Properties

Label 17.10.a.b.1.4
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 1.4
Root \(-4.12962\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.12962 q^{2} -254.074 q^{3} -494.946 q^{4} +151.544 q^{5} -1049.23 q^{6} +9407.97 q^{7} -4158.31 q^{8} +44870.8 q^{9} +O(q^{10})\) \(q+4.12962 q^{2} -254.074 q^{3} -494.946 q^{4} +151.544 q^{5} -1049.23 q^{6} +9407.97 q^{7} -4158.31 q^{8} +44870.8 q^{9} +625.818 q^{10} -56967.2 q^{11} +125753. q^{12} -60874.5 q^{13} +38851.3 q^{14} -38503.4 q^{15} +236240. q^{16} +83521.0 q^{17} +185299. q^{18} +1.00994e6 q^{19} -75006.0 q^{20} -2.39032e6 q^{21} -235253. q^{22} +1.35979e6 q^{23} +1.05652e6 q^{24} -1.93016e6 q^{25} -251388. q^{26} -6.39958e6 q^{27} -4.65644e6 q^{28} +3.12503e6 q^{29} -159004. q^{30} +2.97426e6 q^{31} +3.10463e6 q^{32} +1.44739e7 q^{33} +344910. q^{34} +1.42572e6 q^{35} -2.22086e7 q^{36} +681625. q^{37} +4.17068e6 q^{38} +1.54666e7 q^{39} -630165. q^{40} -4.09135e6 q^{41} -9.87113e6 q^{42} +1.00085e7 q^{43} +2.81957e7 q^{44} +6.79989e6 q^{45} +5.61542e6 q^{46} +2.54570e7 q^{47} -6.00226e7 q^{48} +4.81562e7 q^{49} -7.97082e6 q^{50} -2.12206e7 q^{51} +3.01296e7 q^{52} -3.14563e7 q^{53} -2.64278e7 q^{54} -8.63302e6 q^{55} -3.91212e7 q^{56} -2.56601e8 q^{57} +1.29052e7 q^{58} -9.03573e7 q^{59} +1.90571e7 q^{60} +9.87113e7 q^{61} +1.22826e7 q^{62} +4.22143e8 q^{63} -1.08134e8 q^{64} -9.22514e6 q^{65} +5.97717e7 q^{66} +1.32700e8 q^{67} -4.13384e7 q^{68} -3.45488e8 q^{69} +5.88767e6 q^{70} +4.18554e8 q^{71} -1.86587e8 q^{72} +4.80282e7 q^{73} +2.81485e6 q^{74} +4.90404e8 q^{75} -4.99868e8 q^{76} -5.35945e8 q^{77} +6.38714e7 q^{78} +3.49030e7 q^{79} +3.58007e7 q^{80} +7.42778e8 q^{81} -1.68957e7 q^{82} -2.05650e8 q^{83} +1.18308e9 q^{84} +1.26571e7 q^{85} +4.13311e7 q^{86} -7.93991e8 q^{87} +2.36887e8 q^{88} -2.03866e8 q^{89} +2.80810e7 q^{90} -5.72705e8 q^{91} -6.73023e8 q^{92} -7.55684e8 q^{93} +1.05128e8 q^{94} +1.53050e8 q^{95} -7.88808e8 q^{96} +1.24300e9 q^{97} +1.98867e8 q^{98} -2.55616e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.12962 0.182505 0.0912526 0.995828i \(-0.470913\pi\)
0.0912526 + 0.995828i \(0.470913\pi\)
\(3\) −254.074 −1.81099 −0.905493 0.424360i \(-0.860499\pi\)
−0.905493 + 0.424360i \(0.860499\pi\)
\(4\) −494.946 −0.966692
\(5\) 151.544 0.108436 0.0542179 0.998529i \(-0.482733\pi\)
0.0542179 + 0.998529i \(0.482733\pi\)
\(6\) −1049.23 −0.330514
\(7\) 9407.97 1.48100 0.740499 0.672057i \(-0.234589\pi\)
0.740499 + 0.672057i \(0.234589\pi\)
\(8\) −4158.31 −0.358931
\(9\) 44870.8 2.27967
\(10\) 625.818 0.0197901
\(11\) −56967.2 −1.17316 −0.586581 0.809891i \(-0.699526\pi\)
−0.586581 + 0.809891i \(0.699526\pi\)
\(12\) 125753. 1.75067
\(13\) −60874.5 −0.591140 −0.295570 0.955321i \(-0.595510\pi\)
−0.295570 + 0.955321i \(0.595510\pi\)
\(14\) 38851.3 0.270290
\(15\) −38503.4 −0.196376
\(16\) 236240. 0.901185
\(17\) 83521.0 0.242536
\(18\) 185299. 0.416052
\(19\) 1.00994e6 1.77789 0.888947 0.458010i \(-0.151438\pi\)
0.888947 + 0.458010i \(0.151438\pi\)
\(20\) −75006.0 −0.104824
\(21\) −2.39032e6 −2.68207
\(22\) −235253. −0.214108
\(23\) 1.35979e6 1.01320 0.506602 0.862180i \(-0.330901\pi\)
0.506602 + 0.862180i \(0.330901\pi\)
\(24\) 1.05652e6 0.650020
\(25\) −1.93016e6 −0.988242
\(26\) −251388. −0.107886
\(27\) −6.39958e6 −2.31747
\(28\) −4.65644e6 −1.43167
\(29\) 3.12503e6 0.820472 0.410236 0.911979i \(-0.365446\pi\)
0.410236 + 0.911979i \(0.365446\pi\)
\(30\) −159004. −0.0358396
\(31\) 2.97426e6 0.578431 0.289216 0.957264i \(-0.406606\pi\)
0.289216 + 0.957264i \(0.406606\pi\)
\(32\) 3.10463e6 0.523402
\(33\) 1.44739e7 2.12458
\(34\) 344910. 0.0442640
\(35\) 1.42572e6 0.160593
\(36\) −2.22086e7 −2.20374
\(37\) 681625. 0.0597913 0.0298956 0.999553i \(-0.490483\pi\)
0.0298956 + 0.999553i \(0.490483\pi\)
\(38\) 4.17068e6 0.324475
\(39\) 1.54666e7 1.07055
\(40\) −630165. −0.0389210
\(41\) −4.09135e6 −0.226120 −0.113060 0.993588i \(-0.536065\pi\)
−0.113060 + 0.993588i \(0.536065\pi\)
\(42\) −9.87113e6 −0.489491
\(43\) 1.00085e7 0.446436 0.223218 0.974769i \(-0.428344\pi\)
0.223218 + 0.974769i \(0.428344\pi\)
\(44\) 2.81957e7 1.13409
\(45\) 6.79989e6 0.247198
\(46\) 5.61542e6 0.184915
\(47\) 2.54570e7 0.760970 0.380485 0.924787i \(-0.375757\pi\)
0.380485 + 0.924787i \(0.375757\pi\)
\(48\) −6.00226e7 −1.63203
\(49\) 4.81562e7 1.19336
\(50\) −7.97082e6 −0.180359
\(51\) −2.12206e7 −0.439229
\(52\) 3.01296e7 0.571450
\(53\) −3.14563e7 −0.547603 −0.273801 0.961786i \(-0.588281\pi\)
−0.273801 + 0.961786i \(0.588281\pi\)
\(54\) −2.64278e7 −0.422951
\(55\) −8.63302e6 −0.127213
\(56\) −3.91212e7 −0.531577
\(57\) −2.56601e8 −3.21974
\(58\) 1.29052e7 0.149740
\(59\) −9.03573e7 −0.970798 −0.485399 0.874293i \(-0.661326\pi\)
−0.485399 + 0.874293i \(0.661326\pi\)
\(60\) 1.90571e7 0.189835
\(61\) 9.87113e7 0.912815 0.456408 0.889771i \(-0.349136\pi\)
0.456408 + 0.889771i \(0.349136\pi\)
\(62\) 1.22826e7 0.105567
\(63\) 4.22143e8 3.37619
\(64\) −1.08134e8 −0.805661
\(65\) −9.22514e6 −0.0641007
\(66\) 5.97717e7 0.387747
\(67\) 1.32700e8 0.804516 0.402258 0.915526i \(-0.368225\pi\)
0.402258 + 0.915526i \(0.368225\pi\)
\(68\) −4.13384e7 −0.234457
\(69\) −3.45488e8 −1.83490
\(70\) 5.88767e6 0.0293091
\(71\) 4.18554e8 1.95474 0.977369 0.211541i \(-0.0678482\pi\)
0.977369 + 0.211541i \(0.0678482\pi\)
\(72\) −1.86587e8 −0.818246
\(73\) 4.80282e7 0.197944 0.0989721 0.995090i \(-0.468445\pi\)
0.0989721 + 0.995090i \(0.468445\pi\)
\(74\) 2.81485e6 0.0109122
