Properties

Label 1.38.a.a.1.2
Level 1
Weight 38
Character 1.1
Self dual yes
Analytic conductor 8.671
Analytic rank 1
Dimension 2
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 38 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.67140381246\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Defining polynomial: \(x^{2} - x - 15934380\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3991.29\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+286012. q^{2} -2.05955e7 q^{3} -5.56362e10 q^{4} -8.29715e12 q^{5} -5.89057e12 q^{6} +1.97377e15 q^{7} -5.52218e16 q^{8} -4.49860e17 q^{9} +O(q^{10})\) \(q+286012. q^{2} -2.05955e7 q^{3} -5.56362e10 q^{4} -8.29715e12 q^{5} -5.89057e12 q^{6} +1.97377e15 q^{7} -5.52218e16 q^{8} -4.49860e17 q^{9} -2.37308e18 q^{10} -2.57012e19 q^{11} +1.14586e18 q^{12} +5.42906e20 q^{13} +5.64522e20 q^{14} +1.70884e20 q^{15} -8.14749e21 q^{16} -3.52797e22 q^{17} -1.28665e23 q^{18} +6.82122e23 q^{19} +4.61622e23 q^{20} -4.06509e22 q^{21} -7.35084e24 q^{22} -8.19547e22 q^{23} +1.13732e24 q^{24} -3.91685e24 q^{25} +1.55278e26 q^{26} +1.85389e25 q^{27} -1.09813e26 q^{28} -1.51991e27 q^{29} +4.88749e25 q^{30} +2.60785e27 q^{31} +5.25934e27 q^{32} +5.29330e26 q^{33} -1.00904e28 q^{34} -1.63767e28 q^{35} +2.50285e28 q^{36} -1.30205e29 q^{37} +1.95095e29 q^{38} -1.11814e28 q^{39} +4.58183e29 q^{40} -4.07079e29 q^{41} -1.16266e28 q^{42} -2.92424e30 q^{43} +1.42992e30 q^{44} +3.73255e30 q^{45} -2.34400e28 q^{46} +3.58323e30 q^{47} +1.67802e29 q^{48} -1.46663e31 q^{49} -1.12027e30 q^{50} +7.26605e29 q^{51} -3.02052e31 q^{52} +3.56714e31 q^{53} +5.30236e30 q^{54} +2.13247e32 q^{55} -1.08995e32 q^{56} -1.40487e31 q^{57} -4.34713e32 q^{58} -3.03666e32 q^{59} -9.50736e30 q^{60} +1.16214e33 q^{61} +7.45875e32 q^{62} -8.87921e32 q^{63} +2.62402e33 q^{64} -4.50457e33 q^{65} +1.51395e32 q^{66} -2.44324e33 q^{67} +1.96283e33 q^{68} +1.68790e30 q^{69} -4.68393e33 q^{70} +6.30224e33 q^{71} +2.48421e34 q^{72} +1.02725e34 q^{73} -3.72400e34 q^{74} +8.06697e31 q^{75} -3.79507e34 q^{76} -5.07283e34 q^{77} -3.19803e33 q^{78} +1.20547e35 q^{79} +6.76010e34 q^{80} +2.02183e35 q^{81} -1.16430e35 q^{82} -3.26699e35 q^{83} +2.26166e33 q^{84} +2.92721e35 q^{85} -8.36366e35 q^{86} +3.13034e34 q^{87} +1.41927e36 q^{88} -1.56115e36 q^{89} +1.06755e36 q^{90} +1.07157e36 q^{91} +4.55965e33 q^{92} -5.37100e34 q^{93} +1.02485e36 q^{94} -5.65967e36 q^{95} -1.08319e35 q^{96} -1.07155e36 q^{97} -4.19474e36 q^{98} +1.15619e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 194400q^{2} + 13991400q^{3} + 37720269824q^{4} + 5529584385900q^{5} - 22506543847296q^{6} - 3448443953486000q^{7} - 34044043043635200q^{8} - 898947378401769414q^{9} + O(q^{10}) \) \( 2q - 194400q^{2} + 13991400q^{3} + 37720269824q^{4} + 5529584385900q^{5} - 22506543847296q^{6} - 3448443953486000q^{7} - 34044043043635200q^{8} - 898947378401769414q^{9} - 9015609355013275200q^{10} - 26734036354848538056q^{11} + 4374774798370099200q^{12} + \)\(53\!\cdots\!00\)\(q^{13} + \)\(31\!\cdots\!48\)\(q^{14} + \)\(64\!\cdots\!00\)\(q^{15} - \)\(31\!\cdots\!08\)\(q^{16} - \)\(89\!\cdots\!00\)\(q^{17} + \)\(87\!\cdots\!00\)\(q^{18} + \)\(37\!\cdots\!20\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(22\!\cdots\!56\)\(q^{21} - \)\(68\!\cdots\!00\)\(q^{22} - \)\(26\!\cdots\!00\)\(q^{23} + \)\(18\!\cdots\!60\)\(q^{24} + \)\(11\!\cdots\!50\)\(q^{25} + \)\(16\!\cdots\!44\)\(q^{26} - \)\(12\!\cdots\!00\)\(q^{27} - \)\(61\!\cdots\!00\)\(q^{28} - \)\(12\!\cdots\!20\)\(q^{29} - \)\(18\!\cdots\!00\)\(q^{30} + \)\(26\!\cdots\!24\)\(q^{31} + \)\(13\!\cdots\!00\)\(q^{32} + \)\(49\!\cdots\!00\)\(q^{33} + \)\(15\!\cdots\!08\)\(q^{34} - \)\(91\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!68\)\(q^{36} - \)\(68\!\cdots\!00\)\(q^{37} + \)\(34\!\cdots\!00\)\(q^{38} - \)\(11\!\cdots\!68\)\(q^{39} + \)\(75\!\cdots\!00\)\(q^{40} - \)\(12\!\cdots\!36\)\(q^{41} + \)\(78\!\cdots\!00\)\(q^{42} - \)\(25\!\cdots\!00\)\(q^{43} + \)\(13\!\cdots\!28\)\(q^{44} - \)\(24\!\cdots\!00\)\(q^{45} + \)\(12\!\cdots\!84\)\(q^{46} + \)\(42\!\cdots\!00\)\(q^{47} - \)\(62\!\cdots\!00\)\(q^{48} - \)\(38\!\cdots\!86\)\(q^{49} - \)\(58\!\cdots\!00\)\(q^{50} - \)\(11\!\cdots\!76\)\(q^{51} - \)\(31\!\cdots\!00\)\(q^{52} + \)\(15\!\cdots\!00\)\(q^{53} + \)\(20\!\cdots\!20\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} - \)\(22\!\cdots\!80\)\(q^{56} - \)\(24\!\cdots\!00\)\(q^{57} - \)\(55\!\cdots\!00\)\(q^{58} - \)\(23\!\cdots\!40\)\(q^{59} + \)\(35\!\cdots\!00\)\(q^{60} + \)\(10\!\cdots\!44\)\(q^{61} + \)\(18\!\cdots\!00\)\(q^{62} + \)\(15\!\cdots\!00\)\(q^{63} + \)\(18\!\cdots\!64\)\(q^{64} - \)\(46\!\cdots\!00\)\(q^{65} + \)\(16\!\cdots\!88\)\(q^{66} - \)\(10\!\cdots\!00\)\(q^{67} - \)\(30\!\cdots\!00\)\(q^{68} - \)\(90\!\cdots\!48\)\(q^{69} + \)\(31\!\cdots\!00\)\(q^{70} - \)\(74\!\cdots\!16\)\(q^{71} + \)\(15\!\cdots\!00\)\(q^{72} + \)\(19\!\cdots\!00\)\(q^{73} - \)\(67\!\cdots\!72\)\(q^{74} + \)\(41\!\cdots\!00\)\(q^{75} - \)\(66\!\cdots\!60\)\(q^{76} - \)\(45\!\cdots\!00\)\(q^{77} - \)\(29\!\cdots\!00\)\(q^{78} + \)\(27\!\cdots\!80\)\(q^{79} - \)\(25\!\cdots\!00\)\(q^{80} + \)\(40\!\cdots\!42\)\(q^{81} + \)\(29\!\cdots\!00\)\(q^{82} - \)\(47\!\cdots\!00\)\(q^{83} - \)\(15\!\cdots\!72\)\(q^{84} - \)\(45\!\cdots\!00\)\(q^{85} - \)\(10\!\cdots\!36\)\(q^{86} + \)\(39\!\cdots\!00\)\(q^{87} + \)\(13\!\cdots\!00\)\(q^{88} - \)\(13\!\cdots\!60\)\(q^{89} + \)\(40\!\cdots\!00\)\(q^{90} + \)\(11\!\cdots\!84\)\(q^{91} - \)\(24\!\cdots\!00\)\(q^{92} - \)\(13\!\cdots\!00\)\(q^{93} + \)\(70\!\cdots\!88\)\(q^{94} - \)\(99\!\cdots\!00\)\(q^{95} + \)\(17\!\cdots\!64\)\(q^{96} + \)\(60\!\cdots\!00\)\(q^{97} - \)\(94\!\cdots\!00\)\(q^{98} + \)\(12\!\cdots\!92\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 286012. 0.771488 0.385744 0.922606i \(-0.373945\pi\)
0.385744 + 0.922606i \(0.373945\pi\)
\(3\) −2.05955e7 −0.0306923 −0.0153462 0.999882i \(-0.504885\pi\)
−0.0153462 + 0.999882i \(0.504885\pi\)
\(4\) −5.56362e10 −0.404807
