Properties

Label 43.6.a.b.1.8
Level 43
Weight 6
Character 43.1
Self dual yes
Analytic conductor 6.897
Analytic rank 0
Dimension 10
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-6.91219\) of \(x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.91219 q^{2} +12.8799 q^{3} +30.6028 q^{4} +79.5677 q^{5} +101.908 q^{6} -172.354 q^{7} -11.0549 q^{8} -77.1083 q^{9} +O(q^{10})\) \(q+7.91219 q^{2} +12.8799 q^{3} +30.6028 q^{4} +79.5677 q^{5} +101.908 q^{6} -172.354 q^{7} -11.0549 q^{8} -77.1083 q^{9} +629.555 q^{10} +452.247 q^{11} +394.161 q^{12} -22.7429 q^{13} -1363.70 q^{14} +1024.82 q^{15} -1066.76 q^{16} -521.824 q^{17} -610.096 q^{18} +1558.56 q^{19} +2434.99 q^{20} -2219.90 q^{21} +3578.27 q^{22} -3464.36 q^{23} -142.385 q^{24} +3206.01 q^{25} -179.946 q^{26} -4122.96 q^{27} -5274.51 q^{28} +4324.79 q^{29} +8108.60 q^{30} -3987.66 q^{31} -8086.64 q^{32} +5824.90 q^{33} -4128.77 q^{34} -13713.8 q^{35} -2359.73 q^{36} +10080.4 q^{37} +12331.6 q^{38} -292.926 q^{39} -879.609 q^{40} -16408.5 q^{41} -17564.3 q^{42} +1849.00 q^{43} +13840.0 q^{44} -6135.33 q^{45} -27410.7 q^{46} +24153.7 q^{47} -13739.7 q^{48} +12898.8 q^{49} +25366.6 q^{50} -6721.04 q^{51} -695.997 q^{52} +21214.2 q^{53} -32621.7 q^{54} +35984.2 q^{55} +1905.34 q^{56} +20074.0 q^{57} +34218.6 q^{58} -25849.7 q^{59} +31362.5 q^{60} +28577.7 q^{61} -31551.2 q^{62} +13289.9 q^{63} -29846.8 q^{64} -1809.60 q^{65} +46087.7 q^{66} +66762.2 q^{67} -15969.3 q^{68} -44620.6 q^{69} -108506. q^{70} -10031.8 q^{71} +852.421 q^{72} +32145.0 q^{73} +79758.3 q^{74} +41293.1 q^{75} +47696.2 q^{76} -77946.5 q^{77} -2317.69 q^{78} -21913.4 q^{79} -84879.4 q^{80} -34366.0 q^{81} -129827. q^{82} -66782.4 q^{83} -67935.1 q^{84} -41520.3 q^{85} +14629.6 q^{86} +55702.8 q^{87} -4999.53 q^{88} +48984.7 q^{89} -48543.9 q^{90} +3919.82 q^{91} -106019. q^{92} -51360.7 q^{93} +191108. q^{94} +124011. q^{95} -104155. q^{96} +93075.8 q^{97} +102058. q^{98} -34872.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.91219 1.39869 0.699346 0.714784i \(-0.253475\pi\)
0.699346 + 0.714784i \(0.253475\pi\)
\(3\) 12.8799 0.826246 0.413123 0.910675i \(-0.364438\pi\)
0.413123 + 0.910675i \(0.364438\pi\)
\(4\) 30.6028 0.956338
\(5\) 79.5677 1.42335 0.711675 0.702509i \(-0.247937\pi\)
0.711675 + 0.702509i \(0.247937\pi\)
\(6\) 101.908 1.15566
\(7\) −172.354 −1.32946 −0.664730 0.747083i \(-0.731454\pi\)
−0.664730 + 0.747083i \(0.731454\pi\)
\(8\) −11.0549 −0.0610700
\(9\) −77.1083 −0.317318
\(10\) 629.555 1.99083
\(11\) 452.247 1.12692 0.563461 0.826142i \(-0.309469\pi\)
0.563461 + 0.826142i \(0.309469\pi\)
\(12\) 394.161 0.790170
\(13\) −22.7429 −0.0373240 −0.0186620 0.999826i \(-0.505941\pi\)
−0.0186620 + 0.999826i \(0.505941\pi\)
\(14\) −1363.70 −1.85950
\(15\) 1024.82 1.17604
\(16\) −1066.76 −1.04176
\(17\) −521.824 −0.437927 −0.218964 0.975733i \(-0.570268\pi\)
−0.218964 + 0.975733i \(0.570268\pi\)
\(18\) −610.096 −0.443830
\(19\) 1558.56 0.990463 0.495232 0.868761i \(-0.335083\pi\)
0.495232 + 0.868761i \(0.335083\pi\)
\(20\) 2434.99 1.36120
\(21\) −2219.90 −1.09846
\(22\) 3578.27 1.57622
\(23\) −3464.36 −1.36554 −0.682769 0.730635i \(-0.739224\pi\)
−0.682769 + 0.730635i \(0.739224\pi\)
\(24\) −142.385 −0.0504588
\(25\) 3206.01 1.02592
\(26\) −179.946 −0.0522047
\(27\) −4122.96 −1.08843
\(28\) −5274.51 −1.27141
\(29\) 4324.79 0.954926 0.477463 0.878652i \(-0.341556\pi\)
0.477463 + 0.878652i \(0.341556\pi\)
\(30\) 8108.60 1.64491
\(31\) −3987.66 −0.745271 −0.372635 0.927978i \(-0.621546\pi\)
−0.372635 + 0.927978i \(0.621546\pi\)
\(32\) −8086.64 −1.39602
\(33\) 5824.90 0.931115
\(34\) −4128.77 −0.612525
\(35\) −13713.8 −1.89229
\(36\) −2359.73 −0.303463
\(37\) 10080.4 1.21053 0.605264 0.796025i \(-0.293068\pi\)
0.605264 + 0.796025i \(0.293068\pi\)
\(38\) 12331.6 1.38535
\(39\) −292.926 −0.0308388
\(40\) −879.609 −0.0869240
\(41\) −16408.5 −1.52444 −0.762219 0.647319i \(-0.775890\pi\)
−0.762219 + 0.647319i \(0.775890\pi\)
\(42\) −17564.3 −1.53641
\(43\) 1849.00 0.152499
\(44\) 13840.0 1.07772
\(45\) −6135.33 −0.451654
\(46\) −27410.7 −1.90997
\(47\) 24153.7 1.59492 0.797459 0.603373i \(-0.206177\pi\)
0.797459 + 0.603373i \(0.206177\pi\)
\(48\) −13739.7 −0.860746
\(49\) 12898.8 0.767465
\(50\) 25366.6 1.43495
\(51\) −6721.04 −0.361835
\(52\) −695.997 −0.0356943
\(53\) 21214.2 1.03738 0.518688 0.854963i \(-0.326420\pi\)
0.518688 + 0.854963i \(0.326420\pi\)
\(54\) −32621.7 −1.52238
\(55\) 35984.2 1.60400
\(56\) 1905.34 0.0811902
\(57\) 20074.0 0.818366
\(58\) 34218.6 1.33565
\(59\) −25849.7 −0.966775 −0.483387 0.875407i \(-0.660594\pi\)
−0.483387 + 0.875407i \(0.660594\pi\)
\(60\) 31362.5 1.12469
\(61\) 28577.7 0.983338 0.491669 0.870782i \(-0.336387\pi\)
0.491669 + 0.870782i \(0.336387\pi\)
\(62\) −31551.2 −1.04240
\(63\) 13289.9 0.421862
\(64\) −29846.8 −0.910852
\(65\) −1809.60 −0.0531250
\(66\) 46087.7 1.30234
\(67\) 66762.2 1.81695 0.908477 0.417935i \(-0.137246\pi\)
0.908477 + 0.417935i \(0.137246\pi\)
\(68\) −15969.3 −0.418806
\(69\) −44620.6 −1.12827
\(70\) −108506. −2.64673
\(71\) −10031.8 −0.236173 −0.118087 0.993003i \(-0.537676\pi\)
−0.118087 + 0.993003i \(0.537676\pi\)
\(72\) 852.421 0.0193786
\(73\) 32145.0 0.706003 0.353001 0.935623i \(-0.385161\pi\)
