Properties

Label 320.6.l.a.81.13
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 81.13
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.88400 - 7.88400i) q^{3} +(17.6777 - 17.6777i) q^{5} +208.047i q^{7} -118.685i q^{9} +O(q^{10})\) \(q+(-7.88400 - 7.88400i) q^{3} +(17.6777 - 17.6777i) q^{5} +208.047i q^{7} -118.685i q^{9} +(-117.724 + 117.724i) q^{11} +(-192.926 - 192.926i) q^{13} -278.742 q^{15} -961.739 q^{17} +(1107.22 + 1107.22i) q^{19} +(1640.24 - 1640.24i) q^{21} -2636.65i q^{23} -625.000i q^{25} +(-2851.53 + 2851.53i) q^{27} +(3437.64 + 3437.64i) q^{29} +2302.12 q^{31} +1856.27 q^{33} +(3677.78 + 3677.78i) q^{35} +(10541.5 - 10541.5i) q^{37} +3042.06i q^{39} -8634.65i q^{41} +(5912.40 - 5912.40i) q^{43} +(-2098.08 - 2098.08i) q^{45} -5889.22 q^{47} -26476.4 q^{49} +(7582.35 + 7582.35i) q^{51} +(-12424.3 + 12424.3i) q^{53} +4162.17i q^{55} -17458.7i q^{57} +(-12930.4 + 12930.4i) q^{59} +(-24417.8 - 24417.8i) q^{61} +24692.0 q^{63} -6820.96 q^{65} +(-13983.9 - 13983.9i) q^{67} +(-20787.4 + 20787.4i) q^{69} -48733.1i q^{71} -88373.4i q^{73} +(-4927.50 + 4927.50i) q^{75} +(-24492.0 - 24492.0i) q^{77} -39883.7 q^{79} +16122.4 q^{81} +(-45453.5 - 45453.5i) q^{83} +(-17001.3 + 17001.3i) q^{85} -54204.8i q^{87} +19622.1i q^{89} +(40137.6 - 40137.6i) q^{91} +(-18149.9 - 18149.9i) q^{93} +39146.2 q^{95} +51026.8 q^{97} +(13972.1 + 13972.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

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
\(3\) −7.88400 7.88400i −0.505759 0.505759i 0.407463 0.913222i \(-0.366414\pi\)
−0.913222 + 0.407463i \(0.866414\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 208.047i 1.60478i 0.596800 + 0.802390i \(0.296438\pi\)
−0.596800 + 0.802390i \(0.703562\pi\)
\(8\) 0 0
\(9\) 118.685i 0.488416i
\(10\) 0 0
\(11\) −117.724 + 117.724i −0.293348 + 0.293348i −0.838401 0.545054i \(-0.816509\pi\)
0.545054 + 0.838401i \(0.316509\pi\)
\(12\) 0 0
\(13\) −192.926 192.926i −0.316616 0.316616i 0.530850 0.847466i \(-0.321873\pi\)
−0.847466 + 0.530850i \(0.821873\pi\)
\(14\) 0 0
\(15\) −278.742 −0.319870
\(16\) 0 0
\(17\) −961.739 −0.807114 −0.403557 0.914954i \(-0.632226\pi\)
−0.403557 + 0.914954i \(0.632226\pi\)
\(18\) 0 0
\(19\) 1107.22 + 1107.22i 0.703639 + 0.703639i 0.965190 0.261550i \(-0.0842338\pi\)
−0.261550 + 0.965190i \(0.584234\pi\)
\(20\) 0 0
\(21\) 1640.24 1640.24i 0.811632 0.811632i
\(22\) 0 0
\(23\) 2636.65i 1.03928i −0.854385 0.519641i \(-0.826066\pi\)
0.854385 0.519641i \(-0.173934\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −2851.53 + 2851.53i −0.752780 + 0.752780i
\(28\) 0 0
\(29\) 3437.64 + 3437.64i 0.759042 + 0.759042i 0.976148 0.217106i \(-0.0696617\pi\)
−0.217106 + 0.976148i \(0.569662\pi\)
\(30\) 0 0
\(31\) 2302.12 0.430253 0.215126 0.976586i \(-0.430984\pi\)
0.215126 + 0.976586i \(0.430984\pi\)
\(32\) 0 0
\(33\) 1856.27 0.296726
\(34\) 0 0
\(35\) 3677.78 + 3677.78i 0.507476 + 0.507476i
\(36\) 0 0
\(37\) 10541.5 10541.5i 1.26590 1.26590i 0.317710 0.948188i \(-0.397086\pi\)
0.948188 0.317710i \(-0.102914\pi\)
\(38\) 0 0
\(39\) 3042.06i 0.320262i
\(40\) 0 0
\(41\) 8634.65i 0.802204i −0.916033 0.401102i \(-0.868627\pi\)
0.916033 0.401102i \(-0.131373\pi\)
\(42\) 0 0
\(43\) 5912.40 5912.40i 0.487633 0.487633i −0.419926 0.907558i \(-0.637944\pi\)
0.907558 + 0.419926i \(0.137944\pi\)
\(44\) 0 0
\(45\) −2098.08 2098.08i −0.154451 0.154451i
\(46\) 0 0
\(47\) −5889.22 −0.388878 −0.194439 0.980915i \(-0.562289\pi\)
−0.194439 + 0.980915i \(0.562289\pi\)
\(48\) 0 0
\(49\) −26476.4 −1.57532
\(50\) 0 0
\(51\) 7582.35 + 7582.35i 0.408205 + 0.408205i
\(52\) 0 0
\(53\) −12424.3 + 12424.3i −0.607552 + 0.607552i −0.942306 0.334754i \(-0.891347\pi\)
0.334754 + 0.942306i \(0.391347\pi\)
\(54\) 0 0
\(55\) 4162.17i 0.185529i
\(56\) 0 0
\(57\) 17458.7i 0.711744i
\(58\) 0 0
\(59\) −12930.4 + 12930.4i −0.483595 + 0.483595i −0.906278 0.422683i \(-0.861088\pi\)
