Properties

Label 320.6.l.a.81.4
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 81.4
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-17.6894 - 17.6894i) q^{3} +(17.6777 - 17.6777i) q^{5} +145.744i q^{7} +382.828i q^{9} +O(q^{10})\) \(q+(-17.6894 - 17.6894i) q^{3} +(17.6777 - 17.6777i) q^{5} +145.744i q^{7} +382.828i q^{9} +(-499.361 + 499.361i) q^{11} +(-139.026 - 139.026i) q^{13} -625.414 q^{15} +2249.81 q^{17} +(-870.316 - 870.316i) q^{19} +(2578.13 - 2578.13i) q^{21} -306.863i q^{23} -625.000i q^{25} +(2473.47 - 2473.47i) q^{27} +(-3027.13 - 3027.13i) q^{29} +8495.03 q^{31} +17666.8 q^{33} +(2576.42 + 2576.42i) q^{35} +(-9933.99 + 9933.99i) q^{37} +4918.57i q^{39} -3882.30i q^{41} +(4843.29 - 4843.29i) q^{43} +(6767.50 + 6767.50i) q^{45} -10166.3 q^{47} -4434.45 q^{49} +(-39797.6 - 39797.6i) q^{51} +(954.691 - 954.691i) q^{53} +17655.1i q^{55} +30790.7i q^{57} +(23925.2 - 23925.2i) q^{59} +(-4569.75 - 4569.75i) q^{61} -55795.0 q^{63} -4915.32 q^{65} +(-6793.71 - 6793.71i) q^{67} +(-5428.21 + 5428.21i) q^{69} -55530.4i q^{71} -41830.3i q^{73} +(-11055.9 + 11055.9i) q^{75} +(-72779.1 - 72779.1i) q^{77} -63349.3 q^{79} +5518.99 q^{81} +(-13456.0 - 13456.0i) q^{83} +(39771.3 - 39771.3i) q^{85} +107096. i q^{87} +91427.3i q^{89} +(20262.3 - 20262.3i) q^{91} +(-150272. - 150272. i) q^{93} -30770.3 q^{95} -134371. q^{97} +(-191169. - 191169. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

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
\(3\) −17.6894 17.6894i −1.13477 1.13477i −0.989373 0.145401i \(-0.953553\pi\)
−0.145401 0.989373i \(-0.546447\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 145.744i 1.12421i 0.827066 + 0.562104i \(0.190008\pi\)
−0.827066 + 0.562104i \(0.809992\pi\)
\(8\) 0 0
\(9\) 382.828i 1.57542i
\(10\) 0 0
\(11\) −499.361 + 499.361i −1.24432 + 1.24432i −0.286133 + 0.958190i \(0.592370\pi\)
−0.958190 + 0.286133i \(0.907630\pi\)
\(12\) 0 0
\(13\) −139.026 139.026i −0.228159 0.228159i 0.583764 0.811923i \(-0.301579\pi\)
−0.811923 + 0.583764i \(0.801579\pi\)
\(14\) 0 0
\(15\) −625.414 −0.717694
\(16\) 0 0
\(17\) 2249.81 1.88809 0.944045 0.329817i \(-0.106987\pi\)
0.944045 + 0.329817i \(0.106987\pi\)
\(18\) 0 0
\(19\) −870.316 870.316i −0.553086 0.553086i 0.374244 0.927330i \(-0.377902\pi\)
−0.927330 + 0.374244i \(0.877902\pi\)
\(20\) 0 0
\(21\) 2578.13 2578.13i 1.27572 1.27572i
\(22\) 0 0
\(23\) 306.863i 0.120955i −0.998170 0.0604776i \(-0.980738\pi\)
0.998170 0.0604776i \(-0.0192624\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) 2473.47 2473.47i 0.652975 0.652975i
\(28\) 0 0
\(29\) −3027.13 3027.13i −0.668400 0.668400i 0.288946 0.957346i \(-0.406695\pi\)
−0.957346 + 0.288946i \(0.906695\pi\)
\(30\) 0 0
\(31\) 8495.03 1.58767 0.793836 0.608132i \(-0.208081\pi\)
0.793836 + 0.608132i \(0.208081\pi\)
\(32\) 0 0
\(33\) 17666.8 2.82405
\(34\) 0 0
\(35\) 2576.42 + 2576.42i 0.355506 + 0.355506i
\(36\) 0 0
\(37\) −9933.99 + 9933.99i −1.19294 + 1.19294i −0.216704 + 0.976237i \(0.569531\pi\)
−0.976237 + 0.216704i \(0.930469\pi\)
\(38\) 0 0
\(39\) 4918.57i 0.517818i
\(40\) 0 0
\(41\) 3882.30i 0.360686i −0.983604 0.180343i \(-0.942279\pi\)
0.983604 0.180343i \(-0.0577208\pi\)
\(42\) 0 0
\(43\) 4843.29 4843.29i 0.399456 0.399456i −0.478585 0.878041i \(-0.658850\pi\)
0.878041 + 0.478585i \(0.158850\pi\)
\(44\) 0 0
\(45\) 6767.50 + 6767.50i 0.498193 + 0.498193i
\(46\) 0 0
\(47\) −10166.3 −0.671299 −0.335650 0.941987i \(-0.608956\pi\)
−0.335650 + 0.941987i \(0.608956\pi\)
\(48\) 0 0
\(49\) −4434.45 −0.263845
\(50\) 0 0
\(51\) −39797.6 39797.6i −2.14255 2.14255i
\(52\) 0 0
\(53\) 954.691 954.691i 0.0466845 0.0466845i −0.683379 0.730064i \(-0.739490\pi\)
0.730064 + 0.683379i \(0.239490\pi\)
\(54\) 0 0
\(55\) 17655.1i 0.786979i
\(56\) 0 0
\(57\) 30790.7i 1.25526i
\(58\) 0 0
\(59\) 23925.2 23925.2i 0.894799 0.894799i −0.100171 0.994970i \(-0.531939\pi\)
