Properties

Label 43.10.a.a.1.15
Level 43
Weight 10
Character 43.1
Self dual yes
Analytic conductor 22.147
Analytic rank 1
Dimension 15
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.1465409550\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: multiple of \( 2^{10}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(-45.0936\) of \(x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} - 32493903147264 x^{6} - 1516975415483904 x^{5} + 10892588268404224 x^{4} + 139803541742443008 x^{3} - 1349125586394823680 x^{2} + 2103623681144094720 x + 529838441422848000\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+43.0936 q^{2} -179.621 q^{3} +1345.05 q^{4} -1330.99 q^{5} -7740.49 q^{6} -743.545 q^{7} +35899.3 q^{8} +12580.5 q^{9} +O(q^{10})\) \(q+43.0936 q^{2} -179.621 q^{3} +1345.05 q^{4} -1330.99 q^{5} -7740.49 q^{6} -743.545 q^{7} +35899.3 q^{8} +12580.5 q^{9} -57356.9 q^{10} -60876.5 q^{11} -241599. q^{12} -104090. q^{13} -32042.0 q^{14} +239072. q^{15} +858359. q^{16} -344506. q^{17} +542140. q^{18} -626694. q^{19} -1.79025e6 q^{20} +133556. q^{21} -2.62338e6 q^{22} +1.13084e6 q^{23} -6.44824e6 q^{24} -181604. q^{25} -4.48560e6 q^{26} +1.27575e6 q^{27} -1.00011e6 q^{28} +3.51526e6 q^{29} +1.03025e7 q^{30} -6.97177e6 q^{31} +1.86093e7 q^{32} +1.09347e7 q^{33} -1.48460e7 q^{34} +989648. q^{35} +1.69215e7 q^{36} +7.60065e6 q^{37} -2.70065e7 q^{38} +1.86967e7 q^{39} -4.77814e7 q^{40} +3.04443e7 q^{41} +5.75540e6 q^{42} -3.41880e6 q^{43} -8.18822e7 q^{44} -1.67445e7 q^{45} +4.87317e7 q^{46} +3.57930e7 q^{47} -1.54179e8 q^{48} -3.98007e7 q^{49} -7.82595e6 q^{50} +6.18803e7 q^{51} -1.40006e8 q^{52} -9.41168e7 q^{53} +5.49766e7 q^{54} +8.10257e7 q^{55} -2.66927e7 q^{56} +1.12567e8 q^{57} +1.51485e8 q^{58} -1.25011e8 q^{59} +3.21565e8 q^{60} +1.62742e8 q^{61} -3.00439e8 q^{62} -9.35420e6 q^{63} +3.62462e8 q^{64} +1.38542e8 q^{65} +4.71214e8 q^{66} +1.76153e8 q^{67} -4.63379e8 q^{68} -2.03121e8 q^{69} +4.26474e7 q^{70} -7.75938e7 q^{71} +4.51632e8 q^{72} -4.14592e8 q^{73} +3.27539e8 q^{74} +3.26198e7 q^{75} -8.42937e8 q^{76} +4.52644e7 q^{77} +8.05706e8 q^{78} +3.87411e8 q^{79} -1.14246e9 q^{80} -4.76773e8 q^{81} +1.31195e9 q^{82} +1.61425e7 q^{83} +1.79640e8 q^{84} +4.58532e8 q^{85} -1.47328e8 q^{86} -6.31412e8 q^{87} -2.18542e9 q^{88} -1.53813e8 q^{89} -7.21580e8 q^{90} +7.73955e7 q^{91} +1.52103e9 q^{92} +1.25227e9 q^{93} +1.54245e9 q^{94} +8.34120e8 q^{95} -3.34261e9 q^{96} +1.02217e9 q^{97} -1.71516e9 q^{98} -7.65859e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 43.0936 1.90448 0.952242 0.305345i \(-0.0987716\pi\)
0.952242 + 0.305345i \(0.0987716\pi\)
\(3\) −179.621 −1.28030 −0.640148 0.768252i \(-0.721127\pi\)
−0.640148 + 0.768252i \(0.721127\pi\)
\(4\) 1345.05 2.62706
\(5\) −1330.99 −0.952375 −0.476188 0.879344i \(-0.657982\pi\)
−0.476188 + 0.879344i \(0.657982\pi\)
\(6\) −7740.49 −2.43830
\(7\) −743.545 −0.117049 −0.0585243 0.998286i \(-0.518640\pi\)
−0.0585243 + 0.998286i \(0.518640\pi\)
\(8\) 35899.3 3.09871
\(9\) 12580.5 0.639157
\(10\) −57356.9 −1.81378
\(11\) −60876.5 −1.25367 −0.626834 0.779153i \(-0.715650\pi\)
−0.626834 + 0.779153i \(0.715650\pi\)
\(12\) −241599. −3.36341
\(13\) −104090. −1.01080 −0.505398 0.862887i \(-0.668654\pi\)
−0.505398 + 0.862887i \(0.668654\pi\)
\(14\) −32042.0 −0.222917
\(15\) 239072. 1.21932
\(16\) 858359. 3.27438
\(17\) −344506. −1.00041 −0.500203 0.865908i \(-0.666741\pi\)
−0.500203 + 0.865908i \(0.666741\pi\)
\(18\) 542140. 1.21726
\(19\) −626694. −1.10323 −0.551613 0.834100i \(-0.685987\pi\)
−0.551613 + 0.834100i \(0.685987\pi\)
\(20\) −1.79025e6 −2.50195
\(21\) 133556. 0.149857
\(22\) −2.62338e6 −2.38759
\(23\) 1.13084e6 0.842605 0.421303 0.906920i \(-0.361573\pi\)
0.421303 + 0.906920i \(0.361573\pi\)
\(24\) −6.44824e6 −3.96726
\(25\) −181604. −0.0929811
\(26\) −4.48560e6 −1.92504
\(27\) 1.27575e6 0.461986
\(28\) −1.00011e6 −0.307494
\(29\) 3.51526e6 0.922924 0.461462 0.887160i \(-0.347325\pi\)
0.461462 + 0.887160i \(0.347325\pi\)
\(30\) 1.03025e7 2.32218
\(31\) −6.97177e6 −1.35586 −0.677931 0.735125i \(-0.737123\pi\)
−0.677931 + 0.735125i \(0.737123\pi\)
\(32\) 1.86093e7 3.13730
\(33\) 1.09347e7 1.60507
\(34\) −1.48460e7 −1.90526
\(35\) 989648. 0.111474
\(36\) 1.69215e7 1.67910
\(37\) 7.60065e6 0.666719 0.333360 0.942800i \(-0.391818\pi\)
0.333360 + 0.942800i \(0.391818\pi\)
\(38\) −2.70065e7 −2.10108
\(39\) 1.86967e7 1.29412
\(40\) −4.77814e7 −2.95113
\(41\) 3.04443e7 1.68259 0.841296 0.540575i \(-0.181793\pi\)
0.841296 + 0.540575i \(0.181793\pi\)
\(42\) 5.75540e6 0.285400
\(43\) −3.41880e6 −0.152499
\(44\) −8.18822e7 −3.29346
\(45\) −1.67445e7 −0.608718
\(46\) 4.87317e7 1.60473
\(47\) 3.57930e7 1.06994 0.534968 0.844872i \(-0.320324\pi\)
0.534968 + 0.844872i \(0.320324\pi\)
\(48\) −1.54179e8 −4.19217
\(49\) −3.98007e7 −0.986300
\(50\) −7.82595e6 −0.177081
\(51\) 6.18803e7 1.28082
\(52\) −1.40006e8 −2.65542
\(53\) −9.41168e7 −1.63842 −0.819211 0.573492i \(-0.805588\pi\)
−0.819211 + 0.573492i \(0.805588\pi\)
\(54\) 5.49766e7 0.879844
\(55\) 8.10257e7 1.19396
\(56\) −2.66927e7 −0.362699
\(57\) 1.12567e8 1.41246
\(58\) 1.51485e8 1.75769
\(59\) −1.25011e8 −1.34312 −0.671561 0.740949i \(-0.734376\pi\)
−0.671561 + 0.740949i \(0.734376\pi\)
\(60\) 3.21565e8 3.20323
\(61\) 1.62742e8 1.50493 0.752464 0.658633i \(-0.228865\pi\)
0.752464 + 0.658633i \(0.228865\pi\)
\(62\) −3.00439e8 −2.58222
\(63\) −9.35420e6 −0.0748125
\(64\) 3.62462e8 2.70055
\(65\) 1.38542e8 0.962656
