Properties

Label 245.6.a.a.1.1
Level $245$
Weight $6$
Character 245.1
Self dual yes
Analytic conductor $39.294$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.2940358542\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 245.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.00000 q^{2} -1.00000 q^{3} +32.0000 q^{4} -25.0000 q^{5} +8.00000 q^{6} -242.000 q^{9} +O(q^{10})\) \(q-8.00000 q^{2} -1.00000 q^{3} +32.0000 q^{4} -25.0000 q^{5} +8.00000 q^{6} -242.000 q^{9} +200.000 q^{10} -453.000 q^{11} -32.0000 q^{12} +969.000 q^{13} +25.0000 q^{15} -1024.00 q^{16} -1637.00 q^{17} +1936.00 q^{18} +1550.00 q^{19} -800.000 q^{20} +3624.00 q^{22} -1654.00 q^{23} +625.000 q^{25} -7752.00 q^{26} +485.000 q^{27} -4985.00 q^{29} -200.000 q^{30} -1192.00 q^{31} +8192.00 q^{32} +453.000 q^{33} +13096.0 q^{34} -7744.00 q^{36} -11018.0 q^{37} -12400.0 q^{38} -969.000 q^{39} +1728.00 q^{41} -10814.0 q^{43} -14496.0 q^{44} +6050.00 q^{45} +13232.0 q^{46} -26237.0 q^{47} +1024.00 q^{48} -5000.00 q^{50} +1637.00 q^{51} +31008.0 q^{52} +25936.0 q^{53} -3880.00 q^{54} +11325.0 q^{55} -1550.00 q^{57} +39880.0 q^{58} +4580.00 q^{59} +800.000 q^{60} +12488.0 q^{61} +9536.00 q^{62} -32768.0 q^{64} -24225.0 q^{65} -3624.00 q^{66} -15848.0 q^{67} -52384.0 q^{68} +1654.00 q^{69} +51792.0 q^{71} -4846.00 q^{73} +88144.0 q^{74} -625.000 q^{75} +49600.0 q^{76} +7752.00 q^{78} +62765.0 q^{79} +25600.0 q^{80} +58321.0 q^{81} -13824.0 q^{82} +23644.0 q^{83} +40925.0 q^{85} +86512.0 q^{86} +4985.00 q^{87} +147300. q^{89} -48400.0 q^{90} -52928.0 q^{92} +1192.00 q^{93} +209896. q^{94} -38750.0 q^{95} -8192.00 q^{96} +8343.00 q^{97} +109626. q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) −1.00000 −0.0641500 −0.0320750 0.999485i \(-0.510212\pi\)
−0.0320750 + 0.999485i \(0.510212\pi\)
\(4\) 32.0000 1.00000
\(5\) −25.0000 −0.447214
\(6\) 8.00000 0.0907218
\(7\) 0 0
\(8\) 0 0
\(9\) −242.000 −0.995885
\(10\) 200.000 0.632456
\(11\) −453.000 −1.12880 −0.564399 0.825502i \(-0.690892\pi\)
−0.564399 + 0.825502i \(0.690892\pi\)
\(12\) −32.0000 −0.0641500
\(13\) 969.000 1.59025 0.795125 0.606446i \(-0.207405\pi\)
0.795125 + 0.606446i \(0.207405\pi\)
\(14\) 0 0
\(15\) 25.0000 0.0286888
\(16\) −1024.00 −1.00000
\(17\) −1637.00 −1.37381 −0.686905 0.726748i \(-0.741031\pi\)
−0.686905 + 0.726748i \(0.741031\pi\)
\(18\) 1936.00 1.40839
\(19\) 1550.00 0.985026 0.492513 0.870305i \(-0.336078\pi\)
0.492513 + 0.870305i \(0.336078\pi\)
\(20\) −800.000 −0.447214
\(21\) 0 0
\(22\) 3624.00 1.59636
\(23\) −1654.00 −0.651952 −0.325976 0.945378i \(-0.605693\pi\)
−0.325976 + 0.945378i \(0.605693\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) −7752.00 −2.24895
\(27\) 485.000 0.128036
\(28\) 0 0
\(29\) −4985.00 −1.10070 −0.550352 0.834933i \(-0.685506\pi\)
−0.550352 + 0.834933i \(0.685506\pi\)
\(30\) −200.000 −0.0405720
\(31\) −1192.00 −0.222778 −0.111389 0.993777i \(-0.535530\pi\)
−0.111389 + 0.993777i \(0.535530\pi\)
\(32\) 8192.00 1.41421
\(33\) 453.000 0.0724125
\(34\) 13096.0 1.94286
\(35\) 0 0
\(36\) −7744.00 −0.995885
\(37\) −11018.0 −1.32312 −0.661559 0.749893i \(-0.730105\pi\)
−0.661559 + 0.749893i \(0.730105\pi\)
\(38\) −12400.0 −1.39304
\(39\) −969.000 −0.102015
\(40\) 0 0
\(41\) 1728.00 0.160540 0.0802702 0.996773i \(-0.474422\pi\)
0.0802702 + 0.996773i \(0.474422\pi\)
\(42\) 0 0
\(43\) −10814.0 −0.891898 −0.445949 0.895058i \(-0.647134\pi\)
−0.445949 + 0.895058i \(0.647134\pi\)
\(44\) −14496.0 −1.12880
\(45\) 6050.00 0.445373
\(46\) 13232.0 0.922000
\(47\) −26237.0 −1.73249 −0.866243 0.499624i \(-0.833472\pi\)
−0.866243 + 0.499624i \(0.833472\pi\)
\(48\) 1024.00 0.0641500
\(49\) 0 0
\(50\) −5000.00 −0.282843
\(51\) 1637.00 0.0881299
\(52\) 31008.0 1.59025
\(53\) 25936.0 1.26827 0.634137 0.773220i \(-0.281355\pi\)
0.634137 + 0.773220i \(0.281355\pi\)
\(54\) −3880.00 −0.181070
\(55\) 11325.0 0.504814
\(56\) 0 0
\(57\) −1550.00 −0.0631894
\(58\) 39880.0 1.55663
\(59\) 4580.00 0.171291 0.0856457 0.996326i \(-0.472705\pi\)
0.0856457 + 0.996326i \(0.472705\pi\)
\(60\) 800.000 0.0286888
\(61\) 12488.0 0.429703 0.214851 0.976647i \(-0.431073\pi\)
0.214851 + 0.976647i \(0.431073\pi\)
\(62\) 9536.00 0.315055
\(63\) 0 0
\(64\) −32768.0 −1.00000
\(65\) −24225.0 −0.711181
\(66\) −3624.00 −0.102407
\(67\) −15848.0 −0.431308 −0.215654 0.976470i \(-0.569188\pi\)
−0.215654 + 0.976470i \(0.569188\pi\)
\(68\) −52384.0 −1.37381
\(69\) 1654.00 0.0418228
\(70\) 0 0
\(71\) 51792.0 1.21932 0.609659 0.792664i \(-0.291306\pi\)
0.609659 + 0.792664i \(0.291306\pi\)
\(72\) 0 0
\(73\) −4846.00 −0.106433 −0.0532165 0.998583i \(-0.516947\pi\)
−0.0532165 + 0.998583i \(0.516947\pi\)
\(74\) 88144.0 1.87117
\(75\) −625.000 −0.0128300
\(76\) 49600.0 0.985026
\(77\) 0 0
\(78\) 7752.00 0.144270
\(79\) 62765.0 1.13149 0.565744 0.824581i \(-0.308589\pi\)
0.565744 + 0.824581i \(0.308589\pi\)
