Properties

Label 177.10.a.c.1.4
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-36.1747 q^{2} -81.0000 q^{3} +796.607 q^{4} +898.892 q^{5} +2930.15 q^{6} -4674.69 q^{7} -10295.5 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-36.1747 q^{2} -81.0000 q^{3} +796.607 q^{4} +898.892 q^{5} +2930.15 q^{6} -4674.69 q^{7} -10295.5 q^{8} +6561.00 q^{9} -32517.1 q^{10} -58345.2 q^{11} -64525.1 q^{12} +57332.9 q^{13} +169105. q^{14} -72810.3 q^{15} -35424.5 q^{16} -510308. q^{17} -237342. q^{18} -168147. q^{19} +716063. q^{20} +378650. q^{21} +2.11062e6 q^{22} +2.17501e6 q^{23} +833939. q^{24} -1.14512e6 q^{25} -2.07400e6 q^{26} -531441. q^{27} -3.72389e6 q^{28} +244852. q^{29} +2.63389e6 q^{30} +6.46606e6 q^{31} +6.55279e6 q^{32} +4.72596e6 q^{33} +1.84602e7 q^{34} -4.20204e6 q^{35} +5.22654e6 q^{36} -4.04614e6 q^{37} +6.08266e6 q^{38} -4.64396e6 q^{39} -9.25459e6 q^{40} -8.50617e6 q^{41} -1.36975e7 q^{42} -1.02337e7 q^{43} -4.64781e7 q^{44} +5.89763e6 q^{45} -7.86802e7 q^{46} -3.48588e7 q^{47} +2.86939e6 q^{48} -1.85009e7 q^{49} +4.14243e7 q^{50} +4.13350e7 q^{51} +4.56718e7 q^{52} -5.20000e7 q^{53} +1.92247e7 q^{54} -5.24460e7 q^{55} +4.81285e7 q^{56} +1.36199e7 q^{57} -8.85743e6 q^{58} +1.21174e7 q^{59} -5.80011e7 q^{60} +2.99414e7 q^{61} -2.33907e8 q^{62} -3.06706e7 q^{63} -2.18908e8 q^{64} +5.15361e7 q^{65} -1.70960e8 q^{66} -2.13498e8 q^{67} -4.06515e8 q^{68} -1.76176e8 q^{69} +1.52007e8 q^{70} -1.52154e8 q^{71} -6.75491e7 q^{72} +1.83932e8 q^{73} +1.46368e8 q^{74} +9.27546e7 q^{75} -1.33947e8 q^{76} +2.72745e8 q^{77} +1.67994e8 q^{78} +7.72399e7 q^{79} -3.18428e7 q^{80} +4.30467e7 q^{81} +3.07708e8 q^{82} -1.73619e8 q^{83} +3.01635e8 q^{84} -4.58712e8 q^{85} +3.70202e8 q^{86} -1.98330e7 q^{87} +6.00695e8 q^{88} -6.72303e8 q^{89} -2.13345e8 q^{90} -2.68013e8 q^{91} +1.73263e9 q^{92} -5.23751e8 q^{93} +1.26100e9 q^{94} -1.51146e8 q^{95} -5.30776e8 q^{96} +1.37731e9 q^{97} +6.69264e8 q^{98} -3.82803e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −36.1747 −1.59871 −0.799355 0.600859i \(-0.794825\pi\)
−0.799355 + 0.600859i \(0.794825\pi\)
\(3\) −81.0000 −0.577350
\(4\) 796.607 1.55587
\(5\) 898.892 0.643195 0.321597 0.946876i \(-0.395780\pi\)
0.321597 + 0.946876i \(0.395780\pi\)
\(6\) 2930.15 0.923015
\(7\) −4674.69 −0.735888 −0.367944 0.929848i \(-0.619938\pi\)
−0.367944 + 0.929848i \(0.619938\pi\)
\(8\) −10295.5 −0.888678
\(9\) 6561.00 0.333333
\(10\) −32517.1 −1.02828
\(11\) −58345.2 −1.20154 −0.600769 0.799422i \(-0.705139\pi\)
−0.600769 + 0.799422i \(0.705139\pi\)
\(12\) −64525.1 −0.898283
\(13\) 57332.9 0.556748 0.278374 0.960473i \(-0.410204\pi\)
0.278374 + 0.960473i \(0.410204\pi\)
\(14\) 169105. 1.17647
\(15\) −72810.3 −0.371349
\(16\) −35424.5 −0.135134
\(17\) −510308. −1.48188 −0.740939 0.671573i \(-0.765619\pi\)
−0.740939 + 0.671573i \(0.765619\pi\)
\(18\) −237342. −0.532903
\(19\) −168147. −0.296004 −0.148002 0.988987i \(-0.547284\pi\)
−0.148002 + 0.988987i \(0.547284\pi\)
\(20\) 716063. 1.00073
\(21\) 378650. 0.424865
\(22\) 2.11062e6 1.92091
\(23\) 2.17501e6 1.62064 0.810318 0.585990i \(-0.199294\pi\)
0.810318 + 0.585990i \(0.199294\pi\)
\(24\) 833939. 0.513079
\(25\) −1.14512e6 −0.586300
\(26\) −2.07400e6 −0.890079
\(27\) −531441. −0.192450
\(28\) −3.72389e6 −1.14495
\(29\) 244852. 0.0642853 0.0321427 0.999483i \(-0.489767\pi\)
0.0321427 + 0.999483i \(0.489767\pi\)
\(30\) 2.63389e6 0.593679
\(31\) 6.46606e6 1.25751 0.628756 0.777603i \(-0.283565\pi\)
0.628756 + 0.777603i \(0.283565\pi\)
\(32\) 6.55279e6 1.10472
\(33\) 4.72596e6 0.693709
\(34\) 1.84602e7 2.36909
\(35\) −4.20204e6 −0.473319
\(36\) 5.22654e6 0.518624
\(37\) −4.04614e6 −0.354922 −0.177461 0.984128i \(-0.556788\pi\)
−0.177461 + 0.984128i \(0.556788\pi\)
\(38\) 6.08266e6 0.473224
\(39\) −4.64396e6 −0.321439
\(40\) −9.25459e6 −0.571593
\(41\) −8.50617e6 −0.470118 −0.235059 0.971981i \(-0.575528\pi\)
−0.235059 + 0.971981i \(0.575528\pi\)
\(42\) −1.36975e7 −0.679236
\(43\) −1.02337e7 −0.456485 −0.228242 0.973604i \(-0.573298\pi\)
−0.228242 + 0.973604i \(0.573298\pi\)
\(44\) −4.64781e7 −1.86944
\(45\) 5.89763e6 0.214398
\(46\) −7.86802e7 −2.59093
\(47\) −3.48588e7 −1.04201 −0.521005 0.853554i \(-0.674443\pi\)
−0.521005 + 0.853554i \(0.674443\pi\)
\(48\) 2.86939e6 0.0780195
\(49\) −1.85009e7 −0.458470
\(50\) 4.14243e7 0.937324
\(51\) 4.13350e7 0.855562
\(52\) 4.56718e7 0.866229
\(53\) −5.20000e7 −0.905237 −0.452618 0.891704i \(-0.649510\pi\)
−0.452618 + 0.891704i \(0.649510\pi\)
\(54\) 1.92247e7 0.307672
\(55\) −5.24460e7 −0.772823
\(56\) 4.81285e7 0.653967
\(57\) 1.36199e7 0.170898
\(58\) −8.85743e6 −0.102774
\(59\) 1.21174e7 0.130189
\(60\) −5.80011e7 −0.577771
\(61\) 2.99414e7 0.276878 0.138439 0.990371i \(-0.455792\pi\)
0.138439 + 0.990371i \(0.455792\pi\)
\(62\) −2.33907e8 −2.01040
\(63\) −3.06706e7 −0.245296
\(64\) −2.18908e8 −1.63099
\(65\) 5.15361e7 0.358098
\(66\) −1.70960e8 −1.10904
\(67\) −2.13498e8 −1.29437 −0.647183 0.762335i \(-0.724053\pi\)
−0.647183 + 0.762335i \(0.724053\pi\)
\(68\) −4.06515e8 −2.30561
\(69\) −1.76176e8 −0.935675
\(70\) 1.52007e8 0.756700
\(71\) −1.52154e8 −0.710592 −0.355296 0.934754i \(-0.615620\pi\)
−0.355296 + 0.934754i \(0.615620\pi\)
\(72\) −6.75491e7 −0.296226
\(73\) 1.83932e8 0.758063 0.379032 0.925384i \(-0.376257\pi\)
0.379032 + 0.925384i \(0.376257\pi\)
\(74\) 1.46368e8 0.567417
\(75\) 9.27546e7 0.338501
\(76\) −1.33947e8 −0.460544