\(66\) 4.71214e8 3.05682
\(67\) 1.76153e8 1.06796 0.533978 0.845498i \(-0.320697\pi\)
0.533978 + 0.845498i \(0.320697\pi\)
\(68\) −4.63379e8 −2.62813
\(69\) −2.03121e8 −1.07878
\(70\) 4.26474e7 0.212301
\(71\) −7.75938e7 −0.362380 −0.181190 0.983448i \(-0.557995\pi\)
−0.181190 + 0.983448i \(0.557995\pi\)
\(72\) 4.51632e8 1.98056
\(73\) −4.14592e8 −1.70871 −0.854354 0.519692i \(-0.826047\pi\)
−0.854354 + 0.519692i \(0.826047\pi\)
\(74\) 3.27539e8 1.26976
\(75\) 3.26198e7 0.119043
\(76\) −8.42937e8 −2.89824
\(77\) 4.52644e7 0.146740
\(78\) 8.05706e8 2.46462
\(79\) 3.87411e8 1.11905 0.559526 0.828813i \(-0.310983\pi\)
0.559526 + 0.828813i \(0.310983\pi\)
\(80\) −1.14246e9 −3.11844
\(81\) −4.76773e8 −1.23064
\(82\) 1.31195e9 3.20447
\(83\) 1.61425e7 0.0373354 0.0186677 0.999826i \(-0.494058\pi\)
0.0186677 + 0.999826i \(0.494058\pi\)
\(84\) 1.79640e8 0.393683
\(85\) 4.58532e8 0.952763
\(86\) −1.47328e8 −0.290431
\(87\) −6.31412e8 −1.18162
\(88\) −2.18542e9 −3.88475
\(89\) −1.53813e8 −0.259859 −0.129929 0.991523i \(-0.541475\pi\)
−0.129929 + 0.991523i \(0.541475\pi\)
\(90\) −7.21580e8 −1.15929
\(91\) 7.73955e7 0.118312
\(92\) 1.52103e9 2.21357
\(93\) 1.25227e9 1.73591
\(94\) 1.54245e9 2.03768
\(95\) 8.34120e8 1.05069
\(96\) −3.34261e9 −4.01667
\(97\) 1.02217e9 1.17233 0.586167 0.810190i \(-0.300636\pi\)
0.586167 + 0.810190i \(0.300636\pi\)
\(98\) −1.71516e9 −1.87839
\(99\) −7.65859e8 −0.801291
\(100\) −2.44267e8 −0.244267
\(101\) −6.67110e8 −0.637898 −0.318949 0.947772i \(-0.603330\pi\)
−0.318949 + 0.947772i \(0.603330\pi\)
\(102\) 2.66664e9 2.43929
\(103\) 6.79368e7 0.0594754 0.0297377 0.999558i \(-0.490533\pi\)
0.0297377 + 0.999558i \(0.490533\pi\)
\(104\) −3.73675e9 −3.13216
\(105\) −1.77761e8 −0.142720
\(106\) −4.05583e9 −3.12035
\(107\) −1.71864e9 −1.26753 −0.633766 0.773525i \(-0.718492\pi\)
−0.633766 + 0.773525i \(0.718492\pi\)
\(108\) 1.71595e9 1.21366
\(109\) −1.49887e9 −1.01706 −0.508530 0.861045i \(-0.669811\pi\)
−0.508530 + 0.861045i \(0.669811\pi\)
\(110\) 3.49169e9 2.27388
\(111\) −1.36523e9 −0.853598
\(112\) −6.38229e8 −0.383262
\(113\) −4.77264e8 −0.275363 −0.137681 0.990477i \(-0.543965\pi\)
−0.137681 + 0.990477i \(0.543965\pi\)
\(114\) 4.85092e9 2.69000
\(115\) −1.50512e9 −0.802476
\(116\) 4.72821e9 2.42458
\(117\) −1.30951e9 −0.646057
\(118\) −5.38718e9 −2.55795
\(119\) 2.56156e8 0.117096
\(120\) 8.58252e9 3.77832
\(121\) 1.34800e9 0.571684
\(122\) 7.01314e9 2.86611
\(123\) −5.46842e9 −2.15421
\(124\) −9.37741e9 −3.56193
\(125\) 2.84129e9 1.04093
\(126\) −4.03105e8 −0.142479
\(127\) 1.95999e9 0.668556 0.334278 0.942475i \(-0.391508\pi\)
0.334278 + 0.942475i \(0.391508\pi\)
\(128\) 6.09179e9 2.00586
\(129\) 6.14087e8 0.195243
\(130\) 5.97027e9 1.83336
\(131\) −3.31045e9 −0.982123 −0.491061 0.871125i \(-0.663391\pi\)
−0.491061 + 0.871125i \(0.663391\pi\)
\(132\) 1.47077e10 4.21660
\(133\) 4.65975e8 0.129131
\(134\) 7.59106e9 2.03391
\(135\) −1.69800e9 −0.439984
\(136\) −1.23675e10 −3.09997
\(137\) −6.47943e9 −1.57143 −0.785713 0.618591i \(-0.787704\pi\)
−0.785713 + 0.618591i \(0.787704\pi\)
\(138\) −8.75321e9 −2.05453
\(139\) −6.83083e9 −1.55206 −0.776028 0.630699i \(-0.782768\pi\)
−0.776028 + 0.630699i \(0.782768\pi\)
\(140\) 1.33113e9 0.292849
\(141\) −6.42916e9 −1.36984
\(142\) −3.34379e9 −0.690147
\(143\) 6.33662e9 1.26720
\(144\) 1.07986e10 2.09284
\(145\) −4.67875e9 −0.878970
\(146\) −1.78662e10 −3.25421
\(147\) 7.14903e9 1.26276
\(148\) 1.02233e10 1.75151
\(149\) −5.71164e9 −0.949341 −0.474671 0.880164i \(-0.657433\pi\)
−0.474671 + 0.880164i \(0.657433\pi\)
\(150\) 1.40570e9 0.226716
\(151\) 6.90224e9 1.08042 0.540211 0.841530i \(-0.318344\pi\)
0.540211 + 0.841530i \(0.318344\pi\)
\(152\) −2.24979e10 −3.41857
\(153\) −4.33407e9 −0.639417
\(154\) 1.95061e9 0.279464
\(155\) 9.27933e9 1.29129
\(156\) 2.51480e10 3.39972
\(157\) 6.65621e8 0.0874336 0.0437168 0.999044i \(-0.486080\pi\)
0.0437168 + 0.999044i \(0.486080\pi\)
\(158\) 1.66949e10 2.13122
\(159\) 1.69053e10 2.09766
\(160\) −2.47687e10 −2.98788
\(161\) −8.40827e8 −0.0986258
\(162\) −2.05459e10 −2.34373
\(163\) −7.03047e9 −0.780082 −0.390041 0.920798i \(-0.627539\pi\)
−0.390041 + 0.920798i \(0.627539\pi\)
\(164\) 4.09492e10 4.42027
\(165\) −1.45539e10 −1.52863
\(166\) 6.95639e8 0.0711046
\(167\) 7.10666e9 0.707036 0.353518 0.935428i \(-0.384985\pi\)
0.353518 + 0.935428i \(0.384985\pi\)
\(168\) 4.79456e9 0.464363
\(169\) 2.30190e8 0.0217068
\(170\) 1.97598e10 1.81452
\(171\) −7.88414e9 −0.705135
\(172\) −4.59847e9 −0.400623
\(173\) −1.52722e10 −1.29627 −0.648134 0.761527i \(-0.724450\pi\)
−0.648134 + 0.761527i \(0.724450\pi\)
\(174\) −2.72098e10 −2.25037
\(175\) 1.35031e8 0.0108833
\(176\) −5.22539e10 −4.10499
\(177\) 2.24546e10 1.71959
\(178\) −6.62834e9 −0.494897
\(179\) −3.28112e8 −0.0238882 −0.0119441 0.999929i \(-0.503802\pi\)
−0.0119441 + 0.999929i \(0.503802\pi\)
\(180\) −2.25223e10 −1.59914
\(181\) 1.38266e9 0.0957554 0.0478777 0.998853i \(-0.484754\pi\)
0.0478777 + 0.998853i \(0.484754\pi\)
\(182\) 3.33525e9 0.225324
\(183\) −2.92318e10 −1.92675
\(184\) 4.05961e10 2.61099
\(185\) −1.01164e10 −0.634967
\(186\) 5.39649e10 3.30600
\(187\) 2.09723e10 1.25418
\(188\) 4.81436e10 2.81079
\(189\) −9.48578e8 −0.0540748
\(190\) 3.59452e10 2.00101
\(191\) 1.10617e10 0.601411 0.300706 0.953717i \(-0.402778\pi\)
0.300706 + 0.953717i \(0.402778\pi\)
\(192\) −6.51055e10 −3.45750
\(193\) 1.56904e10 0.814005 0.407003 0.913427i \(-0.366574\pi\)
