Properties

Label 17.10.a.b.1.5
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 2986 x^{5} + 8252 x^{4} + 2252056 x^{3} - 10388768 x^{2} - 243559296 x - 675998208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-5.44491\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.44491 q^{2} +106.475 q^{3} -482.353 q^{4} +1303.94 q^{5} +579.746 q^{6} +9199.27 q^{7} -5414.17 q^{8} -8346.12 q^{9} +O(q^{10})\) \(q+5.44491 q^{2} +106.475 q^{3} -482.353 q^{4} +1303.94 q^{5} +579.746 q^{6} +9199.27 q^{7} -5414.17 q^{8} -8346.12 q^{9} +7099.84 q^{10} +62238.4 q^{11} -51358.4 q^{12} +141901. q^{13} +50089.2 q^{14} +138837. q^{15} +217485. q^{16} +83521.0 q^{17} -45443.9 q^{18} -941163. q^{19} -628959. q^{20} +979491. q^{21} +338883. q^{22} +568165. q^{23} -576472. q^{24} -252865. q^{25} +772638. q^{26} -2.98439e6 q^{27} -4.43730e6 q^{28} -1.83597e6 q^{29} +755954. q^{30} -7.34903e6 q^{31} +3.95624e6 q^{32} +6.62682e6 q^{33} +454765. q^{34} +1.19953e7 q^{35} +4.02577e6 q^{36} -8.01674e6 q^{37} -5.12455e6 q^{38} +1.51089e7 q^{39} -7.05975e6 q^{40} +1.95674e7 q^{41} +5.33324e6 q^{42} +3.46966e7 q^{43} -3.00209e7 q^{44} -1.08828e7 q^{45} +3.09361e6 q^{46} -5.63645e7 q^{47} +2.31567e7 q^{48} +4.42730e7 q^{49} -1.37683e6 q^{50} +8.89288e6 q^{51} -6.84463e7 q^{52} -3.28783e7 q^{53} -1.62498e7 q^{54} +8.11551e7 q^{55} -4.98064e7 q^{56} -1.00210e8 q^{57} -9.99672e6 q^{58} +1.04852e8 q^{59} -6.69683e7 q^{60} +5.69264e7 q^{61} -4.00148e7 q^{62} -7.67782e7 q^{63} -8.98109e7 q^{64} +1.85030e8 q^{65} +3.60825e7 q^{66} -1.58325e7 q^{67} -4.02866e7 q^{68} +6.04952e7 q^{69} +6.53134e7 q^{70} -9.81097e7 q^{71} +4.51873e7 q^{72} -6.27365e7 q^{73} -4.36505e7 q^{74} -2.69238e7 q^{75} +4.53973e8 q^{76} +5.72548e8 q^{77} +8.22665e7 q^{78} -1.38282e8 q^{79} +2.83587e8 q^{80} -1.53486e8 q^{81} +1.06543e8 q^{82} -6.69421e8 q^{83} -4.72460e8 q^{84} +1.08906e8 q^{85} +1.88920e8 q^{86} -1.95485e8 q^{87} -3.36969e8 q^{88} -4.21417e7 q^{89} -5.92561e7 q^{90} +1.30538e9 q^{91} -2.74056e8 q^{92} -7.82486e8 q^{93} -3.06900e8 q^{94} -1.22722e9 q^{95} +4.21240e8 q^{96} -4.11288e8 q^{97} +2.41063e8 q^{98} -5.19449e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.44491 0.240633 0.120317 0.992736i \(-0.461609\pi\)
0.120317 + 0.992736i \(0.461609\pi\)
\(3\) 106.475 0.758929 0.379465 0.925206i \(-0.376108\pi\)
0.379465 + 0.925206i \(0.376108\pi\)
\(4\) −482.353 −0.942096
\(5\) 1303.94 0.933024 0.466512 0.884515i \(-0.345511\pi\)
0.466512 + 0.884515i \(0.345511\pi\)
\(6\) 579.746 0.182624
\(7\) 9199.27 1.44815 0.724073 0.689723i \(-0.242268\pi\)
0.724073 + 0.689723i \(0.242268\pi\)
\(8\) −5414.17 −0.467333
\(9\) −8346.12 −0.424027
\(10\) 7099.84 0.224517
\(11\) 62238.4 1.28171 0.640857 0.767660i \(-0.278579\pi\)
0.640857 + 0.767660i \(0.278579\pi\)
\(12\) −51358.4 −0.714984
\(13\) 141901. 1.37797 0.688985 0.724775i \(-0.258056\pi\)
0.688985 + 0.724775i \(0.258056\pi\)
\(14\) 50089.2 0.348472
\(15\) 138837. 0.708099
\(16\) 217485. 0.829640
\(17\) 83521.0 0.242536
\(18\) −45443.9 −0.102035
\(19\) −941163. −1.65681 −0.828407 0.560127i \(-0.810753\pi\)
−0.828407 + 0.560127i \(0.810753\pi\)
\(20\) −628959. −0.878997
\(21\) 979491. 1.09904
\(22\) 338883. 0.308423
\(23\) 568165. 0.423349 0.211675 0.977340i \(-0.432108\pi\)
0.211675 + 0.977340i \(0.432108\pi\)
\(24\) −576472. −0.354673
\(25\) −252865. −0.129467
\(26\) 772638. 0.331586
\(27\) −2.98439e6 −1.08074
\(28\) −4.43730e6 −1.36429
\(29\) −1.83597e6 −0.482032 −0.241016 0.970521i \(-0.577481\pi\)
−0.241016 + 0.970521i \(0.577481\pi\)
\(30\) 755954. 0.170392
\(31\) −7.34903e6 −1.42923 −0.714615 0.699518i \(-0.753398\pi\)
−0.714615 + 0.699518i \(0.753398\pi\)
\(32\) 3.95624e6 0.666972
\(33\) 6.62682e6 0.972730
\(34\) 454765. 0.0583622
\(35\) 1.19953e7 1.35115
\(36\) 4.02577e6 0.399474
\(37\) −8.01674e6 −0.703218 −0.351609 0.936147i \(-0.614365\pi\)
−0.351609 + 0.936147i \(0.614365\pi\)
\(38\) −5.12455e6 −0.398685
\(39\) 1.51089e7 1.04578
\(40\) −7.05975e6 −0.436033
\(41\) 1.95674e7 1.08145 0.540724 0.841200i \(-0.318150\pi\)
0.540724 + 0.841200i \(0.318150\pi\)
\(42\) 5.33324e6 0.264466
\(43\) 3.46966e7 1.54767 0.773835 0.633387i \(-0.218336\pi\)
0.773835 + 0.633387i \(0.218336\pi\)
\(44\) −3.00209e7 −1.20750
\(45\) −1.08828e7 −0.395627
\(46\) 3.09361e6 0.101872
\(47\) −5.63645e7 −1.68486 −0.842432 0.538802i \(-0.818877\pi\)
−0.842432 + 0.538802i \(0.818877\pi\)
\(48\) 2.31567e7 0.629638
\(49\) 4.42730e7 1.09713
\(50\) −1.37683e6 −0.0311541
\(51\) 8.89288e6 0.184067
\(52\) −6.84463e7 −1.29818
\(53\) −3.28783e7 −0.572359 −0.286179 0.958176i \(-0.592385\pi\)
−0.286179 + 0.958176i \(0.592385\pi\)
\(54\) −1.62498e7 −0.260061
\(55\) 8.11551e7 1.19587
\(56\) −4.98064e7 −0.676767
\(57\) −1.00210e8 −1.25740
\(58\) −9.99672e6 −0.115993
\(59\) 1.04852e8 1.12653 0.563267 0.826275i \(-0.309544\pi\)
0.563267 + 0.826275i \(0.309544\pi\)
\(60\) −6.69683e7 −0.667097
\(61\) 5.69264e7 0.526416 0.263208 0.964739i \(-0.415219\pi\)
0.263208 + 0.964739i \(0.415219\pi\)
\(62\) −4.00148e7 −0.343921
\(63\) −7.67782e7 −0.614052
\(64\) −8.98109e7 −0.669144
\(65\) 1.85030e8 1.28568
\(66\) 3.60825e7 0.234072
\(67\) −1.58325e7 −0.0959872 −0.0479936 0.998848i \(-0.515283\pi\)
−0.0479936 + 0.998848i \(0.515283\pi\)
\(68\) −4.02866e7 −0.228492
\(69\) 6.04952e7 0.321292
\(70\) 6.53134e7 0.325133
\(71\) −9.81097e7 −0.458194 −0.229097 0.973404i \(-0.573577\pi\)
−0.229097 + 0.973404i \(0.573577\pi\)
\(72\) 4.51873e7 0.198162