\(77\) 2.72745e8 0.884197
\(78\) 1.67994e8 0.513887
\(79\) 7.72399e7 0.223110 0.111555 0.993758i \(-0.464417\pi\)
0.111555 + 0.993758i \(0.464417\pi\)
\(80\) −3.18428e7 −0.0869174
\(81\) 4.30467e7 0.111111
\(82\) 3.07708e8 0.751582
\(83\) −1.73619e8 −0.401555 −0.200778 0.979637i \(-0.564347\pi\)
−0.200778 + 0.979637i \(0.564347\pi\)
\(84\) 3.01635e8 0.661035
\(85\) −4.58712e8 −0.953136
\(86\) 3.70202e8 0.729787
\(87\) −1.98330e7 −0.0371152
\(88\) 6.00695e8 1.06778
\(89\) −6.72303e8 −1.13582 −0.567911 0.823090i \(-0.692248\pi\)
−0.567911 + 0.823090i \(0.692248\pi\)
\(90\) −2.13345e8 −0.342761
\(91\) −2.68013e8 −0.409704
\(92\) 1.73263e9 2.52150
\(93\) −5.23751e8 −0.726024
\(94\) 1.26100e9 1.66587
\(95\) −1.51146e8 −0.190388
\(96\) −5.30776e8 −0.637809
\(97\) 1.37731e9 1.57964 0.789820 0.613338i \(-0.210174\pi\)
0.789820 + 0.613338i \(0.210174\pi\)
\(98\) 6.69264e8 0.732960
\(99\) −3.82803e8 −0.400513
\(100\) −9.12209e8 −0.912209
\(101\) −7.06551e7 −0.0675612 −0.0337806 0.999429i \(-0.510755\pi\)
−0.0337806 + 0.999429i \(0.510755\pi\)
\(102\) −1.49528e9 −1.36780
\(103\) 3.47159e8 0.303921 0.151961 0.988387i \(-0.451441\pi\)
0.151961 + 0.988387i \(0.451441\pi\)
\(104\) −5.90274e8 −0.494770
\(105\) 3.40365e8 0.273271
\(106\) 1.88108e9 1.44721
\(107\) −2.17084e9 −1.60103 −0.800516 0.599311i \(-0.795441\pi\)
−0.800516 + 0.599311i \(0.795441\pi\)
\(108\) −4.23349e8 −0.299428
\(109\) 1.68021e9 1.14010 0.570051 0.821609i \(-0.306923\pi\)
0.570051 + 0.821609i \(0.306923\pi\)
\(110\) 1.89722e9 1.23552
\(111\) 3.27737e8 0.204914
\(112\) 1.65599e8 0.0994433
\(113\) −3.34940e8 −0.193248 −0.0966239 0.995321i \(-0.530804\pi\)
−0.0966239 + 0.995321i \(0.530804\pi\)
\(114\) −4.92695e8 −0.273216
\(115\) 1.95510e9 1.04238
\(116\) 1.95050e8 0.100020
\(117\) 3.76161e8 0.185583
\(118\) −4.38342e8 −0.208134
\(119\) 2.38553e9 1.09050
\(120\) 7.49622e8 0.330010
\(121\) 1.04621e9 0.443695
\(122\) −1.08312e9 −0.442647
\(123\) 6.89000e8 0.271423
\(124\) 5.15090e9 1.95653
\(125\) −2.78499e9 −1.02030
\(126\) 1.10950e9 0.392157
\(127\) 4.31503e9 1.47186 0.735931 0.677056i \(-0.236745\pi\)
0.735931 + 0.677056i \(0.236745\pi\)
\(128\) 4.56388e9 1.50276
\(129\) 8.28933e8 0.263552
\(130\) −1.86430e9 −0.572494
\(131\) −4.44468e9 −1.31862 −0.659310 0.751871i \(-0.729152\pi\)
−0.659310 + 0.751871i \(0.729152\pi\)
\(132\) 3.76473e9 1.07932
\(133\) 7.86034e8 0.217826
\(134\) 7.72322e9 2.06932
\(135\) −4.77708e8 −0.123783
\(136\) 5.25390e9 1.31691
\(137\) −2.71704e9 −0.658951 −0.329476 0.944164i \(-0.606872\pi\)
−0.329476 + 0.944164i \(0.606872\pi\)
\(138\) 6.37310e9 1.49587
\(139\) −1.44384e9 −0.328060 −0.164030 0.986455i \(-0.552449\pi\)
−0.164030 + 0.986455i \(0.552449\pi\)
\(140\) −3.34737e9 −0.736424
\(141\) 2.82356e9 0.601605
\(142\) 5.50411e9 1.13603
\(143\) −3.34510e9 −0.668954
\(144\) −2.32420e8 −0.0450446
\(145\) 2.20095e8 0.0413480
\(146\) −6.65369e9 −1.21192
\(147\) 1.49857e9 0.264698
\(148\) −3.22318e9 −0.552213
\(149\) 2.95833e9 0.491709 0.245855 0.969307i \(-0.420931\pi\)
0.245855 + 0.969307i \(0.420931\pi\)
\(150\) −3.35537e9 −0.541164
\(151\) 4.00966e9 0.627640 0.313820 0.949482i \(-0.398391\pi\)
0.313820 + 0.949482i \(0.398391\pi\)
\(152\) 1.73116e9 0.263052
\(153\) −3.34813e9 −0.493959
\(154\) −9.86647e9 −1.41357
\(155\) 5.81229e9 0.808825
\(156\) −3.69941e9 −0.500118
\(157\) 1.25451e10 1.64788 0.823940 0.566678i \(-0.191771\pi\)
0.823940 + 0.566678i \(0.191771\pi\)
\(158\) −2.79413e9 −0.356689
\(159\) 4.21200e9 0.522639
\(160\) 5.89025e9 0.710549
\(161\) −1.01675e10 −1.19261
\(162\) −1.55720e9 −0.177634
\(163\) 1.20770e10 1.34003 0.670013 0.742349i \(-0.266288\pi\)
0.670013 + 0.742349i \(0.266288\pi\)
\(164\) −6.77607e9 −0.731443
\(165\) 4.24813e9 0.446190
\(166\) 6.28060e9 0.641970
\(167\) −8.77986e9 −0.873501 −0.436750 0.899583i \(-0.643871\pi\)
−0.436750 + 0.899583i \(0.643871\pi\)
\(168\) −3.89841e9 −0.377568
\(169\) −7.31744e9 −0.690031
\(170\) 1.65937e10 1.52379
\(171\) −1.10321e9 −0.0986680
\(172\) −8.15226e9 −0.710232
\(173\) −3.23450e9 −0.274536 −0.137268 0.990534i \(-0.543832\pi\)
−0.137268 + 0.990534i \(0.543832\pi\)
\(174\) 7.17451e8 0.0593364
\(175\) 5.35307e9 0.431451
\(176\) 2.06685e9 0.162368
\(177\) −9.81506e8 −0.0751646
\(178\) 2.43204e10 1.81585
\(179\) 2.22715e10 1.62147 0.810737 0.585411i \(-0.199067\pi\)
0.810737 + 0.585411i \(0.199067\pi\)
\(180\) 4.69809e9 0.333576
\(181\) −2.16773e10 −1.50125 −0.750623 0.660731i \(-0.770247\pi\)
−0.750623 + 0.660731i \(0.770247\pi\)
\(182\) 9.69530e9 0.654998
\(183\) −2.42526e9 −0.159856
\(184\) −2.23929e10 −1.44022
\(185\) −3.63704e9 −0.228284
\(186\) 1.89465e10 1.16070
\(187\) 2.97740e10 1.78053
\(188\) −2.77687e10 −1.62123
\(189\) 2.48432e9 0.141622
\(190\) 5.46765e9 0.304375
\(191\) 2.81443e10 1.53017 0.765086 0.643928i \(-0.222696\pi\)
0.765086 + 0.643928i \(0.222696\pi\)
\(192\) 1.77315e10 0.941652
\(193\) −4.41397e9 −0.228992 −0.114496 0.993424i \(-0.536525\pi\)
−0.114496 + 0.993424i \(0.536525\pi\)
\(194\) −4.98237e10 −2.52539
\(195\) −4.17442e9 −0.206748
\(196\) −1.47379e10 −0.713320
\(197\) −2.04044e10 −0.965219 −0.482609 0.875836i \(-0.660311\pi\)
−0.482609 + 0.875836i \(0.660311\pi\)
\(198\) 1.38478e10 0.640304
\(199\) 1.01977e10 0.460962 0.230481 0.973077i \(-0.425970\pi\)
0.230481 + 0.973077i \(0.425970\pi\)
\(200\) 1.17896e10 0.521032
\(201\) 1.72933e10 0.747303
\(202\) 2.55592e9 0.108011
\(203\) −1.14460e9 −0.0473068
