Properties

Label 43.10.a.a.1.10
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 1.10
Root \(-17.0644\) 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

\(f(q)\) \(=\) \(q+15.0644 q^{2} +34.0074 q^{3} -285.063 q^{4} +1876.98 q^{5} +512.302 q^{6} -7041.18 q^{7} -12007.3 q^{8} -18526.5 q^{9} +O(q^{10})\) \(q+15.0644 q^{2} +34.0074 q^{3} -285.063 q^{4} +1876.98 q^{5} +512.302 q^{6} -7041.18 q^{7} -12007.3 q^{8} -18526.5 q^{9} +28275.7 q^{10} -2479.03 q^{11} -9694.23 q^{12} +103059. q^{13} -106071. q^{14} +63831.2 q^{15} -34931.2 q^{16} -529570. q^{17} -279091. q^{18} -431982. q^{19} -535058. q^{20} -239452. q^{21} -37345.2 q^{22} -100577. q^{23} -408337. q^{24} +1.56994e6 q^{25} +1.55253e6 q^{26} -1.29940e6 q^{27} +2.00718e6 q^{28} -7.09806e6 q^{29} +961582. q^{30} -3.27053e6 q^{31} +5.62152e6 q^{32} -84305.4 q^{33} -7.97768e6 q^{34} -1.32162e7 q^{35} +5.28121e6 q^{36} -4.41240e6 q^{37} -6.50756e6 q^{38} +3.50477e6 q^{39} -2.25375e7 q^{40} +1.81476e7 q^{41} -3.60721e6 q^{42} -3.41880e6 q^{43} +706679. q^{44} -3.47739e7 q^{45} -1.51514e6 q^{46} +5.52154e7 q^{47} -1.18792e6 q^{48} +9.22462e6 q^{49} +2.36502e7 q^{50} -1.80093e7 q^{51} -2.93783e7 q^{52} -8.53713e6 q^{53} -1.95748e7 q^{54} -4.65310e6 q^{55} +8.45456e7 q^{56} -1.46906e7 q^{57} -1.06928e8 q^{58} -1.92252e7 q^{59} -1.81959e7 q^{60} -9.01048e6 q^{61} -4.92687e7 q^{62} +1.30448e8 q^{63} +1.02570e8 q^{64} +1.93440e8 q^{65} -1.27001e6 q^{66} +1.40140e8 q^{67} +1.50961e8 q^{68} -3.42037e6 q^{69} -1.99094e8 q^{70} +2.63642e8 q^{71} +2.22453e8 q^{72} -1.09424e8 q^{73} -6.64703e7 q^{74} +5.33895e7 q^{75} +1.23142e8 q^{76} +1.74553e7 q^{77} +5.27973e7 q^{78} -6.39726e7 q^{79} -6.55653e7 q^{80} +3.20468e8 q^{81} +2.73383e8 q^{82} +4.71378e8 q^{83} +6.82588e7 q^{84} -9.93994e8 q^{85} -5.15023e7 q^{86} -2.41386e8 q^{87} +2.97665e7 q^{88} -1.07301e9 q^{89} -5.23850e8 q^{90} -7.25657e8 q^{91} +2.86708e7 q^{92} -1.11222e8 q^{93} +8.31790e8 q^{94} -8.10822e8 q^{95} +1.91173e8 q^{96} -2.81023e8 q^{97} +1.38964e8 q^{98} +4.59278e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.0644 0.665761 0.332880 0.942969i \(-0.391980\pi\)
0.332880 + 0.942969i \(0.391980\pi\)
\(3\) 34.0074 0.242397 0.121199 0.992628i \(-0.461326\pi\)
0.121199 + 0.992628i \(0.461326\pi\)
\(4\) −285.063 −0.556763
\(5\) 1876.98 1.34306 0.671530 0.740978i \(-0.265638\pi\)
0.671530 + 0.740978i \(0.265638\pi\)
\(6\) 512.302 0.161378
\(7\) −7041.18 −1.10842 −0.554210 0.832377i \(-0.686980\pi\)
−0.554210 + 0.832377i \(0.686980\pi\)
\(8\) −12007.3 −1.03643
\(9\) −18526.5 −0.941244
\(10\) 28275.7 0.894156
\(11\) −2479.03 −0.0510523 −0.0255261 0.999674i \(-0.508126\pi\)
−0.0255261 + 0.999674i \(0.508126\pi\)
\(12\) −9694.23 −0.134958
\(13\) 103059. 1.00079 0.500393 0.865799i \(-0.333189\pi\)
0.500393 + 0.865799i \(0.333189\pi\)
\(14\) −106071. −0.737942
\(15\) 63831.2 0.325554
\(16\) −34931.2 −0.133252
\(17\) −529570. −1.53781 −0.768906 0.639361i \(-0.779199\pi\)
−0.768906 + 0.639361i \(0.779199\pi\)
\(18\) −279091. −0.626643
\(19\) −431982. −0.760456 −0.380228 0.924893i \(-0.624154\pi\)
−0.380228 + 0.924893i \(0.624154\pi\)
\(20\) −535058. −0.747766
\(21\) −239452. −0.268678
\(22\) −37345.2 −0.0339886
\(23\) −100577. −0.0749419 −0.0374709 0.999298i \(-0.511930\pi\)
−0.0374709 + 0.999298i \(0.511930\pi\)
\(24\) −408337. −0.251228
\(25\) 1.56994e6 0.803808
\(26\) 1.55253e6 0.666283
\(27\) −1.29940e6 −0.470552
\(28\) 2.00718e6 0.617127
\(29\) −7.09806e6 −1.86358 −0.931792 0.362994i \(-0.881755\pi\)
−0.931792 + 0.362994i \(0.881755\pi\)
\(30\) 961582. 0.216741
\(31\) −3.27053e6 −0.636049 −0.318025 0.948082i \(-0.603020\pi\)
−0.318025 + 0.948082i \(0.603020\pi\)
\(32\) 5.62152e6 0.947717
\(33\) −84305.4 −0.0123749
\(34\) −7.97768e6 −1.02381
\(35\) −1.32162e7 −1.48867
\(36\) 5.28121e6 0.524050
\(37\) −4.41240e6 −0.387050 −0.193525 0.981095i \(-0.561992\pi\)
−0.193525 + 0.981095i \(0.561992\pi\)
\(38\) −6.50756e6 −0.506281
\(39\) 3.50477e6 0.242587
\(40\) −2.25375e7 −1.39199
\(41\) 1.81476e7 1.00298 0.501488 0.865164i \(-0.332786\pi\)
0.501488 + 0.865164i \(0.332786\pi\)
\(42\) −3.60721e6 −0.178875
\(43\) −3.41880e6 −0.152499
\(44\) 706679. 0.0284240
\(45\) −3.47739e7 −1.26415
\(46\) −1.51514e6 −0.0498933
\(47\) 5.52154e7 1.65052 0.825259 0.564755i \(-0.191029\pi\)
0.825259 + 0.564755i \(0.191029\pi\)
\(48\) −1.18792e6 −0.0322999
\(49\) 9.22462e6 0.228595
\(50\) 2.36502e7 0.535144
\(51\) −1.80093e7 −0.372761
\(52\) −2.93783e7 −0.557200
\(53\) −8.53713e6 −0.148618 −0.0743089 0.997235i \(-0.523675\pi\)
−0.0743089 + 0.997235i \(0.523675\pi\)
\(54\) −1.95748e7 −0.313275
\(55\) −4.65310e6 −0.0685662
\(56\) 8.45456e7 1.14880
\(57\) −1.46906e7 −0.184332
\(58\) −1.06928e8 −1.24070
\(59\) −1.92252e7 −0.206556 −0.103278 0.994653i \(-0.532933\pi\)
−0.103278 + 0.994653i \(0.532933\pi\)
\(60\) −1.81959e7 −0.181256
\(61\) −9.01048e6 −0.0833228 −0.0416614 0.999132i \(-0.513265\pi\)
−0.0416614 + 0.999132i \(0.513265\pi\)
\(62\) −4.92687e7 −0.423457
\(63\) 1.30448e8 1.04329
\(64\) 1.02570e8 0.764205
\(65\) 1.93440e8 1.34411
\(66\) −1.27001e6 −0.00823873
\(67\) 1.40140e8 0.849625 0.424812 0.905281i \(-0.360340\pi\)
0.424812 + 0.905281i \(0.360340\pi\)
\(68\) 1.50961e8 0.856197
\(69\) −3.42037e6 −0.0181657
\(70\) −1.99094e8 −0.991100
\(71\) 2.63642e8 1.23127 0.615633 0.788033i \(-0.288900\pi\)
0.615633 + 0.788033i \(0.288900\pi\)
\(72\) 2.22453e8 0.975534
\(73\) −1.09424e8 −0.450982 −0.225491 0.974245i \(-0.572399\pi\)
