Properties

Label 320.6.l.a.81.8
Level 320
Weight 6
Character 320.81
Analytic conductor 51.323
Analytic rank 0
Dimension 80
CM no
Inner twists 2

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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 81.8
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-14.9697 - 14.9697i) q^{3} +(17.6777 - 17.6777i) q^{5} -66.6523i q^{7} +205.184i q^{9} +O(q^{10})\) \(q+(-14.9697 - 14.9697i) q^{3} +(17.6777 - 17.6777i) q^{5} -66.6523i q^{7} +205.184i q^{9} +(34.0729 - 34.0729i) q^{11} +(292.234 + 292.234i) q^{13} -529.259 q^{15} +610.554 q^{17} +(702.298 + 702.298i) q^{19} +(-997.765 + 997.765i) q^{21} +2859.14i q^{23} -625.000i q^{25} +(-566.093 + 566.093i) q^{27} +(4762.59 + 4762.59i) q^{29} +775.382 q^{31} -1020.12 q^{33} +(-1178.26 - 1178.26i) q^{35} +(-6929.77 + 6929.77i) q^{37} -8749.32i q^{39} +1051.16i q^{41} +(-5645.72 + 5645.72i) q^{43} +(3627.18 + 3627.18i) q^{45} +2247.96 q^{47} +12364.5 q^{49} +(-9139.81 - 9139.81i) q^{51} +(17582.1 - 17582.1i) q^{53} -1204.66i q^{55} -21026.4i q^{57} +(-22506.6 + 22506.6i) q^{59} +(35680.2 + 35680.2i) q^{61} +13676.0 q^{63} +10332.0 q^{65} +(-14570.0 - 14570.0i) q^{67} +(42800.5 - 42800.5i) q^{69} -37150.7i q^{71} -77602.0i q^{73} +(-9356.07 + 9356.07i) q^{75} +(-2271.04 - 2271.04i) q^{77} +103892. q^{79} +66808.2 q^{81} +(30433.5 + 30433.5i) q^{83} +(10793.2 - 10793.2i) q^{85} -142589. i q^{87} -55535.9i q^{89} +(19478.1 - 19478.1i) q^{91} +(-11607.2 - 11607.2i) q^{93} +24830.0 q^{95} +33028.6 q^{97} +(6991.23 + 6991.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

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
\(3\) −14.9697 14.9697i −0.960307 0.960307i 0.0389348 0.999242i \(-0.487604\pi\)
−0.999242 + 0.0389348i \(0.987604\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 66.6523i 0.514127i −0.966395 0.257063i \(-0.917245\pi\)
0.966395 0.257063i \(-0.0827549\pi\)
\(8\) 0 0
\(9\) 205.184i 0.844379i
\(10\) 0 0
\(11\) 34.0729 34.0729i 0.0849040 0.0849040i −0.663379 0.748283i \(-0.730878\pi\)
0.748283 + 0.663379i \(0.230878\pi\)
\(12\) 0 0
\(13\) 292.234 + 292.234i 0.479593 + 0.479593i 0.905001 0.425409i \(-0.139870\pi\)
−0.425409 + 0.905001i \(0.639870\pi\)
\(14\) 0 0
\(15\) −529.259 −0.607351
\(16\) 0 0
\(17\) 610.554 0.512391 0.256196 0.966625i \(-0.417531\pi\)
0.256196 + 0.966625i \(0.417531\pi\)
\(18\) 0 0
\(19\) 702.298 + 702.298i 0.446311 + 0.446311i 0.894126 0.447815i \(-0.147798\pi\)
−0.447815 + 0.894126i \(0.647798\pi\)
\(20\) 0 0
\(21\) −997.765 + 997.765i −0.493719 + 0.493719i
\(22\) 0 0
\(23\) 2859.14i 1.12698i 0.826123 + 0.563489i \(0.190541\pi\)
−0.826123 + 0.563489i \(0.809459\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −566.093 + 566.093i −0.149444 + 0.149444i
\(28\) 0 0
\(29\) 4762.59 + 4762.59i 1.05159 + 1.05159i 0.998595 + 0.0529987i \(0.0168779\pi\)
0.0529987 + 0.998595i \(0.483122\pi\)
\(30\) 0 0
\(31\) 775.382 0.144914 0.0724572 0.997372i \(-0.476916\pi\)
0.0724572 + 0.997372i \(0.476916\pi\)
\(32\) 0 0
\(33\) −1020.12 −0.163068
\(34\) 0 0
\(35\) −1178.26 1178.26i −0.162581 0.162581i
\(36\) 0 0
\(37\) −6929.77 + 6929.77i −0.832174 + 0.832174i −0.987814 0.155640i \(-0.950256\pi\)
0.155640 + 0.987814i \(0.450256\pi\)
\(38\) 0 0
\(39\) 8749.32i 0.921113i
\(40\) 0 0
\(41\) 1051.16i 0.0976585i 0.998807 + 0.0488292i \(0.0155490\pi\)
−0.998807 + 0.0488292i \(0.984451\pi\)
\(42\) 0 0
\(43\) −5645.72 + 5645.72i −0.465638 + 0.465638i −0.900498 0.434860i \(-0.856798\pi\)
0.434860 + 0.900498i \(0.356798\pi\)
\(44\) 0 0
\(45\) 3627.18 + 3627.18i 0.267016 + 0.267016i
\(46\) 0 0
\(47\) 2247.96 0.148437 0.0742187 0.997242i \(-0.476354\pi\)
0.0742187 + 0.997242i \(0.476354\pi\)
\(48\) 0 0
\(49\) 12364.5 0.735674
\(50\) 0 0
\(51\) −9139.81 9139.81i −0.492053 0.492053i
\(52\) 0 0
\(53\) 17582.1 17582.1i 0.859769 0.859769i −0.131541 0.991311i \(-0.541993\pi\)
0.991311 + 0.131541i \(0.0419926\pi\)
\(54\) 0 0
