Properties

Label 177.10.a.d.1.11
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.53527 q^{2} +81.0000 q^{3} -509.643 q^{4} +521.717 q^{5} -124.357 q^{6} +11357.2 q^{7} +1568.49 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-1.53527 q^{2} +81.0000 q^{3} -509.643 q^{4} +521.717 q^{5} -124.357 q^{6} +11357.2 q^{7} +1568.49 q^{8} +6561.00 q^{9} -800.975 q^{10} +95119.1 q^{11} -41281.1 q^{12} +58936.0 q^{13} -17436.4 q^{14} +42259.1 q^{15} +258529. q^{16} -89268.2 q^{17} -10072.9 q^{18} +308991. q^{19} -265890. q^{20} +919936. q^{21} -146033. q^{22} +2.23300e6 q^{23} +127048. q^{24} -1.68094e6 q^{25} -90482.4 q^{26} +531441. q^{27} -5.78813e6 q^{28} -7.46892e6 q^{29} -64879.0 q^{30} +6.83914e6 q^{31} -1.19998e6 q^{32} +7.70465e6 q^{33} +137050. q^{34} +5.92527e6 q^{35} -3.34377e6 q^{36} -1.22568e7 q^{37} -474384. q^{38} +4.77381e6 q^{39} +818311. q^{40} +5.99927e6 q^{41} -1.41235e6 q^{42} -2.75963e7 q^{43} -4.84768e7 q^{44} +3.42299e6 q^{45} -3.42825e6 q^{46} -1.84158e6 q^{47} +2.09409e7 q^{48} +8.86331e7 q^{49} +2.58068e6 q^{50} -7.23072e6 q^{51} -3.00363e7 q^{52} +2.55383e7 q^{53} -815903. q^{54} +4.96253e7 q^{55} +1.78137e7 q^{56} +2.50283e7 q^{57} +1.14668e7 q^{58} -1.21174e7 q^{59} -2.15371e7 q^{60} +7.45458e7 q^{61} -1.04999e7 q^{62} +7.45148e7 q^{63} -1.30525e8 q^{64} +3.07479e7 q^{65} -1.18287e7 q^{66} +795340. q^{67} +4.54949e7 q^{68} +1.80873e8 q^{69} -9.09686e6 q^{70} +2.30879e8 q^{71} +1.02909e7 q^{72} +5.28924e7 q^{73} +1.88174e7 q^{74} -1.36156e8 q^{75} -1.57475e8 q^{76} +1.08029e9 q^{77} -7.32907e6 q^{78} -4.07537e8 q^{79} +1.34879e8 q^{80} +4.30467e7 q^{81} -9.21047e6 q^{82} -6.59317e8 q^{83} -4.68839e8 q^{84} -4.65728e7 q^{85} +4.23676e7 q^{86} -6.04982e8 q^{87} +1.49194e8 q^{88} -5.89798e8 q^{89} -5.25520e6 q^{90} +6.69349e8 q^{91} -1.13803e9 q^{92} +5.53971e8 q^{93} +2.82732e6 q^{94} +1.61206e8 q^{95} -9.71984e7 q^{96} +1.40309e9 q^{97} -1.36075e8 q^{98} +6.24077e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.53527 −0.0678498 −0.0339249 0.999424i \(-0.510801\pi\)
−0.0339249 + 0.999424i \(0.510801\pi\)
\(3\) 81.0000 0.577350
\(4\) −509.643 −0.995396
\(5\) 521.717 0.373311 0.186655 0.982425i \(-0.440235\pi\)
0.186655 + 0.982425i \(0.440235\pi\)
\(6\) −124.357 −0.0391731
\(7\) 11357.2 1.78785 0.893925 0.448216i \(-0.147940\pi\)
0.893925 + 0.448216i \(0.147940\pi\)
\(8\) 1568.49 0.135387
\(9\) 6561.00 0.333333
\(10\) −800.975 −0.0253291
\(11\) 95119.1 1.95885 0.979424 0.201813i \(-0.0646832\pi\)
0.979424 + 0.201813i \(0.0646832\pi\)
\(12\) −41281.1 −0.574692
\(13\) 58936.0 0.572315 0.286158 0.958183i \(-0.407622\pi\)
0.286158 + 0.958183i \(0.407622\pi\)
\(14\) −17436.4 −0.121305
\(15\) 42259.1 0.215531
\(16\) 258529. 0.986210
\(17\) −89268.2 −0.259225 −0.129612 0.991565i \(-0.541373\pi\)
−0.129612 + 0.991565i \(0.541373\pi\)
\(18\) −10072.9 −0.0226166
\(19\) 308991. 0.543945 0.271973 0.962305i \(-0.412324\pi\)
0.271973 + 0.962305i \(0.412324\pi\)
\(20\) −265890. −0.371592
\(21\) 919936. 1.03222
\(22\) −146033. −0.132907
\(23\) 2.23300e6 1.66385 0.831925 0.554888i \(-0.187239\pi\)
0.831925 + 0.554888i \(0.187239\pi\)
\(24\) 127048. 0.0781659
\(25\) −1.68094e6 −0.860639
\(26\) −90482.4 −0.0388315
\(27\) 531441. 0.192450
\(28\) −5.78813e6 −1.77962
\(29\) −7.46892e6 −1.96095 −0.980475 0.196643i \(-0.936996\pi\)
−0.980475 + 0.196643i \(0.936996\pi\)
\(30\) −64879.0 −0.0146237
\(31\) 6.83914e6 1.33007 0.665034 0.746813i \(-0.268417\pi\)
0.665034 + 0.746813i \(0.268417\pi\)
\(32\) −1.19998e6 −0.202301
\(33\) 7.70465e6 1.13094
\(34\) 137050. 0.0175883
\(35\) 5.92527e6 0.667424
\(36\) −3.34377e6 −0.331799
\(37\) −1.22568e7 −1.07515 −0.537574 0.843217i \(-0.680659\pi\)
−0.537574 + 0.843217i \(0.680659\pi\)
\(38\) −474384. −0.0369066
\(39\) 4.77381e6 0.330426
\(40\) 818311. 0.0505415
\(41\) 5.99927e6 0.331567 0.165783 0.986162i \(-0.446985\pi\)
0.165783 + 0.986162i \(0.446985\pi\)
\(42\) −1.41235e6 −0.0700357
\(43\) −2.75963e7 −1.23096 −0.615478 0.788154i \(-0.711037\pi\)
−0.615478 + 0.788154i \(0.711037\pi\)
\(44\) −4.84768e7 −1.94983
\(45\) 3.42299e6 0.124437
\(46\) −3.42825e6 −0.112892
\(47\) −1.84158e6 −0.0550492 −0.0275246 0.999621i \(-0.508762\pi\)
−0.0275246 + 0.999621i \(0.508762\pi\)
\(48\) 2.09409e7 0.569389
\(49\) 8.86331e7 2.19641
\(50\) 2.58068e6 0.0583942
\(51\) −7.23072e6 −0.149663
\(52\) −3.00363e7 −0.569681
\(53\) 2.55383e7 0.444581 0.222290 0.974981i \(-0.428647\pi\)
0.222290 + 0.974981i \(0.428647\pi\)
\(54\) −815903. −0.0130577
\(55\) 4.96253e7 0.731259
\(56\) 1.78137e7 0.242052
\(57\) 2.50283e7 0.314047
\(58\) 1.14668e7 0.133050
\(59\) −1.21174e7 −0.130189
\(60\) −2.15371e7 −0.214539
\(61\) 7.45458e7 0.689349 0.344674 0.938722i \(-0.387989\pi\)
0.344674 + 0.938722i \(0.387989\pi\)
\(62\) −1.04999e7 −0.0902449
\(63\) 7.45148e7 0.595950
\(64\) −1.30525e8 −0.972484
\(65\) 3.07479e7 0.213651
\(66\) −1.18287e7 −0.0767342
\(67\) 795340. 0.00482188 0.00241094 0.999997i \(-0.499233\pi\)
0.00241094 + 0.999997i \(0.499233\pi\)
\(68\) 4.54949e7 0.258031
\(69\) 1.80873e8 0.960624
\(70\) −9.09686e6 −0.0452846
\(71\) 2.30879e8 1.07825 0.539127 0.842224i \(-0.318754\pi\)
0.539127 + 0.842224i \(0.318754\pi\)
\(72\) 1.02909e7 0.0451291
\(73\) 5.28924e7 0.217992 0.108996 0.994042i \(-0.465236\pi\)
0.108996 + 0.994042i \(0.465236\pi\)
\(74\) 1.88174e7 0.0729486
\(75\) −1.36156e8 −0.496890
\(76\) −1.57475e8 −0.541441
\(77\) 1.08029e9 3.50213
\(78\) −7.32907e6 −0.0224194
