Properties

Label 177.12.a.c.1.2
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-81.8884 q^{2} -243.000 q^{3} +4657.72 q^{4} -12268.5 q^{5} +19898.9 q^{6} -65634.7 q^{7} -213706. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-81.8884 q^{2} -243.000 q^{3} +4657.72 q^{4} -12268.5 q^{5} +19898.9 q^{6} -65634.7 q^{7} -213706. q^{8} +59049.0 q^{9} +1.00465e6 q^{10} +614467. q^{11} -1.13182e6 q^{12} +1.74232e6 q^{13} +5.37472e6 q^{14} +2.98124e6 q^{15} +7.96101e6 q^{16} -1.11473e6 q^{17} -4.83543e6 q^{18} +1.46733e7 q^{19} -5.71431e7 q^{20} +1.59492e7 q^{21} -5.03177e7 q^{22} +5.31182e7 q^{23} +5.19304e7 q^{24} +1.01688e8 q^{25} -1.42676e8 q^{26} -1.43489e7 q^{27} -3.05708e8 q^{28} -1.59287e8 q^{29} -2.44129e8 q^{30} +4.50702e7 q^{31} -2.14246e8 q^{32} -1.49315e8 q^{33} +9.12837e7 q^{34} +8.05238e8 q^{35} +2.75033e8 q^{36} +7.33231e8 q^{37} -1.20157e9 q^{38} -4.23385e8 q^{39} +2.62184e9 q^{40} -3.90985e7 q^{41} -1.30606e9 q^{42} +9.67989e8 q^{43} +2.86201e9 q^{44} -7.24442e8 q^{45} -4.34976e9 q^{46} +1.84099e9 q^{47} -1.93453e9 q^{48} +2.33058e9 q^{49} -8.32704e9 q^{50} +2.70880e8 q^{51} +8.11525e9 q^{52} +3.64445e9 q^{53} +1.17501e9 q^{54} -7.53858e9 q^{55} +1.40265e10 q^{56} -3.56561e9 q^{57} +1.30438e10 q^{58} -7.14924e8 q^{59} +1.38858e10 q^{60} +1.84441e9 q^{61} -3.69073e9 q^{62} -3.87566e9 q^{63} +1.24009e9 q^{64} -2.13757e10 q^{65} +1.22272e10 q^{66} -1.36376e10 q^{67} -5.19211e9 q^{68} -1.29077e10 q^{69} -6.59397e10 q^{70} -2.07952e10 q^{71} -1.26191e10 q^{72} +1.69766e10 q^{73} -6.00431e10 q^{74} -2.47101e10 q^{75} +6.83441e10 q^{76} -4.03303e10 q^{77} +3.46703e10 q^{78} +3.36122e10 q^{79} -9.76695e10 q^{80} +3.48678e9 q^{81} +3.20171e9 q^{82} +2.76507e10 q^{83} +7.42870e10 q^{84} +1.36761e10 q^{85} -7.92671e10 q^{86} +3.87067e10 q^{87} -1.31315e11 q^{88} -1.44161e10 q^{89} +5.93234e10 q^{90} -1.14357e11 q^{91} +2.47409e11 q^{92} -1.09521e10 q^{93} -1.50755e11 q^{94} -1.80019e11 q^{95} +5.20617e10 q^{96} +1.18137e11 q^{97} -1.90848e11 q^{98} +3.62837e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −81.8884 −1.80950 −0.904748 0.425947i \(-0.859941\pi\)
−0.904748 + 0.425947i \(0.859941\pi\)
\(3\) −243.000 −0.577350
\(4\) 4657.72 2.27428
\(5\) −12268.5 −1.75572 −0.877861 0.478915i \(-0.841030\pi\)
−0.877861 + 0.478915i \(0.841030\pi\)
\(6\) 19898.9 1.04471
\(7\) −65634.7 −1.47603 −0.738013 0.674786i \(-0.764236\pi\)
−0.738013 + 0.674786i \(0.764236\pi\)
\(8\) −213706. −2.30580
\(9\) 59049.0 0.333333
\(10\) 1.00465e6 3.17697
\(11\) 614467. 1.15037 0.575187 0.818022i \(-0.304929\pi\)
0.575187 + 0.818022i \(0.304929\pi\)
\(12\) −1.13182e6 −1.31305
\(13\) 1.74232e6 1.30149 0.650744 0.759297i \(-0.274457\pi\)
0.650744 + 0.759297i \(0.274457\pi\)
\(14\) 5.37472e6 2.67086
\(15\) 2.98124e6 1.01367
\(16\) 7.96101e6 1.89805
\(17\) −1.11473e6 −0.190415 −0.0952076 0.995457i \(-0.530351\pi\)
−0.0952076 + 0.995457i \(0.530351\pi\)
\(18\) −4.83543e6 −0.603165
\(19\) 1.46733e7 1.35951 0.679756 0.733438i \(-0.262086\pi\)
0.679756 + 0.733438i \(0.262086\pi\)
\(20\) −5.71431e7 −3.99300
\(21\) 1.59492e7 0.852184
\(22\) −5.03177e7 −2.08160
\(23\) 5.31182e7 1.72084 0.860419 0.509587i \(-0.170202\pi\)
0.860419 + 0.509587i \(0.170202\pi\)
\(24\) 5.19304e7 1.33125
\(25\) 1.01688e8 2.08256
\(26\) −1.42676e8 −2.35504
\(27\) −1.43489e7 −0.192450
\(28\) −3.05708e8 −3.35689
\(29\) −1.59287e8 −1.44209 −0.721043 0.692891i \(-0.756337\pi\)
−0.721043 + 0.692891i \(0.756337\pi\)
\(30\) −2.44129e8 −1.83423
\(31\) 4.50702e7 0.282749 0.141374 0.989956i \(-0.454848\pi\)
0.141374 + 0.989956i \(0.454848\pi\)
\(32\) −2.14246e8 −1.12872
\(33\) −1.49315e8 −0.664168
\(34\) 9.12837e7 0.344556
\(35\) 8.05238e8 2.59149
\(36\) 2.75033e8 0.758092
\(37\) 7.33231e8 1.73833 0.869163 0.494526i \(-0.164658\pi\)
0.869163 + 0.494526i \(0.164658\pi\)
\(38\) −1.20157e9 −2.46003
\(39\) −4.23385e8 −0.751415
\(40\) 2.62184e9 4.04834
\(41\) −3.90985e7 −0.0527046 −0.0263523 0.999653i \(-0.508389\pi\)
−0.0263523 + 0.999653i \(0.508389\pi\)
\(42\) −1.30606e9 −1.54202
\(43\) 9.67989e8 1.00414 0.502070 0.864827i \(-0.332572\pi\)
0.502070 + 0.864827i \(0.332572\pi\)
\(44\) 2.86201e9 2.61627
\(45\) −7.24442e8 −0.585241
\(46\) −4.34976e9 −3.11385
\(47\) 1.84099e9 1.17088 0.585440 0.810716i \(-0.300922\pi\)
0.585440 + 0.810716i \(0.300922\pi\)
\(48\) −1.93453e9 −1.09584
\(49\) 2.33058e9 1.17865
\(50\) −8.32704e9 −3.76839
\(51\) 2.70880e8 0.109936
\(52\) 8.11525e9 2.95994
\(53\) 3.64445e9 1.19706 0.598528 0.801102i \(-0.295752\pi\)
0.598528 + 0.801102i \(0.295752\pi\)
\(54\) 1.17501e9 0.348238
\(55\) −7.53858e9 −2.01974
\(56\) 1.40265e10 3.40342
\(57\) −3.56561e9 −0.784915
\(58\) 1.30438e10 2.60945
\(59\) −7.14924e8 −0.130189
\(60\) 1.38858e10 2.30536
\(61\) 1.84441e9 0.279604 0.139802 0.990179i \(-0.455353\pi\)
0.139802 + 0.990179i \(0.455353\pi\)
\(62\) −3.69073e9 −0.511633
\(63\) −3.87566e9 −0.492009
\(64\) 1.24009e9 0.144366
\(65\) −2.13757e10 −2.28505
\(66\) 1.22272e10 1.20181
\(67\) −1.36376e10 −1.23403 −0.617017 0.786950i \(-0.711659\pi\)
−0.617017 + 0.786950i \(0.711659\pi\)
\(68\) −5.19211e9 −0.433057
\(69\) −1.29077e10 −0.993526
\(70\) −6.59397e10 −4.68930
\(71\) −2.07952e10 −1.36786 −0.683930 0.729548i \(-0.739731\pi\)
−0.683930 + 0.729548i \(0.739731\pi\)
\(72\) −1.26191e10 −0.768599
\(73\) 1.69766e10 0.958465 0.479232 0.877688i \(-0.340915\pi\)
0.479232 + 0.877688i \(0.340915\pi\)