\(80\) 25600.0 0.447214
\(81\) 58321.0 0.987671
\(82\) −13824.0 −0.227038
\(83\) 23644.0 0.376726 0.188363 0.982099i \(-0.439682\pi\)
0.188363 + 0.982099i \(0.439682\pi\)
\(84\) 0 0
\(85\) 40925.0 0.614386
\(86\) 86512.0 1.26133
\(87\) 4985.00 0.0706101
\(88\) 0 0
\(89\) 147300. 1.97119 0.985593 0.169133i \(-0.0540967\pi\)
0.985593 + 0.169133i \(0.0540967\pi\)
\(90\) −48400.0 −0.629853
\(91\) 0 0
\(92\) −52928.0 −0.651952
\(93\) 1192.00 0.0142912
\(94\) 209896. 2.45010
\(95\) −38750.0 −0.440517
\(96\) −8192.00 −0.0907218
\(97\) 8343.00 0.0900312 0.0450156 0.998986i \(-0.485666\pi\)
0.0450156 + 0.998986i \(0.485666\pi\)
\(98\) 0 0
\(99\) 109626. 1.12415
\(100\) 20000.0 0.200000
\(101\) 11878.0 0.115862 0.0579308 0.998321i \(-0.481550\pi\)
0.0579308 + 0.998321i \(0.481550\pi\)
\(102\) −13096.0 −0.124634
\(103\) 132439. 1.23005 0.615025 0.788508i \(-0.289146\pi\)
0.615025 + 0.788508i \(0.289146\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −207488. −1.79361
\(107\) 136842. 1.15547 0.577737 0.816223i \(-0.303936\pi\)
0.577737 + 0.816223i \(0.303936\pi\)
\(108\) 15520.0 0.128036
\(109\) 109485. 0.882650 0.441325 0.897347i \(-0.354509\pi\)
0.441325 + 0.897347i \(0.354509\pi\)
\(110\) −90600.0 −0.713915
\(111\) 11018.0 0.0848780
\(112\) 0 0
\(113\) −200934. −1.48033 −0.740163 0.672428i \(-0.765252\pi\)
−0.740163 + 0.672428i \(0.765252\pi\)
\(114\) 12400.0 0.0893634
\(115\) 41350.0 0.291562
\(116\) −159520. −1.10070
\(117\) −234498. −1.58371
\(118\) −36640.0 −0.242243
\(119\) 0 0
\(120\) 0 0
\(121\) 44158.0 0.274186
\(122\) −99904.0 −0.607692
\(123\) −1728.00 −0.0102987
\(124\) −38144.0 −0.222778
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 330692. 1.81934 0.909671 0.415329i \(-0.136334\pi\)
0.909671 + 0.415329i \(0.136334\pi\)
\(128\) 0 0
\(129\) 10814.0 0.0572153
\(130\) 193800. 1.00576
\(131\) −43982.0 −0.223922 −0.111961 0.993713i \(-0.535713\pi\)
−0.111961 + 0.993713i \(0.535713\pi\)
\(132\) 14496.0 0.0724125
\(133\) 0 0
\(134\) 126784. 0.609962
\(135\) −12125.0 −0.0572595
\(136\) 0 0
\(137\) −99748.0 −0.454049 −0.227025 0.973889i \(-0.572900\pi\)
−0.227025 + 0.973889i \(0.572900\pi\)
\(138\) −13232.0 −0.0591463
\(139\) −258930. −1.13670 −0.568349 0.822787i \(-0.692418\pi\)
−0.568349 + 0.822787i \(0.692418\pi\)
\(140\) 0 0
\(141\) 26237.0 0.111139
\(142\) −414336. −1.72438
\(143\) −438957. −1.79507
\(144\) 247808. 0.995885
\(145\) 124625. 0.492249
\(146\) 38768.0 0.150519
\(147\) 0 0
\(148\) −352576. −1.32312
\(149\) −498430. −1.83924 −0.919620 0.392809i \(-0.871503\pi\)
−0.919620 + 0.392809i \(0.871503\pi\)
\(150\) 5000.00 0.0181444
\(151\) −245803. −0.877293 −0.438647 0.898660i \(-0.644542\pi\)
−0.438647 + 0.898660i \(0.644542\pi\)
\(152\) 0 0
\(153\) 396154. 1.36816
\(154\) 0 0
\(155\) 29800.0 0.0996293
\(156\) −31008.0 −0.102015
\(157\) 85478.0 0.276761 0.138381 0.990379i \(-0.455810\pi\)
0.138381 + 0.990379i \(0.455810\pi\)
\(158\) −502120. −1.60017
\(159\) −25936.0 −0.0813599
\(160\) −204800. −0.632456
\(161\) 0 0
\(162\) −466568. −1.39678
\(163\) 193026. 0.569045 0.284523 0.958669i \(-0.408165\pi\)
0.284523 + 0.958669i \(0.408165\pi\)
\(164\) 55296.0 0.160540
\(165\) −11325.0 −0.0323838
\(166\) −189152. −0.532771
\(167\) 157783. 0.437793 0.218897 0.975748i \(-0.429754\pi\)
0.218897 + 0.975748i \(0.429754\pi\)
\(168\) 0 0
\(169\) 567668. 1.52889
\(170\) −327400. −0.868873
\(171\) −375100. −0.980972
\(172\) −346048. −0.891898
\(173\) 265659. 0.674853 0.337427 0.941352i \(-0.390444\pi\)
0.337427 + 0.941352i \(0.390444\pi\)
\(174\) −39880.0 −0.0998578
\(175\) 0 0
\(176\) 463872. 1.12880
\(177\) −4580.00 −0.0109883
\(178\) −1.17840e6 −2.78768
\(179\) 183660. 0.428432 0.214216 0.976786i \(-0.431280\pi\)
0.214216 + 0.976786i \(0.431280\pi\)
\(180\) 193600. 0.445373
\(181\) 635048. 1.44082 0.720411 0.693548i \(-0.243953\pi\)
0.720411 + 0.693548i \(0.243953\pi\)
\(182\) 0 0
\(183\) −12488.0 −0.0275655
\(184\) 0 0
\(185\) 275450. 0.591716
\(186\) −9536.00 −0.0202108
\(187\) 741561. 1.55075
\(188\) −839584. −1.73249
\(189\) 0 0
\(190\) 310000. 0.622985
\(191\) −226613. −0.449471 −0.224735 0.974420i \(-0.572152\pi\)
−0.224735 + 0.974420i \(0.572152\pi\)
\(192\) 32768.0 0.0641500
\(193\) 46476.0 0.0898122 0.0449061 0.998991i \(-0.485701\pi\)
0.0449061 + 0.998991i \(0.485701\pi\)
\(194\) −66744.0 −0.127323
\(195\) 24225.0 0.0456223
\(196\) 0 0
\(197\) 204972. 0.376295 0.188148 0.982141i \(-0.439752\pi\)
0.188148 + 0.982141i \(0.439752\pi\)
\(198\) −877008. −1.58979
\(199\) 953020. 1.70596 0.852981 0.521942i \(-0.174792\pi\)
0.852981 + 0.521942i \(0.174792\pi\)
\(200\) 0 0
\(201\) 15848.0 0.0276684
\(202\) −95024.0 −0.163853
\(203\) 0 0
\(204\) 52384.0 0.0881299
\(205\) −43200.0 −0.0717958
\(206\) −1.05951e6 −1.73955
\(207\) 400268. 0.649270
\(208\) −992256. −1.59025
\(209\) −702150. −1.11190