\(79\) −4.07537e8 −1.17719 −0.588593 0.808429i \(-0.700318\pi\)
−0.588593 + 0.808429i \(0.700318\pi\)
\(80\) 1.34879e8 0.368163
\(81\) 4.30467e7 0.111111
\(82\) −9.21047e6 −0.0224967
\(83\) −6.59317e8 −1.52491 −0.762453 0.647043i \(-0.776005\pi\)
−0.762453 + 0.647043i \(0.776005\pi\)
\(84\) −4.68839e8 −1.02746
\(85\) −4.65728e7 −0.0967714
\(86\) 4.23676e7 0.0835201
\(87\) −6.04982e8 −1.13216
\(88\) 1.49194e8 0.265203
\(89\) −5.89798e8 −0.996433 −0.498216 0.867053i \(-0.666011\pi\)
−0.498216 + 0.867053i \(0.666011\pi\)
\(90\) −5.25520e6 −0.00844302
\(91\) 6.69349e8 1.02321
\(92\) −1.13803e9 −1.65619
\(93\) 5.53971e8 0.767916
\(94\) 2.82732e6 0.00373508
\(95\) 1.61206e8 0.203061
\(96\) −9.71984e7 −0.116799
\(97\) 1.40309e9 1.60921 0.804605 0.593811i \(-0.202377\pi\)
0.804605 + 0.593811i \(0.202377\pi\)
\(98\) −1.36075e8 −0.149026
\(99\) 6.24077e8 0.652949
\(100\) 8.56677e8 0.856677
\(101\) −1.10370e9 −1.05537 −0.527686 0.849439i \(-0.676940\pi\)
−0.527686 + 0.849439i \(0.676940\pi\)
\(102\) 1.11011e7 0.0101546
\(103\) 3.30692e8 0.289505 0.144752 0.989468i \(-0.453761\pi\)
0.144752 + 0.989468i \(0.453761\pi\)
\(104\) 9.24407e7 0.0774842
\(105\) 4.79947e8 0.385337
\(106\) −3.92081e7 −0.0301647
\(107\) −1.59893e9 −1.17924 −0.589621 0.807680i \(-0.700723\pi\)
−0.589621 + 0.807680i \(0.700723\pi\)
\(108\) −2.70845e8 −0.191564
\(109\) −4.91275e8 −0.333354 −0.166677 0.986012i \(-0.553304\pi\)
−0.166677 + 0.986012i \(0.553304\pi\)
\(110\) −7.61881e7 −0.0496158
\(111\) −9.92798e8 −0.620737
\(112\) 2.93617e9 1.76320
\(113\) 1.37860e9 0.795401 0.397701 0.917515i \(-0.369808\pi\)
0.397701 + 0.917515i \(0.369808\pi\)
\(114\) −3.84251e7 −0.0213080
\(115\) 1.16500e9 0.621133
\(116\) 3.80648e9 1.95192
\(117\) 3.86679e8 0.190772
\(118\) 1.86034e7 0.00883329
\(119\) −1.01384e9 −0.463455
\(120\) 6.62832e7 0.0291802
\(121\) 6.68970e9 2.83709
\(122\) −1.14448e8 −0.0467722
\(123\) 4.85941e8 0.191430
\(124\) −3.48552e9 −1.32395
\(125\) −1.89595e9 −0.694596
\(126\) −1.14400e8 −0.0404351
\(127\) −9.76735e8 −0.333165 −0.166583 0.986027i \(-0.553273\pi\)
−0.166583 + 0.986027i \(0.553273\pi\)
\(128\) 8.14780e8 0.268284
\(129\) −2.23530e9 −0.710692
\(130\) −4.72062e7 −0.0144962
\(131\) −4.62441e8 −0.137194 −0.0685970 0.997644i \(-0.521852\pi\)
−0.0685970 + 0.997644i \(0.521852\pi\)
\(132\) −3.92662e9 −1.12574
\(133\) 3.50929e9 0.972493
\(134\) −1.22106e6 −0.000327163 0
\(135\) 2.77262e8 0.0718437
\(136\) −1.40017e8 −0.0350957
\(137\) 3.68274e9 0.893158 0.446579 0.894744i \(-0.352642\pi\)
0.446579 + 0.894744i \(0.352642\pi\)
\(138\) −2.77689e8 −0.0651782
\(139\) 8.61871e9 1.95828 0.979142 0.203176i \(-0.0651265\pi\)
0.979142 + 0.203176i \(0.0651265\pi\)
\(140\) −3.01977e9 −0.664351
\(141\) −1.49168e8 −0.0317827
\(142\) −3.54460e8 −0.0731593
\(143\) 5.60594e9 1.12108
\(144\) 1.69621e9 0.328737
\(145\) −3.89666e9 −0.732044
\(146\) −8.12039e7 −0.0147907
\(147\) 7.17928e9 1.26810
\(148\) 6.24657e9 1.07020
\(149\) 1.16878e9 0.194265 0.0971324 0.995271i \(-0.469033\pi\)
0.0971324 + 0.995271i \(0.469033\pi\)
\(150\) 2.09035e8 0.0337139
\(151\) 7.56814e9 1.18466 0.592329 0.805696i \(-0.298208\pi\)
0.592329 + 0.805696i \(0.298208\pi\)
\(152\) 4.84651e8 0.0736433
\(153\) −5.85688e8 −0.0864082
\(154\) −1.65853e9 −0.237619
\(155\) 3.56810e9 0.496529
\(156\) −2.43294e9 −0.328905
\(157\) −8.83066e9 −1.15996 −0.579982 0.814629i \(-0.696940\pi\)
−0.579982 + 0.814629i \(0.696940\pi\)
\(158\) 6.25678e8 0.0798719
\(159\) 2.06860e9 0.256679
\(160\) −6.26050e8 −0.0755213
\(161\) 2.53607e10 2.97472
\(162\) −6.60882e7 −0.00753887
\(163\) −5.52494e8 −0.0613032 −0.0306516 0.999530i \(-0.509758\pi\)
−0.0306516 + 0.999530i \(0.509758\pi\)
\(164\) −3.05748e9 −0.330040
\(165\) 4.01965e9 0.422193
\(166\) 1.01223e9 0.103465
\(167\) 1.63432e10 1.62597 0.812987 0.582282i \(-0.197840\pi\)
0.812987 + 0.582282i \(0.197840\pi\)
\(168\) 1.44291e9 0.139749
\(169\) −7.13105e9 −0.672455
\(170\) 7.15016e7 0.00656592
\(171\) 2.02729e9 0.181315
\(172\) 1.40642e10 1.22529
\(173\) 1.38478e9 0.117537 0.0587685 0.998272i \(-0.481283\pi\)
0.0587685 + 0.998272i \(0.481283\pi\)
\(174\) 9.28809e8 0.0768165
\(175\) −1.90908e10 −1.53869
\(176\) 2.45911e10 1.93184
\(177\) −9.81506e8 −0.0751646
\(178\) 9.05496e8 0.0676078
\(179\) −1.93204e10 −1.40662 −0.703312 0.710881i \(-0.748297\pi\)
−0.703312 + 0.710881i \(0.748297\pi\)
\(180\) −1.74450e9 −0.123864
\(181\) −2.47164e10 −1.71171 −0.855857 0.517212i \(-0.826970\pi\)
−0.855857 + 0.517212i \(0.826970\pi\)
\(182\) −1.02763e9 −0.0694249
\(183\) 6.03821e9 0.397996
\(184\) 3.50245e9 0.225264
\(185\) −6.39457e9 −0.401364
\(186\) −8.50492e8 −0.0521029
\(187\) −8.49111e9 −0.507782
\(188\) 9.38550e8 0.0547958
\(189\) 6.03570e9 0.344072
\(190\) −2.47494e8 −0.0137776
\(191\) 7.09375e9 0.385679 0.192839 0.981230i \(-0.438230\pi\)
0.192839 + 0.981230i \(0.438230\pi\)
\(192\) −1.05725e10 −0.561464
\(193\) 1.79947e10 0.933548 0.466774 0.884377i \(-0.345416\pi\)
0.466774 + 0.884377i \(0.345416\pi\)
\(194\) −2.15412e9 −0.109185
\(195\) 2.49058e9 0.123352
\(196\) −4.51712e10 −2.18630
\(197\) 2.83463e10 1.34091 0.670453 0.741952i \(-0.266100\pi\)
0.670453 + 0.741952i \(0.266100\pi\)
\(198\) −9.58124e8 −0.0443025
\(199\) −3.68752e10 −1.66685 −0.833423 0.552635i \(-0.813622\pi\)
−0.833423 + 0.552635i \(0.813622\pi\)
\(200\) −2.63654e9 −0.116520
\(201\) 6.44225e7 0.00278391
\(202\) 1.69448e9 0.0716068
\(203\) −8.48262e10 −3.50589
\(204\) 3.68509e9 0.148974
