Properties

Label 29.12.a.a.1.3
Level $29$
Weight $12$
Character 29.1
Self dual yes
Analytic conductor $22.282$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.2819522362\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + 1279291654973975 x^{2} - 65244901875230266 x - 758324542468966858\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-56.7551\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-59.7551 q^{2} -392.705 q^{3} +1522.68 q^{4} -6379.08 q^{5} +23466.1 q^{6} -23005.8 q^{7} +31390.8 q^{8} -22929.7 q^{9} +O(q^{10})\) \(q-59.7551 q^{2} -392.705 q^{3} +1522.68 q^{4} -6379.08 q^{5} +23466.1 q^{6} -23005.8 q^{7} +31390.8 q^{8} -22929.7 q^{9} +381183. q^{10} +522514. q^{11} -597963. q^{12} +1.47979e6 q^{13} +1.37472e6 q^{14} +2.50510e6 q^{15} -4.99420e6 q^{16} +4.61480e6 q^{17} +1.37017e6 q^{18} +1.36307e7 q^{19} -9.71327e6 q^{20} +9.03450e6 q^{21} -3.12229e7 q^{22} -5.58468e7 q^{23} -1.23273e7 q^{24} -8.13546e6 q^{25} -8.84253e7 q^{26} +7.85711e7 q^{27} -3.50304e7 q^{28} +2.05111e7 q^{29} -1.49692e8 q^{30} -1.47320e8 q^{31} +2.34141e8 q^{32} -2.05194e8 q^{33} -2.75758e8 q^{34} +1.46756e8 q^{35} -3.49146e7 q^{36} -1.64673e8 q^{37} -8.14503e8 q^{38} -5.81123e8 q^{39} -2.00244e8 q^{40} +9.49494e6 q^{41} -5.39858e8 q^{42} +7.59458e8 q^{43} +7.95619e8 q^{44} +1.46271e8 q^{45} +3.33713e9 q^{46} +1.65847e9 q^{47} +1.96125e9 q^{48} -1.44806e9 q^{49} +4.86136e8 q^{50} -1.81226e9 q^{51} +2.25325e9 q^{52} +3.15983e9 q^{53} -4.69503e9 q^{54} -3.33316e9 q^{55} -7.22171e8 q^{56} -5.35284e9 q^{57} -1.22565e9 q^{58} +2.72696e9 q^{59} +3.81445e9 q^{60} +2.15540e9 q^{61} +8.80314e9 q^{62} +5.27517e8 q^{63} -3.76299e9 q^{64} -9.43973e9 q^{65} +1.22614e10 q^{66} -1.36283e10 q^{67} +7.02685e9 q^{68} +2.19313e10 q^{69} -8.76942e9 q^{70} +9.15005e9 q^{71} -7.19783e8 q^{72} -2.13411e10 q^{73} +9.84006e9 q^{74} +3.19484e9 q^{75} +2.07551e10 q^{76} -1.20209e10 q^{77} +3.47251e10 q^{78} -3.95516e10 q^{79} +3.18584e10 q^{80} -2.67934e10 q^{81} -5.67371e8 q^{82} +2.56121e10 q^{83} +1.37566e10 q^{84} -2.94382e10 q^{85} -4.53815e10 q^{86} -8.05483e9 q^{87} +1.64021e10 q^{88} -6.50080e10 q^{89} -8.74042e9 q^{90} -3.40439e10 q^{91} -8.50365e10 q^{92} +5.78534e10 q^{93} -9.91019e10 q^{94} -8.69512e10 q^{95} -9.19483e10 q^{96} +1.86954e10 q^{97} +8.65290e10 q^{98} -1.19811e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} + O(q^{10}) \) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} - 685834q^{10} - 612246q^{11} + 2578538q^{12} + 1510364q^{13} + 3955400q^{14} - 2462818q^{15} + 3024818q^{16} - 3291098q^{17} - 27885614q^{18} - 44121388q^{19} - 49472662q^{20} - 46916800q^{21} - 43435618q^{22} - 88684076q^{23} - 224700678q^{24} - 44195521q^{25} - 324999762q^{26} - 236304286q^{27} - 391274848q^{28} + 225622639q^{29} - 494910382q^{30} - 292235934q^{31} - 632542514q^{32} - 1079766410q^{33} - 1113307936q^{34} - 1312820120q^{35} - 2236726492q^{36} - 1380429338q^{37} - 1222857284q^{38} - 1186931090q^{39} - 2713154106q^{40} - 1062067494q^{41} + 205598960q^{42} + 74588594q^{43} + 52891466q^{44} + 4527996830q^{45} - 87670324q^{46} - 1821239394q^{47} + 2666035542q^{48} + 4692522003q^{49} + 9494259926q^{50} + 8768158380q^{51} + 3266669866q^{52} + 7818635688q^{53} + 17402728558q^{54} - 191002682q^{55} + 11263587512q^{56} + 15495358340q^{57} - 656356768q^{58} + 1230002712q^{59} + 31834046430q^{60} - 18602654230q^{61} + 22075953162q^{62} - 9964531456q^{63} + 11813658086q^{64} + 32245789334q^{65} + 42677188354q^{66} + 27481284652q^{67} + 29588811820q^{68} - 20565315068q^{69} + 42862666712q^{70} - 20347168516q^{71} + 47061083616q^{72} - 57740010478q^{73} - 2640709564q^{74} - 23544691000q^{75} - 33350650772q^{76} + 871959792q^{77} - 15384525342q^{78} - 120245016462q^{79} - 84319695274q^{80} - 48880047865q^{81} - 111495532412q^{82} - 142463983824q^{83} - 134146226376q^{84} - 181628566552q^{85} + 47870165542q^{86} - 20141948318q^{87} - 180608014462q^{88} - 96700717270q^{89} - 25522461244q^{90} - 355162031176q^{91} - 22429477796q^{92} - 172582115142q^{93} + 172608565078q^{94} - 195922150708q^{95} + 226391047758q^{96} - 303190852014q^{97} - 123776497136q^{98} - 139125462440q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −59.7551 −1.32041 −0.660207 0.751084i \(-0.729532\pi\)
−0.660207 + 0.751084i \(0.729532\pi\)
\(3\) −392.705 −0.933039 −0.466519 0.884511i \(-0.654492\pi\)
−0.466519 + 0.884511i \(0.654492\pi\)
\(4\) 1522.68 0.743494
\(5\) −6379.08 −0.912900 −0.456450 0.889749i \(-0.650879\pi\)
−0.456450 + 0.889749i \(0.650879\pi\)
\(6\) 23466.1 1.23200
\(7\) −23005.8 −0.517367 −0.258683 0.965962i \(-0.583289\pi\)
−0.258683 + 0.965962i \(0.583289\pi\)
\(8\) 31390.8 0.338694
\(9\) −22929.7 −0.129439
\(10\) 381183. 1.20541
\(11\) 522514. 0.978223 0.489112 0.872221i \(-0.337321\pi\)
0.489112 + 0.872221i \(0.337321\pi\)
\(12\) −597963. −0.693709
\(13\) 1.47979e6 1.10538 0.552692 0.833386i \(-0.313601\pi\)
0.552692 + 0.833386i \(0.313601\pi\)
\(14\) 1.37472e6 0.683138
\(15\) 2.50510e6 0.851771
\(16\) −4.99420e6 −1.19071
\(17\) 4.61480e6 0.788286 0.394143 0.919049i \(-0.371041\pi\)
0.394143 + 0.919049i \(0.371041\pi\)
\(18\) 1.37017e6 0.170913
\(19\) 1.36307e7 1.26291 0.631456 0.775412i \(-0.282458\pi\)
0.631456 + 0.775412i \(0.282458\pi\)
\(20\) −9.71327e6 −0.678736
\(21\) 9.03450e6 0.482723
\(22\) −3.12229e7 −1.29166
\(23\) −5.58468e7 −1.80923 −0.904617 0.426225i \(-0.859843\pi\)
−0.904617 + 0.426225i \(0.859843\pi\)
\(24\) −1.23273e7 −0.316014
\(25\) −8.13546e6 −0.166614
\(26\) −8.84253e7 −1.45956
\(27\) 7.85711e7 1.05381
\(28\) −3.50304e7 −0.384659
\(29\) 2.05111e7 0.185695
\(30\) −1.49692e8 −1.12469
\(31\) −1.47320e8 −0.924215 −0.462108 0.886824i \(-0.652907\pi\)
−0.462108 + 0.886824i \(0.652907\pi\)