\(210\) 0 0
\(211\) −223523. −0.345634 −0.172817 0.984954i \(-0.555287\pi\)
−0.172817 + 0.984954i \(0.555287\pi\)
\(212\) 829952. 1.26827
\(213\) −51792.0 −0.0782193
\(214\) −1.09474e6 −1.63409
\(215\) 270350. 0.398869
\(216\) 0 0
\(217\) 0 0
\(218\) −875880. −1.24826
\(219\) 4846.00 0.00682768
\(220\) 362400. 0.504814
\(221\) −1.58625e6 −2.18470
\(222\) −88144.0 −0.120036
\(223\) −1.01480e6 −1.36653 −0.683264 0.730171i \(-0.739440\pi\)
−0.683264 + 0.730171i \(0.739440\pi\)
\(224\) 0 0
\(225\) −151250. −0.199177
\(226\) 1.60747e6 2.09350
\(227\) −999797. −1.28780 −0.643898 0.765111i \(-0.722684\pi\)
−0.643898 + 0.765111i \(0.722684\pi\)
\(228\) −49600.0 −0.0631894
\(229\) 851120. 1.07251 0.536256 0.844055i \(-0.319838\pi\)
0.536256 + 0.844055i \(0.319838\pi\)
\(230\) −330800. −0.412331
\(231\) 0 0
\(232\) 0 0
\(233\) 1.09270e6 1.31859 0.659295 0.751885i \(-0.270855\pi\)
0.659295 + 0.751885i \(0.270855\pi\)
\(234\) 1.87598e6 2.23970
\(235\) 655925. 0.774791
\(236\) 146560. 0.171291
\(237\) −62765.0 −0.0725850
\(238\) 0 0
\(239\) 765905. 0.867322 0.433661 0.901076i \(-0.357222\pi\)
0.433661 + 0.901076i \(0.357222\pi\)
\(240\) −25600.0 −0.0286888
\(241\) 1.21094e6 1.34301 0.671505 0.741000i \(-0.265648\pi\)
0.671505 + 0.741000i \(0.265648\pi\)
\(242\) −353264. −0.387758
\(243\) −176176. −0.191395
\(244\) 399616. 0.429703
\(245\) 0 0
\(246\) 13824.0 0.0145645
\(247\) 1.50195e6 1.56644
\(248\) 0 0
\(249\) −23644.0 −0.0241670
\(250\) 125000. 0.126491
\(251\) −278262. −0.278785 −0.139393 0.990237i \(-0.544515\pi\)
−0.139393 + 0.990237i \(0.544515\pi\)
\(252\) 0 0
\(253\) 749262. 0.735923
\(254\) −2.64554e6 −2.57294
\(255\) −40925.0 −0.0394129
\(256\) 1.04858e6 1.00000
\(257\) 352998. 0.333380 0.166690 0.986009i \(-0.446692\pi\)
0.166690 + 0.986009i \(0.446692\pi\)
\(258\) −86512.0 −0.0809146
\(259\) 0 0
\(260\) −775200. −0.711181
\(261\) 1.20637e6 1.09617
\(262\) 351856. 0.316674
\(263\) −1.55809e6 −1.38901 −0.694503 0.719490i \(-0.744376\pi\)
−0.694503 + 0.719490i \(0.744376\pi\)
\(264\) 0 0
\(265\) −648400. −0.567190
\(266\) 0 0
\(267\) −147300. −0.126452
\(268\) −507136. −0.431308
\(269\) 1.21963e6 1.02766 0.513828 0.857893i \(-0.328227\pi\)
0.513828 + 0.857893i \(0.328227\pi\)
\(270\) 97000.0 0.0809771
\(271\) −405792. −0.335645 −0.167823 0.985817i \(-0.553674\pi\)
−0.167823 + 0.985817i \(0.553674\pi\)
\(272\) 1.67629e6 1.37381
\(273\) 0 0
\(274\) 797984. 0.642122
\(275\) −283125. −0.225760
\(276\) 52928.0 0.0418228
\(277\) 652442. 0.510908 0.255454 0.966821i \(-0.417775\pi\)
0.255454 + 0.966821i \(0.417775\pi\)
\(278\) 2.07144e6 1.60753
\(279\) 288464. 0.221861
\(280\) 0 0
\(281\) 118827. 0.0897737 0.0448869 0.998992i \(-0.485707\pi\)
0.0448869 + 0.998992i \(0.485707\pi\)
\(282\) −209896. −0.157174
\(283\) −1.48801e6 −1.10443 −0.552217 0.833700i \(-0.686218\pi\)
−0.552217 + 0.833700i \(0.686218\pi\)
\(284\) 1.65734e6 1.21932
\(285\) 38750.0 0.0282592
\(286\) 3.51166e6 2.53862
\(287\) 0 0
\(288\) −1.98246e6 −1.40839
\(289\) 1.25991e6 0.887351
\(290\) −997000. −0.696146
\(291\) −8343.00 −0.00577550
\(292\) −155072. −0.106433
\(293\) −1.89580e6 −1.29010 −0.645050 0.764140i \(-0.723164\pi\)
−0.645050 + 0.764140i \(0.723164\pi\)
\(294\) 0 0
\(295\) −114500. −0.0766038
\(296\) 0 0
\(297\) −219705. −0.144527
\(298\) 3.98744e6 2.60108
\(299\) −1.60273e6 −1.03677
\(300\) −20000.0 −0.0128300
\(301\) 0 0
\(302\) 1.96642e6 1.24068
\(303\) −11878.0 −0.00743253
\(304\) −1.58720e6 −0.985026
\(305\) −312200. −0.192169
\(306\) −3.16923e6 −1.93486
\(307\) 821853. 0.497678 0.248839 0.968545i \(-0.419951\pi\)
0.248839 + 0.968545i \(0.419951\pi\)
\(308\) 0 0
\(309\) −132439. −0.0789078
\(310\) −238400. −0.140897
\(311\) 2.09600e6 1.22882 0.614412 0.788985i \(-0.289393\pi\)
0.614412 + 0.788985i \(0.289393\pi\)
\(312\) 0 0
\(313\) −394571. −0.227648 −0.113824 0.993501i \(-0.536310\pi\)
−0.113824 + 0.993501i \(0.536310\pi\)
\(314\) −683824. −0.391399
\(315\) 0 0
\(316\) 2.00848e6 1.13149
\(317\) 321422. 0.179650 0.0898250 0.995958i \(-0.471369\pi\)
0.0898250 + 0.995958i \(0.471369\pi\)
\(318\) 207488. 0.115060
\(319\) 2.25820e6 1.24247
\(320\) 819200. 0.447214
\(321\) −136842. −0.0741237
\(322\) 0 0
\(323\) −2.53735e6 −1.35324
\(324\) 1.86627e6 0.987671
\(325\) 605625. 0.318050
\(326\) −1.54421e6 −0.804752
\(327\) −109485. −0.0566220
\(328\) 0 0
\(329\) 0 0
\(330\) 90600.0 0.0457977
\(331\) −2.23259e6 −1.12005 −0.560027 0.828475i \(-0.689209\pi\)
−0.560027 + 0.828475i \(0.689209\pi\)
\(332\) 756608. 0.376726
\(333\) 2.66636e6 1.31767
\(334\) −1.26226e6 −0.619133
\(335\) 396200. 0.192887
\(336\) 0 0
\(337\) −3.65656e6 −1.75387 −0.876936 0.480608i \(-0.840416\pi\)
−0.876936 + 0.480608i \(0.840416\pi\)
\(338\) −4.54134e6 −2.16218
\(339\) 200934. 0.0949629
\(340\) 1.30960e6 0.614386
\(341\) 539976. 0.251471
\(342\) 3.00080e6 1.38730
\(343\) 0 0
