Properties

Label 177.10.a.d.1.16
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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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 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+22.7532 q^{2} +81.0000 q^{3} +5.71029 q^{4} -1397.96 q^{5} +1843.01 q^{6} -3353.38 q^{7} -11519.7 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+22.7532 q^{2} +81.0000 q^{3} +5.71029 q^{4} -1397.96 q^{5} +1843.01 q^{6} -3353.38 q^{7} -11519.7 q^{8} +6561.00 q^{9} -31808.2 q^{10} +35617.8 q^{11} +462.534 q^{12} -147759. q^{13} -76300.2 q^{14} -113235. q^{15} -265035. q^{16} +65139.2 q^{17} +149284. q^{18} +699375. q^{19} -7982.78 q^{20} -271624. q^{21} +810421. q^{22} +996679. q^{23} -933099. q^{24} +1179.05 q^{25} -3.36199e6 q^{26} +531441. q^{27} -19148.8 q^{28} -3.88707e6 q^{29} -2.57647e6 q^{30} +2.43647e6 q^{31} -132304. q^{32} +2.88504e6 q^{33} +1.48213e6 q^{34} +4.68790e6 q^{35} +37465.2 q^{36} +1.41307e7 q^{37} +1.59131e7 q^{38} -1.19684e7 q^{39} +1.61042e7 q^{40} -1.02547e7 q^{41} -6.18032e6 q^{42} +2.85692e7 q^{43} +203388. q^{44} -9.17204e6 q^{45} +2.26777e7 q^{46} +2.87214e7 q^{47} -2.14678e7 q^{48} -2.91085e7 q^{49} +26827.2 q^{50} +5.27627e6 q^{51} -843744. q^{52} +7.51619e7 q^{53} +1.20920e7 q^{54} -4.97924e7 q^{55} +3.86300e7 q^{56} +5.66494e7 q^{57} -8.84436e7 q^{58} -1.21174e7 q^{59} -646605. q^{60} +1.55086e8 q^{61} +5.54377e7 q^{62} -2.20015e7 q^{63} +1.32688e8 q^{64} +2.06561e8 q^{65} +6.56441e7 q^{66} -1.39101e8 q^{67} +371964. q^{68} +8.07310e7 q^{69} +1.06665e8 q^{70} +1.41817e8 q^{71} -7.55810e7 q^{72} +2.22968e8 q^{73} +3.21520e8 q^{74} +95503.2 q^{75} +3.99364e6 q^{76} -1.19440e8 q^{77} -2.72321e8 q^{78} -7.34739e7 q^{79} +3.70510e8 q^{80} +4.30467e7 q^{81} -2.33328e8 q^{82} -1.06550e8 q^{83} -1.55105e6 q^{84} -9.10622e7 q^{85} +6.50041e8 q^{86} -3.14853e8 q^{87} -4.10308e8 q^{88} -1.11107e7 q^{89} -2.08694e8 q^{90} +4.95490e8 q^{91} +5.69133e6 q^{92} +1.97354e8 q^{93} +6.53506e8 q^{94} -9.77702e8 q^{95} -1.07166e7 q^{96} -1.97748e8 q^{97} -6.62312e8 q^{98} +2.33688e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.7532 1.00556 0.502780 0.864414i \(-0.332310\pi\)
0.502780 + 0.864414i \(0.332310\pi\)
\(3\) 81.0000 0.577350
\(4\) 5.71029 0.0111529
\(5\) −1397.96 −1.00030 −0.500151 0.865938i \(-0.666722\pi\)
−0.500151 + 0.865938i \(0.666722\pi\)
\(6\) 1843.01 0.580561
\(7\) −3353.38 −0.527887 −0.263944 0.964538i \(-0.585023\pi\)
−0.263944 + 0.964538i \(0.585023\pi\)
\(8\) −11519.7 −0.994346
\(9\) 6561.00 0.333333
\(10\) −31808.2 −1.00586
\(11\) 35617.8 0.733500 0.366750 0.930320i \(-0.380470\pi\)
0.366750 + 0.930320i \(0.380470\pi\)
\(12\) 462.534 0.00643914
\(13\) −147759. −1.43485 −0.717427 0.696634i \(-0.754680\pi\)
−0.717427 + 0.696634i \(0.754680\pi\)
\(14\) −76300.2 −0.530823
\(15\) −113235. −0.577525
\(16\) −265035. −1.01103
\(17\) 65139.2 0.189157 0.0945784 0.995517i \(-0.469850\pi\)
0.0945784 + 0.995517i \(0.469850\pi\)
\(18\) 149284. 0.335187
\(19\) 699375. 1.23117 0.615587 0.788069i \(-0.288919\pi\)
0.615587 + 0.788069i \(0.288919\pi\)
\(20\) −7982.78 −0.0111563
\(21\) −271624. −0.304776
\(22\) 810421. 0.737579
\(23\) 996679. 0.742643 0.371321 0.928504i \(-0.378905\pi\)
0.371321 + 0.928504i \(0.378905\pi\)
\(24\) −933099. −0.574086
\(25\) 1179.05 0.000603674 0
\(26\) −3.36199e6 −1.44283
\(27\) 531441. 0.192450
\(28\) −19148.8 −0.00588748
\(29\) −3.88707e6 −1.02054 −0.510272 0.860013i \(-0.670455\pi\)
−0.510272 + 0.860013i \(0.670455\pi\)
\(30\) −2.57647e6 −0.580736
\(31\) 2.43647e6 0.473843 0.236921 0.971529i \(-0.423862\pi\)
0.236921 + 0.971529i \(0.423862\pi\)
\(32\) −132304. −0.0223048
\(33\) 2.88504e6 0.423486
\(34\) 1.48213e6 0.190209
\(35\) 4.68790e6 0.528047
\(36\) 37465.2 0.00371764
\(37\) 1.41307e7 1.23953 0.619765 0.784787i \(-0.287228\pi\)
0.619765 + 0.784787i \(0.287228\pi\)
\(38\) 1.59131e7 1.23802
\(39\) −1.19684e7 −0.828413
\(40\) 1.61042e7 0.994646
\(41\) −1.02547e7 −0.566755 −0.283378 0.959008i \(-0.591455\pi\)
−0.283378 + 0.959008i \(0.591455\pi\)
\(42\) −6.18032e6 −0.306471
\(43\) 2.85692e7 1.27435 0.637176 0.770718i \(-0.280102\pi\)
0.637176 + 0.770718i \(0.280102\pi\)
\(44\) 203388. 0.00818066
\(45\) −9.17204e6 −0.333434
\(46\) 2.26777e7 0.746773
\(47\) 2.87214e7 0.858550 0.429275 0.903174i \(-0.358769\pi\)
0.429275 + 0.903174i \(0.358769\pi\)
\(48\) −2.14678e7 −0.583718
\(49\) −2.91085e7 −0.721335
\(50\) 26827.2 0.000607031 0
\(51\) 5.27627e6 0.109210
\(52\) −843744. −0.0160028
\(53\) 7.51619e7 1.30845 0.654224 0.756301i \(-0.272996\pi\)
0.654224 + 0.756301i \(0.272996\pi\)
\(54\) 1.20920e7 0.193520
\(55\) −4.97924e7 −0.733721
\(56\) 3.86300e7 0.524903
\(57\) 5.66494e7 0.710818
\(58\) −8.84436e7 −1.02622
\(59\) −1.21174e7 −0.130189
\(60\) −646605. −0.00644108
\(61\) 1.55086e8 1.43413 0.717064 0.697008i \(-0.245486\pi\)
0.717064 + 0.697008i \(0.245486\pi\)
\(62\) 5.54377e7 0.476478
\(63\) −2.20015e7 −0.175962
\(64\) 1.32688e8 0.988600
\(65\) 2.06561e8 1.43529
\(66\) 6.56441e7 0.425841
\(67\) −1.39101e8 −0.843321 −0.421660 0.906754i \(-0.638553\pi\)
−0.421660 + 0.906754i \(0.638553\pi\)
\(68\) 371964. 0.00210965
\(69\) 8.07310e7 0.428765
\(70\) 1.06665e8 0.530983
\(71\) 1.41817e8 0.662318 0.331159 0.943575i \(-0.392560\pi\)
0.331159 + 0.943575i \(0.392560\pi\)
\(72\) −7.55810e7 −0.331449
\(73\) 2.22968e8 0.918947 0.459474 0.888191i \(-0.348038\pi\)
0.459474 + 0.888191i \(0.348038\pi\)
\(74\) 3.21520e8 1.24642
