Properties

Label 320.6.l.a.81.19
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 81.19
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.19

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.82595 - 2.82595i) q^{3} +(17.6777 - 17.6777i) q^{5} -197.416i q^{7} -227.028i q^{9} +O(q^{10})\) \(q+(-2.82595 - 2.82595i) q^{3} +(17.6777 - 17.6777i) q^{5} -197.416i q^{7} -227.028i q^{9} +(541.655 - 541.655i) q^{11} +(-657.010 - 657.010i) q^{13} -99.9125 q^{15} +152.646 q^{17} +(428.008 + 428.008i) q^{19} +(-557.887 + 557.887i) q^{21} +2103.77i q^{23} -625.000i q^{25} +(-1328.28 + 1328.28i) q^{27} +(-1313.03 - 1313.03i) q^{29} +8014.55 q^{31} -3061.38 q^{33} +(-3489.85 - 3489.85i) q^{35} +(-4174.18 + 4174.18i) q^{37} +3713.36i q^{39} -6836.92i q^{41} +(-367.257 + 367.257i) q^{43} +(-4013.33 - 4013.33i) q^{45} +6123.69 q^{47} -22165.9 q^{49} +(-431.370 - 431.370i) q^{51} +(-8837.44 + 8837.44i) q^{53} -19150.4i q^{55} -2419.06i q^{57} +(23628.5 - 23628.5i) q^{59} +(34685.8 + 34685.8i) q^{61} -44818.9 q^{63} -23228.8 q^{65} +(12889.4 + 12889.4i) q^{67} +(5945.16 - 5945.16i) q^{69} -56725.7i q^{71} +41485.9i q^{73} +(-1766.22 + 1766.22i) q^{75} +(-106931. - 106931. i) q^{77} -106416. q^{79} -47660.5 q^{81} +(49167.0 + 49167.0i) q^{83} +(2698.42 - 2698.42i) q^{85} +7421.13i q^{87} -62632.3i q^{89} +(-129704. + 129704. i) q^{91} +(-22648.8 - 22648.8i) q^{93} +15132.4 q^{95} +27802.9 q^{97} +(-122971. - 122971. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

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
\(3\) −2.82595 2.82595i −0.181285 0.181285i 0.610631 0.791916i \(-0.290916\pi\)
−0.791916 + 0.610631i \(0.790916\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 197.416i 1.52278i −0.648296 0.761389i \(-0.724518\pi\)
0.648296 0.761389i \(-0.275482\pi\)
\(8\) 0 0
\(9\) 227.028i 0.934272i
\(10\) 0 0
\(11\) 541.655 541.655i 1.34971 1.34971i 0.463739 0.885972i \(-0.346507\pi\)
0.885972 0.463739i \(-0.153493\pi\)
\(12\) 0 0
\(13\) −657.010 657.010i −1.07824 1.07824i −0.996668 0.0815680i \(-0.974007\pi\)
−0.0815680 0.996668i \(-0.525993\pi\)
\(14\) 0 0
\(15\) −99.9125 −0.114655
\(16\) 0 0
\(17\) 152.646 0.128104 0.0640520 0.997947i \(-0.479598\pi\)
0.0640520 + 0.997947i \(0.479598\pi\)
\(18\) 0 0
\(19\) 428.008 + 428.008i 0.272000 + 0.272000i 0.829905 0.557905i \(-0.188395\pi\)
−0.557905 + 0.829905i \(0.688395\pi\)
\(20\) 0 0
\(21\) −557.887 + 557.887i −0.276057 + 0.276057i
\(22\) 0 0
\(23\) 2103.77i 0.829237i 0.909995 + 0.414619i \(0.136085\pi\)
−0.909995 + 0.414619i \(0.863915\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −1328.28 + 1328.28i −0.350654 + 0.350654i
\(28\) 0 0
\(29\) −1313.03 1313.03i −0.289921 0.289921i 0.547128 0.837049i \(-0.315721\pi\)
−0.837049 + 0.547128i \(0.815721\pi\)
\(30\) 0 0
\(31\) 8014.55 1.49787 0.748937 0.662642i \(-0.230565\pi\)
0.748937 + 0.662642i \(0.230565\pi\)
\(32\) 0 0
\(33\) −3061.38 −0.489365
\(34\) 0 0
\(35\) −3489.85 3489.85i −0.481544 0.481544i
\(36\) 0 0
\(37\) −4174.18 + 4174.18i −0.501265 + 0.501265i −0.911831 0.410566i \(-0.865331\pi\)
0.410566 + 0.911831i \(0.365331\pi\)
\(38\) 0 0
\(39\) 3713.36i 0.390936i
\(40\) 0 0
\(41\) 6836.92i 0.635186i −0.948227 0.317593i \(-0.897126\pi\)
0.948227 0.317593i \(-0.102874\pi\)
\(42\) 0 0
\(43\) −367.257 + 367.257i −0.0302900 + 0.0302900i −0.722090 0.691800i \(-0.756818\pi\)
0.691800 + 0.722090i \(0.256818\pi\)
\(44\) 0 0
\(45\) −4013.33 4013.33i −0.295443 0.295443i
\(46\) 0 0
\(47\) 6123.69 0.404360 0.202180 0.979348i \(-0.435197\pi\)
0.202180 + 0.979348i \(0.435197\pi\)
\(48\) 0 0
\(49\) −22165.9 −1.31885
\(50\) 0 0
\(51\) −431.370 431.370i −0.0232233 0.0232233i
\(52\) 0 0
\(53\) −8837.44 + 8837.44i −0.432152 + 0.432152i −0.889360 0.457208i \(-0.848850\pi\)
0.457208 + 0.889360i \(0.348850\pi\)
\(54\) 0 0
\(55\) 19150.4i 0.853632i
\(56\) 0 0
\(57\) 2419.06i 0.0986189i
\(58\) 0 0