\(205\) 3.12992e9 0.123777
\(206\) −5.07700e8 −0.0196428
\(207\) 1.46507e10 0.554617
\(208\) 1.52367e10 0.564423
\(209\) 2.93910e10 1.06551
\(210\) −7.36846e8 −0.0261451
\(211\) −3.93354e10 −1.36619 −0.683097 0.730328i \(-0.739367\pi\)
−0.683097 + 0.730328i \(0.739367\pi\)
\(212\) −1.30154e10 −0.442534
\(213\) 1.87012e10 0.622530
\(214\) 2.45478e9 0.0800113
\(215\) −1.43975e10 −0.459529
\(216\) 8.33562e8 0.0260553
\(217\) 7.76737e10 2.37796
\(218\) 7.54239e8 0.0226180
\(219\) 4.28428e9 0.125858
\(220\) −2.52912e10 −0.727893
\(221\) −5.26110e9 −0.148358
\(222\) 1.52421e9 0.0421169
\(223\) 1.37882e10 0.373366 0.186683 0.982420i \(-0.440226\pi\)
0.186683 + 0.982420i \(0.440226\pi\)
\(224\) −1.36284e10 −0.361685
\(225\) −1.10286e10 −0.286880
\(226\) −2.11652e9 −0.0539678
\(227\) −1.75195e10 −0.437931 −0.218965 0.975733i \(-0.570268\pi\)
−0.218965 + 0.975733i \(0.570268\pi\)
\(228\) −1.27555e10 −0.312601
\(229\) −6.95923e10 −1.67225 −0.836126 0.548537i \(-0.815185\pi\)
−0.836126 + 0.548537i \(0.815185\pi\)
\(230\) −1.78858e9 −0.0421438
\(231\) 8.75035e10 2.02195
\(232\) −1.17149e10 −0.265488
\(233\) −1.86095e10 −0.413649 −0.206825 0.978378i \(-0.566313\pi\)
−0.206825 + 0.978378i \(0.566313\pi\)
\(234\) −5.93655e8 −0.0129438
\(235\) −9.60787e8 −0.0205505
\(236\) 6.17553e9 0.129590
\(237\) −3.30105e10 −0.679649
\(238\) 1.55651e9 0.0314453
\(239\) 8.01476e10 1.58891 0.794456 0.607321i \(-0.207756\pi\)
0.794456 + 0.607321i \(0.207756\pi\)
\(240\) 1.09252e10 0.212559
\(241\) −4.83756e9 −0.0923739 −0.0461870 0.998933i \(-0.514707\pi\)
−0.0461870 + 0.998933i \(0.514707\pi\)
\(242\) −1.02705e10 −0.192496
\(243\) 3.48678e9 0.0641500
\(244\) −3.79918e10 −0.686175
\(245\) 4.62414e10 0.819943
\(246\) −7.46048e8 −0.0129885
\(247\) 1.82107e10 0.311308
\(248\) 1.07272e10 0.180074
\(249\) −5.34047e10 −0.880405
\(250\) 2.91079e9 0.0471282
\(251\) −7.62361e9 −0.121235 −0.0606177 0.998161i \(-0.519307\pi\)
−0.0606177 + 0.998161i \(0.519307\pi\)
\(252\) −3.79759e10 −0.593207
\(253\) 2.12401e11 3.25923
\(254\) 1.49955e9 0.0226052
\(255\) −3.77239e9 −0.0558710
\(256\) 6.55777e10 0.954281
\(257\) 5.48861e10 0.784808 0.392404 0.919793i \(-0.371644\pi\)
0.392404 + 0.919793i \(0.371644\pi\)
\(258\) 3.43178e9 0.0482203
\(259\) −1.39203e11 −1.92220
\(260\) −1.56705e10 −0.212668
\(261\) −4.90036e10 −0.653650
\(262\) 7.09970e8 0.00930859
\(263\) −9.52195e9 −0.122723 −0.0613614 0.998116i \(-0.519544\pi\)
−0.0613614 + 0.998116i \(0.519544\pi\)
\(264\) 1.20847e10 0.153115
\(265\) 1.33238e10 0.165967
\(266\) −5.38769e9 −0.0659834
\(267\) −4.77736e10 −0.575291
\(268\) −4.05339e8 −0.00479968
\(269\) 2.50707e10 0.291932 0.145966 0.989290i \(-0.453371\pi\)
0.145966 + 0.989290i \(0.453371\pi\)
\(270\) −4.25671e8 −0.00487458
\(271\) 5.35620e9 0.0603247 0.0301623 0.999545i \(-0.490398\pi\)
0.0301623 + 0.999545i \(0.490398\pi\)
\(272\) −2.30784e10 −0.255650
\(273\) 5.42173e10 0.590753
\(274\) −5.65398e9 −0.0606006
\(275\) −1.59889e11 −1.68586
\(276\) −9.21808e10 −0.956202
\(277\) −1.39810e11 −1.42685 −0.713426 0.700730i \(-0.752858\pi\)
−0.713426 + 0.700730i \(0.752858\pi\)
\(278\) −1.32320e10 −0.132869
\(279\) 4.48716e10 0.443356
\(280\) 9.29374e9 0.0903607
\(281\) 5.63482e10 0.539140 0.269570 0.962981i \(-0.413118\pi\)
0.269570 + 0.962981i \(0.413118\pi\)
\(282\) 2.29013e8 0.00215645
\(283\) −1.49244e11 −1.38312 −0.691559 0.722320i \(-0.743076\pi\)
−0.691559 + 0.722320i \(0.743076\pi\)
\(284\) −1.17666e11 −1.07329
\(285\) 1.30577e10 0.117237
\(286\) −8.60661e9 −0.0760650
\(287\) 6.81351e10 0.592792
\(288\) −7.87307e9 −0.0674338
\(289\) −1.10619e11 −0.932803
\(290\) 5.98242e9 0.0496690
\(291\) 1.13650e11 0.929077
\(292\) −2.69562e10 −0.216988
\(293\) 8.99234e10 0.712801 0.356400 0.934333i \(-0.384004\pi\)
0.356400 + 0.934333i \(0.384004\pi\)
\(294\) −1.10221e10 −0.0860402
\(295\) −6.32184e9 −0.0486009
\(296\) −1.92247e10 −0.145561
\(297\) 5.05502e10 0.376981
\(298\) −1.79439e9 −0.0131808
\(299\) 1.31604e11 0.952247
\(300\) 6.93908e10 0.494603
\(301\) −3.13417e11 −2.20076
\(302\) −1.16191e10 −0.0803789
\(303\) −8.93999e10 −0.609319
\(304\) 7.98833e10 0.536444
\(305\) 3.88919e10 0.257341
\(306\) 8.99187e8 0.00586278
\(307\) −4.75255e10 −0.305354 −0.152677 0.988276i \(-0.548789\pi\)
−0.152677 + 0.988276i \(0.548789\pi\)
\(308\) −5.50562e11 −3.48601
\(309\) 2.67860e10 0.167146
\(310\) −5.47798e9 −0.0336894
\(311\) −2.58316e11 −1.56578 −0.782888 0.622163i \(-0.786254\pi\)
−0.782888 + 0.622163i \(0.786254\pi\)
\(312\) 7.48770e9 0.0447355
\(313\) 1.53447e11 0.903669 0.451835 0.892102i \(-0.350770\pi\)
0.451835 + 0.892102i \(0.350770\pi\)
\(314\) 1.35574e10 0.0787034
\(315\) 3.88757e10 0.222475
\(316\) 2.07698e11 1.17177
\(317\) 6.64771e9 0.0369747 0.0184874 0.999829i \(-0.494115\pi\)
0.0184874 + 0.999829i \(0.494115\pi\)
\(318\) −3.17585e9 −0.0174156
\(319\) −7.10437e11 −3.84120
\(320\) −6.80970e10 −0.363039
\(321\) −1.29513e11 −0.680835
\(322\) −3.89355e10 −0.201834
\(323\) −2.75831e10 −0.141004
\(324\) −2.19385e10 −0.110600
\(325\) −9.90676e10 −0.492557
\(326\) 8.48225e8 0.00415941
\(327\) −3.97933e10 −0.192462
\(328\) 9.40981e9 0.0448899
\(329\) −2.09153e10 −0.0984198
\(330\) −6.17123e9 −0.0286457
\(331\) 1.80447e11 0.826272 0.413136 0.910669i \(-0.364433\pi\)
0.413136 + 0.910669i \(0.364433\pi\)
\(332\) 3.36017e11 1.51789
\(333\) −8.04166e10 −0.358382
\(334\) −2.50912e10 −0.110322
\(335\) 4.14943e8 0.00180006
\(336\) 2.37830e11 1.01798
