Properties

Label 320.6.l.a.81.1
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 81.1
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-21.2511 - 21.2511i) q^{3} +(-17.6777 + 17.6777i) q^{5} +169.621i q^{7} +660.222i q^{9} +O(q^{10})\) \(q+(-21.2511 - 21.2511i) q^{3} +(-17.6777 + 17.6777i) q^{5} +169.621i q^{7} +660.222i q^{9} +(-379.002 + 379.002i) q^{11} +(10.8362 + 10.8362i) q^{13} +751.341 q^{15} -1788.05 q^{17} +(1092.33 + 1092.33i) q^{19} +(3604.64 - 3604.64i) q^{21} +2097.19i q^{23} -625.000i q^{25} +(8866.44 - 8866.44i) q^{27} +(100.133 + 100.133i) q^{29} -3154.58 q^{31} +16108.4 q^{33} +(-2998.50 - 2998.50i) q^{35} +(7283.15 - 7283.15i) q^{37} -460.565i q^{39} +13081.0i q^{41} +(-1355.74 + 1355.74i) q^{43} +(-11671.2 - 11671.2i) q^{45} -18498.7 q^{47} -11964.3 q^{49} +(37998.0 + 37998.0i) q^{51} +(-10148.2 + 10148.2i) q^{53} -13399.7i q^{55} -46426.4i q^{57} +(-5697.28 + 5697.28i) q^{59} +(-16810.4 - 16810.4i) q^{61} -111987. q^{63} -383.119 q^{65} +(-8866.04 - 8866.04i) q^{67} +(44567.6 - 44567.6i) q^{69} +23103.9i q^{71} +134.268i q^{73} +(-13282.0 + 13282.0i) q^{75} +(-64286.6 - 64286.6i) q^{77} +26974.0 q^{79} -216410. q^{81} +(20245.8 + 20245.8i) q^{83} +(31608.5 - 31608.5i) q^{85} -4255.86i q^{87} +101494. i q^{89} +(-1838.05 + 1838.05i) q^{91} +(67038.5 + 67038.5i) q^{93} -38619.6 q^{95} -47842.6 q^{97} +(-250225. - 250225. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

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
\(3\) −21.2511 21.2511i −1.36326 1.36326i −0.869725 0.493536i \(-0.835704\pi\)
−0.493536 0.869725i \(-0.664296\pi\)
\(4\) 0 0
\(5\) −17.6777 + 17.6777i −0.316228 + 0.316228i
\(6\) 0 0
\(7\) 169.621i 1.30838i 0.756330 + 0.654191i \(0.226991\pi\)
−0.756330 + 0.654191i \(0.773009\pi\)
\(8\) 0 0
\(9\) 660.222i 2.71696i
\(10\) 0 0
\(11\) −379.002 + 379.002i −0.944408 + 0.944408i −0.998534 0.0541263i \(-0.982763\pi\)
0.0541263 + 0.998534i \(0.482763\pi\)
\(12\) 0 0
\(13\) 10.8362 + 10.8362i 0.0177836 + 0.0177836i 0.715943 0.698159i \(-0.245997\pi\)
−0.698159 + 0.715943i \(0.745997\pi\)
\(14\) 0 0
\(15\) 751.341 0.862202
\(16\) 0 0
\(17\) −1788.05 −1.50057 −0.750286 0.661114i \(-0.770084\pi\)
−0.750286 + 0.661114i \(0.770084\pi\)
\(18\) 0 0
\(19\) 1092.33 + 1092.33i 0.694174 + 0.694174i 0.963148 0.268973i \(-0.0866843\pi\)
−0.268973 + 0.963148i \(0.586684\pi\)
\(20\) 0 0
\(21\) 3604.64 3604.64i 1.78367 1.78367i
\(22\) 0 0
\(23\) 2097.19i 0.826642i 0.910585 + 0.413321i \(0.135631\pi\)
−0.910585 + 0.413321i \(0.864369\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) 8866.44 8866.44i 2.34067 2.34067i
\(28\) 0 0
\(29\) 100.133 + 100.133i 0.0221096 + 0.0221096i 0.718075 0.695966i \(-0.245023\pi\)
−0.695966 + 0.718075i \(0.745023\pi\)
\(30\) 0 0
\(31\) −3154.58 −0.589573 −0.294787 0.955563i \(-0.595249\pi\)
−0.294787 + 0.955563i \(0.595249\pi\)
\(32\) 0 0
\(33\) 16108.4 2.57495
\(34\) 0 0
\(35\) −2998.50 2998.50i −0.413747 0.413747i
\(36\) 0 0
\(37\) 7283.15 7283.15i 0.874611 0.874611i −0.118360 0.992971i \(-0.537764\pi\)
0.992971 + 0.118360i \(0.0377637\pi\)
\(38\) 0 0
\(39\) 460.565i 0.0484874i
\(40\) 0 0
\(41\) 13081.0i 1.21529i 0.794208 + 0.607646i \(0.207886\pi\)
−0.794208 + 0.607646i \(0.792114\pi\)
\(42\) 0 0
\(43\) −1355.74 + 1355.74i −0.111817 + 0.111817i −0.760801 0.648985i \(-0.775194\pi\)
0.648985 + 0.760801i \(0.275194\pi\)
\(44\) 0 0
\(45\) −11671.2 11671.2i −0.859179 0.859179i
\(46\) 0 0
\(47\) −18498.7 −1.22151 −0.610754 0.791820i \(-0.709134\pi\)
−0.610754 + 0.791820i \(0.709134\pi\)
\(48\) 0 0
\(49\) −11964.3 −0.711862
\(50\) 0 0
\(51\) 37998.0 + 37998.0i 2.04567 + 2.04567i
\(52\) 0 0
\(53\) −10148.2 + 10148.2i −0.496247 + 0.496247i −0.910267 0.414021i \(-0.864124\pi\)
0.414021 + 0.910267i \(0.364124\pi\)
\(54\) 0 0
\(55\) 13399.7i 0.597296i
\(56\) 0 0
\(57\) 46426.4i 1.89268i
\(58\) 0 0
\(59\) −5697.28 + 5697.28i −0.213077 + 0.213077i −0.805573 0.592496i \(-0.798143\pi\)