−0.225491 + 0.974245i \(0.572399\pi\)
\(74\) −6.64703e7 −0.257683
\(75\) 5.33895e7 0.194841
\(76\) 1.23142e8 0.423394
\(77\) 1.74553e7 0.0565874
\(78\) 5.27973e7 0.161505
\(79\) −6.39726e7 −0.184787 −0.0923937 0.995723i \(-0.529452\pi\)
−0.0923937 + 0.995723i \(0.529452\pi\)
\(80\) −6.55653e7 −0.178966
\(81\) 3.20468e8 0.827183
\(82\) 2.73383e8 0.667742
\(83\) 4.71378e8 1.09023 0.545115 0.838362i \(-0.316486\pi\)
0.545115 + 0.838362i \(0.316486\pi\)
\(84\) 6.82588e7 0.149590
\(85\) −9.93994e8 −2.06537
\(86\) −5.15023e7 −0.101528
\(87\) −2.41386e8 −0.451727
\(88\) 2.97665e7 0.0529122
\(89\) −1.07301e9 −1.81279 −0.906395 0.422431i \(-0.861177\pi\)
−0.906395 + 0.422431i \(0.861177\pi\)
\(90\) −5.23850e8 −0.841619
\(91\) −7.25657e8 −1.10929
\(92\) 2.86708e7 0.0417249
\(93\) −1.11222e8 −0.154177
\(94\) 8.31790e8 1.09885
\(95\) −8.10822e8 −1.02134
\(96\) 1.91173e8 0.229724
\(97\) −2.81023e8 −0.322306 −0.161153 0.986929i \(-0.551521\pi\)
−0.161153 + 0.986929i \(0.551521\pi\)
\(98\) 1.38964e8 0.152189
\(99\) 4.59278e7 0.0480526
\(100\) −4.47531e8 −0.447531
\(101\) 9.66718e8 0.924387 0.462193 0.886779i \(-0.347063\pi\)
0.462193 + 0.886779i \(0.347063\pi\)
\(102\) −2.71300e8 −0.248170
\(103\) 7.64929e8 0.669659 0.334829 0.942279i \(-0.391321\pi\)
0.334829 + 0.942279i \(0.391321\pi\)
\(104\) −1.23746e9 −1.03725
\(105\) −4.49447e8 −0.360850
\(106\) −1.28607e8 −0.0989438
\(107\) −6.83281e8 −0.503932 −0.251966 0.967736i \(-0.581077\pi\)
−0.251966 + 0.967736i \(0.581077\pi\)
\(108\) 3.70412e8 0.261986
\(109\) 1.06256e9 0.721001 0.360501 0.932759i \(-0.382606\pi\)
0.360501 + 0.932759i \(0.382606\pi\)
\(110\) −7.00963e7 −0.0456487
\(111\) −1.50054e8 −0.0938198
\(112\) 2.45957e8 0.147699
\(113\) −2.75197e9 −1.58778 −0.793889 0.608062i \(-0.791947\pi\)
−0.793889 + 0.608062i \(0.791947\pi\)
\(114\) −2.21305e8 −0.122721
\(115\) −1.88782e8 −0.100651
\(116\) 2.02339e9 1.03757
\(117\) −1.90932e9 −0.941983
\(118\) −2.89617e8 −0.137517
\(119\) 3.72880e9 1.70454
\(120\) −7.66441e8 −0.337414
\(121\) −2.35180e9 −0.997394
\(122\) −1.35738e8 −0.0554730
\(123\) 6.17150e8 0.243119
\(124\) 9.32307e8 0.354129
\(125\) −7.19235e8 −0.263497
\(126\) 1.96513e9 0.694583
\(127\) 4.95413e8 0.168986 0.0844929 0.996424i \(-0.473073\pi\)
0.0844929 + 0.996424i \(0.473073\pi\)
\(128\) −1.33306e9 −0.438940
\(129\) −1.16264e8 −0.0369652
\(130\) 2.91407e9 0.894858
\(131\) 3.75757e9 1.11477 0.557387 0.830253i \(-0.311804\pi\)
0.557387 + 0.830253i \(0.311804\pi\)
\(132\) 2.40323e7 0.00688990
\(133\) 3.04166e9 0.842904
\(134\) 2.11114e9 0.565646
\(135\) −2.43896e9 −0.631979
\(136\) 6.35871e9 1.59384
\(137\) −5.56301e9 −1.34917 −0.674586 0.738197i \(-0.735678\pi\)
−0.674586 + 0.738197i \(0.735678\pi\)
\(138\) −5.15259e7 −0.0120940
\(139\) −2.23267e9 −0.507292 −0.253646 0.967297i \(-0.581630\pi\)
−0.253646 + 0.967297i \(0.581630\pi\)
\(140\) 3.76744e9 0.828838
\(141\) 1.87773e9 0.400081
\(142\) 3.97162e9 0.819728
\(143\) −2.55487e8 −0.0510924
\(144\) 6.47154e8 0.125423
\(145\) −1.33229e10 −2.50290
\(146\) −1.64841e9 −0.300246
\(147\) 3.13705e8 0.0554107
\(148\) 1.25781e9 0.215495
\(149\) 2.53385e9 0.421156 0.210578 0.977577i \(-0.432465\pi\)
0.210578 + 0.977577i \(0.432465\pi\)
\(150\) 8.04282e8 0.129717
\(151\) −8.68661e9 −1.35973 −0.679867 0.733335i \(-0.737963\pi\)
−0.679867 + 0.733335i \(0.737963\pi\)
\(152\) 5.18693e9 0.788160
\(153\) 9.81108e9 1.44746
\(154\) 2.62955e8 0.0376736
\(155\) −6.13873e9 −0.854252
\(156\) −9.99078e8 −0.135064
\(157\) −1.63159e8 −0.0214320 −0.0107160 0.999943i \(-0.503411\pi\)
−0.0107160 + 0.999943i \(0.503411\pi\)
\(158\) −9.63712e8 −0.123024
\(159\) −2.90325e8 −0.0360245
\(160\) 1.05515e10 1.27284
\(161\) 7.08183e8 0.0830671
\(162\) 4.82767e9 0.550706
\(163\) −1.74840e10 −1.93998 −0.969991 0.243141i \(-0.921822\pi\)
−0.969991 + 0.243141i \(0.921822\pi\)
\(164\) −5.17319e9 −0.558420
\(165\) −1.58240e8 −0.0166203
\(166\) 7.10104e9 0.725831
\(167\) 1.29270e10 1.28610 0.643048 0.765826i \(-0.277669\pi\)
0.643048 + 0.765826i \(0.277669\pi\)
\(168\) 2.87517e9 0.278466
\(169\) 1.66620e7 0.00157122
\(170\) −1.49740e10 −1.37504
\(171\) 8.00311e9 0.715774
\(172\) 9.74572e8 0.0849055
\(173\) 2.03436e10 1.72671 0.863356 0.504595i \(-0.168358\pi\)
0.863356 + 0.504595i \(0.168358\pi\)
\(174\) −3.63635e9 −0.300742
\(175\) −1.10542e10 −0.890957
\(176\) 8.65957e7 0.00680282
\(177\) −6.53799e8 −0.0500685
\(178\) −1.61643e10 −1.20688
\(179\) −1.34136e10 −0.976581 −0.488290 0.872681i \(-0.662379\pi\)
−0.488290 + 0.872681i \(0.662379\pi\)
\(180\) 9.91274e9 0.703830
\(181\) 2.32509e10 1.61022 0.805111 0.593124i \(-0.202106\pi\)
0.805111 + 0.593124i \(0.202106\pi\)
\(182\) −1.09316e10 −0.738522
\(183\) −3.06423e8 −0.0201972
\(184\) 1.20766e9 0.0776721
\(185\) −8.28199e9 −0.519831
\(186\) −1.67550e9 −0.102645
\(187\) 1.31282e9 0.0785088
\(188\) −1.57399e10 −0.918947
\(189\) 9.14934e9 0.521569
\(190\) −1.22146e10 −0.679966
\(191\) −2.42046e10 −1.31598 −0.657988 0.753029i \(-0.728592\pi\)
−0.657988 + 0.753029i \(0.728592\pi\)
\(192\) 3.48813e9 0.185241
\(193\) −2.49753e10 −1.29570 −0.647848 0.761770i \(-0.724331\pi\)
−0.647848 + 0.761770i \(0.724331\pi\)
\(194\) −4.23345e9 −0.214579
\(195\) 6.57838e9 0.325809
\(196\) −2.62959e9 −0.127273
\(197\) −1.22394e10 −0.578977 −0.289489 0.957181i \(-0.593485\pi\)
−0.289489 + 0.957181i \(0.593485\pi\)
\(198\) 6.91876e8 0.0319915
\(199\) −2.35676e10 −1.06531 −0.532655 0.846332i \(-0.678806\pi\)
