645387
\(66\) 0 0
\(67\) −49797.3 49797.3i −1.35525 1.35525i −0.879678 0.475570i \(-0.842242\pi\)
−0.475570 0.879678i \(-0.657758\pi\)
\(68\) 0 0
\(69\) 13928.1 13928.1i 0.352185 0.352185i
\(70\) 0 0
\(71\) 70220.5i 1.65317i −0.562811 0.826586i \(-0.690280\pi\)
0.562811 0.826586i \(-0.309720\pi\)
\(72\) 0 0
\(73\) 54478.8i 1.19652i −0.801302 0.598260i \(-0.795859\pi\)
0.801302 0.598260i \(-0.204141\pi\)
\(74\) 0 0
\(75\) −2412.52 + 2412.52i −0.0495243 + 0.0495243i
\(76\) 0 0
\(77\) 5473.61 + 5473.61i 0.105208 + 0.105208i
\(78\) 0 0
\(79\) 69249.4 1.24838 0.624192 0.781271i \(-0.285428\pi\)
0.624192 + 0.781271i \(0.285428\pi\)
\(80\) 0 0
\(81\) −38213.0 −0.647141
\(82\) 0 0
\(83\) 21656.9 + 21656.9i 0.345066 + 0.345066i 0.858268 0.513202i \(-0.171541\pi\)
−0.513202 + 0.858268i \(0.671541\pi\)
\(84\) 0 0
\(85\) 37026.4 37026.4i 0.555859 0.555859i
\(86\) 0 0
\(87\) 45993.8i 0.651480i
\(88\) 0 0
\(89\) 3328.58i 0.0445435i 0.999752 + 0.0222718i \(0.00708990\pi\)
−0.999752 + 0.0222718i \(0.992910\pi\)
\(90\) 0 0
\(91\) −12666.4 + 12666.4i −0.160343 + 0.160343i
\(92\) 0 0
\(93\) −39812.5 39812.5i −0.477323 0.477323i
\(94\) 0 0
\(95\) −13092.7 −0.148840
\(96\) 0 0
\(97\) 128648. 1.38826 0.694132 0.719848i \(-0.255788\pi\)
0.694132 + 0.719848i \(0.255788\pi\)
\(98\) 0 0
\(99\) −57287.2 57287.2i −0.587449 0.587449i
\(100\) 0 0
\(101\) 6522.13 6522.13i 0.0636189 0.0636189i −0.674582 0.738200i \(-0.735676\pi\)
0.738200 + 0.674582i \(0.235676\pi\)
\(102\) 0 0
\(103\) 138377.i 1.28520i −0.766202 0.642600i \(-0.777856\pi\)
0.766202 0.642600i \(-0.222144\pi\)
\(104\) 0 0
\(105\) 2780.03i 0.0246080i
\(106\) 0 0
\(107\) 55482.2 55482.2i 0.468483 0.468483i −0.432940 0.901423i \(-0.642524\pi\)
0.901423 + 0.432940i \(0.142524\pi\)
\(108\) 0 0
\(109\) −71569.6 71569.6i −0.576982 0.576982i 0.357089 0.934071i \(-0.383769\pi\)
−0.934071 + 0.357089i \(0.883769\pi\)
\(110\) 0 0
\(111\) −21850.0 −0.168324
\(112\) 0 0
\(113\) 56679.7 0.417572 0.208786 0.977961i \(-0.433049\pi\)
0.208786 + 0.977961i \(0.433049\pi\)
\(114\) 0 0
\(115\) −63786.2 63786.2i −0.449762 0.449762i
\(116\) 0 0
\(117\) 132567. 132567.i 0.895307 0.895307i
\(118\) 0 0
\(119\) 42666.8i 0.276200i
\(120\) 0 0
\(121\) 16649.9i 0.103383i
\(122\) 0 0
\(123\) −11284.9 + 11284.9i −0.0672569 + 0.0672569i
\(124\) 0 0
\(125\) 11048.5 + 11048.5i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) 12378.2 0.0681002 0.0340501 0.999420i \(-0.489159\pi\)
0.0340501 + 0.999420i \(0.489159\pi\)
\(128\) 0 0
\(129\) −54874.0 −0.290330
\(130\) 0 0
\(131\) −106355. 106355.i −0.541476 0.541476i 0.382485 0.923962i \(-0.375068\pi\)
−0.923962 + 0.382485i \(0.875068\pi\)
\(132\) 0 0
\(133\) −7543.59 + 7543.59i −0.0369785 + 0.0369785i
\(134\) 0 0
\(135\) 62258.9i 0.294014i
\(136\) 0 0
\(137\) 12703.6i 0.0578264i 0.999582 + 0.0289132i \(0.00920465\pi\)
−0.999582 + 0.0289132i \(0.990795\pi\)
\(138\) 0 0
\(139\) −94848.3 + 94848.3i −0.416383 + 0.416383i −0.883955 0.467572i \(-0.845129\pi\)
0.467572 + 0.883955i \(0.345129\pi\)
\(140\) 0 0
\(141\) −1815.96 1815.96i −0.00769235 0.00769235i
\(142\) 0 0
\(143\) 334156. 1.36650
\(144\) 0 0
\(145\) 210636. 0.831980
\(146\) 0 0
\(147\) −63273.8 63273.8i −0.241508 0.241508i
\(148\) 0 0
\(149\) 227916. 227916.i 0.841026 0.841026i −0.147966 0.988992i \(-0.547273\pi\)
0.988992 + 0.147966i \(0.0472727\pi\)
\(150\) 0 0
\(151\) 17188.0i 0.0613454i −0.999529 0.0306727i \(-0.990235\pi\)