\(32\) 2.34141e8 1.23354
\(33\) −2.05194e8 −0.912720
\(34\) −2.75758e8 −1.04086
\(35\) 1.46756e8 0.472304
\(36\) −3.49146e7 −0.0962372
\(37\) −1.64673e8 −0.390403 −0.195201 0.980763i \(-0.562536\pi\)
−0.195201 + 0.980763i \(0.562536\pi\)
\(38\) −8.14503e8 −1.66757
\(39\) −5.81123e8 −1.03137
\(40\) −2.00244e8 −0.309194
\(41\) 9.49494e6 0.0127991 0.00639957 0.999980i \(-0.497963\pi\)
0.00639957 + 0.999980i \(0.497963\pi\)
\(42\) −5.39858e8 −0.637395
\(43\) 7.59458e8 0.787820 0.393910 0.919149i \(-0.371122\pi\)
0.393910 + 0.919149i \(0.371122\pi\)
\(44\) 7.95619e8 0.727303
\(45\) 1.46271e8 0.118165
\(46\) 3.33713e9 2.38894
\(47\) 1.65847e9 1.05480 0.527398 0.849618i \(-0.323168\pi\)
0.527398 + 0.849618i \(0.323168\pi\)
\(48\) 1.96125e9 1.11098
\(49\) −1.44806e9 −0.732332
\(50\) 4.86136e8 0.220000
\(51\) −1.81226e9 −0.735501
\(52\) 2.25325e9 0.821846
\(53\) 3.15983e9 1.03788 0.518940 0.854811i \(-0.326327\pi\)
0.518940 + 0.854811i \(0.326327\pi\)
\(54\) −4.69503e9 −1.39147
\(55\) −3.33316e9 −0.893020
\(56\) −7.22171e8 −0.175229
\(57\) −5.35284e9 −1.17834
\(58\) −1.22565e9 −0.245195
\(59\) 2.72696e9 0.496584 0.248292 0.968685i \(-0.420131\pi\)
0.248292 + 0.968685i \(0.420131\pi\)
\(60\) 3.81445e9 0.633286
\(61\) 2.15540e9 0.326748 0.163374 0.986564i \(-0.447762\pi\)
0.163374 + 0.986564i \(0.447762\pi\)
\(62\) 8.80314e9 1.22035
\(63\) 5.27517e8 0.0669674
\(64\) −3.76299e9 −0.438070
\(65\) −9.43973e9 −1.00910
\(66\) 1.22614e10 1.20517
\(67\) −1.36283e10 −1.23319 −0.616594 0.787281i \(-0.711488\pi\)
−0.616594 + 0.787281i \(0.711488\pi\)
\(68\) 7.02685e9 0.586086
\(69\) 2.19313e10 1.68809
\(70\) −8.76942e9 −0.623637
\(71\) 9.15005e9 0.601870 0.300935 0.953645i \(-0.402701\pi\)
0.300935 + 0.953645i \(0.402701\pi\)
\(72\) −7.19783e8 −0.0438402
\(73\) −2.13411e10 −1.20487 −0.602437 0.798166i \(-0.705804\pi\)
−0.602437 + 0.798166i \(0.705804\pi\)
\(74\) 9.84006e9 0.515493
\(75\) 3.19484e9 0.155458
\(76\) 2.07551e10 0.938967
\(77\) −1.20209e10 −0.506100
\(78\) 3.47251e10 1.36183
\(79\) −3.95516e10 −1.44616 −0.723078 0.690766i \(-0.757273\pi\)
−0.723078 + 0.690766i \(0.757273\pi\)
\(80\) 3.18584e10 1.08700
\(81\) −2.67934e10 −0.853807
\(82\) −5.67371e8 −0.0169002
\(83\) 2.56121e10 0.713699 0.356850 0.934162i \(-0.383851\pi\)
0.356850 + 0.934162i \(0.383851\pi\)
\(84\) 1.37566e10 0.358902
\(85\) −2.94382e10 −0.719626
\(86\) −4.53815e10 −1.04025
\(87\) −8.05483e9 −0.173261
\(88\) 1.64021e10 0.331318
\(89\) −6.50080e10 −1.23402 −0.617009 0.786956i \(-0.711656\pi\)
−0.617009 + 0.786956i \(0.711656\pi\)
\(90\) −8.74042e9 −0.156027
\(91\) −3.40439e10 −0.571889
\(92\) −8.50365e10 −1.34516
\(93\) 5.78534e10 0.862329
\(94\) −9.91019e10 −1.39277
\(95\) −8.69512e10 −1.15291
\(96\) −9.19483e10 −1.15094
\(97\) 1.86954e10 0.221050 0.110525 0.993873i \(-0.464747\pi\)
0.110525 + 0.993873i \(0.464747\pi\)
\(98\) 8.65290e10 0.966981
\(99\) −1.19811e10 −0.126620
\(100\) −1.23877e10 −0.123877
\(101\) 6.62726e10 0.627432 0.313716 0.949517i \(-0.398426\pi\)
0.313716 + 0.949517i \(0.398426\pi\)
\(102\) 1.08292e11 0.971166
\(103\) 5.60992e10 0.476817 0.238409 0.971165i \(-0.423374\pi\)
0.238409 + 0.971165i \(0.423374\pi\)
\(104\) 4.64519e10 0.374387
\(105\) −5.76318e10 −0.440678
\(106\) −1.88816e11 −1.37043
\(107\) −8.31258e10 −0.572961 −0.286481 0.958086i \(-0.592485\pi\)
−0.286481 + 0.958086i \(0.592485\pi\)
\(108\) 1.19638e11 0.783502
\(109\) −5.57921e9 −0.0347318 −0.0173659 0.999849i \(-0.505528\pi\)
−0.0173659 + 0.999849i \(0.505528\pi\)
\(110\) 1.99173e11 1.17916
\(111\) 6.46679e10 0.364261
\(112\) 1.14896e11 0.616034
\(113\) 1.83190e11 0.935341 0.467670 0.883903i \(-0.345093\pi\)
0.467670 + 0.883903i \(0.345093\pi\)
\(114\) 3.19860e11 1.55590
\(115\) 3.56251e11 1.65165
\(116\) 3.12318e10 0.138063
\(117\) −3.39313e10 −0.143080
\(118\) −1.62950e11 −0.655696
\(119\) −1.06167e11 −0.407833
\(120\) 7.86370e10 0.288489
\(121\) −1.22910e10 −0.0430791
\(122\) −1.28796e11 −0.431443
\(123\) −3.72871e9 −0.0119421
\(124\) −2.24321e11 −0.687149
\(125\) 3.63375e11 1.06500
\(126\) −3.15219e10 −0.0884248
\(127\) 5.37204e11 1.44284 0.721421 0.692497i \(-0.243489\pi\)
0.721421 + 0.692497i \(0.243489\pi\)
\(128\) −2.54662e11 −0.655103
\(129\) −2.98243e11 −0.735067
\(130\) 5.64072e11 1.33244
\(131\) −1.80822e11 −0.409506 −0.204753 0.978814i \(-0.565639\pi\)
−0.204753 + 0.978814i \(0.565639\pi\)
\(132\) −3.12444e11 −0.678602
\(133\) −3.13585e11 −0.653388
\(134\) 8.14359e11 1.62832
\(135\) −5.01212e11 −0.962023
\(136\) 1.44862e11 0.266988
\(137\) −9.68864e10 −0.171514 −0.0857570 0.996316i \(-0.527331\pi\)
−0.0857570 + 0.996316i \(0.527331\pi\)
\(138\) −1.31051e12 −2.22897
\(139\) −8.65857e11 −1.41535 −0.707677 0.706536i \(-0.750257\pi\)
−0.707677 + 0.706536i \(0.750257\pi\)
\(140\) 2.23462e11 0.351155
\(141\) −6.51288e11 −0.984166
\(142\) −5.46762e11 −0.794717
\(143\) 7.73213e11 1.08131
\(144\) 1.14516e11 0.154124
\(145\) −1.30842e11 −0.169521
\(146\) 1.27524e12 1.59093
\(147\) 5.68660e11 0.683294
\(148\) −2.50744e11 −0.290262
\(149\) −1.20498e12 −1.34418 −0.672089 0.740471i \(-0.734603\pi\)
−0.672089 + 0.740471i \(0.734603\pi\)
\(150\) −1.90908e11 −0.205268
\(151\) −1.40735e12 −1.45891 −0.729457 0.684027i \(-0.760227\pi\)
−0.729457 + 0.684027i \(0.760227\pi\)
\(152\) 4.27878e11 0.427740
\(153\) −1.05816e11 −0.102035
\(154\) 7.18308e11 0.668262
\(155\) 9.39768e11 0.843716
\(156\) −8.84862e11 −0.766814
\(157\) −9.92000e10 −0.0829973 −0.0414986 0.999139i \(-0.513213\pi\)
−0.0414986 + 0.999139i \(0.513213\pi\)
\(158\) 2.36341e12 1.90953
\(159\) −1.24088e12 −0.968381
\(160\) −1.49360e12 −1.12610
\(161\) 1.28480e12 0.936038
\(162\) 1.60104e12 1.12738
\(163\) −2.51668e12 −1.71315 −0.856577 0.516019i \(-0.827413\pi\)