\(75\) 95503.2 0.000348532 0
\(76\) 3.99364e6 0.0137312
\(77\) −1.19440e8 −0.387205
\(78\) −2.72321e8 −0.833020
\(79\) −7.34739e7 −0.212232 −0.106116 0.994354i \(-0.533842\pi\)
−0.106116 + 0.994354i \(0.533842\pi\)
\(80\) 3.70510e8 1.01133
\(81\) 4.30467e7 0.111111
\(82\) −2.33328e8 −0.569907
\(83\) −1.06550e8 −0.246435 −0.123218 0.992380i \(-0.539321\pi\)
−0.123218 + 0.992380i \(0.539321\pi\)
\(84\) −1.55105e6 −0.00339914
\(85\) −9.10622e7 −0.189214
\(86\) 6.50041e8 1.28144
\(87\) −3.14853e8 −0.589211
\(88\) −4.10308e8 −0.729353
\(89\) −1.11107e7 −0.0187710 −0.00938552 0.999956i \(-0.502988\pi\)
−0.00938552 + 0.999956i \(0.502988\pi\)
\(90\) −2.08694e8 −0.335288
\(91\) 4.95490e8 0.757441
\(92\) 5.69133e6 0.00828263
\(93\) 1.97354e8 0.273573
\(94\) 6.53506e8 0.863325
\(95\) −9.77702e8 −1.23154
\(96\) −1.07166e7 −0.0128777
\(97\) −1.97748e8 −0.226798 −0.113399 0.993550i \(-0.536174\pi\)
−0.113399 + 0.993550i \(0.536174\pi\)
\(98\) −6.62312e8 −0.725346
\(99\) 2.33688e8 0.244500
\(100\) 6732.73 6.73273e−6 0
\(101\) 1.98613e8 0.189916 0.0949580 0.995481i \(-0.469728\pi\)
0.0949580 + 0.995481i \(0.469728\pi\)
\(102\) 1.20052e8 0.109817
\(103\) 2.21392e7 0.0193818 0.00969090 0.999953i \(-0.496915\pi\)
0.00969090 + 0.999953i \(0.496915\pi\)
\(104\) 1.70214e9 1.42674
\(105\) 3.79720e8 0.304868
\(106\) 1.71018e9 1.31572
\(107\) −1.02274e9 −0.754293 −0.377146 0.926154i \(-0.623095\pi\)
−0.377146 + 0.926154i \(0.623095\pi\)
\(108\) 3.03468e6 0.00214638
\(109\) 1.36334e8 0.0925092 0.0462546 0.998930i \(-0.485271\pi\)
0.0462546 + 0.998930i \(0.485271\pi\)
\(110\) −1.13294e9 −0.737801
\(111\) 1.14459e9 0.715643
\(112\) 8.88763e8 0.533709
\(113\) −4.89261e8 −0.282285 −0.141143 0.989989i \(-0.545078\pi\)
−0.141143 + 0.989989i \(0.545078\pi\)
\(114\) 1.28896e9 0.714771
\(115\) −1.39332e9 −0.742867
\(116\) −2.21963e7 −0.0113820
\(117\) −9.69444e8 −0.478284
\(118\) −2.75709e8 −0.130913
\(119\) −2.18436e8 −0.0998535
\(120\) 1.30444e9 0.574259
\(121\) −1.08932e9 −0.461978
\(122\) 3.52871e9 1.44210
\(123\) −8.30631e8 −0.327216
\(124\) 1.39130e7 0.00528472
\(125\) 2.72875e9 0.999698
\(126\) −5.00606e8 −0.176941
\(127\) 2.13822e9 0.729348 0.364674 0.931135i \(-0.381180\pi\)
0.364674 + 0.931135i \(0.381180\pi\)
\(128\) 3.08681e9 1.01640
\(129\) 2.31410e9 0.735747
\(130\) 4.69994e9 1.44327
\(131\) −1.28564e9 −0.381415 −0.190708 0.981647i \(-0.561078\pi\)
−0.190708 + 0.981647i \(0.561078\pi\)
\(132\) 1.64744e7 0.00472311
\(133\) −2.34527e9 −0.649921
\(134\) −3.16499e9 −0.848011
\(135\) −7.42936e8 −0.192508
\(136\) −7.50386e8 −0.188087
\(137\) −3.57302e9 −0.866548 −0.433274 0.901262i \(-0.642642\pi\)
−0.433274 + 0.901262i \(0.642642\pi\)
\(138\) 1.83689e9 0.431149
\(139\) 2.69381e9 0.612068 0.306034 0.952021i \(-0.400998\pi\)
0.306034 + 0.952021i \(0.400998\pi\)
\(140\) 2.67693e7 0.00588926
\(141\) 2.32644e9 0.495684
\(142\) 3.22680e9 0.666001
\(143\) −5.26283e9 −1.05246
\(144\) −1.73890e9 −0.337010
\(145\) 5.43399e9 1.02085
\(146\) 5.07326e9 0.924057
\(147\) −2.35779e9 −0.416463
\(148\) 8.06907e7 0.0138244
\(149\) 9.84181e9 1.63582 0.817912 0.575343i \(-0.195132\pi\)
0.817912 + 0.575343i \(0.195132\pi\)
\(150\) 2.17301e6 0.000350470 0
\(151\) −9.15733e9 −1.43342 −0.716708 0.697373i \(-0.754352\pi\)
−0.716708 + 0.697373i \(0.754352\pi\)
\(152\) −8.05662e9 −1.22421
\(153\) 4.27378e8 0.0630523
\(154\) −2.71765e9 −0.389359
\(155\) −3.40610e9 −0.473986
\(156\) −6.83433e7 −0.00923922
\(157\) 6.83830e9 0.898255 0.449128 0.893468i \(-0.351735\pi\)
0.449128 + 0.893468i \(0.351735\pi\)
\(158\) −1.67177e9 −0.213412
\(159\) 6.08811e9 0.755432
\(160\) 1.84956e8 0.0223115
\(161\) −3.34224e9 −0.392032
\(162\) 9.79453e8 0.111729
\(163\) 3.20037e9 0.355104 0.177552 0.984111i \(-0.443182\pi\)
0.177552 + 0.984111i \(0.443182\pi\)
\(164\) −5.85573e7 −0.00632097
\(165\) −4.03319e9 −0.423614
\(166\) −2.42436e9 −0.247806
\(167\) −2.62703e9 −0.261361 −0.130680 0.991425i \(-0.541716\pi\)
−0.130680 + 0.991425i \(0.541716\pi\)
\(168\) 3.12903e9 0.303053
\(169\) 1.12281e10 1.05880
\(170\) −2.07196e9 −0.190266
\(171\) 4.58860e9 0.410391
\(172\) 1.63138e8 0.0142127
\(173\) 3.99041e9 0.338696 0.169348 0.985556i \(-0.445834\pi\)
0.169348 + 0.985556i \(0.445834\pi\)
\(174\) −7.16393e9 −0.592488
\(175\) −3.95380e6 −0.000318672 0
\(176\) −9.43997e9 −0.741589
\(177\) −9.81506e8 −0.0751646
\(178\) −2.52806e8 −0.0188754
\(179\) 1.49455e10 1.08811 0.544055 0.839050i \(-0.316888\pi\)
0.544055 + 0.839050i \(0.316888\pi\)
\(180\) −5.23750e7 −0.00371876
\(181\) −1.02993e8 −0.00713271 −0.00356636 0.999994i \(-0.501135\pi\)
−0.00356636 + 0.999994i \(0.501135\pi\)
\(182\) 1.12740e10 0.761653
\(183\) 1.25619e10 0.827994
\(184\) −1.14815e10 −0.738444
\(185\) −1.97543e10 −1.23990
\(186\) 4.49045e9 0.275094
\(187\) 2.32011e9 0.138747
\(188\) 1.64008e8 0.00957534
\(189\) −1.78212e9 −0.101592
\(190\) −2.22459e10 −1.23839
\(191\) −7.24464e9 −0.393883 −0.196941 0.980415i \(-0.563101\pi\)
−0.196941 + 0.980415i \(0.563101\pi\)
\(192\) 1.07477e10 0.570768
\(193\) 2.51260e10 1.30351 0.651756 0.758429i \(-0.274033\pi\)
0.651756 + 0.758429i \(0.274033\pi\)
\(194\) −4.49942e9 −0.228060
\(195\) 1.67315e10 0.828663
\(196\) −1.66218e8 −0.00804499
\(197\) 3.06233e9 0.144862 0.0724309 0.997373i \(-0.476924\pi\)
0.0724309 + 0.997373i \(0.476924\pi\)
\(198\) 5.31717e9 0.245860
\(199\) 4.33802e10 1.96089 0.980444 0.196800i \(-0.0630550\pi\)
0.980444 + 0.196800i \(0.0630550\pi\)
\(200\) −1.35824e7 −0.000600261 0