0.999529 0.0306727i \(-0.00976496\pi\)
\(152\) 0 0
\(153\) 446554.i 1.54222i
\(154\) 0 0
\(155\) −182328. + 182328.i −0.609571 + 0.609571i
\(156\) 0 0
\(157\) −36276.9 36276.9i −0.117458 0.117458i 0.645935 0.763393i \(-0.276468\pi\)
−0.763393 + 0.645935i \(0.776468\pi\)
\(158\) 0 0
\(159\) 45812.4 0.143711
\(160\) 0 0
\(161\) −73503.1 −0.223481
\(162\) 0 0
\(163\) 41418.5 + 41418.5i 0.122103 + 0.122103i 0.765518 0.643415i \(-0.222483\pi\)
−0.643415 + 0.765518i \(0.722483\pi\)
\(164\) 0 0
\(165\) 36670.5 36670.5i 0.104859 0.104859i
\(166\) 0 0
\(167\) 400566.i 1.11143i −0.831372 0.555717i \(-0.812444\pi\)
0.831372 0.555717i \(-0.187556\pi\)
\(168\) 0 0
\(169\) 401971.i 1.08262i
\(170\) 0 0
\(171\) 78951.8 78951.8i 0.206477 0.206477i
\(172\) 0 0
\(173\) −241650. 241650.i −0.613862 0.613862i 0.330088 0.943950i \(-0.392922\pi\)
−0.943950 + 0.330088i \(0.892922\pi\)
\(174\) 0 0
\(175\) 12731.6 0.0314260
\(176\) 0 0
\(177\) −64891.9 −0.155689
\(178\) 0 0
\(179\) −143567. 143567.i −0.334905 0.334905i 0.519541 0.854446i \(-0.326103\pi\)
−0.854446 + 0.519541i \(0.826103\pi\)
\(180\) 0 0
\(181\) 189284. 189284.i 0.429454 0.429454i −0.458988 0.888442i \(-0.651788\pi\)
0.888442 + 0.458988i \(0.151788\pi\)
\(182\) 0 0
\(183\) 212674.i 0.469446i
\(184\) 0 0
\(185\) 100066.i 0.214960i
\(186\) 0 0
\(187\) −562804. + 562804.i −1.17694 + 1.17694i
\(188\) 0 0
\(189\) −35871.6 35871.6i −0.0730459 0.0730459i
\(190\) 0 0
\(191\) 218440. 0.433259 0.216630 0.976254i \(-0.430494\pi\)
0.216630 + 0.976254i \(0.430494\pi\)
\(192\) 0 0
\(193\) −627669. −1.21293 −0.606467 0.795109i \(-0.707414\pi\)
−0.606467 + 0.795109i \(0.707414\pi\)
\(194\) 0 0
\(195\) 84858.4 + 84858.4i 0.159812 + 0.159812i
\(196\) 0 0
\(197\) −145767. + 145767.i −0.267605 + 0.267605i −0.828134 0.560530i \(-0.810598\pi\)
0.560530 + 0.828134i \(0.310598\pi\)
\(198\) 0 0
\(199\) 874377.i 1.56519i 0.622534 + 0.782593i \(0.286103\pi\)
−0.622534 + 0.782593i \(0.713897\pi\)
\(200\) 0 0
\(201\) 384439.i 0.671177i
\(202\) 0 0
\(203\) 121362. 121362.i 0.206701 0.206701i
\(204\) 0 0
\(205\) 51681.3 + 51681.3i 0.0858912 + 0.0858912i
\(206\) 0 0
\(207\) 769289. 1.24785
\(208\) 0 0
\(209\) 199010. 0.315144
\(210\) 0 0
\(211\) −278056. 278056.i −0.429958 0.429958i 0.458656 0.888614i \(-0.348331\pi\)
−0.888614 + 0.458656i \(0.848331\pi\)
\(212\) 0 0
\(213\) −271053. + 271053.i −0.409361 + 0.409361i
\(214\) 0 0
\(215\) 251304.i 0.370770i
\(216\) 0 0
\(217\) 210103.i 0.302888i
\(218\) 0 0
\(219\) −210290. + 210290.i −0.296284 + 0.296284i
\(220\) 0 0
\(221\) −1.30237e6 1.30237e6i −1.79372 1.79372i
\(222\) 0 0
\(223\) 1.12642e6 1.51684 0.758420 0.651767i \(-0.225972\pi\)
0.758420 + 0.651767i \(0.225972\pi\)
\(224\) 0 0
\(225\) −133250. −0.175473
\(226\) 0 0
\(227\) 290194. + 290194.i 0.373787 + 0.373787i 0.868854 0.495068i \(-0.164857\pi\)
−0.495068 + 0.868854i \(0.664857\pi\)
\(228\) 0 0
\(229\) 726941. 726941.i 0.916031 0.916031i −0.0807066 0.996738i \(-0.525718\pi\)
0.996738 + 0.0807066i \(0.0257177\pi\)
\(230\) 0 0
\(231\) 42256.7i 0.0521033i
\(232\) 0 0
\(233\) 929560.i 1.12173i 0.827908 + 0.560864i \(0.189531\pi\)
−0.827908 + 0.560864i \(0.810469\pi\)
\(234\) 0 0
\(235\) −8316.50 + 8316.50i −0.00982360 + 0.00982360i
\(236\) 0 0
\(237\) −267305. 267305.i −0.309127 0.309127i
\(238\) 0 0
\(239\) −743046. −0.841436 −0.420718 0.907192i \(-0.638222\pi\)