−0.856577 + 0.516019i \(0.827413\pi\)
\(164\) 1.44577e10 0.00951609
\(165\) 1.30895e12 0.833222
\(166\) −1.53045e12 −0.942379
\(167\) −3.10127e12 −1.84756 −0.923782 0.382919i \(-0.874919\pi\)
−0.923782 + 0.382919i \(0.874919\pi\)
\(168\) 2.83600e11 0.163495
\(169\) 3.97632e11 0.221873
\(170\) 1.75908e12 0.950204
\(171\) −3.12548e11 −0.163470
\(172\) 1.15641e12 0.585740
\(173\) 3.96206e12 1.94387 0.971936 0.235244i \(-0.0755888\pi\)
0.971936 + 0.235244i \(0.0755888\pi\)
\(174\) 4.81318e11 0.228776
\(175\) 1.87163e11 0.0862007
\(176\) −2.60954e12 −1.16478
\(177\) −1.07089e12 −0.463332
\(178\) 3.88456e12 1.62942
\(179\) −3.65706e12 −1.48744 −0.743721 0.668490i \(-0.766941\pi\)
−0.743721 + 0.668490i \(0.766941\pi\)
\(180\) 2.22723e11 0.0878549
\(181\) −4.32276e11 −0.165397 −0.0826987 0.996575i \(-0.526354\pi\)
−0.0826987 + 0.996575i \(0.526354\pi\)
\(182\) 2.03430e12 0.755130
\(183\) −8.46436e11 −0.304869
\(184\) −1.75307e12 −0.612777
\(185\) 1.05046e12 0.356399
\(186\) −3.45704e12 −1.13863
\(187\) 2.41130e12 0.771120
\(188\) 2.52531e12 0.784235
\(189\) −1.80759e12 −0.545206
\(190\) 5.19578e12 1.52232
\(191\) 1.14191e12 0.325048 0.162524 0.986705i \(-0.448037\pi\)
0.162524 + 0.986705i \(0.448037\pi\)
\(192\) 1.47775e12 0.408736
\(193\) −2.21005e12 −0.594068 −0.297034 0.954867i \(-0.595997\pi\)
−0.297034 + 0.954867i \(0.595997\pi\)
\(194\) −1.11715e12 −0.291878
\(195\) 3.70703e12 0.941533
\(196\) −2.20493e12 −0.544484
\(197\) 4.19072e12 1.00629 0.503146 0.864201i \(-0.332176\pi\)
0.503146 + 0.864201i \(0.332176\pi\)
\(198\) 7.15933e11 0.167191
\(199\) −4.05306e12 −0.920643 −0.460322 0.887752i \(-0.652266\pi\)
−0.460322 + 0.887752i \(0.652266\pi\)
\(200\) −2.55379e11 −0.0564313
\(201\) 5.35189e12 1.15061
\(202\) −3.96013e12 −0.828470
\(203\) −4.71876e11 −0.0960726
\(204\) −2.75948e12 −0.546841
\(205\) −6.05690e10 −0.0116843
\(206\) −3.35222e12 −0.629596
\(207\) 1.28055e12 0.234186
\(208\) −7.39039e12 −1.31619
\(209\) 7.12222e12 1.23541
\(210\) 3.44380e12 0.581877
\(211\) −4.84297e12 −0.797184 −0.398592 0.917128i \(-0.630501\pi\)
−0.398592 + 0.917128i \(0.630501\pi\)
\(212\) 4.81140e12 0.771657
\(213\) −3.59327e12 −0.561568
\(214\) 4.96720e12 0.756546
\(215\) −4.84464e12 −0.719201
\(216\) 2.46641e12 0.356919
\(217\) 3.38922e12 0.478158
\(218\) 3.33387e11 0.0458604
\(219\) 8.38078e12 1.12419
\(220\) −5.07532e12 −0.663955
\(221\) 6.82896e12 0.871358
\(222\) −3.86424e12 −0.480975
\(223\) −1.05727e11 −0.0128383 −0.00641915 0.999979i \(-0.502043\pi\)
−0.00641915 + 0.999979i \(0.502043\pi\)
\(224\) −5.38660e12 −0.638191
\(225\) 1.86544e11 0.0215664
\(226\) −1.09465e13 −1.23504
\(227\) 7.03256e12 0.774410 0.387205 0.921994i \(-0.373441\pi\)
0.387205 + 0.921994i \(0.373441\pi\)
\(228\) −8.15064e12 −0.876093
\(229\) 1.66758e13 1.74981 0.874905 0.484294i \(-0.160923\pi\)
0.874905 + 0.484294i \(0.160923\pi\)
\(230\) −2.12878e13 −2.18086
\(231\) 4.72065e12 0.472211
\(232\) 6.43861e11 0.0628939
\(233\) −3.37844e12 −0.322298 −0.161149 0.986930i \(-0.551520\pi\)
−0.161149 + 0.986930i \(0.551520\pi\)
\(234\) 2.02757e12 0.188925
\(235\) −1.05795e13 −0.962923
\(236\) 4.15227e12 0.369207
\(237\) 1.55321e13 1.34932
\(238\) 6.34404e12 0.538508
\(239\) −4.13774e12 −0.343222 −0.171611 0.985165i \(-0.554897\pi\)
−0.171611 + 0.985165i \(0.554897\pi\)
\(240\) −1.25110e13 −1.01421
\(241\) −2.20806e13 −1.74952 −0.874758 0.484559i \(-0.838980\pi\)
−0.874758 + 0.484559i \(0.838980\pi\)
\(242\) 7.34448e11 0.0568822
\(243\) −3.39676e12 −0.257176
\(244\) 3.28197e12 0.242936
\(245\) 9.23728e12 0.668545
\(246\) 2.22810e11 0.0157685
\(247\) 2.01706e13 1.39600
\(248\) −4.62450e12 −0.313026
\(249\) −1.00580e13 −0.665909
\(250\) −2.17135e13 −1.40624
\(251\) −9.99788e12 −0.633435 −0.316718 0.948520i \(-0.602581\pi\)
−0.316718 + 0.948520i \(0.602581\pi\)
\(252\) 8.03238e11 0.0497899
\(253\) −2.91807e13 −1.76984
\(254\) −3.21007e13 −1.90515
\(255\) 1.15605e13 0.671439
\(256\) 2.29240e13 1.30308
\(257\) −1.92790e13 −1.07264 −0.536319 0.844016i \(-0.680185\pi\)
−0.536319 + 0.844016i \(0.680185\pi\)
\(258\) 1.78216e13 0.970593
\(259\) 3.78844e12 0.201981
\(260\) −1.43737e13 −0.750263
\(261\) −4.70315e11 −0.0240362
\(262\) 1.08051e13 0.540717
\(263\) 1.38093e13 0.676729 0.338364 0.941015i \(-0.390126\pi\)
0.338364 + 0.941015i \(0.390126\pi\)
\(264\) −6.44120e12 −0.309133
\(265\) −2.01568e13 −0.947479
\(266\) 1.87383e13 0.862743
\(267\) 2.55290e13 1.15139
\(268\) −2.07514e13 −0.916869
\(269\) 2.07270e13 0.897219 0.448609 0.893728i \(-0.351919\pi\)
0.448609 + 0.893728i \(0.351919\pi\)
\(270\) 2.99500e13 1.27027
\(271\) 1.20155e13 0.499356 0.249678 0.968329i \(-0.419675\pi\)
0.249678 + 0.968329i \(0.419675\pi\)
\(272\) −2.30472e13 −0.938620
\(273\) 1.33692e13 0.533594
\(274\) 5.78946e12 0.226470
\(275\) −4.25089e12 −0.162986
\(276\) 3.33943e13 1.25508
\(277\) 3.13772e13 1.15605 0.578024 0.816020i \(-0.303824\pi\)
0.578024 + 0.816020i \(0.303824\pi\)
\(278\) 5.17394e13 1.86885
\(279\) 3.37802e12 0.119630
\(280\) 4.60679e12 0.159966
\(281\) 1.59297e13 0.542404 0.271202 0.962522i \(-0.412579\pi\)
0.271202 + 0.962522i \(0.412579\pi\)
\(282\) 3.89178e13 1.29951
\(283\) 4.36081e13 1.42805 0.714023 0.700123i \(-0.246871\pi\)
0.714023 + 0.700123i \(0.246871\pi\)
\(284\) 1.39326e13 0.447487
\(285\) 3.41462e13 1.07571
\(286\) −4.62035e13 −1.42778
\(287\) −2.18439e11 −0.00662185
\(288\) −5.36879e12 −0.159668
\(289\) −1.29755e13 −0.378605
\(290\) 7.81850e12 0.223838
\(291\) −7.34179e12 −0.206248
\(292\) −3.24957e13 −0.895818
\(293\) −5.68721e13 −1.53861 −0.769303 0.638885i \(-0.779396\pi\)
−0.769303 + 0.638885i \(0.779396\pi\)
\(294\) −3.39804e13 −0.902231
\(295\) −1.73955e13 −0.453331
\(296\) −5.16922e12 −0.132227