\(59\) 23628.5 23628.5i 0.883704 0.883704i −0.110205 0.993909i \(-0.535151\pi\)
0.993909 + 0.110205i \(0.0351508\pi\)
\(60\) 0 0
\(61\) 34685.8 + 34685.8i 1.19351 + 1.19351i 0.976074 + 0.217437i \(0.0697698\pi\)
0.217437 + 0.976074i \(0.430230\pi\)
\(62\) 0 0
\(63\) −44818.9 −1.42269
\(64\) 0 0
\(65\) −23228.8 −0.681936
\(66\) 0 0
\(67\) 12889.4 + 12889.4i 0.350790 + 0.350790i 0.860403 0.509613i \(-0.170212\pi\)
−0.509613 + 0.860403i \(0.670212\pi\)
\(68\) 0 0
\(69\) 5945.16 5945.16i 0.150328 0.150328i
\(70\) 0 0
\(71\) 56725.7i 1.33547i −0.744399 0.667735i \(-0.767264\pi\)
0.744399 0.667735i \(-0.232736\pi\)
\(72\) 0 0
\(73\) 41485.9i 0.911158i 0.890195 + 0.455579i \(0.150568\pi\)
−0.890195 + 0.455579i \(0.849432\pi\)
\(74\) 0 0
\(75\) −1766.22 + 1766.22i −0.0362570 + 0.0362570i
\(76\) 0 0
\(77\) −106931. 106931.i −2.05531 2.05531i
\(78\) 0 0
\(79\) −106416. −1.91839 −0.959196 0.282743i \(-0.908756\pi\)
−0.959196 + 0.282743i \(0.908756\pi\)
\(80\) 0 0
\(81\) −47660.5 −0.807135
\(82\) 0 0
\(83\) 49167.0 + 49167.0i 0.783390 + 0.783390i 0.980401 0.197011i \(-0.0631235\pi\)
−0.197011 + 0.980401i \(0.563124\pi\)
\(84\) 0 0
\(85\) 2698.42 2698.42i 0.0405100 0.0405100i
\(86\) 0 0
\(87\) 7421.13i 0.105117i
\(88\) 0 0
\(89\) 62632.3i 0.838154i −0.907951 0.419077i \(-0.862354\pi\)
0.907951 0.419077i \(-0.137646\pi\)
\(90\) 0 0
\(91\) −129704. + 129704.i −1.64191 + 1.64191i
\(92\) 0 0
\(93\) −22648.8 22648.8i −0.271542 0.271542i
\(94\) 0 0
\(95\) 15132.4 0.172028
\(96\) 0 0
\(97\) 27802.9 0.300027 0.150014 0.988684i \(-0.452068\pi\)
0.150014 + 0.988684i \(0.452068\pi\)
\(98\) 0 0
\(99\) −122971. 122971.i −1.26100 1.26100i
\(100\) 0 0
\(101\) −86867.1 + 86867.1i −0.847328 + 0.847328i −0.989799 0.142471i \(-0.954495\pi\)
0.142471 + 0.989799i \(0.454495\pi\)
\(102\) 0 0
\(103\) 37838.9i 0.351436i −0.984441 0.175718i \(-0.943775\pi\)
0.984441 0.175718i \(-0.0562246\pi\)
\(104\) 0 0
\(105\) 19724.3i 0.174594i
\(106\) 0 0
\(107\) −1871.29 + 1871.29i −0.0158009 + 0.0158009i −0.714963 0.699162i \(-0.753557\pi\)
0.699162 + 0.714963i \(0.253557\pi\)
\(108\) 0 0
\(109\) 39905.8 + 39905.8i 0.321714 + 0.321714i 0.849424 0.527710i \(-0.176949\pi\)
−0.527710 + 0.849424i \(0.676949\pi\)
\(110\) 0 0
\(111\) 23592.1 0.181743
\(112\) 0 0
\(113\) 179127. 1.31967 0.659834 0.751412i \(-0.270627\pi\)
0.659834 + 0.751412i \(0.270627\pi\)
\(114\) 0 0
\(115\) 37189.8 + 37189.8i 0.262228 + 0.262228i
\(116\) 0 0
\(117\) −149160. + 149160.i −1.00736 + 1.00736i
\(118\) 0 0
\(119\) 30134.7i 0.195074i
\(120\) 0 0
\(121\) 425729.i 2.64344i
\(122\) 0 0
\(123\) −19320.8 + 19320.8i −0.115150 + 0.115150i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) −54658.8 −0.300712 −0.150356 0.988632i \(-0.548042\pi\)
−0.150356 + 0.988632i \(0.548042\pi\)
\(128\) 0 0
\(129\) 2075.70 0.0109822
\(130\) 0 0
\(131\) −75263.3 75263.3i −0.383182 0.383182i 0.489065 0.872247i \(-0.337338\pi\)
−0.872247 + 0.489065i \(0.837338\pi\)
\(132\) 0 0
\(133\) 84495.5 84495.5i 0.414195 0.414195i
\(134\) 0 0
\(135\) 46961.7i 0.221773i
\(136\) 0 0
\(137\) 82268.7i 0.374484i −0.982314 0.187242i \(-0.940045\pi\)
0.982314 0.187242i \(-0.0599549\pi\)
\(138\) 0 0
\(139\) 30619.7 30619.7i 0.134420 0.134420i −0.636696 0.771115i \(-0.719699\pi\)
0.771115 + 0.636696i \(0.219699\pi\)
\(140\) 0 0
\(141\) −17305.2 17305.2i −0.0733044 0.0733044i
\(142\) 0 0
\(143\) −711745. −2.91061
\(144\) 0 0
\(145\) −46422.6 −0.183362
\(146\) 0 0
\(147\) 62639.8 + 62639.8i 0.239088 + 0.239088i
\(148\) 0 0
\(149\) −209646. + 209646.i −0.773607 + 0.773607i −0.978735 0.205128i \(-0.934239\pi\)
0.205128 + 0.978735i \(0.434239\pi\)
\(150\) 0 0
\(151\) 202737.i 0.723586i −0.932258 0.361793i \(-0.882165\pi\)
0.932258 0.361793i \(-0.117835\pi\)
\(152\) 0 0
\(153\) 34654.9i 0.119684i
\(154\) 0 0
\(155\) 141679. 141679.i 0.473669 0.473669i
\(156\) 0 0
\(157\) 343510. + 343510.i 1.11222 + 1.11222i 0.992850 + 0.119369i \(0.0380872\pi\)