0.353001 + 0.935623i \(0.385161\pi\)
\(74\) 79758.3 1.69315
\(75\) 41293.1 0.847665
\(76\) 47696.2 0.947217
\(77\) −77946.5 −1.49820
\(78\) −2317.69 −0.0431339
\(79\) −21913.4 −0.395040 −0.197520 0.980299i \(-0.563289\pi\)
−0.197520 + 0.980299i \(0.563289\pi\)
\(80\) −84879.4 −1.48278
\(81\) −34366.0 −0.581991
\(82\) −129827. −2.13222
\(83\) −66782.4 −1.06406 −0.532031 0.846725i \(-0.678571\pi\)
−0.532031 + 0.846725i \(0.678571\pi\)
\(84\) −67935.1 −1.05050
\(85\) −41520.3 −0.623323
\(86\) 14629.6 0.213298
\(87\) 55702.8 0.789004
\(88\) −4999.53 −0.0688212
\(89\) 48984.7 0.655520 0.327760 0.944761i \(-0.393706\pi\)
0.327760 + 0.944761i \(0.393706\pi\)
\(90\) −48543.9 −0.631725
\(91\) 3919.82 0.0496207
\(92\) −106019. −1.30591
\(93\) −51360.7 −0.615777
\(94\) 191108. 2.23080
\(95\) 124011. 1.40978
\(96\) −104155. −1.15346
\(97\) 93075.8 1.00440 0.502201 0.864751i \(-0.332524\pi\)
0.502201 + 0.864751i \(0.332524\pi\)
\(98\) 102058. 1.07345
\(99\) −34872.0 −0.357593
\(100\) 98112.9 0.981129
\(101\) 47004.9 0.458500 0.229250 0.973368i \(-0.426373\pi\)
0.229250 + 0.973368i \(0.426373\pi\)
\(102\) −53178.2 −0.506096
\(103\) −51489.8 −0.478220 −0.239110 0.970992i \(-0.576856\pi\)
−0.239110 + 0.970992i \(0.576856\pi\)
\(104\) 251.420 0.00227938
\(105\) −176632. −1.56349
\(106\) 167851. 1.45097
\(107\) 74331.3 0.627642 0.313821 0.949482i \(-0.398391\pi\)
0.313821 + 0.949482i \(0.398391\pi\)
\(108\) −126174. −1.04091
\(109\) −204775. −1.65086 −0.825430 0.564505i \(-0.809067\pi\)
−0.825430 + 0.564505i \(0.809067\pi\)
\(110\) 284714. 2.24351
\(111\) 129835. 1.00019
\(112\) 183860. 1.38497
\(113\) 125866. 0.927281 0.463640 0.886023i \(-0.346543\pi\)
0.463640 + 0.886023i \(0.346543\pi\)
\(114\) 158830. 1.14464
\(115\) −275651. −1.94364
\(116\) 132351. 0.913232
\(117\) 1753.67 0.0118436
\(118\) −204528. −1.35222
\(119\) 89938.3 0.582207
\(120\) −11329.3 −0.0718206
\(121\) 43476.5 0.269955
\(122\) 226112. 1.37539
\(123\) −211340. −1.25956
\(124\) −122034. −0.712731
\(125\) 6445.88 0.0368984
\(126\) 105152. 0.590054
\(127\) −318214. −1.75069 −0.875347 0.483495i \(-0.839367\pi\)
−0.875347 + 0.483495i \(0.839367\pi\)
\(128\) 22618.8 0.122024
\(129\) 23814.9 0.126001
\(130\) −14317.9 −0.0743055
\(131\) −261871. −1.33324 −0.666620 0.745398i \(-0.732260\pi\)
−0.666620 + 0.745398i \(0.732260\pi\)
\(132\) 178258. 0.890460
\(133\) −268623. −1.31678
\(134\) 528236. 2.54136
\(135\) −328054. −1.54921
\(136\) 5768.69 0.0267442
\(137\) −20837.0 −0.0948492 −0.0474246 0.998875i \(-0.515101\pi\)
−0.0474246 + 0.998875i \(0.515101\pi\)
\(138\) −353047. −1.57810
\(139\) −182520. −0.801260 −0.400630 0.916240i \(-0.631209\pi\)
−0.400630 + 0.916240i \(0.631209\pi\)
\(140\) −419680. −1.80967
\(141\) 311097. 1.31779
\(142\) −79373.1 −0.330334
\(143\) −10285.4 −0.0420612
\(144\) 82255.9 0.330568
\(145\) 344113. 1.35919
\(146\) 254337. 0.987480
\(147\) 166135. 0.634115
\(148\) 308489. 1.15767
\(149\) 478460. 1.76555 0.882775 0.469796i \(-0.155673\pi\)
0.882775 + 0.469796i \(0.155673\pi\)
\(150\) 326719. 1.18562
\(151\) 244853. 0.873901 0.436951 0.899485i \(-0.356058\pi\)
0.436951 + 0.899485i \(0.356058\pi\)
\(152\) −17229.6 −0.0604876
\(153\) 40237.0 0.138962
\(154\) −616727. −2.09552
\(155\) −317289. −1.06078
\(156\) −8964.37 −0.0294923
\(157\) 12990.1 0.0420594 0.0210297 0.999779i \(-0.493306\pi\)
0.0210297 + 0.999779i \(0.493306\pi\)
\(158\) −173383. −0.552539
\(159\) 273236. 0.857128
\(160\) −643435. −1.98703
\(161\) 597095. 1.81543
\(162\) −271910. −0.814026
\(163\) 43866.4 0.129319 0.0646596 0.997907i \(-0.479404\pi\)
0.0646596 + 0.997907i \(0.479404\pi\)
\(164\) −502147. −1.45788
\(165\) 463473. 1.32530
\(166\) −528395. −1.48829
\(167\) 454884. 1.26215 0.631073 0.775724i \(-0.282615\pi\)
0.631073 + 0.775724i \(0.282615\pi\)
\(168\) 24540.6 0.0670830
\(169\) −370776. −0.998607
\(170\) −328517. −0.871837
\(171\) −120178. −0.314292
\(172\) 56584.6 0.145840
\(173\) −649198. −1.64916 −0.824579 0.565747i \(-0.808588\pi\)
−0.824579 + 0.565747i \(0.808588\pi\)
\(174\) 440731. 1.10357
\(175\) −552568. −1.36392
\(176\) −482438. −1.17398
\(177\) −332941. −0.798793
\(178\) 387577. 0.916870
\(179\) −570828. −1.33160 −0.665798 0.746132i \(-0.731909\pi\)
−0.665798 + 0.746132i \(0.731909\pi\)
\(180\) −187758. −0.431934
\(181\) −90744.3 −0.205884 −0.102942 0.994687i \(-0.532826\pi\)
−0.102942 + 0.994687i \(0.532826\pi\)
\(182\) 31014.4 0.0694041
\(183\) 368078. 0.812479
\(184\) 38298.0 0.0833934
\(185\) 802076. 1.72300
\(186\) −406376. −0.861282
\(187\) −235994. −0.493510
\(188\) 739170. 1.52528
\(189\) 710607. 1.44702
\(190\) 981196. 1.97184
\(191\) −546924. −1.08478 −0.542392 0.840126i \(-0.682481\pi\)
−0.542392 + 0.840126i \(0.682481\pi\)
\(192\) −384424. −0.752588
\(193\) 25064.4 0.0484356 0.0242178 0.999707i \(-0.492290\pi\)
0.0242178 + 0.999707i \(0.492290\pi\)
\(194\) 736434. 1.40485
\(195\) −23307.5 −0.0438943
\(196\) 394739. 0.733956
\(197\) 579350. 1.06359 0.531797 0.846872i \(-0.321517\pi\)
0.531797 + 0.846872i \(0.321517\pi\)
\(198\) −275914. −0.500162
\(199\) 411324. 0.736295 0.368147 0.929767i \(-0.379992\pi\)
0.368147 + 0.929767i \(0.379992\pi\)
\(200\) −35442.0 −0.0626532
\(201\) 859891. 1.50125
\(202\) 371912. 0.641301