\(5\) −8.29715e12 −0.972711 −0.486356 0.873761i \(-0.661674\pi\)
−0.486356 + 0.873761i \(0.661674\pi\)
\(6\) −5.89057e12 −0.0236788
\(7\) 1.97377e15 0.458124 0.229062 0.973412i \(-0.426434\pi\)
0.229062 + 0.973412i \(0.426434\pi\)
\(8\) −5.52218e16 −1.08379
\(9\) −4.49860e17 −0.999058
\(10\) −2.37308e18 −0.750435
\(11\) −2.57012e19 −1.39376 −0.696881 0.717187i \(-0.745429\pi\)
−0.696881 + 0.717187i \(0.745429\pi\)
\(12\) 1.14586e18 0.0124245
\(13\) 5.42906e20 1.33898 0.669488 0.742823i \(-0.266514\pi\)
0.669488 + 0.742823i \(0.266514\pi\)
\(14\) 5.64522e20 0.353437
\(15\) 1.70884e20 0.0298548
\(16\) −8.14749e21 −0.431325
\(17\) −3.52797e22 −0.608443 −0.304221 0.952601i \(-0.598396\pi\)
−0.304221 + 0.952601i \(0.598396\pi\)
\(18\) −1.28665e23 −0.770761
\(19\) 6.82122e23 1.50287 0.751433 0.659809i \(-0.229363\pi\)
0.751433 + 0.659809i \(0.229363\pi\)
\(20\) 4.61622e23 0.393760
\(21\) −4.06509e22 −0.0140609
\(22\) −7.35084e24 −1.07527
\(23\) −8.19547e22 −0.00526755 −0.00263378 0.999997i \(-0.500838\pi\)
−0.00263378 + 0.999997i \(0.500838\pi\)
\(24\) 1.13732e24 0.0332641
\(25\) −3.91685e24 −0.0538328
\(26\) 1.55278e26 1.03300
\(27\) 1.85389e25 0.0613558
\(28\) −1.09813e26 −0.185452
\(29\) −1.51991e27 −1.34108 −0.670541 0.741872i \(-0.733938\pi\)
−0.670541 + 0.741872i \(0.733938\pi\)
\(30\) 4.88749e25 0.0230326
\(31\) 2.60785e27 0.670025 0.335012 0.942214i \(-0.391260\pi\)
0.335012 + 0.942214i \(0.391260\pi\)
\(32\) 5.25934e27 0.751030
\(33\) 5.29330e26 0.0427778
\(34\) −1.00904e28 −0.469406
\(35\) −1.63767e28 −0.445623
\(36\) 2.50285e28 0.404426
\(37\) −1.30205e29 −1.26734 −0.633672 0.773602i \(-0.718453\pi\)
−0.633672 + 0.773602i \(0.718453\pi\)
\(38\) 1.95095e29 1.15944
\(39\) −1.11814e28 −0.0410963
\(40\) 4.58183e29 1.05422
\(41\) −4.07079e29 −0.593168 −0.296584 0.955007i \(-0.595847\pi\)
−0.296584 + 0.955007i \(0.595847\pi\)
\(42\) −1.16266e28 −0.0108478
\(43\) −2.92424e30 −1.76541 −0.882706 0.469926i \(-0.844281\pi\)
−0.882706 + 0.469926i \(0.844281\pi\)
\(44\) 1.42992e30 0.564204
\(45\) 3.73255e30 0.971795
\(46\) −2.34400e28 −0.00406385
\(47\) 3.58323e30 0.417315 0.208658 0.977989i \(-0.433091\pi\)
0.208658 + 0.977989i \(0.433091\pi\)
\(48\) 1.67802e29 0.0132384
\(49\) −1.46663e31 −0.790122
\(50\) −1.12027e30 −0.0415313
\(51\) 7.26605e29 0.0186745
\(52\) −3.02052e31 −0.542027
\(53\) 3.56714e31 0.450005 0.225002 0.974358i \(-0.427761\pi\)
0.225002 + 0.974358i \(0.427761\pi\)
\(54\) 5.30236e30 0.0473352
\(55\) 2.13247e32 1.35573
\(56\) −1.08995e32 −0.496511
\(57\) −1.40487e31 −0.0461265
\(58\) −4.34713e32 −1.03463
\(59\) −3.03666e32 −0.526785 −0.263393 0.964689i \(-0.584841\pi\)
−0.263393 + 0.964689i \(0.584841\pi\)
\(60\) −9.50736e30 −0.0120854
\(61\) 1.16214e33 1.08807 0.544034 0.839063i \(-0.316896\pi\)
0.544034 + 0.839063i \(0.316896\pi\)
\(62\) 7.45875e32 0.516916
\(63\) −8.87921e32 −0.457693
\(64\) 2.62402e33 1.01073
\(65\) −4.50457e33 −1.30244
\(66\) 1.51395e32 0.0330026
\(67\) −2.44324e33 −0.403257 −0.201628 0.979462i \(-0.564623\pi\)
−0.201628 + 0.979462i \(0.564623\pi\)
\(68\) 1.96283e33 0.246302
\(69\) 1.68790e30 0.000161673 0
\(70\) −4.68393e33 −0.343792
\(71\) 6.30224e33 0.355808 0.177904 0.984048i \(-0.443068\pi\)
0.177904 + 0.984048i \(0.443068\pi\)
\(72\) 2.48421e34 1.08277
\(73\) 1.02725e34 0.346899 0.173450 0.984843i \(-0.444509\pi\)
0.173450 + 0.984843i \(0.444509\pi\)
\(74\) −3.72400e34 −0.977740
\(75\) 8.06697e31 0.00165226
\(76\) −3.79507e34 −0.608371
\(77\) −5.07283e34 −0.638516
\(78\) −3.19803e33 −0.0317053
\(79\) 1.20547e35 0.944182 0.472091 0.881550i \(-0.343499\pi\)
0.472091 + 0.881550i \(0.343499\pi\)
\(80\) 6.76010e34 0.419554
\(81\) 2.02183e35 0.997175
\(82\) −1.16430e35 −0.457622
\(83\) −3.26699e35 −1.02613 −0.513066 0.858349i \(-0.671490\pi\)
−0.513066 + 0.858349i \(0.671490\pi\)
\(84\) 2.26166e33 0.00569195
\(85\) 2.92721e35 0.591839
\(86\) −8.36366e35 −1.36199
\(87\) 3.13034e34 0.0411610
\(88\) 1.41927e36 1.51055
\(89\) −1.56115e36 −1.34812 −0.674062 0.738674i \(-0.735452\pi\)
−0.674062 + 0.738674i \(0.735452\pi\)
\(90\) 1.06755e36 0.749728
\(91\) 1.07157e36 0.613418
\(92\) 4.55965e33 0.00213234
\(93\) −5.37100e34 −0.0205646
\(94\) 1.02485e36 0.321954
\(95\) −5.65967e36 −1.46186
\(96\) −1.08319e35 −0.0230509
\(97\) −1.07155e36 −0.188251 −0.0941254 0.995560i \(-0.530005\pi\)
−0.0941254 + 0.995560i \(0.530005\pi\)
\(98\) −4.19474e36 −0.609569
\(99\) 1.15619e37 1.39245
\(100\) 2.17919e35 0.0217919
\(101\) 1.29521e37 1.07744 0.538721 0.842484i \(-0.318908\pi\)
0.538721 + 0.842484i \(0.318908\pi\)
\(102\) 2.07817e35 0.0144072
\(103\) −3.39568e36 −0.196534 −0.0982672 0.995160i \(-0.531330\pi\)
−0.0982672 + 0.995160i \(0.531330\pi\)
\(104\) −2.99802e37 −1.45117
\(105\) 3.37287e35 0.0136772
\(106\) 1.02025e37 0.347173
\(107\) −1.58608e37 −0.453653 −0.226827 0.973935i \(-0.572835\pi\)
−0.226827 + 0.973935i \(0.572835\pi\)
\(108\) −1.03144e36 −0.0248372
\(109\) −1.06858e36 −0.0216978 −0.0108489 0.999941i \(-0.503453\pi\)
−0.0108489 + 0.999941i \(0.503453\pi\)
\(110\) 6.09911e37 1.04593
\(111\) 2.68163e36 0.0388977
\(112\) −1.60813e37 −0.197600
\(113\) 1.64170e37 0.171136 0.0855682 0.996332i \(-0.472729\pi\)
0.0855682 + 0.996332i \(0.472729\pi\)
\(114\) −4.01809e36 −0.0355860
\(115\) 6.79990e35 0.00512381
\(116\) 8.45622e37 0.542879
\(117\) −2.44232e38 −1.33771
\(118\) −8.68520e37 −0.406408
\(119\) −6.96341e37 −0.278743
\(120\) −9.43654e36 −0.0323564
\(121\) 3.20512e38 0.942572
\(122\) 3.32386e38 0.839432
\(123\) 8.38402e36 0.0182057
\(124\) −1.45091e38 −0.271231
\(125\) 6.36196e38 1.02508
\(126\) −2.53956e38 −0.353104
\(127\) −1.42456e39 −1.71124 −0.855619 0.517606i \(-0.826823\pi\)
−0.855619 + 0.517606i \(0.826823\pi\)
\(128\) 2.76609e37 0.0287397
\(129\) 6.02262e37 0.0541846
\(130\) −1.28836e39 −1.00481
\(131\) 2.12044e39 1.43518 0.717590 0.696466i \(-0.245245\pi\)
0.717590 + 0.696466i \(0.245245\pi\)
\(132\) −2.94499e37 −0.0173168
\(133\) 1.34635e39 0.688500
\(134\) −6.98795e38 −0.311108
\(135\) −1.53820e38 −0.0596815
\(136\) 1.94821e39 0.659425
