Properties

Label 320.6.l.a.81.18
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 81.18
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.18

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.58258 - 3.58258i) q^{3} +(17.6777 - 17.6777i) q^{5} +149.558i q^{7} -217.330i q^{9} +O(q^{10})\) \(q+(-3.58258 - 3.58258i) q^{3} +(17.6777 - 17.6777i) q^{5} +149.558i q^{7} -217.330i q^{9} +(38.8975 - 38.8975i) q^{11} +(683.576 + 683.576i) q^{13} -126.663 q^{15} -929.208 q^{17} +(-900.333 - 900.333i) q^{19} +(535.804 - 535.804i) q^{21} +507.581i q^{23} -625.000i q^{25} +(-1649.17 + 1649.17i) q^{27} +(584.811 + 584.811i) q^{29} +5061.59 q^{31} -278.707 q^{33} +(2643.84 + 2643.84i) q^{35} +(-10345.7 + 10345.7i) q^{37} -4897.93i q^{39} -1291.09i q^{41} +(-3874.63 + 3874.63i) q^{43} +(-3841.89 - 3841.89i) q^{45} +1375.42 q^{47} -5560.57 q^{49} +(3328.96 + 3328.96i) q^{51} +(-8947.98 + 8947.98i) q^{53} -1375.23i q^{55} +6451.03i q^{57} +(32361.6 - 32361.6i) q^{59} +(8808.44 + 8808.44i) q^{61} +32503.5 q^{63} +24168.1 q^{65} +(36446.3 + 36446.3i) q^{67} +(1818.45 - 1818.45i) q^{69} +45094.7i q^{71} +86532.8i q^{73} +(-2239.11 + 2239.11i) q^{75} +(5817.43 + 5817.43i) q^{77} +55508.6 q^{79} -40994.7 q^{81} +(-26808.7 - 26808.7i) q^{83} +(-16426.2 + 16426.2i) q^{85} -4190.27i q^{87} +54453.4i q^{89} +(-102234. + 102234. i) q^{91} +(-18133.6 - 18133.6i) q^{93} -31831.6 q^{95} +110499. q^{97} +(-8453.60 - 8453.60i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.58258 3.58258i −0.229823 0.229823i 0.582796 0.812619i \(-0.301959\pi\)
−0.812619 + 0.582796i \(0.801959\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 149.558i 1.15362i 0.816877 + 0.576812i \(0.195703\pi\)
−0.816877 + 0.576812i \(0.804297\pi\)
\(8\) 0 0
\(9\) 217.330i 0.894363i
\(10\) 0 0
\(11\) 38.8975 38.8975i 0.0969259 0.0969259i −0.656981 0.753907i \(-0.728167\pi\)
0.753907 + 0.656981i \(0.228167\pi\)
\(12\) 0 0
\(13\) 683.576 + 683.576i 1.12183 + 1.12183i 0.991466 + 0.130368i \(0.0416157\pi\)
0.130368 + 0.991466i \(0.458384\pi\)
\(14\) 0 0
\(15\) −126.663 −0.145353
\(16\) 0 0
\(17\) −929.208 −0.779813 −0.389907 0.920854i \(-0.627493\pi\)
−0.389907 + 0.920854i \(0.627493\pi\)
\(18\) 0 0
\(19\) −900.333 900.333i −0.572162 0.572162i 0.360570 0.932732i \(-0.382582\pi\)
−0.932732 + 0.360570i \(0.882582\pi\)
\(20\) 0 0
\(21\) 535.804 535.804i 0.265129 0.265129i
\(22\) 0 0
\(23\) 507.581i 0.200072i 0.994984 + 0.100036i \(0.0318958\pi\)
−0.994984 + 0.100036i \(0.968104\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −1649.17 + 1649.17i −0.435368 + 0.435368i
\(28\) 0 0
\(29\) 584.811 + 584.811i 0.129128 + 0.129128i 0.768717 0.639589i \(-0.220895\pi\)
−0.639589 + 0.768717i \(0.720895\pi\)
\(30\) 0 0
\(31\) 5061.59 0.945982 0.472991 0.881067i \(-0.343174\pi\)
0.472991 + 0.881067i \(0.343174\pi\)
\(32\) 0 0
\(33\) −278.707 −0.0445516
\(34\) 0 0
\(35\) 2643.84 + 2643.84i 0.364808 + 0.364808i
\(36\) 0 0
\(37\) −10345.7 + 10345.7i −1.24238 + 1.24238i −0.283375 + 0.959009i \(0.591454\pi\)
−0.959009 + 0.283375i \(0.908546\pi\)
\(38\) 0 0
\(39\) 4897.93i 0.515646i
\(40\) 0 0
\(41\) 1291.09i 0.119949i −0.998200 0.0599746i \(-0.980898\pi\)
0.998200 0.0599746i \(-0.0191020\pi\)
\(42\) 0 0
\(43\) −3874.63 + 3874.63i −0.319565 + 0.319565i −0.848600 0.529035i \(-0.822554\pi\)
0.529035 + 0.848600i \(0.322554\pi\)
\(44\) 0 0
\(45\) −3841.89 3841.89i −0.282822 0.282822i
\(46\) 0 0
\(47\) 1375.42 0.0908219 0.0454110 0.998968i \(-0.485540\pi\)
0.0454110 + 0.998968i \(0.485540\pi\)
\(48\) 0 0
\(49\) −5560.57 −0.330848
\(50\) 0 0
\(51\) 3328.96 + 3328.96i 0.179219 + 0.179219i
\(52\) 0 0
\(53\) −8947.98 + 8947.98i −0.437558 + 0.437558i −0.891189 0.453631i \(-0.850128\pi\)
0.453631 + 0.891189i \(0.350128\pi\)
\(54\) 0 0
\(55\) 1375.23i 0.0613013i
\(56\) 0 0
\(57\) 6451.03i 0.262992i
\(58\) 0 0
\(59\) 32361.6 32361.6i 1.21032 1.21032i 0.239399 0.970921i \(-0.423050\pi\)