0.592496 + 0.805573i \(0.298143\pi\)
\(60\) 0 0
\(61\) −16810.4 16810.4i −0.578434 0.578434i 0.356037 0.934472i \(-0.384128\pi\)
−0.934472 + 0.356037i \(0.884128\pi\)
\(62\) 0 0
\(63\) −111987. −3.55482
\(64\) 0 0
\(65\) −383.119 −0.0112473
\(66\) 0 0
\(67\) −8866.04 8866.04i −0.241292 0.241292i 0.576093 0.817384i \(-0.304577\pi\)
−0.817384 + 0.576093i \(0.804577\pi\)
\(68\) 0 0
\(69\) 44567.6 44567.6i 1.12693 1.12693i
\(70\) 0 0
\(71\) 23103.9i 0.543925i 0.962308 + 0.271962i \(0.0876726\pi\)
−0.962308 + 0.271962i \(0.912327\pi\)
\(72\) 0 0
\(73\) 134.268i 0.00294894i 0.999999 + 0.00147447i \(0.000469338\pi\)
−0.999999 + 0.00147447i \(0.999531\pi\)
\(74\) 0 0
\(75\) −13282.0 + 13282.0i −0.272652 + 0.272652i
\(76\) 0 0
\(77\) −64286.6 64286.6i −1.23565 1.23565i
\(78\) 0 0
\(79\) 26974.0 0.486270 0.243135 0.969993i \(-0.421824\pi\)
0.243135 + 0.969993i \(0.421824\pi\)
\(80\) 0 0
\(81\) −216410. −3.66492
\(82\) 0 0
\(83\) 20245.8 + 20245.8i 0.322581 + 0.322581i 0.849757 0.527175i \(-0.176749\pi\)
−0.527175 + 0.849757i \(0.676749\pi\)
\(84\) 0 0
\(85\) 31608.5 31608.5i 0.474522 0.474522i
\(86\) 0 0
\(87\) 4255.86i 0.0602823i
\(88\) 0 0
\(89\) 101494.i 1.35821i 0.734041 + 0.679105i \(0.237632\pi\)
−0.734041 + 0.679105i \(0.762368\pi\)
\(90\) 0 0
\(91\) −1838.05 + 1838.05i −0.0232678 + 0.0232678i
\(92\) 0 0
\(93\) 67038.5 + 67038.5i 0.803743 + 0.803743i
\(94\) 0 0
\(95\) −38619.6 −0.439034
\(96\) 0 0
\(97\) −47842.6 −0.516280 −0.258140 0.966107i \(-0.583110\pi\)
−0.258140 + 0.966107i \(0.583110\pi\)
\(98\) 0 0
\(99\) −250225. 250225.i −2.56592 2.56592i
\(100\) 0 0
\(101\) −95106.3 + 95106.3i −0.927696 + 0.927696i −0.997557 0.0698605i \(-0.977745\pi\)
0.0698605 + 0.997557i \(0.477745\pi\)
\(102\) 0 0
\(103\) 25847.2i 0.240060i 0.992770 + 0.120030i \(0.0382991\pi\)
−0.992770 + 0.120030i \(0.961701\pi\)
\(104\) 0 0
\(105\) 127443.i 1.12809i
\(106\) 0 0
\(107\) 110256. 110256.i 0.930985 0.930985i −0.0667822 0.997768i \(-0.521273\pi\)
0.997768 + 0.0667822i \(0.0212733\pi\)
\(108\) 0 0
\(109\) −73554.2 73554.2i −0.592982 0.592982i 0.345454 0.938436i \(-0.387725\pi\)
−0.938436 + 0.345454i \(0.887725\pi\)
\(110\) 0 0
\(111\) −309550. −2.38465
\(112\) 0 0
\(113\) 116163. 0.855801 0.427901 0.903826i \(-0.359253\pi\)
0.427901 + 0.903826i \(0.359253\pi\)
\(114\) 0 0
\(115\) −37073.4 37073.4i −0.261407 0.261407i
\(116\) 0 0
\(117\) −7154.32 + 7154.32i −0.0483174 + 0.0483174i
\(118\) 0 0
\(119\) 303290.i 1.96332i
\(120\) 0 0
\(121\) 126234.i 0.783812i
\(122\) 0 0
\(123\) 277986. 277986.i 1.65676 1.65676i
\(124\) 0 0
\(125\) 11048.5 + 11048.5i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) 206963. 1.13863 0.569317 0.822118i \(-0.307208\pi\)
0.569317 + 0.822118i \(0.307208\pi\)
\(128\) 0 0
\(129\) 57622.2 0.304871
\(130\) 0 0
\(131\) 138422. + 138422.i 0.704738 + 0.704738i 0.965424 0.260685i \(-0.0839485\pi\)
−0.260685 + 0.965424i \(0.583949\pi\)
\(132\) 0 0
\(133\) −185282. + 185282.i −0.908245 + 0.908245i
\(134\) 0 0
\(135\) 313476.i 1.48037i
\(136\) 0 0
\(137\) 230300.i 1.04831i −0.851621 0.524157i \(-0.824380\pi\)
0.851621 0.524157i \(-0.175620\pi\)
\(138\) 0 0
\(139\) −32332.2 + 32332.2i −0.141938 + 0.141938i −0.774505 0.632568i \(-0.782001\pi\)
0.632568 + 0.774505i \(0.282001\pi\)
\(140\) 0 0
\(141\) 393118. + 393118.i 1.66523 + 1.66523i
\(142\) 0 0
\(143\) −8213.91 −0.0335900
\(144\) 0 0
\(145\) −3540.22 −0.0139833
\(146\) 0 0
\(147\) 254254. + 254254.i 0.970454 + 0.970454i
\(148\) 0 0
\(149\) 142412. 142412.i 0.525510 0.525510i −0.393720 0.919230i \(-0.628812\pi\)
0.919230 + 0.393720i \(0.128812\pi\)
\(150\) 0 0
\(151\) 101751.i 0.363158i −0.983376 0.181579i \(-0.941879\pi\)
0.983376 0.181579i \(-0.0581208\pi\)
\(152\) 0 0
\(153\) 1.18051e6i 4.07700i
\(154\) 0 0
\(155\) 55765.7 55765.7i 0.186440 0.186440i
\(156\) 0 0
\(157\) −35410.6 35410.6i −0.114653 0.114653i 0.647453 0.762106i \(-0.275834\pi\)