\(74\) −6.00431e10 −3.14549
\(75\) −2.47101e10 −1.20237
\(76\) 6.83441e10 3.09191
\(77\) −4.03303e10 −1.69798
\(78\) 3.46703e10 1.35968
\(79\) 3.36122e10 1.22899 0.614494 0.788922i \(-0.289360\pi\)
0.614494 + 0.788922i \(0.289360\pi\)
\(80\) −9.76695e10 −3.33245
\(81\) 3.48678e9 0.111111
\(82\) 3.20171e9 0.0953688
\(83\) 2.76507e10 0.770507 0.385254 0.922811i \(-0.374114\pi\)
0.385254 + 0.922811i \(0.374114\pi\)
\(84\) 7.42870e10 1.93810
\(85\) 1.36761e10 0.334316
\(86\) −7.92671e10 −1.81699
\(87\) 3.87067e10 0.832588
\(88\) −1.31315e11 −2.65253
\(89\) −1.44161e10 −0.273655 −0.136827 0.990595i \(-0.543691\pi\)
−0.136827 + 0.990595i \(0.543691\pi\)
\(90\) 5.93234e10 1.05899
\(91\) −1.14357e11 −1.92103
\(92\) 2.47409e11 3.91366
\(93\) −1.09521e10 −0.163245
\(94\) −1.50755e11 −2.11870
\(95\) −1.80019e11 −2.38693
\(96\) 5.20617e10 0.651668
\(97\) 1.18137e11 1.39683 0.698413 0.715695i \(-0.253890\pi\)
0.698413 + 0.715695i \(0.253890\pi\)
\(98\) −1.90848e11 −2.13277
\(99\) 3.62837e10 0.383458
\(100\) 4.73632e11 4.73632
\(101\) −3.07269e10 −0.290905 −0.145453 0.989365i \(-0.546464\pi\)
−0.145453 + 0.989365i \(0.546464\pi\)
\(102\) −2.21819e10 −0.198929
\(103\) 4.65828e10 0.395932 0.197966 0.980209i \(-0.436566\pi\)
0.197966 + 0.980209i \(0.436566\pi\)
\(104\) −3.72344e11 −3.00097
\(105\) −1.95673e11 −1.49620
\(106\) −2.98438e11 −2.16607
\(107\) −1.33118e11 −0.917542 −0.458771 0.888555i \(-0.651710\pi\)
−0.458771 + 0.888555i \(0.651710\pi\)
\(108\) −6.68331e10 −0.437684
\(109\) 1.35886e11 0.845921 0.422960 0.906148i \(-0.360991\pi\)
0.422960 + 0.906148i \(0.360991\pi\)
\(110\) 6.17322e11 3.65470
\(111\) −1.78175e11 −1.00362
\(112\) −5.22518e11 −2.80158
\(113\) 1.99811e11 1.02020 0.510102 0.860114i \(-0.329608\pi\)
0.510102 + 0.860114i \(0.329608\pi\)
\(114\) 2.91982e11 1.42030
\(115\) −6.51679e11 −3.02131
\(116\) −7.41913e11 −3.27970
\(117\) 1.02882e11 0.433830
\(118\) 5.85440e10 0.235576
\(119\) 7.31651e10 0.281058
\(120\) −6.37108e11 −2.33731
\(121\) 9.22580e10 0.323359
\(122\) −1.51036e11 −0.505943
\(123\) 9.50093e9 0.0304290
\(124\) 2.09924e11 0.643048
\(125\) −6.48505e11 −1.90068
\(126\) 3.17372e11 0.890288
\(127\) −2.45066e11 −0.658208 −0.329104 0.944294i \(-0.606747\pi\)
−0.329104 + 0.944294i \(0.606747\pi\)
\(128\) 3.37226e11 0.867493
\(129\) −2.35221e11 −0.579740
\(130\) 1.75042e12 4.13479
\(131\) −3.48684e11 −0.789659 −0.394830 0.918754i \(-0.629196\pi\)
−0.394830 + 0.918754i \(0.629196\pi\)
\(132\) −6.95469e11 −1.51050
\(133\) −9.63078e11 −2.00668
\(134\) 1.11676e12 2.23298
\(135\) 1.76039e11 0.337889
\(136\) 2.38225e11 0.439059
\(137\) 7.91794e10 0.140168 0.0700840 0.997541i \(-0.477673\pi\)
0.0700840 + 0.997541i \(0.477673\pi\)
\(138\) 1.05699e12 1.79778
\(139\) 5.35686e11 0.875646 0.437823 0.899061i \(-0.355750\pi\)
0.437823 + 0.899061i \(0.355750\pi\)
\(140\) 3.75057e12 5.89377
\(141\) −4.47359e11 −0.676007
\(142\) 1.70288e12 2.47514
\(143\) 1.07060e12 1.49720
\(144\) 4.70090e11 0.632684
\(145\) 1.95421e12 2.53190
\(146\) −1.39019e12 −1.73434
\(147\) −5.66332e11 −0.680496
\(148\) 3.41518e12 3.95343
\(149\) −1.13785e12 −1.26928 −0.634642 0.772806i \(-0.718852\pi\)
−0.634642 + 0.772806i \(0.718852\pi\)
\(150\) 2.02347e12 2.17568
\(151\) 7.52312e11 0.779875 0.389937 0.920841i \(-0.372497\pi\)
0.389937 + 0.920841i \(0.372497\pi\)
\(152\) −3.13577e12 −3.13476
\(153\) −6.58239e10 −0.0634717
\(154\) 3.30259e12 3.07249
\(155\) −5.52944e11 −0.496428
\(156\) −1.97201e12 −1.70892
\(157\) 1.57758e12 1.31991 0.659954 0.751306i \(-0.270576\pi\)
0.659954 + 0.751306i \(0.270576\pi\)
\(158\) −2.75245e12 −2.22385
\(159\) −8.85602e11 −0.691121
\(160\) 2.62847e12 1.98172
\(161\) −3.48639e12 −2.54000
\(162\) −2.85527e11 −0.201055
\(163\) 1.11569e12 0.759470 0.379735 0.925095i \(-0.376015\pi\)
0.379735 + 0.925095i \(0.376015\pi\)
\(164\) −1.82110e11 −0.119865
\(165\) 1.83187e12 1.16610
\(166\) −2.26427e12 −1.39423
\(167\) 1.00214e12 0.597020 0.298510 0.954407i \(-0.403510\pi\)
0.298510 + 0.954407i \(0.403510\pi\)
\(168\) −3.40844e12 −1.96496
\(169\) 1.24353e12 0.693874
\(170\) −1.11991e12 −0.604944
\(171\) 8.66444e11 0.453171
\(172\) 4.50862e12 2.28369
\(173\) 1.17842e12 0.578156 0.289078 0.957306i \(-0.406651\pi\)
0.289078 + 0.957306i \(0.406651\pi\)
\(174\) −3.16963e12 −1.50657
\(175\) −6.67423e12 −3.07392
\(176\) 4.89178e12 2.18347
\(177\) 1.73727e11 0.0751646
\(178\) 1.18051e12 0.495177
\(179\) −1.28029e12 −0.520735 −0.260368 0.965510i \(-0.583844\pi\)
−0.260368 + 0.965510i \(0.583844\pi\)
\(180\) −3.37424e12 −1.33100
\(181\) 2.22754e12 0.852302 0.426151 0.904652i \(-0.359869\pi\)
0.426151 + 0.904652i \(0.359869\pi\)
\(182\) 9.36450e12 3.47610
\(183\) −4.48192e11 −0.161430
\(184\) −1.13516e13 −3.96790
\(185\) −8.99563e12 −3.05202
\(186\) 8.96848e11 0.295391
\(187\) −6.84967e11 −0.219049
\(188\) 8.57479e12 2.66290
\(189\) 9.41786e11 0.284061
\(190\) 1.47415e13 4.31913
\(191\) 1.46958e11 0.0418320 0.0209160 0.999781i \(-0.493342\pi\)
0.0209160 + 0.999781i \(0.493342\pi\)
\(192\) −3.01343e11 −0.0833496
\(193\) −7.03816e12 −1.89188 −0.945941 0.324338i \(-0.894859\pi\)
−0.945941 + 0.324338i \(0.894859\pi\)
\(194\) −9.67407e12 −2.52755
\(195\) 5.19429e12 1.31928
\(196\) 1.08552e13 2.68058
\(197\) 4.74360e12 1.13905 0.569527 0.821973i \(-0.307127\pi\)
0.569527 + 0.821973i \(0.307127\pi\)
\(198\) −2.97121e12 −0.693865
\(199\) −6.90796e12 −1.56913 −0.784563 0.620049i \(-0.787113\pi\)
