Properties

Label 177.14.a.b.1.20
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
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: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+52.9360 q^{2} -729.000 q^{3} -5389.78 q^{4} -33150.0 q^{5} -38590.4 q^{6} -413060. q^{7} -718965. q^{8} +531441. q^{9} +O(q^{10})\) \(q+52.9360 q^{2} -729.000 q^{3} -5389.78 q^{4} -33150.0 q^{5} -38590.4 q^{6} -413060. q^{7} -718965. q^{8} +531441. q^{9} -1.75483e6 q^{10} +2.37030e6 q^{11} +3.92915e6 q^{12} -1.44816e7 q^{13} -2.18658e7 q^{14} +2.41664e7 q^{15} +6.09389e6 q^{16} -9.80573e7 q^{17} +2.81324e7 q^{18} +2.31816e8 q^{19} +1.78671e8 q^{20} +3.01121e8 q^{21} +1.25474e8 q^{22} +7.61140e8 q^{23} +5.24126e8 q^{24} -1.21779e8 q^{25} -7.66597e8 q^{26} -3.87420e8 q^{27} +2.22630e9 q^{28} -2.21082e9 q^{29} +1.27927e9 q^{30} +6.65917e8 q^{31} +6.21235e9 q^{32} -1.72795e9 q^{33} -5.19076e9 q^{34} +1.36930e10 q^{35} -2.86435e9 q^{36} +3.56511e9 q^{37} +1.22714e10 q^{38} +1.05571e10 q^{39} +2.38337e10 q^{40} +5.94111e10 q^{41} +1.59401e10 q^{42} +3.00720e9 q^{43} -1.27754e10 q^{44} -1.76173e10 q^{45} +4.02917e10 q^{46} +7.04075e10 q^{47} -4.44245e9 q^{48} +7.37295e10 q^{49} -6.44648e9 q^{50} +7.14837e10 q^{51} +7.80524e10 q^{52} -2.38186e11 q^{53} -2.05085e10 q^{54} -7.85755e10 q^{55} +2.96976e11 q^{56} -1.68994e11 q^{57} -1.17032e11 q^{58} -4.21805e10 q^{59} -1.30251e11 q^{60} +4.48921e11 q^{61} +3.52510e10 q^{62} -2.19517e11 q^{63} +2.78936e11 q^{64} +4.80064e11 q^{65} -9.14708e10 q^{66} -1.96931e11 q^{67} +5.28507e11 q^{68} -5.54871e11 q^{69} +7.24850e11 q^{70} -4.00518e11 q^{71} -3.82088e11 q^{72} -2.04862e11 q^{73} +1.88723e11 q^{74} +8.87767e10 q^{75} -1.24943e12 q^{76} -9.79076e11 q^{77} +5.58849e11 q^{78} +1.96050e12 q^{79} -2.02013e11 q^{80} +2.82430e11 q^{81} +3.14499e12 q^{82} +4.20575e11 q^{83} -1.62297e12 q^{84} +3.25060e12 q^{85} +1.59189e11 q^{86} +1.61169e12 q^{87} -1.70416e12 q^{88} +4.35059e11 q^{89} -9.32589e11 q^{90} +5.98176e12 q^{91} -4.10237e12 q^{92} -4.85453e11 q^{93} +3.72709e12 q^{94} -7.68469e12 q^{95} -4.52880e12 q^{96} -6.74801e12 q^{97} +3.90295e12 q^{98} +1.25968e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 52.9360 0.584866 0.292433 0.956286i \(-0.405535\pi\)
0.292433 + 0.956286i \(0.405535\pi\)
\(3\) −729.000 −0.577350
\(4\) −5389.78 −0.657932
\(5\) −33150.0 −0.948809 −0.474405 0.880307i \(-0.657337\pi\)
−0.474405 + 0.880307i \(0.657337\pi\)
\(6\) −38590.4 −0.337673
\(7\) −413060. −1.32702 −0.663508 0.748170i \(-0.730933\pi\)
−0.663508 + 0.748170i \(0.730933\pi\)
\(8\) −718965. −0.969668
\(9\) 531441. 0.333333
\(10\) −1.75483e6 −0.554926
\(11\) 2.37030e6 0.403414 0.201707 0.979446i \(-0.435351\pi\)
0.201707 + 0.979446i \(0.435351\pi\)
\(12\) 3.92915e6 0.379857
\(13\) −1.44816e7 −0.832116 −0.416058 0.909338i \(-0.636589\pi\)
−0.416058 + 0.909338i \(0.636589\pi\)
\(14\) −2.18658e7 −0.776126
\(15\) 2.41664e7 0.547795
\(16\) 6.09389e6 0.0908060
\(17\) −9.80573e7 −0.985285 −0.492642 0.870232i \(-0.663969\pi\)
−0.492642 + 0.870232i \(0.663969\pi\)
\(18\) 2.81324e7 0.194955
\(19\) 2.31816e8 1.13043 0.565216 0.824943i \(-0.308793\pi\)
0.565216 + 0.824943i \(0.308793\pi\)
\(20\) 1.78671e8 0.624252
\(21\) 3.01121e8 0.766153
\(22\) 1.25474e8 0.235943
\(23\) 7.61140e8 1.07210 0.536048 0.844188i \(-0.319917\pi\)
0.536048 + 0.844188i \(0.319917\pi\)
\(24\) 5.24126e8 0.559838
\(25\) −1.21779e8 −0.0997611
\(26\) −7.66597e8 −0.486676
\(27\) −3.87420e8 −0.192450
\(28\) 2.22630e9 0.873085
\(29\) −2.21082e9 −0.690187 −0.345093 0.938568i \(-0.612153\pi\)
−0.345093 + 0.938568i \(0.612153\pi\)
\(30\) 1.27927e9 0.320387
\(31\) 6.65917e8 0.134763 0.0673813 0.997727i \(-0.478536\pi\)
0.0673813 + 0.997727i \(0.478536\pi\)
\(32\) 6.21235e9 1.02278
\(33\) −1.72795e9 −0.232911
\(34\) −5.19076e9 −0.576259
\(35\) 1.36930e10 1.25908
\(36\) −2.86435e9 −0.219311
\(37\) 3.56511e9 0.228435 0.114217 0.993456i \(-0.463564\pi\)
0.114217 + 0.993456i \(0.463564\pi\)
\(38\) 1.22714e10 0.661151
\(39\) 1.05571e10 0.480422
\(40\) 2.38337e10 0.920030
\(41\) 5.94111e10 1.95332 0.976658 0.214801i \(-0.0689101\pi\)
0.976658 + 0.214801i \(0.0689101\pi\)
\(42\) 1.59401e10 0.448097
\(43\) 3.00720e9 0.0725467 0.0362734 0.999342i \(-0.488451\pi\)
0.0362734 + 0.999342i \(0.488451\pi\)
\(44\) −1.27754e10 −0.265419
\(45\) −1.76173e10 −0.316270
\(46\) 4.02917e10 0.627032
\(47\) 7.04075e10 0.952759 0.476379 0.879240i \(-0.341949\pi\)
0.476379 + 0.879240i \(0.341949\pi\)
\(48\) −4.44245e9 −0.0524269
\(49\) 7.37295e10 0.760969
\(50\) −6.44648e9 −0.0583469
\(51\) 7.14837e10 0.568854
\(52\) 7.80524e10 0.547475
\(53\) −2.38186e11 −1.47612 −0.738061 0.674734i \(-0.764258\pi\)
−0.738061 + 0.674734i \(0.764258\pi\)
\(54\) −2.05085e10 −0.112558
\(55\) −7.85755e10 −0.382763
\(56\) 2.96976e11 1.28676
\(57\) −1.68994e11 −0.652655
\(58\) −1.17032e11 −0.403667
\(59\) −4.21805e10 −0.130189
\(60\) −1.30251e11 −0.360412
\(61\) 4.48921e11 1.11564 0.557822 0.829961i \(-0.311637\pi\)
0.557822 + 0.829961i \(0.311637\pi\)
\(62\) 3.52510e10 0.0788180
\(63\) −2.19517e11 −0.442338
\(64\) 2.78936e11 0.507382
\(65\) 4.80064e11 0.789519
\(66\) −9.14708e10 −0.136222
\(67\) −1.96931e11 −0.265967 −0.132984 0.991118i \(-0.542456\pi\)
−0.132984 + 0.991118i \(0.542456\pi\)
\(68\) 5.28507e11 0.648250
\(69\) −5.54871e11 −0.618975
\(70\) 7.24850e11 0.736395
\(71\) −4.00518e11 −0.371059 −0.185529 0.982639i \(-0.559400\pi\)
−0.185529 + 0.982639i \(0.559400\pi\)
\(72\) −3.82088e11 −0.323223