0.994970 + 0.100171i \(0.0319391\pi\)
\(60\) 0 0
\(61\) −4569.75 4569.75i −0.157242 0.157242i 0.624102 0.781343i \(-0.285465\pi\)
−0.781343 + 0.624102i \(0.785465\pi\)
\(62\) 0 0
\(63\) −55795.0 −1.77110
\(64\) 0 0
\(65\) −4915.32 −0.144301
\(66\) 0 0
\(67\) −6793.71 6793.71i −0.184893 0.184893i 0.608591 0.793484i \(-0.291735\pi\)
−0.793484 + 0.608591i \(0.791735\pi\)
\(68\) 0 0
\(69\) −5428.21 + 5428.21i −0.137257 + 0.137257i
\(70\) 0 0
\(71\) 55530.4i 1.30733i −0.756784 0.653665i \(-0.773231\pi\)
0.756784 0.653665i \(-0.226769\pi\)
\(72\) 0 0
\(73\) 41830.3i 0.918721i −0.888250 0.459360i \(-0.848079\pi\)
0.888250 0.459360i \(-0.151921\pi\)
\(74\) 0 0
\(75\) −11055.9 + 11055.9i −0.226955 + 0.226955i
\(76\) 0 0
\(77\) −72779.1 72779.1i −1.39888 1.39888i
\(78\) 0 0
\(79\) −63349.3 −1.14202 −0.571011 0.820943i \(-0.693448\pi\)
−0.571011 + 0.820943i \(0.693448\pi\)
\(80\) 0 0
\(81\) 5518.99 0.0934646
\(82\) 0 0
\(83\) −13456.0 13456.0i −0.214398 0.214398i 0.591735 0.806133i \(-0.298443\pi\)
−0.806133 + 0.591735i \(0.798443\pi\)
\(84\) 0 0
\(85\) 39771.3 39771.3i 0.597066 0.597066i
\(86\) 0 0
\(87\) 107096.i 1.51697i
\(88\) 0 0
\(89\) 91427.3i 1.22349i 0.791054 + 0.611746i \(0.209532\pi\)
−0.791054 + 0.611746i \(0.790468\pi\)
\(90\) 0 0
\(91\) 20262.3 20262.3i 0.256499 0.256499i
\(92\) 0 0
\(93\) −150272. 150272.i −1.80165 1.80165i
\(94\) 0 0
\(95\) −30770.3 −0.349802
\(96\) 0 0
\(97\) −134371. −1.45003 −0.725014 0.688734i \(-0.758167\pi\)
−0.725014 + 0.688734i \(0.758167\pi\)
\(98\) 0 0
\(99\) −191169. 191169.i −1.96034 1.96034i
\(100\) 0 0
\(101\) −43169.3 + 43169.3i −0.421087 + 0.421087i −0.885578 0.464491i \(-0.846237\pi\)
0.464491 + 0.885578i \(0.346237\pi\)
\(102\) 0 0
\(103\) 63502.8i 0.589793i −0.955529 0.294897i \(-0.904715\pi\)
0.955529 0.294897i \(-0.0952853\pi\)
\(104\) 0 0
\(105\) 91150.6i 0.806838i
\(106\) 0 0
\(107\) 24015.3 24015.3i 0.202782 0.202782i −0.598409 0.801191i \(-0.704200\pi\)
0.801191 + 0.598409i \(0.204200\pi\)
\(108\) 0 0
\(109\) 96045.6 + 96045.6i 0.774304 + 0.774304i 0.978856 0.204552i \(-0.0655738\pi\)
−0.204552 + 0.978856i \(0.565574\pi\)
\(110\) 0 0
\(111\) 351452. 2.70744
\(112\) 0 0
\(113\) −89096.9 −0.656397 −0.328198 0.944609i \(-0.606441\pi\)
−0.328198 + 0.944609i \(0.606441\pi\)
\(114\) 0 0
\(115\) −5424.62 5424.62i −0.0382494 0.0382494i
\(116\) 0 0
\(117\) 53223.1 53223.1i 0.359447 0.359447i
\(118\) 0 0
\(119\) 327897.i 2.12261i
\(120\) 0 0
\(121\) 337672.i 2.09668i
\(122\) 0 0
\(123\) −68675.5 + 68675.5i −0.409297 + 0.409297i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) −92362.1 −0.508141 −0.254071 0.967186i \(-0.581770\pi\)
−0.254071 + 0.967186i \(0.581770\pi\)
\(128\) 0 0
\(129\) −171349. −0.906584
\(130\) 0 0
\(131\) 72978.2 + 72978.2i 0.371548 + 0.371548i 0.868041 0.496493i \(-0.165379\pi\)
−0.496493 + 0.868041i \(0.665379\pi\)
\(132\) 0 0
\(133\) 126844. 126844.i 0.621784 0.621784i
\(134\) 0 0
\(135\) 87450.3i 0.412978i
\(136\) 0 0
\(137\) 74846.8i 0.340700i −0.985384 0.170350i \(-0.945510\pi\)
0.985384 0.170350i \(-0.0544898\pi\)
\(138\) 0 0
\(139\) −12794.3 + 12794.3i −0.0561666 + 0.0561666i −0.734632 0.678466i \(-0.762645\pi\)
0.678466 + 0.734632i \(0.262645\pi\)
\(140\) 0 0
\(141\) 179835. + 179835.i 0.761773 + 0.761773i
\(142\) 0 0
\(143\) 138849. 0.567808
\(144\) 0 0
\(145\) −107025. −0.422733
\(146\) 0 0
\(147\) 78442.6 + 78442.6i 0.299405 + 0.299405i
\(148\) 0 0
\(149\) 87143.8 87143.8i 0.321567 0.321567i −0.527801 0.849368i \(-0.676983\pi\)
0.849368 + 0.527801i \(0.176983\pi\)
\(150\) 0 0
\(151\) 401715.i 1.43376i −0.697197 0.716879i \(-0.745570\pi\)
0.697197 0.716879i \(-0.254430\pi\)
\(152\) 0 0
\(153\) 861288.i 2.97454i
\(154\) 0 0
\(155\) 150172. 150172.i 0.502066 0.502066i
\(156\) 0 0
\(157\) 63529.6 + 63529.6i 0.205696 + 0.205696i 0.802435 0.596739i \(-0.203537\pi\)
−0.596739 + 0.802435i \(0.703537\pi\)
\(158\) 0 0
\(159\) −33775.8 −0.105953
\(160\) 0 0