−0.532655 + 0.846332i \(0.678806\pi\)
\(200\) −1.88507e10 −0.833092
\(201\) 4.76581e9 0.205946
\(202\) 1.45631e10 0.615420
\(203\) 4.99787e10 2.06563
\(204\) 5.13378e9 0.207540
\(205\) 3.40626e10 1.34706
\(206\) 1.15232e10 0.445832
\(207\) 1.86334e9 0.0705386
\(208\) −3.59998e9 −0.133357
\(209\) 1.07090e9 0.0388230
\(210\) −6.77067e9 −0.240240
\(211\) −5.46004e10 −1.89638 −0.948188 0.317710i \(-0.897086\pi\)
−0.948188 + 0.317710i \(0.897086\pi\)
\(212\) 2.43362e9 0.0827448
\(213\) 8.96577e9 0.298455
\(214\) −1.02932e10 −0.335498
\(215\) −6.41703e9 −0.204815
\(216\) 1.56023e10 0.487695
\(217\) 2.30284e10 0.705010
\(218\) 1.60069e10 0.480014
\(219\) −3.72122e9 −0.109317
\(220\) 1.32642e9 0.0381751
\(221\) −5.45770e10 −1.53902
\(222\) −2.26048e9 −0.0624615
\(223\) 2.69840e10 0.730693 0.365347 0.930872i \(-0.380950\pi\)
0.365347 + 0.930872i \(0.380950\pi\)
\(224\) −3.95821e10 −1.05047
\(225\) −2.90855e10 −0.756579
\(226\) −4.14568e10 −1.05708
\(227\) 2.28428e10 0.570995 0.285498 0.958379i \(-0.407841\pi\)
0.285498 + 0.958379i \(0.407841\pi\)
\(228\) 4.18773e9 0.102629
\(229\) 4.78347e9 0.114943 0.0574716 0.998347i \(-0.481696\pi\)
0.0574716 + 0.998347i \(0.481696\pi\)
\(230\) −2.84389e9 −0.0670097
\(231\) 5.93609e8 0.0137166
\(232\) 8.52286e10 1.93148
\(233\) 2.54149e10 0.564920 0.282460 0.959279i \(-0.408850\pi\)
0.282460 + 0.959279i \(0.408850\pi\)
\(234\) −2.87629e10 −0.627135
\(235\) 1.03638e11 2.21674
\(236\) 5.48039e9 0.115003
\(237\) −2.17554e9 −0.0447919
\(238\) 5.61723e10 1.13482
\(239\) 4.29227e10 0.850936 0.425468 0.904974i \(-0.360110\pi\)
0.425468 + 0.904974i \(0.360110\pi\)
\(240\) −2.22970e9 −0.0433807
\(241\) 3.36684e10 0.642903 0.321451 0.946926i \(-0.395829\pi\)
0.321451 + 0.946926i \(0.395829\pi\)
\(242\) −3.54286e10 −0.664025
\(243\) 3.64744e10 0.671059
\(244\) 2.56855e9 0.0463910
\(245\) 1.73145e10 0.307016
\(246\) 9.29703e9 0.161859
\(247\) −4.45196e10 −0.761053
\(248\) 3.92703e10 0.659222
\(249\) 1.60303e10 0.264268
\(250\) −1.08349e10 −0.175426
\(251\) 3.34718e10 0.532289 0.266145 0.963933i \(-0.414250\pi\)
0.266145 + 0.963933i \(0.414250\pi\)
\(252\) −3.71860e10 −0.580867
\(253\) 2.49334e8 0.00382595
\(254\) 7.46311e9 0.112504
\(255\) −3.38031e10 −0.500640
\(256\) −7.25976e10 −1.05643
\(257\) −3.86792e10 −0.553068 −0.276534 0.961004i \(-0.589186\pi\)
−0.276534 + 0.961004i \(0.589186\pi\)
\(258\) −1.75146e9 −0.0246100
\(259\) 3.10685e10 0.429014
\(260\) −5.51425e10 −0.748353
\(261\) 1.31502e11 1.75409
\(262\) 5.66057e10 0.742172
\(263\) 3.69446e10 0.476157 0.238078 0.971246i \(-0.423483\pi\)
0.238078 + 0.971246i \(0.423483\pi\)
\(264\) 1.01228e9 0.0128258
\(265\) −1.60240e10 −0.199602
\(266\) 4.58209e10 0.561172
\(267\) −3.64902e10 −0.439415
\(268\) −3.99488e10 −0.473039
\(269\) −1.65605e11 −1.92836 −0.964182 0.265242i \(-0.914548\pi\)
−0.964182 + 0.265242i \(0.914548\pi\)
\(270\) −3.67416e10 −0.420747
\(271\) 3.88648e10 0.437718 0.218859 0.975756i \(-0.429766\pi\)
0.218859 + 0.975756i \(0.429766\pi\)
\(272\) 1.84985e10 0.204917
\(273\) −2.46777e10 −0.268889
\(274\) −8.38036e10 −0.898225
\(275\) −3.89193e9 −0.0410362
\(276\) 9.75019e8 0.0101140
\(277\) 1.49820e10 0.152901 0.0764506 0.997073i \(-0.475641\pi\)
0.0764506 + 0.997073i \(0.475641\pi\)
\(278\) −3.36339e10 −0.337735
\(279\) 6.05915e10 0.598678
\(280\) 1.58691e11 1.54291
\(281\) −1.83669e11 −1.75734 −0.878672 0.477425i \(-0.841570\pi\)
−0.878672 + 0.477425i \(0.841570\pi\)
\(282\) 2.82870e10 0.266358
\(283\) 9.42540e10 0.873495 0.436748 0.899584i \(-0.356130\pi\)
0.436748 + 0.899584i \(0.356130\pi\)
\(284\) −7.51544e10 −0.685523
\(285\) −2.75739e10 −0.247569
\(286\) −3.84876e9 −0.0340153
\(287\) −1.27780e11 −1.11172
\(288\) −1.04147e11 −0.892033
\(289\) 1.61857e11 1.36487
\(290\) −2.00703e11 −1.66633
\(291\) −9.55684e9 −0.0781260
\(292\) 3.11926e10 0.251090
\(293\) −1.43511e11 −1.13758 −0.568790 0.822483i \(-0.692588\pi\)
−0.568790 + 0.822483i \(0.692588\pi\)
\(294\) 4.72579e9 0.0368903
\(295\) −3.60854e10 −0.277417
\(296\) 5.29810e10 0.401151
\(297\) 3.22127e9 0.0240227
\(298\) 3.81711e10 0.280389
\(299\) −1.03654e10 −0.0750007
\(300\) −1.52193e10 −0.108480
\(301\) 2.40724e10 0.169032
\(302\) −1.30859e11 −0.905258
\(303\) 3.28755e10 0.224069
\(304\) 1.50897e10 0.101332
\(305\) −1.69125e10 −0.111907
\(306\) 1.47798e11 0.963659
\(307\) −2.47841e11 −1.59240 −0.796198 0.605037i \(-0.793158\pi\)
−0.796198 + 0.605037i \(0.793158\pi\)
\(308\) −4.97586e9 −0.0315057
\(309\) 2.60132e10 0.162323
\(310\) −9.24766e10 −0.568727
\(311\) −3.23810e11 −1.96276 −0.981382 0.192066i \(-0.938481\pi\)
−0.981382 + 0.192066i \(0.938481\pi\)
\(312\) −4.20828e10 −0.251425
\(313\) 2.55636e11 1.50547 0.752735 0.658323i \(-0.228734\pi\)
0.752735 + 0.658323i \(0.228734\pi\)
\(314\) −2.45790e9 −0.0142686
\(315\) 2.44849e11 1.40120
\(316\) 1.82362e10 0.102883
\(317\) 2.16477e11 1.20405 0.602025 0.798477i \(-0.294361\pi\)
0.602025 + 0.798477i \(0.294361\pi\)
\(318\) −4.37359e9 −0.0239837
\(319\) 1.75963e10 0.0951402
\(320\) 1.92522e11 1.02637
\(321\) −2.32366e10 −0.122152
\(322\) 1.06684e10 0.0553028
\(323\) 2.28765e11 1.16944
\(324\) −9.13534e10 −0.460545
\(325\) 1.61796e11 0.804440
\(326\) −2.63387e11 −1.29156
\(327\) 3.61350e10 0.174769
\(328\) −2.17903e11 −1.03952
\(329\) −3.88782e11 −1.82947
\(330\) −2.38379e9 −0.0110651
\(331\) −4.68906e10 −0.214714 −0.107357 0.994221i \(-0.534239\pi\)
−0.107357 + 0.994221i \(0.534239\pi\)
\(332\) −1.34372e11 −0.606999
\(333\) 8.17463e10 0.364308