\(201\) −1.12672e10 −0.486891
\(202\) 4.51909e9 0.190972
\(203\) 1.30348e10 0.538732
\(204\) 3.01291e7 0.00121801
\(205\) 1.43357e10 0.566926
\(206\) 5.03738e8 0.0194896
\(207\) 6.53921e9 0.247548
\(208\) 3.91612e10 1.45068
\(209\) 2.49102e10 0.903065
\(210\) 8.63987e9 0.306563
\(211\) 4.08132e10 1.41752 0.708761 0.705449i \(-0.249254\pi\)
0.708761 + 0.705449i \(0.249254\pi\)
\(212\) 4.29196e8 0.0145930
\(213\) 1.14872e10 0.382389
\(214\) −2.32707e10 −0.758487
\(215\) −3.99387e10 −1.27474
\(216\) −6.12206e9 −0.191362
\(217\) −8.17042e9 −0.250136
\(218\) 3.10204e9 0.0930237
\(219\) 1.80604e10 0.530554
\(220\) −2.84329e8 −0.00818313
\(221\) −9.62487e9 −0.271412
\(222\) 2.60431e10 0.719623
\(223\) −3.62409e10 −0.981357 −0.490678 0.871341i \(-0.663251\pi\)
−0.490678 + 0.871341i \(0.663251\pi\)
\(224\) 4.43665e8 0.0117744
\(225\) 7.73576e6 0.000201225 0
\(226\) −1.11323e10 −0.283855
\(227\) −7.23329e10 −1.80809 −0.904044 0.427440i \(-0.859416\pi\)
−0.904044 + 0.427440i \(0.859416\pi\)
\(228\) 3.23485e8 0.00792769
\(229\) −4.66680e10 −1.12140 −0.560698 0.828020i \(-0.689467\pi\)
−0.560698 + 0.828020i \(0.689467\pi\)
\(230\) −3.17026e10 −0.746998
\(231\) −9.67464e9 −0.223553
\(232\) 4.47781e10 1.01477
\(233\) −6.49657e10 −1.44405 −0.722025 0.691867i \(-0.756789\pi\)
−0.722025 + 0.691867i \(0.756789\pi\)
\(234\) −2.20580e10 −0.480944
\(235\) −4.01515e10 −0.858809
\(236\) −6.91937e7 −0.00145199
\(237\) −5.95139e9 −0.122532
\(238\) −4.97013e9 −0.100409
\(239\) 1.27226e10 0.252223 0.126111 0.992016i \(-0.459750\pi\)
0.126111 + 0.992016i \(0.459750\pi\)
\(240\) 3.00113e10 0.583894
\(241\) −3.06114e10 −0.584530 −0.292265 0.956337i \(-0.594409\pi\)
−0.292265 + 0.956337i \(0.594409\pi\)
\(242\) −2.47856e10 −0.464547
\(243\) 3.48678e9 0.0641500
\(244\) 8.85585e8 0.0159947
\(245\) 4.06926e10 0.721553
\(246\) −1.88995e10 −0.329036
\(247\) −1.03339e11 −1.76655
\(248\) −2.80675e10 −0.471163
\(249\) −8.63057e9 −0.142280
\(250\) 6.20879e10 1.00526
\(251\) −5.69376e9 −0.0905455 −0.0452728 0.998975i \(-0.514416\pi\)
−0.0452728 + 0.998975i \(0.514416\pi\)
\(252\) −1.25635e8 −0.00196249
\(253\) 3.54995e10 0.544728
\(254\) 4.86514e10 0.733404
\(255\) −7.37604e9 −0.109243
\(256\) 2.29898e9 0.0334546
\(257\) 8.08853e10 1.15657 0.578283 0.815836i \(-0.303723\pi\)
0.578283 + 0.815836i \(0.303723\pi\)
\(258\) 5.26533e10 0.739839
\(259\) −4.73857e10 −0.654333
\(260\) 1.17952e9 0.0160076
\(261\) −2.55031e10 −0.340181
\(262\) −2.92525e10 −0.383536
\(263\) 1.13968e10 0.146886 0.0734432 0.997299i \(-0.476601\pi\)
0.0734432 + 0.997299i \(0.476601\pi\)
\(264\) −3.32349e10 −0.421092
\(265\) −1.05074e11 −1.30884
\(266\) −5.33625e10 −0.653535
\(267\) −8.99970e8 −0.0108375
\(268\) −7.94306e8 −0.00940548
\(269\) 6.01816e10 0.700775 0.350387 0.936605i \(-0.386050\pi\)
0.350387 + 0.936605i \(0.386050\pi\)
\(270\) −1.69042e10 −0.193579
\(271\) −1.89338e10 −0.213244 −0.106622 0.994300i \(-0.534003\pi\)
−0.106622 + 0.994300i \(0.534003\pi\)
\(272\) −1.72642e10 −0.191243
\(273\) 4.01347e10 0.437309
\(274\) −8.12978e10 −0.871367
\(275\) 4.19952e7 0.000442795 0
\(276\) 4.60997e8 0.00478198
\(277\) 1.06645e11 1.08838 0.544192 0.838960i \(-0.316836\pi\)
0.544192 + 0.838960i \(0.316836\pi\)
\(278\) 6.12929e10 0.615472
\(279\) 1.59857e10 0.157948
\(280\) −5.40034e10 −0.525061
\(281\) 8.24661e10 0.789036 0.394518 0.918888i \(-0.370912\pi\)
0.394518 + 0.918888i \(0.370912\pi\)
\(282\) 5.29340e10 0.498441
\(283\) −1.52295e11 −1.41139 −0.705695 0.708516i \(-0.749365\pi\)
−0.705695 + 0.708516i \(0.749365\pi\)
\(284\) 8.09817e8 0.00738677
\(285\) −7.91938e10 −0.711033
\(286\) −1.19747e11 −1.05832
\(287\) 3.43879e10 0.299183
\(288\) −8.68047e8 −0.00743493
\(289\) −1.14345e11 −0.964220
\(290\) 1.23641e11 1.02653
\(291\) −1.60176e10 −0.130942
\(292\) 1.27321e9 0.0102489
\(293\) 1.93446e10 0.153340 0.0766700 0.997057i \(-0.475571\pi\)
0.0766700 + 0.997057i \(0.475571\pi\)
\(294\) −5.36473e10 −0.418779
\(295\) 1.69396e10 0.130228
\(296\) −1.62782e11 −1.23252
\(297\) 1.89288e10 0.141162
\(298\) 2.23933e11 1.64492
\(299\) −1.47268e11 −1.06558
\(300\) 545351. 3.88714e−6 0
\(301\) −9.58032e10 −0.672714
\(302\) −2.08359e11 −1.44139
\(303\) 1.60877e10 0.109648
\(304\) −1.85359e11 −1.24475
\(305\) −2.16804e11 −1.43456
\(306\) 9.72424e9 0.0634029
\(307\) 1.74407e10 0.112057 0.0560287 0.998429i \(-0.482156\pi\)
0.0560287 + 0.998429i \(0.482156\pi\)
\(308\) −6.82037e8 −0.00431847
\(309\) 1.79327e9 0.0111901
\(310\) −7.74999e10 −0.476621
\(311\) −4.21904e10 −0.255736 −0.127868 0.991791i \(-0.540813\pi\)
−0.127868 + 0.991791i \(0.540813\pi\)
\(312\) 1.37873e11 0.823729
\(313\) −6.79419e10 −0.400118 −0.200059 0.979784i \(-0.564113\pi\)
−0.200059 + 0.979784i \(0.564113\pi\)
\(314\) 1.55594e11 0.903251
\(315\) 3.07573e10 0.176016
\(316\) −4.19557e8 −0.00236701
\(317\) −1.45150e11 −0.807328 −0.403664 0.914907i \(-0.632264\pi\)
−0.403664 + 0.914907i \(0.632264\pi\)
\(318\) 1.38524e11 0.759633
\(319\) −1.38449e11 −0.748569
\(320\) −1.85493e11 −0.988898
\(321\) −8.28423e10 −0.435491
\(322\) −7.60468e10 −0.394212
\(323\) 4.55567e10 0.232885
\(324\) 2.45809e8 0.00123921
\(325\) −1.74215e8 −0.000866184 0
\(326\) 7.28188e10 0.357079
\(327\) 1.10431e10 0.0534102
\(328\) 1.18131e11 0.563551
\(329\) −9.63138e10 −0.453218
\(330\) −9.17681e10 −0.425970
\(331\) 2.49225e10 0.114121 0.0570606 0.998371i \(-0.481827\pi\)
0.0570606 + 0.998371i \(0.481827\pi\)
\(332\) −6.08433e8 −0.00274847
\(333\) 9.27118e10 0.413177
