Properties

Label 177.14.a.c.1.7
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-107.990 q^{2} +729.000 q^{3} +3469.94 q^{4} +5614.85 q^{5} -78725.0 q^{6} -441395. q^{7} +509938. q^{8} +531441. q^{9} +O(q^{10})\) \(q-107.990 q^{2} +729.000 q^{3} +3469.94 q^{4} +5614.85 q^{5} -78725.0 q^{6} -441395. q^{7} +509938. q^{8} +531441. q^{9} -606350. q^{10} -9.58760e6 q^{11} +2.52958e6 q^{12} -1.04119e6 q^{13} +4.76664e7 q^{14} +4.09323e6 q^{15} -8.34941e7 q^{16} +8.94693e7 q^{17} -5.73906e7 q^{18} -1.31769e8 q^{19} +1.94832e7 q^{20} -3.21777e8 q^{21} +1.03537e9 q^{22} -6.51675e8 q^{23} +3.71745e8 q^{24} -1.18918e9 q^{25} +1.12438e8 q^{26} +3.87420e8 q^{27} -1.53161e9 q^{28} -4.82241e9 q^{29} -4.42029e8 q^{30} +6.29557e9 q^{31} +4.83916e9 q^{32} -6.98936e9 q^{33} -9.66183e9 q^{34} -2.47837e9 q^{35} +1.84407e9 q^{36} -1.75409e10 q^{37} +1.42298e10 q^{38} -7.59024e8 q^{39} +2.86322e9 q^{40} -3.34544e10 q^{41} +3.47488e10 q^{42} +1.01527e10 q^{43} -3.32684e10 q^{44} +2.98396e9 q^{45} +7.03747e10 q^{46} -7.21820e10 q^{47} -6.08672e10 q^{48} +9.79404e10 q^{49} +1.28420e11 q^{50} +6.52231e10 q^{51} -3.61285e9 q^{52} -1.09457e11 q^{53} -4.18377e10 q^{54} -5.38329e10 q^{55} -2.25084e11 q^{56} -9.60597e10 q^{57} +5.20774e11 q^{58} -4.21805e10 q^{59} +1.42032e10 q^{60} -2.31061e11 q^{61} -6.79861e11 q^{62} -2.34575e11 q^{63} +1.61401e11 q^{64} -5.84610e9 q^{65} +7.54784e11 q^{66} +1.73456e11 q^{67} +3.10453e11 q^{68} -4.75071e11 q^{69} +2.67640e11 q^{70} +1.31392e12 q^{71} +2.71002e11 q^{72} +1.72064e12 q^{73} +1.89425e12 q^{74} -8.66910e11 q^{75} -4.57231e11 q^{76} +4.23191e12 q^{77} +8.19674e10 q^{78} -2.25052e12 q^{79} -4.68807e11 q^{80} +2.82430e11 q^{81} +3.61276e12 q^{82} +2.25693e12 q^{83} -1.11655e12 q^{84} +5.02357e11 q^{85} -1.09639e12 q^{86} -3.51554e12 q^{87} -4.88908e12 q^{88} -3.90720e12 q^{89} -3.22239e11 q^{90} +4.59574e11 q^{91} -2.26127e12 q^{92} +4.58947e12 q^{93} +7.79497e12 q^{94} -7.39864e11 q^{95} +3.52775e12 q^{96} -9.75846e12 q^{97} -1.05766e13 q^{98} -5.09524e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −107.990 −1.19314 −0.596569 0.802562i \(-0.703470\pi\)
−0.596569 + 0.802562i \(0.703470\pi\)
\(3\) 729.000 0.577350
\(4\) 3469.94 0.423576
\(5\) 5614.85 0.160706 0.0803532 0.996766i \(-0.474395\pi\)
0.0803532 + 0.996766i \(0.474395\pi\)
\(6\) −78725.0 −0.688858
\(7\) −441395. −1.41804 −0.709022 0.705186i \(-0.750863\pi\)
−0.709022 + 0.705186i \(0.750863\pi\)
\(8\) 509938. 0.687752
\(9\) 531441. 0.333333
\(10\) −606350. −0.191745
\(11\) −9.58760e6 −1.63176 −0.815882 0.578219i \(-0.803748\pi\)
−0.815882 + 0.578219i \(0.803748\pi\)
\(12\) 2.52958e6 0.244552
\(13\) −1.04119e6 −0.0598269 −0.0299134 0.999552i \(-0.509523\pi\)
−0.0299134 + 0.999552i \(0.509523\pi\)
\(14\) 4.76664e7 1.69192
\(15\) 4.09323e6 0.0927839
\(16\) −8.34941e7 −1.24416
\(17\) 8.94693e7 0.898993 0.449496 0.893282i \(-0.351604\pi\)
0.449496 + 0.893282i \(0.351604\pi\)
\(18\) −5.73906e7 −0.397712
\(19\) −1.31769e8 −0.642562 −0.321281 0.946984i \(-0.604113\pi\)
−0.321281 + 0.946984i \(0.604113\pi\)
\(20\) 1.94832e7 0.0680714
\(21\) −3.21777e8 −0.818709
\(22\) 1.03537e9 1.94692
\(23\) −6.51675e8 −0.917910 −0.458955 0.888460i \(-0.651776\pi\)
−0.458955 + 0.888460i \(0.651776\pi\)
\(24\) 3.71745e8 0.397074
\(25\) −1.18918e9 −0.974173
\(26\) 1.12438e8 0.0713817
\(27\) 3.87420e8 0.192450
\(28\) −1.53161e9 −0.600650
\(29\) −4.82241e9 −1.50549 −0.752744 0.658313i \(-0.771270\pi\)
−0.752744 + 0.658313i \(0.771270\pi\)
\(30\) −4.42029e8 −0.110704
\(31\) 6.29557e9 1.27404 0.637021 0.770846i \(-0.280166\pi\)
0.637021 + 0.770846i \(0.280166\pi\)
\(32\) 4.83916e9 0.796700
\(33\) −6.98936e9 −0.942099
\(34\) −9.66183e9 −1.07262
\(35\) −2.47837e9 −0.227889
\(36\) 1.84407e9 0.141192
\(37\) −1.75409e10 −1.12393 −0.561966 0.827160i \(-0.689955\pi\)
−0.561966 + 0.827160i \(0.689955\pi\)
\(38\) 1.42298e10 0.766665
\(39\) −7.59024e8 −0.0345411
\(40\) 2.86322e9 0.110526
\(41\) −3.34544e10 −1.09991 −0.549956 0.835193i \(-0.685356\pi\)
−0.549956 + 0.835193i \(0.685356\pi\)
\(42\) 3.47488e10 0.976832
\(43\) 1.01527e10 0.244926 0.122463 0.992473i \(-0.460921\pi\)
0.122463 + 0.992473i \(0.460921\pi\)
\(44\) −3.32684e10 −0.691177
\(45\) 2.98396e9 0.0535688
\(46\) 7.03747e10 1.09519
\(47\) −7.21820e10 −0.976771 −0.488386 0.872628i \(-0.662414\pi\)
−0.488386 + 0.872628i \(0.662414\pi\)
\(48\) −6.08672e10 −0.718316
\(49\) 9.79404e10 1.01085
\(50\) 1.28420e11 1.16232
\(51\) 6.52231e10 0.519034
\(52\) −3.61285e9 −0.0253413
\(53\) −1.09457e11 −0.678347 −0.339173 0.940724i \(-0.610147\pi\)
−0.339173 + 0.940724i \(0.610147\pi\)
\(54\) −4.18377e10 −0.229619
\(55\) −5.38329e10 −0.262235
\(56\) −2.25084e11 −0.975264
\(57\) −9.60597e10 −0.370984
\(58\) 5.20774e11 1.79625
\(59\) −4.21805e10 −0.130189
\(60\) 1.42032e10 0.0393011
\(61\) −2.31061e11 −0.574226 −0.287113 0.957897i \(-0.592695\pi\)
−0.287113 + 0.957897i \(0.592695\pi\)
\(62\) −6.79861e11 −1.52011
\(63\) −2.34575e11 −0.472682
\(64\) 1.61401e11 0.293586
\(65\) −5.84610e9 −0.00961456
\(66\) 7.54784e11 1.12405
\(67\) 1.73456e11 0.234263 0.117131 0.993116i \(-0.462630\pi\)
0.117131 + 0.993116i \(0.462630\pi\)
\(68\) 3.10453e11 0.380792
\(69\) −4.75071e11 −0.529955
\(70\) 2.67640e11 0.271903
\(71\) 1.31392e12 1.21728 0.608639 0.793447i \(-0.291716\pi\)
0.608639 + 0.793447i \(0.291716\pi\)
\(72\) 2.71002e11 0.229251
\(73\) 1.72064e12 1.33073 0.665365 0.746518i \(-0.268276\pi\)
0.665365 + 0.746518i \(0.268276\pi\)