−0.420718 + 0.907192i \(0.638222\pi\)
\(240\) 0 0
\(241\) −226030. −0.250682 −0.125341 0.992114i \(-0.540003\pi\)
−0.125341 + 0.992114i \(0.540003\pi\)
\(242\) 0 0
\(243\) 575414. + 575414.i 0.625122 + 0.625122i
\(244\) 0 0
\(245\) −289773. + 289773.i −0.308420 + 0.308420i
\(246\) 0 0
\(247\) 460525.i 0.480298i
\(248\) 0 0
\(249\) 167193.i 0.170891i
\(250\) 0 0
\(251\) −904818. + 904818.i −0.906519 + 0.906519i −0.995989 0.0894704i \(-0.971483\pi\)
0.0894704 + 0.995989i \(0.471483\pi\)
\(252\) 0 0
\(253\) 969554. + 969554.i 0.952294 + 0.952294i
\(254\) 0 0
\(255\) −285847. −0.275285
\(256\) 0 0
\(257\) −296966. −0.280462 −0.140231 0.990119i \(-0.544785\pi\)
−0.140231 + 0.990119i \(0.544785\pi\)
\(258\) 0 0
\(259\) 57654.7 + 57654.7i 0.0534054 + 0.0534054i
\(260\) 0 0
\(261\) −1.27018e6 + 1.27018e6i −1.15416 + 1.15416i
\(262\) 0 0
\(263\) 1.00748e6i 0.898144i 0.893495 + 0.449072i \(0.148245\pi\)
−0.893495 + 0.449072i \(0.851755\pi\)
\(264\) 0 0
\(265\) 209806.i 0.183528i
\(266\) 0 0
\(267\) 12848.4 12848.4i 0.0110299 0.0110299i
\(268\) 0 0
\(269\) 612624. + 612624.i 0.516195 + 0.516195i 0.916418 0.400223i \(-0.131067\pi\)
−0.400223 + 0.916418i \(0.631067\pi\)
\(270\) 0 0
\(271\) 1.44682e6 1.19672 0.598358 0.801229i \(-0.295820\pi\)
0.598358 + 0.801229i \(0.295820\pi\)
\(272\) 0 0
\(273\) 97785.3 0.0794085
\(274\) 0 0
\(275\) −167938. 167938.i −0.133912 0.133912i
\(276\) 0 0
\(277\) −134739. + 134739.i −0.105510 + 0.105510i −0.757891 0.652381i \(-0.773770\pi\)
0.652381 + 0.757891i \(0.273770\pi\)
\(278\) 0 0
\(279\) 2.19895e6i 1.69124i
\(280\) 0 0
\(281\) 718447.i 0.542786i 0.962469 + 0.271393i \(0.0874844\pi\)
−0.962469 + 0.271393i \(0.912516\pi\)
\(282\) 0 0
\(283\) −23252.5 + 23252.5i −0.0172585 + 0.0172585i −0.715683 0.698425i \(-0.753885\pi\)
0.698425 + 0.715683i \(0.253885\pi\)
\(284\) 0 0
\(285\) 50538.3 + 50538.3i 0.0368560 + 0.0368560i
\(286\) 0 0
\(287\) 59554.1 0.0426783
\(288\) 0 0
\(289\) 2.96720e6 2.08979
\(290\) 0 0
\(291\) −496584. 496584.i −0.343764 0.343764i
\(292\) 0 0
\(293\) 509773. 509773.i 0.346903 0.346903i −0.512052 0.858954i \(-0.671114\pi\)
0.858954 + 0.512052i \(0.171114\pi\)
\(294\) 0 0
\(295\) 297183.i 0.198824i
\(296\) 0 0
\(297\) 946339.i 0.622524i
\(298\) 0 0
\(299\) −2.24363e6 + 2.24363e6i −1.45135 + 1.45135i
\(300\) 0 0
\(301\) 144793. + 144793.i 0.0921155 + 0.0921155i
\(302\) 0 0
\(303\) −50351.3 −0.0315068
\(304\) 0 0
\(305\) 973974. 0.599512
\(306\) 0 0
\(307\) −1.48996e6 1.48996e6i −0.902253 0.902253i 0.0933775 0.995631i \(-0.470234\pi\)
−0.995631 + 0.0933775i \(0.970234\pi\)
\(308\) 0 0
\(309\) −534140. + 534140.i −0.318243 + 0.318243i
\(310\) 0 0
\(311\) 431469.i 0.252958i −0.991969 0.126479i \(-0.959632\pi\)
0.991969 0.126479i \(-0.0403676\pi\)
\(312\) 0 0
\(313\) 1.81612e6i 1.04781i 0.851776 + 0.523906i \(0.175526\pi\)
−0.851776 + 0.523906i \(0.824474\pi\)
\(314\) 0 0
\(315\) −76774.4 + 76774.4i −0.0435953 + 0.0435953i
\(316\) 0 0
\(317\) 735496. + 735496.i 0.411086 + 0.411086i 0.882117 0.471031i \(-0.156118\pi\)
−0.471031 + 0.882117i \(0.656118\pi\)
\(318\) 0 0
\(319\) −3.20168e6 −1.76158
\(320\) 0 0
\(321\) −428326. −0.232013
\(322\) 0 0
\(323\) −775642. 775642.i −0.413671 0.413671i
\(324\) 0 0
\(325\) 388623. 388623.i 0.204089 0.204089i
\(326\) 0 0
\(327\) 552522.i 0.285746i
\(328\) 0 0
\(329\) 9583.39i 0.00488123i
\(330\) 0 0