−0.784563 + 0.620049i \(0.787113\pi\)
\(200\) −2.17312e13 −4.80196
\(201\) 3.31394e12 0.712470
\(202\) 2.51618e12 0.526392
\(203\) 1.04547e13 2.12856
\(204\) 1.26168e12 0.250025
\(205\) 4.79679e11 0.0925347
\(206\) −3.81459e12 −0.716438
\(207\) 3.13657e12 0.573613
\(208\) 1.38707e13 2.47029
\(209\) 9.01626e12 1.56395
\(210\) 1.60233e13 2.70737
\(211\) 2.87436e12 0.473139 0.236569 0.971615i \(-0.423977\pi\)
0.236569 + 0.971615i \(0.423977\pi\)
\(212\) 1.69748e13 2.72244
\(213\) 5.05323e12 0.789734
\(214\) 1.09008e13 1.66029
\(215\) −1.18758e13 −1.76299
\(216\) 3.06644e12 0.443751
\(217\) −2.95817e12 −0.417345
\(218\) −1.11275e13 −1.53069
\(219\) −4.12532e12 −0.553370
\(220\) −3.51126e13 −4.59344
\(221\) −1.94223e12 −0.247823
\(222\) 1.45905e13 1.81605
\(223\) −9.28787e11 −0.112782 −0.0563910 0.998409i \(-0.517959\pi\)
−0.0563910 + 0.998409i \(0.517959\pi\)
\(224\) 1.40619e13 1.66602
\(225\) 6.00455e12 0.694187
\(226\) −1.63622e13 −1.84606
\(227\) 2.76808e11 0.0304815 0.0152408 0.999884i \(-0.495149\pi\)
0.0152408 + 0.999884i \(0.495149\pi\)
\(228\) −1.66076e13 −1.78511
\(229\) 2.06500e12 0.216683 0.108341 0.994114i \(-0.465446\pi\)
0.108341 + 0.994114i \(0.465446\pi\)
\(230\) 5.33650e13 5.46705
\(231\) 9.80027e12 0.980330
\(232\) 3.40405e13 3.32515
\(233\) 1.37762e13 1.31423 0.657117 0.753788i \(-0.271776\pi\)
0.657117 + 0.753788i \(0.271776\pi\)
\(234\) −8.42489e12 −0.785013
\(235\) −2.25861e13 −2.05574
\(236\) −3.32991e12 −0.296085
\(237\) −8.16776e12 −0.709556
\(238\) −5.99138e12 −0.508573
\(239\) 1.12934e13 0.936776 0.468388 0.883523i \(-0.344835\pi\)
0.468388 + 0.883523i \(0.344835\pi\)
\(240\) 2.37337e13 1.92399
\(241\) 1.59171e13 1.26116 0.630581 0.776123i \(-0.282817\pi\)
0.630581 + 0.776123i \(0.282817\pi\)
\(242\) −7.55487e12 −0.585116
\(243\) −8.47289e11 −0.0641500
\(244\) 8.59075e12 0.635897
\(245\) −2.85927e13 −2.06939
\(246\) −7.78016e11 −0.0550612
\(247\) 2.55657e13 1.76939
\(248\) −9.63176e12 −0.651961
\(249\) −6.71912e12 −0.444853
\(250\) 5.31051e13 3.43927
\(251\) 1.23833e12 0.0784569 0.0392284 0.999230i \(-0.487510\pi\)
0.0392284 + 0.999230i \(0.487510\pi\)
\(252\) −1.80517e13 −1.11896
\(253\) 3.26394e13 1.97961
\(254\) 2.00681e13 1.19102
\(255\) −3.32329e12 −0.193018
\(256\) −3.01546e13 −1.71409
\(257\) −2.89910e13 −1.61299 −0.806494 0.591242i \(-0.798638\pi\)
−0.806494 + 0.591242i \(0.798638\pi\)
\(258\) 1.92619e13 1.04904
\(259\) −4.81253e13 −2.56581
\(260\) −9.95618e13 −5.19684
\(261\) −9.40573e12 −0.480695
\(262\) 2.85532e13 1.42889
\(263\) 2.19744e13 1.07686 0.538432 0.842669i \(-0.319017\pi\)
0.538432 + 0.842669i \(0.319017\pi\)
\(264\) 3.19095e13 1.53144
\(265\) −4.47119e13 −2.10170
\(266\) 7.88649e13 3.63107
\(267\) 3.50312e12 0.157995
\(268\) −6.35201e13 −2.80653
\(269\) 1.88848e13 0.817476 0.408738 0.912652i \(-0.365969\pi\)
0.408738 + 0.912652i \(0.365969\pi\)
\(270\) −1.44156e13 −0.611409
\(271\) −2.90121e13 −1.20573 −0.602863 0.797845i \(-0.705973\pi\)
−0.602863 + 0.797845i \(0.705973\pi\)
\(272\) −8.87440e12 −0.361418
\(273\) 2.77887e13 1.10911
\(274\) −6.48387e12 −0.253633
\(275\) 6.24837e13 2.39572
\(276\) −6.01205e13 −2.25955
\(277\) 4.19714e13 1.54638 0.773188 0.634177i \(-0.218661\pi\)
0.773188 + 0.634177i \(0.218661\pi\)
\(278\) −4.38665e13 −1.58448
\(279\) 2.66135e12 0.0942496
\(280\) −1.72084e14 −5.97545
\(281\) 3.40504e13 1.15941 0.579706 0.814826i \(-0.303167\pi\)
0.579706 + 0.814826i \(0.303167\pi\)
\(282\) 3.66336e13 1.22323
\(283\) 2.11301e12 0.0691951 0.0345976 0.999401i \(-0.488985\pi\)
0.0345976 + 0.999401i \(0.488985\pi\)
\(284\) −9.68580e13 −3.11089
\(285\) 4.37447e13 1.37809
\(286\) −8.76698e13 −2.70917
\(287\) 2.56622e12 0.0777934
\(288\) −1.26510e13 −0.376241
\(289\) −3.30293e13 −0.963742
\(290\) −1.60027e14 −4.58147
\(291\) −2.87073e13 −0.806457
\(292\) 7.90724e13 2.17981
\(293\) −1.32074e13 −0.357311 −0.178656 0.983912i \(-0.557175\pi\)
−0.178656 + 0.983912i \(0.557175\pi\)
\(294\) 4.63760e13 1.23135
\(295\) 8.77104e12 0.228576
\(296\) −1.56695e14 −4.00822
\(297\) −8.81693e12 −0.221389
\(298\) 9.31763e13 2.29676
\(299\) 9.25490e13 2.23965
\(300\) −1.15093e14 −2.73451
\(301\) −6.35336e13 −1.48214
\(302\) −6.16057e13 −1.41118
\(303\) 7.46664e12 0.167954
\(304\) 1.16814e14 2.58043
\(305\) −2.26281e13 −0.490908
\(306\) 5.39021e12 0.114852
\(307\) 2.80769e13 0.587608 0.293804 0.955866i \(-0.405079\pi\)
0.293804 + 0.955866i \(0.405079\pi\)
\(308\) −1.87847e14 −3.86168
\(309\) −1.13196e13 −0.228592
\(310\) 4.52797e13 0.898285
\(311\) −1.42706e13 −0.278139 −0.139069 0.990283i \(-0.544411\pi\)
−0.139069 + 0.990283i \(0.544411\pi\)
\(312\) 9.04797e13 1.73261
\(313\) −6.35564e13 −1.19582 −0.597910 0.801564i \(-0.704002\pi\)
−0.597910 + 0.801564i \(0.704002\pi\)
\(314\) −1.29186e14 −2.38837
\(315\) 4.75485e13 0.863831
\(316\) 1.56556e14 2.79506
\(317\) 8.71235e13 1.52866 0.764328 0.644828i \(-0.223071\pi\)
0.764328 + 0.644828i \(0.223071\pi\)
\(318\) 7.25205e13 1.25058
\(319\) −9.78765e13 −1.65894
\(320\) −1.52141e13 −0.253466
\(321\) 3.23477e13 0.529743
\(322\) 2.85495e14 4.59612
\(323\) −1.63568e13 −0.258872
\(324\) 1.62404e13 0.252697
\(325\) 1.77173e14 2.71043
\(326\) −9.13618e13 −1.37426
\(327\) −3.30203e13 −0.488393
\(328\) 8.35556e12 0.121526
\(329\) −1.20832e14 −1.72825
\(330\) −1.50009e14 −2.11004
\(331\) 7.31864e13 1.01246 0.506229 0.862399i \(-0.331039\pi\)
0.506229 + 0.862399i \(0.331039\pi\)