\(74\) 1.89425e12 1.34101
\(75\) −8.66910e11 −0.562439
\(76\) −4.57231e11 −0.272174
\(77\) 4.23191e12 2.31391
\(78\) 8.19674e10 0.0412122
\(79\) −2.25052e12 −1.04162 −0.520808 0.853674i \(-0.674369\pi\)
−0.520808 + 0.853674i \(0.674369\pi\)
\(80\) −4.68807e11 −0.199944
\(81\) 2.82430e11 0.111111
\(82\) 3.61276e12 1.31235
\(83\) 2.25693e12 0.757725 0.378862 0.925453i \(-0.376315\pi\)
0.378862 + 0.925453i \(0.376315\pi\)
\(84\) −1.11655e12 −0.346786
\(85\) 5.02357e11 0.144474
\(86\) −1.09639e12 −0.292230
\(87\) −3.51554e12 −0.869194
\(88\) −4.88908e12 −1.12225
\(89\) −3.90720e12 −0.833356 −0.416678 0.909054i \(-0.636806\pi\)
−0.416678 + 0.909054i \(0.636806\pi\)
\(90\) −3.22239e11 −0.0639149
\(91\) 4.59574e11 0.0848372
\(92\) −2.26127e12 −0.388805
\(93\) 4.58947e12 0.735569
\(94\) 7.79497e12 1.16542
\(95\) −7.39864e11 −0.103264
\(96\) 3.52775e12 0.459975
\(97\) −9.75846e12 −1.18950 −0.594751 0.803910i \(-0.702749\pi\)
−0.594751 + 0.803910i \(0.702749\pi\)
\(98\) −1.05766e13 −1.20608
\(99\) −5.09524e12 −0.543921
\(100\) −4.12637e12 −0.412637
\(101\) −4.75087e12 −0.445332 −0.222666 0.974895i \(-0.571476\pi\)
−0.222666 + 0.974895i \(0.571476\pi\)
\(102\) −7.04347e12 −0.619278
\(103\) −2.35557e13 −1.94381 −0.971904 0.235378i \(-0.924367\pi\)
−0.971904 + 0.235378i \(0.924367\pi\)
\(104\) −5.30940e11 −0.0411461
\(105\) −1.80673e12 −0.131572
\(106\) 1.18204e13 0.809361
\(107\) −2.68262e13 −1.72808 −0.864041 0.503422i \(-0.832074\pi\)
−0.864041 + 0.503422i \(0.832074\pi\)
\(108\) 1.34432e12 0.0815173
\(109\) −1.67914e13 −0.958989 −0.479494 0.877545i \(-0.659180\pi\)
−0.479494 + 0.877545i \(0.659180\pi\)
\(110\) 5.81344e12 0.312882
\(111\) −1.27873e13 −0.648903
\(112\) 3.68539e13 1.76427
\(113\) 1.40641e12 0.0635482 0.0317741 0.999495i \(-0.489884\pi\)
0.0317741 + 0.999495i \(0.489884\pi\)
\(114\) 1.03735e13 0.442634
\(115\) −3.65906e12 −0.147514
\(116\) −1.67335e13 −0.637689
\(117\) −5.53329e11 −0.0199423
\(118\) 4.55509e12 0.155333
\(119\) −3.94913e13 −1.27481
\(120\) 2.08729e12 0.0638123
\(121\) 5.73993e13 1.66265
\(122\) 2.49524e13 0.685130
\(123\) −2.43883e13 −0.635035
\(124\) 2.18452e13 0.539654
\(125\) −1.35311e13 −0.317262
\(126\) 2.53319e13 0.563974
\(127\) 5.02216e13 1.06210 0.531051 0.847340i \(-0.321797\pi\)
0.531051 + 0.847340i \(0.321797\pi\)
\(128\) −5.70721e13 −1.14699
\(129\) 7.40129e12 0.141408
\(130\) 6.31323e11 0.0114715
\(131\) −7.45761e13 −1.28925 −0.644624 0.764500i \(-0.722986\pi\)
−0.644624 + 0.764500i \(0.722986\pi\)
\(132\) −2.42526e13 −0.399051
\(133\) 5.81622e13 0.911182
\(134\) −1.87316e13 −0.279508
\(135\) 2.17531e12 0.0309280
\(136\) 4.56238e13 0.618284
\(137\) −5.10006e13 −0.659010 −0.329505 0.944154i \(-0.606882\pi\)
−0.329505 + 0.944154i \(0.606882\pi\)
\(138\) 5.13031e13 0.632310
\(139\) −2.16189e12 −0.0254236 −0.0127118 0.999919i \(-0.504046\pi\)
−0.0127118 + 0.999919i \(0.504046\pi\)
\(140\) −8.59977e12 −0.0965283
\(141\) −5.26207e13 −0.563939
\(142\) −1.41891e14 −1.45238
\(143\) 9.98247e12 0.0976233
\(144\) −4.43722e13 −0.414720
\(145\) −2.70771e13 −0.241942
\(146\) −1.85812e14 −1.58774
\(147\) 7.13985e13 0.583615
\(148\) −6.08658e13 −0.476071
\(149\) 1.34291e14 1.00539 0.502696 0.864463i \(-0.332342\pi\)
0.502696 + 0.864463i \(0.332342\pi\)
\(150\) 9.36180e13 0.671067
\(151\) −1.49735e14 −1.02795 −0.513977 0.857804i \(-0.671829\pi\)
−0.513977 + 0.857804i \(0.671829\pi\)
\(152\) −6.71941e13 −0.441924
\(153\) 4.75477e13 0.299664
\(154\) −4.57006e14 −2.76082
\(155\) 3.53487e13 0.204747
\(156\) −2.63377e12 −0.0146308
\(157\) −8.62203e12 −0.0459475 −0.0229737 0.999736i \(-0.507313\pi\)
−0.0229737 + 0.999736i \(0.507313\pi\)
\(158\) 2.43035e14 1.24279
\(159\) −7.97944e13 −0.391644
\(160\) 2.71712e13 0.128035
\(161\) 2.87646e14 1.30164
\(162\) −3.04997e13 −0.132571
\(163\) −1.36347e14 −0.569411 −0.284706 0.958615i \(-0.591896\pi\)
−0.284706 + 0.958615i \(0.591896\pi\)
\(164\) −1.16085e14 −0.465897
\(165\) −3.92442e13 −0.151401
\(166\) −2.43727e14 −0.904069
\(167\) −1.40374e14 −0.500759 −0.250379 0.968148i \(-0.580555\pi\)
−0.250379 + 0.968148i \(0.580555\pi\)
\(168\) −1.64086e14 −0.563069
\(169\) −3.01791e14 −0.996421
\(170\) −5.42497e13 −0.172377
\(171\) −7.00275e13 −0.214187
\(172\) 3.52291e13 0.103745
\(173\) 2.88987e14 0.819557 0.409778 0.912185i \(-0.365606\pi\)
0.409778 + 0.912185i \(0.365606\pi\)
\(174\) 3.79644e14 1.03707
\(175\) 5.24896e14 1.38142
\(176\) 8.00508e14 2.03017
\(177\) −3.07496e13 −0.0751646
\(178\) 4.21940e14 0.994307
\(179\) 3.70795e14 0.842537 0.421268 0.906936i \(-0.361585\pi\)
0.421268 + 0.906936i \(0.361585\pi\)
\(180\) 1.03542e13 0.0226905
\(181\) 5.97550e14 1.26317 0.631587 0.775305i \(-0.282404\pi\)
0.631587 + 0.775305i \(0.282404\pi\)
\(182\) −4.96296e13 −0.101222
\(183\) −1.68443e14 −0.331529
\(184\) −3.32314e14 −0.631295
\(185\) −9.84895e13 −0.180623
\(186\) −4.95619e14 −0.877634
\(187\) −8.57796e14 −1.46694
\(188\) −2.50467e14 −0.413737
\(189\) −1.71005e14 −0.272903
\(190\) 7.98983e13 0.123208
\(191\) −5.89234e14 −0.878155 −0.439077 0.898449i \(-0.644695\pi\)
−0.439077 + 0.898449i \(0.644695\pi\)
\(192\) 1.17661e14 0.169502
\(193\) −5.66671e14 −0.789239 −0.394619 0.918845i \(-0.629124\pi\)
−0.394619 + 0.918845i \(0.629124\pi\)
\(194\) 1.05382e15 1.41924
\(195\) −4.26181e12 −0.00555097
\(196\) 3.39847e14 0.428173
\(197\) −3.03408e14 −0.369825 −0.184912 0.982755i \(-0.559200\pi\)
−0.184912 + 0.982755i \(0.559200\pi\)
\(198\) 5.50237e14 0.648973