\(55\) 1204.66i 0.0536980i
\(56\) 0 0
\(57\) 21026.4i 0.857191i
\(58\) 0 0
\(59\) −22506.6 + 22506.6i −0.841744 + 0.841744i −0.989086 0.147341i \(-0.952928\pi\)
0.147341 + 0.989086i \(0.452928\pi\)
\(60\) 0 0
\(61\) 35680.2 + 35680.2i 1.22773 + 1.22773i 0.964821 + 0.262906i \(0.0846811\pi\)
0.262906 + 0.964821i \(0.415319\pi\)
\(62\) 0 0
\(63\) 13676.0 0.434118
\(64\) 0 0
\(65\) 10332.0 0.303321
\(66\) 0 0
\(67\) −14570.0 14570.0i −0.396526 0.396526i 0.480480 0.877006i \(-0.340462\pi\)
−0.877006 + 0.480480i \(0.840462\pi\)
\(68\) 0 0
\(69\) 42800.5 42800.5i 1.08225 1.08225i
\(70\) 0 0
\(71\) 37150.7i 0.874624i −0.899310 0.437312i \(-0.855930\pi\)
0.899310 0.437312i \(-0.144070\pi\)
\(72\) 0 0
\(73\) 77602.0i 1.70438i −0.523235 0.852188i \(-0.675275\pi\)
0.523235 0.852188i \(-0.324725\pi\)
\(74\) 0 0
\(75\) −9356.07 + 9356.07i −0.192061 + 0.192061i
\(76\) 0 0
\(77\) −2271.04 2271.04i −0.0436514 0.0436514i
\(78\) 0 0
\(79\) 103892. 1.87290 0.936450 0.350800i \(-0.114090\pi\)
0.936450 + 0.350800i \(0.114090\pi\)
\(80\) 0 0
\(81\) 66808.2 1.13140
\(82\) 0 0
\(83\) 30433.5 + 30433.5i 0.484905 + 0.484905i 0.906694 0.421789i \(-0.138598\pi\)
−0.421789 + 0.906694i \(0.638598\pi\)
\(84\) 0 0
\(85\) 10793.2 10793.2i 0.162032 0.162032i
\(86\) 0 0
\(87\) 142589.i 2.01970i
\(88\) 0 0
\(89\) 55535.9i 0.743188i −0.928395 0.371594i \(-0.878811\pi\)
0.928395 0.371594i \(-0.121189\pi\)
\(90\) 0 0
\(91\) 19478.1 19478.1i 0.246571 0.246571i
\(92\) 0 0
\(93\) −11607.2 11607.2i −0.139162 0.139162i
\(94\) 0 0
\(95\) 24830.0 0.282272
\(96\) 0 0
\(97\) 33028.6 0.356419 0.178209 0.983993i \(-0.442970\pi\)
0.178209 + 0.983993i \(0.442970\pi\)
\(98\) 0 0
\(99\) 6991.23 + 6991.23i 0.0716911 + 0.0716911i
\(100\) 0 0
\(101\) −69109.8 + 69109.8i −0.674119 + 0.674119i −0.958663 0.284544i \(-0.908158\pi\)
0.284544 + 0.958663i \(0.408158\pi\)
\(102\) 0 0
\(103\) 59252.8i 0.550321i −0.961398 0.275161i \(-0.911269\pi\)
0.961398 0.275161i \(-0.0887310\pi\)
\(104\) 0 0
\(105\) 35276.3i 0.312256i
\(106\) 0 0
\(107\) 132571. 132571.i 1.11941 1.11941i 0.127585 0.991828i \(-0.459277\pi\)
0.991828 0.127585i \(-0.0407226\pi\)
\(108\) 0 0
\(109\) −151453. 151453.i −1.22099 1.22099i −0.967281 0.253708i \(-0.918350\pi\)
−0.253708 0.967281i \(-0.581650\pi\)
\(110\) 0 0
\(111\) 207473. 1.59829
\(112\) 0 0
\(113\) −27934.3 −0.205798 −0.102899 0.994692i \(-0.532812\pi\)
−0.102899 + 0.994692i \(0.532812\pi\)
\(114\) 0 0
\(115\) 50542.9 + 50542.9i 0.356382 + 0.356382i
\(116\) 0 0
\(117\) −59961.8 + 59961.8i −0.404958 + 0.404958i
\(118\) 0 0
\(119\) 40694.8i 0.263434i
\(120\) 0 0
\(121\) 158729.i 0.985583i
\(122\) 0 0
\(123\) 15735.6 15735.6i 0.0937821 0.0937821i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) 15092.5 0.0830333 0.0415166 0.999138i \(-0.486781\pi\)
0.0415166 + 0.999138i \(0.486781\pi\)
\(128\) 0 0
\(129\) 169030. 0.894310
\(130\) 0 0
\(131\) 225439. + 225439.i 1.14776 + 1.14776i 0.986993 + 0.160765i \(0.0513960\pi\)
0.160765 + 0.986993i \(0.448604\pi\)
\(132\) 0 0
\(133\) 46809.8 46809.8i 0.229460 0.229460i
\(134\) 0 0
\(135\) 20014.4i 0.0945166i
\(136\) 0 0
\(137\) 183393.i 0.834798i 0.908723 + 0.417399i \(0.137058\pi\)
−0.908723 + 0.417399i \(0.862942\pi\)
\(138\) 0 0
\(139\) −227165. + 227165.i −0.997252 + 0.997252i −0.999996 0.00274377i \(-0.999127\pi\)
0.00274377 + 0.999996i \(0.499127\pi\)
\(140\) 0 0
\(141\) −33651.2 33651.2i −0.142545 0.142545i
\(142\) 0 0
\(143\) 19914.6 0.0814386
\(144\) 0 0
\(145\) 168383. 0.665086
\(146\) 0 0
\(147\) −185092. 185092.i −0.706473 0.706473i
\(148\) 0 0
\(149\) 126186. 126186.i 0.465636 0.465636i −0.434862 0.900497i \(-0.643203\pi\)
0.900497 + 0.434862i \(0.143203\pi\)
\(150\) 0 0
\(151\) 406653.i 1.45138i 0.688021 + 0.725691i \(0.258480\pi\)
−0.688021 + 0.725691i \(0.741520\pi\)
\(152\) 0 0
\(153\) 125276.i 0.432652i
\(154\) 0 0
\(155\) 13706.9 13706.9i 0.0458259 0.0458259i
\(156\) 0 0