\(334\) −5.97734e10 −0.262814
\(335\) 1.94458e11 0.843575
\(336\) 7.19898e10 0.308137
\(337\) −4.53476e11 −1.91522 −0.957612 0.288060i \(-0.906990\pi\)
−0.957612 + 0.288060i \(0.906990\pi\)
\(338\) 2.55475e11 1.06469
\(339\) −3.96302e10 −0.162977
\(340\) −5.19992e8 −0.00211029
\(341\) 8.67818e10 0.347563
\(342\) 1.04406e11 0.412673
\(343\) 2.32933e11 0.908671
\(344\) −3.29109e11 −1.26715
\(345\) −1.12859e11 −0.428894
\(346\) 9.07948e10 0.340580
\(347\) 2.24806e10 0.0832387 0.0416194 0.999134i \(-0.486748\pi\)
0.0416194 + 0.999134i \(0.486748\pi\)
\(348\) −1.79790e9 −0.00657142
\(349\) 6.47369e9 0.0233581 0.0116790 0.999932i \(-0.496282\pi\)
0.0116790 + 0.999932i \(0.496282\pi\)
\(350\) −8.99619e7 −0.000320444 0
\(351\) −7.85249e10 −0.276138
\(352\) −4.71238e9 −0.0163606
\(353\) 2.09469e11 0.718016 0.359008 0.933335i \(-0.383115\pi\)
0.359008 + 0.933335i \(0.383115\pi\)
\(354\) −2.23325e10 −0.0755826
\(355\) −1.98255e11 −0.662517
\(356\) −6.34456e7 −0.000209352 0
\(357\) −1.76933e10 −0.0576505
\(358\) 3.40059e11 1.09416
\(359\) 4.81083e11 1.52860 0.764301 0.644859i \(-0.223084\pi\)
0.764301 + 0.644859i \(0.223084\pi\)
\(360\) 1.05660e11 0.331549
\(361\) 1.66438e11 0.515787
\(362\) −2.34343e9 −0.00717238
\(363\) −8.82349e10 −0.266723
\(364\) 2.82939e9 0.00844767
\(365\) −3.11702e11 −0.919224
\(366\) 2.85825e11 0.832598
\(367\) −1.18448e11 −0.340823 −0.170412 0.985373i \(-0.554510\pi\)
−0.170412 + 0.985373i \(0.554510\pi\)
\(368\) −2.64155e11 −0.750833
\(369\) −6.72811e10 −0.188918
\(370\) −4.49474e11 −1.24680
\(371\) −2.52046e11 −0.690713
\(372\) 1.12695e9 0.00305114
\(373\) 2.72138e11 0.727946 0.363973 0.931409i \(-0.381420\pi\)
0.363973 + 0.931409i \(0.381420\pi\)
\(374\) 5.27901e10 0.139518
\(375\) 2.21029e11 0.577176
\(376\) −3.30863e11 −0.853696
\(377\) 5.74348e11 1.46433
\(378\) −4.05491e10 −0.102157
\(379\) −3.37404e11 −0.839991 −0.419995 0.907526i \(-0.637968\pi\)
−0.419995 + 0.907526i \(0.637968\pi\)
\(380\) −5.58296e9 −0.0137353
\(381\) 1.73196e11 0.421089
\(382\) −1.64839e11 −0.396073
\(383\) 5.80008e11 1.37733 0.688667 0.725077i \(-0.258196\pi\)
0.688667 + 0.725077i \(0.258196\pi\)
\(384\) 2.50032e11 0.586820
\(385\) 1.66973e11 0.387322
\(386\) 5.71698e11 1.31076
\(387\) 1.87442e11 0.424784
\(388\) −1.12920e9 −0.00252946
\(389\) −4.48244e11 −0.992525 −0.496262 0.868173i \(-0.665295\pi\)
−0.496262 + 0.868173i \(0.665295\pi\)
\(390\) 3.80695e11 0.833271
\(391\) 6.49228e10 0.140476
\(392\) 3.35322e11 0.717257
\(393\) −1.04137e11 −0.220210
\(394\) 6.96779e10 0.145667
\(395\) 1.02714e11 0.212296
\(396\) 1.33443e9 0.00272689
\(397\) 4.48520e11 0.906200 0.453100 0.891460i \(-0.350318\pi\)
0.453100 + 0.891460i \(0.350318\pi\)
\(398\) 9.87040e11 1.97179
\(399\) −1.89967e11 −0.375232
\(400\) −3.12490e8 −0.000610332 0
\(401\) 2.37587e11 0.458852 0.229426 0.973326i \(-0.426315\pi\)
0.229426 + 0.973326i \(0.426315\pi\)
\(402\) −2.56364e11 −0.489599
\(403\) −3.60010e11 −0.679895
\(404\) 1.13414e9 0.00211812
\(405\) −6.01778e10 −0.111145
\(406\) 2.96585e11 0.541728
\(407\) 5.03306e11 0.909196
\(408\) −6.07813e10 −0.108592
\(409\) 9.97089e11 1.76189 0.880946 0.473217i \(-0.156907\pi\)
0.880946 + 0.473217i \(0.156907\pi\)
\(410\) 3.26184e11 0.570079
\(411\) −2.89415e11 −0.500302
\(412\) 1.26421e8 0.000216164 0
\(413\) 4.06341e10 0.0687251
\(414\) 1.48788e11 0.248924
\(415\) 1.48953e11 0.246510
\(416\) 1.95490e10 0.0320041
\(417\) 2.18198e11 0.353378
\(418\) 5.66788e11 0.908087
\(419\) 9.76087e11 1.54713 0.773563 0.633720i \(-0.218473\pi\)
0.773563 + 0.633720i \(0.218473\pi\)
\(420\) 2.16831e9 0.00340017
\(421\) 1.69685e11 0.263254 0.131627 0.991299i \(-0.457980\pi\)
0.131627 + 0.991299i \(0.457980\pi\)
\(422\) 9.28633e11 1.42541
\(423\) 1.88441e11 0.286183
\(424\) −8.65845e11 −1.30105
\(425\) 7.68024e7 0.000114189 0
\(426\) 2.61371e11 0.384516
\(427\) −5.20061e11 −0.757058
\(428\) −5.84017e9 −0.00841256
\(429\) −4.26290e11 −0.607641
\(430\) −9.08734e11 −1.28183
\(431\) 9.50235e11 1.32643 0.663214 0.748430i \(-0.269192\pi\)
0.663214 + 0.748430i \(0.269192\pi\)
\(432\) −1.40850e11 −0.194573
\(433\) 1.24774e12 1.70581 0.852903 0.522069i \(-0.174840\pi\)
0.852903 + 0.522069i \(0.174840\pi\)
\(434\) −1.85903e11 −0.251527
\(435\) 4.40153e11 0.589389
\(436\) 7.78507e8 0.00103175
\(437\) 6.97053e11 0.914322
\(438\) 4.10934e11 0.533505
\(439\) −8.46452e11 −1.08771 −0.543854 0.839180i \(-0.683035\pi\)
−0.543854 + 0.839180i \(0.683035\pi\)
\(440\) 5.73595e11 0.729573
\(441\) −1.90981e11 −0.240445
\(442\) −2.18997e11 −0.272922
\(443\) −9.24332e11 −1.14028 −0.570140 0.821548i \(-0.693111\pi\)
−0.570140 + 0.821548i \(0.693111\pi\)
\(444\) 6.53594e9 0.00798151
\(445\) 1.55324e10 0.0187767
\(446\) −8.24598e11 −0.986814
\(447\) 7.97186e11 0.944444
\(448\) −4.44952e11 −0.521869
\(449\) 1.46015e12 1.69547 0.847734 0.530421i \(-0.177966\pi\)
0.847734 + 0.530421i \(0.177966\pi\)
\(450\) 1.76014e8 0.000202344 0
\(451\) −3.65250e11 −0.415715
\(452\) −2.79382e9 −0.00314830
\(453\) −7.41744e11 −0.827584
\(454\) −1.64581e12 −1.81814
\(455\) −6.92678e11 −0.757670
\(456\) −6.52586e11 −0.706799
\(457\) −1.36049e12 −1.45905 −0.729527 0.683953i \(-0.760260\pi\)
−0.729527 + 0.683953i \(0.760260\pi\)
\(458\) −1.06185e12 −1.12763
\(459\) 3.46176e10 0.0364033
\(460\) −7.95627e9 −0.00828513
\(461\) 1.78435e12 1.84003 0.920017 0.391878i \(-0.128174\pi\)
0.920017 + 0.391878i \(0.128174\pi\)
\(462\) −2.20129e11 −0.224796
\(463\) −1.15110e12 −1.16412 −0.582059 0.813146i \(-0.697753\pi\)