\(331\) 1.14396e6 1.14396e6i 0.573907 0.573907i −0.359311 0.933218i \(-0.616988\pi\)
0.933218 + 0.359311i \(0.116988\pi\)
\(332\) 0 0
\(333\) −603419. 603419.i −0.298200 0.298200i
\(334\) 0 0
\(335\) 1.76060e6 0.857134
\(336\) 0 0
\(337\) −3.71312e6 −1.78100 −0.890500 0.454983i \(-0.849645\pi\)
−0.890500 + 0.454983i \(0.849645\pi\)
\(338\) 0 0
\(339\) −218785. 218785.i −0.103400 0.103400i
\(340\) 0 0
\(341\) 2.77140e6 2.77140e6i 1.29066 1.29066i
\(342\) 0 0
\(343\) 676284.i 0.310380i
\(344\) 0 0
\(345\) 492434.i 0.222741i
\(346\) 0 0
\(347\) 2.30050e6 2.30050e6i 1.02565 1.02565i 0.0259845 0.999662i \(-0.491728\pi\)
0.999662 0.0259845i \(-0.00827206\pi\)
\(348\) 0 0
\(349\) −458011. 458011.i −0.201286 0.201286i 0.599265 0.800551i \(-0.295460\pi\)
−0.800551 + 0.599265i \(0.795460\pi\)
\(350\) 0 0
\(351\) −2.18991e6 −0.948763
\(352\) 0 0
\(353\) 1.98245e6 0.846768 0.423384 0.905950i \(-0.360842\pi\)
0.423384 + 0.905950i \(0.360842\pi\)
\(354\) 0 0
\(355\) 1.24133e6 + 1.24133e6i 0.522779 + 0.522779i
\(356\) 0 0
\(357\) −164695. + 164695.i −0.0683929 + 0.0683929i
\(358\) 0 0
\(359\) 3.42438e6i 1.40232i 0.713006 + 0.701158i \(0.247333\pi\)
−0.713006 + 0.701158i \(0.752667\pi\)
\(360\) 0 0
\(361\) 2.20183e6i 0.889233i
\(362\) 0 0
\(363\) 64269.3 64269.3i 0.0255998 0.0255998i
\(364\) 0 0
\(365\) 963057. + 963057.i 0.378373 + 0.378373i
\(366\) 0 0
\(367\) 553446. 0.214491 0.107246 0.994233i \(-0.465797\pi\)
0.107246 + 0.994233i \(0.465797\pi\)
\(368\) 0 0
\(369\) −623298. −0.238303
\(370\) 0 0
\(371\) −120883. 120883.i −0.0455964 0.0455964i
\(372\) 0 0
\(373\) −1.82003e6 + 1.82003e6i −0.677341 + 0.677341i −0.959398 0.282057i \(-0.908983\pi\)
0.282057 + 0.959398i \(0.408983\pi\)
\(374\) 0 0
\(375\) 85295.5i 0.0313219i
\(376\) 0 0
\(377\) 7.40895e6i 2.68475i
\(378\) 0 0
\(379\) 3.47422e6 3.47422e6i 1.24239 1.24239i 0.283388 0.959005i \(-0.408542\pi\)
0.959005 0.283388i \(-0.0914584\pi\)
\(380\) 0 0
\(381\) −47780.3 47780.3i −0.0168631 0.0168631i
\(382\) 0 0
\(383\) 1.64390e6 0.572634 0.286317 0.958135i \(-0.407569\pi\)
0.286317 + 0.958135i \(0.407569\pi\)
\(384\) 0 0
\(385\) −193521. −0.0665391
\(386\) 0 0
\(387\) −1.51542e6 1.51542e6i −0.514346 0.514346i
\(388\) 0 0
\(389\) 1.26514e6 1.26514e6i 0.423902 0.423902i −0.462643 0.886545i \(-0.653099\pi\)
0.886545 + 0.462643i \(0.153099\pi\)
\(390\) 0 0
\(391\) 7.55768e6i 2.50004i
\(392\) 0 0
\(393\) 821068.i 0.268162i
\(394\) 0 0
\(395\) −1.22417e6 + 1.22417e6i −0.394774 + 0.394774i
\(396\) 0 0
\(397\) −881275. 881275.i −0.280631 0.280631i 0.552730 0.833361i \(-0.313586\pi\)
−0.833361 + 0.552730i \(0.813586\pi\)
\(398\) 0 0
\(399\) 58237.1 0.0183133
\(400\) 0 0
\(401\) −1.43364e6 −0.445225 −0.222613 0.974907i \(-0.571459\pi\)
−0.222613 + 0.974907i \(0.571459\pi\)
\(402\) 0 0
\(403\) 6.41323e6 + 6.41323e6i 1.96705 + 1.96705i
\(404\) 0 0
\(405\) 675517. 675517.i 0.204644 0.204644i
\(406\) 0 0
\(407\) 1.52101e6i 0.455140i
\(408\) 0 0
\(409\) 2.61233e6i 0.772182i −0.922461 0.386091i \(-0.873825\pi\)
0.922461 0.386091i \(-0.126175\pi\)
\(410\) 0 0
\(411\) 49036.5 49036.5i 0.0143191 0.0143191i
\(412\) 0 0
\(413\) 171227. + 171227.i 0.0493967 + 0.0493967i
\(414\) 0 0
\(415\) −765689. −0.218239
\(416\) 0 0
\(417\) 732235. 0.206210
\(418\) 0 0
\(419\) −1.79144e6 1.79144e6i −0.498502 0.498502i 0.412470 0.910971i \(-0.364666\pi\)
−0.910971 + 0.412470i \(0.864666\pi\)
\(420\) 0 0