\(204\) 3.29277e10 1.33115
\(205\) −7.64613e9 −0.302377
\(206\) −1.25584e10 −0.485882
\(207\) 1.42702e10 0.540212
\(208\) −2.03099e9 −0.0752355
\(209\) 9.81055e9 0.355660
\(210\) −1.23126e10 −0.436881
\(211\) −1.33425e10 −0.463410 −0.231705 0.972786i \(-0.574430\pi\)
−0.231705 + 0.972786i \(0.574430\pi\)
\(212\) −4.14236e10 −1.40843
\(213\) 1.23245e10 0.410260
\(214\) 7.85293e10 2.55959
\(215\) −9.19903e9 −0.293609
\(216\) 5.47148e9 0.171026
\(217\) −3.02268e10 −0.925387
\(218\) −6.07810e10 −1.82269
\(219\) −1.48985e10 −0.437668
\(220\) −4.17788e10 −1.20241
\(221\) −2.92574e10 −0.825033
\(222\) −1.18558e10 −0.327598
\(223\) −2.17210e10 −0.588178 −0.294089 0.955778i \(-0.595016\pi\)
−0.294089 + 0.955778i \(0.595016\pi\)
\(224\) −3.06323e10 −0.812948
\(225\) −7.51312e9 −0.195433
\(226\) 1.21164e10 0.308947
\(227\) 3.32500e10 0.831141 0.415571 0.909561i \(-0.363582\pi\)
0.415571 + 0.909561i \(0.363582\pi\)
\(228\) 1.08497e10 0.265895
\(229\) −9.20653e9 −0.221226 −0.110613 0.993864i \(-0.535281\pi\)
−0.110613 + 0.993864i \(0.535281\pi\)
\(230\) −7.07250e10 −1.66647
\(231\) −2.20924e10 −0.510492
\(232\) −2.52088e9 −0.0571290
\(233\) 5.05237e10 1.12303 0.561517 0.827465i \(-0.310218\pi\)
0.561517 + 0.827465i \(0.310218\pi\)
\(234\) −1.36075e10 −0.296693
\(235\) −3.13343e10 −0.670215
\(236\) 9.65277e9 0.202557
\(237\) −6.25643e9 −0.128813
\(238\) −8.62958e10 −1.74338
\(239\) 1.89053e10 0.374794 0.187397 0.982284i \(-0.439995\pi\)
0.187397 + 0.982284i \(0.439995\pi\)
\(240\) 2.57927e9 0.0501818
\(241\) −3.30262e10 −0.630640 −0.315320 0.948985i \(-0.602112\pi\)
−0.315320 + 0.948985i \(0.602112\pi\)
\(242\) −3.78463e10 −0.709340
\(243\) −3.48678e9 −0.0641500
\(244\) 2.38515e10 0.430787
\(245\) −1.66303e10 −0.294885
\(246\) −2.49243e10 −0.433926
\(247\) −9.64035e9 −0.164800
\(248\) −6.65716e10 −1.11752
\(249\) 1.40631e10 0.231838
\(250\) 1.00746e11 1.63116
\(251\) −8.61853e8 −0.0137057 −0.00685285 0.999977i \(-0.502181\pi\)
−0.00685285 + 0.999977i \(0.502181\pi\)
\(252\) −2.44324e10 −0.381649
\(253\) −1.26901e11 −1.94726
\(254\) −1.56095e11 −2.35308
\(255\) 3.71557e10 0.550293
\(256\) −5.30162e10 −0.771488
\(257\) 1.23018e11 1.75902 0.879510 0.475881i \(-0.157871\pi\)
0.879510 + 0.475881i \(0.157871\pi\)
\(258\) −2.99864e10 −0.421342
\(259\) 1.89144e10 0.261183
\(260\) 4.10540e10 0.557154
\(261\) 1.60647e9 0.0214284
\(262\) 1.60785e11 2.10809
\(263\) 2.48000e10 0.319632 0.159816 0.987147i \(-0.448910\pi\)
0.159816 + 0.987147i \(0.448910\pi\)
\(264\) −4.86563e10 −0.616484
\(265\) −4.67424e10 −0.582244
\(266\) −2.84345e10 −0.348240
\(267\) 5.44566e10 0.655767
\(268\) −1.70074e11 −2.01387
\(269\) −1.65665e11 −1.92906 −0.964528 0.263979i \(-0.914965\pi\)
−0.964528 + 0.263979i \(0.914965\pi\)
\(270\) 1.72809e10 0.197893
\(271\) 3.14041e10 0.353691 0.176846 0.984239i \(-0.443411\pi\)
0.176846 + 0.984239i \(0.443411\pi\)
\(272\) 1.80774e10 0.200252
\(273\) 2.17091e10 0.236543
\(274\) 9.82880e10 1.05347
\(275\) 6.68121e10 0.704463
\(276\) −1.40343e11 −1.45579
\(277\) 1.64597e11 1.67982 0.839911 0.542725i \(-0.182607\pi\)
0.839911 + 0.542725i \(0.182607\pi\)
\(278\) 5.22306e10 0.524473
\(279\) 4.24238e10 0.419170
\(280\) 4.32623e10 0.420628
\(281\) −1.74325e11 −1.66794 −0.833971 0.551808i \(-0.813938\pi\)
−0.833971 + 0.551808i \(0.813938\pi\)
\(282\) −1.02141e11 −0.961791
\(283\) 1.53298e11 1.42069 0.710344 0.703855i \(-0.248540\pi\)
0.710344 + 0.703855i \(0.248540\pi\)
\(284\) −1.21207e11 −1.10559
\(285\) 1.22428e10 0.109921
\(286\) 1.21008e11 1.06946
\(287\) 3.97637e10 0.345954
\(288\) 4.29929e10 0.368239
\(289\) 1.41826e11 1.19596
\(290\) −7.96187e9 −0.0661034
\(291\) −1.11562e11 −0.912006
\(292\) 1.46522e11 1.17945
\(293\) 5.26361e10 0.417233 0.208617 0.977997i \(-0.433104\pi\)
0.208617 + 0.977997i \(0.433104\pi\)
\(294\) −5.42104e10 −0.423174
\(295\) 1.08922e10 0.0837368
\(296\) 4.16572e10 0.315411
\(297\) 3.10070e10 0.231236
\(298\) −1.07017e11 −0.786100
\(299\) 1.24700e11 0.902286
\(300\) 7.38889e10 0.526664
\(301\) 4.78395e10 0.335921
\(302\) −1.45048e11 −1.00341
\(303\) 5.72306e9 0.0390064
\(304\) 5.95652e9 0.0400001
\(305\) 2.69141e10 0.178086
\(306\) 1.21118e11 0.789697
\(307\) 2.34703e11 1.50798 0.753991 0.656885i \(-0.228126\pi\)
0.753991 + 0.656885i \(0.228126\pi\)
\(308\) 2.17271e11 1.37570
\(309\) −2.81199e10 −0.175469
\(310\) −2.10258e11 −1.29308
\(311\) 3.48562e10 0.211280 0.105640 0.994404i \(-0.466311\pi\)
0.105640 + 0.994404i \(0.466311\pi\)
\(312\) 4.78122e10 0.285656
\(313\) 1.77039e11 1.04260 0.521301 0.853373i \(-0.325447\pi\)
0.521301 + 0.853373i \(0.325447\pi\)
\(314\) −4.53814e11 −2.63448
\(315\) −2.75696e10 −0.157773
\(316\) 6.15298e10 0.347131
\(317\) 2.30912e8 0.00128434 0.000642169 1.00000i \(-0.499796\pi\)
0.000642169 1.00000i \(0.499796\pi\)
\(318\) −1.52368e11 −0.835547
\(319\) −1.42859e10 −0.0772413
\(320\) −1.96774e11 −1.04904
\(321\) 1.75838e11 0.924357
\(322\) 3.67805e11 1.90663
\(323\) 8.58067e10 0.438642
\(324\) 3.42913e10 0.172875
\(325\) −6.56529e10 −0.326422
\(326\) −4.36880e11 −2.14231
\(327\) −1.36097e11 −0.658238
\(328\) 8.75757e10 0.417783
\(329\) 1.62954e11 0.766802
\(330\) −1.53675e11 −0.713328
\(331\) 7.38318e9 0.0338078 0.0169039 0.999857i \(-0.494619\pi\)
0.0169039 + 0.999857i \(0.494619\pi\)
\(332\) −1.38306e11 −0.624769
\(333\) −2.65467e10 −0.118307
\(334\) 3.17608e11 1.39647
\(335\) −1.91912e11 −0.832530