\(334\) 1.94738e11 0.856232
\(335\) 2.63041e11 1.14110
\(336\) 8.36436e9 0.0358019
\(337\) −4.29929e11 −1.81578 −0.907888 0.419212i \(-0.862306\pi\)
−0.907888 + 0.419212i \(0.862306\pi\)
\(338\) 2.51003e8 0.00104605
\(339\) −9.35871e10 −0.384873
\(340\) 2.83351e11 1.14992
\(341\) 8.10776e9 0.0324718
\(342\) 1.20562e11 0.476534
\(343\) 2.19185e11 0.855041
\(344\) 4.10506e10 0.158054
\(345\) −6.41997e9 −0.0243976
\(346\) 3.06465e11 1.14958
\(347\) 3.36146e11 1.24465 0.622323 0.782761i \(-0.286189\pi\)
0.622323 + 0.782761i \(0.286189\pi\)
\(348\) 6.88102e10 0.251505
\(349\) 9.78546e10 0.353075 0.176537 0.984294i \(-0.443510\pi\)
0.176537 + 0.984294i \(0.443510\pi\)
\(350\) −1.66526e11 −0.593164
\(351\) −1.33915e11 −0.470921
\(352\) −1.39359e10 −0.0483831
\(353\) −1.75851e11 −0.602778 −0.301389 0.953501i \(-0.597450\pi\)
−0.301389 + 0.953501i \(0.597450\pi\)
\(354\) −9.84912e9 −0.0333336
\(355\) 4.94851e11 1.65366
\(356\) 3.05874e11 1.00929
\(357\) 1.26807e11 0.413176
\(358\) −2.02069e11 −0.650169
\(359\) 5.43941e10 0.172833 0.0864165 0.996259i \(-0.472458\pi\)
0.0864165 + 0.996259i \(0.472458\pi\)
\(360\) 4.17541e11 1.31020
\(361\) −1.36080e11 −0.421707
\(362\) 3.50261e11 1.07202
\(363\) −7.99786e10 −0.241765
\(364\) 2.06858e11 0.617612
\(365\) −2.05387e11 −0.605695
\(366\) −4.61609e9 −0.0134465
\(367\) 3.85965e11 1.11058 0.555291 0.831656i \(-0.312607\pi\)
0.555291 + 0.831656i \(0.312607\pi\)
\(368\) 3.51329e9 0.00998616
\(369\) −3.36211e11 −0.944045
\(370\) −1.24764e11 −0.346083
\(371\) 6.01115e10 0.164731
\(372\) 3.17053e10 0.0858398
\(373\) −1.93481e11 −0.517545 −0.258772 0.965938i \(-0.583318\pi\)
−0.258772 + 0.965938i \(0.583318\pi\)
\(374\) 1.97769e10 0.0522681
\(375\) −2.44593e10 −0.0638709
\(376\) −6.62989e11 −1.71065
\(377\) −7.31519e11 −1.86505
\(378\) 1.37830e11 0.347240
\(379\) 1.36906e10 0.0340837 0.0170419 0.999855i \(-0.494575\pi\)
0.0170419 + 0.999855i \(0.494575\pi\)
\(380\) 2.31135e11 0.568643
\(381\) 1.68477e10 0.0409617
\(382\) −3.64629e11 −0.876125
\(383\) −4.49622e11 −1.06771 −0.533855 0.845576i \(-0.679257\pi\)
−0.533855 + 0.845576i \(0.679257\pi\)
\(384\) −4.53339e10 −0.106398
\(385\) 3.27633e10 0.0760002
\(386\) −3.76239e11 −0.862623
\(387\) 6.33384e10 0.143538
\(388\) 8.01090e10 0.179448
\(389\) 3.88202e10 0.0859577 0.0429789 0.999076i \(-0.486315\pi\)
0.0429789 + 0.999076i \(0.486315\pi\)
\(390\) 9.90997e10 0.216911
\(391\) 5.32627e10 0.115247
\(392\) −1.10763e11 −0.236923
\(393\) 1.27785e11 0.270218
\(394\) −1.84379e11 −0.385460
\(395\) −1.20075e11 −0.248180
\(396\) −1.30923e10 −0.0267539
\(397\) −1.19424e11 −0.241288 −0.120644 0.992696i \(-0.538496\pi\)
−0.120644 + 0.992696i \(0.538496\pi\)
\(398\) −3.55032e11 −0.709241
\(399\) 1.03439e11 0.204318
\(400\) −5.48399e10 −0.107109
\(401\) 6.09718e11 1.17755 0.588775 0.808297i \(-0.299610\pi\)
0.588775 + 0.808297i \(0.299610\pi\)
\(402\) 7.17942e10 0.137111
\(403\) −3.37058e11 −0.636549
\(404\) −2.75575e11 −0.514664
\(405\) 6.01512e11 1.11096
\(406\) 7.52902e11 1.37522
\(407\) 1.09385e10 0.0197598
\(408\) 2.16243e11 0.386341
\(409\) 9.60444e9 0.0169714 0.00848569 0.999964i \(-0.497299\pi\)
0.00848569 + 0.999964i \(0.497299\pi\)
\(410\) 5.13135e11 0.896817
\(411\) −1.89183e11 −0.327035
\(412\) −2.18053e11 −0.372841
\(413\) 1.35368e11 0.228950
\(414\) 2.80702e10 0.0469618
\(415\) 8.84768e11 1.46424
\(416\) 5.79348e11 0.948462
\(417\) −7.59272e10 −0.122966
\(418\) 1.61325e10 0.0258468
\(419\) 3.47797e11 0.551269 0.275634 0.961263i \(-0.411112\pi\)
0.275634 + 0.961263i \(0.411112\pi\)
\(420\) 1.28121e11 0.200908
\(421\) −3.74682e11 −0.581291 −0.290645 0.956831i \(-0.593870\pi\)
−0.290645 + 0.956831i \(0.593870\pi\)
\(422\) −8.22524e11 −1.26253
\(423\) −1.02295e12 −1.55354
\(424\) 1.02508e11 0.154032
\(425\) −8.31393e11 −1.23611
\(426\) 1.35064e11 0.198700
\(427\) 6.34444e10 0.0923566
\(428\) 1.94778e11 0.280571
\(429\) −8.68843e9 −0.0123846
\(430\) −9.66690e10 −0.136357
\(431\) −1.23917e12 −1.72975 −0.864875 0.501987i \(-0.832603\pi\)
−0.864875 + 0.501987i \(0.832603\pi\)
\(432\) 4.53898e10 0.0627020
\(433\) −5.28782e11 −0.722905 −0.361453 0.932390i \(-0.617719\pi\)
−0.361453 + 0.932390i \(0.617719\pi\)
\(434\) 3.46910e11 0.469368
\(435\) −4.53078e11 −0.606696
\(436\) −3.02897e11 −0.401427
\(437\) 4.34475e10 0.0569900
\(438\) −5.60580e10 −0.0727787
\(439\) 1.10920e12 1.42534 0.712669 0.701500i \(-0.247486\pi\)
0.712669 + 0.701500i \(0.247486\pi\)
\(440\) 5.58712e10 0.0710642
\(441\) −1.70900e11 −0.215163
\(442\) −8.22172e11 −1.02462
\(443\) 1.21790e12 1.50243 0.751213 0.660059i \(-0.229469\pi\)
0.751213 + 0.660059i \(0.229469\pi\)
\(444\) 4.27748e10 0.0522354
\(445\) −2.01402e12 −2.43469
\(446\) 4.06500e11 0.486467
\(447\) 8.61697e10 0.102087
\(448\) −7.22213e11 −0.847060
\(449\) −9.78940e11 −1.13670 −0.568352 0.822785i \(-0.692419\pi\)
−0.568352 + 0.822785i \(0.692419\pi\)
\(450\) −4.38156e11 −0.503701
\(451\) −4.49884e10 −0.0512042
\(452\) 7.84482e11 0.884016
\(453\) −2.95409e11 −0.329596
\(454\) 3.44114e11 0.380146
\(455\) −1.36205e12 −1.48984
\(456\) 1.76394e11 0.191048
\(457\) 9.91411e11 1.06324 0.531619 0.846983i \(-0.321584\pi\)
0.531619 + 0.846983i \(0.321584\pi\)
\(458\) 7.20602e10 0.0765246
\(459\) 6.88126e11 0.723620
\(460\) 5.38146e10 0.0560390
\(461\) 1.84663e11 0.190426 0.0952130 0.995457i \(-0.469647\pi\)
0.0952130 + 0.995457i \(0.469647\pi\)
\(462\) 8.94239e9 0.00913198
\(463\) 8.46043e11 0.855614 0.427807 0.903870i \(-0.359286\pi\)