\(332\) 1.28789e14 1.75235
\(333\) 4.32965e13 0.579442
\(334\) −8.20638e13 −1.08030
\(335\) 1.67313e14 2.16662
\(336\) 1.26972e14 1.61749
\(337\) −7.55866e13 −0.947284 −0.473642 0.880717i \(-0.657061\pi\)
−0.473642 + 0.880717i \(0.657061\pi\)
\(338\) −1.01831e14 −1.25556
\(339\) −4.85540e13 −0.589015
\(340\) 6.36993e13 0.760327
\(341\) 2.76942e13 0.325267
\(342\) −7.09517e13 −0.820011
\(343\) −2.31859e13 −0.263698
\(344\) −2.06865e14 −2.31534
\(345\) 1.58358e14 1.74436
\(346\) −9.64987e13 −1.04617
\(347\) 9.47376e13 1.01090 0.505452 0.862854i \(-0.331326\pi\)
0.505452 + 0.862854i \(0.331326\pi\)
\(348\) 1.80285e14 1.89354
\(349\) −6.81483e12 −0.0704556 −0.0352278 0.999379i \(-0.511216\pi\)
−0.0352278 + 0.999379i \(0.511216\pi\)
\(350\) 5.46542e14 5.56224
\(351\) −2.50004e13 −0.250472
\(352\) −1.31647e14 −1.29845
\(353\) −8.85389e13 −0.859752 −0.429876 0.902888i \(-0.641443\pi\)
−0.429876 + 0.902888i \(0.641443\pi\)
\(354\) −1.42262e13 −0.136010
\(355\) 2.55125e14 2.40158
\(356\) −6.71462e13 −0.622366
\(357\) −1.77791e13 −0.162269
\(358\) 1.04841e14 0.942269
\(359\) 1.09759e14 0.971449 0.485724 0.874112i \(-0.338556\pi\)
0.485724 + 0.874112i \(0.338556\pi\)
\(360\) 1.54817e14 1.34945
\(361\) 9.88156e13 0.848274
\(362\) −1.82410e14 −1.54224
\(363\) −2.24187e13 −0.186691
\(364\) −5.32642e14 −4.36896
\(365\) −2.08278e14 −1.68280
\(366\) 3.67018e13 0.292106
\(367\) −1.27385e14 −0.998745 −0.499373 0.866387i \(-0.666436\pi\)
−0.499373 + 0.866387i \(0.666436\pi\)
\(368\) 4.22874e14 3.26624
\(369\) −2.30873e12 −0.0175682
\(370\) 7.36638e14 5.52261
\(371\) −2.39202e14 −1.76689
\(372\) −5.10116e13 −0.371264
\(373\) −1.67487e14 −1.20111 −0.600554 0.799584i \(-0.705053\pi\)
−0.600554 + 0.799584i \(0.705053\pi\)
\(374\) 5.60908e13 0.396368
\(375\) 1.57587e14 1.09736
\(376\) −3.93429e14 −2.69981
\(377\) −2.77529e14 −1.87686
\(378\) −7.71214e13 −0.514008
\(379\) 8.74232e13 0.574263 0.287132 0.957891i \(-0.407298\pi\)
0.287132 + 0.957891i \(0.407298\pi\)
\(380\) −8.38478e14 −5.42853
\(381\) 5.95511e13 0.380016
\(382\) −1.20341e13 −0.0756949
\(383\) 1.33470e14 0.827541 0.413770 0.910381i \(-0.364212\pi\)
0.413770 + 0.910381i \(0.364212\pi\)
\(384\) −8.19459e13 −0.500847
\(385\) 4.94792e14 2.98118
\(386\) 5.76344e14 3.42335
\(387\) 5.71588e13 0.334713
\(388\) 5.50249e14 3.17676
\(389\) −2.38319e14 −1.35655 −0.678276 0.734808i \(-0.737272\pi\)
−0.678276 + 0.734808i \(0.737272\pi\)
\(390\) −4.25352e14 −2.38722
\(391\) −5.92126e13 −0.327674
\(392\) −4.98059e14 −2.71773
\(393\) 8.47302e13 0.455910
\(394\) −3.88446e14 −2.06111
\(395\) −4.12370e14 −2.15776
\(396\) 1.68999e14 0.872088
\(397\) 3.31386e14 1.68650 0.843249 0.537523i \(-0.180640\pi\)
0.843249 + 0.537523i \(0.180640\pi\)
\(398\) 5.65682e14 2.83933
\(399\) 2.34028e14 1.15855
\(400\) 8.09536e14 3.95281
\(401\) −2.88745e14 −1.39066 −0.695330 0.718691i \(-0.744742\pi\)
−0.695330 + 0.718691i \(0.744742\pi\)
\(402\) −2.71373e14 −1.28921
\(403\) 7.85270e13 0.367994
\(404\) −1.43117e14 −0.661599
\(405\) −4.27776e13 −0.195080
\(406\) −8.56122e14 −3.85161
\(407\) 4.50546e14 1.99972
\(408\) −5.78886e13 −0.253491
\(409\) 3.50854e14 1.51582 0.757911 0.652358i \(-0.226220\pi\)
0.757911 + 0.652358i \(0.226220\pi\)
\(410\) −3.92802e13 −0.167441
\(411\) −1.92406e13 −0.0809260
\(412\) 2.16970e14 0.900459
\(413\) 4.69238e13 0.192162
\(414\) −2.56849e14 −1.03795
\(415\) −3.39232e14 −1.35280
\(416\) −3.73285e14 −1.46902
\(417\) −1.30172e14 −0.505555
\(418\) −7.38328e14 −2.82996
\(419\) −8.89563e13 −0.336511 −0.168256 0.985743i \(-0.553813\pi\)
−0.168256 + 0.985743i \(0.553813\pi\)
\(420\) −9.11388e14 −3.40277
\(421\) −1.68005e14 −0.619113 −0.309556 0.950881i \(-0.600181\pi\)
−0.309556 + 0.950881i \(0.600181\pi\)
\(422\) −2.35377e14 −0.856142
\(423\) 1.08708e14 0.390293
\(424\) −7.78839e14 −2.76017
\(425\) −1.13354e14 −0.396551
\(426\) −4.13801e14 −1.42902
\(427\) −1.21057e14 −0.412703
\(428\) −6.20026e14 −2.08674
\(429\) −2.60156e14 −0.864408
\(430\) 9.72487e14 3.19012
\(431\) −1.33060e14 −0.430946 −0.215473 0.976510i \(-0.569129\pi\)
−0.215473 + 0.976510i \(0.569129\pi\)
\(432\) −1.14232e14 −0.365280
\(433\) −3.10508e14 −0.980370 −0.490185 0.871619i \(-0.663071\pi\)
−0.490185 + 0.871619i \(0.663071\pi\)
\(434\) 2.42240e14 0.755183
\(435\) −4.74873e14 −1.46179
\(436\) 6.32919e14 1.92386
\(437\) 7.79419e14 2.33950
\(438\) 3.37816e14 1.00132
\(439\) 5.94518e14 1.74024 0.870122 0.492837i \(-0.164040\pi\)
0.870122 + 0.492837i \(0.164040\pi\)
\(440\) 1.61104e15 4.65710
\(441\) 1.37619e14 0.392885
\(442\) 1.59046e14 0.448435
\(443\) −6.10093e14 −1.69893 −0.849465 0.527645i \(-0.823075\pi\)
−0.849465 + 0.527645i \(0.823075\pi\)
\(444\) −8.29889e14 −2.28251
\(445\) 1.76864e14 0.480462
\(446\) 7.60569e13 0.204078
\(447\) 2.76496e14 0.732821
\(448\) −8.13931e13 −0.213088
\(449\) 3.25417e14 0.841560 0.420780 0.907163i \(-0.361756\pi\)
0.420780 + 0.907163i \(0.361756\pi\)
\(450\) −4.91703e14 −1.25613
\(451\) −2.40247e13 −0.0606300
\(452\) 9.30661e14 2.32023
\(453\) −1.82812e14 −0.450261
\(454\) −2.26674e13 −0.0551562
\(455\) 1.40299e15 3.37280
\(456\) 7.61991e14 1.80985
\(457\) −5.63579e14 −1.32256 −0.661281 0.750139i \(-0.729987\pi\)
−0.661281 + 0.750139i \(0.729987\pi\)
\(458\) −1.69100e14 −0.392087
\(459\) 1.59952e13 0.0366454
\(460\) −3.03534e15 −6.87130
\(461\) 1.78681e14 0.399691 0.199846 0.979827i \(-0.435956\pi\)
0.199846 + 0.979827i \(0.435956\pi\)