0.970921 0.239399i \(-0.0769504\pi\)
\(60\) 0 0
\(61\) 8808.44 + 8808.44i 0.303092 + 0.303092i 0.842222 0.539130i \(-0.181247\pi\)
−0.539130 + 0.842222i \(0.681247\pi\)
\(62\) 0 0
\(63\) 32503.5 1.03176
\(64\) 0 0
\(65\) 24168.1 0.709510
\(66\) 0 0
\(67\) 36446.3 + 36446.3i 0.991898 + 0.991898i 0.999967 0.00806945i \(-0.00256861\pi\)
−0.00806945 + 0.999967i \(0.502569\pi\)
\(68\) 0 0
\(69\) 1818.45 1818.45i 0.0459811 0.0459811i
\(70\) 0 0
\(71\) 45094.7i 1.06165i 0.847483 + 0.530823i \(0.178117\pi\)
−0.847483 + 0.530823i \(0.821883\pi\)
\(72\) 0 0
\(73\) 86532.8i 1.90053i 0.311450 + 0.950263i \(0.399186\pi\)
−0.311450 + 0.950263i \(0.600814\pi\)
\(74\) 0 0
\(75\) −2239.11 + 2239.11i −0.0459646 + 0.0459646i
\(76\) 0 0
\(77\) 5817.43 + 5817.43i 0.111816 + 0.111816i
\(78\) 0 0
\(79\) 55508.6 1.00067 0.500337 0.865831i \(-0.333209\pi\)
0.500337 + 0.865831i \(0.333209\pi\)
\(80\) 0 0
\(81\) −40994.7 −0.694248
\(82\) 0 0
\(83\) −26808.7 26808.7i −0.427150 0.427150i 0.460506 0.887656i \(-0.347668\pi\)
−0.887656 + 0.460506i \(0.847668\pi\)
\(84\) 0 0
\(85\) −16426.2 + 16426.2i −0.246599 + 0.246599i
\(86\) 0 0
\(87\) 4190.27i 0.0593531i
\(88\) 0 0
\(89\) 54453.4i 0.728702i 0.931262 + 0.364351i \(0.118709\pi\)
−0.931262 + 0.364351i \(0.881291\pi\)
\(90\) 0 0
\(91\) −102234. + 102234.i −1.29417 + 1.29417i
\(92\) 0 0
\(93\) −18133.6 18133.6i −0.217408 0.217408i
\(94\) 0 0
\(95\) −31831.6 −0.361867
\(96\) 0 0
\(97\) 110499. 1.19242 0.596208 0.802830i \(-0.296673\pi\)
0.596208 + 0.802830i \(0.296673\pi\)
\(98\) 0 0
\(99\) −8453.60 8453.60i −0.0866869 0.0866869i
\(100\) 0 0
\(101\) 16243.2 16243.2i 0.158442 0.158442i −0.623434 0.781876i \(-0.714263\pi\)
0.781876 + 0.623434i \(0.214263\pi\)
\(102\) 0 0
\(103\) 190349.i 1.76790i 0.467582 + 0.883949i \(0.345125\pi\)
−0.467582 + 0.883949i \(0.654875\pi\)
\(104\) 0 0
\(105\) 18943.5i 0.167682i
\(106\) 0 0
\(107\) −148544. + 148544.i −1.25428 + 1.25428i −0.300497 + 0.953783i \(0.597153\pi\)
−0.953783 + 0.300497i \(0.902847\pi\)
\(108\) 0 0
\(109\) 97591.1 + 97591.1i 0.786763 + 0.786763i 0.980962 0.194199i \(-0.0622107\pi\)
−0.194199 + 0.980962i \(0.562211\pi\)
\(110\) 0 0
\(111\) 74128.7 0.571056
\(112\) 0 0
\(113\) 152239. 1.12158 0.560791 0.827957i \(-0.310497\pi\)
0.560791 + 0.827957i \(0.310497\pi\)
\(114\) 0 0
\(115\) 8972.86 + 8972.86i 0.0632683 + 0.0632683i
\(116\) 0 0
\(117\) 148562. 148562.i 1.00333 1.00333i
\(118\) 0 0
\(119\) 138970.i 0.899611i
\(120\) 0 0
\(121\) 158025.i 0.981211i
\(122\) 0 0
\(123\) −4625.44 + 4625.44i −0.0275671 + 0.0275671i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) 104375. 0.574234 0.287117 0.957896i \(-0.407303\pi\)
0.287117 + 0.957896i \(0.407303\pi\)
\(128\) 0 0
\(129\) 27762.4 0.146887
\(130\) 0 0
\(131\) 7019.50 + 7019.50i 0.0357378 + 0.0357378i 0.724750 0.689012i \(-0.241955\pi\)
−0.689012 + 0.724750i \(0.741955\pi\)
\(132\) 0 0
\(133\) 134652. 134652.i 0.660060 0.660060i
\(134\) 0 0
\(135\) 58307.0i 0.275351i
\(136\) 0 0
\(137\) 80126.5i 0.364733i −0.983231 0.182366i \(-0.941624\pi\)
0.983231 0.182366i \(-0.0583757\pi\)
\(138\) 0 0
\(139\) −121893. + 121893.i −0.535110 + 0.535110i −0.922089 0.386979i \(-0.873519\pi\)
0.386979 + 0.922089i \(0.373519\pi\)
\(140\) 0 0
\(141\) −4927.55 4927.55i −0.0208729 0.0208729i
\(142\) 0 0
\(143\) 53178.8 0.217469
\(144\) 0 0
\(145\) 20676.2 0.0816677
\(146\) 0 0
\(147\) 19921.2 + 19921.2i 0.0760365 + 0.0760365i
\(148\) 0 0
\(149\) −359884. + 359884.i −1.32800 + 1.32800i −0.420880 + 0.907116i \(0.638279\pi\)
−0.907116 + 0.420880i \(0.861721\pi\)
\(150\) 0 0
\(151\) 355270.i 1.26799i −0.773336 0.633996i \(-0.781414\pi\)
0.773336 0.633996i \(-0.218586\pi\)
\(152\) 0 0
\(153\) 201945.i 0.697436i
\(154\) 0 0
\(155\) 89477.2 89477.2i 0.299146 0.299146i
\(156\) 0 0
\(157\) −237892. 237892.i −0.770248 0.770248i 0.207901 0.978150i \(-0.433337\pi\)
−0.978150 + 0.207901i \(0.933337\pi\)