\(73\) −2.04862e11 −0.158440 −0.0792198 0.996857i \(-0.525243\pi\)
−0.0792198 + 0.996857i \(0.525243\pi\)
\(74\) 1.88723e11 0.133604
\(75\) 8.87767e10 0.0575971
\(76\) −1.24943e12 −0.743747
\(77\) −9.79076e11 −0.535337
\(78\) 5.58849e11 0.280983
\(79\) 1.96050e12 0.907384 0.453692 0.891159i \(-0.350107\pi\)
0.453692 + 0.891159i \(0.350107\pi\)
\(80\) −2.02013e11 −0.0861576
\(81\) 2.82430e11 0.111111
\(82\) 3.14499e12 1.14243
\(83\) 4.20575e11 0.141200 0.0706002 0.997505i \(-0.477509\pi\)
0.0706002 + 0.997505i \(0.477509\pi\)
\(84\) −1.62297e12 −0.504076
\(85\) 3.25060e12 0.934847
\(86\) 1.59189e11 0.0424301
\(87\) 1.61169e12 0.398479
\(88\) −1.70416e12 −0.391178
\(89\) 4.35059e11 0.0927925 0.0463962 0.998923i \(-0.485226\pi\)
0.0463962 + 0.998923i \(0.485226\pi\)
\(90\) −9.32589e11 −0.184975
\(91\) 5.98176e12 1.10423
\(92\) −4.10237e12 −0.705366
\(93\) −4.85453e11 −0.0778052
\(94\) 3.72709e12 0.557236
\(95\) −7.68469e12 −1.07256
\(96\) −4.52880e12 −0.590501
\(97\) −6.74801e12 −0.822545 −0.411272 0.911513i \(-0.634915\pi\)
−0.411272 + 0.911513i \(0.634915\pi\)
\(98\) 3.90295e12 0.445065
\(99\) 1.25968e12 0.134471
\(100\) 6.56360e11 0.0656360
\(101\) −8.27950e10 −0.00776095 −0.00388048 0.999992i \(-0.501235\pi\)
−0.00388048 + 0.999992i \(0.501235\pi\)
\(102\) 3.78406e12 0.332704
\(103\) −4.93712e12 −0.407410 −0.203705 0.979032i \(-0.565298\pi\)
−0.203705 + 0.979032i \(0.565298\pi\)
\(104\) 1.04117e13 0.806876
\(105\) −9.98216e12 −0.726933
\(106\) −1.26086e13 −0.863334
\(107\) 7.69066e12 0.495415 0.247708 0.968835i \(-0.420323\pi\)
0.247708 + 0.968835i \(0.420323\pi\)
\(108\) 2.08811e12 0.126619
\(109\) 3.61733e12 0.206593 0.103296 0.994651i \(-0.467061\pi\)
0.103296 + 0.994651i \(0.467061\pi\)
\(110\) −4.15948e12 −0.223865
\(111\) −2.59897e12 −0.131887
\(112\) −2.51714e12 −0.120501
\(113\) −3.57321e13 −1.61454 −0.807269 0.590184i \(-0.799055\pi\)
−0.807269 + 0.590184i \(0.799055\pi\)
\(114\) −8.94585e12 −0.381716
\(115\) −2.52318e13 −1.01721
\(116\) 1.19158e13 0.454096
\(117\) −7.69610e12 −0.277372
\(118\) −2.23287e12 −0.0761431
\(119\) 4.05035e13 1.30749
\(120\) −1.73748e13 −0.531179
\(121\) −2.89044e13 −0.837257
\(122\) 2.37641e13 0.652502
\(123\) −4.33107e13 −1.12775
\(124\) −3.58914e12 −0.0886645
\(125\) 4.45033e13 1.04346
\(126\) −1.16204e13 −0.258709
\(127\) 3.87874e13 0.820288 0.410144 0.912021i \(-0.365478\pi\)
0.410144 + 0.912021i \(0.365478\pi\)
\(128\) −3.61258e13 −0.726027
\(129\) −2.19225e12 −0.0418849
\(130\) 2.54127e13 0.461763
\(131\) −1.07756e13 −0.186286 −0.0931428 0.995653i \(-0.529691\pi\)
−0.0931428 + 0.995653i \(0.529691\pi\)
\(132\) 9.31326e12 0.153240
\(133\) −9.57537e13 −1.50010
\(134\) −1.04248e13 −0.155555
\(135\) 1.28430e13 0.182598
\(136\) 7.04998e13 0.955399
\(137\) −1.24590e13 −0.160990 −0.0804952 0.996755i \(-0.525650\pi\)
−0.0804952 + 0.996755i \(0.525650\pi\)
\(138\) −2.93727e13 −0.362017
\(139\) −1.48455e13 −0.174581 −0.0872906 0.996183i \(-0.527821\pi\)
−0.0872906 + 0.996183i \(0.527821\pi\)
\(140\) −7.38020e13 −0.828391
\(141\) −5.13271e13 −0.550076
\(142\) −2.12018e13 −0.217020
\(143\) −3.43257e13 −0.335687
\(144\) 3.23854e12 0.0302687
\(145\) 7.32888e13 0.654855
\(146\) −1.08446e13 −0.0926660
\(147\) −5.37488e13 −0.439346
\(148\) −1.92152e13 −0.150295
\(149\) 3.89395e13 0.291528 0.145764 0.989319i \(-0.453436\pi\)
0.145764 + 0.989319i \(0.453436\pi\)
\(150\) 4.69948e12 0.0336866
\(151\) 1.15177e14 0.790706 0.395353 0.918529i \(-0.370622\pi\)
0.395353 + 0.918529i \(0.370622\pi\)
\(152\) −1.66667e14 −1.09614
\(153\) −5.21116e13 −0.328428
\(154\) −5.18284e13 −0.313100
\(155\) −2.20752e13 −0.127864
\(156\) −5.69002e13 −0.316085
\(157\) 1.43467e14 0.764550 0.382275 0.924049i \(-0.375141\pi\)
0.382275 + 0.924049i \(0.375141\pi\)
\(158\) 1.03781e14 0.530698
\(159\) 1.73637e14 0.852240
\(160\) −2.05940e14 −0.970420
\(161\) −3.14396e14 −1.42269
\(162\) 1.49507e13 0.0649851
\(163\) −9.35409e11 −0.00390645 −0.00195322 0.999998i \(-0.500622\pi\)
−0.00195322 + 0.999998i \(0.500622\pi\)
\(164\) −3.20213e14 −1.28515
\(165\) 5.72816e13 0.220988
\(166\) 2.22636e13 0.0825833
\(167\) 3.04805e14 1.08734 0.543670 0.839299i \(-0.317034\pi\)
0.543670 + 0.839299i \(0.317034\pi\)
\(168\) −2.16495e14 −0.742913
\(169\) −9.31593e13 −0.307583
\(170\) 1.72074e14 0.546760
\(171\) 1.23196e14 0.376810
\(172\) −1.62082e13 −0.0477308
\(173\) 2.18937e14 0.620896 0.310448 0.950590i \(-0.399521\pi\)
0.310448 + 0.950590i \(0.399521\pi\)
\(174\) 8.53164e13 0.233057
\(175\) 5.03019e13 0.132385
\(176\) 1.44444e13 0.0366324
\(177\) 3.07496e13 0.0751646
\(178\) 2.30303e13 0.0542712
\(179\) 1.26997e14 0.288569 0.144284 0.989536i \(-0.453912\pi\)
0.144284 + 0.989536i \(0.453912\pi\)
\(180\) 9.49532e13 0.208084
\(181\) −8.92312e14 −1.88628 −0.943140 0.332396i \(-0.892143\pi\)
−0.943140 + 0.332396i \(0.892143\pi\)
\(182\) 3.16650e14 0.645827
\(183\) −3.27263e14 −0.644117
\(184\) −5.47233e14 −1.03958
\(185\) −1.18184e14 −0.216741
\(186\) −2.56980e13 −0.0455056
\(187\) −2.32425e14 −0.397478
\(188\) −3.79481e14 −0.626850
\(189\) 1.60028e14 0.255384
\(190\) −4.06797e14 −0.627306
\(191\) −1.04194e15 −1.55284 −0.776418 0.630219i \(-0.782965\pi\)
−0.776418 + 0.630219i \(0.782965\pi\)
\(192\) −2.03344e14 −0.292937
\(193\) 9.41290e14 1.31099 0.655497 0.755198i \(-0.272459\pi\)
0.655497 + 0.755198i \(0.272459\pi\)
\(194\) −3.57213e14 −0.481078
\(195\) −3.49967e14 −0.455829
\(196\) −3.97386e14 −0.500666
\(197\) −1.45040e15 −1.76790 −0.883950 0.467581i \(-0.845126\pi\)