\(203\) −745393. −1.26954
\(204\) −205683. −0.346037
\(205\) −1.30559e6 −2.16981
\(206\) −407397. −0.668883
\(207\) 267131. 0.433310
\(208\) 24261.2 0.0388825
\(209\) 704852. 1.11618
\(210\) −1.39755e6 −2.18685
\(211\) −385582. −0.596225 −0.298113 0.954531i \(-0.596357\pi\)
−0.298113 + 0.954531i \(0.596357\pi\)
\(212\) 649213. 0.992083
\(213\) −129208. −0.195137
\(214\) 588123. 0.877878
\(215\) 147121. 0.217059
\(216\) 45578.7 0.0664703
\(217\) 687288. 0.990808
\(218\) −1.62022e6 −2.30904
\(219\) 414024. 0.583332
\(220\) 1.10122e6 1.53397
\(221\) 11867.8 0.0163452
\(222\) 1.02728e6 1.39896
\(223\) −1.03807e6 −1.39786 −0.698930 0.715190i \(-0.746340\pi\)
−0.698930 + 0.715190i \(0.746340\pi\)
\(224\) 1.39376e6 1.85596
\(225\) −247210. −0.325544
\(226\) 995874. 1.29698
\(227\) 1.14006e6 1.46846 0.734229 0.678902i \(-0.237544\pi\)
0.734229 + 0.678902i \(0.237544\pi\)
\(228\) 614322. 0.782634
\(229\) 548999. 0.691804 0.345902 0.938271i \(-0.387573\pi\)
0.345902 + 0.938271i \(0.387573\pi\)
\(230\) −2.18100e6 −2.71855
\(231\) −1.00394e6 −1.23788
\(232\) −47809.9 −0.0583174
\(233\) −1.11203e6 −1.34191 −0.670957 0.741496i \(-0.734117\pi\)
−0.670957 + 0.741496i \(0.734117\pi\)
\(234\) 13875.4 0.0165655
\(235\) 1.92185e6 2.27013
\(236\) −791073. −0.924563
\(237\) −282242. −0.326400
\(238\) 711609. 0.814328
\(239\) −1.28067e6 −1.45025 −0.725123 0.688620i \(-0.758217\pi\)
−0.725123 + 0.688620i \(0.758217\pi\)
\(240\) −1.09324e6 −1.22514
\(241\) 725022. 0.804097 0.402049 0.915618i \(-0.368298\pi\)
0.402049 + 0.915618i \(0.368298\pi\)
\(242\) 343995. 0.377584
\(243\) 559249. 0.607561
\(244\) 874558. 0.940403
\(245\) 1.02633e6 1.09237
\(246\) −1.67216e6 −1.76174
\(247\) −35446.1 −0.0369680
\(248\) 44083.0 0.0455137
\(249\) −860150. −0.879176
\(250\) 51001.1 0.0516095
\(251\) −1.43637e6 −1.43907 −0.719533 0.694458i \(-0.755644\pi\)
−0.719533 + 0.694458i \(0.755644\pi\)
\(252\) 406708. 0.403442
\(253\) −1.56675e6 −1.53886
\(254\) −2.51777e6 −2.44868
\(255\) −534777. −0.515018
\(256\) 1.13406e6 1.08153
\(257\) 607070. 0.573331 0.286666 0.958031i \(-0.407453\pi\)
0.286666 + 0.958031i \(0.407453\pi\)
\(258\) 188428. 0.176237
\(259\) −1.73740e6 −1.60935
\(260\) −55378.9 −0.0508055
\(261\) −333477. −0.303015
\(262\) −2.07197e6 −1.86479
\(263\) 169221. 0.150856 0.0754282 0.997151i \(-0.475968\pi\)
0.0754282 + 0.997151i \(0.475968\pi\)
\(264\) −64393.4 −0.0568632
\(265\) 1.68796e6 1.47655
\(266\) −2.12540e6 −1.84177
\(267\) 630918. 0.541620
\(268\) 2.04311e6 1.73762
\(269\) 1.41683e6 1.19382 0.596908 0.802310i \(-0.296396\pi\)
0.596908 + 0.802310i \(0.296396\pi\)
\(270\) −2.59563e6 −2.16687
\(271\) 947582. 0.783779 0.391889 0.920012i \(-0.371822\pi\)
0.391889 + 0.920012i \(0.371822\pi\)
\(272\) 556660. 0.456213
\(273\) 50486.9 0.0409989
\(274\) −164866. −0.132665
\(275\) 1.44991e6 1.15614
\(276\) −1.36552e6 −1.07901
\(277\) 37913.3 0.0296888 0.0148444 0.999890i \(-0.495275\pi\)
0.0148444 + 0.999890i \(0.495275\pi\)
\(278\) −1.44413e6 −1.12072
\(279\) 307482. 0.236488
\(280\) 151604. 0.115562
\(281\) −2.05268e6 −1.55080 −0.775400 0.631471i \(-0.782452\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(282\) 2.46146e6 1.84319
\(283\) −2.35101e6 −1.74497 −0.872487 0.488636i \(-0.837494\pi\)
−0.872487 + 0.488636i \(0.837494\pi\)
\(284\) −307000. −0.225861
\(285\) 1.59724e6 1.16482
\(286\) −81380.2 −0.0588307
\(287\) 2.82807e6 2.02668
\(288\) 623547. 0.442984
\(289\) −1.14756e6 −0.808220
\(290\) 2.72269e6 1.90109
\(291\) 1.19881e6 0.829882
\(292\) 983727. 0.675177
\(293\) 1.11432e6 0.758300 0.379150 0.925335i \(-0.376216\pi\)
0.379150 + 0.925335i \(0.376216\pi\)
\(294\) 1.31449e6 0.886931
\(295\) −2.05680e6 −1.37606
\(296\) −111438. −0.0739269
\(297\) −1.86460e6 −1.22657
\(298\) 3.78567e6 2.46946
\(299\) 78789.7 0.0509673
\(300\) 1.26368e6 0.810654
\(301\) −318682. −0.202741
\(302\) 1.93732e6 1.22232
\(303\) 605418. 0.378834
\(304\) −1.66260e6 −1.03182
\(305\) 2.27386e6 1.39963
\(306\) 318363. 0.194365
\(307\) −1.15903e6 −0.701854 −0.350927 0.936403i \(-0.614134\pi\)
−0.350927 + 0.936403i \(0.614134\pi\)
\(308\) −2.38538e6 −1.43278
\(309\) −663183. −0.395127
\(310\) −2.51045e6 −1.48371
\(311\) −1.18671e6 −0.695736 −0.347868 0.937543i \(-0.613094\pi\)
−0.347868 + 0.937543i \(0.613094\pi\)
\(312\) 3238.26 0.00188332
\(313\) 571287. 0.329605 0.164802 0.986327i \(-0.447301\pi\)
0.164802 + 0.986327i \(0.447301\pi\)
\(314\) 102780. 0.0588282
\(315\) 1.05745e6 0.600457
\(316\) −670610. −0.377792
\(317\) −796360. −0.445104 −0.222552 0.974921i \(-0.571439\pi\)
−0.222552 + 0.974921i \(0.571439\pi\)
\(318\) 2.16190e6 1.19886
\(319\) 1.95587e6 1.07613
\(320\) −2.37484e6 −1.29646
\(321\) 957379. 0.518587
\(322\) 4.72433e6 2.53922
\(323\) −813292. −0.433751
\(324\) −1.05170e6 −0.556580
\(325\) −72914.0 −0.0382915
\(326\) 347080. 0.180878
\(327\) −2.63748e6 −1.36402
\(328\) 181394. 0.0930975
\(329\) −4.16297e6 −2.12038
\(330\) 3.66709e6 1.85369
\(331\) −390295. −0.195805 −0.0979023 0.995196i \(-0.531213\pi\)
−0.0979023 + 0.995196i \(0.531213\pi\)
\(332\) −2.04373e6 −1.01760
\(333\) −777285. −0.384122
\(334\) 3.59913e6 1.76535
\(335\) 5.31212e6 2.58616
\(336\) 2.36809e6 1.14433
\(337\) 765533. 0.367189 0.183594 0.983002i \(-0.441227\pi\)