\(158\) 0 0
\(159\) 64113.8 0.201122
\(160\) 0 0
\(161\) −75912.8 −0.230808
\(162\) 0 0
\(163\) −7842.29 7842.29i −0.0231193 0.0231193i 0.695453 0.718572i \(-0.255204\pi\)
−0.718572 + 0.695453i \(0.755204\pi\)
\(164\) 0 0
\(165\) −4926.89 + 4926.89i −0.0140884 + 0.0140884i
\(166\) 0 0
\(167\) 221862.i 0.615590i 0.951453 + 0.307795i \(0.0995910\pi\)
−0.951453 + 0.307795i \(0.900409\pi\)
\(168\) 0 0
\(169\) 563259.i 1.51702i
\(170\) 0 0
\(171\) −195669. + 195669.i −0.511720 + 0.511720i
\(172\) 0 0
\(173\) −407014. 407014.i −1.03394 1.03394i −0.999404 0.0345330i \(-0.989006\pi\)
−0.0345330 0.999404i \(-0.510994\pi\)
\(174\) 0 0
\(175\) 93473.7 0.230725
\(176\) 0 0
\(177\) −231876. −0.556318
\(178\) 0 0
\(179\) 109397. + 109397.i 0.255195 + 0.255195i 0.823096 0.567902i \(-0.192245\pi\)
−0.567902 + 0.823096i \(0.692245\pi\)
\(180\) 0 0
\(181\) 122240. 122240.i 0.277342 0.277342i −0.554705 0.832047i \(-0.687169\pi\)
0.832047 + 0.554705i \(0.187169\pi\)
\(182\) 0 0
\(183\) 63113.9i 0.139315i
\(184\) 0 0
\(185\) 365776.i 0.785753i
\(186\) 0 0
\(187\) −36143.9 + 36143.9i −0.0755841 + 0.0755841i
\(188\) 0 0
\(189\) −246647. 246647.i −0.502251 0.502251i
\(190\) 0 0
\(191\) 103925. 0.206129 0.103064 0.994675i \(-0.467135\pi\)
0.103064 + 0.994675i \(0.467135\pi\)
\(192\) 0 0
\(193\) 591953. 1.14391 0.571957 0.820283i \(-0.306184\pi\)
0.571957 + 0.820283i \(0.306184\pi\)
\(194\) 0 0
\(195\) −86584.1 86584.1i −0.163061 0.163061i
\(196\) 0 0
\(197\) 434216. 434216.i 0.797151 0.797151i −0.185494 0.982645i \(-0.559389\pi\)
0.982645 + 0.185494i \(0.0593886\pi\)
\(198\) 0 0
\(199\) 838962.i 1.50179i −0.660421 0.750895i \(-0.729622\pi\)
0.660421 0.750895i \(-0.270378\pi\)
\(200\) 0 0
\(201\) 261144.i 0.455922i
\(202\) 0 0
\(203\) −87463.1 + 87463.1i −0.148965 + 0.148965i
\(204\) 0 0
\(205\) −22823.5 22823.5i −0.0379313 0.0379313i
\(206\) 0 0
\(207\) 110313. 0.178937
\(208\) 0 0
\(209\) −70041.3 −0.110915
\(210\) 0 0
\(211\) −403638. 403638.i −0.624145 0.624145i 0.322443 0.946589i \(-0.395496\pi\)
−0.946589 + 0.322443i \(0.895496\pi\)
\(212\) 0 0
\(213\) 161555. 161555.i 0.243990 0.243990i
\(214\) 0 0
\(215\) 136989.i 0.202111i
\(216\) 0 0
\(217\) 757001.i 1.09131i
\(218\) 0 0
\(219\) 310011. 310011.i 0.436784 0.436784i
\(220\) 0 0
\(221\) −635184. 635184.i −0.874821 0.874821i
\(222\) 0 0
\(223\) 771172. 1.03846 0.519229 0.854635i \(-0.326219\pi\)
0.519229 + 0.854635i \(0.326219\pi\)
\(224\) 0 0
\(225\) −135831. −0.178873
\(226\) 0 0
\(227\) −651907. 651907.i −0.839694 0.839694i 0.149125 0.988818i \(-0.452354\pi\)
−0.988818 + 0.149125i \(0.952354\pi\)
\(228\) 0 0
\(229\) 170285. 170285.i 0.214579 0.214579i −0.591630 0.806210i \(-0.701515\pi\)
0.806210 + 0.591630i \(0.201515\pi\)
\(230\) 0 0
\(231\) 41682.8i 0.0513957i
\(232\) 0 0
\(233\) 1.27649e6i 1.54038i −0.637812 0.770192i \(-0.720160\pi\)
0.637812 0.770192i \(-0.279840\pi\)
\(234\) 0 0
\(235\) 24314.2 24314.2i 0.0287204 0.0287204i
\(236\) 0 0
\(237\) −198864. 198864.i −0.229978 0.229978i
\(238\) 0 0
\(239\) 1.40814e6 1.59459 0.797297 0.603587i \(-0.206262\pi\)
0.797297 + 0.603587i \(0.206262\pi\)
\(240\) 0 0
\(241\) −897800. −0.995719 −0.497860 0.867258i \(-0.665881\pi\)
−0.497860 + 0.867258i \(0.665881\pi\)
\(242\) 0 0
\(243\) 547615. + 547615.i 0.594922 + 0.594922i
\(244\) 0 0
\(245\) −98297.9 + 98297.9i −0.104623 + 0.104623i
\(246\) 0 0
\(247\) 1.23089e6i 1.28374i
\(248\) 0 0
\(249\) 192089.i 0.196338i
\(250\) 0 0
\(251\) −848905. + 848905.i −0.850501 + 0.850501i −0.990195 0.139694i \(-0.955388\pi\)
0.139694 + 0.990195i \(0.455388\pi\)
\(252\) 0 0
\(253\) 19743.6 + 19743.6i 0.0193922 + 0.0193922i
\(254\) 0 0
\(255\) 117697. 0.113348
\(256\) 0 0
\(257\) 368924. 0.348421 0.174211 0.984708i \(-0.444263\pi\)
0.174211 + 0.984708i \(0.444263\pi\)
\(258\) 0 0
\(259\) −1.54728e6 1.54728e6i −1.43324 1.43324i
\(260\) 0 0
\(261\) 127097. 127097.i 0.115487 0.115487i