\(161\) 44723.5 0.135979
\(162\) 0 0
\(163\) 22561.0 + 22561.0i 0.0665103 + 0.0665103i 0.739579 0.673069i \(-0.235024\pi\)
−0.673069 + 0.739579i \(0.735024\pi\)
\(164\) 0 0
\(165\) 312307. 312307.i 0.893043 0.893043i
\(166\) 0 0
\(167\) 69435.4i 0.192659i −0.995349 0.0963296i \(-0.969290\pi\)
0.995349 0.0963296i \(-0.0307103\pi\)
\(168\) 0 0
\(169\) 332636.i 0.895887i
\(170\) 0 0
\(171\) 333181. 333181.i 0.871345 0.871345i
\(172\) 0 0
\(173\) 114267. + 114267.i 0.290272 + 0.290272i 0.837188 0.546916i \(-0.184198\pi\)
−0.546916 + 0.837188i \(0.684198\pi\)
\(174\) 0 0
\(175\) 91090.3 0.224842
\(176\) 0 0
\(177\) −846443. −2.03079
\(178\) 0 0
\(179\) −343413. 343413.i −0.801095 0.801095i 0.182171 0.983267i \(-0.441687\pi\)
−0.983267 + 0.182171i \(0.941687\pi\)
\(180\) 0 0
\(181\) 551806. 551806.i 1.25196 1.25196i 0.297117 0.954841i \(-0.403975\pi\)
0.954841 0.297117i \(-0.0960250\pi\)
\(182\) 0 0
\(183\) 161672.i 0.356867i
\(184\) 0 0
\(185\) 351219.i 0.754483i
\(186\) 0 0
\(187\) −1.12347e6 + 1.12347e6i −2.34939 + 2.34939i
\(188\) 0 0
\(189\) 360494. + 360494.i 0.734081 + 0.734081i
\(190\) 0 0
\(191\) 318668. 0.632056 0.316028 0.948750i \(-0.397651\pi\)
0.316028 + 0.948750i \(0.397651\pi\)
\(192\) 0 0
\(193\) −948125. −1.83220 −0.916099 0.400953i \(-0.868679\pi\)
−0.916099 + 0.400953i \(0.868679\pi\)
\(194\) 0 0
\(195\) 86948.9 + 86948.9i 0.163749 + 0.163749i
\(196\) 0 0
\(197\) 414665. 414665.i 0.761258 0.761258i −0.215291 0.976550i \(-0.569070\pi\)
0.976550 + 0.215291i \(0.0690701\pi\)
\(198\) 0 0
\(199\) 174075.i 0.311604i −0.987788 0.155802i \(-0.950204\pi\)
0.987788 0.155802i \(-0.0497962\pi\)
\(200\) 0 0
\(201\) 240353.i 0.419623i
\(202\) 0 0
\(203\) 441188. 441188.i 0.751421 0.751421i
\(204\) 0 0
\(205\) −68630.0 68630.0i −0.114059 0.114059i
\(206\) 0 0
\(207\) 117476. 0.190556
\(208\) 0 0
\(209\) 869204. 1.37644
\(210\) 0 0
\(211\) −710866. 710866.i −1.09921 1.09921i −0.994503 0.104710i \(-0.966609\pi\)
−0.104710 0.994503i \(-0.533391\pi\)
\(212\) 0 0
\(213\) −982298. + 982298.i −1.48352 + 1.48352i
\(214\) 0 0
\(215\) 171236.i 0.252638i
\(216\) 0 0
\(217\) 1.23810e6i 1.78487i
\(218\) 0 0
\(219\) −739951. + 739951.i −1.04254 + 1.04254i
\(220\) 0 0
\(221\) −312782. 312782.i −0.430785 0.430785i
\(222\) 0 0
\(223\) 344479. 0.463874 0.231937 0.972731i \(-0.425494\pi\)
0.231937 + 0.972731i \(0.425494\pi\)
\(224\) 0 0
\(225\) 239267. 0.315085
\(226\) 0 0
\(227\) 423003. + 423003.i 0.544852 + 0.544852i 0.924947 0.380095i \(-0.124109\pi\)
−0.380095 + 0.924947i \(0.624109\pi\)
\(228\) 0 0
\(229\) 13077.0 13077.0i 0.0164786 0.0164786i −0.698819 0.715298i \(-0.746291\pi\)
0.715298 + 0.698819i \(0.246291\pi\)
\(230\) 0 0
\(231\) 2.57483e6i 3.17482i
\(232\) 0 0
\(233\) 906564.i 1.09398i −0.837140 0.546989i \(-0.815774\pi\)
0.837140 0.546989i \(-0.184226\pi\)
\(234\) 0 0
\(235\) −179716. + 179716.i −0.212284 + 0.212284i
\(236\) 0 0
\(237\) 1.12061e6 + 1.12061e6i 1.29594 + 1.29594i
\(238\) 0 0
\(239\) 127219. 0.144065 0.0720325 0.997402i \(-0.477051\pi\)
0.0720325 + 0.997402i \(0.477051\pi\)
\(240\) 0 0
\(241\) 1.16404e6 1.29100 0.645501 0.763760i \(-0.276649\pi\)
0.645501 + 0.763760i \(0.276649\pi\)
\(242\) 0 0
\(243\) −698680. 698680.i −0.759037 0.759037i
\(244\) 0 0
\(245\) −78390.7 + 78390.7i −0.0834352 + 0.0834352i
\(246\) 0 0
\(247\) 241993.i 0.252384i
\(248\) 0 0
\(249\) 476056.i 0.486586i
\(250\) 0 0
\(251\) 1.13028e6 1.13028e6i 1.13240 1.13240i 0.142627 0.989776i \(-0.454445\pi\)
0.989776 0.142627i \(-0.0455550\pi\)
\(252\) 0 0
\(253\) 153235. + 153235.i 0.150507 + 0.150507i
\(254\) 0 0
\(255\) −1.40706e6 −1.35507
\(256\) 0 0
\(257\) −857575. −0.809914 −0.404957 0.914336i \(-0.632714\pi\)
−0.404957 + 0.914336i \(0.632714\pi\)
\(258\) 0 0
\(259\) −1.44782e6 1.44782e6i −1.34112 1.34112i
\(260\) 0 0
\(261\) 1.15887e6 1.15887e6i 1.05301 1.05301i
\(262\) 0 0
\(263\) 1.81966e6i 1.62219i 0.584915 + 0.811095i \(0.301128\pi\)