\(344\) 0 0
\(345\) −41350.0 −0.0187037
\(346\) −2.12527e6 −0.954386
\(347\) −1.88962e6 −0.842462 −0.421231 0.906953i \(-0.638402\pi\)
−0.421231 + 0.906953i \(0.638402\pi\)
\(348\) 159520. 0.0706101
\(349\) 2.69329e6 1.18364 0.591820 0.806070i \(-0.298410\pi\)
0.591820 + 0.806070i \(0.298410\pi\)
\(350\) 0 0
\(351\) 469965. 0.203609
\(352\) −3.71098e6 −1.59636
\(353\) 1.57468e6 0.672598 0.336299 0.941755i \(-0.390825\pi\)
0.336299 + 0.941755i \(0.390825\pi\)
\(354\) 36640.0 0.0155399
\(355\) −1.29480e6 −0.545295
\(356\) 4.71360e6 1.97119
\(357\) 0 0
\(358\) −1.46928e6 −0.605894
\(359\) 4.05576e6 1.66087 0.830436 0.557114i \(-0.188091\pi\)
0.830436 + 0.557114i \(0.188091\pi\)
\(360\) 0 0
\(361\) −73599.0 −0.0297238
\(362\) −5.08038e6 −2.03763
\(363\) −44158.0 −0.0175891
\(364\) 0 0
\(365\) 121150. 0.0475983
\(366\) 99904.0 0.0389834
\(367\) 4.90628e6 1.90146 0.950731 0.310018i \(-0.100335\pi\)
0.950731 + 0.310018i \(0.100335\pi\)
\(368\) 1.69370e6 0.651952
\(369\) −418176. −0.159880
\(370\) −2.20360e6 −0.836813
\(371\) 0 0
\(372\) 38144.0 0.0142912
\(373\) −3.45336e6 −1.28520 −0.642599 0.766202i \(-0.722144\pi\)
−0.642599 + 0.766202i \(0.722144\pi\)
\(374\) −5.93249e6 −2.19310
\(375\) 15625.0 0.00573775
\(376\) 0 0
\(377\) −4.83046e6 −1.75039
\(378\) 0 0
\(379\) −4.23466e6 −1.51433 −0.757165 0.653224i \(-0.773416\pi\)
−0.757165 + 0.653224i \(0.773416\pi\)
\(380\) −1.24000e6 −0.440517
\(381\) −330692. −0.116711
\(382\) 1.81290e6 0.635648
\(383\) 1.86460e6 0.649516 0.324758 0.945797i \(-0.394717\pi\)
0.324758 + 0.945797i \(0.394717\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −371808. −0.127014
\(387\) 2.61699e6 0.888228
\(388\) 266976. 0.0900312
\(389\) −4.81502e6 −1.61333 −0.806666 0.591008i \(-0.798730\pi\)
−0.806666 + 0.591008i \(0.798730\pi\)
\(390\) −193800. −0.0645197
\(391\) 2.70760e6 0.895658
\(392\) 0 0
\(393\) 43982.0 0.0143646
\(394\) −1.63978e6 −0.532162
\(395\) −1.56912e6 −0.506017
\(396\) 3.50803e6 1.12415
\(397\) −1.21376e6 −0.386505 −0.193253 0.981149i \(-0.561904\pi\)
−0.193253 + 0.981149i \(0.561904\pi\)
\(398\) −7.62416e6 −2.41259
\(399\) 0 0
\(400\) −640000. −0.200000
\(401\) 5.90442e6 1.83365 0.916824 0.399291i \(-0.130744\pi\)
0.916824 + 0.399291i \(0.130744\pi\)
\(402\) −126784. −0.0391291
\(403\) −1.15505e6 −0.354272
\(404\) 380096. 0.115862
\(405\) −1.45802e6 −0.441700
\(406\) 0 0
\(407\) 4.99115e6 1.49353
\(408\) 0 0
\(409\) −4.84289e6 −1.43152 −0.715758 0.698348i \(-0.753919\pi\)
−0.715758 + 0.698348i \(0.753919\pi\)
\(410\) 345600. 0.101535
\(411\) 99748.0 0.0291273
\(412\) 4.23805e6 1.23005
\(413\) 0 0
\(414\) −3.20214e6 −0.918206
\(415\) −591100. −0.168477
\(416\) 7.93805e6 2.24895
\(417\) 258930. 0.0729193
\(418\) 5.61720e6 1.57246
\(419\) −270360. −0.0752328 −0.0376164 0.999292i \(-0.511977\pi\)
−0.0376164 + 0.999292i \(0.511977\pi\)
\(420\) 0 0
\(421\) 3.13648e6 0.862456 0.431228 0.902243i \(-0.358080\pi\)
0.431228 + 0.902243i \(0.358080\pi\)
\(422\) 1.78818e6 0.488800
\(423\) 6.34935e6 1.72536
\(424\) 0 0
\(425\) −1.02312e6 −0.274762
\(426\) 414336. 0.110619
\(427\) 0 0
\(428\) 4.37894e6 1.15547
\(429\) 438957. 0.115154
\(430\) −2.16280e6 −0.564086
\(431\) −1.87703e6 −0.486719 −0.243360 0.969936i \(-0.578250\pi\)
−0.243360 + 0.969936i \(0.578250\pi\)
\(432\) −496640. −0.128036
\(433\) −3.20357e6 −0.821134 −0.410567 0.911830i \(-0.634669\pi\)
−0.410567 + 0.911830i \(0.634669\pi\)
\(434\) 0 0
\(435\) −124625. −0.0315778
\(436\) 3.50352e6 0.882650
\(437\) −2.56370e6 −0.642190
\(438\) −38768.0 −0.00965580
\(439\) 6.27209e6 1.55328 0.776642 0.629942i \(-0.216921\pi\)
0.776642 + 0.629942i \(0.216921\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.26900e7 3.08963
\(443\) 724986. 0.175517 0.0877587 0.996142i \(-0.472030\pi\)
0.0877587 + 0.996142i \(0.472030\pi\)
\(444\) 352576. 0.0848780
\(445\) −3.68250e6 −0.881541
\(446\) 8.11841e6 1.93256
\(447\) 498430. 0.117987
\(448\) 0 0
\(449\) −875985. −0.205060 −0.102530 0.994730i \(-0.532694\pi\)
−0.102530 + 0.994730i \(0.532694\pi\)
\(450\) 1.21000e6 0.281679
\(451\) −782784. −0.181218
\(452\) −6.42989e6 −1.48033
\(453\) 245803. 0.0562784
\(454\) 7.99838e6 1.82122
\(455\) 0 0
\(456\) 0 0
\(457\) −832668. −0.186501 −0.0932505 0.995643i \(-0.529726\pi\)
−0.0932505 + 0.995643i \(0.529726\pi\)
\(458\) −6.80896e6 −1.51676
\(459\) −793945. −0.175897
\(460\) 1.32320e6 0.291562
\(461\) −5.92115e6 −1.29764 −0.648820 0.760942i \(-0.724737\pi\)
−0.648820 + 0.760942i \(0.724737\pi\)
\(462\) 0 0
\(463\) 682776. 0.148022 0.0740109 0.997257i \(-0.476420\pi\)
0.0740109 + 0.997257i \(0.476420\pi\)
\(464\) 5.10464e6 1.10070
\(465\) −29800.0 −0.00639122
\(466\) −8.74157e6 −1.86477
\(467\) 5.41667e6 1.14932 0.574659 0.818393i \(-0.305135\pi\)
0.574659 + 0.818393i \(0.305135\pi\)
\(468\) −7.50394e6 −1.58371
\(469\) 0 0
\(470\) −5.24740e6 −1.09572