0.407003 + 0.913427i \(0.366574\pi\)
\(194\) 4.40490e10 2.23269
\(195\) −2.48850e10 −1.23248
\(196\) −5.35342e10 −2.59107
\(197\) −1.54645e10 −0.731538 −0.365769 0.930706i \(-0.619194\pi\)
−0.365769 + 0.930706i \(0.619194\pi\)
\(198\) −3.30036e10 −1.52605
\(199\) 1.72181e10 0.778300 0.389150 0.921174i \(-0.372769\pi\)
0.389150 + 0.921174i \(0.372769\pi\)
\(200\) −6.51944e9 −0.288121
\(201\) −3.16407e10 −1.36730
\(202\) −2.87482e10 −1.21487
\(203\) −2.61375e9 −0.108027
\(204\) 8.32324e10 3.36478
\(205\) −4.05209e10 −1.60246
\(206\) 2.92764e9 0.113270
\(207\) 1.42265e10 0.538557
\(208\) −8.93464e10 −3.30973
\(209\) 3.81509e10 1.38308
\(210\) −7.66036e9 −0.271808
\(211\) 2.45117e10 0.851337 0.425669 0.904879i \(-0.360039\pi\)
0.425669 + 0.904879i \(0.360039\pi\)
\(212\) −1.26592e11 −4.30423
\(213\) 1.39374e10 0.463954
\(214\) −7.40625e10 −2.41400
\(215\) 4.55037e9 0.145236
\(216\) 4.57985e10 1.43156
\(217\) 5.18383e9 0.158702
\(218\) −6.45918e10 −1.93697
\(219\) 7.44692e10 2.18765
\(220\) 1.08984e11 3.13661
\(221\) 3.58596e10 1.01121
\(222\) −5.88327e10 −1.62566
\(223\) 3.43688e9 0.0930664 0.0465332 0.998917i \(-0.485183\pi\)
0.0465332 + 0.998917i \(0.485183\pi\)
\(224\) −1.38369e10 −0.367216
\(225\) −2.28467e9 −0.0594295
\(226\) −2.05670e10 −0.524424
\(227\) 1.17388e10 0.293431 0.146716 0.989179i \(-0.453130\pi\)
0.146716 + 0.989179i \(0.453130\pi\)
\(228\) 1.51409e11 3.71060
\(229\) −8.32583e8 −0.0200064 −0.0100032 0.999950i \(-0.503184\pi\)
−0.0100032 + 0.999950i \(0.503184\pi\)
\(230\) −6.48612e10 −1.52830
\(231\) −8.13042e9 −0.187871
\(232\) 1.26195e11 2.85987
\(233\) −7.38751e9 −0.164209 −0.0821044 0.996624i \(-0.526164\pi\)
−0.0821044 + 0.996624i \(0.526164\pi\)
\(234\) −5.64312e10 −1.23041
\(235\) −4.76400e10 −1.01898
\(236\) −1.68147e11 −3.52846
\(237\) −6.95870e10 −1.43272
\(238\) 1.10387e10 0.223008
\(239\) 3.60402e10 0.714492 0.357246 0.934010i \(-0.383716\pi\)
0.357246 + 0.934010i \(0.383716\pi\)
\(240\) 2.05210e11 3.99252
\(241\) 5.35383e10 1.02232 0.511161 0.859485i \(-0.329216\pi\)
0.511161 + 0.859485i \(0.329216\pi\)
\(242\) 5.80902e10 1.08876
\(243\) 6.05277e10 1.11359
\(244\) 2.18897e11 3.95354
\(245\) 5.29742e10 0.939327
\(246\) −2.35654e11 −4.10267
\(247\) 6.52325e10 1.11514
\(248\) −2.50282e11 −4.20142
\(249\) −2.89953e9 −0.0478003
\(250\) 1.22441e11 1.98243
\(251\) 8.37307e10 1.33154 0.665768 0.746159i \(-0.268104\pi\)
0.665768 + 0.746159i \(0.268104\pi\)
\(252\) −1.25819e10 −0.196537
\(253\) −6.88413e10 −1.05635
\(254\) 8.44630e10 1.27325
\(255\) −8.23618e10 −1.21982
\(256\) 7.69365e10 1.11957
\(257\) −9.28756e10 −1.32801 −0.664007 0.747726i \(-0.731146\pi\)
−0.664007 + 0.747726i \(0.731146\pi\)
\(258\) 2.64632e10 0.371838
\(259\) −5.65143e9 −0.0780386
\(260\) 1.86346e11 2.52896
\(261\) 4.42238e10 0.589894
\(262\) −1.42659e11 −1.87044
\(263\) 4.81389e10 0.620434 0.310217 0.950666i \(-0.399598\pi\)
0.310217 + 0.950666i \(0.399598\pi\)
\(264\) 3.92547e11 4.97363
\(265\) 1.25268e11 1.56039
\(266\) 2.00805e10 0.245928
\(267\) 2.76279e10 0.332696
\(268\) 2.36935e11 2.80558
\(269\) −5.22733e10 −0.608688 −0.304344 0.952562i \(-0.598437\pi\)
−0.304344 + 0.952562i \(0.598437\pi\)
\(270\) −7.31730e10 −0.837942
\(271\) −1.23731e9 −0.0139354 −0.00696768 0.999976i \(-0.502218\pi\)
−0.00696768 + 0.999976i \(0.502218\pi\)
\(272\) −2.95710e11 −3.27571
\(273\) −1.39018e10 −0.151475
\(274\) −2.79221e11 −2.99276
\(275\) 1.10554e10 0.116567
\(276\) −2.73209e11 −2.83403
\(277\) −1.26159e10 −0.128754 −0.0643768 0.997926i \(-0.520506\pi\)
−0.0643768 + 0.997926i \(0.520506\pi\)
\(278\) −2.94365e11 −2.95586
\(279\) −8.77086e10 −0.866609
\(280\) 3.55276e10 0.345426
\(281\) 3.54512e10 0.339197 0.169599 0.985513i \(-0.445753\pi\)
0.169599 + 0.985513i \(0.445753\pi\)
\(282\) −2.77055e11 −2.60883
\(283\) −4.93389e10 −0.457247 −0.228624 0.973515i \(-0.573422\pi\)
−0.228624 + 0.973515i \(0.573422\pi\)
\(284\) −1.04368e11 −0.951994
\(285\) −1.49825e11 −1.34519
\(286\) 2.73068e11 2.41337
\(287\) −2.26367e10 −0.196945
\(288\) 2.34115e11 2.00522
\(289\) 9.64955e7 0.000813704 0
\(290\) −2.01624e11 −1.67398
\(291\) −1.83603e11 −1.50093
\(292\) −5.57648e11 −4.48888
\(293\) 8.58588e9 0.0680582 0.0340291 0.999421i \(-0.489166\pi\)
0.0340291 + 0.999421i \(0.489166\pi\)
\(294\) 3.08077e11 2.40490
\(295\) 1.66388e11 1.27916
\(296\) 2.72858e11 2.06597
\(297\) −7.76632e10 −0.579177
\(298\) −2.46135e11 −1.80800
\(299\) −1.17708e11 −0.851701
\(300\) 4.38753e10 0.312734
\(301\) 2.54203e9 0.0178497
\(302\) 2.97442e11 2.05765
\(303\) 1.19827e11 0.816699
\(304\) −5.37928e11 −3.61238
\(305\) −2.16607e11 −1.43326
\(306\) −1.86770e11 −1.21776
\(307\) −1.78128e11 −1.14448 −0.572241 0.820085i \(-0.693926\pi\)
−0.572241 + 0.820085i \(0.693926\pi\)
\(308\) 6.08831e10 0.385495
\(309\) −1.22028e10 −0.0761461
\(310\) 3.99879e11 2.45924
\(311\) −1.70733e11 −1.03489 −0.517447 0.855715i \(-0.673118\pi\)
−0.517447 + 0.855715i \(0.673118\pi\)
\(312\) 6.71197e11 4.01009
\(313\) 1.90876e11 1.12409 0.562046 0.827106i \(-0.310015\pi\)
0.562046 + 0.827106i \(0.310015\pi\)
\(314\) 2.86840e10 0.166516
\(315\) 1.24503e10 0.0712496
\(316\) 5.21089e11 2.93982
\(317\) 9.34241e10 0.519628 0.259814 0.965659i \(-0.416339\pi\)
0.259814 + 0.965659i \(0.416339\pi\)
\(318\) 7.28510e11 3.99497
\(319\) −2.13997e11 −1.15704
\(320\) −4.82431e11 −2.57194
\(321\) 3.08704e11 1.62282
\(322\) −3.62342e10 −0.187831
\(323\) 2.15900e11 1.10367
\(324\) −6.41286e11 −3.23295
\(325\) 1.89031e10 0.0939849