\(73\) −6.27365e7 −0.258564 −0.129282 0.991608i \(-0.541267\pi\)
−0.129282 + 0.991608i \(0.541267\pi\)
\(74\) −4.36505e7 −0.169218
\(75\) −2.69238e7 −0.0982563
\(76\) 4.53973e8 1.56088
\(77\) 5.72548e8 1.85611
\(78\) 8.22665e7 0.251650
\(79\) −1.38282e8 −0.399433 −0.199717 0.979854i \(-0.564002\pi\)
−0.199717 + 0.979854i \(0.564002\pi\)
\(80\) 2.83587e8 0.774073
\(81\) −1.53486e8 −0.396175
\(82\) 1.06543e8 0.260233
\(83\) −6.69421e8 −1.54827 −0.774137 0.633018i \(-0.781816\pi\)
−0.774137 + 0.633018i \(0.781816\pi\)
\(84\) −4.72460e8 −1.03540
\(85\) 1.08906e8 0.226291
\(86\) 1.88920e8 0.372421
\(87\) −1.95485e8 −0.365828
\(88\) −3.36969e8 −0.598988
\(89\) −4.21417e7 −0.0711963 −0.0355981 0.999366i \(-0.511334\pi\)
−0.0355981 + 0.999366i \(0.511334\pi\)
\(90\) −5.92561e7 −0.0952011
\(91\) 1.30538e9 1.99550
\(92\) −2.74056e8 −0.398836
\(93\) −7.82486e8 −1.08468
\(94\) −3.06900e8 −0.405435
\(95\) −1.22722e9 −1.54585
\(96\) 4.21240e8 0.506185
\(97\) −4.11288e8 −0.471707 −0.235854 0.971789i \(-0.575789\pi\)
−0.235854 + 0.971789i \(0.575789\pi\)
\(98\) 2.41063e8 0.264005
\(99\) −5.19449e8 −0.543481
\(100\) 1.21970e8 0.121970
\(101\) 1.81470e7 0.0173524 0.00867620 0.999962i \(-0.497238\pi\)
0.00867620 + 0.999962i \(0.497238\pi\)
\(102\) 4.84210e7 0.0442928
\(103\) 7.17681e8 0.628296 0.314148 0.949374i \(-0.398281\pi\)
0.314148 + 0.949374i \(0.398281\pi\)
\(104\) −7.68275e8 −0.643971
\(105\) 1.27720e9 1.02543
\(106\) −1.79020e8 −0.137729
\(107\) −7.18789e8 −0.530120 −0.265060 0.964232i \(-0.585392\pi\)
−0.265060 + 0.964232i \(0.585392\pi\)
\(108\) 1.43953e9 1.01816
\(109\) 3.41476e8 0.231708 0.115854 0.993266i \(-0.463040\pi\)
0.115854 + 0.993266i \(0.463040\pi\)
\(110\) 4.41883e8 0.287766
\(111\) −8.53581e8 −0.533693
\(112\) 2.00070e9 1.20144
\(113\) −1.70781e9 −0.985339 −0.492670 0.870216i \(-0.663979\pi\)
−0.492670 + 0.870216i \(0.663979\pi\)
\(114\) −5.45636e8 −0.302574
\(115\) 7.40853e8 0.394995
\(116\) 8.85588e8 0.454120
\(117\) −1.18432e9 −0.584296
\(118\) 5.70912e8 0.271082
\(119\) 7.68332e8 0.351227
\(120\) −7.51685e8 −0.330918
\(121\) 1.51567e9 0.642792
\(122\) 3.09959e8 0.126673
\(123\) 2.08343e9 0.820743
\(124\) 3.54482e9 1.34647
\(125\) −2.87648e9 −1.05382
\(126\) −4.18051e8 −0.147762
\(127\) 1.94335e9 0.662880 0.331440 0.943476i \(-0.392466\pi\)
0.331440 + 0.943476i \(0.392466\pi\)
\(128\) −2.51461e9 −0.827991
\(129\) 3.69431e9 1.17457
\(130\) 1.00747e9 0.309377
\(131\) 3.30692e9 0.981075 0.490538 0.871420i \(-0.336800\pi\)
0.490538 + 0.871420i \(0.336800\pi\)
\(132\) −3.19647e9 −0.916405
\(133\) −8.65802e9 −2.39931
\(134\) −8.62067e7 −0.0230977
\(135\) −3.89147e9 −1.00835
\(136\) −4.52197e8 −0.113345
\(137\) −4.83938e9 −1.17367 −0.586836 0.809706i \(-0.699627\pi\)
−0.586836 + 0.809706i \(0.699627\pi\)
\(138\) 3.29391e8 0.0773137
\(139\) 3.57524e9 0.812342 0.406171 0.913797i \(-0.366864\pi\)
0.406171 + 0.913797i \(0.366864\pi\)
\(140\) −5.78597e9 −1.27292
\(141\) −6.00139e9 −1.27869
\(142\) −5.34199e8 −0.110257
\(143\) 8.83168e9 1.76616
\(144\) −1.81516e9 −0.351789
\(145\) −2.39400e9 −0.449747
\(146\) −3.41595e8 −0.0622191
\(147\) 4.71396e9 0.832641
\(148\) 3.86690e9 0.662499
\(149\) −2.20680e9 −0.366796 −0.183398 0.983039i \(-0.558710\pi\)
−0.183398 + 0.983039i \(0.558710\pi\)
\(150\) −1.46598e8 −0.0236438
\(151\) 7.78978e9 1.21935 0.609676 0.792651i \(-0.291300\pi\)
0.609676 + 0.792651i \(0.291300\pi\)
\(152\) 5.09561e9 0.774284
\(153\) −6.97076e8 −0.102842
\(154\) 3.11747e9 0.446642
\(155\) −9.58269e9 −1.33351
\(156\) −7.28780e9 −0.985226
\(157\) 5.99611e9 0.787627 0.393814 0.919190i \(-0.371155\pi\)
0.393814 + 0.919190i \(0.371155\pi\)
\(158\) −7.52935e8 −0.0961171
\(159\) −3.50071e9 −0.434380
\(160\) 5.15870e9 0.622301
\(161\) 5.22670e9 0.613072
\(162\) −8.35719e8 −0.0953329
\(163\) 2.20096e9 0.244212 0.122106 0.992517i \(-0.461035\pi\)
0.122106 + 0.992517i \(0.461035\pi\)
\(164\) −9.43839e9 −1.01883
\(165\) 8.64098e9 0.907580
\(166\) −3.64494e9 −0.372567
\(167\) −1.54378e9 −0.153589 −0.0767946 0.997047i \(-0.524469\pi\)
−0.0767946 + 0.997047i \(0.524469\pi\)
\(168\) −5.30313e9 −0.513618
\(169\) 9.53135e9 0.898802
\(170\) 5.92986e8 0.0544533
\(171\) 7.85506e9 0.702533
\(172\) −1.67360e10 −1.45805
\(173\) 1.36568e10 1.15916 0.579578 0.814917i \(-0.303217\pi\)
0.579578 + 0.814917i \(0.303217\pi\)
\(174\) −1.06440e9 −0.0880304
\(175\) −2.32618e9 −0.187487
\(176\) 1.35359e10 1.06336
\(177\) 1.11641e10 0.854959
\(178\) −2.29458e8 −0.0171322
\(179\) 7.48481e9 0.544932 0.272466 0.962165i \(-0.412161\pi\)
0.272466 + 0.962165i \(0.412161\pi\)
\(180\) 5.24937e9 0.372718
\(181\) −1.98188e10 −1.37254 −0.686269 0.727348i \(-0.740753\pi\)
−0.686269 + 0.727348i \(0.740753\pi\)
\(182\) 7.10771e9 0.480185
\(183\) 6.06123e9 0.399513
\(184\) −3.07614e9 −0.197845
\(185\) −1.04534e10 −0.656119
\(186\) −4.26057e9 −0.261011
\(187\) 5.19821e9 0.310861
\(188\) 2.71876e10 1.58730
\(189\) −2.74543e10 −1.56506
\(190\) −6.68211e9 −0.371982
\(191\) −3.54665e10 −1.92827 −0.964137 0.265405i \(-0.914494\pi\)
−0.964137 + 0.265405i \(0.914494\pi\)
\(192\) −9.56260e9 −0.507833
\(193\) −1.16540e10 −0.604599 −0.302299 0.953213i \(-0.597754\pi\)
−0.302299 + 0.953213i \(0.597754\pi\)
\(194\) −2.23943e9 −0.113509
\(195\) 1.97011e10 0.975739
\(196\) −2.13552e10 −1.03360
\(197\) 4.99943e9 0.236495 0.118248 0.992984i \(-0.462272\pi\)
0.118248 + 0.992984i \(0.462272\pi\)
\(198\) −2.82835e9 −0.130780
\(199\) −1.90482e9 −0.0861026 −0.0430513 0.999073i \(-0.513708\pi\)