0.119369 + 0.992850i \(0.461913\pi\)
\(158\) 0 0
\(159\) 49948.4 0.156685
\(160\) 0 0
\(161\) 415317. 1.26274
\(162\) 0 0
\(163\) 163012. + 163012.i 0.480564 + 0.480564i 0.905312 0.424748i \(-0.139637\pi\)
−0.424748 + 0.905312i \(0.639637\pi\)
\(164\) 0 0
\(165\) −54118.1 + 54118.1i −0.154751 + 0.154751i
\(166\) 0 0
\(167\) 12174.1i 0.0337790i 0.999857 + 0.0168895i \(0.00537634\pi\)
−0.999857 + 0.0168895i \(0.994624\pi\)
\(168\) 0 0
\(169\) 492032.i 1.32518i
\(170\) 0 0
\(171\) 97169.9 97169.9i 0.254121 0.254121i
\(172\) 0 0
\(173\) −536526. 536526.i −1.36294 1.36294i −0.870152 0.492783i \(-0.835980\pi\)
−0.492783 0.870152i \(-0.664020\pi\)
\(174\) 0 0
\(175\) −123385. −0.304555
\(176\) 0 0
\(177\) −133546. −0.320404
\(178\) 0 0
\(179\) 496149. + 496149.i 1.15739 + 1.15739i 0.985035 + 0.172356i \(0.0551378\pi\)
0.172356 + 0.985035i \(0.444862\pi\)
\(180\) 0 0
\(181\) 189857. 189857.i 0.430754 0.430754i −0.458131 0.888885i \(-0.651481\pi\)
0.888885 + 0.458131i \(0.151481\pi\)
\(182\) 0 0
\(183\) 196041.i 0.432731i
\(184\) 0 0
\(185\) 147580.i 0.317028i
\(186\) 0 0
\(187\) 82681.3 82681.3i 0.172903 0.172903i
\(188\) 0 0
\(189\) 262223. + 262223.i 0.533968 + 0.533968i
\(190\) 0 0
\(191\) 216777. 0.429962 0.214981 0.976618i \(-0.431031\pi\)
0.214981 + 0.976618i \(0.431031\pi\)
\(192\) 0 0
\(193\) −129059. −0.249399 −0.124700 0.992195i \(-0.539797\pi\)
−0.124700 + 0.992195i \(0.539797\pi\)
\(194\) 0 0
\(195\) 65643.6 + 65643.6i 0.123625 + 0.123625i
\(196\) 0 0
\(197\) −384351. + 384351.i −0.705607 + 0.705607i −0.965608 0.260001i \(-0.916277\pi\)
0.260001 + 0.965608i \(0.416277\pi\)
\(198\) 0 0
\(199\) 754358.i 1.35035i −0.737660 0.675173i \(-0.764069\pi\)
0.737660 0.675173i \(-0.235931\pi\)
\(200\) 0 0
\(201\) 72849.9i 0.127186i
\(202\) 0 0
\(203\) −259213. + 259213.i −0.441485 + 0.441485i
\(204\) 0 0
\(205\) −120861. 120861.i −0.200863 0.200863i
\(206\) 0 0
\(207\) 477615. 0.774733
\(208\) 0 0
\(209\) 463665. 0.734242
\(210\) 0 0
\(211\) 508214. + 508214.i 0.785851 + 0.785851i 0.980811 0.194960i \(-0.0624577\pi\)
−0.194960 + 0.980811i \(0.562458\pi\)
\(212\) 0 0
\(213\) −160304. + 160304.i −0.242101 + 0.242101i
\(214\) 0 0
\(215\) 12984.5i 0.0191571i
\(216\) 0 0
\(217\) 1.58220e6i 2.28093i
\(218\) 0 0
\(219\) 117237. 117237.i 0.165179 0.165179i
\(220\) 0 0
\(221\) −100290. 100290.i −0.138126 0.138126i
\(222\) 0 0
\(223\) −162588. −0.218940 −0.109470 0.993990i \(-0.534915\pi\)
−0.109470 + 0.993990i \(0.534915\pi\)
\(224\) 0 0
\(225\) −141892. −0.186854
\(226\) 0 0
\(227\) 517939. + 517939.i 0.667135 + 0.667135i 0.957052 0.289917i \(-0.0936275\pi\)
−0.289917 + 0.957052i \(0.593628\pi\)
\(228\) 0 0
\(229\) −814473. + 814473.i −1.02633 + 1.02633i −0.0266888 + 0.999644i \(0.508496\pi\)
−0.999644 + 0.0266888i \(0.991504\pi\)
\(230\) 0 0
\(231\) 604364.i 0.745193i
\(232\) 0 0
\(233\) 453287.i 0.546995i −0.961873 0.273498i \(-0.911819\pi\)
0.961873 0.273498i \(-0.0881805\pi\)
\(234\) 0 0
\(235\) 108252. 108252.i 0.127870 0.127870i
\(236\) 0 0
\(237\) 300725. + 300725.i 0.347776 + 0.347776i
\(238\) 0 0
\(239\) 1.02509e6 1.16083 0.580413 0.814322i \(-0.302891\pi\)
0.580413 + 0.814322i \(0.302891\pi\)
\(240\) 0 0
\(241\) 1.33741e6 1.48328 0.741638 0.670800i \(-0.234049\pi\)
0.741638 + 0.670800i \(0.234049\pi\)
\(242\) 0 0
\(243\) 457458. + 457458.i 0.496976 + 0.496976i
\(244\) 0 0
\(245\) −391842. + 391842.i −0.417057 + 0.417057i
\(246\) 0 0
\(247\) 562412.i 0.586559i
\(248\) 0 0
\(249\) 277887.i 0.284034i
\(250\) 0 0
\(251\) 949915. 949915.i 0.951701 0.951701i −0.0471855 0.998886i \(-0.515025\pi\)
0.998886 + 0.0471855i \(0.0150252\pi\)
\(252\) 0 0
\(253\) 1.13952e6 + 1.13952e6i 1.11923 + 1.11923i
\(254\) 0 0
\(255\) −15251.2 −0.0146877
\(256\) 0 0
\(257\) 1.04686e6 0.988681 0.494341 0.869268i \(-0.335410\pi\)
0.494341 + 0.869268i \(0.335410\pi\)
\(258\) 0 0
\(259\) 824048. + 824048.i 0.763314 + 0.763314i
\(260\) 0 0
\(261\) −298095. + 298095.i −0.270865 + 0.270865i