\(336\) −1.34135e10 −0.0574136
\(337\) 4.06055e11 1.71495 0.857473 0.514530i \(-0.172033\pi\)
0.857473 + 0.514530i \(0.172033\pi\)
\(338\) 2.64706e11 1.10316
\(339\) 2.71302e10 0.111572
\(340\) −3.65413e11 −1.48296
\(341\) −3.77263e11 −1.51095
\(342\) 3.99083e10 0.157741
\(343\) 2.75126e11 1.07327
\(344\) 1.05362e11 0.405668
\(345\) −1.58363e11 −0.601821
\(346\) 1.17007e11 0.438904
\(347\) 5.29349e11 1.96002 0.980008 0.198957i \(-0.0637555\pi\)
0.980008 + 0.198957i \(0.0637555\pi\)
\(348\) −1.57991e10 −0.0577464
\(349\) 3.08680e11 1.11377 0.556884 0.830591i \(-0.311997\pi\)
0.556884 + 0.830591i \(0.311997\pi\)
\(350\) −1.93646e11 −0.689765
\(351\) −3.04691e10 −0.107146
\(352\) −3.82324e11 −1.32736
\(353\) 3.72155e11 1.27567 0.637833 0.770175i \(-0.279831\pi\)
0.637833 + 0.770175i \(0.279831\pi\)
\(354\) 3.55057e10 0.120166
\(355\) −1.36770e11 −0.457049
\(356\) −5.35561e11 −1.76719
\(357\) −1.93228e11 −0.629598
\(358\) −8.05663e11 −2.59227
\(359\) 5.49485e11 1.74595 0.872973 0.487769i \(-0.162189\pi\)
0.872973 + 0.487769i \(0.162189\pi\)
\(360\) −6.07193e10 −0.190531
\(361\) −2.94414e11 −0.912382
\(362\) 7.84170e11 2.40006
\(363\) −8.47430e10 −0.256167
\(364\) −2.13501e11 −0.637447
\(365\) 1.65335e11 0.487582
\(366\) 8.77328e10 0.255563
\(367\) −3.94449e11 −1.13499 −0.567497 0.823376i \(-0.692088\pi\)
−0.567497 + 0.823376i \(0.692088\pi\)
\(368\) −7.70486e10 −0.219003
\(369\) −5.58090e10 −0.156706
\(370\) 1.31569e11 0.364960
\(371\) 2.43084e11 0.666152
\(372\) −4.17223e11 −1.12960
\(373\) −3.12062e11 −0.834739 −0.417369 0.908737i \(-0.637048\pi\)
−0.417369 + 0.908737i \(0.637048\pi\)
\(374\) −1.07706e12 −2.84656
\(375\) 2.25584e11 0.589071
\(376\) 3.58890e11 0.926011
\(377\) 1.40381e10 0.0357908
\(378\) −8.98695e10 −0.226412
\(379\) −1.54226e11 −0.383955 −0.191977 0.981399i \(-0.561490\pi\)
−0.191977 + 0.981399i \(0.561490\pi\)
\(380\) −1.20404e11 −0.296220
\(381\) −3.49518e11 −0.849780
\(382\) −1.01811e12 −2.44630
\(383\) 4.33365e11 1.02911 0.514553 0.857459i \(-0.327958\pi\)
0.514553 + 0.857459i \(0.327958\pi\)
\(384\) −3.69675e11 −0.867619
\(385\) 2.45169e11 0.568711
\(386\) 1.59674e11 0.366092
\(387\) −6.71436e10 −0.152162
\(388\) 1.09717e12 2.45772
\(389\) −2.14366e11 −0.474660 −0.237330 0.971429i \(-0.576272\pi\)
−0.237330 + 0.971429i \(0.576272\pi\)
\(390\) 1.51008e11 0.330530
\(391\) −1.10992e12 −2.40158
\(392\) 1.90477e11 0.407432
\(393\) 3.60019e11 0.761306
\(394\) 7.38122e11 1.54310
\(395\) 6.94303e10 0.143503
\(396\) −3.04943e11 −0.623147
\(397\) 3.59774e10 0.0726895 0.0363448 0.999339i \(-0.488429\pi\)
0.0363448 + 0.999339i \(0.488429\pi\)
\(398\) −3.68900e11 −0.736944
\(399\) −6.36688e10 −0.125762
\(400\) 4.05652e10 0.0792290
\(401\) 2.39655e11 0.462846 0.231423 0.972853i \(-0.425662\pi\)
0.231423 + 0.972853i \(0.425662\pi\)
\(402\) −6.25581e11 −1.19472
\(403\) 3.70718e11 0.700117
\(404\) −5.62843e10 −0.105117
\(405\) 3.86944e10 0.0714661
\(406\) 4.14057e10 0.0756298
\(407\) 2.36073e11 0.426452
\(408\) −4.25566e11 −0.760320
\(409\) 8.16510e11 1.44280 0.721401 0.692518i \(-0.243499\pi\)
0.721401 + 0.692518i \(0.243499\pi\)
\(410\) 2.76596e11 0.483414
\(411\) 2.20080e11 0.380446
\(412\) 2.76549e11 0.472862
\(413\) −5.66449e10 −0.0958044
\(414\) −5.16221e11 −0.863642
\(415\) −1.56065e11 −0.258278
\(416\) 3.75691e11 0.615050
\(417\) 1.16951e11 0.189406
\(418\) −3.54894e11 −0.568597
\(419\) 1.35929e10 0.0215452 0.0107726 0.999942i \(-0.496571\pi\)
0.0107726 + 0.999942i \(0.496571\pi\)
\(420\) 2.71137e11 0.425175
\(421\) −1.99138e11 −0.308948 −0.154474 0.987997i \(-0.549368\pi\)
−0.154474 + 0.987997i \(0.549368\pi\)
\(422\) 4.82660e11 0.740858
\(423\) −2.28708e11 −0.347337
\(424\) 5.35369e11 0.804464
\(425\) 5.84363e11 0.868825
\(426\) −4.45833e11 −0.655887
\(427\) −1.39967e11 −0.203751
\(428\) −1.72930e12 −2.49100
\(429\) 2.70953e11 0.386221
\(430\) 3.32772e11 0.469395
\(431\) 7.02282e11 0.980310 0.490155 0.871635i \(-0.336940\pi\)
0.490155 + 0.871635i \(0.336940\pi\)
\(432\) 1.88260e10 0.0260065
\(433\) −2.80736e11 −0.383798 −0.191899 0.981415i \(-0.561465\pi\)
−0.191899 + 0.981415i \(0.561465\pi\)
\(434\) 1.09344e12 1.47942
\(435\) −1.78277e10 −0.0238723
\(436\) 1.33846e12 1.77385
\(437\) −3.65721e11 −0.479715
\(438\) 5.38949e11 0.699704
\(439\) 5.49999e11 0.706760 0.353380 0.935480i \(-0.385032\pi\)
0.353380 + 0.935480i \(0.385032\pi\)
\(440\) 5.39960e11 0.686791
\(441\) −1.21384e11 −0.152823
\(442\) 1.05838e12 1.31899
\(443\) −1.23621e11 −0.152501 −0.0762507 0.997089i \(-0.524295\pi\)
−0.0762507 + 0.997089i \(0.524295\pi\)
\(444\) 2.61078e11 0.318820
\(445\) −6.04328e11 −0.730555
\(446\) 7.85751e11 0.940325
\(447\) −2.39625e11 −0.283888
\(448\) 1.02333e12 1.20022
\(449\) −8.83485e11 −1.02587 −0.512933 0.858429i \(-0.671441\pi\)
−0.512933 + 0.858429i \(0.671441\pi\)
\(450\) 2.71785e11 0.312441
\(451\) 4.96294e11 0.564865
\(452\) −2.66816e11 −0.300669
\(453\) −3.24782e11 −0.362368
\(454\) −1.20281e12 −1.32875
\(455\) −2.40915e11 −0.263520
\(456\) −1.40224e11 −0.151873
\(457\) −9.77143e11 −1.04794 −0.523969 0.851738i \(-0.675549\pi\)
−0.523969 + 0.851738i \(0.675549\pi\)
\(458\) 3.33043e11 0.353676
\(459\) 2.71199e11 0.285187
\(460\) 1.55744e12 1.62182
\(461\) 2.51148e11 0.258986 0.129493 0.991580i \(-0.458665\pi\)
0.129493 + 0.991580i \(0.458665\pi\)
\(462\) 7.99184e11 0.816128
\(463\) 4.80930e11 0.486371 0.243185 0.969980i \(-0.421808\pi\)