−0.883950 + 0.467581i \(0.845126\pi\)
\(198\) 6.66822e13 0.0786477
\(199\) 9.13225e14 1.04240 0.521198 0.853436i \(-0.325485\pi\)
0.521198 + 0.853436i \(0.325485\pi\)
\(200\) 8.75547e13 0.0967351
\(201\) 1.43563e14 0.153556
\(202\) −4.38284e12 −0.00453912
\(203\) 9.13201e14 0.915888
\(204\) −3.85281e14 −0.374267
\(205\) −1.96948e15 −1.85332
\(206\) −2.61351e14 −0.238280
\(207\) 4.04501e14 0.357365
\(208\) −8.82491e13 −0.0755611
\(209\) 5.49473e14 0.456032
\(210\) −5.28416e14 −0.425158
\(211\) 2.36901e15 1.84812 0.924062 0.382242i \(-0.124848\pi\)
0.924062 + 0.382242i \(0.124848\pi\)
\(212\) 1.28377e15 0.971188
\(213\) 2.91978e14 0.214231
\(214\) 4.07113e14 0.289751
\(215\) −9.96889e13 −0.0688330
\(216\) 2.78542e14 0.186613
\(217\) −2.75064e14 −0.178832
\(218\) 1.91487e14 0.120829
\(219\) 1.49345e14 0.0914752
\(220\) 4.23505e14 0.251832
\(221\) 1.42002e15 0.819871
\(222\) −1.37579e14 −0.0771361
\(223\) 2.40543e15 1.30982 0.654909 0.755707i \(-0.272707\pi\)
0.654909 + 0.755707i \(0.272707\pi\)
\(224\) −2.56607e15 −1.35724
\(225\) −6.47182e13 −0.0332537
\(226\) −1.89151e15 −0.944288
\(227\) 3.69060e15 1.79031 0.895156 0.445753i \(-0.147064\pi\)
0.895156 + 0.445753i \(0.147064\pi\)
\(228\) 9.10838e14 0.429402
\(229\) −2.39631e14 −0.109802 −0.0549012 0.998492i \(-0.517484\pi\)
−0.0549012 + 0.998492i \(0.517484\pi\)
\(230\) −1.33567e15 −0.594934
\(231\) 7.13747e14 0.309077
\(232\) 1.58950e15 0.669252
\(233\) 1.57644e15 0.645452 0.322726 0.946493i \(-0.395401\pi\)
0.322726 + 0.946493i \(0.395401\pi\)
\(234\) −4.07401e14 −0.162225
\(235\) −2.33401e15 −0.903986
\(236\) 2.27344e14 0.0856554
\(237\) −1.42920e15 −0.523878
\(238\) 2.14410e15 0.764705
\(239\) −3.05022e15 −1.05863 −0.529315 0.848425i \(-0.677551\pi\)
−0.529315 + 0.848425i \(0.677551\pi\)
\(240\) 1.47267e14 0.0497431
\(241\) −3.78943e15 −1.24584 −0.622922 0.782284i \(-0.714055\pi\)
−0.622922 + 0.782284i \(0.714055\pi\)
\(242\) −1.53008e15 −0.489683
\(243\) −2.05891e14 −0.0641500
\(244\) −2.41958e15 −0.734018
\(245\) −2.44414e15 −0.722014
\(246\) −2.29270e15 −0.659581
\(247\) −3.35705e15 −0.940650
\(248\) −4.78771e14 −0.130675
\(249\) −3.06599e14 −0.0815220
\(250\) 2.35583e15 0.610286
\(251\) −1.61252e14 −0.0407030 −0.0203515 0.999793i \(-0.506479\pi\)
−0.0203515 + 0.999793i \(0.506479\pi\)
\(252\) 1.18315e15 0.291028
\(253\) 1.80413e15 0.432498
\(254\) 2.05325e15 0.479759
\(255\) −2.36969e15 −0.539734
\(256\) −4.19740e15 −0.932010
\(257\) −6.41643e15 −1.38908 −0.694541 0.719453i \(-0.744393\pi\)
−0.694541 + 0.719453i \(0.744393\pi\)
\(258\) −1.16049e14 −0.0244970
\(259\) −1.47261e15 −0.303136
\(260\) −2.58744e15 −0.519450
\(261\) −1.17492e15 −0.230062
\(262\) −5.70419e14 −0.108952
\(263\) −5.44228e15 −1.01407 −0.507036 0.861925i \(-0.669259\pi\)
−0.507036 + 0.861925i \(0.669259\pi\)
\(264\) 1.24234e15 0.225847
\(265\) 7.89586e15 1.40056
\(266\) −5.06882e15 −0.877357
\(267\) −3.17158e14 −0.0535738
\(268\) 1.06142e15 0.174988
\(269\) 6.88971e15 1.10869 0.554347 0.832286i \(-0.312968\pi\)
0.554347 + 0.832286i \(0.312968\pi\)
\(270\) 6.79857e14 0.106796
\(271\) 1.04055e16 1.59574 0.797868 0.602833i \(-0.205961\pi\)
0.797868 + 0.602833i \(0.205961\pi\)
\(272\) −5.97550e14 −0.0894698
\(273\) −4.36070e15 −0.637528
\(274\) −6.59531e14 −0.0941578
\(275\) −2.88652e14 −0.0402450
\(276\) 2.99063e15 0.407243
\(277\) −1.29214e16 −1.71866 −0.859331 0.511420i \(-0.829120\pi\)
−0.859331 + 0.511420i \(0.829120\pi\)
\(278\) −7.85860e14 −0.102107
\(279\) 3.53896e14 0.0449208
\(280\) −9.84476e15 −1.22089
\(281\) −4.81022e15 −0.582873 −0.291436 0.956590i \(-0.594133\pi\)
−0.291436 + 0.956590i \(0.594133\pi\)
\(282\) −2.71705e15 −0.321721
\(283\) 4.84010e15 0.560070 0.280035 0.959990i \(-0.409654\pi\)
0.280035 + 0.959990i \(0.409654\pi\)
\(284\) 2.15870e15 0.244131
\(285\) 5.60214e15 0.619245
\(286\) −1.81706e15 −0.196332
\(287\) −2.45403e16 −2.59208
\(288\) 3.30150e15 0.340926
\(289\) −2.89353e14 −0.0292141
\(290\) 3.87962e15 0.383003
\(291\) 4.91930e15 0.474896
\(292\) 1.10416e15 0.104242
\(293\) −1.84190e16 −1.70069 −0.850346 0.526224i \(-0.823607\pi\)
−0.850346 + 0.526224i \(0.823607\pi\)
\(294\) −2.84525e15 −0.256958
\(295\) 1.39829e15 0.123524
\(296\) −2.56319e15 −0.221506
\(297\) −9.18303e14 −0.0776371
\(298\) 2.06130e15 0.170505
\(299\) −1.10225e16 −0.892108
\(300\) −4.78486e14 −0.0378950
\(301\) −1.24216e15 −0.0962706
\(302\) 6.09701e15 0.462457
\(303\) 6.03575e13 0.00448079
\(304\) 1.41266e15 0.102650
\(305\) −1.48817e16 −1.05853
\(306\) −2.75858e15 −0.192086
\(307\) 1.62920e16 1.11064 0.555321 0.831636i \(-0.312595\pi\)
0.555321 + 0.831636i \(0.312595\pi\)
\(308\) 5.27700e15 0.352215
\(309\) 3.59916e15 0.235218
\(310\) −1.16857e15 −0.0747833
\(311\) −2.56749e15 −0.160904 −0.0804519 0.996758i \(-0.525636\pi\)
−0.0804519 + 0.996758i \(0.525636\pi\)
\(312\) −7.59016e15 −0.465850
\(313\) −1.03513e16 −0.622237 −0.311119 0.950371i \(-0.600704\pi\)
−0.311119 + 0.950371i \(0.600704\pi\)
\(314\) 7.59460e15 0.447159
\(315\) 7.27700e15 0.419695
\(316\) −1.05667e16 −0.596996
\(317\) 7.88032e15 0.436173 0.218086 0.975929i \(-0.430019\pi\)
0.218086 + 0.975929i \(0.430019\pi\)
\(318\) 9.19167e15 0.498446
\(319\) −5.24031e15 −0.278431
\(320\) −9.24674e15 −0.481408
\(321\) −5.60649e15 −0.286028
\(322\) −1.66429e16 −0.832081
\(323\) −2.27312e16 −1.11380
\(324\) −1.52223e15 −0.0731035
\(325\) 1.76355e15 0.0830128
\(326\) −4.95168e13 −0.00228475
\(327\) −2.63703e15 −0.119277
\(328\) −4.27145e16 −1.89407