0.427807 + 0.903870i \(0.359286\pi\)
\(464\) 2.47944e11 0.248326
\(465\) −2.08762e11 −0.207068
\(466\) 3.82861e11 0.376101
\(467\) 1.63330e11 0.158906 0.0794530 0.996839i \(-0.474683\pi\)
0.0794530 + 0.996839i \(0.474683\pi\)
\(468\) 5.44277e11 0.524461
\(469\) −9.86755e11 −0.941741
\(470\) 1.56125e12 1.47582
\(471\) −5.54862e9 −0.00519506
\(472\) 2.30843e11 0.214081
\(473\) 8.47532e9 0.00778540
\(474\) −3.27733e10 −0.0298207
\(475\) −6.78184e11 −0.611261
\(476\) −1.06294e12 −0.949026
\(477\) 1.58163e11 0.139885
\(478\) 6.46607e11 0.566519
\(479\) 1.37723e12 1.19536 0.597679 0.801736i \(-0.296090\pi\)
0.597679 + 0.801736i \(0.296090\pi\)
\(480\) 3.58828e11 0.308533
\(481\) −4.54737e11 −0.387354
\(482\) 5.07195e11 0.428019
\(483\) 2.40834e10 0.0201352
\(484\) 6.70411e11 0.555312
\(485\) −5.27474e11 −0.432876
\(486\) 5.49467e11 0.446764
\(487\) −2.11605e12 −1.70469 −0.852347 0.522977i \(-0.824821\pi\)
−0.852347 + 0.522977i \(0.824821\pi\)
\(488\) 1.08192e11 0.0863583
\(489\) −5.94586e11 −0.470246
\(490\) 2.60833e11 0.204399
\(491\) −1.23880e11 −0.0961907 −0.0480954 0.998843i \(-0.515315\pi\)
−0.0480954 + 0.998843i \(0.515315\pi\)
\(492\) −1.75927e11 −0.135359
\(493\) 3.75892e12 2.86584
\(494\) −6.70663e11 −0.506679
\(495\) 8.62056e10 0.0645375
\(496\) 1.14244e11 0.0847549
\(497\) −1.85635e12 −1.36476
\(498\) 2.41488e11 0.175939
\(499\) −2.30366e10 −0.0166328 −0.00831641 0.999965i \(-0.502647\pi\)
−0.00831641 + 0.999965i \(0.502647\pi\)
\(500\) 2.05027e11 0.146705
\(501\) 4.39613e11 0.311746
\(502\) 5.04234e11 0.354377
\(503\) 1.75621e12 1.22327 0.611633 0.791142i \(-0.290513\pi\)
0.611633 + 0.791142i \(0.290513\pi\)
\(504\) −1.56633e12 −1.08130
\(505\) 1.81451e12 1.24151
\(506\) 3.75608e9 0.00254717
\(507\) 5.66629e8 0.000380858 0
\(508\) −1.41224e11 −0.0940850
\(509\) 1.05347e12 0.695650 0.347825 0.937559i \(-0.386920\pi\)
0.347825 + 0.937559i \(0.386920\pi\)
\(510\) −5.09225e11 −0.333307
\(511\) 7.70473e11 0.499877
\(512\) −4.11115e11 −0.264392
\(513\) 5.61319e11 0.357834
\(514\) −5.82681e11 −0.368211
\(515\) 1.43576e12 0.899392
\(516\) 3.31426e10 0.0205809
\(517\) −1.36881e11 −0.0842627
\(518\) 4.68030e11 0.285620
\(519\) 6.91831e11 0.418550
\(520\) −2.32269e12 −1.39308
\(521\) −7.44126e11 −0.442463 −0.221231 0.975221i \(-0.571008\pi\)
−0.221231 + 0.975221i \(0.571008\pi\)
\(522\) 1.98101e12 1.16780
\(523\) 9.32642e11 0.545076 0.272538 0.962145i \(-0.412137\pi\)
0.272538 + 0.962145i \(0.412137\pi\)
\(524\) −1.07114e12 −0.620664
\(525\) −3.75925e11 −0.215965
\(526\) 5.56549e11 0.317006
\(527\) 1.73198e12 0.978125
\(528\) 2.94489e9 0.00164898
\(529\) −1.79104e12 −0.994384
\(530\) −2.41393e11 −0.132887
\(531\) 3.56176e11 0.194419
\(532\) −8.67064e11 −0.469298
\(533\) 1.87027e12 1.00376
\(534\) −5.49704e11 −0.292545
\(535\) −1.28251e12 −0.676811
\(536\) −1.68271e12 −0.880577
\(537\) −4.56163e11 −0.236720
\(538\) −2.49475e12 −1.28383
\(539\) −2.28681e10 −0.0116703
\(540\) 6.95256e11 0.351862
\(541\) 1.74928e12 0.877952 0.438976 0.898499i \(-0.355341\pi\)
0.438976 + 0.898499i \(0.355341\pi\)
\(542\) 5.85477e11 0.291416
\(543\) 7.90701e11 0.390313
\(544\) −2.97699e12 −1.45741
\(545\) 1.99441e12 0.968347
\(546\) −3.71756e11 −0.179015
\(547\) −2.83590e12 −1.35440 −0.677202 0.735797i \(-0.736808\pi\)
−0.677202 + 0.735797i \(0.736808\pi\)
\(548\) 1.58581e12 0.751168
\(549\) 1.66933e11 0.0784270
\(550\) −5.86297e10 −0.0273203
\(551\) 3.06623e12 1.41717
\(552\) 4.10694e10 0.0188275
\(553\) 4.50443e11 0.204822
\(554\) 2.25695e11 0.101796
\(555\) −2.81649e11 −0.126005
\(556\) 6.36450e11 0.282441
\(557\) −4.44074e11 −0.195482 −0.0977410 0.995212i \(-0.531162\pi\)
−0.0977410 + 0.995212i \(0.531162\pi\)
\(558\) 9.12777e11 0.398576
\(559\) −3.52338e11 −0.152618
\(560\) 4.61657e11 0.198369
\(561\) 4.46456e10 0.0190303
\(562\) −2.76687e12 −1.16997
\(563\) 2.66977e11 0.111992 0.0559959 0.998431i \(-0.482167\pi\)
0.0559959 + 0.998431i \(0.482167\pi\)
\(564\) −5.35271e11 −0.222750
\(565\) −5.16539e12 −2.13248
\(566\) 1.41988e12 0.581539
\(567\) −2.25647e12 −0.916866
\(568\) −3.16563e12 −1.27612
\(569\) 1.98776e12 0.794985 0.397492 0.917606i \(-0.369881\pi\)
0.397492 + 0.917606i \(0.369881\pi\)
\(570\) −4.15386e11 −0.164822
\(571\) 1.77358e11 0.0698215 0.0349107 0.999390i \(-0.488885\pi\)
0.0349107 + 0.999390i \(0.488885\pi\)
\(572\) 7.28297e10 0.0284463
\(573\) −8.23135e11 −0.318989
\(574\) −1.92494e12 −0.740139
\(575\) −1.57900e11 −0.0602389
\(576\) −1.90026e12 −0.719303
\(577\) −2.44961e12 −0.920039 −0.460020 0.887909i \(-0.652158\pi\)
−0.460020 + 0.887909i \(0.652158\pi\)
\(578\) 2.43828e12 0.908675
\(579\) −8.49344e11 −0.314073
\(580\) 3.79787e12 1.39352
\(581\) −3.31906e12 −1.20843
\(582\) −1.43968e11 −0.0520132
\(583\) 2.11638e10 0.00758727
\(584\) 1.31389e12 0.467412
\(585\) −3.58377e12 −1.26514
\(586\) −2.16192e12 −0.757356
\(587\) −3.96669e12 −1.37898 −0.689488 0.724297i \(-0.742164\pi\)
−0.689488 + 0.724297i \(0.742164\pi\)
\(588\) −8.94256e10 −0.0308506
\(589\) 1.41281e12 0.483687
\(590\) −5.43606e11 −0.184693
\(591\) −4.16229e11 −0.140342
\(592\) 1.54131e11 0.0515752
\(593\) −1.37473e12 −0.456531 −0.228265 0.973599i \(-0.573305\pi\)
−0.228265 + 0.973599i \(0.573305\pi\)
\(594\) 4.85266e10 0.0159934
\(595\) 6.99889e12 2.28930
\(596\) −7.22307e11 −0.234484
\(597\) −8.01471e11 −0.258228
\(598\) −1.56149e11 −0.0499325
\(599\) −1.83622e12 −0.582779 −0.291389 0.956605i \(-0.594118\pi\)