\(137\) −1.25855e39 −0.371999 −0.185999 0.982550i \(-0.559552\pi\)
−0.185999 + 0.982550i \(0.559552\pi\)
\(138\) 4.82760e35 0.000124729 0
\(139\) −3.12966e39 −0.707494 −0.353747 0.935341i \(-0.615093\pi\)
−0.353747 + 0.935341i \(0.615093\pi\)
\(140\) 9.11138e38 0.180391
\(141\) −7.37986e37 −0.0128084
\(142\) 1.80251e39 0.274501
\(143\) −1.39533e40 −1.86621
\(144\) 3.66523e39 0.430918
\(145\) 1.26109e40 1.30449
\(146\) 2.93806e39 0.267628
\(147\) 3.02061e38 0.0242507
\(148\) 7.24409e39 0.513029
\(149\) 2.99066e39 0.186991 0.0934956 0.995620i \(-0.470196\pi\)
0.0934956 + 0.995620i \(0.470196\pi\)
\(150\) 2.30725e37 0.00127469
\(151\) −7.06984e39 −0.345411 −0.172706 0.984973i \(-0.555251\pi\)
−0.172706 + 0.984973i \(0.555251\pi\)
\(152\) −3.76680e40 −1.62879
\(153\) 1.58709e40 0.607870
\(154\) −1.45089e40 −0.492607
\(155\) −2.16377e40 −0.651740
\(156\) 6.22094e38 0.0166361
\(157\) 7.04676e40 1.67435 0.837174 0.546937i \(-0.184206\pi\)
0.837174 + 0.546937i \(0.184206\pi\)
\(158\) 3.44779e40 0.728425
\(159\) −7.34673e38 −0.0138117
\(160\) −4.36376e40 −0.730535
\(161\) −1.61760e38 −0.00241319
\(162\) 5.78267e40 0.769308
\(163\) −8.16698e40 −0.969596 −0.484798 0.874626i \(-0.661107\pi\)
−0.484798 + 0.874626i \(0.661107\pi\)
\(164\) 2.26484e40 0.240119
\(165\) −4.39193e39 −0.0416105
\(166\) −9.34397e40 −0.791648
\(167\) −3.94031e40 −0.298728 −0.149364 0.988782i \(-0.547723\pi\)
−0.149364 + 0.988782i \(0.547723\pi\)
\(168\) 2.24482e39 0.0152391
\(169\) 1.30346e41 0.792856
\(170\) 8.37216e40 0.456597
\(171\) −3.06859e41 −1.50145
\(172\) 1.62693e41 0.714651
\(173\) 2.61566e41 1.03212 0.516058 0.856554i \(-0.327399\pi\)
0.516058 + 0.856554i \(0.327399\pi\)
\(174\) 8.95315e39 0.0317552
\(175\) −7.73098e39 −0.0246621
\(176\) 2.09400e41 0.601164
\(177\) 6.25416e39 0.0161683
\(178\) −4.46508e41 −1.04006
\(179\) −4.21879e41 −0.885946 −0.442973 0.896535i \(-0.646076\pi\)
−0.442973 + 0.896535i \(0.646076\pi\)
\(180\) −2.07665e41 −0.393389
\(181\) −9.51260e40 −0.162647 −0.0813234 0.996688i \(-0.525915\pi\)
−0.0813234 + 0.996688i \(0.525915\pi\)
\(182\) 3.06483e41 0.473244
\(183\) −2.39349e40 −0.0333954
\(184\) 4.52568e39 0.00570892
\(185\) 1.08033e42 1.23276
\(186\) −1.53617e40 −0.0158654
\(187\) 9.06730e41 0.848024
\(188\) −1.99357e41 −0.168932
\(189\) 3.65917e40 0.0281086
\(190\) −1.61873e42 −1.12780
\(191\) −2.61439e41 −0.165292 −0.0826462 0.996579i \(-0.526337\pi\)
−0.0826462 + 0.996579i \(0.526337\pi\)
\(192\) −5.40431e40 −0.0310218
\(193\) −6.27072e41 −0.326969 −0.163485 0.986546i \(-0.552273\pi\)
−0.163485 + 0.986546i \(0.552273\pi\)
\(194\) −3.06477e41 −0.145233
\(195\) 9.27742e40 0.0399748
\(196\) 8.15980e41 0.319847
\(197\) −1.81081e42 −0.646021 −0.323010 0.946395i \(-0.604695\pi\)
−0.323010 + 0.946395i \(0.604695\pi\)
\(198\) 3.30685e42 1.07426
\(199\) −3.78123e41 −0.111906 −0.0559528 0.998433i \(-0.517820\pi\)
−0.0559528 + 0.998433i \(0.517820\pi\)
\(200\) 2.16295e41 0.0583435
\(201\) 5.03198e40 0.0123769
\(202\) 3.70445e42 0.831233
\(203\) −2.99996e42 −0.614383
\(204\) −4.04255e40 −0.00755958
\(205\) 3.37760e42 0.576981
\(206\) −9.71205e41 −0.151624
\(207\) 3.68681e40 0.00526259
\(208\) −4.42332e42 −0.577533
\(209\) −1.75313e43 −2.09464
\(210\) 9.64680e40 0.0105518
\(211\) 1.66783e43 1.67081 0.835404 0.549637i \(-0.185234\pi\)
0.835404 + 0.549637i \(0.185234\pi\)
\(212\) −1.98462e42 −0.182165
\(213\) −1.29798e41 −0.0109206
\(214\) −4.53636e42 −0.349988
\(215\) 2.42628e43 1.71724
\(216\) −1.02375e42 −0.0664968
\(217\) 5.14730e42 0.306955
\(218\) −3.05626e41 −0.0167396
\(219\) −2.11568e41 −0.0106472
\(220\) −1.18642e43 −0.548808
\(221\) −1.91536e43 −0.814690
\(222\) 7.66979e41 0.0300091
\(223\) −3.60083e43 −1.29647 −0.648236 0.761439i \(-0.724493\pi\)
−0.648236 + 0.761439i \(0.724493\pi\)
\(224\) 1.03808e43 0.344065
\(225\) 1.76203e42 0.0537821
\(226\) 4.69546e42 0.132030
\(227\) 6.76307e43 1.75253 0.876265 0.481830i \(-0.160028\pi\)
0.876265 + 0.481830i \(0.160028\pi\)
\(228\) 7.81615e41 0.0186723
\(229\) −5.09302e43 −1.12207 −0.561033 0.827793i \(-0.689596\pi\)
−0.561033 + 0.827793i \(0.689596\pi\)
\(230\) 1.94485e41 0.00395295
\(231\) 1.04478e42 0.0195976
\(232\) 8.39322e43 1.45345
\(233\) 1.79375e43 0.286865 0.143432 0.989660i \(-0.454186\pi\)
0.143432 + 0.989660i \(0.454186\pi\)
\(234\) −6.98531e43 −1.03203
\(235\) −2.97306e43 −0.405927
\(236\) 1.68948e43 0.213246
\(237\) −2.48273e42 −0.0289792
\(238\) −1.99162e43 −0.215046
\(239\) −2.86950e43 −0.286711 −0.143356 0.989671i \(-0.545789\pi\)
−0.143356 + 0.989671i \(0.545789\pi\)
\(240\) −1.39228e42 −0.0128771
\(241\) −1.12255e44 −0.961372 −0.480686 0.876893i \(-0.659612\pi\)
−0.480686 + 0.876893i \(0.659612\pi\)
\(242\) 9.16701e43 0.727182
\(243\) −1.25119e43 −0.0919614
\(244\) −6.46571e43 −0.440458
\(245\) 1.21689e44 0.768561
\(246\) 2.39793e42 0.0140455
\(247\) 3.70328e44 2.01230
\(248\) −1.44010e44 −0.726167
\(249\) 6.72854e42 0.0314944
\(250\) 1.81960e44 0.790833
\(251\) −4.02278e44 −1.62391 −0.811955 0.583720i \(-0.801597\pi\)
−0.811955 + 0.583720i \(0.801597\pi\)
\(252\) 4.94006e43 0.185277
\(253\) 2.10633e42 0.00734171
\(254\) −4.07440e44 −1.32020
\(255\) −6.02875e42 −0.0181649
\(256\) −3.52731e44 −0.988562
\(257\) 5.42969e44 1.41583 0.707917 0.706296i \(-0.249635\pi\)
0.707917 + 0.706296i \(0.249635\pi\)
\(258\) 1.72254e43 0.0418028
\(259\) −2.56994e44 −0.580601
\(260\) 2.50618e44 0.527235
\(261\) 6.83747e44 1.33982
\(262\) 6.06470e44 1.10722
\(263\) −7.98181e44 −1.35806 −0.679031 0.734109i \(-0.737600\pi\)
−0.679031 + 0.734109i \(0.737600\pi\)
\(264\) −2.92305e43 −0.0463622
\(265\) −2.95971e44 −0.437725
\(266\) 3.85073e44 0.531169
\(267\) 3.21528e43 0.0413771
\(268\) 1.35933e44 0.163241
\(269\) −1.02189e45 −1.14548 −0.572739 0.819738i \(-0.694119\pi\)
−0.572739 + 0.819738i \(0.694119\pi\)
\(270\) −4.39945e43 −0.0460435
\(271\) −2.63101e44 −0.257152 −0.128576 0.991700i \(-0.541041\pi\)
−0.128576 + 0.991700i \(0.541041\pi\)
\(272\) 2.87441e44 0.262436
\(273\) −2.20696e43 −0.0188272
\(274\) −3.59961e44 −0.286992