\(262\) 0 0
\(263\) 1.88612e6i 1.68144i 0.541472 + 0.840719i \(0.317867\pi\)
−0.541472 + 0.840719i \(0.682133\pi\)
\(264\) 0 0
\(265\) 312451.i 0.273317i
\(266\) 0 0
\(267\) −176996. + 176996.i −0.151945 + 0.151945i
\(268\) 0 0
\(269\) −225955. 225955.i −0.190388 0.190388i 0.605476 0.795864i \(-0.292983\pi\)
−0.795864 + 0.605476i \(0.792983\pi\)
\(270\) 0 0
\(271\) −751159. −0.621310 −0.310655 0.950523i \(-0.600548\pi\)
−0.310655 + 0.950523i \(0.600548\pi\)
\(272\) 0 0
\(273\) 733075. 0.595308
\(274\) 0 0
\(275\) −338534. 338534.i −0.269942 0.269942i
\(276\) 0 0
\(277\) 991598. 991598.i 0.776491 0.776491i −0.202742 0.979232i \(-0.564985\pi\)
0.979232 + 0.202742i \(0.0649852\pi\)
\(278\) 0 0
\(279\) 1.81953e6i 1.39942i
\(280\) 0 0
\(281\) 1.15437e6i 0.872126i 0.899916 + 0.436063i \(0.143627\pi\)
−0.899916 + 0.436063i \(0.856373\pi\)
\(282\) 0 0
\(283\) −1.22003e6 + 1.22003e6i −0.905530 + 0.905530i −0.995908 0.0903777i \(-0.971193\pi\)
0.0903777 + 0.995908i \(0.471193\pi\)
\(284\) 0 0
\(285\) −42763.4 42763.4i −0.0311860 0.0311860i
\(286\) 0 0
\(287\) −1.34971e6 −0.967246
\(288\) 0 0
\(289\) −1.39656e6 −0.983589
\(290\) 0 0
\(291\) −78569.6 78569.6i −0.0543904 0.0543904i
\(292\) 0 0
\(293\) 203103. 203103.i 0.138213 0.138213i −0.634615 0.772828i \(-0.718841\pi\)
0.772828 + 0.634615i \(0.218841\pi\)
\(294\) 0 0
\(295\) 835395.i 0.558903i
\(296\) 0 0
\(297\) 1.43893e6i 0.946564i
\(298\) 0 0
\(299\) 1.38220e6 1.38220e6i 0.894114 0.894114i
\(300\) 0 0
\(301\) 72502.2 + 72502.2i 0.0461249 + 0.0461249i
\(302\) 0 0
\(303\) 490965. 0.307216
\(304\) 0 0
\(305\) 1.22633e6 0.754843
\(306\) 0 0
\(307\) −559308. 559308.i −0.338692 0.338692i 0.517183 0.855875i \(-0.326981\pi\)
−0.855875 + 0.517183i \(0.826981\pi\)
\(308\) 0 0
\(309\) −106931. + 106931.i −0.0637100 + 0.0637100i
\(310\) 0 0
\(311\) 1.23935e6i 0.726598i −0.931673 0.363299i \(-0.881650\pi\)
0.931673 0.363299i \(-0.118350\pi\)
\(312\) 0 0
\(313\) 859630.i 0.495965i −0.968765 0.247982i \(-0.920233\pi\)
0.968765 0.247982i \(-0.0797675\pi\)
\(314\) 0 0
\(315\) −792293. + 792293.i −0.449893 + 0.449893i
\(316\) 0 0
\(317\) 227313. + 227313.i 0.127051 + 0.127051i 0.767773 0.640722i \(-0.221365\pi\)
−0.640722 + 0.767773i \(0.721365\pi\)
\(318\) 0 0
\(319\) −1.42242e6 −0.782619
\(320\) 0 0
\(321\) 10576.4 0.00572894
\(322\) 0 0
\(323\) 65333.7 + 65333.7i 0.0348442 + 0.0348442i
\(324\) 0 0
\(325\) −410631. + 410631.i −0.215647 + 0.215647i
\(326\) 0 0
\(327\) 225544.i 0.116644i
\(328\) 0 0
\(329\) 1.20891e6i 0.615750i
\(330\) 0 0
\(331\) −781848. + 781848.i −0.392240 + 0.392240i −0.875485 0.483245i \(-0.839458\pi\)
0.483245 + 0.875485i \(0.339458\pi\)
\(332\) 0 0
\(333\) 947656. + 947656.i 0.468317 + 0.468317i
\(334\) 0 0
\(335\) 455711. 0.221859
\(336\) 0 0
\(337\) 3.22360e6 1.54620 0.773102 0.634282i \(-0.218704\pi\)
0.773102 + 0.634282i \(0.218704\pi\)
\(338\) 0 0
\(339\) −506204. 506204.i −0.239236 0.239236i
\(340\) 0 0
\(341\) 4.34112e6 4.34112e6i 2.02170 2.02170i
\(342\) 0 0
\(343\) 1.05793e6i 0.485537i
\(344\) 0 0
\(345\) 210193.i 0.0950760i
\(346\) 0 0
\(347\) −336317. + 336317.i −0.149942 + 0.149942i −0.778092 0.628150i \(-0.783812\pi\)
0.628150 + 0.778092i \(0.283812\pi\)
\(348\) 0 0
\(349\) −1.30701e6 1.30701e6i −0.574400 0.574400i 0.358955 0.933355i \(-0.383133\pi\)
−0.933355 + 0.358955i \(0.883133\pi\)
\(350\) 0 0
\(351\) 1.74538e6 0.756176
\(352\) 0 0
\(353\) −4.18476e6 −1.78745 −0.893725 0.448615i \(-0.851917\pi\)
−0.893725 + 0.448615i \(0.851917\pi\)
\(354\) 0 0
\(355\) −1.00278e6 1.00278e6i −0.422313 0.422313i
\(356\) 0 0
\(357\) −85159.1 + 85159.1i −0.0353639 + 0.0353639i
\(358\) 0 0
\(359\) 1.30242e6i 0.533354i 0.963786 + 0.266677i \(0.0859257\pi\)
−0.963786 + 0.266677i \(0.914074\pi\)
\(360\) 0 0
\(361\) 2.10972e6i 0.852032i
\(362\) 0 0
\(363\) −1.20309e6 + 1.20309e6i −0.479216 + 0.479216i
\(364\) 0 0
\(365\) 733374. + 733374.i 0.288133 + 0.288133i