−0.584915 + 0.811095i \(0.698872\pi\)
\(264\) 0 0
\(265\) 33753.4i 0.0295259i
\(266\) 0 0
\(267\) 1.61729e6 1.61729e6i 1.38839 1.38839i
\(268\) 0 0
\(269\) −852235. 852235.i −0.718090 0.718090i 0.250124 0.968214i \(-0.419529\pi\)
−0.968214 + 0.250124i \(0.919529\pi\)
\(270\) 0 0
\(271\) 1.02596e6 0.848609 0.424305 0.905520i \(-0.360519\pi\)
0.424305 + 0.905520i \(0.360519\pi\)
\(272\) 0 0
\(273\) −716855. −0.582136
\(274\) 0 0
\(275\) 312101. + 312101.i 0.248865 + 0.248865i
\(276\) 0 0
\(277\) 684167. 684167.i 0.535751 0.535751i −0.386527 0.922278i \(-0.626325\pi\)
0.922278 + 0.386527i \(0.126325\pi\)
\(278\) 0 0
\(279\) 3.25213e6i 2.50125i
\(280\) 0 0
\(281\) 729777.i 0.551346i 0.961251 + 0.275673i \(0.0889008\pi\)
−0.961251 + 0.275673i \(0.911099\pi\)
\(282\) 0 0
\(283\) 1.54419e6 1.54419e6i 1.14613 1.14613i 0.158829 0.987306i \(-0.449228\pi\)
0.987306 0.158829i \(-0.0507717\pi\)
\(284\) 0 0
\(285\) 544308. + 544308.i 0.396947 + 0.396947i
\(286\) 0 0
\(287\) 565824. 0.405487
\(288\) 0 0
\(289\) 3.64177e6 2.56488
\(290\) 0 0
\(291\) 2.37694e6 + 2.37694e6i 1.64545 + 1.64545i
\(292\) 0 0
\(293\) −193823. + 193823.i −0.131898 + 0.131898i −0.769973 0.638076i \(-0.779731\pi\)
0.638076 + 0.769973i \(0.279731\pi\)
\(294\) 0 0
\(295\) 845883.i 0.565920i
\(296\) 0 0
\(297\) 2.47031e6i 1.62502i
\(298\) 0 0
\(299\) −42662.0 + 42662.0i −0.0275971 + 0.0275971i
\(300\) 0 0
\(301\) 705882. + 705882.i 0.449072 + 0.449072i
\(302\) 0 0
\(303\) 1.52728e6 0.955677
\(304\) 0 0
\(305\) −161565. −0.0994483
\(306\) 0 0
\(307\) 925679. + 925679.i 0.560550 + 0.560550i 0.929464 0.368913i \(-0.120270\pi\)
−0.368913 + 0.929464i \(0.620270\pi\)
\(308\) 0 0
\(309\) −1.12333e6 + 1.12333e6i −0.669282 + 0.669282i
\(310\) 0 0
\(311\) 2.38575e6i 1.39870i −0.714779 0.699350i \(-0.753473\pi\)
0.714779 0.699350i \(-0.246527\pi\)
\(312\) 0 0
\(313\) 1.58579e6i 0.914922i −0.889230 0.457461i \(-0.848759\pi\)
0.889230 0.457461i \(-0.151241\pi\)
\(314\) 0 0
\(315\) −986326. + 986326.i −0.560072 + 0.560072i
\(316\) 0 0
\(317\) −475855. 475855.i −0.265966 0.265966i 0.561506 0.827473i \(-0.310222\pi\)
−0.827473 + 0.561506i \(0.810222\pi\)
\(318\) 0 0
\(319\) 3.02326e6 1.66341
\(320\) 0 0
\(321\) −849631. −0.460222
\(322\) 0 0
\(323\) −1.95804e6 1.95804e6i −1.04428 1.04428i
\(324\) 0 0
\(325\) −86891.4 + 86891.4i −0.0456319 + 0.0456319i
\(326\) 0 0
\(327\) 3.39797e6i 1.75732i
\(328\) 0 0
\(329\) 1.48168e6i 0.754681i
\(330\) 0 0
\(331\) 342774. 342774.i 0.171964 0.171964i −0.615878 0.787842i \(-0.711198\pi\)
0.787842 + 0.615878i \(0.211198\pi\)
\(332\) 0 0
\(333\) −3.80301e6 3.80301e6i −1.87939 1.87939i
\(334\) 0 0
\(335\) −240194. −0.116937
\(336\) 0 0
\(337\) −730000. −0.350145 −0.175072 0.984556i \(-0.556016\pi\)
−0.175072 + 0.984556i \(0.556016\pi\)
\(338\) 0 0
\(339\) 1.57607e6 + 1.57607e6i 0.744862 + 0.744862i
\(340\) 0 0
\(341\) −4.24209e6 + 4.24209e6i −1.97558 + 1.97558i
\(342\) 0 0
\(343\) 1.80323e6i 0.827592i
\(344\) 0 0
\(345\) 191916.i 0.0868088i
\(346\) 0 0
\(347\) 1.23141e6 1.23141e6i 0.549008 0.549008i −0.377146 0.926154i \(-0.623094\pi\)
0.926154 + 0.377146i \(0.123094\pi\)
\(348\) 0 0
\(349\) 12105.3 + 12105.3i 0.00531999 + 0.00531999i 0.709762 0.704442i \(-0.248803\pi\)
−0.704442 + 0.709762i \(0.748803\pi\)
\(350\) 0 0
\(351\) −687753. −0.297965
\(352\) 0 0
\(353\) −1.88586e6 −0.805513 −0.402756 0.915307i \(-0.631948\pi\)
−0.402756 + 0.915307i \(0.631948\pi\)
\(354\) 0 0
\(355\) −981648. 981648.i −0.413414 0.413414i
\(356\) 0 0
\(357\) 5.80029e6 5.80029e6i 2.40868 2.40868i
\(358\) 0 0
\(359\) 1.37593e6i 0.563455i 0.959494 + 0.281727i \(0.0909074\pi\)
−0.959494 + 0.281727i \(0.909093\pi\)
\(360\) 0 0
\(361\) 961200.i 0.388191i
\(362\) 0 0
\(363\) −5.97321e6 + 5.97321e6i −2.37926 + 2.37926i
\(364\) 0 0
\(365\) −739462. 739462.i −0.290525 0.290525i
\(366\) 0 0
\(367\) −2.12929e6 −0.825219 −0.412610 0.910908i \(-0.635383\pi\)