\(262\) 0 0
\(263\) 244595.i 0.218051i 0.994039 + 0.109026i \(0.0347731\pi\)
−0.994039 + 0.109026i \(0.965227\pi\)
\(264\) 0 0
\(265\) 316359.i 0.276736i
\(266\) 0 0
\(267\) 195084. 195084.i 0.167472 0.167472i
\(268\) 0 0
\(269\) −565231. 565231.i −0.476261 0.476261i 0.427673 0.903934i \(-0.359334\pi\)
−0.903934 + 0.427673i \(0.859334\pi\)
\(270\) 0 0
\(271\) −1.22976e6 −1.01718 −0.508588 0.861010i \(-0.669832\pi\)
−0.508588 + 0.861010i \(0.669832\pi\)
\(272\) 0 0
\(273\) 732525. 0.594861
\(274\) 0 0
\(275\) −24310.9 24310.9i −0.0193852 0.0193852i
\(276\) 0 0
\(277\) −1.36759e6 + 1.36759e6i −1.07092 + 1.07092i −0.0736368 + 0.997285i \(0.523461\pi\)
−0.997285 + 0.0736368i \(0.976539\pi\)
\(278\) 0 0
\(279\) 1.10004e6i 0.846051i
\(280\) 0 0
\(281\) 905343.i 0.683986i −0.939702 0.341993i \(-0.888898\pi\)
0.939702 0.341993i \(-0.111102\pi\)
\(282\) 0 0
\(283\) −1.73786e6 + 1.73786e6i −1.28988 + 1.28988i −0.355024 + 0.934857i \(0.615527\pi\)
−0.934857 + 0.355024i \(0.884473\pi\)
\(284\) 0 0
\(285\) 114039. + 114039.i 0.0831653 + 0.0831653i
\(286\) 0 0
\(287\) 193093. 0.138376
\(288\) 0 0
\(289\) −556429. −0.391891
\(290\) 0 0
\(291\) −395871. 395871.i −0.274044 0.274044i
\(292\) 0 0
\(293\) 1.03306e6 1.03306e6i 0.703005 0.703005i −0.262050 0.965054i \(-0.584398\pi\)
0.965054 + 0.262050i \(0.0843984\pi\)
\(294\) 0 0
\(295\) 1.14416e6i 0.765474i
\(296\) 0 0
\(297\) 128297.i 0.0843968i
\(298\) 0 0
\(299\) −346970. + 346970.i −0.224447 + 0.224447i
\(300\) 0 0
\(301\) −579481. 579481.i −0.368658 0.368658i
\(302\) 0 0
\(303\) −116385. −0.0728269
\(304\) 0 0
\(305\) 311425. 0.191692
\(306\) 0 0
\(307\) 433474. + 433474.i 0.262493 + 0.262493i 0.826066 0.563573i \(-0.190574\pi\)
−0.563573 + 0.826066i \(0.690574\pi\)
\(308\) 0 0
\(309\) 681941. 681941.i 0.406303 0.406303i
\(310\) 0 0
\(311\) 2.34286e6i 1.37355i 0.726868 + 0.686777i \(0.240975\pi\)
−0.726868 + 0.686777i \(0.759025\pi\)
\(312\) 0 0
\(313\) 692967.i 0.399808i 0.979815 + 0.199904i \(0.0640631\pi\)
−0.979815 + 0.199904i \(0.935937\pi\)
\(314\) 0 0
\(315\) 574585. 574585.i 0.326271 0.326271i
\(316\) 0 0
\(317\) −2.00689e6 2.00689e6i −1.12170 1.12170i −0.991486 0.130211i \(-0.958434\pi\)
−0.130211 0.991486i \(-0.541566\pi\)
\(318\) 0 0
\(319\) 45495.3 0.0250317
\(320\) 0 0
\(321\) 1.06434e6 0.576524
\(322\) 0 0
\(323\) 836596. + 836596.i 0.446180 + 0.446180i
\(324\) 0 0
\(325\) 427235. 427235.i 0.224367 0.224367i
\(326\) 0 0
\(327\) 699257.i 0.361632i
\(328\) 0 0
\(329\) 205705.i 0.104774i
\(330\) 0 0
\(331\) 1.85751e6 1.85751e6i 0.931885 0.931885i −0.0659391 0.997824i \(-0.521004\pi\)
0.997824 + 0.0659391i \(0.0210043\pi\)
\(332\) 0 0
\(333\) 2.24843e6 + 2.24843e6i 1.11114 + 1.11114i
\(334\) 0 0
\(335\) 1.28857e6 0.627331
\(336\) 0 0
\(337\) 892674. 0.428172 0.214086 0.976815i \(-0.431323\pi\)
0.214086 + 0.976815i \(0.431323\pi\)
\(338\) 0 0
\(339\) −545410. 545410.i −0.257765 0.257765i
\(340\) 0 0
\(341\) 196883. 196883.i 0.0916902 0.0916902i
\(342\) 0 0
\(343\) 1.68199e6i 0.771949i
\(344\) 0 0
\(345\) 64292.0i 0.0290810i
\(346\) 0 0
\(347\) 50929.3 50929.3i 0.0227062 0.0227062i −0.695663 0.718369i \(-0.744889\pi\)
0.718369 + 0.695663i \(0.244889\pi\)
\(348\) 0 0
\(349\) 1.60405e6 + 1.60405e6i 0.704944 + 0.704944i 0.965467 0.260524i \(-0.0838952\pi\)
−0.260524 + 0.965467i \(0.583895\pi\)
\(350\) 0 0
\(351\) −2.25467e6 −0.976820
\(352\) 0 0
\(353\) −594017. −0.253724 −0.126862 0.991920i \(-0.540491\pi\)
−0.126862 + 0.991920i \(0.540491\pi\)
\(354\) 0 0
\(355\) 797169. + 797169.i 0.335722 + 0.335722i
\(356\) 0 0
\(357\) −497873. + 497873.i −0.206751 + 0.206751i
\(358\) 0 0
\(359\) 3.26627e6i 1.33757i 0.743457 + 0.668784i \(0.233185\pi\)
−0.743457 + 0.668784i \(0.766815\pi\)
\(360\) 0 0
\(361\) 854901.i 0.345261i
\(362\) 0 0
\(363\) 566138. 566138.i 0.225505 0.225505i
\(364\) 0 0
\(365\) 1.52970e6 + 1.52970e6i 0.600999 + 0.600999i
\(366\) 0 0