\(366\) 0 0
\(367\) −442787. −0.171605 −0.0858025 0.996312i \(-0.527345\pi\)
−0.0858025 + 0.996312i \(0.527345\pi\)
\(368\) 0 0
\(369\) −1.55217e6 −0.593436
\(370\) 0 0
\(371\) 1.74465e6 + 1.74465e6i 0.658071 + 0.658071i
\(372\) 0 0
\(373\) −3.38472e6 + 3.38472e6i −1.25965 + 1.25965i −0.308392 + 0.951259i \(0.599791\pi\)
−0.951259 + 0.308392i \(0.900209\pi\)
\(374\) 0 0
\(375\) 62445.3i 0.0229309i
\(376\) 0 0
\(377\) 1.72535e6i 0.625207i
\(378\) 0 0
\(379\) 1.74454e6 1.74454e6i 0.623852 0.623852i −0.322662 0.946514i \(-0.604578\pi\)
0.946514 + 0.322662i \(0.104578\pi\)
\(380\) 0 0
\(381\) 154463. + 154463.i 0.0545146 + 0.0545146i
\(382\) 0 0
\(383\) −3.91329e6 −1.36315 −0.681577 0.731746i \(-0.738706\pi\)
−0.681577 + 0.731746i \(0.738706\pi\)
\(384\) 0 0
\(385\) −3.78058e6 −1.29989
\(386\) 0 0
\(387\) 83377.6 + 83377.6i 0.0282991 + 0.0282991i
\(388\) 0 0
\(389\) 521316. 521316.i 0.174674 0.174674i −0.614356 0.789029i \(-0.710584\pi\)
0.789029 + 0.614356i \(0.210584\pi\)
\(390\) 0 0
\(391\) 321132.i 0.106229i
\(392\) 0 0
\(393\) 425381.i 0.138930i
\(394\) 0 0
\(395\) −1.88118e6 + 1.88118e6i −0.606649 + 0.606649i
\(396\) 0 0
\(397\) −2.14350e6 2.14350e6i −0.682569 0.682569i 0.278009 0.960578i \(-0.410325\pi\)
−0.960578 + 0.278009i \(0.910325\pi\)
\(398\) 0 0
\(399\) −477561. −0.150175
\(400\) 0 0
\(401\) −2.38412e6 −0.740403 −0.370201 0.928952i \(-0.620711\pi\)
−0.370201 + 0.928952i \(0.620711\pi\)
\(402\) 0 0
\(403\) −5.26564e6 5.26564e6i −1.61506 1.61506i
\(404\) 0 0
\(405\) −842527. + 842527.i −0.255238 + 0.255238i
\(406\) 0 0
\(407\) 4.52193e6i 1.35312i
\(408\) 0 0
\(409\) 4.74247e6i 1.40183i 0.713244 + 0.700916i \(0.247225\pi\)
−0.713244 + 0.700916i \(0.752775\pi\)
\(410\) 0 0
\(411\) −232488. + 232488.i −0.0678883 + 0.0678883i
\(412\) 0 0
\(413\) −4.66464e6 4.66464e6i −1.34568 1.34568i
\(414\) 0 0
\(415\) 1.73831e6 0.495459
\(416\) 0 0
\(417\) −173059. −0.0487366
\(418\) 0 0
\(419\) −1.30162e6 1.30162e6i −0.362199 0.362199i 0.502423 0.864622i \(-0.332442\pi\)
−0.864622 + 0.502423i \(0.832442\pi\)
\(420\) 0 0
\(421\) 945631. 945631.i 0.260026 0.260026i −0.565039 0.825064i \(-0.691139\pi\)
0.825064 + 0.565039i \(0.191139\pi\)
\(422\) 0 0
\(423\) 1.39025e6i 0.377782i
\(424\) 0 0
\(425\) 95403.6i 0.0256208i
\(426\) 0 0
\(427\) 6.84751e6 6.84751e6i 1.81745 1.81745i
\(428\) 0 0
\(429\) 2.01136e6 + 2.01136e6i 0.527650 + 0.527650i
\(430\) 0 0
\(431\) 5.90106e6 1.53016 0.765080 0.643935i \(-0.222699\pi\)
0.765080 + 0.643935i \(0.222699\pi\)
\(432\) 0 0
\(433\) −3.70654e6 −0.950055 −0.475027 0.879971i \(-0.657562\pi\)
−0.475027 + 0.879971i \(0.657562\pi\)
\(434\) 0 0
\(435\) 131188. + 131188.i 0.0332408 + 0.0332408i
\(436\) 0 0
\(437\) −900432. + 900432.i −0.225552 + 0.225552i
\(438\) 0 0
\(439\) 2.43564e6i 0.603186i 0.953437 + 0.301593i \(0.0975184\pi\)
−0.953437 + 0.301593i \(0.902482\pi\)
\(440\) 0 0
\(441\) 5.03228e6i 1.23216i
\(442\) 0 0
\(443\) −4.75839e6 + 4.75839e6i −1.15200 + 1.15200i −0.165843 + 0.986152i \(0.553034\pi\)
−0.986152 + 0.165843i \(0.946966\pi\)
\(444\) 0 0
\(445\) −1.10719e6 1.10719e6i −0.265047 0.265047i
\(446\) 0 0
\(447\) 1.18490e6 0.280487
\(448\) 0 0
\(449\) 1.20625e6 0.282372 0.141186 0.989983i \(-0.454908\pi\)
0.141186 + 0.989983i \(0.454908\pi\)
\(450\) 0 0
\(451\) −3.70325e6 3.70325e6i −0.857317 0.857317i
\(452\) 0 0
\(453\) −572925. + 572925.i −0.131175 + 0.131175i
\(454\) 0 0
\(455\) 4.58573e6i 1.03844i
\(456\) 0 0
\(457\) 8.30542e6i 1.86025i −0.367245 0.930124i \(-0.619699\pi\)
0.367245 0.930124i \(-0.380301\pi\)
\(458\) 0 0
\(459\) −202756. + 202756.i −0.0449202 + 0.0449202i
\(460\) 0 0
\(461\) −3.51089e6 3.51089e6i −0.769422 0.769422i 0.208583 0.978005i \(-0.433115\pi\)
−0.978005 + 0.208583i \(0.933115\pi\)
\(462\) 0 0
\(463\) −558945. −0.121176 −0.0605880 0.998163i \(-0.519298\pi\)
−0.0605880 + 0.998163i \(0.519298\pi\)
\(464\) 0 0
\(465\) −800754. −0.171738
\(466\) 0 0