\(326\) −3.02968e11 −1.48565
\(327\) 2.69229e11 1.30214
\(328\) 1.09293e12 5.21386
\(329\) −2.66137e10 −0.125235
\(330\) −6.27178e11 −2.91124
\(331\) 5.97363e10 0.273535 0.136767 0.990603i \(-0.456329\pi\)
0.136767 + 0.990603i \(0.456329\pi\)
\(332\) 2.17126e10 0.0980822
\(333\) 9.56202e10 0.426138
\(334\) 3.06251e11 1.34654
\(335\) −2.34457e11 −1.01710
\(336\) 1.14639e11 0.490688
\(337\) 1.79056e11 0.756230 0.378115 0.925759i \(-0.376572\pi\)
0.378115 + 0.925759i \(0.376572\pi\)
\(338\) 9.91969e9 0.0413403
\(339\) 8.57263e10 0.352546
\(340\) 6.16751e11 2.50296
\(341\) 4.24417e11 1.69980
\(342\) −3.39756e11 −1.34292
\(343\) 5.95984e10 0.232494
\(344\) −1.22732e11 −0.472548
\(345\) 2.70351e11 1.02741
\(346\) −6.58134e11 −2.46872
\(347\) −3.88777e11 −1.43952 −0.719760 0.694223i \(-0.755748\pi\)
−0.719760 + 0.694223i \(0.755748\pi\)
\(348\) −8.49284e11 −3.10417
\(349\) −4.77801e11 −1.72398 −0.861991 0.506923i \(-0.830783\pi\)
−0.861991 + 0.506923i \(0.830783\pi\)
\(350\) 5.81895e9 0.0207271
\(351\) −1.32793e11 −0.466973
\(352\) −1.13287e12 −3.93313
\(353\) −5.04077e11 −1.72787 −0.863933 0.503606i \(-0.832006\pi\)
−0.863933 + 0.503606i \(0.832006\pi\)
\(354\) 9.67649e11 3.27494
\(355\) 1.03276e11 0.345122
\(356\) −2.06887e11 −0.682665
\(357\) −4.60108e10 −0.149918
\(358\) −1.41395e10 −0.0454946
\(359\) 4.17951e11 1.32801 0.664004 0.747729i \(-0.268856\pi\)
0.664004 + 0.747729i \(0.268856\pi\)
\(360\) −6.01115e11 −1.88624
\(361\) 7.00577e10 0.217107
\(362\) 5.95839e10 0.182365
\(363\) −2.42129e11 −0.731925
\(364\) 1.04101e11 0.310813
\(365\) 5.51816e11 1.62733
\(366\) −1.25970e12 −3.66947
\(367\) 5.55628e11 1.59877 0.799387 0.600817i \(-0.205158\pi\)
0.799387 + 0.600817i \(0.205158\pi\)
\(368\) 9.70662e11 2.75901
\(369\) 3.83005e11 1.07544
\(370\) −4.35950e11 −1.20928
\(371\) 6.99801e10 0.191775
\(372\) 1.68438e12 4.56033
\(373\) −6.91524e11 −1.84977 −0.924885 0.380247i \(-0.875839\pi\)
−0.924885 + 0.380247i \(0.875839\pi\)
\(374\) 9.03772e11 2.38856
\(375\) −5.10354e11 −1.33270
\(376\) 1.28494e12 3.31542
\(377\) −3.65902e11 −0.932887
\(378\) −4.08776e10 −0.102985
\(379\) 5.21767e11 1.29897 0.649486 0.760373i \(-0.274984\pi\)
0.649486 + 0.760373i \(0.274984\pi\)
\(380\) 1.12194e12 2.76021
\(381\) −3.52055e11 −0.855949
\(382\) 4.76688e11 1.14538
\(383\) −6.52757e11 −1.55009 −0.775045 0.631906i \(-0.782273\pi\)
−0.775045 + 0.631906i \(0.782273\pi\)
\(384\) −1.09421e12 −2.56809
\(385\) −6.02463e10 −0.139752
\(386\) 6.76157e11 1.55026
\(387\) −4.30103e10 −0.0974706
\(388\) 1.37488e12 3.07979
\(389\) 3.45861e11 0.765823 0.382912 0.923785i \(-0.374921\pi\)
0.382912 + 0.923785i \(0.374921\pi\)
\(390\) −1.07238e12 −2.34725
\(391\) −3.89579e11 −0.842948
\(392\) −1.42882e12 −3.05625
\(393\) 5.94624e11 1.25741
\(394\) −6.66419e11 −1.39320
\(395\) −5.15639e11 −1.06576
\(396\) −1.03012e12 −2.10504
\(397\) 1.97139e11 0.398305 0.199152 0.979969i \(-0.436181\pi\)
0.199152 + 0.979969i \(0.436181\pi\)
\(398\) 7.41990e11 1.48226
\(399\) −8.36988e10 −0.165326
\(400\) −1.55881e11 −0.304455
\(401\) −9.67496e11 −1.86853 −0.934263 0.356584i \(-0.883941\pi\)
−0.934263 + 0.356584i \(0.883941\pi\)
\(402\) −1.36351e12 −2.60400
\(403\) 7.25691e11 1.37050
\(404\) −8.97300e11 −1.67580
\(405\) 6.34578e11 1.17203
\(406\) −1.12636e11 −0.205736
\(407\) −4.62701e11 −0.835845
\(408\) 2.22146e12 3.96888
\(409\) −7.33241e11 −1.29566 −0.647831 0.761784i \(-0.724324\pi\)
−0.647831 + 0.761784i \(0.724324\pi\)
\(410\) −1.74619e12 −3.05186
\(411\) 1.16384e12 2.01189
\(412\) 9.13786e10 0.156245
\(413\) 9.29516e10 0.157211
\(414\) 6.13071e11 1.02567
\(415\) −2.14855e10 −0.0355573
\(416\) −1.93704e12 −3.17116
\(417\) 1.22696e12 1.98709
\(418\) 1.64406e12 2.63405
\(419\) 1.00496e11 0.159289 0.0796443 0.996823i \(-0.474622\pi\)
0.0796443 + 0.996823i \(0.474622\pi\)
\(420\) −2.39098e11 −0.374934
\(421\) 8.88132e10 0.137787 0.0688935 0.997624i \(-0.478053\pi\)
0.0688935 + 0.997624i \(0.478053\pi\)
\(422\) 1.05629e12 1.62136
\(423\) 4.50295e11 0.683858
\(424\) −3.37872e12 −5.07699
\(425\) 6.25636e10 0.0930189
\(426\) 6.00614e11 0.883592
\(427\) −1.21006e11 −0.176150
\(428\) −2.31167e12 −3.32988
\(429\) −1.13819e12 −1.62239
\(430\) 1.96092e11 0.276599
\(431\) 4.61691e11 0.644471 0.322236 0.946660i \(-0.395566\pi\)
0.322236 + 0.946660i \(0.395566\pi\)
\(432\) 1.09505e12 1.51272
\(433\) 5.27475e11 0.721119 0.360559 0.932736i \(-0.382586\pi\)
0.360559 + 0.932736i \(0.382586\pi\)
\(434\) 2.23390e11 0.302245
\(435\) 8.40400e11 1.12534
\(436\) −2.01607e12 −2.67187
\(437\) −7.08688e11 −0.929584
\(438\) 3.20914e12 4.16635
\(439\) 7.31485e11 0.939973 0.469986 0.882674i \(-0.344259\pi\)
0.469986 + 0.882674i \(0.344259\pi\)
\(440\) 2.90876e12 3.69974
\(441\) −5.00714e11 −0.630400
\(442\) 1.54532e12 1.92583
\(443\) −4.46593e11 −0.550929 −0.275464 0.961311i \(-0.588832\pi\)
−0.275464 + 0.961311i \(0.588832\pi\)
\(444\) −1.83631e12 −2.24245
\(445\) 2.04723e11 0.247483
\(446\) 1.48108e11 0.177243
\(447\) 1.02593e12 1.21544
\(448\) −2.69507e11 −0.316096
\(449\) −3.25387e11 −0.377826 −0.188913 0.981994i \(-0.560496\pi\)
−0.188913 + 0.981994i \(0.560496\pi\)
\(450\) −9.84546e10 −0.113183
\(451\) −1.85334e12 −2.10941
\(452\) −6.41945e11 −0.723394
\(453\) −1.23978e12 −1.38326
\(454\) 5.05865e11 0.558835
\(455\) −1.03012e11 −0.112678
\(456\) 4.04108e12 4.37679
\(457\) −1.70489e12 −1.82841 −0.914203 0.405257i \(-0.867182\pi\)
−0.914203 + 0.405257i \(0.867182\pi\)
\(458\) −3.58790e10 −0.0381018