\(337\) 2.39924e10 0.101330 0.0506650 0.998716i \(-0.483866\pi\)
0.0506650 + 0.998716i \(0.483866\pi\)
\(338\) 1.09481e10 0.0456260
\(339\) 1.11667e11 0.459225
\(340\) 2.37355e10 0.0963259
\(341\) 6.50533e11 2.60540
\(342\) −3.11243e9 −0.0123022
\(343\) 5.48321e11 2.13900
\(344\) −4.32846e10 −0.166656
\(345\) 9.43648e10 0.358611
\(346\) −2.12601e9 −0.00797486
\(347\) −2.11491e11 −0.783084 −0.391542 0.920160i \(-0.628058\pi\)
−0.391542 + 0.920160i \(0.628058\pi\)
\(348\) 3.08325e11 1.12694
\(349\) −1.24571e11 −0.449470 −0.224735 0.974420i \(-0.572152\pi\)
−0.224735 + 0.974420i \(0.572152\pi\)
\(350\) 2.93094e10 0.104400
\(351\) 3.13210e10 0.110142
\(352\) −1.14141e11 −0.396278
\(353\) −3.97716e10 −0.136329 −0.0681644 0.997674i \(-0.521714\pi\)
−0.0681644 + 0.997674i \(0.521714\pi\)
\(354\) 1.50687e9 0.00509990
\(355\) 1.20453e11 0.402524
\(356\) 3.00586e11 0.991845
\(357\) −8.21210e10 −0.267576
\(358\) 2.96620e10 0.0954392
\(359\) 9.64259e10 0.306386 0.153193 0.988196i \(-0.451044\pi\)
0.153193 + 0.988196i \(0.451044\pi\)
\(360\) 5.36894e9 0.0168472
\(361\) −2.27212e11 −0.704124
\(362\) 3.79462e10 0.116140
\(363\) 5.41866e11 1.63799
\(364\) −3.41129e11 −1.01850
\(365\) 2.75949e10 0.0813787
\(366\) −9.27026e9 −0.0270039
\(367\) −2.75007e11 −0.791308 −0.395654 0.918400i \(-0.629482\pi\)
−0.395654 + 0.918400i \(0.629482\pi\)
\(368\) 5.77296e11 1.64091
\(369\) 3.93612e10 0.110522
\(370\) 9.81736e9 0.0272325
\(371\) 2.90044e11 0.794844
\(372\) −2.82327e11 −0.764380
\(373\) −2.04623e11 −0.547348 −0.273674 0.961822i \(-0.588239\pi\)
−0.273674 + 0.961822i \(0.588239\pi\)
\(374\) 1.30361e10 0.0344529
\(375\) −1.53572e11 −0.401025
\(376\) −2.88851e9 −0.00745296
\(377\) −4.40188e11 −1.12228
\(378\) −9.26640e9 −0.0233452
\(379\) 1.24424e11 0.309761 0.154881 0.987933i \(-0.450501\pi\)
0.154881 + 0.987933i \(0.450501\pi\)
\(380\) −8.21576e10 −0.202126
\(381\) −7.91155e10 −0.192353
\(382\) −1.08908e10 −0.0261682
\(383\) 2.31365e11 0.549418 0.274709 0.961527i \(-0.411418\pi\)
0.274709 + 0.961527i \(0.411418\pi\)
\(384\) 6.59972e10 0.154894
\(385\) 5.63606e11 1.30738
\(386\) −2.76266e10 −0.0633411
\(387\) −1.81059e11 −0.410318
\(388\) −7.15075e11 −1.60180
\(389\) 5.89622e11 1.30557 0.652785 0.757543i \(-0.273600\pi\)
0.652785 + 0.757543i \(0.273600\pi\)
\(390\) −3.82371e9 −0.00836939
\(391\) −1.99336e11 −0.431311
\(392\) 1.39020e11 0.297366
\(393\) −3.74577e10 −0.0792090
\(394\) −4.35191e10 −0.0909802
\(395\) −2.12619e11 −0.439456
\(396\) −3.18056e11 −0.649944
\(397\) −1.17251e11 −0.236897 −0.118448 0.992960i \(-0.537792\pi\)
−0.118448 + 0.992960i \(0.537792\pi\)
\(398\) 5.66132e10 0.113095
\(399\) 2.84252e11 0.561469
\(400\) −4.34571e11 −0.848771
\(401\) 6.92604e10 0.133763 0.0668814 0.997761i \(-0.478695\pi\)
0.0668814 + 0.997761i \(0.478695\pi\)
\(402\) −9.89057e7 −0.000188888 0
\(403\) 4.03072e11 0.761219
\(404\) 5.62494e11 1.05051
\(405\) 2.24582e10 0.0414790
\(406\) 1.30231e11 0.237874
\(407\) −1.16585e12 −2.10605
\(408\) −1.13413e10 −0.0202625
\(409\) 5.32844e11 0.941554 0.470777 0.882252i \(-0.343974\pi\)
0.470777 + 0.882252i \(0.343974\pi\)
\(410\) −4.80526e9 −0.00839827
\(411\) 2.98302e11 0.515665
\(412\) −1.68535e11 −0.288172
\(413\) −1.37620e11 −0.232758
\(414\) −2.24928e10 −0.0376306
\(415\) −3.43977e11 −0.569264
\(416\) −7.07220e10 −0.115780
\(417\) 6.98116e11 1.13062
\(418\) −4.51230e10 −0.0722944
\(419\) 1.03837e12 1.64584 0.822920 0.568157i \(-0.192343\pi\)
0.822920 + 0.568157i \(0.192343\pi\)
\(420\) −2.44601e11 −0.383563
\(421\) −8.26226e11 −1.28183 −0.640914 0.767613i \(-0.721444\pi\)
−0.640914 + 0.767613i \(0.721444\pi\)
\(422\) 6.03903e10 0.0926960
\(423\) −1.20826e10 −0.0183497
\(424\) 4.00567e10 0.0601905
\(425\) 1.50054e11 0.223099
\(426\) −2.87113e10 −0.0422386
\(427\) 8.46634e11 1.23245
\(428\) 8.14884e11 1.17381
\(429\) 4.54081e11 0.647255
\(430\) 2.21039e10 0.0311789
\(431\) 5.76904e11 0.805297 0.402649 0.915355i \(-0.368090\pi\)
0.402649 + 0.915355i \(0.368090\pi\)
\(432\) 1.37393e11 0.189796
\(433\) 8.37477e11 1.14493 0.572463 0.819930i \(-0.305988\pi\)
0.572463 + 0.819930i \(0.305988\pi\)
\(434\) −1.19250e11 −0.161344
\(435\) −3.15630e11 −0.422646
\(436\) 2.50375e11 0.331820
\(437\) 6.89979e11 0.905043
\(438\) −6.57751e9 −0.00853942
\(439\) 8.78080e11 1.12835 0.564175 0.825655i \(-0.309194\pi\)
0.564175 + 0.825655i \(0.309194\pi\)
\(440\) 7.78370e10 0.0990032
\(441\) 5.81522e11 0.732137
\(442\) 8.07720e9 0.0100661
\(443\) 5.02232e11 0.619566 0.309783 0.950807i \(-0.399744\pi\)
0.309783 + 0.950807i \(0.399744\pi\)
\(444\) 5.05972e11 0.617879
\(445\) −3.07708e11 −0.371979
\(446\) −2.11685e10 −0.0253328
\(447\) 9.46711e10 0.112159
\(448\) −1.48240e12 −1.73866
\(449\) 1.17433e12 1.36358 0.681792 0.731546i \(-0.261201\pi\)
0.681792 + 0.731546i \(0.261201\pi\)
\(450\) 1.69319e10 0.0194647
\(451\) 5.70645e11 0.649489
\(452\) −7.02595e11 −0.791739
\(453\) 6.13020e11 0.683963
\(454\) 2.68971e10 0.0297135
\(455\) 3.49211e11 0.381977
\(456\) 3.92567e10 0.0425180
\(457\) −1.37774e12 −1.47755 −0.738776 0.673951i \(-0.764596\pi\)
−0.738776 + 0.673951i \(0.764596\pi\)
\(458\) 1.06843e11 0.113462
\(459\) −4.74408e10 −0.0498878
\(460\) −5.93733e11 −0.618273
\(461\) 3.12616e11 0.322372 0.161186 0.986924i \(-0.448468\pi\)
0.161186 + 0.986924i \(0.448468\pi\)
\(462\) −1.34341e11 −0.137189
\(463\) −3.22766e10 −0.0326417 −0.0163209 0.999867i \(-0.505195\pi\)
−0.0163209 + 0.999867i \(0.505195\pi\)
\(464\) −1.93093e12 −1.93391