0.422683 + 0.906278i \(0.361088\pi\)
\(60\) 0 0
\(61\) −24417.8 24417.8i −0.840197 0.840197i 0.148687 0.988884i \(-0.452495\pi\)
−0.988884 + 0.148687i \(0.952495\pi\)
\(62\) 0 0
\(63\) 24692.0 0.783800
\(64\) 0 0
\(65\) −6820.96 −0.200245
\(66\) 0 0
\(67\) −13983.9 13983.9i −0.380576 0.380576i 0.490734 0.871310i \(-0.336729\pi\)
−0.871310 + 0.490734i \(0.836729\pi\)
\(68\) 0 0
\(69\) −20787.4 + 20787.4i −0.525626 + 0.525626i
\(70\) 0 0
\(71\) 48733.1i 1.14730i −0.819099 0.573652i \(-0.805526\pi\)
0.819099 0.573652i \(-0.194474\pi\)
\(72\) 0 0
\(73\) 88373.4i 1.94095i −0.241203 0.970475i \(-0.577542\pi\)
0.241203 0.970475i \(-0.422458\pi\)
\(74\) 0 0
\(75\) −4927.50 + 4927.50i −0.101152 + 0.101152i
\(76\) 0 0
\(77\) −24492.0 24492.0i −0.470758 0.470758i
\(78\) 0 0
\(79\) −39883.7 −0.718998 −0.359499 0.933145i \(-0.617052\pi\)
−0.359499 + 0.933145i \(0.617052\pi\)
\(80\) 0 0
\(81\) 16122.4 0.273034
\(82\) 0 0
\(83\) −45453.5 45453.5i −0.724222 0.724222i 0.245240 0.969462i \(-0.421133\pi\)
−0.969462 + 0.245240i \(0.921133\pi\)
\(84\) 0 0
\(85\) −17001.3 + 17001.3i −0.255232 + 0.255232i
\(86\) 0 0
\(87\) 54204.8i 0.767785i
\(88\) 0 0
\(89\) 19622.1i 0.262585i 0.991344 + 0.131293i \(0.0419128\pi\)
−0.991344 + 0.131293i \(0.958087\pi\)
\(90\) 0 0
\(91\) 40137.6 40137.6i 0.508098 0.508098i
\(92\) 0 0
\(93\) −18149.9 18149.9i −0.217604 0.217604i
\(94\) 0 0
\(95\) 39146.2 0.445021
\(96\) 0 0
\(97\) 51026.8 0.550642 0.275321 0.961352i \(-0.411216\pi\)
0.275321 + 0.961352i \(0.411216\pi\)
\(98\) 0 0
\(99\) 13972.1 + 13972.1i 0.143276 + 0.143276i
\(100\) 0 0
\(101\) 123045. 123045.i 1.20022 1.20022i 0.226120 0.974100i \(-0.427396\pi\)
0.974100 0.226120i \(-0.0726040\pi\)
\(102\) 0 0
\(103\) 212680.i 1.97530i −0.156683 0.987649i \(-0.550080\pi\)
0.156683 0.987649i \(-0.449920\pi\)
\(104\) 0 0
\(105\) 57991.2i 0.513321i
\(106\) 0 0
\(107\) −106075. + 106075.i −0.895678 + 0.895678i −0.995050 0.0993727i \(-0.968316\pi\)
0.0993727 + 0.995050i \(0.468316\pi\)
\(108\) 0 0
\(109\) −17617.5 17617.5i −0.142029 0.142029i 0.632517 0.774546i \(-0.282022\pi\)
−0.774546 + 0.632517i \(0.782022\pi\)
\(110\) 0 0
\(111\) −166219. −1.28048
\(112\) 0 0
\(113\) 71983.2 0.530317 0.265158 0.964205i \(-0.414576\pi\)
0.265158 + 0.964205i \(0.414576\pi\)
\(114\) 0 0
\(115\) −46609.9 46609.9i −0.328650 0.328650i
\(116\) 0 0
\(117\) −22897.4 + 22897.4i −0.154640 + 0.154640i
\(118\) 0 0
\(119\) 200087.i 1.29524i
\(120\) 0 0
\(121\) 133333.i 0.827894i
\(122\) 0 0
\(123\) −68075.6 + 68075.6i −0.405722 + 0.405722i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) −239532. −1.31781 −0.658906 0.752225i \(-0.728980\pi\)
−0.658906 + 0.752225i \(0.728980\pi\)
\(128\) 0 0
\(129\) −93226.7 −0.493249
\(130\) 0 0
\(131\) 132808. + 132808.i 0.676155 + 0.676155i 0.959128 0.282973i \(-0.0913206\pi\)
−0.282973 + 0.959128i \(0.591321\pi\)
\(132\) 0 0
\(133\) −230353. + 230353.i −1.12919 + 1.12919i
\(134\) 0 0
\(135\) 100817.i 0.476100i
\(136\) 0 0
\(137\) 155055.i 0.705802i −0.935661 0.352901i \(-0.885195\pi\)
0.935661 0.352901i \(-0.114805\pi\)
\(138\) 0 0
\(139\) 262037. 262037.i 1.15034 1.15034i 0.163851 0.986485i \(-0.447608\pi\)
0.986485 0.163851i \(-0.0523917\pi\)
\(140\) 0 0
\(141\) 46430.6 + 46430.6i 0.196678 + 0.196678i
\(142\) 0 0
\(143\) 45424.0 0.185757
\(144\) 0 0
\(145\) 121539. 0.480060
\(146\) 0 0
\(147\) 208740. + 208740.i 0.796731 + 0.796731i
\(148\) 0 0
\(149\) −192042. + 192042.i −0.708646 + 0.708646i −0.966250 0.257604i \(-0.917067\pi\)
0.257604 + 0.966250i \(0.417067\pi\)
\(150\) 0 0
\(151\) 427260.i 1.52493i −0.647029 0.762466i \(-0.723989\pi\)
0.647029 0.762466i \(-0.276011\pi\)
\(152\) 0 0
\(153\) 114144.i 0.394207i
\(154\) 0 0
\(155\) 40696.1 40696.1i 0.136058 0.136058i
\(156\) 0 0
\(157\) −229660. 229660.i −0.743595 0.743595i 0.229673 0.973268i \(-0.426234\pi\)
−0.973268 + 0.229673i \(0.926234\pi\)
\(158\) 0 0
\(159\) 195907. 0.614549
\(160\) 0 0