\(199\) 7.49175e14 0.855142 0.427571 0.903982i \(-0.359369\pi\)
0.427571 + 0.903982i \(0.359369\pi\)
\(200\) −6.06406e14 −0.669990
\(201\) 1.26449e14 0.135252
\(202\) 5.13048e14 0.531342
\(203\) 2.12859e15 2.13485
\(204\) 2.26320e14 0.219850
\(205\) −1.87842e14 −0.176763
\(206\) 2.54379e15 2.31923
\(207\) −3.46327e14 −0.305970
\(208\) 8.69329e13 0.0744342
\(209\) 1.26335e15 1.04851
\(210\) 1.95109e14 0.156983
\(211\) 6.38277e14 0.497936 0.248968 0.968512i \(-0.419909\pi\)
0.248968 + 0.968512i \(0.419909\pi\)
\(212\) −3.79810e14 −0.287332
\(213\) 9.57849e14 0.702796
\(214\) 2.89697e15 2.06184
\(215\) 5.70056e13 0.0393612
\(216\) 1.97560e14 0.132358
\(217\) −2.77883e15 −1.80665
\(218\) 1.81331e15 1.14421
\(219\) 1.25434e15 0.768298
\(220\) −1.86797e14 −0.111076
\(221\) −9.31542e13 −0.0537839
\(222\) 1.38091e15 0.774230
\(223\) 2.42026e15 1.31789 0.658946 0.752190i \(-0.271002\pi\)
0.658946 + 0.752190i \(0.271002\pi\)
\(224\) −2.13598e15 −1.12976
\(225\) −6.31977e14 −0.324724
\(226\) −1.51879e14 −0.0758218
\(227\) 2.13210e15 1.03428 0.517141 0.855900i \(-0.326996\pi\)
0.517141 + 0.855900i \(0.326996\pi\)
\(228\) −3.33321e14 −0.157140
\(229\) −1.66361e15 −0.762292 −0.381146 0.924515i \(-0.624470\pi\)
−0.381146 + 0.924515i \(0.624470\pi\)
\(230\) 3.95143e14 0.176004
\(231\) 3.08507e15 1.33594
\(232\) −2.45913e15 −1.03540
\(233\) −1.58920e15 −0.650677 −0.325338 0.945598i \(-0.605478\pi\)
−0.325338 + 0.945598i \(0.605478\pi\)
\(234\) 5.97542e13 0.0237939
\(235\) −4.05291e14 −0.156973
\(236\) −1.46364e14 −0.0551449
\(237\) −1.64063e15 −0.601377
\(238\) 4.26468e15 1.52103
\(239\) 5.29417e15 1.83743 0.918716 0.394918i \(-0.129227\pi\)
0.918716 + 0.394918i \(0.129227\pi\)
\(240\) −3.41760e14 −0.115438
\(241\) 3.21625e14 0.105740 0.0528700 0.998601i \(-0.483163\pi\)
0.0528700 + 0.998601i \(0.483163\pi\)
\(242\) −6.19857e15 −1.98377
\(243\) 2.05891e14 0.0641500
\(244\) −8.01767e14 −0.243228
\(245\) 5.49920e14 0.162450
\(246\) 2.63370e15 0.757684
\(247\) 1.37196e14 0.0384425
\(248\) 3.21035e15 0.876226
\(249\) 1.64531e15 0.437472
\(250\) 1.46123e15 0.378537
\(251\) 6.74063e15 1.70146 0.850729 0.525605i \(-0.176161\pi\)
0.850729 + 0.525605i \(0.176161\pi\)
\(252\) −8.13962e14 −0.200217
\(253\) 6.24799e15 1.49781
\(254\) −5.42346e15 −1.26723
\(255\) 3.66218e14 0.0834120
\(256\) 4.84105e15 1.07493
\(257\) 5.56284e15 1.20429 0.602145 0.798386i \(-0.294313\pi\)
0.602145 + 0.798386i \(0.294313\pi\)
\(258\) −7.99268e14 −0.168719
\(259\) 7.74246e15 1.59379
\(260\) −2.02856e13 −0.00407250
\(261\) −2.56283e15 −0.501829
\(262\) 8.05351e15 1.53825
\(263\) −3.16501e15 −0.589743 −0.294871 0.955537i \(-0.595277\pi\)
−0.294871 + 0.955537i \(0.595277\pi\)
\(264\) −3.56414e15 −0.647931
\(265\) −6.14587e14 −0.109015
\(266\) −6.28096e15 −1.08717
\(267\) −2.84835e15 −0.481138
\(268\) 6.01882e14 0.0992282
\(269\) 1.06354e16 1.71145 0.855725 0.517432i \(-0.173112\pi\)
0.855725 + 0.517432i \(0.173112\pi\)
\(270\) −2.34913e14 −0.0369013
\(271\) −4.20543e15 −0.644927 −0.322463 0.946582i \(-0.604511\pi\)
−0.322463 + 0.946582i \(0.604511\pi\)
\(272\) −7.47016e15 −1.11849
\(273\) 3.35029e14 0.0489808
\(274\) 5.50758e15 0.786289
\(275\) 1.14013e16 1.58962
\(276\) −1.64847e15 −0.224477
\(277\) −2.75757e15 −0.366782 −0.183391 0.983040i \(-0.558707\pi\)
−0.183391 + 0.983040i \(0.558707\pi\)
\(278\) 2.33463e14 0.0303338
\(279\) 3.34572e15 0.424681
\(280\) −1.26381e15 −0.156731
\(281\) −6.56319e15 −0.795286 −0.397643 0.917540i \(-0.630172\pi\)
−0.397643 + 0.917540i \(0.630172\pi\)
\(282\) 5.68253e15 0.672857
\(283\) −7.25297e15 −0.839275 −0.419637 0.907692i \(-0.637843\pi\)
−0.419637 + 0.907692i \(0.637843\pi\)
\(284\) 4.55923e15 0.515611
\(285\) −5.39361e14 −0.0596194
\(286\) −1.07801e15 −0.116478
\(287\) 1.47666e16 1.55973
\(288\) 2.57173e15 0.265567
\(289\) −1.89982e15 −0.191812
\(290\) 2.92407e15 0.288669
\(291\) −7.11392e15 −0.686759
\(292\) 5.97050e15 0.563666
\(293\) 1.91677e16 1.76983 0.884914 0.465754i \(-0.154217\pi\)
0.884914 + 0.465754i \(0.154217\pi\)
\(294\) −7.71036e15 −0.696333
\(295\) −2.36837e14 −0.0209222
\(296\) −8.94476e15 −0.772988
\(297\) −3.71443e15 −0.314033
\(298\) −1.45021e16 −1.19957
\(299\) 6.78515e14 0.0549157
\(300\) −3.00812e15 −0.238236
\(301\) −4.48133e15 −0.347316
\(302\) 1.61700e16 1.22649
\(303\) −3.46338e15 −0.257112
\(304\) 1.10020e16 0.799450
\(305\) −1.29737e15 −0.0922818
\(306\) −5.13469e15 −0.357540
\(307\) −2.39237e16 −1.63090 −0.815451 0.578825i \(-0.803511\pi\)
−0.815451 + 0.578825i \(0.803511\pi\)
\(308\) 1.46845e16 0.980119
\(309\) −1.71721e16 −1.12226
\(310\) −3.81732e15 −0.244291
\(311\) 1.29630e16 0.812388 0.406194 0.913787i \(-0.366856\pi\)
0.406194 + 0.913787i \(0.366856\pi\)
\(312\) −3.87055e14 −0.0237557
\(313\) 5.96928e15 0.358826 0.179413 0.983774i \(-0.442580\pi\)
0.179413 + 0.983774i \(0.442580\pi\)
\(314\) 9.31097e14 0.0548217
\(315\) −1.31711e15 −0.0759630
\(316\) −7.80917e15 −0.441204
\(317\) −2.23734e16 −1.23836 −0.619180 0.785249i \(-0.712535\pi\)
−0.619180 + 0.785249i \(0.712535\pi\)
\(318\) 8.61704e15 0.467285
\(319\) 4.62353e16 2.45660
\(320\) 9.06242e14 0.0471812
\(321\) −1.95563e16 −0.997709
\(322\) −3.10630e16 −1.55303
\(323\) −1.17893e16 −0.577659
\(324\) 9.80013e14 0.0470640
\(325\) 1.23815e15 0.0582818
\(326\) 1.47242e16 0.679386
\(327\) −1.22409e16 −0.553672
\(328\) −1.70597e16 −0.756468
\(329\) 3.18608e16 1.38511
\(330\) 4.23800e15 0.180643
\(331\) −8.39910e15 −0.351035 −0.175518 0.984476i \(-0.556160\pi\)