\(367\) −4.74678e6 −1.83964 −0.919822 0.392337i \(-0.871667\pi\)
−0.919822 + 0.392337i \(0.871667\pi\)
\(368\) 0 0
\(369\) −280593. −0.107278
\(370\) 0 0
\(371\) −1.33824e6 1.33824e6i −0.504777 0.504777i
\(372\) 0 0
\(373\) 1.07649e6 1.07649e6i 0.400624 0.400624i −0.477829 0.878453i \(-0.658576\pi\)
0.878453 + 0.477829i \(0.158576\pi\)
\(374\) 0 0
\(375\) 79164.6i 0.0290705i
\(376\) 0 0
\(377\) 799525.i 0.289720i
\(378\) 0 0
\(379\) −1.07695e6 + 1.07695e6i −0.385122 + 0.385122i −0.872943 0.487821i \(-0.837792\pi\)
0.487821 + 0.872943i \(0.337792\pi\)
\(380\) 0 0
\(381\) −373933. 373933.i −0.131972 0.131972i
\(382\) 0 0
\(383\) 1.61998e6 0.564302 0.282151 0.959370i \(-0.408952\pi\)
0.282151 + 0.959370i \(0.408952\pi\)
\(384\) 0 0
\(385\) 205677. 0.0707187
\(386\) 0 0
\(387\) 842074. + 842074.i 0.285807 + 0.285807i
\(388\) 0 0
\(389\) −1.61689e6 + 1.61689e6i −0.541759 + 0.541759i −0.924044 0.382285i \(-0.875137\pi\)
0.382285 + 0.924044i \(0.375137\pi\)
\(390\) 0 0
\(391\) 471649.i 0.156019i
\(392\) 0 0
\(393\) 50295.9i 0.0164267i
\(394\) 0 0
\(395\) 981263. 981263.i 0.316441 0.316441i
\(396\) 0 0
\(397\) −400667. 400667.i −0.127587 0.127587i 0.640430 0.768017i \(-0.278756\pi\)
−0.768017 + 0.640430i \(0.778756\pi\)
\(398\) 0 0
\(399\) −964803. −0.303394
\(400\) 0 0
\(401\) −1.51826e6 −0.471503 −0.235751 0.971813i \(-0.575755\pi\)
−0.235751 + 0.971813i \(0.575755\pi\)
\(402\) 0 0
\(403\) 3.45998e6 + 3.45998e6i 1.06123 + 1.06123i
\(404\) 0 0
\(405\) −724690. + 724690.i −0.219541 + 0.219541i
\(406\) 0 0
\(407\) 804844.i 0.240838i
\(408\) 0 0
\(409\) 1.49322e6i 0.441382i −0.975344 0.220691i \(-0.929169\pi\)
0.975344 0.220691i \(-0.0708313\pi\)
\(410\) 0 0
\(411\) −287060. + 287060.i −0.0838239 + 0.0838239i
\(412\) 0 0
\(413\) 4.83994e6 + 4.83994e6i 1.39625 + 1.39625i
\(414\) 0 0
\(415\) −947830. −0.270153
\(416\) 0 0
\(417\) 873386. 0.245961
\(418\) 0 0
\(419\) 4.75505e6 + 4.75505e6i 1.32318 + 1.32318i 0.911185 + 0.411998i \(0.135169\pi\)
0.411998 + 0.911185i \(0.364831\pi\)
\(420\) 0 0
\(421\) −2.48208e6 + 2.48208e6i −0.682511 + 0.682511i −0.960565 0.278054i \(-0.910311\pi\)
0.278054 + 0.960565i \(0.410311\pi\)
\(422\) 0 0
\(423\) 298920.i 0.0812277i
\(424\) 0 0
\(425\) 580755.i 0.155963i
\(426\) 0 0
\(427\) −1.31737e6 + 1.31737e6i −0.349654 + 0.349654i
\(428\) 0 0
\(429\) −190517. 190517.i −0.0499794 0.0499794i
\(430\) 0 0
\(431\) 1.70333e6 0.441677 0.220838 0.975310i \(-0.429121\pi\)
0.220838 + 0.975310i \(0.429121\pi\)
\(432\) 0 0
\(433\) 3.13406e6 0.803319 0.401659 0.915789i \(-0.368434\pi\)
0.401659 + 0.915789i \(0.368434\pi\)
\(434\) 0 0
\(435\) −74074.2 74074.2i −0.0187691 0.0187691i
\(436\) 0 0
\(437\) 456992. 456992.i 0.114474 0.114474i
\(438\) 0 0
\(439\) 3.94725e6i 0.977537i −0.872414 0.488768i \(-0.837446\pi\)
0.872414 0.488768i \(-0.162554\pi\)
\(440\) 0 0
\(441\) 1.20848e6i 0.295899i
\(442\) 0 0
\(443\) 2.77891e6 2.77891e6i 0.672767 0.672767i −0.285586 0.958353i \(-0.592188\pi\)
0.958353 + 0.285586i \(0.0921883\pi\)
\(444\) 0 0
\(445\) 962610. + 962610.i 0.230436 + 0.230436i
\(446\) 0 0
\(447\) 2.57863e6 0.610408
\(448\) 0 0
\(449\) −666721. −0.156073 −0.0780366 0.996950i \(-0.524865\pi\)
−0.0780366 + 0.996950i \(0.524865\pi\)
\(450\) 0 0
\(451\) −50220.2 50220.2i −0.0116262 0.0116262i
\(452\) 0 0
\(453\) −1.27279e6 + 1.27279e6i −0.291413 + 0.291413i
\(454\) 0 0
\(455\) 3.61452e6i 0.818507i
\(456\) 0 0
\(457\) 687743.i 0.154041i −0.997030 0.0770204i \(-0.975459\pi\)
0.997030 0.0770204i \(-0.0245407\pi\)
\(458\) 0 0
\(459\) 1.53242e6 1.53242e6i 0.339506 0.339506i
\(460\) 0 0
\(461\) 1.34081e6 + 1.34081e6i 0.293843 + 0.293843i 0.838596 0.544753i \(-0.183377\pi\)
−0.544753 + 0.838596i \(0.683377\pi\)
\(462\) 0 0
\(463\) 8.72731e6 1.89203 0.946015 0.324124i \(-0.105070\pi\)
0.946015 + 0.324124i \(0.105070\pi\)
\(464\) 0 0
\(465\) −641119. −0.137501
\(466\) 0 0