−0.291389 + 0.956605i \(0.594118\pi\)
\(600\) −6.41063e11 −0.201939
\(601\) 2.11756e12 0.662064 0.331032 0.943620i \(-0.392603\pi\)
0.331032 + 0.943620i \(0.392603\pi\)
\(602\) 3.62637e11 0.112535
\(603\) −2.59631e12 −0.799704
\(604\) 2.47623e12 0.757050
\(605\) −4.41429e12 −1.33956
\(606\) 4.95252e11 0.149176
\(607\) 6.21202e12 1.85731 0.928654 0.370947i \(-0.120967\pi\)
0.928654 + 0.370947i \(0.120967\pi\)
\(608\) −2.42839e12 −0.720697
\(609\) 1.69965e12 0.500703
\(610\) −2.54778e11 −0.0745035
\(611\) 5.69045e12 1.65181
\(612\) −2.79677e12 −0.805890
\(613\) 1.80823e12 0.517228 0.258614 0.965981i \(-0.416734\pi\)
0.258614 + 0.965981i \(0.416734\pi\)
\(614\) −3.73359e12 −1.06015
\(615\) 1.15838e12 0.326523
\(616\) −2.09591e11 −0.0586489
\(617\) −5.17980e11 −0.143890 −0.0719449 0.997409i \(-0.522921\pi\)
−0.0719449 + 0.997409i \(0.522921\pi\)
\(618\) 3.91875e11 0.108068
\(619\) 4.80654e12 1.31591 0.657953 0.753059i \(-0.271423\pi\)
0.657953 + 0.753059i \(0.271423\pi\)
\(620\) 1.74992e12 0.475616
\(621\) 1.30691e11 0.0352640
\(622\) −4.87801e12 −1.30673
\(623\) 7.55524e12 2.00933
\(624\) −1.22426e11 −0.0323253
\(625\) −4.41628e12 −1.15770
\(626\) 3.85101e12 1.00228
\(627\) 3.64184e10 0.00941058
\(628\) 4.65106e10 0.0119326
\(629\) 2.33667e12 0.595210
\(630\) 3.68852e12 0.932867
\(631\) 6.50796e12 1.63423 0.817114 0.576476i \(-0.195572\pi\)
0.817114 + 0.576476i \(0.195572\pi\)
\(632\) 7.68138e11 0.191519
\(633\) −1.85681e12 −0.459676
\(634\) 3.26110e12 0.801609
\(635\) 9.29881e11 0.226958
\(636\) 8.27609e10 0.0200571
\(637\) 9.50680e11 0.228774
\(638\) 2.65079e11 0.0633406
\(639\) −4.88436e12 −1.15892
\(640\) −2.50213e12 −0.589522
\(641\) −3.48179e12 −0.814595 −0.407297 0.913296i \(-0.633529\pi\)
−0.407297 + 0.913296i \(0.633529\pi\)
\(642\) −3.50046e11 −0.0813238
\(643\) −1.58721e12 −0.366172 −0.183086 0.983097i \(-0.558609\pi\)
−0.183086 + 0.983097i \(0.558609\pi\)
\(644\) −2.01876e11 −0.0462487
\(645\) −2.18226e11 −0.0496465
\(646\) 3.44621e12 0.778566
\(647\) −1.50095e12 −0.336741 −0.168371 0.985724i \(-0.553851\pi\)
−0.168371 + 0.985724i \(0.553851\pi\)
\(648\) −3.84795e12 −0.857319
\(649\) 4.76599e10 0.0105451
\(650\) 2.43737e12 0.535564
\(651\) 7.83136e11 0.170892
\(652\) 4.98405e12 1.08011
\(653\) −6.01788e12 −1.29519 −0.647596 0.761984i \(-0.724226\pi\)
−0.647596 + 0.761984i \(0.724226\pi\)
\(654\) 5.44354e11 0.116354
\(655\) 7.05290e12 1.49721
\(656\) −6.33917e11 −0.133649
\(657\) 2.02724e12 0.424484
\(658\) −5.85678e12 −1.21799
\(659\) 6.45564e12 1.33338 0.666691 0.745334i \(-0.267710\pi\)
0.666691 + 0.745334i \(0.267710\pi\)
\(660\) 4.51082e10 0.00925354
\(661\) 6.32975e12 1.28967 0.644837 0.764320i \(-0.276925\pi\)
0.644837 + 0.764320i \(0.276925\pi\)
\(662\) −7.06380e11 −0.142948
\(663\) −1.85602e12 −0.373054
\(664\) −5.65998e12 −1.12995
\(665\) 5.70914e12 1.13207
\(666\) 1.23146e12 0.242542
\(667\) 7.13904e11 0.139660
\(668\) −3.68500e12 −0.716051
\(669\) 9.17656e11 0.177118
\(670\) 3.96257e12 0.759697
\(671\) 2.23373e10 0.00425382
\(672\) −1.34608e12 −0.254631
\(673\) −2.05876e12 −0.386846 −0.193423 0.981115i \(-0.561959\pi\)
−0.193423 + 0.981115i \(0.561959\pi\)
\(674\) −6.47664e12 −1.20887
\(675\) −2.03998e12 −0.378233
\(676\) −4.74970e9 −0.000874795 0
\(677\) 1.82789e12 0.334427 0.167213 0.985921i \(-0.446523\pi\)
0.167213 + 0.985921i \(0.446523\pi\)
\(678\) −1.40984e12 −0.256233
\(679\) 1.97873e12 0.357250
\(680\) 1.19352e13 2.14062
\(681\) 7.76823e11 0.138408
\(682\) 1.22139e11 0.0216184
\(683\) −5.70420e11 −0.100300 −0.0501501 0.998742i \(-0.515970\pi\)
−0.0501501 + 0.998742i \(0.515970\pi\)
\(684\) −2.28139e12 −0.398517
\(685\) −1.04417e13 −1.81202
\(686\) 3.30190e12 0.569253
\(687\) 1.62673e11 0.0278619
\(688\) 1.19423e11 0.0203208
\(689\) −8.79829e11 −0.148734
\(690\) −9.67133e10 −0.0162430
\(691\) 7.86912e11 0.131303 0.0656515 0.997843i \(-0.479087\pi\)
0.0656515 + 0.997843i \(0.479087\pi\)
\(692\) −5.79919e12 −0.961369
\(693\) −3.23386e11 −0.0532625
\(694\) 5.06386e12 0.828636
\(695\) −4.19068e12 −0.681323
\(696\) 2.89840e12 0.468184
\(697\) −9.61040e12 −1.54239
\(698\) 1.47413e12 0.235063
\(699\) 8.64294e11 0.136935
\(700\) 3.15114e12 0.496052
\(701\) 5.46260e12 0.854415 0.427207 0.904154i \(-0.359497\pi\)
0.427207 + 0.904154i \(0.359497\pi\)
\(702\) −2.01736e12 −0.313521
\(703\) 1.90607e12 0.294334
\(704\) −2.54274e11 −0.0390144
\(705\) 3.52447e12 0.537332
\(706\) −2.64909e12 −0.401306
\(707\) −6.80684e12 −1.02461
\(708\) 1.86374e11 0.0278763
\(709\) −7.21721e12 −1.07266 −0.536329 0.844009i \(-0.680189\pi\)
−0.536329 + 0.844009i \(0.680189\pi\)
\(710\) 7.45466e12 1.10094
\(711\) 1.18519e12 0.173930
\(712\) 1.28839e13 1.87883
\(713\) 3.28941e11 0.0476667
\(714\) 1.91027e12 0.275076
\(715\) −4.79544e11 −0.0686201
\(716\) 3.82373e12 0.543724
\(717\) 1.45969e12 0.206264
\(718\) 8.19416e11 0.115065
\(719\) −9.38428e12 −1.30955 −0.654773 0.755825i \(-0.727236\pi\)
−0.654773 + 0.755825i \(0.727236\pi\)
\(720\) 1.21470e12 0.168450
\(721\) −5.38600e12 −0.742263
\(722\) −2.04996e12 −0.280756
\(723\) 1.14497e12 0.155838
\(724\) −6.62795e12 −0.896512
\(725\) −1.11435e13 −1.49796
\(726\) −1.20483e12 −0.160958
\(727\) −1.35930e13 −1.80472 −0.902362 0.430980i \(-0.858168\pi\)
−0.902362 + 0.430980i \(0.858168\pi\)
\(728\) 8.71319e12 1.14970
\(729\) −5.06737e12 −0.664521
\(730\) −3.09403e12 −0.403248
\(731\) 1.81050e12 0.234514
\(732\) 8.73496e10 0.0112450
\(733\) −1.32485e13 −1.69512 −0.847559 0.530701i \(-0.821929\pi\)