\(297\) 4.10545e13 1.03086
\(298\) 7.20040e13 1.77487
\(299\) −8.26417e13 −1.99990
\(300\) 4.86470e12 0.115582
\(301\) −1.74720e13 −0.407592
\(302\) 8.40965e13 1.92637
\(303\) −2.60256e13 −0.585418
\(304\) −6.80744e13 −1.50376
\(305\) −1.37495e13 −0.298288
\(306\) 6.32306e12 0.134728
\(307\) −8.79181e13 −1.84000 −0.919998 0.391922i \(-0.871810\pi\)
−0.919998 + 0.391922i \(0.871810\pi\)
\(308\) −1.83039e13 −0.376283
\(309\) −2.20304e13 −0.444889
\(310\) −5.61560e13 −1.11405
\(311\) −8.36586e12 −0.163053 −0.0815264 0.996671i \(-0.525980\pi\)
−0.0815264 + 0.996671i \(0.525980\pi\)
\(312\) −1.82419e13 −0.349317
\(313\) 8.42618e12 0.158539 0.0792697 0.996853i \(-0.474741\pi\)
0.0792697 + 0.996853i \(0.474741\pi\)
\(314\) 5.92771e12 0.109591
\(315\) −3.36508e12 −0.0611346
\(316\) −6.02243e13 −1.07521
\(317\) −9.64046e13 −1.69150 −0.845750 0.533580i \(-0.820846\pi\)
−0.845750 + 0.533580i \(0.820846\pi\)
\(318\) 7.41491e13 1.27866
\(319\) 1.07174e13 0.181652
\(320\) 2.40044e13 0.399914
\(321\) 3.26439e13 0.534595
\(322\) −7.67734e13 −1.23596
\(323\) 6.29029e13 0.995535
\(324\) −4.07976e13 −0.634800
\(325\) −1.20388e13 −0.184173
\(326\) 1.50385e14 2.26207
\(327\) 2.19099e12 0.0324061
\(328\) 2.98054e11 0.00433499
\(329\) −3.81544e13 −0.545717
\(330\) −7.82164e13 −1.10020
\(331\) −2.88602e13 −0.399251 −0.199625 0.979872i \(-0.563973\pi\)
−0.199625 + 0.979872i \(0.563973\pi\)
\(332\) 3.89989e13 0.530631
\(333\) 3.77591e12 0.0505334
\(334\) 1.85317e14 2.43955
\(335\) 8.69359e13 1.12578
\(336\) −4.51201e13 −0.574783
\(337\) 4.06845e13 0.509876 0.254938 0.966957i \(-0.417945\pi\)
0.254938 + 0.966957i \(0.417945\pi\)
\(338\) −2.37606e13 −0.292964
\(339\) −7.19396e13 −0.872709
\(340\) −4.48248e13 −0.535038
\(341\) −7.69769e13 −0.904089
\(342\) 1.86763e13 0.215848
\(343\) 7.88038e13 0.896251
\(344\) 2.38400e13 0.266830
\(345\) −1.39902e14 −1.54105
\(346\) −2.36754e14 −2.56672
\(347\) −6.27388e12 −0.0669460 −0.0334730 0.999440i \(-0.510657\pi\)
−0.0334730 + 0.999440i \(0.510657\pi\)
\(348\) −1.22649e13 −0.128818
\(349\) 1.09741e12 0.0113457 0.00567283 0.999984i \(-0.498194\pi\)
0.00567283 + 0.999984i \(0.498194\pi\)
\(350\) −1.11840e13 −0.113821
\(351\) 1.16269e14 1.16486
\(352\) 1.22342e14 1.20668
\(353\) 5.86214e13 0.569240 0.284620 0.958640i \(-0.408133\pi\)
0.284620 + 0.958640i \(0.408133\pi\)
\(354\) 6.39912e13 0.611790
\(355\) −5.83689e13 −0.549447
\(356\) −9.89861e13 −0.917486
\(357\) 4.16924e13 0.380524
\(358\) 2.18528e14 1.96404
\(359\) 5.82298e13 0.515378 0.257689 0.966228i \(-0.417039\pi\)
0.257689 + 0.966228i \(0.417039\pi\)
\(360\) 4.59155e12 0.0400217
\(361\) 6.93053e13 0.594945
\(362\) 2.58307e13 0.218393
\(363\) 4.82672e12 0.0401944
\(364\) −5.18378e13 −0.425196
\(365\) 1.36137e14 1.09993
\(366\) 5.05789e13 0.402553
\(367\) −2.00272e14 −1.57021 −0.785104 0.619364i \(-0.787390\pi\)
−0.785104 + 0.619364i \(0.787390\pi\)
\(368\) 2.78910e14 2.15427
\(369\) −2.17716e11 −0.00165671
\(370\) −6.27705e13 −0.470594
\(371\) −7.26945e13 −0.536964
\(372\) 8.80920e13 0.641136
\(373\) 1.06705e14 0.765219 0.382609 0.923910i \(-0.375026\pi\)
0.382609 + 0.923910i \(0.375026\pi\)
\(374\) −1.44087e14 −1.01820
\(375\) −1.42699e14 −0.993688
\(376\) 5.20606e13 0.357253
\(377\) 3.03523e13 0.205265
\(378\) 1.08013e14 0.719898
\(379\) −2.74715e14 −1.80454 −0.902269 0.431173i \(-0.858100\pi\)
−0.902269 + 0.431173i \(0.858100\pi\)
\(380\) −1.32399e14 −0.857183
\(381\) −2.10963e14 −1.34623
\(382\) −6.82348e13 −0.429198
\(383\) 1.78808e14 1.10865 0.554323 0.832302i \(-0.312977\pi\)
0.554323 + 0.832302i \(0.312977\pi\)
\(384\) 1.00007e14 0.611237
\(385\) 7.66820e13 0.462019
\(386\) 1.32062e14 0.784416
\(387\) −1.74142e13 −0.101975
\(388\) 2.84671e13 0.164350
\(389\) 3.37178e13 0.191927 0.0959635 0.995385i \(-0.469407\pi\)
0.0959635 + 0.995385i \(0.469407\pi\)
\(390\) −2.21514e14 −1.24321
\(391\) −2.57722e14 −1.42619
\(392\) −4.54557e13 −0.248036
\(393\) 7.10098e13 0.382085
\(394\) −2.50417e14 −1.32872
\(395\) 2.52303e14 1.32020
\(396\) −1.82433e13 −0.0941415
\(397\) 6.71565e13 0.341775 0.170887 0.985291i \(-0.445337\pi\)
0.170887 + 0.985291i \(0.445337\pi\)
\(398\) 2.42191e14 1.21563
\(399\) 1.23146e14 0.609636
\(400\) 4.06302e13 0.198389
\(401\) 3.26275e14 1.57141 0.785706 0.618600i \(-0.212300\pi\)
0.785706 + 0.618600i \(0.212300\pi\)
\(402\) −3.19803e14 −1.51929
\(403\) −2.18004e14 −1.02161
\(404\) 1.00912e14 0.466492
\(405\) 1.70917e14 0.779440
\(406\) 2.81970e13 0.126856
\(407\) −8.60439e13 −0.381901
\(408\) −5.68881e13 −0.249110
\(409\) 2.71137e14 1.17142 0.585708 0.810522i \(-0.300817\pi\)
0.585708 + 0.810522i \(0.300817\pi\)
\(410\) 3.61931e12 0.0154282
\(411\) 3.80478e13 0.160029
\(412\) 8.54209e13 0.354511
\(413\) −6.27359e13 −0.256916
\(414\) −7.65195e13 −0.309222
\(415\) −1.63381e14 −0.651536
\(416\) 3.46480e14 1.36353
\(417\) 3.40026e14 1.32058
\(418\) −4.25589e14 −1.63125
\(419\) −4.36462e14 −1.65109 −0.825543 0.564339i \(-0.809131\pi\)
−0.825543 + 0.564339i \(0.809131\pi\)
\(420\) −8.77546e13 −0.327641
\(421\) 3.35884e14 1.23776 0.618881 0.785485i \(-0.287586\pi\)
0.618881 + 0.785485i \(0.287586\pi\)
\(422\) 2.89392e14 1.05261
\(423\) −3.80282e13 −0.136532
\(424\) 9.91896e13 0.351523
\(425\) −3.75435e13 −0.131340
\(426\) 2.14716e14 0.741502
\(427\) −4.95867e13 −0.169049
\(428\) −1.26574e14 −0.425993
\(429\) −3.03645e14 −1.00891
\(430\) 2.89492e14 0.949643
\(431\) −3.93344e14 −1.27394 −0.636968 0.770890i \(-0.719812\pi\)
−0.636968 + 0.770890i \(0.719812\pi\)
\(432\) −3.92400e14 −1.25478
\(433\) 3.57057e14 1.12734 0.563668 0.826001i \(-0.309390\pi\)
0.563668 + 0.826001i \(0.309390\pi\)
\(434\) −2.02524e14 −0.631367
\(435\) 5.13824e13 0.158170
\(436\) −8.49534e12 −0.0258229