\(75\) 4.90404e8 1.78969
\(76\) −4.99868e8 −1.71868
\(77\) −5.35945e8 −1.73745
\(78\) 6.38714e7 0.195380
\(79\) 3.49030e7 0.100819 0.0504093 0.998729i \(-0.483947\pi\)
0.0504093 + 0.998729i \(0.483947\pi\)
\(80\) 3.58007e7 0.0977207
\(81\) 7.42778e8 1.91724
\(82\) −1.68957e7 −0.0412681
\(83\) −2.05650e8 −0.475638 −0.237819 0.971309i \(-0.576433\pi\)
−0.237819 + 0.971309i \(0.576433\pi\)
\(84\) 1.18308e9 2.59273
\(85\) 1.26571e7 0.0262995
\(86\) 4.13311e7 0.0814769
\(87\) −7.93991e8 −1.48586
\(88\) 2.36887e8 0.421084
\(89\) −2.03866e8 −0.344422 −0.172211 0.985060i \(-0.555091\pi\)
−0.172211 + 0.985060i \(0.555091\pi\)
\(90\) 2.80810e7 0.0451150
\(91\) −5.72705e8 −0.875477
\(92\) −6.73023e8 −0.979456
\(93\) −7.55684e8 −1.04753
\(94\) 1.05128e8 0.138881
\(95\) 1.53050e8 0.192787
\(96\) −7.88808e8 −0.947875
\(97\) 1.24300e9 1.42560 0.712798 0.701369i \(-0.247427\pi\)
0.712798 + 0.701369i \(0.247427\pi\)
\(98\) 1.98867e8 0.217794
\(99\) −2.55616e9 −2.67443
\(100\) 9.55325e8 0.955325
\(101\) −2.02496e9 −1.93629 −0.968144 0.250395i \(-0.919440\pi\)
−0.968144 + 0.250395i \(0.919440\pi\)
\(102\) −8.76328e7 −0.0801615
\(103\) 1.16276e9 1.01794 0.508970 0.860785i \(-0.330027\pi\)
0.508970 + 0.860785i \(0.330027\pi\)
\(104\) 2.53135e8 0.212179
\(105\) −3.62238e8 −0.290832
\(106\) −1.29902e8 −0.0999403
\(107\) 1.31593e9 0.970520 0.485260 0.874370i \(-0.338725\pi\)
0.485260 + 0.874370i \(0.338725\pi\)
\(108\) 3.16745e9 2.24028
\(109\) −1.79000e8 −0.121460 −0.0607302 0.998154i \(-0.519343\pi\)
−0.0607302 + 0.998154i \(0.519343\pi\)
\(110\) −3.56511e7 −0.0232170
\(111\) −1.73184e8 −0.108281
\(112\) 2.22254e9 1.33465
\(113\) 2.53572e9 1.46301 0.731506 0.681835i \(-0.238818\pi\)
0.731506 + 0.681835i \(0.238818\pi\)
\(114\) −1.05966e9 −0.587619
\(115\) 2.06068e8 0.109868
\(116\) −1.54672e9 −0.793144
\(117\) −2.73149e9 −1.34761
\(118\) −3.73141e8 −0.177176
\(119\) 7.85763e8 0.359195
\(120\) 1.60109e8 0.0704854
\(121\) 8.87314e8 0.376308
\(122\) 4.07640e8 0.166593
\(123\) 1.03951e9 0.409500
\(124\) −1.47210e9 −0.559165
\(125\) −5.88487e8 −0.215597
\(126\) 1.74329e9 0.616172
\(127\) 4.05326e9 1.38257 0.691287 0.722581i \(-0.257044\pi\)
0.691287 + 0.722581i \(0.257044\pi\)
\(128\) −2.03613e9 −0.670440
\(129\) −2.54289e9 −0.808490
\(130\) −3.80963e7 −0.0116987
\(131\) −2.93543e9 −0.870865 −0.435432 0.900221i \(-0.643405\pi\)
−0.435432 + 0.900221i \(0.643405\pi\)
\(132\) −7.16381e9 −2.05381
\(133\) 9.50151e9 2.63306
\(134\) 5.48001e8 0.146828
\(135\) −9.69816e8 −0.251297
\(136\) −3.47306e8 −0.0870536
\(137\) −4.82610e9 −1.17045 −0.585226 0.810870i \(-0.698994\pi\)
−0.585226 + 0.810870i \(0.698994\pi\)
\(138\) −1.42673e9 −0.334879
\(139\) 2.65630e9 0.603546 0.301773 0.953380i \(-0.402421\pi\)
0.301773 + 0.953380i \(0.402421\pi\)
\(140\) −7.05653e8 −0.155244
\(141\) −6.46798e9 −1.37811
\(142\) 1.72847e9 0.356750
\(143\) 3.46785e9 0.693502
\(144\) 1.06003e10 2.05441
\(145\) 4.73579e8 0.0889685
\(146\) 1.98338e8 0.0361259
\(147\) −1.22353e10 −2.16115
\(148\) −3.37368e8 −0.0577998
\(149\) −2.85114e9 −0.473894 −0.236947 0.971523i \(-0.576147\pi\)
−0.236947 + 0.971523i \(0.576147\pi\)
\(150\) 2.02518e9 0.326628
\(151\) −8.37259e9 −1.31058 −0.655290 0.755378i \(-0.727454\pi\)
−0.655290 + 0.755378i \(0.727454\pi\)
\(152\) −4.19965e9 −0.638142
\(153\) 3.74766e9 0.552902
\(154\) −2.21325e9 −0.317094
\(155\) 4.50731e8 0.0627227
\(156\) −7.65516e9 −1.03489
\(157\) 8.37311e9 1.09986 0.549931 0.835210i \(-0.314654\pi\)
0.549931 + 0.835210i \(0.314654\pi\)
\(158\) 1.44136e8 0.0183999
\(159\) 7.99223e9 0.991702
\(160\) 4.70488e8 0.0567555
\(161\) 1.27929e10 1.50055
\(162\) 3.06739e9 0.349906
\(163\) −2.12079e8 −0.0235317 −0.0117659 0.999931i \(-0.503745\pi\)
−0.0117659 + 0.999931i \(0.503745\pi\)
\(164\) 2.02500e9 0.218588
\(165\) 2.19343e9 0.230381
\(166\) −8.49256e8 −0.0868064
\(167\) −9.27756e9 −0.923017 −0.461509 0.887136i \(-0.652692\pi\)
−0.461509 + 0.887136i \(0.652692\pi\)
\(168\) 9.93969e9 0.962678
\(169\) −6.89880e9 −0.650554
\(170\) 5.22689e7 0.00479980
\(171\) 4.53170e10 4.05302
\(172\) −4.95365e9 −0.431566
\(173\) −1.29744e10 −1.10123 −0.550617 0.834758i \(-0.685608\pi\)
−0.550617 + 0.834758i \(0.685608\pi\)
\(174\) −3.27888e9 −0.271178
\(175\) −1.81589e10 −1.46358
\(176\) −1.34579e10 −1.05724
\(177\) 2.29575e10 1.75810
\(178\) −8.41890e8 −0.0628587
\(179\) 2.58172e10 1.87962 0.939812 0.341692i \(-0.111000\pi\)
0.939812 + 0.341692i \(0.111000\pi\)
\(180\) −3.36558e9 −0.238965
\(181\) 2.61713e9 0.181248 0.0906238 0.995885i \(-0.471114\pi\)
0.0906238 + 0.995885i \(0.471114\pi\)
\(182\) −2.36505e9 −0.159779
\(183\) −2.50800e10 −1.65310
\(184\) −5.65443e9 −0.363671
\(185\) 1.03296e8 0.00648352
\(186\) −3.12069e9 −0.191180
\(187\) −4.75796e9 −0.284533
\(188\) −1.25999e10 −0.735623
\(189\) −6.02070e10 −3.43217
\(190\) 6.32040e8 0.0351847
\(191\) 8.25575e8 0.0448855 0.0224428 0.999748i \(-0.492856\pi\)
0.0224428 + 0.999748i \(0.492856\pi\)
\(192\) 2.74741e10 1.45904
\(193\) 1.88810e10 0.979530 0.489765 0.871855i \(-0.337083\pi\)
0.489765 + 0.871855i \(0.337083\pi\)
\(194\) 5.13310e9 0.260179
\(195\) 2.34387e9 0.116086
\(196\) −2.38347e10 −1.15361
\(197\) 1.73273e10 0.819659 0.409829 0.912162i \(-0.365588\pi\)
0.409829 + 0.912162i \(0.365588\pi\)
\(198\) −1.05560e10 −0.488096
\(199\) 2.14638e10 0.970216 0.485108 0.874454i \(-0.338780\pi\)
0.485108 + 0.874454i \(0.338780\pi\)
\(200\) 8.02619e9 0.354711
\(201\) −3.37157e10 −1.45697