\(161\) 548547. 1.66782
\(162\) 0 0
\(163\) −336280. 336280.i −0.991363 0.991363i 0.00860016 0.999963i \(-0.497262\pi\)
−0.999963 + 0.00860016i \(0.997262\pi\)
\(164\) 0 0
\(165\) 32814.5 32814.5i 0.0938332 0.0938332i
\(166\) 0 0
\(167\) 338007.i 0.937852i 0.883237 + 0.468926i \(0.155359\pi\)
−0.883237 + 0.468926i \(0.844641\pi\)
\(168\) 0 0
\(169\) 296852.i 0.799509i
\(170\) 0 0
\(171\) 131411. 131411.i 0.343669 0.343669i
\(172\) 0 0
\(173\) 144268. + 144268.i 0.366485 + 0.366485i 0.866194 0.499709i \(-0.166560\pi\)
−0.499709 + 0.866194i \(0.666560\pi\)
\(174\) 0 0
\(175\) 130029. 0.320956
\(176\) 0 0
\(177\) 203886. 0.489165
\(178\) 0 0
\(179\) 385415. + 385415.i 0.899075 + 0.899075i 0.995354 0.0962793i \(-0.0306942\pi\)
−0.0962793 + 0.995354i \(0.530694\pi\)
\(180\) 0 0
\(181\) −135597. + 135597.i −0.307647 + 0.307647i −0.843996 0.536349i \(-0.819803\pi\)
0.536349 + 0.843996i \(0.319803\pi\)
\(182\) 0 0
\(183\) 385019.i 0.849875i
\(184\) 0 0
\(185\) 372699.i 0.800624i
\(186\) 0 0
\(187\) 113220. 113220.i 0.236765 0.236765i
\(188\) 0 0
\(189\) −593250. 593250.i −1.20805 1.20805i
\(190\) 0 0
\(191\) 70124.0 0.139086 0.0695430 0.997579i \(-0.477846\pi\)
0.0695430 + 0.997579i \(0.477846\pi\)
\(192\) 0 0
\(193\) 714068. 1.37990 0.689948 0.723859i \(-0.257633\pi\)
0.689948 + 0.723859i \(0.257633\pi\)
\(194\) 0 0
\(195\) 53776.5 + 53776.5i 0.101276 + 0.101276i
\(196\) 0 0
\(197\) −441131. + 441131.i −0.809845 + 0.809845i −0.984610 0.174765i \(-0.944083\pi\)
0.174765 + 0.984610i \(0.444083\pi\)
\(198\) 0 0
\(199\) 135153.i 0.241931i −0.992657 0.120966i \(-0.961401\pi\)
0.992657 0.120966i \(-0.0385991\pi\)
\(200\) 0 0
\(201\) 220498.i 0.384960i
\(202\) 0 0
\(203\) −715190. + 715190.i −1.21810 + 1.21810i
\(204\) 0 0
\(205\) −152640. 152640.i −0.253679 0.253679i
\(206\) 0 0
\(207\) −312931. −0.507602
\(208\) 0 0
\(209\) −260693. −0.412822
\(210\) 0 0
\(211\) 672860. + 672860.i 1.04044 + 1.04044i 0.999147 + 0.0412971i \(0.0131490\pi\)
0.0412971 + 0.999147i \(0.486851\pi\)
\(212\) 0 0
\(213\) −384212. + 384212.i −0.580259 + 0.580259i
\(214\) 0 0
\(215\) 209035.i 0.308406i
\(216\) 0 0
\(217\) 478948.i 0.690461i
\(218\) 0 0
\(219\) −696736. + 696736.i −0.981652 + 0.981652i
\(220\) 0 0
\(221\) 185545. + 185545.i 0.255545 + 0.255545i
\(222\) 0 0
\(223\) −1.33714e6 −1.80059 −0.900293 0.435285i \(-0.856648\pi\)
−0.900293 + 0.435285i \(0.856648\pi\)
\(224\) 0 0
\(225\) −74178.2 −0.0976832
\(226\) 0 0
\(227\) 24080.3 + 24080.3i 0.0310168 + 0.0310168i 0.722445 0.691428i \(-0.243018\pi\)
−0.691428 + 0.722445i \(0.743018\pi\)
\(228\) 0 0
\(229\) 332429. 332429.i 0.418900 0.418900i −0.465925 0.884824i \(-0.654278\pi\)
0.884824 + 0.465925i \(0.154278\pi\)
\(230\) 0 0
\(231\) 386191.i 0.476181i
\(232\) 0 0
\(233\) 909342.i 1.09733i −0.836042 0.548665i \(-0.815136\pi\)
0.836042 0.548665i \(-0.184864\pi\)
\(234\) 0 0
\(235\) −104108. + 104108.i −0.122974 + 0.122974i
\(236\) 0 0
\(237\) 314443. + 314443.i 0.363640 + 0.363640i
\(238\) 0 0
\(239\) 259767. 0.294164 0.147082 0.989124i \(-0.453012\pi\)
0.147082 + 0.989124i \(0.453012\pi\)
\(240\) 0 0
\(241\) 199206. 0.220932 0.110466 0.993880i \(-0.464766\pi\)
0.110466 + 0.993880i \(0.464766\pi\)
\(242\) 0 0
\(243\) 565812. + 565812.i 0.614690 + 0.614690i
\(244\) 0 0
\(245\) −468040. + 468040.i −0.498159 + 0.498159i
\(246\) 0 0
\(247\) 427223.i 0.445567i
\(248\) 0 0
\(249\) 716711.i 0.732564i
\(250\) 0 0
\(251\) −522423. + 522423.i −0.523405 + 0.523405i −0.918598 0.395193i \(-0.870678\pi\)
0.395193 + 0.918598i \(0.370678\pi\)
\(252\) 0 0
\(253\) 310397. + 310397.i 0.304871 + 0.304871i
\(254\) 0 0
\(255\) 268077. 0.258172
\(256\) 0 0
\(257\) 1.24541e6 1.17620 0.588099 0.808789i \(-0.299877\pi\)
0.588099 + 0.808789i \(0.299877\pi\)
\(258\) 0 0
\(259\) 2.19312e6 + 2.19312e6i 2.03149 + 2.03149i
\(260\) 0 0
\(261\) 407997. 407997.i 0.370728 0.370728i
\(262\) 0 0