−0.847559 + 0.530701i \(0.821929\pi\)
\(734\) 5.81435e12 0.739382
\(735\) 5.88819e11 0.0744198
\(736\) −5.65397e11 −0.0710237
\(737\) −3.47413e11 −0.0433753
\(738\) −5.06483e12 −0.628508
\(739\) −6.06380e10 −0.00747903 −0.00373951 0.999993i \(-0.501190\pi\)
−0.00373951 + 0.999993i \(0.501190\pi\)
\(740\) 2.36089e12 0.289423
\(741\) −1.51399e12 −0.184477
\(742\) 9.05546e11 0.109671
\(743\) 8.45052e12 1.01726 0.508632 0.860984i \(-0.330151\pi\)
0.508632 + 0.860984i \(0.330151\pi\)
\(744\) 1.33548e12 0.159793
\(745\) 4.75600e12 0.565638
\(746\) −2.91468e12 −0.344561
\(747\) −8.73298e12 −1.02617
\(748\) −3.74236e11 −0.0437108
\(749\) 4.81110e12 0.558569
\(750\) −3.68466e11 −0.0425227
\(751\) 5.00951e12 0.574666 0.287333 0.957831i \(-0.407231\pi\)
0.287333 + 0.957831i \(0.407231\pi\)
\(752\) −1.92874e12 −0.219935
\(753\) 1.13829e12 0.129025
\(754\) −1.10199e13 −1.24167
\(755\) −1.63046e13 −1.82620
\(756\) −2.60814e12 −0.290390
\(757\) 5.80549e12 0.642551 0.321276 0.946986i \(-0.395888\pi\)
0.321276 + 0.946986i \(0.395888\pi\)
\(758\) 2.06242e11 0.0226916
\(759\) 8.47920e9 0.000927400 0
\(760\) 9.73578e12 1.05855
\(761\) 1.32066e13 1.42745 0.713723 0.700429i \(-0.247008\pi\)
0.713723 + 0.700429i \(0.247008\pi\)
\(762\) 2.53801e11 0.0272707
\(763\) −7.48171e12 −0.799172
\(764\) 6.89983e12 0.732686
\(765\) 1.84152e13 1.94402
\(766\) −6.77331e12 −0.710839
\(767\) −1.98133e12 −0.206718
\(768\) −2.46885e12 −0.256076
\(769\) −8.98106e12 −0.926102 −0.463051 0.886332i \(-0.653245\pi\)
−0.463051 + 0.886332i \(0.653245\pi\)
\(770\) 4.93561e11 0.0505979
\(771\) −1.31538e12 −0.134062
\(772\) 7.11952e12 0.721395
\(773\) −3.75046e12 −0.377813 −0.188906 0.981995i \(-0.560494\pi\)
−0.188906 + 0.981995i \(0.560494\pi\)
\(774\) 9.54158e11 0.0955621
\(775\) −5.13453e12 −0.511262
\(776\) 3.37432e12 0.334048
\(777\) 1.05656e12 0.103992
\(778\) 5.84805e11 0.0572272
\(779\) −7.83941e12 −0.762719
\(780\) −1.87525e12 −0.181399
\(781\) −6.53577e11 −0.0628589
\(782\) 8.02373e11 0.0767266
\(783\) 9.22325e12 0.876912
\(784\) −3.22228e11 −0.0304607
\(785\) −3.06247e11 −0.0287845
\(786\) 1.92501e12 0.179900
\(787\) 8.97788e12 0.834233 0.417117 0.908853i \(-0.363041\pi\)
0.417117 + 0.908853i \(0.363041\pi\)
\(788\) 3.48899e12 0.322353
\(789\) 1.25639e12 0.115419
\(790\) −1.80887e12 −0.165229
\(791\) 1.93771e13 1.75993
\(792\) −5.51469e11 −0.0498032
\(793\) −9.28611e11 −0.0833882
\(794\) −1.79906e12 −0.160640
\(795\) −5.44936e11 −0.0483830
\(796\) 6.71823e12 0.593125
\(797\) −9.78357e12 −0.858884 −0.429442 0.903094i \(-0.641290\pi\)
−0.429442 + 0.903094i \(0.641290\pi\)
\(798\) 1.55825e12 0.136027
\(799\) −2.92405e13 −2.53819
\(800\) 8.82544e12 0.761783
\(801\) 1.98791e13 1.70628
\(802\) 9.18507e12 0.783967
\(803\) 2.71265e11 0.0230236
\(804\) −1.35855e12 −0.114663
\(805\) 1.32925e12 0.111564
\(806\) −5.07759e12 −0.423789
\(807\) −5.63180e12 −0.467430
\(808\) −1.16077e13 −0.958063
\(809\) −2.21862e13 −1.82102 −0.910511 0.413485i \(-0.864311\pi\)
−0.910511 + 0.413485i \(0.864311\pi\)
\(810\) 9.06145e12 0.739631
\(811\) 2.78479e12 0.226047 0.113023 0.993592i \(-0.463946\pi\)
0.113023 + 0.993592i \(0.463946\pi\)
\(812\) −1.42471e13 −1.15007
\(813\) 1.32169e12 0.106102
\(814\) 1.64782e11 0.0131553
\(815\) −3.28172e13 −2.60551
\(816\) 6.29087e11 0.0496712
\(817\) 1.47686e12 0.115968
\(818\) 1.44685e11 0.0112989
\(819\) 1.34439e13 1.04411
\(820\) −9.70998e12 −0.749991
\(821\) 1.16501e13 0.894920 0.447460 0.894304i \(-0.352329\pi\)
0.447460 + 0.894304i \(0.352329\pi\)
\(822\) −2.84994e12 −0.217727
\(823\) 8.62542e11 0.0655361 0.0327681 0.999463i \(-0.489568\pi\)
0.0327681 + 0.999463i \(0.489568\pi\)
\(824\) −9.18473e12 −0.694055
\(825\) −1.32354e11 −0.00994706
\(826\) 2.03925e12 0.152426
\(827\) 3.07127e12 0.228320 0.114160 0.993462i \(-0.463582\pi\)
0.114160 + 0.993462i \(0.463582\pi\)
\(828\) −5.31170e11 −0.0392733
\(829\) 1.65764e13 1.21897 0.609487 0.792796i \(-0.291375\pi\)
0.609487 + 0.792796i \(0.291375\pi\)
\(830\) 1.33285e13 0.974835
\(831\) 5.09498e11 0.0370628
\(832\) 1.05707e13 0.764805
\(833\) −4.88509e12 −0.351536
\(834\) −1.14380e12 −0.0818659
\(835\) 2.42637e13 1.72730
\(836\) −3.05272e11 −0.0216152
\(837\) 4.24974e12 0.299294
\(838\) 5.23937e12 0.367013
\(839\) 9.91022e12 0.690486 0.345243 0.938513i \(-0.387797\pi\)
0.345243 + 0.938513i \(0.387797\pi\)
\(840\) 5.39665e12 0.373996
\(841\) 3.58753e13 2.47294
\(842\) −5.64437e12 −0.387000
\(843\) −6.24609e12 −0.425975
\(844\) 1.55645e13 1.05583
\(845\) 3.12742e10 0.00211024
\(846\) −1.54102e13 −1.03429
\(847\) 1.65595e13 1.10553
\(848\) 2.98213e11 0.0198036
\(849\) 3.20533e12 0.211733
\(850\) −1.25245e13 −0.822951
\(851\) 4.43787e11 0.0290062
\(852\) −2.55580e12 −0.166169
\(853\) −2.84458e13 −1.83970 −0.919852 0.392266i \(-0.871691\pi\)
−0.919852 + 0.392266i \(0.871691\pi\)
\(854\) 9.55755e11 0.0614874
\(855\) 1.50217e13 0.961327
\(856\) 8.20436e12 0.522291
\(857\) −9.16254e12 −0.580232 −0.290116 0.956991i \(-0.593694\pi\)
−0.290116 + 0.956991i \(0.593694\pi\)
\(858\) −1.30886e11 −0.00824520
\(859\) −1.59098e13 −0.997002 −0.498501 0.866889i \(-0.666116\pi\)
−0.498501 + 0.866889i \(0.666116\pi\)
\(860\) 1.82926e12 0.114033
\(861\) −4.34547e12 −0.269477
\(862\) −1.86674e13 −1.15160
\(863\) −6.71369e12 −0.412015 −0.206007 0.978550i \(-0.566047\pi\)
−0.206007 + 0.978550i \(0.566047\pi\)
\(864\) −7.30463e12 −0.445950
\(865\) 3.81845e13 2.31908
\(866\) −7.96581e12 −0.481282