\(421\) −1.02803e6 + 1.02803e6i −0.282684 + 0.282684i −0.834179 0.551494i \(-0.814058\pi\)
0.551494 + 0.834179i \(0.314058\pi\)
\(422\) 0 0
\(423\) 100301.i 0.0272554i
\(424\) 0 0
\(425\) 1.30908e6i 0.351556i
\(426\) 0 0
\(427\) 561172. 561172.i 0.148945 0.148945i
\(428\) 0 0
\(429\) −1.28985e6 1.28985e6i −0.338374 0.338374i
\(430\) 0 0
\(431\) −2.46985e6 −0.640438 −0.320219 0.947343i \(-0.603757\pi\)
−0.320219 + 0.947343i \(0.603757\pi\)
\(432\) 0 0
\(433\) 2.37472e6 0.608685 0.304343 0.952563i \(-0.401563\pi\)
0.304343 + 0.952563i \(0.401563\pi\)
\(434\) 0 0
\(435\) −813063. 813063.i −0.206016 0.206016i
\(436\) 0 0
\(437\) −1.33622e6 + 1.33622e6i −0.334713 + 0.334713i
\(438\) 0 0
\(439\) 2.14558e6i 0.531352i −0.964062 0.265676i \(-0.914405\pi\)
0.964062 0.265676i \(-0.0855952\pi\)
\(440\) 0 0
\(441\) 3.49479e6i 0.855705i
\(442\) 0 0
\(443\) 202439. 202439.i 0.0490100 0.0490100i −0.682177 0.731187i \(-0.738967\pi\)
0.731187 + 0.682177i \(0.238967\pi\)
\(444\) 0 0
\(445\) −58841.6 58841.6i −0.0140859 0.0140859i
\(446\) 0 0
\(447\) −1.75953e6 −0.416512
\(448\) 0 0
\(449\) −7.11149e6 −1.66473 −0.832367 0.554225i \(-0.813015\pi\)
−0.832367 + 0.554225i \(0.813015\pi\)
\(450\) 0 0
\(451\) −785559. 785559.i −0.181860 0.181860i
\(452\) 0 0
\(453\) −66346.2 + 66346.2i −0.0151904 + 0.0151904i
\(454\) 0 0
\(455\) 447824.i 0.101410i
\(456\) 0 0
\(457\) 3.03083e6i 0.678846i −0.940634 0.339423i \(-0.889768\pi\)
0.940634 0.339423i \(-0.110232\pi\)
\(458\) 0 0
\(459\) 3.68836e6 3.68836e6i 0.817150 0.817150i
\(460\) 0 0
\(461\) −4.79592e6 4.79592e6i −1.05104 1.05104i −0.998625 0.0524147i \(-0.983308\pi\)
−0.0524147 0.998625i \(-0.516692\pi\)
\(462\) 0 0
\(463\) −3.25096e6 −0.704789 −0.352395 0.935851i \(-0.614633\pi\)
−0.352395 + 0.935851i \(0.614633\pi\)
\(464\) 0 0
\(465\) 1.40758e6 0.301885
\(466\) 0 0
\(467\) 3.68299e6 + 3.68299e6i 0.781463 + 0.781463i 0.980078 0.198615i \(-0.0636443\pi\)
−0.198615 + 0.980078i \(0.563644\pi\)
\(468\) 0 0
\(469\) 1.01440e6 1.01440e6i 0.212950 0.212950i
\(470\) 0 0
\(471\) 280060.i 0.0581700i
\(472\) 0 0
\(473\) 3.81984e6i 0.785041i
\(474\) 0 0
\(475\) 231449. 231449.i 0.0470674 0.0470674i
\(476\) 0 0
\(477\) 1.26517e6 + 1.26517e6i 0.254597 + 0.254597i
\(478\) 0 0
\(479\) 629120. 0.125284 0.0626419 0.998036i \(-0.480047\pi\)
0.0626419 + 0.998036i \(0.480047\pi\)
\(480\) 0 0
\(481\) 3.51974e6 0.693661
\(482\) 0 0
\(483\) 283724. + 283724.i 0.0553387 + 0.0553387i
\(484\) 0 0
\(485\) −2.27419e6 + 2.27419e6i −0.439008 + 0.439008i
\(486\) 0 0
\(487\) 639056.i 0.122100i −0.998135 0.0610501i \(-0.980555\pi\)
0.998135 0.0610501i \(-0.0194450\pi\)
\(488\) 0 0
\(489\) 319754.i 0.0604704i
\(490\) 0 0
\(491\) 306275. 306275.i 0.0573334 0.0573334i −0.677859 0.735192i \(-0.737092\pi\)
0.735192 + 0.677859i \(0.237092\pi\)
\(492\) 0 0
\(493\) 1.24786e7 + 1.24786e7i 2.31232 + 2.31232i
\(494\) 0 0
\(495\) 2.02541e6 0.371535
\(496\) 0 0
\(497\) 1.43043e6 0.259763
\(498\) 0 0
\(499\) 3.63733e6 + 3.63733e6i 0.653931 + 0.653931i 0.953937 0.300007i \(-0.0969889\pi\)
−0.300007 + 0.953937i \(0.596989\pi\)
\(500\) 0 0
\(501\) −1.54620e6 + 1.54620e6i −0.275215 + 0.275215i
\(502\) 0 0
\(503\) 8.04809e6i 1.41832i 0.705050 + 0.709158i \(0.250925\pi\)
−0.705050 + 0.709158i \(0.749075\pi\)
\(504\) 0 0
\(505\) 230592.i 0.0402361i
\(506\) 0 0
\(507\) 1.55162e6 1.55162e6i 0.268081 0.268081i
\(508\) 0 0
\(509\) 2.18413e6 + 2.18413e6i 0.373666 + 0.373666i 0.868811 0.495145i \(-0.164885\pi\)