\(462\) −8.02529e14 −1.77390
\(463\) 5.69718e14 1.24441 0.622207 0.782853i \(-0.286236\pi\)
0.622207 + 0.782853i \(0.286236\pi\)
\(464\) −1.26808e15 −2.73715
\(465\) 1.34365e14 0.286613
\(466\) −1.12811e15 −2.37810
\(467\) −3.81172e13 −0.0794105 −0.0397052 0.999211i \(-0.512642\pi\)
−0.0397052 + 0.999211i \(0.512642\pi\)
\(468\) 4.79197e14 0.986648
\(469\) 8.95101e14 1.82147
\(470\) 1.84954e15 3.71985
\(471\) −3.83352e14 −0.762049
\(472\) 1.52783e14 0.300189
\(473\) 5.94797e14 1.15514
\(474\) 6.68845e14 1.28394
\(475\) 1.49209e15 2.83127
\(476\) 3.40782e14 0.639203
\(477\) 2.15201e14 0.399019
\(478\) −9.24798e14 −1.69509
\(479\) −8.91177e13 −0.161480 −0.0807400 0.996735i \(-0.525728\pi\)
−0.0807400 + 0.996735i \(0.525728\pi\)
\(480\) −6.38718e14 −1.14415
\(481\) 1.27753e15 2.26241
\(482\) −1.30343e15 −2.28207
\(483\) 8.47193e14 1.46647
\(484\) 4.29712e14 0.735407
\(485\) −1.44936e15 −2.45244
\(486\) 6.93831e13 0.116079
\(487\) −1.20100e15 −1.98670 −0.993350 0.115137i \(-0.963269\pi\)
−0.993350 + 0.115137i \(0.963269\pi\)
\(488\) −3.94161e14 −0.644711
\(489\) −2.71112e14 −0.438480
\(490\) 2.34141e15 3.74455
\(491\) −4.53460e14 −0.717118 −0.358559 0.933507i \(-0.616732\pi\)
−0.358559 + 0.933507i \(0.616732\pi\)
\(492\) 4.42526e13 0.0692040
\(493\) 1.77562e14 0.274595
\(494\) −2.09353e15 −3.20170
\(495\) −4.45146e14 −0.673245
\(496\) 3.58805e14 0.536672
\(497\) 1.36488e15 2.01900
\(498\) 5.50218e14 0.804959
\(499\) −2.32270e13 −0.0336079 −0.0168039 0.999859i \(-0.505349\pi\)
−0.0168039 + 0.999859i \(0.505349\pi\)
\(500\) −3.02055e15 −4.32266
\(501\) −2.43520e14 −0.344689
\(502\) −1.01405e14 −0.141967
\(503\) −1.06144e15 −1.46985 −0.734926 0.678148i \(-0.762783\pi\)
−0.734926 + 0.678148i \(0.762783\pi\)
\(504\) 8.28250e14 1.13447
\(505\) 3.76973e14 0.510749
\(506\) −2.67279e15 −3.58209
\(507\) −3.02178e14 −0.400608
\(508\) −1.14145e15 −1.49695
\(509\) 4.13158e14 0.536005 0.268002 0.963418i \(-0.413636\pi\)
0.268002 + 0.963418i \(0.413636\pi\)
\(510\) 2.72139e14 0.349265
\(511\) −1.11426e15 −1.41472
\(512\) 1.77867e15 2.23415
\(513\) −2.10546e14 −0.261638
\(514\) 2.37403e15 2.91870
\(515\) −5.71501e14 −0.695148
\(516\) −1.09559e15 −1.31849
\(517\) 1.13122e15 1.34695
\(518\) 3.94091e15 4.64283
\(519\) −2.86355e14 −0.333799
\(520\) 4.56810e15 5.26887
\(521\) 1.20058e15 1.37019 0.685097 0.728452i \(-0.259760\pi\)
0.685097 + 0.728452i \(0.259760\pi\)
\(522\) 7.70220e14 0.869816
\(523\) −2.39919e14 −0.268105 −0.134052 0.990974i \(-0.542799\pi\)
−0.134052 + 0.990974i \(0.542799\pi\)
\(524\) −1.62407e15 −1.79590
\(525\) 1.62184e15 1.77473
\(526\) −1.79945e15 −1.94858
\(527\) −5.02413e13 −0.0538397
\(528\) −1.18870e15 −1.26063
\(529\) 1.86873e15 1.96128
\(530\) 3.66139e15 3.80302
\(531\) −4.22156e13 −0.0433963
\(532\) −4.48574e15 −4.56373
\(533\) −6.81222e13 −0.0685945
\(534\) −2.86865e14 −0.285891
\(535\) 1.63316e15 1.61095
\(536\) 2.91443e15 2.84543
\(537\) 3.11111e14 0.300647
\(538\) −1.54645e15 −1.47922
\(539\) 1.43207e15 1.35589
\(540\) 8.19941e14 0.768452
\(541\) −1.53994e15 −1.42862 −0.714312 0.699827i \(-0.753260\pi\)
−0.714312 + 0.699827i \(0.753260\pi\)
\(542\) 2.37576e15 2.18176
\(543\) −5.41292e14 −0.492077
\(544\) 2.38827e14 0.214926
\(545\) −1.66712e15 −1.48520
\(546\) −2.27557e15 −2.00693
\(547\) −1.77377e15 −1.54870 −0.774349 0.632759i \(-0.781923\pi\)
−0.774349 + 0.632759i \(0.781923\pi\)
\(548\) 3.68795e14 0.318781
\(549\) 1.08911e14 0.0932015
\(550\) −5.11669e15 −4.33505
\(551\) −2.33726e15 −1.96053
\(552\) 2.75845e15 2.29087
\(553\) −2.20612e15 −1.81402
\(554\) −3.43697e15 −2.79816
\(555\) 2.18594e15 1.76208
\(556\) 2.49507e15 1.99146
\(557\) −1.34692e15 −1.06448 −0.532242 0.846592i \(-0.678650\pi\)
−0.532242 + 0.846592i \(0.678650\pi\)
\(558\) −2.17934e14 −0.170544
\(559\) 1.68655e15 1.30688
\(560\) 6.41051e15 4.91879
\(561\) 1.66447e14 0.126468
\(562\) −2.78834e15 −2.09795
\(563\) −5.37127e14 −0.400204 −0.200102 0.979775i \(-0.564127\pi\)
−0.200102 + 0.979775i \(0.564127\pi\)
\(564\) −2.08367e15 −1.53743
\(565\) −2.45137e15 −1.79120
\(566\) −1.73031e14 −0.125208
\(567\) −2.28854e14 −0.164003
\(568\) 4.44404e15 3.15401
\(569\) 8.67485e14 0.609740 0.304870 0.952394i \(-0.401387\pi\)
0.304870 + 0.952394i \(0.401387\pi\)
\(570\) −3.58218e15 −2.49365
\(571\) 6.22355e14 0.429081 0.214541 0.976715i \(-0.431175\pi\)
0.214541 + 0.976715i \(0.431175\pi\)
\(572\) 4.98655e15 3.40504
\(573\) −3.57107e13 −0.0241517
\(574\) −2.10143e14 −0.140767
\(575\) 5.40146e15 3.58375
\(576\) 7.32262e13 0.0481219
\(577\) −2.49549e15 −1.62438 −0.812191 0.583392i \(-0.801725\pi\)
−0.812191 + 0.583392i \(0.801725\pi\)
\(578\) 2.70471e15 1.74389
\(579\) 1.71027e15 1.09228
\(580\) 9.10215e15 5.75824
\(581\) −1.81485e15 −1.13729
\(582\) 2.35080e15 1.45928
\(583\) 2.23939e15 1.37706
\(584\) −3.62800e15 −2.21002
\(585\) −1.26221e15 −0.761684
\(586\) 1.08154e15 0.646553
\(587\) −4.10477e14 −0.243097 −0.121549 0.992585i \(-0.538786\pi\)
−0.121549 + 0.992585i \(0.538786\pi\)
\(588\) −2.63781e15 −1.54764
\(589\) 6.61330e14 0.384400
\(590\) −7.18247e14 −0.413607
\(591\) −1.15270e15 −0.657633
\(592\) 5.83725e15 3.29943
\(593\) 3.87690e14 0.217112 0.108556 0.994090i \(-0.465377\pi\)
0.108556 + 0.994090i \(0.465377\pi\)
\(594\) 7.22005e14 0.400603
\(595\) −8.97625e14 −0.493460
\(596\) −5.29976e15 −2.88670
\(597\) 1.67863e15 0.905935
\(598\) −7.57870e15 −4.05264