0.183594 + 0.983002i \(0.441227\pi\)
\(338\) −2.93365e6 −1.39674
\(339\) 1.62114e6 0.766162
\(340\) −1.27064e6 −0.596108
\(341\) −1.80341e6 −0.839863
\(342\) −950868. −0.439597
\(343\) 673595. 0.309146
\(344\) −20440.4 −0.00931309
\(345\) −3.55036e6 −1.60592
\(346\) −5.13658e6 −2.30666
\(347\) −1.47170e6 −0.656140 −0.328070 0.944653i \(-0.606398\pi\)
−0.328070 + 0.944653i \(0.606398\pi\)
\(348\) 1.70466e6 0.754554
\(349\) 3.61738e6 1.58975 0.794877 0.606770i \(-0.207535\pi\)
0.794877 + 0.606770i \(0.207535\pi\)
\(350\) −4.37202e6 −1.90771
\(351\) 93768.2 0.0406245
\(352\) −3.65716e6 −1.57321
\(353\) 500946. 0.213971 0.106985 0.994261i \(-0.465880\pi\)
0.106985 + 0.994261i \(0.465880\pi\)
\(354\) −2.63430e6 −1.11727
\(355\) −798203. −0.336157
\(356\) 1.49907e6 0.626898
\(357\) 1.15840e6 0.481046
\(358\) −4.51650e6 −1.86249
\(359\) −3.84739e6 −1.57554 −0.787770 0.615969i \(-0.788765\pi\)
−0.787770 + 0.615969i \(0.788765\pi\)
\(360\) 67825.1 0.0275825
\(361\) −47002.6 −0.0189825
\(362\) −717987. −0.287968
\(363\) 559973. 0.223049
\(364\) 119958. 0.0474542
\(365\) 2.55770e6 1.00489
\(366\) 2.91230e6 1.13641
\(367\) 2.28572e6 0.885844 0.442922 0.896560i \(-0.353942\pi\)
0.442922 + 0.896560i \(0.353942\pi\)
\(368\) 3.69563e6 1.42256
\(369\) 1.26523e6 0.483732
\(370\) 6.34618e6 2.40995
\(371\) −3.65634e6 −1.37915
\(372\) −1.57178e6 −0.588891
\(373\) −753658. −0.280480 −0.140240 0.990118i \(-0.544787\pi\)
−0.140240 + 0.990118i \(0.544787\pi\)
\(374\) −1.86723e6 −0.690268
\(375\) 83022.3 0.0304871
\(376\) −267015. −0.0974017
\(377\) −98358.3 −0.0356416
\(378\) 5.62246e6 2.02394
\(379\) −3.54911e6 −1.26917 −0.634587 0.772851i \(-0.718830\pi\)
−0.634587 + 0.772851i \(0.718830\pi\)
\(380\) 3.79507e6 1.34822
\(381\) −4.09857e6 −1.44650
\(382\) −4.32737e6 −1.51728
\(383\) 2.29101e6 0.798049 0.399025 0.916940i \(-0.369349\pi\)
0.399025 + 0.916940i \(0.369349\pi\)
\(384\) 291327. 0.100821
\(385\) −6.20202e6 −2.13246
\(386\) 198314. 0.0677464
\(387\) −142573. −0.0483906
\(388\) 2.84838e6 0.960547
\(389\) 3.75998e6 1.25983 0.629914 0.776665i \(-0.283090\pi\)
0.629914 + 0.776665i \(0.283090\pi\)
\(390\) −184413. −0.0613946
\(391\) 1.80779e6 0.598006
\(392\) −142594. −0.0468691
\(393\) −3.37287e6 −1.10158
\(394\) 4.58393e6 1.48764
\(395\) −1.74359e6 −0.562280
\(396\) −1.06718e6 −0.341980
\(397\) 5.66320e6 1.80337 0.901686 0.432392i \(-0.142330\pi\)
0.901686 + 0.432392i \(0.142330\pi\)
\(398\) 3.25448e6 1.02985
\(399\) −3.45983e6 −1.08799
\(400\) −3.42004e6 −1.06876
\(401\) 3.53734e6 1.09854 0.549270 0.835645i \(-0.314906\pi\)
0.549270 + 0.835645i \(0.314906\pi\)
\(402\) 6.80362e6 2.09979
\(403\) 90691.1 0.0278165
\(404\) 1.43848e6 0.438481
\(405\) −2.73442e6 −0.828377
\(406\) −5.89769e6 −1.77569
\(407\) 4.55885e6 1.36417
\(408\) 74300.1 0.0220973
\(409\) −2.11034e6 −0.623798 −0.311899 0.950115i \(-0.600965\pi\)
−0.311899 + 0.950115i \(0.600965\pi\)
\(410\) −1.03301e7 −3.03489
\(411\) −268378. −0.0783688
\(412\) −1.57573e6 −0.457340
\(413\) 4.45529e6 1.28529
\(414\) 2.11359e6 0.606066
\(415\) −5.31372e6 −1.51453
\(416\) 183914. 0.0521052
\(417\) −2.35084e6 −0.662038
\(418\) 5.57693e6 1.56119
\(419\) 896357. 0.249428 0.124714 0.992193i \(-0.460199\pi\)
0.124714 + 0.992193i \(0.460199\pi\)
\(420\) −5.40544e6 −1.49523
\(421\) 4.09292e6 1.12545 0.562727 0.826643i \(-0.309752\pi\)
0.562727 + 0.826643i \(0.309752\pi\)
\(422\) −3.05080e6 −0.833935
\(423\) −1.86245e6 −0.506096
\(424\) −234520. −0.0633526
\(425\) −1.67297e6 −0.449280
\(426\) −1.02232e6 −0.272937
\(427\) −4.92547e6 −1.30731
\(428\) 2.27475e6 0.600238
\(429\) −132475. −0.0347529
\(430\) 1.16405e6 0.303598
\(431\) −1.18319e6 −0.306804 −0.153402 0.988164i \(-0.549023\pi\)
−0.153402 + 0.988164i \(0.549023\pi\)
\(432\) 4.39820e6 1.13388
\(433\) 1.63492e6 0.419061 0.209530 0.977802i \(-0.432806\pi\)
0.209530 + 0.977802i \(0.432806\pi\)
\(434\) 5.43796e6 1.38583
\(435\) 4.43214e6 1.12303
\(436\) −6.26668e6 −1.57878
\(437\) −5.39940e6 −1.35251
\(438\) 3.27584e6 0.815901
\(439\) −2.23900e6 −0.554488 −0.277244 0.960800i \(-0.589421\pi\)
−0.277244 + 0.960800i \(0.589421\pi\)
\(440\) −397801. −0.0979566
\(441\) −994603. −0.243531
\(442\) 93900.4 0.0228619
\(443\) 4.42567e6 1.07144 0.535722 0.844394i \(-0.320039\pi\)
0.535722 + 0.844394i \(0.320039\pi\)
\(444\) 3.97331e6 0.956522
\(445\) 3.89760e6 0.933034
\(446\) −8.21339e6 −1.95517
\(447\) 6.16252e6 1.45878
\(448\) 5.14421e6 1.21094
\(449\) 824623. 0.193037 0.0965183 0.995331i \(-0.469229\pi\)
0.0965183 + 0.995331i \(0.469229\pi\)
\(450\) −1.95597e6 −0.455336
\(451\) −7.42071e6 −1.71792
\(452\) 3.85184e6 0.886794
\(453\) 3.15368e6 0.722057
\(454\) 9.02034e6 2.05392
\(455\) 311891. 0.0706276
\(456\) −221916. −0.0499776
\(457\) 4.78062e6 1.07076 0.535382 0.844610i \(-0.320168\pi\)
0.535382 + 0.844610i \(0.320168\pi\)
\(458\) 4.34379e6 0.967621
\(459\) 2.15146e6 0.476652
\(460\) −8.43570e6 −1.85877
\(461\) 177573. 0.0389157 0.0194578 0.999811i \(-0.493806\pi\)
0.0194578 + 0.999811i \(0.493806\pi\)
\(462\) −7.94339e6 −1.73141
\(463\) 8.24149e6 1.78671 0.893353 0.449355i \(-0.148346\pi\)
0.893353 + 0.449355i \(0.148346\pi\)
\(464\) −4.61350e6 −0.994800
\(465\) −4.08665e6 −0.876466
\(466\) −8.79856e6 −1.87692