0.243185 + 0.969980i \(0.421808\pi\)
\(464\) −8.67375e9 −0.00868712
\(465\) −4.70795e11 −0.466975
\(466\) −1.82768e12 −1.79541
\(467\) −5.63309e10 −0.0548051 −0.0274026 0.999624i \(-0.508724\pi\)
−0.0274026 + 0.999624i \(0.508724\pi\)
\(468\) 2.99652e11 0.288743
\(469\) 9.98036e11 0.952508
\(470\) 1.13351e12 1.07148
\(471\) −1.01615e12 −0.951404
\(472\) −1.24755e11 −0.115696
\(473\) 5.97089e11 0.548484
\(474\) 2.26324e11 0.205934
\(475\) 1.92548e11 0.173547
\(476\) 1.90033e12 1.69667
\(477\) −3.41172e11 −0.301746
\(478\) −6.83892e11 −0.599186
\(479\) 2.33976e11 0.203078 0.101539 0.994832i \(-0.467623\pi\)
0.101539 + 0.994832i \(0.467623\pi\)
\(480\) −4.77110e11 −0.410236
\(481\) −2.31977e11 −0.197602
\(482\) 1.19471e12 1.00821
\(483\) 8.23566e11 0.688552
\(484\) 8.33418e11 0.690333
\(485\) 1.23805e12 1.01602
\(486\) 1.26133e11 0.102557
\(487\) −1.54104e12 −1.24147 −0.620733 0.784022i \(-0.713165\pi\)
−0.620733 + 0.784022i \(0.713165\pi\)
\(488\) −3.08264e11 −0.246055
\(489\) −9.78234e11 −0.773665
\(490\) 6.01596e11 0.471436
\(491\) −4.63630e11 −0.360002 −0.180001 0.983666i \(-0.557610\pi\)
−0.180001 + 0.983666i \(0.557610\pi\)
\(492\) 5.48862e11 0.422299
\(493\) −1.24950e11 −0.0952630
\(494\) 3.48736e11 0.263467
\(495\) −3.44098e11 −0.257608
\(496\) −2.29057e11 −0.169932
\(497\) 7.11272e11 0.522916
\(498\) −5.08729e11 −0.370642
\(499\) 2.14250e12 1.54692 0.773462 0.633843i \(-0.218523\pi\)
0.773462 + 0.633843i \(0.218523\pi\)
\(500\) −2.21854e12 −1.58746
\(501\) 7.11168e11 0.504316
\(502\) 3.11772e10 0.0219114
\(503\) 8.16297e11 0.568581 0.284291 0.958738i \(-0.408242\pi\)
0.284291 + 0.958738i \(0.408242\pi\)
\(504\) 3.15771e11 0.217989
\(505\) −6.35113e10 −0.0434550
\(506\) 4.59061e12 3.11310
\(507\) 5.92712e11 0.398390
\(508\) 3.43738e12 2.29003
\(509\) −1.36465e12 −0.901136 −0.450568 0.892742i \(-0.648779\pi\)
−0.450568 + 0.892742i \(0.648779\pi\)
\(510\) −1.34409e12 −0.879759
\(511\) −8.59827e11 −0.557849
\(512\) −4.18863e11 −0.269375
\(513\) 8.93601e10 0.0569660
\(514\) −4.45015e12 −2.81216
\(515\) 3.12058e11 0.195480
\(516\) 6.60333e11 0.410053
\(517\) 2.03384e12 1.25202
\(518\) −6.84223e11 −0.417555
\(519\) 2.61995e11 0.158504
\(520\) −5.30592e11 −0.318234
\(521\) −1.64297e12 −0.976920 −0.488460 0.872586i \(-0.662441\pi\)
−0.488460 + 0.872586i \(0.662441\pi\)
\(522\) −5.81136e10 −0.0342579
\(523\) 2.27813e12 1.33144 0.665719 0.746203i \(-0.268125\pi\)
0.665719 + 0.746203i \(0.268125\pi\)
\(524\) −3.54066e12 −2.05160
\(525\) −4.33599e11 −0.249098
\(526\) −8.97132e11 −0.511000
\(527\) −3.29968e12 −1.86348
\(528\) −1.67415e11 −0.0937435
\(529\) 2.92951e12 1.62646
\(530\) 1.69089e12 0.930838
\(531\) 7.95020e10 0.0433963
\(532\) 6.26160e11 0.338909
\(533\) −4.87683e11 −0.261737
\(534\) −1.96995e12 −1.04838
\(535\) −1.95135e12 −1.02978
\(536\) 2.19808e12 1.15028
\(537\) −1.80399e12 −0.936158
\(538\) 5.99287e12 3.08400
\(539\) 1.07944e12 0.550869
\(540\) −3.80545e11 −0.192590
\(541\) −3.39774e12 −1.70530 −0.852652 0.522479i \(-0.825007\pi\)
−0.852652 + 0.522479i \(0.825007\pi\)
\(542\) −1.13603e12 −0.565450
\(543\) 1.75586e12 0.866745
\(544\) −3.34394e12 −1.63706
\(545\) 1.51033e12 0.733308
\(546\) −7.85319e11 −0.378163
\(547\) −2.14411e11 −0.102401 −0.0512005 0.998688i \(-0.516305\pi\)
−0.0512005 + 0.998688i \(0.516305\pi\)
\(548\) −2.16441e12 −1.02524
\(549\) 1.96446e11 0.0922927
\(550\) −2.41691e12 −1.12623
\(551\) −4.11710e10 −0.0190287
\(552\) 1.81383e12 0.831514
\(553\) −3.61072e11 −0.164184
\(554\) −5.95424e12 −2.68555
\(555\) 2.94600e11 0.131800
\(556\) −1.15018e12 −0.510420
\(557\) 2.17048e12 0.955450 0.477725 0.878510i \(-0.341462\pi\)
0.477725 + 0.878510i \(0.341462\pi\)
\(558\) −1.53467e12 −0.670132
\(559\) −5.86730e11 −0.254147
\(560\) 1.48855e11 0.0639614
\(561\) −2.41169e12 −1.02799
\(562\) 6.30615e12 2.66656
\(563\) 9.89772e11 0.415191 0.207595 0.978215i \(-0.433436\pi\)
0.207595 + 0.978215i \(0.433436\pi\)
\(564\) 2.24927e12 0.936020
\(565\) −3.01075e11 −0.124296
\(566\) −5.54552e12 −2.27127
\(567\) −2.01230e11 −0.0817653
\(568\) 1.56651e12 0.631488
\(569\) −3.94076e12 −1.57607 −0.788033 0.615632i \(-0.788901\pi\)
−0.788033 + 0.615632i \(0.788901\pi\)
\(570\) −4.42880e11 −0.175731
\(571\) −8.16947e11 −0.321611 −0.160806 0.986986i \(-0.551409\pi\)
−0.160806 + 0.986986i \(0.551409\pi\)
\(572\) −2.66473e12 −1.04081
\(573\) −2.27969e12 −0.883446
\(574\) −1.43844e12 −0.553080
\(575\) −2.49064e12 −0.950180
\(576\) −1.43625e12 −0.543663
\(577\) 7.47676e11 0.280816 0.140408 0.990094i \(-0.455159\pi\)
0.140408 + 0.990094i \(0.455159\pi\)
\(578\) −5.13052e12 −1.91199
\(579\) 3.57531e11 0.132209
\(580\) 1.75329e11 0.0643322
\(581\) 8.11614e11 0.295499
\(582\) 4.03572e12 1.45803
\(583\) 3.03395e12 1.08768
\(584\) −1.89369e12 −0.673674
\(585\) 3.38128e11 0.119366
\(586\) −1.90409e12 −0.667035
\(587\) −2.57396e12 −0.894808 −0.447404 0.894332i \(-0.647651\pi\)
−0.447404 + 0.894332i \(0.647651\pi\)
\(588\) 1.19377e12 0.411836
\(589\) −1.08725e12 −0.372228
\(590\) −3.94022e11 −0.133871
\(591\) 1.65276e12 0.557269
\(592\) 1.43332e11 0.0479619
\(593\) 2.53540e12 0.841979 0.420989 0.907066i \(-0.361683\pi\)
0.420989 + 0.907066i \(0.361683\pi\)
\(594\) −1.12167e12 −0.369680
\(595\) 2.14433e12 0.701401
\(596\) 2.35662e12 0.765037
\(597\) −8.26017e11 −0.266136
\(598\) −4.51096e12 −1.44249
\(599\) 3.20638e12 1.01764 0.508820 0.860873i \(-0.330082\pi\)
0.508820 + 0.860873i \(0.330082\pi\)