\(467\) −2.74891e6 2.74891e6i −0.583268 0.583268i 0.352532 0.935800i \(-0.385321\pi\)
−0.935800 + 0.352532i \(0.885321\pi\)
\(468\) 0 0
\(469\) 2.54458e6 2.54458e6i 0.534175 0.534175i
\(470\) 0 0
\(471\) 1.94149e6i 0.403257i
\(472\) 0 0
\(473\) 397853.i 0.0817654i
\(474\) 0 0
\(475\) 267505. 267505.i 0.0543999 0.0543999i
\(476\) 0 0
\(477\) 2.00634e6 + 2.00634e6i 0.403747 + 0.403747i
\(478\) 0 0
\(479\) 1.32442e6 0.263746 0.131873 0.991267i \(-0.457901\pi\)
0.131873 + 0.991267i \(0.457901\pi\)
\(480\) 0 0
\(481\) 5.48496e6 1.08096
\(482\) 0 0
\(483\) −1.17367e6 1.17367e6i −0.228916 0.228916i
\(484\) 0 0
\(485\) 491490. 491490.i 0.0948769 0.0948769i
\(486\) 0 0
\(487\) 8.10722e6i 1.54899i −0.632578 0.774496i \(-0.718003\pi\)
0.632578 0.774496i \(-0.281997\pi\)
\(488\) 0 0
\(489\) 921329.i 0.174238i
\(490\) 0 0
\(491\) 406525. 406525.i 0.0760998 0.0760998i −0.668032 0.744132i \(-0.732863\pi\)
0.744132 + 0.668032i \(0.232863\pi\)
\(492\) 0 0
\(493\) −200429. 200429.i −0.0371400 0.0371400i
\(494\) 0 0
\(495\) −4.34767e6 −0.797524
\(496\) 0 0
\(497\) −1.11985e7 −2.03362
\(498\) 0 0
\(499\) −193908. 193908.i −0.0348614 0.0348614i 0.689461 0.724323i \(-0.257847\pi\)
−0.724323 + 0.689461i \(0.757847\pi\)
\(500\) 0 0
\(501\) 34403.5 34403.5i 0.00612362 0.00612362i
\(502\) 0 0
\(503\) 1.67379e6i 0.294973i −0.989064 0.147486i \(-0.952882\pi\)
0.989064 0.147486i \(-0.0471183\pi\)
\(504\) 0 0
\(505\) 3.07121e6i 0.535897i
\(506\) 0 0
\(507\) 1.39046e6 1.39046e6i 0.240236 0.240236i
\(508\) 0 0
\(509\) 1.50765e6 + 1.50765e6i 0.257932 + 0.257932i 0.824213 0.566280i \(-0.191618\pi\)
−0.566280 + 0.824213i \(0.691618\pi\)
\(510\) 0 0
\(511\) 8.18996e6 1.38749
\(512\) 0 0
\(513\) −1.13703e6 −0.190756
\(514\) 0 0
\(515\) −668904. 668904.i −0.111134 0.111134i
\(516\) 0 0
\(517\) 3.31692e6 3.31692e6i 0.545769 0.545769i
\(518\) 0 0
\(519\) 3.03239e6i 0.494159i
\(520\) 0 0
\(521\) 2.57563e6i 0.415708i 0.978160 + 0.207854i \(0.0666479\pi\)
−0.978160 + 0.207854i \(0.933352\pi\)
\(522\) 0 0
\(523\) 2.13633e6 2.13633e6i 0.341518 0.341518i −0.515420 0.856938i \(-0.672364\pi\)
0.856938 + 0.515420i \(0.172364\pi\)
\(524\) 0 0
\(525\) 348679. + 348679.i 0.0552113 + 0.0552113i
\(526\) 0 0
\(527\) 1.22339e6 0.191883
\(528\) 0 0
\(529\) 2.01049e6 0.312365
\(530\) 0 0
\(531\) −5.36434e6 5.36434e6i −0.825619 0.825619i
\(532\) 0 0
\(533\) −4.49192e6 + 4.49192e6i −0.684880 + 0.684880i
\(534\) 0 0
\(535\) 66160.2i 0.00999338i
\(536\) 0 0
\(537\) 2.80419e6i 0.419635i
\(538\) 0 0
\(539\) −1.20063e7 + 1.20063e7i −1.78007 + 1.78007i
\(540\) 0 0
\(541\) 1.65184e6 + 1.65184e6i 0.242647 + 0.242647i 0.817944 0.575297i \(-0.195114\pi\)
−0.575297 + 0.817944i \(0.695114\pi\)
\(542\) 0 0
\(543\) −1.07305e6 −0.156178
\(544\) 0 0
\(545\) 1.41088e6 0.203470
\(546\) 0 0
\(547\) 6.74481e6 + 6.74481e6i 0.963833 + 0.963833i 0.999368 0.0355356i \(-0.0113137\pi\)
−0.0355356 + 0.999368i \(0.511314\pi\)
\(548\) 0 0
\(549\) 7.87464e6 7.87464e6i 1.11506 1.11506i
\(550\) 0 0
\(551\) 1.12398e6i 0.157717i
\(552\) 0 0
\(553\) 2.10081e7i 2.92128i
\(554\) 0 0
\(555\) 417053. 417053.i 0.0574723 0.0574723i
\(556\) 0 0
\(557\) 3.42824e6 + 3.42824e6i 0.468202 + 0.468202i 0.901332 0.433130i \(-0.142591\pi\)
−0.433130 + 0.901332i \(0.642591\pi\)
\(558\) 0 0
\(559\) 482583. 0.0653194
\(560\) 0 0
\(561\) −467307. −0.0626895
\(562\) 0 0
\(563\) 9.10019e6 + 9.10019e6i 1.20998 + 1.20998i 0.971031 + 0.238952i \(0.0768040\pi\)
0.238952 + 0.971031i \(0.423196\pi\)
\(564\) 0 0
\(565\) 3.16654e6 3.16654e6i 0.417316 0.417316i
\(566\) 0 0
\(567\) 9.40893e6i 1.22909i
\(568\) 0 0
\(569\) 5.49614e6i 0.711668i −0.934549 0.355834i \(-0.884197\pi\)
0.934549 0.355834i \(-0.115803\pi\)
\(570\) 0 0
\(571\) 6.26904e6 6.26904e6i 0.804657 0.804657i −0.179162 0.983820i \(-0.557339\pi\)
0.983820 + 0.179162i \(0.0573387\pi\)
\(572\) 0 0
\(573\) −612602. 612602.i −0.0779457 0.0779457i
\(574\) 0 0
\(575\) 1.31486e6 0.165847