−0.412610 + 0.910908i \(0.635383\pi\)
\(368\) 0 0
\(369\) 1.48625e6 0.568233
\(370\) 0 0
\(371\) 139141. + 139141.i 0.0524832 + 0.0524832i
\(372\) 0 0
\(373\) −1.07538e6 + 1.07538e6i −0.400212 + 0.400212i −0.878308 0.478096i \(-0.841327\pi\)
0.478096 + 0.878308i \(0.341327\pi\)
\(374\) 0 0
\(375\) 390884.i 0.143539i
\(376\) 0 0
\(377\) 841701.i 0.305003i
\(378\) 0 0
\(379\) −68100.6 + 68100.6i −0.0243530 + 0.0243530i −0.719178 0.694825i \(-0.755482\pi\)
0.694825 + 0.719178i \(0.255482\pi\)
\(380\) 0 0
\(381\) 1.63383e6 + 1.63383e6i 0.576625 + 0.576625i
\(382\) 0 0
\(383\) −3.78678e6 −1.31908 −0.659542 0.751667i \(-0.729250\pi\)
−0.659542 + 0.751667i \(0.729250\pi\)
\(384\) 0 0
\(385\) −2.57313e6 −0.884728
\(386\) 0 0
\(387\) 1.85414e6 + 1.85414e6i 0.629312 + 0.629312i
\(388\) 0 0
\(389\) −349779. + 349779.i −0.117198 + 0.117198i −0.763273 0.646076i \(-0.776409\pi\)
0.646076 + 0.763273i \(0.276409\pi\)
\(390\) 0 0
\(391\) 690381.i 0.228374i
\(392\) 0 0
\(393\) 2.58188e6i 0.843246i
\(394\) 0 0
\(395\) −1.11987e6 + 1.11987e6i −0.361139 + 0.361139i
\(396\) 0 0
\(397\) −988780. 988780.i −0.314864 0.314864i 0.531926 0.846791i \(-0.321468\pi\)
−0.846791 + 0.531926i \(0.821468\pi\)
\(398\) 0 0
\(399\) −4.48757e6 −1.41117
\(400\) 0 0
\(401\) −2.30396e6 −0.715508 −0.357754 0.933816i \(-0.616457\pi\)
−0.357754 + 0.933816i \(0.616457\pi\)
\(402\) 0 0
\(403\) −1.18103e6 1.18103e6i −0.362242 0.362242i
\(404\) 0 0
\(405\) 97562.9 97562.9i 0.0295561 0.0295561i
\(406\) 0 0
\(407\) 9.92129e6i 2.96881i
\(408\) 0 0
\(409\) 3.24798e6i 0.960075i −0.877248 0.480038i \(-0.840623\pi\)
0.877248 0.480038i \(-0.159377\pi\)
\(410\) 0 0
\(411\) −1.32399e6 + 1.32399e6i −0.386617 + 0.386617i
\(412\) 0 0
\(413\) 3.48696e6 + 3.48696e6i 1.00594 + 1.00594i
\(414\) 0 0
\(415\) −475741. −0.135597
\(416\) 0 0
\(417\) 452645. 0.127473
\(418\) 0 0
\(419\) −4.61891e6 4.61891e6i −1.28530 1.28530i −0.937610 0.347689i \(-0.886966\pi\)
−0.347689 0.937610i \(-0.613034\pi\)
\(420\) 0 0
\(421\) −253169. + 253169.i −0.0696153 + 0.0696153i −0.741057 0.671442i \(-0.765675\pi\)
0.671442 + 0.741057i \(0.265675\pi\)
\(422\) 0 0
\(423\) 3.89193e6i 1.05758i
\(424\) 0 0
\(425\) 1.40613e6i 0.377618i
\(426\) 0 0
\(427\) 666015. 666015.i 0.176772 0.176772i
\(428\) 0 0
\(429\) −2.45614e6 2.45614e6i −0.644333 0.644333i
\(430\) 0 0
\(431\) −4.39929e6 −1.14075 −0.570374 0.821385i \(-0.693202\pi\)
−0.570374 + 0.821385i \(0.693202\pi\)
\(432\) 0 0
\(433\) 4.71386e6 1.20825 0.604125 0.796889i \(-0.293523\pi\)
0.604125 + 0.796889i \(0.293523\pi\)
\(434\) 0 0
\(435\) 1.89321e6 + 1.89321e6i 0.479707 + 0.479707i
\(436\) 0 0
\(437\) −267068. + 267068.i −0.0668987 + 0.0668987i
\(438\) 0 0
\(439\) 5.00924e6i 1.24054i −0.784388 0.620270i \(-0.787023\pi\)
0.784388 0.620270i \(-0.212977\pi\)
\(440\) 0 0
\(441\) 1.69763e6i 0.415668i
\(442\) 0 0
\(443\) 121497. 121497.i 0.0294141 0.0294141i −0.692247 0.721661i \(-0.743379\pi\)
0.721661 + 0.692247i \(0.243379\pi\)
\(444\) 0 0
\(445\) 1.61622e6 + 1.61622e6i 0.386902 + 0.386902i
\(446\) 0 0
\(447\) −3.08304e6 −0.729811
\(448\) 0 0
\(449\) −3.37166e6 −0.789274 −0.394637 0.918837i \(-0.629130\pi\)
−0.394637 + 0.918837i \(0.629130\pi\)
\(450\) 0 0
\(451\) 1.93867e6 + 1.93867e6i 0.448810 + 0.448810i
\(452\) 0 0
\(453\) −7.10609e6 + 7.10609e6i −1.62699 + 1.62699i
\(454\) 0 0
\(455\) 716380.i 0.162224i
\(456\) 0 0
\(457\) 5.73334e6i 1.28415i −0.766640 0.642077i \(-0.778073\pi\)
0.766640 0.642077i \(-0.221927\pi\)
\(458\) 0 0
\(459\) 5.56482e6 5.56482e6i 1.23288 1.23288i
\(460\) 0 0
\(461\) 1.24910e6 + 1.24910e6i 0.273744 + 0.273744i 0.830606 0.556861i \(-0.187995\pi\)
−0.556861 + 0.830606i \(0.687995\pi\)
\(462\) 0 0
\(463\) 1.47038e6 0.318769 0.159384 0.987217i \(-0.449049\pi\)
0.159384 + 0.987217i \(0.449049\pi\)
\(464\) 0 0
\(465\) −5.31291e6 −1.13946
\(466\) 0 0
\(467\) 5.39068e6 + 5.39068e6i 1.14380 + 1.14380i 0.987748 + 0.156056i \(0.0498780\pi\)