\(157\) −355078. 355078.i −1.14967 1.14967i −0.986617 0.163058i \(-0.947864\pi\)
−0.163058 0.986617i \(-0.552136\pi\)
\(158\) 0 0
\(159\) −526399. −1.65129
\(160\) 0 0
\(161\) 190568. 0.579410
\(162\) 0 0
\(163\) 300694. + 300694.i 0.886454 + 0.886454i 0.994181 0.107727i \(-0.0343571\pi\)
−0.107727 + 0.994181i \(0.534357\pi\)
\(164\) 0 0
\(165\) −18033.4 + 18033.4i −0.0515665 + 0.0515665i
\(166\) 0 0
\(167\) 12377.8i 0.0343441i −0.999853 0.0171721i \(-0.994534\pi\)
0.999853 0.0171721i \(-0.00546630\pi\)
\(168\) 0 0
\(169\) 200491.i 0.539982i
\(170\) 0 0
\(171\) −144100. + 144100.i −0.376855 + 0.376855i
\(172\) 0 0
\(173\) −207386. 207386.i −0.526823 0.526823i 0.392800 0.919624i \(-0.371506\pi\)
−0.919624 + 0.392800i \(0.871506\pi\)
\(174\) 0 0
\(175\) −41657.7 −0.102825
\(176\) 0 0
\(177\) 673835. 1.61667
\(178\) 0 0
\(179\) 66148.3 + 66148.3i 0.154307 + 0.154307i 0.780039 0.625731i \(-0.215199\pi\)
−0.625731 + 0.780039i \(0.715199\pi\)
\(180\) 0 0
\(181\) −100739. + 100739.i −0.228560 + 0.228560i −0.812091 0.583531i \(-0.801671\pi\)
0.583531 + 0.812091i \(0.301671\pi\)
\(182\) 0 0
\(183\) 1.06824e6i 2.35799i
\(184\) 0 0
\(185\) 245004.i 0.526313i
\(186\) 0 0
\(187\) 20803.4 20803.4i 0.0435040 0.0435040i
\(188\) 0 0
\(189\) 37731.4 + 37731.4i 0.0768331 + 0.0768331i
\(190\) 0 0
\(191\) −3731.48 −0.00740113 −0.00370056 0.999993i \(-0.501178\pi\)
−0.00370056 + 0.999993i \(0.501178\pi\)
\(192\) 0 0
\(193\) −113488. −0.219309 −0.109654 0.993970i \(-0.534974\pi\)
−0.109654 + 0.993970i \(0.534974\pi\)
\(194\) 0 0
\(195\) −154668. 154668.i −0.291281 0.291281i
\(196\) 0 0
\(197\) −299753. + 299753.i −0.550298 + 0.550298i −0.926527 0.376228i \(-0.877221\pi\)
0.376228 + 0.926527i \(0.377221\pi\)
\(198\) 0 0
\(199\) 754680.i 1.35092i −0.737396 0.675460i \(-0.763945\pi\)
0.737396 0.675460i \(-0.236055\pi\)
\(200\) 0 0
\(201\) 436216.i 0.761572i
\(202\) 0 0
\(203\) 317437. 317437.i 0.540652 0.540652i
\(204\) 0 0
\(205\) 18582.1 + 18582.1i 0.0308823 + 0.0308823i
\(206\) 0 0
\(207\) −586650. −0.951597
\(208\) 0 0
\(209\) 47858.7 0.0757871
\(210\) 0 0
\(211\) 440226. + 440226.i 0.680722 + 0.680722i 0.960163 0.279441i \(-0.0901490\pi\)
−0.279441 + 0.960163i \(0.590149\pi\)
\(212\) 0 0
\(213\) −556136. + 556136.i −0.839908 + 0.839908i
\(214\) 0 0
\(215\) 199606.i 0.294495i
\(216\) 0 0
\(217\) 51681.0i 0.0745043i
\(218\) 0 0
\(219\) −1.16168e6 + 1.16168e6i −1.63673 + 1.63673i
\(220\) 0 0
\(221\) 178425. + 178425.i 0.245739 + 0.245739i
\(222\) 0 0
\(223\) 597053. 0.803990 0.401995 0.915642i \(-0.368317\pi\)
0.401995 + 0.915642i \(0.368317\pi\)
\(224\) 0 0
\(225\) 128240. 0.168876
\(226\) 0 0
\(227\) −515972. 515972.i −0.664602 0.664602i 0.291859 0.956461i \(-0.405726\pi\)
−0.956461 + 0.291859i \(0.905726\pi\)
\(228\) 0 0
\(229\) 414064. 414064.i 0.521769 0.521769i −0.396336 0.918105i \(-0.629719\pi\)
0.918105 + 0.396336i \(0.129719\pi\)
\(230\) 0 0
\(231\) 67993.6i 0.0838375i
\(232\) 0 0
\(233\) 556837.i 0.671952i 0.941870 + 0.335976i \(0.109066\pi\)
−0.941870 + 0.335976i \(0.890934\pi\)
\(234\) 0 0
\(235\) 39738.6 39738.6i 0.0469400 0.0469400i
\(236\) 0 0
\(237\) −1.55523e6 1.55523e6i −1.79856 1.79856i
\(238\) 0 0
\(239\) −16833.0 −0.0190619 −0.00953097 0.999955i \(-0.503034\pi\)
−0.00953097 + 0.999955i \(0.503034\pi\)
\(240\) 0 0
\(241\) 416006. 0.461378 0.230689 0.973027i \(-0.425902\pi\)
0.230689 + 0.973027i \(0.425902\pi\)
\(242\) 0 0
\(243\) −862539. 862539.i −0.937050 0.937050i
\(244\) 0 0
\(245\) 218575. 218575.i 0.232641 0.232641i
\(246\) 0 0
\(247\) 410471.i 0.428095i
\(248\) 0 0
\(249\) 911162.i 0.931316i
\(250\) 0 0
\(251\) −1.23509e6 + 1.23509e6i −1.23741 + 1.23741i −0.276359 + 0.961054i \(0.589128\pi\)
−0.961054 + 0.276359i \(0.910872\pi\)
\(252\) 0 0
\(253\) 97419.3 + 97419.3i 0.0956850 + 0.0956850i
\(254\) 0 0
\(255\) −323141. −0.311202
\(256\) 0 0
\(257\) 77341.0 0.0730427 0.0365214 0.999333i \(-0.488372\pi\)
0.0365214 + 0.999333i \(0.488372\pi\)
\(258\) 0 0