\(329\) −2.90825e16 −1.26433
\(330\) 3.03226e15 0.129249
\(331\) 1.80611e16 0.754855 0.377427 0.926039i \(-0.376809\pi\)
0.377427 + 0.926039i \(0.376809\pi\)
\(332\) −2.26680e15 −0.0929002
\(333\) 1.89465e15 0.0761449
\(334\) 1.61352e16 0.635949
\(335\) 6.52828e15 0.252352
\(336\) 1.83500e15 0.0695713
\(337\) −1.30441e16 −0.485087 −0.242543 0.970141i \(-0.577982\pi\)
−0.242543 + 0.970141i \(0.577982\pi\)
\(338\) −4.93148e15 −0.179895
\(339\) 2.60487e16 0.932154
\(340\) −1.75200e16 −0.615066
\(341\) 1.57842e15 0.0543651
\(342\) 6.52152e15 0.220384
\(343\) 9.56625e15 0.317198
\(344\) −2.16208e15 −0.0703463
\(345\) 1.83940e16 0.587289
\(346\) 1.15896e16 0.363141
\(347\) 2.45147e16 0.753851 0.376925 0.926244i \(-0.376981\pi\)
0.376925 + 0.926244i \(0.376981\pi\)
\(348\) −8.68664e15 −0.262172
\(349\) −1.99669e16 −0.591489 −0.295744 0.955267i \(-0.595568\pi\)
−0.295744 + 0.955267i \(0.595568\pi\)
\(350\) 2.66278e15 0.0774272
\(351\) 5.61046e15 0.160141
\(352\) 1.47251e16 0.412603
\(353\) −3.57892e16 −0.984502 −0.492251 0.870453i \(-0.663826\pi\)
−0.492251 + 0.870453i \(0.663826\pi\)
\(354\) 1.62776e15 0.0439612
\(355\) 1.32772e16 0.352064
\(356\) −2.34487e15 −0.0610511
\(357\) −2.95271e16 −0.754878
\(358\) 6.72273e15 0.168774
\(359\) −4.42811e15 −0.109170 −0.0545852 0.998509i \(-0.517384\pi\)
−0.0545852 + 0.998509i \(0.517384\pi\)
\(360\) 1.26662e16 0.306677
\(361\) 1.16855e16 0.277875
\(362\) −4.72355e16 −1.10322
\(363\) 2.10713e16 0.483391
\(364\) −3.22403e16 −0.726508
\(365\) 6.79120e15 0.150329
\(366\) −1.73240e16 −0.376722
\(367\) −7.27825e16 −1.55488 −0.777442 0.628955i \(-0.783483\pi\)
−0.777442 + 0.628955i \(0.783483\pi\)
\(368\) 4.63830e15 0.0973527
\(369\) 3.15735e16 0.651105
\(370\) −6.25617e15 −0.126764
\(371\) 9.83849e16 1.95884
\(372\) 2.61649e15 0.0511905
\(373\) 2.72476e16 0.523868 0.261934 0.965086i \(-0.415640\pi\)
0.261934 + 0.965086i \(0.415640\pi\)
\(374\) −1.23037e16 −0.232471
\(375\) −3.24429e16 −0.602444
\(376\) −5.06206e16 −0.923860
\(377\) 3.20161e16 0.574315
\(378\) 8.47124e15 0.149366
\(379\) 3.61868e14 0.00627185 0.00313592 0.999995i \(-0.499002\pi\)
0.00313592 + 0.999995i \(0.499002\pi\)
\(380\) 4.14188e16 0.705674
\(381\) −2.82760e16 −0.473594
\(382\) −5.51561e16 −0.908200
\(383\) 6.39805e16 1.03575 0.517876 0.855456i \(-0.326723\pi\)
0.517876 + 0.855456i \(0.326723\pi\)
\(384\) 2.63357e16 0.419172
\(385\) 3.24564e16 0.507932
\(386\) 4.98281e16 0.766756
\(387\) 1.59815e15 0.0241822
\(388\) 3.63703e16 0.541178
\(389\) 7.05074e16 1.03172 0.515860 0.856673i \(-0.327472\pi\)
0.515860 + 0.856673i \(0.327472\pi\)
\(390\) −1.85259e16 −0.266599
\(391\) −7.46353e16 −1.05632
\(392\) −5.30090e16 −0.737887
\(393\) 7.85543e15 0.107552
\(394\) −7.67785e16 −1.03398
\(395\) −6.49907e16 −0.860934
\(396\) −6.78937e15 −0.0884730
\(397\) 8.31775e16 1.06627 0.533135 0.846030i \(-0.321014\pi\)
0.533135 + 0.846030i \(0.321014\pi\)
\(398\) 4.83425e16 0.609662
\(399\) 6.98045e16 0.866083
\(400\) −7.42106e14 −0.00905891
\(401\) 1.42240e17 1.70837 0.854187 0.519966i \(-0.174056\pi\)
0.854187 + 0.519966i \(0.174056\pi\)
\(402\) 7.59965e15 0.0898099
\(403\) −9.64352e15 −0.112138
\(404\) 4.46247e14 0.00510618
\(405\) −9.36255e15 −0.105423
\(406\) 4.83413e16 0.535672
\(407\) 8.45039e15 0.0921538
\(408\) −5.13943e16 −0.551600
\(409\) 1.76353e17 1.86287 0.931433 0.363912i \(-0.118559\pi\)
0.931433 + 0.363912i \(0.118559\pi\)
\(410\) −1.04256e17 −1.08395
\(411\) 9.08262e15 0.0929478
\(412\) 2.66100e16 0.268048
\(413\) 1.74231e16 0.172763
\(414\) 2.14127e16 0.209011
\(415\) −1.39421e16 −0.133972
\(416\) −8.99646e16 −0.851069
\(417\) 1.08223e16 0.100795
\(418\) 2.90869e16 0.266718
\(419\) −7.54584e16 −0.681266 −0.340633 0.940196i \(-0.610641\pi\)
−0.340633 + 0.940196i \(0.610641\pi\)
\(420\) 5.38016e16 0.478272
\(421\) 1.61204e16 0.141105 0.0705525 0.997508i \(-0.477524\pi\)
0.0705525 + 0.997508i \(0.477524\pi\)
\(422\) 1.25406e17 1.08091
\(423\) 3.74174e16 0.317586
\(424\) 1.71247e17 1.43135
\(425\) 1.19413e16 0.0982931
\(426\) 1.54561e16 0.125296
\(427\) −1.85431e17 −1.48048
\(428\) −4.14510e16 −0.325949
\(429\) 2.50234e16 0.193809
\(430\) −5.27713e15 −0.0402581
\(431\) 2.11458e16 0.158899 0.0794496 0.996839i \(-0.474684\pi\)
0.0794496 + 0.996839i \(0.474684\pi\)
\(432\) −2.36090e15 −0.0174756
\(433\) −1.96271e17 −1.43115 −0.715574 0.698537i \(-0.753835\pi\)
−0.715574 + 0.698537i \(0.753835\pi\)
\(434\) −1.45608e16 −0.104593
\(435\) −5.34275e16 −0.378081
\(436\) −1.94966e16 −0.135924
\(437\) 1.76444e17 1.21193
\(438\) 7.90572e15 0.0535007
\(439\) 1.63153e17 1.08786 0.543932 0.839129i \(-0.316935\pi\)
0.543932 + 0.839129i \(0.316935\pi\)
\(440\) 5.64931e16 0.371153
\(441\) 3.91829e16 0.253656
\(442\) 7.51704e16 0.479515
\(443\) 9.43420e16 0.593036 0.296518 0.955027i \(-0.404175\pi\)
0.296518 + 0.955027i \(0.404175\pi\)
\(444\) 1.40079e16 0.0867726
\(445\) −1.44222e16 −0.0880424
\(446\) 1.27334e17 0.766068
\(447\) −2.83869e16 −0.168314
\(448\) −1.15217e17 −0.673303
\(449\) 8.35783e16 0.481385 0.240692 0.970601i \(-0.422626\pi\)
0.240692 + 0.970601i \(0.422626\pi\)
\(450\) −3.42592e15 −0.0194490
\(451\) 1.40822e17 0.787995
\(452\) 1.92588e17 1.06226
\(453\) −8.39639e16 −0.456514
\(454\) 1.95366e17 1.04709
\(455\) −1.98295e17 −1.04770
\(456\) 1.21501e17 0.632858
\(457\) 2.88918e17 1.48361 0.741805 0.670615i \(-0.233970\pi\)
0.741805 + 0.670615i \(0.233970\pi\)
\(458\) −1.26851e16 −0.0642196
\(459\) 3.79894e16 0.189618
\(460\) 1.35994e17 0.669257