\(437\) −7.61229e14 −2.28490
\(438\) −5.00794e14 −1.48440
\(439\) −3.37901e14 −0.989087 −0.494543 0.869153i \(-0.664665\pi\)
−0.494543 + 0.869153i \(0.664665\pi\)
\(440\) −1.04630e14 −0.302460
\(441\) 3.32036e13 0.0947923
\(442\) −4.08065e14 −1.15055
\(443\) 4.40752e14 1.22737 0.613683 0.789552i \(-0.289687\pi\)
0.613683 + 0.789552i \(0.289687\pi\)
\(444\) 9.84683e13 0.270826
\(445\) 4.14691e14 1.12653
\(446\) 6.31771e12 0.0169519
\(447\) 4.73203e14 1.25417
\(448\) 8.65707e13 0.226643
\(449\) −4.87159e14 −1.25984 −0.629920 0.776660i \(-0.716913\pi\)
−0.629920 + 0.776660i \(0.716913\pi\)
\(450\) −1.11470e13 −0.0284766
\(451\) 4.96124e12 0.0125204
\(452\) 2.78939e14 0.695421
\(453\) 5.52674e14 1.36122
\(454\) −4.20231e14 −1.02254
\(455\) 2.17169e14 0.522077
\(456\) −1.68030e14 −0.399098
\(457\) −3.43377e14 −0.805809 −0.402905 0.915242i \(-0.631999\pi\)
−0.402905 + 0.915242i \(0.631999\pi\)
\(458\) −9.96464e14 −2.31048
\(459\) 3.62590e14 0.830704
\(460\) 5.42455e14 1.22799
\(461\) 1.17693e14 0.263266 0.131633 0.991299i \(-0.457978\pi\)
0.131633 + 0.991299i \(0.457978\pi\)
\(462\) −2.82083e14 −0.623514
\(463\) 6.04064e14 1.31943 0.659717 0.751514i \(-0.270676\pi\)
0.659717 + 0.751514i \(0.270676\pi\)
\(464\) −1.02437e14 −0.221109
\(465\) −3.69052e14 −0.787220
\(466\) 2.01879e14 0.425568
\(467\) −6.03902e14 −1.25812 −0.629062 0.777355i \(-0.716561\pi\)
−0.629062 + 0.777355i \(0.716561\pi\)
\(468\) −5.16664e13 −0.106379
\(469\) 3.13530e14 0.638011
\(470\) 6.32179e14 1.27146
\(471\) 3.89564e13 0.0774397
\(472\) 8.56014e13 0.168190
\(473\) 3.96827e14 0.770664
\(474\) −9.28124e14 −1.78166
\(475\) −1.10892e14 −0.210419
\(476\) −1.61658e14 −0.303221
\(477\) −7.24541e13 −0.134342
\(478\) 2.47251e14 0.453195
\(479\) −6.97054e14 −1.26305 −0.631526 0.775355i \(-0.717571\pi\)
−0.631526 + 0.775355i \(0.717571\pi\)
\(480\) 5.86546e14 1.05069
\(481\) −2.43682e14 −0.431545
\(482\) 1.31943e15 2.31009
\(483\) −5.04548e14 −0.873359
\(484\) −1.87152e13 −0.0320290
\(485\) −1.19260e14 −0.201797
\(486\) 2.02974e14 0.339579
\(487\) −3.79054e14 −0.627035 −0.313517 0.949582i \(-0.601507\pi\)
−0.313517 + 0.949582i \(0.601507\pi\)
\(488\) 6.76597e13 0.110668
\(489\) 9.88314e14 1.59844
\(490\) −5.51975e14 −0.882757
\(491\) 2.28692e14 0.361662 0.180831 0.983514i \(-0.442121\pi\)
0.180831 + 0.983514i \(0.442121\pi\)
\(492\) −5.67762e12 −0.00887888
\(493\) 9.46548e13 0.146381
\(494\) −1.20530e15 −1.84330
\(495\) 7.64284e13 0.115592
\(496\) 7.35747e14 1.10047
\(497\) −2.10504e14 −0.311387
\(498\) 6.01017e14 0.879276
\(499\) 4.01402e14 0.580800 0.290400 0.956905i \(-0.406212\pi\)
0.290400 + 0.956905i \(0.406212\pi\)
\(500\) 5.53303e14 0.791823
\(501\) 1.21789e15 1.72385
\(502\) 5.97424e14 0.836397
\(503\) 3.05669e13 0.0423280 0.0211640 0.999776i \(-0.493263\pi\)
0.0211640 + 0.999776i \(0.493263\pi\)
\(504\) 1.65592e13 0.0226815
\(505\) −4.22758e14 −0.572782
\(506\) 1.74370e15 2.33692
\(507\) −1.56152e14 −0.207016
\(508\) 8.17988e14 1.07274
\(509\) −9.50285e14 −1.23284 −0.616419 0.787418i \(-0.711417\pi\)
−0.616419 + 0.787418i \(0.711417\pi\)
\(510\) −6.90800e14 −0.886577
\(511\) 4.90971e14 0.623362
\(512\) −8.48278e14 −1.06550
\(513\) 1.07098e15 1.33087
\(514\) 1.15202e15 1.41633
\(515\) −3.57861e14 −0.435286
\(516\) −4.54127e14 −0.546518
\(517\) 8.66572e14 1.03183
\(518\) −2.26379e14 −0.266699
\(519\) −1.55592e15 −1.81371
\(520\) −2.96321e14 −0.341777
\(521\) −1.22076e15 −1.39322 −0.696612 0.717448i \(-0.745310\pi\)
−0.696612 + 0.717448i \(0.745310\pi\)
\(522\) 2.81038e13 0.0317378
\(523\) −7.59341e14 −0.848550 −0.424275 0.905533i \(-0.639471\pi\)
−0.424275 + 0.905533i \(0.639471\pi\)
\(524\) −2.75334e14 −0.304465
\(525\) −7.34999e13 −0.0804286
\(526\) −8.25176e14 −0.893562
\(527\) −6.79854e14 −0.728546
\(528\) 1.02478e15 1.08679
\(529\) 2.16605e15 2.27333
\(530\) 1.20447e15 1.25107
\(531\) −6.25284e13 −0.0642773
\(532\) −4.77488e14 −0.485790
\(533\) 1.40506e13 0.0141480
\(534\) −1.52549e15 −1.52031
\(535\) 5.30266e14 0.523056
\(536\) −4.27802e14 −0.417673
\(537\) 1.43615e15 1.38784
\(538\) −1.23854e15 −1.18470
\(539\) −7.56631e14 −0.716384
\(540\) −7.63183e14 −0.715258
\(541\) 1.08760e15 1.00898 0.504491 0.863417i \(-0.331680\pi\)
0.504491 + 0.863417i \(0.331680\pi\)
\(542\) −7.17987e14 −0.659357
\(543\) 1.69757e14 0.154322
\(544\) 1.08051e15 0.972380
\(545\) 3.55903e13 0.0317066
\(546\) −7.98879e14 −0.704565
\(547\) −2.03385e15 −1.77578 −0.887888 0.460059i \(-0.847828\pi\)
−0.887888 + 0.460059i \(0.847828\pi\)
\(548\) −1.47527e14 −0.127520
\(549\) −4.94227e13 −0.0422940
\(550\) 2.54013e14 0.215209
\(551\) 2.79581e14 0.234517
\(552\) 6.88441e14 0.571744
\(553\) 9.09918e14 0.748193
\(554\) −1.87495e15 −1.52646
\(555\) −4.12522e14 −0.332534
\(556\) −1.31842e15 −1.05231
\(557\) 1.33949e15 1.05861 0.529305 0.848432i \(-0.322453\pi\)
0.529305 + 0.848432i \(0.322453\pi\)
\(558\) −2.01854e14 −0.157961
\(559\) 1.12384e15 0.870844
\(560\) −7.32929e14 −0.562377
\(561\) −9.46928e14 −0.719484
\(562\) −9.51882e14 −0.716198
\(563\) −2.15377e15 −1.60474 −0.802369 0.596829i \(-0.796427\pi\)
−0.802369 + 0.596829i \(0.796427\pi\)
\(564\) −9.91701e14 −0.731722
\(565\) −1.16858e15 −0.853872
\(566\) −2.60581e15 −1.88561
\(567\) 6.16403e14 0.441731
\(568\) 2.87227e14 0.203850
\(569\) −3.66146e14 −0.257357 −0.128679 0.991686i \(-0.541074\pi\)
−0.128679 + 0.991686i \(0.541074\pi\)
\(570\) −2.04041e15 −1.42038
\(571\) 1.16726e15 0.804767 0.402384 0.915471i \(-0.368182\pi\)
0.402384 + 0.915471i \(0.368182\pi\)
\(572\) 1.17735e15 0.803949
\(573\) −4.48433e14 −0.303282
\(574\) 1.30528e13 0.00874359
\(575\) 4.54339e14 0.301444
\(576\) 8.62845e13 0.0567034
\(577\) 1.33412e15 0.868419 0.434209 0.900812i \(-0.357028\pi\)