\(576\) 0 0
\(577\) 2.00756e6 0.251031 0.125516 0.992092i \(-0.459941\pi\)
0.125516 + 0.992092i \(0.459941\pi\)
\(578\) 0 0
\(579\) 364714. + 364714.i 0.0452123 + 0.0452123i
\(580\) 0 0
\(581\) 9.70632e6 9.70632e6i 1.19293 1.19293i
\(582\) 0 0
\(583\) 9.57368e6i 1.16656i
\(584\) 0 0
\(585\) 5.27359e6i 0.637114i
\(586\) 0 0
\(587\) −5.11196e6 + 5.11196e6i −0.612339 + 0.612339i −0.943555 0.331216i \(-0.892541\pi\)
0.331216 + 0.943555i \(0.392541\pi\)
\(588\) 0 0
\(589\) 3.43030e6 + 3.43030e6i 0.407421 + 0.407421i
\(590\) 0 0
\(591\) 2.17232e6 0.255832
\(592\) 0 0
\(593\) −5.60846e6 −0.654948 −0.327474 0.944860i \(-0.606197\pi\)
−0.327474 + 0.944860i \(0.606197\pi\)
\(594\) 0 0
\(595\) −532710. 532710.i −0.0616877 0.0616877i
\(596\) 0 0
\(597\) −2.13178e6 + 2.13178e6i −0.244797 + 0.244797i
\(598\) 0 0
\(599\) 3.57303e6i 0.406883i 0.979087 + 0.203441i \(0.0652126\pi\)
−0.979087 + 0.203441i \(0.934787\pi\)
\(600\) 0 0
\(601\) 7.00344e6i 0.790907i 0.918486 + 0.395453i \(0.129413\pi\)
−0.918486 + 0.395453i \(0.870587\pi\)
\(602\) 0 0
\(603\) 2.92626e6 2.92626e6i 0.327733 0.327733i
\(604\) 0 0
\(605\) −7.52589e6 7.52589e6i −0.835929 0.835929i
\(606\) 0 0
\(607\) 7.15190e6 0.787861 0.393930 0.919140i \(-0.371115\pi\)
0.393930 + 0.919140i \(0.371115\pi\)
\(608\) 0 0
\(609\) 1.46505e6 0.160069
\(610\) 0 0
\(611\) −4.02332e6 4.02332e6i −0.435995 0.435995i
\(612\) 0 0
\(613\) 1.00171e7 1.00171e7i 1.07669 1.07669i 0.0798818 0.996804i \(-0.474546\pi\)
0.996804 0.0798818i \(-0.0254543\pi\)
\(614\) 0 0
\(615\) 683094.i 0.0728270i
\(616\) 0 0
\(617\) 6.37727e6i 0.674407i −0.941432 0.337203i \(-0.890519\pi\)
0.941432 0.337203i \(-0.109481\pi\)
\(618\) 0 0
\(619\) 1.04107e7 1.04107e7i 1.09208 1.09208i 0.0967688 0.995307i \(-0.469149\pi\)
0.995307 0.0967688i \(-0.0308508\pi\)
\(620\) 0 0
\(621\) −2.79439e6 2.79439e6i −0.290776 0.290776i
\(622\) 0 0
\(623\) −1.23646e7 −1.27632
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) −1.31030e6 1.31030e6i −0.133107 0.133107i
\(628\) 0 0
\(629\) −637171. + 637171.i −0.0642140 + 0.0642140i
\(630\) 0 0
\(631\) 7.50163e6i 0.750036i −0.927018 0.375018i \(-0.877637\pi\)
0.927018 0.375018i \(-0.122363\pi\)
\(632\) 0 0
\(633\) 2.87238e6i 0.284926i
\(634\) 0 0
\(635\) −966241. + 966241.i −0.0950935 + 0.0950935i
\(636\) 0 0
\(637\) 1.45632e7 + 1.45632e7i 1.42203 + 1.42203i
\(638\) 0 0
\(639\) −1.28783e7 −1.24769
\(640\) 0 0
\(641\) 1.89084e7 1.81765 0.908825 0.417177i \(-0.136980\pi\)
0.908825 + 0.417177i \(0.136980\pi\)
\(642\) 0 0
\(643\) −5.88611e6 5.88611e6i −0.561437 0.561437i 0.368278 0.929716i \(-0.379947\pi\)
−0.929716 + 0.368278i \(0.879947\pi\)
\(644\) 0 0
\(645\) 36693.6 36693.6i 0.00347289 0.00347289i
\(646\) 0 0
\(647\) 1.84161e6i 0.172956i −0.996254 0.0864782i \(-0.972439\pi\)
0.996254 0.0864782i \(-0.0275613\pi\)
\(648\) 0 0
\(649\) 2.55970e7i 2.38549i
\(650\) 0 0
\(651\) −4.47122e6 + 4.47122e6i −0.413498 + 0.413498i
\(652\) 0 0
\(653\) 7.63776e6 + 7.63776e6i 0.700944 + 0.700944i 0.964613 0.263670i \(-0.0849328\pi\)
−0.263670 + 0.964613i \(0.584933\pi\)
\(654\) 0 0
\(655\) −2.66096e6 −0.242345
\(656\) 0 0
\(657\) 9.41846e6 0.851269
\(658\) 0 0
\(659\) −4.80399e6 4.80399e6i −0.430912 0.430912i 0.458027 0.888939i \(-0.348556\pi\)
−0.888939 + 0.458027i \(0.848556\pi\)
\(660\) 0 0
\(661\) 2.67220e6 2.67220e6i 0.237884 0.237884i −0.578089 0.815974i \(-0.696201\pi\)
0.815974 + 0.578089i \(0.196201\pi\)
\(662\) 0 0
\(663\) 566829.i 0.0500804i
\(664\) 0 0
\(665\) 2.98737e6i 0.261960i
\(666\) 0 0
\(667\) 2.76232e6 2.76232e6i 0.240413 0.240413i
\(668\) 0 0
\(669\) 459465. + 459465.i 0.0396906 + 0.0396906i
\(670\) 0 0
\(671\) 3.75754e7 3.22179
\(672\) 0 0
\(673\) −7.91971e6 −0.674019 −0.337009 0.941501i \(-0.609415\pi\)
−0.337009 + 0.941501i \(0.609415\pi\)
\(674\) 0 0
\(675\) 830173. + 830173.i 0.0701309 + 0.0701309i
\(676\) 0 0
\(677\) −8.95269e6 + 8.95269e6i −0.750727 + 0.750727i −0.974615 0.223888i \(-0.928125\pi\)