\(461\) 2.60150e16 0.126232 0.0631159 0.998006i \(-0.479896\pi\)
0.0631159 + 0.998006i \(0.479896\pi\)
\(462\) 3.77829e16 0.180768
\(463\) 8.30710e16 0.391898 0.195949 0.980614i \(-0.437221\pi\)
0.195949 + 0.980614i \(0.437221\pi\)
\(464\) −1.34725e16 −0.0626731
\(465\) 1.60928e16 0.0738223
\(466\) 8.34504e16 0.377503
\(467\) −2.52906e17 −1.12824 −0.564118 0.825694i \(-0.690784\pi\)
−0.564118 + 0.825694i \(0.690784\pi\)
\(468\) 4.14803e16 0.182492
\(469\) 8.13444e16 0.352943
\(470\) −1.23553e17 −0.528711
\(471\) −1.04588e17 −0.441413
\(472\) 3.03263e16 0.126240
\(473\) 7.12798e15 0.0292664
\(474\) −7.56564e16 −0.306398
\(475\) −2.82302e16 −0.112773
\(476\) −2.18305e17 −0.860238
\(477\) −1.26582e17 −0.492041
\(478\) −1.61466e17 −0.619157
\(479\) −4.06289e16 −0.153693 −0.0768466 0.997043i \(-0.524485\pi\)
−0.0768466 + 0.997043i \(0.524485\pi\)
\(480\) 1.50130e17 0.560273
\(481\) −5.16284e16 −0.190084
\(482\) −2.00598e17 −0.728652
\(483\) 2.29195e17 0.821389
\(484\) 1.55788e17 0.550858
\(485\) 2.23697e17 0.780438
\(486\) −1.08991e16 −0.0375192
\(487\) 1.91152e17 0.649293 0.324647 0.945835i \(-0.394755\pi\)
0.324647 + 0.945835i \(0.394755\pi\)
\(488\) −3.22758e17 −1.08180
\(489\) 6.81913e14 0.00225539
\(490\) −1.29383e17 −0.422282
\(491\) 2.73363e17 0.880461 0.440231 0.897885i \(-0.354897\pi\)
0.440231 + 0.897885i \(0.354897\pi\)
\(492\) 2.33435e17 0.741981
\(493\) 2.16787e17 0.680030
\(494\) −1.77709e17 −0.550154
\(495\) −4.17583e16 −0.127588
\(496\) 4.05802e15 0.0122372
\(497\) 1.65438e17 0.492401
\(498\) −1.62301e16 −0.0476795
\(499\) 2.57000e17 0.745211 0.372605 0.927990i \(-0.378465\pi\)
0.372605 + 0.927990i \(0.378465\pi\)
\(500\) −2.39863e17 −0.686528
\(501\) −2.22203e17 −0.627776
\(502\) −8.53604e15 −0.0238058
\(503\) −6.49415e17 −1.78785 −0.893923 0.448220i \(-0.852058\pi\)
−0.893923 + 0.448220i \(0.852058\pi\)
\(504\) 1.57825e17 0.428921
\(505\) 2.74466e15 0.00736366
\(506\) 9.55035e16 0.252954
\(507\) 6.79131e16 0.177583
\(508\) −2.09055e17 −0.539694
\(509\) −1.17905e17 −0.300514 −0.150257 0.988647i \(-0.548010\pi\)
−0.150257 + 0.988647i \(0.548010\pi\)
\(510\) −1.25442e17 −0.315672
\(511\) 8.46205e16 0.210252
\(512\) 7.37489e16 0.180926
\(513\) −8.98101e16 −0.217552
\(514\) −3.39660e17 −0.812427
\(515\) 1.63666e17 0.386554
\(516\) 1.18157e16 0.0275574
\(517\) 1.66887e17 0.384356
\(518\) −7.79539e16 −0.177294
\(519\) −1.59605e17 −0.358475
\(520\) −3.45150e17 −0.765571
\(521\) 3.63292e17 0.795811 0.397906 0.917426i \(-0.369737\pi\)
0.397906 + 0.917426i \(0.369737\pi\)
\(522\) −6.21956e16 −0.134556
\(523\) 3.36655e17 0.719323 0.359662 0.933083i \(-0.382892\pi\)
0.359662 + 0.933083i \(0.382892\pi\)
\(524\) 5.80782e16 0.122563
\(525\) −3.66701e16 −0.0764322
\(526\) −2.88093e17 −0.593096
\(527\) −6.52980e16 −0.132779
\(528\) −1.05299e16 −0.0211497
\(529\) 7.52972e16 0.149388
\(530\) 4.17975e17 0.819139
\(531\) −2.24165e16 −0.0433963
\(532\) 5.16091e17 0.986963
\(533\) −8.60366e17 −1.62539
\(534\) −1.67891e16 −0.0313335
\(535\) −2.54946e17 −0.470054
\(536\) 1.41587e17 0.257900
\(537\) −9.25810e16 −0.166605
\(538\) 3.64714e17 0.648437
\(539\) 1.74761e17 0.306986
\(540\) −6.92209e16 −0.120137
\(541\) 6.16378e17 1.05698 0.528488 0.848941i \(-0.322759\pi\)
0.528488 + 0.848941i \(0.322759\pi\)
\(542\) 5.50824e17 0.933291
\(543\) 6.50496e17 1.08904
\(544\) −6.09166e17 −1.00773
\(545\) −1.19914e17 −0.196017
\(546\) −2.30838e17 −0.372868
\(547\) 2.56338e17 0.409163 0.204581 0.978850i \(-0.434417\pi\)
0.204581 + 0.978850i \(0.434417\pi\)
\(548\) 6.71513e16 0.105921
\(549\) 2.38575e17 0.371881
\(550\) −1.52801e16 −0.0235380
\(551\) −5.12503e17 −0.780209
\(552\) 3.98933e17 0.600200
\(553\) −8.09804e17 −1.20411
\(554\) −6.84007e17 −1.00519
\(555\) 8.61559e16 0.125135
\(556\) 8.00137e16 0.114863
\(557\) 6.80740e17 0.965878 0.482939 0.875654i \(-0.339569\pi\)
0.482939 + 0.875654i \(0.339569\pi\)
\(558\) 1.87338e16 0.0262727
\(559\) −4.35490e16 −0.0603673
\(560\) 8.34433e16 0.114332
\(561\) 1.69438e17 0.229484
\(562\) −2.54634e17 −0.340903
\(563\) −3.41798e17 −0.452340 −0.226170 0.974088i \(-0.572621\pi\)
−0.226170 + 0.974088i \(0.572621\pi\)
\(564\) 2.76642e17 0.361912
\(565\) 1.18452e18 1.53189
\(566\) 2.56216e17 0.327566
\(567\) −1.16660e17 −0.147446
\(568\) 2.87959e17 0.359804
\(569\) 1.11798e18 1.38103 0.690516 0.723318i \(-0.257384\pi\)
0.690516 + 0.723318i \(0.257384\pi\)
\(570\) 2.96555e17 0.362175
\(571\) −2.93875e17 −0.354836 −0.177418 0.984136i \(-0.556774\pi\)
−0.177418 + 0.984136i \(0.556774\pi\)
\(572\) 1.85008e17 0.220859
\(573\) 7.59573e17 0.896530
\(574\) −1.29907e18 −1.51602
\(575\) −9.26906e16 −0.106953
\(576\) 1.48238e17 0.169127
\(577\) −8.64918e17 −0.975735 −0.487868 0.872918i \(-0.662225\pi\)
−0.487868 + 0.872918i \(0.662225\pi\)
\(578\) −1.53172e16 −0.0170863
\(579\) −6.86200e17 −0.756903
\(580\) −3.95010e17 −0.430850
\(581\) −1.73723e17 −0.187375
\(582\) 2.60408e17 0.277751
\(583\) −5.64571e17 −0.595488
\(584\) 1.47289e17 0.153634
\(585\) 2.55126e17 0.263173
\(586\) −9.75027e17 −0.994677
\(587\) −1.34860e17 −0.136061 −0.0680306 0.997683i \(-0.521672\pi\)
−0.0680306 + 0.997683i \(0.521672\pi\)
\(588\) 2.89694e17 0.289059
\(589\) 1.54370e17 0.152340
\(590\) 7.40197e16 0.0722452
\(591\) 1.05734e18 1.02070
\(592\) 2.17254e16 0.0207433
\(593\) 2.81323e17 0.265675 0.132837 0.991138i \(-0.457591\pi\)
0.132837 + 0.991138i \(0.457591\pi\)
\(594\) −4.86113e16 −0.0454073
\(595\) −1.34269e18 −1.24056
\(596\) −2.09875e17 −0.191805