0.434209 + 0.900812i \(0.357028\pi\)
\(578\) 7.75354e14 0.499916
\(579\) 8.67896e14 0.554288
\(580\) −1.99230e14 −0.126038
\(581\) −5.89227e14 −0.369244
\(582\) 4.38710e14 0.272333
\(583\) 1.65106e15 1.01528
\(584\) −6.69915e14 −0.408084
\(585\) 2.16450e14 0.130617
\(586\) 3.39840e15 2.03160
\(587\) −1.53095e15 −0.906677 −0.453339 0.891338i \(-0.649767\pi\)
−0.453339 + 0.891338i \(0.649767\pi\)
\(588\) 8.65885e14 0.508025
\(589\) −2.00808e15 −1.16720
\(590\) 1.03947e15 0.598585
\(591\) −1.64572e15 −0.938909
\(592\) 8.22410e14 0.464857
\(593\) 4.73205e14 0.265002 0.132501 0.991183i \(-0.457699\pi\)
0.132501 + 0.991183i \(0.457699\pi\)
\(594\) −2.45322e15 −1.36116
\(595\) 6.77249e14 0.372310
\(596\) −1.83480e15 −0.999388
\(597\) 1.59166e15 0.858996
\(598\) 4.93827e15 2.64069
\(599\) 1.14171e15 0.604932 0.302466 0.953160i \(-0.402190\pi\)
0.302466 + 0.953160i \(0.402190\pi\)
\(600\) 1.00289e14 0.0526525
\(601\) 1.00013e15 0.520290 0.260145 0.965570i \(-0.416230\pi\)
0.260145 + 0.965570i \(0.416230\pi\)
\(602\) 1.04404e15 0.538190
\(603\) 3.12493e14 0.159623
\(604\) −2.14294e15 −1.08469
\(605\) 7.84050e13 0.0393269
\(606\) 1.55516e15 0.772994
\(607\) −1.84033e15 −0.906480 −0.453240 0.891388i \(-0.649732\pi\)
−0.453240 + 0.891388i \(0.649732\pi\)
\(608\) 3.19150e15 1.55785
\(609\) 1.85308e14 0.0896394
\(610\) 8.21601e14 0.393864
\(611\) 2.45419e15 1.16595
\(612\) −1.61124e14 −0.0758624
\(613\) −3.47262e15 −1.62041 −0.810205 0.586146i \(-0.800644\pi\)
−0.810205 + 0.586146i \(0.800644\pi\)
\(614\) 5.25356e15 2.42956
\(615\) 2.37857e13 0.0109019
\(616\) −3.77344e14 −0.171413
\(617\) 3.14997e15 1.41820 0.709101 0.705107i \(-0.249101\pi\)
0.709101 + 0.705107i \(0.249101\pi\)
\(618\) 1.31643e15 0.587438
\(619\) 4.65762e14 0.205999 0.103000 0.994681i \(-0.467156\pi\)
0.103000 + 0.994681i \(0.467156\pi\)
\(620\) 1.43096e15 0.627298
\(621\) −4.38794e15 −1.90659
\(622\) 4.99903e14 0.215297
\(623\) 1.49556e15 0.638440
\(624\) 2.90225e15 1.22806
\(625\) −1.92076e15 −0.805625
\(626\) −5.03508e14 −0.209338
\(627\) −2.79693e15 −1.15268
\(628\) −1.51050e14 −0.0617080
\(629\) −7.59933e14 −0.307749
\(630\) 2.01081e14 0.0807229
\(631\) −3.09320e15 −1.23097 −0.615483 0.788150i \(-0.711039\pi\)
−0.615483 + 0.788150i \(0.711039\pi\)
\(632\) −1.24156e15 −0.489805
\(633\) 1.90186e15 0.743803
\(634\) 5.76067e15 2.23348
\(635\) −3.42687e15 −1.31717
\(636\) −1.88946e15 −0.719986
\(637\) −2.14283e15 −0.809507
\(638\) −6.40417e14 −0.239855
\(639\) −2.09808e14 −0.0779054
\(640\) 1.62451e15 0.598044
\(641\) −2.63890e15 −0.963170 −0.481585 0.876399i \(-0.659939\pi\)
−0.481585 + 0.876399i \(0.659939\pi\)
\(642\) −1.95064e15 −0.705887
\(643\) 1.40968e15 0.505777 0.252889 0.967495i \(-0.418619\pi\)
0.252889 + 0.967495i \(0.418619\pi\)
\(644\) 1.95633e15 0.695939
\(645\) 1.90252e15 0.671042
\(646\) −3.75877e15 −1.31452
\(647\) −5.04497e15 −1.74938 −0.874692 0.484679i \(-0.838936\pi\)
−0.874692 + 0.484679i \(0.838936\pi\)
\(648\) −8.41065e14 −0.289179
\(649\) 1.42487e15 0.485770
\(650\) 7.19381e14 0.243184
\(651\) −1.33097e15 −0.446140
\(652\) −3.83209e15 −1.27372
\(653\) −3.65428e15 −1.20442 −0.602212 0.798336i \(-0.705714\pi\)
−0.602212 + 0.798336i \(0.705714\pi\)
\(654\) −1.30923e14 −0.0427895
\(655\) 1.15348e15 0.373838
\(656\) −4.74196e13 −0.0152401
\(657\) 4.89347e14 0.155958
\(658\) 2.27992e15 0.720572
\(659\) 1.48389e15 0.465085 0.232543 0.972586i \(-0.425296\pi\)
0.232543 + 0.972586i \(0.425296\pi\)
\(660\) 1.99310e15 0.619496
\(661\) 3.44956e15 1.06330 0.531650 0.846964i \(-0.321572\pi\)
0.531650 + 0.846964i \(0.321572\pi\)
\(662\) 1.72455e15 0.527177
\(663\) −2.68177e15 −0.813011
\(664\) 8.03983e14 0.241726
\(665\) 2.00038e15 0.596478
\(666\) −2.25630e14 −0.0667250
\(667\) −1.14548e15 −0.335966
\(668\) −4.72223e15 −1.37365
\(669\) 4.15194e13 0.0119786
\(670\) −5.19486e15 −1.48649
\(671\) 1.12623e15 0.319633
\(672\) 2.11535e15 0.595457
\(673\) −2.06156e15 −0.575591 −0.287795 0.957692i \(-0.592922\pi\)
−0.287795 + 0.957692i \(0.592922\pi\)
\(674\) −2.43111e15 −0.673247
\(675\) −6.39213e14 −0.175580
\(676\) 6.05465e14 0.164961
\(677\) 2.89101e15 0.781290 0.390645 0.920541i \(-0.372252\pi\)
0.390645 + 0.920541i \(0.372252\pi\)
\(678\) 4.29876e15 1.15234
\(679\) −4.30104e14 −0.114364
\(680\) −9.24088e14 −0.243733
\(681\) −2.76172e15 −0.722555
\(682\) 4.59976e15 1.19377
\(683\) 4.53396e15 1.16725 0.583625 0.812023i \(-0.301634\pi\)
0.583625 + 0.812023i \(0.301634\pi\)
\(684\) −4.75909e14 −0.121539
\(685\) 6.18046e14 0.156575
\(686\) −4.70893e15 −1.18342
\(687\) −6.54866e15 −1.63264
\(688\) −3.79289e15 −0.938066
\(689\) 4.67590e15 1.14725
\(690\) 8.35984e15 2.03483
\(691\) 3.83758e15 0.926677 0.463339 0.886181i \(-0.346651\pi\)
0.463339 + 0.886181i \(0.346651\pi\)
\(692\) 6.03294e15 1.44526
\(693\) 2.75635e14 0.0655091
\(694\) 3.74897e14 0.0883964
\(695\) 5.52337e15 1.29208
\(696\) −2.52848e14 −0.0586824
\(697\) 4.38172e13 0.0100894
\(698\) −6.55759e13 −0.0149810
\(699\) 1.32673e15 0.300717
\(700\) 2.84989e14 0.0640897
\(701\) −5.70841e15 −1.27370 −0.636848 0.770989i \(-0.719762\pi\)
−0.636848 + 0.770989i \(0.719762\pi\)
\(702\) −6.94768e15 −1.53810
\(703\) −2.24461e15 −0.493044
\(704\) −1.96622e15 −0.428530
\(705\) 4.15462e15 0.898445
\(706\) −3.50293e15 −0.751633
\(707\) −1.52466e15 −0.324612
\(708\) −1.63062e15 −0.344484
\(709\) −6.92299e15 −1.45124 −0.725620 0.688095i \(-0.758447\pi\)
−0.725620 + 0.688095i \(0.758447\pi\)
\(710\) 3.48784e15 0.725497
\(711\) 9.06908e14 0.187189
\(712\) −2.04065e15 −0.417955
\(713\) 8.22736e15 1.67212
\(714\) −2.49134e15 −0.502449
\(715\) −4.93239e15 −0.987129
\(716\) −5.56852e15 −1.10591
\(717\) 1.62491e15 0.320239
\(718\) −3.47953e15 −0.680512