\(259\) 461885. + 461885.i 0.427843 + 0.427843i
\(260\) 0 0
\(261\) −977207. + 977207.i −0.887943 + 0.887943i
\(262\) 0 0
\(263\) 1.43109e6i 1.27579i −0.770124 0.637894i \(-0.779806\pi\)
0.770124 0.637894i \(-0.220194\pi\)
\(264\) 0 0
\(265\) 621622.i 0.543766i
\(266\) 0 0
\(267\) −831356. + 831356.i −0.713689 + 0.713689i
\(268\) 0 0
\(269\) 1.03735e6 + 1.03735e6i 0.874067 + 0.874067i 0.992913 0.118846i \(-0.0379194\pi\)
−0.118846 + 0.992913i \(0.537919\pi\)
\(270\) 0 0
\(271\) 654430. 0.541302 0.270651 0.962677i \(-0.412761\pi\)
0.270651 + 0.962677i \(0.412761\pi\)
\(272\) 0 0
\(273\) −583162. −0.473568
\(274\) 0 0
\(275\) −21295.6 21295.6i −0.0169808 0.0169808i
\(276\) 0 0
\(277\) −1.12490e6 + 1.12490e6i −0.880876 + 0.880876i −0.993624 0.112748i \(-0.964035\pi\)
0.112748 + 0.993624i \(0.464035\pi\)
\(278\) 0 0
\(279\) 159096.i 0.122363i
\(280\) 0 0
\(281\) 2.15244e6i 1.62617i 0.582148 + 0.813083i \(0.302213\pi\)
−0.582148 + 0.813083i \(0.697787\pi\)
\(282\) 0 0
\(283\) −1.07730e6 + 1.07730e6i −0.799597 + 0.799597i −0.983032 0.183435i \(-0.941278\pi\)
0.183435 + 0.983032i \(0.441278\pi\)
\(284\) 0 0
\(285\) −371697. 371697.i −0.271067 0.271067i
\(286\) 0 0
\(287\) 70062.3 0.0502088
\(288\) 0 0
\(289\) −1.04708e6 −0.737455
\(290\) 0 0
\(291\) −494428. 494428.i −0.342271 0.342271i
\(292\) 0 0
\(293\) 201738. 201738.i 0.137283 0.137283i −0.635125 0.772409i \(-0.719052\pi\)
0.772409 + 0.635125i \(0.219052\pi\)
\(294\) 0 0
\(295\) 795729.i 0.532366i
\(296\) 0 0
\(297\) 38576.9i 0.0253768i
\(298\) 0 0
\(299\) −835538. + 835538.i −0.540491 + 0.540491i
\(300\) 0 0
\(301\) 376300. + 376300.i 0.239397 + 0.239397i
\(302\) 0 0
\(303\) 2.06911e6 1.29472
\(304\) 0 0
\(305\) 1.26148e6 0.776483
\(306\) 0 0
\(307\) 2.33520e6 + 2.33520e6i 1.41409 + 1.41409i 0.716310 + 0.697783i \(0.245830\pi\)
0.697783 + 0.716310i \(0.254170\pi\)
\(308\) 0 0
\(309\) −886997. + 886997.i −0.528477 + 0.528477i
\(310\) 0 0
\(311\) 1.50514e6i 0.882420i −0.897404 0.441210i \(-0.854549\pi\)
0.897404 0.441210i \(-0.145451\pi\)
\(312\) 0 0
\(313\) 1.17646e6i 0.678763i −0.940649 0.339381i \(-0.889782\pi\)
0.940649 0.339381i \(-0.110218\pi\)
\(314\) 0 0
\(315\) 241760. 241760.i 0.137280 0.137280i
\(316\) 0 0
\(317\) 851779. + 851779.i 0.476079 + 0.476079i 0.903875 0.427796i \(-0.140710\pi\)
−0.427796 + 0.903875i \(0.640710\pi\)
\(318\) 0 0
\(319\) 324551. 0.178569
\(320\) 0 0
\(321\) −3.96911e6 −2.14996
\(322\) 0 0
\(323\) 428791. + 428791.i 0.228686 + 0.228686i
\(324\) 0 0
\(325\) 182646. 182646.i 0.0959185 0.0959185i
\(326\) 0 0
\(327\) 4.53441e6i 2.34505i
\(328\) 0 0
\(329\) 149831.i 0.0763156i
\(330\) 0 0
\(331\) 435282. 435282.i 0.218374 0.218374i −0.589439 0.807813i \(-0.700651\pi\)
0.807813 + 0.589439i \(0.200651\pi\)
\(332\) 0 0
\(333\) −1.42188e6 1.42188e6i −0.702671 0.702671i
\(334\) 0 0
\(335\) −515126. −0.250785
\(336\) 0 0
\(337\) 2.88013e6 1.38146 0.690728 0.723115i \(-0.257290\pi\)
0.690728 + 0.723115i \(0.257290\pi\)
\(338\) 0 0
\(339\) 418168. + 418168.i 0.197629 + 0.197629i
\(340\) 0 0
\(341\) 26419.5 26419.5i 0.0123038 0.0123038i
\(342\) 0 0
\(343\) 1.94435e6i 0.892356i
\(344\) 0 0
\(345\) 1.51323e6i 0.684472i
\(346\) 0 0
\(347\) 2.63293e6 2.63293e6i 1.17386 1.17386i 0.192577 0.981282i \(-0.438315\pi\)
0.981282 0.192577i \(-0.0616846\pi\)
\(348\) 0 0
\(349\) 2.54010e6 + 2.54010e6i 1.11632 + 1.11632i 0.992277 + 0.124040i \(0.0395852\pi\)
0.124040 + 0.992277i \(0.460415\pi\)
\(350\) 0 0
\(351\) −330863. −0.143344
\(352\) 0 0
\(353\) −1.69643e6 −0.724603 −0.362302 0.932061i \(-0.618009\pi\)
−0.362302 + 0.932061i \(0.618009\pi\)
\(354\) 0 0
\(355\) −656738. 656738.i −0.276581 0.276581i
\(356\) 0 0
\(357\) −609189. + 609189.i −0.252977 + 0.252977i
\(358\) 0 0
\(359\) 2.86875e6i 1.17478i −0.809304 0.587390i \(-0.800156\pi\)
0.809304 0.587390i \(-0.199844\pi\)
\(360\) 0 0
\(361\) 1.48965e6i 0.601613i
\(362\) 0 0
\(363\) 2.37613e6 2.37613e6i 0.946462 0.946462i
\(364\) 0 0