−0.175518 + 0.984476i \(0.556160\pi\)
\(332\) 7.83142e15 0.320954
\(333\) −9.32195e15 −0.374644
\(334\) 1.51590e16 0.597474
\(335\) 9.73930e14 0.0376475
\(336\) 2.68665e16 1.01860
\(337\) 6.82874e15 0.253949 0.126974 0.991906i \(-0.459473\pi\)
0.126974 + 0.991906i \(0.459473\pi\)
\(338\) 3.25906e16 1.18887
\(339\) 1.02528e15 0.0366896
\(340\) 1.74315e15 0.0611957
\(341\) −6.03593e16 −2.07894
\(342\) 7.56230e15 0.255555
\(343\) −4.64057e14 −0.0153872
\(344\) 5.17722e15 0.168448
\(345\) −2.66745e15 −0.0851672
\(346\) −3.12079e16 −0.977844
\(347\) −2.67733e16 −0.823305 −0.411653 0.911341i \(-0.635048\pi\)
−0.411653 + 0.911341i \(0.635048\pi\)
\(348\) −1.21987e16 −0.368170
\(349\) 5.66261e16 1.67746 0.838729 0.544549i \(-0.183299\pi\)
0.838729 + 0.544549i \(0.183299\pi\)
\(350\) −5.66838e16 −1.64823
\(351\) −4.03377e14 −0.0115137
\(352\) −4.63959e16 −1.30003
\(353\) −1.05506e16 −0.290229 −0.145114 0.989415i \(-0.546355\pi\)
−0.145114 + 0.989415i \(0.546355\pi\)
\(354\) 3.32066e15 0.0896817
\(355\) 7.37747e15 0.195624
\(356\) −1.35577e16 −0.352990
\(357\) −2.87891e16 −0.736013
\(358\) −4.00423e16 −1.00526
\(359\) 4.74699e16 1.17032 0.585159 0.810918i \(-0.301032\pi\)
0.585159 + 0.810918i \(0.301032\pi\)
\(360\) 1.52163e15 0.0368421
\(361\) −2.46899e16 −0.587113
\(362\) −6.45297e16 −1.50714
\(363\) 4.18441e16 0.959933
\(364\) 1.59469e15 0.0359350
\(365\) 9.66111e15 0.213857
\(366\) 1.81903e16 0.395560
\(367\) 1.91625e16 0.409375 0.204688 0.978827i \(-0.434382\pi\)
0.204688 + 0.978827i \(0.434382\pi\)
\(368\) 5.44110e16 1.14203
\(369\) −1.77790e16 −0.366638
\(370\) 1.06359e16 0.215508
\(371\) 4.83139e16 0.961926
\(372\) 1.59252e16 0.311569
\(373\) −4.60121e16 −0.884635 −0.442318 0.896858i \(-0.645844\pi\)
−0.442318 + 0.896858i \(0.645844\pi\)
\(374\) 9.26337e16 1.75026
\(375\) −9.86418e15 −0.183171
\(376\) −3.68083e16 −0.671777
\(377\) 5.02103e15 0.0900687
\(378\) 1.84669e16 0.325611
\(379\) 4.29578e15 0.0744539 0.0372269 0.999307i \(-0.488148\pi\)
0.0372269 + 0.999307i \(0.488148\pi\)
\(380\) −2.56728e15 −0.0437401
\(381\) 3.66116e16 0.613205
\(382\) 6.36317e16 1.04776
\(383\) −3.00763e16 −0.486892 −0.243446 0.969914i \(-0.578278\pi\)
−0.243446 + 0.969914i \(0.578278\pi\)
\(384\) −4.16056e16 −0.662215
\(385\) 2.37616e16 0.371861
\(386\) 6.11950e16 0.941670
\(387\) 5.39554e15 0.0816420
\(388\) −3.38613e16 −0.503845
\(389\) 1.20445e17 1.76244 0.881221 0.472705i \(-0.156722\pi\)
0.881221 + 0.472705i \(0.156722\pi\)
\(390\) 4.60235e14 0.00662307
\(391\) −5.83049e16 −0.825194
\(392\) 4.99435e16 0.695215
\(393\) −5.43660e16 −0.744348
\(394\) 3.27651e16 0.441252
\(395\) −1.26363e16 −0.167394
\(396\) −1.76802e16 −0.230392
\(397\) 4.39605e16 0.563539 0.281770 0.959482i \(-0.409079\pi\)
0.281770 + 0.959482i \(0.409079\pi\)
\(398\) −8.09038e16 −1.02030
\(399\) 4.24003e16 0.526071
\(400\) 9.92893e16 1.21203
\(401\) −1.97572e16 −0.237294 −0.118647 0.992937i \(-0.537856\pi\)
−0.118647 + 0.992937i \(0.537856\pi\)
\(402\) −1.36553e16 −0.161374
\(403\) −6.55485e15 −0.0762220
\(404\) −1.64852e16 −0.188632
\(405\) 1.58580e15 0.0178563
\(406\) −2.29867e17 −2.54717
\(407\) 1.68175e17 1.83399
\(408\) 3.32597e16 0.356967
\(409\) −4.32602e16 −0.456969 −0.228485 0.973548i \(-0.573377\pi\)
−0.228485 + 0.973548i \(0.573377\pi\)
\(410\) 2.02851e16 0.210903
\(411\) −3.71795e16 −0.380479
\(412\) −8.17367e16 −0.823351
\(413\) 1.86183e16 0.184614
\(414\) 3.74000e16 0.365064
\(415\) 1.26723e16 0.121771
\(416\) −5.03846e15 −0.0476641
\(417\) −1.57602e15 −0.0146783
\(418\) −1.36430e17 −1.25102
\(419\) −2.75196e16 −0.248456 −0.124228 0.992254i \(-0.539645\pi\)
−0.124228 + 0.992254i \(0.539645\pi\)
\(420\) −6.26924e15 −0.0557307
\(421\) −1.15862e17 −1.01416 −0.507081 0.861899i \(-0.669275\pi\)
−0.507081 + 0.861899i \(0.669275\pi\)
\(422\) −6.89278e16 −0.594106
\(423\) −3.83605e16 −0.325590
\(424\) −5.58164e16 −0.466535
\(425\) −1.06395e17 −0.875775
\(426\) −1.03439e17 −0.838532
\(427\) 1.01989e17 0.814278
\(428\) −9.30852e16 −0.731975
\(429\) 7.27722e15 0.0563629
\(430\) −6.15607e15 −0.0469633
\(431\) 1.39883e17 1.05114 0.525572 0.850749i \(-0.323851\pi\)
0.525572 + 0.850749i \(0.323851\pi\)
\(432\) −3.23473e16 −0.239439
\(433\) 1.04847e17 0.764512 0.382256 0.924057i \(-0.375147\pi\)
0.382256 + 0.924057i \(0.375147\pi\)
\(434\) 3.00087e17 2.15558
\(435\) −1.97392e16 −0.139685
\(436\) −5.82650e16 −0.406205
\(437\) 8.58706e16 0.589814
\(438\) −1.35457e17 −0.916685
\(439\) −1.13279e17 −0.755321 −0.377661 0.925944i \(-0.623271\pi\)
−0.377661 + 0.925944i \(0.623271\pi\)
\(440\) −2.74514e16 −0.180353
\(441\) 5.20495e16 0.336950
\(442\) 1.00598e16 0.0641716
\(443\) −1.06437e17 −0.669065 −0.334533 0.942384i \(-0.608578\pi\)
−0.334533 + 0.942384i \(0.608578\pi\)
\(444\) −4.43712e16 −0.274860
\(445\) −2.19383e16 −0.133926
\(446\) −2.61365e17 −1.57243
\(447\) 9.78980e16 0.580463
\(448\) −7.12415e16 −0.416319
\(449\) −1.73315e17 −0.998242 −0.499121 0.866532i \(-0.666344\pi\)
−0.499121 + 0.866532i \(0.666344\pi\)
\(450\) 6.82475e16 0.387441
\(451\) 3.20747e17 1.79480
\(452\) 4.88017e15 0.0269175
\(453\) −1.09157e17 −0.593490
\(454\) −2.30246e17 −1.23404
\(455\) 2.58044e15 0.0136339
\(456\) −4.89845e16 −0.255145
\(457\) 3.33307e17 1.71155 0.855775 0.517349i \(-0.173081\pi\)
0.855775 + 0.517349i \(0.173081\pi\)
\(458\) 1.79654e17 0.909519
\(459\) 3.46622e16 0.173011
\(460\) −1.26967e16 −0.0624834
\(461\) 1.90878e16 0.0926191 0.0463096 0.998927i \(-0.485254\pi\)