\(867\) 5.50432e12 0.330840
\(868\) −6.56454e12 −0.392523
\(869\) 1.58590e11 0.00943381
\(870\) −6.82537e12 −0.403914
\(871\) 1.44427e13 0.850292
\(872\) −1.27585e13 −0.747268
\(873\) 5.20636e12 0.303368
\(874\) 6.54513e11 0.0379417
\(875\) 5.06426e12 0.292065
\(876\) 1.06078e12 0.0608635
\(877\) 4.21446e12 0.240571 0.120286 0.992739i \(-0.461619\pi\)
0.120286 + 0.992739i \(0.461619\pi\)
\(878\) 1.67094e13 0.948934
\(879\) −4.88044e12 −0.275746
\(880\) 1.62539e11 0.00913660
\(881\) −8.50983e12 −0.475915 −0.237957 0.971276i \(-0.576478\pi\)
−0.237957 + 0.971276i \(0.576478\pi\)
\(882\) −2.57451e12 −0.143247
\(883\) 2.12668e13 1.17728 0.588639 0.808396i \(-0.299664\pi\)
0.588639 + 0.808396i \(0.299664\pi\)
\(884\) 1.55579e13 0.856869
\(885\) −1.22717e12 −0.0672450
\(886\) 1.83469e13 1.00026
\(887\) −2.61674e13 −1.41940 −0.709700 0.704504i \(-0.751170\pi\)
−0.709700 + 0.704504i \(0.751170\pi\)
\(888\) 1.80174e12 0.0972377
\(889\) −3.48829e12 −0.187307
\(890\) −3.03400e13 −1.62092
\(891\) −7.94450e11 −0.0422296
\(892\) −7.69214e12 −0.406823
\(893\) −2.38521e13 −1.25515
\(894\) 1.29810e12 0.0679655
\(895\) −2.51772e13 −1.31161
\(896\) 9.38632e12 0.486530
\(897\) −3.52500e11 −0.0181800
\(898\) −1.47472e13 −0.756773
\(899\) 2.32144e13 1.18533
\(900\) 8.29118e12 0.421235
\(901\) 4.52101e12 0.228546
\(902\) −6.77725e11 −0.0340898
\(903\) 8.18639e11 0.0409730
\(904\) 3.30437e13 1.64562
\(905\) 4.36415e13 2.16262
\(906\) −4.45017e12 −0.219432
\(907\) 1.63634e13 0.802861 0.401431 0.915889i \(-0.368513\pi\)
0.401431 + 0.915889i \(0.368513\pi\)
\(908\) −6.51162e12 −0.317909
\(909\) −1.79099e13 −0.870073
\(910\) −2.05185e13 −0.991878
\(911\) −3.39916e13 −1.63508 −0.817540 0.575872i \(-0.804663\pi\)
−0.817540 + 0.575872i \(0.804663\pi\)
\(912\) 5.13159e11 0.0245627
\(913\) −1.16856e12 −0.0556587
\(914\) 1.49350e13 0.707862
\(915\) −5.75150e11 −0.0271260
\(916\) −1.36359e12 −0.0639961
\(917\) −2.64577e13 −1.23564
\(918\) 1.03662e13 0.481758
\(919\) −2.19737e12 −0.101621 −0.0508106 0.998708i \(-0.516180\pi\)
−0.0508106 + 0.998708i \(0.516180\pi\)
\(920\) 2.26676e12 0.104318
\(921\) −8.42843e12 −0.385992
\(922\) 2.78185e12 0.126778
\(923\) 2.71707e13 1.23223
\(924\) −1.69216e11 −0.00763690
\(925\) −6.92719e12 −0.311114
\(926\) 1.27452e13 0.569634
\(927\) −1.41715e13 −0.630312
\(928\) −3.99019e13 −1.76615
\(929\) −1.08879e12 −0.0479596 −0.0239798 0.999712i \(-0.507634\pi\)
−0.0239798 + 0.999712i \(0.507634\pi\)
\(930\) −3.14488e12 −0.137858
\(931\) −3.98487e12 −0.173836
\(932\) −7.24484e12 −0.314526
\(933\) −1.10119e13 −0.475768
\(934\) 2.46048e12 0.105793
\(935\) 2.46414e12 0.105442
\(936\) 2.29258e13 0.976300
\(937\) 3.72812e13 1.58002 0.790008 0.613096i \(-0.210076\pi\)
0.790008 + 0.613096i \(0.210076\pi\)
\(938\) −1.48649e13 −0.626974
\(939\) 8.69350e12 0.364922
\(940\) −2.95434e13 −1.23420
\(941\) 1.01973e13 0.423966 0.211983 0.977273i \(-0.432008\pi\)
0.211983 + 0.977273i \(0.432008\pi\)
\(942\) −8.35868e10 −0.00345867
\(943\) −1.82523e12 −0.0751649
\(944\) 6.71561e11 0.0275240
\(945\) 1.71732e13 0.700498
\(946\) 1.27676e11 0.00518321
\(947\) −1.73267e13 −0.700070 −0.350035 0.936737i \(-0.613830\pi\)
−0.350035 + 0.936737i \(0.613830\pi\)
\(948\) 6.20165e11 0.0249385
\(949\) −1.12771e13 −0.451336
\(950\) −1.02165e13 −0.406953
\(951\) 7.36180e12 0.291858
\(952\) −4.47728e13 −1.76664
\(953\) −3.24945e13 −1.27612 −0.638060 0.769986i \(-0.720263\pi\)
−0.638060 + 0.769986i \(0.720263\pi\)
\(954\) 2.38264e12 0.0931302
\(955\) −4.54316e13 −1.76743
\(956\) −1.22357e13 −0.473769
\(957\) 5.98405e11 0.0230617
\(958\) 2.07473e13 0.795822
\(959\) 3.91701e13 1.49545
\(960\) 6.54716e12 0.248790
\(961\) −1.57432e13 −0.595441
\(962\) −6.85037e12 −0.257885
\(963\) 1.26588e13 0.474323
\(964\) −9.59759e12 −0.357944
\(965\) −4.68782e13 −1.74020
\(966\) 3.62803e11 0.0134052
\(967\) −2.07087e13 −0.761611 −0.380805 0.924655i \(-0.624353\pi\)
−0.380805 + 0.924655i \(0.624353\pi\)
\(968\) 2.82388e13 1.03373
\(969\) 7.77968e12 0.283468
\(970\) −7.94611e12 −0.288192
\(971\) 3.71042e13 1.33948 0.669740 0.742596i \(-0.266406\pi\)
0.669740 + 0.742596i \(0.266406\pi\)
\(972\) −1.03975e13 −0.373621
\(973\) 1.57206e13 0.562292
\(974\) −3.18772e13 −1.13492
\(975\) 5.50227e12 0.194994
\(976\) 3.14747e11 0.0111029
\(977\) −1.12430e13 −0.394783 −0.197392 0.980325i \(-0.563247\pi\)
−0.197392 + 0.980325i \(0.563247\pi\)
\(978\) −8.95711e12 −0.313071
\(979\) 2.66002e12 0.0925471
\(980\) −4.93570e12 −0.170935
\(981\) −1.96856e13 −0.678638
\(982\) −1.86618e12 −0.0640400
\(983\) −7.97289e12 −0.272349 −0.136174 0.990685i \(-0.543481\pi\)
−0.136174 + 0.990685i \(0.543481\pi\)
\(984\) −7.41031e12 −0.251976
\(985\) −2.29731e13 −0.777601
\(986\) 5.66261e13 1.90796
\(987\) −1.32214e13 −0.443457
\(988\) 1.26909e13 0.423726
\(989\) 3.43854e11 0.0114285
\(990\) 1.29864e12 0.0429665
\(991\) 2.75569e13 0.907609 0.453804 0.891101i \(-0.350066\pi\)
0.453804 + 0.891101i \(0.350066\pi\)
\(992\) −1.83854e13 −0.602795
\(993\) −1.59462e12 −0.0520459
\(994\) −2.79649e13 −0.908603
\(995\) −4.42359e13 −1.43077
\(996\) −4.56964e12 −0.147135
\(997\) 1.33441e13 0.427722 0.213861 0.976864i \(-0.431396\pi\)
0.213861 + 0.976864i \(0.431396\pi\)
\(998\) −3.47033e11 −0.0110735
\(999\) 5.73349e12 0.182127
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.1.10 15
3.2 odd 2 387.10.a.c.1.6 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.10 15 1.1 even 1 trivial
387.10.a.c.1.6 15 3.2 odd 2