\(599\) −3.99439e14 −0.211642 −0.105821 0.994385i \(-0.533747\pi\)
−0.105821 + 0.994385i \(0.533747\pi\)
\(600\) 5.28068e15 2.77241
\(601\) −1.59334e15 −0.828896 −0.414448 0.910073i \(-0.636025\pi\)
−0.414448 + 0.910073i \(0.636025\pi\)
\(602\) 5.20267e15 2.68192
\(603\) −8.05288e14 −0.411345
\(604\) 3.50406e15 1.77365
\(605\) −1.13187e15 −0.567728
\(606\) −6.11432e14 −0.303913
\(607\) −1.83861e15 −0.905631 −0.452816 0.891604i \(-0.649580\pi\)
−0.452816 + 0.891604i \(0.649580\pi\)
\(608\) −3.14369e15 −1.53451
\(609\) −2.54050e15 −1.22892
\(610\) 1.85298e15 0.888295
\(611\) 3.20759e15 1.52389
\(612\) −3.06589e14 −0.144352
\(613\) −2.85879e15 −1.33398 −0.666992 0.745065i \(-0.732418\pi\)
−0.666992 + 0.745065i \(0.732418\pi\)
\(614\) −2.29917e15 −1.06327
\(615\) −1.16562e14 −0.0534249
\(616\) 8.61882e15 3.91520
\(617\) 4.04258e15 1.82008 0.910040 0.414520i \(-0.136051\pi\)
0.910040 + 0.414520i \(0.136051\pi\)
\(618\) 9.26947e14 0.413636
\(619\) 1.66600e15 0.736847 0.368423 0.929658i \(-0.379898\pi\)
0.368423 + 0.929658i \(0.379898\pi\)
\(620\) −2.57545e15 −1.12901
\(621\) −7.62188e14 −0.331175
\(622\) 1.16860e15 0.503291
\(623\) 9.46197e14 0.403922
\(624\) −3.37057e15 −1.42623
\(625\) 2.99096e15 1.25450
\(626\) 5.20454e15 2.16383
\(627\) −2.19095e15 −0.902945
\(628\) 7.34793e15 3.00183
\(629\) −8.17356e14 −0.331004
\(630\) −3.89367e15 −1.56310
\(631\) −2.22420e15 −0.885140 −0.442570 0.896734i \(-0.645933\pi\)
−0.442570 + 0.896734i \(0.645933\pi\)
\(632\) −7.18311e15 −2.83379
\(633\) −6.98471e14 −0.273167
\(634\) −7.13441e15 −2.76610
\(635\) 3.00659e15 1.15563
\(636\) −4.12488e15 −1.57180
\(637\) 4.06063e15 1.53400
\(638\) 8.01496e15 3.00184
\(639\) −1.22793e15 −0.455953
\(640\) −4.13725e15 −1.52308
\(641\) −3.13841e15 −1.14549 −0.572743 0.819735i \(-0.694121\pi\)
−0.572743 + 0.819735i \(0.694121\pi\)
\(642\) −2.64890e15 −0.958568
\(643\) −2.20899e15 −0.792563 −0.396281 0.918129i \(-0.629700\pi\)
−0.396281 + 0.918129i \(0.629700\pi\)
\(644\) −1.62386e16 −5.77666
\(645\) 2.88581e15 1.01786
\(646\) 1.33943e15 0.468428
\(647\) −2.86406e15 −0.993137 −0.496568 0.867998i \(-0.665407\pi\)
−0.496568 + 0.867998i \(0.665407\pi\)
\(648\) −7.45145e14 −0.256200
\(649\) −4.39297e14 −0.149766
\(650\) −1.45084e16 −4.90451
\(651\) 7.18836e14 0.240954
\(652\) 5.19655e15 1.72724
\(653\) 2.31705e15 0.763681 0.381841 0.924228i \(-0.375290\pi\)
0.381841 + 0.924228i \(0.375290\pi\)
\(654\) 2.70398e15 0.883744
\(655\) 4.27782e15 1.38642
\(656\) −3.11263e14 −0.100036
\(657\) 1.00245e15 0.319488
\(658\) 9.89478e15 3.12726
\(659\) −1.43478e14 −0.0449691 −0.0224846 0.999747i \(-0.507158\pi\)
−0.0224846 + 0.999747i \(0.507158\pi\)
\(660\) 8.53235e15 2.65202
\(661\) 3.98885e15 1.22953 0.614766 0.788710i \(-0.289250\pi\)
0.614766 + 0.788710i \(0.289250\pi\)
\(662\) −5.99312e15 −1.83204
\(663\) 4.71961e14 0.143081
\(664\) −5.90911e15 −1.77663
\(665\) 1.18155e16 3.52317
\(666\) −3.54549e15 −1.04850
\(667\) −8.46102e15 −2.48159
\(668\) 4.66769e15 1.35779
\(669\) 2.25695e14 0.0651147
\(670\) −1.37010e16 −3.92049
\(671\) 1.13333e15 0.321649
\(672\) −3.41705e15 −0.961879
\(673\) −5.12540e14 −0.143102 −0.0715509 0.997437i \(-0.522795\pi\)
−0.0715509 + 0.997437i \(0.522795\pi\)
\(674\) 6.18967e15 1.71411
\(675\) −1.45911e15 −0.400789
\(676\) 5.79202e15 1.57806
\(677\) 2.83003e15 0.764809 0.382405 0.923995i \(-0.375096\pi\)
0.382405 + 0.923995i \(0.375096\pi\)
\(678\) 3.97601e15 1.06582
\(679\) −7.75390e15 −2.06175
\(680\) −2.92265e15 −0.770865
\(681\) −6.72644e13 −0.0175985
\(682\) −2.26783e15 −0.588568
\(683\) 1.48113e15 0.381312 0.190656 0.981657i \(-0.438938\pi\)
0.190656 + 0.981657i \(0.438938\pi\)
\(684\) 4.03565e15 1.03064
\(685\) −9.71411e14 −0.246096
\(686\) 1.89866e15 0.477160
\(687\) −5.01795e14 −0.125102
\(688\) 7.70617e15 1.90591
\(689\) 6.34981e15 1.55796
\(690\) −1.29677e16 −3.15641
\(691\) 6.00640e15 1.45039 0.725195 0.688544i \(-0.241750\pi\)
0.725195 + 0.688544i \(0.241750\pi\)
\(692\) 5.48873e15 1.31489
\(693\) −2.38147e15 −0.565994
\(694\) −7.75791e15 −1.82923
\(695\) −6.57205e15 −1.53739
\(696\) −8.27184e15 −1.91978
\(697\) 4.35844e13 0.0100358
\(698\) 5.58056e14 0.127489
\(699\) −3.34762e15 −0.758774
\(700\) −3.10867e16 −6.99093
\(701\) 1.87164e15 0.417613 0.208806 0.977957i \(-0.433042\pi\)
0.208806 + 0.977957i \(0.433042\pi\)
\(702\) 2.04725e15 0.453227
\(703\) 1.07589e16 2.36327
\(704\) 7.61996e14 0.166075
\(705\) 5.48842e15 1.18688
\(706\) 7.25031e15 1.55572
\(707\) 2.01675e15 0.429384
\(708\) 8.09169e14 0.170945
\(709\) 6.18607e15 1.29676 0.648382 0.761315i \(-0.275446\pi\)
0.648382 + 0.761315i \(0.275446\pi\)
\(710\) −2.08918e16 −4.34565
\(711\) 1.98476e15 0.409663
\(712\) 3.08080e15 0.630992
\(713\) 2.39405e15 0.486565
\(714\) 1.45590e15 0.293625
\(715\) −1.31346e16 −2.62866
\(716\) −5.96323e15 −1.18430
\(717\) −2.74429e15 −0.540848
\(718\) −8.98798e15 −1.75783
\(719\) −3.83167e14 −0.0743668 −0.0371834 0.999308i \(-0.511839\pi\)
−0.0371834 + 0.999308i \(0.511839\pi\)
\(720\) −5.76729e15 −1.11082
\(721\) −3.05745e15 −0.584407
\(722\) −8.09186e15 −1.53495
\(723\) −3.86786e15 −0.728133
\(724\) 1.03752e16 1.93837
\(725\) −1.61975e16 −3.00323
\(726\) 1.83583e15 0.337817
\(727\) −5.51247e15 −1.00672 −0.503358 0.864078i \(-0.667902\pi\)
−0.503358 + 0.864078i \(0.667902\pi\)
\(728\) 2.44387e16 4.42951
\(729\) 2.05891e14 0.0370370
\(730\) 1.70555e16 3.04502
\(731\) −1.07905e15 −0.191203