0.0463096 + 0.998927i \(0.485254\pi\)
\(462\) −3.33158e17 −1.59396
\(463\) −8.20003e15 −0.0386847 −0.0193423 0.999813i \(-0.506157\pi\)
−0.0193423 + 0.999813i \(0.506157\pi\)
\(464\) 4.02643e17 1.87307
\(465\) 2.57692e16 0.118211
\(466\) 1.71619e17 0.776347
\(467\) 2.90621e17 1.29648 0.648242 0.761435i \(-0.275505\pi\)
0.648242 + 0.761435i \(0.275505\pi\)
\(468\) −1.92002e15 −0.00844709
\(469\) −7.65626e16 −0.332195
\(470\) 4.37676e16 0.187291
\(471\) −6.28546e15 −0.0265278
\(472\) −2.15094e16 −0.0895377
\(473\) −9.73396e16 −0.399661
\(474\) 1.77172e17 0.717525
\(475\) 1.56697e17 0.625967
\(476\) −1.37032e17 −0.539980
\(477\) −5.81701e16 −0.226116
\(478\) −5.71720e17 −2.19231
\(479\) 4.11421e17 1.55634 0.778172 0.628051i \(-0.216147\pi\)
0.778172 + 0.628051i \(0.216147\pi\)
\(480\) 1.98078e16 0.0739210
\(481\) 1.82633e16 0.0672414
\(482\) −3.47325e16 −0.126162
\(483\) 2.09694e17 0.751501
\(484\) 1.99172e17 0.704260
\(485\) −5.47923e16 −0.191161
\(486\) −2.22343e16 −0.0765398
\(487\) −8.50507e16 −0.288895 −0.144447 0.989512i \(-0.546140\pi\)
−0.144447 + 0.989512i \(0.546140\pi\)
\(488\) −1.17827e17 −0.394925
\(489\) −9.93970e16 −0.328750
\(490\) −5.93862e16 −0.193825
\(491\) 5.33038e17 1.71683 0.858417 0.512953i \(-0.171448\pi\)
0.858417 + 0.512953i \(0.171448\pi\)
\(492\) −8.46258e16 −0.268986
\(493\) −4.31458e17 −1.35342
\(494\) −1.48159e16 −0.0458672
\(495\) −2.86090e16 −0.0874116
\(496\) −5.25643e17 −1.58511
\(497\) −5.79958e17 −1.72616
\(498\) −1.77677e17 −0.521965
\(499\) 1.21583e16 0.0352549 0.0176274 0.999845i \(-0.494389\pi\)
0.0176274 + 0.999845i \(0.494389\pi\)
\(500\) −4.69521e16 −0.134385
\(501\) −1.02332e17 −0.289113
\(502\) −7.27923e17 −2.03007
\(503\) −3.19223e17 −0.878826 −0.439413 0.898285i \(-0.644814\pi\)
−0.439413 + 0.898285i \(0.644814\pi\)
\(504\) −1.19619e17 −0.325088
\(505\) −2.66754e16 −0.0715677
\(506\) −6.74724e17 −1.78710
\(507\) −2.20006e17 −0.575284
\(508\) 1.74266e17 0.449882
\(509\) 3.64045e17 0.927875 0.463938 0.885868i \(-0.346436\pi\)
0.463938 + 0.885868i \(0.346436\pi\)
\(510\) −3.95481e16 −0.0995220
\(511\) −7.59479e17 −1.88704
\(512\) −5.52523e16 −0.135549
\(513\) −5.10501e16 −0.123661
\(514\) −6.00734e17 −1.43688
\(515\) −1.32261e17 −0.312382
\(516\) 2.56820e16 0.0598971
\(517\) 6.92052e17 1.59386
\(518\) −8.36111e17 −1.90161
\(519\) 2.10672e17 0.473171
\(520\) −2.98115e15 −0.00661244
\(521\) 9.58656e16 0.209999 0.105000 0.994472i \(-0.466516\pi\)
0.105000 + 0.994472i \(0.466516\pi\)
\(522\) 2.76761e17 0.598751
\(523\) 5.04150e17 1.07721 0.538603 0.842560i \(-0.318952\pi\)
0.538603 + 0.842560i \(0.318952\pi\)
\(524\) −2.58775e17 −0.546095
\(525\) 3.82649e17 0.797564
\(526\) 3.41791e17 0.703644
\(527\) 5.63260e17 1.14535
\(528\) 5.83570e17 1.17212
\(529\) −7.93563e16 −0.157442
\(530\) 6.63695e16 0.130069
\(531\) −2.24165e16 −0.0433963
\(532\) 2.01819e17 0.385955
\(533\) 3.48323e16 0.0658044
\(534\) 3.07594e17 0.574064
\(535\) −1.50625e17 −0.277714
\(536\) 8.84518e16 0.161115
\(537\) 2.70309e17 0.486439
\(538\) −1.14852e18 −2.04199
\(539\) −9.39013e17 −1.64947
\(540\) 7.54818e15 0.0131004
\(541\) −1.00143e18 −1.71727 −0.858634 0.512590i \(-0.828686\pi\)
−0.858634 + 0.512590i \(0.828686\pi\)
\(542\) 4.54147e17 0.769486
\(543\) 4.35614e17 0.729294
\(544\) 4.32956e17 0.716228
\(545\) −9.42810e16 −0.154116
\(546\) −3.61800e16 −0.0584408
\(547\) 2.37772e17 0.379528 0.189764 0.981830i \(-0.439228\pi\)
0.189764 + 0.981830i \(0.439228\pi\)
\(548\) −1.76969e17 −0.279141
\(549\) −1.22795e17 −0.191409
\(550\) −1.23124e18 −1.89664
\(551\) 6.35445e17 0.967370
\(552\) −2.42257e17 −0.364478
\(553\) 9.93369e17 1.47706
\(554\) 2.97791e17 0.437621
\(555\) −7.17988e16 −0.104283
\(556\) −7.50161e15 −0.0107688
\(557\) −8.07829e17 −1.14620 −0.573101 0.819485i \(-0.694260\pi\)
−0.573101 + 0.819485i \(0.694260\pi\)
\(558\) −3.61306e17 −0.506702
\(559\) −1.05708e16 −0.0146532
\(560\) 2.06929e17 0.283530
\(561\) −6.25333e17 −0.846940
\(562\) 7.08761e17 0.948886
\(563\) 8.75664e17 1.15886 0.579432 0.815020i \(-0.303274\pi\)
0.579432 + 0.815020i \(0.303274\pi\)
\(564\) −1.82590e17 −0.238871
\(565\) 7.89681e15 0.0102126
\(566\) 7.83252e17 1.00137
\(567\) −1.24663e17 −0.157561
\(568\) 6.70018e17 0.837187
\(569\) 8.68202e17 1.07248 0.536242 0.844064i \(-0.319843\pi\)
0.536242 + 0.844064i \(0.319843\pi\)
\(570\) 5.82458e16 0.0711342
\(571\) 8.14188e17 0.983082 0.491541 0.870854i \(-0.336434\pi\)
0.491541 + 0.870854i \(0.336434\pi\)
\(572\) 3.46385e16 0.0413509
\(573\) −4.29552e17 −0.507003
\(574\) −1.59465e18 −1.86097
\(575\) 7.74956e17 0.894203
\(576\) 8.57750e16 0.0978622
\(577\) −1.09707e17 −0.123763 −0.0618816 0.998083i \(-0.519710\pi\)
−0.0618816 + 0.998083i \(0.519710\pi\)
\(578\) 2.05163e17 0.228859
\(579\) −4.13103e17 −0.455667
\(580\) −9.39559e16 −0.102481
\(581\) −9.96199e17 −1.07449
\(582\) 7.68235e17 0.819398
\(583\) 1.04943e18 1.10690
\(584\) 8.77417e17 0.915213
\(585\) −3.10686e15 −0.00320485
\(586\) −2.06993e18 −2.11165
\(587\) −6.34760e17 −0.640416 −0.320208 0.947347i \(-0.603753\pi\)
−0.320208 + 0.947347i \(0.603753\pi\)
\(588\) 2.47748e17 0.247206
\(589\) −8.29562e17 −0.818652
\(590\) 2.55762e16 0.0249630
\(591\) −2.21184e17 −0.213518
\(592\) 1.46456e18 1.39835
\(593\) 4.62954e17 0.437202 0.218601 0.975814i \(-0.429851\pi\)
0.218601 + 0.975814i \(0.429851\pi\)
\(594\) 4.01123e17 0.374685
\(595\) −2.21738e17 −0.204870
\(596\) 4.65981e17 0.425860
\(597\) 5.46149e17 0.493717
\(598\) −7.32731e16 −0.0655220