\(467\) −670605. 670605.i −0.142290 0.142290i 0.632374 0.774664i \(-0.282081\pi\)
−0.774664 + 0.632374i \(0.782081\pi\)
\(468\) 0 0
\(469\) −5.45084e6 + 5.45084e6i −1.14428 + 1.14428i
\(470\) 0 0
\(471\) 1.70454e6i 0.354041i
\(472\) 0 0
\(473\) 301427.i 0.0619482i
\(474\) 0 0
\(475\) −562708. + 562708.i −0.114432 + 0.114432i
\(476\) 0 0
\(477\) 1.94467e6 + 1.94467e6i 0.391336 + 0.391336i
\(478\) 0 0
\(479\) −4.74802e6 −0.945526 −0.472763 0.881190i \(-0.656743\pi\)
−0.472763 + 0.881190i \(0.656743\pi\)
\(480\) 0 0
\(481\) −1.41442e7 −2.78750
\(482\) 0 0
\(483\) 271964. + 271964.i 0.0530449 + 0.0530449i
\(484\) 0 0
\(485\) 1.95336e6 1.95336e6i 0.377075 0.377075i
\(486\) 0 0
\(487\) 4.78477e6i 0.914195i 0.889417 + 0.457097i \(0.151111\pi\)
−0.889417 + 0.457097i \(0.848889\pi\)
\(488\) 0 0
\(489\) 56191.3i 0.0106267i
\(490\) 0 0
\(491\) 6.20974e6 6.20974e6i 1.16244 1.16244i 0.178497 0.983940i \(-0.442876\pi\)
0.983940 0.178497i \(-0.0571236\pi\)
\(492\) 0 0
\(493\) −543411. 543411.i −0.100696 0.100696i
\(494\) 0 0
\(495\) −298880. −0.0548256
\(496\) 0 0
\(497\) −6.74427e6 −1.22474
\(498\) 0 0
\(499\) 619633. + 619633.i 0.111399 + 0.111399i 0.760609 0.649210i \(-0.224900\pi\)
−0.649210 + 0.760609i \(0.724900\pi\)
\(500\) 0 0
\(501\) 794838. 794838.i 0.141477 0.141477i
\(502\) 0 0
\(503\) 786743.i 0.138648i −0.997594 0.0693239i \(-0.977916\pi\)
0.997594 0.0693239i \(-0.0220842\pi\)
\(504\) 0 0
\(505\) 574285.i 0.100207i
\(506\) 0 0
\(507\) 2.01792e6 2.01792e6i 0.348646 0.348646i
\(508\) 0 0
\(509\) 1.52004e6 + 1.52004e6i 0.260052 + 0.260052i 0.825075 0.565023i \(-0.191133\pi\)
−0.565023 + 0.825075i \(0.691133\pi\)
\(510\) 0 0
\(511\) −1.29417e7 −2.19249
\(512\) 0 0
\(513\) 2.96960e6 0.498202
\(514\) 0 0
\(515\) 3.36493e6 + 3.36493e6i 0.559059 + 0.559059i
\(516\) 0 0
\(517\) 53500.4 53500.4i 0.00880299 0.00880299i
\(518\) 0 0
\(519\) 2.91632e6i 0.475244i
\(520\) 0 0
\(521\) 7.53189e6i 1.21565i −0.794070 0.607827i \(-0.792041\pi\)
0.794070 0.607827i \(-0.207959\pi\)
\(522\) 0 0
\(523\) 3.36602e6 3.36602e6i 0.538099 0.538099i −0.384871 0.922970i \(-0.625754\pi\)
0.922970 + 0.384871i \(0.125754\pi\)
\(524\) 0 0
\(525\) −334877. 334877.i −0.0530258 0.0530258i
\(526\) 0 0
\(527\) −4.70327e6 −0.737690
\(528\) 0 0
\(529\) 6.17870e6 0.959971
\(530\) 0 0
\(531\) −7.03316e6 7.03316e6i −1.08247 1.08247i
\(532\) 0 0
\(533\) 882559. 882559.i 0.134563 0.134563i
\(534\) 0 0
\(535\) 5.25181e6i 0.793276i
\(536\) 0 0
\(537\) 783845.i 0.117299i
\(538\) 0 0
\(539\) −216292. + 216292.i −0.0320678 + 0.0320678i
\(540\) 0 0
\(541\) 6.26679e6 + 6.26679e6i 0.920560 + 0.920560i 0.997069 0.0765086i \(-0.0243773\pi\)
−0.0765086 + 0.997069i \(0.524377\pi\)
\(542\) 0 0
\(543\) −875866. −0.127479
\(544\) 0 0
\(545\) 3.45037e6 0.497593
\(546\) 0 0
\(547\) −1.14604e6 1.14604e6i −0.163770 0.163770i 0.620465 0.784234i \(-0.286944\pi\)
−0.784234 + 0.620465i \(0.786944\pi\)
\(548\) 0 0
\(549\) 1.91434e6 1.91434e6i 0.271074 0.271074i
\(550\) 0 0
\(551\) 1.05305e6i 0.147764i
\(552\) 0 0
\(553\) 8.30175e6i 1.15440i
\(554\) 0 0
\(555\) 1.31042e6 1.31042e6i 0.180584 0.180584i
\(556\) 0 0
\(557\) −5.80858e6 5.80858e6i −0.793291 0.793291i 0.188737 0.982028i \(-0.439561\pi\)
−0.982028 + 0.188737i \(0.939561\pi\)
\(558\) 0 0
\(559\) −5.29720e6 −0.716997
\(560\) 0 0
\(561\) 258977. 0.0347419
\(562\) 0 0
\(563\) 2.59073e6 + 2.59073e6i 0.344470 + 0.344470i 0.858045 0.513575i \(-0.171679\pi\)
−0.513575 + 0.858045i \(0.671679\pi\)
\(564\) 0 0
\(565\) 2.69124e6 2.69124e6i 0.354675 0.354675i
\(566\) 0 0
\(567\) 6.13108e6i 0.800901i
\(568\) 0 0
\(569\) 1.06981e7i 1.38524i −0.721304 0.692618i \(-0.756457\pi\)
0.721304 0.692618i \(-0.243543\pi\)
\(570\) 0 0
\(571\) −2.78779e6 + 2.78779e6i −0.357824 + 0.357824i −0.863010 0.505187i \(-0.831424\pi\)
0.505187 + 0.863010i \(0.331424\pi\)
\(572\) 0 0
\(573\) −372321. 372321.i −0.0473731 0.0473731i
\(574\) 0 0
\(575\) 317238. 0.0400144
\(576\) 0 0