−0.0430513 + 0.999073i \(0.513708\pi\)
\(200\) 1.36906e9 0.0605043
\(201\) −1.68576e9 −0.0728475
\(202\) 9.88091e7 0.00417557
\(203\) −1.68896e10 −0.698052
\(204\) −4.28951e9 −0.173409
\(205\) 2.55147e10 1.00902
\(206\) 3.90771e9 0.151189
\(207\) −4.74197e9 −0.179511
\(208\) 3.08613e10 1.14322
\(209\) −5.85765e10 −2.12356
\(210\) 6.95423e9 0.246753
\(211\) 4.45582e10 1.54759 0.773797 0.633434i \(-0.218355\pi\)
0.773797 + 0.633434i \(0.218355\pi\)
\(212\) 1.58590e10 0.539216
\(213\) −1.04462e10 −0.347737
\(214\) −3.91374e9 −0.127565
\(215\) 4.52422e10 1.44401
\(216\) 1.61580e10 0.505063
\(217\) −6.76057e10 −2.06973
\(218\) 1.85931e9 0.0557567
\(219\) −6.67986e9 −0.196232
\(220\) −3.91454e10 −1.12662
\(221\) 1.18517e10 0.334207
\(222\) −4.64768e9 −0.128424
\(223\) −1.00748e10 −0.272812 −0.136406 0.990653i \(-0.543555\pi\)
−0.136406 + 0.990653i \(0.543555\pi\)
\(224\) 3.63945e10 0.965873
\(225\) 2.11044e9 0.0548975
\(226\) −9.29886e9 −0.237106
\(227\) 7.51701e10 1.87901 0.939505 0.342536i \(-0.111286\pi\)
0.939505 + 0.342536i \(0.111286\pi\)
\(228\) 4.83367e10 1.18460
\(229\) 8.19379e10 1.96891 0.984453 0.175647i \(-0.0562016\pi\)
0.984453 + 0.175647i \(0.0562016\pi\)
\(230\) 4.03388e9 0.0950490
\(231\) 6.09619e10 1.40866
\(232\) 9.94027e9 0.225269
\(233\) −4.97304e10 −1.10540 −0.552701 0.833380i \(-0.686403\pi\)
−0.552701 + 0.833380i \(0.686403\pi\)
\(234\) −6.44853e9 −0.140601
\(235\) −7.34959e10 −1.57202
\(236\) −5.05759e10 −1.06130
\(237\) −1.47236e10 −0.303142
\(238\) 4.18350e9 0.0845170
\(239\) −4.06399e10 −0.805680 −0.402840 0.915270i \(-0.631977\pi\)
−0.402840 + 0.915270i \(0.631977\pi\)
\(240\) 3.01949e10 0.587467
\(241\) −3.05939e10 −0.584196 −0.292098 0.956388i \(-0.594353\pi\)
−0.292098 + 0.956388i \(0.594353\pi\)
\(242\) 8.25269e9 0.154677
\(243\) 4.23994e10 0.780067
\(244\) −2.74586e10 −0.495934
\(245\) 5.77293e10 1.02364
\(246\) 1.13441e10 0.197498
\(247\) −1.33552e11 −2.28304
\(248\) 3.97889e10 0.667927
\(249\) −7.12765e10 −1.17503
\(250\) −1.56622e10 −0.253584
\(251\) 2.05450e10 0.326719 0.163359 0.986567i \(-0.447767\pi\)
0.163359 + 0.986567i \(0.447767\pi\)
\(252\) 3.70342e10 0.578496
\(253\) 3.53617e10 0.542613
\(254\) 1.05814e10 0.159511
\(255\) 1.15958e10 0.171739
\(256\) 3.22914e10 0.469901
\(257\) −8.98169e10 −1.28428 −0.642139 0.766588i \(-0.721953\pi\)
−0.642139 + 0.766588i \(0.721953\pi\)
\(258\) 2.01152e10 0.282641
\(259\) −7.37482e10 −1.01836
\(260\) −8.92498e10 −1.21123
\(261\) 1.53233e10 0.204394
\(262\) 1.80059e10 0.236080
\(263\) 1.43373e11 1.84785 0.923923 0.382577i \(-0.124963\pi\)
0.923923 + 0.382577i \(0.124963\pi\)
\(264\) −3.58787e10 −0.454589
\(265\) −4.28714e10 −0.534024
\(266\) −4.71422e10 −0.577354
\(267\) −4.48703e9 −0.0540329
\(268\) 7.63686e9 0.0904291
\(269\) −1.67468e11 −1.95005 −0.975025 0.222094i \(-0.928711\pi\)
−0.975025 + 0.222094i \(0.928711\pi\)
\(270\) −2.11887e10 −0.242643
\(271\) 4.52996e10 0.510190 0.255095 0.966916i \(-0.417893\pi\)
0.255095 + 0.966916i \(0.417893\pi\)
\(272\) 1.81646e10 0.201217
\(273\) 1.38991e11 1.51444
\(274\) −2.63500e10 −0.282425
\(275\) −1.57379e10 −0.165940
\(276\) −2.91800e10 −0.302688
\(277\) 1.93194e9 0.0197167 0.00985836 0.999951i \(-0.496862\pi\)
0.00985836 + 0.999951i \(0.496862\pi\)
\(278\) 1.94669e10 0.195477
\(279\) 6.13358e10 0.606032
\(280\) −6.49445e10 −0.631439
\(281\) 1.16694e11 1.11653 0.558265 0.829662i \(-0.311467\pi\)
0.558265 + 0.829662i \(0.311467\pi\)
\(282\) −3.26771e10 −0.307696
\(283\) −1.65132e8 −0.00153036 −0.000765180 1.00000i \(-0.500244\pi\)
−0.000765180 1.00000i \(0.500244\pi\)
\(284\) 4.73235e10 0.431662
\(285\) −1.30668e11 −1.17319
\(286\) 4.80877e10 0.424998
\(287\) 1.80006e11 1.56609
\(288\) −3.30192e10 −0.282814
\(289\) 6.97576e9 0.0588235
\(290\) −1.30351e10 −0.108224
\(291\) −4.37918e10 −0.357993
\(292\) 3.02611e10 0.243592
\(293\) 6.45700e10 0.511831 0.255915 0.966699i \(-0.417623\pi\)
0.255915 + 0.966699i \(0.417623\pi\)
\(294\) 2.56671e10 0.200361
\(295\) 1.36721e11 1.05108
\(296\) 4.34040e10 0.328637
\(297\) −1.85744e11 −1.38519
\(298\) −1.20158e10 −0.0882633
\(299\) 8.06230e10 0.583363
\(300\) 1.29868e10 0.0925669
\(301\) 3.19183e11 2.24125
\(302\) 4.24147e10 0.293417
\(303\) 1.93220e9 0.0131692
\(304\) −2.04689e11 −1.37456
\(305\) 7.42286e10 0.491159
\(306\) −3.79552e9 −0.0247471
\(307\) 8.54538e10 0.549046 0.274523 0.961581i \(-0.411480\pi\)
0.274523 + 0.961581i \(0.411480\pi\)
\(308\) −2.76170e11 −1.74863
\(309\) 7.64150e10 0.476832
\(310\) −5.21769e10 −0.320886
\(311\) −7.31980e10 −0.443688 −0.221844 0.975082i \(-0.571208\pi\)
−0.221844 + 0.975082i \(0.571208\pi\)
\(312\) −8.18019e10 −0.488729
\(313\) 1.60425e10 0.0944764 0.0472382 0.998884i \(-0.484958\pi\)
0.0472382 + 0.998884i \(0.484958\pi\)
\(314\) 3.26483e10 0.189530
\(315\) −1.00114e11 −0.572925
\(316\) 6.67008e10 0.376304
\(317\) 8.53822e10 0.474899 0.237449 0.971400i \(-0.423689\pi\)
0.237449 + 0.971400i \(0.423689\pi\)
\(318\) −1.90611e10 −0.104526
\(319\) −1.14268e11 −0.617827
\(320\) −1.17108e11 −0.624327
\(321\) −7.65329e10 −0.402324
\(322\) 2.84589e10 0.147526
\(323\) −7.86069e10 −0.401836
\(324\) 7.40345e10 0.373235
\(325\) −3.58818e10 −0.178402
\(326\) 1.19840e10 0.0587656
\(327\) 3.63586e10 0.175850
\(328\) −1.05941e11 −0.505397
\(329\) −5.18512e11 −2.43993
\(330\) 4.70494e10 0.218394
\(331\) 5.68636e10 0.260380 0.130190 0.991489i \(-0.458441\pi\)
0.130190 + 0.991489i \(0.458441\pi\)
\(332\) 3.22897e11 1.45862