\(600\) −9.54959e11 −0.300818
\(601\) −2.22462e12 −0.695537 −0.347769 0.937580i \(-0.613061\pi\)
−0.347769 + 0.937580i \(0.613061\pi\)
\(602\) −1.73058e12 −0.537041
\(603\) −1.40076e12 −0.431455
\(604\) 3.19412e12 0.976528
\(605\) 9.40430e11 0.285382
\(606\) −2.07030e11 −0.0623600
\(607\) 1.85983e12 0.556062 0.278031 0.960572i \(-0.410318\pi\)
0.278031 + 0.960572i \(0.410318\pi\)
\(608\) −1.10183e12 −0.327001
\(609\) 9.27130e10 0.0273126
\(610\) −9.73609e11 −0.284709
\(611\) −1.99855e12 −0.580137
\(612\) −2.66714e12 −0.768537
\(613\) 4.96907e11 0.142136 0.0710679 0.997471i \(-0.477359\pi\)
0.0710679 + 0.997471i \(0.477359\pi\)
\(614\) −8.49031e12 −2.41083
\(615\) 6.19336e11 0.174578
\(616\) −2.80806e12 −0.785767
\(617\) −4.67093e12 −1.29754 −0.648769 0.760985i \(-0.724716\pi\)
−0.648769 + 0.760985i \(0.724716\pi\)
\(618\) 1.01723e12 0.280524
\(619\) −3.58040e11 −0.0980220 −0.0490110 0.998798i \(-0.515607\pi\)
−0.0490110 + 0.998798i \(0.515607\pi\)
\(620\) 4.63011e12 1.25843
\(621\) −1.15589e12 −0.311892
\(622\) −1.26091e12 −0.337776
\(623\) 3.14281e12 0.835837
\(624\) 1.64510e11 0.0434372
\(625\) −2.66843e11 −0.0699514
\(626\) −6.40432e12 −1.66682
\(627\) −7.94655e11 −0.205341
\(628\) 9.99350e12 2.56389
\(629\) 2.06478e12 0.525951
\(630\) 9.97321e11 0.252233
\(631\) 9.90994e11 0.248851 0.124425 0.992229i \(-0.460291\pi\)
0.124425 + 0.992229i \(0.460291\pi\)
\(632\) −7.95227e11 −0.198273
\(633\) 1.08074e12 0.267550
\(634\) −8.35315e9 −0.00205328
\(635\) 3.87875e12 0.946694
\(636\) 3.35531e12 0.813159
\(637\) −1.06071e12 −0.255252
\(638\) 5.16788e11 0.123486
\(639\) −9.98281e11 −0.236864
\(640\) 4.10244e12 0.966568
\(641\) −3.94375e12 −0.922675 −0.461337 0.887225i \(-0.652630\pi\)
−0.461337 + 0.887225i \(0.652630\pi\)
\(642\) −6.36087e12 −1.47778
\(643\) 6.09002e12 1.40498 0.702489 0.711695i \(-0.252072\pi\)
0.702489 + 0.711695i \(0.252072\pi\)
\(644\) −8.09948e12 −1.85554
\(645\) 7.45121e11 0.169515
\(646\) −3.10403e12 −0.701260
\(647\) −8.53763e12 −1.91544 −0.957719 0.287704i \(-0.907108\pi\)
−0.957719 + 0.287704i \(0.907108\pi\)
\(648\) −4.43190e11 −0.0987420
\(649\) −7.06989e11 −0.156427
\(650\) 2.37497e12 0.521854
\(651\) 2.44837e12 0.534272
\(652\) 9.62059e12 2.08491
\(653\) −2.31918e12 −0.499144 −0.249572 0.968356i \(-0.580290\pi\)
−0.249572 + 0.968356i \(0.580290\pi\)
\(654\) 4.92326e12 1.05233
\(655\) −3.99529e12 −0.848130
\(656\) 3.01327e11 0.0635288
\(657\) 1.20678e12 0.252688
\(658\) −5.89480e12 −1.22589
\(659\) 3.93884e12 0.813549 0.406774 0.913529i \(-0.366654\pi\)
0.406774 + 0.913529i \(0.366654\pi\)
\(660\) 3.38409e12 0.694214
\(661\) −4.00845e12 −0.816714 −0.408357 0.912822i \(-0.633898\pi\)
−0.408357 + 0.912822i \(0.633898\pi\)
\(662\) −2.67084e11 −0.0540489
\(663\) 2.36985e12 0.476333
\(664\) 1.78750e12 0.356853
\(665\) 7.06560e11 0.140104
\(666\) 9.60318e11 0.189139
\(667\) 5.32554e11 0.104183
\(668\) −6.99409e12 −1.35906
\(669\) 1.75940e12 0.339584
\(670\) 6.94234e12 1.33097
\(671\) −1.74694e12 −0.332680
\(672\) 2.48121e12 0.469356
\(673\) −1.29844e12 −0.243979 −0.121990 0.992531i \(-0.538927\pi\)
−0.121990 + 0.992531i \(0.538927\pi\)
\(674\) −1.46889e13 −2.74170
\(675\) 6.08563e11 0.112834
\(676\) −5.82912e12 −1.07360
\(677\) 8.66231e12 1.58484 0.792419 0.609978i \(-0.208822\pi\)
0.792419 + 0.609978i \(0.208822\pi\)
\(678\) −9.81425e11 −0.178371
\(679\) −6.43849e12 −1.16244
\(680\) 4.72269e12 0.847031
\(681\) −2.69325e12 −0.479860
\(682\) 1.36474e13 2.41557
\(683\) 3.03372e12 0.533436 0.266718 0.963775i \(-0.414061\pi\)
0.266718 + 0.963775i \(0.414061\pi\)
\(684\) −8.78825e11 −0.153515
\(685\) −2.44233e12 −0.423834
\(686\) −9.95261e12 −1.71585
\(687\) 7.45729e11 0.127725
\(688\) 3.62525e11 0.0616865
\(689\) −2.98131e12 −0.503989
\(690\) 5.72873e12 0.962137
\(691\) 7.07473e11 0.118048 0.0590240 0.998257i \(-0.481201\pi\)
0.0590240 + 0.998257i \(0.481201\pi\)
\(692\) −2.57663e12 −0.427144
\(693\) 1.78948e12 0.294732
\(694\) −1.91490e13 −3.13350
\(695\) −1.29786e12 −0.211007
\(696\) 2.04191e11 0.0329834
\(697\) 4.34077e12 0.696657
\(698\) −1.11664e13 −1.78059
\(699\) −4.09242e12 −0.648384
\(700\) 4.26429e12 0.671283
\(701\) 5.38606e12 0.842442 0.421221 0.906958i \(-0.361602\pi\)
0.421221 + 0.906958i \(0.361602\pi\)
\(702\) 1.10221e12 0.171296
\(703\) 6.80345e11 0.105058
\(704\) 1.27722e13 1.95970
\(705\) 2.53808e12 0.386949
\(706\) −1.34626e13 −2.03942
\(707\) 3.30290e11 0.0497174
\(708\) −7.81874e11 −0.116947
\(709\) −5.97478e12 −0.888002 −0.444001 0.896026i \(-0.646441\pi\)
−0.444001 + 0.896026i \(0.646441\pi\)
\(710\) 4.94760e12 0.730689
\(711\) 5.06771e11 0.0743701
\(712\) 6.92173e12 1.00938
\(713\) 1.40637e13 2.03797
\(714\) 6.98996e12 1.00654
\(715\) −3.00688e12 −0.430268
\(716\) 1.77416e13 2.52281
\(717\) −1.53133e12 −0.216387
\(718\) −1.98774e13 −2.79126
\(719\) −3.16517e12 −0.441689 −0.220844 0.975309i \(-0.570881\pi\)
−0.220844 + 0.975309i \(0.570881\pi\)
\(720\) −2.08921e11 −0.0289725
\(721\) −1.62286e12 −0.223652
\(722\) 1.06503e13 1.45863
\(723\) 2.67512e12 0.364100
\(724\) −1.72683e13 −2.33575
\(725\) −2.80384e11 −0.0376905
\(726\) 3.06555e12 0.409537
\(727\) 5.47097e12 0.726372 0.363186 0.931717i \(-0.381689\pi\)
0.363186 + 0.931717i \(0.381689\pi\)
\(728\) 2.75935e12 0.364095
\(729\) 2.82430e11 0.0370370
\(730\) −5.98095e12 −0.779502
\(731\) 5.22236e12 0.676454
\(732\) −1.93198e12 −0.248715