−0.762106 + 0.647453i \(0.775834\pi\)
\(158\) 0 0
\(159\) 431320. 1.35303
\(160\) 0 0
\(161\) −355727. −1.08156
\(162\) 0 0
\(163\) −301633. 301633.i −0.889221 0.889221i 0.105227 0.994448i \(-0.466443\pi\)
−0.994448 + 0.105227i \(0.966443\pi\)
\(164\) 0 0
\(165\) −284760. + 284760.i −0.814270 + 0.814270i
\(166\) 0 0
\(167\) 157537.i 0.437111i 0.975824 + 0.218556i \(0.0701345\pi\)
−0.975824 + 0.218556i \(0.929865\pi\)
\(168\) 0 0
\(169\) 371058.i 0.999367i
\(170\) 0 0
\(171\) −721178. + 721178.i −1.88605 + 1.88605i
\(172\) 0 0
\(173\) 35638.7 + 35638.7i 0.0905329 + 0.0905329i 0.750923 0.660390i \(-0.229609\pi\)
−0.660390 + 0.750923i \(0.729609\pi\)
\(174\) 0 0
\(175\) 106013. 0.261676
\(176\) 0 0
\(177\) 242147. 0.580960
\(178\) 0 0
\(179\) −63778.3 63778.3i −0.148779 0.148779i 0.628794 0.777572i \(-0.283549\pi\)
−0.777572 + 0.628794i \(0.783549\pi\)
\(180\) 0 0
\(181\) −370078. + 370078.i −0.839647 + 0.839647i −0.988812 0.149166i \(-0.952341\pi\)
0.149166 + 0.988812i \(0.452341\pi\)
\(182\) 0 0
\(183\) 714482.i 1.57711i
\(184\) 0 0
\(185\) 257498.i 0.553152i
\(186\) 0 0
\(187\) 677673. 677673.i 1.41715 1.41715i
\(188\) 0 0
\(189\) 1.50393e6 + 1.50393e6i 3.06249 + 3.06249i
\(190\) 0 0
\(191\) −168330. −0.333870 −0.166935 0.985968i \(-0.553387\pi\)
−0.166935 + 0.985968i \(0.553387\pi\)
\(192\) 0 0
\(193\) −541728. −1.04686 −0.523429 0.852069i \(-0.675347\pi\)
−0.523429 + 0.852069i \(0.675347\pi\)
\(194\) 0 0
\(195\) 8141.71 + 8141.71i 0.0153331 + 0.0153331i
\(196\) 0 0
\(197\) 585746. 585746.i 1.07534 1.07534i 0.0784142 0.996921i \(-0.475014\pi\)
0.996921 0.0784142i \(-0.0249857\pi\)
\(198\) 0 0
\(199\) 127714.i 0.228615i −0.993445 0.114307i \(-0.963535\pi\)
0.993445 0.114307i \(-0.0364649\pi\)
\(200\) 0 0
\(201\) 376827.i 0.657887i
\(202\) 0 0
\(203\) −16984.6 + 16984.6i −0.0289278 + 0.0289278i
\(204\) 0 0
\(205\) −231241. 231241.i −0.384309 0.384309i
\(206\) 0 0
\(207\) −1.38461e6 −2.24596
\(208\) 0 0
\(209\) −827988. −1.31117
\(210\) 0 0
\(211\) −644768. 644768.i −0.997005 0.997005i 0.00299074 0.999996i \(-0.499048\pi\)
−0.999996 + 0.00299074i \(0.999048\pi\)
\(212\) 0 0
\(213\) 490983. 490983.i 0.741511 0.741511i
\(214\) 0 0
\(215\) 47932.8i 0.0707191i
\(216\) 0 0
\(217\) 535084.i 0.771387i
\(218\) 0 0
\(219\) 2853.35 2853.35i 0.00402017 0.00402017i
\(220\) 0 0
\(221\) −19375.7 19375.7i −0.0266856 0.0266856i
\(222\) 0 0
\(223\) 1.44076e6 1.94013 0.970064 0.242851i \(-0.0780825\pi\)
0.970064 + 0.242851i \(0.0780825\pi\)
\(224\) 0 0
\(225\) 412639. 0.543393
\(226\) 0 0
\(227\) −517029. 517029.i −0.665963 0.665963i 0.290816 0.956779i \(-0.406073\pi\)
−0.956779 + 0.290816i \(0.906073\pi\)
\(228\) 0 0
\(229\) −920463. + 920463.i −1.15989 + 1.15989i −0.175394 + 0.984498i \(0.556120\pi\)
−0.984498 + 0.175394i \(0.943880\pi\)
\(230\) 0 0
\(231\) 2.73233e6i 3.36902i
\(232\) 0 0
\(233\) 1.24039e6i 1.49682i 0.663238 + 0.748409i \(0.269182\pi\)
−0.663238 + 0.748409i \(0.730818\pi\)
\(234\) 0 0
\(235\) 327014. 327014.i 0.386275 0.386275i
\(236\) 0 0
\(237\) −573228. 573228.i −0.662912 0.662912i
\(238\) 0 0
\(239\) −1.34665e6 −1.52496 −0.762482 0.647009i \(-0.776020\pi\)
−0.762482 + 0.647009i \(0.776020\pi\)
\(240\) 0 0
\(241\) 32567.7 0.0361197 0.0180599 0.999837i \(-0.494251\pi\)
0.0180599 + 0.999837i \(0.494251\pi\)
\(242\) 0 0
\(243\) 2.44442e6 + 2.44442e6i 2.65558 + 2.65558i
\(244\) 0 0
\(245\) 211500. 211500.i 0.225111 0.225111i
\(246\) 0 0
\(247\) 23673.4i 0.0246899i
\(248\) 0 0
\(249\) 860492.i 0.879525i
\(250\) 0 0
\(251\) 292306. 292306.i 0.292856 0.292856i −0.545351 0.838207i \(-0.683604\pi\)
0.838207 + 0.545351i \(0.183604\pi\)
\(252\) 0 0
\(253\) −794838. 794838.i −0.780687 0.780687i
\(254\) 0 0
\(255\) −1.34343e6 −1.29380
\(256\) 0 0
\(257\) 1.04416e6 0.986130 0.493065 0.869993i \(-0.335877\pi\)
0.493065 + 0.869993i \(0.335877\pi\)
\(258\) 0 0
\(259\) 1.23537e6 + 1.23537e6i 1.14432 + 1.14432i
\(260\) 0 0