\(471\) −85478.0 −0.0177542
\(472\) 0 0
\(473\) 4.89874e6 1.00677
\(474\) 502120. 0.102651
\(475\) 968750. 0.197005
\(476\) 0 0
\(477\) −6.27651e6 −1.26306
\(478\) −6.12724e6 −1.22658
\(479\) −1.98599e6 −0.395493 −0.197746 0.980253i \(-0.563362\pi\)
−0.197746 + 0.980253i \(0.563362\pi\)
\(480\) 204800. 0.0405720
\(481\) −1.06764e7 −2.10409
\(482\) −9.68750e6 −1.89930
\(483\) 0 0
\(484\) 1.41306e6 0.274186
\(485\) −208575. −0.0402632
\(486\) 1.40941e6 0.270674
\(487\) −1.06974e6 −0.204388 −0.102194 0.994764i \(-0.532586\pi\)
−0.102194 + 0.994764i \(0.532586\pi\)
\(488\) 0 0
\(489\) −193026. −0.0365043
\(490\) 0 0
\(491\) 4.59246e6 0.859689 0.429844 0.902903i \(-0.358568\pi\)
0.429844 + 0.902903i \(0.358568\pi\)
\(492\) −55296.0 −0.0102987
\(493\) 8.16045e6 1.51216
\(494\) −1.20156e7 −2.21528
\(495\) −2.74065e6 −0.502737
\(496\) 1.22061e6 0.222778
\(497\) 0 0
\(498\) 189152. 0.0341773
\(499\) 1.96066e6 0.352492 0.176246 0.984346i \(-0.443605\pi\)
0.176246 + 0.984346i \(0.443605\pi\)
\(500\) −500000. −0.0894427
\(501\) −157783. −0.0280844
\(502\) 2.22610e6 0.394262
\(503\) −3.51483e6 −0.619419 −0.309709 0.950831i \(-0.600232\pi\)
−0.309709 + 0.950831i \(0.600232\pi\)
\(504\) 0 0
\(505\) −296950. −0.0518149
\(506\) −5.99410e6 −1.04075
\(507\) −567668. −0.0980787
\(508\) 1.05821e7 1.81934
\(509\) 1.45211e6 0.248431 0.124215 0.992255i \(-0.460359\pi\)
0.124215 + 0.992255i \(0.460359\pi\)
\(510\) 327400. 0.0557382
\(511\) 0 0
\(512\) −8.38861e6 −1.41421
\(513\) 751750. 0.126119
\(514\) −2.82398e6 −0.471470
\(515\) −3.31098e6 −0.550095
\(516\) 346048. 0.0572153
\(517\) 1.18854e7 1.95563
\(518\) 0 0
\(519\) −265659. −0.0432918
\(520\) 0 0
\(521\) 4.24240e6 0.684726 0.342363 0.939568i \(-0.388773\pi\)
0.342363 + 0.939568i \(0.388773\pi\)
\(522\) −9.65096e6 −1.55022
\(523\) 7.56012e6 1.20858 0.604289 0.796765i \(-0.293457\pi\)
0.604289 + 0.796765i \(0.293457\pi\)
\(524\) −1.40742e6 −0.223922
\(525\) 0 0
\(526\) 1.24648e7 1.96435
\(527\) 1.95130e6 0.306054
\(528\) −463872. −0.0724125
\(529\) −3.70063e6 −0.574958
\(530\) 5.18720e6 0.802127
\(531\) −1.10836e6 −0.170586
\(532\) 0 0
\(533\) 1.67443e6 0.255299
\(534\) 1.17840e6 0.178830
\(535\) −3.42105e6 −0.516743
\(536\) 0 0
\(537\) −183660. −0.0274839
\(538\) −9.75704e6 −1.45332
\(539\) 0 0
\(540\) −388000. −0.0572595
\(541\) 1.24065e6 0.182245 0.0911224 0.995840i \(-0.470955\pi\)
0.0911224 + 0.995840i \(0.470955\pi\)
\(542\) 3.24634e6 0.474674
\(543\) −635048. −0.0924287
\(544\) −1.34103e7 −1.94286
\(545\) −2.73712e6 −0.394733
\(546\) 0 0
\(547\) −1.85057e6 −0.264446 −0.132223 0.991220i \(-0.542211\pi\)
−0.132223 + 0.991220i \(0.542211\pi\)
\(548\) −3.19194e6 −0.454049
\(549\) −3.02210e6 −0.427935
\(550\) 2.26500e6 0.319272
\(551\) −7.72675e6 −1.08422
\(552\) 0 0
\(553\) 0 0
\(554\) −5.21954e6 −0.722533
\(555\) −275450. −0.0379586
\(556\) −8.28576e6 −1.13670
\(557\) 7.77555e6 1.06192 0.530962 0.847396i \(-0.321831\pi\)
0.530962 + 0.847396i \(0.321831\pi\)
\(558\) −2.30771e6 −0.313759
\(559\) −1.04788e7 −1.41834
\(560\) 0 0
\(561\) −741561. −0.0994809
\(562\) −950616. −0.126959
\(563\) −8.37716e6 −1.11385 −0.556924 0.830564i \(-0.688018\pi\)
−0.556924 + 0.830564i \(0.688018\pi\)
\(564\) 839584. 0.111139
\(565\) 5.02335e6 0.662022
\(566\) 1.19041e7 1.56191
\(567\) 0 0
\(568\) 0 0
\(569\) −6.15591e6 −0.797098 −0.398549 0.917147i \(-0.630486\pi\)
−0.398549 + 0.917147i \(0.630486\pi\)
\(570\) −310000. −0.0399645
\(571\) 7.21513e6 0.926092 0.463046 0.886334i \(-0.346757\pi\)
0.463046 + 0.886334i \(0.346757\pi\)
\(572\) −1.40466e7 −1.79507
\(573\) 226613. 0.0288336
\(574\) 0 0
\(575\) −1.03375e6 −0.130390
\(576\) 7.92986e6 0.995885
\(577\) −1.36699e7 −1.70933 −0.854666 0.519177i \(-0.826238\pi\)
−0.854666 + 0.519177i \(0.826238\pi\)
\(578\) −1.00793e7 −1.25490
\(579\) −46476.0 −0.00576146
\(580\) 3.98800e6 0.492249
\(581\) 0 0
\(582\) 66744.0 0.00816779
\(583\) −1.17490e7 −1.43163
\(584\) 0 0
\(585\) 5.86245e6 0.708255
\(586\) 1.51664e7 1.82448
\(587\) 1.00686e7 1.20608 0.603040 0.797711i \(-0.293956\pi\)
0.603040 + 0.797711i \(0.293956\pi\)
\(588\) 0 0
\(589\) −1.84760e6 −0.219442
\(590\) 916000. 0.108334
\(591\) −204972. −0.0241394
\(592\) 1.12824e7 1.32312
\(593\) −9.80615e6 −1.14515 −0.572574 0.819853i \(-0.694055\pi\)
−0.572574 + 0.819853i \(0.694055\pi\)
\(594\) 1.75764e6 0.204392
\(595\) 0 0
\(596\) −1.59498e7 −1.83924
\(597\) −953020. −0.109438
\(598\) 1.28218e7 1.46621
\(599\) 8.26257e6 0.940911 0.470455 0.882424i \(-0.344090\pi\)
0.470455 + 0.882424i \(0.344090\pi\)
\(600\) 0 0
\(601\) 3.59492e6 0.405978 0.202989 0.979181i \(-0.434934\pi\)
0.202989 + 0.979181i \(0.434934\pi\)
\(602\) 0 0
\(603\) 3.83522e6 0.429533
\(604\) −7.86570e6 −0.877293
\(605\) −1.10395e6 −0.122620
\(606\) 95024.0 0.0105112
\(607\) 1.32969e7 1.46480 0.732401 0.680873i \(-0.238400\pi\)