\(275\) 1.00668e44 0.0750301
\(276\) −9.39085e40 −6.54465e−5 0
\(277\) 1.60882e45 1.04865 0.524327 0.851517i \(-0.324317\pi\)
0.524327 + 0.851517i \(0.324317\pi\)
\(278\) −8.95119e44 −0.545823
\(279\) −1.17317e45 −0.669393
\(280\) 9.04350e44 0.482962
\(281\) 2.86236e45 1.43106 0.715529 0.698583i \(-0.246186\pi\)
0.715529 + 0.698583i \(0.246186\pi\)
\(282\) −2.11073e43 −0.00988151
\(283\) 7.97480e44 0.349680 0.174840 0.984597i \(-0.444059\pi\)
0.174840 + 0.984597i \(0.444059\pi\)
\(284\) −3.50633e44 −0.144033
\(285\) 1.16564e44 0.0448678
\(286\) −3.99082e45 −1.43976
\(287\) −8.03482e44 −0.271745
\(288\) −2.36597e45 −0.750322
\(289\) −2.11744e45 −0.629797
\(290\) 3.60688e45 1.00639
\(291\) 2.20692e43 0.00577786
\(292\) −5.71523e44 −0.140427
\(293\) 5.17198e44 0.119290 0.0596452 0.998220i \(-0.481003\pi\)
0.0596452 + 0.998220i \(0.481003\pi\)
\(294\) 8.63931e43 0.0187091
\(295\) 2.51956e45 0.512410
\(296\) 7.19013e45 1.37354
\(297\) −4.76473e44 −0.0855153
\(298\) 8.55364e44 0.144261
\(299\) −4.44937e43 −0.00705312
\(300\) −4.48816e42 −0.000668844 0
\(301\) −5.77178e45 −0.808778
\(302\) −2.02206e45 −0.266480
\(303\) −2.66755e44 −0.0330692
\(304\) −5.55758e45 −0.648223
\(305\) −9.64245e45 −1.05838
\(306\) 4.53927e45 0.468964
\(307\) 9.59117e45 0.932850 0.466425 0.884561i \(-0.345542\pi\)
0.466425 + 0.884561i \(0.345542\pi\)
\(308\) 2.82233e45 0.258476
\(309\) 6.99360e43 0.00603210
\(310\) −6.18864e45 −0.502810
\(311\) −5.05857e45 −0.387222 −0.193611 0.981078i \(-0.562020\pi\)
−0.193611 + 0.981078i \(0.562020\pi\)
\(312\) 6.17459e44 0.0445398
\(313\) 5.12462e45 0.348410 0.174205 0.984709i \(-0.444264\pi\)
0.174205 + 0.984709i \(0.444264\pi\)
\(314\) 2.01546e46 1.29174
\(315\) 7.36722e45 0.445203
\(316\) −6.70679e45 −0.382211
\(317\) −2.14514e46 −1.15308 −0.576541 0.817068i \(-0.695598\pi\)
−0.576541 + 0.817068i \(0.695598\pi\)
\(318\) −2.10125e44 −0.0106556
\(319\) 3.90635e46 1.86915
\(320\) −2.17719e46 −0.983153
\(321\) 3.26661e44 0.0139237
\(322\) −4.62652e43 −0.00186175
\(323\) −2.40651e46 −0.914408
\(324\) −1.12487e46 −0.403663
\(325\) −2.12648e45 −0.0720808
\(326\) −2.33585e46 −0.748032
\(327\) 2.20080e43 0.000665958 0
\(328\) 2.24796e46 0.642870
\(329\) 7.07248e45 0.191182
\(330\) −1.25614e45 −0.0321020
\(331\) 1.85276e46 0.447714 0.223857 0.974622i \(-0.428135\pi\)
0.223857 + 0.974622i \(0.428135\pi\)
\(332\) 1.81763e46 0.415385
\(333\) 5.85738e46 1.26615
\(334\) −1.12698e46 −0.230465
\(335\) 2.02719e46 0.392253
\(336\) 3.31203e44 0.00606482
\(337\) −9.22947e46 −1.59965 −0.799823 0.600236i \(-0.795073\pi\)
−0.799823 + 0.600236i \(0.795073\pi\)
\(338\) 3.72805e46 0.611679
\(339\) −3.38117e44 −0.00525258
\(340\) −1.62859e46 −0.239581
\(341\) −6.70248e46 −0.933855
\(342\) −8.77653e46 −1.15835
\(343\) −6.55854e46 −0.820099
\(344\) 1.61481e47 1.91334
\(345\) −1.40048e43 −0.000157262 0
\(346\) 7.48110e46 0.796265
\(347\) −5.27249e46 −0.532011 −0.266005 0.963972i \(-0.585704\pi\)
−0.266005 + 0.963972i \(0.585704\pi\)
\(348\) −1.74160e45 −0.0166622
\(349\) 9.71277e46 0.881196 0.440598 0.897704i \(-0.354766\pi\)
0.440598 + 0.897704i \(0.354766\pi\)
\(350\) −2.21115e45 −0.0190265
\(351\) 1.00649e46 0.0821539
\(352\) −1.35171e47 −1.04676
\(353\) 1.73375e47 1.27396 0.636979 0.770881i \(-0.280184\pi\)
0.636979 + 0.770881i \(0.280184\pi\)
\(354\) 1.78876e45 0.0124736
\(355\) −5.22906e46 −0.346098
\(356\) 8.68566e46 0.545730
\(357\) 1.43415e45 0.00855526
\(358\) −1.20662e47 −0.683497
\(359\) −1.13075e47 −0.608301 −0.304150 0.952624i \(-0.598373\pi\)
−0.304150 + 0.952624i \(0.598373\pi\)
\(360\) −2.06118e47 −1.05322
\(361\) 2.59283e47 1.25861
\(362\) −2.72072e46 −0.125480
\(363\) −6.60111e45 −0.0289297
\(364\) −5.96183e46 −0.248316
\(365\) −8.52325e46 −0.337433
\(366\) −6.84566e45 −0.0257641
\(367\) −8.74068e46 −0.312768 −0.156384 0.987696i \(-0.549984\pi\)
−0.156384 + 0.987696i \(0.549984\pi\)
\(368\) 6.67725e44 0.00227202
\(369\) 1.83129e47 0.592609
\(370\) 3.08986e47 0.951059
\(371\) 7.04073e46 0.206158
\(372\) 2.98822e45 0.00832470
\(373\) 2.70122e47 0.716056 0.358028 0.933711i \(-0.383449\pi\)
0.358028 + 0.933711i \(0.383449\pi\)
\(374\) 2.59335e47 0.654240
\(375\) −1.31028e46 −0.0314620
\(376\) −1.97872e47 −0.452283
\(377\) −8.25170e47 −1.79568
\(378\) 1.04657e46 0.0216854
\(379\) −4.13508e47 −0.815940 −0.407970 0.912995i \(-0.633763\pi\)
−0.407970 + 0.912995i \(0.633763\pi\)
\(380\) 3.14883e47 0.591769
\(381\) 2.93395e46 0.0525219
\(382\) −7.47746e46 −0.127521
\(383\) −6.64131e47 −1.07914 −0.539569 0.841942i \(-0.681413\pi\)
−0.539569 + 0.841942i \(0.681413\pi\)
\(384\) −5.69691e44 −0.000882088 0
\(385\) 4.20901e47 0.621092
\(386\) −1.79350e47 −0.252253
\(387\) 1.31550e48 1.76375
\(388\) 5.96172e46 0.0762052
\(389\) 4.74132e46 0.0577872 0.0288936 0.999582i \(-0.490802\pi\)
0.0288936 + 0.999582i \(0.490802\pi\)
\(390\) 2.65345e46 0.0308401
\(391\) 2.89134e45 0.00320500
\(392\) 8.09901e47 0.856327
\(393\) −4.36716e46 −0.0440491
\(394\) −5.17912e47 −0.498397
\(395\) −1.00020e48 −0.918417
\(396\) −6.43262e47 −0.563673
\(397\) 6.00594e47 0.502292 0.251146 0.967949i \(-0.419193\pi\)
0.251146 + 0.967949i \(0.419193\pi\)
\(398\) −1.08148e47 −0.0863337
\(399\) −2.77289e46 −0.0211317
\(400\) 3.19125e46 0.0232194
\(401\) −9.30169e47 −0.646235 −0.323118 0.946359i \(-0.604731\pi\)
−0.323118 + 0.946359i \(0.604731\pi\)
\(402\) 1.43921e46 0.00954863
\(403\) 1.41582e48 0.897147
\(404\) −7.20605e47 −0.436156
\(405\) −1.67754e48 −0.969963
\(406\) −8.58024e47 −0.473989
\(407\) 3.34641e48 1.76637
\(408\) −4.01244e46 −0.0202393
\(409\) −2.60436e47 −0.125551 −0.0627755 0.998028i \(-0.519995\pi\)
−0.0627755 + 0.998028i \(0.519995\pi\)
\(410\) 9.66033e47 0.445134
\(411\) 2.59206e46 0.0114175
\(412\) 1.88923e47 0.0795585
\(413\) −5.99367e47 −0.241333
\(414\) 1.05447e46 0.00406002
\(415\) 2.71067e48 0.998130
\(416\) 2.85533e48 1.00561
\(417\) 6.44570e46 0.0217147
\(418\) −5.01417e48 −1.61599
\(419\) −3.92255e48 −1.20951 −0.604755 0.796412i \(-0.706729\pi\)
−0.604755 + 0.796412i \(0.706729\pi\)