\(459\) −4.39503e11 −0.462173
\(460\) −2.02447e12 −2.10815
\(461\) −4.25542e11 −0.438821 −0.219411 0.975633i \(-0.570413\pi\)
−0.219411 + 0.975633i \(0.570413\pi\)
\(462\) −3.50369e11 −0.357797
\(463\) 1.43391e12 1.45013 0.725065 0.688681i \(-0.241810\pi\)
0.725065 + 0.688681i \(0.241810\pi\)
\(464\) 3.01735e12 3.02200
\(465\) −1.66676e12 −1.65323
\(466\) −3.18354e11 −0.312733
\(467\) −3.64292e11 −0.354424 −0.177212 0.984173i \(-0.556708\pi\)
−0.177212 + 0.984173i \(0.556708\pi\)
\(468\) −1.76136e12 −1.69723
\(469\) −1.30978e11 −0.125003
\(470\) −2.05298e12 −1.94063
\(471\) −1.19559e11 −0.111941
\(472\) −4.48782e12 −4.16194
\(473\) 2.08125e11 0.191183
\(474\) −2.99875e12 −2.72859
\(475\) 1.13810e11 0.102579
\(476\) 3.44543e11 0.307619
\(477\) −1.18404e12 −1.04721
\(478\) 1.55310e12 1.36074
\(479\) 1.17368e12 1.01869 0.509344 0.860563i \(-0.329888\pi\)
0.509344 + 0.860563i \(0.329888\pi\)
\(480\) 4.44897e12 3.82537
\(481\) −7.91150e11 −0.673917
\(482\) 2.30716e12 1.94700
\(483\) 1.51030e11 0.126270
\(484\) 1.81314e12 1.50185
\(485\) −1.36050e12 −1.11650
\(486\) 2.60835e12 2.12082
\(487\) −2.54555e11 −0.205070 −0.102535 0.994729i \(-0.532695\pi\)
−0.102535 + 0.994729i \(0.532695\pi\)
\(488\) 5.84233e12 4.66333
\(489\) 1.26282e12 0.998735
\(490\) 2.28285e12 1.78893
\(491\) −1.23895e11 −0.0962028 −0.0481014 0.998842i \(-0.515317\pi\)
−0.0481014 + 0.998842i \(0.515317\pi\)
\(492\) −7.35532e12 −5.65925
\(493\) −1.21103e12 −0.923300
\(494\) 2.81110e12 2.12376
\(495\) 1.01935e12 0.763130
\(496\) −5.98429e12 −4.43961
\(497\) 5.76945e10 0.0424161
\(498\) −1.24951e11 −0.0910349
\(499\) −1.43556e12 −1.03650 −0.518250 0.855229i \(-0.673416\pi\)
−0.518250 + 0.855229i \(0.673416\pi\)
\(500\) 3.82169e12 2.73458
\(501\) −1.27650e12 −0.905215
\(502\) 3.60825e12 2.53589
\(503\) −2.19255e12 −1.52719 −0.763595 0.645695i \(-0.776568\pi\)
−0.763595 + 0.645695i \(0.776568\pi\)
\(504\) −3.35809e11 −0.231822
\(505\) 8.87914e11 0.607519
\(506\) −2.96662e12 −2.01180
\(507\) −4.13468e10 −0.0277911
\(508\) 2.63630e12 1.75633
\(509\) 8.92806e11 0.589559 0.294779 0.955565i \(-0.404754\pi\)
0.294779 + 0.955565i \(0.404754\pi\)
\(510\) −3.54926e12 −2.32312
\(511\) 3.08268e11 0.200002
\(512\) 1.96471e11 0.126352
\(513\) −7.99505e11 −0.509674
\(514\) −4.00234e12 −2.52918
\(515\) −9.04228e10 −0.0566429
\(516\) 8.25980e11 0.512916
\(517\) −2.17895e12 −1.34135
\(518\) −2.43540e11 −0.148623
\(519\) 2.74320e12 1.65961
\(520\) 4.97356e12 2.98299
\(521\) 1.73495e12 1.03161 0.515807 0.856705i \(-0.327492\pi\)
0.515807 + 0.856705i \(0.327492\pi\)
\(522\) 1.90576e12 1.12344
\(523\) 2.26368e12 1.32299 0.661497 0.749948i \(-0.269921\pi\)
0.661497 + 0.749948i \(0.269921\pi\)
\(524\) −4.45273e12 −2.58009
\(525\) −2.42543e10 −0.0139339
\(526\) 2.07448e12 1.18161
\(527\) 2.40182e12 1.35641
\(528\) 9.38587e12 5.25560
\(529\) −5.22364e11 −0.290017
\(530\) 5.39825e12 2.97174
\(531\) −1.57271e12 −0.858466
\(532\) 6.26762e11 0.339235
\(533\) −3.16894e12 −1.70076
\(534\) 1.19059e12 0.633615
\(535\) 2.28749e12 1.20717
\(536\) 6.32376e12 3.30928
\(537\) 5.89356e10 0.0305839
\(538\) −2.25264e12 −1.15924
\(539\) 2.42293e12 1.23649
\(540\) −2.28391e12 −1.15586
\(541\) 7.85800e11 0.394388 0.197194 0.980364i \(-0.436817\pi\)
0.197194 + 0.980364i \(0.436817\pi\)
\(542\) −5.33202e10 −0.0265397
\(543\) −2.48355e11 −0.122595
\(544\) −6.41102e12 −3.13857
\(545\) 1.99498e12 0.968622
\(546\) −5.99079e11 −0.288481
\(547\) −8.14762e11 −0.389124 −0.194562 0.980890i \(-0.562329\pi\)
−0.194562 + 0.980890i \(0.562329\pi\)
\(548\) −8.71518e12 −4.12823
\(549\) 2.04738e12 0.961886
\(550\) 4.76417e11 0.222001
\(551\) −2.20299e12 −1.01819
\(552\) −7.29190e12 −3.34283
\(553\) −2.88058e11 −0.130984
\(554\) −5.43664e11 −0.245209
\(555\) 1.81710e12 0.812946
\(556\) −9.18784e12 −4.07734
\(557\) 2.73409e12 1.20355 0.601775 0.798666i \(-0.294460\pi\)
0.601775 + 0.798666i \(0.294460\pi\)
\(558\) −3.77968e12 −1.65044
\(559\) 3.55862e11 0.154145
\(560\) 8.49473e11 0.365009
\(561\) −3.76706e12 −1.60572
\(562\) 1.52772e12 0.645996
\(563\) 9.71533e11 0.407540 0.203770 0.979019i \(-0.434681\pi\)
0.203770 + 0.979019i \(0.434681\pi\)
\(564\) −8.64757e12 −3.59864
\(565\) 6.35231e11 0.262249
\(566\) −2.12619e12 −0.870820
\(567\) 3.54503e11 0.144044
\(568\) −2.78556e12 −1.12291
\(569\) 2.53670e12 1.01453 0.507265 0.861790i \(-0.330657\pi\)
0.507265 + 0.861790i \(0.330657\pi\)
\(570\) −6.45650e12 −2.56189
\(571\) 4.31961e12 1.70052 0.850261 0.526361i \(-0.176444\pi\)
0.850261 + 0.526361i \(0.176444\pi\)
\(572\) 8.52310e12 3.32901
\(573\) −1.98691e12 −0.769984
\(574\) −9.75497e11 −0.375079
\(575\) −2.05364e11 −0.0783464
\(576\) 4.55996e12 1.72608
\(577\) 1.89784e12 0.712801 0.356401 0.934333i \(-0.384004\pi\)
0.356401 + 0.934333i \(0.384004\pi\)
\(578\) 4.15833e9 0.00154969
\(579\) −2.81832e12 −1.04217
\(580\) −6.29318e12 −2.30911
\(581\) −1.20027e10 −0.00437005
\(582\) −7.91211e12 −2.85850
\(583\) 5.72950e12 2.05404
\(584\) −1.48835e13 −5.29479
\(585\) 1.74293e12 0.615289
\(586\) 3.69996e11 0.129616
\(587\) 2.77649e12 0.965216 0.482608 0.875837i \(-0.339690\pi\)
0.482608 + 0.875837i \(0.339690\pi\)
\(588\) 9.61583e12 3.31733
\(589\) 4.36917e12 1.49582
\(590\) 7.17026e12 2.43613
\(591\) 2.77773e12 0.936585
\(592\) 6.52409e12 2.18309
\(593\) −2.88583e11 −0.0958352 −0.0479176 0.998851i \(-0.515258\pi\)
−0.0479176 + 0.998851i \(0.515258\pi\)
\(594\) −3.34678e12 −1.10303
\(595\) −3.40940e11 −0.111520