−0.495145 + 0.868811i \(0.664885\pi\)
\(510\) 0 0
\(511\) 1.10976e6 0.188009
\(512\) 0 0
\(513\) −1.30422e6 −0.218805
\(514\) 0 0
\(515\) 2.44618e6 + 2.44618e6i 0.406416 + 0.406416i
\(516\) 0 0
\(517\) 126411. 126411.i 0.0207998 0.0207998i
\(518\) 0 0
\(519\) 1.86555e6i 0.304011i
\(520\) 0 0
\(521\) 7.59494e6i 1.22583i −0.790149 0.612914i \(-0.789997\pi\)
0.790149 0.612914i \(-0.210003\pi\)
\(522\) 0 0
\(523\) 7.40239e6 7.40239e6i 1.18336 1.18336i 0.204495 0.978868i \(-0.434445\pi\)
0.978868 0.204495i \(-0.0655553\pi\)
\(524\) 0 0
\(525\) −49144.5 49144.5i −0.00778174 0.00778174i
\(526\) 0 0
\(527\) −2.16030e7 −3.38835
\(528\) 0 0
\(529\) −6.58344e6 −1.02285
\(530\) 0 0
\(531\) −1.79208e6 1.79208e6i −0.275817 0.275817i
\(532\) 0 0
\(533\) 1.81785e6 1.81785e6i 0.277165 0.277165i
\(534\) 0 0
\(535\) 1.96159e6i 0.296295i
\(536\) 0 0
\(537\) 1.10835e6i 0.165859i
\(538\) 0 0
\(539\) 4.40457e6 4.40457e6i 0.653027 0.653027i
\(540\) 0 0
\(541\) −4.81695e6 4.81695e6i −0.707585 0.707585i 0.258442 0.966027i \(-0.416791\pi\)
−0.966027 + 0.258442i \(0.916791\pi\)
\(542\) 0 0
\(543\) −1.46128e6 −0.212684
\(544\) 0 0
\(545\) 2.53037e6 0.364915
\(546\) 0 0
\(547\) −6.11181e6 6.11181e6i −0.873377 0.873377i 0.119462 0.992839i \(-0.461883\pi\)
−0.992839 + 0.119462i \(0.961883\pi\)
\(548\) 0 0
\(549\) −5.87327e6 + 5.87327e6i −0.831667 + 0.831667i
\(550\) 0 0
\(551\) 4.41248e6i 0.619161i
\(552\) 0 0
\(553\) 1.41065e6i 0.196158i
\(554\) 0 0
\(555\) 386258. 386258.i 0.0532286 0.0532286i
\(556\) 0 0
\(557\) 3.95240e6 + 3.95240e6i 0.539788 + 0.539788i 0.923467 0.383679i \(-0.125343\pi\)
−0.383679 + 0.923467i \(0.625343\pi\)
\(558\) 0 0
\(559\) 8.83943e6 1.19645
\(560\) 0 0
\(561\) 4.34488e6 0.582869
\(562\) 0 0
\(563\) 1.30447e6 + 1.30447e6i 0.173445 + 0.173445i 0.788491 0.615046i \(-0.210863\pi\)
−0.615046 + 0.788491i \(0.710863\pi\)
\(564\) 0 0
\(565\) −1.00196e6 + 1.00196e6i −0.132048 + 0.132048i
\(566\) 0 0
\(567\) 778422.i 0.101685i
\(568\) 0 0
\(569\) 259548.i 0.0336075i 0.999859 + 0.0168038i \(0.00534906\pi\)
−0.999859 + 0.0168038i \(0.994651\pi\)
\(570\) 0 0
\(571\) −8.20992e6 + 8.20992e6i −1.05378 + 1.05378i −0.0553069 + 0.998469i \(0.517614\pi\)
−0.998469 + 0.0553069i \(0.982386\pi\)
\(572\) 0 0
\(573\) −843184. 843184.i −0.107284 0.107284i
\(574\) 0 0
\(575\) 2.25518e6 0.284454
\(576\) 0 0
\(577\) −32512.1 −0.00406542 −0.00203271 0.999998i \(-0.500647\pi\)
−0.00203271 + 0.999998i \(0.500647\pi\)
\(578\) 0 0
\(579\) 2.42282e6 + 2.42282e6i 0.300348 + 0.300348i
\(580\) 0 0
\(581\) −441165. + 441165.i −0.0542201 + 0.0542201i
\(582\) 0 0
\(583\) 3.18906e6i 0.388589i
\(584\) 0 0
\(585\) 4.68696e6i 0.566242i
\(586\) 0 0
\(587\) −7.33552e6 + 7.33552e6i −0.878690 + 0.878690i −0.993399 0.114709i \(-0.963406\pi\)
0.114709 + 0.993399i \(0.463406\pi\)
\(588\) 0 0
\(589\) 3.81947e6 + 3.81947e6i 0.453643 + 0.453643i
\(590\) 0 0
\(591\) 1.12533e6 0.132529
\(592\) 0 0
\(593\) 3.74815e6 0.437704 0.218852 0.975758i \(-0.429769\pi\)
0.218852 + 0.975758i \(0.429769\pi\)
\(594\) 0 0
\(595\) 754250. + 754250.i 0.0873420 + 0.0873420i
\(596\) 0 0
\(597\) 3.37512e6 3.37512e6i 0.387573 0.387573i
\(598\) 0 0
\(599\) 32116.0i 0.00365725i −0.999998 0.00182862i \(-0.999418\pi\)
0.999998 0.00182862i \(-0.000582069\pi\)
\(600\) 0 0
\(601\) 1.53233e7i 1.73047i 0.501364 + 0.865236i \(0.332832\pi\)
−0.501364 + 0.865236i \(0.667168\pi\)