\(420\) −1.87654e46 −0.00553663
\(421\) −3.86983e48 −1.09263 −0.546315 0.837580i \(-0.683970\pi\)
−0.546315 + 0.837580i \(0.683970\pi\)
\(422\) 4.77019e48 1.28901
\(423\) −1.61195e48 −0.416922
\(424\) −1.96984e48 −0.487711
\(425\) 1.38185e47 0.0327542
\(426\) −3.71238e46 −0.00842509
\(427\) 2.29380e48 0.498471
\(428\) 8.82433e47 0.183642
\(429\) 2.87377e47 0.0572785
\(430\) 6.93945e48 1.32483
\(431\) 2.97992e48 0.544973 0.272487 0.962160i \(-0.412154\pi\)
0.272487 + 0.962160i \(0.412154\pi\)
\(432\) −1.51046e47 −0.0264643
\(433\) −2.20884e48 −0.370798 −0.185399 0.982663i \(-0.559358\pi\)
−0.185399 + 0.982663i \(0.559358\pi\)
\(434\) 1.47219e48 0.236812
\(435\) −2.59729e47 −0.0400377
\(436\) 5.94517e46 0.00878344
\(437\) −5.59031e46 −0.00791643
\(438\) −6.05109e46 −0.00821414
\(439\) −1.14225e49 −1.48650 −0.743252 0.669011i \(-0.766718\pi\)
−0.743252 + 0.669011i \(0.766718\pi\)
\(440\) −1.17759e49 −1.46933
\(441\) 6.59779e48 0.789378
\(442\) −5.47814e48 −0.628523
\(443\) 8.78568e48 0.966733 0.483366 0.875418i \(-0.339414\pi\)
0.483366 + 0.875418i \(0.339414\pi\)
\(444\) −1.49196e47 −0.0157461
\(445\) 1.29531e49 1.31134
\(446\) −1.02988e49 −1.00021
\(447\) −6.15943e46 −0.00573920
\(448\) 5.17921e48 0.463042
\(449\) −8.94932e48 −0.767773 −0.383886 0.923380i \(-0.625415\pi\)
−0.383886 + 0.923380i \(0.625415\pi\)
\(450\) 5.03962e47 0.0414922
\(451\) 1.04624e49 0.826735
\(452\) −9.13380e47 −0.0692772
\(453\) 1.45607e47 0.0106015
\(454\) 1.93432e49 1.35205
\(455\) −8.89101e48 −0.596678
\(456\) 7.75793e47 0.0499915
\(457\) 3.77717e48 0.233731 0.116866 0.993148i \(-0.462715\pi\)
0.116866 + 0.993148i \(0.462715\pi\)
\(458\) −1.45666e49 −0.865661
\(459\) −6.54048e47 −0.0373315
\(460\) −3.78321e46 −0.00207415
\(461\) 8.89831e48 0.468641 0.234320 0.972159i \(-0.424714\pi\)
0.234320 + 0.972159i \(0.424714\pi\)
\(462\) 2.98819e47 0.0151193
\(463\) −3.35423e49 −1.63059 −0.815294 0.579047i \(-0.803425\pi\)
−0.815294 + 0.579047i \(0.803425\pi\)
\(464\) 1.23835e49 0.578442
\(465\) 4.45640e47 0.0200034
\(466\) 5.13034e48 0.221313
\(467\) −3.67520e49 −1.52377 −0.761884 0.647714i \(-0.775725\pi\)
−0.761884 + 0.647714i \(0.775725\pi\)
\(468\) 1.35881e49 0.541516
\(469\) −4.82240e48 −0.184742
\(470\) −8.50330e48 −0.313168
\(471\) −1.45132e48 −0.0513897
\(472\) 1.67690e49 0.570925
\(473\) 7.51563e49 2.46056
\(474\) −7.10091e47 −0.0223571
\(475\) −2.67177e48 −0.0809035
\(476\) 3.87418e48 0.112837
\(477\) −1.60471e49 −0.449581
\(478\) −8.20711e48 −0.221194
\(479\) 4.73384e49 1.22746 0.613730 0.789516i \(-0.289669\pi\)
0.613730 + 0.789516i \(0.289669\pi\)
\(480\) 8.98740e47 0.0224218
\(481\) −7.06889e49 −1.69694
\(482\) −3.21063e49 −0.741686
\(483\) 3.33153e45 7.40666e−5 0
\(484\) −1.78321e49 −0.381560
\(485\) 8.89084e48 0.183114
\(486\) −3.57854e48 −0.0709471
\(487\) 7.97298e48 0.152172 0.0760860 0.997101i \(-0.475758\pi\)
0.0760860 + 0.997101i \(0.475758\pi\)
\(488\) −6.41754e49 −1.17924
\(489\) 1.68203e48 0.0297592
\(490\) 3.48044e49 0.592935
\(491\) 3.59851e49 0.590358 0.295179 0.955442i \(-0.404621\pi\)
0.295179 + 0.955442i \(0.404621\pi\)
\(492\) −4.66455e47 −0.00736980
\(493\) 5.36220e49 0.815972
\(494\) 1.05918e50 1.55247
\(495\) −9.59311e49 −1.35445
\(496\) −2.12474e49 −0.288998
\(497\) 1.24392e49 0.163004
\(498\) 1.92444e48 0.0242975
\(499\) 7.98372e49 0.971282 0.485641 0.874158i \(-0.338586\pi\)
0.485641 + 0.874158i \(0.338586\pi\)
\(500\) −3.53955e49 −0.414957
\(501\) 8.11529e47 0.00916866
\(502\) −1.15056e50 −1.25283
\(503\) 6.32137e49 0.663443 0.331721 0.943377i \(-0.392371\pi\)
0.331721 + 0.943377i \(0.392371\pi\)
\(504\) 4.90326e49 0.496043
\(505\) −1.07465e50 −1.04804
\(506\) 6.02436e47 0.00566404
\(507\) −2.68455e48 −0.0243346
\(508\) 7.92569e49 0.692721
\(509\) −1.42477e50 −1.20078 −0.600392 0.799706i \(-0.704989\pi\)
−0.600392 + 0.799706i \(0.704989\pi\)
\(510\) −1.72429e48 −0.0140140
\(511\) 2.02756e49 0.158923
\(512\) −1.04687e50 −0.791403
\(513\) 1.26458e49 0.0922095
\(514\) 1.55295e50 1.09230
\(515\) 2.81745e49 0.191171
\(516\) −3.35076e48 −0.0219343
\(517\) −9.20932e49 −0.581638
\(518\) −7.35034e49 −0.447927
\(519\) −5.38710e48 −0.0316781
\(520\) 2.48751e50 1.41157
\(521\) 1.18735e50 0.650251 0.325125 0.945671i \(-0.394593\pi\)
0.325125 + 0.945671i \(0.394593\pi\)
\(522\) 1.95560e50 1.03365
\(523\) 6.66586e49 0.340075 0.170038 0.985438i \(-0.445611\pi\)
0.170038 + 0.985438i \(0.445611\pi\)
\(524\) −1.17973e50 −0.580971
\(525\) 1.59224e47 0.000756938 0
\(526\) −2.28289e50 −1.04773
\(527\) −9.20040e49 −0.407672
\(528\) −4.31271e48 −0.0184511
\(529\) −2.42057e50 −0.999972
\(530\) −8.46513e49 −0.337699
\(531\) 1.36607e50 0.526289
\(532\) −7.49061e49 −0.278709
\(533\) −2.21006e50 −0.794238
\(534\) 9.19607e48 0.0319219
\(535\) 1.31599e50 0.441274
\(536\) 1.34920e50 0.437046
\(537\) 8.68884e48 0.0271918
\(538\) −2.92272e50 −0.883722
\(539\) 3.76942e50 1.10124
\(540\) 8.55799e48 0.0241595
\(541\) 7.31652e50 1.99597 0.997987 0.0634127i \(-0.0201984\pi\)
0.997987 + 0.0634127i \(0.0201984\pi\)
\(542\) −7.52499e49 −0.198390
\(543\) 1.95917e48 0.00499201
\(544\) −1.85548e50 −0.456959
\(545\) 8.86616e48 0.0211057
\(546\) −6.31218e48 −0.0145250
\(547\) 1.90668e50 0.424143 0.212072 0.977254i \(-0.431979\pi\)
0.212072 + 0.977254i \(0.431979\pi\)
\(548\) 7.00212e49 0.150588
\(549\) −5.22800e50 −1.08704
\(550\) 2.87922e49 0.0578848
\(551\) −1.03677e51 −2.01547
\(552\) −9.32089e46 −0.000175220 0
\(553\) 2.37933e50 0.432553
\(554\) 4.60142e50 0.809024
\(555\) −2.22499e49 −0.0378363
\(556\) 1.74122e50 0.286399
\(557\) 6.78617e50 1.07970 0.539851 0.841761i \(-0.318481\pi\)
0.539851 + 0.841761i \(0.318481\pi\)
\(558\) −3.35539e50 −0.516429
\(559\) −1.58759e51 −2.36384
\(560\) 1.33429e50 0.192208
\(561\) −1.86746e49 −0.0260279
\(562\) 8.18669e50 1.10404
\(563\) 6.45010e50 0.841708 0.420854 0.907128i \(-0.361730\pi\)
0.420854 + 0.907128i \(0.361730\pi\)
\(564\) 4.10587e48 0.00518492
\(565\) −1.36214e50 −0.166466
\(566\) 2.28089e50 0.269774
\(567\) 3.99063e50 0.456830