\(263\) 1.93577e6i 1.72570i −0.505462 0.862849i \(-0.668678\pi\)
0.505462 0.862849i \(-0.331322\pi\)
\(264\) 0 0
\(265\) 439266.i 0.384249i
\(266\) 0 0
\(267\) 154701. 154701.i 0.132805 0.132805i
\(268\) 0 0
\(269\) 629021. + 629021.i 0.530010 + 0.530010i 0.920575 0.390565i \(-0.127720\pi\)
−0.390565 + 0.920575i \(0.627720\pi\)
\(270\) 0 0
\(271\) 1.61018e6 1.33184 0.665921 0.746023i \(-0.268039\pi\)
0.665921 + 0.746023i \(0.268039\pi\)
\(272\) 0 0
\(273\) −632890. −0.513951
\(274\) 0 0
\(275\) 73577.4 + 73577.4i 0.0586696 + 0.0586696i
\(276\) 0 0
\(277\) −1.05351e6 + 1.05351e6i −0.824974 + 0.824974i −0.986817 0.161842i \(-0.948256\pi\)
0.161842 + 0.986817i \(0.448256\pi\)
\(278\) 0 0
\(279\) 273227.i 0.210142i
\(280\) 0 0
\(281\) 14414.9i 0.0108904i 0.999985 + 0.00544522i \(0.00173328\pi\)
−0.999985 + 0.00544522i \(0.998267\pi\)
\(282\) 0 0
\(283\) 328025. 328025.i 0.243468 0.243468i −0.574815 0.818283i \(-0.694926\pi\)
0.818283 + 0.574815i \(0.194926\pi\)
\(284\) 0 0
\(285\) −308628. 308628.i −0.225073 0.225073i
\(286\) 0 0
\(287\) 1.79641e6 1.28736
\(288\) 0 0
\(289\) −494914. −0.348566
\(290\) 0 0
\(291\) −402296. 402296.i −0.278492 0.278492i
\(292\) 0 0
\(293\) 1.52796e6 1.52796e6i 1.03978 1.03978i 0.0406088 0.999175i \(-0.487070\pi\)
0.999175 0.0406088i \(-0.0129297\pi\)
\(294\) 0 0
\(295\) 457158.i 0.305852i
\(296\) 0 0
\(297\) 671385.i 0.441652i
\(298\) 0 0
\(299\) −508679. + 508679.i −0.329053 + 0.329053i
\(300\) 0 0
\(301\) 1.23005e6 + 1.23005e6i 0.782543 + 0.782543i
\(302\) 0 0
\(303\) −1.94017e6 −1.21404
\(304\) 0 0
\(305\) −863298. −0.531387
\(306\) 0 0
\(307\) −588349. 588349.i −0.356278 0.356278i 0.506161 0.862439i \(-0.331064\pi\)
−0.862439 + 0.506161i \(0.831064\pi\)
\(308\) 0 0
\(309\) −1.67677e6 + 1.67677e6i −0.999025 + 0.999025i
\(310\) 0 0
\(311\) 133732.i 0.0784036i 0.999231 + 0.0392018i \(0.0124815\pi\)
−0.999231 + 0.0392018i \(0.987518\pi\)
\(312\) 0 0
\(313\) 2.56615e6i 1.48054i 0.672307 + 0.740272i \(0.265303\pi\)
−0.672307 + 0.740272i \(0.734697\pi\)
\(314\) 0 0
\(315\) 436497. 436497.i 0.247859 0.247859i
\(316\) 0 0
\(317\) 1.19775e6 + 1.19775e6i 0.669448 + 0.669448i 0.957588 0.288140i \(-0.0930370\pi\)
−0.288140 + 0.957588i \(0.593037\pi\)
\(318\) 0 0
\(319\) −809385. −0.445327
\(320\) 0 0
\(321\) 1.67258e6 0.905994
\(322\) 0 0
\(323\) −1.06486e6 1.06486e6i −0.567917 0.567917i
\(324\) 0 0
\(325\) −120579. + 120579.i −0.0633231 + 0.0633231i
\(326\) 0 0
\(327\) 277793.i 0.143665i
\(328\) 0 0
\(329\) 1.22523e6i 0.624063i
\(330\) 0 0
\(331\) 174005. 174005.i 0.0872955 0.0872955i −0.662111 0.749406i \(-0.730339\pi\)
0.749406 + 0.662111i \(0.230339\pi\)
\(332\) 0 0
\(333\) −1.25112e6 1.25112e6i −0.618284 0.618284i
\(334\) 0 0
\(335\) −494406. −0.240697
\(336\) 0 0
\(337\) 3.44408e6 1.65196 0.825978 0.563703i \(-0.190624\pi\)
0.825978 + 0.563703i \(0.190624\pi\)
\(338\) 0 0
\(339\) −567516. 567516.i −0.268212 0.268212i
\(340\) 0 0
\(341\) −271014. + 271014.i −0.126214 + 0.126214i
\(342\) 0 0
\(343\) 2.01168e6i 0.923257i
\(344\) 0 0
\(345\) 734945.i 0.332435i
\(346\) 0 0
\(347\) 315686. 315686.i 0.140745 0.140745i −0.633224 0.773969i \(-0.718269\pi\)
0.773969 + 0.633224i \(0.218269\pi\)
\(348\) 0 0
\(349\) −623357. 623357.i −0.273951 0.273951i 0.556737 0.830689i \(-0.312053\pi\)
−0.830689 + 0.556737i \(0.812053\pi\)
\(350\) 0 0
\(351\) 1.10027e6 0.476684
\(352\) 0 0
\(353\) −3.20077e6 −1.36716 −0.683578 0.729878i \(-0.739577\pi\)
−0.683578 + 0.729878i \(0.739577\pi\)
\(354\) 0 0
\(355\) −861488. 861488.i −0.362809 0.362809i
\(356\) 0 0
\(357\) −1.57748e6 + 1.57748e6i −0.655079 + 0.655079i
\(358\) 0 0
\(359\) 1.76174e6i 0.721449i 0.932672 + 0.360724i \(0.117471\pi\)
−0.932672 + 0.360724i \(0.882529\pi\)
\(360\) 0 0
\(361\) 24224.3i 0.00978323i
\(362\) 0 0
\(363\) 1.05120e6 1.05120e6i 0.418715 0.418715i
\(364\) 0 0
\(365\) −1.56224e6 1.56224e6i −0.613782 0.613782i
\(366\) 0 0
\(367\) 322537. 0.125001 0.0625006 0.998045i \(-0.480092\pi\)