\(333\) 6.69087e10 0.298183
\(334\) −8.40574e9 −0.0369587
\(335\) −2.06447e10 −0.0895583
\(336\) 2.13025e11 0.911807
\(337\) 3.07106e11 1.29704 0.648521 0.761197i \(-0.275388\pi\)
0.648521 + 0.761197i \(0.275388\pi\)
\(338\) 5.18974e10 0.216282
\(339\) −1.81838e11 −0.747803
\(340\) −5.25313e10 −0.213188
\(341\) −4.57392e11 −1.83187
\(342\) 4.27701e10 0.169053
\(343\) 3.60556e10 0.140653
\(344\) −1.87853e11 −0.723278
\(345\) 7.88821e10 0.299773
\(346\) 7.43602e10 0.278932
\(347\) 3.34687e10 0.123924 0.0619621 0.998079i \(-0.480264\pi\)
0.0619621 + 0.998079i \(0.480264\pi\)
\(348\) 9.42928e10 0.344645
\(349\) −3.80974e11 −1.37462 −0.687308 0.726366i \(-0.741208\pi\)
−0.687308 + 0.726366i \(0.741208\pi\)
\(350\) −1.26658e10 −0.0451157
\(351\) −4.23488e11 −1.48922
\(352\) 2.46230e11 0.854868
\(353\) 2.09902e11 0.719499 0.359750 0.933049i \(-0.382862\pi\)
0.359750 + 0.933049i \(0.382862\pi\)
\(354\) 6.07878e10 0.205732
\(355\) −1.27929e11 −0.427506
\(356\) 2.03272e10 0.0670737
\(357\) 8.18080e10 0.266556
\(358\) 4.07542e10 0.131129
\(359\) 3.14148e11 0.998181 0.499091 0.866550i \(-0.333668\pi\)
0.499091 + 0.866550i \(0.333668\pi\)
\(360\) 5.89215e10 0.184890
\(361\) 5.63101e11 1.74503
\(362\) −1.07912e11 −0.330279
\(363\) 1.61381e11 0.487834
\(364\) −6.29656e11 −1.87995
\(365\) −8.18047e10 −0.241246
\(366\) 3.30029e10 0.0961361
\(367\) 2.40379e11 0.691671 0.345835 0.938295i \(-0.387596\pi\)
0.345835 + 0.938295i \(0.387596\pi\)
\(368\) 1.23567e11 0.351227
\(369\) −1.63312e11 −0.458563
\(370\) −5.69176e10 −0.157884
\(371\) −3.02457e11 −0.828859
\(372\) 3.77435e11 1.02188
\(373\) 2.93908e11 0.786179 0.393089 0.919500i \(-0.371406\pi\)
0.393089 + 0.919500i \(0.371406\pi\)
\(374\) 2.83038e10 0.0748037
\(375\) −3.06273e11 −0.799774
\(376\) 3.05167e11 0.787393
\(377\) −2.60526e11 −0.664225
\(378\) −1.49486e11 −0.376606
\(379\) 3.76034e11 0.936161 0.468081 0.883686i \(-0.344946\pi\)
0.468081 + 0.883686i \(0.344946\pi\)
\(380\) 5.91953e11 1.45634
\(381\) 2.06918e11 0.503079
\(382\) −1.93112e11 −0.464007
\(383\) 3.73836e11 0.887741 0.443870 0.896091i \(-0.353605\pi\)
0.443870 + 0.896091i \(0.353605\pi\)
\(384\) −2.67742e11 −0.628386
\(385\) 7.46568e11 1.73179
\(386\) −6.34550e10 −0.145487
\(387\) −2.89582e11 −0.656253
\(388\) 1.98386e11 0.444394
\(389\) −4.62613e10 −0.102434 −0.0512171 0.998688i \(-0.516310\pi\)
−0.0512171 + 0.998688i \(0.516310\pi\)
\(390\) 1.07271e11 0.234795
\(391\) 4.74537e10 0.102677
\(392\) −2.39701e11 −0.512724
\(393\) 3.52103e11 0.744567
\(394\) 2.72215e10 0.0569087
\(395\) −1.80312e11 −0.372681
\(396\) 2.50558e11 0.512011
\(397\) −3.36827e11 −0.680534 −0.340267 0.940329i \(-0.610517\pi\)
−0.340267 + 0.940329i \(0.610517\pi\)
\(398\) −1.03716e10 −0.0207192
\(399\) −9.21861e11 −1.82091
\(400\) −5.49944e10 −0.107411
\(401\) −9.81350e11 −1.89528 −0.947642 0.319335i \(-0.896541\pi\)
−0.947642 + 0.319335i \(0.896541\pi\)
\(402\) −9.17884e9 −0.0175295
\(403\) −1.04283e12 −1.96944
\(404\) −8.75328e9 −0.0163476
\(405\) −2.00137e11 −0.369640
\(406\) −9.19626e10 −0.167975
\(407\) −4.98949e11 −0.901325
\(408\) −4.81475e10 −0.0860208
\(409\) 8.17703e11 1.44491 0.722455 0.691418i \(-0.243014\pi\)
0.722455 + 0.691418i \(0.243014\pi\)
\(410\) 1.38925e11 0.242803
\(411\) −5.15272e11 −0.890734
\(412\) −3.46176e11 −0.591915
\(413\) 9.64566e11 1.63139
\(414\) −2.58196e10 −0.0431965
\(415\) −8.72885e11 −1.44458
\(416\) 5.61394e11 0.919068
\(417\) 3.80673e11 0.616510
\(418\) −3.18944e11 −0.511000
\(419\) −4.18196e11 −0.662852 −0.331426 0.943481i \(-0.607530\pi\)
−0.331426 + 0.943481i \(0.607530\pi\)
\(420\) −6.16060e11 −0.966053
\(421\) 3.11784e11 0.483709 0.241855 0.970313i \(-0.422244\pi\)
0.241855 + 0.970313i \(0.422244\pi\)
\(422\) 2.42616e11 0.372403
\(423\) 4.70424e11 0.714427
\(424\) 1.78009e11 0.267482
\(425\) −2.11196e10 −0.0314004
\(426\) −5.68787e10 −0.0836771
\(427\) 5.23681e11 0.762328
\(428\) 3.46710e11 0.499424
\(429\) 9.40351e11 1.34039
\(430\) 2.46340e11 0.347478
\(431\) 8.66540e11 1.20960 0.604799 0.796378i \(-0.293253\pi\)
0.604799 + 0.796378i \(0.293253\pi\)
\(432\) −6.49061e11 −0.896621
\(433\) 2.95119e11 0.403461 0.201730 0.979441i \(-0.435344\pi\)
0.201730 + 0.979441i \(0.435344\pi\)
\(434\) −3.68107e11 −0.498047
\(435\) −2.54901e11 −0.341326
\(436\) −1.64712e11 −0.218291
\(437\) −5.34736e11 −0.701411
\(438\) −3.63713e10 −0.0472199
\(439\) 5.48786e11 0.705201 0.352600 0.935774i \(-0.385297\pi\)
0.352600 + 0.935774i \(0.385297\pi\)
\(440\) −4.39387e11 −0.558870
\(441\) −3.69508e11 −0.465211
\(442\) 6.45315e10 0.0804214
\(443\) −1.03597e12 −1.27800 −0.638999 0.769207i \(-0.720651\pi\)
−0.638999 + 0.769207i \(0.720651\pi\)
\(444\) 4.11727e11 0.502790
\(445\) −5.49503e10 −0.0664278
\(446\) −5.48562e10 −0.0656476
\(447\) −2.34968e11 −0.278372
\(448\) −8.26195e11 −0.969018
\(449\) −1.04924e12 −1.21833 −0.609167 0.793042i \(-0.708496\pi\)
−0.609167 + 0.793042i \(0.708496\pi\)
\(450\) 1.14912e10 0.0132102
\(451\) 1.21784e12 1.38611
\(452\) 8.23766e11 0.928284
\(453\) 8.29415e11 0.925401
\(454\) 4.09295e11 0.452153
\(455\) 1.70214e12 1.86185
\(456\) 5.42555e11 0.587627
\(457\) 1.13929e11 0.122183 0.0610917 0.998132i \(-0.480542\pi\)
0.0610917 + 0.998132i \(0.480542\pi\)
\(458\) 4.46145e11 0.473785
\(459\) −2.49260e11 −0.262117
\(460\) −3.57352e11 −0.372123
\(461\) 1.04783e12 1.08053 0.540264 0.841496i \(-0.318325\pi\)
0.540264 + 0.841496i \(0.318325\pi\)
\(462\) 3.31932e11 0.338970
\(463\) 1.26218e11 0.127646 0.0638231 0.997961i \(-0.479671\pi\)