\(577\) 1.25782e6 0.157282 0.0786412 0.996903i \(-0.474942\pi\)
0.0786412 + 0.996903i \(0.474942\pi\)
\(578\) 0 0
\(579\) −2.12072e6 2.12072e6i −0.262898 0.262898i
\(580\) 0 0
\(581\) 4.00945e6 4.00945e6i 0.492770 0.492770i
\(582\) 0 0
\(583\) 696108.i 0.0848214i
\(584\) 0 0
\(585\) 5.25245e6i 0.634559i
\(586\) 0 0
\(587\) −1.10160e7 + 1.10160e7i −1.31956 + 1.31956i −0.405430 + 0.914126i \(0.632878\pi\)
−0.914126 + 0.405430i \(0.867122\pi\)
\(588\) 0 0
\(589\) −4.55712e6 4.55712e6i −0.541255 0.541255i
\(590\) 0 0
\(591\) −3.11123e6 −0.366407
\(592\) 0 0
\(593\) 1.26173e7 1.47343 0.736713 0.676206i \(-0.236377\pi\)
0.736713 + 0.676206i \(0.236377\pi\)
\(594\) 0 0
\(595\) −2.45667e6 2.45667e6i −0.284482 0.284482i
\(596\) 0 0
\(597\) −3.00565e6 + 3.00565e6i −0.345146 + 0.345146i
\(598\) 0 0
\(599\) 1.05389e7i 1.20013i −0.799950 0.600067i \(-0.795141\pi\)
0.799950 0.600067i \(-0.204859\pi\)
\(600\) 0 0
\(601\) 1.10876e7i 1.25214i −0.779769 0.626068i \(-0.784663\pi\)
0.779769 0.626068i \(-0.215337\pi\)
\(602\) 0 0
\(603\) 7.92089e6 7.92089e6i 0.887117 0.887117i
\(604\) 0 0
\(605\) 2.79351e6 + 2.79351e6i 0.310286 + 0.310286i
\(606\) 0 0
\(607\) −890974. −0.0981506 −0.0490753 0.998795i \(-0.515627\pi\)
−0.0490753 + 0.998795i \(0.515627\pi\)
\(608\) 0 0
\(609\) 626688. 0.0684712
\(610\) 0 0
\(611\) 940204. + 940204.i 0.101887 + 0.101887i
\(612\) 0 0
\(613\) −8.88039e6 + 8.88039e6i −0.954510 + 0.954510i −0.999009 0.0444991i \(-0.985831\pi\)
0.0444991 + 0.999009i \(0.485831\pi\)
\(614\) 0 0
\(615\) 163534.i 0.0174349i
\(616\) 0 0
\(617\) 8.90147e6i 0.941345i −0.882308 0.470672i \(-0.844011\pi\)
0.882308 0.470672i \(-0.155989\pi\)
\(618\) 0 0
\(619\) −6.71588e6 + 6.71588e6i −0.704493 + 0.704493i −0.965372 0.260879i \(-0.915988\pi\)
0.260879 + 0.965372i \(0.415988\pi\)
\(620\) 0 0
\(621\) −837089. 837089.i −0.0871049 0.0871049i
\(622\) 0 0
\(623\) −8.14394e6 −0.840648
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) 250929. + 250929.i 0.0254907 + 0.0254907i
\(628\) 0 0
\(629\) 9.61332e6 9.61332e6i 0.968828 0.968828i
\(630\) 0 0
\(631\) 5.38492e6i 0.538401i 0.963084 + 0.269201i \(0.0867595\pi\)
−0.963084 + 0.269201i \(0.913241\pi\)
\(632\) 0 0
\(633\) 2.89213e6i 0.286886i
\(634\) 0 0
\(635\) 1.84511e6 1.84511e6i 0.181589 0.181589i
\(636\) 0 0
\(637\) −3.80107e6 3.80107e6i −0.371157 0.371157i
\(638\) 0 0
\(639\) 9.80044e6 0.949496
\(640\) 0 0
\(641\) −1.79300e7 −1.72359 −0.861796 0.507254i \(-0.830661\pi\)
−0.861796 + 0.507254i \(0.830661\pi\)
\(642\) 0 0
\(643\) −2.14350e6 2.14350e6i −0.204454 0.204454i 0.597451 0.801905i \(-0.296180\pi\)
−0.801905 + 0.597451i \(0.796180\pi\)
\(644\) 0 0
\(645\) 490774. 490774.i 0.0464496 0.0464496i
\(646\) 0 0
\(647\) 1.97136e7i 1.85143i −0.378227 0.925713i \(-0.623466\pi\)
0.378227 0.925713i \(-0.376534\pi\)
\(648\) 0 0
\(649\) 2.51757e6i 0.234623i
\(650\) 0 0
\(651\) 2.71202e6 2.71202e6i 0.250807 0.250807i
\(652\) 0 0
\(653\) 1.07789e7 + 1.07789e7i 0.989216 + 0.989216i 0.999942 0.0107266i \(-0.00341445\pi\)
−0.0107266 + 0.999942i \(0.503414\pi\)
\(654\) 0 0
\(655\) 248177. 0.0226026
\(656\) 0 0
\(657\) 1.88062e7 1.69976
\(658\) 0 0
\(659\) −2.31615e6 2.31615e6i −0.207755 0.207755i 0.595557 0.803313i \(-0.296931\pi\)
−0.803313 + 0.595557i \(0.796931\pi\)
\(660\) 0 0
\(661\) −5.60044e6 + 5.60044e6i −0.498561 + 0.498561i −0.910990 0.412429i \(-0.864680\pi\)
0.412429 + 0.910990i \(0.364680\pi\)
\(662\) 0 0
\(663\) 4.55120e6i 0.402107i
\(664\) 0 0
\(665\) 4.76066e6i 0.417458i
\(666\) 0 0
\(667\) −296839. + 296839.i −0.0258349 + 0.0258349i
\(668\) 0 0
\(669\) −2.76279e6 2.76279e6i −0.238661 0.238661i
\(670\) 0 0
\(671\) 685252. 0.0587549
\(672\) 0 0
\(673\) −6.07594e6 −0.517101 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(674\) 0 0
\(675\) 1.03073e6 + 1.03073e6i 0.0870736 + 0.0870736i
\(676\) 0 0
\(677\) −2.38722e6 + 2.38722e6i −0.200180 + 0.200180i −0.800077 0.599897i \(-0.795208\pi\)