\(596\) −7.68246e12 −2.49397
\(597\) −3.09273e12 −0.996455
\(598\) −5.07247e12 −1.62205
\(599\) 2.66006e12 0.844250 0.422125 0.906538i \(-0.361284\pi\)
0.422125 + 0.906538i \(0.361284\pi\)
\(600\) 1.17103e12 0.368880
\(601\) 3.96050e12 1.23827 0.619134 0.785286i \(-0.287484\pi\)
0.619134 + 0.785286i \(0.287484\pi\)
\(602\) 1.09545e11 0.0339946
\(603\) 2.21610e12 0.682592
\(604\) 9.28388e12 2.83833
\(605\) −1.79417e12 −0.544458
\(606\) 5.16376e12 1.55539
\(607\) 6.64259e12 1.98604 0.993020 0.117944i \(-0.0376303\pi\)
0.993020 + 0.117944i \(0.0376303\pi\)
\(608\) −1.16623e13 −3.46115
\(609\) 4.69484e11 0.138307
\(610\) −9.33438e12 −2.72962
\(611\) −3.72569e12 −1.08149
\(612\) −5.82956e12 −1.67979
\(613\) −5.81304e12 −1.66277 −0.831383 0.555700i \(-0.812450\pi\)
−0.831383 + 0.555700i \(0.812450\pi\)
\(614\) −7.67616e12 −2.17965
\(615\) 7.27839e12 2.05162
\(616\) 1.62496e12 0.454705
\(617\) −4.96503e12 −1.37924 −0.689618 0.724173i \(-0.742222\pi\)
−0.689618 + 0.724173i \(0.742222\pi\)
\(618\) −5.25864e11 −0.145019
\(619\) −1.48949e11 −0.0407784 −0.0203892 0.999792i \(-0.506491\pi\)
−0.0203892 + 0.999792i \(0.506491\pi\)
\(620\) 1.24812e13 3.39230
\(621\) 1.44266e12 0.389271
\(622\) −7.35749e12 −1.97094
\(623\) 1.14367e11 0.0304161
\(624\) 1.60485e13 4.23743
\(625\) −3.42702e12 −0.898373
\(626\) 8.22552e12 2.14081
\(627\) −6.85269e12 −1.77075
\(628\) 8.95296e11 0.229693
\(629\) −2.61847e12 −0.666990
\(630\) 5.36527e11 0.135694
\(631\) −6.80747e11 −0.170944 −0.0854719 0.996341i \(-0.527240\pi\)
−0.0854719 + 0.996341i \(0.527240\pi\)
\(632\) 1.39078e13 3.46762
\(633\) −4.40280e12 −1.08996
\(634\) 4.02598e12 0.989622
\(635\) −2.60872e12 −0.636716
\(636\) 2.27386e13 5.51069
\(637\) 4.14285e12 0.996947
\(638\) −9.22187e12 −2.20357
\(639\) −9.76171e11 −0.231618
\(640\) −8.10808e12 −1.91033
\(641\) −3.88893e12 −0.909848 −0.454924 0.890530i \(-0.650334\pi\)
−0.454924 + 0.890530i \(0.650334\pi\)
\(642\) 1.33031e13 3.09063
\(643\) −3.00480e11 −0.0693213 −0.0346606 0.999399i \(-0.511035\pi\)
−0.0346606 + 0.999399i \(0.511035\pi\)
\(644\) −1.13096e12 −0.259096
\(645\) −8.17340e11 −0.185945
\(646\) 9.30389e12 2.10193
\(647\) −2.32257e12 −0.521074 −0.260537 0.965464i \(-0.583900\pi\)
−0.260537 + 0.965464i \(0.583900\pi\)
\(648\) −1.71158e13 −3.81338
\(649\) 7.61026e12 1.68383
\(650\) 8.14602e11 0.178993
\(651\) −9.31122e11 −0.203185
\(652\) −9.45636e12 −2.04932
\(653\) −5.89953e12 −1.26972 −0.634860 0.772627i \(-0.718942\pi\)
−0.634860 + 0.772627i \(0.718942\pi\)
\(654\) 1.16020e13 2.47990
\(655\) 4.40615e12 0.935349
\(656\) 2.61321e13 5.50944
\(657\) −5.21578e12 −1.09213
\(658\) −1.14688e12 −0.238507
\(659\) −2.83678e12 −0.585924 −0.292962 0.956124i \(-0.594641\pi\)
−0.292962 + 0.956124i \(0.594641\pi\)
\(660\) −1.95758e13 −4.01579
\(661\) 6.55557e12 1.33568 0.667842 0.744303i \(-0.267218\pi\)
0.667842 + 0.744303i \(0.267218\pi\)
\(662\) 2.57425e12 0.520942
\(663\) −6.44111e12 −1.29464
\(664\) 5.79505e11 0.115691
\(665\) −6.20206e11 −0.122981
\(666\) 4.12061e12 0.811574
\(667\) 3.97518e12 0.777661
\(668\) 9.55884e12 1.85742
\(669\) −6.17335e11 −0.119153
\(670\) −1.01036e13 −1.93704
\(671\) −9.90718e12 −1.88668
\(672\) 2.48539e12 0.470145
\(673\) −7.59974e11 −0.142801 −0.0714004 0.997448i \(-0.522747\pi\)
−0.0714004 + 0.997448i \(0.522747\pi\)
\(674\) 7.71615e12 1.44023
\(675\) −2.31681e11 −0.0429559
\(676\) 3.09618e11 0.0570250
\(677\) −7.68314e12 −1.40569 −0.702845 0.711343i \(-0.748087\pi\)
−0.702845 + 0.711343i \(0.748087\pi\)
\(678\) 3.69425e12 0.671418
\(679\) −7.60031e11 −0.137220
\(680\) 1.64610e13 2.95233
\(681\) −2.10852e12 −0.375679
\(682\) 1.82896e13 3.23725
\(683\) −3.85374e12 −0.677624 −0.338812 0.940854i \(-0.610025\pi\)
−0.338812 + 0.940854i \(0.610025\pi\)
\(684\) −1.06046e13 −1.85243
\(685\) 8.62402e12 1.49659
\(686\) 2.56831e12 0.442780
\(687\) 1.49549e11 0.0256141
\(688\) −2.93456e12 −0.499338
\(689\) 9.79660e12 1.65611
\(690\) 1.16504e13 1.95668
\(691\) 1.15096e11 0.0192048 0.00960239 0.999954i \(-0.496943\pi\)
0.00960239 + 0.999954i \(0.496943\pi\)
\(692\) −2.05420e13 −3.40537
\(693\) 5.69451e11 0.0937900
\(694\) −1.67538e13 −2.74154
\(695\) 9.09174e12 1.47814
\(696\) −2.26672e13 −3.66148
\(697\) −1.04882e13 −1.68328
\(698\) −2.05902e13 −3.28330
\(699\) 1.32695e12 0.210236
\(700\) 1.81624e11 0.0285911
\(701\) −2.15689e12 −0.337362 −0.168681 0.985671i \(-0.553951\pi\)
−0.168681 + 0.985671i \(0.553951\pi\)
\(702\) −5.72250e12 −0.889342
\(703\) −4.76328e12 −0.735542
\(704\) −2.20654e13 −3.38559
\(705\) 8.55712e12 1.30460
\(706\) −2.17224e13 −3.29069
\(707\) 4.96027e11 0.0746651
\(708\) 3.02027e13 4.51747
\(709\) 9.13106e12 1.35710 0.678552 0.734552i \(-0.262608\pi\)
0.678552 + 0.734552i \(0.262608\pi\)
\(710\) 4.45054e12 0.657279
\(711\) 4.87384e12 0.715250
\(712\) −5.52177e12 −0.805227
\(713\) −7.88393e12 −1.14246
\(714\) −1.98277e12 −0.285516
\(715\) −8.43395e12 −1.20685
\(716\) −4.41328e11 −0.0627556
\(717\) −6.47357e12 −0.914760
\(718\) 1.80110e13 2.52917
\(719\) 7.17755e12 1.00160 0.500802 0.865562i \(-0.333038\pi\)
0.500802 + 0.865562i \(0.333038\pi\)
\(720\) −1.43728e13 −1.99317
\(721\) −5.05141e10 −0.00696151
\(722\) 3.01904e12 0.413477
\(723\) −9.61658e12 −1.30888
\(724\) 1.85976e12 0.251555
\(725\) −6.38384e11 −0.0858145
\(726\) −1.04342e13 −1.39394
\(727\) 1.54751e12 0.205461 0.102730 0.994709i \(-0.467242\pi\)
0.102730 + 0.994709i \(0.467242\pi\)
\(728\) 2.77844e12 0.366615
\(729\) −1.48769e12 −0.195091