\(732\) −2.08755e15 −0.367135
\(733\) 5.39658e15 0.941991 0.470995 0.882136i \(-0.343895\pi\)
0.470995 + 0.882136i \(0.343895\pi\)
\(734\) 1.04314e16 1.80722
\(735\) 6.94803e15 1.19476
\(736\) −1.13803e16 −1.94235
\(737\) −8.37987e15 −1.41960
\(738\) 1.89058e14 0.0317896
\(739\) −4.28606e15 −0.715342 −0.357671 0.933848i \(-0.616429\pi\)
−0.357671 + 0.933848i \(0.616429\pi\)
\(740\) −4.18991e16 −6.94113
\(741\) −6.21245e15 −1.02156
\(742\) 1.95879e16 3.19718
\(743\) −3.44325e15 −0.557866 −0.278933 0.960311i \(-0.589981\pi\)
−0.278933 + 0.960311i \(0.589981\pi\)
\(744\) 2.34052e15 0.376410
\(745\) 1.39596e16 2.22851
\(746\) 1.37152e16 2.17340
\(747\) 1.63275e15 0.256836
\(748\) −3.19038e15 −0.498177
\(749\) 8.73715e15 1.35432
\(750\) −1.29045e16 −1.98566
\(751\) −1.02592e16 −1.56709 −0.783547 0.621332i \(-0.786592\pi\)
−0.783547 + 0.621332i \(0.786592\pi\)
\(752\) 1.46561e16 2.22239
\(753\) −3.00914e14 −0.0452971
\(754\) 2.27264e16 3.39617
\(755\) −9.22973e15 −1.36924
\(756\) 4.38657e15 0.646034
\(757\) −8.42991e15 −1.23252 −0.616262 0.787541i \(-0.711354\pi\)
−0.616262 + 0.787541i \(0.711354\pi\)
\(758\) −7.15895e15 −1.03913
\(759\) −7.93136e15 −1.14293
\(760\) 3.84711e16 5.50376
\(761\) −1.18345e16 −1.68088 −0.840439 0.541907i \(-0.817703\pi\)
−0.840439 + 0.541907i \(0.817703\pi\)
\(762\) −4.87654e15 −0.687638
\(763\) −8.91885e15 −1.24860
\(764\) 6.84487e14 0.0951376
\(765\) 8.07559e14 0.111439
\(766\) −1.09296e16 −1.49743
\(767\) −1.24563e15 −0.169439
\(768\) 7.32757e15 0.989631
\(769\) −8.62931e15 −1.15713 −0.578564 0.815637i \(-0.696387\pi\)
−0.578564 + 0.815637i \(0.696387\pi\)
\(770\) −4.05178e16 −5.39444
\(771\) 7.04482e15 0.931260
\(772\) −3.27818e16 −4.30266
\(773\) −3.26142e15 −0.425030 −0.212515 0.977158i \(-0.568165\pi\)
−0.212515 + 0.977158i \(0.568165\pi\)
\(774\) −4.68064e15 −0.605662
\(775\) 4.58308e15 0.588842
\(776\) −2.52466e16 −3.22079
\(777\) 1.16945e16 1.48137
\(778\) 1.95156e16 2.45467
\(779\) −5.73704e14 −0.0716526
\(780\) 2.41935e16 3.00040
\(781\) −1.27779e16 −1.57355
\(782\) 4.84882e15 0.592924
\(783\) 2.28559e15 0.277529
\(784\) 1.85538e16 2.23715
\(785\) −1.93545e16 −2.31739
\(786\) −6.93842e15 −0.824967
\(787\) 2.49094e15 0.294105 0.147053 0.989129i \(-0.453021\pi\)
0.147053 + 0.989129i \(0.453021\pi\)
\(788\) 2.20943e16 2.59052
\(789\) −5.33978e15 −0.621728
\(790\) 3.37684e16 3.90446
\(791\) −1.31145e16 −1.50585
\(792\) −7.75402e15 −0.884175
\(793\) 3.21356e15 0.363902
\(794\) −2.71367e16 −3.05171
\(795\) 1.08650e16 1.21342
\(796\) −3.21753e16 −3.56862
\(797\) 2.02263e15 0.222790 0.111395 0.993776i \(-0.464468\pi\)
0.111395 + 0.993776i \(0.464468\pi\)
\(798\) −1.91642e16 −2.09640
\(799\) −2.05221e15 −0.222953
\(800\) −2.17861e16 −2.35063
\(801\) −8.51257e14 −0.0912183
\(802\) 2.36449e16 2.51639
\(803\) 1.04316e16 1.10259
\(804\) 1.54354e16 1.62035
\(805\) 4.27728e16 4.45954
\(806\) −6.43045e15 −0.665884
\(807\) −4.58901e15 −0.471970
\(808\) 6.56651e15 0.670768
\(809\) 7.96662e15 0.808272 0.404136 0.914699i \(-0.367572\pi\)
0.404136 + 0.914699i \(0.367572\pi\)
\(810\) 3.50299e15 0.352997
\(811\) −2.21596e15 −0.221793 −0.110896 0.993832i \(-0.535372\pi\)
−0.110896 + 0.993832i \(0.535372\pi\)
\(812\) 4.86952e16 4.84092
\(813\) 7.04995e15 0.696126
\(814\) −3.68945e16 −3.61849
\(815\) −1.36878e16 −1.33342
\(816\) 2.15648e15 0.208665
\(817\) 1.42036e16 1.36514
\(818\) −2.87309e16 −2.74287
\(819\) −6.75266e15 −0.640344
\(820\) 2.23421e15 0.210449
\(821\) 7.19699e15 0.673385 0.336692 0.941615i \(-0.390692\pi\)
0.336692 + 0.941615i \(0.390692\pi\)
\(822\) 1.57558e15 0.146435
\(823\) 2.87425e15 0.265354 0.132677 0.991159i \(-0.457643\pi\)
0.132677 + 0.991159i \(0.457643\pi\)
\(824\) −9.95501e15 −0.912939
\(825\) −1.51835e16 −1.38317
\(826\) −3.84252e15 −0.347717
\(827\) 8.45798e15 0.760302 0.380151 0.924924i \(-0.375872\pi\)
0.380151 + 0.924924i \(0.375872\pi\)
\(828\) 1.46093e16 1.30455
\(829\) 4.09434e15 0.363190 0.181595 0.983373i \(-0.441874\pi\)
0.181595 + 0.983373i \(0.441874\pi\)
\(830\) 2.77792e16 2.44788
\(831\) −1.01991e16 −0.892800
\(832\) 2.16064e15 0.187890
\(833\) −2.59798e15 −0.224434
\(834\) 1.06596e16 0.914799
\(835\) −1.22948e16 −1.04820
\(836\) 4.19952e16 3.55685
\(837\) −6.46709e14 −0.0544150
\(838\) 7.28449e15 0.608915
\(839\) 2.31251e15 0.192040 0.0960201 0.995379i \(-0.469389\pi\)
0.0960201 + 0.995379i \(0.469389\pi\)
\(840\) 4.18164e16 3.44993
\(841\) 1.31718e16 1.07961
\(842\) 1.37576e16 1.12028
\(843\) −8.27426e15 −0.669387
\(844\) 1.33880e16 1.07605
\(845\) −1.52563e16 −1.21825
\(846\) −8.90196e15 −0.706234
\(847\) −6.05533e15 −0.477286
\(848\) 2.90135e16 2.27208
\(849\) −5.13461e14 −0.0399498
\(850\) 9.28242e15 0.717558
\(851\) 3.89479e16 2.99138
\(852\) 2.35365e16 1.79607
\(853\) −2.06938e15 −0.156899 −0.0784496 0.996918i \(-0.524997\pi\)
−0.0784496 + 0.996918i \(0.524997\pi\)
\(854\) 9.91320e15 0.746785
\(855\) −1.06300e16 −0.795642
\(856\) 2.84480e16 2.11566
\(857\) 1.04644e16 0.773248 0.386624 0.922237i \(-0.373641\pi\)
0.386624 + 0.922237i \(0.373641\pi\)
\(858\) 2.13038e16 1.56414
\(859\) 7.94158e15 0.579354 0.289677 0.957124i \(-0.406452\pi\)
0.289677 + 0.957124i \(0.406452\pi\)
\(860\) −5.53139e16 −4.00952
\(861\) −6.23590e14 −0.0449140
\(862\) 1.08961e16 0.779796
\(863\) 1.14766e16 0.816122 0.408061 0.912955i \(-0.366205\pi\)
0.408061 + 0.912955i \(0.366205\pi\)
\(864\) 3.07419e15 0.217223