\(465\) 2.89016e11 0.286671
\(466\) 2.85705e10 0.0280660
\(467\) −1.30750e12 −1.27208 −0.636042 0.771654i \(-0.719429\pi\)
−0.636042 + 0.771654i \(0.719429\pi\)
\(468\) −1.97068e11 −0.189894
\(469\) 9.03286e9 0.00862079
\(470\) 1.47506e9 0.00139434
\(471\) −7.15283e11 −0.669706
\(472\) −1.90060e10 −0.0176259
\(473\) −2.62493e12 −2.41125
\(474\) 5.06799e10 0.0461141
\(475\) −5.19395e11 −0.468140
\(476\) 5.16696e11 0.461322
\(477\) 1.67557e11 0.148194
\(478\) −1.23048e11 −0.107807
\(479\) 1.17526e12 1.02006 0.510029 0.860157i \(-0.329635\pi\)
0.510029 + 0.860157i \(0.329635\pi\)
\(480\) −5.07101e10 −0.0436022
\(481\) −7.22364e11 −0.615323
\(482\) 7.42694e9 0.00626756
\(483\) 2.05422e12 1.71745
\(484\) −3.40936e12 −2.82403
\(485\) 7.32016e11 0.600735
\(486\) −5.35314e9 −0.00435257
\(487\) 2.59684e11 0.209201 0.104601 0.994514i \(-0.466644\pi\)
0.104601 + 0.994514i \(0.466644\pi\)
\(488\) 1.16925e11 0.0933291
\(489\) −4.47520e10 −0.0353934
\(490\) −7.09929e10 −0.0556330
\(491\) −1.23696e12 −0.960484 −0.480242 0.877136i \(-0.659451\pi\)
−0.480242 + 0.877136i \(0.659451\pi\)
\(492\) −2.47656e11 −0.190549
\(493\) 6.66736e11 0.508327
\(494\) −2.79583e10 −0.0211222
\(495\) 3.25592e11 0.243753
\(496\) 1.76812e12 1.31173
\(497\) 2.62214e12 1.92776
\(498\) 8.19904e10 0.0597353
\(499\) 4.52497e10 0.0326711 0.0163355 0.999867i \(-0.494800\pi\)
0.0163355 + 0.999867i \(0.494800\pi\)
\(500\) 9.66259e11 0.691399
\(501\) 1.32380e12 0.938756
\(502\) 1.17043e10 0.00822579
\(503\) −2.79106e11 −0.194408 −0.0972039 0.995264i \(-0.530990\pi\)
−0.0972039 + 0.995264i \(0.530990\pi\)
\(504\) 1.16876e11 0.0806841
\(505\) −5.75821e11 −0.393982
\(506\) −3.26093e11 −0.221138
\(507\) −5.77615e11 −0.388242
\(508\) 4.97786e11 0.331632
\(509\) −1.97812e12 −1.30624 −0.653119 0.757255i \(-0.726540\pi\)
−0.653119 + 0.757255i \(0.726540\pi\)
\(510\) 5.79163e9 0.00379083
\(511\) 6.00711e11 0.389737
\(512\) −5.17846e11 −0.333032
\(513\) 1.64211e11 0.104682
\(514\) −8.42647e10 −0.0532491
\(515\) 1.72528e11 0.108075
\(516\) 1.13920e12 0.707420
\(517\) −1.75170e11 −0.107833
\(518\) 2.13713e11 0.130421
\(519\) 1.12167e11 0.0678600
\(520\) 4.82279e10 0.0289257
\(521\) −1.73104e11 −0.102929 −0.0514645 0.998675i \(-0.516389\pi\)
−0.0514645 + 0.998675i \(0.516389\pi\)
\(522\) 7.52335e10 0.0443500
\(523\) −2.59134e12 −1.51449 −0.757245 0.653131i \(-0.773455\pi\)
−0.757245 + 0.653131i \(0.773455\pi\)
\(524\) 2.35680e11 0.136562
\(525\) −1.54635e12 −0.888366
\(526\) 1.46187e10 0.00832671
\(527\) −6.10518e11 −0.344787
\(528\) 1.99188e12 1.11535
\(529\) 3.18515e12 1.76840
\(530\) −2.04555e10 −0.0112608
\(531\) −7.95020e10 −0.0433963
\(532\) −1.78848e12 −0.968016
\(533\) 3.53573e11 0.189761
\(534\) 7.33452e10 0.0390334
\(535\) −8.34190e11 −0.440223
\(536\) 1.24749e9 0.000652821 0
\(537\) −1.56496e12 −0.812115
\(538\) −3.84902e10 −0.0198075
\(539\) 8.43070e12 4.30243
\(540\) −1.41305e11 −0.0715129
\(541\) 8.44449e11 0.423824 0.211912 0.977289i \(-0.432031\pi\)
0.211912 + 0.977289i \(0.432031\pi\)
\(542\) −8.22319e9 −0.00409302
\(543\) −2.00203e12 −0.988259
\(544\) 1.07120e11 0.0524415
\(545\) −2.56307e11 −0.124445
\(546\) −8.32380e10 −0.0400825
\(547\) −2.86951e12 −1.37045 −0.685227 0.728329i \(-0.740297\pi\)
−0.685227 + 0.728329i \(0.740297\pi\)
\(548\) −1.87688e12 −0.889046
\(549\) 4.89095e11 0.229783
\(550\) 2.45472e11 0.114385
\(551\) −2.30783e12 −1.06665
\(552\) 2.83699e11 0.130056
\(553\) −4.62849e12 −2.10463
\(554\) 2.14645e11 0.0968117
\(555\) −5.17960e11 −0.231728
\(556\) −4.39247e12 −1.94927
\(557\) 3.23987e12 1.42619 0.713097 0.701065i \(-0.247292\pi\)
0.713097 + 0.701065i \(0.247292\pi\)
\(558\) −6.88899e10 −0.0300816
\(559\) −1.62641e12 −0.704494
\(560\) 1.53185e12 0.658220
\(561\) −6.87780e11 −0.293168
\(562\) −8.65095e10 −0.0365806
\(563\) 4.45164e11 0.186738 0.0933690 0.995632i \(-0.470236\pi\)
0.0933690 + 0.995632i \(0.470236\pi\)
\(564\) 7.60226e10 0.0316364
\(565\) 7.19241e11 0.296932
\(566\) 2.29130e11 0.0938443
\(567\) 4.88892e11 0.198650
\(568\) 3.62132e11 0.145982
\(569\) 4.19474e12 1.67764 0.838821 0.544407i \(-0.183245\pi\)
0.838821 + 0.544407i \(0.183245\pi\)
\(570\) −2.00470e10 −0.00795451
\(571\) 3.05784e12 1.20380 0.601898 0.798573i \(-0.294411\pi\)
0.601898 + 0.798573i \(0.294411\pi\)
\(572\) −2.85703e12 −1.11592
\(573\) 5.74594e11 0.222672
\(574\) −1.04605e11 −0.0402208
\(575\) −3.75354e12 −1.43197
\(576\) −8.56372e11 −0.324161
\(577\) −3.45286e12 −1.29684 −0.648422 0.761281i \(-0.724571\pi\)
−0.648422 + 0.761281i \(0.724571\pi\)
\(578\) 1.69830e11 0.0632905
\(579\) 1.45757e12 0.538984
\(580\) 1.98591e12 0.728674
\(581\) −7.48802e12 −2.72630
\(582\) −1.74483e11 −0.0630377
\(583\) 2.42918e12 0.870866
\(584\) 8.29614e10 0.0295133
\(585\) 2.01737e11 0.0712171
\(586\) −1.38056e11 −0.0483634
\(587\) 7.15734e11 0.248817 0.124409 0.992231i \(-0.460297\pi\)
0.124409 + 0.992231i \(0.460297\pi\)
\(588\) −3.65887e12 −1.26226
\(589\) 2.11324e12 0.723484
\(590\) 9.70571e9 0.00329756
\(591\) 2.29605e12 0.774173
\(592\) −3.16873e12 −1.06032
\(593\) −3.03726e11 −0.100864 −0.0504320 0.998727i \(-0.516060\pi\)
−0.0504320 + 0.998727i \(0.516060\pi\)
\(594\) −7.76080e10 −0.0255781
\(595\) −5.28938e11 −0.173013
\(596\) −5.95660e11 −0.193371
\(597\) −2.98689e12 −0.962354
\(598\) −2.02047e11 −0.0646098
\(599\) −2.28392e12 −0.724870 −0.362435 0.932009i \(-0.618055\pi\)
−0.362435 + 0.932009i \(0.618055\pi\)
\(600\) −2.13560e11 −0.0672726