\(467\) 2.93483e6 0.622718 0.311359 0.950292i \(-0.399216\pi\)
0.311359 + 0.950292i \(0.399216\pi\)
\(468\) 53667.1 0.0113265
\(469\) −1.15067e7 −2.41557
\(470\) 1.52061e7 3.17521
\(471\) 167311. 0.0347514
\(472\) 285765. 0.0590410
\(473\) 836205. 0.171854
\(474\) −2.23315e6 −0.456533
\(475\) 4.99675e6 1.01614
\(476\) 2.75236e6 0.556786
\(477\) −1.63579e6 −0.329178
\(478\) −1.01329e7 −2.02845
\(479\) 7.53163e6 1.49986 0.749929 0.661518i \(-0.230088\pi\)
0.749929 + 0.661518i \(0.230088\pi\)
\(480\) −8.28738e6 −1.64178
\(481\) −229258. −0.0451817
\(482\) 5.73651e6 1.12468
\(483\) 7.69053e6 1.49999
\(484\) 1.33050e6 0.258168
\(485\) 7.40582e6 1.42961
\(486\) 4.42489e6 0.849790
\(487\) −2.30284e6 −0.439988 −0.219994 0.975501i \(-0.570604\pi\)
−0.219994 + 0.975501i \(0.570604\pi\)
\(488\) −315922. −0.0600525
\(489\) 564995. 0.106849
\(490\) 8.12049e6 1.52789
\(491\) 4.43974e6 0.831100 0.415550 0.909570i \(-0.363589\pi\)
0.415550 + 0.909570i \(0.363589\pi\)
\(492\) −6.46760e6 −1.20457
\(493\) −2.25678e6 −0.418188
\(494\) −280456. −0.0517068
\(495\) −2.77468e6 −0.508980
\(496\) 4.25387e6 0.776390
\(497\) 1.72901e6 0.313983
\(498\) −6.80567e6 −1.22970
\(499\) 7.95785e6 1.43069 0.715343 0.698774i \(-0.246271\pi\)
0.715343 + 0.698774i \(0.246271\pi\)
\(500\) 197262. 0.0352873
\(501\) 5.85886e6 1.04284
\(502\) −1.13648e7 −2.01281
\(503\) −4.75804e6 −0.838510 −0.419255 0.907868i \(-0.637709\pi\)
−0.419255 + 0.907868i \(0.637709\pi\)
\(504\) −146918. −0.0257631
\(505\) 3.74007e6 0.652606
\(506\) −1.23964e7 −2.15238
\(507\) −4.77555e6 −0.825095
\(508\) −9.73825e6 −1.67425
\(509\) −5.42576e6 −0.928252 −0.464126 0.885769i \(-0.653632\pi\)
−0.464126 + 0.885769i \(0.653632\pi\)
\(510\) −4.23126e6 −0.720352
\(511\) −5.54031e6 −0.938603
\(512\) 8.24912e6 1.39070
\(513\) −6.42587e6 −1.07805
\(514\) 4.80325e6 0.801914
\(515\) −4.09692e6 −0.680675
\(516\) 728804. 0.120500
\(517\) 1.09234e7 1.79735
\(518\) −1.37466e7 −2.25098
\(519\) −8.36161e6 −1.36261
\(520\) 20004.9 0.00324435
\(521\) −8.88444e6 −1.43396 −0.716978 0.697096i \(-0.754475\pi\)
−0.716978 + 0.697096i \(0.754475\pi\)
\(522\) −2.63853e6 −0.423825
\(523\) −5.03938e6 −0.805606 −0.402803 0.915287i \(-0.631964\pi\)
−0.402803 + 0.915287i \(0.631964\pi\)
\(524\) −8.01397e6 −1.27503
\(525\) −7.11702e6 −1.12694
\(526\) 1.33891e6 0.211002
\(527\) 2.08086e6 0.326374
\(528\) −6.21375e6 −0.969995
\(529\) 5.56545e6 0.864692
\(530\) 1.33555e7 2.06524
\(531\) 1.99323e6 0.306775
\(532\) −8.22061e6 −1.25929
\(533\) 373178. 0.0568981
\(534\) 4.99195e6 0.757560
\(535\) 5.91436e6 0.893354
\(536\) −738047. −0.110961
\(537\) −7.35221e6 −1.10023
\(538\) 1.12102e7 1.66978
\(539\) 5.83344e6 0.864874
\(540\) −1.00394e7 −1.48157
\(541\) 3.49430e6 0.513295 0.256648 0.966505i \(-0.417382\pi\)
0.256648 + 0.966505i \(0.417382\pi\)
\(542\) 7.49745e6 1.09626
\(543\) −1.16878e6 −0.170111
\(544\) 4.21980e6 0.611357
\(545\) −1.62934e7 −2.34975
\(546\) 399462. 0.0573448
\(547\) −2.50382e6 −0.357796 −0.178898 0.983868i \(-0.557253\pi\)
−0.178898 + 0.983868i \(0.557253\pi\)
\(548\) −637671. −0.0907079
\(549\) −2.20358e6 −0.312031
\(550\) 1.14720e7 1.61708
\(551\) 6.74042e6 0.945819
\(552\) 493274. 0.0689034
\(553\) 3.77685e6 0.525190
\(554\) 299977. 0.0415254
\(555\) 1.03307e7 1.42362
\(556\) −5.58563e6 −0.766276
\(557\) −1.53305e6 −0.209371 −0.104686 0.994505i \(-0.533384\pi\)
−0.104686 + 0.994505i \(0.533384\pi\)
\(558\) 2.43286e6 0.330774
\(559\) −42051.7 −0.00569185
\(560\) 1.46293e7 1.97130
\(561\) −3.03957e6 −0.407761
\(562\) −1.62412e7 −2.16909
\(563\) 8.52078e6 1.13294 0.566472 0.824081i \(-0.308308\pi\)
0.566472 + 0.824081i \(0.308308\pi\)
\(564\) 9.52043e6 1.26026
\(565\) 1.00148e7 1.31984
\(566\) −1.86017e7 −2.44068
\(567\) 5.92311e6 0.773734
\(568\) 110900. 0.0144231
\(569\) −429293. −0.0555870 −0.0277935 0.999614i \(-0.508848\pi\)
−0.0277935 + 0.999614i \(0.508848\pi\)
\(570\) 1.26377e7 1.62922
\(571\) −6.30376e6 −0.809114 −0.404557 0.914513i \(-0.632574\pi\)
−0.404557 + 0.914513i \(0.632574\pi\)
\(572\) −314763. −0.0402247
\(573\) −7.04432e6 −0.896298
\(574\) 2.23762e7 2.83470
\(575\) −1.11068e7 −1.40094
\(576\) 2.30144e6 0.289030
\(577\) −8.10411e6 −1.01337 −0.506683 0.862133i \(-0.669128\pi\)
−0.506683 + 0.862133i \(0.669128\pi\)
\(578\) −9.07969e6 −1.13045
\(579\) 322827. 0.0400197
\(580\) 1.05308e7 1.29985
\(581\) 1.15102e7 1.41463
\(582\) 9.48519e6 1.16075
\(583\) 9.59405e6 1.16904
\(584\) −355358. −0.0431156
\(585\) 139535. 0.0168575
\(586\) 8.81672e6 1.06063
\(587\) 5.93951e6 0.711468 0.355734 0.934587i \(-0.384231\pi\)
0.355734 + 0.934587i \(0.384231\pi\)
\(588\) 5.08420e6 0.606428
\(589\) −6.21499e6 −0.738163
\(590\) −1.62738e7 −1.92468
\(591\) 7.46197e6 0.878789
\(592\) −1.07534e7 −1.26107
\(593\) −1.03054e6 −0.120345 −0.0601727 0.998188i \(-0.519165\pi\)
−0.0601727 + 0.998188i \(0.519165\pi\)
\(594\) −1.47531e7 −1.71560
\(595\) 7.15618e6 0.828684
\(596\) 1.46422e7 1.68846
\(597\) 5.29781e6 0.608360
\(598\) 623399. 0.0712875
\(599\) 8.75551e6 0.997044 0.498522 0.866877i \(-0.333876\pi\)
0.498522 + 0.866877i \(0.333876\pi\)
\(600\) −456489. −0.0517669
\(601\) −6.36534e6 −0.718845 −0.359423 0.933175i \(-0.617026\pi\)
−0.359423 + 0.933175i \(0.617026\pi\)
\(602\) −2.52147e6 −0.283572