\(365\) −1.37182e6 1.37182e6i −0.538971 0.538971i
\(366\) 0 0
\(367\) −231568. −0.0897457 −0.0448729 0.998993i \(-0.514288\pi\)
−0.0448729 + 0.998993i \(0.514288\pi\)
\(368\) 0 0
\(369\) −215682. −0.0824608
\(370\) 0 0
\(371\) −1.17189e6 1.17189e6i −0.442030 0.442030i
\(372\) 0 0
\(373\) 1.46826e6 1.46826e6i 0.546427 0.546427i −0.378979 0.925405i \(-0.623725\pi\)
0.925405 + 0.378979i \(0.123725\pi\)
\(374\) 0 0
\(375\) 330787.i 0.121470i
\(376\) 0 0
\(377\) 2.78358e6i 1.00867i
\(378\) 0 0
\(379\) −460062. + 460062.i −0.164520 + 0.164520i −0.784566 0.620046i \(-0.787114\pi\)
0.620046 + 0.784566i \(0.287114\pi\)
\(380\) 0 0
\(381\) −225930. 225930.i −0.0797375 0.0797375i
\(382\) 0 0
\(383\) 278081. 0.0968665 0.0484333 0.998826i \(-0.484577\pi\)
0.0484333 + 0.998826i \(0.484577\pi\)
\(384\) 0 0
\(385\) −80293.4 −0.0276076
\(386\) 0 0
\(387\) −1.15841e6 1.15841e6i −0.393175 0.393175i
\(388\) 0 0
\(389\) 3.81927e6 3.81927e6i 1.27969 1.27969i 0.338855 0.940839i \(-0.389960\pi\)
0.940839 0.338855i \(-0.110040\pi\)
\(390\) 0 0
\(391\) 1.74566e6i 0.577454i
\(392\) 0 0
\(393\) 6.74950e6i 2.20440i
\(394\) 0 0
\(395\) 1.83657e6 1.83657e6i 0.592263 0.592263i
\(396\) 0 0
\(397\) −978913. 978913.i −0.311722 0.311722i 0.533854 0.845576i \(-0.320743\pi\)
−0.845576 + 0.533854i \(0.820743\pi\)
\(398\) 0 0
\(399\) −1.40146e6 −0.440704
\(400\) 0 0
\(401\) −1.86658e6 −0.579677 −0.289838 0.957076i \(-0.593602\pi\)
−0.289838 + 0.957076i \(0.593602\pi\)
\(402\) 0 0
\(403\) 226593. + 226593.i 0.0694999 + 0.0694999i
\(404\) 0 0
\(405\) 1.18101e6 1.18101e6i 0.357781 0.357781i
\(406\) 0 0
\(407\) 472235.i 0.141310i
\(408\) 0 0
\(409\) 4.49733e6i 1.32937i 0.747123 + 0.664686i \(0.231435\pi\)
−0.747123 + 0.664686i \(0.768565\pi\)
\(410\) 0 0
\(411\) 2.74534e6 2.74534e6i 0.801663 0.801663i
\(412\) 0 0
\(413\) 1.50012e6 + 1.50012e6i 0.432763 + 0.432763i
\(414\) 0 0
\(415\) 1.07599e6 0.306681
\(416\) 0 0
\(417\) 6.80120e6 1.91534
\(418\) 0 0
\(419\) 289805. + 289805.i 0.0806438 + 0.0806438i 0.746278 0.665634i \(-0.231839\pi\)
−0.665634 + 0.746278i \(0.731839\pi\)
\(420\) 0 0
\(421\) 3.18738e6 3.18738e6i 0.876452 0.876452i −0.116714 0.993166i \(-0.537236\pi\)
0.993166 + 0.116714i \(0.0372360\pi\)
\(422\) 0 0
\(423\) 461245.i 0.125337i
\(424\) 0 0
\(425\) 381596.i 0.102478i
\(426\) 0 0
\(427\) 2.37816e6 2.37816e6i 0.631207 0.631207i
\(428\) 0 0
\(429\) −298115. 298115.i −0.0782061 0.0782061i
\(430\) 0 0
\(431\) −1.40103e6 −0.363290 −0.181645 0.983364i \(-0.558142\pi\)
−0.181645 + 0.983364i \(0.558142\pi\)
\(432\) 0 0
\(433\) 4.92875e6 1.26333 0.631666 0.775241i \(-0.282372\pi\)
0.631666 + 0.775241i \(0.282372\pi\)
\(434\) 0 0
\(435\) −2.52064e6 2.52064e6i −0.638687 0.638687i
\(436\) 0 0
\(437\) −2.00797e6 + 2.00797e6i −0.502983 + 0.502983i
\(438\) 0 0
\(439\) 489017.i 0.121105i −0.998165 0.0605526i \(-0.980714\pi\)
0.998165 0.0605526i \(-0.0192863\pi\)
\(440\) 0 0
\(441\) 2.53699e6i 0.621188i
\(442\) 0 0
\(443\) 5.39962e6 5.39962e6i 1.30724 1.30724i 0.383833 0.923403i \(-0.374604\pi\)
0.923403 0.383833i \(-0.125396\pi\)
\(444\) 0 0
\(445\) −981746. 981746.i −0.235017 0.235017i
\(446\) 0 0
\(447\) −3.77794e6 −0.894307
\(448\) 0 0
\(449\) −1.48009e6 −0.346475 −0.173237 0.984880i \(-0.555423\pi\)
−0.173237 + 0.984880i \(0.555423\pi\)
\(450\) 0 0
\(451\) 35816.2 + 35816.2i 0.00829159 + 0.00829159i
\(452\) 0 0
\(453\) 6.08748e6 6.08748e6i 1.39377 1.39377i
\(454\) 0 0
\(455\) 688654.i 0.155945i
\(456\) 0 0
\(457\) 5.01425e6i 1.12309i 0.827445 + 0.561546i \(0.189793\pi\)
−0.827445 + 0.561546i \(0.810207\pi\)
\(458\) 0 0
\(459\) −345630. + 345630.i −0.0765738 + 0.0765738i
\(460\) 0 0
\(461\) 1.39558e6 + 1.39558e6i 0.305845 + 0.305845i 0.843295 0.537450i \(-0.180612\pi\)
−0.537450 + 0.843295i \(0.680612\pi\)
\(462\) 0 0
\(463\) −4.41497e6 −0.957139 −0.478570 0.878050i \(-0.658845\pi\)
−0.478570 + 0.878050i \(0.658845\pi\)
\(464\) 0 0
\(465\) −410378. −0.0880139
\(466\) 0 0