\(599\) −1.37740e18 −1.21838 −0.609192 0.793023i \(-0.708506\pi\)
−0.609192 + 0.793023i \(0.708506\pi\)
\(600\) −4.42070e17 −0.386819
\(601\) −8.29177e17 −0.717734 −0.358867 0.933389i \(-0.616837\pi\)
−0.358867 + 0.933389i \(0.616837\pi\)
\(602\) 4.83941e17 0.414395
\(603\) 9.21817e16 0.0780876
\(604\) −5.19572e17 −0.435417
\(605\) 3.22288e17 0.267199
\(606\) 3.74012e17 0.306770
\(607\) 1.98534e18 1.61105 0.805525 0.592562i \(-0.201883\pi\)
0.805525 + 0.592562i \(0.201883\pi\)
\(608\) −6.37652e17 −0.511930
\(609\) 1.55174e18 1.23256
\(610\) 1.40104e17 0.110105
\(611\) 7.51549e16 0.0584372
\(612\) 1.64987e17 0.126931
\(613\) −1.90822e18 −1.45256 −0.726282 0.687397i \(-0.758753\pi\)
−0.726282 + 0.687397i \(0.758753\pi\)
\(614\) 2.58353e18 1.94589
\(615\) −1.36936e17 −0.102054
\(616\) 2.15801e18 1.59140
\(617\) −3.31213e16 −0.0241687 −0.0120843 0.999927i \(-0.503847\pi\)
−0.0120843 + 0.999927i \(0.503847\pi\)
\(618\) 1.85442e18 1.33901
\(619\) −2.33375e18 −1.66749 −0.833747 0.552146i \(-0.813809\pi\)
−0.833747 + 0.552146i \(0.813809\pi\)
\(620\) 1.22658e17 0.0867259
\(621\) −2.52472e17 −0.176652
\(622\) −1.39988e18 −0.969290
\(623\) 1.72462e18 1.18174
\(624\) 6.33741e16 0.0429746
\(625\) 1.37566e18 0.923187
\(626\) −6.44625e17 −0.428128
\(627\) 9.20982e17 0.605358
\(628\) −2.99179e16 −0.0194623
\(629\) −1.56937e18 −1.01041
\(630\) 1.42235e17 0.0906342
\(631\) −1.41731e18 −0.893870 −0.446935 0.894566i \(-0.647484\pi\)
−0.446935 + 0.894566i \(0.647484\pi\)
\(632\) −1.14763e18 −0.716373
\(633\) 4.65304e17 0.287483
\(634\) 2.41611e18 1.47753
\(635\) 2.81987e17 0.170687
\(636\) −2.76882e17 −0.165891
\(637\) −1.01974e17 −0.0604761
\(638\) −4.99297e18 −2.93106
\(639\) 6.98272e17 0.405760
\(640\) −3.20452e17 −0.184329
\(641\) −1.06228e18 −0.604872 −0.302436 0.953170i \(-0.597800\pi\)
−0.302436 + 0.953170i \(0.597800\pi\)
\(642\) 2.11189e18 1.19040
\(643\) −2.13065e18 −1.18889 −0.594443 0.804138i \(-0.702627\pi\)
−0.594443 + 0.804138i \(0.702627\pi\)
\(644\) 9.98113e17 0.551343
\(645\) 4.15571e16 0.0227252
\(646\) 1.27313e18 0.689226
\(647\) −8.87594e17 −0.475704 −0.237852 0.971301i \(-0.576443\pi\)
−0.237852 + 0.971301i \(0.576443\pi\)
\(648\) 1.44021e17 0.0764169
\(649\) 4.04410e17 0.212438
\(650\) −1.33709e17 −0.0695381
\(651\) −2.02577e18 −1.04307
\(652\) −4.73116e17 −0.241189
\(653\) −1.93108e17 −0.0974686 −0.0487343 0.998812i \(-0.515519\pi\)
−0.0487343 + 0.998812i \(0.515519\pi\)
\(654\) 1.32190e18 0.660607
\(655\) −4.18734e17 −0.207190
\(656\) 2.79325e18 1.36847
\(657\) 9.14416e17 0.443577
\(658\) −3.44066e18 −1.65262
\(659\) −1.37220e18 −0.652622 −0.326311 0.945262i \(-0.605806\pi\)
−0.326311 + 0.945262i \(0.605806\pi\)
\(660\) −1.36175e17 −0.0641300
\(661\) 2.68051e18 1.24999 0.624997 0.780627i \(-0.285100\pi\)
0.624997 + 0.780627i \(0.285100\pi\)
\(662\) 9.07022e17 0.418833
\(663\) −6.79094e16 −0.0310522
\(664\) 1.15090e18 0.521127
\(665\) 3.26572e17 0.146433
\(666\) 1.00668e18 0.447002
\(667\) 3.14264e18 1.38190
\(668\) −4.87088e17 −0.212110
\(669\) 1.76437e18 0.760886
\(670\) −1.05175e17 −0.0449187
\(671\) 2.21532e18 0.937001
\(672\) −1.55713e18 −0.652265
\(673\) −1.49388e16 −0.00619750 −0.00309875 0.999995i \(-0.500986\pi\)
−0.00309875 + 0.999995i \(0.500986\pi\)
\(674\) −7.37439e17 −0.302996
\(675\) −4.60711e17 −0.187480
\(676\) −1.04720e18 −0.422060
\(677\) 1.94890e18 0.777970 0.388985 0.921244i \(-0.372826\pi\)
0.388985 + 0.921244i \(0.372826\pi\)
\(678\) −1.10720e17 −0.0437757
\(679\) 4.30733e18 1.68677
\(680\) 2.56171e17 0.0993622
\(681\) 1.55430e18 0.597143
\(682\) 6.51823e18 2.48046
\(683\) 3.07859e18 1.16042 0.580212 0.814465i \(-0.302970\pi\)
0.580212 + 0.814465i \(0.302970\pi\)
\(684\) −2.42991e17 −0.0907248
\(685\) −2.86361e17 −0.105907
\(686\) 5.01137e16 0.0183590
\(687\) −1.21277e18 −0.440109
\(688\) −8.47687e17 −0.304727
\(689\) 1.13965e17 0.0405834
\(690\) 2.88059e17 0.101616
\(691\) −2.21151e17 −0.0772825 −0.0386413 0.999253i \(-0.512303\pi\)
−0.0386413 + 0.999253i \(0.512303\pi\)
\(692\) 1.00277e18 0.347145
\(693\) 2.24901e18 0.771305
\(694\) 2.89127e18 0.982316
\(695\) −1.21387e16 −0.00408573
\(696\) −1.79270e18 −0.597790
\(697\) −2.99314e18 −0.988813
\(698\) −6.11508e18 −2.00144
\(699\) −1.15853e18 −0.375668
\(700\) 1.82136e18 0.585138
\(701\) −3.85220e18 −1.22614 −0.613072 0.790027i \(-0.710067\pi\)
−0.613072 + 0.790027i \(0.710067\pi\)
\(702\) 4.35608e16 0.0137374
\(703\) 2.31135e18 0.722197
\(704\) −1.54745e18 −0.479064
\(705\) −2.95457e17 −0.0906286
\(706\) 1.13936e18 0.346283
\(707\) 2.09701e18 0.631501
\(708\) −1.06699e17 −0.0318380
\(709\) 6.13648e18 1.81434 0.907171 0.420763i \(-0.138238\pi\)
0.907171 + 0.420763i \(0.138238\pi\)
\(710\) −7.96696e17 −0.233407
\(711\) −1.19602e18 −0.347205
\(712\) −1.99243e18 −0.573142
\(713\) −4.10266e18 −1.16946
\(714\) 3.10895e18 0.878164
\(715\) 5.60501e16 0.0156887
\(716\) 1.28663e18 0.356879
\(717\) 3.85945e18 1.06084
\(718\) −5.12629e18 −1.39635
\(719\) 9.80939e17 0.264791 0.132396 0.991197i \(-0.457733\pi\)
0.132396 + 0.991197i \(0.457733\pi\)
\(720\) −2.49143e17 −0.0666481
\(721\) 1.03973e19 2.75641
\(722\) 2.66627e18 0.700507
\(723\) 2.34465e17 0.0610491
\(724\) 2.07346e18 0.535051
\(725\) 5.73470e18 1.46661
\(726\) −4.51876e18 −1.14533
\(727\) 2.54365e18 0.638975 0.319488 0.947590i \(-0.396489\pi\)
0.319488 + 0.947590i \(0.396489\pi\)
\(728\) 2.34354e17 0.0583470
\(729\) 1.50095e17 0.0370370
\(730\) −1.04331e18 −0.255161
\(731\) 9.08351e17 0.220187