\(603\) −5.14792e6 −0.576552
\(604\) 7.49318e6 0.835745
\(605\) 3.45932e6 0.384240
\(606\) 4.79019e6 0.529872
\(607\) 1.44657e7 1.59356 0.796779 0.604270i \(-0.206535\pi\)
0.796779 + 0.604270i \(0.206535\pi\)
\(608\) −1.26035e7 −1.38271
\(609\) −9.60058e6 −1.04895
\(610\) 1.79912e7 1.95766
\(611\) −549325. −0.0595287
\(612\) 1.23136e6 0.132895
\(613\) −1.78097e7 −1.91428 −0.957142 0.289619i \(-0.906471\pi\)
−0.957142 + 0.289619i \(0.906471\pi\)
\(614\) −9.17043e6 −0.981678
\(615\) −1.68158e7 −1.79279
\(616\) 861687. 0.0914951
\(617\) 4.11393e6 0.435054 0.217527 0.976054i \(-0.430201\pi\)
0.217527 + 0.976054i \(0.430201\pi\)
\(618\) −5.24723e6 −0.552661
\(619\) −3.56813e6 −0.374295 −0.187148 0.982332i \(-0.559924\pi\)
−0.187148 + 0.982332i \(0.559924\pi\)
\(620\) −9.70993e6 −1.01446
\(621\) 1.42834e7 1.48629
\(622\) −9.38950e6 −0.973120
\(623\) −8.44270e6 −0.871488
\(624\) 312482. 0.0321265
\(625\) −9.50590e6 −0.973404
\(626\) 4.52013e6 0.461015
\(627\) 9.07843e6 0.922235
\(628\) 397534. 0.0402230
\(629\) −5.26021e6 −0.530123
\(630\) 8.36672e6 0.839854
\(631\) 8.10764e6 0.810627 0.405314 0.914178i \(-0.367162\pi\)
0.405314 + 0.914178i \(0.367162\pi\)
\(632\) 242249. 0.0241251
\(633\) −4.96625e6 −0.492629
\(634\) −6.30095e6 −0.622562
\(635\) −2.53196e7 −2.49185
\(636\) 8.36180e6 0.819704
\(637\) −293356. −0.0286448
\(638\) 1.54752e7 1.50517
\(639\) 773531. 0.0749421
\(640\) 1.79972e6 0.173682
\(641\) 1.15748e7 1.11267 0.556335 0.830958i \(-0.312207\pi\)
0.556335 + 0.830958i \(0.312207\pi\)
\(642\) 7.57497e6 0.725343
\(643\) −865667. −0.0825702 −0.0412851 0.999147i \(-0.513145\pi\)
−0.0412851 + 0.999147i \(0.513145\pi\)
\(644\) 1.82728e7 1.73616
\(645\) 1.89490e6 0.179344
\(646\) −6.43493e6 −0.606684
\(647\) −3.32273e6 −0.312057 −0.156029 0.987753i \(-0.549869\pi\)
−0.156029 + 0.987753i \(0.549869\pi\)
\(648\) 379911. 0.0355422
\(649\) −1.16904e7 −1.08948
\(650\) −576910. −0.0535580
\(651\) 8.85220e6 0.818651
\(652\) 1.34244e6 0.123673
\(653\) −1.42689e7 −1.30951 −0.654754 0.755842i \(-0.727228\pi\)
−0.654754 + 0.755842i \(0.727228\pi\)
\(654\) −2.08682e7 −1.90784
\(655\) −2.08364e7 −1.89767
\(656\) 1.75039e7 1.58809
\(657\) −2.47865e6 −0.224027
\(658\) −3.29382e7 −2.96576
\(659\) −1.73298e6 −0.155446 −0.0777230 0.996975i \(-0.524765\pi\)
−0.0777230 + 0.996975i \(0.524765\pi\)
\(660\) 1.41836e7 1.26744
\(661\) 456270. 0.0406180 0.0203090 0.999794i \(-0.493535\pi\)
0.0203090 + 0.999794i \(0.493535\pi\)
\(662\) −3.08809e6 −0.273870
\(663\) 152856. 0.0135051
\(664\) 738269. 0.0649822
\(665\) −2.13737e7 −1.87424
\(666\) −6.15003e6 −0.537269
\(667\) −1.49826e7 −1.30399
\(668\) 1.39207e7 1.20704
\(669\) −1.33702e7 −1.15498
\(670\) 4.20305e7 3.61724
\(671\) 1.29242e7 1.10815
\(672\) 1.79515e7 1.53348
\(673\) −1.34881e7 −1.14793 −0.573963 0.818881i \(-0.694595\pi\)
−0.573963 + 0.818881i \(0.694595\pi\)
\(674\) 6.05705e6 0.513584
\(675\) −1.32183e7 −1.11664
\(676\) −1.13468e7 −0.955005
\(677\) 1.96810e7 1.65035 0.825174 0.564879i \(-0.191077\pi\)
0.825174 + 0.564879i \(0.191077\pi\)
\(678\) 1.28268e7 1.07162
\(679\) −1.60420e7 −1.33531
\(680\) 459001. 0.0380664
\(681\) 1.46838e7 1.21331
\(682\) −1.42689e7 −1.17471
\(683\) 6.25887e6 0.513386 0.256693 0.966493i \(-0.417367\pi\)
0.256693 + 0.966493i \(0.417367\pi\)
\(684\) −3.67777e6 −0.300569
\(685\) −1.65795e6 −0.135004
\(686\) 5.32962e6 0.432400
\(687\) 7.07106e6 0.571600
\(688\) −1.97244e6 −0.158866
\(689\) −482472. −0.0387190
\(690\) −2.80911e7 −2.24619
\(691\) 3.10391e6 0.247295 0.123647 0.992326i \(-0.460541\pi\)
0.123647 + 0.992326i \(0.460541\pi\)
\(692\) −1.98673e7 −1.57715
\(693\) 6.01032e6 0.475406
\(694\) −1.16444e7 −0.917738
\(695\) −1.45227e7 −1.14047
\(696\) −615786. −0.0481845
\(697\) 8.56236e6 0.667593
\(698\) 2.86214e7 2.22358
\(699\) −1.43228e7 −1.10875
\(700\) −1.69101e7 −1.30437
\(701\) 5.25605e6 0.403984 0.201992 0.979387i \(-0.435258\pi\)
0.201992 + 0.979387i \(0.435258\pi\)
\(702\) 741912. 0.0568211
\(703\) 1.57109e7 1.19898
\(704\) −1.34981e7 −1.02646
\(705\) 2.47532e7 1.87568
\(706\) 3.96358e6 0.299279
\(707\) −8.10147e6 −0.609558
\(708\) −1.01889e7 −0.763916
\(709\) 8.29295e6 0.619574 0.309787 0.950806i \(-0.399742\pi\)
0.309787 + 0.950806i \(0.399742\pi\)
\(710\) −6.31554e6 −0.470180
\(711\) 1.68970e6 0.125353
\(712\) −541519. −0.0400326
\(713\) 1.38147e7 1.01770
\(714\) 9.16545e6 0.672835
\(715\) −818387. −0.0598678
\(716\) −1.74689e7 −1.27346
\(717\) −1.64949e7 −1.19826
\(718\) −3.04413e7 −2.20370
\(719\) 3.71146e6 0.267746 0.133873 0.990999i \(-0.457259\pi\)
0.133873 + 0.990999i \(0.457259\pi\)
\(720\) 6.54491e6 0.470514
\(721\) 8.87445e6 0.635775
\(722\) −371894. −0.0265507
\(723\) 9.33821e6 0.664382
\(724\) −2.77703e6 −0.196895
\(725\) 1.38653e7 0.979681
\(726\) 4.43061e6 0.311977
\(727\) −3.10084e6 −0.217592 −0.108796 0.994064i \(-0.534700\pi\)
−0.108796 + 0.994064i \(0.534700\pi\)
\(728\) −43333.1 −0.00303034
\(729\) 1.55540e7 1.08399
\(730\) 2.02370e7 1.40553
\(731\) −964853. −0.0667833
\(732\) 1.12642e7 0.777004
\(733\) −1.69858e7 −1.16769 −0.583844 0.811866i \(-0.698452\pi\)
−0.583844 + 0.811866i \(0.698452\pi\)
\(734\) 1.80850e7 1.23902
\(735\) 1.32190e7 0.902567
\(736\) 2.80150e7 1.90632
\(737\) 3.01930e7 2.04757