\(597\) −6.65741e17 −0.601828
\(598\) −5.83487e17 −0.521763
\(599\) 9.72310e17 0.860064 0.430032 0.902814i \(-0.358502\pi\)
0.430032 + 0.902814i \(0.358502\pi\)
\(600\) −6.38273e16 −0.0558501
\(601\) −7.39160e17 −0.639815 −0.319908 0.947449i \(-0.603652\pi\)
−0.319908 + 0.947449i \(0.603652\pi\)
\(602\) −6.57548e16 −0.0563054
\(603\) −1.04657e17 −0.0886558
\(604\) −6.20778e17 −0.520231
\(605\) 9.58181e17 0.794397
\(606\) 3.19509e15 0.00262066
\(607\) −7.29265e17 −0.591778 −0.295889 0.955222i \(-0.595616\pi\)
−0.295889 + 0.955222i \(0.595616\pi\)
\(608\) 1.44012e18 1.15618
\(609\) −6.65724e17 −0.528788
\(610\) −7.87780e17 −0.619100
\(611\) −1.01961e18 −0.792806
\(612\) 2.80870e17 0.216083
\(613\) −5.44643e17 −0.414590 −0.207295 0.978278i \(-0.566466\pi\)
−0.207295 + 0.978278i \(0.566466\pi\)
\(614\) 8.62432e17 0.649576
\(615\) 1.43575e18 1.07002
\(616\) 7.03922e17 0.519099
\(617\) 4.00338e17 0.292128 0.146064 0.989275i \(-0.453339\pi\)
0.146064 + 0.989275i \(0.453339\pi\)
\(618\) 1.90525e17 0.137571
\(619\) −2.37123e18 −1.69428 −0.847140 0.531370i \(-0.821677\pi\)
−0.847140 + 0.531370i \(0.821677\pi\)
\(620\) 1.18980e17 0.0841257
\(621\) −2.94881e17 −0.206325
\(622\) −1.35913e17 −0.0941071
\(623\) −1.79705e17 −0.123137
\(624\) 6.43336e16 0.0436252
\(625\) −1.32663e18 −0.890287
\(626\) −5.47956e17 −0.363925
\(627\) −4.00566e17 −0.263290
\(628\) −7.73258e17 −0.503022
\(629\) −3.49585e17 −0.225073
\(630\) 3.85215e17 0.245465
\(631\) −1.48994e18 −0.939676 −0.469838 0.882753i \(-0.655688\pi\)
−0.469838 + 0.882753i \(0.655688\pi\)
\(632\) −1.40953e18 −0.879861
\(633\) −1.72701e18 −1.06702
\(634\) 4.17153e17 0.255103
\(635\) −1.28580e18 −0.778297
\(636\) −9.35866e17 −0.560715
\(637\) −1.06772e18 −0.633214
\(638\) −2.77401e17 −0.162845
\(639\) −2.12852e17 −0.123686
\(640\) 1.19757e18 0.688861
\(641\) 1.23302e18 0.702088 0.351044 0.936359i \(-0.385827\pi\)
0.351044 + 0.936359i \(0.385827\pi\)
\(642\) −2.96786e17 −0.167288
\(643\) −2.58757e18 −1.44385 −0.721924 0.691972i \(-0.756742\pi\)
−0.721924 + 0.691972i \(0.756742\pi\)
\(644\) 1.69453e18 0.936031
\(645\) 7.26732e16 0.0397408
\(646\) −1.20330e18 −0.651422
\(647\) 1.27248e18 0.681984 0.340992 0.940066i \(-0.389237\pi\)
0.340992 + 0.940066i \(0.389237\pi\)
\(648\) −2.03057e17 −0.107741
\(649\) −9.99806e16 −0.0525200
\(650\) 9.33551e16 0.0485514
\(651\) 2.00521e17 0.103249
\(652\) 5.04165e15 0.00257018
\(653\) −5.94769e17 −0.300201 −0.150101 0.988671i \(-0.547960\pi\)
−0.150101 + 0.988671i \(0.547960\pi\)
\(654\) −1.39594e17 −0.0697608
\(655\) 3.57212e17 0.176749
\(656\) 3.62045e17 0.177373
\(657\) −1.08872e17 −0.0528132
\(658\) −1.53951e18 −0.739461
\(659\) 1.13181e18 0.538294 0.269147 0.963099i \(-0.413258\pi\)
0.269147 + 0.963099i \(0.413258\pi\)
\(660\) −3.08735e17 −0.145395
\(661\) −5.06120e17 −0.236017 −0.118009 0.993013i \(-0.537651\pi\)
−0.118009 + 0.993013i \(0.537651\pi\)
\(662\) 9.56085e17 0.441489
\(663\) −1.03520e18 −0.473353
\(664\) −3.02379e17 −0.136917
\(665\) 3.17424e18 1.42331
\(666\) 1.00295e17 0.0445346
\(667\) −1.68274e18 −0.739946
\(668\) −1.64283e18 −0.715396
\(669\) −1.75356e18 −0.756224
\(670\) 3.45581e17 0.147592
\(671\) 1.06408e18 0.450067
\(672\) 1.87067e18 0.783603
\(673\) 7.45977e17 0.309476 0.154738 0.987956i \(-0.450547\pi\)
0.154738 + 0.987956i \(0.450547\pi\)
\(674\) −6.90502e17 −0.283711
\(675\) 4.71796e16 0.0191990
\(676\) 5.02108e17 0.202369
\(677\) −1.68066e18 −0.670895 −0.335448 0.942059i \(-0.608888\pi\)
−0.335448 + 0.942059i \(0.608888\pi\)
\(678\) 1.37891e18 0.545185
\(679\) 2.78733e18 1.09153
\(680\) −2.33707e18 −0.906491
\(681\) −2.69045e18 −1.03364
\(682\) 8.35555e16 0.0317963
\(683\) −8.15123e16 −0.0307248 −0.0153624 0.999882i \(-0.504890\pi\)
−0.0153624 + 0.999882i \(0.504890\pi\)
\(684\) −6.64001e17 −0.247916
\(685\) 4.13017e17 0.152749
\(686\) 5.06399e17 0.185518
\(687\) 1.74691e17 0.0633944
\(688\) 1.83256e16 0.00658768
\(689\) 3.44930e18 1.22830
\(690\) 9.73704e17 0.343485
\(691\) −4.27942e17 −0.149547 −0.0747734 0.997201i \(-0.523823\pi\)
−0.0747734 + 0.997201i \(0.523823\pi\)
\(692\) −1.18002e18 −0.408507
\(693\) −5.20321e17 −0.178446
\(694\) 1.29771e18 0.440902
\(695\) 4.92128e17 0.165644
\(696\) −1.15875e18 −0.386393
\(697\) −5.82569e18 −1.92457
\(698\) −1.05697e18 −0.345942
\(699\) −1.14922e18 −0.372652
\(700\) −2.71116e17 −0.0871000
\(701\) 2.89387e18 0.921110 0.460555 0.887631i \(-0.347650\pi\)
0.460555 + 0.887631i \(0.347650\pi\)
\(702\) 2.96995e17 0.0936609
\(703\) 8.26449e17 0.258230
\(704\) 6.61162e17 0.204685
\(705\) 1.70149e18 0.521917
\(706\) −1.89454e18 −0.575802
\(707\) 3.41993e16 0.0102989
\(708\) −1.65734e17 −0.0494532
\(709\) −2.73955e18 −0.809988 −0.404994 0.914319i \(-0.632726\pi\)
−0.404994 + 0.914319i \(0.632726\pi\)
\(710\) 7.02841e17 0.205910
\(711\) 1.04189e18 0.302461
\(712\) −3.12792e17 −0.0899779
\(713\) 5.06856e17 0.144478
\(714\) −1.56305e18 −0.441503
\(715\) 1.13790e18 0.318503
\(716\) −6.84487e17 −0.189859
\(717\) 2.22361e18 0.611200
\(718\) −2.34407e17 −0.0638500
\(719\) −1.31729e18 −0.355585 −0.177793 0.984068i \(-0.556896\pi\)
−0.177793 + 0.984068i \(0.556896\pi\)
\(720\) −1.07358e17 −0.0287192
\(721\) 2.03932e18 0.540639
\(722\) 6.18583e17 0.162520
\(723\) 2.76250e18 0.719288
\(724\) 4.80936e18 1.24104
\(725\) 2.69231e17 0.0688538
\(726\) 1.11543e18 0.282719
\(727\) −6.78555e18 −1.70456 −0.852278 0.523088i \(-0.824780\pi\)
−0.852278 + 0.523088i \(0.824780\pi\)
\(728\) −4.30068e18 −1.07074
\(729\) 1.50095e17 0.0370370