\(601\) −1.41623e12 −0.442789 −0.221395 0.975184i \(-0.571061\pi\)
−0.221395 + 0.975184i \(0.571061\pi\)
\(602\) 4.81179e11 0.149321
\(603\) 5.21822e9 0.00160729
\(604\) −3.85705e12 −1.17920
\(605\) 3.49013e12 1.05911
\(606\) 1.37253e11 0.0413422
\(607\) 6.68445e11 0.199856 0.0999278 0.994995i \(-0.468139\pi\)
0.0999278 + 0.994995i \(0.468139\pi\)
\(608\) −3.70783e11 −0.110041
\(609\) −6.87092e12 −2.02412
\(610\) −5.97094e10 −0.0174606
\(611\) −1.08536e11 −0.0315055
\(612\) 2.98492e11 0.0860105
\(613\) 3.29593e12 0.942771 0.471385 0.881927i \(-0.343754\pi\)
0.471385 + 0.881927i \(0.343754\pi\)
\(614\) 7.29643e10 0.0207182
\(615\) 2.53524e11 0.0714629
\(616\) 1.69443e12 0.474144
\(617\) −3.51993e12 −0.977802 −0.488901 0.872339i \(-0.662602\pi\)
−0.488901 + 0.872339i \(0.662602\pi\)
\(618\) −4.11237e10 −0.0113408
\(619\) 5.42052e12 1.48400 0.741998 0.670402i \(-0.233878\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(620\) −1.81846e12 −0.494243
\(621\) 1.18671e12 0.320208
\(622\) 3.96584e11 0.106238
\(623\) −6.69847e12 −1.78147
\(624\) 1.23417e12 0.325870
\(625\) 2.29393e12 0.601339
\(626\) −2.35582e11 −0.0613138
\(627\) 2.38067e12 0.615170
\(628\) 4.50048e12 1.15462
\(629\) 1.09414e12 0.278705
\(630\) −5.96845e10 −0.0150949
\(631\) 1.04898e12 0.263413 0.131706 0.991289i \(-0.457954\pi\)
0.131706 + 0.991289i \(0.457954\pi\)
\(632\) −6.39220e11 −0.159376
\(633\) −3.18617e12 −0.788772
\(634\) −1.02060e10 −0.00250873
\(635\) −5.09580e11 −0.124374
\(636\) −1.05425e12 −0.255497
\(637\) 5.22368e12 1.25704
\(638\) 1.09071e12 0.260625
\(639\) 1.51479e12 0.359418
\(640\) 4.25085e11 0.100153
\(641\) 2.12024e12 0.496049 0.248024 0.968754i \(-0.420219\pi\)
0.248024 + 0.968754i \(0.420219\pi\)
\(642\) 1.98837e11 0.0461945
\(643\) 1.63431e12 0.377038 0.188519 0.982070i \(-0.439631\pi\)
0.188519 + 0.982070i \(0.439631\pi\)
\(644\) −1.29249e13 −2.96102
\(645\) −1.16619e12 −0.265309
\(646\) 4.23474e10 0.00956710
\(647\) −3.43085e12 −0.769719 −0.384860 0.922975i \(-0.625750\pi\)
−0.384860 + 0.922975i \(0.625750\pi\)
\(648\) 6.75185e10 0.0150430
\(649\) −1.15259e12 −0.255020
\(650\) 1.52095e11 0.0334199
\(651\) 6.29157e12 1.37292
\(652\) 2.81575e11 0.0610210
\(653\) 3.32537e11 0.0715699 0.0357850 0.999360i \(-0.488607\pi\)
0.0357850 + 0.999360i \(0.488607\pi\)
\(654\) 6.10933e10 0.0130585
\(655\) −2.41263e11 −0.0512160
\(656\) 1.55099e12 0.326995
\(657\) 3.47027e11 0.0726640
\(658\) 3.21105e10 0.00667776
\(659\) 4.48045e11 0.0925417 0.0462709 0.998929i \(-0.485266\pi\)
0.0462709 + 0.998929i \(0.485266\pi\)
\(660\) −2.04859e12 −0.420249
\(661\) −4.98017e12 −1.01470 −0.507350 0.861740i \(-0.669375\pi\)
−0.507350 + 0.861740i \(0.669375\pi\)
\(662\) −2.77034e11 −0.0560624
\(663\) −4.26149e11 −0.0856547
\(664\) −1.03414e12 −0.206453
\(665\) 1.83086e12 0.363042
\(666\) 1.23461e11 0.0243162
\(667\) −1.66781e13 −3.26273
\(668\) −8.32920e12 −1.61849
\(669\) 1.11684e12 0.215563
\(670\) −6.37047e8 −0.000122134 0
\(671\) 7.09073e12 1.35033
\(672\) −1.10390e12 −0.208819
\(673\) 8.54363e12 1.60537 0.802684 0.596404i \(-0.203404\pi\)
0.802684 + 0.596404i \(0.203404\pi\)
\(674\) −3.68347e10 −0.00687523
\(675\) −8.93318e11 −0.165630
\(676\) 3.63429e12 0.669360
\(677\) 4.76231e11 0.0871301 0.0435651 0.999051i \(-0.486128\pi\)
0.0435651 + 0.999051i \(0.486128\pi\)
\(678\) −1.71438e11 −0.0311583
\(679\) 1.59352e13 2.87703
\(680\) −7.30491e10 −0.0131016
\(681\) −1.41908e12 −0.252839
\(682\) −9.98742e11 −0.176776
\(683\) 1.00532e13 1.76771 0.883856 0.467759i \(-0.154938\pi\)
0.883856 + 0.467759i \(0.154938\pi\)
\(684\) −1.03320e12 −0.180480
\(685\) 1.92135e12 0.333425
\(686\) −8.41819e11 −0.145131
\(687\) −5.63698e12 −0.965475
\(688\) −7.13444e12 −1.21398
\(689\) 1.50512e12 0.254440
\(690\) −1.44875e11 −0.0243317
\(691\) −4.48639e12 −0.748594 −0.374297 0.927309i \(-0.622116\pi\)
−0.374297 + 0.927309i \(0.622116\pi\)
\(692\) −7.05745e11 −0.116996
\(693\) 7.08778e12 1.16738
\(694\) 3.24694e11 0.0531321
\(695\) 4.49653e12 0.731048
\(696\) −9.48911e11 −0.153279
\(697\) −5.35544e11 −0.0859503
\(698\) 1.91249e11 0.0304965
\(699\) −1.50737e12 −0.238820
\(700\) 9.72948e12 1.53161
\(701\) 7.82510e12 1.22394 0.611968 0.790882i \(-0.290378\pi\)
0.611968 + 0.790882i \(0.290378\pi\)
\(702\) −4.80861e10 −0.00747312
\(703\) −3.78723e12 −0.584821
\(704\) −1.24154e13 −1.90495
\(705\) −7.78237e10 −0.0118648
\(706\) 6.10601e10 0.00924988
\(707\) −1.25350e13 −1.88685
\(708\) 5.00218e11 0.0748186
\(709\) −6.85312e12 −1.01854 −0.509272 0.860605i \(-0.670085\pi\)
−0.509272 + 0.860605i \(0.670085\pi\)
\(710\) −1.84928e11 −0.0273112
\(711\) −2.67385e12 −0.392396
\(712\) −9.25094e11 −0.134904
\(713\) 1.52718e13 2.21303
\(714\) 1.26078e11 0.0181550
\(715\) 2.92472e12 0.418511
\(716\) 9.84652e12 1.40015
\(717\) 6.49196e12 0.917359
\(718\) −1.48039e11 −0.0207882
\(719\) 1.16115e13 1.62035 0.810174 0.586189i \(-0.199372\pi\)
0.810174 + 0.586189i \(0.199372\pi\)
\(720\) 8.84942e11 0.122721
\(721\) 3.75574e12 0.517591
\(722\) 3.48831e11 0.0477747
\(723\) −3.91842e11 −0.0533321
\(724\) 1.25965e13 1.70383
\(725\) 1.25548e13 1.68767
\(726\) −8.31908e11 −0.111138
\(727\) −1.05133e13 −1.39584 −0.697920 0.716176i \(-0.745891\pi\)
−0.697920 + 0.716176i \(0.745891\pi\)
\(728\) 1.04987e12 0.138530
\(729\) 2.82430e11 0.0370370
\(730\) −4.23655e10 −0.00552153
\(731\) 2.46347e12 0.319094
\(732\) −3.07733e12 −0.396164
\(733\) −8.91599e12 −1.14078 −0.570390 0.821374i \(-0.693208\pi\)