\(261\) −66109.7 + 66109.7i −0.0600709 + 0.0600709i
\(262\) 0 0
\(263\) 645063.i 0.575059i −0.957772 0.287530i \(-0.907166\pi\)
0.957772 0.287530i \(-0.0928340\pi\)
\(264\) 0 0
\(265\) 358792.i 0.313854i
\(266\) 0 0
\(267\) 2.15687e6 2.15687e6i 1.85160 1.85160i
\(268\) 0 0
\(269\) 1.50774e6 + 1.50774e6i 1.27042 + 1.27042i 0.945870 + 0.324547i \(0.105212\pi\)
0.324547 + 0.945870i \(0.394788\pi\)
\(270\) 0 0
\(271\) 52832.6 0.0436997 0.0218499 0.999761i \(-0.493044\pi\)
0.0218499 + 0.999761i \(0.493044\pi\)
\(272\) 0 0
\(273\) 78121.4 0.0634401
\(274\) 0 0
\(275\) 236876. + 236876.i 0.188882 + 0.188882i
\(276\) 0 0
\(277\) 977130. 977130.i 0.765161 0.765161i −0.212089 0.977250i \(-0.568027\pi\)
0.977250 + 0.212089i \(0.0680267\pi\)
\(278\) 0 0
\(279\) 2.08273e6i 1.60185i
\(280\) 0 0
\(281\) 581362.i 0.439219i −0.975588 0.219610i \(-0.929522\pi\)
0.975588 0.219610i \(-0.0704783\pi\)
\(282\) 0 0
\(283\) −590873. + 590873.i −0.438559 + 0.438559i −0.891527 0.452968i \(-0.850365\pi\)
0.452968 + 0.891527i \(0.350365\pi\)
\(284\) 0 0
\(285\) 820710. + 820710.i 0.598519 + 0.598519i
\(286\) 0 0
\(287\) −2.21881e6 −1.59007
\(288\) 0 0
\(289\) 1.77726e6 1.25171
\(290\) 0 0
\(291\) 1.01671e6 + 1.01671e6i 0.703825 + 0.703825i
\(292\) 0 0
\(293\) 1.64681e6 1.64681e6i 1.12066 1.12066i 0.129016 0.991643i \(-0.458818\pi\)
0.991643 0.129016i \(-0.0411818\pi\)
\(294\) 0 0
\(295\) 201429.i 0.134762i
\(296\) 0 0
\(297\) 6.72080e6i 4.42109i
\(298\) 0 0
\(299\) −22725.6 + 22725.6i −0.0147007 + 0.0147007i
\(300\) 0 0
\(301\) −229963. 229963.i −0.146299 0.146299i
\(302\) 0 0
\(303\) 4.04223e6 2.52938
\(304\) 0 0
\(305\) 594338. 0.365834
\(306\) 0 0
\(307\) 1.06448e6 + 1.06448e6i 0.644601 + 0.644601i 0.951683 0.307082i \(-0.0993525\pi\)
−0.307082 + 0.951683i \(0.599352\pi\)
\(308\) 0 0
\(309\) 549282. 549282.i 0.327265 0.327265i
\(310\) 0 0
\(311\) 938055.i 0.549955i −0.961451 0.274978i \(-0.911330\pi\)
0.961451 0.274978i \(-0.0886705\pi\)
\(312\) 0 0
\(313\) 851057.i 0.491018i −0.969394 0.245509i \(-0.921045\pi\)
0.969394 0.245509i \(-0.0789551\pi\)
\(314\) 0 0
\(315\) 1.97968e6 1.97968e6i 1.12413 1.12413i
\(316\) 0 0
\(317\) −2.34483e6 2.34483e6i −1.31058 1.31058i −0.920986 0.389595i \(-0.872615\pi\)
−0.389595 0.920986i \(-0.627385\pi\)
\(318\) 0 0
\(319\) −75900.9 −0.0417609
\(320\) 0 0
\(321\) −4.68613e6 −2.53835
\(322\) 0 0
\(323\) −1.95313e6 1.95313e6i −1.04166 1.04166i
\(324\) 0 0
\(325\) 6772.65 6772.65i 0.00355672 0.00355672i
\(326\) 0 0
\(327\) 3.12622e6i 1.61678i
\(328\) 0 0
\(329\) 3.13776e6i 1.59820i
\(330\) 0 0
\(331\) 2.43713e6 2.43713e6i 1.22267 1.22267i 0.255992 0.966679i \(-0.417598\pi\)
0.966679 0.255992i \(-0.0824021\pi\)
\(332\) 0 0
\(333\) 4.80849e6 + 4.80849e6i 2.37629 + 2.37629i
\(334\) 0 0
\(335\) 313462. 0.152606
\(336\) 0 0
\(337\) 2.39700e6 1.14972 0.574861 0.818251i \(-0.305056\pi\)
0.574861 + 0.818251i \(0.305056\pi\)
\(338\) 0 0
\(339\) −2.46860e6 2.46860e6i −1.16668 1.16668i
\(340\) 0 0
\(341\) 1.19559e6 1.19559e6i 0.556798 0.556798i
\(342\) 0 0
\(343\) 821430.i 0.376994i
\(344\) 0 0
\(345\) 1.57570e6i 0.712733i
\(346\) 0 0
\(347\) −2.82591e6 + 2.82591e6i −1.25989 + 1.25989i −0.308751 + 0.951143i \(0.599911\pi\)
−0.951143 + 0.308751i \(0.900089\pi\)
\(348\) 0 0
\(349\) −724297. 724297.i −0.318312 0.318312i 0.529806 0.848119i \(-0.322265\pi\)
−0.848119 + 0.529806i \(0.822265\pi\)
\(350\) 0 0
\(351\) 192158. 0.0832511
\(352\) 0 0
\(353\) 714440. 0.305161 0.152580 0.988291i \(-0.451242\pi\)
0.152580 + 0.988291i \(0.451242\pi\)
\(354\) 0 0
\(355\) −408422. 408422.i −0.172004 0.172004i
\(356\) 0 0
\(357\) −6.44526e6 + 6.44526e6i −2.67652 + 2.67652i
\(358\) 0 0
\(359\) 2.73797e6i 1.12122i −0.828078 0.560612i \(-0.810566\pi\)
0.828078 0.560612i \(-0.189434\pi\)
\(360\) 0 0
\(361\) 89743.0i 0.0362437i
\(362\) 0 0
\(363\) −2.68261e6 + 2.68261e6i −1.06854 + 1.06854i
\(364\) 0 0
\(365\) −2373.55 2373.55i −0.000932536 0.000932536i