0.0638231 + 0.997961i \(0.479671\pi\)
\(464\) −3.99297e11 −0.399913
\(465\) −1.02032e12 −1.01204
\(466\) −2.70778e11 −0.265997
\(467\) −1.20765e12 −1.17494 −0.587470 0.809246i \(-0.699876\pi\)
−0.587470 + 0.809246i \(0.699876\pi\)
\(468\) 5.71261e11 0.550463
\(469\) −1.45648e11 −0.139003
\(470\) −4.00179e11 −0.378280
\(471\) 6.38434e11 0.597753
\(472\) −5.67688e11 −0.526467
\(473\) 2.15946e12 1.98367
\(474\) −8.01686e10 −0.0729460
\(475\) 2.37988e11 0.214503
\(476\) −3.70607e11 −0.330889
\(477\) 2.74406e11 0.242695
\(478\) −2.21281e11 −0.193874
\(479\) −1.58750e12 −1.37786 −0.688930 0.724828i \(-0.741919\pi\)
−0.688930 + 0.724828i \(0.741919\pi\)
\(480\) 5.49272e11 0.472282
\(481\) −1.13758e12 −0.969014
\(482\) −1.66581e11 −0.140577
\(483\) 5.56512e11 0.465278
\(484\) −7.31088e11 −0.605572
\(485\) −5.36294e11 −0.440114
\(486\) 2.30861e11 0.187710
\(487\) 9.39880e11 0.757167 0.378584 0.925567i \(-0.376411\pi\)
0.378584 + 0.925567i \(0.376411\pi\)
\(488\) −3.08209e11 −0.246012
\(489\) 2.34347e11 0.185340
\(490\) 3.14331e11 0.246323
\(491\) 9.66438e11 0.750425 0.375213 0.926939i \(-0.377570\pi\)
0.375213 + 0.926939i \(0.377570\pi\)
\(492\) −1.00495e12 −0.773218
\(493\) −1.53342e11 −0.116910
\(494\) −7.27178e11 −0.549376
\(495\) −6.77330e11 −0.507081
\(496\) −1.59830e12 −1.18575
\(497\) −9.02538e11 −0.663532
\(498\) −3.88094e11 −0.282752
\(499\) −1.22995e12 −0.888045 −0.444022 0.896016i \(-0.646449\pi\)
−0.444022 + 0.896016i \(0.646449\pi\)
\(500\) 1.38748e12 0.992799
\(501\) −1.64373e11 −0.116563
\(502\) 1.11866e11 0.0786195
\(503\) −1.98521e12 −1.38277 −0.691386 0.722485i \(-0.743000\pi\)
−0.691386 + 0.722485i \(0.743000\pi\)
\(504\) 4.15690e11 0.286967
\(505\) 2.36626e10 0.0161902
\(506\) 1.92541e11 0.130571
\(507\) 1.01485e12 0.682127
\(508\) −9.37382e11 −0.624496
\(509\) 2.25974e12 1.49221 0.746104 0.665830i \(-0.231922\pi\)
0.746104 + 0.665830i \(0.231922\pi\)
\(510\) 6.31381e10 0.0413262
\(511\) −5.77130e11 −0.374438
\(512\) 1.46330e12 0.941065
\(513\) 2.80880e12 1.79058
\(514\) −4.89045e11 −0.309040
\(515\) 9.35813e11 0.586215
\(516\) −1.78196e12 −1.10656
\(517\) −3.50803e12 −2.15952
\(518\) −4.01553e11 −0.245052
\(519\) 1.45411e12 0.879717
\(520\) −1.00178e12 −0.600840
\(521\) 4.78832e11 0.284717 0.142358 0.989815i \(-0.454531\pi\)
0.142358 + 0.989815i \(0.454531\pi\)
\(522\) 8.34338e10 0.0491841
\(523\) −9.37326e11 −0.547814 −0.273907 0.961756i \(-0.588316\pi\)
−0.273907 + 0.961756i \(0.588316\pi\)
\(524\) −1.59510e12 −0.924267
\(525\) −2.47679e11 −0.142290
\(526\) 7.80653e11 0.444654
\(527\) −6.13798e11 −0.346639
\(528\) 1.44123e12 0.807016
\(529\) −1.47834e12 −0.820775
\(530\) −2.33431e11 −0.128504
\(531\) −8.75110e11 −0.477680
\(532\) 4.17622e12 2.26038
\(533\) 2.77663e12 1.49020
\(534\) −2.44315e10 −0.0130021
\(535\) −9.37257e11 −0.494614
\(536\) 8.57199e10 0.0448580
\(537\) 7.96944e11 0.413565
\(538\) −9.11847e11 −0.469247
\(539\) 2.75548e12 1.40620
\(540\) 1.87706e12 0.949963
\(541\) −3.44109e12 −1.72706 −0.863532 0.504293i \(-0.831753\pi\)
−0.863532 + 0.504293i \(0.831753\pi\)
\(542\) 2.46652e11 0.122769
\(543\) −2.11021e12 −1.04166
\(544\) 3.30429e11 0.161765
\(545\) 4.45264e11 0.216189
\(546\) 7.56792e11 0.364426
\(547\) 8.05238e11 0.384575 0.192288 0.981339i \(-0.438409\pi\)
0.192288 + 0.981339i \(0.438409\pi\)
\(548\) 2.33429e12 1.10571
\(549\) −4.75114e11 −0.223215
\(550\) −8.56917e10 −0.0399307
\(551\) 1.72795e12 0.798637
\(552\) −3.27531e11 −0.150151
\(553\) −1.27210e12 −0.578438
\(554\) 1.05192e10 0.00474450
\(555\) −1.11302e12 −0.497948
\(556\) −1.72453e12 −0.765304
\(557\) −2.13503e11 −0.0939842 −0.0469921 0.998895i \(-0.514964\pi\)
−0.0469921 + 0.998895i \(0.514964\pi\)
\(558\) 3.33968e11 0.145832
\(559\) 4.92347e12 2.13264
\(560\) 2.60880e12 1.12097
\(561\) 5.53479e11 0.235922
\(562\) 6.35390e11 0.268675
\(563\) −1.94290e12 −0.815010 −0.407505 0.913203i \(-0.633601\pi\)
−0.407505 + 0.913203i \(0.633601\pi\)
\(564\) 2.89479e12 1.20465
\(565\) −2.22688e12 −0.919345
\(566\) −8.99132e8 −0.000368256 0
\(567\) −1.41196e12 −0.573719
\(568\) 5.31182e11 0.214129
\(569\) −9.66618e11 −0.386589 −0.193295 0.981141i \(-0.561917\pi\)
−0.193295 + 0.981141i \(0.561917\pi\)
\(570\) −7.11476e11 −0.282308
\(571\) 3.96159e12 1.55958 0.779788 0.626043i \(-0.215327\pi\)
0.779788 + 0.626043i \(0.215327\pi\)
\(572\) −4.25999e12 −1.66390
\(573\) −3.77629e12 −1.46342
\(574\) 9.80116e11 0.376855
\(575\) −1.43669e11 −0.0548098
\(576\) 7.49573e11 0.283735
\(577\) 2.21488e12 0.831876 0.415938 0.909393i \(-0.363453\pi\)
0.415938 + 0.909393i \(0.363453\pi\)
\(578\) 3.79824e10 0.0141549
\(579\) −1.24086e12 −0.458847
\(580\) 1.15475e12 0.423705
\(581\) −6.15819e12 −2.24213
\(582\) −2.38442e11 −0.0861450
\(583\) −2.04629e12 −0.733600
\(584\) 3.39666e11 0.120835
\(585\) −1.54428e12 −0.545162
\(586\) 3.51578e11 0.123164
\(587\) −6.70503e11 −0.233093 −0.116546 0.993185i \(-0.537182\pi\)
−0.116546 + 0.993185i \(0.537182\pi\)
\(588\) −2.27379e12 −0.784427
\(589\) 6.91664e12 2.36797
\(590\) 7.44435e11 0.252926
\(591\) 5.32314e11 0.179483
\(592\) −1.74352e12 −0.583418
\(593\) −4.14332e12 −1.37595 −0.687975 0.725735i \(-0.741500\pi\)
−0.687975 + 0.725735i \(0.741500\pi\)
\(594\) −1.01136e12 −0.333324
\(595\) 1.00186e12 0.327703
\(596\) 1.06445e12 0.345556
\(597\) −2.02816e11 −0.0653458
\(598\) 4.38986e11 0.140377
\(599\) 2.11940e12 0.672653 0.336327 0.941745i \(-0.390815\pi\)
0.336327 + 0.941745i \(0.390815\pi\)