\(467\) 833822. + 833822.i 0.176922 + 0.176922i 0.790013 0.613091i \(-0.210074\pi\)
−0.613091 + 0.790013i \(0.710074\pi\)
\(468\) 0 0
\(469\) −971121. + 971121.i −0.203864 + 0.203864i
\(470\) 0 0
\(471\) 1.06308e7i 2.20808i
\(472\) 0 0
\(473\) 384733.i 0.0790690i
\(474\) 0 0
\(475\) 438936. 438936.i 0.0892622 0.0892622i
\(476\) 0 0
\(477\) 3.60757e6 + 3.60757e6i 0.725971 + 0.725971i
\(478\) 0 0
\(479\) 5.84747e6 1.16447 0.582236 0.813020i \(-0.302178\pi\)
0.582236 + 0.813020i \(0.302178\pi\)
\(480\) 0 0
\(481\) −4.05023e6 −0.798210
\(482\) 0 0
\(483\) −2.85275e6 2.85275e6i −0.556411 0.556411i
\(484\) 0 0
\(485\) 583868. 583868.i 0.112709 0.112709i
\(486\) 0 0
\(487\) 5.71510e6i 1.09195i 0.837802 + 0.545974i \(0.183840\pi\)
−0.837802 + 0.545974i \(0.816160\pi\)
\(488\) 0 0
\(489\) 9.00261e6i 1.70254i
\(490\) 0 0
\(491\) −2.06011e6 + 2.06011e6i −0.385645 + 0.385645i −0.873131 0.487486i \(-0.837914\pi\)
0.487486 + 0.873131i \(0.337914\pi\)
\(492\) 0 0
\(493\) 2.90781e6 + 2.90781e6i 0.538827 + 0.538827i
\(494\) 0 0
\(495\) 247177. 0.0453414
\(496\) 0 0
\(497\) −2.47618e6 −0.449668
\(498\) 0 0
\(499\) 4.78177e6 + 4.78177e6i 0.859680 + 0.859680i 0.991300 0.131620i \(-0.0420179\pi\)
−0.131620 + 0.991300i \(0.542018\pi\)
\(500\) 0 0
\(501\) −185292. + 185292.i −0.0329809 + 0.0329809i
\(502\) 0 0
\(503\) 4.52174e6i 0.796867i −0.917197 0.398433i \(-0.869554\pi\)
0.917197 0.398433i \(-0.130446\pi\)
\(504\) 0 0
\(505\) 2.44340e6i 0.426350i
\(506\) 0 0
\(507\) −3.00130e6 + 3.00130e6i −0.518548 + 0.518548i
\(508\) 0 0
\(509\) 296532. + 296532.i 0.0507314 + 0.0507314i 0.732017 0.681286i \(-0.238579\pi\)
−0.681286 + 0.732017i \(0.738579\pi\)
\(510\) 0 0
\(511\) −5.17235e6 −0.876265
\(512\) 0 0
\(513\) −795132. −0.133397
\(514\) 0 0
\(515\) −1.04745e6 1.04745e6i −0.174027 0.174027i
\(516\) 0 0
\(517\) 76594.5 76594.5i 0.0126029 0.0126029i
\(518\) 0 0
\(519\) 6.20903e6i 1.01182i
\(520\) 0 0
\(521\) 458362.i 0.0739800i −0.999316 0.0369900i \(-0.988223\pi\)
0.999316 0.0369900i \(-0.0117770\pi\)
\(522\) 0 0
\(523\) −1.31189e6 + 1.31189e6i −0.209721 + 0.209721i −0.804149 0.594428i \(-0.797379\pi\)
0.594428 + 0.804149i \(0.297379\pi\)
\(524\) 0 0
\(525\) 623603. + 623603.i 0.0987439 + 0.0987439i
\(526\) 0 0
\(527\) 473412. 0.0742528
\(528\) 0 0
\(529\) −1.73834e6 −0.270082
\(530\) 0 0
\(531\) −4.61800e6 4.61800e6i −0.710751 0.710751i
\(532\) 0 0
\(533\) −307185. + 307185.i −0.0468363 + 0.0468363i
\(534\) 0 0
\(535\) 4.68710e6i 0.707979i
\(536\) 0 0
\(537\) 1.98044e6i 0.296364i
\(538\) 0 0
\(539\) 421294. 421294.i 0.0624616 0.0624616i
\(540\) 0 0
\(541\) 7.50591e6 + 7.50591e6i 1.10258 + 1.10258i 0.994098 + 0.108481i \(0.0345988\pi\)
0.108481 + 0.994098i \(0.465401\pi\)
\(542\) 0 0
\(543\) 3.01606e6 0.438975
\(544\) 0 0
\(545\) −5.35467e6 −0.772221
\(546\) 0 0
\(547\) 3.64329e6 + 3.64329e6i 0.520626 + 0.520626i 0.917760 0.397135i \(-0.129995\pi\)
−0.397135 + 0.917760i \(0.629995\pi\)
\(548\) 0 0
\(549\) −7.32100e6 + 7.32100e6i −1.03667 + 1.03667i
\(550\) 0 0
\(551\) 6.68951e6i 0.938675i
\(552\) 0 0
\(553\) 6.92465e6i 0.962908i
\(554\) 0 0
\(555\) 3.66764e6 3.66764e6i 0.505422 0.505422i
\(556\) 0 0
\(557\) −2.00393e6 2.00393e6i −0.273681 0.273681i 0.556899 0.830580i \(-0.311991\pi\)
−0.830580 + 0.556899i \(0.811991\pi\)
\(558\) 0 0
\(559\) −3.29974e6 −0.446633
\(560\) 0 0
\(561\) −622841. −0.0835545
\(562\) 0 0
\(563\) −4.20161e6 4.20161e6i −0.558656 0.558656i 0.370269 0.928925i \(-0.379266\pi\)
−0.928925 + 0.370269i \(0.879266\pi\)
\(564\) 0 0
\(565\) −493813. + 493813.i −0.0650791 + 0.0650791i
\(566\) 0 0
\(567\) 4.45292e6i 0.581684i
\(568\) 0 0
\(569\) 4.05098e6i 0.524541i 0.964994 + 0.262271i \(0.0844713\pi\)
−0.964994 + 0.262271i \(0.915529\pi\)
\(570\) 0 0
\(571\) −7.13511e6 + 7.13511e6i −0.915820 + 0.915820i −0.996722 0.0809020i \(-0.974220\pi\)
0.0809020 + 0.996722i \(0.474220\pi\)
\(572\) 0 0
\(573\) 55859.2 + 55859.2i 0.00710735 + 0.00710735i