0.223888 + 0.974615i \(0.428125\pi\)
\(678\) 0 0
\(679\) 5.48872e6i 0.456874i
\(680\) 0 0
\(681\) 2.92734e6i 0.241883i
\(682\) 0 0
\(683\) 843476. 843476.i 0.0691865 0.0691865i −0.671667 0.740853i \(-0.734421\pi\)
0.740853 + 0.671667i \(0.234421\pi\)
\(684\) 0 0
\(685\) −1.45432e6 1.45432e6i −0.118422 0.118422i
\(686\) 0 0
\(687\) 4.60333e6 0.372117
\(688\) 0 0
\(689\) 1.16126e7 0.931924
\(690\) 0 0
\(691\) 5.68228e6 + 5.68228e6i 0.452717 + 0.452717i 0.896256 0.443538i \(-0.146277\pi\)
−0.443538 + 0.896256i \(0.646277\pi\)
\(692\) 0 0
\(693\) −2.42763e7 + 2.42763e7i −1.92022 + 1.92022i
\(694\) 0 0
\(695\) 1.08257e6i 0.0850146i
\(696\) 0 0
\(697\) 1.04363e6i 0.0813698i
\(698\) 0 0
\(699\) −1.28097e6 + 1.28097e6i −0.0991620 + 0.0991620i
\(700\) 0 0
\(701\) 1.14378e7 + 1.14378e7i 0.879118 + 0.879118i 0.993443 0.114325i \(-0.0364705\pi\)
−0.114325 + 0.993443i \(0.536471\pi\)
\(702\) 0 0
\(703\) −3.57317e6 −0.272688
\(704\) 0 0
\(705\) −611833. −0.0463618
\(706\) 0 0
\(707\) 1.71489e7 + 1.71489e7i 1.29029 + 1.29029i
\(708\) 0 0
\(709\) −1.13313e7 + 1.13313e7i −0.846576 + 0.846576i −0.989704 0.143128i \(-0.954284\pi\)
0.143128 + 0.989704i \(0.454284\pi\)
\(710\) 0 0
\(711\) 2.41593e7i 1.79230i
\(712\) 0 0
\(713\) 1.68608e7i 1.24209i
\(714\) 0 0
\(715\) −1.25820e7 + 1.25820e7i −0.920417 + 0.920417i
\(716\) 0 0
\(717\) −2.89685e6 2.89685e6i −0.210440 0.210440i
\(718\) 0 0
\(719\) −3.31295e6 −0.238997 −0.119499 0.992834i \(-0.538129\pi\)
−0.119499 + 0.992834i \(0.538129\pi\)
\(720\) 0 0
\(721\) −7.46999e6 −0.535158
\(722\) 0 0
\(723\) −3.77946e6 3.77946e6i −0.268896 0.268896i
\(724\) 0 0
\(725\) −820644. + 820644.i −0.0579842 + 0.0579842i
\(726\) 0 0
\(727\) 1.99116e7i 1.39723i −0.715496 0.698617i \(-0.753799\pi\)
0.715496 0.698617i \(-0.246201\pi\)
\(728\) 0 0
\(729\) 8.99599e6i 0.626946i
\(730\) 0 0
\(731\) −56060.2 + 56060.2i −0.00388026 + 0.00388026i
\(732\) 0 0
\(733\) −7.01608e6 7.01608e6i −0.482319 0.482319i 0.423553 0.905872i \(-0.360783\pi\)
−0.905872 + 0.423553i \(0.860783\pi\)
\(734\) 0 0
\(735\) 2.21465e6 0.151212
\(736\) 0 0
\(737\) 1.39633e7 0.946930
\(738\) 0 0
\(739\) 1.40622e7 + 1.40622e7i 0.947199 + 0.947199i 0.998674 0.0514751i \(-0.0163923\pi\)
−0.0514751 + 0.998674i \(0.516392\pi\)
\(740\) 0 0
\(741\) −1.58935e6 + 1.58935e6i −0.106334 + 0.106334i
\(742\) 0 0
\(743\) 6.27904e6i 0.417274i −0.977993 0.208637i \(-0.933097\pi\)
0.977993 0.208637i \(-0.0669027\pi\)
\(744\) 0 0
\(745\) 7.41210e6i 0.489272i
\(746\) 0 0
\(747\) 1.11623e7 1.11623e7i 0.731899 0.731899i
\(748\) 0 0
\(749\) 369422. + 369422.i 0.0240613 + 0.0240613i
\(750\) 0 0
\(751\) 6.01668e6 0.389275 0.194638 0.980875i \(-0.437647\pi\)
0.194638 + 0.980875i \(0.437647\pi\)
\(752\) 0 0
\(753\) −5.36883e6 −0.345058
\(754\) 0 0
\(755\) −3.58392e6 3.58392e6i −0.228818 0.228818i
\(756\) 0 0
\(757\) 3.36457e6 3.36457e6i 0.213398 0.213398i −0.592311 0.805709i \(-0.701784\pi\)
0.805709 + 0.592311i \(0.201784\pi\)
\(758\) 0 0
\(759\) 6.44045e6i 0.405799i
\(760\) 0 0
\(761\) 1.95367e7i 1.22290i 0.791284 + 0.611448i \(0.209413\pi\)
−0.791284 + 0.611448i \(0.790587\pi\)
\(762\) 0 0
\(763\) 7.87803e6 7.87803e6i 0.489899 0.489899i
\(764\) 0 0
\(765\) −612617. 612617.i −0.0378474 0.0378474i
\(766\) 0 0
\(767\) −3.10484e7 −1.90568
\(768\) 0 0
\(769\) −2.30217e6 −0.140386 −0.0701928 0.997533i \(-0.522361\pi\)
−0.0701928 + 0.997533i \(0.522361\pi\)
\(770\) 0 0
\(771\) −2.95838e6 2.95838e6i −0.179233 0.179233i
\(772\) 0 0
\(773\) 3.83662e6 3.83662e6i 0.230941 0.230941i −0.582145 0.813085i \(-0.697786\pi\)
0.813085 + 0.582145i \(0.197786\pi\)
\(774\) 0 0
\(775\) 5.00910e6i 0.299575i
\(776\) 0 0
\(777\) 4.65744e6i 0.276755i
\(778\) 0 0
\(779\) 2.92626e6 2.92626e6i 0.172770 0.172770i
\(780\) 0 0
\(781\) −3.07257e7 3.07257e7i −1.80250 1.80250i
\(782\) 0 0
\(783\) 3.48814e6 0.203324
\(784\) 0 0
\(785\) 1.21449e7 0.703429
\(786\) 0 0