\(730\) 3.59499e17 0.0879223
\(731\) −2.94878e17 −0.0714792
\(732\) 1.76388e18 0.423785
\(733\) −5.28441e18 −1.25841 −0.629203 0.777241i \(-0.716619\pi\)
−0.629203 + 0.777241i \(0.716619\pi\)
\(734\) −3.85282e18 −0.909398
\(735\) 1.78178e18 0.416855
\(736\) 4.72847e18 1.09651
\(737\) −4.66786e17 −0.107295
\(738\) 1.67138e18 0.380809
\(739\) −5.56521e18 −1.25688 −0.628439 0.777859i \(-0.716306\pi\)
−0.628439 + 0.777859i \(0.716306\pi\)
\(740\) 6.36983e17 0.142601
\(741\) 2.44729e18 0.543084
\(742\) 5.20811e18 1.14566
\(743\) 5.01347e18 1.09323 0.546614 0.837385i \(-0.315916\pi\)
0.546614 + 0.837385i \(0.315916\pi\)
\(744\) 3.49024e17 0.0754452
\(745\) −1.29085e18 −0.276604
\(746\) 1.44238e18 0.306392
\(747\) 2.23511e17 0.0470668
\(748\) 1.25272e18 0.261513
\(749\) −3.17671e18 −0.657423
\(750\) −1.71740e18 −0.352349
\(751\) −5.55282e18 −1.12942 −0.564708 0.825291i \(-0.691011\pi\)
−0.564708 + 0.825291i \(0.691011\pi\)
\(752\) 4.29056e17 0.0865163
\(753\) 1.17553e17 0.0234999
\(754\) 1.69481e18 0.335897
\(755\) −3.81812e18 −0.750229
\(756\) −8.62515e17 −0.168025
\(757\) −2.69428e18 −0.520379 −0.260189 0.965558i \(-0.583785\pi\)
−0.260189 + 0.965558i \(0.583785\pi\)
\(758\) 1.91559e16 0.00366819
\(759\) −1.31521e18 −0.249703
\(760\) 5.52503e18 1.04003
\(761\) 6.36065e18 1.18714 0.593569 0.804783i \(-0.297718\pi\)
0.593569 + 0.804783i \(0.297718\pi\)
\(762\) −1.49682e18 −0.276989
\(763\) −1.49417e18 −0.274152
\(764\) 5.61582e18 1.02166
\(765\) 1.72750e18 0.311616
\(766\) 3.38687e18 0.605776
\(767\) 6.10840e17 0.108332
\(768\) 3.05990e18 0.538096
\(769\) −4.04769e18 −0.705806 −0.352903 0.935660i \(-0.614806\pi\)
−0.352903 + 0.935660i \(0.614806\pi\)
\(770\) 1.71811e18 0.297072
\(771\) 4.67758e18 0.801987
\(772\) −5.07334e18 −0.862545
\(773\) −5.86398e18 −0.988611 −0.494306 0.869288i \(-0.664578\pi\)
−0.494306 + 0.869288i \(0.664578\pi\)
\(774\) 8.45998e16 0.0141434
\(775\) −8.10945e16 −0.0134441
\(776\) 4.85159e18 0.797595
\(777\) 1.07353e18 0.175016
\(778\) 3.73238e18 0.603418
\(779\) 1.37724e19 2.20809
\(780\) 1.88624e18 0.299904
\(781\) −9.49348e17 −0.149690
\(782\) −3.95089e18 −0.617805
\(783\) 8.56517e17 0.132826
\(784\) 4.49300e17 0.0691006
\(785\) −4.75595e18 −0.725412
\(786\) 4.15835e17 0.0629035
\(787\) −3.23596e18 −0.485476 −0.242738 0.970092i \(-0.578045\pi\)
−0.242738 + 0.970092i \(0.578045\pi\)
\(788\) 7.81734e18 1.16316
\(789\) 3.96742e18 0.585474
\(790\) −3.44035e18 −0.503531
\(791\) 1.47595e19 2.14252
\(792\) −9.05663e17 −0.130393
\(793\) −6.50108e18 −0.928345
\(794\) 4.40309e18 0.623626
\(795\) −5.75608e18 −0.808613
\(796\) −4.92208e18 −0.685826
\(797\) −1.27032e19 −1.75564 −0.877819 0.478993i \(-0.841002\pi\)
−0.877819 + 0.478993i \(0.841002\pi\)
\(798\) 3.69517e18 0.506542
\(799\) −6.90397e18 −0.938739
\(800\) −7.56532e17 −0.102033
\(801\) 2.31208e17 0.0309308
\(802\) 7.52961e18 0.999170
\(803\) −4.85586e17 −0.0639168
\(804\) −7.73772e17 −0.101030
\(805\) 1.04222e19 1.34986
\(806\) −5.10490e17 −0.0655857
\(807\) −5.02260e18 −0.640104
\(808\) 5.95267e16 0.00752555
\(809\) 3.77318e18 0.473197 0.236599 0.971607i \(-0.423967\pi\)
0.236599 + 0.971607i \(0.423967\pi\)
\(810\) −4.95616e17 −0.0616585
\(811\) −4.85204e18 −0.598809 −0.299405 0.954126i \(-0.596788\pi\)
−0.299405 + 0.954126i \(0.596788\pi\)
\(812\) −4.92195e18 −0.602592
\(813\) −7.58558e18 −0.921298
\(814\) 4.47330e17 0.0538976
\(815\) 3.10088e16 0.00370647
\(816\) 4.35614e17 0.0516554
\(817\) 6.97117e17 0.0820091
\(818\) 9.33544e18 1.08953
\(819\) 3.17895e18 0.368077
\(820\) 1.06151e19 1.21936
\(821\) −3.20579e18 −0.365346 −0.182673 0.983174i \(-0.558475\pi\)
−0.182673 + 0.983174i \(0.558475\pi\)
\(822\) 4.80798e17 0.0543620
\(823\) −1.19960e19 −1.34567 −0.672834 0.739794i \(-0.734923\pi\)
−0.672834 + 0.739794i \(0.734923\pi\)
\(824\) 3.54961e18 0.395052
\(825\) 2.10427e17 0.0232355
\(826\) 9.22309e17 0.101043
\(827\) 7.99788e18 0.869339 0.434669 0.900590i \(-0.356865\pi\)
0.434669 + 0.900590i \(0.356865\pi\)
\(828\) −2.18017e18 −0.235122
\(829\) −4.06021e18 −0.434454 −0.217227 0.976121i \(-0.569701\pi\)
−0.217227 + 0.976121i \(0.569701\pi\)
\(830\) −7.38038e17 −0.0783558
\(831\) 9.41969e18 0.992270
\(832\) −4.03943e18 −0.422200
\(833\) −7.22972e18 −0.749771
\(834\) 5.72892e17 0.0589513
\(835\) −1.01043e19 −1.03168
\(836\) −2.96154e18 −0.300038
\(837\) −2.57990e17 −0.0259351
\(838\) −3.99447e18 −0.398449
\(839\) 7.42606e18 0.735031 0.367515 0.930017i \(-0.380209\pi\)
0.367515 + 0.930017i \(0.380209\pi\)
\(840\) 7.17683e18 0.704883
\(841\) −5.37290e18 −0.523642
\(842\) 8.53350e17 0.0825275
\(843\) 3.50665e18 0.336522
\(844\) −1.27684e19 −1.21594
\(845\) 3.08823e18 0.291838
\(846\) 1.98073e18 0.185745
\(847\) 1.19392e19 1.11105
\(848\) −1.45148e18 −0.134041
\(849\) −3.52843e18 −0.323357
\(850\) 6.32124e17 0.0574883
\(851\) 2.71355e18 0.244904
\(852\) −1.57369e18 −0.140949
\(853\) 1.36262e19 1.21117 0.605587 0.795779i \(-0.292938\pi\)
0.605587 + 0.795779i \(0.292938\pi\)
\(854\) −9.81599e18 −0.865880
\(855\) −4.08396e18 −0.357521
\(856\) −5.52932e18 −0.480388
\(857\) −3.25642e17 −0.0280779 −0.0140390 0.999901i \(-0.504469\pi\)
−0.0140390 + 0.999901i \(0.504469\pi\)
\(858\) 1.32464e18 0.113352
\(859\) −1.73799e19 −1.47602 −0.738009 0.674790i \(-0.764234\pi\)
−0.738009 + 0.674790i \(0.764234\pi\)
\(860\) 5.37301e17 0.0452874
\(861\) 1.78899e19 1.49654
\(862\) 1.11937e18 0.0929348
\(863\) −1.97071e19 −1.62388 −0.811939 0.583743i \(-0.801588\pi\)