−0.570390 + 0.821374i \(0.693208\pi\)
\(734\) 4.22208e11 0.0536901
\(735\) 3.74556e12 0.473394
\(736\) −2.67956e12 −0.336599
\(737\) 7.56520e10 0.00944532
\(738\) −6.04299e10 −0.00749891
\(739\) −3.97006e12 −0.489663 −0.244831 0.969566i \(-0.578733\pi\)
−0.244831 + 0.969566i \(0.578733\pi\)
\(740\) 3.25895e12 0.399516
\(741\) 1.47507e12 0.179734
\(742\) −4.45295e11 −0.0539300
\(743\) −1.12649e13 −1.35606 −0.678028 0.735036i \(-0.737165\pi\)
−0.678028 + 0.735036i \(0.737165\pi\)
\(744\) 8.68899e11 0.103966
\(745\) 6.09773e11 0.0725212
\(746\) 3.14150e11 0.0371375
\(747\) −4.32578e12 −0.508302
\(748\) 4.32743e12 0.505444
\(749\) −1.81594e13 −2.10831
\(750\) 2.35774e11 0.0272095
\(751\) −2.00731e12 −0.230268 −0.115134 0.993350i \(-0.536730\pi\)
−0.115134 + 0.993350i \(0.536730\pi\)
\(752\) −4.76103e11 −0.0542901
\(753\) −6.17513e11 −0.0699952
\(754\) 6.75805e11 0.0761466
\(755\) 3.94843e12 0.442246
\(756\) −3.07605e12 −0.342488
\(757\) −2.31160e12 −0.255848 −0.127924 0.991784i \(-0.540831\pi\)
−0.127924 + 0.991784i \(0.540831\pi\)
\(758\) −1.91024e11 −0.0210172
\(759\) 1.72045e13 1.88172
\(760\) 2.52851e11 0.0274918
\(761\) −7.94917e12 −0.859193 −0.429597 0.903021i \(-0.641344\pi\)
−0.429597 + 0.903021i \(0.641344\pi\)
\(762\) 1.21463e11 0.0130511
\(763\) −5.57953e12 −0.595987
\(764\) −3.61528e12 −0.383903
\(765\) −3.05564e11 −0.0322571
\(766\) −3.55207e11 −0.0372779
\(767\) −7.14148e11 −0.0745091
\(768\) 5.31179e12 0.550955
\(769\) −9.28671e12 −0.957621 −0.478810 0.877918i \(-0.658932\pi\)
−0.478810 + 0.877918i \(0.658932\pi\)
\(770\) −8.65285e11 −0.0887056
\(771\) 4.44577e12 0.453109
\(772\) −9.17087e12 −0.929250
\(773\) −4.08955e12 −0.411972 −0.205986 0.978555i \(-0.566040\pi\)
−0.205986 + 0.978555i \(0.566040\pi\)
\(774\) 2.77974e11 0.0278400
\(775\) −1.14962e13 −1.14471
\(776\) 2.20074e12 0.217866
\(777\) −1.12754e13 −1.10978
\(778\) −9.05227e11 −0.0885828
\(779\) 1.85372e12 0.180354
\(780\) −1.26931e12 −0.122784
\(781\) 2.19610e13 2.11214
\(782\) 3.06034e11 0.0292644
\(783\) −3.96929e12 −0.377385
\(784\) 2.29142e13 2.16612
\(785\) −4.60711e12 −0.433027
\(786\) 5.75075e10 0.00537432
\(787\) 1.69890e13 1.57864 0.789318 0.613985i \(-0.210434\pi\)
0.789318 + 0.613985i \(0.210434\pi\)
\(788\) −1.44465e13 −1.33473
\(789\) −7.71278e11 −0.0708540
\(790\) 3.26427e11 0.0298170
\(791\) 1.56571e13 1.42206
\(792\) 9.78860e11 0.0884010
\(793\) 4.39343e12 0.394525
\(794\) 1.80011e11 0.0160734
\(795\) 1.07923e12 0.0958209
\(796\) 1.87932e13 1.65917
\(797\) 1.39053e13 1.22072 0.610362 0.792123i \(-0.291024\pi\)
0.610362 + 0.792123i \(0.291024\pi\)
\(798\) −4.36403e11 −0.0380956
\(799\) 1.64395e11 0.0142701
\(800\) 2.01709e12 0.174109
\(801\) −3.86966e12 −0.332144
\(802\) −1.06333e11 −0.00907578
\(803\) 5.03108e12 0.427013
\(804\) −3.28325e10 −0.00277110
\(805\) 1.32311e13 1.11049
\(806\) −6.18822e11 −0.0516485
\(807\) 2.03073e12 0.168547
\(808\) −1.73115e12 −0.142884
\(809\) −1.89067e12 −0.155184 −0.0775921 0.996985i \(-0.524723\pi\)
−0.0775921 + 0.996985i \(0.524723\pi\)
\(810\) −3.44794e10 −0.00281434
\(811\) −6.08028e12 −0.493548 −0.246774 0.969073i \(-0.579371\pi\)
−0.246774 + 0.969073i \(0.579371\pi\)
\(812\) 4.32311e13 3.48975
\(813\) 4.33852e11 0.0348285
\(814\) 1.78989e12 0.142895
\(815\) −2.88246e11 −0.0228851
\(816\) −1.86935e12 −0.147600
\(817\) −8.52701e12 −0.669572
\(818\) −8.18058e11 −0.0638843
\(819\) 4.39160e12 0.341071
\(820\) −1.59514e12 −0.123208
\(821\) 1.01770e13 0.781768 0.390884 0.920440i \(-0.372169\pi\)
0.390884 + 0.920440i \(0.372169\pi\)
\(822\) −4.57973e11 −0.0349878
\(823\) 1.27885e13 0.971671 0.485836 0.874050i \(-0.338515\pi\)
0.485836 + 0.874050i \(0.338515\pi\)
\(824\) 5.18688e11 0.0391953
\(825\) −1.29510e13 −0.973333
\(826\) 2.11283e11 0.0157926
\(827\) −1.42977e12 −0.106290 −0.0531449 0.998587i \(-0.516925\pi\)
−0.0531449 + 0.998587i \(0.516925\pi\)
\(828\) −7.46664e12 −0.552063
\(829\) −1.01993e12 −0.0750023 −0.0375011 0.999297i \(-0.511940\pi\)
−0.0375011 + 0.999297i \(0.511940\pi\)
\(830\) 5.28097e11 0.0386244
\(831\) −1.13246e13 −0.823794
\(832\) −7.69259e12 −0.556568
\(833\) −7.91211e12 −0.569364
\(834\) −1.07179e12 −0.0767121
\(835\) 8.52654e12 0.606993
\(836\) −1.49789e13 −1.06060
\(837\) 3.63460e12 0.255972
\(838\) −1.59417e12 −0.111670
\(839\) −2.59347e13 −1.80697 −0.903487 0.428616i \(-0.859001\pi\)
−0.903487 + 0.428616i \(0.859001\pi\)
\(840\) 7.52793e11 0.0521698
\(841\) 4.12776e13 2.84533
\(842\) 1.26848e12 0.0869718
\(843\) 4.56421e12 0.311273
\(844\) 2.00470e13 1.35990
\(845\) −3.72039e12 −0.251035
\(846\) 1.85501e10 0.00124503
\(847\) 7.59765e13 5.07229
\(848\) 6.60239e12 0.438450
\(849\) −1.20888e13 −0.798543
\(850\) −2.30373e11 −0.0151372
\(851\) −2.73694e13 −1.78888
\(852\) −9.53092e12 −0.619664
\(853\) −7.48082e12 −0.483814 −0.241907 0.970299i \(-0.577773\pi\)
−0.241907 + 0.970299i \(0.577773\pi\)
\(854\) −1.29981e12 −0.0836217
\(855\) 1.05767e12 0.0676868
\(856\) −2.50791e12 −0.159654
\(857\) 9.78179e12 0.619448 0.309724 0.950827i \(-0.399763\pi\)
0.309724 + 0.950827i \(0.399763\pi\)
\(858\) −6.97135e11 −0.0439161
\(859\) 4.63523e12 0.290471 0.145235 0.989397i \(-0.453606\pi\)
0.145235 + 0.989397i \(0.453606\pi\)
\(860\) 7.33756e12 0.457413
\(861\) 5.51894e12 0.342248
\(862\) −8.85702e11 −0.0546393
\(863\) −2.36590e13 −1.45194 −0.725968 0.687729i \(-0.758608\pi\)
−0.725968 + 0.687729i \(0.758608\pi\)
\(864\) −6.37718e11 −0.0389329
\(865\) 7.22466e11 0.0438778