\(574\) 0 0
\(575\) 1.78696e6 0.225396
\(576\) 0 0
\(577\) −1.29452e7 −1.61871 −0.809355 0.587320i \(-0.800183\pi\)
−0.809355 + 0.587320i \(0.800183\pi\)
\(578\) 0 0
\(579\) 1.69888e6 + 1.69888e6i 0.210604 + 0.210604i
\(580\) 0 0
\(581\) 2.02846e6 2.02846e6i 0.249303 0.249303i
\(582\) 0 0
\(583\) 1.19815e6i 0.145996i
\(584\) 0 0
\(585\) 2.11997e6i 0.256118i
\(586\) 0 0
\(587\) 243385. 243385.i 0.0291540 0.0291540i −0.692379 0.721534i \(-0.743438\pi\)
0.721534 + 0.692379i \(0.243438\pi\)
\(588\) 0 0
\(589\) 544549. + 544549.i 0.0646768 + 0.0646768i
\(590\) 0 0
\(591\) 8.97443e6 1.05691
\(592\) 0 0
\(593\) −1.13600e7 −1.32661 −0.663305 0.748349i \(-0.730847\pi\)
−0.663305 + 0.748349i \(0.730847\pi\)
\(594\) 0 0
\(595\) −719390. 719390.i −0.0833051 0.0833051i
\(596\) 0 0
\(597\) −1.12973e7 + 1.12973e7i −1.29730 + 1.29730i
\(598\) 0 0
\(599\) 4.77277e6i 0.543505i −0.962367 0.271752i \(-0.912397\pi\)
0.962367 0.271752i \(-0.0876032\pi\)
\(600\) 0 0
\(601\) 6.29410e6i 0.710800i 0.934714 + 0.355400i \(0.115655\pi\)
−0.934714 + 0.355400i \(0.884345\pi\)
\(602\) 0 0
\(603\) 2.98952e6 2.98952e6i 0.334818 0.334818i
\(604\) 0 0
\(605\) 2.80596e6 + 2.80596e6i 0.311669 + 0.311669i
\(606\) 0 0
\(607\) 1.46495e6 0.161380 0.0806901 0.996739i \(-0.474288\pi\)
0.0806901 + 0.996739i \(0.474288\pi\)
\(608\) 0 0
\(609\) −9.50388e6 −1.03838
\(610\) 0 0
\(611\) 656929. + 656929.i 0.0711895 + 0.0711895i
\(612\) 0 0
\(613\) 6.75338e6 6.75338e6i 0.725888 0.725888i −0.243910 0.969798i \(-0.578430\pi\)
0.969798 + 0.243910i \(0.0784300\pi\)
\(614\) 0 0
\(615\) 556337.i 0.0593130i
\(616\) 0 0
\(617\) 1.41502e7i 1.49641i −0.663468 0.748205i \(-0.730916\pi\)
0.663468 0.748205i \(-0.269084\pi\)
\(618\) 0 0
\(619\) 5.04550e6 5.04550e6i 0.529271 0.529271i −0.391084 0.920355i \(-0.627900\pi\)
0.920355 + 0.391084i \(0.127900\pi\)
\(620\) 0 0
\(621\) −1.61854e6 1.61854e6i −0.168420 0.168420i
\(622\) 0 0
\(623\) −3.70160e6 −0.382093
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) −716431. 716431.i −0.0727789 0.0727789i
\(628\) 0 0
\(629\) −4.23100e6 + 4.23100e6i −0.426399 + 0.426399i
\(630\) 0 0
\(631\) 1.77040e7i 1.77010i 0.465495 + 0.885051i \(0.345876\pi\)
−0.465495 + 0.885051i \(0.654124\pi\)
\(632\) 0 0
\(633\) 1.31801e7i 1.30740i
\(634\) 0 0
\(635\) 266800. 266800.i 0.0262574 0.0262574i
\(636\) 0 0
\(637\) 3.61332e6 + 3.61332e6i 0.352824 + 0.352824i
\(638\) 0 0
\(639\) 7.62274e6 0.738514
\(640\) 0 0
\(641\) −1.04525e7 −1.00479 −0.502395 0.864638i \(-0.667548\pi\)
−0.502395 + 0.864638i \(0.667548\pi\)
\(642\) 0 0
\(643\) 5.43319e6 + 5.43319e6i 0.518236 + 0.518236i 0.917037 0.398801i \(-0.130574\pi\)
−0.398801 + 0.917037i \(0.630574\pi\)
\(644\) 0 0
\(645\) 2.98805e6 2.98805e6i 0.282806 0.282806i
\(646\) 0 0
\(647\) 1.39010e7i 1.30552i −0.757563 0.652762i \(-0.773610\pi\)
0.757563 0.652762i \(-0.226390\pi\)
\(648\) 0 0
\(649\) 1.53373e6i 0.142935i
\(650\) 0 0
\(651\) −773649. + 773649.i −0.0715470 + 0.0715470i
\(652\) 0 0
\(653\) −1.15514e7 1.15514e7i −1.06011 1.06011i −0.998074 0.0620336i \(-0.980241\pi\)
−0.0620336 0.998074i \(-0.519759\pi\)
\(654\) 0 0
\(655\) 7.97046e6 0.725906
\(656\) 0 0
\(657\) 1.59227e7 1.43914
\(658\) 0 0
\(659\) −1.20268e7 1.20268e7i −1.07879 1.07879i −0.996618 0.0821756i \(-0.973813\pi\)
−0.0821756 0.996618i \(-0.526187\pi\)
\(660\) 0 0
\(661\) −3.95930e6 + 3.95930e6i −0.352464 + 0.352464i −0.861026 0.508562i \(-0.830177\pi\)
0.508562 + 0.861026i \(0.330177\pi\)
\(662\) 0 0
\(663\) 5.34193e6i 0.471970i
\(664\) 0 0
\(665\) 1.65498e6i 0.145123i
\(666\) 0 0
\(667\) −1.36169e7 + 1.36169e7i −1.18512 + 1.18512i
\(668\) 0 0
\(669\) −8.93770e6 8.93770e6i −0.772077 0.772077i
\(670\) 0 0
\(671\) 2.43146e6 0.208478
\(672\) 0 0
\(673\) 1.00027e7 0.851297 0.425649 0.904889i \(-0.360046\pi\)
0.425649 + 0.904889i \(0.360046\pi\)
\(674\) 0 0
\(675\) 353808. + 353808.i 0.0298888 + 0.0298888i
\(676\) 0 0