0.0625006 + 0.998045i \(0.480092\pi\)
\(368\) 0 0
\(369\) −1.02480e6 −0.391809
\(370\) 0 0
\(371\) −2.58484e6 2.58484e6i −0.974987 0.974987i
\(372\) 0 0
\(373\) 1.70422e6 1.70422e6i 0.634238 0.634238i −0.314890 0.949128i \(-0.601968\pi\)
0.949128 + 0.314890i \(0.101968\pi\)
\(374\) 0 0
\(375\) 174213.i 0.0639740i
\(376\) 0 0
\(377\) 1.32642e6i 0.480649i
\(378\) 0 0
\(379\) 1.11070e6 1.11070e6i 0.397191 0.397191i −0.480050 0.877241i \(-0.659381\pi\)
0.877241 + 0.480050i \(0.159381\pi\)
\(380\) 0 0
\(381\) 1.88847e6 + 1.88847e6i 0.666495 + 0.666495i
\(382\) 0 0
\(383\) −4.30045e6 −1.49802 −0.749009 0.662559i \(-0.769470\pi\)
−0.749009 + 0.662559i \(0.769470\pi\)
\(384\) 0 0
\(385\) −865924. −0.297734
\(386\) 0 0
\(387\) −701714. 701714.i −0.238167 0.238167i
\(388\) 0 0
\(389\) 4.14998e6 4.14998e6i 1.39050 1.39050i 0.566313 0.824190i \(-0.308369\pi\)
0.824190 0.566313i \(-0.191631\pi\)
\(390\) 0 0
\(391\) 2.53577e6i 0.838820i
\(392\) 0 0
\(393\) 2.09412e6i 0.683943i
\(394\) 0 0
\(395\) −705051. + 705051.i −0.227367 + 0.227367i
\(396\) 0 0
\(397\) −1.05760e6 1.05760e6i −0.336781 0.336781i 0.518374 0.855154i \(-0.326538\pi\)
−0.855154 + 0.518374i \(0.826538\pi\)
\(398\) 0 0
\(399\) 3.63221e6 1.14219
\(400\) 0 0
\(401\) 653994. 0.203101 0.101551 0.994830i \(-0.467620\pi\)
0.101551 + 0.994830i \(0.467620\pi\)
\(402\) 0 0
\(403\) −444139. 444139.i −0.136225 0.136225i
\(404\) 0 0
\(405\) 285006. 285006.i 0.0863410 0.0863410i
\(406\) 0 0
\(407\) 2.48197e6i 0.742696i
\(408\) 0 0
\(409\) 3.75150e6i 1.10891i −0.832214 0.554455i \(-0.812927\pi\)
0.832214 0.554455i \(-0.187073\pi\)
\(410\) 0 0
\(411\) −1.22245e6 + 1.22245e6i −0.356966 + 0.356966i
\(412\) 0 0
\(413\) −2.69012e6 2.69012e6i −0.776063 0.776063i
\(414\) 0 0
\(415\) −1.60702e6 −0.458039
\(416\) 0 0
\(417\) −4.13179e6 −1.16359
\(418\) 0 0
\(419\) −191869. 191869.i −0.0533913 0.0533913i 0.679907 0.733298i \(-0.262020\pi\)
−0.733298 + 0.679907i \(0.762020\pi\)
\(420\) 0 0
\(421\) 1.78024e6 1.78024e6i 0.489523 0.489523i −0.418633 0.908156i \(-0.637491\pi\)
0.908156 + 0.418633i \(0.137491\pi\)
\(422\) 0 0
\(423\) 698962.i 0.189934i
\(424\) 0 0
\(425\) 601087.i 0.161423i
\(426\) 0 0
\(427\) 5.08003e6 5.08003e6i 1.34833 1.34833i
\(428\) 0 0
\(429\) −358123. 358123.i −0.0939483 0.0939483i
\(430\) 0 0
\(431\) −2.05116e6 −0.531871 −0.265936 0.963991i \(-0.585681\pi\)
−0.265936 + 0.963991i \(0.585681\pi\)
\(432\) 0 0
\(433\) −4.88523e6 −1.25217 −0.626087 0.779753i \(-0.715345\pi\)
−0.626087 + 0.779753i \(0.715345\pi\)
\(434\) 0 0
\(435\) −958214. 958214.i −0.242795 0.242795i
\(436\) 0 0
\(437\) 2.91936e6 2.91936e6i 0.731280 0.731280i
\(438\) 0 0
\(439\) 4.22642e6i 1.04667i −0.852126 0.523337i \(-0.824687\pi\)
0.852126 0.523337i \(-0.175313\pi\)
\(440\) 0 0
\(441\) 3.14235e6i 0.769410i
\(442\) 0 0
\(443\) −3.63313e6 + 3.63313e6i −0.879573 + 0.879573i −0.993490 0.113918i \(-0.963660\pi\)
0.113918 + 0.993490i \(0.463660\pi\)
\(444\) 0 0
\(445\) 346873. + 346873.i 0.0830368 + 0.0830368i
\(446\) 0 0
\(447\) 3.02811e6 0.716808
\(448\) 0 0
\(449\) −1.68435e6 −0.394291 −0.197145 0.980374i \(-0.563167\pi\)
−0.197145 + 0.980374i \(0.563167\pi\)
\(450\) 0 0
\(451\) 1.01650e6 + 1.01650e6i 0.235325 + 0.235325i
\(452\) 0 0
\(453\) −3.36852e6 + 3.36852e6i −0.771248 + 0.771248i
\(454\) 0 0
\(455\) 1.41908e6i 0.321350i
\(456\) 0 0
\(457\) 3.26840e6i 0.732056i −0.930604 0.366028i \(-0.880717\pi\)
0.930604 0.366028i \(-0.119283\pi\)
\(458\) 0 0
\(459\) 2.74242e6 2.74242e6i 0.607579 0.607579i
\(460\) 0 0
\(461\) −5.01159e6 5.01159e6i −1.09831 1.09831i −0.994609 0.103697i \(-0.966933\pi\)
−0.103697 0.994609i \(-0.533067\pi\)
\(462\) 0 0
\(463\) 455834. 0.0988221 0.0494110 0.998779i \(-0.484266\pi\)
0.0494110 + 0.998779i \(0.484266\pi\)
\(464\) 0 0
\(465\) −641696. −0.137625
\(466\) 0 0
\(467\) 277375. + 277375.i 0.0588539 + 0.0588539i 0.735921 0.677067i \(-0.236749\pi\)