0.156056 + 0.987748i \(0.450122\pi\)
\(468\) 0 0
\(469\) 990146. 990146.i 0.207858 0.207858i
\(470\) 0 0
\(471\) 2.24760e6i 0.466838i
\(472\) 0 0
\(473\) 4.83710e6i 0.994104i
\(474\) 0 0
\(475\) −543947. + 543947.i −0.110617 + 0.110617i
\(476\) 0 0
\(477\) 365482. + 365482.i 0.0735479 + 0.0735479i
\(478\) 0 0
\(479\) 7.61161e6 1.51578 0.757892 0.652380i \(-0.226229\pi\)
0.757892 + 0.652380i \(0.226229\pi\)
\(480\) 0 0
\(481\) 2.76217e6 0.544361
\(482\) 0 0
\(483\) −791131. 791131.i −0.154305 0.154305i
\(484\) 0 0
\(485\) −2.37537e6 + 2.37537e6i −0.458539 + 0.458539i
\(486\) 0 0
\(487\) 8.28314e6i 1.58261i 0.611425 + 0.791303i \(0.290597\pi\)
−0.611425 + 0.791303i \(0.709403\pi\)
\(488\) 0 0
\(489\) 798179.i 0.150948i
\(490\) 0 0
\(491\) −1.99372e6 + 1.99372e6i −0.373216 + 0.373216i −0.868647 0.495431i \(-0.835010\pi\)
0.495431 + 0.868647i \(0.335010\pi\)
\(492\) 0 0
\(493\) −6.81046e6 6.81046e6i −1.26200 1.26200i
\(494\) 0 0
\(495\) −6.75886e6 −1.23982
\(496\) 0 0
\(497\) 8.09325e6 1.46971
\(498\) 0 0
\(499\) −5.05666e6 5.05666e6i −0.909101 0.909101i 0.0870987 0.996200i \(-0.472240\pi\)
−0.996200 + 0.0870987i \(0.972240\pi\)
\(500\) 0 0
\(501\) −1.22827e6 + 1.22827e6i −0.218625 + 0.218625i
\(502\) 0 0
\(503\) 8.55756e6i 1.50810i −0.656817 0.754050i \(-0.728098\pi\)
0.656817 0.754050i \(-0.271902\pi\)
\(504\) 0 0
\(505\) 1.52627e6i 0.266319i
\(506\) 0 0
\(507\) −5.88413e6 + 5.88413e6i −1.01663 + 1.01663i
\(508\) 0 0
\(509\) 7.62878e6 + 7.62878e6i 1.30515 + 1.30515i 0.924872 + 0.380277i \(0.124172\pi\)
0.380277 + 0.924872i \(0.375828\pi\)
\(510\) 0 0
\(511\) 6.09653e6 1.03283
\(512\) 0 0
\(513\) −4.30540e6 −0.722303
\(514\) 0 0
\(515\) −1.12258e6 1.12258e6i −0.186509 0.186509i
\(516\) 0 0
\(517\) 5.07663e6 5.07663e6i 0.835313 0.835313i
\(518\) 0 0
\(519\) 4.04262e6i 0.658786i
\(520\) 0 0
\(521\) 2.21623e6i 0.357702i −0.983876 0.178851i \(-0.942762\pi\)
0.983876 0.178851i \(-0.0572380\pi\)
\(522\) 0 0
\(523\) −1.14782e6 + 1.14782e6i −0.183493 + 0.183493i −0.792876 0.609383i \(-0.791417\pi\)
0.609383 + 0.792876i \(0.291417\pi\)
\(524\) 0 0
\(525\) −1.61133e6 1.61133e6i −0.255145 0.255145i
\(526\) 0 0
\(527\) 1.91122e7 2.99767
\(528\) 0 0
\(529\) 6.34218e6 0.985370
\(530\) 0 0
\(531\) 9.15923e6 + 9.15923e6i 1.40969 + 1.40969i
\(532\) 0 0
\(533\) −539741. + 539741.i −0.0822939 + 0.0822939i
\(534\) 0 0
\(535\) 849069.i 0.128250i
\(536\) 0 0
\(537\) 1.21495e7i 1.81812i
\(538\) 0 0
\(539\) 2.21439e6 2.21439e6i 0.328309 0.328309i
\(540\) 0 0
\(541\) 3.06045e6 + 3.06045e6i 0.449564 + 0.449564i 0.895210 0.445645i \(-0.147026\pi\)
−0.445645 + 0.895210i \(0.647026\pi\)
\(542\) 0 0
\(543\) −1.95222e7 −2.84138
\(544\) 0 0
\(545\) 3.39573e6 0.489713
\(546\) 0 0
\(547\) −578599. 578599.i −0.0826817 0.0826817i 0.664556 0.747238i \(-0.268621\pi\)
−0.747238 + 0.664556i \(0.768621\pi\)
\(548\) 0 0
\(549\) 1.74943e6 1.74943e6i 0.247722 0.247722i
\(550\) 0 0
\(551\) 5.26912e6i 0.739366i
\(552\) 0 0
\(553\) 9.23281e6i 1.28387i
\(554\) 0 0
\(555\) 6.21285e6 6.21285e6i 0.856167 0.856167i
\(556\) 0 0
\(557\) −1.05759e6 1.05759e6i −0.144437 0.144437i 0.631190 0.775628i \(-0.282567\pi\)
−0.775628 + 0.631190i \(0.782567\pi\)
\(558\) 0 0
\(559\) −1.34669e6 −0.182279
\(560\) 0 0
\(561\) 3.97468e7 5.33206
\(562\) 0 0
\(563\) −1.20855e6 1.20855e6i −0.160692 0.160692i 0.622181 0.782873i \(-0.286247\pi\)
−0.782873 + 0.622181i \(0.786247\pi\)
\(564\) 0 0
\(565\) −1.57503e6 + 1.57503e6i −0.207571 + 0.207571i
\(566\) 0 0
\(567\) 804363.i 0.105074i
\(568\) 0 0
\(569\) 240008.i 0.0310775i 0.999879 + 0.0155387i \(0.00494633\pi\)
−0.999879 + 0.0155387i \(0.995054\pi\)
\(570\) 0 0
\(571\) 3.15859e6 3.15859e6i 0.405418 0.405418i −0.474719 0.880137i \(-0.657450\pi\)
0.880137 + 0.474719i \(0.157450\pi\)
\(572\) 0 0
\(573\) −5.63704e6 5.63704e6i −0.717240 0.717240i
\(574\) 0 0
\(575\) −191789. −0.0241910
\(576\) 0 0