\(202\) −8.36231e9 −0.353382
\(203\) 2.94002e10 1.21512
\(204\) 1.05030e10 0.424599
\(205\) −6.20018e8 −0.0245195
\(206\) 4.80175e9 0.185779
\(207\) 6.10149e10 2.30977
\(208\) −1.43810e10 −0.532726
\(209\) −5.75336e10 −2.08576
\(210\) −1.49591e9 −0.0530784
\(211\) 7.73227e9 0.268557 0.134278 0.990944i \(-0.457128\pi\)
0.134278 + 0.990944i \(0.457128\pi\)
\(212\) 1.55692e10 0.529363
\(213\) −1.06344e11 −3.54001
\(214\) 5.43427e9 0.177125
\(215\) 1.51672e9 0.0484096
\(216\) 2.66114e10 0.831814
\(217\) 2.79818e10 0.856656
\(218\) −7.39204e8 −0.0221672
\(219\) −1.22027e10 −0.358475
\(220\) 4.27288e9 0.122975
\(221\) −5.08430e9 −0.143372
\(222\) −7.15182e8 −0.0197619
\(223\) 9.27651e9 0.251196 0.125598 0.992081i \(-0.459915\pi\)
0.125598 + 0.992081i \(0.459915\pi\)
\(224\) 2.92083e10 0.775158
\(225\) −8.66078e10 −2.25287
\(226\) 1.04715e10 0.267007
\(227\) −1.00921e10 −0.252270 −0.126135 0.992013i \(-0.540257\pi\)
−0.126135 + 0.992013i \(0.540257\pi\)
\(228\) 1.27004e11 3.11250
\(229\) −2.70436e10 −0.649837 −0.324918 0.945742i \(-0.605337\pi\)
−0.324918 + 0.945742i \(0.605337\pi\)
\(230\) 8.50981e8 0.0200514
\(231\) 1.36170e11 3.14650
\(232\) −1.29948e10 −0.294493
\(233\) 6.83620e10 1.51954 0.759771 0.650191i \(-0.225311\pi\)
0.759771 + 0.650191i \(0.225311\pi\)
\(234\) −1.12800e10 −0.245945
\(235\) 3.85785e9 0.0825164
\(236\) 4.47220e10 0.938463
\(237\) −8.86795e9 −0.182581
\(238\) 3.24490e9 0.0655549
\(239\) −2.57344e10 −0.510179 −0.255090 0.966917i \(-0.582105\pi\)
−0.255090 + 0.966917i \(0.582105\pi\)
\(240\) −9.09605e9 −0.176971
\(241\) −1.97738e10 −0.377584 −0.188792 0.982017i \(-0.560457\pi\)
−0.188792 + 0.982017i \(0.560457\pi\)
\(242\) 3.66427e9 0.0686781
\(243\) −6.27578e10 −1.15462
\(244\) −4.88568e10 −0.882411
\(245\) 7.29777e9 0.129402
\(246\) 4.29277e9 0.0747359
\(247\) −6.14798e10 −1.05098
\(248\) −1.23679e10 −0.207617
\(249\) 5.22504e10 0.861375
\(250\) −2.43023e9 −0.0393475
\(251\) 3.35205e10 0.533063 0.266532 0.963826i \(-0.414122\pi\)
0.266532 + 0.963826i \(0.414122\pi\)
\(252\) −2.08938e11 −3.26374
\(253\) −7.74635e10 −1.18865
\(254\) 1.67384e10 0.252327
\(255\) −3.21584e9 −0.0476281
\(256\) 4.69562e10 0.683303
\(257\) −9.22091e10 −1.31848 −0.659242 0.751931i \(-0.729123\pi\)
−0.659242 + 0.751931i \(0.729123\pi\)
\(258\) −1.05012e10 −0.147554
\(259\) 6.41271e9 0.0885508
\(260\) 4.56595e9 0.0619656
\(261\) 1.40223e11 1.87041
\(262\) −1.21222e10 −0.158937
\(263\) 1.83512e10 0.236518 0.118259 0.992983i \(-0.462269\pi\)
0.118259 + 0.992983i \(0.462269\pi\)
\(264\) −6.01869e10 −0.762578
\(265\) −4.76700e9 −0.0593798
\(266\) 3.92376e10 0.480546
\(267\) 5.17972e10 0.623743
\(268\) −6.56795e10 −0.777719
\(269\) −9.60172e10 −1.11806 −0.559029 0.829148i \(-0.688826\pi\)
−0.559029 + 0.829148i \(0.688826\pi\)
\(270\) −4.00497e9 −0.0458630
\(271\) −1.61081e11 −1.81419 −0.907097 0.420922i \(-0.861706\pi\)
−0.907097 + 0.420922i \(0.861706\pi\)
\(272\) 1.97310e10 0.218569
\(273\) 1.45510e11 1.58548
\(274\) −1.99300e10 −0.213614
\(275\) 1.09956e11 1.15937
\(276\) 1.70998e11 1.77378
\(277\) 5.34317e10 0.545305 0.272653 0.962113i \(-0.412099\pi\)
0.272653 + 0.962113i \(0.412099\pi\)
\(278\) 1.09695e10 0.110150
\(279\) 1.33458e11 1.31863
\(280\) −5.92857e9 −0.0576419
\(281\) 1.48954e11 1.42520 0.712599 0.701572i \(-0.247518\pi\)
0.712599 + 0.701572i \(0.247518\pi\)
\(282\) −2.67103e10 −0.251511
\(283\) −5.51543e10 −0.511140 −0.255570 0.966790i \(-0.582263\pi\)
−0.255570 + 0.966790i \(0.582263\pi\)
\(284\) −2.07162e11 −1.88963
\(285\) −3.88862e10 −0.349135
\(286\) 1.43209e10 0.126568
\(287\) −3.84913e10 −0.334883
\(288\) 1.39307e11 1.19319
\(289\) 6.97576e9 0.0588235
\(290\) 1.95570e9 0.0162372
\(291\) −3.15813e11 −2.58174
\(292\) −2.37714e10 −0.191351
\(293\) −1.58399e11 −1.25559 −0.627794 0.778379i \(-0.716042\pi\)
−0.627794 + 0.778379i \(0.716042\pi\)
\(294\) −5.05270e10 −0.394421
\(295\) −1.36931e10 −0.105269
\(296\) −2.83441e9 −0.0214610
\(297\) 3.64566e11 2.71877
\(298\) −1.17741e10 −0.0864880
\(299\) −8.27766e10 −0.598945
\(300\) −2.42724e11 −1.73008
\(301\) 9.41592e10 0.661171
\(302\) −3.45756e10 −0.239188
\(303\) 5.14490e11 3.50659
\(304\) 2.38589e11 1.60221
\(305\) 1.49591e10 0.0989818
\(306\) 1.54764e10 0.100907
\(307\) 2.33754e11 1.50188 0.750942 0.660368i \(-0.229600\pi\)
0.750942 + 0.660368i \(0.229600\pi\)
\(308\) 2.65264e11 1.67958
\(309\) −2.95427e11 −1.84347
\(310\) 1.86135e9 0.0114472
\(311\) −2.24488e11 −1.36073 −0.680363 0.732875i \(-0.738178\pi\)
−0.680363 + 0.732875i \(0.738178\pi\)
\(312\) −6.43150e10 −0.384253
\(313\) −2.83464e10 −0.166935 −0.0834676 0.996510i \(-0.526599\pi\)
−0.0834676 + 0.996510i \(0.526599\pi\)
\(314\) 3.45777e10 0.200730
\(315\) 6.39731e10 0.366100
\(316\) −1.72751e10 −0.0974604
\(317\) −1.13413e11 −0.630807 −0.315404 0.948958i \(-0.602140\pi\)
−0.315404 + 0.948958i \(0.602140\pi\)
\(318\) 3.30049e10 0.180991
\(319\) −1.78024e11 −0.962546
\(320\) −1.63870e10 −0.0873626
\(321\) −3.34343e11 −1.75760
\(322\) 5.28297e10 0.273859
\(323\) 8.43515e10 0.431203
\(324\) −3.67635e11 −1.85338
\(325\) 1.17497e11 0.584189
\(326\) −8.75807e8 −0.00429466
\(327\) 4.54794e10 0.219963
\(328\) 1.70131e10 0.0811616
\(329\) 2.39499e11 1.12699
\(330\) 9.05803e9 0.0420456
\(331\) −4.08556e10 −0.187079 −0.0935397 0.995616i \(-0.529818\pi\)
−0.0935397 + 0.995616i \(0.529818\pi\)
\(332\) 1.01786e11 0.459796
\(333\) 3.05851e10 0.136305
\(334\) −3.83128e10 −0.168455
\(335\) 2.01099e10 0.0872384