−0.677067 + 0.735921i \(0.736749\pi\)
\(468\) 0 0
\(469\) 2.90930e6 2.90930e6i 0.610741 0.610741i
\(470\) 0 0
\(471\) 3.62128e6i 0.752160i
\(472\) 0 0
\(473\) 1.39206e6i 0.286092i
\(474\) 0 0
\(475\) 692013. 692013.i 0.140728 0.140728i
\(476\) 0 0
\(477\) 1.47458e6 + 1.47458e6i 0.296738 + 0.296738i
\(478\) 0 0
\(479\) −5.13891e6 −1.02337 −0.511684 0.859173i \(-0.670978\pi\)
−0.511684 + 0.859173i \(0.670978\pi\)
\(480\) 0 0
\(481\) −4.06746e6 −0.801606
\(482\) 0 0
\(483\) −4.32474e6 4.32474e6i −0.843514 0.843514i
\(484\) 0 0
\(485\) 902035. 902035.i 0.174128 0.174128i
\(486\) 0 0
\(487\) 3.67637e6i 0.702420i 0.936297 + 0.351210i \(0.114230\pi\)
−0.936297 + 0.351210i \(0.885770\pi\)
\(488\) 0 0
\(489\) 5.30247e6i 1.00278i
\(490\) 0 0
\(491\) 1.38862e6 1.38862e6i 0.259943 0.259943i −0.565088 0.825031i \(-0.691158\pi\)
0.825031 + 0.565088i \(0.191158\pi\)
\(492\) 0 0
\(493\) −3.30612e6 3.30612e6i −0.612634 0.612634i
\(494\) 0 0
\(495\) 493987. 0.0906155
\(496\) 0 0
\(497\) 1.01388e7 1.84117
\(498\) 0 0
\(499\) −1.15528e6 1.15528e6i −0.207699 0.207699i 0.595590 0.803289i \(-0.296918\pi\)
−0.803289 + 0.595590i \(0.796918\pi\)
\(500\) 0 0
\(501\) 2.66485e6 2.66485e6i 0.474327 0.474327i
\(502\) 0 0
\(503\) 3.23595e6i 0.570271i 0.958487 + 0.285135i \(0.0920386\pi\)
−0.958487 + 0.285135i \(0.907961\pi\)
\(504\) 0 0
\(505\) 4.35030e6i 0.759085i
\(506\) 0 0
\(507\) −2.34038e6 + 2.34038e6i −0.404359 + 0.404359i
\(508\) 0 0
\(509\) 7.03415e6 + 7.03415e6i 1.20342 + 1.20342i 0.973120 + 0.230301i \(0.0739709\pi\)
0.230301 + 0.973120i \(0.426029\pi\)
\(510\) 0 0
\(511\) 1.83858e7 3.11480
\(512\) 0 0
\(513\) −6.31454e6 −1.05937
\(514\) 0 0
\(515\) −3.75968e6 3.75968e6i −0.624644 0.624644i
\(516\) 0 0
\(517\) 693302. 693302.i 0.114076 0.114076i
\(518\) 0 0
\(519\) 2.27483e6i 0.370706i
\(520\) 0 0
\(521\) 1.02322e7i 1.65149i 0.564042 + 0.825746i \(0.309246\pi\)
−0.564042 + 0.825746i \(0.690754\pi\)
\(522\) 0 0
\(523\) 1.85939e6 1.85939e6i 0.297246 0.297246i −0.542688 0.839934i \(-0.682593\pi\)
0.839934 + 0.542688i \(0.182593\pi\)
\(524\) 0 0
\(525\) −1.02515e6 1.02515e6i −0.162326 0.162326i
\(526\) 0 0
\(527\) −2.21404e6 −0.347263
\(528\) 0 0
\(529\) −515597. −0.0801072
\(530\) 0 0
\(531\) 1.53464e6 + 1.53464e6i 0.236195 + 0.236195i
\(532\) 0 0
\(533\) −1.66585e6 + 1.66585e6i −0.253990 + 0.253990i
\(534\) 0 0
\(535\) 3.75030e6i 0.566476i
\(536\) 0 0
\(537\) 6.07722e6i 0.909430i
\(538\) 0 0
\(539\) 3.11690e6 3.11690e6i 0.462116 0.462116i
\(540\) 0 0
\(541\) 5.40070e6 + 5.40070e6i 0.793336 + 0.793336i 0.982035 0.188699i \(-0.0604271\pi\)
−0.188699 + 0.982035i \(0.560427\pi\)
\(542\) 0 0
\(543\) 2.13809e6 0.311191
\(544\) 0 0
\(545\) −622873. −0.0898273
\(546\) 0 0
\(547\) 7.23243e6 + 7.23243e6i 1.03351 + 1.03351i 0.999419 + 0.0340941i \(0.0108546\pi\)
0.0340941 + 0.999419i \(0.489145\pi\)
\(548\) 0 0
\(549\) −2.89802e6 + 2.89802e6i −0.410366 + 0.410366i
\(550\) 0 0
\(551\) 7.61246e6i 1.06818i
\(552\) 0 0
\(553\) 8.29767e6i 1.15383i
\(554\) 0 0
\(555\) −2.93836e6 + 2.93836e6i −0.404923 + 0.404923i
\(556\) 0 0
\(557\) 3.43079e6 + 3.43079e6i 0.468550 + 0.468550i 0.901445 0.432894i \(-0.142508\pi\)
−0.432894 + 0.901445i \(0.642508\pi\)
\(558\) 0 0
\(559\) −2.28131e6 −0.308784
\(560\) 0 0
\(561\) −1.78525e6 −0.239492
\(562\) 0 0
\(563\) −5.24831e6 5.24831e6i −0.697828 0.697828i 0.266114 0.963942i \(-0.414260\pi\)
−0.963942 + 0.266114i \(0.914260\pi\)
\(564\) 0 0
\(565\) 1.27250e6 1.27250e6i 0.167701 0.167701i
\(566\) 0 0
\(567\) 3.35421e6i 0.438160i
\(568\) 0 0
\(569\) 8.98310e6i 1.16318i 0.813483 + 0.581588i \(0.197569\pi\)
−0.813483 + 0.581588i \(0.802431\pi\)
\(570\) 0 0
\(571\) 2.67366e6 2.67366e6i 0.343176 0.343176i −0.514384 0.857560i \(-0.671979\pi\)
0.857560 + 0.514384i \(0.171979\pi\)
\(572\) 0 0
\(573\) −552858. 552858.i −0.0703439 0.0703439i
\(574\) 0 0
\(575\) −1.64791e6 −0.207856
\(576\) 0 0