\(577\) −1.19096e7 −1.48922 −0.744608 0.667502i \(-0.767364\pi\)
−0.744608 + 0.667502i \(0.767364\pi\)
\(578\) 0 0
\(579\) 1.67717e7 + 1.67717e7i 2.07913 + 2.07913i
\(580\) 0 0
\(581\) 1.96114e6 1.96114e6i 0.241028 0.241028i
\(582\) 0 0
\(583\) 953471.i 0.116181i
\(584\) 0 0
\(585\) 1.88172e6i 0.227335i
\(586\) 0 0
\(587\) −3.44065e6 + 3.44065e6i −0.412141 + 0.412141i −0.882484 0.470343i \(-0.844130\pi\)
0.470343 + 0.882484i \(0.344130\pi\)
\(588\) 0 0
\(589\) −7.39336e6 7.39336e6i −0.878119 0.878119i
\(590\) 0 0
\(591\) −1.46703e7 −1.72771
\(592\) 0 0
\(593\) −6.77775e6 −0.791496 −0.395748 0.918359i \(-0.629515\pi\)
−0.395748 + 0.918359i \(0.629515\pi\)
\(594\) 0 0
\(595\) 5.79645e6 + 5.79645e6i 0.671227 + 0.671227i
\(596\) 0 0
\(597\) −3.07927e6 + 3.07927e6i −0.353600 + 0.353600i
\(598\) 0 0
\(599\) 1.75030e7i 1.99318i 0.0825337 + 0.996588i \(0.473699\pi\)
−0.0825337 + 0.996588i \(0.526301\pi\)
\(600\) 0 0
\(601\) 1.22316e7i 1.38133i −0.723175 0.690664i \(-0.757318\pi\)
0.723175 0.690664i \(-0.242682\pi\)
\(602\) 0 0
\(603\) 2.60082e6 2.60082e6i 0.291285 0.291285i
\(604\) 0 0
\(605\) −5.96926e6 5.96926e6i −0.663028 0.663028i
\(606\) 0 0
\(607\) 7.53728e6 0.830315 0.415158 0.909750i \(-0.363726\pi\)
0.415158 + 0.909750i \(0.363726\pi\)
\(608\) 0 0
\(609\) −1.56087e7 −1.70539
\(610\) 0 0
\(611\) 1.41338e6 + 1.41338e6i 0.153163 + 0.153163i
\(612\) 0 0
\(613\) −3.06505e6 + 3.06505e6i −0.329448 + 0.329448i −0.852377 0.522928i \(-0.824839\pi\)
0.522928 + 0.852377i \(0.324839\pi\)
\(614\) 0 0
\(615\) 2.42804e6i 0.258862i
\(616\) 0 0
\(617\) 8.57289e6i 0.906597i −0.891359 0.453299i \(-0.850247\pi\)
0.891359 0.453299i \(-0.149753\pi\)
\(618\) 0 0
\(619\) −4.50028e6 + 4.50028e6i −0.472077 + 0.472077i −0.902586 0.430509i \(-0.858334\pi\)
0.430509 + 0.902586i \(0.358334\pi\)
\(620\) 0 0
\(621\) −759015. 759015.i −0.0789808 0.0789808i
\(622\) 0 0
\(623\) −1.33250e7 −1.37546
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) −1.53757e7 1.53757e7i −1.56194 1.56194i
\(628\) 0 0
\(629\) −2.23495e7 + 2.23495e7i −2.25238 + 2.25238i
\(630\) 0 0
\(631\) 5.75361e6i 0.575263i 0.957741 + 0.287632i \(0.0928679\pi\)
−0.957741 + 0.287632i \(0.907132\pi\)
\(632\) 0 0
\(633\) 2.51496e7i 2.49472i
\(634\) 0 0
\(635\) −1.63275e6 + 1.63275e6i −0.160688 + 0.160688i
\(636\) 0 0
\(637\) 616504. + 616504.i 0.0601987 + 0.0601987i
\(638\) 0 0
\(639\) 2.12586e7 2.05960
\(640\) 0 0
\(641\) −1.59854e7 −1.53666 −0.768329 0.640055i \(-0.778912\pi\)
−0.768329 + 0.640055i \(0.778912\pi\)
\(642\) 0 0
\(643\) 4.24577e6 + 4.24577e6i 0.404976 + 0.404976i 0.879982 0.475007i \(-0.157554\pi\)
−0.475007 + 0.879982i \(0.657554\pi\)
\(644\) 0 0
\(645\) −3.02906e6 + 3.02906e6i −0.286687 + 0.286687i
\(646\) 0 0
\(647\) 1.87607e7i 1.76192i 0.473186 + 0.880962i \(0.343104\pi\)
−0.473186 + 0.880962i \(0.656896\pi\)
\(648\) 0 0
\(649\) 2.38946e7i 2.22684i
\(650\) 0 0
\(651\) 2.19013e7 2.19013e7i 2.02543 2.02543i
\(652\) 0 0
\(653\) 9.42037e6 + 9.42037e6i 0.864540 + 0.864540i 0.991861 0.127322i \(-0.0406381\pi\)
−0.127322 + 0.991861i \(0.540638\pi\)
\(654\) 0 0
\(655\) 2.58017e6 0.234987
\(656\) 0 0
\(657\) 1.60138e7 1.44737
\(658\) 0 0
\(659\) −5.03540e6 5.03540e6i −0.451669 0.451669i 0.444239 0.895908i \(-0.353474\pi\)
−0.895908 + 0.444239i \(0.853474\pi\)
\(660\) 0 0
\(661\) −518766. + 518766.i −0.0461815 + 0.0461815i −0.729820 0.683639i \(-0.760396\pi\)
0.683639 + 0.729820i \(0.260396\pi\)
\(662\) 0 0
\(663\) 1.10658e7i 0.977688i
\(664\) 0 0
\(665\) 4.48460e6i 0.393251i
\(666\) 0 0
\(667\) −928914. + 928914.i −0.0808465 + 0.0808465i
\(668\) 0 0
\(669\) −6.09361e6 6.09361e6i −0.526392 0.526392i
\(670\) 0 0
\(671\) 4.56391e6 0.391319
\(672\) 0 0
\(673\) 1.42161e7 1.20988 0.604942 0.796270i \(-0.293196\pi\)
0.604942 + 0.796270i \(0.293196\pi\)
\(674\) 0 0
\(675\) −1.54592e6 1.54592e6i −0.130595 0.130595i
\(676\) 0 0
\(677\) −1.12363e7 + 1.12363e7i −0.942214 + 0.942214i −0.998419 0.0562048i \(-0.982100\pi\)