−0.582059 + 0.813146i \(0.697753\pi\)
\(464\) 1.03021e12 1.03180
\(465\) −2.75894e11 −0.273656
\(466\) −1.47818e12 −1.45208
\(467\) 7.32203e11 0.712370 0.356185 0.934416i \(-0.384077\pi\)
0.356185 + 0.934416i \(0.384077\pi\)
\(468\) −5.53581e9 −0.00533426
\(469\) 4.66457e11 0.445178
\(470\) −9.13578e11 −0.863585
\(471\) 5.53903e11 0.518608
\(472\) 1.39589e11 0.129453
\(473\) 1.01757e12 0.934737
\(474\) −1.35413e11 −0.123214
\(475\) 8.24599e8 0.000743228 0
\(476\) −1.24733e9 −0.00111366
\(477\) 4.93137e11 0.436149
\(478\) 2.89480e11 0.253625
\(479\) 5.44537e11 0.472626 0.236313 0.971677i \(-0.424061\pi\)
0.236313 + 0.971677i \(0.424061\pi\)
\(480\) 1.49815e10 0.0128816
\(481\) −2.08794e12 −1.77854
\(482\) −6.96509e11 −0.587781
\(483\) −2.70722e11 −0.226340
\(484\) −6.22033e9 −0.00515240
\(485\) 2.76445e11 0.226867
\(486\) 7.93357e10 0.0645068
\(487\) −3.03937e11 −0.244852 −0.122426 0.992478i \(-0.539067\pi\)
−0.122426 + 0.992478i \(0.539067\pi\)
\(488\) −1.78655e12 −1.42602
\(489\) 2.59230e11 0.205019
\(490\) 9.25889e11 0.725565
\(491\) 6.20518e11 0.481823 0.240912 0.970547i \(-0.422554\pi\)
0.240912 + 0.970547i \(0.422554\pi\)
\(492\) −4.74314e9 −0.00364941
\(493\) −2.53201e11 −0.193043
\(494\) −2.35129e12 −1.77638
\(495\) −3.26688e11 −0.244574
\(496\) −6.45751e11 −0.479068
\(497\) −4.75567e11 −0.349629
\(498\) −1.96374e11 −0.143071
\(499\) −2.20381e12 −1.59119 −0.795593 0.605831i \(-0.792841\pi\)
−0.795593 + 0.605831i \(0.792841\pi\)
\(500\) 1.55820e10 0.0111495
\(501\) −2.12789e11 −0.150897
\(502\) −1.29551e11 −0.0910491
\(503\) 2.05035e12 1.42815 0.714073 0.700072i \(-0.246849\pi\)
0.714073 + 0.700072i \(0.246849\pi\)
\(504\) 2.53452e11 0.174968
\(505\) −2.77654e11 −0.189973
\(506\) 8.07729e11 0.547758
\(507\) 9.09475e11 0.611301
\(508\) 1.22098e10 0.00813436
\(509\) 9.88432e11 0.652705 0.326352 0.945248i \(-0.394180\pi\)
0.326352 + 0.945248i \(0.394180\pi\)
\(510\) −1.67829e11 −0.109850
\(511\) −7.47697e11 −0.485101
\(512\) −1.52814e12 −0.982761
\(513\) 3.71677e11 0.236939
\(514\) 1.84040e12 1.16300
\(515\) −3.09498e10 −0.0193876
\(516\) 1.32142e10 0.00820573
\(517\) 1.02299e12 0.629747
\(518\) −1.07818e12 −0.657971
\(519\) 3.23223e11 0.195546
\(520\) −2.37953e12 −1.42717
\(521\) −2.84286e11 −0.169039 −0.0845193 0.996422i \(-0.526935\pi\)
−0.0845193 + 0.996422i \(0.526935\pi\)
\(522\) −5.80278e11 −0.342073
\(523\) 2.36673e12 1.38322 0.691609 0.722273i \(-0.256902\pi\)
0.691609 + 0.722273i \(0.256902\pi\)
\(524\) −7.34137e9 −0.00425389
\(525\) −3.20258e8 −0.000183985 0
\(526\) 2.59314e11 0.147703
\(527\) 1.58710e11 0.0896306
\(528\) −7.64637e11 −0.428157
\(529\) −8.07784e11 −0.448482
\(530\) −2.39077e12 −1.31612
\(531\) −7.95020e10 −0.0433963
\(532\) −1.33922e10 −0.00724851
\(533\) 1.51522e12 0.813211
\(534\) −2.04773e10 −0.0108977
\(535\) 1.42976e12 0.754520
\(536\) 1.60240e12 0.838553
\(537\) 1.21059e12 0.628220
\(538\) 1.36933e12 0.704672
\(539\) −1.03678e12 −0.529099
\(540\) −4.24238e9 −0.00214703
\(541\) 2.27027e12 1.13943 0.569717 0.821841i \(-0.307053\pi\)
0.569717 + 0.821841i \(0.307053\pi\)
\(542\) −4.30806e11 −0.214430
\(543\) −8.34245e9 −0.00411807
\(544\) −8.61817e9 −0.00421910
\(545\) −1.90590e11 −0.0925372
\(546\) 9.13195e11 0.439741
\(547\) 2.45903e12 1.17441 0.587206 0.809437i \(-0.300228\pi\)
0.587206 + 0.809437i \(0.300228\pi\)
\(548\) −2.04030e10 −0.00966454
\(549\) 1.01752e12 0.478043
\(550\) 9.55528e8 0.000445257 0
\(551\) −2.71852e12 −1.25647
\(552\) −9.30000e11 −0.426341
\(553\) 2.46386e11 0.112035
\(554\) 2.42653e12 1.09444
\(555\) −1.60010e12 −0.715859
\(556\) 1.53824e10 0.00682635
\(557\) 3.65527e12 1.60906 0.804529 0.593914i \(-0.202418\pi\)
0.804529 + 0.593914i \(0.202418\pi\)
\(558\) 3.63727e11 0.158826
\(559\) −4.22134e12 −1.82851
\(560\) −1.24246e12 −0.533870
\(561\) 1.87929e11 0.0801053
\(562\) 1.87637e12 0.793424
\(563\) −4.28647e12 −1.79809 −0.899047 0.437852i \(-0.855739\pi\)
−0.899047 + 0.437852i \(0.855739\pi\)
\(564\) 1.32846e10 0.00552832
\(565\) 6.83970e11 0.282370
\(566\) −3.46521e12 −1.41924
\(567\) −1.44352e11 −0.0586542
\(568\) −1.63370e12 −0.658573
\(569\) −2.55612e12 −1.02230 −0.511148 0.859493i \(-0.670779\pi\)
−0.511148 + 0.859493i \(0.670779\pi\)
\(570\) −1.80192e12 −0.714987
\(571\) −3.28901e12 −1.29480 −0.647400 0.762150i \(-0.724144\pi\)
−0.647400 + 0.762150i \(0.724144\pi\)
\(572\) −3.00523e10 −0.0117380
\(573\) −5.86816e11 −0.227408
\(574\) 7.82436e11 0.300847
\(575\) 1.17514e9 0.000448314 0
\(576\) 8.70563e11 0.329533
\(577\) −2.30318e12 −0.865040 −0.432520 0.901624i \(-0.642375\pi\)
−0.432520 + 0.901624i \(0.642375\pi\)
\(578\) −2.60171e12 −0.969582
\(579\) 2.03520e12 0.752583
\(580\) 3.10297e10 0.0113855
\(581\) 3.57303e11 0.130090
\(582\) −3.64453e11 −0.131670
\(583\) 2.67710e12 0.959746
\(584\) −2.56854e12 −0.913751
\(585\) 1.35525e12 0.478429
\(586\) 4.40152e11 0.154193
\(587\) 1.35652e12 0.471579 0.235790 0.971804i \(-0.424232\pi\)
0.235790 + 0.971804i \(0.424232\pi\)
\(588\) −1.34636e10 −0.00464477
\(589\) 1.70401e12 0.583382
\(590\) 3.85432e11 0.130952
\(591\) 2.48049e11 0.0836360
\(592\) −3.74514e12 −1.25320
\(593\) −1.38959e12 −0.461468 −0.230734 0.973017i \(-0.574113\pi\)
−0.230734 + 0.973017i \(0.574113\pi\)
\(594\) 4.30691e11 0.141947
\(595\) 3.05366e11 0.0998836
\(596\) 5.61996e10 0.0182442
\(597\) 3.51380e12 1.13212
\(598\) −3.35082e12 −1.07151
\(599\) 1.04751e12 0.332459 0.166230 0.986087i \(-0.446841\pi\)