\(577\) −2.47918e6 −0.310005 −0.155003 0.987914i \(-0.549539\pi\)
−0.155003 + 0.987914i \(0.549539\pi\)
\(578\) 0 0
\(579\) −5.62972e6 5.62972e6i −0.697895 0.697895i
\(580\) 0 0
\(581\) 9.45644e6 9.45644e6i 1.16222 1.16222i
\(582\) 0 0
\(583\) 2.92528e6i 0.356448i
\(584\) 0 0
\(585\) 809547.i 0.0978030i
\(586\) 0 0
\(587\) −3.20495e6 + 3.20495e6i −0.383906 + 0.383906i −0.872507 0.488601i \(-0.837507\pi\)
0.488601 + 0.872507i \(0.337507\pi\)
\(588\) 0 0
\(589\) 2.54895e6 + 2.54895e6i 0.302743 + 0.302743i
\(590\) 0 0
\(591\) 6.95575e6 0.819172
\(592\) 0 0
\(593\) 3.73079e6 0.435677 0.217838 0.975985i \(-0.430099\pi\)
0.217838 + 0.975985i \(0.430099\pi\)
\(594\) 0 0
\(595\) −3.53706e6 3.53706e6i −0.409591 0.409591i
\(596\) 0 0
\(597\) −1.06554e6 + 1.06554e6i −0.122359 + 0.122359i
\(598\) 0 0
\(599\) 2.96317e6i 0.337434i 0.985665 + 0.168717i \(0.0539625\pi\)
−0.985665 + 0.168717i \(0.946038\pi\)
\(600\) 0 0
\(601\) 1.10701e7i 1.25016i 0.780561 + 0.625079i \(0.214933\pi\)
−0.780561 + 0.625079i \(0.785067\pi\)
\(602\) 0 0
\(603\) −1.65968e6 + 1.65968e6i −0.185879 + 0.185879i
\(604\) 0 0
\(605\) 2.35702e6 + 2.35702e6i 0.261803 + 0.261803i
\(606\) 0 0
\(607\) −1.42525e7 −1.57007 −0.785036 0.619450i \(-0.787356\pi\)
−0.785036 + 0.619450i \(0.787356\pi\)
\(608\) 0 0
\(609\) 1.12771e7 1.23212
\(610\) 0 0
\(611\) 1.13618e6 + 1.13618e6i 0.123125 + 0.123125i
\(612\) 0 0
\(613\) −5.52901e6 + 5.52901e6i −0.594287 + 0.594287i −0.938787 0.344499i \(-0.888049\pi\)
0.344499 + 0.938787i \(0.388049\pi\)
\(614\) 0 0
\(615\) 2.40683e6i 0.256601i
\(616\) 0 0
\(617\) 1.12751e7i 1.19236i 0.802852 + 0.596178i \(0.203315\pi\)
−0.802852 + 0.596178i \(0.796685\pi\)
\(618\) 0 0
\(619\) −7.49743e6 + 7.49743e6i −0.786476 + 0.786476i −0.980915 0.194438i \(-0.937712\pi\)
0.194438 + 0.980915i \(0.437712\pi\)
\(620\) 0 0
\(621\) 7.51848e6 + 7.51848e6i 0.782350 + 0.782350i
\(622\) 0 0
\(623\) −4.08231e6 −0.421392
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) 2.05530e6 + 2.05530e6i 0.208788 + 0.208788i
\(628\) 0 0
\(629\) −1.01382e7 + 1.01382e7i −1.02172 + 1.02172i
\(630\) 0 0
\(631\) 7.22894e6i 0.722771i −0.932416 0.361386i \(-0.882304\pi\)
0.932416 0.361386i \(-0.117696\pi\)
\(632\) 0 0
\(633\) 1.06097e7i 1.05243i
\(634\) 0 0
\(635\) −4.23436e6 + 4.23436e6i −0.416729 + 0.416729i
\(636\) 0 0
\(637\) 5.10798e6 + 5.10798e6i 0.498770 + 0.498770i
\(638\) 0 0
\(639\) −5.78389e6 −0.560361
\(640\) 0 0
\(641\) −1.53670e7 −1.47722 −0.738610 0.674133i \(-0.764517\pi\)
−0.738610 + 0.674133i \(0.764517\pi\)
\(642\) 0 0
\(643\) 288960. + 288960.i 0.0275620 + 0.0275620i 0.720753 0.693191i \(-0.243796\pi\)
−0.693191 + 0.720753i \(0.743796\pi\)
\(644\) 0 0
\(645\) −1.64803e6 + 1.64803e6i −0.155979 + 0.155979i
\(646\) 0 0
\(647\) 1.39042e7i 1.30583i −0.757432 0.652914i \(-0.773546\pi\)
0.757432 0.652914i \(-0.226454\pi\)
\(648\) 0 0
\(649\) 3.04443e6i 0.283723i
\(650\) 0 0
\(651\) 3.77603e6 3.77603e6i 0.349207 0.349207i
\(652\) 0 0
\(653\) 2.44568e6 + 2.44568e6i 0.224449 + 0.224449i 0.810369 0.585920i \(-0.199267\pi\)
−0.585920 + 0.810369i \(0.699267\pi\)
\(654\) 0 0
\(655\) 4.69548e6 0.427638
\(656\) 0 0
\(657\) −1.04886e7 −0.947990
\(658\) 0 0
\(659\) 5.00967e6 + 5.00967e6i 0.449361 + 0.449361i 0.895142 0.445781i \(-0.147074\pi\)
−0.445781 + 0.895142i \(0.647074\pi\)
\(660\) 0 0
\(661\) 1.37540e7 1.37540e7i 1.22441 1.22441i 0.258359 0.966049i \(-0.416818\pi\)
0.966049 0.258359i \(-0.0831816\pi\)
\(662\) 0 0
\(663\) 2.92567e6i 0.258488i
\(664\) 0 0
\(665\) 8.14422e6i 0.714160i
\(666\) 0 0
\(667\) 9.06387e6 9.06387e6i 0.788859 0.788859i
\(668\) 0 0
\(669\) 1.05420e7 + 1.05420e7i 0.910662 + 0.910662i
\(670\) 0 0
\(671\) 5.74911e6 0.492940
\(672\) 0 0
\(673\) −2.01324e7 −1.71339 −0.856696 0.515821i \(-0.827487\pi\)
−0.856696 + 0.515821i \(0.827487\pi\)
\(674\) 0 0
\(675\) 1.78220e6 + 1.78220e6i 0.150556 + 0.150556i
\(676\) 0 0
\(677\) −2.09354e6 + 2.09354e6i −0.175554 + 0.175554i −0.789414 0.613861i \(-0.789616\pi\)