\(568\) −3.48021e50 −0.385621
\(569\) 2.68168e50 0.287627 0.143814 0.989605i \(-0.454063\pi\)
0.143814 + 0.989605i \(0.454063\pi\)
\(570\) 3.33387e49 0.0346149
\(571\) −3.44946e50 −0.346724 −0.173362 0.984858i \(-0.555463\pi\)
−0.173362 + 0.984858i \(0.555463\pi\)
\(572\) 7.76311e50 0.755456
\(573\) 5.38448e48 0.00507321
\(574\) −2.29805e50 −0.209648
\(575\) 3.21004e47 0.000283567 0
\(576\) −1.18044e51 −1.00978
\(577\) 2.52648e50 0.209297 0.104648 0.994509i \(-0.466628\pi\)
0.104648 + 0.994509i \(0.466628\pi\)
\(578\) −6.05612e50 −0.485881
\(579\) 1.29149e49 0.0100355
\(580\) −7.01625e50 −0.528065
\(581\) −6.44830e50 −0.470096
\(582\) 6.31206e48 0.00445754
\(583\) −9.16799e50 −0.627199
\(584\) −5.67266e50 −0.375966
\(585\) 2.02643e51 1.30121
\(586\) 1.47925e50 0.0920311
\(587\) 1.13653e51 0.685134 0.342567 0.939493i \(-0.388704\pi\)
0.342567 + 0.939493i \(0.388704\pi\)
\(588\) −1.68055e49 −0.00981685
\(589\) 1.77887e51 1.00696
\(590\) 7.20624e50 0.395318
\(591\) 3.72945e49 0.0198279
\(592\) 1.06084e51 0.546636
\(593\) −1.23614e51 −0.617383 −0.308692 0.951162i \(-0.599891\pi\)
−0.308692 + 0.951162i \(0.599891\pi\)
\(594\) −1.36277e50 −0.0659740
\(595\) 5.77765e50 0.271136
\(596\) −1.66389e50 −0.0756954
\(597\) 7.78766e48 0.00343464
\(598\) −1.27257e49 −0.00544140
\(599\) −4.59427e51 −1.90467 −0.952336 0.305052i \(-0.901326\pi\)
−0.952336 + 0.305052i \(0.901326\pi\)
\(600\) −4.45472e48 −0.00179070
\(601\) −1.48401e49 −0.00578442 −0.00289221 0.999996i \(-0.500921\pi\)
−0.00289221 + 0.999996i \(0.500921\pi\)
\(602\) −1.65080e51 −0.623962
\(603\) 1.09911e51 0.402877
\(604\) 3.93340e50 0.139825
\(605\) −2.65933e51 −0.916850
\(606\) −7.62951e49 −0.0255125
\(607\) 2.59968e51 0.843198 0.421599 0.906782i \(-0.361469\pi\)
0.421599 + 0.906782i \(0.361469\pi\)
\(608\) 3.58751e51 1.12870
\(609\) 6.17859e49 0.0188568
\(610\) −2.75785e51 −0.816525
\(611\) 1.94536e51 0.558775
\(612\) −8.82998e50 −0.246070
\(613\) 1.49376e50 0.0403890 0.0201945 0.999796i \(-0.493571\pi\)
0.0201945 + 0.999796i \(0.493571\pi\)
\(614\) 2.74319e51 0.719682
\(615\) −6.95635e49 −0.0177089
\(616\) 2.80131e51 0.692018
\(617\) −6.30081e51 −1.51050 −0.755250 0.655437i \(-0.772484\pi\)
−0.755250 + 0.655437i \(0.772484\pi\)
\(618\) 2.00025e49 0.00465369
\(619\) 5.97852e51 1.34995 0.674974 0.737842i \(-0.264155\pi\)
0.674974 + 0.737842i \(0.264155\pi\)
\(620\) 1.20384e51 0.263829
\(621\) −1.51935e48 −0.000323195 0
\(622\) −1.44681e51 −0.298737
\(623\) −3.08136e51 −0.617609
\(624\) 9.11007e49 0.0177258
\(625\) −4.99363e51 −0.943269
\(626\) 1.46570e51 0.268794
\(627\) 3.61068e50 0.0642893
\(628\) −3.92055e51 −0.677787
\(629\) 4.59358e51 0.771106
\(630\) 2.10711e51 0.343469
\(631\) −3.17011e51 −0.501800 −0.250900 0.968013i \(-0.580727\pi\)
−0.250900 + 0.968013i \(0.580727\pi\)
\(632\) −6.65683e51 −1.02330
\(633\) −3.43499e50 −0.0512810
\(634\) −6.13536e51 −0.889588
\(635\) 1.18198e52 1.66454
\(636\) 4.08744e49 0.00559107
\(637\) −7.96244e51 −1.05795
\(638\) 1.11726e52 1.44203
\(639\) −2.83512e51 −0.355473
\(640\) −2.29507e50 −0.0279554
\(641\) 1.15243e52 1.36377 0.681885 0.731459i \(-0.261160\pi\)
0.681885 + 0.731459i \(0.261160\pi\)
\(642\) 9.34289e49 0.0107420
\(643\) 1.66832e52 1.86370 0.931851 0.362842i \(-0.118193\pi\)
0.931851 + 0.362842i \(0.118193\pi\)
\(644\) 8.99971e48 0.000976877 0
\(645\) −4.99706e50 −0.0527060
\(646\) −6.88289e51 −0.705455
\(647\) −1.67531e52 −1.66865 −0.834327 0.551270i \(-0.814144\pi\)
−0.834327 + 0.551270i \(0.814144\pi\)
\(648\) −1.11649e52 −1.08073
\(649\) 7.80457e51 0.734213
\(650\) −6.08199e50 −0.0556095
\(651\) −1.06011e50 −0.00942116
\(652\) 4.54380e51 0.392499
\(653\) −9.01096e51 −0.756619 −0.378309 0.925679i \(-0.623494\pi\)
−0.378309 + 0.925679i \(0.623494\pi\)
\(654\) 6.29454e48 0.000513778 0
\(655\) −1.75936e52 −1.39602
\(656\) 3.31668e51 0.255848
\(657\) −4.62118e51 −0.346572
\(658\) 2.02281e51 0.147495
\(659\) 1.92183e52 1.36249 0.681247 0.732054i \(-0.261438\pi\)
0.681247 + 0.732054i \(0.261438\pi\)
\(660\) 2.44351e50 0.0168442
\(661\) −1.12368e51 −0.0753213 −0.0376606 0.999291i \(-0.511991\pi\)
−0.0376606 + 0.999291i \(0.511991\pi\)
\(662\) 5.29910e51 0.345405
\(663\) 3.94478e50 0.0250048
\(664\) 1.80409e52 1.11211
\(665\) −1.11709e52 −0.669712
\(666\) 1.67528e52 0.976819
\(667\) 1.24564e50 0.00706422
\(668\) 2.19224e51 0.120927
\(669\) 7.41611e50 0.0397918
\(670\) 5.79801e51 0.302618
\(671\) −2.98684e52 −1.51651
\(672\) −2.13797e50 −0.0105602
\(673\) 6.07438e51 0.291893 0.145946 0.989292i \(-0.453377\pi\)
0.145946 + 0.989292i \(0.453377\pi\)
\(674\) −2.63974e52 −1.23411
\(675\) −7.26143e49 −0.00330295
\(676\) −7.25197e51 −0.320954
\(677\) 3.94010e52 1.69675 0.848373 0.529398i \(-0.177582\pi\)
0.848373 + 0.529398i \(0.177582\pi\)
\(678\) −9.67055e49 −0.00405230
\(679\) −2.11500e51 −0.0862423
\(680\) −1.61646e52 −0.641430
\(681\) −1.39289e51 −0.0537892
\(682\) −1.91699e52 −0.720457
\(683\) −2.05041e52 −0.749993 −0.374996 0.927026i \(-0.622356\pi\)
−0.374996 + 0.927026i \(0.622356\pi\)
\(684\) 1.70725e52 0.607798
\(685\) 1.04424e52 0.361847
\(686\) −1.87582e52 −0.632696
\(687\) 1.04893e51 0.0344389
\(688\) 2.38252e52 0.761465
\(689\) 1.93662e52 0.602545
\(690\) −4.00553e48 −0.000121325 0
\(691\) 4.63109e51 0.136565 0.0682825 0.997666i \(-0.478248\pi\)
0.0682825 + 0.997666i \(0.478248\pi\)
\(692\) −1.45525e52 −0.417808
\(693\) 2.28206e52 0.637915
\(694\) −1.50799e52 −0.410440
\(695\) 2.59672e52 0.688188
\(696\) −1.72863e51 −0.0446099
\(697\) 1.43616e52 0.360909
\(698\) 2.77797e52 0.679832
\(699\) −3.69433e50 −0.00880456
\(700\) 4.30122e50 0.00998340
\(701\) −6.34322e51 −0.143392 −0.0716962 0.997427i \(-0.522841\pi\)
−0.0716962 + 0.997427i \(0.522841\pi\)
\(702\) 2.87868e51 0.0633807
\(703\) −8.88154e52 −1.90465
\(704\) −6.74404e52 −1.40872
\(705\) 6.12318e50 0.0124589
\(706\) 4.95873e52 0.982842
\(707\) 2.55645e52 0.493602
\(708\) −3.47958e50 −0.00654503
\(709\) −7.70939e52 −1.41275 −0.706374 0.707839i \(-0.749670\pi\)
−0.706374 + 0.707839i \(0.749670\pi\)
\(710\) −1.49557e52 −0.267010