\(600\) 1.45770e11 0.0459185
\(601\) 4.44856e12 1.39086 0.695431 0.718593i \(-0.255213\pi\)
0.695431 + 0.718593i \(0.255213\pi\)
\(602\) 1.73792e12 0.539320
\(603\) 1.32140e11 0.0407011
\(604\) −3.75742e12 −1.14875
\(605\) 1.97634e12 0.599740
\(606\) 1.05207e10 0.00316896
\(607\) 8.59588e11 0.257005 0.128502 0.991709i \(-0.458983\pi\)
0.128502 + 0.991709i \(0.458983\pi\)
\(608\) −3.72347e12 −1.10505
\(609\) −1.79832e12 −0.529772
\(610\) 4.04168e11 0.118189
\(611\) −7.99816e12 −2.32169
\(612\) 3.36237e11 0.0968866
\(613\) −5.43289e12 −1.55403 −0.777013 0.629484i \(-0.783266\pi\)
−0.777013 + 0.629484i \(0.783266\pi\)
\(614\) 4.65289e11 0.132119
\(615\) 2.71667e12 0.765772
\(616\) −3.09987e12 −0.867422
\(617\) −1.22774e12 −0.341053 −0.170527 0.985353i \(-0.554547\pi\)
−0.170527 + 0.985353i \(0.554547\pi\)
\(618\) 4.16073e11 0.114742
\(619\) 4.33143e12 1.18583 0.592917 0.805264i \(-0.297976\pi\)
0.592917 + 0.805264i \(0.297976\pi\)
\(620\) 4.62224e12 1.25629
\(621\) −1.69563e12 −0.457529
\(622\) −3.98557e11 −0.106766
\(623\) −3.87673e11 −0.103103
\(624\) 3.28595e12 0.867622
\(625\) −3.25688e12 −0.853771
\(626\) 8.73502e10 0.0227342
\(627\) −6.23692e12 −1.61163
\(628\) −2.89224e12 −0.742020
\(629\) −6.69566e11 −0.170555
\(630\) −5.45113e11 −0.137865
\(631\) 1.79967e12 0.451919 0.225959 0.974137i \(-0.427448\pi\)
0.225959 + 0.974137i \(0.427448\pi\)
\(632\) 7.48683e11 0.186669
\(633\) 4.74433e12 1.17451
\(634\) 4.64899e11 0.114277
\(635\) 2.53402e12 0.618483
\(636\) 1.68858e12 0.409227
\(637\) 6.28238e12 1.51181
\(638\) −6.22180e11 −0.148670
\(639\) 8.18835e11 0.194286
\(640\) −3.27890e12 −0.772535
\(641\) 5.02365e12 1.17532 0.587662 0.809106i \(-0.300048\pi\)
0.587662 + 0.809106i \(0.300048\pi\)
\(642\) −4.16715e11 −0.0968125
\(643\) 4.60458e12 1.06229 0.531143 0.847283i \(-0.321763\pi\)
0.531143 + 0.847283i \(0.321763\pi\)
\(644\) −2.52111e12 −0.577572
\(645\) 4.81716e12 1.09590
\(646\) −4.28008e11 −0.0966953
\(647\) 4.15507e12 0.932201 0.466100 0.884732i \(-0.345659\pi\)
0.466100 + 0.884732i \(0.345659\pi\)
\(648\) 8.31000e11 0.185146
\(649\) 6.52584e12 1.44390
\(650\) −1.95373e11 −0.0429295
\(651\) −7.19830e12 −1.57078
\(652\) −1.06164e12 −0.230071
\(653\) 3.43743e11 0.0739817 0.0369909 0.999316i \(-0.488223\pi\)
0.0369909 + 0.999316i \(0.488223\pi\)
\(654\) 1.97969e11 0.0423154
\(655\) 4.31202e12 0.915367
\(656\) 4.25562e12 0.897212
\(657\) 5.23606e11 0.109638
\(658\) −2.82325e12 −0.587129
\(659\) 2.39727e12 0.495145 0.247572 0.968869i \(-0.420367\pi\)
0.247572 + 0.968869i \(0.420367\pi\)
\(660\) −4.16800e12 −0.855027
\(661\) −2.09899e12 −0.427665 −0.213833 0.976870i \(-0.568595\pi\)
−0.213833 + 0.976870i \(0.568595\pi\)
\(662\) 3.09617e11 0.0626563
\(663\) 1.26191e12 0.253639
\(664\) 3.62436e12 0.723560
\(665\) −1.12895e13 −2.23861
\(666\) 3.64312e11 0.0717529
\(667\) −1.04314e12 −0.204068
\(668\) 7.44646e11 0.144696
\(669\) −1.07271e12 −0.207045
\(670\) −1.12408e11 −0.0215507
\(671\) 3.54301e12 0.674715
\(672\) 3.87510e12 0.733029
\(673\) −1.61276e12 −0.303042 −0.151521 0.988454i \(-0.548417\pi\)
−0.151521 + 0.988454i \(0.548417\pi\)
\(674\) 1.67217e12 0.312112
\(675\) 7.54650e11 0.139920
\(676\) −4.59747e12 −0.846758
\(677\) 2.64830e12 0.484527 0.242264 0.970210i \(-0.422110\pi\)
0.242264 + 0.970210i \(0.422110\pi\)
\(678\) −9.90094e11 −0.179946
\(679\) −3.78355e12 −0.683101
\(680\) −5.89637e11 −0.105754
\(681\) 8.00373e12 1.42604
\(682\) −2.49046e12 −0.440808
\(683\) −9.69821e12 −1.70529 −0.852645 0.522491i \(-0.825003\pi\)
−0.852645 + 0.522491i \(0.825003\pi\)
\(684\) −3.78891e12 −0.661853
\(685\) −6.31026e12 −1.09506
\(686\) 1.96320e11 0.0338458
\(687\) 8.72432e12 1.49426
\(688\) 7.54598e12 1.28401
\(689\) −4.66546e12 −0.788693
\(690\) 4.29506e11 0.0721355
\(691\) −7.85953e12 −1.31143 −0.655715 0.755008i \(-0.727633\pi\)
−0.655715 + 0.755008i \(0.727633\pi\)
\(692\) −6.58740e12 −1.09204
\(693\) −4.77855e12 −0.787040
\(694\) 1.82234e11 0.0298203
\(695\) 4.66190e12 0.757934
\(696\) 1.05839e12 0.170964
\(697\) 1.63429e12 0.262290
\(698\) −2.07437e12 −0.330779
\(699\) −5.29503e12 −0.838922
\(700\) 1.12204e12 0.176631
\(701\) 1.35808e12 0.212419 0.106210 0.994344i \(-0.466129\pi\)
0.106210 + 0.994344i \(0.466129\pi\)
\(702\) −2.30586e12 −0.358356
\(703\) 7.54506e12 1.16510
\(704\) −5.58969e12 −0.857651
\(705\) −7.82546e12 −1.19305
\(706\) 1.14290e12 0.173136
\(707\) 1.66940e11 0.0251288
\(708\) −5.38505e12 −0.805453
\(709\) 8.38924e12 1.24685 0.623426 0.781883i \(-0.285740\pi\)
0.623426 + 0.781883i \(0.285740\pi\)
\(710\) −6.96563e11 −0.102872
\(711\) 1.15412e12 0.169370
\(712\) 2.28162e11 0.0332724
\(713\) −4.17546e12 −0.605064
\(714\) 4.45438e11 0.0641424
\(715\) 1.15160e13 1.64787
\(716\) −3.61032e12 −0.513378
\(717\) −4.32713e12 −0.611454
\(718\) 1.71051e12 0.240196
\(719\) 1.05644e12 0.147423 0.0737117 0.997280i \(-0.476516\pi\)
0.0737117 + 0.997280i \(0.476516\pi\)
\(720\) −2.36685e12 −0.328228
\(721\) 6.60214e12 0.909864
\(722\) 3.06604e12 0.419913
\(723\) −3.25748e12 −0.443363
\(724\) 9.55967e12 1.29306
\(725\) 4.64254e11 0.0624072
\(726\) 8.78704e11 0.117389
\(727\) 1.20219e12 0.159614 0.0798068 0.996810i \(-0.474570\pi\)
0.0798068 + 0.996810i \(0.474570\pi\)
\(728\) −7.06757e12 −0.932564
\(729\) 7.53554e12 0.988190
\(730\) −4.45419e11 −0.0580519
\(731\) 2.89789e12 0.375365
\(732\) −2.92365e12 −0.376379
\(733\) −1.38044e13 −1.76624 −0.883121 0.469146i \(-0.844562\pi\)
−0.883121 + 0.469146i \(0.844562\pi\)