0.732401 + 0.680873i \(0.238400\pi\)
\(608\) 1.26976e7 1.39304
\(609\) 0 0
\(610\) 2.49760e6 0.271768
\(611\) −2.54237e7 −2.75508
\(612\) 1.26769e7 1.36816
\(613\) 2.50327e6 0.269064 0.134532 0.990909i \(-0.457047\pi\)
0.134532 + 0.990909i \(0.457047\pi\)
\(614\) −6.57482e6 −0.703823
\(615\) 43200.0 0.00460570
\(616\) 0 0
\(617\) 1.88254e6 0.199082 0.0995409 0.995033i \(-0.468263\pi\)
0.0995409 + 0.995033i \(0.468263\pi\)
\(618\) 1.05951e6 0.111592
\(619\) −8.21487e6 −0.861736 −0.430868 0.902415i \(-0.641792\pi\)
−0.430868 + 0.902415i \(0.641792\pi\)
\(620\) 953600. 0.0996293
\(621\) −802190. −0.0834734
\(622\) −1.67680e7 −1.73782
\(623\) 0 0
\(624\) 992256. 0.102015
\(625\) 390625. 0.0400000
\(626\) 3.15657e6 0.321943
\(627\) 702150. 0.0713282
\(628\) 2.73530e6 0.276761
\(629\) 1.80365e7 1.81771
\(630\) 0 0
\(631\) 1.61155e7 1.61128 0.805638 0.592408i \(-0.201823\pi\)
0.805638 + 0.592408i \(0.201823\pi\)
\(632\) 0 0
\(633\) 223523. 0.0221724
\(634\) −2.57138e6 −0.254064
\(635\) −8.26730e6 −0.813635
\(636\) −829952. −0.0813599
\(637\) 0 0
\(638\) −1.80656e7 −1.75712
\(639\) −1.25337e7 −1.21430
\(640\) 0 0
\(641\) −8.50544e6 −0.817620 −0.408810 0.912619i \(-0.634056\pi\)
−0.408810 + 0.912619i \(0.634056\pi\)
\(642\) 1.09474e6 0.104827
\(643\) 1.32191e7 1.26088 0.630440 0.776238i \(-0.282874\pi\)
0.630440 + 0.776238i \(0.282874\pi\)
\(644\) 0 0
\(645\) −270350. −0.0255875
\(646\) 2.02988e7 1.91377
\(647\) −1.89115e6 −0.177609 −0.0888047 0.996049i \(-0.528305\pi\)
−0.0888047 + 0.996049i \(0.528305\pi\)
\(648\) 0 0
\(649\) −2.07474e6 −0.193353
\(650\) −4.84500e6 −0.449791
\(651\) 0 0
\(652\) 6.17683e6 0.569045
\(653\) 4.90587e6 0.450228 0.225114 0.974332i \(-0.427725\pi\)
0.225114 + 0.974332i \(0.427725\pi\)
\(654\) 875880. 0.0800756
\(655\) 1.09955e6 0.100141
\(656\) −1.76947e6 −0.160540
\(657\) 1.17273e6 0.105995
\(658\) 0 0
\(659\) 1.36367e7 1.22319 0.611597 0.791169i \(-0.290527\pi\)
0.611597 + 0.791169i \(0.290527\pi\)
\(660\) −362400. −0.0323838
\(661\) 2.22345e6 0.197935 0.0989677 0.995091i \(-0.468446\pi\)
0.0989677 + 0.995091i \(0.468446\pi\)
\(662\) 1.78607e7 1.58399
\(663\) 1.58625e6 0.140149
\(664\) 0 0
\(665\) 0 0
\(666\) −2.13308e7 −1.86347
\(667\) 8.24519e6 0.717606
\(668\) 5.04906e6 0.437793
\(669\) 1.01480e6 0.0876629
\(670\) −3.16960e6 −0.272783
\(671\) −5.65706e6 −0.485048
\(672\) 0 0
\(673\) 4.88484e6 0.415731 0.207865 0.978157i \(-0.433348\pi\)
0.207865 + 0.978157i \(0.433348\pi\)
\(674\) 2.92525e7 2.48035
\(675\) 303125. 0.0256072
\(676\) 1.81654e7 1.52889
\(677\) 1.98785e7 1.66691 0.833453 0.552590i \(-0.186360\pi\)
0.833453 + 0.552590i \(0.186360\pi\)
\(678\) −1.60747e6 −0.134298
\(679\) 0 0
\(680\) 0 0
\(681\) 999797. 0.0826122
\(682\) −4.31981e6 −0.355634
\(683\) 4.27870e6 0.350962 0.175481 0.984483i \(-0.443852\pi\)
0.175481 + 0.984483i \(0.443852\pi\)
\(684\) −1.20032e7 −0.980972
\(685\) 2.49370e6 0.203057
\(686\) 0 0
\(687\) −851120. −0.0688017
\(688\) 1.10735e7 0.891898
\(689\) 2.51320e7 2.01687
\(690\) 330800. 0.0264510
\(691\) −9.48925e6 −0.756026 −0.378013 0.925800i \(-0.623393\pi\)
−0.378013 + 0.925800i \(0.623393\pi\)
\(692\) 8.50109e6 0.674853
\(693\) 0 0
\(694\) 1.51169e7 1.19142
\(695\) 6.47325e6 0.508347
\(696\) 0 0
\(697\) −2.82874e6 −0.220552
\(698\) −2.15463e7 −1.67392
\(699\) −1.09270e6 −0.0845875
\(700\) 0 0
\(701\) −5.86385e6 −0.450700 −0.225350 0.974278i \(-0.572353\pi\)
−0.225350 + 0.974278i \(0.572353\pi\)
\(702\) −3.75972e6 −0.287947
\(703\) −1.70779e7 −1.30331
\(704\) 1.48439e7 1.12880
\(705\) −655925. −0.0497029
\(706\) −1.25974e7 −0.951197
\(707\) 0 0
\(708\) −146560. −0.0109883
\(709\) −2.66670e6 −0.199232 −0.0996161 0.995026i \(-0.531761\pi\)
−0.0996161 + 0.995026i \(0.531761\pi\)
\(710\) 1.03584e7 0.771164
\(711\) −1.51891e7 −1.12683
\(712\) 0 0
\(713\) 1.97157e6 0.145241
\(714\) 0 0
\(715\) 1.09739e7 0.802781
\(716\) 5.87712e6 0.428432
\(717\) −765905. −0.0556387
\(718\) −3.24461e7 −2.34883
\(719\) 4.46629e6 0.322199 0.161100 0.986938i \(-0.448496\pi\)
0.161100 + 0.986938i \(0.448496\pi\)
\(720\) −6.19520e6 −0.445373
\(721\) 0 0
\(722\) 588792. 0.0420358
\(723\) −1.21094e6 −0.0861541
\(724\) 2.03215e7 1.44082
\(725\) −3.11562e6 −0.220141
\(726\) 353264. 0.0248747
\(727\) 7.47757e6 0.524716 0.262358 0.964971i \(-0.415500\pi\)
0.262358 + 0.964971i \(0.415500\pi\)
\(728\) 0 0
\(729\) −1.39958e7 −0.975393
\(730\) −969200. −0.0673141
\(731\) 1.77025e7 1.22530
\(732\) −399616. −0.0275655
\(733\) 4.39751e6 0.302306 0.151153 0.988510i \(-0.451701\pi\)
0.151153 + 0.988510i \(0.451701\pi\)
\(734\) −3.92503e7 −2.68907
\(735\) 0 0
\(736\) −1.35496e7 −0.922000
\(737\) 7.17914e6 0.486860
\(738\) 3.34541e6 0.226104
\(739\) 2.84036e7 1.91321 0.956603 0.291395i \(-0.0941195\pi\)
0.956603 + 0.291395i \(0.0941195\pi\)
\(740\) 8.81440e6 0.591716
\(741\) −1.50195e6 −0.100487
\(742\) 0 0