\(733\) −2.58003e12 −0.330108 −0.165054 0.986285i \(-0.552780\pi\)
−0.165054 + 0.986285i \(0.552780\pi\)
\(734\) 1.42691e13 1.81452
\(735\) 1.34706e12 0.170252
\(736\) 1.42524e13 1.79035
\(737\) 1.24566e13 1.55523
\(738\) 2.01887e12 0.250527
\(739\) 7.87394e12 0.971163 0.485582 0.874191i \(-0.338608\pi\)
0.485582 + 0.874191i \(0.338608\pi\)
\(740\) −2.89729e12 −0.355181
\(741\) 7.80868e11 0.0951471
\(742\) −8.79348e12 −1.06498
\(743\) 1.97110e12 0.237279 0.118640 0.992937i \(-0.462147\pi\)
0.118640 + 0.992937i \(0.462147\pi\)
\(744\) 5.39230e12 0.645202
\(745\) 2.65922e12 0.316265
\(746\) 1.12887e13 1.33450
\(747\) −1.13911e12 −0.133852
\(748\) 2.37182e13 2.77028
\(749\) 1.01480e13 1.17818
\(750\) −8.16042e12 −0.941753
\(751\) 1.05866e13 1.21444 0.607219 0.794535i \(-0.292285\pi\)
0.607219 + 0.794535i \(0.292285\pi\)
\(752\) 1.23486e12 0.140811
\(753\) 6.98101e10 0.00791299
\(754\) −5.07822e11 −0.0572190
\(755\) 3.60425e12 0.403695
\(756\) 1.97903e12 0.220345
\(757\) 6.82958e12 0.755897 0.377949 0.925827i \(-0.376630\pi\)
0.377949 + 0.925827i \(0.376630\pi\)
\(758\) 5.57906e12 0.613832
\(759\) 1.02790e13 1.12425
\(760\) 1.55613e12 0.169194
\(761\) 3.87107e12 0.418409 0.209204 0.977872i \(-0.432913\pi\)
0.209204 + 0.977872i \(0.432913\pi\)
\(762\) 1.26437e13 1.35855
\(763\) −7.85445e12 −0.838987
\(764\) 2.24199e13 2.38075
\(765\) −3.00961e12 −0.317712
\(766\) −1.56769e13 −1.64524
\(767\) 6.94723e11 0.0724824
\(768\) 4.29432e12 0.445419
\(769\) −3.32827e12 −0.343202 −0.171601 0.985167i \(-0.554894\pi\)
−0.171601 + 0.985167i \(0.554894\pi\)
\(770\) −8.86890e12 −0.909204
\(771\) −9.96448e12 −1.01557
\(772\) −3.51619e12 −0.356283
\(773\) 1.09993e13 1.10805 0.554023 0.832502i \(-0.313092\pi\)
0.554023 + 0.832502i \(0.313092\pi\)
\(774\) 2.42890e12 0.243262
\(775\) −7.40440e12 −0.737279
\(776\) −1.41801e13 −1.40379
\(777\) −1.53207e12 −0.150794
\(778\) 7.75462e12 0.758844
\(779\) 1.43029e12 0.139157
\(780\) −3.32537e12 −0.321673
\(781\) 8.87744e12 0.853804
\(782\) 4.01511e13 3.83944
\(783\) −1.30124e11 −0.0123717
\(784\) 6.55385e11 0.0619547
\(785\) 1.12767e13 1.05991
\(786\) −1.30236e13 −1.21711
\(787\) −4.00733e12 −0.372365 −0.186182 0.982515i \(-0.559612\pi\)
−0.186182 + 0.982515i \(0.559612\pi\)
\(788\) −1.62543e13 −1.50176
\(789\) −2.00880e12 −0.184540
\(790\) −2.51162e12 −0.229420
\(791\) 1.56574e12 0.142209
\(792\) 3.94116e12 0.355927
\(793\) 1.71663e12 0.154151
\(794\) −1.30147e12 −0.116209
\(795\) 3.78614e12 0.336158
\(796\) 8.12358e12 0.717198
\(797\) −1.15951e13 −1.01792 −0.508959 0.860791i \(-0.669970\pi\)
−0.508959 + 0.860791i \(0.669970\pi\)
\(798\) 2.30320e12 0.201056
\(799\) 1.77887e13 1.54413
\(800\) −7.50372e12 −0.647697
\(801\) −4.41098e12 −0.378607
\(802\) −8.66944e12 −0.739956
\(803\) −1.07316e13 −0.910842
\(804\) 1.37760e13 1.16271
\(805\) −9.13947e12 −0.767078
\(806\) −1.34106e13 −1.11928
\(807\) 1.34188e13 1.11374
\(808\) 7.27433e11 0.0600401
\(809\) 8.25765e12 0.677779 0.338890 0.940826i \(-0.389949\pi\)
0.338890 + 0.940826i \(0.389949\pi\)
\(810\) −1.39976e12 −0.114254
\(811\) −8.98093e12 −0.729000 −0.364500 0.931203i \(-0.618760\pi\)
−0.364500 + 0.931203i \(0.618760\pi\)
\(812\) −9.11800e11 −0.0736033
\(813\) −2.54373e12 −0.204204
\(814\) −8.53984e12 −0.681774
\(815\) 1.08559e13 0.861898
\(816\) −1.46427e12 −0.115615
\(817\) 1.72077e12 0.135121
\(818\) −2.95370e13 −2.30662
\(819\) −1.75844e12 −0.136568
\(820\) −6.09096e12 −0.470461
\(821\) −1.51505e13 −1.16381 −0.581905 0.813257i \(-0.697692\pi\)
−0.581905 + 0.813257i \(0.697692\pi\)
\(822\) −7.96133e12 −0.608222
\(823\) 1.47489e12 0.112063 0.0560313 0.998429i \(-0.482155\pi\)
0.0560313 + 0.998429i \(0.482155\pi\)
\(824\) −3.57419e12 −0.270088
\(825\) −5.41178e12 −0.406722
\(826\) 2.04911e12 0.153163
\(827\) 1.16616e13 0.866925 0.433463 0.901172i \(-0.357292\pi\)
0.433463 + 0.901172i \(0.357292\pi\)
\(828\) 1.13678e13 0.840501
\(829\) 2.04853e13 1.50642 0.753210 0.657780i \(-0.228505\pi\)
0.753210 + 0.657780i \(0.228505\pi\)
\(830\) 5.64558e12 0.412912
\(831\) −1.33324e13 −0.969845
\(832\) −1.25506e13 −0.908050
\(833\) 9.44116e12 0.679396
\(834\) −4.23068e12 −0.302805
\(835\) −7.89214e12 −0.561831
\(836\) 7.81515e12 0.553362
\(837\) −3.43633e12 −0.242008
\(838\) −4.91720e11 −0.0344445
\(839\) 8.04580e12 0.560584 0.280292 0.959915i \(-0.409569\pi\)
0.280292 + 0.959915i \(0.409569\pi\)
\(840\) −3.50425e12 −0.242850
\(841\) −1.44472e13 −0.995867
\(842\) 7.20376e12 0.493918
\(843\) 1.41203e13 0.962987
\(844\) −1.06287e13 −0.721007
\(845\) −6.57759e12 −0.443825
\(846\) 8.27345e12 0.555290
\(847\) −4.89070e12 −0.326510
\(848\) 1.84208e12 0.122328
\(849\) −1.24172e13 −0.820234
\(850\) −2.11391e13 −1.38900
\(851\) −8.80038e12 −0.575199
\(852\) 9.81775e12 0.638313
\(853\) −2.14040e13 −1.38428 −0.692140 0.721763i \(-0.743332\pi\)
−0.692140 + 0.721763i \(0.743332\pi\)
\(854\) 5.06326e12 0.325739
\(855\) −9.91668e11 −0.0634627
\(856\) 2.23500e13 1.42280
\(857\) 2.80212e13 1.77449 0.887245 0.461299i \(-0.152617\pi\)
0.887245 + 0.461299i \(0.152617\pi\)
\(858\) −9.80163e12 −0.617455
\(859\) −1.79329e13 −1.12378 −0.561891 0.827211i \(-0.689926\pi\)
−0.561891 + 0.827211i \(0.689926\pi\)
\(860\) −7.32801e12 −0.456818
\(861\) −3.22086e12 −0.199737
\(862\) −2.54048e13 −1.56723
\(863\) −1.96418e13 −1.20540 −0.602701 0.797967i \(-0.705909\pi\)
−0.602701 + 0.797967i \(0.705909\pi\)
\(864\) −3.48242e12 −0.212603
\(865\) −2.90747e12 −0.176580