\(366\) 0 0
\(367\) −1.70699e6 −0.661555 −0.330777 0.943709i \(-0.607311\pi\)
−0.330777 + 0.943709i \(0.607311\pi\)
\(368\) 0 0
\(369\) −8.63635e6 −3.30190
\(370\) 0 0
\(371\) −1.72134e6 1.72134e6i −0.649280 0.649280i
\(372\) 0 0
\(373\) 1.59619e6 1.59619e6i 0.594036 0.594036i −0.344683 0.938719i \(-0.612014\pi\)
0.938719 + 0.344683i \(0.112014\pi\)
\(374\) 0 0
\(375\) 469588.i 0.172440i
\(376\) 0 0
\(377\) 2170.12i 0.000786377i
\(378\) 0 0
\(379\) −2.12185e6 + 2.12185e6i −0.758782 + 0.758782i −0.976101 0.217319i \(-0.930269\pi\)
0.217319 + 0.976101i \(0.430269\pi\)
\(380\) 0 0
\(381\) −4.39820e6 4.39820e6i −1.55225 1.55225i
\(382\) 0 0
\(383\) −3.39113e6 −1.18127 −0.590633 0.806940i \(-0.701122\pi\)
−0.590633 + 0.806940i \(0.701122\pi\)
\(384\) 0 0
\(385\) 2.27288e6 0.781491
\(386\) 0 0
\(387\) −895092. 895092.i −0.303802 0.303802i
\(388\) 0 0
\(389\) −4.15607e6 + 4.15607e6i −1.39254 + 1.39254i −0.572958 + 0.819585i \(0.694204\pi\)
−0.819585 + 0.572958i \(0.805796\pi\)
\(390\) 0 0
\(391\) 3.74987e6i 1.24044i
\(392\) 0 0
\(393\) 5.88326e6i 1.92149i
\(394\) 0 0
\(395\) −476837. + 476837.i −0.153772 + 0.153772i
\(396\) 0 0
\(397\) −3.36699e6 3.36699e6i −1.07217 1.07217i −0.997184 0.0749888i \(-0.976108\pi\)
−0.0749888 0.997184i \(-0.523892\pi\)
\(398\) 0 0
\(399\) 7.87489e6 2.47635
\(400\) 0 0
\(401\) 4.35505e6 1.35248 0.676242 0.736680i \(-0.263607\pi\)
0.676242 + 0.736680i \(0.263607\pi\)
\(402\) 0 0
\(403\) −34183.8 34183.8i −0.0104848 0.0104848i
\(404\) 0 0
\(405\) 3.82563e6 3.82563e6i 1.15895 1.15895i
\(406\) 0 0
\(407\) 5.52065e6i 1.65198i
\(408\) 0 0
\(409\) 377060.i 0.111456i 0.998446 + 0.0557279i \(0.0177479\pi\)
−0.998446 + 0.0557279i \(0.982252\pi\)
\(410\) 0 0
\(411\) −4.89413e6 + 4.89413e6i −1.42913 + 1.42913i
\(412\) 0 0
\(413\) −966378. 966378.i −0.278786 0.278786i
\(414\) 0 0
\(415\) −715796. −0.204018
\(416\) 0 0
\(417\) 1.37419e6 0.386996
\(418\) 0 0
\(419\) 48525.8 + 48525.8i 0.0135032 + 0.0135032i 0.713826 0.700323i \(-0.246961\pi\)
−0.700323 + 0.713826i \(0.746961\pi\)
\(420\) 0 0
\(421\) −1.37804e6 + 1.37804e6i −0.378929 + 0.378929i −0.870716 0.491787i \(-0.836344\pi\)
0.491787 + 0.870716i \(0.336344\pi\)
\(422\) 0 0
\(423\) 1.22132e7i 3.31879i
\(424\) 0 0
\(425\) 1.11753e6i 0.300114i
\(426\) 0 0
\(427\) 2.85140e6 2.85140e6i 0.756813 0.756813i
\(428\) 0 0
\(429\) 174555. + 174555.i 0.0457919 + 0.0457919i
\(430\) 0 0
\(431\) −1.22831e6 −0.318503 −0.159251 0.987238i \(-0.550908\pi\)
−0.159251 + 0.987238i \(0.550908\pi\)
\(432\) 0 0
\(433\) −3.43096e6 −0.879418 −0.439709 0.898140i \(-0.644918\pi\)
−0.439709 + 0.898140i \(0.644918\pi\)
\(434\) 0 0
\(435\) 75233.7 + 75233.7i 0.0190629 + 0.0190629i
\(436\) 0 0
\(437\) −2.29081e6 + 2.29081e6i −0.573834 + 0.573834i
\(438\) 0 0
\(439\) 3.48221e6i 0.862371i 0.902263 + 0.431185i \(0.141904\pi\)
−0.902263 + 0.431185i \(0.858096\pi\)
\(440\) 0 0
\(441\) 7.89907e6i 1.93410i
\(442\) 0 0
\(443\) 2.92993e6 2.92993e6i 0.709330 0.709330i −0.257064 0.966394i \(-0.582755\pi\)
0.966394 + 0.257064i \(0.0827552\pi\)
\(444\) 0 0
\(445\) −1.79418e6 1.79418e6i −0.429504 0.429504i
\(446\) 0 0
\(447\) −6.05283e6 −1.43281
\(448\) 0 0
\(449\) 6.52284e6 1.52694 0.763469 0.645845i \(-0.223495\pi\)
0.763469 + 0.645845i \(0.223495\pi\)
\(450\) 0 0
\(451\) −4.95771e6 4.95771e6i −1.14773 1.14773i
\(452\) 0 0
\(453\) −2.16232e6 + 2.16232e6i −0.495079 + 0.495079i
\(454\) 0 0
\(455\) 64985.0i 0.0147158i
\(456\) 0 0
\(457\) 260871.i 0.0584299i −0.999573 0.0292150i \(-0.990699\pi\)
0.999573 0.0292150i \(-0.00930074\pi\)
\(458\) 0 0
\(459\) −1.58536e7 + 1.58536e7i −3.51234 + 3.51234i
\(460\) 0 0
\(461\) 4.25443e6 + 4.25443e6i 0.932372 + 0.932372i 0.997854 0.0654817i \(-0.0208584\pi\)
−0.0654817 + 0.997854i \(0.520858\pi\)
\(462\) 0 0
\(463\) 4.35973e6 0.945163 0.472582 0.881287i \(-0.343322\pi\)
0.472582 + 0.881287i \(0.343322\pi\)
\(464\) 0 0
\(465\) −2.37017e6 −0.508332
\(466\) 0 0