0.166230 + 0.986087i \(0.446841\pi\)
\(600\) −1.10017e9 −0.000346561 0
\(601\) 3.83855e12 1.20014 0.600071 0.799947i \(-0.295139\pi\)
0.600071 + 0.799947i \(0.295139\pi\)
\(602\) −2.17983e12 −0.676455
\(603\) −9.12640e11 −0.281107
\(604\) −5.22910e10 −0.0159868
\(605\) 1.52283e12 0.462117
\(606\) 3.66047e11 0.110258
\(607\) −5.75921e11 −0.172192 −0.0860962 0.996287i \(-0.527439\pi\)
−0.0860962 + 0.996287i \(0.527439\pi\)
\(608\) −9.25302e10 −0.0274611
\(609\) 1.05582e12 0.311037
\(610\) −4.93300e12 −1.44254
\(611\) −4.24384e12 −1.23189
\(612\) 2.44045e9 0.000703217 0
\(613\) 5.65749e12 1.61827 0.809137 0.587620i \(-0.199935\pi\)
0.809137 + 0.587620i \(0.199935\pi\)
\(614\) 3.96832e11 0.112681
\(615\) 1.16119e12 0.327315
\(616\) 1.37592e12 0.385016
\(617\) 4.56000e12 1.26672 0.633361 0.773856i \(-0.281675\pi\)
0.633361 + 0.773856i \(0.281675\pi\)
\(618\) 4.08028e10 0.0112523
\(619\) 2.72974e12 0.747332 0.373666 0.927563i \(-0.378101\pi\)
0.373666 + 0.927563i \(0.378101\pi\)
\(620\) −1.94498e10 −0.00528632
\(621\) 5.29676e11 0.142922
\(622\) −9.59968e11 −0.257158
\(623\) 3.72585e10 0.00990899
\(624\) 3.17206e12 0.837549
\(625\) −3.81700e12 −1.00060
\(626\) −1.54590e12 −0.402343
\(627\) 2.01773e12 0.521385
\(628\) 3.90487e10 0.0100182
\(629\) 9.20465e11 0.234466
\(630\) 6.99829e11 0.176994
\(631\) −2.98551e12 −0.749698 −0.374849 0.927086i \(-0.622306\pi\)
−0.374849 + 0.927086i \(0.622306\pi\)
\(632\) 8.46400e11 0.211032
\(633\) 3.30587e12 0.818407
\(634\) −3.30263e12 −0.811817
\(635\) −2.98915e12 −0.729568
\(636\) 3.47649e10 0.00842527
\(637\) 4.30102e12 1.03501
\(638\) −3.15016e12 −0.752732
\(639\) 9.30463e11 0.220773
\(640\) −4.31526e12 −1.01671
\(641\) 3.08549e12 0.721878 0.360939 0.932590i \(-0.382456\pi\)
0.360939 + 0.932590i \(0.382456\pi\)
\(642\) −1.88493e12 −0.437913
\(643\) 4.78998e11 0.110506 0.0552528 0.998472i \(-0.482404\pi\)
0.0552528 + 0.998472i \(0.482404\pi\)
\(644\) −1.90852e10 −0.00437230
\(645\) −3.23503e12 −0.735970
\(646\) 1.03656e12 0.234180
\(647\) −5.97540e11 −0.134060 −0.0670298 0.997751i \(-0.521352\pi\)
−0.0670298 + 0.997751i \(0.521352\pi\)
\(648\) −4.95887e11 −0.110483
\(649\) −4.31594e11 −0.0954935
\(650\) −3.96395e9 −0.000871001 0
\(651\) −6.61804e11 −0.144416
\(652\) 1.82750e10 0.00396044
\(653\) 5.25724e12 1.13148 0.565742 0.824582i \(-0.308590\pi\)
0.565742 + 0.824582i \(0.308590\pi\)
\(654\) 2.51265e11 0.0537072
\(655\) 1.79728e12 0.381530
\(656\) 2.71785e12 0.573006
\(657\) 1.46290e12 0.306316
\(658\) −2.19145e12 −0.455738
\(659\) −4.38391e11 −0.0905476 −0.0452738 0.998975i \(-0.514416\pi\)
−0.0452738 + 0.998975i \(0.514416\pi\)
\(660\) −2.30307e10 −0.00472453
\(661\) −1.47713e12 −0.300963 −0.150482 0.988613i \(-0.548082\pi\)
−0.150482 + 0.988613i \(0.548082\pi\)
\(662\) 5.67069e11 0.114756
\(663\) −7.79614e11 −0.156700
\(664\) 1.22743e12 0.245042
\(665\) 3.27860e12 0.650117
\(666\) 2.10950e12 0.415475
\(667\) −3.87416e12 −0.757900
\(668\) −1.50011e10 −0.00291493
\(669\) −2.93551e12 −0.566587
\(670\) 4.42455e12 0.848266
\(671\) 5.52382e12 1.05193
\(672\) 3.59369e10 0.00679796
\(673\) 6.94568e12 1.30511 0.652555 0.757742i \(-0.273697\pi\)
0.652555 + 0.757742i \(0.273697\pi\)
\(674\) −1.03181e13 −1.92588
\(675\) 6.26596e8 0.000116177 0
\(676\) 6.41156e10 0.0118087
\(677\) −2.09846e12 −0.383930 −0.191965 0.981402i \(-0.561486\pi\)
−0.191965 + 0.981402i \(0.561486\pi\)
\(678\) −9.01715e11 −0.163884
\(679\) 6.63125e11 0.119724
\(680\) 1.04901e12 0.188144
\(681\) −5.85896e12 −1.04390
\(682\) 1.97457e12 0.349496
\(683\) −8.36376e12 −1.47065 −0.735323 0.677717i \(-0.762970\pi\)
−0.735323 + 0.677717i \(0.762970\pi\)
\(684\) 2.62023e10 0.00457706
\(685\) 4.99495e12 0.866810
\(686\) 5.29997e12 0.913724
\(687\) −3.78011e12 −0.647439
\(688\) −7.57183e12 −1.28841
\(689\) −1.11058e13 −1.87743
\(690\) −2.56791e12 −0.431280
\(691\) −2.29427e12 −0.382819 −0.191410 0.981510i \(-0.561306\pi\)
−0.191410 + 0.981510i \(0.561306\pi\)
\(692\) 2.27864e10 0.00377745
\(693\) −7.83645e11 −0.129068
\(694\) 5.11507e11 0.0837016
\(695\) −3.76585e12 −0.612253
\(696\) 3.62702e12 0.585880
\(697\) −6.67983e11 −0.107206
\(698\) 1.47297e11 0.0234880
\(699\) −5.26222e12 −0.833723
\(700\) −2.25774e7 −3.55412e−6 0
\(701\) −8.27605e12 −1.29447 −0.647235 0.762291i \(-0.724075\pi\)
−0.647235 + 0.762291i \(0.724075\pi\)
\(702\) −1.78670e12 −0.277673
\(703\) 9.88269e12 1.52608
\(704\) 4.72604e12 0.725138
\(705\) −3.25227e12 −0.495834
\(706\) 4.76610e12 0.722008
\(707\) −6.66025e11 −0.100254
\(708\) −5.60469e9 −0.000838304 0
\(709\) 6.39004e11 0.0949720 0.0474860 0.998872i \(-0.484879\pi\)
0.0474860 + 0.998872i \(0.484879\pi\)
\(710\) −4.51095e12 −0.666202
\(711\) −4.82062e11 −0.0707441
\(712\) 1.27993e11 0.0186649
\(713\) 2.42838e12 0.351896
\(714\) −4.02581e11 −0.0579710
\(715\) 7.35725e12 1.05278
\(716\) 8.53433e10 0.0121356
\(717\) 1.03053e12 0.145621
\(718\) 1.09462e13 1.53710
\(719\) 6.07965e12 0.848396 0.424198 0.905569i \(-0.360556\pi\)
0.424198 + 0.905569i \(0.360556\pi\)
\(720\) 2.43091e12 0.337111
\(721\) −7.42411e10 −0.0102314
\(722\) 3.78701e12 0.518655
\(723\) −2.47953e12 −0.337479
\(724\) −5.88121e8 −7.95505e−5 0
\(725\) −4.58306e9 −0.000616076 0
\(726\) −2.00763e12 −0.268206
\(727\) 2.87181e12 0.381286 0.190643 0.981659i \(-0.438943\pi\)
0.190643 + 0.981659i \(0.438943\pi\)
\(728\) −5.70792e12 −0.753158
\(729\) 2.82430e11 0.0370370
\(730\) −7.09223e12 −0.924336
\(731\) 1.86097e12 0.241052
\(732\) 7.17324e10 0.00923454