\(738\) 1.00108e7 0.676591
\(739\) 1.13197e7 0.762473 0.381236 0.924478i \(-0.375498\pi\)
0.381236 + 0.924478i \(0.375498\pi\)
\(740\) 2.45458e7 1.64777
\(741\) −456542. −0.0305447
\(742\) −2.89297e7 −1.92901
\(743\) −9.42589e6 −0.626398 −0.313199 0.949688i \(-0.601401\pi\)
−0.313199 + 0.949688i \(0.601401\pi\)
\(744\) 567785. 0.0376055
\(745\) 3.80699e7 2.51299
\(746\) −5.96309e6 −0.392305
\(747\) 5.14947e6 0.337646
\(748\) −7.22206e6 −0.471962
\(749\) −1.28113e7 −0.834425
\(750\) 656888. 0.0426421
\(751\) −3.73658e6 −0.241754 −0.120877 0.992667i \(-0.538571\pi\)
−0.120877 + 0.992667i \(0.538571\pi\)
\(752\) −2.57661e7 −1.66152
\(753\) −1.85002e7 −1.18902
\(754\) −778230. −0.0498516
\(755\) 1.94824e7 1.24387
\(756\) 2.17466e7 1.38384
\(757\) 1.39033e7 0.881815 0.440908 0.897552i \(-0.354657\pi\)
0.440908 + 0.897552i \(0.354657\pi\)
\(758\) −2.80812e7 −1.77518
\(759\) −2.01795e7 −1.27147
\(760\) −1.37092e6 −0.0860950
\(761\) −2.95291e7 −1.84837 −0.924185 0.381946i \(-0.875254\pi\)
−0.924185 + 0.381946i \(0.875254\pi\)
\(762\) −3.24286e7 −2.02321
\(763\) 3.52937e7 2.19475
\(764\) −1.67374e7 −1.03742
\(765\) 3.20156e6 0.197792
\(766\) 1.81269e7 1.11622
\(767\) 587897. 0.0360839
\(768\) 1.46066e7 0.893606
\(769\) −9.04293e6 −0.551434 −0.275717 0.961239i \(-0.588915\pi\)
−0.275717 + 0.961239i \(0.588915\pi\)
\(770\) −4.90716e7 −2.98265
\(771\) 7.81899e6 0.473713
\(772\) 767041. 0.0463207
\(773\) −661253. −0.0398033 −0.0199016 0.999802i \(-0.506335\pi\)
−0.0199016 + 0.999802i \(0.506335\pi\)
\(774\) −1.12807e6 −0.0676834
\(775\) −1.27845e7 −0.764591
\(776\) −1.02894e6 −0.0613388
\(777\) −2.23775e7 −1.32972
\(778\) 2.97497e7 1.76211
\(779\) −2.55736e7 −1.50990
\(780\) −713274. −0.0419778
\(781\) −4.53683e6 −0.266149
\(782\) 1.43036e7 0.836426
\(783\) −1.78309e7 −1.03937
\(784\) −1.37599e7 −0.799511
\(785\) 1.03359e6 0.0598653
\(786\) −2.66868e7 −1.54078
\(787\) −6.46523e6 −0.372089 −0.186045 0.982541i \(-0.559567\pi\)
−0.186045 + 0.982541i \(0.559567\pi\)
\(788\) 1.77297e7 1.01715
\(789\) 2.17954e6 0.124644
\(790\) −1.37957e7 −0.786456
\(791\) −2.16934e7 −1.23278
\(792\) 385505. 0.0218382
\(793\) −649940. −0.0367021
\(794\) 4.48083e7 2.52236
\(795\) 2.17408e7 1.21999
\(796\) 1.25877e7 0.704146
\(797\) 2.62978e7 1.46647 0.733234 0.679976i \(-0.238010\pi\)
0.733234 + 0.679976i \(0.238010\pi\)
\(798\) −2.73749e7 −1.52176
\(799\) −1.26040e7 −0.698458
\(800\) −2.59259e7 −1.43222
\(801\) −3.77713e6 −0.208008
\(802\) 2.79881e7 1.53652
\(803\) 1.45375e7 0.795610
\(804\) 2.63151e7 1.43570
\(805\) 4.75095e7 2.58399
\(806\) 717565. 0.0389066
\(807\) 1.82486e7 0.986385
\(808\) −519632. −0.0280006
\(809\) −9.92533e6 −0.533180 −0.266590 0.963810i \(-0.585897\pi\)
−0.266590 + 0.963810i \(0.585897\pi\)
\(810\) −2.16353e7 −1.15864
\(811\) 1.86128e7 0.993712 0.496856 0.867833i \(-0.334488\pi\)
0.496856 + 0.867833i \(0.334488\pi\)
\(812\) −2.28111e7 −1.21411
\(813\) 1.22048e7 0.647594
\(814\) 3.60705e7 1.90805
\(815\) 3.49035e6 0.184066
\(816\) 7.16972e6 0.376944
\(817\) 2.88177e6 0.151044
\(818\) −1.66974e7 −0.872501
\(819\) −302251. −0.0157456
\(820\) −3.99546e7 −2.07507
\(821\) 1.08487e7 0.561718 0.280859 0.959749i \(-0.409381\pi\)
0.280859 + 0.959749i \(0.409381\pi\)
\(822\) −2.12346e6 −0.109614
\(823\) −1.29473e7 −0.666316 −0.333158 0.942871i \(-0.608114\pi\)
−0.333158 + 0.942871i \(0.608114\pi\)
\(824\) 569212. 0.0292049
\(825\) 1.86747e7 0.955253
\(826\) 3.52511e7 1.79772
\(827\) 2.79589e7 1.42153 0.710767 0.703428i \(-0.248348\pi\)
0.710767 + 0.703428i \(0.248348\pi\)
\(828\) 8.17496e6 0.414390
\(829\) −1.95464e7 −0.987825 −0.493913 0.869512i \(-0.664434\pi\)
−0.493913 + 0.869512i \(0.664434\pi\)
\(830\) −4.20432e7 −2.11836
\(831\) 488319. 0.0245302
\(832\) 678803. 0.0339966
\(833\) −6.73090e6 −0.336094
\(834\) −1.86003e7 −0.925987
\(835\) 3.61940e7 1.79647
\(836\) 2.15705e7 1.06744
\(837\) 1.64410e7 0.811174
\(838\) 7.09215e6 0.348873
\(839\) 1.66180e7 0.815031 0.407516 0.913198i \(-0.366395\pi\)
0.407516 + 0.913198i \(0.366395\pi\)
\(840\) 1.95264e6 0.0954826
\(841\) −1.80736e6 −0.0881161
\(842\) 3.23840e7 1.57416
\(843\) −2.64383e7 −1.28134
\(844\) −1.17999e7 −0.570193
\(845\) −2.95018e7 −1.42137
\(846\) −1.47360e7 −0.707873
\(847\) −7.49334e6 −0.358894
\(848\) −2.26304e7 −1.08069
\(849\) −3.02808e7 −1.44178
\(850\) −1.32369e7 −0.628404
\(851\) −3.49222e7 −1.65302
\(852\) −3.95412e6 −0.186617
\(853\) −1.69144e7 −0.795947 −0.397974 0.917397i \(-0.630286\pi\)
−0.397974 + 0.917397i \(0.630286\pi\)
\(854\) −3.89713e7 −1.82852
\(855\) −9.56225e6 −0.447347
\(856\) −821721. −0.0383301
\(857\) 767365. 0.0356903 0.0178451 0.999841i \(-0.494319\pi\)
0.0178451 + 0.999841i \(0.494319\pi\)
\(858\) −1.04817e6 −0.0486086
\(859\) 1.25709e7 0.581278 0.290639 0.956833i \(-0.406132\pi\)
0.290639 + 0.956833i \(0.406132\pi\)
\(860\) 4.50230e6 0.207581
\(861\) 3.64252e7 1.67454
\(862\) −9.36163e6 −0.429124
\(863\) 4.15225e6 0.189783 0.0948913 0.995488i \(-0.469750\pi\)
0.0948913 + 0.995488i \(0.469750\pi\)
\(864\) 3.33409e7 1.51947
\(865\) −5.16552e7 −2.34733
\(866\) 1.29358e7 0.586137
\(867\) −1.47804e7 −0.667788
\(868\) 2.10329e7 0.947547
\(869\) −9.91025e6 −0.445180
\(870\) 3.50680e7 1.57077
\(871\) −1.51837e6 −0.0678159
\(872\) 2.26375e6 0.100818