\(467\) −1.89257e6 1.89257e6i −0.401569 0.401569i 0.477216 0.878786i \(-0.341646\pi\)
−0.878786 + 0.477216i \(0.841646\pi\)
\(468\) 0 0
\(469\) 1.50387e6 1.50387e6i 0.315702 0.315702i
\(470\) 0 0
\(471\) 1.50503e6i 0.312603i
\(472\) 0 0
\(473\) 1.02766e6i 0.211201i
\(474\) 0 0
\(475\) 682704. 682704.i 0.138835 0.138835i
\(476\) 0 0
\(477\) −6.70004e6 6.70004e6i −1.34828 1.34828i
\(478\) 0 0
\(479\) 3.95775e6 0.788151 0.394075 0.919078i \(-0.371065\pi\)
0.394075 + 0.919078i \(0.371065\pi\)
\(480\) 0 0
\(481\) 157844. 0.0311075
\(482\) 0 0
\(483\) 7.55960e6 + 7.55960e6i 1.47445 + 1.47445i
\(484\) 0 0
\(485\) 845746. 845746.i 0.163262 0.163262i
\(486\) 0 0
\(487\) 453914.i 0.0867264i 0.999059 + 0.0433632i \(0.0138073\pi\)
−0.999059 + 0.0433632i \(0.986193\pi\)
\(488\) 0 0
\(489\) 1.28201e7i 2.42448i
\(490\) 0 0
\(491\) 5.41878e6 5.41878e6i 1.01437 1.01437i 0.0144777 0.999895i \(-0.495391\pi\)
0.999895 0.0144777i \(-0.00460855\pi\)
\(492\) 0 0
\(493\) −179042. 179042.i −0.0331770 0.0331770i
\(494\) 0 0
\(495\) 8.84680e6 1.62283
\(496\) 0 0
\(497\) −3.91890e6 −0.711661
\(498\) 0 0
\(499\) −5.16769e6 5.16769e6i −0.929063 0.929063i 0.0685828 0.997645i \(-0.478152\pi\)
−0.997645 + 0.0685828i \(0.978152\pi\)
\(500\) 0 0
\(501\) 3.34785e6 3.34785e6i 0.595897 0.595897i
\(502\) 0 0
\(503\) 9.19408e6i 1.62027i 0.586240 + 0.810137i \(0.300607\pi\)
−0.586240 + 0.810137i \(0.699393\pi\)
\(504\) 0 0
\(505\) 3.36252e6i 0.586727i
\(506\) 0 0
\(507\) −7.88541e6 + 7.88541e6i −1.36240 + 1.36240i
\(508\) 0 0
\(509\) −913921. 913921.i −0.156356 0.156356i 0.624594 0.780950i \(-0.285265\pi\)
−0.780950 + 0.624594i \(0.785265\pi\)
\(510\) 0 0
\(511\) −22774.7 −0.00385833
\(512\) 0 0
\(513\) 1.93701e7 3.24967
\(514\) 0 0
\(515\) −456918. 456918.i −0.0759137 0.0759137i
\(516\) 0 0
\(517\) 7.01104e6 7.01104e6i 1.15360 1.15360i
\(518\) 0 0
\(519\) 1.51473e6i 0.246840i
\(520\) 0 0
\(521\) 7.10507e6i 1.14676i 0.819288 + 0.573382i \(0.194369\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(522\) 0 0
\(523\) 5.26173e6 5.26173e6i 0.841152 0.841152i −0.147857 0.989009i \(-0.547238\pi\)
0.989009 + 0.147857i \(0.0472376\pi\)
\(524\) 0 0
\(525\) −2.25290e6 2.25290e6i −0.356733 0.356733i
\(526\) 0 0
\(527\) 5.64055e6 0.884697
\(528\) 0 0
\(529\) 2.03815e6 0.316663
\(530\) 0 0
\(531\) −3.76147e6 3.76147e6i −0.578923 0.578923i
\(532\) 0 0
\(533\) −141749. + 141749.i −0.0216123 + 0.0216123i
\(534\) 0 0
\(535\) 3.89814e6i 0.588807i
\(536\) 0 0
\(537\) 2.71072e6i 0.405648i
\(538\) 0 0
\(539\) 4.53448e6 4.53448e6i 0.672288 0.672288i
\(540\) 0 0
\(541\) −1.53164e6 1.53164e6i −0.224989 0.224989i 0.585606 0.810596i \(-0.300857\pi\)
−0.810596 + 0.585606i \(0.800857\pi\)
\(542\) 0 0
\(543\) 1.57292e7 2.28932
\(544\) 0 0
\(545\) 2.60053e6 0.375035
\(546\) 0 0
\(547\) 3.29041e6 + 3.29041e6i 0.470198 + 0.470198i 0.901979 0.431780i \(-0.142114\pi\)
−0.431780 + 0.901979i \(0.642114\pi\)
\(548\) 0 0
\(549\) 1.10986e7 1.10986e7i 1.57159 1.57159i
\(550\) 0 0
\(551\) 218755.i 0.0306958i
\(552\) 0 0
\(553\) 4.57535e6i 0.636226i
\(554\) 0 0
\(555\) 5.47213e6 5.47213e6i 0.754091 0.754091i
\(556\) 0 0
\(557\) −712454. 712454.i −0.0973014 0.0973014i 0.656780 0.754082i \(-0.271918\pi\)
−0.754082 + 0.656780i \(0.771918\pi\)
\(558\) 0 0
\(559\) −29382.3 −0.00397701
\(560\) 0 0
\(561\) −2.88027e7 −3.86390
\(562\) 0 0
\(563\) 368542. + 368542.i 0.0490023 + 0.0490023i 0.731183 0.682181i \(-0.238968\pi\)
−0.682181 + 0.731183i \(0.738968\pi\)
\(564\) 0 0
\(565\) −2.05350e6 + 2.05350e6i −0.270628 + 0.270628i
\(566\) 0 0
\(567\) 3.67077e7i 4.79512i
\(568\) 0 0
\(569\) 2.45410e6i 0.317769i −0.987297 0.158884i \(-0.949210\pi\)
0.987297 0.158884i \(-0.0507897\pi\)
\(570\) 0 0
\(571\) −2.20689e6 + 2.20689e6i −0.283263 + 0.283263i −0.834409 0.551146i \(-0.814191\pi\)
0.551146 + 0.834409i \(0.314191\pi\)
\(572\) 0 0
\(573\) 3.57720e6 + 3.57720e6i 0.455152 + 0.455152i
\(574\) 0 0
\(575\) 1.31074e6 0.165328