\(866\) −1.28575e12 −0.0776830
\(867\) −8.96014e12 −0.538554
\(868\) −3.95859e13 −2.36702
\(869\) −3.87646e13 −2.30593
\(870\) 4.84576e11 0.0286764
\(871\) 4.68741e10 0.00275963
\(872\) −7.70563e11 −0.0451319
\(873\) 9.20567e12 0.536403
\(874\) −1.05930e12 −0.0614070
\(875\) −2.15328e13 −1.24183
\(876\) −2.18345e12 −0.125278
\(877\) 2.87031e13 1.63844 0.819219 0.573481i \(-0.194407\pi\)
0.819219 + 0.573481i \(0.194407\pi\)
\(878\) −1.34809e12 −0.0765583
\(879\) 7.28379e12 0.411536
\(880\) 1.28296e13 0.721175
\(881\) 6.60321e12 0.369287 0.184643 0.982806i \(-0.440887\pi\)
0.184643 + 0.982806i \(0.440887\pi\)
\(882\) −8.92790e11 −0.0496753
\(883\) −3.16627e13 −1.75277 −0.876385 0.481611i \(-0.840052\pi\)
−0.876385 + 0.481611i \(0.840052\pi\)
\(884\) 2.68129e12 0.147675
\(885\) −5.12069e11 −0.0280597
\(886\) −7.71060e11 −0.0420374
\(887\) 2.15265e13 1.16766 0.583831 0.811875i \(-0.301553\pi\)
0.583831 + 0.811875i \(0.301553\pi\)
\(888\) −1.55720e12 −0.0840399
\(889\) −1.10930e13 −0.595650
\(890\) 4.72413e11 0.0252387
\(891\) 4.09457e12 0.217650
\(892\) −7.02704e12 −0.371647
\(893\) −5.69033e11 −0.0299438
\(894\) −1.45345e11 −0.00760996
\(895\) −1.00798e13 −0.525108
\(896\) 9.25364e12 0.479652
\(897\) 1.06599e13 0.549780
\(898\) −1.80291e12 −0.0925189
\(899\) −5.10810e13 −2.60820
\(900\) 5.62066e12 0.285559
\(901\) −2.27976e12 −0.115246
\(902\) −8.76092e11 −0.0440677
\(903\) −2.53868e13 −1.27061
\(904\) 2.16233e12 0.107687
\(905\) −1.28950e13 −0.639001
\(906\) −9.41148e11 −0.0464068
\(907\) −2.11783e13 −1.03910 −0.519550 0.854440i \(-0.673901\pi\)
−0.519550 + 0.854440i \(0.673901\pi\)
\(908\) 8.92869e12 0.435915
\(909\) −7.24139e12 −0.351791
\(910\) −5.36132e11 −0.0259171
\(911\) 1.02131e13 0.491273 0.245636 0.969362i \(-0.421003\pi\)
0.245636 + 0.969362i \(0.421003\pi\)
\(912\) 6.47054e12 0.309716
\(913\) −6.27137e13 −2.98706
\(914\) 2.11519e12 0.100252
\(915\) 3.15024e12 0.148576
\(916\) 3.54672e13 1.66455
\(917\) −5.25205e12 −0.245282
\(918\) 7.28342e10 0.00338488
\(919\) −2.95207e13 −1.36523 −0.682616 0.730777i \(-0.739158\pi\)
−0.682616 + 0.730777i \(0.739158\pi\)
\(920\) 1.82729e12 0.0840935
\(921\) −3.84957e12 −0.176296
\(922\) −4.79949e11 −0.0218729
\(923\) 1.36071e13 0.617101
\(924\) −4.45955e13 −2.01265
\(925\) 2.06028e13 0.925314
\(926\) 4.95532e10 0.00221474
\(927\) 2.16967e12 0.0965016
\(928\) 8.96255e12 0.396703
\(929\) −1.45132e12 −0.0639280 −0.0319640 0.999489i \(-0.510176\pi\)
−0.0319640 + 0.999489i \(0.510176\pi\)
\(930\) −4.43717e11 −0.0194506
\(931\) 2.73869e13 1.19473
\(932\) 9.48418e12 0.411745
\(933\) −2.09236e13 −0.904001
\(934\) 2.00736e12 0.0863107
\(935\) −4.42996e12 −0.189560
\(936\) 6.06503e11 0.0258281
\(937\) 2.21200e13 0.937467 0.468734 0.883340i \(-0.344710\pi\)
0.468734 + 0.883340i \(0.344710\pi\)
\(938\) −1.38678e10 −0.000584919 0
\(939\) 1.24292e13 0.521734
\(940\) 4.89658e11 0.0204559
\(941\) 1.25780e12 0.0522947 0.0261473 0.999658i \(-0.491676\pi\)
0.0261473 + 0.999658i \(0.491676\pi\)
\(942\) 1.09815e12 0.0454394
\(943\) 1.33964e13 0.551677
\(944\) −3.13269e12 −0.128394
\(945\) 3.14893e12 0.128446
\(946\) 4.02997e12 0.163603
\(947\) 2.05492e13 0.830272 0.415136 0.909759i \(-0.363734\pi\)
0.415136 + 0.909759i \(0.363734\pi\)
\(948\) 1.68236e13 0.676520
\(949\) 3.11726e12 0.124760
\(950\) 7.97409e11 0.0317632
\(951\) 5.38464e11 0.0213474
\(952\) −1.59020e12 −0.0627459
\(953\) −8.87114e12 −0.348387 −0.174193 0.984711i \(-0.555732\pi\)
−0.174193 + 0.984711i \(0.555732\pi\)
\(954\) −2.57244e11 −0.0100549
\(955\) 3.70093e12 0.143978
\(956\) −4.08467e13 −1.58160
\(957\) −5.75454e13 −2.21772
\(958\) −1.80434e12 −0.0692107
\(959\) 4.18257e13 1.59683
\(960\) −5.51586e12 −0.209601
\(961\) 2.03343e13 0.769083
\(962\) 1.10902e12 0.0417496
\(963\) −1.04906e13 −0.393080
\(964\) 2.46543e12 0.0919487
\(965\) 9.38815e12 0.348503
\(966\) −3.15377e12 −0.116529
\(967\) −3.66535e13 −1.34802 −0.674011 0.738722i \(-0.735430\pi\)
−0.674011 + 0.738722i \(0.735430\pi\)
\(968\) 1.04928e13 0.384105
\(969\) −2.23423e12 −0.0814087
\(970\) −1.12384e12 −0.0407598
\(971\) 7.42335e12 0.267987 0.133993 0.990982i \(-0.457220\pi\)
0.133993 + 0.990982i \(0.457220\pi\)
\(972\) −1.77702e12 −0.0638547
\(973\) 9.78847e13 3.50112
\(974\) −3.98683e11 −0.0141943
\(975\) −8.02447e12 −0.284378
\(976\) 1.92723e13 0.679843
\(977\) −3.60999e13 −1.26760 −0.633798 0.773498i \(-0.718505\pi\)
−0.633798 + 0.773498i \(0.718505\pi\)
\(978\) 6.87062e10 0.00240144
\(979\) −5.61010e13 −1.95186
\(980\) −2.35666e13 −0.816169
\(981\) −3.22326e12 −0.111118
\(982\) 1.89907e12 0.0651687
\(983\) 2.65953e13 0.908479 0.454239 0.890880i \(-0.349911\pi\)
0.454239 + 0.890880i \(0.349911\pi\)
\(984\) 7.62195e11 0.0259172
\(985\) 1.47888e13 0.500575
\(986\) −1.02362e12 −0.0344899
\(987\) −1.69414e12 −0.0568227
\(988\) −9.28096e12 −0.309875
\(989\) −6.16225e13 −2.04812
\(990\) −4.99870e11 −0.0165386
\(991\) −4.31087e13 −1.41982 −0.709910 0.704292i \(-0.751264\pi\)
−0.709910 + 0.704292i \(0.751264\pi\)
\(992\) −8.20683e12 −0.269075
\(993\) 1.46162e13 0.477048
\(994\) −4.02569e12 −0.130798
\(995\) −1.92384e13 −0.622251
\(996\) 2.72173e13 0.876352
\(997\) −2.69692e13 −0.864451 −0.432226 0.901765i \(-0.642272\pi\)
−0.432226 + 0.901765i \(0.642272\pi\)
\(998\) −6.94704e10 −0.00221673
\(999\) −6.51375e12 −0.206912
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 177.10.a.d.1.11 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.11 22 1.1 even 1 trivial