\(719\) 4.05045e15 0.786130 0.393065 0.919511i \(-0.371415\pi\)
0.393065 + 0.919511i \(0.371415\pi\)
\(720\) −7.30505e14 −0.140700
\(721\) −1.29061e15 −0.246689
\(722\) −4.14134e15 −0.785573
\(723\) 8.67118e15 1.63237
\(724\) −6.58216e14 −0.122972
\(725\) −1.66868e14 −0.0309395
\(726\) −2.88421e14 −0.0530733
\(727\) −2.30565e15 −0.421071 −0.210535 0.977586i \(-0.567521\pi\)
−0.210535 + 0.977586i \(0.567521\pi\)
\(728\) −1.06866e15 −0.193695
\(729\) 6.08029e15 1.09376
\(730\) −8.13488e15 −1.45236
\(731\) 3.50475e15 0.621028
\(732\) −1.28885e15 −0.226668
\(733\) −2.90432e15 −0.506959 −0.253479 0.967341i \(-0.581575\pi\)
−0.253479 + 0.967341i \(0.581575\pi\)
\(734\) 1.19673e16 2.07333
\(735\) −3.62753e15 −0.623779
\(736\) −1.30760e16 −2.23176
\(737\) −7.12096e15 −1.20633
\(738\) 1.30097e13 0.00218754
\(739\) −1.98996e15 −0.332123 −0.166062 0.986115i \(-0.553105\pi\)
−0.166062 + 0.986115i \(0.553105\pi\)
\(740\) 1.59951e15 0.264980
\(741\) −7.92110e15 −1.30252
\(742\) 4.34387e15 0.709015
\(743\) −7.35941e15 −1.19235 −0.596176 0.802854i \(-0.703314\pi\)
−0.596176 + 0.802854i \(0.703314\pi\)
\(744\) 1.81606e15 0.292065
\(745\) 7.68669e15 1.22710
\(746\) −6.37616e15 −1.01041
\(747\) −5.87278e14 −0.0923805
\(748\) 3.67162e15 0.573323
\(749\) 1.91238e15 0.296431
\(750\) 8.52702e15 1.31208
\(751\) −1.82500e15 −0.278768 −0.139384 0.990238i \(-0.544512\pi\)
−0.139384 + 0.990238i \(0.544512\pi\)
\(752\) −8.28272e15 −1.25596
\(753\) 3.92622e15 0.591020
\(754\) −1.81371e15 −0.271034
\(755\) 8.97761e15 1.33184
\(756\) −2.75238e15 −0.405358
\(757\) 7.72752e15 1.12983 0.564915 0.825149i \(-0.308909\pi\)
0.564915 + 0.825149i \(0.308909\pi\)
\(758\) 1.64156e16 2.38274
\(759\) 1.14594e16 1.65132
\(760\) −2.72947e15 −0.390484
\(761\) −1.22550e16 −1.74060 −0.870298 0.492526i \(-0.836074\pi\)
−0.870298 + 0.492526i \(0.836074\pi\)
\(762\) 1.26061e16 1.77758
\(763\) 1.28354e14 0.0179691
\(764\) 1.73876e15 0.241671
\(765\) 6.75010e14 0.0931477
\(766\) −1.06847e16 −1.46387
\(767\) 4.03534e15 0.548915
\(768\) −9.00237e15 −1.21582
\(769\) 2.18975e15 0.293629 0.146815 0.989164i \(-0.453098\pi\)
0.146815 + 0.989164i \(0.453098\pi\)
\(770\) −4.58214e15 −0.610056
\(771\) 7.57097e15 1.00081
\(772\) −3.36519e15 −0.441686
\(773\) 1.21172e16 1.57912 0.789559 0.613675i \(-0.210310\pi\)
0.789559 + 0.613675i \(0.210310\pi\)
\(774\) 1.04059e15 0.134649
\(775\) 1.19852e15 0.153988
\(776\) 5.86864e14 0.0748683
\(777\) −1.48774e15 −0.188456
\(778\) −2.01481e15 −0.253423
\(779\) 1.29422e14 0.0161642
\(780\) 5.64461e15 0.700025
\(781\) 4.78103e15 0.588763
\(782\) 1.54002e16 1.88317
\(783\) 1.61158e15 0.195688
\(784\) 7.23190e15 0.871995
\(785\) 6.32805e14 0.0757682
\(786\) −4.24320e15 −0.504510
\(787\) 1.10648e16 1.30642 0.653211 0.757176i \(-0.273422\pi\)
0.653211 + 0.757176i \(0.273422\pi\)
\(788\) 6.38111e15 0.748172
\(789\) −5.42298e15 −0.631414
\(790\) −1.50764e16 −1.74321
\(791\) −4.21443e15 −0.483914
\(792\) −3.76096e14 −0.0428855
\(793\) 3.18955e15 0.361182
\(794\) −4.01295e15 −0.451285
\(795\) 7.91569e15 0.884035
\(796\) −6.17150e15 −0.684493
\(797\) 2.33358e15 0.257041 0.128520 0.991707i \(-0.458977\pi\)
0.128520 + 0.991707i \(0.458977\pi\)
\(798\) −7.35863e15 −0.804973
\(799\) 7.65349e15 0.831481
\(800\) −1.90484e15 −0.205525
\(801\) 1.49062e15 0.159730
\(802\) −1.94966e16 −2.07491
\(803\) −1.11510e16 −1.17864
\(804\) 8.14920e15 0.855474
\(805\) −8.19584e15 −0.854508
\(806\) 1.30268e16 1.34895
\(807\) −8.13959e15 −0.837140
\(808\) 2.08035e15 0.212507
\(809\) 2.40076e15 0.243575 0.121787 0.992556i \(-0.461137\pi\)
0.121787 + 0.992556i \(0.461137\pi\)
\(810\) −1.02132e16 −1.02918
\(811\) −2.60209e15 −0.260440 −0.130220 0.991485i \(-0.541568\pi\)
−0.130220 + 0.991485i \(0.541568\pi\)
\(812\) −7.18514e14 −0.0714294
\(813\) −4.71854e15 −0.465919
\(814\) 5.14157e15 0.504268
\(815\) 1.60541e16 1.56394
\(816\) 9.05077e15 0.875769
\(817\) 1.03519e16 0.994947
\(818\) −1.62018e16 −1.54675
\(819\) 7.80617e14 0.0740247
\(820\) −9.22269e13 −0.00868723
\(821\) 1.18775e16 1.11132 0.555659 0.831410i \(-0.312466\pi\)
0.555659 + 0.831410i \(0.312466\pi\)
\(822\) −2.27355e15 −0.211305
\(823\) −1.52923e16 −1.41180 −0.705901 0.708311i \(-0.749457\pi\)
−0.705901 + 0.708311i \(0.749457\pi\)
\(824\) 1.76100e15 0.161495
\(825\) 1.66935e15 0.152072
\(826\) 3.74879e15 0.339235
\(827\) −1.82433e16 −1.63992 −0.819959 0.572422i \(-0.806004\pi\)
−0.819959 + 0.572422i \(0.806004\pi\)
\(828\) 1.94987e15 0.174116
\(829\) 1.24346e16 1.10302 0.551508 0.834170i \(-0.314053\pi\)
0.551508 + 0.834170i \(0.314053\pi\)
\(830\) 9.76288e15 0.860297
\(831\) −1.23220e16 −1.07864
\(832\) −5.56846e15 −0.484236
\(833\) −6.68250e15 −0.577287
\(834\) −2.03183e16 −1.74371
\(835\) 1.97833e16 1.68664
\(836\) 1.08448e16 0.918520
\(837\) −1.15751e16 −0.973948
\(838\) 2.60809e16 2.18012
\(839\) −1.21441e16 −1.00850 −0.504249 0.863558i \(-0.668231\pi\)
−0.504249 + 0.863558i \(0.668231\pi\)
\(840\) −1.80911e15 −0.149255
\(841\) 4.20707e14 0.0344828
\(842\) −2.00708e16 −1.63436
\(843\) −6.25568e15 −0.506084
\(844\) −7.37428e15 −0.592702
\(845\) −2.53653e15 −0.202548
\(846\) 2.27238e15 0.180279
\(847\) 2.82764e14 0.0222877
\(848\) −1.57808e16 −1.23581
\(849\) −1.71251e16 −1.33242
\(850\) 2.24342e15 0.173423
\(851\) 9.19645e15 0.706330
\(852\) −5.47139e15 −0.417522
\(853\) 3.30637e15 0.250687 0.125343 0.992113i \(-0.459997\pi\)
0.125343 + 0.992113i \(0.459997\pi\)
\(854\) 2.96306e15 0.223214
\(855\) 1.99377e15 0.149232
\(856\) −2.60939e15 −0.194058
\(857\) −1.61448e16 −1.19299 −0.596495 0.802617i \(-0.703441\pi\)
−0.596495 + 0.802617i \(0.703441\pi\)
\(858\) 1.81443e16 1.33217
\(859\) −2.41473e16 −1.76160 −0.880799 0.473491i \(-0.842994\pi\)
−0.880799 + 0.473491i \(0.842994\pi\)