\(576\) 0 0
\(577\) 7.03399e6 0.879553 0.439777 0.898107i \(-0.355058\pi\)
0.439777 + 0.898107i \(0.355058\pi\)
\(578\) 0 0
\(579\) 1.15123e7 + 1.15123e7i 1.42714 + 1.42714i
\(580\) 0 0
\(581\) −3.43411e6 + 3.43411e6i −0.422059 + 0.422059i
\(582\) 0 0
\(583\) 7.69234e6i 0.937319i
\(584\) 0 0
\(585\) 252944.i 0.0305586i
\(586\) 0 0
\(587\) −5.32556e6 + 5.32556e6i −0.637926 + 0.637926i −0.950043 0.312118i \(-0.898962\pi\)
0.312118 + 0.950043i \(0.398962\pi\)
\(588\) 0 0
\(589\) −3.44584e6 3.44584e6i −0.409267 0.409267i
\(590\) 0 0
\(591\) −2.48955e7 −2.93193
\(592\) 0 0
\(593\) 8.24117e6 0.962392 0.481196 0.876613i \(-0.340203\pi\)
0.481196 + 0.876613i \(0.340203\pi\)
\(594\) 0 0
\(595\) 5.36146e6 + 5.36146e6i 0.620856 + 0.620856i
\(596\) 0 0
\(597\) −2.71406e6 + 2.71406e6i −0.311662 + 0.311662i
\(598\) 0 0
\(599\) 5.71298e6i 0.650572i −0.945616 0.325286i \(-0.894539\pi\)
0.945616 0.325286i \(-0.105461\pi\)
\(600\) 0 0
\(601\) 6.26506e6i 0.707521i 0.935336 + 0.353761i \(0.115097\pi\)
−0.935336 + 0.353761i \(0.884903\pi\)
\(602\) 0 0
\(603\) 5.85355e6 5.85355e6i 0.655581 0.655581i
\(604\) 0 0
\(605\) 2.23152e6 + 2.23152e6i 0.247863 + 0.247863i
\(606\) 0 0
\(607\) −1.00536e7 −1.10752 −0.553760 0.832676i \(-0.686807\pi\)
−0.553760 + 0.832676i \(0.686807\pi\)
\(608\) 0 0
\(609\) 721883. 0.0788722
\(610\) 0 0
\(611\) −200456. 200456.i −0.0217228 0.0217228i
\(612\) 0 0
\(613\) −8.73964e6 + 8.73964e6i −0.939382 + 0.939382i −0.998265 0.0588831i \(-0.981246\pi\)
0.0588831 + 0.998265i \(0.481246\pi\)
\(614\) 0 0
\(615\) 9.82828e6i 1.04783i
\(616\) 0 0
\(617\) 1.44012e7i 1.52295i 0.648194 + 0.761475i \(0.275525\pi\)
−0.648194 + 0.761475i \(0.724475\pi\)
\(618\) 0 0
\(619\) 8.63486e6 8.63486e6i 0.905792 0.905792i −0.0901369 0.995929i \(-0.528730\pi\)
0.995929 + 0.0901369i \(0.0287305\pi\)
\(620\) 0 0
\(621\) 1.85946e7 + 1.85946e7i 1.93490 + 1.93490i
\(622\) 0 0
\(623\) −1.72156e7 −1.77706
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) 1.75957e7 + 1.75957e7i 1.78746 + 1.78746i
\(628\) 0 0
\(629\) −1.30226e7 + 1.30226e7i −1.31242 + 1.31242i
\(630\) 0 0
\(631\) 1.80181e7i 1.80150i 0.434334 + 0.900752i \(0.356984\pi\)
−0.434334 + 0.900752i \(0.643016\pi\)
\(632\) 0 0
\(633\) 2.74041e7i 2.71836i
\(634\) 0 0
\(635\) −3.65863e6 + 3.65863e6i −0.360067 + 0.360067i
\(636\) 0 0
\(637\) −129648. 129648.i −0.0126595 0.0126595i
\(638\) 0 0
\(639\) −1.52537e7 −1.47782
\(640\) 0 0
\(641\) 6.76428e6 0.650245 0.325122 0.945672i \(-0.394595\pi\)
0.325122 + 0.945672i \(0.394595\pi\)
\(642\) 0 0
\(643\) −1.24694e7 1.24694e7i −1.18937 1.18937i −0.977240 0.212134i \(-0.931959\pi\)
−0.212134 0.977240i \(-0.568041\pi\)
\(644\) 0 0
\(645\) −1.01863e6 + 1.01863e6i −0.0964086 + 0.0964086i
\(646\) 0 0
\(647\) 1.76781e7i 1.66025i 0.557574 + 0.830127i \(0.311732\pi\)
−0.557574 + 0.830127i \(0.688268\pi\)
\(648\) 0 0
\(649\) 4.31856e6i 0.402464i
\(650\) 0 0
\(651\) −1.13711e7 + 1.13711e7i −1.05160 + 1.05160i
\(652\) 0 0
\(653\) −6.23084e6 6.23084e6i −0.571826 0.571826i 0.360812 0.932638i \(-0.382499\pi\)
−0.932638 + 0.360812i \(0.882499\pi\)
\(654\) 0 0
\(655\) −4.89397e6 −0.445716
\(656\) 0 0
\(657\) −88646.7 −0.00801215
\(658\) 0 0
\(659\) 7.26417e6 + 7.26417e6i 0.651587 + 0.651587i 0.953375 0.301788i \(-0.0975834\pi\)
−0.301788 + 0.953375i \(0.597583\pi\)
\(660\) 0 0
\(661\) −4.99304e6 + 4.99304e6i −0.444489 + 0.444489i −0.893518 0.449028i \(-0.851770\pi\)
0.449028 + 0.893518i \(0.351770\pi\)
\(662\) 0 0
\(663\) 823512.i 0.0727589i
\(664\) 0 0
\(665\) 6.55069e6i 0.574425i
\(666\) 0 0
\(667\) −209997. + 209997.i −0.0182767 + 0.0182767i
\(668\) 0 0
\(669\) −3.06178e7 3.06178e7i −2.64490 2.64490i
\(670\) 0 0
\(671\) 1.27424e7 1.09256
\(672\) 0 0
\(673\) 1.16798e7 0.994028 0.497014 0.867742i \(-0.334430\pi\)
0.497014 + 0.867742i \(0.334430\pi\)
\(674\) 0 0
\(675\) −5.54153e6 5.54153e6i −0.468134 0.468134i
\(676\) 0 0