\(734\) 1.30884e12 0.166439
\(735\) 6.14672e12 0.776874
\(736\) 2.24780e12 0.282362
\(737\) −9.85390e11 −0.123028
\(738\) −8.89219e11 −0.110346
\(739\) −1.03973e13 −1.28240 −0.641198 0.767375i \(-0.721562\pi\)
−0.641198 + 0.767375i \(0.721562\pi\)
\(740\) 5.04220e12 0.618127
\(741\) −1.42199e13 −1.73267
\(742\) −1.64685e12 −0.199451
\(743\) 7.06440e12 0.850405 0.425202 0.905098i \(-0.360203\pi\)
0.425202 + 0.905098i \(0.360203\pi\)
\(744\) 4.23651e12 0.506909
\(745\) −2.87753e12 −0.342229
\(746\) 1.60030e12 0.189181
\(747\) 5.58707e12 0.656510
\(748\) −2.50737e12 −0.292861
\(749\) −6.61233e12 −0.767691
\(750\) −1.66763e12 −0.192452
\(751\) 5.52292e12 0.633562 0.316781 0.948499i \(-0.397398\pi\)
0.316781 + 0.948499i \(0.397398\pi\)
\(752\) −1.22584e13 −1.39783
\(753\) 2.18752e12 0.247956
\(754\) −1.41854e12 −0.159835
\(755\) 1.01574e13 1.13768
\(756\) 1.32426e13 1.47444
\(757\) −5.93646e12 −0.657046 −0.328523 0.944496i \(-0.606551\pi\)
−0.328523 + 0.944496i \(0.606551\pi\)
\(758\) 2.04747e12 0.225272
\(759\) 3.76513e12 0.411805
\(760\) 6.64438e12 0.722425
\(761\) −1.16527e13 −1.25949 −0.629745 0.776802i \(-0.716840\pi\)
−0.629745 + 0.776802i \(0.716840\pi\)
\(762\) 1.12665e12 0.121058
\(763\) 3.14133e12 0.335547
\(764\) 1.71074e13 1.81662
\(765\) −9.08945e11 −0.0959536
\(766\) 2.03550e12 0.213620
\(767\) 1.48786e13 1.55233
\(768\) 3.43822e12 0.356622
\(769\) −3.13586e12 −0.323361 −0.161681 0.986843i \(-0.551691\pi\)
−0.161681 + 0.986843i \(0.551691\pi\)
\(770\) 4.06500e12 0.416728
\(771\) −9.56324e12 −0.974676
\(772\) 5.62134e12 0.569590
\(773\) 1.41981e13 1.43029 0.715143 0.698979i \(-0.246362\pi\)
0.715143 + 0.698979i \(0.246362\pi\)
\(774\) −1.57675e12 −0.157917
\(775\) 1.85831e12 0.185038
\(776\) 2.22678e12 0.220445
\(777\) −7.85232e12 −0.772865
\(778\) −2.51889e11 −0.0246491
\(779\) −1.84161e13 −1.79176
\(780\) −9.50286e12 −0.919239
\(781\) −6.10619e12 −0.587274
\(782\) 2.58381e11 0.0247076
\(783\) 5.47927e12 0.520949
\(784\) 9.62871e12 0.910219
\(785\) 7.81856e12 0.734875
\(786\) 1.91717e12 0.179168
\(787\) −7.60742e12 −0.706889 −0.353444 0.935456i \(-0.614990\pi\)
−0.353444 + 0.935456i \(0.614990\pi\)
\(788\) −2.41149e12 −0.222801
\(789\) 1.52656e13 1.40238
\(790\) −9.81782e11 −0.0896795
\(791\) −1.57106e13 −1.42691
\(792\) 2.81238e12 0.253987
\(793\) 8.07790e12 0.725386
\(794\) −1.83399e12 −0.163759
\(795\) −4.56472e12 −0.405286
\(796\) 9.18798e11 0.0811169
\(797\) 8.82832e11 0.0775025 0.0387513 0.999249i \(-0.487662\pi\)
0.0387513 + 0.999249i \(0.487662\pi\)
\(798\) −5.01945e12 −0.438171
\(799\) −4.70762e12 −0.408640
\(800\) −1.00040e12 −0.0863510
\(801\) 3.51720e11 0.0301891
\(802\) −5.34337e12 −0.456069
\(803\) −3.90462e12 −0.331405
\(804\) 8.13133e11 0.0686293
\(805\) 6.81530e12 0.572010
\(806\) −5.67814e12 −0.473913
\(807\) −1.78311e13 −1.47995
\(808\) −9.82511e10 −0.00810935
\(809\) 1.36683e13 1.12188 0.560940 0.827856i \(-0.310440\pi\)
0.560940 + 0.827856i \(0.310440\pi\)
\(810\) −1.08973e12 −0.0889479
\(811\) −1.63530e13 −1.32741 −0.663703 0.747996i \(-0.731016\pi\)
−0.663703 + 0.747996i \(0.731016\pi\)
\(812\) 8.14676e12 0.657632
\(813\) 4.82326e12 0.387198
\(814\) −2.71674e12 −0.216889
\(815\) 2.86992e12 0.227856
\(816\) 1.93407e12 0.152710
\(817\) −3.26551e13 −2.56420
\(818\) 4.45232e12 0.347694
\(819\) −1.08949e13 −0.846146
\(820\) −1.23071e13 −0.950590
\(821\) −4.83235e12 −0.371206 −0.185603 0.982625i \(-0.559424\pi\)
−0.185603 + 0.982625i \(0.559424\pi\)
\(822\) −2.80561e12 −0.214340
\(823\) −1.61695e13 −1.22856 −0.614282 0.789087i \(-0.710554\pi\)
−0.614282 + 0.789087i \(0.710554\pi\)
\(824\) −3.88565e12 −0.293623
\(825\) −1.67569e12 −0.125937
\(826\) 5.25198e12 0.392566
\(827\) 1.37247e13 1.02030 0.510149 0.860086i \(-0.329590\pi\)
0.510149 + 0.860086i \(0.329590\pi\)
\(828\) 2.28730e12 0.169117
\(829\) 2.58304e13 1.89949 0.949743 0.313031i \(-0.101344\pi\)
0.949743 + 0.313031i \(0.101344\pi\)
\(830\) −4.75278e12 −0.347613
\(831\) 2.05703e11 0.0149636
\(832\) −1.27442e13 −0.922060
\(833\) 3.69773e12 0.266092
\(834\) 2.07273e12 0.148353
\(835\) −2.01299e12 −0.143302
\(836\) 2.82545e13 2.00060
\(837\) 2.19324e13 1.54462
\(838\) −2.27704e12 −0.159504
\(839\) −5.42716e11 −0.0378132 −0.0189066 0.999821i \(-0.506019\pi\)
−0.0189066 + 0.999821i \(0.506019\pi\)
\(840\) −6.91496e12 −0.479218
\(841\) −1.11363e13 −0.767645
\(842\) 1.69764e12 0.116397
\(843\) 1.24250e13 0.847368
\(844\) −2.14928e13 −1.45798
\(845\) 1.24283e13 0.838604
\(846\) 2.56142e12 0.171915
\(847\) 1.39431e13 0.930857
\(848\) −7.15054e12 −0.474851
\(849\) −1.75824e10 −0.00116143
\(850\) −1.14994e11 −0.00755598
\(851\) −4.55483e12 −0.297707
\(852\) 5.03876e12 0.327601
\(853\) −1.71048e13 −1.10623 −0.553116 0.833104i \(-0.686561\pi\)
−0.553116 + 0.833104i \(0.686561\pi\)
\(854\) 2.85140e12 0.183442
\(855\) 1.02425e13 0.655480
\(856\) 3.89164e12 0.247743
\(857\) −6.06810e12 −0.384272 −0.192136 0.981368i \(-0.561542\pi\)
−0.192136 + 0.981368i \(0.561542\pi\)
\(858\) 5.12013e12 0.322544
\(859\) −1.87986e13 −1.17803 −0.589016 0.808122i \(-0.700484\pi\)
−0.589016 + 0.808122i \(0.700484\pi\)
\(860\) −2.18227e13 −1.36040
\(861\) 1.91661e13 1.18855
\(862\) 4.71824e12 0.291070
\(863\) −6.53337e12 −0.400949 −0.200474 0.979699i \(-0.564248\pi\)
−0.200474 + 0.979699i \(0.564248\pi\)
\(864\) −1.18070e13 −0.720820
\(865\) 1.78077e13 1.08152
\(866\) 1.60690e12 0.0970862
\(867\) 7.42742e11 0.0446429
\(868\) 3.26098e13 1.94989