\(865\) −1.44574e16 −1.01508
\(866\) 2.54270e16 1.77397
\(867\) 8.02611e15 0.556417
\(868\) −1.37783e16 −0.949156
\(869\) 2.06536e16 1.41379
\(870\) 3.88866e16 2.64511
\(871\) −2.37611e16 −1.60608
\(872\) −2.90396e16 −1.95052
\(873\) 6.97588e15 0.465608
\(874\) −6.38254e16 −4.23332
\(875\) 4.25644e16 2.80545
\(876\) −1.92146e16 −1.25852
\(877\) −2.61506e16 −1.70209 −0.851046 0.525090i \(-0.824031\pi\)
−0.851046 + 0.525090i \(0.824031\pi\)
\(878\) −4.86841e16 −3.14896
\(879\) 3.20941e15 0.206294
\(880\) −6.00147e16 −3.83357
\(881\) 9.22917e14 0.0585862 0.0292931 0.999571i \(-0.490674\pi\)
0.0292931 + 0.999571i \(0.490674\pi\)
\(882\) −1.12694e16 −0.710923
\(883\) 6.31286e15 0.395769 0.197885 0.980225i \(-0.436593\pi\)
0.197885 + 0.980225i \(0.436593\pi\)
\(884\) −9.04634e15 −0.563618
\(885\) −2.13136e15 −0.131968
\(886\) 4.99596e16 3.07421
\(887\) 2.29576e16 1.40393 0.701966 0.712211i \(-0.252306\pi\)
0.701966 + 0.712211i \(0.252306\pi\)
\(888\) 3.80770e16 2.31415
\(889\) 1.60848e16 0.971532
\(890\) −1.44831e16 −0.869394
\(891\) 2.14251e15 0.127819
\(892\) −4.32603e15 −0.256497
\(893\) 2.70133e16 1.59182
\(894\) −2.26419e16 −1.32604
\(895\) 1.57072e16 0.914267
\(896\) −2.21337e16 −1.28044
\(897\) −2.24894e16 −1.29306
\(898\) −2.66479e16 −1.52280
\(899\) −7.17910e15 −0.407748
\(900\) 2.79675e16 1.57877
\(901\) −4.06259e15 −0.227938
\(902\) 1.96735e15 0.109710
\(903\) 1.54387e16 0.855712
\(904\) −4.27006e16 −2.35238
\(905\) −2.73285e16 −1.49641
\(906\) 1.49702e16 0.814745
\(907\) −1.33216e16 −0.720636 −0.360318 0.932830i \(-0.617332\pi\)
−0.360318 + 0.932830i \(0.617332\pi\)
\(908\) 1.28929e15 0.0693234
\(909\) −1.81439e15 −0.0969684
\(910\) −1.14888e17 −6.10307
\(911\) −4.14245e15 −0.218729 −0.109364 0.994002i \(-0.534882\pi\)
−0.109364 + 0.994002i \(0.534882\pi\)
\(912\) −2.83859e16 −1.48981
\(913\) 1.69904e16 0.886371
\(914\) 4.61506e16 2.39317
\(915\) 5.49864e15 0.283426
\(916\) 9.61818e15 0.492797
\(917\) 2.28858e16 1.16556
\(918\) −1.30982e15 −0.0663098
\(919\) −2.51113e16 −1.26367 −0.631836 0.775102i \(-0.717698\pi\)
−0.631836 + 0.775102i \(0.717698\pi\)
\(920\) 1.39267e17 6.96653
\(921\) −6.82268e15 −0.339256
\(922\) −1.46319e16 −0.723239
\(923\) −3.62319e16 −1.78025
\(924\) 4.56469e16 2.22954
\(925\) 7.45604e16 3.62017
\(926\) −4.66534e16 −2.25176
\(927\) 2.75067e15 0.131977
\(928\) 3.41265e16 1.62771
\(929\) 2.94286e16 1.39535 0.697675 0.716415i \(-0.254218\pi\)
0.697675 + 0.716415i \(0.254218\pi\)
\(930\) −1.10030e16 −0.518625
\(931\) 3.41974e16 1.60239
\(932\) 6.41658e16 2.98893
\(933\) 3.46777e15 0.160584
\(934\) 3.12136e15 0.143693
\(935\) 8.40350e15 0.384589
\(936\) −2.19866e16 −1.00032
\(937\) −1.14822e16 −0.519347 −0.259673 0.965697i \(-0.583615\pi\)
−0.259673 + 0.965697i \(0.583615\pi\)
\(938\) −7.32984e16 −3.29594
\(939\) 1.54442e16 0.690407
\(940\) −1.05200e17 −4.67532
\(941\) −3.44099e16 −1.52034 −0.760171 0.649724i \(-0.774885\pi\)
−0.760171 + 0.649724i \(0.774885\pi\)
\(942\) 3.13921e16 1.37893
\(943\) −2.07684e15 −0.0906961
\(944\) −5.69152e15 −0.247105
\(945\) −1.15543e16 −0.498733
\(946\) −4.87070e16 −2.09021
\(947\) 1.75216e16 0.747563 0.373782 0.927517i \(-0.378061\pi\)
0.373782 + 0.927517i \(0.378061\pi\)
\(948\) −3.80431e16 −1.61373
\(949\) 2.95788e16 1.24743
\(950\) −1.22185e17 −5.12317
\(951\) −2.11710e16 −0.882570
\(952\) −1.56358e16 −0.648062
\(953\) 2.42597e16 0.999713 0.499856 0.866108i \(-0.333386\pi\)
0.499856 + 0.866108i \(0.333386\pi\)
\(954\) −1.76225e16 −0.722023
\(955\) −1.80295e15 −0.0734455
\(956\) 5.26014e16 2.13049
\(957\) 2.37840e16 0.957787
\(958\) 7.29771e15 0.292197
\(959\) −5.19691e15 −0.206892
\(960\) 3.69702e15 0.146339
\(961\) −2.33771e16 −0.920053
\(962\) −1.04615e17 −4.09382
\(963\) −7.86048e15 −0.305847
\(964\) 7.41375e16 2.86823
\(965\) 8.63476e16 3.32162
\(966\) −6.93753e16 −2.65357
\(967\) −9.87645e15 −0.375626 −0.187813 0.982205i \(-0.560140\pi\)
−0.187813 + 0.982205i \(0.560140\pi\)
\(968\) −1.97161e16 −0.745599
\(969\) 3.97471e15 0.149460
\(970\) 1.18686e17 4.43768
\(971\) 9.14735e15 0.340087 0.170043 0.985437i \(-0.445609\pi\)
0.170043 + 0.985437i \(0.445609\pi\)
\(972\) −3.94643e15 −0.145895
\(973\) −3.51596e16 −1.29248
\(974\) 9.83476e16 3.59492
\(975\) −4.30530e16 −1.56487
\(976\) 1.46834e16 0.530704
\(977\) −2.21369e16 −0.795603 −0.397801 0.917472i \(-0.630227\pi\)
−0.397801 + 0.917472i \(0.630227\pi\)
\(978\) 2.22009e16 0.793428
\(979\) −8.85823e15 −0.314805
\(980\) −1.33177e17 −4.70636
\(981\) 8.02394e15 0.281974
\(982\) 3.71331e16 1.29762
\(983\) 1.98996e16 0.691513 0.345756 0.938324i \(-0.387622\pi\)
0.345756 + 0.938324i \(0.387622\pi\)
\(984\) −2.03040e15 −0.0701631
\(985\) −5.81968e16 −1.99986
\(986\) −1.45403e16 −0.496879
\(987\) 2.93623e16 0.997805
\(988\) 1.19078e17 4.02408
\(989\) 5.14178e16 1.72796
\(990\) 3.64523e16 1.21823
\(991\) 2.64736e16 0.879849 0.439925 0.898035i \(-0.355005\pi\)
0.439925 + 0.898035i \(0.355005\pi\)
\(992\) −9.65610e15 −0.319145
\(993\) −1.77843e16 −0.584542
\(994\) −1.11768e17 −3.65337
\(995\) 8.47502e16 2.75495
\(996\) −3.12958e16 −1.01172
\(997\) 3.83411e16 1.23265 0.616327 0.787491i \(-0.288620\pi\)
0.616327 + 0.787491i \(0.288620\pi\)
\(998\) 1.90203e15 0.0608133
\(999\) −1.05211e16 −0.334541
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 177.12.a.c.1.2 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.2 27 1.1 even 1 trivial