\(336\) −5.64691e11 −2.41704
\(337\) 1.14143e11 0.482075 0.241037 0.970516i \(-0.422512\pi\)
0.241037 + 0.970516i \(0.422512\pi\)
\(338\) −2.84894e10 −0.118729
\(339\) −6.44261e11 −2.64949
\(340\) −6.26457e9 −0.0254236
\(341\) −1.69435e11 −0.678593
\(342\) 1.87142e11 0.739697
\(343\) 7.34065e10 0.286359
\(344\) −4.16182e10 −0.160240
\(345\) −5.23565e10 −0.198969
\(346\) −5.35793e10 −0.200981
\(347\) −1.30233e11 −0.482213 −0.241106 0.970499i \(-0.577510\pi\)
−0.241106 + 0.970499i \(0.577510\pi\)
\(348\) 3.92983e11 1.43637
\(349\) 1.52443e11 0.550039 0.275020 0.961439i \(-0.411316\pi\)
0.275020 + 0.961439i \(0.411316\pi\)
\(350\) −7.49892e10 −0.267112
\(351\) 3.89571e11 1.36995
\(352\) −1.76862e11 −0.614035
\(353\) 4.83570e11 1.65757 0.828787 0.559565i \(-0.189032\pi\)
0.828787 + 0.559565i \(0.189032\pi\)
\(354\) 9.48056e10 0.320863
\(355\) 6.34292e10 0.211964
\(356\) 1.00903e11 0.332950
\(357\) −1.99642e11 −0.650497
\(358\) 1.06615e11 0.343041
\(359\) −3.20450e11 −1.01820 −0.509102 0.860706i \(-0.670023\pi\)
−0.509102 + 0.860706i \(0.670023\pi\)
\(360\) −2.82760e10 −0.0887272
\(361\) 6.97298e11 2.16091
\(362\) 1.08078e10 0.0330786
\(363\) −2.25444e11 −0.681488
\(364\) 2.83458e11 0.846316
\(365\) 7.27836e9 0.0214642
\(366\) −1.03571e11 −0.301699
\(367\) −1.77614e11 −0.511070 −0.255535 0.966800i \(-0.582252\pi\)
−0.255535 + 0.966800i \(0.582252\pi\)
\(368\) 3.21237e11 0.913084
\(369\) −1.83582e11 −0.515480
\(370\) 4.26573e8 0.00118328
\(371\) −2.95939e11 −0.810999
\(372\) 3.74023e11 1.01264
\(373\) 4.80280e11 1.28471 0.642355 0.766407i \(-0.277958\pi\)
0.642355 + 0.766407i \(0.277958\pi\)
\(374\) −1.96486e10 −0.0519288
\(375\) 1.49520e11 0.390443
\(376\) −1.05858e11 −0.273136
\(377\) −1.90235e11 −0.485014
\(378\) −2.48632e11 −0.626389
\(379\) 3.81929e11 0.950837 0.475419 0.879760i \(-0.342297\pi\)
0.475419 + 0.879760i \(0.342297\pi\)
\(380\) −7.57518e10 −0.186366
\(381\) −1.02983e12 −2.50382
\(382\) 3.40931e9 0.00819184
\(383\) 3.63419e11 0.863004 0.431502 0.902112i \(-0.357984\pi\)
0.431502 + 0.902112i \(0.357984\pi\)
\(384\) 5.17327e11 1.21416
\(385\) −8.12191e10 −0.188402
\(386\) 7.79714e10 0.178769
\(387\) 4.49088e11 1.01773
\(388\) −6.15216e11 −1.37811
\(389\) −6.51726e11 −1.44308 −0.721542 0.692370i \(-0.756566\pi\)
−0.721542 + 0.692370i \(0.756566\pi\)
\(390\) 9.67930e9 0.0211862
\(391\) 1.13571e11 0.245738
\(392\) −2.00248e11 −0.428333
\(393\) 7.45818e11 1.57713
\(394\) 7.15552e10 0.149592
\(395\) 5.28932e9 0.0109323
\(396\) 1.26516e12 2.58535
\(397\) 2.04054e11 0.412276 0.206138 0.978523i \(-0.433910\pi\)
0.206138 + 0.978523i \(0.433910\pi\)
\(398\) 8.86375e10 0.177069
\(399\) −2.41409e12 −4.76843
\(400\) −4.55981e11 −0.890589
\(401\) −2.48041e11 −0.479042 −0.239521 0.970891i \(-0.576990\pi\)
−0.239521 + 0.970891i \(0.576990\pi\)
\(402\) −1.39233e11 −0.265904
\(403\) −1.81057e11 −0.341934
\(404\) 1.00225e12 1.87179
\(405\) 1.12563e11 0.207897
\(406\) 1.21412e11 0.221765
\(407\) −3.88303e10 −0.0701448
\(408\) 8.82415e10 0.157653
\(409\) −2.59982e11 −0.459397 −0.229698 0.973262i \(-0.573774\pi\)
−0.229698 + 0.973262i \(0.573774\pi\)
\(410\) −2.56044e9 −0.00447494
\(411\) 1.22619e12 2.11967
\(412\) −5.75503e11 −0.984033
\(413\) −8.50078e11 −1.43775
\(414\) 2.51968e11 0.421546
\(415\) −3.11649e10 −0.0515762
\(416\) −1.88993e11 −0.309404
\(417\) −6.74898e11 −1.09301
\(418\) −2.37592e11 −0.380661
\(419\) −5.23470e11 −0.829714 −0.414857 0.909887i \(-0.636168\pi\)
−0.414857 + 0.909887i \(0.636168\pi\)
\(420\) 1.79288e11 0.281145
\(421\) 4.04503e11 0.627555 0.313778 0.949497i \(-0.398405\pi\)
0.313778 + 0.949497i \(0.398405\pi\)
\(422\) 3.19313e10 0.0490130
\(423\) 1.14228e12 1.73476
\(424\) 1.30805e11 0.196552
\(425\) −1.61209e11 −0.239684
\(426\) −4.39159e11 −0.646069
\(427\) 9.28673e11 1.35188
\(428\) −6.51313e11 −0.938194
\(429\) −8.81092e11 −1.25592
\(430\) 6.26347e9 0.00883501
\(431\) −5.97189e11 −0.833612 −0.416806 0.908995i \(-0.636851\pi\)
−0.416806 + 0.908995i \(0.636851\pi\)
\(432\) −1.51184e12 −2.08847
\(433\) −8.45782e11 −1.15628 −0.578140 0.815938i \(-0.696221\pi\)
−0.578140 + 0.815938i \(0.696221\pi\)
\(434\) 1.15554e11 0.156344
\(435\) −1.20324e11 −0.161121
\(436\) 8.85956e10 0.117415
\(437\) 1.37331e12 1.80137
\(438\) −5.03926e10 −0.0654234
\(439\) 4.42347e11 0.568424 0.284212 0.958761i \(-0.408268\pi\)
0.284212 + 0.958761i \(0.408268\pi\)
\(440\) 3.58987e10 0.0456606
\(441\) 2.16081e12 2.72046
\(442\) −2.09962e10 −0.0261662
\(443\) −2.05741e11 −0.253807 −0.126903 0.991915i \(-0.540504\pi\)
−0.126903 + 0.991915i \(0.540504\pi\)
\(444\) 8.57165e10 0.104675
\(445\) −3.08946e10 −0.0373476
\(446\) 3.83085e10 0.0458446
\(447\) 7.24403e11 0.858215
\(448\) −1.01732e12 −1.19318
\(449\) 1.29191e12 1.50012 0.750059 0.661371i \(-0.230025\pi\)
0.750059 + 0.661371i \(0.230025\pi\)
\(450\) −3.57657e11 −0.411160
\(451\) 2.33073e11 0.265275
\(452\) −1.25504e12 −1.41428
\(453\) 2.12726e12 2.37344
\(454\) −4.16766e10 −0.0460406
\(455\) −8.67898e10 −0.0949330
\(456\) 1.06702e12 1.15567
\(457\) −2.65686e11 −0.284935 −0.142467 0.989799i \(-0.545504\pi\)
−0.142467 + 0.989799i \(0.545504\pi\)
\(458\) −1.11680e11 −0.118599
\(459\) −5.34499e11 −0.562070
\(460\) −1.01992e11 −0.106208
\(461\) 4.14119e11 0.427043 0.213521 0.976938i \(-0.431507\pi\)
0.213521 + 0.976938i \(0.431507\pi\)
\(462\) 5.62330e11 0.574252
\(463\) 5.26394e11 0.532349 0.266175 0.963925i \(-0.414240\pi\)
0.266175 + 0.963925i \(0.414240\pi\)
\(464\) 7.38259e11 0.739397