\(677\) −6.60241e6 + 6.60241e6i −0.553645 + 0.553645i −0.927491 0.373846i \(-0.878039\pi\)
0.373846 + 0.927491i \(0.378039\pi\)
\(678\) 0 0
\(679\) 8.11511e6i 0.675492i
\(680\) 0 0
\(681\) 2.19749e7i 1.81576i
\(682\) 0 0
\(683\) −851589. + 851589.i −0.0698519 + 0.0698519i −0.741170 0.671318i \(-0.765729\pi\)
0.671318 + 0.741170i \(0.265729\pi\)
\(684\) 0 0
\(685\) 4.07116e6 + 4.07116e6i 0.331506 + 0.331506i
\(686\) 0 0
\(687\) 3.91218e7 3.16247
\(688\) 0 0
\(689\) −219936. −0.0176501
\(690\) 0 0
\(691\) 2.38682e6 + 2.38682e6i 0.190163 + 0.190163i 0.795766 0.605604i \(-0.207068\pi\)
−0.605604 + 0.795766i \(0.707068\pi\)
\(692\) 0 0
\(693\) 4.24435e7 4.24435e7i 3.35720 3.35720i
\(694\) 0 0
\(695\) 1.14311e6i 0.0897693i
\(696\) 0 0
\(697\) 2.33894e7i 1.82363i
\(698\) 0 0
\(699\) 2.63597e7 2.63597e7i 2.04055 2.04055i
\(700\) 0 0
\(701\) −9.80021e6 9.80021e6i −0.753252 0.753252i 0.221833 0.975085i \(-0.428796\pi\)
−0.975085 + 0.221833i \(0.928796\pi\)
\(702\) 0 0
\(703\) 1.59112e7 1.21426
\(704\) 0 0
\(705\) −1.38988e7 −1.05319
\(706\) 0 0
\(707\) −1.61320e7 1.61320e7i −1.21378 1.21378i
\(708\) 0 0
\(709\) 7.08067e6 7.08067e6i 0.529004 0.529004i −0.391272 0.920275i \(-0.627965\pi\)
0.920275 + 0.391272i \(0.127965\pi\)
\(710\) 0 0
\(711\) 1.78088e7i 1.32118i
\(712\) 0 0
\(713\) 6.61575e6i 0.487366i
\(714\) 0 0
\(715\) 145203. 145203.i 0.0106221 0.0106221i
\(716\) 0 0
\(717\) 2.86178e7 + 2.86178e7i 2.07893 + 2.07893i
\(718\) 0 0
\(719\) −2.03907e7 −1.47099 −0.735495 0.677531i \(-0.763050\pi\)
−0.735495 + 0.677531i \(0.763050\pi\)
\(720\) 0 0
\(721\) −4.38422e6 −0.314090
\(722\) 0 0
\(723\) −692100. 692100.i −0.0492406 0.0492406i
\(724\) 0 0
\(725\) 62582.9 62582.9i 0.00442191 0.00442191i
\(726\) 0 0
\(727\) 6.88695e6i 0.483271i −0.970367 0.241636i \(-0.922316\pi\)
0.970367 0.241636i \(-0.0776838\pi\)
\(728\) 0 0
\(729\) 5.13056e7i 3.57558i
\(730\) 0 0
\(731\) 2.42414e6 2.42414e6i 0.167789 0.167789i
\(732\) 0 0
\(733\) 8.97843e6 + 8.97843e6i 0.617221 + 0.617221i 0.944818 0.327597i \(-0.106239\pi\)
−0.327597 + 0.944818i \(0.606239\pi\)
\(734\) 0 0
\(735\) −8.98925e6 −0.613769
\(736\) 0 0
\(737\) 6.72049e6 0.455756
\(738\) 0 0
\(739\) 1.28144e7 + 1.28144e7i 0.863153 + 0.863153i 0.991703 0.128550i \(-0.0410322\pi\)
−0.128550 + 0.991703i \(0.541032\pi\)
\(740\) 0 0
\(741\) 503087. 503087.i 0.0336587 0.0336587i
\(742\) 0 0
\(743\) 1.59231e7i 1.05817i 0.848568 + 0.529087i \(0.177465\pi\)
−0.848568 + 0.529087i \(0.822535\pi\)
\(744\) 0 0
\(745\) 5.03502e6i 0.332362i
\(746\) 0 0
\(747\) −1.33667e7 + 1.33667e7i −0.876442 + 0.876442i
\(748\) 0 0
\(749\) 1.87017e7 + 1.87017e7i 1.21808 + 1.21808i
\(750\) 0 0
\(751\) 2.14541e7 1.38807 0.694034 0.719942i \(-0.255832\pi\)
0.694034 + 0.719942i \(0.255832\pi\)
\(752\) 0 0
\(753\) −1.24237e7 −0.798478
\(754\) 0 0
\(755\) 1.79872e6 + 1.79872e6i 0.114841 + 0.114841i
\(756\) 0 0
\(757\) 1.08813e7 1.08813e7i 0.690145 0.690145i −0.272119 0.962264i \(-0.587724\pi\)
0.962264 + 0.272119i \(0.0877244\pi\)
\(758\) 0 0
\(759\) 3.37824e7i 2.12856i
\(760\) 0 0
\(761\) 2.31444e6i 0.144872i 0.997373 + 0.0724361i \(0.0230773\pi\)
−0.997373 + 0.0724361i \(0.976923\pi\)
\(762\) 0 0
\(763\) 1.24763e7 1.24763e7i 0.775846 0.775846i
\(764\) 0 0
\(765\) 2.08686e7 + 2.08686e7i 1.28926 + 1.28926i
\(766\) 0 0
\(767\) −123474. −0.00757857
\(768\) 0 0
\(769\) 2.53993e7 1.54884 0.774418 0.632675i \(-0.218043\pi\)
0.774418 + 0.632675i \(0.218043\pi\)
\(770\) 0 0
\(771\) −2.21896e7 2.21896e7i −1.34435 1.34435i
\(772\) 0 0
\(773\) −2.08318e7 + 2.08318e7i −1.25394 + 1.25394i −0.300004 + 0.953938i \(0.596988\pi\)
−0.953938 + 0.300004i \(0.903012\pi\)
\(774\) 0 0
\(775\) 1.97162e6i 0.117915i
\(776\) 0 0
\(777\) 5.25062e7i 3.12003i
\(778\) 0 0
\(779\) −1.42887e7 + 1.42887e7i −0.843625 + 0.843625i
\(780\) 0 0
\(781\) −8.75640e6 8.75640e6i −0.513687 0.513687i
\(782\) 0 0
\(783\) 1.77564e6 0.103502
\(784\) 0 0
\(785\) 1.25196e6 0.0725128
\(786\) 0 0 </