\(733\) 8.02066e11 0.102622 0.0513112 0.998683i \(-0.483660\pi\)
0.0513112 + 0.998683i \(0.483660\pi\)
\(734\) −2.69507e12 −0.342719
\(735\) 3.29610e12 0.416589
\(736\) −1.31865e11 −0.0165645
\(737\) −4.95446e12 −0.618576
\(738\) −1.53086e12 −0.189969
\(739\) 1.42081e13 1.75241 0.876204 0.481941i \(-0.160068\pi\)
0.876204 + 0.481941i \(0.160068\pi\)
\(740\) −1.12803e11 −0.0138286
\(741\) −8.37043e12 −1.01992
\(742\) −5.73487e12 −0.694554
\(743\) −8.54638e12 −1.02880 −0.514402 0.857549i \(-0.671986\pi\)
−0.514402 + 0.857549i \(0.671986\pi\)
\(744\) −2.27347e12 −0.272026
\(745\) −1.37585e13 −1.63632
\(746\) 6.19202e12 0.731994
\(747\) −6.99076e11 −0.0821451
\(748\) 1.32485e10 0.00154743
\(749\) 3.42965e12 0.398182
\(750\) 5.02912e12 0.580386
\(751\) 1.18674e13 1.36136 0.680682 0.732579i \(-0.261684\pi\)
0.680682 + 0.732579i \(0.261684\pi\)
\(752\) −7.61219e12 −0.868019
\(753\) −4.61194e11 −0.0522765
\(754\) 1.30683e13 1.47247
\(755\) 1.28016e13 1.43385
\(756\) −1.01764e10 −0.00113305
\(757\) −1.14291e13 −1.26498 −0.632488 0.774570i \(-0.717966\pi\)
−0.632488 + 0.774570i \(0.717966\pi\)
\(758\) −7.67705e12 −0.844662
\(759\) 2.87546e12 0.314499
\(760\) 1.12629e13 1.22458
\(761\) 8.11619e12 0.877246 0.438623 0.898671i \(-0.355466\pi\)
0.438623 + 0.898671i \(0.355466\pi\)
\(762\) 3.94076e12 0.423431
\(763\) −4.57180e11 −0.0488345
\(764\) −4.13690e10 −0.00439294
\(765\) −5.97459e11 −0.0630713
\(766\) 1.31971e13 1.38499
\(767\) 1.79044e12 0.186802
\(768\) 1.86218e11 0.0193150
\(769\) −7.35224e12 −0.758143 −0.379072 0.925367i \(-0.623757\pi\)
−0.379072 + 0.925367i \(0.623757\pi\)
\(770\) 3.79917e12 0.389476
\(771\) 6.55171e12 0.667744
\(772\) 1.43477e11 0.0145380
\(773\) 1.27079e13 1.28017 0.640085 0.768304i \(-0.278899\pi\)
0.640085 + 0.768304i \(0.278899\pi\)
\(774\) 4.26492e12 0.427146
\(775\) 2.87273e9 0.000286047 0
\(776\) 2.27801e12 0.225516
\(777\) −3.83824e12 −0.377779
\(778\) −1.01990e13 −0.998044
\(779\) −7.17188e12 −0.697774
\(780\) 9.55415e10 0.00924200
\(781\) 5.05122e12 0.485810
\(782\) 1.47721e12 0.141257
\(783\) −2.06575e12 −0.196404
\(784\) 7.71476e12 0.729290
\(785\) −9.55970e12 −0.898527
\(786\) −2.36945e12 −0.221435
\(787\) −1.81646e13 −1.68787 −0.843935 0.536445i \(-0.819767\pi\)
−0.843935 + 0.536445i \(0.819767\pi\)
\(788\) 1.74868e10 0.00161563
\(789\) 9.23140e11 0.0848049
\(790\) 2.33708e12 0.213477
\(791\) 1.64068e12 0.149015
\(792\) −2.69203e12 −0.243118
\(793\) −2.29152e13 −2.05776
\(794\) 1.02053e13 0.911240
\(795\) −8.51096e12 −0.755660
\(796\) 2.47714e11 0.0218696
\(797\) 2.04779e13 1.79773 0.898863 0.438230i \(-0.144394\pi\)
0.898863 + 0.438230i \(0.144394\pi\)
\(798\) −4.32236e12 −0.377319
\(799\) 1.87089e12 0.162401
\(800\) −1.55993e8 −1.34648e−5 0
\(801\) −7.28976e10 −0.00625701
\(802\) 5.40587e12 0.461404
\(803\) 7.94165e12 0.674048
\(804\) −6.43388e10 −0.00543026
\(805\) 4.67233e12 0.392150
\(806\) −8.19139e12 −0.683675
\(807\) 4.87471e12 0.404593
\(808\) −2.28797e12 −0.188842
\(809\) 2.77264e12 0.227575 0.113788 0.993505i \(-0.463702\pi\)
0.113788 + 0.993505i \(0.463702\pi\)
\(810\) −1.36924e12 −0.111763
\(811\) 4.45984e12 0.362014 0.181007 0.983482i \(-0.442064\pi\)
0.181007 + 0.983482i \(0.442064\pi\)
\(812\) 7.44327e10 0.00600844
\(813\) −1.53364e12 −0.123116
\(814\) 1.14518e13 0.914252
\(815\) −4.47400e12 −0.355211
\(816\) −1.39840e12 −0.110414
\(817\) 1.99806e13 1.56895
\(818\) 2.26870e13 1.77169
\(819\) 3.25091e12 0.252480
\(820\) 8.18610e10 0.00632288
\(821\) −7.92103e12 −0.608468 −0.304234 0.952597i \(-0.598400\pi\)
−0.304234 + 0.952597i \(0.598400\pi\)
\(822\) −6.58512e12 −0.503084
\(823\) 9.57400e12 0.727435 0.363718 0.931509i \(-0.381507\pi\)
0.363718 + 0.931509i \(0.381507\pi\)
\(824\) −2.55038e11 −0.0192722
\(825\) 3.40161e9 0.000255648 0
\(826\) 9.24557e11 0.0691073
\(827\) −1.26247e13 −0.938524 −0.469262 0.883059i \(-0.655480\pi\)
−0.469262 + 0.883059i \(0.655480\pi\)
\(828\) 3.73408e10 0.00276088
\(829\) 4.32575e12 0.318101 0.159051 0.987270i \(-0.449157\pi\)
0.159051 + 0.987270i \(0.449157\pi\)
\(830\) 3.38917e12 0.247881
\(831\) 8.63826e12 0.628379
\(832\) −1.96057e13 −1.41850
\(833\) −1.89610e12 −0.136445
\(834\) 4.96472e12 0.355343
\(835\) 3.67249e12 0.261440
\(836\) 1.42245e11 0.0100718
\(837\) 1.29484e12 0.0911910
\(838\) 2.22092e13 1.55573
\(839\) 2.32435e11 0.0161947 0.00809735 0.999967i \(-0.497423\pi\)
0.00809735 + 0.999967i \(0.497423\pi\)
\(840\) −4.37427e12 −0.303144
\(841\) 6.02196e11 0.0415103
\(842\) 3.86089e12 0.264718
\(843\) 6.67975e12 0.455550
\(844\) 2.33055e11 0.0158095
\(845\) −1.56965e13 −1.05912
\(846\) 4.28765e12 0.287775
\(847\) 3.65290e12 0.243872
\(848\) −1.99205e13 −1.32288
\(849\) −1.23359e13 −0.814866
\(850\) 1.74750e9 0.000114824 0
\(851\) 1.40838e13 0.920529
\(852\) 6.55952e10 0.00426475
\(853\) −1.00294e13 −0.648644 −0.324322 0.945947i \(-0.605136\pi\)
−0.324322 + 0.945947i \(0.605136\pi\)
\(854\) −1.18331e13 −0.761268
\(855\) −6.41470e12 −0.410515
\(856\) 1.17817e13 0.750028
\(857\) 1.21511e13 0.769487 0.384743 0.923024i \(-0.374290\pi\)
0.384743 + 0.923024i \(0.374290\pi\)
\(858\) −9.69947e12 −0.611020
\(859\) −1.02223e13 −0.640588 −0.320294 0.947318i \(-0.603782\pi\)
−0.320294 + 0.947318i \(0.603782\pi\)
\(860\) −2.28061e11 −0.0142170
\(861\) 2.78542e12 0.172733
\(862\) 2.16209e13 1.33380
\(863\) 1.52014e13 0.932897 0.466449 0.884548i \(-0.345533\pi\)
0.466449 + 0.884548i \(0.345533\pi\)
\(864\) −7.03118e10 −0.00429256
\(865\) −5.57845e12 −0.338798