\(465\) −1.14519e11 −0.113590
\(466\) 2.82309e11 0.277324
\(467\) 5.24754e11 0.510540 0.255270 0.966870i \(-0.417836\pi\)
0.255270 + 0.966870i \(0.417836\pi\)
\(468\) 1.35194e12 1.30272
\(469\) 1.24844e12 1.19149
\(470\) 1.59315e10 0.0150597
\(471\) −2.12739e12 −1.99184
\(472\) 3.75733e11 0.348450
\(473\) −5.70154e11 −0.523741
\(474\) −3.66213e10 −0.0333220
\(475\) −1.94935e12 −1.75699
\(476\) −3.88910e11 −0.347231
\(477\) −1.41147e12 −1.24836
\(478\) −1.06273e11 −0.0931103
\(479\) −6.90731e11 −0.599514 −0.299757 0.954016i \(-0.596906\pi\)
−0.299757 + 0.954016i \(0.596906\pi\)
\(480\) −1.19539e11 −0.102784
\(481\) −4.14936e10 −0.0353450
\(482\) −8.16582e10 −0.0689109
\(483\) −3.25034e12 −2.71748
\(484\) −4.39173e11 −0.363774
\(485\) 1.88368e11 0.154586
\(486\) −2.59166e11 −0.210724
\(487\) 5.21019e11 0.419733 0.209867 0.977730i \(-0.432697\pi\)
0.209867 + 0.977730i \(0.432697\pi\)
\(488\) −4.10472e11 −0.327638
\(489\) 5.38839e10 0.0426157
\(490\) 3.01370e10 0.0236166
\(491\) 3.74675e11 0.290930 0.145465 0.989363i \(-0.453532\pi\)
0.145465 + 0.989363i \(0.453532\pi\)
\(492\) −5.14500e11 −0.395861
\(493\) 2.61006e11 0.198994
\(494\) −2.53888e11 −0.191810
\(495\) −3.87371e11 −0.290003
\(496\) 7.02641e11 0.521274
\(497\) 3.93774e12 2.89496
\(498\) 2.15774e11 0.157205
\(499\) −1.96144e12 −1.41619 −0.708096 0.706116i \(-0.750446\pi\)
−0.708096 + 0.706116i \(0.750446\pi\)
\(500\) 2.91269e11 0.208415
\(501\) 2.35719e12 1.67157
\(502\) 1.38427e11 0.0972868
\(503\) 7.20856e11 0.502103 0.251051 0.967974i \(-0.419224\pi\)
0.251051 + 0.967974i \(0.419224\pi\)
\(504\) −1.75540e12 −1.21182
\(505\) −3.06870e11 −0.209963
\(506\) −3.19895e11 −0.216935
\(507\) 1.75281e12 1.17814
\(508\) −2.00615e12 −1.33652
\(509\) 4.96970e11 0.328171 0.164085 0.986446i \(-0.447533\pi\)
0.164085 + 0.986446i \(0.447533\pi\)
\(510\) −1.32802e10 −0.00869238
\(511\) 4.51847e11 0.293155
\(512\) 1.23641e12 0.795146
\(513\) −6.46321e12 −4.12022
\(514\) −3.80789e11 −0.240630
\(515\) 1.76209e11 0.110381
\(516\) 1.25860e12 0.781560
\(517\) −1.45022e12 −0.892740
\(518\) 2.64820e10 0.0161610
\(519\) 3.29646e12 1.99432
\(520\) 3.83609e10 0.0230078
\(521\) −7.85633e11 −0.467143 −0.233572 0.972340i \(-0.575041\pi\)
−0.233572 + 0.972340i \(0.575041\pi\)
\(522\) 5.79067e11 0.341359
\(523\) −1.28047e12 −0.748363 −0.374182 0.927355i \(-0.622076\pi\)
−0.374182 + 0.927355i \(0.622076\pi\)
\(524\) 1.45288e12 0.841858
\(525\) 4.61371e12 2.65053
\(526\) 7.57835e10 0.0431657
\(527\) 2.48413e11 0.140290
\(528\) 3.41932e12 1.91464
\(529\) 4.78790e10 0.0265824
\(530\) −1.96859e10 −0.0108371
\(531\) −4.05440e12 −2.21310
\(532\) −4.70274e12 −2.54535
\(533\) 2.49059e11 0.133669
\(534\) 2.13903e11 0.113836
\(535\) 1.99420e11 0.105239
\(536\) −5.51808e11 −0.288766
\(537\) −6.55950e12 −3.40397
\(538\) −3.96515e11 −0.204051
\(539\) −2.74332e12 −1.40000
\(540\) 4.80007e11 0.242927
\(541\) 2.82997e12 1.42035 0.710174 0.704026i \(-0.248616\pi\)
0.710174 + 0.704026i \(0.248616\pi\)
\(542\) −6.65205e11 −0.331100
\(543\) −6.64947e11 −0.328237
\(544\) 2.59302e11 0.126944
\(545\) −2.71264e10 −0.0131707
\(546\) 6.00900e11 0.289358
\(547\) 3.65687e12 1.74649 0.873247 0.487278i \(-0.162010\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(548\) 2.38866e12 1.13147
\(549\) 4.42926e12 2.08092
\(550\) 4.54076e11 0.211590
\(551\) 3.15611e12 1.45871
\(552\) 1.43665e12 0.658603
\(553\) 3.28366e11 0.149312
\(554\) 2.20652e11 0.0995210
\(555\) −2.62449e10 −0.0117416
\(556\) −1.31473e12 −0.583443
\(557\) −8.41201e11 −0.370298 −0.185149 0.982710i \(-0.559277\pi\)
−0.185149 + 0.982710i \(0.559277\pi\)
\(558\) 5.51129e11 0.240658
\(559\) −6.09260e11 −0.263906
\(560\) 3.36812e11 0.144724
\(561\) 1.20888e12 0.515286
\(562\) 6.15125e11 0.260106
\(563\) 2.93812e12 1.23249 0.616243 0.787556i \(-0.288654\pi\)
0.616243 + 0.787556i \(0.288654\pi\)
\(564\) 3.20130e12 1.33220
\(565\) 3.84272e11 0.158643
\(566\) −2.27766e11 −0.0932858
\(567\) 6.98803e12 2.83943
\(568\) −1.74047e12 −0.701617
\(569\) −2.06188e12 −0.824627 −0.412313 0.911042i \(-0.635279\pi\)
−0.412313 + 0.911042i \(0.635279\pi\)
\(570\) −1.60585e11 −0.0637190
\(571\) −2.23269e12 −0.878955 −0.439477 0.898254i \(-0.644836\pi\)
−0.439477 + 0.898254i \(0.644836\pi\)
\(572\) −1.71640e12 −0.670403
\(573\) −2.09757e11 −0.0812871
\(574\) −1.58954e11 −0.0611179
\(575\) −2.62461e12 −1.00129
\(576\) −4.85206e12 −1.83665
\(577\) −9.94350e11 −0.373464 −0.186732 0.982411i \(-0.559790\pi\)
−0.186732 + 0.982411i \(0.559790\pi\)
\(578\) 2.88072e10 0.0107356
\(579\) −4.79719e12 −1.77392
\(580\) −2.34396e11 −0.0860052
\(581\) −1.93475e12 −0.704420
\(582\) −1.30419e12 −0.471180
\(583\) 1.79198e12 0.642427
\(584\) −1.99716e11 −0.0710484
\(585\) −4.13940e11 −0.146129
\(586\) −6.54126e11 −0.229151
\(587\) −4.22018e12 −1.46710 −0.733549 0.679636i \(-0.762138\pi\)
−0.733549 + 0.679636i \(0.762138\pi\)
\(588\) 6.05580e12 2.08917
\(589\) 3.00384e12 1.02839
\(590\) −5.65472e10 −0.0192122
\(591\) −4.40243e12 −1.48439
\(592\) 1.61027e11 0.0538830
\(593\) −4.49622e12 −1.49314 −0.746571 0.665305i \(-0.768301\pi\)
−0.746571 + 0.665305i \(0.768301\pi\)
\(594\) 1.50552e12 0.496189
\(595\) 1.19077e11 0.0389496
\(596\) 1.41116e12 0.458109
\(597\) −5.45341e12 −1.75705
\(598\) −3.41836e11 −0.109311
\(599\) 1.61824e11 0.0513598 0.0256799 0.999670i \(-0.491825\pi\)
0.0256799 + 0.999670i \(0.491825\pi\)
\(600\) −2.03925e12 −0.642377
\(601\) −3.79766e12 −1.18735 −0.593677 0.804703i \(-0.702324\pi\)