\(602\) 0 0
\(603\) −1.06168e7 + 1.06168e7i −1.18905 + 1.18905i
\(604\) 0 0
\(605\) −294332. 294332.i −0.0326925 0.0326925i
\(606\) 0 0
\(607\) 9.26259e6 1.02038 0.510189 0.860063i \(-0.329576\pi\)
0.510189 + 0.860063i \(0.329576\pi\)
\(608\) 0 0
\(609\) −936921. −0.102367
\(610\) 0 0
\(611\) 292526. + 292526.i 0.0317001 + 0.0317001i
\(612\) 0 0
\(613\) −4.22409e6 + 4.22409e6i −0.454027 + 0.454027i −0.896689 0.442662i \(-0.854034\pi\)
0.442662 + 0.896689i \(0.354034\pi\)
\(614\) 0 0
\(615\) 398983.i 0.0425370i
\(616\) 0 0
\(617\) 1.06955e7i 1.13107i −0.824725 0.565534i \(-0.808670\pi\)
0.824725 0.565534i \(-0.191330\pi\)
\(618\) 0 0
\(619\) −1.29776e6 + 1.29776e6i −0.136135 + 0.136135i −0.771890 0.635756i \(-0.780689\pi\)
0.635756 + 0.771890i \(0.280689\pi\)
\(620\) 0 0
\(621\) −6.35402e6 6.35402e6i −0.661180 0.661180i
\(622\) 0 0
\(623\) −67805.2 −0.00699911
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) −768185. 768185.i −0.0780364 0.0780364i
\(628\) 0 0
\(629\) −5.92813e6 + 5.92813e6i −0.597436 + 0.597436i
\(630\) 0 0
\(631\) 1.23969e6i 0.123948i −0.998078 0.0619738i \(-0.980260\pi\)
0.998078 0.0619738i \(-0.0197395\pi\)
\(632\) 0 0
\(633\) 2.14661e6i 0.212934i
\(634\) 0 0
\(635\) −218818. + 218818.i −0.0215352 + 0.0215352i
\(636\) 0 0
\(637\) 1.01925e7 + 1.01925e7i 0.995252 + 0.995252i
\(638\) 0 0
\(639\) −1.49710e7 −1.45044
\(640\) 0 0
\(641\) 3.96999e6 0.381632 0.190816 0.981626i \(-0.438887\pi\)
0.190816 + 0.981626i \(0.438887\pi\)
\(642\) 0 0
\(643\) 5.11306e6 + 5.11306e6i 0.487701 + 0.487701i 0.907580 0.419879i \(-0.137928\pi\)
−0.419879 + 0.907580i \(0.637928\pi\)
\(644\) 0 0
\(645\) 970044. 970044.i 0.0918105 0.0918105i
\(646\) 0 0
\(647\) 1.08958e7i 1.02329i 0.859196 + 0.511646i \(0.170964\pi\)
−0.859196 + 0.511646i \(0.829036\pi\)
\(648\) 0 0
\(649\) 4.51720e6i 0.420976i
\(650\) 0 0
\(651\) 811004. 811004.i 0.0750016 0.0750016i
\(652\) 0 0
\(653\) 7.99690e6 + 7.99690e6i 0.733903 + 0.733903i 0.971391 0.237488i \(-0.0763240\pi\)
−0.237488 + 0.971391i \(0.576324\pi\)
\(654\) 0 0
\(655\) 3.76022e6 0.342460
\(656\) 0 0
\(657\) −1.16149e7 −1.04979
\(658\) 0 0
\(659\) −5.10943e6 5.10943e6i −0.458310 0.458310i 0.439791 0.898100i \(-0.355053\pi\)
−0.898100 + 0.439791i \(0.855053\pi\)
\(660\) 0 0
\(661\) −1.30768e6 + 1.30768e6i −0.116412 + 0.116412i −0.762913 0.646501i \(-0.776232\pi\)
0.646501 + 0.762913i \(0.276232\pi\)
\(662\) 0 0
\(663\) 1.00544e7i 0.888327i
\(664\) 0 0
\(665\) 266706.i 0.0233872i
\(666\) 0 0
\(667\) 2.14971e7 2.14971e7i 1.87096 1.87096i
\(668\) 0 0
\(669\) −4.34803e6 4.34803e6i −0.375602 0.375602i
\(670\) 0 0
\(671\) −1.48045e7 −1.26936
\(672\) 0 0
\(673\) 1.39705e7 1.18898 0.594491 0.804102i \(-0.297353\pi\)
0.594491 + 0.804102i \(0.297353\pi\)
\(674\) 0 0
\(675\) 1.10059e6 + 1.10059e6i 0.0929752 + 0.0929752i
\(676\) 0 0
\(677\) 3.27475e6 3.27475e6i 0.274603 0.274603i −0.556347 0.830950i \(-0.687797\pi\)
0.830950 + 0.556347i \(0.187797\pi\)
\(678\) 0 0
\(679\) 2.62063e6i 0.218138i
\(680\) 0 0
\(681\) 2.24032e6i 0.185115i
\(682\) 0 0
\(683\) −1.37218e7 + 1.37218e7i −1.12554 + 1.12554i −0.134641 + 0.990894i \(0.542988\pi\)
−0.990894 + 0.134641i \(0.957012\pi\)
\(684\) 0 0
\(685\) −224571. 224571.i −0.0182863 0.0182863i
\(686\) 0 0
\(687\) −5.61203e6 −0.453658
\(688\) 0 0
\(689\) −7.37973e6 −0.592233
\(690\) 0 0
\(691\) −1.41091e7 1.41091e7i −1.12410 1.12410i −0.991119 0.132978i \(-0.957546\pi\)