\(866\) 2.83902e13 1.71529
\(867\) −9.26193e12 −0.556692
\(868\) −4.66555e10 −0.00278974
\(869\) −2.61698e12 −0.155672
\(870\) 1.00149e13 0.592667
\(871\) 2.05533e13 1.21004
\(872\) −1.57053e12 −0.0919862
\(873\) −1.29743e12 −0.0755994
\(874\) 1.58602e13 0.919406
\(875\) −9.15053e12 −0.527728
\(876\) 1.03130e11 0.00591723
\(877\) −5.03270e12 −0.287278 −0.143639 0.989630i \(-0.545880\pi\)
−0.143639 + 0.989630i \(0.545880\pi\)
\(878\) −1.92595e13 −1.09376
\(879\) 1.56691e12 0.0885308
\(880\) 1.31967e13 0.741813
\(881\) 1.51352e13 0.846439 0.423220 0.906027i \(-0.360900\pi\)
0.423220 + 0.906027i \(0.360900\pi\)
\(882\) −4.34543e12 −0.241782
\(883\) 3.10810e13 1.72057 0.860283 0.509817i \(-0.170287\pi\)
0.860283 + 0.509817i \(0.170287\pi\)
\(884\) −5.49608e10 −0.00302704
\(885\) 1.37211e12 0.0751873
\(886\) −2.10316e13 −1.14662
\(887\) 2.22009e13 1.20424 0.602122 0.798404i \(-0.294322\pi\)
0.602122 + 0.798404i \(0.294322\pi\)
\(888\) −1.31854e13 −0.711597
\(889\) −7.17025e12 −0.385014
\(890\) 3.53413e11 0.0188811
\(891\) 1.53323e12 0.0815000
\(892\) −2.06946e11 −0.0109450
\(893\) 2.00871e13 1.05702
\(894\) 1.81386e13 0.949696
\(895\) −2.08933e13 −1.08844
\(896\) −1.03513e13 −0.536546
\(897\) −1.19287e13 −0.615215
\(898\) 3.32232e13 1.70490
\(899\) −9.47075e12 −0.483577
\(900\) 4.41734e7 2.24424e−6 0
\(901\) 4.89598e12 0.247502
\(902\) −8.31062e12 −0.418027
\(903\) −7.76006e12 −0.388392
\(904\) 5.63616e12 0.280689
\(905\) 1.43981e11 0.00713487
\(906\) −1.68771e13 −0.832186
\(907\) −2.69908e13 −1.32429 −0.662145 0.749376i \(-0.730354\pi\)
−0.662145 + 0.749376i \(0.730354\pi\)
\(908\) −4.13042e11 −0.0201654
\(909\) 1.30310e12 0.0633054
\(910\) −1.57607e13 −0.761883
\(911\) −6.41073e12 −0.308372 −0.154186 0.988042i \(-0.549276\pi\)
−0.154186 + 0.988042i \(0.549276\pi\)
\(912\) −1.50141e13 −0.718657
\(913\) −3.79509e12 −0.180760
\(914\) −3.09555e13 −1.46717
\(915\) −1.75612e13 −0.828244
\(916\) −2.66488e11 −0.0125068
\(917\) 4.31123e12 0.201344
\(918\) 7.87663e11 0.0366057
\(919\) −3.08233e13 −1.42548 −0.712738 0.701431i \(-0.752545\pi\)
−0.712738 + 0.701431i \(0.752545\pi\)
\(920\) 1.60507e13 0.738667
\(921\) 1.41269e12 0.0646964
\(922\) 4.05998e13 1.85027
\(923\) −2.09547e13 −0.950329
\(924\) −5.52450e10 −0.00249327
\(925\) 1.66609e10 0.000748273 0
\(926\) −2.61912e13 −1.17059
\(927\) 1.45255e11 0.00646060
\(928\) 5.14275e11 0.0227630
\(929\) −1.27614e13 −0.562119 −0.281060 0.959690i \(-0.590686\pi\)
−0.281060 + 0.959690i \(0.590686\pi\)
\(930\) −6.27749e12 −0.275177
\(931\) −2.03577e13 −0.888088
\(932\) −3.70973e11 −0.0161054
\(933\) −3.41742e12 −0.147649
\(934\) 1.66600e13 0.716331
\(935\) −3.24344e12 −0.138788
\(936\) 1.11677e13 0.475580
\(937\) −4.60555e13 −1.95188 −0.975940 0.218037i \(-0.930035\pi\)
−0.975940 + 0.218037i \(0.930035\pi\)
\(938\) 1.06134e13 0.447654
\(939\) −5.50329e12 −0.231008
\(940\) −2.29277e11 −0.00957823
\(941\) −2.31569e12 −0.0962782 −0.0481391 0.998841i \(-0.515329\pi\)
−0.0481391 + 0.998841i \(0.515329\pi\)
\(942\) 1.26031e13 0.521492
\(943\) −1.02206e13 −0.420897
\(944\) 3.21153e12 0.131625
\(945\) 2.49134e12 0.101623
\(946\) 2.31530e13 0.939935
\(947\) 1.36583e13 0.551853 0.275926 0.961179i \(-0.411015\pi\)
0.275926 + 0.961179i \(0.411015\pi\)
\(948\) −3.39842e10 −0.00136659
\(949\) −3.29455e13 −1.31855
\(950\) 1.87623e10 0.000747361 0
\(951\) −1.17571e13 −0.466111
\(952\) 2.51633e12 0.0992889
\(953\) 3.99596e13 1.56929 0.784645 0.619946i \(-0.212845\pi\)
0.784645 + 0.619946i \(0.212845\pi\)
\(954\) 1.12205e13 0.438575
\(955\) 1.01278e13 0.394001
\(956\) 7.26495e10 0.00281302
\(957\) −1.12144e13 −0.432186
\(958\) 1.23900e13 0.475254
\(959\) 1.19817e13 0.457440
\(960\) −1.50249e13 −0.570941
\(961\) −2.05032e13 −0.775473
\(962\) −4.75074e13 −1.78844
\(963\) −6.71022e12 −0.251431
\(964\) −1.74800e11 −0.00651921
\(965\) −3.51252e13 −1.30391
\(966\) −6.15979e12 −0.227598
\(967\) 2.52200e13 0.927525 0.463762 0.885960i \(-0.346499\pi\)
0.463762 + 0.885960i \(0.346499\pi\)
\(968\) 1.25487e13 0.459366
\(969\) 3.69009e12 0.134456
\(970\) 6.29002e12 0.228128
\(971\) 3.42705e13 1.23718 0.618591 0.785713i \(-0.287704\pi\)
0.618591 + 0.785713i \(0.287704\pi\)
\(972\) 1.99106e10 0.000715460 0
\(973\) −9.03335e12 −0.323103
\(974\) −6.91556e12 −0.246213
\(975\) −1.41114e10 −0.000500092 0
\(976\) −4.11032e13 −1.44994
\(977\) 1.42817e13 0.501481 0.250741 0.968054i \(-0.419326\pi\)
0.250741 + 0.968054i \(0.419326\pi\)
\(978\) 5.89832e12 0.206160
\(979\) −3.95740e11 −0.0137686
\(980\) 2.32367e11 0.00804741
\(981\) 8.94488e11 0.0308364
\(982\) 1.41188e13 0.484503
\(983\) −2.29765e13 −0.784863 −0.392431 0.919781i \(-0.628366\pi\)
−0.392431 + 0.919781i \(0.628366\pi\)
\(984\) 9.56864e12 0.325366
\(985\) −4.28103e12 −0.144905
\(986\) −5.76114e12 −0.194116
\(987\) −7.80142e12 −0.261665
\(988\) −5.90094e11 −0.0197022
\(989\) 2.84743e13 0.946388
\(990\) −7.43321e12 −0.245934
\(991\) 6.00264e12 0.197702 0.0988510 0.995102i \(-0.468483\pi\)
0.0988510 + 0.995102i \(0.468483\pi\)
\(992\) −3.22355e11 −0.0105690
\(993\) 2.01873e12 0.0658879
\(994\) −1.08207e13 −0.351573
\(995\) −6.06440e13 −1.96148
\(996\) −4.92831e10 −0.00158683
\(997\) −3.23900e13 −1.03820 −0.519102 0.854712i \(-0.673734\pi\)
−0.519102 + 0.854712i \(0.673734\pi\)
\(998\) −5.01438e13 −1.60004
\(999\) 7.50966e12 0.238548
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.1.16 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.16 22 1.1 even 1 trivial