\(730\) 2.37797e13 3.09923
\(731\) 1.17780e12 0.152561
\(732\) −3.93184e13 −5.06170
\(733\) 5.60399e12 0.717017 0.358508 0.933527i \(-0.383285\pi\)
0.358508 + 0.933527i \(0.383285\pi\)
\(734\) 2.39440e13 3.04484
\(735\) −9.51525e12 −1.20262
\(736\) 2.10441e13 2.64350
\(737\) −1.07236e13 −1.33886
\(738\) 1.65051e13 2.04816
\(739\) −1.36939e12 −0.168899 −0.0844494 0.996428i \(-0.526913\pi\)
−0.0844494 + 0.996428i \(0.526913\pi\)
\(740\) −1.36070e13 −1.66810
\(741\) −1.17171e13 −1.42770
\(742\) 3.01569e12 0.365232
\(743\) −4.16784e12 −0.501720 −0.250860 0.968023i \(-0.580713\pi\)
−0.250860 + 0.968023i \(0.580713\pi\)
\(744\) 4.49557e13 5.37906
\(745\) 7.60210e12 0.904129
\(746\) −2.98002e13 −3.52286
\(747\) 2.03082e11 0.0238632
\(748\) 2.82089e13 3.29480
\(749\) 1.27789e12 0.148363
\(750\) −2.19930e13 −2.53810
\(751\) −4.35477e12 −0.499557 −0.249779 0.968303i \(-0.580358\pi\)
−0.249779 + 0.968303i \(0.580358\pi\)
\(752\) 3.07233e13 3.50338
\(753\) −1.50397e13 −1.70476
\(754\) −1.57680e13 −1.77667
\(755\) −9.18677e12 −1.02897
\(756\) −1.27589e12 −0.142058
\(757\) 1.07979e13 1.19511 0.597556 0.801827i \(-0.296138\pi\)
0.597556 + 0.801827i \(0.296138\pi\)
\(758\) 2.24848e13 2.47387
\(759\) 1.23653e13 1.35244
\(760\) 2.99443e13 3.25577
\(761\) −1.64930e13 −1.78266 −0.891328 0.453359i \(-0.850226\pi\)
−0.891328 + 0.453359i \(0.850226\pi\)
\(762\) −1.51713e13 −1.63014
\(763\) 1.11448e12 0.119045
\(764\) 1.48786e13 1.57994
\(765\) 5.76858e12 0.608965
\(766\) −2.81296e13 −2.95212
\(767\) 1.30124e13 1.35762
\(768\) −1.38194e13 −1.43339
\(769\) 1.66475e13 1.71665 0.858323 0.513109i \(-0.171506\pi\)
0.858323 + 0.513109i \(0.171506\pi\)
\(770\) −2.59623e12 −0.266155
\(771\) 1.66824e13 1.70025
\(772\) 2.11045e13 2.13844
\(773\) 1.53370e12 0.154502 0.0772509 0.997012i \(-0.475386\pi\)
0.0772509 + 0.997012i \(0.475386\pi\)
\(774\) −1.85347e12 −0.185631
\(775\) 1.26610e12 0.126070
\(776\) 3.66952e13 3.63272
\(777\) 1.01511e12 0.0999124
\(778\) 1.49044e13 1.45850
\(779\) −1.90793e13 −1.85628
\(780\) −3.34717e13 −3.23781
\(781\) 4.72364e12 0.454304
\(782\) −1.67884e13 −1.60538
\(783\) 4.48459e12 0.426378
\(784\) −3.41633e13 −3.22952
\(785\) −8.85931e11 −0.0832696
\(786\) 2.56245e13 2.39471
\(787\) −5.66934e12 −0.526801 −0.263400 0.964687i \(-0.584844\pi\)
−0.263400 + 0.964687i \(0.584844\pi\)
\(788\) −2.08005e13 −1.92179
\(789\) −8.64674e12 −0.794339
\(790\) −2.22207e13 −2.02972
\(791\) 3.54867e11 0.0322308
\(792\) −2.74938e13 −2.48297
\(793\) −1.69398e13 −1.52117
\(794\) 8.49542e12 0.758565
\(795\) −2.25007e13 −1.99776
\(796\) 2.31593e13 2.04464
\(797\) 1.69239e13 1.48572 0.742860 0.669446i \(-0.233469\pi\)
0.742860 + 0.669446i \(0.233469\pi\)
\(798\) −3.60688e12 −0.314861
\(799\) −1.23309e13 −1.07037
\(800\) −3.37952e12 −0.291709
\(801\) −1.93505e12 −0.166091
\(802\) −4.16928e13 −3.55858
\(803\) 2.52389e13 2.14215
\(804\) −4.25584e13 −3.59198
\(805\) 1.11913e12 0.0939287
\(806\) 3.12726e13 2.61009
\(807\) 9.38936e12 0.779301
\(808\) −2.39488e13 −1.97666
\(809\) 1.54138e13 1.26515 0.632575 0.774499i \(-0.281998\pi\)
0.632575 + 0.774499i \(0.281998\pi\)
\(810\) 2.73462e13 2.23211
\(811\) −6.33063e12 −0.513870 −0.256935 0.966429i \(-0.582713\pi\)
−0.256935 + 0.966429i \(0.582713\pi\)
\(812\) −3.51564e12 −0.283793
\(813\) 2.22247e11 0.0178414
\(814\) −1.99394e13 −1.59185
\(815\) 9.35745e12 0.742931
\(816\) 5.31155e13 4.19388
\(817\) 2.14254e12 0.168240
\(818\) −3.15979e13 −2.46757
\(819\) 9.73676e11 0.0756201
\(820\) −5.45028e13 −4.20975
\(821\) −1.35648e13 −1.04200 −0.521000 0.853557i \(-0.674441\pi\)
−0.521000 + 0.853557i \(0.674441\pi\)
\(822\) 5.01539e13 3.83161
\(823\) 6.80965e11 0.0517399 0.0258700 0.999665i \(-0.491764\pi\)
0.0258700 + 0.999665i \(0.491764\pi\)
\(824\) 2.43888e12 0.184297
\(825\) −1.98578e12 −0.149241
\(826\) 4.00562e12 0.299405
\(827\) 2.18527e13 1.62454 0.812270 0.583281i \(-0.198231\pi\)
0.812270 + 0.583281i \(0.198231\pi\)
\(828\) 1.91354e13 1.41482
\(829\) −8.42772e12 −0.619747 −0.309874 0.950778i \(-0.600287\pi\)
−0.309874 + 0.950778i \(0.600287\pi\)
\(830\) −9.25885e11 −0.0677183
\(831\) 2.26607e12 0.164843
\(832\) −3.77286e13 −2.72970
\(833\) 1.37116e13 0.986701
\(834\) 5.28740e13 3.78438
\(835\) −9.45886e12 −0.673364
\(836\) 5.13151e13 3.63343
\(837\) −8.89424e12 −0.626389
\(838\) 4.33072e12 0.303363
\(839\) −1.21585e13 −0.847130 −0.423565 0.905866i \(-0.639221\pi\)
−0.423565 + 0.905866i \(0.639221\pi\)
\(840\) −6.38149e12 −0.442247
\(841\) −2.15012e12 −0.148211
\(842\) 3.82728e12 0.262413
\(843\) −6.36776e12 −0.434273
\(844\) 3.29695e13 2.23651
\(845\) −3.06379e11 −0.0206730
\(846\) 1.94048e13 1.30240
\(847\) −1.00230e12 −0.0669149
\(848\) −8.07860e13 −5.36482
\(849\) 8.86229e12 0.585411
\(850\) 2.69609e12 0.177153
\(851\) 8.59508e12 0.561781
\(852\) 1.87466e13 1.21883
\(853\) 1.08092e13 0.699072 0.349536 0.936923i \(-0.386339\pi\)
0.349536 + 0.936923i \(0.386339\pi\)
\(854\) −5.21459e12 −0.335475
\(855\) 1.04937e13 0.671553
\(856\) −6.16981e13 −3.92771
\(857\) 5.36363e12 0.339660 0.169830 0.985473i \(-0.445678\pi\)
0.169830 + 0.985473i \(0.445678\pi\)
\(858\) −4.90486e13 −3.08982
\(859\) −9.61783e12 −0.602709 −0.301355 0.953512i \(-0.597439\pi\)
−0.301355 + 0.953512i \(0.597439\pi\)
\(860\) 6.12050e12 0.381543
\(861\) 4.06602e12 0.252148
\(862\) 1.98959e13 1.22738
\(863\) 1.95919e13 1.20234 0.601171 0.799121i \(-0.294701\pi\)
0.601171 + 0.799121i \(0.294701\pi\)
\(864\) 2.37408e13 1.44939
\(865\) 2.03271e13 1.23453