−0.811939 + 0.583743i \(0.801588\pi\)
\(864\) −2.40679e18 −0.196834
\(865\) −7.25776e18 −0.589112
\(866\) −1.03898e19 −0.837029
\(867\) 2.10938e17 0.0168668
\(868\) 1.48253e18 0.117659
\(869\) 4.64698e18 0.366051
\(870\) −2.82824e18 −0.221127
\(871\) 2.85187e18 0.221316
\(872\) −2.60073e18 −0.200327
\(873\) −3.58617e18 −0.274182
\(874\) 9.34025e18 0.708817
\(875\) −1.83825e19 −1.38469
\(876\) −8.04935e17 −0.0601844
\(877\) −1.41182e19 −1.04781 −0.523905 0.851776i \(-0.675525\pi\)
−0.523905 + 0.851776i \(0.675525\pi\)
\(878\) 8.63665e18 0.636255
\(879\) 1.34274e19 0.981895
\(880\) −4.78831e17 −0.0347572
\(881\) −2.43112e19 −1.75171 −0.875857 0.482571i \(-0.839703\pi\)
−0.875857 + 0.482571i \(0.839703\pi\)
\(882\) 2.07419e18 0.148355
\(883\) 4.75021e18 0.337263 0.168631 0.985679i \(-0.446065\pi\)
0.168631 + 0.985679i \(0.446065\pi\)
\(884\) −7.65361e18 −0.539419
\(885\) −1.01935e18 −0.0713169
\(886\) 4.99409e18 0.346846
\(887\) 4.03966e18 0.278510 0.139255 0.990257i \(-0.455529\pi\)
0.139255 + 0.990257i \(0.455529\pi\)
\(888\) 1.86857e18 0.127886
\(889\) −1.60215e19 −1.08853
\(890\) −7.63454e17 −0.0514930
\(891\) 6.69443e17 0.0448238
\(892\) −1.29647e19 −0.861771
\(893\) 1.63216e19 1.07703
\(894\) −1.50269e18 −0.0984410
\(895\) −4.20996e18 −0.273797
\(896\) 1.49221e19 0.963449
\(897\) 8.03540e18 0.515059
\(898\) 4.42430e18 0.281546
\(899\) −1.47222e18 −0.0930113
\(900\) 3.48817e17 0.0218787
\(901\) 2.33558e19 1.45440
\(902\) 7.45457e18 0.460872
\(903\) 9.05531e17 0.0555819
\(904\) 2.56901e19 1.56557
\(905\) 2.95802e19 1.78972
\(906\) −4.44472e18 −0.267000
\(907\) 1.36175e19 0.812175 0.406088 0.913834i \(-0.366893\pi\)
0.406088 + 0.913834i \(0.366893\pi\)
\(908\) −1.98915e19 −1.17790
\(909\) −4.40007e16 −0.00258698
\(910\) −1.04970e19 −0.612766
\(911\) 2.27922e19 1.32104 0.660522 0.750806i \(-0.270335\pi\)
0.660522 + 0.750806i \(0.270335\pi\)
\(912\) −1.02983e18 −0.0592650
\(913\) 9.96889e17 0.0569622
\(914\) 1.52942e19 0.867714
\(915\) 1.08488e19 0.611145
\(916\) 1.29156e18 0.0722424
\(917\) 4.45098e18 0.247204
\(918\) 2.01101e18 0.110901
\(919\) 2.16005e19 1.18281 0.591403 0.806376i \(-0.298574\pi\)
0.591403 + 0.806376i \(0.298574\pi\)
\(920\) 1.81408e19 0.986360
\(921\) −1.18768e19 −0.641229
\(922\) 1.37713e18 0.0738286
\(923\) 5.80013e18 0.308764
\(924\) −3.84694e18 −0.203351
\(925\) −4.34155e17 −0.0227889
\(926\) 4.39745e18 0.229208
\(927\) −2.62379e18 −0.135803
\(928\) −1.37344e19 −0.705907
\(929\) 2.24565e19 1.14614 0.573072 0.819505i \(-0.305752\pi\)
0.573072 + 0.819505i \(0.305752\pi\)
\(930\) 8.51889e17 0.0431761
\(931\) 1.70917e19 0.860223
\(932\) −8.49665e18 −0.424663
\(933\) 1.87170e18 0.0928978
\(934\) −1.33878e19 −0.659867
\(935\) 7.70490e18 0.377130
\(936\) 5.53323e18 0.268959
\(937\) −1.93776e19 −0.935392 −0.467696 0.883890i \(-0.654916\pi\)
−0.467696 + 0.883890i \(0.654916\pi\)
\(938\) 4.30605e18 0.206424
\(939\) 7.54609e18 0.359249
\(940\) 1.25798e19 0.594761
\(941\) 1.11702e19 0.524481 0.262241 0.965003i \(-0.415539\pi\)
0.262241 + 0.965003i \(0.415539\pi\)
\(942\) −5.53646e18 −0.258167
\(943\) 4.52201e19 2.09414
\(944\) −2.57044e17 −0.0118219
\(945\) −5.30493e18 −0.242311
\(946\) 3.77327e17 0.0171169
\(947\) 4.05530e18 0.182704 0.0913519 0.995819i \(-0.470881\pi\)
0.0913519 + 0.995819i \(0.470881\pi\)
\(948\) 7.70310e18 0.344676
\(949\) 2.96673e18 0.131840
\(950\) −1.49439e18 −0.0659571
\(951\) −5.74475e18 −0.251824
\(952\) −2.91206e19 −1.26783
\(953\) 7.00532e17 0.0302917 0.0151459 0.999885i \(-0.495179\pi\)
0.0151459 + 0.999885i \(0.495179\pi\)
\(954\) −6.70073e18 −0.287778
\(955\) 3.45403e19 1.47334
\(956\) 1.64400e19 0.696506
\(957\) 3.82019e18 0.160752
\(958\) −2.15073e18 −0.0898899
\(959\) 5.14632e18 0.213637
\(960\) 6.74087e18 0.277941
\(961\) −2.39741e19 −0.981839
\(962\) −2.73300e18 −0.111174
\(963\) 4.08713e18 0.165138
\(964\) 2.04242e19 0.819680
\(965\) −3.12038e19 −1.24388
\(966\) 1.21327e19 0.480402
\(967\) −3.90005e19 −1.53390 −0.766952 0.641705i \(-0.778227\pi\)
−0.766952 + 0.641705i \(0.778227\pi\)
\(968\) 2.07813e19 0.811861
\(969\) 1.65710e19 0.643051
\(970\) 1.18416e19 0.456452
\(971\) −1.69465e19 −0.648865 −0.324432 0.945909i \(-0.605173\pi\)
−0.324432 + 0.945909i \(0.605173\pi\)
\(972\) 1.10971e18 0.0422063
\(973\) 6.13207e18 0.231672
\(974\) 1.01188e19 0.379750
\(975\) −1.28563e18 −0.0479275
\(976\) 2.73567e18 0.101307
\(977\) 5.54794e18 0.204088 0.102044 0.994780i \(-0.467462\pi\)
0.102044 + 0.994780i \(0.467462\pi\)
\(978\) 3.60978e16 0.00131910
\(979\) 1.03122e18 0.0374338
\(980\) 1.31733e19 0.475036
\(981\) 1.92240e18 0.0688643
\(982\) 1.44708e19 0.514952
\(983\) −1.85716e19 −0.656525 −0.328263 0.944587i \(-0.606463\pi\)
−0.328263 + 0.944587i \(0.606463\pi\)
\(984\) 3.11389e19 1.09354
\(985\) 4.80809e19 1.67740
\(986\) 1.14758e19 0.397727
\(987\) 2.12012e19 0.729959
\(988\) 1.80938e19 0.618883
\(989\) 2.28890e18 0.0777770
\(990\) −2.21052e18 −0.0746217
\(991\) −2.96463e18 −0.0994242 −0.0497121 0.998764i \(-0.515830\pi\)
−0.0497121 + 0.998764i \(0.515830\pi\)
\(992\) 4.13691e18 0.137832
\(993\) −1.31666e19 −0.435815
\(994\) 8.75763e18 0.287988
\(995\) −3.02734e19 −0.989036
\(996\) 1.65250e18 0.0536359
\(997\) −5.55268e19 −1.79054 −0.895270 0.445525i \(-0.853017\pi\)
−0.895270 + 0.445525i \(0.853017\pi\)
\(998\) 1.36045e19 0.435848
\(999\) −1.38120e18 −0.0439623
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.b.1.20 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.20 31 1.1 even 1 trivial