−0.593677 + 0.804703i \(0.702324\pi\)
\(602\) 3.88842e11 0.120667
\(603\) 5.95437e12 1.83403
\(604\) 4.14398e12 1.26693
\(605\) 1.34467e11 0.0408052
\(606\) 2.12465e12 0.639971
\(607\) 9.59183e11 0.286782 0.143391 0.989666i \(-0.454199\pi\)
0.143391 + 0.989666i \(0.454199\pi\)
\(608\) 3.13550e12 0.930554
\(609\) −7.46984e12 −2.20056
\(610\) 6.17753e10 0.0180647
\(611\) −1.54968e12 −0.449839
\(612\) −1.85489e12 −0.534486
\(613\) 2.49059e12 0.712409 0.356205 0.934408i \(-0.384071\pi\)
0.356205 + 0.934408i \(0.384071\pi\)
\(614\) 9.65315e11 0.274102
\(615\) 1.57531e11 0.0444045
\(616\) 2.22862e12 0.623625
\(617\) −1.31221e12 −0.364519 −0.182259 0.983250i \(-0.558341\pi\)
−0.182259 + 0.983250i \(0.558341\pi\)
\(618\) −1.22000e12 −0.336444
\(619\) 6.10985e12 1.67272 0.836359 0.548182i \(-0.184680\pi\)
0.836359 + 0.548182i \(0.184680\pi\)
\(620\) −2.23087e11 −0.0606335
\(621\) −8.70209e12 −2.34807
\(622\) −9.27049e11 −0.248340
\(623\) −1.91797e12 −0.510088
\(624\) 3.65384e12 0.964760
\(625\) 3.68066e12 0.964863
\(626\) −1.17060e11 −0.0304665
\(627\) 1.46178e13 3.77728
\(628\) −4.14424e12 −1.06323
\(629\) 5.69300e10 0.0145015
\(630\) 2.64185e11 0.0668152
\(631\) −2.63235e12 −0.661016 −0.330508 0.943803i \(-0.607220\pi\)
−0.330508 + 0.943803i \(0.607220\pi\)
\(632\) −1.45137e11 −0.0361869
\(633\) −1.96457e12 −0.486353
\(634\) −4.68353e11 −0.115126
\(635\) 6.14247e11 0.149920
\(636\) −3.95573e12 −0.958670
\(637\) −2.93148e12 −0.705440
\(638\) −7.35173e11 −0.175670
\(639\) 1.87808e13 4.45617
\(640\) −3.08562e11 −0.0726997
\(641\) 4.56614e12 1.06829 0.534144 0.845394i \(-0.320634\pi\)
0.534144 + 0.845394i \(0.320634\pi\)
\(642\) −1.38071e12 −0.320771
\(643\) −6.83172e12 −1.57609 −0.788044 0.615618i \(-0.788906\pi\)
−0.788044 + 0.615618i \(0.788906\pi\)
\(644\) −6.33178e12 −1.45057
\(645\) −3.85359e11 −0.0876692
\(646\) 3.48340e11 0.0786967
\(647\) −3.87609e12 −0.869609 −0.434805 0.900525i \(-0.643183\pi\)
−0.434805 + 0.900525i \(0.643183\pi\)
\(648\) −3.08870e12 −0.688157
\(649\) 5.14740e12 1.13890
\(650\) 4.85220e11 0.106617
\(651\) −7.10945e12 −1.55139
\(652\) 1.04968e11 0.0227479
\(653\) 5.89438e12 1.26861 0.634306 0.773082i \(-0.281286\pi\)
0.634306 + 0.773082i \(0.281286\pi\)
\(654\) 1.87813e11 0.0401444
\(655\) −4.44846e11 −0.0944329
\(656\) −9.66541e11 −0.203776
\(657\) 2.15506e12 0.451248
\(658\) 9.89039e11 0.205682
\(659\) 6.62732e12 1.36884 0.684421 0.729087i \(-0.260055\pi\)
0.684421 + 0.729087i \(0.260055\pi\)
\(660\) −1.08563e12 −0.222707
\(661\) −1.51309e12 −0.308288 −0.154144 0.988048i \(-0.549262\pi\)
−0.154144 + 0.988048i \(0.549262\pi\)
\(662\) −1.68718e11 −0.0341429
\(663\) 1.29179e12 0.259646
\(664\) 8.55155e11 0.170722
\(665\) 1.43989e12 0.285518
\(666\) 1.26305e11 0.0248763
\(667\) 4.24939e12 0.831306
\(668\) 4.59190e12 0.892273
\(669\) −2.35692e12 −0.454913
\(670\) 8.30461e10 0.0159215
\(671\) −5.62331e12 −1.07088
\(672\) −7.42108e12 −1.40380
\(673\) −7.99861e10 −0.0150296 −0.00751479 0.999972i \(-0.502392\pi\)
−0.00751479 + 0.999972i \(0.502392\pi\)
\(674\) 4.71367e11 0.0879811
\(675\) 1.23522e13 2.29022
\(676\) 3.41453e12 0.628885
\(677\) −1.28946e12 −0.235917 −0.117958 0.993019i \(-0.537635\pi\)
−0.117958 + 0.993019i \(0.537635\pi\)
\(678\) −2.66055e12 −0.483546
\(679\) 1.16941e13 2.11131
\(680\) −5.26320e10 −0.00943973
\(681\) 2.56415e12 0.456858
\(682\) −6.99704e11 −0.123847
\(683\) −1.41260e12 −0.248386 −0.124193 0.992258i \(-0.539634\pi\)
−0.124193 + 0.992258i \(0.539634\pi\)
\(684\) −2.24295e13 −3.91802
\(685\) −7.31365e11 −0.126919
\(686\) 3.03141e11 0.0522620
\(687\) 6.87108e12 1.17685
\(688\) 2.36440e12 0.402321
\(689\) 1.91488e12 0.323710
\(690\) −2.16213e11 −0.0363128
\(691\) −2.52816e12 −0.421846 −0.210923 0.977503i \(-0.567647\pi\)
−0.210923 + 0.977503i \(0.567647\pi\)
\(692\) 6.42163e12 1.06455
\(693\) −2.40483e13 −3.96082
\(694\) −5.37813e11 −0.0880063
\(695\) 4.02546e11 0.0654460
\(696\) 3.30166e12 0.533323
\(697\) −3.41713e11 −0.0548422
\(698\) 6.29532e11 0.100385
\(699\) −1.73690e13 −2.75187
\(700\) 8.98767e12 1.41483
\(701\) 6.98644e12 1.09276 0.546380 0.837537i \(-0.316005\pi\)
0.546380 + 0.837537i \(0.316005\pi\)
\(702\) 1.60878e12 0.250023
\(703\) 6.88403e11 0.106303
\(704\) 6.16009e12 0.945171
\(705\) −9.80181e11 −0.149436
\(706\) 1.99696e12 0.302516
\(707\) −1.90507e13 −2.86764
\(708\) −1.13627e13 −1.69954
\(709\) −4.48848e12 −0.667100 −0.333550 0.942732i \(-0.608247\pi\)
−0.333550 + 0.942732i \(0.608247\pi\)
\(710\) 2.61938e11 0.0386844
\(711\) 1.56612e12 0.229833
\(712\) 8.47738e11 0.123624
\(713\) 4.04438e12 0.586069
\(714\) −8.24446e11 −0.118719
\(715\) 5.25530e11 0.0752005
\(716\) −1.27781e13 −1.81702
\(717\) 6.53844e12 0.923928
\(718\) −1.32334e12 −0.185828
\(719\) −7.44881e12 −1.03946 −0.519729 0.854331i \(-0.673967\pi\)
−0.519729 + 0.854331i \(0.673967\pi\)
\(720\) 1.60641e12 0.222771
\(721\) 1.09392e13 1.50757
\(722\) 2.87957e12 0.394376
\(723\) 5.02401e12 0.683799
\(724\) −1.29534e12 −0.175211
\(725\) −6.03181e12 −0.810825
\(726\) −9.30997e11 −0.124375
\(727\) 3.94611e12 0.523920 0.261960 0.965079i \(-0.415631\pi\)
0.261960 + 0.965079i \(0.415631\pi\)
\(728\) 2.38148e12 0.314236
\(729\) 1.32507e12 0.173766
\(730\) 3.00569e10 0.00391734
\(731\) 8.35917e11 0.108277
\(732\) 1.24133e13 1.59803
\(733\) 8.83103e12 1.12991 0.564955 0.825122i \(-0.308894\pi\)
0.564955 + 0.825122i \(0.308894\pi\)
\(734\) −7.33479e11 −0.0932729
\(735\) −1.85418e12 −0.234346