0.599897 + 0.800077i \(0.295208\pi\)
\(678\) 0 0
\(679\) 1.65260e7i 1.37560i
\(680\) 0 0
\(681\) 4.67102e6i 0.385962i
\(682\) 0 0
\(683\) 7.61306e6 7.61306e6i 0.624464 0.624464i −0.322206 0.946670i \(-0.604424\pi\)
0.946670 + 0.322206i \(0.104424\pi\)
\(684\) 0 0
\(685\) −1.41645e6 1.41645e6i −0.115339 0.115339i
\(686\) 0 0
\(687\) −1.22012e6 −0.0986305
\(688\) 0 0
\(689\) −1.22333e7 −0.981734
\(690\) 0 0
\(691\) −1.08249e7 1.08249e7i −0.862439 0.862439i 0.129182 0.991621i \(-0.458765\pi\)
−0.991621 + 0.129182i \(0.958765\pi\)
\(692\) 0 0
\(693\) 1.26430e6 1.26430e6i 0.100004 0.100004i
\(694\) 0 0
\(695\) 4.30958e6i 0.338433i
\(696\) 0 0
\(697\) 1.19969e6i 0.0935380i
\(698\) 0 0
\(699\) −4.57315e6 + 4.57315e6i −0.354016 + 0.354016i
\(700\) 0 0
\(701\) 2.39524e6 + 2.39524e6i 0.184100 + 0.184100i 0.793140 0.609039i \(-0.208445\pi\)
−0.609039 + 0.793140i \(0.708445\pi\)
\(702\) 0 0
\(703\) 1.86292e7 1.42169
\(704\) 0 0
\(705\) −174215. −0.0132012
\(706\) 0 0
\(707\) 2.42930e6 + 2.42930e6i 0.182782 + 0.182782i
\(708\) 0 0
\(709\) 9.09930e6 9.09930e6i 0.679817 0.679817i −0.280141 0.959959i \(-0.590381\pi\)
0.959959 + 0.280141i \(0.0903814\pi\)
\(710\) 0 0
\(711\) 1.20637e7i 0.894966i
\(712\) 0 0
\(713\) 2.56917e6i 0.189264i
\(714\) 0 0
\(715\) 940077. 940077.i 0.0687699 0.0687699i
\(716\) 0 0
\(717\) −5.04477e6 5.04477e6i −0.366474 0.366474i
\(718\) 0 0
\(719\) 6.42870e6 0.463768 0.231884 0.972743i \(-0.425511\pi\)
0.231884 + 0.972743i \(0.425511\pi\)
\(720\) 0 0
\(721\) −2.84682e7 −2.03949
\(722\) 0 0
\(723\) 3.21644e6 + 3.21644e6i 0.228839 + 0.228839i
\(724\) 0 0
\(725\) 365507. 365507.i 0.0258256 0.0258256i
\(726\) 0 0
\(727\) 2.68443e7i 1.88372i −0.336006 0.941860i \(-0.609076\pi\)
0.336006 0.941860i \(-0.390924\pi\)
\(728\) 0 0
\(729\) 6.03795e6i 0.420795i
\(730\) 0 0
\(731\) 3.60034e6 3.60034e6i 0.249201 0.249201i
\(732\) 0 0
\(733\) −1.49935e7 1.49935e7i −1.03072 1.03072i −0.999513 0.0312110i \(-0.990064\pi\)
−0.0312110 0.999513i \(-0.509936\pi\)
\(734\) 0 0
\(735\) 704321. 0.0480897
\(736\) 0 0
\(737\) 2.83534e6 0.192281
\(738\) 0 0
\(739\) −7.73938e6 7.73938e6i −0.521309 0.521309i 0.396658 0.917967i \(-0.370170\pi\)
−0.917967 + 0.396658i \(0.870170\pi\)
\(740\) 0 0
\(741\) −4.40977e6 + 4.40977e6i −0.295033 + 0.295033i
\(742\) 0 0
\(743\) 4.27335e6i 0.283986i 0.989868 + 0.141993i \(0.0453510\pi\)
−0.989868 + 0.141993i \(0.954649\pi\)
\(744\) 0 0
\(745\) 1.27238e7i 0.839899i
\(746\) 0 0
\(747\) −5.82634e6 + 5.82634e6i −0.382027 + 0.382027i
\(748\) 0 0
\(749\) −2.22159e7 2.22159e7i −1.44697 1.44697i
\(750\) 0 0
\(751\) −1.71751e7 −1.11122 −0.555609 0.831444i \(-0.687515\pi\)
−0.555609 + 0.831444i \(0.687515\pi\)
\(752\) 0 0
\(753\) 6.08255e6 0.390929
\(754\) 0 0
\(755\) −6.28035e6 6.28035e6i −0.400974 0.400974i
\(756\) 0 0
\(757\) −5.21393e6 + 5.21393e6i −0.330694 + 0.330694i −0.852850 0.522156i \(-0.825128\pi\)
0.522156 + 0.852850i \(0.325128\pi\)
\(758\) 0 0
\(759\) 141466.i 0.00891352i
\(760\) 0 0
\(761\) 1.79653e7i 1.12454i 0.826955 + 0.562268i \(0.190071\pi\)
−0.826955 + 0.562268i \(0.809929\pi\)
\(762\) 0 0
\(763\) −1.45955e7 + 1.45955e7i −0.907629 + 0.907629i
\(764\) 0 0
\(765\) 3.56992e6 + 3.56992e6i 0.220549 + 0.220549i
\(766\) 0 0
\(767\) 4.42433e7 2.71556
\(768\) 0 0
\(769\) 2.43375e7 1.48409 0.742045 0.670350i \(-0.233856\pi\)
0.742045 + 0.670350i \(0.233856\pi\)
\(770\) 0 0
\(771\) −1.32170e6 1.32170e6i −0.0800751 0.0800751i
\(772\) 0 0
\(773\) 9.33938e6 9.33938e6i 0.562172 0.562172i −0.367752 0.929924i \(-0.619872\pi\)
0.929924 + 0.367752i \(0.119872\pi\)
\(774\) 0 0
\(775\) 3.16350e6i 0.189196i
\(776\) 0 0
\(777\) 1.10865e7i 0.658784i
\(778\) 0 0
\(779\) −1.16241e6 + 1.16241e6i −0.0686304 + 0.0686304i
\(780\) 0 0
\(781\) 1.75407e6 + 1.75407e6i 0.102901 + 0.102901i
\(782\) 0 0
\(783\) −1.92891e6 −0.112436
\(784\) 0 0
\(785\) −8.41075e6 −0.487148
\(786\) 0 0