\(869\) −8.60646e12 −0.511960
\(870\) −1.38791e12 −0.0821345
\(871\) −2.24665e12 −0.132268
\(872\) −1.84881e12 −0.108285
\(873\) 3.43265e12 0.200017
\(874\) −2.91159e12 −0.168783
\(875\) −2.64615e13 −1.52608
\(876\) 3.22205e12 0.184869
\(877\) −1.60851e13 −0.918178 −0.459089 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(878\) 2.98809e12 0.169695
\(879\) 6.87507e12 0.388443
\(880\) 1.76500e13 0.992141
\(881\) 3.30698e13 1.84944 0.924720 0.380647i \(-0.124299\pi\)
0.924720 + 0.380647i \(0.124299\pi\)
\(882\) −2.01194e12 −0.111945
\(883\) −7.25465e12 −0.401599 −0.200800 0.979632i \(-0.564354\pi\)
−0.200800 + 0.979632i \(0.564354\pi\)
\(884\) −5.71670e12 −0.314855
\(885\) 1.45574e13 0.797697
\(886\) −5.64077e12 −0.307529
\(887\) −1.13226e13 −0.614170 −0.307085 0.951682i \(-0.599354\pi\)
−0.307085 + 0.951682i \(0.599354\pi\)
\(888\) 4.62143e12 0.249412
\(889\) 1.78774e13 0.959947
\(890\) −2.99200e11 −0.0159848
\(891\) −9.55274e12 −0.507783
\(892\) 4.85959e12 0.257015
\(893\) 5.30482e13 2.79151
\(894\) −1.27938e12 −0.0669856
\(895\) 9.75974e12 0.508434
\(896\) −2.31326e13 −1.19905
\(897\) 8.58432e12 0.442731
\(898\) −5.71303e12 −0.293172
\(899\) 1.34926e13 0.688934
\(900\) −1.01798e12 −0.0517187
\(901\) −2.74603e12 −0.138817
\(902\) 6.63105e12 0.333544
\(903\) 3.39850e13 1.70095
\(904\) 9.24635e12 0.460482
\(905\) −2.58426e13 −1.28061
\(906\) 4.51609e12 0.222683
\(907\) 3.43776e13 1.68672 0.843360 0.537348i \(-0.180574\pi\)
0.843360 + 0.537348i \(0.180574\pi\)
\(908\) −3.62585e13 −1.77021
\(909\) −1.51457e11 −0.00735788
\(910\) 9.26802e12 0.448024
\(911\) −1.18306e13 −0.569082 −0.284541 0.958664i \(-0.591841\pi\)
−0.284541 + 0.958664i \(0.591841\pi\)
\(912\) −2.17942e13 −1.04319
\(913\) −4.16637e13 −1.98445
\(914\) 6.20334e11 0.0294014
\(915\) 7.90348e12 0.372755
\(916\) −3.95230e13 −1.85490
\(917\) 3.04212e13 1.42074
\(918\) −1.35720e12 −0.0630741
\(919\) −2.68999e13 −1.24403 −0.622015 0.783005i \(-0.713686\pi\)
−0.622015 + 0.783005i \(0.713686\pi\)
\(920\) −4.01110e12 −0.184594
\(921\) 9.09868e12 0.416687
\(922\) 5.70533e12 0.260011
\(923\) −1.39218e13 −0.631378
\(924\) −2.94052e13 −1.32709
\(925\) 2.02716e12 0.0910436
\(926\) 6.87248e11 0.0307160
\(927\) −5.98985e12 −0.266414
\(928\) −7.26356e12 −0.321502
\(929\) −9.83481e12 −0.433207 −0.216603 0.976260i \(-0.569498\pi\)
−0.216603 + 0.976260i \(0.569498\pi\)
\(930\) −5.55553e12 −0.243530
\(931\) −4.16681e13 −1.81773
\(932\) 2.39876e13 1.04139
\(933\) −7.79374e12 −0.336728
\(934\) −6.57556e12 −0.282730
\(935\) 6.77816e12 0.290041
\(936\) 6.41211e12 0.273061
\(937\) 9.23144e12 0.391238 0.195619 0.980680i \(-0.437328\pi\)
0.195619 + 0.980680i \(0.437328\pi\)
\(938\) −7.93039e11 −0.0334489
\(939\) 1.70812e12 0.0717009
\(940\) 3.54509e13 1.48099
\(941\) −1.00553e13 −0.418062 −0.209031 0.977909i \(-0.567031\pi\)
−0.209031 + 0.977909i \(0.567031\pi\)
\(942\) 3.47622e12 0.143839
\(943\) 1.11175e13 0.457830
\(944\) 2.28038e13 0.934617
\(945\) −3.57987e13 −1.46024
\(946\) 1.17581e13 0.477338
\(947\) 3.28956e13 1.32912 0.664558 0.747237i \(-0.268620\pi\)
0.664558 + 0.747237i \(0.268620\pi\)
\(948\) 7.10196e12 0.285588
\(949\) −8.90236e12 −0.356293
\(950\) 1.29582e12 0.0516166
\(951\) 9.09106e12 0.360414
\(952\) −4.15988e12 −0.164140
\(953\) −2.79353e13 −1.09707 −0.548537 0.836126i \(-0.684815\pi\)
−0.548537 + 0.836126i \(0.684815\pi\)
\(954\) 1.49412e12 0.0584006
\(955\) −4.62463e13 −1.79913
\(956\) 1.96028e13 0.759027
\(957\) −1.21667e13 −0.468887
\(958\) −8.64382e12 −0.331559
\(959\) −4.45187e13 −1.69965
\(960\) −1.24691e13 −0.473820
\(961\) 2.75686e13 1.04270
\(962\) −6.19404e12 −0.233177
\(963\) 5.99909e12 0.224785
\(964\) 1.47571e13 0.550368
\(965\) −1.51961e13 −0.564105
\(966\) 3.03016e12 0.111961
\(967\) 3.57620e13 1.31523 0.657617 0.753352i \(-0.271565\pi\)
0.657617 + 0.753352i \(0.271565\pi\)
\(968\) −8.20609e12 −0.300398
\(969\) −8.36965e12 −0.304965
\(970\) −2.92008e12 −0.105906
\(971\) −5.49737e12 −0.198458 −0.0992290 0.995065i \(-0.531638\pi\)
−0.0992290 + 0.995065i \(0.531638\pi\)
\(972\) −2.04515e13 −0.734897
\(973\) 3.28896e13 1.17639
\(974\) 5.11756e12 0.182200
\(975\) −3.82051e12 −0.135394
\(976\) 1.23806e13 0.436736
\(977\) −1.41757e13 −0.497759 −0.248879 0.968534i \(-0.580062\pi\)
−0.248879 + 0.968534i \(0.580062\pi\)
\(978\) 1.27600e12 0.0445990
\(979\) −2.62283e12 −0.0912533
\(980\) −2.78459e13 −0.964371
\(981\) −2.85000e12 −0.0982503
\(982\) 5.26217e12 0.180577
\(983\) 4.48632e13 1.53250 0.766248 0.642545i \(-0.222121\pi\)
0.766248 + 0.642545i \(0.222121\pi\)
\(984\) −1.12801e13 −0.383560
\(985\) 6.51896e12 0.220656
\(986\) −8.34936e11 −0.0281324
\(987\) −5.52085e13 −1.85173
\(988\) 6.44191e13 2.15084
\(989\) 1.97134e13 0.655205
\(990\) −3.68800e12 −0.122021
\(991\) 2.93025e13 0.965101 0.482550 0.875868i \(-0.339711\pi\)
0.482550 + 0.875868i \(0.339711\pi\)
\(992\) −2.90745e13 −0.953257
\(993\) 6.05454e12 0.197610
\(994\) −4.91424e12 −0.159668
\(995\) −2.48378e12 −0.0803357
\(996\) 3.43804e13 1.10699
\(997\) 1.15625e13 0.370616 0.185308 0.982680i \(-0.440672\pi\)
0.185308 + 0.982680i \(0.440672\pi\)
\(998\) −6.69697e12 −0.213693
\(999\) 2.39251e13 0.759993
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 17.10.a.b.1.5 7
3.2 odd 2 153.10.a.f.1.3 7
4.3 odd 2 272.10.a.g.1.4 7
17.16 even 2 289.10.a.b.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.5 7 1.1 even 1 trivial
153.10.a.f.1.3 7 3.2 odd 2
272.10.a.g.1.4 7 4.3 odd 2
289.10.a.b.1.5 7 17.16 even 2