\(711\) −5.42293e52 −0.943293
\(712\) 8.62096e52 1.46109
\(713\) −2.13725e50 −0.00352939
\(714\) 4.10184e50 0.00660028
\(715\) 1.15773e53 1.81529
\(716\) 2.34718e52 0.358637
\(717\) 5.90989e50 0.00879985
\(718\) −3.23407e52 −0.469296
\(719\) 5.22428e52 0.738826 0.369413 0.929265i \(-0.379559\pi\)
0.369413 + 0.929265i \(0.379559\pi\)
\(720\) −3.04110e52 −0.419159
\(721\) −6.70231e51 −0.0900372
\(722\) 7.41579e52 0.971000
\(723\) 2.31196e51 0.0295068
\(724\) 5.29245e51 0.0658406
\(725\) 5.95327e51 0.0721942
\(726\) −1.88800e51 −0.0223189
\(727\) −1.24495e53 −1.43471 −0.717354 0.696708i \(-0.754647\pi\)
−0.717354 + 0.696708i \(0.754647\pi\)
\(728\) −5.91742e52 −0.664816
\(729\) −9.07820e52 −0.994352
\(730\) −2.43775e52 −0.260325
\(731\) 1.03166e53 1.07415
\(732\) 1.33165e51 0.0135187
\(733\) −1.12627e52 −0.111485 −0.0557427 0.998445i \(-0.517753\pi\)
−0.0557427 + 0.998445i \(0.517753\pi\)
\(734\) −2.49994e52 −0.241297
\(735\) −2.50625e51 −0.0235889
\(736\) −4.31028e50 −0.00395609
\(737\) 6.27941e52 0.562044
\(738\) 5.23769e52 0.457191
\(739\) −2.92067e52 −0.248634 −0.124317 0.992243i \(-0.539674\pi\)
−0.124317 + 0.992243i \(0.539674\pi\)
\(740\) −6.01053e52 −0.499029
\(741\) −7.62711e51 −0.0617623
\(742\) 2.01373e52 0.159048
\(743\) 3.47917e52 0.268029 0.134015 0.990979i \(-0.457213\pi\)
0.134015 + 0.990979i \(0.457213\pi\)
\(744\) 2.96596e51 0.0222878
\(745\) −2.48140e52 −0.181889
\(746\) 7.72582e52 0.552429
\(747\) 1.46969e53 1.02516
\(748\) −5.04470e52 −0.343286
\(749\) −3.13055e52 −0.207830
\(750\) −3.74756e51 −0.0242725
\(751\) 1.55213e53 0.980818 0.490409 0.871492i \(-0.336847\pi\)
0.490409 + 0.871492i \(0.336847\pi\)
\(752\) −2.91943e52 −0.179998
\(753\) 8.28513e51 0.0498416
\(754\) −2.36008e53 −1.38534
\(755\) 5.86596e52 0.335985
\(756\) −2.03582e51 −0.0113785
\(757\) −1.00018e51 −0.00545510 −0.00272755 0.999996i \(-0.500868\pi\)
−0.00272755 + 0.999996i \(0.500868\pi\)
\(758\) −1.18268e53 −0.629488
\(759\) −4.33811e49 −0.000225334 0
\(760\) 3.12537e53 1.58435
\(761\) −3.93324e53 −1.94596 −0.972981 0.230886i \(-0.925838\pi\)
−0.972981 + 0.230886i \(0.925838\pi\)
\(762\) 8.39144e51 0.0405200
\(763\) −2.10913e51 −0.00994031
\(764\) 1.45455e52 0.0669115
\(765\) −1.31683e53 −0.591282
\(766\) −1.89949e53 −0.832541
\(767\) −1.64862e53 −0.705353
\(768\) 7.26468e51 0.0303413
\(769\) 4.31322e53 1.75859 0.879295 0.476278i \(-0.158015\pi\)
0.879295 + 0.476278i \(0.158015\pi\)
\(770\) 1.20382e53 0.479165
\(771\) −1.11827e52 −0.0434552
\(772\) 3.48879e52 0.132359
\(773\) 1.93734e53 0.717604 0.358802 0.933414i \(-0.383185\pi\)
0.358802 + 0.933414i \(0.383185\pi\)
\(774\) 3.76247e53 1.36071
\(775\) −1.02145e52 −0.0360693
\(776\) 5.91731e52 0.204024
\(777\) 5.29294e51 0.0178200
\(778\) 1.35607e52 0.0445821
\(779\) −2.77678e53 −0.891452
\(780\) −5.16160e51 −0.0161821
\(781\) −1.61975e53 −0.495911
\(782\) 8.26956e50 0.00247262
\(783\) −2.81776e52 −0.0822832
\(784\) 1.19494e53 0.340799
\(785\) −5.84680e53 −1.62866
\(786\) −1.24906e52 −0.0339833
\(787\) −1.53439e52 −0.0407759 −0.0203880 0.999792i \(-0.506490\pi\)
−0.0203880 + 0.999792i \(0.506490\pi\)
\(788\) 1.00746e53 0.261514
\(789\) 1.64390e52 0.0416821
\(790\) −2.86068e53 −0.708547
\(791\) 3.24034e52 0.0784018
\(792\) −6.38470e53 −1.50912
\(793\) 6.30933e53 1.45690
\(794\) 1.71777e53 0.387512
\(795\) 6.09569e51 0.0134348
\(796\) 2.10374e52 0.0453001
\(797\) 5.82231e53 1.22494 0.612472 0.790493i \(-0.290175\pi\)
0.612472 + 0.790493i \(0.290175\pi\)
\(798\) −7.93079e51 −0.0163028
\(799\) −1.26415e53 −0.253912
\(800\) −2.06001e52 −0.0404300
\(801\) 7.02299e53 1.34685
\(802\) −2.66039e53 −0.498563
\(803\) −2.64015e53 −0.483495
\(804\) −2.79960e51 −0.00501025
\(805\) 1.34215e51 0.00234734
\(806\) 4.04940e53 0.692137
\(807\) 2.10464e52 0.0351574
\(808\) −7.15236e53 −1.16772
\(809\) 7.29683e53 1.16436 0.582179 0.813061i \(-0.302200\pi\)
0.582179 + 0.813061i \(0.302200\pi\)
\(810\) −4.79796e53 −0.748315
\(811\) −8.04109e53 −1.22583 −0.612914 0.790150i \(-0.710003\pi\)
−0.612914 + 0.790150i \(0.710003\pi\)
\(812\) 1.66907e53 0.248706
\(813\) 5.41870e51 0.00789261
\(814\) 9.57113e53 1.36274
\(815\) 6.77627e53 0.943137
\(816\) −5.92000e51 −0.00805479
\(817\) −1.99469e54 −2.65318
\(818\) −7.44878e52 −0.0968611
\(819\) −4.82058e53 −0.612840
\(820\) −1.87917e53 −0.233566
\(821\) −1.06873e52 −0.0129873 −0.00649364 0.999979i \(-0.502067\pi\)
−0.00649364 + 0.999979i \(0.502067\pi\)
\(822\) 7.41360e51 0.00880847
\(823\) 1.55439e54 1.80578 0.902889 0.429874i \(-0.141442\pi\)
0.902889 + 0.429874i \(0.141442\pi\)
\(824\) 1.87516e53 0.213002
\(825\) −2.07331e51 −0.00230285
\(826\) −1.71426e53 −0.186186
\(827\) −1.52865e54 −1.62352 −0.811759 0.583992i \(-0.801490\pi\)
−0.811759 + 0.583992i \(0.801490\pi\)
\(828\) −2.05120e51 −0.00213033
\(829\) 4.48559e53 0.455576 0.227788 0.973711i \(-0.426851\pi\)
0.227788 + 0.973711i \(0.426851\pi\)
\(830\) 7.75284e53 0.770045
\(831\) −3.31346e52 −0.0321857
\(832\) 1.42459e54 1.35335
\(833\) 5.17424e53 0.480744
\(834\) 1.84355e52 0.0167526
\(835\) 3.26934e53 0.290576
\(836\) 9.75378e53 0.847924
\(837\) 4.83467e52 0.0411099
\(838\) −1.12190e54 −0.933122
\(839\) −1.70786e54 −1.38949 −0.694747 0.719254i \(-0.744484\pi\)
−0.694747 + 0.719254i \(0.744484\pi\)
\(840\) −1.86256e52 −0.0148232
\(841\) 1.02566e54 0.798502
\(842\) −1.10682e54 −0.842950
\(843\) −5.89519e52 −0.0439226
\(844\) −9.27918e53 −0.676354
\(845\) −1.08150e54 −0.771220
\(846\) −4.61037e53 −0.321650
\(847\) 6.32617e53 0.431815
\(848\) −2.90633e53 −0.194098
\(849\) −1.64245e52 −0.0107325
\(850\) 3.95226e52 0.0252694
\(851\) 1.06709e52 0.00667580
\(852\) 7.22147e51 0.00442072
\(853\) −1.02278e54 −0.612667 −0.306334 0.951924i \(-0.599102\pi\)
−0.306334 + 0.951924i \(0.599102\pi\)
\(854\) 6.56054e53 0.384564
\(855\) 2.54606e54 1.46048
\(856\) 8.75859e53 0.491666
\(857\) 7.33586e52 0.0403001 0.0201500 0.999797i \(-0.493586\pi\)
0.0201500 + 0.999797i \(0.493586\pi\)
\(858\) 8.21931e52 0.0441896
\(859\) 1.46329e54 0.769938 0.384969 0.922929i \(-0.374212\pi\)