−0.132978 0.991119i \(-0.542454\pi\)
\(692\) 0 0
\(693\) 1.16698e6 1.16698e6i 0.0923057 0.0923057i
\(694\) 0 0
\(695\) 3.35339e6i 0.263343i
\(696\) 0 0
\(697\) 6.12343e6i 0.477434i
\(698\) 0 0
\(699\) 3.58813e6 3.58813e6i 0.277764 0.277764i
\(700\) 0 0
\(701\) −4.66155e6 4.66155e6i −0.358290 0.358290i 0.504892 0.863182i \(-0.331532\pi\)
−0.863182 + 0.504892i \(0.831532\pi\)
\(702\) 0 0
\(703\) 2.09621e6 0.159973
\(704\) 0 0
\(705\) 64203.9 0.00486507
\(706\) 0 0
\(707\) 132860. + 132860.i 0.00999642 + 0.00999642i
\(708\) 0 0
\(709\) −5.95157e6 + 5.95157e6i −0.444648 + 0.444648i −0.893570 0.448923i \(-0.851808\pi\)
0.448923 + 0.893570i \(0.351808\pi\)
\(710\) 0 0
\(711\) 1.47640e7i 1.09529i
\(712\) 0 0
\(713\) 3.72160e7i 2.74161i
\(714\) 0 0
\(715\) −5.90710e6 + 5.90710e6i −0.432125 + 0.432125i
\(716\) 0 0
\(717\) 2.86818e6 + 2.86818e6i 0.208357 + 0.208357i
\(718\) 0 0
\(719\) 1.53105e7 1.10450 0.552251 0.833678i \(-0.313769\pi\)
0.552251 + 0.833678i \(0.313769\pi\)
\(720\) 0 0
\(721\) 2.81882e6 0.201943
\(722\) 0 0
\(723\) 872484. + 872484.i 0.0620743 + 0.0620743i
\(724\) 0 0
\(725\) −3.72356e6 + 3.72356e6i −0.263095 + 0.263095i
\(726\) 0 0
\(727\) 1.84545e7i 1.29499i 0.762070 + 0.647494i \(0.224183\pi\)
−0.762070 + 0.647494i \(0.775817\pi\)
\(728\) 0 0
\(729\) 4.84353e6i 0.337554i
\(730\) 0 0
\(731\) −1.48878e7 + 1.48878e7i −1.03048 + 1.03048i
\(732\) 0 0
\(733\) −4.32766e6 4.32766e6i −0.297504 0.297504i 0.542531 0.840036i \(-0.317466\pi\)
−0.840036 + 0.542531i \(0.817466\pi\)
\(734\) 0 0
\(735\) 2.23707e6 0.152743
\(736\) 0 0
\(737\) −2.67612e7 −1.81484
\(738\) 0 0
\(739\) 1.35979e7 + 1.35979e7i 0.915924 + 0.915924i 0.996730 0.0808056i \(-0.0257493\pi\)
−0.0808056 + 0.996730i \(0.525749\pi\)
\(740\) 0 0
\(741\) 1.77764e6 1.77764e6i 0.118932 0.118932i
\(742\) 0 0
\(743\) 2.95819e6i 0.196586i −0.995157 0.0982932i \(-0.968662\pi\)
0.995157 0.0982932i \(-0.0313383\pi\)
\(744\) 0 0
\(745\) 8.05806e6i 0.531912i
\(746\) 0 0
\(747\) 4.61727e6 4.61727e6i 0.302749 0.302749i
\(748\) 0 0
\(749\) 1.13020e6 + 1.13020e6i 0.0736127 + 0.0736127i
\(750\) 0 0
\(751\) 2.94196e7 1.90343 0.951715 0.306982i \(-0.0993191\pi\)
0.951715 + 0.306982i \(0.0993191\pi\)
\(752\) 0 0
\(753\) 6.98526e6 0.448947
\(754\) 0 0
\(755\) 303843. + 303843.i 0.0193991 + 0.0193991i
\(756\) 0 0
\(757\) 9.32272e6 9.32272e6i 0.591293 0.591293i −0.346688 0.937981i \(-0.612694\pi\)
0.937981 + 0.346688i \(0.112694\pi\)
\(758\) 0 0
\(759\) 7.48503e6i 0.471616i
\(760\) 0 0
\(761\) 5.78866e6i 0.362340i −0.983452 0.181170i \(-0.942012\pi\)
0.983452 0.181170i \(-0.0579884\pi\)
\(762\) 0 0
\(763\) 1.45791e6 1.45791e6i 0.0906611 0.0906611i
\(764\) 0 0
\(765\) −7.89404e6 7.89404e6i −0.487692 0.487692i
\(766\) 0 0
\(767\) 1.04532e7 0.641593
\(768\) 0 0
\(769\) 1.52452e7 0.929647 0.464823 0.885403i \(-0.346118\pi\)
0.464823 + 0.885403i \(0.346118\pi\)
\(770\) 0 0
\(771\) 1.14630e6 + 1.14630e6i 0.0694485 + 0.0694485i
\(772\) 0 0
\(773\) 1.56687e7 1.56687e7i 0.943159 0.943159i −0.0553104 0.998469i \(-0.517615\pi\)
0.998469 + 0.0553104i \(0.0176148\pi\)
\(774\) 0 0
\(775\) 6.44627e6i 0.385526i
\(776\) 0 0
\(777\) 445098.i 0.0264487i
\(778\) 0 0
\(779\) 1.08264e6 1.08264e6i 0.0639204 0.0639204i
\(780\) 0 0
\(781\) −1.88684e7 1.88684e7i −1.10689 1.10689i
\(782\) 0 0
\(783\) 2.09824e7 1.22307
\(784\) 0 0
\(785\) 1.28258e6 0.0742867
\(786\) 0 0