\(866\) 2.27308e13 1.37336
\(867\) −1.73326e10 −0.00104178
\(868\) 6.97253e12 0.416919
\(869\) −2.35842e13 −1.40292
\(870\) 3.62158e13 2.14320
\(871\) −1.83357e13 −1.07948
\(872\) −5.38085e13 −3.15157
\(873\) 1.28595e13 0.749305
\(874\) −3.05399e13 −1.77038
\(875\) −2.11263e12 −0.121839
\(876\) 1.00165e14 5.74709
\(877\) 1.92311e13 1.09775 0.548877 0.835903i \(-0.315056\pi\)
0.548877 + 0.835903i \(0.315056\pi\)
\(878\) 3.15223e13 1.79016
\(879\) −1.54220e12 −0.0871346
\(880\) 6.95492e13 3.90949
\(881\) 1.63419e13 0.913925 0.456963 0.889486i \(-0.348937\pi\)
0.456963 + 0.889486i \(0.348937\pi\)
\(882\) −2.15776e13 −1.20059
\(883\) −3.37986e13 −1.87101 −0.935503 0.353319i \(-0.885053\pi\)
−0.935503 + 0.353319i \(0.885053\pi\)
\(884\) 4.82331e13 2.65650
\(885\) −2.98868e13 −1.63770
\(886\) −1.92453e13 −1.04924
\(887\) −1.58038e13 −0.857244 −0.428622 0.903484i \(-0.641001\pi\)
−0.428622 + 0.903484i \(0.641001\pi\)
\(888\) −4.90108e13 −2.64505
\(889\) −1.45734e12 −0.0782535
\(890\) 8.82222e12 0.471328
\(891\) 2.90243e13 1.54281
\(892\) 4.62279e12 0.244491
\(893\) −2.24313e13 −1.18038
\(894\) 4.42108e13 2.31478
\(895\) 4.36712e11 0.0227505
\(896\) −4.52952e12 −0.234783
\(897\) 2.11428e13 1.09043
\(898\) −1.40221e13 −0.719564
\(899\) −2.45076e13 −1.25136
\(900\) −3.07301e12 −0.156125
\(901\) 3.24238e13 1.63909
\(902\) −7.98671e13 −4.01734
\(903\) −4.56601e11 −0.0228530
\(904\) −1.71334e13 −0.853269
\(905\) −1.84031e12 −0.0911951
\(906\) −5.34267e13 −2.63440
\(907\) −8.09983e12 −0.397414 −0.198707 0.980059i \(-0.563674\pi\)
−0.198707 + 0.980059i \(0.563674\pi\)
\(908\) 1.57893e13 0.770861
\(909\) −8.39260e12 −0.407717
\(910\) −4.43916e12 −0.214593
\(911\) −4.04038e12 −0.194352 −0.0971760 0.995267i \(-0.530981\pi\)
−0.0971760 + 0.995267i \(0.530981\pi\)
\(912\) 9.66230e13 4.62491
\(913\) −9.82701e11 −0.0468062
\(914\) −7.34696e13 −3.48217
\(915\) 3.89071e13 1.83499
\(916\) −1.11987e12 −0.0525579
\(917\) 2.46147e12 0.114956
\(918\) −1.89398e13 −0.880202
\(919\) −1.35982e13 −0.628869 −0.314435 0.949279i \(-0.601815\pi\)
−0.314435 + 0.949279i \(0.601815\pi\)
\(920\) −5.40329e13 −2.48664
\(921\) 3.19954e13 1.46528
\(922\) −1.83381e13 −0.835728
\(923\) 8.07672e12 0.366292
\(924\) −1.09359e13 −0.493548
\(925\) −1.38031e12 −0.0619923
\(926\) 6.17922e13 2.76175
\(927\) 8.54680e11 0.0380141
\(928\) 6.54165e13 2.89549
\(929\) −1.80722e13 −0.796049 −0.398024 0.917375i \(-0.630304\pi\)
−0.398024 + 0.917375i \(0.630304\pi\)
\(930\) −7.18265e13 −3.14856
\(931\) 2.49429e13 1.08811
\(932\) −9.93660e12 −0.431386
\(933\) 3.06672e13 1.32497
\(934\) −1.56986e13 −0.674995
\(935\) −2.79138e13 −1.19445
\(936\) −4.70103e13 −2.00194
\(937\) −2.82959e13 −1.19921 −0.599606 0.800295i \(-0.704676\pi\)
−0.599606 + 0.800295i \(0.704676\pi\)
\(938\) −5.64430e12 −0.238066
\(939\) −3.42852e13 −1.43917
\(940\) −6.40784e13 −2.67692
\(941\) 1.67782e13 0.697579 0.348789 0.937201i \(-0.386593\pi\)
0.348789 + 0.937201i \(0.386593\pi\)
\(942\) −5.15223e12 −0.213190
\(943\) 3.44275e13 1.41776
\(944\) −1.07305e14 −4.39789
\(945\) 1.26254e12 0.0514995
\(946\) 8.96883e12 0.364104
\(947\) −9.22630e12 −0.372780 −0.186390 0.982476i \(-0.559679\pi\)
−0.186390 + 0.982476i \(0.559679\pi\)
\(948\) −9.35983e13 −3.76383
\(949\) 4.31548e13 1.72715
\(950\) 4.90448e12 0.195360
\(951\) −1.67809e13 −0.665277
\(952\) 9.19581e12 0.362847
\(953\) −2.41710e13 −0.949241 −0.474620 0.880191i \(-0.657415\pi\)
−0.474620 + 0.880191i \(0.657415\pi\)
\(954\) −5.10245e13 −1.99439
\(955\) −1.47229e13 −0.572769
\(956\) 4.84761e13 1.87701
\(957\) 3.84382e13 1.48135
\(958\) 5.05782e13 1.94007
\(959\) 4.81775e12 0.183933
\(960\) 8.66545e13 3.29284
\(961\) 2.21660e13 0.838364
\(962\) −3.40935e13 −1.28346
\(963\) −2.16215e13 −0.810152
\(964\) 7.20119e13 2.68570
\(965\) −2.08837e13 −0.775239
\(966\) 6.50841e12 0.240479
\(967\) 4.39048e13 1.61470 0.807352 0.590070i \(-0.200900\pi\)
0.807352 + 0.590070i \(0.200900\pi\)
\(968\) 4.83923e13 1.77148
\(969\) −3.87800e13 −1.41303
\(970\) −5.86286e13 −2.12636
\(971\) −1.38873e13 −0.501339 −0.250670 0.968073i \(-0.580651\pi\)
−0.250670 + 0.968073i \(0.580651\pi\)
\(972\) 8.14130e13 2.92547
\(973\) 5.07904e12 0.181666
\(974\) −1.09697e13 −0.390552
\(975\) −3.39538e12 −0.120328
\(976\) 1.39691e14 4.92771
\(977\) −1.29967e13 −0.456359 −0.228179 0.973619i \(-0.573277\pi\)
−0.228179 + 0.973619i \(0.573277\pi\)
\(978\) 5.44192e13 1.90208
\(979\) 9.36359e12 0.325777
\(980\) 7.12532e13 2.46767
\(981\) −1.88566e13 −0.650061
\(982\) −5.33909e12 −0.183217
\(983\) −1.69991e12 −0.0580679 −0.0290340 0.999578i \(-0.509243\pi\)
−0.0290340 + 0.999578i \(0.509243\pi\)
\(984\) −1.96312e14 −6.67528
\(985\) 2.05830e13 0.696699
\(986\) −5.21875e13 −1.75841
\(987\) 4.78037e12 0.160337
\(988\) 8.77412e13 2.92953
\(989\) −3.86610e12 −0.128496
\(990\) 4.39273e13 1.45337
\(991\) −3.65973e13 −1.20536 −0.602681 0.797982i \(-0.705901\pi\)
−0.602681 + 0.797982i \(0.705901\pi\)
\(992\) −1.29740e14 −4.25374
\(993\) −1.07299e13 −0.350205
\(994\) 2.48626e12 0.0807808
\(995\) −2.29171e13 −0.741234
\(996\) −3.90003e12 −0.125574
\(997\) −7.31096e12 −0.234340 −0.117170 0.993112i \(-0.537382\pi\)
−0.117170 + 0.993112i \(0.537382\pi\)
\(998\) −6.18635e13 −1.97400
\(999\) 9.69652e12 0.308015
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 43.10.a.a.1.15 15
3.2 odd 2 387.10.a.c.1.1 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.15 15 1.1 even 1 trivial
387.10.a.c.1.1 15 3.2 odd 2