\(732\) −5.84488e17 −0.140428
\(733\) −5.65641e18 −1.34699 −0.673496 0.739191i \(-0.735208\pi\)
−0.673496 + 0.739191i \(0.735208\pi\)
\(734\) −2.06936e18 −0.488441
\(735\) 4.00892e17 0.0937907
\(736\) −3.15356e18 −0.731299
\(737\) −1.66303e18 −0.382262
\(738\) 1.91997e18 0.437449
\(739\) 4.68683e17 0.105850 0.0529249 0.998598i \(-0.483146\pi\)
0.0529249 + 0.998598i \(0.483146\pi\)
\(740\) −3.41752e17 −0.0765077
\(741\) 1.00016e17 0.0221948
\(742\) −5.21744e18 −1.14771
\(743\) 5.69331e18 1.24147 0.620737 0.784019i \(-0.286833\pi\)
0.620737 + 0.784019i \(0.286833\pi\)
\(744\) 2.34034e18 0.505889
\(745\) 7.54023e17 0.161573
\(746\) 4.96886e18 1.05549
\(747\) 1.19943e18 0.252575
\(748\) −2.97650e18 −0.621363
\(749\) 1.18409e19 2.45050
\(750\) 1.06524e18 0.218549
\(751\) 3.66106e18 0.744642 0.372321 0.928104i \(-0.378562\pi\)
0.372321 + 0.928104i \(0.378562\pi\)
\(752\) 6.02677e18 1.21526
\(753\) 4.91392e18 0.982337
\(754\) −5.42223e17 −0.107464
\(755\) −8.40741e17 −0.165199
\(756\) −5.93378e17 −0.115595
\(757\) −6.93767e18 −1.33996 −0.669978 0.742381i \(-0.733697\pi\)
−0.669978 + 0.742381i \(0.733697\pi\)
\(758\) −4.63903e17 −0.0888337
\(759\) 4.55479e18 0.864762
\(760\) −3.77285e17 −0.0710200
\(761\) −6.12248e18 −1.14269 −0.571344 0.820711i \(-0.693578\pi\)
−0.571344 + 0.820711i \(0.693578\pi\)
\(762\) −3.95370e18 −0.731638
\(763\) 7.41162e18 1.35989
\(764\) −2.04461e18 −0.371966
\(765\) 2.66973e17 0.0481579
\(766\) 3.24796e18 0.580929
\(767\) 4.39178e16 0.00778880
\(768\) 3.52913e18 0.620611
\(769\) −9.93053e18 −1.73162 −0.865808 0.500377i \(-0.833195\pi\)
−0.865808 + 0.500377i \(0.833195\pi\)
\(770\) −2.56602e18 −0.443681
\(771\) 4.05531e18 0.695298
\(772\) −1.96631e18 −0.334303
\(773\) 3.16993e18 0.534420 0.267210 0.963638i \(-0.413898\pi\)
0.267210 + 0.963638i \(0.413898\pi\)
\(774\) −5.82667e17 −0.0974101
\(775\) −7.48654e18 −1.24114
\(776\) −4.97621e18 −0.818083
\(777\) 5.64425e18 0.920174
\(778\) −1.30069e19 −2.10283
\(779\) 4.40826e18 0.706763
\(780\) −1.47882e16 −0.00235126
\(781\) −1.25973e19 −1.98631
\(782\) 6.29637e18 0.984570
\(783\) −1.86830e18 −0.289731
\(784\) −8.17744e18 −1.25766
\(785\) −4.84114e16 −0.00738406
\(786\) 5.87101e18 0.888109
\(787\) −6.37388e18 −0.956243 −0.478121 0.878294i \(-0.658682\pi\)
−0.478121 + 0.878294i \(0.658682\pi\)
\(788\) −1.05281e18 −0.156649
\(789\) −2.30729e18 −0.340488
\(790\) 1.36461e18 0.199724
\(791\) −6.20784e17 −0.0901142
\(792\) −2.59826e18 −0.374083
\(793\) 2.40577e17 0.0343541
\(794\) −4.74731e18 −0.672380
\(795\) −4.48034e17 −0.0629397
\(796\) 2.59959e18 0.362218
\(797\) −1.04831e19 −1.44880 −0.724402 0.689378i \(-0.757884\pi\)
−0.724402 + 0.689378i \(0.757884\pi\)
\(798\) −4.57882e18 −0.627675
\(799\) −6.45807e18 −0.878110
\(800\) −5.75461e18 −0.776124
\(801\) −2.07644e18 −0.277785
\(802\) 2.13358e18 0.283124
\(803\) −1.64968e19 −2.17144
\(804\) 4.38772e17 0.0572894
\(805\) 1.61509e18 0.209181
\(806\) 7.07862e17 0.0909433
\(807\) 7.75321e18 0.988106
\(808\) −2.42265e18 −0.306278
\(809\) −1.22376e19 −1.53472 −0.767360 0.641216i \(-0.778430\pi\)
−0.767360 + 0.641216i \(0.778430\pi\)
\(810\) −1.71251e17 −0.0213050
\(811\) −6.68310e18 −0.824789 −0.412394 0.911005i \(-0.635307\pi\)
−0.412394 + 0.911005i \(0.635307\pi\)
\(812\) 7.38606e18 0.904272
\(813\) −3.06576e18 −0.372349
\(814\) −1.81613e19 −2.18821
\(815\) −7.65568e17 −0.0915081
\(816\) −5.44575e18 −0.645761
\(817\) −1.33781e18 −0.157380
\(818\) 4.67169e18 0.545227
\(819\) 2.44236e17 0.0282791
\(820\) −6.51798e17 −0.0748726
\(821\) −1.11425e19 −1.26984 −0.634922 0.772576i \(-0.718968\pi\)
−0.634922 + 0.772576i \(0.718968\pi\)
\(822\) 4.01503e18 0.453964
\(823\) −1.21999e19 −1.36854 −0.684270 0.729228i \(-0.739879\pi\)
−0.684270 + 0.729228i \(0.739879\pi\)
\(824\) −1.20119e19 −1.33686
\(825\) 8.31158e18 0.917768
\(826\) −2.01060e18 −0.220269
\(827\) 4.78529e18 0.520143 0.260072 0.965589i \(-0.416254\pi\)
0.260072 + 0.965589i \(0.416254\pi\)
\(828\) −1.20173e18 −0.129602
\(829\) 4.69672e18 0.502562 0.251281 0.967914i \(-0.419148\pi\)
0.251281 + 0.967914i \(0.419148\pi\)
\(830\) −1.36849e18 −0.145290
\(831\) −2.01027e18 −0.211762
\(832\) −1.68048e17 −0.0175644
\(833\) 8.76266e18 0.908747
\(834\) 1.70195e17 0.0175132
\(835\) −7.88177e17 −0.0804751
\(836\) 4.38374e18 0.444124
\(837\) 2.43903e18 0.245190
\(838\) 2.97185e18 0.296443
\(839\) −2.91089e18 −0.288120 −0.144060 0.989569i \(-0.546016\pi\)
−0.144060 + 0.989569i \(0.546016\pi\)
\(840\) −9.21319e17 −0.0904888
\(841\) 1.29950e19 1.26649
\(842\) 1.25120e19 1.21003
\(843\) −4.78456e18 −0.459159
\(844\) 2.21478e18 0.210914
\(845\) −1.69451e18 −0.160131
\(846\) 4.14256e18 0.388474
\(847\) −2.53357e19 −2.35772
\(848\) 9.13905e18 0.843972
\(849\) −5.28742e18 −0.484555
\(850\) 1.14896e19 1.04492
\(851\) 1.14310e19 1.03167
\(852\) 3.32368e18 0.297688
\(853\) 1.64993e19 1.46655 0.733275 0.679932i \(-0.237991\pi\)
0.733275 + 0.679932i \(0.237991\pi\)
\(854\) −1.10139e19 −0.971545
\(855\) −3.93194e17 −0.0344213
\(856\) −1.36797e19 −1.18849
\(857\) −8.81932e18 −0.760431 −0.380215 0.924898i \(-0.624150\pi\)
−0.380215 + 0.924898i \(0.624150\pi\)
\(858\) −7.85870e17 −0.0672486
\(859\) −1.23566e19 −1.04940 −0.524702 0.851286i \(-0.675823\pi\)
−0.524702 + 0.851286i \(0.675823\pi\)
\(860\) 1.97806e17 0.0166725
\(861\) 1.07649e19 0.900508
\(862\) −1.51060e19 −1.25416
\(863\) −7.53367e18 −0.620778 −0.310389 0.950610i \(-0.600459\pi\)
−0.310389 + 0.950610i \(0.600459\pi\)