0.0562048 + 0.998419i \(0.482100\pi\)
\(678\) 0 0
\(679\) 1.95838e7i 1.63013i
\(680\) 0 0
\(681\) 1.49653e7i 1.23657i
\(682\) 0 0
\(683\) −1.05186e7 + 1.05186e7i −0.862790 + 0.862790i −0.991661 0.128871i \(-0.958865\pi\)
0.128871 + 0.991661i \(0.458865\pi\)
\(684\) 0 0
\(685\) −1.32312e6 1.32312e6i −0.107739 0.107739i
\(686\) 0 0
\(687\) −462648. −0.0373989
\(688\) 0 0
\(689\) −265454. −0.0213030
\(690\) 0 0
\(691\) −825671. 825671.i −0.0657827 0.0657827i 0.673450 0.739233i \(-0.264812\pi\)
−0.739233 + 0.673450i \(0.764812\pi\)
\(692\) 0 0
\(693\) 2.78619e7 2.78619e7i 2.20383 2.20383i
\(694\) 0 0
\(695\) 452345.i 0.0355229i
\(696\) 0 0
\(697\) 8.73442e6i 0.681008i
\(698\) 0 0
\(699\) −1.60365e7 + 1.60365e7i −1.24142 + 1.24142i
\(700\) 0 0
\(701\) 1.51900e7 + 1.51900e7i 1.16752 + 1.16752i 0.982790 + 0.184725i \(0.0591395\pi\)
0.184725 + 0.982790i \(0.440860\pi\)
\(702\) 0 0
\(703\) 1.72914e7 1.31960
\(704\) 0 0
\(705\) 6.35812e6 0.481788
\(706\) 0 0
\(707\) −6.29169e6 6.29169e6i −0.473389 0.473389i
\(708\) 0 0
\(709\) 1.65896e7 1.65896e7i 1.23942 1.23942i 0.279185 0.960237i \(-0.409936\pi\)
0.960237 0.279185i \(-0.0900644\pi\)
\(710\) 0 0
\(711\) 2.42519e7i 1.79917i
\(712\) 0 0
\(713\) 2.60681e6i 0.192037i
\(714\) 0 0
\(715\) 2.45452e6 2.45452e6i 0.179557 0.179557i
\(716\) 0 0
\(717\) −2.25043e6 2.25043e6i −0.163481 0.163481i
\(718\) 0 0
\(719\) −4.36503e6 −0.314895 −0.157447 0.987527i \(-0.550326\pi\)
−0.157447 + 0.987527i \(0.550326\pi\)
\(720\) 0 0
\(721\) 9.25518e6 0.663051
\(722\) 0 0
\(723\) −2.05912e7 2.05912e7i −1.46499 1.46499i
\(724\) 0 0
\(725\) −1.89196e6 + 1.89196e6i −0.133680 + 0.133680i
\(726\) 0 0
\(727\) 2.79937e6i 0.196437i −0.995165 0.0982186i \(-0.968686\pi\)
0.995165 0.0982186i \(-0.0313144\pi\)
\(728\) 0 0
\(729\) 2.33773e7i 1.62921i
\(730\) 0 0
\(731\) 1.08964e7 1.08964e7i 0.754209 0.754209i
\(732\) 0 0
\(733\) 9.10632e6 + 9.10632e6i 0.626012 + 0.626012i 0.947062 0.321050i \(-0.104036\pi\)
−0.321050 + 0.947062i \(0.604036\pi\)
\(734\) 0 0
\(735\) 2.77336e6 0.189360
\(736\) 0 0
\(737\) 6.78503e6 0.460133
\(738\) 0 0
\(739\) 1.41829e7 + 1.41829e7i 0.955333 + 0.955333i 0.999044 0.0437113i \(-0.0139182\pi\)
−0.0437113 + 0.999044i \(0.513918\pi\)
\(740\) 0 0
\(741\) 4.28071e6 4.28071e6i 0.286398 0.286398i
\(742\) 0 0
\(743\) 1.55348e7i 1.03236i 0.856479 + 0.516182i \(0.172647\pi\)
−0.856479 + 0.516182i \(0.827353\pi\)
\(744\) 0 0
\(745\) 3.08100e6i 0.203377i
\(746\) 0 0
\(747\) 5.15133e6 5.15133e6i 0.337767 0.337767i
\(748\) 0 0
\(749\) 3.50010e6 + 3.50010e6i 0.227969 + 0.227969i
\(750\) 0 0
\(751\) 2.23946e7 1.44892 0.724458 0.689319i \(-0.242090\pi\)
0.724458 + 0.689319i \(0.242090\pi\)
\(752\) 0 0
\(753\) −3.99879e7 −2.57004
\(754\) 0 0
\(755\) −7.10139e6 7.10139e6i −0.453394 0.453394i
\(756\) 0 0
\(757\) −4.97697e6 + 4.97697e6i −0.315664 + 0.315664i −0.847099 0.531435i \(-0.821653\pi\)
0.531435 + 0.847099i \(0.321653\pi\)
\(758\) 0 0
\(759\) 5.42127e6i 0.341584i
\(760\) 0 0
\(761\) 9.18617e6i 0.575007i −0.957780 0.287503i \(-0.907175\pi\)
0.957780 0.287503i \(-0.0928253\pi\)
\(762\) 0 0
\(763\) −1.39981e7 + 1.39981e7i −0.870479 + 0.870479i
\(764\) 0 0
\(765\) 1.52256e7 + 1.52256e7i 0.940632 + 0.940632i
\(766\) 0 0
\(767\) −6.65246e6 −0.408313
\(768\) 0 0
\(769\) −159069. −0.00969995 −0.00484998 0.999988i \(-0.501544\pi\)
−0.00484998 + 0.999988i \(0.501544\pi\)
\(770\) 0 0
\(771\) 1.51700e7 + 1.51700e7i 0.919070 + 0.919070i
\(772\) 0 0
\(773\) 1.23381e7 1.23381e7i 0.742675 0.742675i −0.230417 0.973092i \(-0.574009\pi\)
0.973092 + 0.230417i \(0.0740089\pi\)
\(774\) 0 0
\(775\) 5.30939e6i 0.317534i
\(776\) 0 0
\(777\) 5.12222e7i 3.04373i
\(778\) 0 0
\(779\) −3.37883e6 + 3.37883e6i −0.199491 + 0.199491i
\(780\) 0 0
\(781\) 2.77297e7 + 2.77297e7i 1.62674 + 1.62674i
\(782\) 0 0
\(783\) −1.49750e7 −0.872897
\(784\) 0 0
\(785\) 2.24611e6 0.130094
\(786\) 0 0