0.613861 + 0.789414i \(0.289616\pi\)
\(678\) 0 0
\(679\) 1.06160e7i 0.883659i
\(680\) 0 0
\(681\) 379698.i 0.0313740i
\(682\) 0 0
\(683\) −73464.0 + 73464.0i −0.00602591 + 0.00602591i −0.710113 0.704087i \(-0.751356\pi\)
0.704087 + 0.710113i \(0.251356\pi\)
\(684\) 0 0
\(685\) −2.74100e6 2.74100e6i −0.223194 0.223194i
\(686\) 0 0
\(687\) −5.24174e6 −0.423724
\(688\) 0 0
\(689\) 4.79395e6 0.384721
\(690\) 0 0
\(691\) 8.05791e6 + 8.05791e6i 0.641989 + 0.641989i 0.951044 0.309055i \(-0.100013\pi\)
−0.309055 + 0.951044i \(0.600013\pi\)
\(692\) 0 0
\(693\) −2.90684e6 + 2.90684e6i −0.229926 + 0.229926i
\(694\) 0 0
\(695\) 9.26439e6i 0.727537i
\(696\) 0 0
\(697\) 8.30428e6i 0.647470i
\(698\) 0 0
\(699\) −7.16926e6 + 7.16926e6i −0.554985 + 0.554985i
\(700\) 0 0
\(701\) −1.51961e7 1.51961e7i −1.16799 1.16799i −0.982681 0.185307i \(-0.940672\pi\)
−0.185307 0.982681i \(-0.559328\pi\)
\(702\) 0 0
\(703\) 2.33436e7 1.78147
\(704\) 0 0
\(705\) 1.64157e6 0.124390
\(706\) 0 0
\(707\) 2.55991e7 + 2.55991e7i 1.92609 + 1.92609i
\(708\) 0 0
\(709\) 3.46603e6 3.46603e6i 0.258951 0.258951i −0.565677 0.824627i \(-0.691385\pi\)
0.824627 + 0.565677i \(0.191385\pi\)
\(710\) 0 0
\(711\) 4.73360e6i 0.351170i
\(712\) 0 0
\(713\) 6.06989e6i 0.447154i
\(714\) 0 0
\(715\) 802990. 802990.i 0.0587415 0.0587415i
\(716\) 0 0
\(717\) −2.04801e6 2.04801e6i −0.148776 0.148776i
\(718\) 0 0
\(719\) −1.14717e7 −0.827568 −0.413784 0.910375i \(-0.635793\pi\)
−0.413784 + 0.910375i \(0.635793\pi\)
\(720\) 0 0
\(721\) 4.42472e7 3.16992
\(722\) 0 0
\(723\) −1.57054e6 1.57054e6i −0.111738 0.111738i
\(724\) 0 0
\(725\) 2.14853e6 2.14853e6i 0.151808 0.151808i
\(726\) 0 0
\(727\) 3.32886e6i 0.233593i −0.993156 0.116796i \(-0.962737\pi\)
0.993156 0.116796i \(-0.0372625\pi\)
\(728\) 0 0
\(729\) 1.28395e7i 0.894804i
\(730\) 0 0
\(731\) −5.68619e6 + 5.68619e6i −0.393575 + 0.393575i
\(732\) 0 0
\(733\) −1.00193e7 1.00193e7i −0.688772 0.688772i 0.273188 0.961961i \(-0.411922\pi\)
−0.961961 + 0.273188i \(0.911922\pi\)
\(734\) 0 0
\(735\) 7.38006e6 0.503897
\(736\) 0 0
\(737\) 3.29248e6 0.223282
\(738\) 0 0
\(739\) 8.02079e6 + 8.02079e6i 0.540264 + 0.540264i 0.923606 0.383342i \(-0.125227\pi\)
−0.383342 + 0.923606i \(0.625227\pi\)
\(740\) 0 0
\(741\) −3.36823e6 + 3.36823e6i −0.225349 + 0.225349i
\(742\) 0 0
\(743\) 1.92310e7i 1.27800i 0.769207 + 0.639000i \(0.220651\pi\)
−0.769207 + 0.639000i \(0.779349\pi\)
\(744\) 0 0
\(745\) 6.78969e6i 0.448187i
\(746\) 0 0
\(747\) −5.39465e6 + 5.39465e6i −0.353722 + 0.353722i
\(748\) 0 0
\(749\) −2.20684e7 2.20684e7i −1.43736 1.43736i
\(750\) 0 0
\(751\) 2.91259e6 0.188443 0.0942214 0.995551i \(-0.469964\pi\)
0.0942214 + 0.995551i \(0.469964\pi\)
\(752\) 0 0
\(753\) 8.23756e6 0.529433
\(754\) 0 0
\(755\) −7.55297e6 7.55297e6i −0.482226 0.482226i
\(756\) 0 0
\(757\) −1.75862e7 + 1.75862e7i −1.11541 + 1.11541i −0.123001 + 0.992407i \(0.539252\pi\)
−0.992407 + 0.123001i \(0.960748\pi\)
\(758\) 0 0
\(759\) 4.89434e6i 0.308383i
\(760\) 0 0
\(761\) 9.66060e6i 0.604704i 0.953196 + 0.302352i \(0.0977717\pi\)
−0.953196 + 0.302352i \(0.902228\pi\)
\(762\) 0 0
\(763\) 3.66526e6 3.66526e6i 0.227926 0.227926i
\(764\) 0 0
\(765\) 2.01780e6 + 2.01780e6i 0.124659 + 0.124659i
\(766\) 0 0
\(767\) 4.98922e6 0.306227
\(768\) 0 0
\(769\) 2.46747e7 1.50465 0.752325 0.658793i \(-0.228932\pi\)
0.752325 + 0.658793i \(0.228932\pi\)
\(770\) 0 0
\(771\) −9.81883e6 9.81883e6i −0.594873 0.594873i
\(772\) 0 0
\(773\) −1.25753e7 + 1.25753e7i −0.756952 + 0.756952i −0.975766 0.218815i \(-0.929781\pi\)
0.218815 + 0.975766i \(0.429781\pi\)
\(774\) 0 0
\(775\) 1.43882e6i 0.0860505i
\(776\) 0 0
\(777\) 3.45812e7i 2.05488i
\(778\) 0 0
\(779\) 9.56046e6 9.56046e6i 0.564462 0.564462i
\(780\) 0 0
\(781\) 5.73705e6 + 5.73705e6i 0.336559 + 0.336559i
\(782\) 0 0
\(783\) −1.96051e7 −1.14278
\(784\) 0 0
\(785\) −8.11972e6 −0.470291
\(786\) 0 0