\(677\) −943407. + 943407.i −0.0791093 + 0.0791093i −0.745554 0.666445i \(-0.767815\pi\)
0.666445 + 0.745554i \(0.267815\pi\)
\(678\) 0 0
\(679\) 2.20143e6i 0.183244i
\(680\) 0 0
\(681\) 1.54479e7i 1.27644i
\(682\) 0 0
\(683\) −1.13632e7 + 1.13632e7i −0.932069 + 0.932069i −0.997835 0.0657662i \(-0.979051\pi\)
0.0657662 + 0.997835i \(0.479051\pi\)
\(684\) 0 0
\(685\) 3.24196e6 + 3.24196e6i 0.263986 + 0.263986i
\(686\) 0 0
\(687\) −1.23968e7 −1.00212
\(688\) 0 0
\(689\) 1.02762e7 0.824678
\(690\) 0 0
\(691\) −2.49054e6 2.49054e6i −0.198426 0.198426i 0.600899 0.799325i \(-0.294809\pi\)
−0.799325 + 0.600899i \(0.794809\pi\)
\(692\) 0 0
\(693\) 465981. 465981.i 0.0368583 0.0368583i
\(694\) 0 0
\(695\) 8.03151e6i 0.630718i
\(696\) 0 0
\(697\) 641791.i 0.0500393i
\(698\) 0 0
\(699\) 8.33569e6 8.33569e6i 0.645281 0.645281i
\(700\) 0 0
\(701\) 1.13666e7 + 1.13666e7i 0.873643 + 0.873643i 0.992867 0.119224i \(-0.0380408\pi\)
−0.119224 + 0.992867i \(0.538041\pi\)
\(702\) 0 0
\(703\) −9.73352e6 −0.742817
\(704\) 0 0
\(705\) −1.18975e6 −0.0901536
\(706\) 0 0
\(707\) 4.60633e6 + 4.60633e6i 0.346582 + 0.346582i
\(708\) 0 0
\(709\) −6.22852e6 + 6.22852e6i −0.465339 + 0.465339i −0.900401 0.435062i \(-0.856727\pi\)
0.435062 + 0.900401i \(0.356727\pi\)
\(710\) 0 0
\(711\) 2.13170e7i 1.58144i
\(712\) 0 0
\(713\) 2.21693e6i 0.163315i
\(714\) 0 0
\(715\) 352043. 352043.i 0.0257532 0.0257532i
\(716\) 0 0
\(717\) 251985. + 251985.i 0.0183053 + 0.0183053i
\(718\) 0 0
\(719\) −2.31572e7 −1.67057 −0.835283 0.549820i \(-0.814696\pi\)
−0.835283 + 0.549820i \(0.814696\pi\)
\(720\) 0 0
\(721\) −3.94934e6 −0.282935
\(722\) 0 0
\(723\) −6.22749e6 6.22749e6i −0.443065 0.443065i
\(724\) 0 0
\(725\) 2.97662e6 2.97662e6i 0.210319 0.210319i
\(726\) 0 0
\(727\) 2.19864e7i 1.54283i −0.636331 0.771416i \(-0.719549\pi\)
0.636331 0.771416i \(-0.280451\pi\)
\(728\) 0 0
\(729\) 9.58950e6i 0.668309i
\(730\) 0 0
\(731\) −3.44702e6 + 3.44702e6i −0.238589 + 0.238589i
\(732\) 0 0
\(733\) −7.72418e6 7.72418e6i −0.530998 0.530998i 0.389872 0.920869i \(-0.372519\pi\)
−0.920869 + 0.389872i \(0.872519\pi\)
\(734\) 0 0
\(735\) −6.54401e6 −0.446813
\(736\) 0 0
\(737\) −992882. −0.0673332
\(738\) 0 0
\(739\) 7.11778e6 + 7.11778e6i 0.479439 + 0.479439i 0.904952 0.425513i \(-0.139906\pi\)
−0.425513 + 0.904952i \(0.639906\pi\)
\(740\) 0 0
\(741\) 6.14463e6 6.14463e6i 0.411102 0.411102i
\(742\) 0 0
\(743\) 1.83694e6i 0.122074i −0.998136 0.0610368i \(-0.980559\pi\)
0.998136 0.0610368i \(-0.0194407\pi\)
\(744\) 0 0
\(745\) 4.46136e6i 0.294494i
\(746\) 0 0
\(747\) −6.24448e6 + 6.24448e6i −0.409444 + 0.409444i
\(748\) 0 0
\(749\) −8.83618e6 8.83618e6i −0.575520 0.575520i
\(750\) 0 0
\(751\) 2.46486e6 0.159475 0.0797375 0.996816i \(-0.474592\pi\)
0.0797375 + 0.996816i \(0.474592\pi\)
\(752\) 0 0
\(753\) 3.69779e7 2.37659
\(754\) 0 0
\(755\) 7.18868e6 + 7.18868e6i 0.458967 + 0.458967i
\(756\) 0 0
\(757\) 737006. 737006.i 0.0467446 0.0467446i −0.683348 0.730093i \(-0.739477\pi\)
0.730093 + 0.683348i \(0.239477\pi\)
\(758\) 0 0
\(759\) 2.91668e6i 0.183774i
\(760\) 0 0
\(761\) 2.99911e7i 1.87729i 0.344887 + 0.938644i \(0.387917\pi\)
−0.344887 + 0.938644i \(0.612083\pi\)
\(762\) 0 0
\(763\) −1.00947e7 + 1.00947e7i −0.627743 + 0.627743i
\(764\) 0 0
\(765\) 2.21459e6 + 2.21459e6i 0.136817 + 0.136817i
\(766\) 0 0
\(767\) −1.31544e7 −0.807389
\(768\) 0 0
\(769\) 1.88084e7 1.14693 0.573464 0.819231i \(-0.305599\pi\)
0.573464 + 0.819231i \(0.305599\pi\)
\(770\) 0 0
\(771\) −1.15777e6 1.15777e6i −0.0701435 0.0701435i
\(772\) 0 0
\(773\) 4.46987e6 4.46987e6i 0.269058 0.269058i −0.559662 0.828721i \(-0.689069\pi\)
0.828721 + 0.559662i \(0.189069\pi\)
\(774\) 0 0
\(775\) 484614.i 0.0289829i
\(776\) 0 0
\(777\) 1.38286e7i 0.821721i
\(778\) 0 0
\(779\) −738229. + 738229.i −0.0435860 + 0.0435860i
\(780\) 0 0
\(781\) −1.26584e6 1.26584e6i −0.0742591 0.0742591i
\(782\) 0 0
\(783\) −5.39213e6 −0.314308
\(784\) 0 0
\(785\) −1.25539e7 −0.727118
\(786\) 0 0