\(873\) −7.17691e6 −0.318715
\(874\) −4.27211e7 −1.89175
\(875\) −1.11097e6 −0.0490549
\(876\) 1.26703e7 0.557862
\(877\) −2.05982e6 −0.0904337 −0.0452168 0.998977i \(-0.514398\pi\)
−0.0452168 + 0.998977i \(0.514398\pi\)
\(878\) −1.77154e7 −0.775558
\(879\) 1.43523e7 0.626542
\(880\) −3.83865e7 −1.67098
\(881\) 3.31902e6 0.144069 0.0720345 0.997402i \(-0.477051\pi\)
0.0720345 + 0.997402i \(0.477051\pi\)
\(882\) −7.86949e6 −0.340624
\(883\) 3.88804e6 0.167814 0.0839071 0.996474i \(-0.473260\pi\)
0.0839071 + 0.996474i \(0.473260\pi\)
\(884\) 363188. 0.0156315
\(885\) −2.64914e7 −1.13696
\(886\) 3.50168e7 1.49862
\(887\) −4.11225e6 −0.175497 −0.0877486 0.996143i \(-0.527967\pi\)
−0.0877486 + 0.996143i \(0.527967\pi\)
\(888\) −1.43531e6 −0.0610818
\(889\) 5.48454e7 2.32748
\(890\) 3.08386e7 1.30503
\(891\) −1.55419e7 −0.655859
\(892\) −3.17678e7 −1.33683
\(893\) 3.76448e7 1.57971
\(894\) 4.87590e7 2.04038
\(895\) −4.54195e7 −1.89533
\(896\) −3.89843e6 −0.162226
\(897\) 1.01480e6 0.0421115
\(898\) 6.52458e6 0.269999
\(899\) −1.72458e7 −0.711679
\(900\) −7.56532e6 −0.311330
\(901\) −1.10701e7 −0.454295
\(902\) −5.87141e7 −2.40285
\(903\) −4.10459e6 −0.167514
\(904\) −1.39143e6 −0.0566291
\(905\) −7.22031e6 −0.293045
\(906\) 2.49525e7 1.00994
\(907\) −4.04945e7 −1.63447 −0.817236 0.576303i \(-0.804495\pi\)
−0.817236 + 0.576303i \(0.804495\pi\)
\(908\) 3.48889e7 1.40434
\(909\) −3.62447e6 −0.145490
\(910\) 2.46774e6 0.0987863
\(911\) −3.27575e7 −1.30772 −0.653860 0.756615i \(-0.726852\pi\)
−0.653860 + 0.756615i \(0.726852\pi\)
\(912\) −2.14141e7 −0.852538
\(913\) −3.02021e7 −1.19911
\(914\) 3.78252e7 1.49767
\(915\) 2.92871e7 1.15644
\(916\) 1.68009e7 0.661599
\(917\) 4.51343e7 1.77249
\(918\) 1.70228e7 0.666690
\(919\) −8.68701e6 −0.339298 −0.169649 0.985505i \(-0.554263\pi\)
−0.169649 + 0.985505i \(0.554263\pi\)
\(920\) 3.04728e6 0.118698
\(921\) −1.49281e7 −0.579904
\(922\) 1.40499e6 0.0544310
\(923\) 228151. 0.00881492
\(924\) −3.07235e7 −1.18383
\(925\) 3.23180e7 1.24191
\(926\) 6.52083e7 2.49905
\(927\) 3.97029e6 0.151748
\(928\) −3.49730e7 −1.33310
\(929\) −6.29057e6 −0.239139 −0.119570 0.992826i \(-0.538151\pi\)
−0.119570 + 0.992826i \(0.538151\pi\)
\(930\) −3.23344e7 −1.22590
\(931\) 2.01035e7 0.760146
\(932\) −3.40311e7 −1.28332
\(933\) −1.52847e7 −0.574849
\(934\) 2.32210e7 0.870990
\(935\) −1.87775e7 −0.702437
\(936\) −19386.5 −0.000723287 0
\(937\) −6.97275e6 −0.259451 −0.129725 0.991550i \(-0.541410\pi\)
−0.129725 + 0.991550i \(0.541410\pi\)
\(938\) −9.10434e7 −3.37863
\(939\) 7.35812e6 0.272335
\(940\) 5.88140e7 2.17101
\(941\) 1.67294e7 0.615894 0.307947 0.951404i \(-0.400358\pi\)
0.307947 + 0.951404i \(0.400358\pi\)
\(942\) 1.32380e6 0.0486065
\(943\) 5.68450e7 2.08168
\(944\) 2.75754e7 1.00714
\(945\) 5.65414e7 2.05962
\(946\) 6.61622e6 0.240371
\(947\) −4.20327e7 −1.52304 −0.761522 0.648140i \(-0.775547\pi\)
−0.761522 + 0.648140i \(0.775547\pi\)
\(948\) −8.63739e6 −0.312149
\(949\) −731071. −0.0263508
\(950\) 3.95352e7 1.42127
\(951\) −1.02570e7 −0.367765
\(952\) −994255. −0.0355554
\(953\) 4.38940e7 1.56557 0.782787 0.622290i \(-0.213798\pi\)
0.782787 + 0.622290i \(0.213798\pi\)
\(954\) −1.29427e7 −0.460419
\(955\) −4.35174e7 −1.54403
\(956\) −3.91920e7 −1.38692
\(957\) 2.51914e7 0.889146
\(958\) 5.95917e7 2.09784
\(959\) 3.59133e6 0.126098
\(960\) −3.05877e7 −1.07120
\(961\) −1.27277e7 −0.444571
\(962\) −1.81394e6 −0.0631952
\(963\) −5.73156e6 −0.199162
\(964\) 2.21877e7 0.768989
\(965\) 1.99432e6 0.0689407
\(966\) 6.08489e7 2.09802
\(967\) 1.42055e6 0.0488530 0.0244265 0.999702i \(-0.492224\pi\)
0.0244265 + 0.999702i \(0.492224\pi\)
\(968\) −480626. −0.0164862
\(969\) −1.04751e7 −0.358385
\(970\) 5.85963e7 1.99959
\(971\) −4.66877e7 −1.58911 −0.794556 0.607191i \(-0.792296\pi\)
−0.794556 + 0.607191i \(0.792296\pi\)
\(972\) 1.71146e7 0.581033
\(973\) 3.14580e7 1.06524
\(974\) −1.82205e7 −0.615407
\(975\) −939125. −0.0316382
\(976\) −3.04855e7 −1.02440
\(977\) 5.11806e6 0.171541 0.0857707 0.996315i \(-0.472665\pi\)
0.0857707 + 0.996315i \(0.472665\pi\)
\(978\) 4.47035e6 0.149449
\(979\) 2.21532e7 0.738720
\(980\) 3.14085e7 1.04468
\(981\) 1.57898e7 0.523848
\(982\) 3.51280e7 1.16245
\(983\) −1.29865e6 −0.0428654 −0.0214327 0.999770i \(-0.506823\pi\)
−0.0214327 + 0.999770i \(0.506823\pi\)
\(984\) 2.33633e6 0.0769214
\(985\) 4.60975e7 1.51387
\(986\) −1.78561e7 −0.584916
\(987\) −5.36187e7 −1.75196
\(988\) −1.08475e6 −0.0353539
\(989\) −6.40560e6 −0.208242
\(990\) −2.19538e7 −0.711906
\(991\) 2.92905e7 0.947422 0.473711 0.880680i \(-0.342914\pi\)
0.473711 + 0.880680i \(0.342914\pi\)
\(992\) 3.22468e7 1.04042
\(993\) −5.02696e6 −0.161783
\(994\) 1.36803e7 0.439165
\(995\) 3.27281e7 1.04800
\(996\) −2.63230e7 −0.840789
\(997\) −2.66478e7 −0.849031 −0.424515 0.905421i \(-0.639555\pi\)
−0.424515 + 0.905421i \(0.639555\pi\)
\(998\) 6.29640e7 2.00109
\(999\) −4.15612e7 −1.31757
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 43.6.a.b.1.8 10
3.2 odd 2 387.6.a.e.1.3 10
4.3 odd 2 688.6.a.h.1.5 10
5.4 even 2 1075.6.a.b.1.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.8 10 1.1 even 1 trivial
387.6.a.e.1.3 10 3.2 odd 2
688.6.a.h.1.5 10 4.3 odd 2
1075.6.a.b.1.3 10 5.4 even 2