\(864\) 1.87479e18 0.153325
\(865\) 1.62262e18 0.131708
\(866\) −1.13225e19 −0.912167
\(867\) −1.38497e18 −0.110743
\(868\) −9.64237e18 −0.765254
\(869\) 2.15771e19 1.69967
\(870\) 2.13165e18 0.166663
\(871\) −1.80600e17 −0.0140152
\(872\) −8.56254e18 −0.659547
\(873\) −5.18605e18 −0.396501
\(874\) −9.27321e18 −0.703730
\(875\) 5.97256e18 0.449892
\(876\) 4.35249e18 0.325433
\(877\) −2.06459e19 −1.53228 −0.766139 0.642675i \(-0.777825\pi\)
−0.766139 + 0.642675i \(0.777825\pi\)
\(878\) 1.22331e19 0.901202
\(879\) 1.39733e19 1.02181
\(880\) 4.49473e18 0.326262
\(881\) 4.71322e18 0.339605 0.169802 0.985478i \(-0.445687\pi\)
0.169802 + 0.985478i \(0.445687\pi\)
\(882\) −5.62085e18 −0.402028
\(883\) −1.89929e19 −1.34848 −0.674242 0.738511i \(-0.735529\pi\)
−0.674242 + 0.738511i \(0.735529\pi\)
\(884\) −3.23239e17 −0.0227816
\(885\) −1.72654e17 −0.0120794
\(886\) 1.14942e19 0.798287
\(887\) 2.12032e19 1.46183 0.730917 0.682466i \(-0.239092\pi\)
0.730917 + 0.682466i \(0.239092\pi\)
\(888\) −6.52073e18 −0.446285
\(889\) −2.21676e19 −1.50611
\(890\) 2.36913e18 0.159792
\(891\) −2.70782e18 −0.181307
\(892\) 8.39814e18 0.558228
\(893\) 9.51136e18 0.627636
\(894\) −1.05720e19 −0.692572
\(895\) 2.08196e18 0.135401
\(896\) 2.51913e19 1.62648
\(897\) 4.94637e17 0.0317056
\(898\) 1.87164e19 1.19104
\(899\) −3.03598e19 −1.91805
\(900\) −2.19292e18 −0.137546
\(901\) −9.79307e18 −0.609829
\(902\) −3.46377e19 −2.14144
\(903\) −3.26689e18 −0.200523
\(904\) 7.17184e17 0.0437055
\(905\) 3.35515e18 0.203000
\(906\) 1.17879e19 0.708115
\(907\) −4.05898e18 −0.242086 −0.121043 0.992647i \(-0.538624\pi\)
−0.121043 + 0.992647i \(0.538624\pi\)
\(908\) 7.39825e18 0.438098
\(909\) −2.52480e18 −0.148444
\(910\) −2.78663e17 −0.0162671
\(911\) 2.16568e19 1.25524 0.627618 0.778521i \(-0.284030\pi\)
0.627618 + 0.778521i \(0.284030\pi\)
\(912\) 8.02042e18 0.461563
\(913\) −2.16386e19 −1.23643
\(914\) −3.59940e19 −2.04211
\(915\) −9.45785e17 −0.0532789
\(916\) −5.77263e18 −0.322889
\(917\) 3.29175e19 1.82821
\(918\) −3.74319e18 −0.206426
\(919\) 1.14013e19 0.624312 0.312156 0.950031i \(-0.398949\pi\)
0.312156 + 0.950031i \(0.398949\pi\)
\(920\) −1.86589e18 −0.101453
\(921\) −1.74403e19 −0.941602
\(922\) −2.06130e18 −0.110507
\(923\) −1.36804e18 −0.0728260
\(924\) 1.07050e19 0.565872
\(925\) 2.08592e19 1.09491
\(926\) 8.85525e17 0.0461561
\(927\) −1.25184e19 −0.647936
\(928\) −2.33364e19 −1.19942
\(929\) 2.09772e19 1.07064 0.535322 0.844648i \(-0.320190\pi\)
0.535322 + 0.844648i \(0.320190\pi\)
\(930\) −2.78282e18 −0.141041
\(931\) −1.29055e19 −0.649535
\(932\) −5.51443e18 −0.275611
\(933\) 9.45004e18 0.469032
\(934\) −3.13843e19 −1.54688
\(935\) −4.81639e18 −0.235747
\(936\) −2.82163e17 −0.0137154
\(937\) 2.77478e19 1.33943 0.669717 0.742616i \(-0.266415\pi\)
0.669717 + 0.742616i \(0.266415\pi\)
\(938\) 8.26803e18 0.396354
\(939\) 4.35160e18 0.207168
\(940\) −1.40633e18 −0.0664902
\(941\) −2.64142e19 −1.24024 −0.620120 0.784507i \(-0.712916\pi\)
−0.620120 + 0.784507i \(0.712916\pi\)
\(942\) 6.78770e17 0.0316513
\(943\) 2.18014e19 1.00962
\(944\) 3.52183e18 0.161976
\(945\) −9.60170e17 −0.0438572
\(946\) 1.05117e19 0.476851
\(947\) 1.13680e19 0.512163 0.256082 0.966655i \(-0.417568\pi\)
0.256082 + 0.966655i \(0.417568\pi\)
\(948\) −5.69289e18 −0.254729
\(949\) −1.79150e18 −0.0796135
\(950\) −1.69218e19 −0.746865
\(951\) −1.63102e19 −0.714967
\(952\) −2.01381e19 −0.876755
\(953\) −2.57112e19 −1.11178 −0.555889 0.831256i \(-0.687622\pi\)
−0.555889 + 0.831256i \(0.687622\pi\)
\(954\) 6.28182e18 0.269787
\(955\) −3.30846e18 −0.141125
\(956\) 1.83704e19 0.778293
\(957\) 3.37056e19 1.41832
\(958\) −4.44296e19 −1.85693
\(959\) 2.25114e19 0.934505
\(960\) 6.60650e17 0.0272401
\(961\) 1.52166e19 0.623184
\(962\) −1.97226e18 −0.0802282
\(963\) −1.42565e19 −0.576027
\(964\) 1.11602e18 0.0447890
\(965\) −3.18177e18 −0.126836
\(966\) −2.26449e19 −0.896643
\(967\) 4.06994e19 1.60072 0.800361 0.599519i \(-0.204641\pi\)
0.800361 + 0.599519i \(0.204641\pi\)
\(968\) 2.92701e19 1.14349
\(969\) −8.59440e18 −0.333511
\(970\) 5.91705e18 0.228081
\(971\) 2.06387e19 0.790239 0.395119 0.918630i \(-0.370703\pi\)
0.395119 + 0.918630i \(0.370703\pi\)
\(972\) 7.14429e17 0.0271724
\(973\) 9.54245e17 0.0360518
\(974\) 9.18467e18 0.344691
\(975\) 9.02614e17 0.0336490
\(976\) 1.92922e19 0.714428
\(977\) −6.87975e18 −0.253080 −0.126540 0.991961i \(-0.540387\pi\)
−0.126540 + 0.991961i \(0.540387\pi\)
\(978\) 1.07339e19 0.392244
\(979\) 3.74606e19 1.35984
\(980\) 1.90819e18 0.0688101
\(981\) −8.92362e18 −0.319663
\(982\) −5.75630e19 −2.04842
\(983\) −9.57656e17 −0.0338541 −0.0169271 0.999857i \(-0.505388\pi\)
−0.0169271 + 0.999857i \(0.505388\pi\)
\(984\) −1.24365e19 −0.436747
\(985\) −1.70359e18 −0.0594332
\(986\) 4.65933e19 1.61482
\(987\) 2.32265e19 0.799691
\(988\) 4.76062e17 0.0162833
\(989\) −6.61623e18 −0.224820
\(990\) 3.08950e18 0.104294
\(991\) 3.70859e19 1.24374 0.621870 0.783120i \(-0.286373\pi\)
0.621870 + 0.783120i \(0.286373\pi\)
\(992\) 3.04652e19 1.01503
\(993\) −6.12294e18 −0.202670
\(994\) 6.26299e19 2.05954
\(995\) 4.20651e18 0.137427
\(996\) 5.70911e18 0.185303
\(997\) −2.10142e19 −0.677633 −0.338816 0.940853i \(-0.610027\pi\)
−0.338816 + 0.940853i \(0.610027\pi\)
\(998\) −1.31298e18 −0.0420639
\(999\) −6.79570e18 −0.216301
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 177.14.a.c.1.7 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.7 31 1.1 even 1 trivial