\(866\) 1.01555e13 0.613582
\(867\) −1.14879e13 −0.690488
\(868\) −2.40789e13 −1.43978
\(869\) −4.50657e12 −0.268076
\(870\) 6.44911e11 0.0381648
\(871\) −1.22405e13 −0.720636
\(872\) −1.72987e13 −1.01318
\(873\) 9.03652e12 0.526547
\(874\) 1.32298e13 0.766925
\(875\) 1.30189e13 0.750826
\(876\) −1.18683e13 −0.680955
\(877\) 2.23088e12 0.127344 0.0636718 0.997971i \(-0.479719\pi\)
0.0636718 + 0.997971i \(0.479719\pi\)
\(878\) −1.98960e13 −1.12990
\(879\) −4.26352e12 −0.240890
\(880\) 1.85787e12 0.104435
\(881\) −2.49429e13 −1.39494 −0.697469 0.716615i \(-0.745691\pi\)
−0.697469 + 0.716615i \(0.745691\pi\)
\(882\) 4.39104e12 0.244320
\(883\) −1.27104e13 −0.703614 −0.351807 0.936073i \(-0.614433\pi\)
−0.351807 + 0.936073i \(0.614433\pi\)
\(884\) −2.33067e13 −1.28365
\(885\) −8.82268e11 −0.0483455
\(886\) 4.47193e12 0.243805
\(887\) −1.03838e13 −0.563251 −0.281625 0.959524i \(-0.590874\pi\)
−0.281625 + 0.959524i \(0.590874\pi\)
\(888\) −3.37423e12 −0.182103
\(889\) −2.01714e13 −1.08313
\(890\) 2.18614e13 1.16794
\(891\) −2.51157e12 −0.133504
\(892\) −1.73031e13 −0.915129
\(893\) 5.86139e12 0.308439
\(894\) 8.66834e12 0.453855
\(895\) 2.00196e13 1.04292
\(896\) −2.13347e13 −1.10586
\(897\) −1.01007e13 −0.520935
\(898\) 3.19598e13 1.64006
\(899\) 1.58322e12 0.0808395
\(900\) −5.98500e12 −0.304070
\(901\) 2.65360e13 1.34145
\(902\) −1.79533e13 −0.903055
\(903\) −3.87500e12 −0.193944
\(904\) 3.44840e12 0.171735
\(905\) −1.94856e13 −0.965594
\(906\) 1.17489e13 0.579322
\(907\) 1.26702e13 0.621659 0.310829 0.950466i \(-0.399393\pi\)
0.310829 + 0.950466i \(0.399393\pi\)
\(908\) 2.64871e13 1.29315
\(909\) −4.63568e11 −0.0225204
\(910\) 8.71503e12 0.421291
\(911\) 2.60368e13 1.25243 0.626217 0.779649i \(-0.284602\pi\)
0.626217 + 0.779649i \(0.284602\pi\)
\(912\) −4.82478e11 −0.0230941
\(913\) 1.01298e13 0.482484
\(914\) 3.53478e13 1.67535
\(915\) −2.18004e12 −0.102818
\(916\) −7.33398e12 −0.344199
\(917\) 2.07775e13 0.970356
\(918\) −9.81052e12 −0.455932
\(919\) 1.59208e13 0.736283 0.368141 0.929770i \(-0.379994\pi\)
0.368141 + 0.929770i \(0.379994\pi\)
\(920\) −2.01288e13 −0.926345
\(921\) −1.90110e13 −0.870634
\(922\) −9.08521e12 −0.414043
\(923\) −8.72342e12 −0.395621
\(924\) −1.75989e13 −0.794260
\(925\) 4.63330e12 0.208091
\(926\) −1.73975e13 −0.777566
\(927\) 2.27771e12 0.101307
\(928\) 1.60446e12 0.0710172
\(929\) 1.91960e13 0.845551 0.422775 0.906234i \(-0.361056\pi\)
0.422775 + 0.906234i \(0.361056\pi\)
\(930\) 1.70309e13 0.746558
\(931\) 3.11087e12 0.135709
\(932\) 4.02475e13 1.74730
\(933\) −2.82336e12 −0.121983
\(934\) 2.03775e12 0.0876175
\(935\) 2.67636e13 1.14523
\(936\) −3.87279e12 −0.164923
\(937\) 4.35148e13 1.84421 0.922103 0.386946i \(-0.126470\pi\)
0.922103 + 0.386946i \(0.126470\pi\)
\(938\) −3.61036e13 −1.52278
\(939\) −1.43401e13 −0.601947
\(940\) −2.49611e13 −1.04277
\(941\) −3.71803e13 −1.54582 −0.772912 0.634514i \(-0.781200\pi\)
−0.772912 + 0.634514i \(0.781200\pi\)
\(942\) 3.67590e13 1.52102
\(943\) −1.85010e13 −0.761890
\(944\) −4.29252e11 −0.0175929
\(945\) 2.23314e12 0.0910903
\(946\) −2.15995e13 −0.876867
\(947\) 2.06568e13 0.834620 0.417310 0.908764i \(-0.362973\pi\)
0.417310 + 0.908764i \(0.362973\pi\)
\(948\) −4.98391e12 −0.200416
\(949\) 1.05454e13 0.422050
\(950\) −6.96536e12 −0.277452
\(951\) −1.87038e10 −0.000741512 0
\(952\) −2.45604e13 −0.969099
\(953\) −1.41965e13 −0.557525 −0.278763 0.960360i \(-0.589924\pi\)
−0.278763 + 0.960360i \(0.589924\pi\)
\(954\) 1.23418e13 0.482404
\(955\) 2.52987e13 0.984199
\(956\) 1.50601e13 0.583131
\(957\) 1.15716e12 0.0445953
\(958\) −8.46402e12 −0.324662
\(959\) 1.27013e13 0.484914
\(960\) 1.59387e13 0.605666
\(961\) 1.53703e13 0.581334
\(962\) 8.39168e12 0.315908
\(963\) −1.42429e13 −0.533678
\(964\) −2.63089e13 −0.981195
\(965\) −3.96768e12 −0.147287
\(966\) −2.97922e13 −1.10079
\(967\) −4.32059e13 −1.58900 −0.794500 0.607264i \(-0.792267\pi\)
−0.794500 + 0.607264i \(0.792267\pi\)
\(968\) −1.07713e13 −0.394302
\(969\) −6.95034e12 −0.253250
\(970\) −4.47861e13 −1.62432
\(971\) 2.39954e13 0.866245 0.433123 0.901335i \(-0.357412\pi\)
0.433123 + 0.901335i \(0.357412\pi\)
\(972\) −2.77760e12 −0.0998093
\(973\) 6.74952e12 0.241416
\(974\) 5.57468e13 1.98474
\(975\) 5.31789e12 0.188460
\(976\) −1.06066e12 −0.0374156
\(977\) 1.45550e13 0.511077 0.255538 0.966799i \(-0.417747\pi\)
0.255538 + 0.966799i \(0.417747\pi\)
\(978\) 3.53873e13 1.23687
\(979\) 3.92256e13 1.36473
\(980\) −1.32478e13 −0.458804
\(981\) 1.10238e13 0.380034
\(982\) 1.67717e13 0.575539
\(983\) 4.62268e13 1.57908 0.789538 0.613701i \(-0.210320\pi\)
0.789538 + 0.613701i \(0.210320\pi\)
\(984\) −7.09363e12 −0.241207
\(985\) −1.83414e13 −0.620824
\(986\) 4.52002e12 0.152298
\(987\) −1.31993e13 −0.442713
\(988\) −7.67956e12 −0.256407
\(989\) −2.22585e13 −0.739796
\(990\) 1.24476e13 0.411840
\(991\) 1.20817e13 0.397922 0.198961 0.980007i \(-0.436243\pi\)
0.198961 + 0.980007i \(0.436243\pi\)
\(992\) 4.23707e13 1.38920
\(993\) −5.98038e11 −0.0195190
\(994\) −2.57300e13 −0.835991
\(995\) 9.16666e12 0.296488
\(996\) 1.12028e13 0.360710
\(997\) −5.11913e13 −1.64085 −0.820423 0.571757i \(-0.806262\pi\)
−0.820423 + 0.571757i \(0.806262\pi\)
\(998\) −7.75043e13 −2.47308
\(999\) 2.15028e12 0.0683048
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.c.1.4 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.4 22 1.1 even 1 trivial