\(736\) 4.22165e12 0.530313
\(737\) −7.55956e12 −0.943828
\(738\) −7.58124e11 −0.0940777
\(739\) −6.70494e12 −0.826980 −0.413490 0.910509i \(-0.635690\pi\)
−0.413490 + 0.910509i \(0.635690\pi\)
\(740\) −5.11260e10 −0.00626756
\(741\) 1.56204e13 1.90332
\(742\) −1.22212e12 −0.148011
\(743\) −8.35278e12 −1.00550 −0.502749 0.864432i \(-0.667678\pi\)
−0.502749 + 0.864432i \(0.667678\pi\)
\(744\) 3.14237e12 0.375992
\(745\) −4.32073e11 −0.0513870
\(746\) 1.98338e12 0.234466
\(747\) −9.22768e12 −1.08430
\(748\) 2.35493e12 0.275056
\(749\) 1.23802e13 1.43734
\(750\) 6.17459e11 0.0712578
\(751\) −1.43369e13 −1.64465 −0.822327 0.569015i \(-0.807325\pi\)
−0.822327 + 0.569015i \(0.807325\pi\)
\(752\) 6.01398e12 0.685775
\(753\) −8.51671e12 −0.965371
\(754\) −7.85597e11 −0.0885175
\(755\) −1.26881e12 −0.142114
\(756\) 2.97992e13 3.31785
\(757\) −1.30485e13 −1.44421 −0.722105 0.691784i \(-0.756825\pi\)
−0.722105 + 0.691784i \(0.756825\pi\)
\(758\) 1.57722e12 0.173533
\(759\) 1.96815e13 2.15263
\(760\) −6.36431e11 −0.0691974
\(761\) −3.25303e10 −0.00351607 −0.00175804 0.999998i \(-0.500560\pi\)
−0.00175804 + 0.999998i \(0.500560\pi\)
\(762\) −4.25281e12 −0.456960
\(763\) −1.68403e12 −0.179883
\(764\) −4.08615e11 −0.0433905
\(765\) 5.67933e11 0.0599544
\(766\) 1.50078e12 0.157503
\(767\) 5.50045e12 0.573877
\(768\) −1.19304e13 −1.23745
\(769\) 1.79023e13 1.84603 0.923016 0.384761i \(-0.125716\pi\)
0.923016 + 0.384761i \(0.125716\pi\)
\(770\) −3.35404e11 −0.0343843
\(771\) 2.34280e13 2.38776
\(772\) −9.34509e12 −0.946903
\(773\) 2.45846e12 0.247660 0.123830 0.992303i \(-0.460482\pi\)
0.123830 + 0.992303i \(0.460482\pi\)
\(774\) 1.85456e12 0.185741
\(775\) −5.74080e12 −0.571630
\(776\) −5.16875e12 −0.511691
\(777\) −1.62930e12 −0.160364
\(778\) −2.69138e12 −0.263370
\(779\) −4.13203e12 −0.402017
\(780\) −1.16009e12 −0.112219
\(781\) −2.38438e13 −2.29322
\(782\) 4.69005e11 0.0448485
\(783\) −1.99989e13 −1.90142
\(784\) 1.13764e13 1.07543
\(785\) 1.26889e12 0.119264
\(786\) 3.07994e12 0.287833
\(787\) −1.50623e13 −1.39961 −0.699803 0.714336i \(-0.746729\pi\)
−0.699803 + 0.714336i \(0.746729\pi\)
\(788\) −8.57609e12 −0.792358
\(789\) −4.66257e12 −0.428331
\(790\) 2.18429e10 0.00199521
\(791\) 2.38559e13 2.16672
\(792\) 1.06293e13 0.959935
\(793\) −6.00900e12 −0.539601
\(794\) 8.42666e11 0.0752425
\(795\) 1.21117e12 0.107536
\(796\) −1.06234e13 −0.937900
\(797\) −1.58318e12 −0.138985 −0.0694924 0.997582i \(-0.522138\pi\)
−0.0694924 + 0.997582i \(0.522138\pi\)
\(798\) −9.96928e12 −0.870263
\(799\) 2.12620e12 0.184562
\(800\) −5.99244e12 −0.517248
\(801\) −9.14765e12 −0.785169
\(802\) −1.02431e12 −0.0874276
\(803\) −2.73603e12 −0.232221
\(804\) 1.66875e13 1.40844
\(805\) 1.93868e12 0.162714
\(806\) −7.47695e11 −0.0624047
\(807\) 2.43955e13 2.02479
\(808\) 8.42039e12 0.694994
\(809\) 1.09269e13 0.896871 0.448435 0.893815i \(-0.351981\pi\)
0.448435 + 0.893815i \(0.351981\pi\)
\(810\) 4.64843e11 0.0379423
\(811\) −1.40564e13 −1.14098 −0.570492 0.821303i \(-0.693247\pi\)
−0.570492 + 0.821303i \(0.693247\pi\)
\(812\) −1.45515e13 −1.17464
\(813\) 4.09267e13 3.28548
\(814\) −1.60354e11 −0.0128018
\(815\) −3.21393e10 −0.00255168
\(816\) −5.01315e12 −0.395826
\(817\) 1.01080e13 0.793716
\(818\) −1.07363e12 −0.0838423
\(819\) −2.56977e13 −1.99580
\(820\) 3.06875e11 0.0237028
\(821\) −8.17487e12 −0.627967 −0.313983 0.949429i \(-0.601664\pi\)
−0.313983 + 0.949429i \(0.601664\pi\)
\(822\) 5.06369e12 0.386852
\(823\) 1.18003e13 0.896587 0.448294 0.893886i \(-0.352032\pi\)
0.448294 + 0.893886i \(0.352032\pi\)
\(824\) −4.83510e12 −0.365370
\(825\) −2.79370e13 −2.09960
\(826\) −3.51050e12 −0.262397
\(827\) 1.45470e13 1.08143 0.540716 0.841205i \(-0.318153\pi\)
0.540716 + 0.841205i \(0.318153\pi\)
\(828\) −3.01991e13 −2.23284
\(829\) −1.06246e13 −0.781301 −0.390650 0.920539i \(-0.627750\pi\)
−0.390650 + 0.920539i \(0.627750\pi\)
\(830\) −1.28699e11 −0.00941293
\(831\) −1.35756e13 −0.987541
\(832\) 6.58260e12 0.476258
\(833\) 4.02205e12 0.289431
\(834\) −2.78707e12 −0.199481
\(835\) −1.40596e12 −0.100088
\(836\) 2.84761e13 2.01628
\(837\) −1.90340e13 −1.34050
\(838\) −2.16173e12 −0.151427
\(839\) −5.78736e12 −0.403229 −0.201614 0.979465i \(-0.564619\pi\)
−0.201614 + 0.979465i \(0.564619\pi\)
\(840\) 1.50630e12 0.104389
\(841\) −4.74131e12 −0.326826
\(842\) 1.67044e12 0.114532
\(843\) −3.78455e13 −2.58101
\(844\) −3.82706e12 −0.259612
\(845\) −1.04547e12 −0.0705433
\(846\) 4.71717e12 0.316603
\(847\) 8.34782e12 0.557311
\(848\) −7.43124e12 −0.493492
\(849\) 1.40133e13 0.925669
\(850\) −6.65731e11 −0.0437435
\(851\) 9.26868e11 0.0605808
\(852\) 5.26345e13 3.42209
\(853\) 1.49513e13 0.966958 0.483479 0.875356i \(-0.339373\pi\)
0.483479 + 0.875356i \(0.339373\pi\)
\(854\) 3.83507e12 0.246725
\(855\) 6.86750e12 0.439492
\(856\) −5.47202e12 −0.348350
\(857\) −1.61752e13 −1.02432 −0.512159 0.858890i \(-0.671154\pi\)
−0.512159 + 0.858890i \(0.671154\pi\)
\(858\) −3.63857e12 −0.229213
\(859\) −2.12735e13 −1.33312 −0.666562 0.745450i \(-0.732235\pi\)
−0.666562 + 0.745450i \(0.732235\pi\)
\(860\) −7.50694e11 −0.0467972
\(861\) 9.77964e12 0.606469
\(862\) −2.46616e12 −0.152139
\(863\) 1.58563e13 0.973093 0.486547 0.873655i \(-0.338256\pi\)
0.486547 + 0.873655i \(0.338256\pi\)
\(864\) −1.98684e13 −1.21297
\(865\) −1.96619e12 −0.119413
\(866\) −3.49276e12 −0.211027
\(867\) −1.77236e12 −0.106529
\(868\) −1.38495e13 −0.828122
\(869\) −1.98832e12 −0.118276