0.384969 + 0.922929i \(0.374212\pi\)
\(860\) −1.34989e54 −0.695149
\(861\) 1.65482e52 0.00834049
\(862\) 8.52292e53 0.420440
\(863\) 2.49462e54 1.20449 0.602247 0.798310i \(-0.294272\pi\)
0.602247 + 0.798310i \(0.294272\pi\)
\(864\) 9.75027e52 0.0460800
\(865\) −2.17025e54 −1.00395
\(866\) −6.31753e53 −0.286066
\(867\) 4.36098e52 0.0193300
\(868\) −2.86376e53 −0.124257
\(869\) −3.09821e54 −1.31597
\(870\) −7.42856e52 −0.0308886
\(871\) −1.32645e54 −0.539951
\(872\) 5.90088e52 0.0235159
\(873\) 4.82049e53 0.188073
\(874\) −1.59889e52 −0.00610742
\(875\) 1.25571e54 0.469612
\(876\) 1.17708e52 0.00431004
\(877\) 4.03070e54 1.44507 0.722534 0.691335i \(-0.242977\pi\)
0.722534 + 0.691335i \(0.242977\pi\)
\(878\) −3.26696e54 −1.14682
\(879\) −1.06520e52 −0.00366130
\(880\) −1.73743e54 −0.584759
\(881\) −2.32935e54 −0.767679 −0.383840 0.923400i \(-0.625398\pi\)
−0.383840 + 0.923400i \(0.625398\pi\)
\(882\) 1.88705e54 0.608995
\(883\) −2.99176e54 −0.945482 −0.472741 0.881202i \(-0.656735\pi\)
−0.472741 + 0.881202i \(0.656735\pi\)
\(884\) 1.06563e54 0.329792
\(885\) −5.18917e52 −0.0157271
\(886\) 2.51281e54 0.745822
\(887\) 5.34771e54 1.55447 0.777233 0.629213i \(-0.216623\pi\)
0.777233 + 0.629213i \(0.216623\pi\)
\(888\) −1.48085e53 −0.0421570
\(889\) −2.81175e54 −0.783960
\(890\) 3.70474e54 1.01168
\(891\) −5.19634e54 −1.38982
\(892\) 2.00337e54 0.524821
\(893\) 2.44420e54 0.627169
\(894\) −1.76167e52 −0.00442772
\(895\) 3.50040e54 0.861770
\(896\) 5.45963e52 0.0131663
\(897\) 9.16372e50 0.000216477 0
\(898\) −2.55961e54 −0.592327
\(899\) −3.96370e54 −0.898558
\(900\) −9.80329e52 −0.0217714
\(901\) −1.25848e54 −0.273802
\(902\) 2.99238e54 0.637816
\(903\) 1.18873e53 0.0248233
\(904\) −9.06576e53 −0.185476
\(905\) 7.89275e53 0.158208
\(906\) 4.16454e52 0.00817891
\(907\) −6.45044e54 −1.24124 −0.620618 0.784113i \(-0.713118\pi\)
−0.620618 + 0.784113i \(0.713118\pi\)
\(908\) −3.76271e54 −0.709436
\(909\) −5.82662e54 −1.07643
\(910\) −2.54293e54 −0.460330
\(911\) 2.81261e54 0.498907 0.249453 0.968387i \(-0.419749\pi\)
0.249453 + 0.968387i \(0.419749\pi\)
\(912\) 1.14461e53 0.0198955
\(913\) 8.39655e54 1.43018
\(914\) 1.08031e54 0.180321
\(915\) 1.98592e53 0.0324841
\(916\) 2.83356e54 0.454220
\(917\) 4.18526e54 0.657491
\(918\) −1.87066e53 −0.0288008
\(919\) 5.50843e54 0.831171 0.415586 0.909554i \(-0.363577\pi\)
0.415586 + 0.909554i \(0.363577\pi\)
\(920\) −3.75503e52 −0.00555314
\(921\) −1.97535e53 −0.0286314
\(922\) 2.54502e54 0.361551
\(923\) 3.42152e54 0.476418
\(924\) −5.81275e52 −0.00793323
\(925\) 5.09992e53 0.0682246
\(926\) −9.59349e54 −1.25798
\(927\) 1.52758e54 0.196349
\(928\) −7.99374e54 −1.00719
\(929\) 9.70568e54 1.19877 0.599384 0.800461i \(-0.295412\pi\)
0.599384 + 0.800461i \(0.295412\pi\)
\(930\) 1.27458e53 0.0154324
\(931\) −1.00042e55 −1.18745
\(932\) −9.97975e53 −0.116125
\(933\) 1.04184e53 0.0118848
\(934\) −1.05115e55 −1.17557
\(935\) −7.52328e54 −0.824883
\(936\) 1.34869e55 1.44980
\(937\) −4.05525e54 −0.427401 −0.213701 0.976899i \(-0.568552\pi\)
−0.213701 + 0.976899i \(0.568552\pi\)
\(938\) −1.37926e54 −0.142526
\(939\) −1.05544e53 −0.0106935
\(940\) 1.65410e54 0.164322
\(941\) 4.56539e54 0.444703 0.222351 0.974967i \(-0.428627\pi\)
0.222351 + 0.974967i \(0.428627\pi\)
\(942\) −4.15094e53 −0.0396465
\(943\) 3.33621e52 0.00312454
\(944\) 2.47411e54 0.227215
\(945\) −3.03607e53 −0.0273415
\(946\) 2.14956e55 1.89829
\(947\) −1.72468e55 −1.49360 −0.746798 0.665051i \(-0.768410\pi\)
−0.746798 + 0.665051i \(0.768410\pi\)
\(948\) 1.38130e53 0.0117310
\(949\) 5.57700e54 0.464490
\(950\) −7.64158e53 −0.0624161
\(951\) 4.41804e53 0.0353908
\(952\) 3.84532e54 0.302099
\(953\) 6.30605e52 0.00485891 0.00242945 0.999997i \(-0.499227\pi\)
0.00242945 + 0.999997i \(0.499227\pi\)
\(954\) −4.58967e54 −0.346846
\(955\) 2.16920e54 0.160782
\(956\) 1.59648e54 0.116063
\(957\) −8.04535e53 −0.0573686
\(958\) 1.35394e55 0.946969
\(959\) −2.48410e54 −0.170422
\(960\) 4.48403e53 0.0301753
\(961\) −8.34809e54 −0.551067
\(962\) −2.02178e55 −1.30917
\(963\) 7.13512e54 0.453226
\(964\) 6.24546e54 0.389170
\(965\) 5.20291e54 0.318047
\(966\) 9.52858e50 5.71415e−5 0
\(967\) −1.73337e55 −1.01977 −0.509883 0.860244i \(-0.670311\pi\)
−0.509883 + 0.860244i \(0.670311\pi\)
\(968\) −1.76992e55 −1.02155
\(969\) 4.95633e53 0.0280653
\(970\) 2.54288e54 0.141270
\(971\) 1.04588e55 0.570067 0.285033 0.958518i \(-0.407995\pi\)
0.285033 + 0.958518i \(0.407995\pi\)
\(972\) 6.96112e53 0.0372266
\(973\) −6.17723e54 −0.324121
\(974\) 2.28037e54 0.117399
\(975\) 4.37961e52 0.00221233
\(976\) −9.46852e54 −0.469311
\(977\) −1.65065e55 −0.802798 −0.401399 0.915903i \(-0.631476\pi\)
−0.401399 + 0.915903i \(0.631476\pi\)
\(978\) 4.81082e53 0.0229588
\(979\) 4.01235e55 1.87896
\(980\) −6.77031e54 −0.311119
\(981\) 4.80711e53 0.0216774
\(982\) 1.02922e55 0.455454
\(983\) 3.82232e55 1.65992 0.829960 0.557823i \(-0.188363\pi\)
0.829960 + 0.557823i \(0.188363\pi\)
\(984\) −4.62981e53 −0.0197312
\(985\) 1.50245e55 0.628392
\(986\) 1.53365e55 0.629512
\(987\) −1.45662e53 −0.00586783
\(988\) −2.06037e55 −0.814593
\(989\) 2.39655e53 0.00929939
\(990\) −2.74374e55 −1.04494
\(991\) −4.27417e55 −1.59768 −0.798838 0.601546i \(-0.794552\pi\)
−0.798838 + 0.601546i \(0.794552\pi\)
\(992\) 1.37156e55 0.503208
\(993\) −3.81585e53 −0.0137414
\(994\) 3.55775e54 0.125756
\(995\) 3.13735e54 0.108852
\(996\) −3.74351e53 −0.0127491
\(997\) −3.39750e55 −1.13579 −0.567896 0.823100i \(-0.692243\pi\)
−0.567896 + 0.823100i \(0.692243\pi\)
\(998\) 2.28344e55 0.749332
\(999\) −2.41386e54 −0.0777588
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 1.38.a.a.1.2 2
3.2 odd 2 9.38.a.a.1.1 2
4.3 odd 2 16.38.a.b.1.2 2
5.2 odd 4 25.38.b.a.24.3 4
5.3 odd 4 25.38.b.a.24.2 4
5.4 even 2 25.38.a.a.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.38.a.a.1.2 2 1.1 even 1 trivial
9.38.a.a.1.1 2 3.2 odd 2
16.38.a.b.1.2 2 4.3 odd 2
25.38.a.a.1.1 2 5.4 even 2
25.38.b.a.24.2 4 5.3 odd 4
25.38.b.a.24.3 4 5.2 odd 4