\(860\) −7.37682e15 −0.534722
\(861\) 8.57820e13 0.00617844
\(862\) 2.35043e16 1.68212
\(863\) −4.67556e14 −0.0332487 −0.0166243 0.999862i \(-0.505292\pi\)
−0.0166243 + 0.999862i \(0.505292\pi\)
\(864\) 1.83967e16 1.29991
\(865\) −2.52743e16 −1.77456
\(866\) −2.13360e16 −1.48855
\(867\) 5.09555e15 0.353253
\(868\) 5.16069e15 0.355508
\(869\) −2.06663e16 −1.41466
\(870\) −3.07036e15 −0.208850
\(871\) −2.01670e16 −1.36315
\(872\) −1.75136e14 −0.0117634
\(873\) −4.28681e14 −0.0286125
\(874\) 4.54874e16 3.01702
\(875\) −8.35975e15 −0.550996
\(876\) 1.27612e16 0.835832
\(877\) −2.90591e16 −1.89140 −0.945701 0.325037i \(-0.894623\pi\)
−0.945701 + 0.325037i \(0.894623\pi\)
\(878\) 2.01913e16 1.30600
\(879\) 2.23340e16 1.43558
\(880\) 1.66465e16 1.06333
\(881\) −1.38771e16 −0.880907 −0.440453 0.897775i \(-0.645182\pi\)
−0.440453 + 0.897775i \(0.645182\pi\)
\(882\) −1.98409e15 −0.125165
\(883\) −2.19395e16 −1.37544 −0.687721 0.725975i \(-0.741389\pi\)
−0.687721 + 0.725975i \(0.741389\pi\)
\(884\) 1.03983e16 0.647850
\(885\) 6.83129e15 0.422975
\(886\) −2.63372e16 −1.62063
\(887\) 8.16450e15 0.499286 0.249643 0.968338i \(-0.419687\pi\)
0.249643 + 0.968338i \(0.419687\pi\)
\(888\) 2.02998e15 0.123373
\(889\) −1.23588e16 −0.746478
\(890\) −2.47799e16 −1.48749
\(891\) −1.39999e16 −0.835213
\(892\) −1.60987e14 −0.00954520
\(893\) 2.26060e16 1.33211
\(894\) −2.82763e16 −1.65602
\(895\) 2.33287e16 1.35789
\(896\) 5.85872e15 0.338929
\(897\) 3.24538e16 1.86598
\(898\) 2.91102e16 1.66351
\(899\) −3.02171e15 −0.171623
\(900\) 2.84046e14 0.0160345
\(901\) 1.45820e16 0.818145
\(902\) −2.96459e14 −0.0165321
\(903\) 6.86132e15 0.380299
\(904\) 5.75048e15 0.316794
\(905\) 2.75752e15 0.150991
\(906\) −3.30251e16 −1.79738
\(907\) 3.62086e16 1.95872 0.979359 0.202129i \(-0.0647859\pi\)
0.979359 + 0.202129i \(0.0647859\pi\)
\(908\) 1.07083e16 0.575769
\(909\) −1.51961e15 −0.0812142
\(910\) −1.29769e16 −0.689358
\(911\) 3.03810e16 1.60417 0.802086 0.597209i \(-0.203724\pi\)
0.802086 + 0.597209i \(0.203724\pi\)
\(912\) 2.67332e16 1.40307
\(913\) 1.33827e16 0.698157
\(914\) 2.05185e16 1.06400
\(915\) 5.39948e15 0.278315
\(916\) 2.53918e16 1.30097
\(917\) 4.15997e15 0.211865
\(918\) −2.16666e16 −1.09687
\(919\) −1.65057e16 −0.830613 −0.415306 0.909682i \(-0.636326\pi\)
−0.415306 + 0.909682i \(0.636326\pi\)
\(920\) 1.11830e16 0.559404
\(921\) 3.45259e16 1.71679
\(922\) −7.03276e15 −0.347621
\(923\) 1.35402e16 0.665297
\(924\) 7.18802e15 0.351086
\(925\) 1.33969e15 0.0650467
\(926\) −3.60959e16 −1.74220
\(927\) −1.28634e15 −0.0617188
\(928\) 4.80250e15 0.229062
\(929\) −3.43050e16 −1.62656 −0.813281 0.581872i \(-0.802321\pi\)
−0.813281 + 0.581872i \(0.802321\pi\)
\(930\) 2.20527e16 1.03946
\(931\) −1.97380e16 −0.924870
\(932\) −5.14427e15 −0.239627
\(933\) 3.28532e15 0.152135
\(934\) 3.60863e16 1.66125
\(935\) −1.53819e16 −0.703955
\(936\) −1.06513e15 −0.0484603
\(937\) −1.98495e16 −0.897803 −0.448901 0.893581i \(-0.648185\pi\)
−0.448901 + 0.893581i \(0.648185\pi\)
\(938\) −1.87350e16 −0.842438
\(939\) −3.30900e15 −0.147923
\(940\) −1.61091e16 −0.715928
\(941\) −3.49305e16 −1.54334 −0.771671 0.636022i \(-0.780579\pi\)
−0.771671 + 0.636022i \(0.780579\pi\)
\(942\) −2.32784e15 −0.102252
\(943\) −5.30261e14 −0.0231566
\(944\) −1.36190e16 −0.591287
\(945\) 1.15308e16 0.497719
\(946\) −2.37125e16 −1.01760
\(947\) 1.18034e16 0.503595 0.251797 0.967780i \(-0.418978\pi\)
0.251797 + 0.967780i \(0.418978\pi\)
\(948\) 2.36504e16 1.00321
\(949\) −3.15805e16 −1.33185
\(950\) 6.62636e15 0.277840
\(951\) 3.78586e16 1.57823
\(952\) −3.33267e15 −0.138131
\(953\) 3.85229e16 1.58748 0.793740 0.608257i \(-0.208131\pi\)
0.793740 + 0.608257i \(0.208131\pi\)
\(954\) 4.32951e15 0.177387
\(955\) −7.28432e15 −0.296736
\(956\) −6.30044e15 −0.255183
\(957\) −4.20876e15 −0.169488
\(958\) 4.16526e16 1.66775
\(959\) 2.22895e15 0.0887356
\(960\) −9.42666e15 −0.373135
\(961\) −3.70521e15 −0.145826
\(962\) 1.45613e16 0.569818
\(963\) 1.90605e15 0.0741636
\(964\) −3.36217e16 −1.30076
\(965\) 1.40981e16 0.542325
\(966\) 3.01493e16 1.15320
\(967\) −1.53557e16 −0.584013 −0.292007 0.956416i \(-0.594323\pi\)
−0.292007 + 0.956416i \(0.594323\pi\)
\(968\) −3.85823e14 −0.0145906
\(969\) −2.47023e16 −0.928873
\(970\) 7.12637e15 0.266455
\(971\) 2.11866e15 0.0787689 0.0393845 0.999224i \(-0.487460\pi\)
0.0393845 + 0.999224i \(0.487460\pi\)
\(972\) −5.17216e15 −0.191209
\(973\) 1.99198e16 0.732257
\(974\) 2.26504e16 0.827946
\(975\) 4.72770e15 0.171840
\(976\) −1.07645e16 −0.389063
\(977\) −2.31006e16 −0.830239 −0.415119 0.909767i \(-0.636260\pi\)
−0.415119 + 0.909767i \(0.636260\pi\)
\(978\) −5.90568e16 −2.11060
\(979\) −3.39676e16 −1.20715
\(980\) 1.40654e16 0.497060
\(981\) 1.27930e14 0.00449565
\(982\) −1.36655e16 −0.477544
\(983\) 3.15129e16 1.09508 0.547538 0.836781i \(-0.315565\pi\)
0.547538 + 0.836781i \(0.315565\pi\)
\(984\) −1.17047e14 −0.00404471
\(985\) −2.67329e16 −0.918644
\(986\) −5.65611e15 −0.193284
\(987\) 1.49834e16 0.509175
\(988\) 3.07133e16 1.03792
\(989\) −4.24133e16 −1.42535
\(990\) −4.56699e15 −0.152629
\(991\) 9.24891e15 0.307387 0.153694 0.988119i \(-0.450883\pi\)
0.153694 + 0.988119i \(0.450883\pi\)
\(992\) −3.44937e16 −1.14005
\(993\) 1.13336e16 0.372517
\(994\) 1.25787e16 0.411160
\(995\) 2.58548e16 0.840455
\(996\) −1.53151e16 −0.495099
\(997\) −7.77459e14 −0.0249950 −0.0124975 0.999922i \(-0.503978\pi\)
−0.0124975 + 0.999922i \(0.503978\pi\)
\(998\) −2.39858e16 −0.766897
\(999\) −1.29385e16 −0.411410
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 29.12.a.a.1.3 11
3.2 odd 2 261.12.a.a.1.9 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.12.a.a.1.3 11 1.1 even 1 trivial
261.12.a.a.1.9 11 3.2 odd 2