\(743\) −1.96012e7 −1.30260 −0.651299 0.758821i \(-0.725776\pi\)
−0.651299 + 0.758821i \(0.725776\pi\)
\(744\) 0 0
\(745\) 1.24608e7 0.822533
\(746\) 2.76269e7 1.81755
\(747\) −5.72185e6 −0.375176
\(748\) 2.37300e7 1.55075
\(749\) 0 0
\(750\) −125000. −0.00811441
\(751\) −2.60344e6 −0.168441 −0.0842206 0.996447i \(-0.526840\pi\)
−0.0842206 + 0.996447i \(0.526840\pi\)
\(752\) 2.68667e7 1.73249
\(753\) 278262. 0.0178841
\(754\) 3.86437e7 2.47543
\(755\) 6.14508e6 0.392337
\(756\) 0 0
\(757\) −2.98869e7 −1.89558 −0.947789 0.318899i \(-0.896687\pi\)
−0.947789 + 0.318899i \(0.896687\pi\)
\(758\) 3.38773e7 2.14159
\(759\) −749262. −0.0472095
\(760\) 0 0
\(761\) −1.21470e7 −0.760338 −0.380169 0.924917i \(-0.624134\pi\)
−0.380169 + 0.924917i \(0.624134\pi\)
\(762\) 2.64554e6 0.165054
\(763\) 0 0
\(764\) −7.25162e6 −0.449471
\(765\) −9.90385e6 −0.611858
\(766\) −1.49168e7 −0.918554
\(767\) 4.43802e6 0.272396
\(768\) −1.04858e6 −0.0641500
\(769\) −4.53845e6 −0.276753 −0.138376 0.990380i \(-0.544188\pi\)
−0.138376 + 0.990380i \(0.544188\pi\)
\(770\) 0 0
\(771\) −352998. −0.0213863
\(772\) 1.48723e6 0.0898122
\(773\) −1.93330e7 −1.16372 −0.581861 0.813288i \(-0.697675\pi\)
−0.581861 + 0.813288i \(0.697675\pi\)
\(774\) −2.09359e7 −1.25614
\(775\) −745000. −0.0445556
\(776\) 0 0
\(777\) 0 0
\(778\) 3.85201e7 2.28160
\(779\) 2.67840e6 0.158136
\(780\) 775200. 0.0456223
\(781\) −2.34618e7 −1.37636
\(782\) −2.16608e7 −1.26665
\(783\) −2.41772e6 −0.140930
\(784\) 0 0
\(785\) −2.13695e6 −0.123771
\(786\) −351856. −0.0203146
\(787\) −1.66392e7 −0.957627 −0.478814 0.877917i \(-0.658933\pi\)
−0.478814 + 0.877917i \(0.658933\pi\)
\(788\) 6.55910e6 0.376295
\(789\) 1.55809e6 0.0891048
\(790\) 1.25530e7 0.715616
\(791\) 0 0
\(792\) 0 0
\(793\) 1.21009e7 0.683335
\(794\) 9.71006e6 0.546601
\(795\) 648400. 0.0363852
\(796\) 3.04966e7 1.70596
\(797\) −1.80409e7 −1.00603 −0.503017 0.864276i \(-0.667777\pi\)
−0.503017 + 0.864276i \(0.667777\pi\)
\(798\) 0 0
\(799\) 4.29500e7 2.38010
\(800\) 5.12000e6 0.282843
\(801\) −3.56466e7 −1.96307
\(802\) −4.72353e7 −2.59317
\(803\) 2.19524e6 0.120141
\(804\) 507136. 0.0276684
\(805\) 0 0
\(806\) 9.24038e6 0.501017
\(807\) −1.21963e6 −0.0659241
\(808\) 0 0
\(809\) 2.33891e7 1.25644 0.628220 0.778036i \(-0.283784\pi\)
0.628220 + 0.778036i \(0.283784\pi\)
\(810\) 1.16642e7 0.624658
\(811\) 2.29037e7 1.22279 0.611397 0.791324i \(-0.290608\pi\)
0.611397 + 0.791324i \(0.290608\pi\)
\(812\) 0 0
\(813\) 405792. 0.0215316
\(814\) −3.99292e7 −2.11218
\(815\) −4.82565e6 −0.254485
\(816\) −1.67629e6 −0.0881299
\(817\) −1.67617e7 −0.878543
\(818\) 3.87431e7 2.02447
\(819\) 0 0
\(820\) −1.38240e6 −0.0717958
\(821\) −1.80745e7 −0.935853 −0.467926 0.883767i \(-0.654999\pi\)
−0.467926 + 0.883767i \(0.654999\pi\)
\(822\) −797984. −0.0411922
\(823\) 1.17989e7 0.607216 0.303608 0.952797i \(-0.401809\pi\)
0.303608 + 0.952797i \(0.401809\pi\)
\(824\) 0 0
\(825\) 283125. 0.0144825
\(826\) 0 0
\(827\) 2.57650e6 0.130999 0.0654993 0.997853i \(-0.479136\pi\)
0.0654993 + 0.997853i \(0.479136\pi\)
\(828\) 1.28086e7 0.649270
\(829\) 3.84340e7 1.94236 0.971178 0.238356i \(-0.0766084\pi\)
0.971178 + 0.238356i \(0.0766084\pi\)
\(830\) 4.72880e6 0.238263
\(831\) −652442. −0.0327747
\(832\) −3.17522e7 −1.59025
\(833\) 0 0
\(834\) −2.07144e6 −0.103123
\(835\) −3.94458e6 −0.195787
\(836\) −2.24688e7 −1.11190
\(837\) −578120. −0.0285236
\(838\) 2.16288e6 0.106395
\(839\) 1.24222e7 0.609247 0.304623 0.952473i \(-0.401469\pi\)
0.304623 + 0.952473i \(0.401469\pi\)
\(840\) 0 0
\(841\) 4.33908e6 0.211547
\(842\) −2.50918e7 −1.21970
\(843\) −118827. −0.00575899
\(844\) −7.15274e6 −0.345634
\(845\) −1.41917e7 −0.683743
\(846\) −5.07948e7 −2.44002
\(847\) 0 0
\(848\) −2.65585e7 −1.26827
\(849\) 1.48801e6 0.0708495
\(850\) 8.18500e6 0.388572
\(851\) 1.82238e7 0.862610
\(852\) −1.65734e6 −0.0782193
\(853\) −7.92067e6 −0.372726 −0.186363 0.982481i \(-0.559670\pi\)
−0.186363 + 0.982481i \(0.559670\pi\)
\(854\) 0 0
\(855\) 9.37750e6 0.438704
\(856\) 0 0
\(857\) −1.48983e7 −0.692924 −0.346462 0.938064i \(-0.612617\pi\)
−0.346462 + 0.938064i \(0.612617\pi\)
\(858\) −3.51166e6 −0.162852
\(859\) 1.38740e7 0.641534 0.320767 0.947158i \(-0.396059\pi\)
0.320767 + 0.947158i \(0.396059\pi\)
\(860\) 8.65120e6 0.398869
\(861\) 0 0
\(862\) 1.50163e7 0.688325
\(863\) 1.25500e7 0.573610 0.286805 0.957989i \(-0.407407\pi\)
0.286805 + 0.957989i \(0.407407\pi\)
\(864\) 3.97312e6 0.181070
\(865\) −6.64147e6 −0.301804
\(866\) 2.56285e7 1.16126
\(867\) −1.25991e6 −0.0569236
\(868\) 0 0
\(869\) −2.84325e7 −1.27722
\(870\) 997000. 0.0446578
\(871\) −1.53567e7 −0.685887
\(872\) 0 0
\(873\) −2.01901e6 −0.0896607
\(874\) 2.05096e7 0.908194
\(875\) 0 0
\(876\) 155072. 0.00682768
\(877\) −2.86002e7 −1.25565 −0.627827 0.778353i \(-0.716056\pi\)
−0.627827 + 0.778353i \(0.716056\pi\)