\(870\) −4.96894e11 −0.0294054
\(871\) −8.07805e12 −0.475582
\(872\) 7.44339e11 0.0435960
\(873\) 5.57742e13 3.24990
\(874\) 5.67126e12 0.328759
\(875\) −5.53647e12 −0.319298
\(876\) 6.03969e12 0.346534
\(877\) −1.59980e13 −0.913203 −0.456601 0.889671i \(-0.650933\pi\)
−0.456601 + 0.889671i \(0.650933\pi\)
\(878\) 1.82672e12 0.103740
\(879\) 4.02451e13 2.27385
\(880\) −2.03947e12 −0.114642
\(881\) 1.84519e13 1.03193 0.515963 0.856611i \(-0.327434\pi\)
0.515963 + 0.856611i \(0.327434\pi\)
\(882\) 8.92332e12 0.496498
\(883\) 2.67143e11 0.0147884 0.00739420 0.999973i \(-0.497646\pi\)
0.00739420 + 0.999973i \(0.497646\pi\)
\(884\) 2.51645e12 0.138597
\(885\) 3.47906e12 0.190641
\(886\) −8.49630e11 −0.0463210
\(887\) 2.38695e13 1.29475 0.647377 0.762170i \(-0.275866\pi\)
0.647377 + 0.762170i \(0.275866\pi\)
\(888\) 7.20150e11 0.0388655
\(889\) 3.81330e13 2.04759
\(890\) −1.27583e11 −0.00681614
\(891\) −4.23140e13 −2.24923
\(892\) −4.59138e12 −0.242829
\(893\) 2.57102e13 1.35292
\(894\) 2.99151e12 0.156629
\(895\) 3.91244e12 0.203819
\(896\) −1.91558e13 −0.992920
\(897\) 2.10314e13 1.08468
\(898\) 5.33512e12 0.273779
\(899\) 9.29467e12 0.474587
\(900\) 4.28662e13 2.17783
\(901\) −2.62726e12 −0.132813
\(902\) 9.62501e11 0.0484141
\(903\) −2.39235e13 −1.19737
\(904\) −1.05443e13 −0.525121
\(905\) 3.96610e11 0.0196537
\(906\) 8.78478e12 0.433166
\(907\) −2.77628e13 −1.36217 −0.681085 0.732205i \(-0.738492\pi\)
−0.681085 + 0.732205i \(0.738492\pi\)
\(908\) 4.99505e12 0.243867
\(909\) −9.08615e13 −4.41410
\(910\) −3.58409e11 −0.0173258
\(911\) 2.28307e13 1.09821 0.549106 0.835753i \(-0.314968\pi\)
0.549106 + 0.835753i \(0.314968\pi\)
\(912\) −6.06194e13 −2.90158
\(913\) 1.17153e13 0.558001
\(914\) −1.09718e12 −0.0520021
\(915\) −3.80072e12 −0.179255
\(916\) 1.33851e13 0.628192
\(917\) −2.76164e13 −1.28975
\(918\) −2.20728e12 −0.102581
\(919\) −5.88802e11 −0.0272301 −0.0136150 0.999907i \(-0.504334\pi\)
−0.0136150 + 0.999907i \(0.504334\pi\)
\(920\) −8.56892e11 −0.0394349
\(921\) −5.93909e13 −2.71989
\(922\) 1.71015e12 0.0779375
\(923\) −2.54792e13 −1.15552
\(924\) −6.73968e13 −3.04170
\(925\) −1.31565e12 −0.0590882
\(926\) 2.17381e12 0.0971565
\(927\) 5.21739e13 2.32057
\(928\) 9.70209e12 0.429437
\(929\) 3.31307e13 1.45935 0.729676 0.683793i \(-0.239671\pi\)
0.729676 + 0.683793i \(0.239671\pi\)
\(930\) −4.72921e11 −0.0207307
\(931\) 4.86350e13 2.12166
\(932\) −3.38355e13 −1.46893
\(933\) 5.70366e13 2.46426
\(934\) 2.16703e12 0.0931761
\(935\) −7.21038e11 −0.0308536
\(936\) 1.13584e13 0.483698
\(937\) −1.19627e13 −0.506993 −0.253496 0.967336i \(-0.581581\pi\)
−0.253496 + 0.967336i \(0.581581\pi\)
\(938\) 5.15558e12 0.217453
\(939\) 7.20208e12 0.302317
\(940\) −1.90943e12 −0.0797679
\(941\) −2.09786e13 −0.872213 −0.436106 0.899895i \(-0.643643\pi\)
−0.436106 + 0.899895i \(0.643643\pi\)
\(942\) −8.78532e12 −0.363520
\(943\) −5.56338e12 −0.229106
\(944\) −2.13460e13 −0.874869
\(945\) −9.12399e12 −0.372170
\(946\) −2.35452e12 −0.0955855
\(947\) 2.72802e13 1.10223 0.551115 0.834429i \(-0.314203\pi\)
0.551115 + 0.834429i \(0.314203\pi\)
\(948\) 4.38916e12 0.176500
\(949\) −2.92369e12 −0.117013
\(950\) −8.05008e12 −0.320659
\(951\) 2.88154e13 1.14238
\(952\) −3.26744e12 −0.128926
\(953\) −1.60893e13 −0.631858 −0.315929 0.948783i \(-0.602316\pi\)
−0.315929 + 0.948783i \(0.602316\pi\)
\(954\) −5.82883e12 −0.227831
\(955\) 1.25111e11 0.00486720
\(956\) 1.27371e13 0.493186
\(957\) 4.52315e13 1.74316
\(958\) −2.85246e12 −0.109414
\(959\) −4.54038e13 −1.73344
\(960\) 4.16353e12 0.158212
\(961\) −1.75934e13 −0.665417
\(962\) −1.71353e11 −0.00645065
\(963\) 5.90467e13 2.21247
\(964\) 9.78696e12 0.365007
\(965\) 2.86130e12 0.106216
\(966\) −1.34227e13 −0.495955
\(967\) −5.02741e13 −1.84895 −0.924475 0.381242i \(-0.875497\pi\)
−0.924475 + 0.381242i \(0.875497\pi\)
\(968\) −3.68972e12 −0.135069
\(969\) −2.14316e13 −0.780902
\(970\) 7.77888e11 0.0282127
\(971\) 3.00761e13 1.08576 0.542881 0.839810i \(-0.317333\pi\)
0.542881 + 0.839810i \(0.317333\pi\)
\(972\) 3.10618e13 1.11616
\(973\) 2.49904e13 0.893851
\(974\) 2.15161e12 0.0766035
\(975\) −2.98531e13 −1.05796
\(976\) 2.33196e13 0.822615
\(977\) −4.15719e13 −1.45974 −0.729868 0.683588i \(-0.760419\pi\)
−0.729868 + 0.683588i \(0.760419\pi\)
\(978\) 2.22520e11 0.00777758
\(979\) 1.16137e13 0.404062
\(980\) −3.61200e12 −0.125092
\(981\) −8.03190e12 −0.276890
\(982\) 1.54727e12 0.0530962
\(983\) −3.65566e12 −0.124875 −0.0624375 0.998049i \(-0.519887\pi\)
−0.0624375 + 0.998049i \(0.519887\pi\)
\(984\) −4.32259e12 −0.146983
\(985\) 2.62584e12 0.0888804
\(986\) 1.07786e12 0.0363174
\(987\) −6.08505e13 −2.04097
\(988\) 3.04292e13 1.01598
\(989\) 1.36094e13 0.452331
\(990\) −1.59969e12 −0.0529271
\(991\) −5.35178e13 −1.76265 −0.881326 0.472509i \(-0.843348\pi\)
−0.881326 + 0.472509i \(0.843348\pi\)
\(992\) 9.23400e12 0.302752
\(993\) 1.03804e13 0.338798
\(994\) 1.62614e13 0.528346
\(995\) 3.25271e12 0.105206
\(996\) −2.58611e13 −0.832684
\(997\) 6.71487e11 0.0215233 0.0107617 0.999942i \(-0.496574\pi\)
0.0107617 + 0.999942i \(0.496574\pi\)
\(998\) −8.09999e12 −0.258462
\(999\) −4.36212e12 −0.138565
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.1.4 7
3.2 odd 2 153.10.a.f.1.4 7
4.3 odd 2 272.10.a.g.1.7 7
17.16 even 2 289.10.a.b.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.4 7 1.1 even 1 trivial
153.10.a.f.1.4 7 3.2 odd 2
272.10.a.g.1.7 7 4.3 odd 2
289.10.a.b.1.4 7 17.16 even 2