\(878\) −5.01767e7 −2.19668
\(879\) 1.89580e6 0.0827600
\(880\) −1.15968e7 −0.504814
\(881\) −4.09608e7 −1.77799 −0.888993 0.457922i \(-0.848594\pi\)
−0.888993 + 0.457922i \(0.848594\pi\)
\(882\) 0 0
\(883\) 1.30504e7 0.563279 0.281639 0.959520i \(-0.409122\pi\)
0.281639 + 0.959520i \(0.409122\pi\)
\(884\) −5.07601e7 −2.18470
\(885\) 114500. 0.00491414
\(886\) −5.79989e6 −0.248219
\(887\) −2.53595e7 −1.08226 −0.541129 0.840939i \(-0.682003\pi\)
−0.541129 + 0.840939i \(0.682003\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 2.94600e7 1.24669
\(891\) −2.64194e7 −1.11488
\(892\) −3.24736e7 −1.36653
\(893\) −4.06674e7 −1.70654
\(894\) −3.98744e6 −0.166859
\(895\) −4.59150e6 −0.191601
\(896\) 0 0
\(897\) 1.60273e6 0.0665087
\(898\) 7.00788e6 0.289999
\(899\) 5.94212e6 0.245212
\(900\) −4.84000e6 −0.199177
\(901\) −4.24572e7 −1.74237
\(902\) 6.26227e6 0.256281
\(903\) 0 0
\(904\) 0 0
\(905\) −1.58762e7 −0.644355
\(906\) −1.96642e6 −0.0795897
\(907\) 1.98595e7 0.801585 0.400793 0.916169i \(-0.368735\pi\)
0.400793 + 0.916169i \(0.368735\pi\)
\(908\) −3.19935e7 −1.28780
\(909\) −2.87448e6 −0.115385
\(910\) 0 0
\(911\) −1.99344e7 −0.795808 −0.397904 0.917427i \(-0.630262\pi\)
−0.397904 + 0.917427i \(0.630262\pi\)
\(912\) 1.58720e6 0.0631894
\(913\) −1.07107e7 −0.425248
\(914\) 6.66134e6 0.263752
\(915\) 312200. 0.0123276
\(916\) 2.72358e7 1.07251
\(917\) 0 0
\(918\) 6.35156e6 0.248756
\(919\) −1.10695e7 −0.432355 −0.216178 0.976354i \(-0.569359\pi\)
−0.216178 + 0.976354i \(0.569359\pi\)
\(920\) 0 0
\(921\) −821853. −0.0319260
\(922\) 4.73692e7 1.83514
\(923\) 5.01864e7 1.93902
\(924\) 0 0
\(925\) −6.88625e6 −0.264624
\(926\) −5.46221e6 −0.209334
\(927\) −3.20502e7 −1.22499
\(928\) −4.08371e7 −1.55663
\(929\) 3.25682e7 1.23810 0.619048 0.785353i \(-0.287519\pi\)
0.619048 + 0.785353i \(0.287519\pi\)
\(930\) 238400. 0.00903855
\(931\) 0 0
\(932\) 3.49663e7 1.31859
\(933\) −2.09600e6 −0.0788291
\(934\) −4.33334e7 −1.62538
\(935\) −1.85390e7 −0.693518
\(936\) 0 0
\(937\) −3.15690e7 −1.17466 −0.587329 0.809348i \(-0.699821\pi\)
−0.587329 + 0.809348i \(0.699821\pi\)
\(938\) 0 0
\(939\) 394571. 0.0146036
\(940\) 2.09896e7 0.774791
\(941\) 3.67997e7 1.35479 0.677393 0.735622i \(-0.263110\pi\)
0.677393 + 0.735622i \(0.263110\pi\)
\(942\) 683824. 0.0251083
\(943\) −2.85811e6 −0.104665
\(944\) −4.68992e6 −0.171291
\(945\) 0 0
\(946\) −3.91899e7 −1.42379
\(947\) 1.88453e7 0.682853 0.341426 0.939909i \(-0.389090\pi\)
0.341426 + 0.939909i \(0.389090\pi\)
\(948\) −2.00848e6 −0.0725850
\(949\) −4.69577e6 −0.169255
\(950\) −7.75000e6 −0.278607
\(951\) −321422. −0.0115246
\(952\) 0 0
\(953\) −1.25120e7 −0.446265 −0.223133 0.974788i \(-0.571628\pi\)
−0.223133 + 0.974788i \(0.571628\pi\)
\(954\) 5.02121e7 1.78623
\(955\) 5.66532e6 0.201009
\(956\) 2.45090e7 0.867322
\(957\) −2.25820e6 −0.0797046
\(958\) 1.58879e7 0.559311
\(959\) 0 0
\(960\) −819200. −0.0286888
\(961\) −2.72083e7 −0.950370
\(962\) 8.54115e7 2.97563
\(963\) −3.31158e7 −1.15072
\(964\) 3.87500e7 1.34301
\(965\) −1.16190e6 −0.0401652
\(966\) 0 0
\(967\) −3.42344e7 −1.17733 −0.588663 0.808379i \(-0.700346\pi\)
−0.588663 + 0.808379i \(0.700346\pi\)
\(968\) 0 0
\(969\) 2.53735e6 0.0868102
\(970\) 1.66860e6 0.0569407
\(971\) 2.62027e7 0.891864 0.445932 0.895067i \(-0.352872\pi\)
0.445932 + 0.895067i \(0.352872\pi\)
\(972\) −5.63763e6 −0.191395
\(973\) 0 0
\(974\) 8.55790e6 0.289048
\(975\) −605625. −0.0204029
\(976\) −1.27877e7 −0.429703
\(977\) −8.01114e6 −0.268508 −0.134254 0.990947i \(-0.542864\pi\)
−0.134254 + 0.990947i \(0.542864\pi\)
\(978\) 1.54421e6 0.0516248
\(979\) −6.67269e7 −2.22507
\(980\) 0 0
\(981\) −2.64954e7 −0.879017
\(982\) −3.67397e7 −1.21578
\(983\) 4.60126e7 1.51877 0.759387 0.650639i \(-0.225499\pi\)
0.759387 + 0.650639i \(0.225499\pi\)
\(984\) 0 0
\(985\) −5.12430e6 −0.168284
\(986\) −6.52836e7 −2.13851
\(987\) 0 0
\(988\) 4.80624e7 1.56644
\(989\) 1.78864e7 0.581475
\(990\) 2.19252e7 0.710977
\(991\) −3.75828e7 −1.21564 −0.607821 0.794074i \(-0.707956\pi\)
−0.607821 + 0.794074i \(0.707956\pi\)
\(992\) −9.76486e6 −0.315055
\(993\) 2.23259e6 0.0718514
\(994\) 0 0
\(995\) −2.38255e7 −0.762929
\(996\) −756608. −0.0241670
\(997\) −2.22066e7 −0.707529 −0.353765 0.935334i \(-0.615099\pi\)
−0.353765 + 0.935334i \(0.615099\pi\)
\(998\) −1.56852e7 −0.498500
\(999\) −5.34373e6 −0.169407
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 245.6.a.a.1.1 1
7.6 odd 2 35.6.a.a.1.1 1
21.20 even 2 315.6.a.a.1.1 1
28.27 even 2 560.6.a.c.1.1 1
35.13 even 4 175.6.b.b.99.2 2
35.27 even 4 175.6.b.b.99.1 2
35.34 odd 2 175.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.6.a.a.1.1 1 7.6 odd 2
175.6.a.a.1.1 1 35.34 odd 2
175.6.b.b.99.1 2 35.27 even 4
175.6.b.b.99.2 2 35.13 even 4
245.6.a.a.1.1 1 1.1 even 1 trivial
315.6.a.a.1.1 1 21.20 even 2
560.6.a.c.1.1 1 28.27 even 2